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: \( 19.9058807142 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.461198431\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.033223319\) \(a_{7}=+0.299236994\) \(a_{8}=-0.353553391\) \(a_{9}=+1.135100855\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.599091316\) \(a_{12}=+0.730599216\) \(a_{13}=+0.572306904\) \(a_{14}=-0.211592508\) \(a_{15}=+0.653467804\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.180151534\) \(a_{18}=-0.802637512\) \(a_{19}=-0.162652296\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.437244627\) \(a_{22}=+1.130728314\) \(a_{23}=-1.517038596\) \(a_{24}=-0.516611660\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.404682093\) \(a_{27}=+0.197409157\) \(a_{28}=+0.149618497\) \(a_{29}=-0.907412760\) \(a_{30}=-0.462071516\)
\(a_{31}=-1.844354156\) \(a_{32}=-0.176776695\) \(a_{33}=-2.336589723\) \(a_{34}=-0.127386371\) \(a_{35}=+0.133822852\)
\(a_{36}=+0.567550427\) \(a_{37}=-1.443154932\) \(a_{38}=+0.115012541\) \(a_{39}=+0.836253951\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.871848908\) \(a_{42}=-0.309178641\) \(a_{43}=+0.150646865\) \(a_{44}=-0.799545658\) \(a_{45}=+0.507632535\)
\(a_{46}=+1.072708279\) \(a_{47}=-0.031262444\) \(a_{48}=+0.365299608\) \(a_{49}=-0.910457221\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.263237138\) \(a_{52}=+0.286153452\) \(a_{53}=+0.247275575\) \(a_{54}=-0.139589354\) \(a_{55}=-0.715135377\)
\(a_{56}=-0.105796254\) \(a_{57}=-0.237667280\) \(a_{58}=+0.641637716\) \(a_{59}=+0.121263381\) \(a_{60}=+0.326733902\)
\(a_{61}=+0.104192581\) \(a_{62}=+1.304155331\) \(a_{63}=+0.339664168\) \(a_{64}=+0.125000000\) \(a_{65}=+0.255943428\)
\(a_{66}=+1.652218438\) \(a_{67}=+0.289109663\) \(a_{68}=+0.090075767\) \(a_{69}=-2.216694417\) \(a_{70}=-0.094627046\)
\(a_{71}=+1.464967674\) \(a_{72}=-0.401318756\) \(a_{73}=-0.927011396\) \(a_{74}=+1.020464639\) \(a_{75}=+0.292239686\)
\(a_{76}=-0.081326148\) \(a_{77}=-0.478507279\) \(a_{78}=-0.591320839\) \(a_{79}=-0.069948324\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.846646904\) \(a_{82}=-1.323597056\) \(a_{83}=+0.347467383\) \(a_{84}=+0.218622313\) \(a_{85}=+0.080566215\)
\(a_{86}=-0.106523420\) \(a_{87}=-1.325910101\) \(a_{88}=+0.565364157\) \(a_{89}=-0.983830243\) \(a_{90}=-0.358950408\)
\(a_{91}=+0.171255398\) \(a_{92}=-0.758519298\) \(a_{93}=-2.694967399\) \(a_{94}=+0.022105886\) \(a_{95}=-0.072740318\)
\(a_{96}=-0.258305830\) \(a_{97}=-0.296286056\) \(a_{98}=+0.643790475\) \(a_{99}=-1.815129920\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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