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: \( 11.5070658355 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.920617422\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.358081603\) \(a_{7}=-0.286223953\) \(a_{8}=+0.353553391\) \(a_{9}=+2.688771282\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.239799523\) \(a_{12}=-0.960308711\) \(a_{13}=+1.375875169\) \(a_{14}=-0.202390898\) \(a_{15}=-0.858926223\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.165991617\) \(a_{18}=+1.901248407\) \(a_{19}=-1.755384023\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.549726710\) \(a_{22}=-0.169563869\) \(a_{23}=-0.433282187\) \(a_{24}=-0.679040802\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.972890662\) \(a_{27}=-3.243483547\) \(a_{28}=-0.143111976\) \(a_{29}=-0.182073571\) \(a_{30}=-0.607352557\)
\(a_{31}=-1.127084523\) \(a_{32}=+0.176776695\) \(a_{33}=+0.460563141\) \(a_{34}=-0.117373798\) \(a_{35}=-0.128003243\)
\(a_{36}=+1.344385641\) \(a_{37}=-0.198006400\) \(a_{38}=-1.241243946\) \(a_{39}=-2.642529820\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.977251822\) \(a_{42}=+0.388715485\) \(a_{43}=+1.006498052\) \(a_{44}=-0.119899761\) \(a_{45}=+1.202455073\)
\(a_{46}=-0.306376773\) \(a_{47}=+0.936622366\) \(a_{48}=-0.480154356\) \(a_{49}=-0.918075849\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.318806392\) \(a_{52}=+0.687937584\) \(a_{53}=-0.863115439\) \(a_{54}=-2.293489211\) \(a_{55}=-0.107241607\)
\(a_{56}=-0.101195449\) \(a_{57}=+3.371421136\) \(a_{58}=-0.128745457\) \(a_{59}=-0.207210154\) \(a_{60}=-0.429463111\)
\(a_{61}=-0.630939423\) \(a_{62}=-0.796969109\) \(a_{63}=-0.769590744\) \(a_{64}=+0.125000000\) \(a_{65}=+0.615310081\)
\(a_{66}=+0.325667320\) \(a_{67}=+0.605983948\) \(a_{68}=-0.082995809\) \(a_{69}=+0.832169317\) \(a_{70}=-0.090511961\)
\(a_{71}=+0.075572370\) \(a_{72}=+0.950624203\) \(a_{73}=-0.226608256\) \(a_{74}=-0.140011668\) \(a_{75}=-0.384123484\)
\(a_{76}=-0.877692011\) \(a_{77}=+0.068636369\) \(a_{78}=-1.868550755\) \(a_{79}=-1.271383387\) \(a_{80}=+0.111803399\)
\(a_{81}=+3.540719728\) \(a_{82}=-0.691021390\) \(a_{83}=-0.887924563\) \(a_{84}=+0.274863355\) \(a_{85}=-0.074233708\)
\(a_{86}=+0.711701598\) \(a_{87}=+0.349693685\) \(a_{88}=-0.084781934\) \(a_{89}=-1.202443652\) \(a_{90}=+0.850264136\)
\(a_{91}=-0.393808411\) \(a_{92}=-0.216641093\) \(a_{93}=+2.164698197\) \(a_{94}=+0.662292026\) \(a_{95}=-0.785031600\)
\(a_{96}=-0.339520401\) \(a_{97}=-0.568421488\) \(a_{98}=-0.649177658\) \(a_{99}=-0.644765977\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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