Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.96964302847 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.135361386\) \(a_{3}=+0.393825250\) \(a_{4}=+0.289045477\) \(a_{5}=+1.488820985\)
\(a_{6}=+0.447133981\) \(a_{7}=+1.706225325\) \(a_{8}=-0.807190313\) \(a_{9}=-0.844901673\) \(a_{10}=+1.690349858\)
\(a_{11}=-0.730214341\) \(a_{12}=+0.113833407\) \(a_{13}=+0.277350098\) \(a_{14}=+1.937182350\) \(a_{15}=+0.586335297\)
\(a_{16}=-1.205498189\) \(a_{17}=-0.778661734\) \(a_{18}=-0.959268734\) \(a_{19}=-0.225862992\) \(a_{20}=+0.430336972\)
\(a_{21}=+0.671954615\) \(a_{22}=-0.829057166\) \(a_{23}=+0.869844229\) \(a_{24}=-0.317891927\) \(a_{25}=+1.216587927\)
\(a_{26}=+0.314892592\) \(a_{27}=-0.726568862\) \(a_{28}=+0.493176713\) \(a_{29}=-0.355634454\) \(a_{30}=+0.665702455\)
\(a_{31}=-1.155408432\) \(a_{32}=-0.561485782\) \(a_{33}=-0.287576845\) \(a_{34}=-0.884062466\) \(a_{35}=+2.540264070\)
\(a_{36}=-0.244215007\) \(a_{37}=-0.209744577\) \(a_{38}=-0.256436119\) \(a_{39}=+0.109227472\) \(a_{40}=-1.201761877\)
\(a_{41}=-0.567803909\) \(a_{42}=+0.762911323\) \(a_{43}=+1.023773013\) \(a_{44}=-0.211065152\) \(a_{45}=-1.257907341\)
\(a_{46}=+0.987587549\) \(a_{47}=-0.174628442\) \(a_{48}=-0.474755626\) \(a_{49}=+1.911204860\) \(a_{50}=+1.381266955\)
\(a_{51}=-0.306656652\) \(a_{52}=+0.080166791\) \(a_{53}=-0.103899569\) \(a_{54}=-0.824918230\) \(a_{55}=-1.087158435\)
\(a_{56}=-1.377248554\) \(a_{57}=-0.088950549\) \(a_{58}=-0.403773626\) \(a_{59}=+1.535065337\) \(a_{60}=+0.169477565\)
\(a_{61}=+0.817781474\) \(a_{62}=-1.311806118\) \(a_{63}=-1.441592631\) \(a_{64}=+0.568008914\) \(a_{65}=+0.412924646\)
\(a_{66}=-0.326503646\) \(a_{67}=-0.997881833\) \(a_{68}=-0.225068652\) \(a_{69}=+0.342566621\) \(a_{70}=+2.884117735\)
\(a_{71}=+0.396088588\) \(a_{72}=+0.681996445\) \(a_{73}=+0.546775732\) \(a_{74}=-0.238135893\) \(a_{75}=+0.479123044\)
\(a_{76}=-0.065284676\) \(a_{77}=-1.245910201\) \(a_{78}=+0.124012654\) \(a_{79}=+0.421206699\) \(a_{80}=-1.794771002\)
\(a_{81}=+0.558760509\) \(a_{82}=-0.644662633\) \(a_{83}=-0.800872283\) \(a_{84}=+0.194225442\) \(a_{85}=-1.159287930\)
\(a_{86}=+1.162352347\) \(a_{87}=-0.140057828\) \(a_{88}=+0.589421942\) \(a_{89}=+0.069180894\) \(a_{90}=-1.428179422\)
\(a_{91}=+0.473221761\) \(a_{92}=+0.251424540\) \(a_{93}=-0.455029014\) \(a_{94}=-0.198266390\) \(a_{95}=-0.336269562\)
\(a_{96}=-0.221127278\) \(a_{97}=+0.488514402\) \(a_{98}=+2.169908199\) \(a_{99}=+0.616959318\) \(a_{100}=+0.351649237\)

Showing 100 of 546 available coefficients

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