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: \( 2.9302569376 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.445304712\) \(a_{3}=+0.577350269\) \(a_{4}=+1.088905709\) \(a_{5}=-0.743553829\)
\(a_{6}=+0.834447064\) \(a_{7}=+0.377964473\) \(a_{8}=+0.128495841\) \(a_{9}=+0.333333333\) \(a_{10}=-1.074661853\)
\(a_{11}=+1.398895728\) \(a_{12}=+0.628680004\) \(a_{13}=-0.788484941\) \(a_{14}=+0.546273834\) \(a_{15}=-0.429291003\)
\(a_{16}=-0.903190065\) \(a_{17}=-1.367106253\) \(a_{18}=+0.481768237\) \(a_{19}=-0.011040481\) \(a_{20}=-0.809660010\)
\(a_{21}=+0.218217890\) \(a_{22}=+2.021830586\) \(a_{23}=+1.653414095\) \(a_{24}=+0.074187108\) \(a_{25}=-0.447127703\)
\(a_{26}=-1.139601000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.411567673\) \(a_{29}=+1.218544105\) \(a_{30}=-0.620456309\)
\(a_{31}=+0.128705035\) \(a_{32}=-1.433880699\) \(a_{33}=+0.807652825\) \(a_{34}=-1.975885107\) \(a_{35}=-0.281036930\)
\(a_{36}=+0.362968568\) \(a_{37}=-0.931199525\) \(a_{38}=-0.015956857\) \(a_{39}=-0.455231988\) \(a_{40}=-0.095543576\)
\(a_{41}=+0.910517159\) \(a_{42}=+0.315391343\) \(a_{43}=-0.380606617\) \(a_{44}=+1.523265557\) \(a_{45}=-0.247851293\)
\(a_{46}=+2.389687156\) \(a_{47}=+0.761432738\) \(a_{48}=-0.521456975\) \(a_{49}=+0.142857146\) \(a_{50}=-0.646235855\)
\(a_{51}=-0.789299223\) \(a_{52}=-0.858585649\) \(a_{53}=-0.168701084\) \(a_{54}=+0.278149021\) \(a_{55}=-1.040154273\)
\(a_{56}=+0.048566864\) \(a_{57}=-0.006374225\) \(a_{58}=+1.761167532\) \(a_{59}=-1.536258190\) \(a_{60}=-0.467457424\)
\(a_{61}=+1.178397879\) \(a_{62}=+0.186017983\) \(a_{63}=+0.125988159\) \(a_{64}=-1.169204427\) \(a_{65}=+0.586281006\)
\(a_{66}=+1.167304441\) \(a_{67}=-0.245643901\) \(a_{68}=-1.488649850\) \(a_{69}=+0.954599133\) \(a_{70}=-0.406183983\)
\(a_{71}=+0.680943631\) \(a_{72}=+0.042831998\) \(a_{73}=-0.419200998\) \(a_{74}=-1.345866355\) \(a_{75}=-0.258149353\)
\(a_{76}=-0.012021438\) \(a_{77}=+0.528734441\) \(a_{78}=-0.657947993\) \(a_{79}=-1.597638562\) \(a_{80}=+0.671564491\)
\(a_{81}=+0.111106999\) \(a_{82}=+1.315978701\) \(a_{83}=+0.408255574\) \(a_{84}=+0.237580322\) \(a_{85}=+1.016538806\)
\(a_{86}=-0.550092558\) \(a_{87}=+0.703526778\) \(a_{88}=+0.179752309\) \(a_{89}=-0.321304032\) \(a_{90}=-0.358220460\)
\(a_{91}=-0.298019284\) \(a_{92}=+1.800412046\) \(a_{93}=+0.074307798\) \(a_{94}=+1.100502163\) \(a_{95}=+0.008209111\)
\(a_{96}=-0.827851484\) \(a_{97}=-0.286670103\) \(a_{98}=+0.206472435\) \(a_{99}=+0.466298876\) \(a_{100}=-0.486878969\)

Showing 100 of 1500 available coefficients

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