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: \( 2.22001009054 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.202530020\) \(a_{3}=+0.746787853\) \(a_{4}=-0.958981591\) \(a_{5}=+1.252304336\)
\(a_{6}=-0.151246958\) \(a_{7}=+0.880478045\) \(a_{8}=+0.396752580\) \(a_{9}=-0.442307903\) \(a_{10}=-0.253629222\)
\(a_{11}=-1.290006416\) \(a_{12}=-0.716155803\) \(a_{13}=+0.608718201\) \(a_{14}=-0.178323235\) \(a_{15}=+0.935205666\)
\(a_{16}=+0.878627284\) \(a_{17}=-0.440375617\) \(a_{18}=+0.089580627\) \(a_{19}=-0.229415733\) \(a_{20}=-1.200936805\)
\(a_{21}=+0.657530308\) \(a_{22}=+0.261265027\) \(a_{23}=+1.319897318\) \(a_{24}=+0.296290011\) \(a_{25}=+0.568266150\)
\(a_{26}=-0.123283716\) \(a_{27}=-1.077098006\) \(a_{28}=-0.844362261\) \(a_{29}=-0.944628932\) \(a_{30}=-0.189407220\)
\(a_{31}=+0.814455568\) \(a_{32}=-0.574700977\) \(a_{33}=-0.963361125\) \(a_{34}=+0.089189281\) \(a_{35}=+1.102626480\)
\(a_{36}=+0.424165127\) \(a_{37}=-0.147921465\) \(a_{38}=+0.046463566\) \(a_{39}=+0.454583342\) \(a_{40}=+0.496855010\)
\(a_{41}=-1.857931602\) \(a_{42}=-0.133169602\) \(a_{43}=+1.724362857\) \(a_{44}=+1.237092417\) \(a_{45}=-0.553904096\)
\(a_{46}=-0.267318848\) \(a_{47}=+0.296360578\) \(a_{48}=+0.656148158\) \(a_{49}=-0.224758403\) \(a_{50}=-0.115090916\)
\(a_{51}=-0.328867180\) \(a_{52}=-0.583749499\) \(a_{53}=+0.312164126\) \(a_{54}=+0.218144615\) \(a_{55}=-1.615480715\)
\(a_{56}=+0.349331904\) \(a_{57}=-0.171324875\) \(a_{58}=+0.191315691\) \(a_{59}=+0.352671819\) \(a_{60}=-0.896844992\)
\(a_{61}=+0.073595422\) \(a_{62}=-0.164951635\) \(a_{63}=-0.389442545\) \(a_{64}=-0.762233071\) \(a_{65}=+0.762300311\)
\(a_{66}=+0.195109562\) \(a_{67}=-0.627300304\) \(a_{68}=+0.422312109\) \(a_{69}=+0.985683330\) \(a_{70}=-0.223314905\)
\(a_{71}=-0.488831380\) \(a_{72}=-0.175486830\) \(a_{73}=+1.593990346\) \(a_{74}=+0.029958511\) \(a_{75}=+0.424374328\)
\(a_{76}=+0.220005425\) \(a_{77}=-1.135822368\) \(a_{78}=-0.092066760\) \(a_{79}=+1.439012542\) \(a_{80}=+1.100308820\)
\(a_{81}=-0.362055797\) \(a_{82}=+0.376286857\) \(a_{83}=+0.396814475\) \(a_{84}=-0.630559528\) \(a_{85}=-0.551484277\)
\(a_{86}=-0.349235156\) \(a_{87}=-0.705437322\) \(a_{88}=-0.511813397\) \(a_{89}=-0.375783590\) \(a_{90}=+0.112182252\)
\(a_{91}=+0.535963023\) \(a_{92}=-1.265757280\) \(a_{93}=+0.608225439\) \(a_{94}=-0.060021980\) \(a_{95}=-0.287298257\)
\(a_{96}=-0.429179691\) \(a_{97}=-0.026608696\) \(a_{98}=+0.045520322\) \(a_{99}=+0.570580059\) \(a_{100}=-0.544956634\)

Showing 100 of 1500 available coefficients

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