Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 42.6434884147 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.774984554\) \(a_{3}=+0.648268795\) \(a_{4}=+2.150570168\) \(a_{5}=+1.455218989\)
\(a_{6}=+1.150667099\) \(a_{7}=+0.219174021\) \(a_{8}=+2.042244276\) \(a_{9}=-0.579747569\) \(a_{10}=+2.582991228\)
\(a_{11}=+1.150222392\) \(a_{12}=+1.394147532\) \(a_{13}=-0.066072238\) \(a_{14}=+0.389030501\) \(a_{15}=+0.943373060\)
\(a_{16}=+1.474381879\) \(a_{17}=-1.266650335\) \(a_{18}=-1.029042980\) \(a_{19}=-0.751786716\) \(a_{20}=+3.129550550\)
\(a_{21}=+0.142083626\) \(a_{22}=+2.041626980\) \(a_{23}=+0.611638327\) \(a_{24}=+1.323923237\) \(a_{25}=+1.117662305\)
\(a_{26}=-0.117277202\) \(a_{27}=-1.024101053\) \(a_{28}=+0.471349110\) \(a_{29}=-0.727799638\) \(a_{30}=+1.674472611\)
\(a_{31}=-0.293790941\) \(a_{32}=+0.574760785\) \(a_{33}=+0.745653284\) \(a_{34}=-2.248284781\) \(a_{35}=+0.318946197\)
\(a_{36}=-1.246787827\) \(a_{37}=+0.842472534\) \(a_{38}=-1.334409808\) \(a_{39}=-0.042832570\) \(a_{40}=+2.971912650\)
\(a_{41}=-0.364546898\) \(a_{42}=+0.252196334\) \(a_{43}=+1.168796531\) \(a_{44}=+2.473633963\) \(a_{45}=-0.843659671\)
\(a_{46}=+1.085648583\) \(a_{47}=+0.425646145\) \(a_{48}=+0.955795764\) \(a_{49}=-0.951962749\) \(a_{50}=+1.983833327\)
\(a_{51}=-0.821129887\) \(a_{52}=-0.142092983\) \(a_{53}=+1.132863594\) \(a_{54}=-1.817763552\) \(a_{55}=+1.673825466\)
\(a_{56}=+0.447606889\) \(a_{57}=-0.487359868\) \(a_{58}=-1.291833116\) \(a_{59}=+0.051703908\) \(a_{60}=+2.028789961\)
\(a_{61}=-0.558856315\) \(a_{62}=-0.521474381\) \(a_{63}=-0.127065607\) \(a_{64}=-0.454190363\) \(a_{65}=-0.096149569\)
\(a_{66}=+1.323523051\) \(a_{67}=+1.025169269\) \(a_{68}=-2.724020398\) \(a_{69}=+0.396505922\) \(a_{70}=+0.566124572\)
\(a_{71}=+1.106732819\) \(a_{72}=-1.183986155\) \(a_{73}=-0.868703418\) \(a_{74}=+1.495375735\) \(a_{75}=+0.724545596\)
\(a_{76}=-1.616770083\) \(a_{77}=+0.252098866\) \(a_{78}=-0.076027150\) \(a_{79}=-0.920531596\) \(a_{80}=+2.145548506\)
\(a_{81}=-0.084145187\) \(a_{82}=-0.647065113\) \(a_{83}=-0.455448206\) \(a_{84}=+0.305560920\) \(a_{85}=-1.843253620\)
\(a_{86}=+2.074595790\) \(a_{87}=-0.471809794\) \(a_{88}=+2.349035097\) \(a_{89}=-1.793585401\) \(a_{90}=-1.497482885\)
\(a_{91}=-0.014481318\) \(a_{92}=+1.315371139\) \(a_{93}=-0.190455499\) \(a_{94}=+0.755515332\) \(a_{95}=-1.094014304\)
\(a_{96}=+0.372599482\) \(a_{97}=+1.051116512\) \(a_{98}=-1.689719175\) \(a_{99}=-0.666838636\) \(a_{100}=+2.403611210\)

Showing 100 of 5000 available coefficients

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