Properties

Level $5$
Weight $0$
Character 5.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.32552437933 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.129511870\) \(a_{3}=+0.804283739\) \(a_{4}=-0.983226676\) \(a_{5}=-0.447213596\)
\(a_{6}=-0.104164291\) \(a_{7}=-1.598177541\) \(a_{8}=+0.256851395\) \(a_{9}=-0.353127668\) \(a_{10}=+0.057919469\)
\(a_{11}=+0.763749451\) \(a_{12}=-0.790793227\) \(a_{13}=-0.551102876\) \(a_{14}=+0.206982963\) \(a_{15}=-0.359686626\)
\(a_{16}=+0.949961376\) \(a_{17}=+0.229847614\) \(a_{18}=+0.045734224\) \(a_{19}=-0.622634648\) \(a_{20}=+0.439712337\)
\(a_{21}=-1.285388208\) \(a_{22}=-0.098914619\) \(a_{23}=+0.917388761\) \(a_{24}=+0.206581400\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.071374364\) \(a_{27}=-1.088298580\) \(a_{28}=+1.571370791\) \(a_{29}=-0.075291958\) \(a_{30}=+0.046583687\)
\(a_{31}=-1.840554077\) \(a_{32}=-0.379882668\) \(a_{33}=+0.614271264\) \(a_{34}=-0.029767994\) \(a_{35}=+0.714726724\)
\(a_{36}=+0.347204543\) \(a_{37}=+0.587551989\) \(a_{38}=+0.080638577\) \(a_{39}=-0.443243081\) \(a_{40}=-0.114867436\)
\(a_{41}=-0.776471739\) \(a_{42}=+0.166473030\) \(a_{43}=+0.522940899\) \(a_{44}=-0.750938836\) \(a_{45}=+0.157923495\)
\(a_{46}=-0.118812733\) \(a_{47}=-1.447498414\) \(a_{48}=+0.764038491\) \(a_{49}=+1.554171451\) \(a_{50}=-0.025902385\)
\(a_{51}=+0.184862696\) \(a_{52}=+0.541859063\) \(a_{53}=-0.460077755\) \(a_{54}=+0.140947641\) \(a_{55}=-0.341559136\)
\(a_{56}=-0.410494228\) \(a_{57}=-0.500774861\) \(a_{58}=+0.009751038\) \(a_{59}=-0.779193900\) \(a_{60}=+0.353653832\)
\(a_{61}=+0.225030119\) \(a_{62}=+0.238373600\) \(a_{63}=+0.564360708\) \(a_{64}=-0.900762057\) \(a_{65}=+0.246460698\)
\(a_{66}=-0.079555420\) \(a_{67}=+1.249307122\) \(a_{68}=-0.225992305\) \(a_{69}=+0.737840863\) \(a_{70}=-0.092565594\)
\(a_{71}=-0.374127433\) \(a_{72}=-0.090701334\) \(a_{73}=-0.916408083\) \(a_{74}=-0.076094959\) \(a_{75}=+0.160856747\)
\(a_{76}=+0.612190997\) \(a_{77}=-1.220607218\) \(a_{78}=+0.057405238\) \(a_{79}=-0.183150792\) \(a_{80}=-0.424835641\)
\(a_{81}=-0.522173183\) \(a_{82}=+0.100562306\) \(a_{83}=+1.676459342\) \(a_{84}=+1.263827992\) \(a_{85}=-0.102790979\)
\(a_{86}=-0.067727071\) \(a_{87}=-0.060556106\) \(a_{88}=+0.196170114\) \(a_{89}=-0.676298149\) \(a_{90}=-0.020452962\)
\(a_{91}=+0.880760259\) \(a_{92}=-0.902001084\) \(a_{93}=-1.480327705\) \(a_{94}=+0.187468064\) \(a_{95}=+0.278450692\)
\(a_{96}=-0.305533327\) \(a_{97}=+1.087157467\) \(a_{98}=-0.201283598\) \(a_{99}=-0.269701067\) \(a_{100}=-0.196645335\)

Showing 100 of 5000 available coefficients

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