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: \( 26.7592831751 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.102073070\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.072176560\) \(a_{7}=-1.152636144\) \(a_{8}=+0.353553391\) \(a_{9}=-0.989581088\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.640849566\) \(a_{12}=+0.051036535\) \(a_{13}=-0.127317104\) \(a_{14}=-0.815036834\) \(a_{15}=-0.045648465\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.365084652\) \(a_{18}=-0.699739498\) \(a_{19}=+0.849228180\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.117653110\) \(a_{22}=+1.160255855\) \(a_{23}=+0.604588038\) \(a_{24}=+0.036088280\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.090026787\) \(a_{27}=-0.203082650\) \(a_{28}=-0.576318072\) \(a_{29}=+1.451638408\) \(a_{30}=-0.032278339\)
\(a_{31}=+0.586992039\) \(a_{32}=+0.176776695\) \(a_{33}=+0.167486553\) \(a_{34}=-0.258153833\) \(a_{35}=+0.515474554\)
\(a_{36}=-0.494790544\) \(a_{37}=+0.173633683\) \(a_{38}=+0.600495005\) \(a_{39}=-0.012995648\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.212923206\) \(a_{42}=-0.083193312\) \(a_{43}=-0.573644454\) \(a_{44}=+0.820424783\) \(a_{45}=+0.442554117\)
\(a_{46}=+0.427508302\) \(a_{47}=-1.103827630\) \(a_{48}=+0.025518268\) \(a_{49}=+0.328570080\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.037265311\) \(a_{52}=-0.063658552\) \(a_{53}=-1.156963898\) \(a_{54}=-0.143601119\) \(a_{55}=-0.733810234\)
\(a_{56}=-0.407518417\) \(a_{57}=+0.086683328\) \(a_{58}=+1.026463362\) \(a_{59}=-0.595470049\) \(a_{60}=-0.022824232\)
\(a_{61}=+0.323622167\) \(a_{62}=+0.415066051\) \(a_{63}=+1.140626930\) \(a_{64}=+0.125000000\) \(a_{65}=+0.056937940\)
\(a_{66}=+0.118430877\) \(a_{67}=-0.361890640\) \(a_{68}=-0.182542326\) \(a_{69}=+0.061712157\) \(a_{70}=+0.364495553\)
\(a_{71}=+1.061240916\) \(a_{72}=-0.349869749\) \(a_{73}=-1.682703151\) \(a_{74}=+0.122777555\) \(a_{75}=+0.020414614\)
\(a_{76}=+0.424614090\) \(a_{77}=-1.891302517\) \(a_{78}=-0.009189311\) \(a_{79}=-1.924245585\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.968851819\) \(a_{82}=-0.857666224\) \(a_{83}=+0.748665462\) \(a_{84}=-0.058826555\) \(a_{85}=+0.163270820\)
\(a_{86}=-0.405627883\) \(a_{87}=+0.148173189\) \(a_{88}=+0.580127928\) \(a_{89}=-0.389725275\) \(a_{90}=+0.312933017\)
\(a_{91}=+0.146750295\) \(a_{92}=+0.302294019\) \(a_{93}=+0.059916080\) \(a_{94}=-0.780524002\) \(a_{95}=-0.379786388\)
\(a_{96}=+0.018044140\) \(a_{97}=-1.586052745\) \(a_{98}=+0.232334132\) \(a_{99}=-1.623753700\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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