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: \( 4.8541487803 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.629400212\) \(a_{3}=+0.414810615\) \(a_{4}=-0.603855373\) \(a_{5}=+0.654069156\)
\(a_{6}=-0.261081889\) \(a_{7}=+1.456959689\) \(a_{8}=+1.009466912\) \(a_{9}=-0.827932154\) \(a_{10}=-0.411671266\)
\(a_{11}=+1.632840686\) \(a_{12}=-0.250485618\) \(a_{13}=-0.277350098\) \(a_{14}=-0.917010737\) \(a_{15}=+0.271314829\)
\(a_{16}=-0.031503316\) \(a_{17}=+0.371973863\) \(a_{18}=+0.521100674\) \(a_{19}=+0.566651134\) \(a_{20}=-0.394963174\)
\(a_{21}=+0.604362344\) \(a_{22}=-1.027710274\) \(a_{23}=+0.464258650\) \(a_{24}=+0.418737590\) \(a_{25}=-0.572193539\)
\(a_{26}=+0.174564211\) \(a_{27}=-0.758245660\) \(a_{28}=-0.879792936\) \(a_{29}=-0.141773160\) \(a_{30}=-0.170765611\)
\(a_{31}=+1.699711814\) \(a_{32}=-0.989638718\) \(a_{33}=+0.677319648\) \(a_{34}=-0.234120429\) \(a_{35}=+0.952952395\)
\(a_{36}=+0.499951279\) \(a_{37}=+0.258538259\) \(a_{38}=-0.356650344\) \(a_{39}=-0.115047765\) \(a_{40}=+0.660261172\)
\(a_{41}=-0.647239297\) \(a_{42}=-0.380385788\) \(a_{43}=+0.203278852\) \(a_{44}=-0.985999621\) \(a_{45}=-0.541524886\)
\(a_{46}=-0.292204493\) \(a_{47}=-0.601108965\) \(a_{48}=-0.013067910\) \(a_{49}=+1.122731534\) \(a_{50}=+0.360138735\)
\(a_{51}=+0.154298707\) \(a_{52}=+0.167479347\) \(a_{53}=-1.945145492\) \(a_{54}=+0.477239980\) \(a_{55}=+1.067990730\)
\(a_{56}=+1.470752598\) \(a_{57}=+0.235052905\) \(a_{58}=+0.089232057\) \(a_{59}=+0.052603547\) \(a_{60}=-0.163834917\)
\(a_{61}=+0.269674331\) \(a_{62}=-1.069798977\) \(a_{63}=-1.206263773\) \(a_{64}=+0.654382136\) \(a_{65}=-0.181406145\)
\(a_{66}=-0.426305131\) \(a_{67}=+1.590197245\) \(a_{68}=-0.224618416\) \(a_{69}=+0.192579416\) \(a_{70}=-0.599788440\)
\(a_{71}=-0.297622326\) \(a_{72}=-0.835770115\) \(a_{73}=-0.156202972\) \(a_{74}=-0.162724035\) \(a_{75}=-0.237351953\)
\(a_{76}=-0.342175332\) \(a_{77}=+2.378983057\) \(a_{78}=+0.072411088\) \(a_{79}=-1.704108895\) \(a_{80}=-0.020605348\)
\(a_{81}=+0.513403806\) \(a_{82}=+0.407372551\) \(a_{83}=-0.838826373\) \(a_{84}=-0.364947448\) \(a_{85}=+0.243296631\)
\(a_{86}=-0.127943752\) \(a_{87}=-0.058809012\) \(a_{88}=+1.648298645\) \(a_{89}=+0.975920141\) \(a_{90}=+0.340835878\)
\(a_{91}=-0.404087913\) \(a_{92}=-0.280345080\) \(a_{93}=+0.705058502\) \(a_{94}=+0.378338110\) \(a_{95}=+0.370629029\)
\(a_{96}=-0.410512645\) \(a_{97}=-0.008667186\) \(a_{98}=-0.706647466\) \(a_{99}=-1.351881306\) \(a_{100}=+0.345522142\)

Showing 100 of 546 available coefficients

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