Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.04447907931 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.701390923\) \(a_{3}=+0.577350269\) \(a_{4}=+1.894731071\) \(a_{5}=+0.436081810\)
\(a_{6}=-0.982298507\) \(a_{7}=-0.377964473\) \(a_{8}=-1.522287323\) \(a_{9}=+0.333333333\) \(a_{10}=-0.741945633\)
\(a_{11}=+0.712029764\) \(a_{12}=+1.093923494\) \(a_{13}=-1.665347249\) \(a_{14}=+0.643065323\) \(a_{15}=+0.251771951\)
\(a_{16}=+0.695274761\) \(a_{17}=+0.318186572\) \(a_{18}=-0.567130308\) \(a_{19}=+1.520356513\) \(a_{20}=+0.826257756\)
\(a_{21}=-0.218217890\) \(a_{22}=-1.211440977\) \(a_{23}=+0.665830595\) \(a_{24}=-0.878892996\) \(a_{25}=-0.809832655\)
\(a_{26}=+2.833406693\) \(a_{27}=+0.192450090\) \(a_{28}=-0.716141031\) \(a_{29}=+0.700649930\) \(a_{30}=-0.428362511\)
\(a_{31}=+1.005929417\) \(a_{32}=+0.339353155\) \(a_{33}=+0.411090576\) \(a_{34}=-0.541359746\) \(a_{35}=-0.164823432\)
\(a_{36}=+0.631577024\) \(a_{37}=-1.029770437\) \(a_{38}=-2.586720770\) \(a_{39}=-0.961488683\) \(a_{40}=-0.663841811\)
\(a_{41}=+1.455786650\) \(a_{42}=+0.371273938\) \(a_{43}=+1.283018802\) \(a_{44}=+1.349104918\) \(a_{45}=+0.145360603\)
\(a_{46}=-1.132838131\) \(a_{47}=+0.562420215\) \(a_{48}=+0.401417071\) \(a_{49}=+0.142857143\) \(a_{50}=+1.377841928\)
\(a_{51}=+0.183705103\) \(a_{52}=-3.155385178\) \(a_{53}=+1.658488229\) \(a_{54}=-0.327432836\) \(a_{55}=+0.310503228\)
\(a_{56}=+0.575370526\) \(a_{57}=+0.877778242\) \(a_{58}=-1.192079431\) \(a_{59}=-1.093322421\) \(a_{60}=+0.477040138\)
\(a_{61}=+1.089442478\) \(a_{62}=-1.711479180\) \(a_{63}=-0.125988158\) \(a_{64}=-1.272647139\) \(a_{65}=-0.726227643\)
\(a_{66}=-0.699425774\) \(a_{67}=+0.064881265\) \(a_{68}=+0.602877985\) \(a_{69}=+0.384417473\) \(a_{70}=+0.280429090\)
\(a_{71}=+0.263986265\) \(a_{72}=-0.507429108\) \(a_{73}=-0.922164362\) \(a_{74}=+1.752042074\) \(a_{75}=-0.467557101\)
\(a_{76}=+2.880666725\) \(a_{77}=-0.269121955\) \(a_{78}=+1.635868117\) \(a_{79}=+1.295546557\) \(a_{80}=+0.303196677\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.476862191\) \(a_{83}=+0.432220142\) \(a_{84}=-0.413464217\) \(a_{85}=+0.138755376\)
\(a_{86}=-2.182916543\) \(a_{87}=+0.404520426\) \(a_{88}=-1.083913883\) \(a_{89}=-1.746350878\) \(a_{90}=-0.247315211\)
\(a_{91}=+0.629442096\) \(a_{92}=+1.261569917\) \(a_{93}=+0.580773620\) \(a_{94}=-0.956896649\) \(a_{95}=+0.662999820\)
\(a_{96}=+0.195925636\) \(a_{97}=+0.263781534\) \(a_{98}=-0.243055846\) \(a_{99}=+0.237343255\) \(a_{100}=-1.534415094\)

Showing 100 of 222 available coefficients

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