Klein and Frauendiener's Period Matrix

genus6.sage

# from the curve f(x,y) = -180*x**5 + 396*y*x**4 - 307*x**3*y**2 + 107*x**2*y**3 = 273*x**3 - 318*x**2*y - 17*x*y**4 + 117*x*y**2 - 68*x + y**5 - 12*y**3 + 19*y = 0
#
# these a- and b-period matrices use a different normalization from that of my own
#
a6 = Matrix(CDF,
[
[0.041441136367794 + 0.027833200726691*I, -0.034538213432710 + 0.027188711893010*I, -0.097853547524326 + 0.026426118256733*I, -0.304059718474855 + 0.060306772513671*I, -0.536899366726663 + 0.087203183867874*I, -2.814882797646379 + 0.543317148745872*I],
[-0.114912806296197 - 0.044601420984340*I, 0.000000000000002 - 0.000000000000002*I, 0.053195632592273 - 0.022598899319034*I, 0.000000000000006 - 0.000000000000006*I, 0.242671354734388 + 0.009863612111086*I, 0.764112818309978 + 0.035735030643330*I],
[0.114912806296198 + 0.016851233729331*I, -0.000000000000003 + 0.054377423786101*I, -0.053195632592272 - 0.080539669725953*I, -0.000000000000009 + 0.120613545027839*I, -0.242671354734385 - 0.237235882811205*I, -0.764112818309973 - 0.538148249906231*I],
[-0.000000000000145 - 0.011064980468868*I, -0.000000000000232 + 0.018296506388701*I, -0.000000000000371 - 0.030253337193984*I, -0.000000000001418 + 0.111441672814486*I, -0.000000000002271 - 0.184269979844065*I, -0.000000000013900 - 1.122369328118062*I],
[0.081988303080824 - 0.027750187255008*I, -0.000000000000001 - 0.000000000000000*I, -0.052735643727852 - 0.103138569044988*I, -0.000000000000002 - 0.000000000000001*I, -0.088120274254757 - 0.227372270700121*I, -0.127496577243115 - 0.502413219262904*I],
[-0.081988303080827 + 0.000000000000001*I, -0.000000000000003 - 0.054377423786097*I, 0.052735643727848 + 0.0000000000000058*I, -0.000000000000006 - 0.120613545027826*I, 0.088120274254749 + 0.000000000000010*I, 0.127496577243099 + 0.000000000000019*I],
]
)

b6 = Matrix(CDF,
[
[0.041441136367794 + 0.027833200726690*I, -0.034538213432710 - 0.009404300883654*I, -0.097853547524326 + 0.026426118256743*I, -0.304059718474855 - 0.162576573110822*I, -0.536899366726663 + 0.087203183867912*I, -2.814882797646379 + 0.543317148746025*I],
[-0.008893776107028 - 0.100911791871047*I, -0.066617940934943 + 0.018040458698884*I, 0.109123013300482 - 0.073253290304226*I, -0.116239263979475 + 0.004585936107792*I, 0.338049660213882 - 0.105519234924677*I, 0.955517317106568 - 0.261883524016635*I],
[-0.008893776107028 - 0.056310370886708*I, -0.066617940934943 - 0.018040458698885*I, 0.109123013300482 - 0.050654390985187*I, -0.116239263979475 - 0.004585936107801*I, 0.338049660213882 - 0.115382847035744*I, 0.955517317106568 - 0.297618554659892*I],
[0.032030533560343 - 0.000000000000020*I, 0.000000000000434 - 0.018296506388225*I, 0.142511462455675 - 0.000000000000020*I, 0.000000000002647 - 0.111441672811588*I, 0.831127378714640 - 0.000000000000147*I, 4.865652776956537 - 0.000000000001017*I],
[0.106019030189168 + 0.028560183631701*I, 0.066617940934943 + 0.072417882484992*I, 0.055927380708208 - 0.052484178059800*I, 0.116239263979479 + 0.125199481135651*I, 0.095378305479493 - 0.111989423664385*I, 0.191404498796592 - 0.204794664603068*I],
[-0.057957575972479 + 0.016041237352642*I, 0.066617940934944 - 0.036336965087211*I, 0.161398668163915 + 0.075083077378845*I, 0.116239263979481 - 0.116027608920027*I, 0.271618853989010 + 0.102125811553314*I, 0.446397653282827 + 0.169059633959730*I],
]
)