Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 26.2945508064 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.024719207\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.724585900\) \(a_{7}=-1.749156195\) \(a_{8}=-0.353553391\) \(a_{9}=+0.050049454\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.742231647\) \(a_{12}=-0.512359604\) \(a_{13}=+0.300496356\) \(a_{14}=+1.236840207\) \(a_{15}=+0.458268361\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.137242362\) \(a_{18}=-0.035390308\) \(a_{19}=+0.683055284\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.792393950\) \(a_{22}=+1.231943812\) \(a_{23}=-0.613399708\) \(a_{24}=+0.362292950\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.212483011\) \(a_{27}=+0.973432571\) \(a_{28}=-0.874578098\) \(a_{29}=+0.659775769\) \(a_{30}=-0.324044666\)
\(a_{31}=-0.787574519\) \(a_{32}=-0.176776695\) \(a_{33}=+1.785298233\) \(a_{34}=+0.804151786\) \(a_{35}=+0.782246431\)
\(a_{36}=+0.025024727\) \(a_{37}=-1.613083912\) \(a_{38}=-0.482993023\) \(a_{39}=-0.307924388\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.127759270\) \(a_{42}=-1.267413917\) \(a_{43}=-0.170472960\) \(a_{44}=-0.871115824\) \(a_{45}=-0.022382796\)
\(a_{46}=+0.433739093\) \(a_{47}=+0.603357281\) \(a_{48}=-0.256179802\) \(a_{49}=+2.059547396\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.165354091\) \(a_{52}=+0.150248178\) \(a_{53}=-0.634877460\) \(a_{54}=-0.688320772\) \(a_{55}=+0.779149679\)
\(a_{56}=+0.618420104\) \(a_{57}=-0.699939869\) \(a_{58}=-0.466531920\) \(a_{59}=+1.463326211\) \(a_{60}=+0.229134181\)
\(a_{61}=+0.483640653\) \(a_{62}=+0.556899283\) \(a_{63}=-0.087544313\) \(a_{64}=+0.125000000\) \(a_{65}=-0.134386056\)
\(a_{66}=-1.262396487\) \(a_{67}=+1.176405094\) \(a_{68}=-0.568621181\) \(a_{69}=+0.628562463\) \(a_{70}=-0.553131756\)
\(a_{71}=-0.149651804\) \(a_{72}=-0.017695154\) \(a_{73}=-1.128148962\) \(a_{74}=+1.140622573\) \(a_{75}=-0.204943841\)
\(a_{76}=+0.341527642\) \(a_{77}=+3.047435279\) \(a_{78}=+0.217735423\) \(a_{79}=-0.726052653\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.047544506\) \(a_{82}=+0.090339446\) \(a_{83}=+1.786108057\) \(a_{84}=+0.896196975\) \(a_{85}=+0.508590246\)
\(a_{86}=+0.120542586\) \(a_{87}=-0.676084903\) \(a_{88}=+0.615971906\) \(a_{89}=+1.524890328\) \(a_{90}=+0.015827027\)
\(a_{91}=-0.525615063\) \(a_{92}=-0.306699854\) \(a_{93}=+0.807042737\) \(a_{94}=-0.426638025\) \(a_{95}=-0.305471609\)
\(a_{96}=+0.181146475\) \(a_{97}=+1.128371887\) \(a_{98}=-1.456319930\) \(a_{99}=-0.087197743\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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