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: \( 6.27128134143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.620374865\) \(a_{3}=+0.577350269\) \(a_{4}=+1.625614703\) \(a_{5}=+1.226698240\)
\(a_{6}=-0.935523864\) \(a_{7}=+0.377964473\) \(a_{8}=-1.013730340\) \(a_{9}=+0.333333333\) \(a_{10}=-1.987710995\)
\(a_{11}=-0.614470312\) \(a_{12}=+0.938549086\) \(a_{13}=+0.738351635\) \(a_{14}=-0.612444132\) \(a_{15}=+0.708234559\)
\(a_{16}=+0.017008459\) \(a_{17}=+1.484118924\) \(a_{18}=-0.540124955\) \(a_{19}=-1.689111650\) \(a_{20}=+1.994138695\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.995672249\) \(a_{23}=+0.962549122\) \(a_{24}=-0.585277484\) \(a_{25}=+0.504788572\)
\(a_{26}=-1.196406431\) \(a_{27}=+0.192450090\) \(a_{28}=+0.614424604\) \(a_{29}=+0.229375949\) \(a_{30}=-1.147605478\)
\(a_{31}=+0.005392272\) \(a_{32}=+0.986170260\) \(a_{33}=-0.354764600\) \(a_{34}=-2.404829001\) \(a_{35}=+0.463648354\)
\(a_{36}=+0.541871568\) \(a_{37}=+1.192650070\) \(a_{38}=+2.736994061\) \(a_{39}=+0.426287515\) \(a_{40}=-1.243541223\)
\(a_{41}=+1.853136378\) \(a_{42}=-0.353594784\) \(a_{43}=-1.092897863\) \(a_{44}=-0.998891974\) \(a_{45}=+0.408899413\)
\(a_{46}=-1.559690404\) \(a_{47}=-0.516188021\) \(a_{48}=+0.009819839\) \(a_{49}=+0.142857143\) \(a_{50}=-0.817946714\)
\(a_{51}=+0.856856460\) \(a_{52}=+1.200275274\) \(a_{53}=-0.309653586\) \(a_{54}=-0.311841288\) \(a_{55}=-0.753769650\)
\(a_{56}=-0.383154054\) \(a_{57}=-0.975209066\) \(a_{58}=-0.371675023\) \(a_{59}=+1.575450012\) \(a_{60}=+1.151316512\)
\(a_{61}=+0.862197225\) \(a_{62}=-0.008737503\) \(a_{63}=+0.125988158\) \(a_{64}=-1.614973961\) \(a_{65}=+0.905734651\)
\(a_{66}=+0.574851641\) \(a_{67}=+0.270007144\) \(a_{68}=+2.412605544\) \(a_{69}=+0.555727995\) \(a_{70}=-0.751284139\)
\(a_{71}=-1.204766545\) \(a_{72}=-0.337910113\) \(a_{73}=+1.383185126\) \(a_{74}=-1.932540196\) \(a_{75}=+0.291439818\)
\(a_{76}=-2.745844732\) \(a_{77}=-0.232247948\) \(a_{78}=-0.690745575\) \(a_{79}=+0.111617277\) \(a_{80}=+0.020864247\)
\(a_{81}=+0.111111111\) \(a_{82}=-3.002775609\) \(a_{83}=+1.324696345\) \(a_{84}=+0.354738211\) \(a_{85}=+1.820566072\)
\(a_{86}=+1.770904227\) \(a_{87}=+0.132430266\) \(a_{88}=+0.622907198\) \(a_{89}=-0.249768076\) \(a_{90}=-0.662570332\)
\(a_{91}=+0.279070687\) \(a_{92}=+1.564734005\) \(a_{93}=+0.003113230\) \(a_{94}=+0.836418095\) \(a_{95}=-2.072030288\)
\(a_{96}=+0.569365665\) \(a_{97}=-1.526562417\) \(a_{98}=-0.231482124\) \(a_{99}=-0.204823437\) \(a_{100}=+0.820591724\)

Showing 100 of 256 available coefficients

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