Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 26.7129034756 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.962945732\) \(a_{3}=-0.577350269\) \(a_{4}=-0.072735517\) \(a_{5}=-0.363414250\)
\(a_{6}=+0.555956978\) \(a_{7}=+1.832638970\) \(a_{8}=+1.032986088\) \(a_{9}=+0.333333333\) \(a_{10}=+0.349948201\)
\(a_{11}=-1.078172929\) \(a_{12}=+0.041993870\) \(a_{13}=+1.841765185\) \(a_{14}=-1.764731875\) \(a_{15}=+0.209817315\)
\(a_{16}=-0.921974028\) \(a_{17}=+0.177332800\) \(a_{18}=-0.320981911\) \(a_{19}=+0.494688301\) \(a_{20}=+0.026433123\)
\(a_{21}=-1.058074602\) \(a_{22}=+1.038222020\) \(a_{23}=-0.526256085\) \(a_{24}=-0.596394796\) \(a_{25}=-0.867930083\)
\(a_{26}=-1.773519925\) \(a_{27}=-0.192450090\) \(a_{28}=-0.133297942\) \(a_{29}=+0.088170930\) \(a_{30}=-0.202042688\)
\(a_{31}=+0.602462066\) \(a_{32}=-0.145175132\) \(a_{33}=+0.622483431\) \(a_{34}=-0.170761863\) \(a_{35}=-0.666007117\)
\(a_{36}=-0.024245172\) \(a_{37}=-0.638388347\) \(a_{38}=-0.476357988\) \(a_{39}=-1.063343625\) \(a_{40}=-0.375401864\)
\(a_{41}=+0.373905060\) \(a_{42}=+1.018868423\) \(a_{43}=+0.032667477\) \(a_{44}=+0.078421465\) \(a_{45}=-0.121138083\)
\(a_{46}=+0.506756051\) \(a_{47}=+0.494815749\) \(a_{48}=+0.532301953\) \(a_{49}=+2.358565593\) \(a_{50}=+0.835769569\)
\(a_{51}=-0.102383140\) \(a_{52}=-0.133961742\) \(a_{53}=+0.158298026\) \(a_{54}=+0.185318993\) \(a_{55}=+0.391823406\)
\(a_{56}=+1.893090559\) \(a_{57}=-0.285608424\) \(a_{58}=-0.084903821\) \(a_{59}=+1.301065865\) \(a_{60}=-0.015261171\)
\(a_{61}=-0.805098824\) \(a_{62}=-0.580138275\) \(a_{63}=+0.610879657\) \(a_{64}=+1.061769802\) \(a_{65}=-0.669323714\)
\(a_{66}=-0.599417763\) \(a_{67}=+1.128699793\) \(a_{68}=-0.012898393\) \(a_{69}=+0.303834092\) \(a_{70}=+0.641328711\)
\(a_{71}=-1.404490906\) \(a_{72}=+0.344328696\) \(a_{73}=-0.645140985\) \(a_{74}=+0.614733334\) \(a_{75}=+0.501099667\)
\(a_{76}=-0.035981409\) \(a_{77}=-1.975901725\) \(a_{78}=+1.023942206\) \(a_{79}=+0.875782981\) \(a_{80}=+0.335058500\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.360050282\) \(a_{83}=-0.215848677\) \(a_{84}=+0.076959603\) \(a_{85}=-0.064445267\)
\(a_{86}=-0.031457008\) \(a_{87}=-0.050905510\) \(a_{88}=-1.113737635\) \(a_{89}=-1.036360009\) \(a_{90}=+0.116649400\)
\(a_{91}=+3.375290651\) \(a_{92}=+0.038277508\) \(a_{93}=-0.347831636\) \(a_{94}=-0.476480714\) \(a_{95}=-0.179776778\)
\(a_{96}=+0.083816902\) \(a_{97}=+0.510788471\) \(a_{98}=-2.271170672\) \(a_{99}=-0.359390976\) \(a_{100}=+0.063129343\)

Showing 100 of 1228 available coefficients

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