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: \( 0.970815416958 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.592042609\) \(a_{3}=-0.299789426\) \(a_{4}=-0.649485549\) \(a_{5}=+0.682172814\)
\(a_{6}=+0.177488114\) \(a_{7}=+0.562396933\) \(a_{8}=+0.976565728\) \(a_{9}=-0.910126300\) \(a_{10}=-0.403875373\)
\(a_{11}=-0.791851160\) \(a_{12}=+0.194708900\) \(a_{13}=+0.277350098\) \(a_{14}=-0.332962948\) \(a_{15}=-0.204508197\)
\(a_{16}=+0.071317027\) \(a_{17}=+0.082417682\) \(a_{18}=+0.538833549\) \(a_{19}=+0.902271900\) \(a_{20}=-0.443061385\)
\(a_{21}=-0.168600654\) \(a_{22}=+0.468809627\) \(a_{23}=+0.160329634\) \(a_{24}=-0.292764079\) \(a_{25}=-0.534640251\)
\(a_{26}=-0.164203076\) \(a_{27}=+0.572635667\) \(a_{28}=-0.365268681\) \(a_{29}=-0.087188229\) \(a_{30}=+0.121077566\)
\(a_{31}=-1.021296533\) \(a_{32}=-1.018788447\) \(a_{33}=+0.237388605\) \(a_{34}=-0.048794779\) \(a_{35}=+0.383651899\)
\(a_{36}=+0.591113879\) \(a_{37}=+1.793325452\) \(a_{38}=-0.534183410\) \(a_{39}=-0.083146627\) \(a_{40}=+0.666186591\)
\(a_{41}=+0.514245518\) \(a_{42}=+0.099818771\) \(a_{43}=-0.628116412\) \(a_{44}=+0.514295885\) \(a_{45}=-0.620863420\)
\(a_{46}=-0.094921975\) \(a_{47}=-1.238731711\) \(a_{48}=-0.021380091\) \(a_{49}=-0.683709689\) \(a_{50}=+0.316529809\)
\(a_{51}=-0.024707949\) \(a_{52}=-0.180134881\) \(a_{53}=+0.354386224\) \(a_{54}=-0.339024715\) \(a_{55}=-0.540179335\)
\(a_{56}=+0.549217571\) \(a_{57}=-0.270491575\) \(a_{58}=+0.051619146\) \(a_{59}=+0.660434616\) \(a_{60}=+0.132825118\)
\(a_{61}=+0.501869060\) \(a_{62}=+0.604651064\) \(a_{63}=-0.511852240\) \(a_{64}=+0.531849144\) \(a_{65}=+0.189200697\)
\(a_{66}=-0.140544169\) \(a_{67}=-0.086873487\) \(a_{68}=-0.053529093\) \(a_{69}=-0.048065129\) \(a_{70}=-0.227138271\)
\(a_{71}=+1.101151619\) \(a_{72}=-0.888798153\) \(a_{73}=+0.997487233\) \(a_{74}=-1.061725080\) \(a_{75}=+0.160279494\)
\(a_{76}=-0.586012560\) \(a_{77}=-0.445334664\) \(a_{78}=+0.049226346\) \(a_{79}=-1.297500197\) \(a_{80}=+0.048650537\)
\(a_{81}=+0.738456182\) \(a_{82}=-0.304455259\) \(a_{83}=+0.703482302\) \(a_{84}=+0.109503688\) \(a_{85}=+0.056223102\)
\(a_{86}=+0.371871680\) \(a_{87}=+0.026138109\) \(a_{88}=-0.773294705\) \(a_{89}=-1.442691169\) \(a_{90}=+0.367577599\)
\(a_{91}=+0.155980845\) \(a_{92}=-0.104131781\) \(a_{93}=+0.306173901\) \(a_{94}=+0.733381954\) \(a_{95}=+0.615505362\)
\(a_{96}=+0.305422004\) \(a_{97}=-0.061097524\) \(a_{98}=+0.404785269\) \(a_{99}=+0.720684567\) \(a_{100}=+0.347241117\)

Showing 100 of 546 available coefficients

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