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: \( 15.5673897311 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.526492832\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.372286652\) \(a_{7}=+1.151886130\) \(a_{8}=+0.353553391\) \(a_{9}=-0.722805298\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.888263699\) \(a_{12}=-0.263246416\) \(a_{13}=-0.569876292\) \(a_{14}=+0.814506493\) \(a_{15}=+0.235454752\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.163204922\) \(a_{18}=-0.511100528\) \(a_{19}=-1.151121294\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.606459790\) \(a_{22}=+0.628097285\) \(a_{23}=+0.627237615\) \(a_{24}=-0.186143326\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.402963391\) \(a_{27}=+0.907044640\) \(a_{28}=+0.575943065\) \(a_{29}=+1.538291447\) \(a_{30}=+0.166491652\)
\(a_{31}=-0.124436535\) \(a_{32}=+0.176776695\) \(a_{33}=-0.467664470\) \(a_{34}=-0.115403307\) \(a_{35}=-0.515139138\)
\(a_{36}=-0.361402649\) \(a_{37}=-0.284818886\) \(a_{38}=-0.813965673\) \(a_{39}=+0.300035783\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.685367416\) \(a_{42}=-0.428831830\) \(a_{43}=-1.253200432\) \(a_{44}=+0.444131850\) \(a_{45}=+0.323248356\)
\(a_{46}=+0.443523971\) \(a_{47}=+1.362778728\) \(a_{48}=-0.131623208\) \(a_{49}=+0.326841656\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.085926221\) \(a_{52}=-0.284938146\) \(a_{53}=+1.334339986\) \(a_{54}=+0.641377416\) \(a_{55}=-0.397243603\)
\(a_{56}=+0.407253247\) \(a_{57}=+0.606057110\) \(a_{58}=+1.087736314\) \(a_{59}=+0.392610084\) \(a_{60}=+0.117727376\)
\(a_{61}=+1.891436423\) \(a_{62}=-0.087989918\) \(a_{63}=-0.832589397\) \(a_{64}=+0.125000000\) \(a_{65}=+0.254856426\)
\(a_{66}=-0.330688718\) \(a_{67}=+0.102914974\) \(a_{68}=-0.081602461\) \(a_{69}=-0.330236108\) \(a_{70}=-0.364258377\)
\(a_{71}=+1.376931774\) \(a_{72}=-0.255550264\) \(a_{73}=+1.266177861\) \(a_{74}=-0.201397366\) \(a_{75}=-0.105298566\)
\(a_{76}=-0.575560647\) \(a_{77}=+1.023178635\) \(a_{78}=+0.212157337\) \(a_{79}=-0.136589092\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.245252798\) \(a_{82}=+1.191734728\) \(a_{83}=-0.169724377\) \(a_{84}=-0.303229895\) \(a_{85}=+0.072987460\)
\(a_{86}=-0.886146524\) \(a_{87}=-0.809899420\) \(a_{88}=+0.314048643\) \(a_{89}=-1.078348565\) \(a_{90}=+0.228571105\)
\(a_{91}=-0.656432596\) \(a_{92}=+0.313618808\) \(a_{93}=+0.065514944\) \(a_{94}=+0.963630080\) \(a_{95}=+0.514797093\)
\(a_{96}=-0.093071663\) \(a_{97}=+1.046836155\) \(a_{98}=+0.231111951\) \(a_{99}=-0.642041714\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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