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: \( 11.9521606244 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.715894435\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.506213810\) \(a_{7}=-1.595477208\) \(a_{8}=+0.353553391\) \(a_{9}=-0.487495157\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.526632824\) \(a_{12}=+0.357947218\) \(a_{13}=-1.884529007\) \(a_{14}=-1.128172753\) \(a_{15}=+0.320157724\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.303654677\) \(a_{18}=-0.344711132\) \(a_{19}=+0.557365631\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.142193255\) \(a_{22}=-0.372385641\) \(a_{23}=+1.723437249\) \(a_{24}=+0.253106905\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.332563240\) \(a_{27}=-1.064889506\) \(a_{28}=-0.797738604\) \(a_{29}=-0.908136166\) \(a_{30}=+0.226385698\)
\(a_{31}=-0.819765595\) \(a_{32}=+0.176776695\) \(a_{33}=-0.377013509\) \(a_{34}=-0.214716281\) \(a_{35}=-0.713519099\)
\(a_{36}=-0.243747579\) \(a_{37}=+0.541787939\) \(a_{38}=+0.394117017\) \(a_{39}=-1.349123830\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.215776642\) \(a_{42}=-0.807652596\) \(a_{43}=+0.250088143\) \(a_{44}=-0.263316412\) \(a_{45}=-0.218014462\)
\(a_{46}=+1.218654166\) \(a_{47}=-1.246080009\) \(a_{48}=+0.178973609\) \(a_{49}=+1.545547523\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.217384693\) \(a_{52}=-0.942264504\) \(a_{53}=+1.037155965\) \(a_{54}=-0.752990591\) \(a_{55}=-0.235517359\)
\(a_{56}=-0.564086377\) \(a_{57}=+0.399014953\) \(a_{58}=-0.642149241\) \(a_{59}=-0.265014525\) \(a_{60}=+0.160078862\)
\(a_{61}=+0.529957614\) \(a_{62}=-0.579661812\) \(a_{63}=+0.777787413\) \(a_{64}=+0.125000000\) \(a_{65}=-0.842786993\)
\(a_{66}=-0.266588808\) \(a_{67}=+0.877698250\) \(a_{68}=-0.151827338\) \(a_{69}=+1.233799137\) \(a_{70}=-0.504534193\)
\(a_{71}=+0.217560643\) \(a_{72}=-0.172355566\) \(a_{73}=-1.098619637\) \(a_{74}=+0.383101925\) \(a_{75}=+0.143178887\)
\(a_{76}=+0.278682815\) \(a_{77}=+0.840230669\) \(a_{78}=-0.953974609\) \(a_{79}=+0.382836585\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.274853314\) \(a_{82}=-0.859683908\) \(a_{83}=+0.042004607\) \(a_{84}=-0.571096628\) \(a_{85}=-0.135798500\)
\(a_{86}=+0.176839022\) \(a_{87}=-0.650129628\) \(a_{88}=-0.186192821\) \(a_{89}=-0.140389229\) \(a_{90}=-0.154159505\)
\(a_{91}=+3.006723084\) \(a_{92}=+0.861718625\) \(a_{93}=-0.586865626\) \(a_{94}=-0.881111624\) \(a_{95}=+0.249261488\)
\(a_{96}=+0.126553452\) \(a_{97}=-0.268518738\) \(a_{98}=+1.092867134\) \(a_{99}=+0.256730938\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

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