Properties

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

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 30.332376131 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106786\) \(a_{3}=-1.773708749\) \(a_{4}=+0.500000006\) \(a_{5}=-0.997668681\)
\(a_{6}=-1.254201493\) \(a_{7}=+0.701723807\) \(a_{8}=+0.353553397\) \(a_{9}=+2.146042728\) \(a_{10}=-0.705458294\)
\(a_{11}=-0.641784268\) \(a_{12}=-0.886854386\) \(a_{13}=+1.458338557\) \(a_{14}=+0.496193665\) \(a_{15}=+1.769573668\)
\(a_{16}=+0.250000006\) \(a_{17}=+0.602738701\) \(a_{18}=+1.517481375\) \(a_{19}=-0.728672655\) \(a_{20}=-0.498834347\)
\(a_{21}=-1.244653656\) \(a_{22}=-0.453810011\) \(a_{23}=+0.599555491\) \(a_{24}=-0.627100754\) \(a_{25}=-0.004657204\)
\(a_{26}=+1.031201089\) \(a_{27}=-2.032746013\) \(a_{28}=+0.350861908\) \(a_{29}=-1.560481591\) \(a_{30}=+1.251277548\)
\(a_{31}=-0.112895112\) \(a_{32}=+0.176776701\) \(a_{33}=+1.138338371\) \(a_{34}=+0.426200625\) \(a_{35}=-0.700087864\)
\(a_{36}=+1.073021377\) \(a_{37}=+0.699852224\) \(a_{38}=-0.515249379\) \(a_{39}=-2.586667857\) \(a_{40}=-0.352729151\)
\(a_{41}=+0.935383614\) \(a_{42}=-0.880103046\) \(a_{43}=-1.380810293\) \(a_{44}=-0.320892138\) \(a_{45}=-2.141039616\)
\(a_{46}=+0.423949756\) \(a_{47}=-0.056076309\) \(a_{48}=-0.443427199\) \(a_{49}=-0.507583699\) \(a_{50}=-0.003293141\)
\(a_{51}=-1.069082907\) \(a_{52}=+0.729169288\) \(a_{53}=-0.216716389\) \(a_{54}=-1.437368499\) \(a_{55}=+0.640288063\)
\(a_{56}=+0.248096836\) \(a_{57}=+1.292453064\) \(a_{58}=-1.103427122\) \(a_{59}=-0.914832512\) \(a_{60}=+0.884786845\)
\(a_{61}=-1.105324904\) \(a_{62}=-0.079828900\) \(a_{63}=+1.505929272\) \(a_{64}=+0.125000005\) \(a_{65}=-1.454938703\)
\(a_{66}=+0.804926786\) \(a_{67}=+0.344358163\) \(a_{68}=+0.301369354\) \(a_{69}=-1.063436821\) \(a_{70}=-0.495036880\)
\(a_{71}=-0.455139466\) \(a_{72}=+0.758740697\) \(a_{73}=+0.939222155\) \(a_{74}=+0.494870257\) \(a_{75}=+0.008260523\)
\(a_{76}=-0.364336332\) \(a_{77}=-0.450355299\) \(a_{78}=-1.829050394\) \(a_{79}=+0.898643468\) \(a_{80}=-0.249417176\)
\(a_{81}=+1.459456661\) \(a_{82}=+0.661416101\) \(a_{83}=-0.351273328\) \(a_{84}=-0.622326836\) \(a_{85}=-0.601333524\)
\(a_{86}=-0.976380328\) \(a_{87}=+2.767839850\) \(a_{88}=-0.226905008\) \(a_{89}=-1.131646034\) \(a_{90}=-1.513943641\)
\(a_{91}=+1.023350884\) \(a_{92}=+0.299777749\) \(a_{93}=+0.200243049\) \(a_{94}=-0.039651938\) \(a_{95}=+0.726973886\)
\(a_{96}=-0.313550381\) \(a_{97}=+0.743159369\) \(a_{98}=-0.358915878\) \(a_{99}=-1.377296460\) \(a_{100}=-0.002328602\)

Showing 100 of 1228 available coefficients

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