Properties

Level $643$
Weight $0$
Character 643.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 643 \)
Weight: \( 0 \)
Character: 643.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.85089434929 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.443479406\) \(a_{3}=-1.827069910\) \(a_{4}=-0.803325904\) \(a_{5}=-1.284487591\)
\(a_{6}=+0.810268010\) \(a_{7}=+0.396074469\) \(a_{8}=+0.799737843\) \(a_{9}=+2.338184497\) \(a_{10}=+0.569643759\)
\(a_{11}=+0.456843803\) \(a_{12}=+1.467732819\) \(a_{13}=-0.864481856\) \(a_{14}=-0.175650894\) \(a_{15}=+2.346848708\)
\(a_{16}=+0.448658505\) \(a_{17}=+1.945031074\) \(a_{18}=-1.036936830\) \(a_{19}=-1.350683033\) \(a_{20}=+1.031862337\)
\(a_{21}=-0.723655859\) \(a_{22}=-0.202600751\) \(a_{23}=+0.216089183\) \(a_{24}=-1.461177206\) \(a_{25}=+0.649908644\)
\(a_{26}=+0.383379843\) \(a_{27}=-2.444956860\) \(a_{28}=-0.318176904\) \(a_{29}=+0.608995728\) \(a_{30}=-1.040779260\)
\(a_{31}=-0.588378178\) \(a_{32}=-0.998708863\) \(a_{33}=-0.834685487\) \(a_{34}=-0.862581382\) \(a_{35}=-0.508752796\)
\(a_{36}=-1.878324539\) \(a_{37}=+1.622306763\) \(a_{38}=+0.599000275\) \(a_{39}=+1.579468878\) \(a_{40}=-1.027253555\)
\(a_{41}=+1.118630625\) \(a_{42}=+0.320926444\) \(a_{43}=-0.279139232\) \(a_{44}=-0.366994399\) \(a_{45}=-3.003369317\)
\(a_{46}=-0.095830995\) \(a_{47}=-1.243827264\) \(a_{48}=-0.819730481\) \(a_{49}=-0.843124956\) \(a_{50}=-0.288221008\)
\(a_{51}=-3.553708045\) \(a_{52}=+0.694460782\) \(a_{53}=-0.398526933\) \(a_{54}=+1.084288164\) \(a_{55}=-0.586810129\)
\(a_{56}=+0.316755822\) \(a_{57}=+2.467792437\) \(a_{58}=-0.270077057\) \(a_{59}=+0.098636151\) \(a_{60}=-1.885284629\)
\(a_{61}=+1.072601818\) \(a_{62}=+0.260933712\) \(a_{63}=+0.926095237\) \(a_{64}=-0.005751853\) \(a_{65}=+1.110416213\)
\(a_{66}=+0.370165772\) \(a_{67}=+0.155985786\) \(a_{68}=-1.562494086\) \(a_{69}=-0.394809928\) \(a_{70}=+0.225621241\)
\(a_{71}=+0.513338483\) \(a_{72}=+1.869934993\) \(a_{73}=+0.344447326\) \(a_{74}=-0.719459723\) \(a_{75}=-1.187428365\)
\(a_{76}=+1.085038628\) \(a_{77}=+0.180944104\) \(a_{78}=-0.700461993\) \(a_{79}=+1.090474351\) \(a_{80}=-0.576296436\)
\(a_{81}=+2.128922912\) \(a_{82}=-0.496089630\) \(a_{83}=-1.473134899\) \(a_{84}=+0.581331308\) \(a_{85}=-2.498368605\)
\(a_{86}=+0.123792162\) \(a_{87}=-1.112677622\) \(a_{88}=+0.365355428\) \(a_{89}=+1.558934608\) \(a_{90}=+1.331932566\)
\(a_{91}=-0.342399288\) \(a_{92}=-0.173589961\) \(a_{93}=+1.075007890\) \(a_{94}=+0.551611886\) \(a_{95}=+1.734935532\)
\(a_{96}=+1.824711048\) \(a_{97}=-1.876225320\) \(a_{98}=+0.373908714\) \(a_{99}=+1.068185101\) \(a_{100}=-0.522088282\)

Showing 100 of 1732 available coefficients

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