Properties

Level $59$
Weight $0$
Character 59.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 59 \)
Weight: \( 0 \)
Character: 59.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.59582968816 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.933619949\) \(a_{3}=-0.234282195\) \(a_{4}=-0.128353790\) \(a_{5}=-0.333036879\)
\(a_{6}=+0.218730531\) \(a_{7}=-1.235810593\) \(a_{8}=+1.053453608\) \(a_{9}=-0.945111853\) \(a_{10}=+0.310929874\)
\(a_{11}=+1.759741855\) \(a_{12}=+0.030071008\) \(a_{13}=+0.064647332\) \(a_{14}=+1.153777424\) \(a_{15}=+0.078024611\)
\(a_{16}=-0.855171515\) \(a_{17}=+0.049447651\) \(a_{18}=+0.882375281\) \(a_{19}=+0.654796609\) \(a_{20}=+0.042746546\)
\(a_{21}=+0.289528418\) \(a_{22}=-1.642930102\) \(a_{23}=+0.029623323\) \(a_{24}=-0.246805423\) \(a_{25}=-0.889086437\)
\(a_{26}=-0.060356039\) \(a_{27}=+0.455705074\) \(a_{28}=+0.158620973\) \(a_{29}=-1.281002317\) \(a_{30}=-0.072845333\)
\(a_{31}=-0.736890468\) \(a_{32}=-0.255048422\) \(a_{33}=-0.412276184\) \(a_{34}=-0.046165313\) \(a_{35}=+0.411570503\)
\(a_{36}=+0.121308688\) \(a_{37}=+0.457059419\) \(a_{38}=-0.611331177\) \(a_{39}=-0.015145719\) \(a_{40}=-0.350838902\)
\(a_{41}=+0.855506832\) \(a_{42}=-0.270309507\) \(a_{43}=+0.708459541\) \(a_{44}=-0.225869536\) \(a_{45}=+0.314757102\)
\(a_{46}=-0.027656925\) \(a_{47}=+1.123411346\) \(a_{48}=+0.200351459\) \(a_{49}=+0.527227823\) \(a_{50}=+0.830068835\)
\(a_{51}=-0.011584704\) \(a_{52}=-0.008297730\) \(a_{53}=+0.150263246\) \(a_{54}=-0.425455348\) \(a_{55}=-0.586058935\)
\(a_{56}=-1.301869129\) \(a_{57}=-0.153407187\) \(a_{58}=+1.195969318\) \(a_{59}=-0.130188911\) \(a_{60}=-0.010014755\)
\(a_{61}=-0.790021948\) \(a_{62}=+0.687975641\) \(a_{63}=+1.167979240\) \(a_{64}=+1.093289810\) \(a_{65}=-0.021529946\)
\(a_{66}=+0.384909270\) \(a_{67}=+0.091009999\) \(a_{68}=-0.006346793\) \(a_{69}=-0.006940217\) \(a_{70}=-0.384250432\)
\(a_{71}=-0.578021271\) \(a_{72}=-0.995631492\) \(a_{73}=-1.208885726\) \(a_{74}=-0.426719791\) \(a_{75}=+0.208297122\)
\(a_{76}=-0.084045626\) \(a_{77}=-2.174707626\) \(a_{78}=+0.014140345\) \(a_{79}=+0.551704513\) \(a_{80}=+0.284803652\)
\(a_{81}=+0.838348268\) \(a_{82}=-0.798718245\) \(a_{83}=+1.393522558\) \(a_{84}=-0.037162070\) \(a_{85}=-0.016467891\)
\(a_{86}=-0.661431961\) \(a_{87}=+0.300116034\) \(a_{88}=+1.853806407\) \(a_{89}=+0.644819499\) \(a_{90}=-0.293863510\)
\(a_{91}=-0.079891857\) \(a_{92}=-0.003802266\) \(a_{93}=+0.172640316\) \(a_{94}=-1.048839244\) \(a_{95}=-0.218071419\)
\(a_{96}=+0.059753304\) \(a_{97}=-0.627653004\) \(a_{98}=-0.492230413\) \(a_{99}=-1.663152886\) \(a_{100}=+0.114117614\)

Showing 100 of 546 available coefficients

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