Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.89514361515 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.091818633\) \(a_{3}=+0.913548892\) \(a_{4}=-0.991569339\) \(a_{5}=-1.154608592\)
\(a_{6}=+0.083880810\) \(a_{7}=-0.693885094\) \(a_{8}=-0.182863174\) \(a_{9}=-0.165428423\) \(a_{10}=-0.106014583\)
\(a_{11}=+0.434455776\) \(a_{12}=-0.905847070\) \(a_{13}=-0.277350098\) \(a_{14}=-0.063711581\) \(a_{15}=-1.054791399\)
\(a_{16}=+0.974779092\) \(a_{17}=-0.359707062\) \(a_{18}=-0.015189412\) \(a_{19}=+1.243347158\) \(a_{20}=+1.144874478\)
\(a_{21}=-0.633897959\) \(a_{22}=+0.039891135\) \(a_{23}=-1.635642689\) \(a_{24}=-0.167054450\) \(a_{25}=+0.333121001\)
\(a_{26}=-0.025465907\) \(a_{27}=-1.064675844\) \(a_{28}=+0.688035184\) \(a_{29}=+1.210033565\) \(a_{30}=-0.096849504\)
\(a_{31}=-1.615260518\) \(a_{32}=+0.272366058\) \(a_{33}=+0.396896593\) \(a_{34}=-0.033027811\) \(a_{35}=+0.801165692\)
\(a_{36}=+0.164033751\) \(a_{37}=+0.613654093\) \(a_{38}=+0.114162436\) \(a_{39}=-0.253372875\) \(a_{40}=+0.211135392\)
\(a_{41}=-0.514772239\) \(a_{42}=-0.058203644\) \(a_{43}=-0.443315417\) \(a_{44}=-0.430793027\) \(a_{45}=+0.191005078\)
\(a_{46}=-0.150182476\) \(a_{47}=-1.002035399\) \(a_{48}=+0.890508359\) \(a_{49}=-0.518523476\) \(a_{50}=+0.030586715\)
\(a_{51}=-0.328609988\) \(a_{52}=+0.275011853\) \(a_{53}=+0.447541607\) \(a_{54}=-0.097757081\) \(a_{55}=-0.501626372\)
\(a_{56}=+0.126886031\) \(a_{57}=+1.135858418\) \(a_{58}=+0.111103628\) \(a_{59}=+1.554303874\) \(a_{60}=+1.045898810\)
\(a_{61}=-1.511811523\) \(a_{62}=-0.148311013\) \(a_{63}=+0.114788317\) \(a_{64}=-0.949770813\) \(a_{65}=+0.320230806\)
\(a_{66}=+0.036442503\) \(a_{67}=-1.037282602\) \(a_{68}=+0.356674494\) \(a_{69}=-1.494239566\) \(a_{70}=+0.073561939\)
\(a_{71}=+0.367718761\) \(a_{72}=+0.030250766\) \(a_{73}=+1.455106412\) \(a_{74}=+0.056344880\) \(a_{75}=+0.304322321\)
\(a_{76}=-1.232864919\) \(a_{77}=-0.301462387\) \(a_{78}=-0.023264351\) \(a_{79}=+0.025157602\) \(a_{80}=-1.125488315\)
\(a_{81}=-0.807205015\) \(a_{82}=-0.047265683\) \(a_{83}=+1.574679148\) \(a_{84}=+0.628553780\) \(a_{85}=+0.415320865\)
\(a_{86}=-0.040704616\) \(a_{87}=+1.105424822\) \(a_{88}=-0.079445962\) \(a_{89}=+0.679852917\) \(a_{90}=+0.017537825\)
\(a_{91}=+0.192449099\) \(a_{92}=+1.621853139\) \(a_{93}=-1.475619456\) \(a_{94}=-0.092005521\) \(a_{95}=-1.435579311\)
\(a_{96}=+0.248819711\) \(a_{97}=-0.537817638\) \(a_{98}=-0.047610117\) \(a_{99}=-0.071871334\) \(a_{100}=-0.330312570\)

Showing 100 of 546 available coefficients

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