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: \( 28.7211104713 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.129685271\) \(a_{4}=+0.500000000\) \(a_{5}=-0.437217724\)
\(a_{6}=-0.798808116\) \(a_{7}=+1.295606540\) \(a_{8}=-0.353553391\) \(a_{9}=+0.276188812\) \(a_{10}=+0.309159617\)
\(a_{11}=-1.170829634\) \(a_{12}=+0.564842635\) \(a_{13}=-1.530484702\) \(a_{14}=-0.916132170\) \(a_{15}=-0.493918423\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.100566244\) \(a_{18}=-0.195294981\) \(a_{19}=+1.164315142\) \(a_{20}=-0.218608862\)
\(a_{21}=+1.463627625\) \(a_{22}=+0.827901574\) \(a_{23}=-0.726033776\) \(a_{24}=-0.399404058\) \(a_{25}=-0.808840662\)
\(a_{26}=+1.082216112\) \(a_{27}=-0.817678839\) \(a_{28}=+0.647803270\) \(a_{29}=+0.558531331\) \(a_{30}=+0.349253066\)
\(a_{31}=+1.457740495\) \(a_{32}=-0.176776695\) \(a_{33}=-1.322668993\) \(a_{34}=+0.071111073\) \(a_{35}=-0.566462142\)
\(a_{36}=+0.138094406\) \(a_{37}=-1.305463959\) \(a_{38}=-0.823295132\) \(a_{39}=-1.728966026\) \(a_{40}=+0.154579809\)
\(a_{41}=-0.042654184\) \(a_{42}=-1.034941019\) \(a_{43}=-0.242140805\) \(a_{44}=-0.585414817\) \(a_{45}=-0.120754643\)
\(a_{46}=+0.513383407\) \(a_{47}=-1.945489777\) \(a_{48}=+0.282421318\) \(a_{49}=+0.678596307\) \(a_{50}=+0.571936717\)
\(a_{51}=-0.113608205\) \(a_{52}=-0.765242351\) \(a_{53}=-1.138273558\) \(a_{54}=+0.578186252\) \(a_{55}=+0.511907467\)
\(a_{56}=-0.458066085\) \(a_{57}=+1.315309667\) \(a_{58}=-0.394941292\) \(a_{59}=-0.562718031\) \(a_{60}=-0.246959211\)
\(a_{61}=+0.447009110\) \(a_{62}=-1.030778189\) \(a_{63}=+0.357832031\) \(a_{64}=+0.125000000\) \(a_{65}=+0.669155038\)
\(a_{66}=+0.935268214\) \(a_{67}=-1.015161247\) \(a_{68}=-0.050283122\) \(a_{69}=-0.820189664\) \(a_{70}=+0.400549222\)
\(a_{71}=-0.281512959\) \(a_{72}=-0.097647491\) \(a_{73}=+0.625573519\) \(a_{74}=+0.923102418\) \(a_{75}=-0.913735383\)
\(a_{76}=+0.582157571\) \(a_{77}=-1.516934531\) \(a_{78}=+1.222563601\) \(a_{79}=+0.208221530\) \(a_{80}=-0.109304431\)
\(a_{81}=-1.199908552\) \(a_{82}=+0.030161063\) \(a_{83}=+0.077906393\) \(a_{84}=+0.731813813\) \(a_{85}=+0.043969344\)
\(a_{86}=+0.171219405\) \(a_{87}=+0.630964618\) \(a_{88}=+0.413950787\) \(a_{89}=-1.119941472\) \(a_{90}=+0.085386427\)
\(a_{91}=-1.982905990\) \(a_{92}=-0.363016888\) \(a_{93}=+1.646787966\) \(a_{94}=+1.375669014\) \(a_{95}=-0.509059216\)
\(a_{96}=-0.199702029\) \(a_{97}=+0.628711069\) \(a_{98}=-0.479840050\) \(a_{99}=-0.323370045\) \(a_{100}=-0.404420331\)

Showing 100 of 1228 available coefficients

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