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: \( 1.32979889047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.809412379\) \(a_{3}=-0.362492529\) \(a_{4}=+2.273973148\) \(a_{5}=+0.030703946\)
\(a_{6}=+0.655898469\) \(a_{7}=+0.575758361\) \(a_{8}=-2.305142779\) \(a_{9}=-0.868599162\) \(a_{10}=-0.055556113\)
\(a_{11}=+1.387641026\) \(a_{12}=-0.824298271\) \(a_{13}=+0.337518944\) \(a_{14}=-1.041784273\) \(a_{15}=-0.011129991\)
\(a_{16}=+1.896980734\) \(a_{17}=-0.180767896\) \(a_{18}=+1.571654121\) \(a_{19}=-0.229415726\) \(a_{20}=+0.069819930\)
\(a_{21}=-0.208708092\) \(a_{22}=-2.510814835\) \(a_{23}=+0.313547098\) \(a_{24}=+0.835597034\) \(a_{25}=-0.999057299\)
\(a_{26}=-0.610710961\) \(a_{27}=+0.677353201\) \(a_{28}=+1.309259023\) \(a_{29}=+0.283379422\) \(a_{30}=+0.020138788\)
\(a_{31}=+0.672108658\) \(a_{32}=-1.127277580\) \(a_{33}=-0.503009461\) \(a_{34}=+0.327083729\) \(a_{35}=+0.017678078\)
\(a_{36}=-1.975171244\) \(a_{37}=-0.755321276\) \(a_{38}=+0.415107606\) \(a_{39}=-0.122348038\) \(a_{40}=-0.070777062\)
\(a_{41}=+1.155129800\) \(a_{42}=+0.377639148\) \(a_{43}=+1.150904872\) \(a_{44}=+3.155458325\) \(a_{45}=-0.026669434\)
\(a_{46}=-0.567335988\) \(a_{47}=-1.722666896\) \(a_{48}=-0.687641345\) \(a_{49}=-0.668502292\) \(a_{50}=+1.807706606\)
\(a_{51}=+0.065526984\) \(a_{52}=+0.767509037\) \(a_{53}=-0.769029024\) \(a_{54}=-1.225611433\) \(a_{55}=+0.042606098\)
\(a_{56}=-1.327205184\) \(a_{57}=+0.083161578\) \(a_{58}=-0.512750239\) \(a_{59}=-0.795783548\) \(a_{60}=-0.025309153\)
\(a_{61}=+0.905044555\) \(a_{62}=-1.216121894\) \(a_{63}=-0.500103070\) \(a_{64}=+0.142729370\) \(a_{65}=+0.010363270\)
\(a_{66}=+0.910151648\) \(a_{67}=+1.288808616\) \(a_{68}=-0.411061375\) \(a_{69}=-0.113658520\) \(a_{70}=-0.031986903\)
\(a_{71}=-0.253357568\) \(a_{72}=+2.002245087\) \(a_{73}=+0.440032414\) \(a_{74}=+1.366687411\) \(a_{75}=+0.362150854\)
\(a_{76}=-0.521685183\) \(a_{77}=+0.798945977\) \(a_{78}=+0.221378156\) \(a_{79}=-0.579171535\) \(a_{80}=+0.058244846\)
\(a_{81}=+0.623063747\) \(a_{82}=-2.090106403\) \(a_{83}=+0.031854359\) \(a_{84}=-0.474596565\) \(a_{85}=-0.005550230\)
\(a_{86}=-2.082461575\) \(a_{87}=-0.102722795\) \(a_{88}=-3.198710595\) \(a_{89}=+1.320544225\) \(a_{90}=+0.048255887\)
\(a_{91}=+0.194329262\) \(a_{92}=+0.712997650\) \(a_{93}=-0.243634320\) \(a_{94}=+3.117014701\) \(a_{95}=-0.007043938\)
\(a_{96}=+0.408629661\) \(a_{97}=+0.712144972\) \(a_{98}=+1.209596394\) \(a_{99}=-1.205303739\) \(a_{100}=-2.271829318\)

Showing 100 of 1500 available coefficients

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