Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.69732758306 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.011060129\) \(a_{3}=-0.577350269\) \(a_{4}=-0.999877674\) \(a_{5}=-1.123681927\)
\(a_{6}=+0.006385568\) \(a_{7}=-0.377964473\) \(a_{8}=+0.022118905\) \(a_{9}=+0.333333333\) \(a_{10}=+0.012428067\)
\(a_{11}=-0.139052801\) \(a_{12}=+0.577279644\) \(a_{13}=+0.282403682\) \(a_{14}=+0.004180336\) \(a_{15}=+0.648758063\)
\(a_{16}=+0.999633036\) \(a_{17}=+1.527721374\) \(a_{18}=-0.003686710\) \(a_{19}=-1.448639178\) \(a_{20}=+1.123544471\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.001537942\) \(a_{23}=-0.740455494\) \(a_{24}=-0.012770356\) \(a_{25}=+0.262661073\)
\(a_{26}=-0.003123421\) \(a_{27}=-0.192450090\) \(a_{28}=+0.377918238\) \(a_{29}=-0.695202842\) \(a_{30}=-0.007175348\)
\(a_{31}=+1.390018501\) \(a_{32}=-0.033174975\) \(a_{33}=+0.080282172\) \(a_{34}=-0.016896795\) \(a_{35}=+0.424711847\)
\(a_{36}=-0.333292558\) \(a_{37}=+0.705416336\) \(a_{38}=+0.016022136\) \(a_{39}=-0.163045842\) \(a_{40}=-0.024854614\)
\(a_{41}=-1.163787347\) \(a_{42}=-0.002413518\) \(a_{43}=+1.159099976\) \(a_{44}=+0.139035792\) \(a_{45}=-0.374560642\)
\(a_{46}=+0.008189533\) \(a_{47}=-0.898955667\) \(a_{48}=-0.577138402\) \(a_{49}=+0.142857143\) \(a_{50}=-0.002905065\)
\(a_{51}=-0.882030347\) \(a_{52}=-0.282369137\) \(a_{53}=+0.484430155\) \(a_{54}=+0.002128523\) \(a_{55}=+0.156251120\)
\(a_{56}=-0.008360160\) \(a_{57}=+0.836372219\) \(a_{58}=+0.007689033\) \(a_{59}=+1.517184054\) \(a_{60}=-0.648678703\)
\(a_{61}=+1.950917829\) \(a_{62}=-0.015373784\) \(a_{63}=-0.125988158\) \(a_{64}=-0.999266116\) \(a_{65}=-0.317331914\)
\(a_{66}=-0.000887931\) \(a_{67}=+0.802650482\) \(a_{68}=-1.527534494\) \(a_{69}=+0.427502179\) \(a_{70}=-0.004697368\)
\(a_{71}=-1.168957063\) \(a_{72}=+0.007372968\) \(a_{73}=-0.170279393\) \(a_{74}=-0.007801996\) \(a_{75}=-0.151647441\)
\(a_{76}=+1.448461971\) \(a_{77}=+0.052557019\) \(a_{78}=+0.001803308\) \(a_{79}=-0.123393918\) \(a_{80}=-1.123269576\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.012871638\) \(a_{83}=+0.946598010\) \(a_{84}=-0.218191196\) \(a_{85}=-1.716672898\)
\(a_{86}=-0.012819795\) \(a_{87}=+0.401375548\) \(a_{88}=-0.003075696\) \(a_{89}=-0.708733458\) \(a_{90}=+0.004142689\)
\(a_{91}=-0.106738559\) \(a_{92}=+0.740364917\) \(a_{93}=-0.802527556\) \(a_{94}=+0.009942566\) \(a_{95}=+1.627809663\)
\(a_{96}=+0.019153581\) \(a_{97}=+1.869959270\) \(a_{98}=-0.001580018\) \(a_{99}=-0.046350934\) \(a_{100}=-0.262628943\)

Showing 100 of 226 available coefficients

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