Properties

Level $499$
Weight $0$
Character 499.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 499 \)
Weight: \( 0 \)
Character: 499.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.78483089027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.164360868\) \(a_{3}=+1.314991915\) \(a_{4}=+0.355736230\) \(a_{5}=+0.536779225\)
\(a_{6}=+1.531125147\) \(a_{7}=+1.605148259\) \(a_{8}=-0.750155526\) \(a_{9}=+0.729203744\) \(a_{10}=+0.625004764\)
\(a_{11}=-1.646744645\) \(a_{12}=+0.467790237\) \(a_{13}=+0.662916321\) \(a_{14}=+1.868971841\) \(a_{15}=+0.705860365\)
\(a_{16}=-1.229187940\) \(a_{17}=+0.208850762\) \(a_{18}=+0.849056250\) \(a_{19}=+0.897424326\) \(a_{20}=+0.190951818\)
\(a_{21}=+2.110756984\) \(a_{22}=-1.917405051\) \(a_{23}=-0.398690040\) \(a_{24}=-0.986448417\) \(a_{25}=-0.711868015\)
\(a_{26}=+0.771873866\) \(a_{27}=-0.356094940\) \(a_{28}=+0.571009400\) \(a_{29}=-1.271537149\) \(a_{30}=+0.821876200\)
\(a_{31}=+0.762376276\) \(a_{32}=-0.681062815\) \(a_{33}=-2.165455877\) \(a_{34}=+0.243177664\) \(a_{35}=+0.861610276\)
\(a_{36}=+0.259404199\) \(a_{37}=+0.007263595\) \(a_{38}=+1.044925762\) \(a_{39}=+0.871729622\) \(a_{40}=-0.402667929\)
\(a_{41}=+0.960454285\) \(a_{42}=+2.457682862\) \(a_{43}=+0.094113734\) \(a_{44}=-0.585806748\) \(a_{45}=+0.391421424\)
\(a_{46}=-0.464219122\) \(a_{47}=-1.608318065\) \(a_{48}=-1.616372220\) \(a_{49}=+1.576501049\) \(a_{50}=-0.828871297\)
\(a_{51}=+0.274637079\) \(a_{52}=+0.235823331\) \(a_{53}=+1.516624691\) \(a_{54}=-0.414622979\) \(a_{55}=-0.883938358\)
\(a_{56}=-1.204110890\) \(a_{57}=+1.180105735\) \(a_{58}=-1.480528087\) \(a_{59}=+1.457250667\) \(a_{60}=+0.251100065\)
\(a_{61}=-1.605291331\) \(a_{62}=+0.887681168\) \(a_{63}=+1.170480082\) \(a_{64}=+0.436185063\) \(a_{65}=+0.355839740\)
\(a_{66}=-2.521372081\) \(a_{67}=-0.981236022\) \(a_{68}=+0.074295727\) \(a_{69}=-0.524274189\) \(a_{70}=+1.003225327\)
\(a_{71}=-0.540006470\) \(a_{72}=-0.547016226\) \(a_{73}=+0.066872042\) \(a_{74}=+0.008457429\) \(a_{75}=-0.936100637\)
\(a_{76}=+0.319246385\) \(a_{77}=-2.643269378\) \(a_{78}=+1.015007860\) \(a_{79}=+0.173481941\) \(a_{80}=-0.659802579\)
\(a_{81}=-1.197465649\) \(a_{82}=+1.118315362\) \(a_{83}=+0.198438341\) \(a_{84}=+0.750872691\) \(a_{85}=+0.112106796\)
\(a_{86}=+0.109582363\) \(a_{87}=-1.672061036\) \(a_{88}=+1.235314576\) \(a_{89}=+0.718597351\) \(a_{90}=+0.455755819\)
\(a_{91}=+1.064079032\) \(a_{92}=-0.141828444\) \(a_{93}=+1.002518614\) \(a_{94}=-1.872662540\) \(a_{95}=+0.481718682\)
\(a_{96}=-0.895592043\) \(a_{97}=-0.163467402\) \(a_{98}=+1.835616139\) \(a_{99}=-1.200812249\) \(a_{100}=-0.253237255\)

Showing 100 of 1542 available coefficients

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