Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.89961904796 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.553126017\) \(a_{3}=-1.740514197\) \(a_{4}=-0.694051610\) \(a_{5}=+1.223990107\)
\(a_{6}=-0.962723685\) \(a_{7}=+0.928443300\) \(a_{8}=-0.937024019\) \(a_{9}=+2.029389668\) \(a_{10}=+0.677020772\)
\(a_{11}=+0.085960601\) \(a_{12}=+1.208006680\) \(a_{13}=-0.277350098\) \(a_{14}=+0.513546144\) \(a_{15}=-2.130372158\)
\(a_{16}=+0.175759246\) \(a_{17}=+0.966640111\) \(a_{18}=+1.122508224\) \(a_{19}=+0.869659927\) \(a_{20}=-0.849512304\)
\(a_{21}=-1.615968744\) \(a_{22}=+0.047547045\) \(a_{23}=+0.924769388\) \(a_{24}=+1.630903608\) \(a_{25}=+0.498151782\)
\(a_{26}=-0.153409555\) \(a_{27}=-1.791667332\) \(a_{28}=-0.644387567\) \(a_{29}=+0.970549802\) \(a_{30}=-1.178364266\)
\(a_{31}=-0.907528139\) \(a_{32}=+1.034241031\) \(a_{33}=-0.149615646\) \(a_{34}=+0.534673794\) \(a_{35}=+1.136405414\)
\(a_{36}=-1.408501166\) \(a_{37}=+1.328981541\) \(a_{38}=+0.481031531\) \(a_{39}=+0.482731783\) \(a_{40}=-1.146908129\)
\(a_{41}=+0.800207860\) \(a_{42}=-0.893834354\) \(a_{43}=-1.744698653\) \(a_{44}=-0.059661093\) \(a_{45}=+2.483952878\)
\(a_{46}=+0.511514008\) \(a_{47}=-0.914763600\) \(a_{48}=-0.305911464\) \(a_{49}=-0.137993039\) \(a_{50}=+0.275540711\)
\(a_{51}=-1.682450836\) \(a_{52}=+0.192495282\) \(a_{53}=+1.561149833\) \(a_{54}=-0.991017814\) \(a_{55}=+0.105214925\)
\(a_{56}=-0.869973672\) \(a_{57}=-1.513655449\) \(a_{58}=+0.536836346\) \(a_{59}=+0.663629303\) \(a_{60}=+1.478588225\)
\(a_{61}=+0.774833421\) \(a_{62}=-0.501977425\) \(a_{63}=+1.884173240\) \(a_{64}=+0.396306375\) \(a_{65}=-0.339473776\)
\(a_{66}=-0.082756306\) \(a_{67}=+0.713112490\) \(a_{68}=-0.670898125\) \(a_{69}=-1.609574248\) \(a_{70}=+0.628575400\)
\(a_{71}=-0.572534403\) \(a_{72}=-1.901586863\) \(a_{73}=-0.074819044\) \(a_{74}=+0.735094266\) \(a_{75}=-0.867040249\)
\(a_{76}=-0.603588872\) \(a_{77}=+0.079809544\) \(a_{78}=+0.267011508\) \(a_{79}=+0.204461153\) \(a_{80}=+0.215127579\)
\(a_{81}=+1.089032758\) \(a_{82}=+0.442615786\) \(a_{83}=-0.265210750\) \(a_{84}=+1.121565708\) \(a_{85}=+1.183157933\)
\(a_{86}=-0.965038217\) \(a_{87}=-1.689255708\) \(a_{88}=-0.080547148\) \(a_{89}=-0.329729447\) \(a_{90}=+1.373938961\)
\(a_{91}=-0.257503840\) \(a_{92}=-0.641837682\) \(a_{93}=+1.579565610\) \(a_{94}=-0.505979546\) \(a_{95}=+1.064455147\)
\(a_{96}=-1.800111197\) \(a_{97}=+1.109796900\) \(a_{98}=-0.076327540\) \(a_{99}=+0.174447555\) \(a_{100}=-0.345743046\)

Showing 100 of 546 available coefficients

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