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: \( 3.10538415095 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.123056156\) \(a_{3}=+1.647499964\) \(a_{4}=+0.261255130\) \(a_{5}=-1.575375230\)
\(a_{6}=+1.850234978\) \(a_{7}=+0.991230915\) \(a_{8}=-0.829651975\) \(a_{9}=+1.714256129\) \(a_{10}=-1.769234851\)
\(a_{11}=+0.074415734\) \(a_{12}=+0.430417818\) \(a_{13}=+0.556995250\) \(a_{14}=+1.113207981\) \(a_{15}=-2.595430631\)
\(a_{16}=-1.193000888\) \(a_{17}=-0.046362766\) \(a_{18}=+1.925205900\) \(a_{19}=-0.229415734\) \(a_{20}=-0.411574862\)
\(a_{21}=+1.633052894\) \(a_{22}=+0.083573048\) \(a_{23}=-0.320453732\) \(a_{24}=-1.366851598\) \(a_{25}=+1.481807113\)
\(a_{26}=+0.625536943\) \(a_{27}=+1.176736943\) \(a_{28}=+0.258964165\) \(a_{29}=-0.457995814\) \(a_{30}=-2.914814349\)
\(a_{31}=-0.259378000\) \(a_{32}=-0.510155016\) \(a_{33}=+0.122599922\) \(a_{34}=-0.052067999\) \(a_{35}=-1.561560627\)
\(a_{36}=+0.447858222\) \(a_{37}=+0.504994357\) \(a_{38}=-0.257646759\) \(a_{39}=+0.917649658\) \(a_{40}=+1.307013163\)
\(a_{41}=+0.543668529\) \(a_{42}=+1.834010117\) \(a_{43}=+1.500494547\) \(a_{44}=+0.019441510\) \(a_{45}=-2.700596649\)
\(a_{46}=-0.359887534\) \(a_{47}=-0.951745698\) \(a_{48}=-1.965468920\) \(a_{49}=-0.017461263\) \(a_{50}=+1.664152600\)
\(a_{51}=-0.076382642\) \(a_{52}=+0.145517826\) \(a_{53}=+0.691341277\) \(a_{54}=+1.321541639\) \(a_{55}=-0.117232677\)
\(a_{56}=-0.822376654\) \(a_{57}=-0.377962444\) \(a_{58}=-0.514354955\) \(a_{59}=+1.187479813\) \(a_{60}=-0.678069541\)
\(a_{61}=-1.693620532\) \(a_{62}=-0.291296047\) \(a_{63}=+1.699223671\) \(a_{64}=+0.620068160\) \(a_{65}=-0.877476537\)
\(a_{66}=+0.137686579\) \(a_{67}=+0.590745565\) \(a_{68}=-0.012112558\) \(a_{69}=-0.527947499\) \(a_{70}=-1.753720316\)
\(a_{71}=-1.421221372\) \(a_{72}=-1.422235907\) \(a_{73}=+1.647875978\) \(a_{74}=+0.567137056\) \(a_{75}=+2.441277175\)
\(a_{76}=-0.059936096\) \(a_{77}=+0.073763213\) \(a_{78}=+1.030572038\) \(a_{79}=-1.530399337\) \(a_{80}=+1.879424015\)
\(a_{81}=+0.224417963\) \(a_{82}=+0.610570296\) \(a_{83}=-1.083763623\) \(a_{84}=+0.426643436\) \(a_{85}=+0.073038704\)
\(a_{86}=+1.685139683\) \(a_{87}=-0.754548102\) \(a_{88}=-0.061739097\) \(a_{89}=+0.318337843\) \(a_{90}=-3.032921744\)
\(a_{91}=+0.552110923\) \(a_{92}=-0.083720219\) \(a_{93}=-0.427325237\) \(a_{94}=-1.068863841\) \(a_{95}=+0.361415875\)
\(a_{96}=-0.840480385\) \(a_{97}=+1.119316863\) \(a_{98}=-0.019610011\) \(a_{99}=+0.127567611\) \(a_{100}=+0.387129767\)

Showing 100 of 1500 available coefficients

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