Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.5228489465 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.441452514\) \(a_{3}=-0.577350269\) \(a_{4}=+1.077785350\) \(a_{5}=+0.927542314\)
\(a_{6}=+0.832222997\) \(a_{7}=+0.341091086\) \(a_{8}=-0.112123888\) \(a_{9}=+0.333333333\) \(a_{10}=-1.337008200\)
\(a_{11}=+0.036646821\) \(a_{12}=-0.622259662\) \(a_{13}=-0.643590740\) \(a_{14}=-0.491666604\) \(a_{15}=-0.535516805\)
\(a_{16}=-0.916164090\) \(a_{17}=-1.507812002\) \(a_{18}=-0.480484171\) \(a_{19}=+1.803589637\) \(a_{20}=+0.999691517\)
\(a_{21}=-0.196929030\) \(a_{22}=-0.052824652\) \(a_{23}=-1.206530665\) \(a_{24}=+0.064734757\) \(a_{25}=-0.139665255\)
\(a_{26}=+0.927705490\) \(a_{27}=-0.192450090\) \(a_{28}=+0.367622976\) \(a_{29}=+1.012400821\) \(a_{30}=+0.771922044\)
\(a_{31}=+0.369419310\) \(a_{32}=+1.432730918\) \(a_{33}=-0.021158052\) \(a_{34}=+2.173439401\) \(a_{35}=+0.316376415\)
\(a_{36}=+0.359261783\) \(a_{37}=+0.720086470\) \(a_{38}=-2.599788817\) \(a_{39}=+0.371577287\) \(a_{40}=-0.103999650\)
\(a_{41}=+1.289661727\) \(a_{42}=+0.283863846\) \(a_{43}=-1.944024326\) \(a_{44}=+0.039497406\) \(a_{45}=+0.309180771\)
\(a_{46}=+1.739156660\) \(a_{47}=+1.120466476\) \(a_{48}=+0.528947584\) \(a_{49}=-0.883656871\) \(a_{50}=+0.201320834\)
\(a_{51}=+0.870535665\) \(a_{52}=-0.693652670\) \(a_{53}=-0.783380796\) \(a_{54}=+0.277407666\) \(a_{55}=+0.033991477\)
\(a_{56}=-0.038244459\) \(a_{57}=-1.041302963\) \(a_{58}=-1.459327709\) \(a_{59}=-0.041282342\) \(a_{60}=-0.577172167\)
\(a_{61}=-1.080367019\) \(a_{62}=-0.532500392\) \(a_{63}=+0.113697029\) \(a_{64}=-1.149049493\) \(a_{65}=-0.596957644\)
\(a_{66}=+0.030498327\) \(a_{67}=+0.324000298\) \(a_{68}=-1.625097686\) \(a_{69}=+0.696590804\) \(a_{70}=-0.456041579\)
\(a_{71}=-0.520506696\) \(a_{72}=-0.037374629\) \(a_{73}=-0.829279466\) \(a_{74}=-1.037970452\) \(a_{75}=+0.080635773\)
\(a_{76}=+1.943882488\) \(a_{77}=+0.012499904\) \(a_{78}=-0.535611014\) \(a_{79}=+0.512880927\) \(a_{80}=-0.849780960\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.858986138\) \(a_{83}=+0.897836387\) \(a_{84}=-0.212247224\) \(a_{85}=-1.398559434\)
\(a_{86}=+2.802218752\) \(a_{87}=-0.584509887\) \(a_{88}=-0.004108984\) \(a_{89}=+1.398891106\) \(a_{90}=-0.445669400\)
\(a_{91}=-0.219523065\) \(a_{92}=-1.300381074\) \(a_{93}=-0.213284338\) \(a_{94}=-1.615099218\) \(a_{95}=+1.672905706\)
\(a_{96}=-0.827187581\) \(a_{97}=+0.961471654\) \(a_{98}=+1.273749418\) \(a_{99}=+0.012215607\) \(a_{100}=-0.150529166\)

Showing 100 of 1228 available coefficients

Rows: Cols: