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: \( 4.03612000975 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.596147239\) \(a_{3}=-0.577350269\) \(a_{4}=-0.644608469\) \(a_{5}=+1.064709997\)
\(a_{6}=+0.344185769\) \(a_{7}=+0.377964473\) \(a_{8}=+0.980428798\) \(a_{9}=+0.333333333\) \(a_{10}=-0.634723925\)
\(a_{11}=-1.476142444\) \(a_{12}=+0.372164873\) \(a_{13}=+1.967287339\) \(a_{14}=-0.225322477\) \(a_{15}=-0.614710603\)
\(a_{16}=+0.060128548\) \(a_{17}=+1.142141698\) \(a_{18}=-0.198715746\) \(a_{19}=+0.444854411\) \(a_{20}=-0.686321081\)
\(a_{21}=-0.218217890\) \(a_{22}=+0.879998243\) \(a_{23}=+0.340771145\) \(a_{24}=-0.566050831\) \(a_{25}=+0.133607377\)
\(a_{26}=-1.172792916\) \(a_{27}=-0.192450090\) \(a_{28}=-0.243639100\) \(a_{29}=-0.003946317\) \(a_{30}=+0.366458029\)
\(a_{31}=+0.721164530\) \(a_{32}=-1.016274266\) \(a_{33}=+0.852251237\) \(a_{34}=-0.680884620\) \(a_{35}=+0.402422553\)
\(a_{36}=-0.214869490\) \(a_{37}=+1.145351739\) \(a_{38}=-0.265198729\) \(a_{39}=-1.135813875\) \(a_{40}=+1.043872343\)
\(a_{41}=-0.590826738\) \(a_{42}=+0.130089993\) \(a_{43}=+0.501256147\) \(a_{44}=+0.951533921\) \(a_{45}=+0.354903333\)
\(a_{46}=-0.203149776\) \(a_{47}=+0.369077538\) \(a_{48}=-0.034715236\) \(a_{49}=+0.142857143\) \(a_{50}=-0.079649666\)
\(a_{51}=-0.659415815\) \(a_{52}=-1.268130085\) \(a_{53}=-0.670404846\) \(a_{54}=+0.114728593\) \(a_{55}=-1.571663605\)
\(a_{56}=+0.370567255\) \(a_{57}=-0.256836834\) \(a_{58}=+0.002352586\) \(a_{59}=+0.084459673\) \(a_{60}=+0.396247661\)
\(a_{61}=+0.422378967\) \(a_{62}=-0.429920244\) \(a_{63}=+0.125988157\) \(a_{64}=+0.545720550\) \(a_{65}=+2.094590497\)
\(a_{66}=-0.508067222\) \(a_{67}=+0.729073745\) \(a_{68}=-0.736234212\) \(a_{69}=-0.196744313\) \(a_{70}=-0.239903093\)
\(a_{71}=+0.605746406\) \(a_{72}=+0.326809599\) \(a_{73}=+1.342652184\) \(a_{74}=-0.682798278\) \(a_{75}=-0.077138259\)
\(a_{76}=-0.286756921\) \(a_{77}=-0.557929402\) \(a_{78}=+0.677112298\) \(a_{79}=-0.895823741\) \(a_{80}=+0.064019454\)
\(a_{81}=+0.111111132\) \(a_{82}=+0.352219794\) \(a_{83}=-1.687857118\) \(a_{84}=+0.140665153\) \(a_{85}=+1.216049380\)
\(a_{86}=-0.298822501\) \(a_{87}=+0.002278458\) \(a_{88}=-1.447253204\) \(a_{89}=-0.291604857\) \(a_{90}=-0.211573943\)
\(a_{91}=+0.743566699\) \(a_{92}=-0.219661765\) \(a_{93}=-0.416364535\) \(a_{94}=-0.220024556\) \(a_{95}=+0.473640938\)
\(a_{96}=+0.586746221\) \(a_{97}=+0.206507513\) \(a_{98}=-0.085163891\) \(a_{99}=-0.492047486\) \(a_{100}=-0.086124447\)

Showing 100 of 1500 available coefficients

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