Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.9956190494 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.685610294\) \(a_{3}=+1.636152370\) \(a_{4}=+1.841282064\) \(a_{5}=+0.224609266\)
\(a_{6}=-2.757915279\) \(a_{7}=+1.357052683\) \(a_{8}=-1.418073708\) \(a_{9}=+1.676994579\) \(a_{10}=-0.378603690\)
\(a_{11}=-0.970642456\) \(a_{12}=+3.012618014\) \(a_{13}=+0.772024846\) \(a_{14}=-2.287461972\) \(a_{15}=+0.367494982\)
\(a_{16}=+0.549037576\) \(a_{17}=-0.145433884\) \(a_{18}=-2.826759325\) \(a_{19}=+0.229415734\) \(a_{20}=+0.413569012\)
\(a_{21}=+2.220344964\) \(a_{22}=+1.636124914\) \(a_{23}=-0.465547405\) \(a_{24}=-2.320184659\) \(a_{25}=-0.949550679\)
\(a_{26}=-1.301333025\) \(a_{27}=+1.107666282\) \(a_{28}=+2.498716767\) \(a_{29}=-0.520200542\) \(a_{30}=-0.619453329\)
\(a_{31}=-0.472796568\) \(a_{32}=+0.492610303\) \(a_{33}=-1.588118945\) \(a_{34}=+0.245144855\) \(a_{35}=+0.304806589\)
\(a_{36}=+3.087820080\) \(a_{37}=+0.347614184\) \(a_{38}=-0.386705522\) \(a_{39}=+1.263150281\) \(a_{40}=-0.318512494\)
\(a_{41}=+1.052755509\) \(a_{42}=-3.742636330\) \(a_{43}=-0.935023123\) \(a_{44}=-1.787226541\) \(a_{45}=+0.376668525\)
\(a_{46}=+0.784731495\) \(a_{47}=-1.492237822\) \(a_{48}=+0.898309138\) \(a_{49}=+0.841591988\) \(a_{50}=+1.600572417\)
\(a_{51}=-0.237952012\) \(a_{52}=+1.421515464\) \(a_{53}=-0.796531556\) \(a_{54}=-1.867093660\) \(a_{55}=-0.218015220\)
\(a_{56}=-1.924400713\) \(a_{57}=+0.375359084\) \(a_{58}=+0.876855353\) \(a_{59}=+1.283626325\) \(a_{60}=+0.676661952\)
\(a_{61}=-0.213386744\) \(a_{62}=+0.796950800\) \(a_{63}=+2.275769925\) \(a_{64}=-1.379386716\) \(a_{65}=+0.173403932\)
\(a_{66}=+2.676949772\) \(a_{67}=-0.764871750\) \(a_{68}=-0.267784846\) \(a_{69}=-0.761706462\) \(a_{70}=-0.513785096\)
\(a_{71}=+0.885587342\) \(a_{72}=-2.378101965\) \(a_{73}=-0.165840883\) \(a_{74}=-0.585942100\) \(a_{75}=-1.553609584\)
\(a_{76}=+0.422419061\) \(a_{77}=-1.317212988\) \(a_{78}=-2.129179029\) \(a_{79}=+1.401796662\) \(a_{80}=+0.123318851\)
\(a_{81}=+0.135316197\) \(a_{82}=-1.774535447\) \(a_{83}=+0.914022229\) \(a_{84}=+4.088281254\) \(a_{85}=-0.032665808\)
\(a_{86}=+1.576084643\) \(a_{87}=-0.851127279\) \(a_{88}=+1.376442573\) \(a_{89}=-1.552698790\) \(a_{90}=-0.634916413\)
\(a_{91}=+1.047678412\) \(a_{92}=-0.857204042\) \(a_{93}=-0.773567260\) \(a_{94}=+2.515331432\) \(a_{95}=+0.051528956\)
\(a_{96}=+0.805985553\) \(a_{97}=+1.313260986\) \(a_{98}=-1.418595990\) \(a_{99}=-1.627762152\) \(a_{100}=-1.748390618\)

Showing 100 of 1500 available coefficients

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