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: \( 25.3582309994 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.003519397\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.002488589\) \(a_{7}=-1.571802236\) \(a_{8}=+0.353553391\) \(a_{9}=-0.999987614\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.274681256\) \(a_{12}=-0.001759698\) \(a_{13}=-0.377653582\) \(a_{14}=-1.111432020\) \(a_{15}=+0.001573922\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.248539932\) \(a_{18}=-0.707098023\) \(a_{19}=-1.247128383\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.005531795\) \(a_{22}=-0.194228979\) \(a_{23}=-1.096298558\) \(a_{24}=-0.001244295\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.267041409\) \(a_{27}=+0.007038750\) \(a_{28}=-0.785901118\) \(a_{29}=-0.973949931\) \(a_{30}=+0.001112931\)
\(a_{31}=-0.062627329\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000966712\) \(a_{34}=+0.175744272\) \(a_{35}=+0.702931329\)
\(a_{36}=-0.499993807\) \(a_{37}=+0.852457826\) \(a_{38}=-0.881852937\) \(a_{39}=+0.001329113\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.643792232\) \(a_{42}=+0.003911570\) \(a_{43}=+0.052588205\) \(a_{44}=-0.137340628\) \(a_{45}=+0.447208056\)
\(a_{46}=-0.775200145\) \(a_{47}=+1.049906231\) \(a_{48}=-0.000879849\) \(a_{49}=+1.470562268\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.000874711\) \(a_{52}=-0.188826791\) \(a_{53}=-1.922908234\) \(a_{54}=+0.004977148\) \(a_{55}=+0.122841192\)
\(a_{56}=-0.555716010\) \(a_{57}=+0.004389139\) \(a_{58}=-0.688686601\) \(a_{59}=-0.291751797\) \(a_{60}=+0.000786961\)
\(a_{61}=-0.034147974\) \(a_{62}=-0.044284209\) \(a_{63}=+1.571782767\) \(a_{64}=+0.125000000\) \(a_{65}=+0.168891816\)
\(a_{66}=+0.000683569\) \(a_{67}=+0.713975524\) \(a_{68}=+0.124269966\) \(a_{69}=+0.003858309\) \(a_{70}=+0.497047510\)
\(a_{71}=+0.926803332\) \(a_{72}=-0.353549011\) \(a_{73}=-1.131379302\) \(a_{74}=+0.602778710\) \(a_{75}=-0.000703879\)
\(a_{76}=-0.623564192\) \(a_{77}=+0.431744612\) \(a_{78}=+0.000939825\) \(a_{79}=+0.820010328\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.999962842\) \(a_{82}=+0.455229853\) \(a_{83}=-0.799635903\) \(a_{84}=+0.002765898\) \(a_{85}=-0.111150437\)
\(a_{86}=+0.037185476\) \(a_{87}=+0.003427716\) \(a_{88}=-0.097114489\) \(a_{89}=+1.641821722\) \(a_{90}=+0.316223849\)
\(a_{91}=+0.593596745\) \(a_{92}=-0.548149279\) \(a_{93}=+0.000220410\) \(a_{94}=+0.742395816\) \(a_{95}=+0.557732768\)
\(a_{96}=-0.000622147\) \(a_{97}=+0.219922805\) \(a_{98}=+1.039844552\) \(a_{99}=+0.274677854\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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