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: \( 4.33588986809 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.221698548\) \(a_{3}=+0.577350269\) \(a_{4}=+0.492547343\) \(a_{5}=+1.623516047\)
\(a_{6}=+0.705347986\) \(a_{7}=+0.377964473\) \(a_{8}=-0.619954174\) \(a_{9}=+0.333333333\) \(a_{10}=+1.983447198\)
\(a_{11}=-0.904885347\) \(a_{12}=+0.284372341\) \(a_{13}=+1.116641735\) \(a_{14}=+0.461758648\) \(a_{15}=+0.937337427\)
\(a_{16}=-1.249944458\) \(a_{17}=-0.174990464\) \(a_{18}=+0.407232849\) \(a_{19}=-1.382548042\) \(a_{20}=+0.799658516\)
\(a_{21}=+0.218217890\) \(a_{22}=-1.105497115\) \(a_{23}=-1.151378723\) \(a_{24}=-0.357930709\) \(a_{25}=+1.635804354\)
\(a_{26}=+1.364199586\) \(a_{27}=+0.192450090\) \(a_{28}=+0.186165397\) \(a_{29}=+0.749825428\) \(a_{30}=+1.145143773\)
\(a_{31}=-0.722757005\) \(a_{32}=-0.907101156\) \(a_{33}=-0.522435799\) \(a_{34}=-0.213785596\) \(a_{35}=+0.613631387\)
\(a_{36}=+0.164182448\) \(a_{37}=-0.815632261\) \(a_{38}=-1.689056936\) \(a_{39}=+0.644693406\) \(a_{40}=-1.006505550\)
\(a_{41}=-0.105296871\) \(a_{42}=+0.266596480\) \(a_{43}=+1.611608125\) \(a_{44}=-0.445698874\) \(a_{45}=+0.541172015\)
\(a_{46}=-1.406637715\) \(a_{47}=+1.022896384\) \(a_{48}=-0.721655769\) \(a_{49}=+0.142857142\) \(a_{50}=+1.998459804\)
\(a_{51}=-0.101030790\) \(a_{52}=+0.549998921\) \(a_{53}=+0.113217197\) \(a_{54}=+0.235115992\) \(a_{55}=-1.469095880\)
\(a_{56}=-0.234320646\) \(a_{57}=-0.798214485\) \(a_{58}=+0.916060639\) \(a_{59}=-0.511348803\) \(a_{60}=+0.461683060\)
\(a_{61}=-0.192366377\) \(a_{62}=-0.882991184\) \(a_{63}=+0.125988158\) \(a_{64}=+0.141740293\) \(a_{65}=+1.812885775\)
\(a_{66}=-0.638259058\) \(a_{67}=+0.751072020\) \(a_{68}=-0.086191087\) \(a_{69}=-0.664748815\) \(a_{70}=+0.749672575\)
\(a_{71}=-0.219204291\) \(a_{72}=-0.206651391\) \(a_{73}=-0.498921952\) \(a_{74}=-0.996456747\) \(a_{75}=+0.944432081\)
\(a_{76}=-0.680970366\) \(a_{77}=-0.342014514\) \(a_{78}=+0.787621002\) \(a_{79}=-1.575051575\) \(a_{80}=-2.029304893\)
\(a_{81}=+0.111111104\) \(a_{82}=-0.128641044\) \(a_{83}=+0.987120599\) \(a_{84}=+0.107482621\) \(a_{85}=-0.284099824\)
\(a_{86}=+1.968899269\) \(a_{87}=+0.432911868\) \(a_{88}=+0.560987425\) \(a_{89}=+1.101285251\) \(a_{90}=+0.661148925\)
\(a_{91}=+0.422050916\) \(a_{92}=-0.567108352\) \(a_{93}=-0.417284081\) \(a_{94}=+1.249671032\) \(a_{95}=-2.244588924\)
\(a_{96}=-0.523715098\) \(a_{97}=-0.285957909\) \(a_{98}=+0.174528369\) \(a_{99}=-0.301628449\) \(a_{100}=+0.805711085\)

Showing 100 of 1500 available coefficients

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