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: \( 11.0484521159 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.727958124\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.221850907\) \(a_{7}=+1.979290423\) \(a_{8}=-0.353553391\) \(a_{9}=+1.985839277\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.116772910\) \(a_{12}=+0.863979062\) \(a_{13}=+0.374262914\) \(a_{14}=-1.399569680\) \(a_{15}=-0.772766365\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.356881387\) \(a_{18}=-1.404200419\) \(a_{19}=-0.332696605\) \(a_{20}=-0.223606798\)
\(a_{21}=+3.420130965\) \(a_{22}=+0.082570917\) \(a_{23}=-0.563583476\) \(a_{24}=-0.610925453\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.264643845\) \(a_{27}=+1.703488987\) \(a_{28}=+0.989645211\) \(a_{29}=-0.142268351\) \(a_{30}=+0.546428337\)
\(a_{31}=+1.422310111\) \(a_{32}=-0.176776695\) \(a_{33}=-0.201778699\) \(a_{34}=+0.252353249\) \(a_{35}=-0.885165587\)
\(a_{36}=+0.992919638\) \(a_{37}=-0.250143500\) \(a_{38}=+0.235252025\) \(a_{39}=+0.646710643\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.751308340\) \(a_{42}=-2.418397798\) \(a_{43}=+1.399326050\) \(a_{44}=-0.058386455\) \(a_{45}=-0.888094323\)
\(a_{46}=+0.398513697\) \(a_{47}=-0.381837657\) \(a_{48}=+0.431989531\) \(a_{49}=+2.917590578\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.616676092\) \(a_{52}=+0.187131457\) \(a_{53}=-0.861283475\) \(a_{54}=-1.204548614\) \(a_{55}=+0.052222433\)
\(a_{56}=-0.699784840\) \(a_{57}=-0.574885801\) \(a_{58}=+0.100598916\) \(a_{59}=+1.370672756\) \(a_{60}=-0.386383183\)
\(a_{61}=-0.909939884\) \(a_{62}=-1.005725125\) \(a_{63}=+3.930552662\) \(a_{64}=+0.125000000\) \(a_{65}=-0.167375464\)
\(a_{66}=+0.142679086\) \(a_{67}=-0.413454521\) \(a_{68}=-0.178440694\) \(a_{69}=-0.973848645\) \(a_{70}=+0.625906589\)
\(a_{71}=+0.539087862\) \(a_{72}=-0.702100209\) \(a_{73}=-0.859809500\) \(a_{74}=+0.176878165\) \(a_{75}=+0.345591625\)
\(a_{76}=-0.166348302\) \(a_{77}=-0.231127503\) \(a_{78}=-0.457293481\) \(a_{79}=-0.652037206\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.957718354\) \(a_{82}=-0.531255222\) \(a_{83}=+0.484594131\) \(a_{84}=+1.710065482\) \(a_{85}=+0.159602208\)
\(a_{86}=-0.989472939\) \(a_{87}=-0.245833750\) \(a_{88}=+0.041285458\) \(a_{89}=-1.220907596\) \(a_{90}=+0.627977518\)
\(a_{91}=+0.740774992\) \(a_{92}=-0.281791738\) \(a_{93}=+2.457692336\) \(a_{94}=+0.269999996\) \(a_{95}=+0.148786445\)
\(a_{96}=-0.305462727\) \(a_{97}=-1.077635518\) \(a_{98}=-2.063048082\) \(a_{99}=-0.231892136\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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