Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.52025624378 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.397599179\) \(a_{3}=-0.235424362\) \(a_{4}=-0.841914893\) \(a_{5}=-0.445453456\)
\(a_{6}=-0.093604533\) \(a_{7}=+0.518692622\) \(a_{8}=-0.732343849\) \(a_{9}=-0.944575370\) \(a_{10}=-0.177111928\)
\(a_{11}=+0.052195536\) \(a_{12}=+0.198207277\) \(a_{13}=-1.420256667\) \(a_{14}=+0.206231761\) \(a_{15}=+0.104870596\)
\(a_{16}=+0.550735579\) \(a_{17}=+0.773615574\) \(a_{18}=-0.375562392\) \(a_{19}=+0.265907641\) \(a_{20}=+0.375033898\)
\(a_{21}=-0.122112880\) \(a_{22}=+0.020752902\) \(a_{23}=+0.208514414\) \(a_{24}=+0.172411584\) \(a_{25}=-0.801571219\)
\(a_{26}=-0.564692885\) \(a_{27}=+0.457800416\) \(a_{28}=-0.436695043\) \(a_{29}=-0.986414240\) \(a_{30}=+0.041696463\)
\(a_{31}=-1.129961893\) \(a_{32}=+0.951315864\) \(a_{33}=-0.012288101\) \(a_{34}=+0.307588917\) \(a_{35}=-0.231053421\)
\(a_{36}=+0.795252071\) \(a_{37}=+0.812383598\) \(a_{38}=+0.105724660\) \(a_{39}=+0.334363020\) \(a_{40}=+0.326225098\)
\(a_{41}=-0.964643083\) \(a_{42}=-0.048551981\) \(a_{43}=+0.889759655\) \(a_{44}=-0.043944199\) \(a_{45}=+0.420764363\)
\(a_{46}=+0.082905160\) \(a_{47}=-0.461158119\) \(a_{48}=-0.129656572\) \(a_{49}=-0.730957964\) \(a_{50}=-0.318704059\)
\(a_{51}=-0.182127953\) \(a_{52}=+1.195735239\) \(a_{53}=-0.860791891\) \(a_{54}=+0.182021070\) \(a_{55}=-0.023250682\)
\(a_{56}=-0.379861351\) \(a_{57}=-0.062601137\) \(a_{58}=-0.392197492\) \(a_{59}=-0.903708624\) \(a_{60}=-0.088292116\)
\(a_{61}=+1.228789026\) \(a_{62}=-0.449271921\) \(a_{63}=-0.489944275\) \(a_{64}=-0.172493173\) \(a_{65}=+0.632658240\)
\(a_{66}=-0.004885739\) \(a_{67}=+0.317972708\) \(a_{68}=-0.651318473\) \(a_{69}=-0.049089373\) \(a_{70}=-0.091866650\)
\(a_{71}=+0.562774643\) \(a_{72}=+0.691753962\) \(a_{73}=+1.440794531\) \(a_{74}=+0.323003052\) \(a_{75}=+0.188709393\)
\(a_{76}=-0.223871603\) \(a_{77}=+0.027073440\) \(a_{78}=+0.132942462\) \(a_{79}=-0.987512017\) \(a_{80}=-0.245327067\)
\(a_{81}=+0.836797999\) \(a_{82}=-0.383541298\) \(a_{83}=-1.090614468\) \(a_{84}=+0.102808652\) \(a_{85}=-0.344609731\)
\(a_{86}=+0.353767708\) \(a_{87}=+0.232225943\) \(a_{88}=-0.038225080\) \(a_{89}=+1.212787798\) \(a_{90}=+0.167295565\)
\(a_{91}=-0.736676654\) \(a_{92}=-0.175551391\) \(a_{93}=+0.266020558\) \(a_{94}=-0.183356090\) \(a_{95}=-0.118449478\)
\(a_{96}=-0.223962930\) \(a_{97}=-0.629907872\) \(a_{98}=-0.290628286\) \(a_{99}=-0.049302618\) \(a_{100}=+0.674854747\)

Showing 100 of 546 available coefficients

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