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: \( 25.7533242596 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.168725066\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.119306638\) \(a_{7}=+1.057567966\) \(a_{8}=+0.353553391\) \(a_{9}=-0.971531852\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.238378379\) \(a_{12}=-0.084362533\) \(a_{13}=-0.938095439\) \(a_{14}=+0.747813481\) \(a_{15}=+0.075456143\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.571456514\) \(a_{18}=-0.686976761\) \(a_{19}=+0.287880281\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.178438225\) \(a_{22}=+0.168558969\) \(a_{23}=-1.772356604\) \(a_{24}=-0.059653319\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.663333646\) \(a_{27}=+0.332646842\) \(a_{28}=+0.528783983\) \(a_{29}=+0.196682007\) \(a_{30}=+0.053355551\)
\(a_{31}=+0.168826783\) \(a_{32}=+0.176776695\) \(a_{33}=-0.040220408\) \(a_{34}=+1.111187558\) \(a_{35}=-0.472958773\)
\(a_{36}=-0.485765926\) \(a_{37}=-1.246648324\) \(a_{38}=+0.203562099\) \(a_{39}=+0.158280215\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.056470010\) \(a_{42}=-0.126174879\) \(a_{43}=+1.038191547\) \(a_{44}=+0.119189190\) \(a_{45}=+0.434482253\)
\(a_{46}=-1.253245373\) \(a_{47}=-1.129357882\) \(a_{48}=-0.042181267\) \(a_{49}=+0.118450004\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.265144104\) \(a_{52}=-0.469047719\) \(a_{53}=+0.967221987\) \(a_{54}=+0.235216838\) \(a_{55}=-0.106606052\)
\(a_{56}=+0.373906740\) \(a_{57}=-0.048572619\) \(a_{58}=+0.139075181\) \(a_{59}=+1.928571630\) \(a_{60}=+0.037728072\)
\(a_{61}=+0.008177341\) \(a_{62}=+0.119378563\) \(a_{63}=-1.027460965\) \(a_{64}=+0.125000000\) \(a_{65}=+0.419529034\)
\(a_{66}=-0.028440123\) \(a_{67}=-1.859614255\) \(a_{68}=+0.785728257\) \(a_{69}=+0.299040985\) \(a_{70}=-0.334432355\)
\(a_{71}=-0.923831902\) \(a_{72}=-0.343488380\) \(a_{73}=-0.460336397\) \(a_{74}=-0.881513484\) \(a_{75}=-0.033745013\)
\(a_{76}=+0.143940140\) \(a_{77}=+0.252101338\) \(a_{78}=+0.111921013\) \(a_{79}=+0.097075543\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.915405992\) \(a_{82}=-0.039930327\) \(a_{83}=-0.493418199\) \(a_{84}=-0.089219113\) \(a_{85}=-0.702776718\)
\(a_{86}=+0.734112283\) \(a_{87}=-0.033185185\) \(a_{88}=+0.084279484\) \(a_{89}=-1.744216332\) \(a_{90}=+0.307225347\)
\(a_{91}=-0.992099686\) \(a_{92}=-0.886178302\) \(a_{93}=-0.028485310\) \(a_{94}=-0.798576617\) \(a_{95}=-0.128743975\)
\(a_{96}=-0.029826660\) \(a_{97}=+1.023740490\) \(a_{98}=+0.083756801\) \(a_{99}=-0.231592188\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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