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: \( 0.86381819348 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.286653241\) \(a_{3}=-1.046408706\) \(a_{4}=-0.917829819\) \(a_{5}=-1.213413556\)
\(a_{6}=-0.299956514\) \(a_{7}=+0.793690924\) \(a_{8}=-0.549752264\) \(a_{9}=+0.094971220\) \(a_{10}=-0.347828975\)
\(a_{11}=-1.616813602\) \(a_{12}=+0.960425152\) \(a_{13}=+0.775102298\) \(a_{14}=+0.227514076\) \(a_{15}=+1.269726527\)
\(a_{16}=+0.760241543\) \(a_{17}=-0.879052973\) \(a_{18}=+0.027223843\) \(a_{19}=+0.496987971\) \(a_{20}=+1.113707233\)
\(a_{21}=-0.830525062\) \(a_{22}=-0.463464934\) \(a_{23}=+1.247944057\) \(a_{24}=+0.575265559\) \(a_{25}=+0.472372554\)
\(a_{26}=+0.222185544\) \(a_{27}=+0.947029954\) \(a_{28}=-0.728473103\) \(a_{29}=+1.084845726\) \(a_{30}=+0.363971297\)
\(a_{31}=-0.980006829\) \(a_{32}=+0.767678021\) \(a_{33}=+1.691847872\) \(a_{34}=-0.251983463\) \(a_{35}=-0.963075294\)
\(a_{36}=-0.087167475\) \(a_{37}=+0.956760578\) \(a_{38}=+0.142463285\) \(a_{39}=-0.811073744\) \(a_{40}=+0.667076852\)
\(a_{41}=-1.212735539\) \(a_{42}=-0.238072741\) \(a_{43}=+1.092102138\) \(a_{44}=+1.483959822\) \(a_{45}=-0.115239411\)
\(a_{46}=+0.357727283\) \(a_{47}=+0.369523605\) \(a_{48}=-0.795523449\) \(a_{49}=-0.370054697\) \(a_{50}=+0.135407200\)
\(a_{51}=+0.919848737\) \(a_{52}=-0.711411954\) \(a_{53}=-0.184439214\) \(a_{54}=+0.271469263\) \(a_{55}=+1.961863643\)
\(a_{56}=-0.436333393\) \(a_{57}=-0.520052560\) \(a_{58}=+0.310974567\) \(a_{59}=+0.407026948\) \(a_{60}=-1.165392981\)
\(a_{61}=-1.523506164\) \(a_{62}=-0.280922285\) \(a_{63}=+0.075377832\) \(a_{64}=-0.540184182\) \(a_{65}=-0.940519665\)
\(a_{66}=+0.484973795\) \(a_{67}=+0.363630101\) \(a_{68}=+0.806821122\) \(a_{69}=-1.305859634\) \(a_{70}=-0.276068668\)
\(a_{71}=-0.545654466\) \(a_{72}=-0.052210677\) \(a_{73}=-1.267044947\) \(a_{74}=+0.274258629\) \(a_{75}=-0.494294775\)
\(a_{76}=-0.456150498\) \(a_{77}=-1.283250229\) \(a_{78}=-0.232496960\) \(a_{79}=+1.632242419\) \(a_{80}=-0.922487476\)
\(a_{81}=-1.085951657\) \(a_{82}=-0.347634619\) \(a_{83}=-0.343607026\) \(a_{84}=+0.762280732\) \(a_{85}=+1.066654839\)
\(a_{86}=+0.313054608\) \(a_{87}=-1.135192046\) \(a_{88}=+0.888846962\) \(a_{89}=-1.014437383\) \(a_{90}=-0.033033747\)
\(a_{91}=+0.615191618\) \(a_{92}=-1.145400343\) \(a_{93}=+1.025487762\) \(a_{94}=+0.105925111\) \(a_{95}=-0.603051986\)
\(a_{96}=-0.803304945\) \(a_{97}=+1.756206573\) \(a_{98}=-0.106077435\) \(a_{99}=-0.153550847\) \(a_{100}=-0.433557687\)

Showing 100 of 1558 available coefficients

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