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: \( 4.60467190452 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.648507873\) \(a_{3}=+0.577350269\) \(a_{4}=+1.717578208\) \(a_{5}=-0.161600133\)
\(a_{6}=-0.951766464\) \(a_{7}=+0.377964473\) \(a_{8}=-1.182933326\) \(a_{9}=+0.333333333\) \(a_{10}=+0.266399092\)
\(a_{11}=-1.170468803\) \(a_{12}=+0.991644241\) \(a_{13}=+0.027008526\) \(a_{14}=-0.623077410\) \(a_{15}=-0.093299881\)
\(a_{16}=+0.232496694\) \(a_{17}=-1.773002755\) \(a_{18}=-0.549502624\) \(a_{19}=+1.071471960\) \(a_{20}=-0.277560868\)
\(a_{21}=+0.218217890\) \(a_{22}=+1.929527037\) \(a_{23}=-1.012028738\) \(a_{24}=-0.682966874\) \(a_{25}=-0.973885397\)
\(a_{26}=-0.044523768\) \(a_{27}=+0.192450090\) \(a_{28}=+0.649183542\) \(a_{29}=+0.369537690\) \(a_{30}=+0.153805588\)
\(a_{31}=-1.905713869\) \(a_{32}=+0.799660696\) \(a_{33}=-0.675770478\) \(a_{34}=+2.922809000\) \(a_{35}=-0.061079109\)
\(a_{36}=+0.572526069\) \(a_{37}=+0.747362989\) \(a_{38}=-1.766329963\) \(a_{39}=+0.015593380\) \(a_{40}=+0.191162183\)
\(a_{41}=-0.960822260\) \(a_{42}=-0.359733910\) \(a_{43}=-1.129427370\) \(a_{44}=-2.010371709\) \(a_{45}=-0.053866711\)
\(a_{46}=+1.668337343\) \(a_{47}=-0.070928552\) \(a_{48}=+0.134232029\) \(a_{49}=+0.142857142\) \(a_{50}=+1.605457744\)
\(a_{51}=-1.023643617\) \(a_{52}=+0.046389258\) \(a_{53}=+1.459803425\) \(a_{54}=-0.317255491\) \(a_{55}=+0.189147912\)
\(a_{56}=-0.447106766\) \(a_{57}=+0.618614632\) \(a_{58}=-0.609185794\) \(a_{59}=+0.030243532\) \(a_{60}=-0.160249846\)
\(a_{61}=+0.227470521\) \(a_{62}=+3.141584341\) \(a_{63}=+0.125988147\) \(a_{64}=-1.550743696\) \(a_{65}=-0.004364608\)
\(a_{66}=+1.114013028\) \(a_{67}=-0.154726269\) \(a_{68}=-3.045270977\) \(a_{69}=-0.584295193\) \(a_{70}=+0.100689409\)
\(a_{71}=+0.212517359\) \(a_{72}=-0.394311038\) \(a_{73}=-0.952542636\) \(a_{74}=-1.232033772\) \(a_{75}=-0.562272998\)
\(a_{76}=+1.840336889\) \(a_{77}=-0.442395622\) \(a_{78}=-0.025705807\) \(a_{79}=-0.920904990\) \(a_{80}=-0.037571500\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.583923064\) \(a_{83}=+0.418308151\) \(a_{84}=+0.374806288\) \(a_{85}=+0.286517479\)
\(a_{86}=+1.861869921\) \(a_{87}=+0.213352687\) \(a_{88}=+1.384586542\) \(a_{89}=+0.178488857\) \(a_{90}=+0.088799720\)
\(a_{91}=+0.010208265\) \(a_{92}=-1.738238523\) \(a_{93}=-1.100264438\) \(a_{94}=+0.116926296\) \(a_{95}=-0.173149987\)
\(a_{96}=+0.461684279\) \(a_{97}=-0.028360815\) \(a_{98}=-0.235501135\) \(a_{99}=-0.390156205\) \(a_{100}=-1.672724329\)

Showing 100 of 1500 available coefficients

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