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: \( 6.89555226831 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.467320078\) \(a_{3}=-0.577350269\) \(a_{4}=-0.781611945\) \(a_{5}=-1.622956964\)
\(a_{6}=-0.269807373\) \(a_{7}=+0.377964473\) \(a_{8}=-0.832583033\) \(a_{9}=+0.333333333\) \(a_{10}=-0.758440375\)
\(a_{11}=-1.693166862\) \(a_{12}=+0.451263867\) \(a_{13}=+1.267405436\) \(a_{14}=+0.176630387\) \(a_{15}=+0.937014640\)
\(a_{16}=+0.392529176\) \(a_{17}=-0.397294402\) \(a_{18}=+0.155773359\) \(a_{19}=+0.651018799\) \(a_{20}=+1.268522549\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.791250870\) \(a_{23}=-0.270901551\) \(a_{24}=+0.480692038\) \(a_{25}=+1.633989307\)
\(a_{26}=+0.592284007\) \(a_{27}=-0.192450090\) \(a_{28}=-0.295421547\) \(a_{29}=+1.236321550\) \(a_{30}=+0.437885755\)
\(a_{31}=-1.218301413\) \(a_{32}=+1.016019799\) \(a_{33}=+0.977550343\) \(a_{34}=-0.185663651\) \(a_{35}=-0.613420074\)
\(a_{36}=-0.260537315\) \(a_{37}=-0.296106627\) \(a_{38}=+0.304234156\) \(a_{39}=-0.731736870\) \(a_{40}=+1.351246432\)
\(a_{41}=-1.193347333\) \(a_{42}=-0.101977602\) \(a_{43}=-0.186032931\) \(a_{44}=+1.323399443\) \(a_{45}=-0.540985655\)
\(a_{46}=-0.126597734\) \(a_{47}=-0.295647137\) \(a_{48}=-0.226626826\) \(a_{49}=+0.142857143\) \(a_{50}=+0.763596010\)
\(a_{51}=+0.229378030\) \(a_{52}=-0.990619227\) \(a_{53}=+0.707801268\) \(a_{54}=-0.089935791\) \(a_{55}=+2.747936949\)
\(a_{56}=-0.314686807\) \(a_{57}=-0.375865879\) \(a_{58}=+0.577757884\) \(a_{59}=-1.156083660\) \(a_{60}=-0.732381835\)
\(a_{61}=-0.233693677\) \(a_{62}=-0.569336712\) \(a_{63}=+0.125988158\) \(a_{64}=+0.082277275\) \(a_{65}=-2.056944478\)
\(a_{66}=+0.456828903\) \(a_{67}=+1.302898139\) \(a_{68}=+0.310530050\) \(a_{69}=+0.156405084\) \(a_{70}=-0.286663517\)
\(a_{71}=+0.635866776\) \(a_{72}=-0.277527678\) \(a_{73}=+0.752169006\) \(a_{74}=-0.138376572\) \(a_{75}=-0.943384166\)
\(a_{76}=-0.508844069\) \(a_{77}=-0.639956921\) \(a_{78}=-0.341955331\) \(a_{79}=+0.546684890\) \(a_{80}=-0.637057960\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.557675169\) \(a_{83}=+1.728773447\) \(a_{84}=+0.170561710\) \(a_{85}=+0.644791716\)
\(a_{86}=-0.086936924\) \(a_{87}=-0.713790580\) \(a_{88}=+1.409702001\) \(a_{89}=+1.121395228\) \(a_{90}=-0.252813458\)
\(a_{91}=+0.479034228\) \(a_{92}=+0.211739888\) \(a_{93}=+0.703386649\) \(a_{94}=-0.138161843\) \(a_{95}=-1.056575493\)
\(a_{96}=-0.586599304\) \(a_{97}=+0.646266789\) \(a_{98}=+0.066760011\) \(a_{99}=-0.564388954\) \(a_{100}=-1.277145559\)

Showing 100 of 268 available coefficients

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