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: \( 3.33220121006 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.641206662\) \(a_{3}=-0.106758353\) \(a_{4}=+1.693559309\) \(a_{5}=-0.930083605\)
\(a_{6}=-0.175212520\) \(a_{7}=+1.488804026\) \(a_{8}=+1.138274159\) \(a_{9}=-0.988602654\) \(a_{10}=-1.526459409\)
\(a_{11}=-0.321665945\) \(a_{12}=-0.180801602\) \(a_{13}=-0.277350098\) \(a_{14}=+2.443435087\) \(a_{15}=+0.099294193\)
\(a_{16}=+0.174583824\) \(a_{17}=+0.344051718\) \(a_{18}=-1.622501262\) \(a_{19}=+1.938949632\) \(a_{20}=-1.575151747\)
\(a_{21}=-0.158942265\) \(a_{22}=-0.527920292\) \(a_{23}=-0.542610443\) \(a_{24}=-0.121520274\) \(a_{25}=-0.134944488\)
\(a_{26}=-0.455188829\) \(a_{27}=+0.212299943\) \(a_{28}=+2.521377918\) \(a_{29}=+0.526021267\) \(a_{30}=+0.162962292\)
\(a_{31}=-0.269765242\) \(a_{32}=-0.851746024\) \(a_{33}=+0.034340526\) \(a_{34}=+0.564659972\) \(a_{35}=-1.384712216\)
\(a_{36}=-1.674257228\) \(a_{37}=+0.027920082\) \(a_{38}=+3.182217055\) \(a_{39}=+0.029609440\) \(a_{40}=-1.058690133\)
\(a_{41}=+0.538224325\) \(a_{42}=-0.260857105\) \(a_{43}=-0.584319357\) \(a_{44}=-0.544760355\) \(a_{45}=+0.919483120\)
\(a_{46}=-0.890535874\) \(a_{47}=-0.865008664\) \(a_{48}=-0.018638281\) \(a_{49}=+1.216537429\) \(a_{50}=-0.221471793\)
\(a_{51}=-0.036730395\) \(a_{52}=-0.469708840\) \(a_{53}=-0.122593746\) \(a_{54}=+0.348428082\) \(a_{55}=+0.299176221\)
\(a_{56}=+1.694667151\) \(a_{57}=-0.206999069\) \(a_{58}=+0.863309609\) \(a_{59}=-0.380477811\) \(a_{60}=+0.168160606\)
\(a_{61}=+1.058140037\) \(a_{62}=-0.442740513\) \(a_{63}=-1.471835612\) \(a_{64}=-1.572475073\) \(a_{65}=+0.257958779\)
\(a_{66}=+0.056359901\) \(a_{67}=+1.147026141\) \(a_{68}=+0.582671990\) \(a_{69}=+0.057928197\) \(a_{70}=-2.272598914\)
\(a_{71}=-1.228648577\) \(a_{72}=-1.125300854\) \(a_{73}=-0.535224328\) \(a_{74}=+0.045822624\) \(a_{75}=+0.014406451\)
\(a_{76}=+3.283726200\) \(a_{77}=-0.478897554\) \(a_{78}=+0.048595210\) \(a_{79}=+1.102929176\) \(a_{80}=-0.162377552\)
\(a_{81}=+0.965937862\) \(a_{82}=+0.883337348\) \(a_{83}=+1.497813258\) \(a_{84}=-0.269178153\) \(a_{85}=-0.319996862\)
\(a_{86}=-0.958988822\) \(a_{87}=-0.056157164\) \(a_{88}=-0.366144033\) \(a_{89}=-1.162509797\) \(a_{90}=+1.509061823\)
\(a_{91}=-0.412919943\) \(a_{92}=-0.918942967\) \(a_{93}=+0.028799693\) \(a_{94}=-1.419657983\) \(a_{95}=-1.803385263\)
\(a_{96}=+0.090931002\) \(a_{97}=-0.205461158\) \(a_{98}=+1.996589334\) \(a_{99}=+0.317999807\) \(a_{100}=-0.228536495\)

Showing 100 of 546 available coefficients

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