Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 21.573637236 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.511266368\) \(a_{4}=+0.500000000\) \(a_{5}=-1.048196527\)
\(a_{6}=+1.068626697\) \(a_{7}=+1.034608335\) \(a_{8}=+0.353553391\) \(a_{9}=+1.283926036\) \(a_{10}=-0.741186872\)
\(a_{11}=+1.326351688\) \(a_{12}=+0.755633184\) \(a_{13}=+0.082602037\) \(a_{14}=+0.731578570\) \(a_{15}=-1.584104158\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.985327540\) \(a_{18}=+0.907872807\) \(a_{19}=+1.239484067\) \(a_{20}=-0.524098264\)
\(a_{21}=+1.563568781\) \(a_{22}=+0.937872273\) \(a_{23}=+0.609964506\) \(a_{24}=+0.534313349\) \(a_{25}=+0.098715959\)
\(a_{26}=+0.058408460\) \(a_{27}=+0.429087869\) \(a_{28}=+0.517304168\) \(a_{29}=+0.722362910\) \(a_{30}=-1.120130792\)
\(a_{31}=-0.530646381\) \(a_{32}=+0.176776695\) \(a_{33}=+2.004470698\) \(a_{34}=-0.696731785\) \(a_{35}=-1.084472863\)
\(a_{36}=+0.641963018\) \(a_{37}=-0.835862541\) \(a_{38}=+0.876447589\) \(a_{39}=+0.124833680\) \(a_{40}=-0.370593436\)
\(a_{41}=-0.064726414\) \(a_{42}=+1.105610088\) \(a_{43}=-1.254026956\) \(a_{44}=+0.663175844\) \(a_{45}=-1.345806811\)
\(a_{46}=+0.431310039\) \(a_{47}=+0.760788351\) \(a_{48}=+0.377816592\) \(a_{49}=+0.070414406\) \(a_{50}=+0.069802724\)
\(a_{51}=-1.489092373\) \(a_{52}=+0.041301018\) \(a_{53}=+0.819676898\) \(a_{54}=+0.303410942\) \(a_{55}=-1.390277232\)
\(a_{56}=+0.365789285\) \(a_{57}=+1.873190584\) \(a_{58}=+0.510787712\) \(a_{59}=-1.672117185\) \(a_{60}=-0.792052079\)
\(a_{61}=-0.104214172\) \(a_{62}=-0.375223654\) \(a_{63}=+1.328360578\) \(a_{64}=+0.125000000\) \(a_{65}=-0.086583168\)
\(a_{66}=+1.417374824\) \(a_{67}=-1.701878926\) \(a_{68}=-0.492663770\) \(a_{69}=+0.921818844\) \(a_{70}=-0.766838116\)
\(a_{71}=+0.400709479\) \(a_{72}=+0.453936403\) \(a_{73}=-0.675732326\) \(a_{74}=-0.591044071\) \(a_{75}=+0.149186108\)
\(a_{76}=+0.619742034\) \(a_{77}=+1.372254511\) \(a_{78}=+0.088270742\) \(a_{79}=-0.991491351\) \(a_{80}=-0.262049132\)
\(a_{81}=-0.635459970\) \(a_{82}=-0.045768487\) \(a_{83}=-0.801089358\) \(a_{84}=+0.781784391\) \(a_{85}=+1.032816905\)
\(a_{86}=-0.886730965\) \(a_{87}=+1.091682772\) \(a_{88}=+0.468936137\) \(a_{89}=-0.268669331\) \(a_{90}=-0.951629123\)
\(a_{91}=+0.085460756\) \(a_{92}=+0.304982253\) \(a_{93}=-0.801948028\) \(a_{94}=+0.537958602\) \(a_{95}=-1.299222894\)
\(a_{96}=+0.267156674\) \(a_{97}=+0.612085603\) \(a_{98}=+0.049790504\) \(a_{99}=+1.702937465\) \(a_{100}=+0.049357979\)

Showing 100 of 1228 available coefficients

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