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: \( 25.1400643416 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.530898051\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.082508393\) \(a_{7}=+0.357741971\) \(a_{8}=+0.353553391\) \(a_{9}=+1.343648842\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.004157226\) \(a_{12}=-0.765449025\) \(a_{13}=+0.411297429\) \(a_{14}=+0.252961773\) \(a_{15}=-0.684638422\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.606268002\) \(a_{18}=+0.950103208\) \(a_{19}=+0.496567556\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.547666485\) \(a_{22}=+0.002939602\) \(a_{23}=+0.071450483\) \(a_{24}=-0.541254196\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.290831201\) \(a_{27}=-0.526091342\) \(a_{28}=+0.178870985\) \(a_{29}=-1.322400709\) \(a_{30}=-0.484112471\)
\(a_{31}=+0.378715821\) \(a_{32}=+0.176776695\) \(a_{33}=-0.006364288\) \(a_{34}=+1.135802997\) \(a_{35}=+0.159987073\)
\(a_{36}=+0.671824421\) \(a_{37}=+1.585449674\) \(a_{38}=+0.351126286\) \(a_{39}=-0.629654433\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.382695236\) \(a_{42}=-0.387258686\) \(a_{43}=+1.058789912\) \(a_{44}=+0.002078613\) \(a_{45}=+0.600898030\)
\(a_{46}=+0.050523121\) \(a_{47}=-0.991885300\) \(a_{48}=-0.382724513\) \(a_{49}=-0.872020683\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.459032553\) \(a_{52}=+0.205648715\) \(a_{53}=-1.134376572\) \(a_{54}=-0.372002756\) \(a_{55}=+0.001859168\)
\(a_{56}=+0.126480887\) \(a_{57}=-0.760194304\) \(a_{58}=-0.935078509\) \(a_{59}=-1.133146158\) \(a_{60}=-0.342319211\)
\(a_{61}=+1.104747550\) \(a_{62}=+0.267792525\) \(a_{63}=+0.480679584\) \(a_{64}=+0.125000000\) \(a_{65}=+0.183937802\)
\(a_{66}=-0.004500231\) \(a_{67}=+0.648416573\) \(a_{68}=+0.803134001\) \(a_{69}=-0.109383405\) \(a_{70}=+0.113127944\)
\(a_{71}=-0.079332224\) \(a_{72}=+0.475051604\) \(a_{73}=-1.716771504\) \(a_{74}=+1.121082216\) \(a_{75}=-0.306179610\)
\(a_{76}=+0.248283778\) \(a_{77}=+0.001487214\) \(a_{78}=-0.445232919\) \(a_{79}=+1.746764887\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.538256632\) \(a_{82}=-0.977713178\) \(a_{83}=+0.026392013\) \(a_{84}=-0.273833243\) \(a_{85}=+0.718344888\)
\(a_{86}=+0.748677527\) \(a_{87}=+2.024460668\) \(a_{88}=+0.001469801\) \(a_{89}=+1.152648517\) \(a_{90}=+0.424899072\)
\(a_{91}=+0.147138353\) \(a_{92}=+0.035725241\) \(a_{93}=-0.579775312\) \(a_{94}=-0.701368821\) \(a_{95}=+0.222071762\)
\(a_{96}=-0.270627098\) \(a_{97}=+0.196288917\) \(a_{98}=-0.616611738\) \(a_{99}=+0.005585851\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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