Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 15.7523478762 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.853799565\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.310834243\) \(a_{7}=-1.382138576\) \(a_{8}=+0.353553391\) \(a_{9}=+2.436572826\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.620315236\) \(a_{12}=-0.926899782\) \(a_{13}=-0.356393014\) \(a_{14}=-0.977319560\) \(a_{15}=+0.829044369\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.709251550\) \(a_{18}=+1.722917168\) \(a_{19}=-0.513428981\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.562207891\) \(a_{22}=+1.145735891\) \(a_{23}=+0.322160788\) \(a_{24}=-0.655417122\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.252007917\) \(a_{27}=-2.663118079\) \(a_{28}=-0.691069288\) \(a_{29}=+0.998406873\) \(a_{30}=+0.586222895\)
\(a_{31}=+0.364561369\) \(a_{32}=+0.176776695\) \(a_{33}=-3.003739679\) \(a_{34}=+0.501516581\) \(a_{35}=+0.618111162\)
\(a_{36}=+1.218286413\) \(a_{37}=+0.395243843\) \(a_{38}=-0.363049114\) \(a_{39}=+0.660681213\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.122515461\) \(a_{42}=+1.811754575\) \(a_{43}=-0.780673149\) \(a_{44}=+0.810157618\) \(a_{45}=-1.089668494\)
\(a_{46}=+0.227802078\) \(a_{47}=-0.954314677\) \(a_{48}=-0.463449891\) \(a_{49}=+0.910307044\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.314810215\) \(a_{52}=-0.178196507\) \(a_{53}=-1.227478343\) \(a_{54}=-1.883108853\) \(a_{55}=-0.724627002\)
\(a_{56}=-0.488659780\) \(a_{57}=+0.951794421\) \(a_{58}=+0.705980270\) \(a_{59}=-0.312811234\) \(a_{60}=+0.414522184\)
\(a_{61}=+0.508481381\) \(a_{62}=+0.257783816\) \(a_{63}=-3.367681296\) \(a_{64}=+0.125000000\) \(a_{65}=+0.159383801\)
\(a_{66}=-2.123964696\) \(a_{67}=+0.505983331\) \(a_{68}=+0.354625775\) \(a_{69}=-0.597221528\) \(a_{70}=+0.437070594\)
\(a_{71}=-1.480698610\) \(a_{72}=+0.861458584\) \(a_{73}=+0.975227008\) \(a_{74}=+0.279479602\) \(a_{75}=-0.370759913\)
\(a_{76}=-0.256714490\) \(a_{77}=-2.239500193\) \(a_{78}=+0.467172166\) \(a_{79}=+0.880709668\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.500314309\) \(a_{82}=-0.793738295\) \(a_{83}=-1.447444399\) \(a_{84}=+1.281103946\) \(a_{85}=-0.317186936\)
\(a_{86}=-0.552019277\) \(a_{87}=-1.850846226\) \(a_{88}=+0.572867945\) \(a_{89}=+0.586115788\) \(a_{90}=-0.770511981\)
\(a_{91}=+0.492584532\) \(a_{92}=+0.161080394\) \(a_{93}=-0.675823707\) \(a_{94}=-0.674802380\) \(a_{95}=+0.229612420\)
\(a_{96}=-0.327708561\) \(a_{97}=-1.584076851\) \(a_{98}=+0.643684284\) \(a_{99}=+3.948016069\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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