Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.7635365926 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.617182648\) \(a_{3}=-0.577350269\) \(a_{4}=-0.619085579\) \(a_{5}=-1.106188873\)
\(a_{6}=+0.356330568\) \(a_{7}=+0.414894461\) \(a_{8}=+0.999271525\) \(a_{9}=+0.333333333\) \(a_{10}=+0.682720578\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.357429226\) \(a_{13}=-1.044658070\) \(a_{14}=-0.256065662\) \(a_{15}=+0.638658444\)
\(a_{16}=+0.002352533\) \(a_{17}=+0.221128522\) \(a_{18}=-0.205727549\) \(a_{19}=-0.682584561\) \(a_{20}=+0.684825579\)
\(a_{21}=-0.239539429\) \(a_{22}=-0.186087570\) \(a_{23}=+1.560149748\) \(a_{24}=-0.576929684\) \(a_{25}=+0.223653822\)
\(a_{26}=+0.644744834\) \(a_{27}=-0.192450090\) \(a_{28}=-0.256855178\) \(a_{29}=+0.959306976\) \(a_{30}=-0.394168909\)
\(a_{31}=+1.351886833\) \(a_{32}=-1.000723468\) \(a_{33}=-0.174077656\) \(a_{34}=-0.136476687\) \(a_{35}=-0.458951636\)
\(a_{36}=-0.206361860\) \(a_{37}=-0.987753335\) \(a_{38}=+0.421279347\) \(a_{39}=+0.603133618\) \(a_{40}=-1.105383042\)
\(a_{41}=+0.537022156\) \(a_{42}=+0.147839579\) \(a_{43}=+0.496123917\) \(a_{44}=-0.186661325\) \(a_{45}=-0.368729624\)
\(a_{46}=-0.962897353\) \(a_{47}=+1.417007901\) \(a_{48}=-0.001358236\) \(a_{49}=-0.827862586\) \(a_{50}=-0.138035258\)
\(a_{51}=-0.127668612\) \(a_{52}=+0.646732746\) \(a_{53}=-0.644189162\) \(a_{54}=+0.118776856\) \(a_{55}=-0.333528494\)
\(a_{56}=+0.414592221\) \(a_{57}=+0.394090380\) \(a_{58}=-0.592067619\) \(a_{59}=+1.739001731\) \(a_{60}=-0.395384232\)
\(a_{61}=+0.687079186\) \(a_{62}=-0.834361095\) \(a_{63}=+0.138298154\) \(a_{64}=+0.615276626\) \(a_{65}=+1.155589133\)
\(a_{66}=+0.107437709\) \(a_{67}=-0.663627756\) \(a_{68}=-0.136897479\) \(a_{69}=-0.900752877\) \(a_{70}=+0.283256986\)
\(a_{71}=-1.373985683\) \(a_{72}=+0.333090508\) \(a_{73}=+1.554460809\) \(a_{74}=+0.609624219\) \(a_{75}=-0.129126595\)
\(a_{76}=+0.422578258\) \(a_{77}=+0.125095387\) \(a_{78}=-0.372243603\) \(a_{79}=-1.206575882\) \(a_{80}=-0.002602346\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.331440756\) \(a_{83}=-1.598705249\) \(a_{84}=+0.148295406\) \(a_{85}=-0.244609911\)
\(a_{86}=-0.306199073\) \(a_{87}=-0.553856141\) \(a_{88}=+0.301291701\) \(a_{89}=+0.179297827\) \(a_{90}=+0.227573526\)
\(a_{91}=-0.433422847\) \(a_{92}=-0.965866210\) \(a_{93}=-0.780512227\) \(a_{94}=-0.874552688\) \(a_{95}=+0.755067446\)
\(a_{96}=+0.577767963\) \(a_{97}=+1.307528917\) \(a_{98}=+0.510942423\) \(a_{99}=+0.100503782\) \(a_{100}=-0.138460856\)

Showing 100 of 316 available coefficients

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