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: \( 30.0339879166 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.363514183\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.257043344\) \(a_{7}=-0.522733629\) \(a_{8}=-0.353553391\) \(a_{9}=-0.867857439\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.622115708\) \(a_{12}=+0.181757092\) \(a_{13}=-0.196432244\) \(a_{14}=+0.369628494\) \(a_{15}=-0.162568485\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.570087022\) \(a_{18}=+0.613667880\) \(a_{19}=-0.122672188\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.190021088\) \(a_{22}=+0.439902236\) \(a_{23}=-1.140900787\) \(a_{24}=-0.128521672\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.138898572\) \(a_{27}=-0.678992671\) \(a_{28}=-0.261366814\) \(a_{29}=-1.258652939\) \(a_{30}=+0.114953278\)
\(a_{31}=+0.075949539\) \(a_{32}=-0.176776695\) \(a_{33}=-0.226147883\) \(a_{34}=+0.403112399\) \(a_{35}=+0.233773586\)
\(a_{36}=-0.433928719\) \(a_{37}=-0.683123839\) \(a_{38}=+0.086742336\) \(a_{39}=-0.071405907\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.527431065\) \(a_{42}=+0.134365200\) \(a_{43}=-0.942029923\) \(a_{44}=-0.311057854\) \(a_{45}=+0.388117645\)
\(a_{46}=+0.806738683\) \(a_{47}=+1.024090186\) \(a_{48}=+0.090878546\) \(a_{49}=-0.726749554\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.207234718\) \(a_{52}=-0.098216122\) \(a_{53}=-0.925602443\) \(a_{54}=+0.480120322\) \(a_{55}=+0.278218603\)
\(a_{56}=+0.184814247\) \(a_{57}=-0.044593080\) \(a_{58}=+0.890002028\) \(a_{59}=+0.646516492\) \(a_{60}=-0.081284242\)
\(a_{61}=-0.002613374\) \(a_{62}=-0.053704434\) \(a_{63}=+0.453658268\) \(a_{64}=+0.125000000\) \(a_{65}=+0.087847170\)
\(a_{66}=+0.159910702\) \(a_{67}=-0.448984168\) \(a_{68}=-0.285043511\) \(a_{69}=-0.414733618\) \(a_{70}=-0.165302888\)
\(a_{71}=-0.803103359\) \(a_{72}=+0.306833940\) \(a_{73}=+1.284287438\) \(a_{74}=+0.483041499\) \(a_{75}=+0.072702837\)
\(a_{76}=-0.061336094\) \(a_{77}=+0.325200801\) \(a_{78}=+0.050491601\) \(a_{79}=+0.598556219\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.621033972\) \(a_{82}=+1.080056864\) \(a_{83}=-0.332227114\) \(a_{84}=-0.095010544\) \(a_{85}=+0.254950667\)
\(a_{86}=+0.666115747\) \(a_{87}=-0.457538195\) \(a_{88}=+0.219951118\) \(a_{89}=-1.191684206\) \(a_{90}=-0.274440619\)
\(a_{91}=+0.102681740\) \(a_{92}=-0.570450393\) \(a_{93}=+0.027608735\) \(a_{94}=-0.724141115\) \(a_{95}=+0.054860670\)
\(a_{96}=-0.064260836\) \(a_{97}=+0.067185798\) \(a_{98}=+0.513889538\) \(a_{99}=+0.539907745\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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