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: \( 6.66320756976 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.312279776\) \(a_{3}=+0.577350269\) \(a_{4}=-0.902481342\) \(a_{5}=+0.554215739\)
\(a_{6}=-0.180294813\) \(a_{7}=-0.377964473\) \(a_{8}=+0.594106447\) \(a_{9}=+0.333333333\) \(a_{10}=-0.173070367\)
\(a_{11}=+1.391174232\) \(a_{12}=-0.521047846\) \(a_{13}=-1.329412722\) \(a_{14}=+0.118030661\) \(a_{15}=+0.319976606\)
\(a_{16}=+0.716953914\) \(a_{17}=-0.571725987\) \(a_{18}=-0.104093259\) \(a_{19}=-1.850515693\) \(a_{20}=-0.500169364\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.434435577\) \(a_{23}=-0.902143232\) \(a_{24}=+0.343007517\) \(a_{25}=-0.692844915\)
\(a_{26}=+0.415148707\) \(a_{27}=+0.192450090\) \(a_{28}=+0.341105885\) \(a_{29}=+0.952819034\) \(a_{30}=-0.099922223\)
\(a_{31}=-1.454850587\) \(a_{32}=-0.817996654\) \(a_{33}=+0.803194817\) \(a_{34}=+0.178538463\) \(a_{35}=-0.209473860\)
\(a_{36}=-0.300827114\) \(a_{37}=-0.255624946\) \(a_{38}=+0.577878625\) \(a_{39}=-0.767536793\) \(a_{40}=+0.329263143\)
\(a_{41}=-1.529948147\) \(a_{42}=+0.068145034\) \(a_{43}=+1.061130277\) \(a_{44}=-1.255508788\) \(a_{45}=+0.184738580\)
\(a_{46}=+0.281721086\) \(a_{47}=+0.170277977\) \(a_{48}=+0.413933535\) \(a_{49}=+0.142857143\) \(a_{50}=+0.216361455\)
\(a_{51}=-0.330086152\) \(a_{52}=+1.199770177\) \(a_{53}=+0.375049974\) \(a_{54}=-0.060098271\) \(a_{55}=+0.771010655\)
\(a_{56}=-0.224551130\) \(a_{57}=-1.068395733\) \(a_{58}=-0.297546114\) \(a_{59}=-0.261023271\) \(a_{60}=-0.288772917\)
\(a_{61}=+0.535211111\) \(a_{62}=+0.454320415\) \(a_{63}=-0.125988158\) \(a_{64}=-0.461510102\) \(a_{65}=-0.736781454\)
\(a_{66}=-0.250821497\) \(a_{67}=-0.320457160\) \(a_{68}=+0.515972036\) \(a_{69}=-0.520852638\) \(a_{70}=+0.065414450\)
\(a_{71}=-1.060696832\) \(a_{72}=+0.198035482\) \(a_{73}=+0.370452161\) \(a_{74}=+0.079826501\) \(a_{75}=-0.400014198\)
\(a_{76}=+1.670055885\) \(a_{77}=-0.525814436\) \(a_{78}=+0.239686217\) \(a_{79}=+0.616355513\) \(a_{80}=+0.397347143\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.477771864\) \(a_{83}=-0.791703515\) \(a_{84}=+0.196937574\) \(a_{85}=-0.316859540\)
\(a_{86}=-0.331369525\) \(a_{87}=+0.550110326\) \(a_{88}=+0.826505580\) \(a_{89}=-0.058346236\) \(a_{90}=-0.057690122\)
\(a_{91}=+0.502470779\) \(a_{92}=+0.814167434\) \(a_{93}=-0.839958378\) \(a_{94}=-0.053174368\) \(a_{95}=-1.025584922\)
\(a_{96}=-0.472270588\) \(a_{97}=-1.721122160\) \(a_{98}=-0.044611397\) \(a_{99}=+0.463724744\) \(a_{100}=+0.625279608\)

Showing 100 of 232 available coefficients

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