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: \( 3.70162757524 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.817977311\) \(a_{3}=+0.649240932\) \(a_{4}=-0.330913119\) \(a_{5}=-1.079398128\)
\(a_{6}=-0.531064352\) \(a_{7}=-0.440100553\) \(a_{8}=+1.088656734\) \(a_{9}=-0.578486212\) \(a_{10}=+0.882923178\)
\(a_{11}=-0.577051891\) \(a_{12}=-0.214842342\) \(a_{13}=+0.277350098\) \(a_{14}=+0.359992266\) \(a_{15}=-0.700789447\)
\(a_{16}=-0.559583388\) \(a_{17}=+0.657541440\) \(a_{18}=+0.473188596\) \(a_{19}=-1.684626089\) \(a_{20}=+0.357187001\)
\(a_{21}=-0.285731293\) \(a_{22}=+0.472015354\) \(a_{23}=+1.028151166\) \(a_{24}=+0.706800513\) \(a_{25}=+0.165100318\)
\(a_{26}=-0.226866087\) \(a_{27}=-1.024817860\) \(a_{28}=+0.145635047\) \(a_{29}=+0.557392840\) \(a_{30}=+0.573229867\)
\(a_{31}=-1.039262093\) \(a_{32}=-0.630930219\) \(a_{33}=-0.374645708\) \(a_{34}=-0.537853979\) \(a_{35}=+0.475043713\)
\(a_{36}=+0.191428677\) \(a_{37}=-1.321923403\) \(a_{38}=+1.377985918\) \(a_{39}=+0.180067036\) \(a_{40}=-1.175094040\)
\(a_{41}=+1.091697093\) \(a_{42}=+0.233721715\) \(a_{43}=+1.942654597\) \(a_{44}=+0.190954041\) \(a_{45}=+0.624416934\)
\(a_{46}=-0.841004326\) \(a_{47}=-0.461966467\) \(a_{48}=-0.363304441\) \(a_{49}=-0.806311504\) \(a_{50}=-0.135048314\)
\(a_{51}=+0.426902818\) \(a_{52}=-0.091778786\) \(a_{53}=-1.658176872\) \(a_{54}=+0.838277757\) \(a_{55}=+0.622868731\)
\(a_{56}=-0.479118430\) \(a_{57}=-1.093728213\) \(a_{58}=-0.455934697\) \(a_{59}=+0.663471026\) \(a_{60}=+0.231900422\)
\(a_{61}=-0.273958311\) \(a_{62}=+0.850092812\) \(a_{63}=+0.254592101\) \(a_{64}=+1.075669992\) \(a_{65}=-0.299371177\)
\(a_{66}=+0.306451689\) \(a_{67}=+0.264558575\) \(a_{68}=-0.217589089\) \(a_{69}=+0.667517822\) \(a_{70}=-0.388574978\)
\(a_{71}=-1.225614657\) \(a_{72}=-0.629772910\) \(a_{73}=-0.516559040\) \(a_{74}=+1.081303350\) \(a_{75}=+0.107189884\)
\(a_{76}=+0.557464874\) \(a_{77}=+0.253960856\) \(a_{78}=-0.147290750\) \(a_{79}=+0.458052262\) \(a_{80}=+0.604013262\)
\(a_{81}=-0.086867491\) \(a_{82}=-0.892983452\) \(a_{83}=-0.113987543\) \(a_{84}=+0.094552233\) \(a_{85}=-0.709748999\)
\(a_{86}=-1.589047383\) \(a_{87}=+0.361882247\) \(a_{88}=-0.628211427\) \(a_{89}=+0.916833068\) \(a_{90}=-0.510758884\)
\(a_{91}=-0.122061931\) \(a_{92}=-0.340228709\) \(a_{93}=-0.674731490\) \(a_{94}=+0.377878088\) \(a_{95}=+1.818382247\)
\(a_{96}=-0.409625724\) \(a_{97}=+0.613540346\) \(a_{98}=+0.659544515\) \(a_{99}=+0.333816563\) \(a_{100}=-0.054633861\)

Showing 100 of 546 available coefficients

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