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: \( 13.3121869995 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.314971969\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.929825596\) \(a_{7}=+0.917647866\) \(a_{8}=-0.353553391\) \(a_{9}=+0.729151280\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.929780429\) \(a_{12}=+0.657485985\) \(a_{13}=-1.856797388\) \(a_{14}=-0.648875029\) \(a_{15}=+0.588073342\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.535991942\) \(a_{18}=-0.515587814\) \(a_{19}=-0.998533767\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.206681221\) \(a_{22}=+1.364560828\) \(a_{23}=+0.201042261\) \(a_{24}=-0.464912798\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.312954024\) \(a_{27}=-0.356158475\) \(a_{28}=+0.458823933\) \(a_{29}=+0.071502012\) \(a_{30}=-0.415830648\)
\(a_{31}=+0.759722033\) \(a_{32}=-0.176776695\) \(a_{33}=-2.537607171\) \(a_{34}=+0.379003537\) \(a_{35}=+0.410384602\)
\(a_{36}=+0.364575640\) \(a_{37}=-0.825097386\) \(a_{38}=+0.706069998\) \(a_{39}=-2.441636518\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.095902793\) \(a_{42}=-0.853252474\) \(a_{43}=-1.161112361\) \(a_{44}=-0.964890215\) \(a_{45}=+0.326086365\)
\(a_{46}=-0.142158346\) \(a_{47}=+1.425181084\) \(a_{48}=+0.328742992\) \(a_{49}=-0.157922394\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.704814379\) \(a_{52}=-0.928398694\) \(a_{53}=+0.198475581\) \(a_{54}=+0.251842073\) \(a_{55}=-0.863024044\)
\(a_{56}=-0.324437514\) \(a_{57}=-1.313043914\) \(a_{58}=-0.050559557\) \(a_{59}=+0.404895280\) \(a_{60}=+0.294036671\)
\(a_{61}=+1.020324162\) \(a_{62}=-0.537204601\) \(a_{63}=+0.669104116\) \(a_{64}=+0.125000000\) \(a_{65}=-0.830385036\)
\(a_{66}=+1.794359239\) \(a_{67}=-0.885586572\) \(a_{68}=-0.267995971\) \(a_{69}=+0.264364938\) \(a_{70}=-0.290185735\)
\(a_{71}=-0.134808088\) \(a_{72}=-0.257793907\) \(a_{73}=-0.726051016\) \(a_{74}=+0.583431957\) \(a_{75}=+0.262994394\)
\(a_{76}=-0.499266884\) \(a_{77}=-1.770858894\) \(a_{78}=+1.726497739\) \(a_{79}=+0.404975315\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.197489689\) \(a_{82}=+0.067813515\) \(a_{83}=-0.188060935\) \(a_{84}=+0.603340611\) \(a_{85}=-0.239702884\)
\(a_{86}=+0.821030424\) \(a_{87}=+0.094023135\) \(a_{88}=+0.682280414\) \(a_{89}=+1.404477437\) \(a_{90}=-0.230577880\)
\(a_{91}=-1.703886153\) \(a_{92}=+0.100521131\) \(a_{93}=+0.999013204\) \(a_{94}=-1.007755209\) \(a_{95}=-0.446557876\)
\(a_{96}=-0.232456399\) \(a_{97}=+0.072427083\) \(a_{98}=+0.111667996\) \(a_{99}=-1.407101825\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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