Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 31.4042589826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.782419767\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.553254323\) \(a_{7}=-0.165907235\) \(a_{8}=+0.353553391\) \(a_{9}=-0.387819308\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.035702969\) \(a_{12}=+0.391209884\) \(a_{13}=+1.602547338\) \(a_{14}=-0.117314131\) \(a_{15}=+0.349908757\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.831474497\) \(a_{18}=-0.274229662\) \(a_{19}=-1.499200791\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.129809100\) \(a_{22}=+0.025245812\) \(a_{23}=-1.152507754\) \(a_{24}=+0.276627162\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.133172090\) \(a_{27}=-1.085857260\) \(a_{28}=-0.082953617\) \(a_{29}=-1.046080547\) \(a_{30}=+0.247422855\)
\(a_{31}=+1.291370617\) \(a_{32}=+0.176776695\) \(a_{33}=+0.027934709\) \(a_{34}=-0.587941255\) \(a_{35}=-0.074195971\)
\(a_{36}=-0.193909654\) \(a_{37}=+0.106697568\) \(a_{38}=-1.060095046\) \(a_{39}=+1.253864715\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.868618888\) \(a_{42}=-0.091788895\) \(a_{43}=+0.634310643\) \(a_{44}=+0.017851485\) \(a_{45}=-0.173438067\)
\(a_{46}=-0.814946048\) \(a_{47}=+0.824542661\) \(a_{48}=+0.195604942\) \(a_{49}=-0.972474789\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.650562083\) \(a_{52}=+0.801273669\) \(a_{53}=-0.791694851\) \(a_{54}=-0.767817032\) \(a_{55}=+0.015966853\)
\(a_{56}=-0.058657065\) \(a_{57}=-1.173004334\) \(a_{58}=-0.739690648\) \(a_{59}=+1.415778059\) \(a_{60}=+0.174954379\)
\(a_{61}=-0.690152712\) \(a_{62}=+0.913136920\) \(a_{63}=+0.064342029\) \(a_{64}=+0.125000000\) \(a_{65}=+0.716680957\)
\(a_{66}=+0.019752822\) \(a_{67}=-0.015333984\) \(a_{68}=-0.415737249\) \(a_{69}=-0.901744849\) \(a_{70}=-0.052464474\)
\(a_{71}=-1.512035460\) \(a_{72}=-0.137114831\) \(a_{73}=-0.705472303\) \(a_{74}=+0.075446574\) \(a_{75}=+0.156483953\)
\(a_{76}=-0.749600396\) \(a_{77}=-0.005923381\) \(a_{78}=+0.886616243\) \(a_{79}=-0.112999942\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.461776877\) \(a_{82}=-1.321313088\) \(a_{83}=-0.894210694\) \(a_{84}=-0.064904550\) \(a_{85}=-0.371846699\)
\(a_{86}=+0.448525357\) \(a_{87}=-0.818474098\) \(a_{88}=+0.012622906\) \(a_{89}=+1.548244980\) \(a_{90}=-0.122639233\)
\(a_{91}=-0.265874198\) \(a_{92}=-0.576253877\) \(a_{93}=+1.010393897\) \(a_{94}=+0.583039707\) \(a_{95}=-0.670462976\)
\(a_{96}=+0.138313581\) \(a_{97}=+0.113565542\) \(a_{98}=-0.687643518\) \(a_{99}=-0.013846301\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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