Properties

Level $971$
Weight $0$
Character 971.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 971 \)
Weight: \( 0 \)
Character: 971.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 0.5787892359 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.639104043\) \(a_{3}=-0.745877347\) \(a_{4}=-0.591545950\) \(a_{5}=-1.648992501\)
\(a_{6}=-0.476693628\) \(a_{7}=+0.452722120\) \(a_{8}=-1.017163541\) \(a_{9}=-0.443666837\) \(a_{10}=-1.053878059\)
\(a_{11}=-0.208074824\) \(a_{12}=+0.441220826\) \(a_{13}=-1.179372145\) \(a_{14}=+0.289336993\) \(a_{15}=+1.229946461\)
\(a_{16}=-0.058527487\) \(a_{17}=+0.150923496\) \(a_{18}=-0.283548859\) \(a_{19}=-0.596480154\) \(a_{20}=+0.975454880\)
\(a_{21}=-0.337675283\) \(a_{22}=-0.132981254\) \(a_{23}=+0.078741562\) \(a_{24}=+0.758679703\) \(a_{25}=+1.719176682\)
\(a_{26}=-0.753741276\) \(a_{27}=+1.076798462\) \(a_{28}=-0.267806030\) \(a_{29}=+0.594585365\) \(a_{30}=+0.786064182\)
\(a_{31}=-0.445522689\) \(a_{32}=+0.979758358\) \(a_{33}=+0.155198065\) \(a_{34}=+0.096455610\) \(a_{35}=-0.746535753\)
\(a_{36}=+0.262449131\) \(a_{37}=-1.454994669\) \(a_{38}=-0.381213403\) \(a_{39}=+0.879667293\) \(a_{40}=+1.677295283\)
\(a_{41}=-0.565581432\) \(a_{42}=-0.215810122\) \(a_{43}=+0.905476212\) \(a_{44}=+0.123085720\) \(a_{45}=+0.731603148\)
\(a_{46}=+0.050323981\) \(a_{47}=+0.810994461\) \(a_{48}=+0.043654248\) \(a_{49}=-0.795042413\) \(a_{50}=+1.098732927\)
\(a_{51}=-0.112570569\) \(a_{52}=+0.697652637\) \(a_{53}=-0.992111853\) \(a_{54}=+0.688186291\) \(a_{55}=+0.343113665\)
\(a_{56}=-0.460492929\) \(a_{57}=+0.444901045\) \(a_{58}=+0.380001748\) \(a_{59}=-0.214899701\) \(a_{60}=-0.727569971\)
\(a_{61}=-1.230765763\) \(a_{62}=-0.284734985\) \(a_{63}=-0.200857779\) \(a_{64}=+0.684694890\) \(a_{65}=+1.944775886\)
\(a_{66}=+0.099187918\) \(a_{67}=+1.750940966\) \(a_{68}=-0.089278097\) \(a_{69}=-0.058731496\) \(a_{70}=-0.477114283\)
\(a_{71}=+0.965100662\) \(a_{72}=+0.451281183\) \(a_{73}=-0.225266915\) \(a_{74}=-0.929893302\) \(a_{75}=-1.282295436\)
\(a_{76}=+0.352845824\) \(a_{77}=-0.094199864\) \(a_{78}=+0.562198776\) \(a_{79}=-0.422778487\) \(a_{80}=+0.096511273\)
\(a_{81}=-0.359493314\) \(a_{82}=-0.361465302\) \(a_{83}=-1.818205869\) \(a_{84}=+0.199750529\) \(a_{85}=-0.248871486\)
\(a_{86}=+0.578693705\) \(a_{87}=-0.443487990\) \(a_{88}=+0.211645920\) \(a_{89}=-0.978280259\) \(a_{90}=+0.467570115\)
\(a_{91}=-0.533928322\) \(a_{92}=-0.046579194\) \(a_{93}=+0.332305626\) \(a_{94}=+0.518309660\) \(a_{95}=+0.983591631\)
\(a_{96}=-0.730779838\) \(a_{97}=+1.297565241\) \(a_{98}=-0.508114719\) \(a_{99}=+0.092316065\) \(a_{100}=-1.016972010\)

Showing 100 of 2590 available coefficients

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