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: \( 20.2676618424 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.353444777\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.957029980\) \(a_{7}=-0.510640443\) \(a_{8}=-0.353553391\) \(a_{9}=+0.831812763\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.572456626\) \(a_{12}=-0.676722388\) \(a_{13}=+0.604548629\) \(a_{14}=+0.361077320\) \(a_{15}=+0.605278905\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.050487646\) \(a_{18}=-0.588180446\) \(a_{19}=+0.458338663\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.691123640\) \(a_{22}=+0.404787962\) \(a_{23}=+0.734765488\) \(a_{24}=+0.478514990\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.427480435\) \(a_{27}=+0.227632137\) \(a_{28}=-0.255320222\) \(a_{29}=-1.698245453\) \(a_{30}=-0.427996818\)
\(a_{31}=-1.399912793\) \(a_{32}=-0.176776695\) \(a_{33}=+0.774788430\) \(a_{34}=+0.742806938\) \(a_{35}=+0.228365349\)
\(a_{36}=+0.415906382\) \(a_{37}=-1.234894804\) \(a_{38}=-0.324094376\) \(a_{39}=-0.818223184\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.181780433\) \(a_{42}=-0.488698213\) \(a_{43}=+0.612492786\) \(a_{44}=-0.286228313\) \(a_{45}=-0.371997977\)
\(a_{46}=-0.519557659\) \(a_{47}=-1.053054112\) \(a_{48}=-0.338361194\) \(a_{49}=-0.739246338\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.421777017\) \(a_{52}=+0.302274315\) \(a_{53}=-0.157701406\) \(a_{54}=-0.160960228\) \(a_{55}=+0.256010386\)
\(a_{56}=+0.180538660\) \(a_{57}=-0.620336069\) \(a_{58}=+1.200840876\) \(a_{59}=-1.795981906\) \(a_{60}=+0.302639452\)
\(a_{61}=-0.786193542\) \(a_{62}=+0.989887829\) \(a_{63}=-0.424757238\) \(a_{64}=+0.125000000\) \(a_{65}=-0.270362366\)
\(a_{66}=-0.547858153\) \(a_{67}=-1.024928796\) \(a_{68}=-0.525243823\) \(a_{69}=-0.994464512\) \(a_{70}=-0.161478687\)
\(a_{71}=-0.730723441\) \(a_{72}=-0.294090223\) \(a_{73}=+1.263340999\) \(a_{74}=+0.873202490\) \(a_{75}=-0.270688955\)
\(a_{76}=+0.229169331\) \(a_{77}=+0.292319505\) \(a_{78}=+0.578571162\) \(a_{79}=+0.161250180\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.139900290\) \(a_{82}=+0.835644958\) \(a_{83}=-1.119649297\) \(a_{84}=+0.345561820\) \(a_{85}=+0.469792357\)
\(a_{86}=-0.433097803\) \(a_{87}=+2.298481438\) \(a_{88}=+0.202393981\) \(a_{89}=+0.665810441\) \(a_{90}=+0.263042292\)
\(a_{91}=-0.308706980\) \(a_{92}=+0.367382744\) \(a_{93}=+1.894704658\) \(a_{94}=+0.744621703\) \(a_{95}=-0.204975281\)
\(a_{96}=+0.239257495\) \(a_{97}=+0.921702768\) \(a_{98}=+0.522726099\) \(a_{99}=-0.476176728\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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