Properties

Level $643$
Weight $0$
Character 643.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 643 \)
Weight: \( 0 \)
Character: 643.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.96569718668 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.422233750\) \(a_{3}=+1.677445110\) \(a_{4}=+1.022748743\) \(a_{5}=-1.839533381\)
\(a_{6}=+2.385718909\) \(a_{7}=-0.356060197\) \(a_{8}=+0.032354143\) \(a_{9}=+1.813822055\) \(a_{10}=-2.616246507\)
\(a_{11}=+0.906163073\) \(a_{12}=+1.715605024\) \(a_{13}=-1.051865347\) \(a_{14}=-0.506400769\) \(a_{15}=-3.085716325\)
\(a_{16}=-0.976733641\) \(a_{17}=+0.177186821\) \(a_{18}=+2.579679019\) \(a_{19}=+1.572163040\) \(a_{20}=-1.881380843\)
\(a_{21}=-0.597271456\) \(a_{22}=+1.288775518\) \(a_{23}=+0.213423851\) \(a_{24}=+0.054272199\) \(a_{25}=+2.383883470\)
\(a_{26}=-1.495998348\) \(a_{27}=+1.365141785\) \(a_{28}=-0.364160233\) \(a_{29}=+0.109589306\) \(a_{30}=-4.388610110\)
\(a_{31}=+1.118464981\) \(a_{32}=-1.421497688\) \(a_{33}=+1.520038726\) \(a_{34}=+0.252001059\) \(a_{35}=+0.654984726\)
\(a_{36}=+1.855084554\) \(a_{37}=+0.035433492\) \(a_{38}=+2.235983344\) \(a_{39}=-1.764446391\) \(a_{40}=-0.059516435\)
\(a_{41}=-1.017632380\) \(a_{42}=-0.849459726\) \(a_{43}=-0.904918641\) \(a_{44}=+0.926777176\) \(a_{45}=-3.336586539\)
\(a_{46}=+0.303538717\) \(a_{47}=+0.869794952\) \(a_{48}=-1.638417085\) \(a_{49}=-0.873221189\) \(a_{50}=+3.390439498\)
\(a_{51}=+0.297221276\) \(a_{52}=-1.075794157\) \(a_{53}=+0.627374742\) \(a_{54}=+1.941550993\) \(a_{55}=-1.666917102\)
\(a_{56}=-0.011520012\) \(a_{57}=+2.637217247\) \(a_{58}=+0.155861653\) \(a_{59}=+1.479611430\) \(a_{60}=-3.155912870\)
\(a_{61}=-1.521531641\) \(a_{62}=+1.590718662\) \(a_{63}=-0.645829999\) \(a_{64}=-1.044968399\) \(a_{65}=+1.934941629\)
\(a_{66}=+2.161850300\) \(a_{67}=+1.062354554\) \(a_{68}=+0.181217594\) \(a_{69}=+0.358006879\) \(a_{70}=+0.931541377\)
\(a_{71}=-1.420675437\) \(a_{72}=+0.058684769\) \(a_{73}=+1.279024906\) \(a_{74}=+0.050394749\) \(a_{75}=+3.998833706\)
\(a_{76}=+1.607927898\) \(a_{77}=-0.322648527\) \(a_{78}=-2.509455242\) \(a_{79}=+0.450404604\) \(a_{80}=+1.796734324\)
\(a_{81}=+0.476128493\) \(a_{82}=-1.447311174\) \(a_{83}=-1.091710063\) \(a_{84}=-0.610858710\) \(a_{85}=-0.325941102\)
\(a_{86}=-1.287005902\) \(a_{87}=+0.183830173\) \(a_{88}=+0.029318096\) \(a_{89}=-1.635632580\) \(a_{90}=-4.745406002\)
\(a_{91}=+0.374527346\) \(a_{92}=+0.218279071\) \(a_{93}=+1.876163586\) \(a_{94}=+1.237051664\) \(a_{95}=-2.892046625\)
\(a_{96}=-2.384484299\) \(a_{97}=+1.478851618\) \(a_{98}=-1.241924419\) \(a_{99}=+1.643618508\) \(a_{100}=+2.438113984\)

Showing 100 of 1846 available coefficients

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