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: \( 24.293655303 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.186283654\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.838829216\) \(a_{7}=+0.418169251\) \(a_{8}=-0.353553391\) \(a_{9}=+0.407268908\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.488892413\) \(a_{12}=+0.593141827\) \(a_{13}=-0.024565001\) \(a_{14}=-0.295690313\) \(a_{15}=+0.530522178\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.461788734\) \(a_{18}=-0.287982606\) \(a_{19}=-0.450445063\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.496067347\) \(a_{22}=+0.345699140\) \(a_{23}=+0.865988831\) \(a_{24}=-0.419414608\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.017370079\) \(a_{27}=-0.703147206\) \(a_{28}=+0.209084625\) \(a_{29}=+0.513582208\) \(a_{30}=-0.375135830\)
\(a_{31}=-0.470133665\) \(a_{32}=-0.176776695\) \(a_{33}=-0.579965078\) \(a_{34}=+0.326533945\) \(a_{35}=+0.187010974\)
\(a_{36}=+0.203634454\) \(a_{37}=+0.025116202\) \(a_{38}=+0.318512759\) \(a_{39}=-0.029141060\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.470337371\) \(a_{42}=-0.350772585\) \(a_{43}=-0.842027206\) \(a_{44}=-0.244446206\) \(a_{45}=+0.182136193\)
\(a_{46}=-0.612346575\) \(a_{47}=-0.525167891\) \(a_{48}=+0.296570914\) \(a_{49}=-0.825134478\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.547812427\) \(a_{52}=-0.012282501\) \(a_{53}=-1.624536258\) \(a_{54}=+0.497200157\) \(a_{55}=-0.218639334\)
\(a_{56}=-0.147845156\) \(a_{57}=-0.534355615\) \(a_{58}=-0.363157462\) \(a_{59}=-0.406536711\) \(a_{60}=+0.265261089\)
\(a_{61}=+0.743175150\) \(a_{62}=+0.332434702\) \(a_{63}=+0.170307334\) \(a_{64}=+0.125000000\) \(a_{65}=-0.010985803\)
\(a_{66}=+0.410097240\) \(a_{67}=+0.191151222\) \(a_{68}=-0.230894367\) \(a_{69}=+1.027308394\) \(a_{70}=-0.132236728\)
\(a_{71}=+1.826760778\) \(a_{72}=-0.143991303\) \(a_{73}=+1.766029609\) \(a_{74}=-0.017759836\) \(a_{75}=+0.237256731\)
\(a_{76}=-0.225222531\) \(a_{77}=-0.204439774\) \(a_{78}=+0.020605841\) \(a_{79}=-1.783565589\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.241400945\) \(a_{82}=+1.039685525\) \(a_{83}=-1.075964726\) \(a_{84}=+0.248033673\) \(a_{85}=-0.206518200\)
\(a_{86}=+0.595403147\) \(a_{87}=+0.609254179\) \(a_{88}=+0.172849570\) \(a_{89}=+0.465877395\) \(a_{90}=-0.128789737\)
\(a_{91}=-0.010272328\) \(a_{92}=+0.432994415\) \(a_{93}=-0.557711882\) \(a_{94}=+0.371349777\) \(a_{95}=-0.201445156\)
\(a_{96}=-0.209707304\) \(a_{97}=-0.775247606\) \(a_{98}=+0.583458185\) \(a_{99}=-0.199110679\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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