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: \( 18.7767490336 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.012972205\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.716279515\) \(a_{7}=+0.380011811\) \(a_{8}=+0.353553391\) \(a_{9}=+0.026112689\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.410488076\) \(a_{12}=-0.506486103\) \(a_{13}=+0.816930551\) \(a_{14}=+0.268708928\) \(a_{15}=+0.453014942\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.937106464\) \(a_{18}=+0.018464459\) \(a_{19}=-1.674934261\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.384941402\) \(a_{22}=-0.290258902\) \(a_{23}=+1.485155718\) \(a_{24}=-0.358139758\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.577657132\) \(a_{27}=+0.986520778\) \(a_{28}=+0.190005905\) \(a_{29}=-0.279204087\) \(a_{30}=+0.320329937\)
\(a_{31}=+0.216037531\) \(a_{32}=+0.176776695\) \(a_{33}=+0.415813011\) \(a_{34}=+0.662634335\) \(a_{35}=-0.169946448\)
\(a_{36}=+0.013056344\) \(a_{37}=+1.055872308\) \(a_{38}=-1.184357374\) \(a_{39}=-0.827527941\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.218740246\) \(a_{42}=-0.272194676\) \(a_{43}=-0.395940885\) \(a_{44}=-0.205244038\) \(a_{45}=-0.011677949\)
\(a_{46}=+1.050163679\) \(a_{47}=-1.125805020\) \(a_{48}=-0.253243051\) \(a_{49}=-0.855591024\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.949262801\) \(a_{52}=+0.408465275\) \(a_{53}=+0.580276141\) \(a_{54}=+0.697575532\) \(a_{55}=+0.183575848\)
\(a_{56}=+0.134354464\) \(a_{57}=+1.696661852\) \(a_{58}=-0.197427103\) \(a_{59}=+0.236827157\) \(a_{60}=+0.226507471\)
\(a_{61}=-0.572756503\) \(a_{62}=+0.152761603\) \(a_{63}=+0.009923130\) \(a_{64}=+0.125000000\) \(a_{65}=-0.365342449\)
\(a_{66}=+0.294024200\) \(a_{67}=-0.835012254\) \(a_{68}=+0.468553232\) \(a_{69}=-1.504421463\) \(a_{70}=-0.120170286\)
\(a_{71}=-1.417707030\) \(a_{72}=+0.009232230\) \(a_{73}=+0.776740714\) \(a_{74}=+0.746614469\) \(a_{75}=-0.202594441\)
\(a_{76}=-0.837467130\) \(a_{77}=-0.155990317\) \(a_{78}=-0.585150619\) \(a_{79}=-0.085400974\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.025430816\) \(a_{82}=-0.861779492\) \(a_{83}=-1.852610446\) \(a_{84}=-0.192470701\) \(a_{85}=-0.419086751\)
\(a_{86}=-0.279972485\) \(a_{87}=+0.282825980\) \(a_{88}=-0.145129451\) \(a_{89}=-0.855890521\) \(a_{90}=-0.008257557\)
\(a_{91}=+0.310443258\) \(a_{92}=+0.742577859\) \(a_{93}=-0.218840015\) \(a_{94}=-0.796064364\) \(a_{95}=+0.749053373\)
\(a_{96}=-0.179069879\) \(a_{97}=-0.058109970\) \(a_{98}=-0.604994215\) \(a_{99}=-0.010718946\) \(a_{100}=+0.099975586\)

Showing 100 of 180 available coefficients

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