Properties

Level $503$
Weight $0$
Character 503.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 503 \)
Weight: \( 0 \)
Character: 503.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.50385607299 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.292787203\) \(a_{3}=-1.467037405\) \(a_{4}=+0.671298763\) \(a_{5}=+1.015534013\)
\(a_{6}=-1.896567345\) \(a_{7}=-1.670757087\) \(a_{8}=-0.424940570\) \(a_{9}=+1.152199244\) \(a_{10}=+1.312869821\)
\(a_{11}=+1.308938876\) \(a_{12}=-0.984820684\) \(a_{13}=-0.936535449\) \(a_{14}=-2.159933190\) \(a_{15}=-1.489826731\)
\(a_{16}=-1.220656754\) \(a_{17}=-1.391454810\) \(a_{18}=+1.489548056\) \(a_{19}=-1.214329226\) \(a_{20}=+0.681726717\)
\(a_{21}=+2.451063170\) \(a_{22}=+1.692179322\) \(a_{23}=-0.107091792\) \(a_{24}=+0.623403963\) \(a_{25}=+0.031309735\)
\(a_{26}=-1.210741054\) \(a_{27}=-0.223281876\) \(a_{28}=-1.121577150\) \(a_{29}=-1.166370389\) \(a_{30}=-1.926029089\)
\(a_{31}=+0.864769409\) \(a_{32}=-1.153108721\) \(a_{33}=-1.920262517\) \(a_{34}=-1.798855184\) \(a_{35}=-1.696710786\)
\(a_{36}=+0.773470097\) \(a_{37}=+0.600629569\) \(a_{38}=-1.569869510\) \(a_{39}=+1.373932687\) \(a_{40}=-0.431541636\)
\(a_{41}=+1.205392084\) \(a_{42}=+3.168703140\) \(a_{43}=+0.492242475\) \(a_{44}=+0.878689259\) \(a_{45}=+1.170097511\)
\(a_{46}=-0.138446828\) \(a_{47}=-1.036308294\) \(a_{48}=+1.790749256\) \(a_{49}=+1.791428986\) \(a_{50}=+0.040476956\)
\(a_{51}=+2.041316422\) \(a_{52}=-0.628695211\) \(a_{53}=-0.186135193\) \(a_{54}=-0.288655755\) \(a_{55}=+1.329272274\)
\(a_{56}=+0.709972564\) \(a_{57}=+1.781466550\) \(a_{58}=-1.507868610\) \(a_{59}=-0.775091766\) \(a_{60}=-1.000118871\)
\(a_{61}=-0.945741182\) \(a_{62}=+1.117962892\) \(a_{63}=-1.925044979\) \(a_{64}=-0.270067463\) \(a_{65}=-0.951083827\)
\(a_{66}=-2.482490724\) \(a_{67}=+0.621198737\) \(a_{68}=-0.934081843\) \(a_{69}=+0.157107499\) \(a_{70}=-2.193486278\)
\(a_{71}=+0.416228626\) \(a_{72}=-0.489616299\) \(a_{73}=+0.872911511\) \(a_{74}=+0.776486088\) \(a_{75}=-0.045932655\)
\(a_{76}=-0.815177701\) \(a_{77}=-2.186918725\) \(a_{78}=+1.776202610\) \(a_{79}=+0.169112893\) \(a_{80}=-1.239618721\)
\(a_{81}=-0.824636273\) \(a_{82}=+1.558315399\) \(a_{83}=-0.272574898\) \(a_{84}=+1.645395926\) \(a_{85}=-1.413069898\)
\(a_{86}=+0.636364646\) \(a_{87}=+1.711108824\) \(a_{88}=-0.556221594\) \(a_{89}=+1.178808379\) \(a_{90}=+1.512687319\)
\(a_{91}=+1.564723015\) \(a_{92}=-0.071890509\) \(a_{93}=-1.268649235\) \(a_{94}=-1.339726213\) \(a_{95}=-1.233192968\)
\(a_{96}=+1.691653567\) \(a_{97}=+0.868377688\) \(a_{98}=+2.315936318\) \(a_{99}=+1.508158125\) \(a_{100}=+0.021018184\)

Showing 100 of 1408 available coefficients

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