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: \( 18.172577593 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.498023981\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.352156134\) \(a_{7}=+0.314171014\) \(a_{8}=-0.353553391\) \(a_{9}=-0.751972114\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.980166354\) \(a_{12}=-0.249011991\) \(a_{13}=-0.770170400\) \(a_{14}=-0.222152454\) \(a_{15}=+0.222723095\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.235926187\) \(a_{18}=+0.531724581\) \(a_{19}=+0.183292339\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.156464699\) \(a_{22}=-0.693082276\) \(a_{23}=-0.269042431\) \(a_{24}=+0.176078067\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.544592712\) \(a_{27}=+0.872524127\) \(a_{28}=+0.157085507\) \(a_{29}=-0.588378264\) \(a_{30}=-0.157489011\)
\(a_{31}=-1.540712525\) \(a_{32}=-0.176776695\) \(a_{33}=-0.488146350\) \(a_{34}=-0.166825007\) \(a_{35}=-0.140501549\)
\(a_{36}=-0.375986057\) \(a_{37}=+0.425069956\) \(a_{38}=-0.129607256\) \(a_{39}=+0.383563329\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.317254570\) \(a_{42}=+0.110637250\) \(a_{43}=-0.776070621\) \(a_{44}=+0.490083177\) \(a_{45}=+0.336292153\)
\(a_{46}=+0.190241728\) \(a_{47}=+0.089990440\) \(a_{48}=-0.124505995\) \(a_{49}=-0.901296574\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.117496899\) \(a_{52}=-0.385085200\) \(a_{53}=-1.476446147\) \(a_{54}=-0.616967727\) \(a_{55}=-0.438343719\)
\(a_{56}=-0.111076227\) \(a_{57}=-0.091283980\) \(a_{58}=+0.416046261\) \(a_{59}=+1.314987430\) \(a_{60}=+0.111361548\)
\(a_{61}=-1.207536721\) \(a_{62}=+1.089448274\) \(a_{63}=-0.236247842\) \(a_{64}=+0.125000000\) \(a_{65}=+0.344430674\)
\(a_{66}=+0.345171594\) \(a_{67}=+0.501937487\) \(a_{68}=+0.117963094\) \(a_{69}=+0.133989583\) \(a_{70}=+0.099349598\)
\(a_{71}=+1.366482144\) \(a_{72}=+0.265862291\) \(a_{73}=+0.922548614\) \(a_{74}=-0.300569849\) \(a_{75}=-0.099604796\)
\(a_{76}=+0.091646169\) \(a_{77}=+0.307939857\) \(a_{78}=-0.271220231\) \(a_{79}=+1.970060309\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.317434175\) \(a_{82}=+0.931439639\) \(a_{83}=+1.143608482\) \(a_{84}=-0.078232350\) \(a_{85}=-0.105509398\)
\(a_{86}=+0.548764799\) \(a_{87}=+0.293026486\) \(a_{88}=-0.346541138\) \(a_{89}=-0.009876722\) \(a_{90}=-0.237794462\)
\(a_{91}=-0.241965215\) \(a_{92}=-0.134521216\) \(a_{93}=+0.767311785\) \(a_{94}=-0.063632850\) \(a_{95}=-0.081970826\)
\(a_{96}=+0.088039034\) \(a_{97}=+0.148917349\) \(a_{98}=+0.637312919\) \(a_{99}=-0.737057765\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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