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: \( 6.740246832 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.706029390\) \(a_{3}=-1.155657660\) \(a_{4}=+1.910536280\) \(a_{5}=+0.425492740\)
\(a_{6}=-1.971585933\) \(a_{7}=+1.566150178\) \(a_{8}=+1.553401654\) \(a_{9}=+0.335544627\) \(a_{10}=+0.725903120\)
\(a_{11}=+1.594459506\) \(a_{12}=-2.207925886\) \(a_{13}=+0.277350098\) \(a_{14}=+2.671898233\) \(a_{15}=-0.491723944\)
\(a_{16}=+0.739612596\) \(a_{17}=+0.078170406\) \(a_{18}=+0.572448996\) \(a_{19}=-0.170458622\) \(a_{20}=+0.812919316\)
\(a_{21}=-1.809933450\) \(a_{22}=+2.720194778\) \(a_{23}=-0.910816568\) \(a_{24}=-1.795200520\) \(a_{25}=-0.818955928\)
\(a_{26}=+0.473167418\) \(a_{27}=+0.767882941\) \(a_{28}=+2.992186734\) \(a_{29}=-1.178119316\) \(a_{30}=-0.838895501\)
\(a_{31}=+0.731770366\) \(a_{32}=-0.291600828\) \(a_{33}=-1.842649341\) \(a_{34}=+0.133361011\) \(a_{35}=+0.666385530\)
\(a_{36}=+0.641070184\) \(a_{37}=+1.177577801\) \(a_{38}=-0.290807418\) \(a_{39}=-0.320521765\) \(a_{40}=+0.660961126\)
\(a_{41}=+0.414994255\) \(a_{42}=-3.087799659\) \(a_{43}=-1.519788230\) \(a_{44}=+3.046272732\) \(a_{45}=+0.142771803\)
\(a_{46}=-1.553879834\) \(a_{47}=+0.850737227\) \(a_{48}=-0.854738962\) \(a_{49}=+1.452826380\) \(a_{50}=-1.397162883\)
\(a_{51}=-0.090338229\) \(a_{52}=+0.529887424\) \(a_{53}=-0.260333239\) \(a_{54}=+1.310030866\) \(a_{55}=+0.678430944\)
\(a_{56}=+2.432860276\) \(a_{57}=+0.196991812\) \(a_{58}=-2.009906178\) \(a_{59}=-0.690117644\) \(a_{60}=-0.939456435\)
\(a_{61}=-0.025054368\) \(a_{62}=+1.248421751\) \(a_{63}=+0.525513277\) \(a_{64}=-1.237092178\) \(a_{65}=+0.118010453\)
\(a_{66}=-3.143613931\) \(a_{67}=-1.542675949\) \(a_{68}=+0.149347398\) \(a_{69}=+1.052592144\) \(a_{70}=+1.136873300\)
\(a_{71}=-0.539116823\) \(a_{72}=+0.521235579\) \(a_{73}=+0.180961877\) \(a_{74}=+2.008982338\) \(a_{75}=+0.946432692\)
\(a_{76}=-0.325667381\) \(a_{77}=+2.497163038\) \(a_{78}=-0.546819551\) \(a_{79}=-0.081458047\) \(a_{80}=+0.314699790\)
\(a_{81}=-1.222954430\) \(a_{82}=+0.707992395\) \(a_{83}=-0.807373103\) \(a_{84}=-3.457943520\) \(a_{85}=+0.033260940\)
\(a_{86}=-2.592803388\) \(a_{87}=+1.361502612\) \(a_{88}=+2.476836032\) \(a_{89}=+0.475190736\) \(a_{90}=+0.243572892\)
\(a_{91}=+0.434371905\) \(a_{92}=-1.740148097\) \(a_{93}=-0.845676029\) \(a_{94}=+1.451382713\) \(a_{95}=-0.072528906\)
\(a_{96}=+0.336990730\) \(a_{97}=-0.782432655\) \(a_{98}=+2.478564503\) \(a_{99}=+0.535012320\) \(a_{100}=-1.564645012\)

Showing 100 of 546 available coefficients

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