Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.03719602046 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.348275136\) \(a_{3}=+0.615841762\) \(a_{4}=+0.817845843\) \(a_{5}=-0.611427328\)
\(a_{6}=-0.830324136\) \(a_{7}=-1.151623859\) \(a_{8}=+0.245593921\) \(a_{9}=-0.620738924\) \(a_{10}=+0.824372264\)
\(a_{11}=+0.442778374\) \(a_{12}=+0.503663625\) \(a_{13}=-0.711344523\) \(a_{14}=+1.552705815\) \(a_{15}=-0.376542483\)
\(a_{16}=-1.148974020\) \(a_{17}=-0.683431041\) \(a_{18}=+0.836926857\) \(a_{19}=+0.229415734\) \(a_{20}=-0.500053298\)
\(a_{21}=-0.709218066\) \(a_{22}=-0.596987072\) \(a_{23}=+1.721195917\) \(a_{24}=+0.151246994\) \(a_{25}=-0.626156623\)
\(a_{26}=+0.959088133\) \(a_{27}=-0.998118712\) \(a_{28}=-0.941850788\) \(a_{29}=+0.326279387\) \(a_{30}=+0.507682867\)
\(a_{31}=-1.645103427\) \(a_{32}=+1.303539193\) \(a_{33}=+0.272681401\) \(a_{34}=+0.921453087\) \(a_{35}=+0.704134304\)
\(a_{36}=-0.507668774\) \(a_{37}=+1.431205795\) \(a_{38}=-0.309315577\) \(a_{39}=-0.438075665\) \(a_{40}=-0.150162836\)
\(a_{41}=-1.671206133\) \(a_{42}=+0.956221086\) \(a_{43}=-0.116369681\) \(a_{44}=+0.362124449\) \(a_{45}=+0.379536746\)
\(a_{46}=-2.320645655\) \(a_{47}=-0.363480602\) \(a_{48}=-0.707586184\) \(a_{49}=+0.326237517\) \(a_{50}=+0.844231407\)
\(a_{51}=-0.420885375\) \(a_{52}=-0.581770178\) \(a_{53}=+0.644179327\) \(a_{54}=+1.345738635\) \(a_{55}=-0.270726809\)
\(a_{56}=-0.282831746\) \(a_{57}=+0.141283730\) \(a_{58}=-0.439914397\) \(a_{59}=-0.395519161\) \(a_{60}=-0.307953716\)
\(a_{61}=+1.630869113\) \(a_{62}=+2.218052090\) \(a_{63}=+0.714857762\) \(a_{64}=-0.608555520\) \(a_{65}=+0.434935582\)
\(a_{66}=-0.367649562\) \(a_{67}=-0.138489190\) \(a_{68}=-0.558941230\) \(a_{69}=+1.059984327\) \(a_{70}=-0.949366762\)
\(a_{71}=-0.774658377\) \(a_{72}=-0.152449670\) \(a_{73}=-0.444561693\) \(a_{74}=-1.929659122\) \(a_{75}=-0.385613377\)
\(a_{76}=+0.187626628\) \(a_{77}=-0.509914098\) \(a_{78}=+0.590646408\) \(a_{79}=-1.557765679\) \(a_{80}=+0.702514083\)
\(a_{81}=+0.006055669\) \(a_{82}=+2.253245738\) \(a_{83}=-0.649823790\) \(a_{84}=-0.580031060\) \(a_{85}=+0.417868409\)
\(a_{86}=+0.156898384\) \(a_{87}=+0.200936491\) \(a_{88}=+0.108743584\) \(a_{89}=+0.500897496\) \(a_{90}=-0.511719877\)
\(a_{91}=+0.819201304\) \(a_{92}=+1.407672957\) \(a_{93}=-1.013123442\) \(a_{94}=+0.490071831\) \(a_{95}=-0.140271069\)
\(a_{96}=+0.802773901\) \(a_{97}=-0.287013659\) \(a_{98}=-0.439857910\) \(a_{99}=-0.274849750\) \(a_{100}=-0.512099553\)

Showing 100 of 1500 available coefficients

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