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: \( 29.5841732525 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.223472010\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.865125355\) \(a_{7}=-1.169752548\) \(a_{8}=-0.353553391\) \(a_{9}=+0.496883759\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.419182601\) \(a_{12}=+0.611736005\) \(a_{13}=-0.978405549\) \(a_{14}=+0.827139959\) \(a_{15}=+0.547153317\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.840520472\) \(a_{18}=-0.351349875\) \(a_{19}=+0.794005491\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.431159501\) \(a_{22}=+0.296406860\) \(a_{23}=+1.088585884\) \(a_{24}=-0.432562677\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.691837198\) \(a_{27}=-0.615548639\) \(a_{28}=-0.584876274\) \(a_{29}=-0.793154328\) \(a_{30}=-0.386895820\)
\(a_{31}=-1.065056177\) \(a_{32}=-0.176776695\) \(a_{33}=-0.512858180\) \(a_{34}=+0.594337725\) \(a_{35}=-0.523129243\)
\(a_{36}=+0.248441879\) \(a_{37}=-1.472230183\) \(a_{38}=-0.561446667\) \(a_{39}=-1.197051803\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.040243629\) \(a_{42}=+1.011982588\) \(a_{43}=+0.691494606\) \(a_{44}=-0.209591301\) \(a_{45}=+0.222213172\)
\(a_{46}=-0.769746460\) \(a_{47}=+1.274865083\) \(a_{48}=+0.305868002\) \(a_{49}=+0.368321023\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.028353271\) \(a_{52}=-0.489202774\) \(a_{53}=-0.770408772\) \(a_{54}=+0.435258617\) \(a_{55}=-0.187464158\)
\(a_{56}=+0.413569979\) \(a_{57}=+0.971443494\) \(a_{58}=+0.560844804\) \(a_{59}=+0.359309897\) \(a_{60}=+0.273576658\)
\(a_{61}=+0.180039922\) \(a_{62}=+0.753108445\) \(a_{63}=-0.581231043\) \(a_{64}=+0.125000000\) \(a_{65}=-0.437556263\)
\(a_{66}=+0.362645497\) \(a_{67}=+0.032692483\) \(a_{68}=-0.420260236\) \(a_{69}=+1.331854359\) \(a_{70}=+0.369908235\)
\(a_{71}=+1.639495627\) \(a_{72}=-0.175674938\) \(a_{73}=-0.276805387\) \(a_{74}=+1.041023946\) \(a_{75}=+0.244694402\)
\(a_{76}=+0.397002745\) \(a_{77}=+0.490339916\) \(a_{78}=+0.846443447\) \(a_{79}=+1.798141253\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.249990289\) \(a_{82}=-0.735563324\) \(a_{83}=+1.517971923\) \(a_{84}=-0.715579750\) \(a_{85}=-0.375892182\)
\(a_{86}=-0.488960525\) \(a_{87}=-0.970402120\) \(a_{88}=+0.148203430\) \(a_{89}=+1.444421297\) \(a_{90}=-0.157128441\)
\(a_{91}=+1.144492383\) \(a_{92}=+0.544292942\) \(a_{93}=-1.303066422\) \(a_{94}=-0.901465745\) \(a_{95}=+0.355090050\)
\(a_{96}=-0.216281339\) \(a_{97}=-0.131009530\) \(a_{98}=-0.260442293\) \(a_{99}=-0.208285027\) \(a_{100}=+0.099975586\)

Showing 100 of 247 available coefficients

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