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: \( 5.42864227935 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.600512037\) \(a_{3}=+0.577350269\) \(a_{4}=+1.561638779\) \(a_{5}=+0.782060427\)
\(a_{6}=+0.924056055\) \(a_{7}=-0.377964473\) \(a_{8}=+0.898909626\) \(a_{9}=+0.333333333\) \(a_{10}=+1.251697126\)
\(a_{11}=+1.445784064\) \(a_{12}=+0.901612570\) \(a_{13}=+0.517967772\) \(a_{14}=-0.604936688\) \(a_{15}=+0.451522798\)
\(a_{16}=-0.122923102\) \(a_{17}=-1.565775593\) \(a_{18}=+0.533504012\) \(a_{19}=+0.516650280\) \(a_{20}=+1.221295890\)
\(a_{21}=-0.218217890\) \(a_{22}=+2.313994797\) \(a_{23}=-1.125977553\) \(a_{24}=+0.518985715\) \(a_{25}=-0.388381489\)
\(a_{26}=+0.829013653\) \(a_{27}=+0.192450090\) \(a_{28}=-0.590243978\) \(a_{29}=-0.881560024\) \(a_{30}=+0.722667673\)
\(a_{31}=-0.377776939\) \(a_{32}=-1.095649531\) \(a_{33}=+0.834723819\) \(a_{34}=-2.506042684\) \(a_{35}=-0.295591057\)
\(a_{36}=+0.520546260\) \(a_{37}=+1.364667240\) \(a_{38}=+0.826904992\) \(a_{39}=+0.299048832\) \(a_{40}=+0.703001646\)
\(a_{41}=+0.502503024\) \(a_{42}=-0.349260360\) \(a_{43}=-1.237249034\) \(a_{44}=+2.257792461\) \(a_{45}=+0.260686809\)
\(a_{46}=-1.802140627\) \(a_{47}=+0.122997953\) \(a_{48}=-0.070969686\) \(a_{49}=+0.142857143\) \(a_{50}=-0.621609248\)
\(a_{51}=-0.904000960\) \(a_{52}=+0.808878558\) \(a_{53}=-1.371187636\) \(a_{54}=+0.308018685\) \(a_{55}=+1.130690502\)
\(a_{56}=-0.339755903\) \(a_{57}=+0.298288178\) \(a_{58}=-1.410947429\) \(a_{59}=+1.862715002\) \(a_{60}=+0.705115511\)
\(a_{61}=+1.077701391\) \(a_{62}=-0.604636537\) \(a_{63}=-0.125988158\) \(a_{64}=-1.630677160\) \(a_{65}=+0.405082096\)
\(a_{66}=+1.335985519\) \(a_{67}=-1.234895294\) \(a_{68}=-2.445175886\) \(a_{69}=-0.650083443\) \(a_{70}=-0.473097045\)
\(a_{71}=+0.685316992\) \(a_{72}=+0.299636542\) \(a_{73}=-0.429127117\) \(a_{74}=+2.184166343\) \(a_{75}=-0.224232157\)
\(a_{76}=+0.806821113\) \(a_{77}=-0.546455012\) \(a_{78}=+0.478631256\) \(a_{79}=+1.500507593\) \(a_{80}=-0.096133294\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.804262138\) \(a_{83}=+1.552885788\) \(a_{84}=-0.340777520\) \(a_{85}=-1.224531129\)
\(a_{86}=-1.980231971\) \(a_{87}=-0.508968917\) \(a_{88}=+1.299629213\) \(a_{89}=+0.015132020\) \(a_{90}=+0.417232375\)
\(a_{91}=-0.195773416\) \(a_{92}=-1.758370211\) \(a_{93}=-0.218109617\) \(a_{94}=+0.196859704\) \(a_{95}=+0.404051738\)
\(a_{96}=-0.632573552\) \(a_{97}=-0.217954620\) \(a_{98}=+0.228644577\) \(a_{99}=+0.481928021\) \(a_{100}=-0.606511595\)

Showing 100 of 268 available coefficients

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