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: \( 9.02977428596 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.939086125\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213596\)
\(a_{6}=+1.371140948\) \(a_{7}=+0.570132136\) \(a_{8}=-0.353553391\) \(a_{9}=+2.760054999\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.588789241\) \(a_{12}=-0.969543062\) \(a_{13}=-0.367206274\) \(a_{14}=-0.403144300\) \(a_{15}=+0.867185678\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.696784301\) \(a_{18}=-1.951653606\) \(a_{19}=-0.490185317\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.105535315\) \(a_{22}=-0.416336865\) \(a_{23}=+1.246281559\) \(a_{24}=+0.685570474\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.259654046\) \(a_{27}=-3.412898228\) \(a_{28}=+0.285066068\) \(a_{29}=+1.686728681\) \(a_{30}=-0.613192873\)
\(a_{31}=+0.223552467\) \(a_{32}=-0.176776695\) \(a_{33}=-1.141713048\) \(a_{34}=+0.492700904\) \(a_{35}=-0.254970843\)
\(a_{36}=+1.380027501\) \(a_{37}=-1.466956940\) \(a_{38}=+0.346613361\) \(a_{39}=+0.712044589\) \(a_{40}=+0.158113885\)
\(a_{41}=-0.538555741\) \(a_{42}=+0.781731510\) \(a_{43}=+0.548127023\) \(a_{44}=+0.294394613\) \(a_{45}=-1.234334135\)
\(a_{46}=-0.881254112\) \(a_{47}=+0.240824224\) \(a_{48}=-0.484771415\) \(a_{49}=-0.674949347\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.351124771\) \(a_{52}=-0.183603137\) \(a_{53}=-1.070947129\) \(a_{54}=+2.413283480\) \(a_{55}=-0.263314554\)
\(a_{56}=-0.201572150\) \(a_{57}=+0.950511547\) \(a_{58}=-1.192697288\) \(a_{59}=-0.403462557\) \(a_{60}=+0.433592839\)
\(a_{61}=-0.842447093\) \(a_{62}=-0.158075465\) \(a_{63}=+1.573596053\) \(a_{64}=+0.125000000\) \(a_{65}=+0.164219638\)
\(a_{66}=+0.807313039\) \(a_{67}=-0.843032546\) \(a_{68}=-0.348392151\) \(a_{69}=-2.416647277\) \(a_{70}=+0.180291611\)
\(a_{71}=+0.965770153\) \(a_{72}=-0.975826802\) \(a_{73}=-0.207169321\) \(a_{74}=+1.037295202\) \(a_{75}=-0.387817225\)
\(a_{76}=-0.245092660\) \(a_{77}=+0.335687663\) \(a_{78}=-0.503491549\) \(a_{79}=+0.487800238\) \(a_{80}=-0.111803401\)
\(a_{81}=+3.857848604\) \(a_{82}=+0.380816426\) \(a_{83}=+0.375138920\) \(a_{84}=-0.552767635\) \(a_{85}=+0.311611439\)
\(a_{86}=-0.387584343\) \(a_{87}=-3.270712211\) \(a_{88}=-0.208168378\) \(a_{89}=-1.693631229\) \(a_{90}=+0.872806005\)
\(a_{91}=-0.209356097\) \(a_{92}=+0.623140779\) \(a_{93}=-0.433487487\) \(a_{94}=-0.170288485\) \(a_{95}=+0.219217539\)
\(a_{96}=+0.342785238\) \(a_{97}=+0.282123477\) \(a_{98}=+0.477261261\) \(a_{99}=+1.625090687\) \(a_{100}=+0.100000000\)

Showing 100 of 2000 available coefficients

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