Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 18.8501464832 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.659820025\) \(a_{4}=+0.500000000\) \(a_{5}=-1.317568704\)
\(a_{6}=-1.173669995\) \(a_{7}=-0.212636446\) \(a_{8}=+0.353553391\) \(a_{9}=+1.755002516\) \(a_{10}=-0.931661765\)
\(a_{11}=+0.147417771\) \(a_{12}=-0.829910013\) \(a_{13}=+0.393408917\) \(a_{14}=-0.150356673\) \(a_{15}=+2.186926920\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.095376878\) \(a_{18}=+1.240974180\) \(a_{19}=+1.063283557\) \(a_{20}=-0.658784352\)
\(a_{21}=+0.352938231\) \(a_{22}=+0.104240105\) \(a_{23}=+0.511296353\) \(a_{24}=-0.586834998\) \(a_{25}=+0.735987290\)
\(a_{26}=+0.278182113\) \(a_{27}=-1.253168295\) \(a_{28}=-0.106318223\) \(a_{29}=+0.763591217\) \(a_{30}=+1.546390855\)
\(a_{31}=-1.892084186\) \(a_{32}=+0.176776695\) \(a_{33}=-0.244686968\) \(a_{34}=+0.067441637\) \(a_{35}=+0.280163126\)
\(a_{36}=+0.877501258\) \(a_{37}=-0.953410080\) \(a_{38}=+0.751855014\) \(a_{39}=-0.652987999\) \(a_{40}=-0.465830883\)
\(a_{41}=-0.307401764\) \(a_{42}=+0.249565016\) \(a_{43}=+1.836682567\) \(a_{44}=+0.073708885\) \(a_{45}=-2.312336391\)
\(a_{46}=+0.361541119\) \(a_{47}=+1.248573224\) \(a_{48}=-0.414955006\) \(a_{49}=-0.954785742\) \(a_{50}=+0.520421604\)
\(a_{51}=-0.158308452\) \(a_{52}=+0.196704459\) \(a_{53}=+1.555196361\) \(a_{54}=-0.886123800\) \(a_{55}=-0.194233041\)
\(a_{56}=-0.075178336\) \(a_{57}=-1.764859341\) \(a_{58}=+0.539940527\) \(a_{59}=+0.438664424\) \(a_{60}=+1.093463460\)
\(a_{61}=+1.163415707\) \(a_{62}=-1.337905558\) \(a_{63}=-0.373177497\) \(a_{64}=+0.125000000\) \(a_{65}=-0.518343277\)
\(a_{66}=-0.173019814\) \(a_{67}=+0.578427943\) \(a_{68}=+0.047688439\) \(a_{69}=-0.848659926\) \(a_{70}=+0.198105246\)
\(a_{71}=+1.089538231\) \(a_{72}=+0.620487090\) \(a_{73}=-0.018809706\) \(a_{74}=-0.674162733\) \(a_{75}=-1.221606442\)
\(a_{76}=+0.531641779\) \(a_{77}=-0.031346391\) \(a_{78}=-0.461732242\) \(a_{79}=+0.887950980\) \(a_{80}=-0.329392176\)
\(a_{81}=+0.325031315\) \(a_{82}=-0.217365872\) \(a_{83}=+0.268900574\) \(a_{84}=+0.176469115\) \(a_{85}=-0.125665590\)
\(a_{86}=+1.298730698\) \(a_{87}=-1.267423993\) \(a_{88}=+0.052120053\) \(a_{89}=-0.547902691\) \(a_{90}=-1.635068742\)
\(a_{91}=-0.083653074\) \(a_{92}=+0.255648177\) \(a_{93}=+3.140519221\) \(a_{94}=+0.882874593\) \(a_{95}=-1.400949139\)
\(a_{96}=-0.293417499\) \(a_{97}=-0.419041400\) \(a_{98}=-0.675135473\) \(a_{99}=+0.258718558\) \(a_{100}=+0.367993645\)

Showing 100 of 1228 available coefficients

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