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: \( 31.0175516329 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.015013390\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.717722851\) \(a_{7}=-0.433182522\) \(a_{8}=+0.353553391\) \(a_{9}=+0.030252182\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.616946289\) \(a_{12}=-0.507506695\) \(a_{13}=+0.579741224\) \(a_{14}=-0.306306299\) \(a_{15}=-0.453927788\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.349390876\) \(a_{18}=+0.021391523\) \(a_{19}=-0.175097472\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.439686060\) \(a_{22}=+0.436246905\) \(a_{23}=-0.213020058\) \(a_{24}=-0.358861425\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.409938951\) \(a_{27}=+0.984307020\) \(a_{28}=-0.216591261\) \(a_{29}=-0.128298658\) \(a_{30}=-0.320975417\)
\(a_{31}=+0.848903084\) \(a_{32}=+0.176776695\) \(a_{33}=-0.626208745\) \(a_{34}=-0.247056658\) \(a_{35}=-0.193725113\)
\(a_{36}=+0.015126091\) \(a_{37}=-1.488519243\) \(a_{38}=-0.123812610\) \(a_{39}=-0.588445105\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.085402928\) \(a_{42}=+0.310904995\) \(a_{43}=+0.869889302\) \(a_{44}=+0.308473145\) \(a_{45}=+0.013529187\)
\(a_{46}=-0.150627928\) \(a_{47}=-1.411257181\) \(a_{48}=-0.253753347\) \(a_{49}=-0.812352902\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.354636417\) \(a_{52}=+0.289870612\) \(a_{53}=+1.719830935\) \(a_{54}=+0.696010169\) \(a_{55}=+0.275906768\)
\(a_{56}=-0.153153150\) \(a_{57}=+0.177726278\) \(a_{58}=-0.090720851\) \(a_{59}=-0.112980914\) \(a_{60}=-0.226963894\)
\(a_{61}=+1.386029344\) \(a_{62}=+0.600265127\) \(a_{63}=-0.013104716\) \(a_{64}=+0.125000000\) \(a_{65}=+0.259268157\)
\(a_{66}=-0.442796450\) \(a_{67}=-1.185983616\) \(a_{68}=-0.174695438\) \(a_{69}=+0.216218211\) \(a_{70}=-0.136984341\)
\(a_{71}=+0.216678765\) \(a_{72}=+0.010695761\) \(a_{73}=+0.042174824\) \(a_{74}=-1.052542050\) \(a_{75}=-0.203002678\)
\(a_{76}=-0.087548736\) \(a_{77}=-0.267250350\) \(a_{78}=-0.416093524\) \(a_{79}=-0.597033666\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.029336987\) \(a_{82}=+0.060388990\) \(a_{83}=-0.726915161\) \(a_{84}=+0.219843030\) \(a_{85}=-0.156252350\)
\(a_{86}=+0.615104625\) \(a_{87}=+0.130224856\) \(a_{88}=+0.218123452\) \(a_{89}=-1.042580937\) \(a_{90}=+0.009566580\)
\(a_{91}=-0.251133766\) \(a_{92}=-0.106510029\) \(a_{93}=-0.861647997\) \(a_{94}=-0.997909523\) \(a_{95}=-0.078305970\)
\(a_{96}=-0.179430713\) \(a_{97}=+0.134789006\) \(a_{98}=-0.574420246\) \(a_{99}=+0.018663971\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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