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: \( 6.78770292015 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.914409838\) \(a_{3}=-0.577350269\) \(a_{4}=-0.163854648\) \(a_{5}=-0.646126967\)
\(a_{6}=+0.527934766\) \(a_{7}=+0.377964473\) \(a_{8}=+1.064240140\) \(a_{9}=+0.333333333\) \(a_{10}=+0.590824855\)
\(a_{11}=+0.579717037\) \(a_{12}=+0.094601525\) \(a_{13}=+0.853027550\) \(a_{14}=-0.345614433\) \(a_{15}=+0.373041578\)
\(a_{16}=-0.809297007\) \(a_{17}=-0.232769084\) \(a_{18}=-0.304803279\) \(a_{19}=-0.865343501\) \(a_{20}=+0.105870906\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.530098962\) \(a_{23}=-0.003029186\) \(a_{24}=-0.614439331\) \(a_{25}=-0.582519943\)
\(a_{26}=-0.780016784\) \(a_{27}=-0.192450090\) \(a_{28}=-0.061931236\) \(a_{29}=+0.667368629\) \(a_{30}=-0.341112889\)
\(a_{31}=+1.472546154\) \(a_{32}=-0.324210995\) \(a_{33}=-0.334699787\) \(a_{34}=+0.212846341\) \(a_{35}=-0.244213039\)
\(a_{36}=-0.054618216\) \(a_{37}=-1.138311465\) \(a_{38}=+0.791278611\) \(a_{39}=-0.492495686\) \(a_{40}=-0.687634254\)
\(a_{41}=+0.136796101\) \(a_{42}=+0.199540586\) \(a_{43}=-1.691631150\) \(a_{44}=-0.094989331\) \(a_{45}=-0.215375656\)
\(a_{46}=+0.002769917\) \(a_{47}=+0.906712444\) \(a_{48}=+0.467247845\) \(a_{49}=+0.142857143\) \(a_{50}=+0.532661967\)
\(a_{51}=+0.134389294\) \(a_{52}=-0.139772529\) \(a_{53}=+1.813150075\) \(a_{54}=+0.175978255\) \(a_{55}=-0.374570811\)
\(a_{56}=+0.402244964\) \(a_{57}=+0.499606303\) \(a_{58}=-0.610248440\) \(a_{59}=-1.229801054\) \(a_{60}=-0.061124596\)
\(a_{61}=-0.554004096\) \(a_{62}=-1.346510691\) \(a_{63}=+0.125988158\) \(a_{64}=+1.105758730\) \(a_{65}=-0.551164104\)
\(a_{66}=+0.306052778\) \(a_{67}=-1.759515872\) \(a_{68}=+0.038140296\) \(a_{69}=+0.001748901\) \(a_{70}=+0.223310805\)
\(a_{71}=+0.995628212\) \(a_{72}=+0.354746713\) \(a_{73}=-0.984601055\) \(a_{74}=+1.040883203\) \(a_{75}=+0.336318046\)
\(a_{76}=+0.141790554\) \(a_{77}=+0.219112444\) \(a_{78}=+0.450342900\) \(a_{79}=-1.709921759\) \(a_{80}=+0.522908620\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.125087700\) \(a_{83}=+0.218742888\) \(a_{84}=+0.035756016\) \(a_{85}=+0.150398383\)
\(a_{86}=+1.546844167\) \(a_{87}=-0.385305457\) \(a_{88}=+0.616958141\) \(a_{89}=-0.957519777\) \(a_{90}=+0.196941618\)
\(a_{91}=+0.322414108\) \(a_{92}=+0.000496346\) \(a_{93}=-0.850174918\) \(a_{94}=-0.829106779\) \(a_{95}=+0.559121771\)
\(a_{96}=+0.187183305\) \(a_{97}=-0.235082647\) \(a_{98}=-0.130629977\) \(a_{99}=+0.193239012\) \(a_{100}=+0.095448600\)

Showing 100 of 240 available coefficients

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