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: \( 1.4463991334 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.508340955\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.359451336\) \(a_{7}=+0.084835778\) \(a_{8}=-0.353553391\) \(a_{9}=-0.741589474\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.245263814\) \(a_{12}=-0.254170477\) \(a_{13}=+1.037936094\) \(a_{14}=-0.059987954\) \(a_{15}=-0.227336986\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.056631553\) \(a_{18}=+0.524382946\) \(a_{19}=-0.313648788\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.043125500\) \(a_{22}=-0.173427706\) \(a_{23}=-1.670386735\) \(a_{24}=+0.179725668\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.733931650\) \(a_{27}=+0.885321256\) \(a_{28}=+0.042417889\) \(a_{29}=+1.265251115\) \(a_{30}=+0.160751524\)
\(a_{31}=+0.556932578\) \(a_{32}=-0.176776695\) \(a_{33}=-0.124677641\) \(a_{34}=+0.040044555\) \(a_{35}=+0.037939713\)
\(a_{36}=-0.370794737\) \(a_{37}=-1.246320407\) \(a_{38}=+0.221783185\) \(a_{39}=-0.527625425\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.409585579\) \(a_{42}=+0.030494334\) \(a_{43}=+0.656277230\) \(a_{44}=+0.122631907\) \(a_{45}=-0.331648895\)
\(a_{46}=+1.181141787\) \(a_{47}=+0.821072406\) \(a_{48}=-0.127085239\) \(a_{49}=-0.992802891\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.028788138\) \(a_{52}=+0.518968047\) \(a_{53}=+1.122603770\) \(a_{54}=-0.626016663\) \(a_{55}=+0.109685312\)
\(a_{56}=-0.029993977\) \(a_{57}=+0.159440524\) \(a_{58}=-0.894667643\) \(a_{59}=-0.243331957\) \(a_{60}=-0.113668493\)
\(a_{61}=-0.381116000\) \(a_{62}=-0.393810803\) \(a_{63}=-0.062913320\) \(a_{64}=+0.125000000\) \(a_{65}=+0.464179132\)
\(a_{66}=+0.088160406\) \(a_{67}=-0.766625000\) \(a_{68}=-0.028315777\) \(a_{69}=+0.849125987\) \(a_{70}=-0.026827428\)
\(a_{71}=-0.335490000\) \(a_{72}=+0.262191473\) \(a_{73}=-0.223340000\) \(a_{74}=+0.881281611\) \(a_{75}=-0.101668191\)
\(a_{76}=-0.156824394\) \(a_{77}=+0.020807146\) \(a_{78}=+0.373087516\) \(a_{79}=+1.316420000\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.291544421\) \(a_{82}=+0.289620740\) \(a_{83}=-1.514809996\) \(a_{84}=-0.021562750\) \(a_{85}=-0.025326401\)
\(a_{86}=-0.464058080\) \(a_{87}=-0.643178959\) \(a_{88}=-0.086713853\) \(a_{89}=-0.864000320\) \(a_{90}=+0.234511183\)
\(a_{91}=+0.088054116\) \(a_{92}=-0.835193367\) \(a_{93}=-0.283111638\) \(a_{94}=-0.580585866\) \(a_{95}=-0.140268002\)
\(a_{96}=+0.089862834\) \(a_{97}=+1.901992798\) \(a_{98}=+0.702017656\) \(a_{99}=-0.181885063\) \(a_{100}=+0.099975586\)

Showing 100 of 106 available coefficients

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