Properties

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

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.26790747396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.901145033\) \(a_{3}=+0.157971054\) \(a_{4}=+2.614352438\) \(a_{5}=-0.993306157\)
\(a_{6}=+0.300325884\) \(a_{7}=-0.330080599\) \(a_{8}=+3.069118120\) \(a_{9}=-0.975045146\) \(a_{10}=-1.888419068\)
\(a_{11}=-0.738368031\) \(a_{12}=+0.412992010\) \(a_{13}=+1.186598892\) \(a_{14}=-0.627531091\) \(a_{15}=-0.156913621\)
\(a_{16}=+3.220486234\) \(a_{17}=+1.469541058\) \(a_{18}=-1.853702237\) \(a_{19}=+0.229415734\) \(a_{20}=-2.596852374\)
\(a_{21}=-0.052143180\) \(a_{22}=-1.403744716\) \(a_{23}=+0.040544490\) \(a_{24}=+0.484831824\) \(a_{25}=-0.013342877\)
\(a_{26}=+2.255896590\) \(a_{27}=-0.311999964\) \(a_{28}=-0.862947019\) \(a_{29}=-1.194861340\) \(a_{30}=-0.298315549\)
\(a_{31}=-0.232105813\) \(a_{32}=+3.053493288\) \(a_{33}=-0.116640775\) \(a_{34}=+2.793810679\) \(a_{35}=+0.327871100\)
\(a_{36}=-2.549111651\) \(a_{37}=+0.213082044\) \(a_{38}=+0.436152581\) \(a_{39}=+0.187448273\) \(a_{40}=-3.048573879\)
\(a_{41}=-0.509880474\) \(a_{42}=-0.099131750\) \(a_{43}=+0.631218330\) \(a_{44}=-1.930354264\) \(a_{45}=+0.968518352\)
\(a_{46}=+0.077080958\) \(a_{47}=+1.035159446\) \(a_{48}=+0.508743597\) \(a_{49}=-0.891046801\) \(a_{50}=-0.025366732\)
\(a_{51}=+0.232144950\) \(a_{52}=+3.102187701\) \(a_{53}=-0.324793473\) \(a_{54}=-0.593157186\) \(a_{55}=+0.733425492\)
\(a_{56}=-1.013056347\) \(a_{57}=+0.036241098\) \(a_{58}=-2.271604669\) \(a_{59}=-0.565096979\) \(a_{60}=-0.410227612\)
\(a_{61}=+0.508819404\) \(a_{62}=-0.441266768\) \(a_{63}=+0.321843622\) \(a_{64}=+2.584647315\) \(a_{65}=-1.178655995\)
\(a_{66}=-0.221751048\) \(a_{67}=+0.255078096\) \(a_{68}=+3.841898248\) \(a_{69}=+0.006404855\) \(a_{70}=+0.623330539\)
\(a_{71}=-1.663305927\) \(a_{72}=-2.992528685\) \(a_{73}=+0.250817383\) \(a_{74}=+0.405099899\) \(a_{75}=-0.002107774\)
\(a_{76}=+0.599773605\) \(a_{77}=+0.243720944\) \(a_{78}=+0.356366328\) \(a_{79}=+0.725763755\) \(a_{80}=-3.198928728\)
\(a_{81}=+0.925758247\) \(a_{82}=-0.969356758\) \(a_{83}=+0.231074060\) \(a_{84}=-0.136320620\) \(a_{85}=-1.459704260\)
\(a_{86}=+1.200037594\) \(a_{87}=-0.188753483\) \(a_{88}=-2.266138651\) \(a_{89}=+0.735676695\) \(a_{90}=+1.841293834\)
\(a_{91}=-0.391673272\) \(a_{92}=+0.105997520\) \(a_{93}=-0.036665918\) \(a_{94}=+1.967988309\) \(a_{95}=-0.227880094\)
\(a_{96}=+0.482363486\) \(a_{97}=+0.187377870\) \(a_{98}=-1.694009202\) \(a_{99}=+0.719942165\) \(a_{100}=-0.034883009\)

Showing 100 of 1500 available coefficients

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