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: \( 4.77954833044 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.538559968\) \(a_{3}=+0.710920609\) \(a_{4}=+1.367166775\) \(a_{5}=-0.030202319\)
\(a_{6}=-1.093793989\) \(a_{7}=+0.338978798\) \(a_{8}=-0.564908101\) \(a_{9}=-0.494591888\) \(a_{10}=+0.046468080\)
\(a_{11}=+0.139762745\) \(a_{12}=+0.971947035\) \(a_{13}=-1.511028197\) \(a_{14}=-0.521539209\) \(a_{15}=-0.021471451\)
\(a_{16}=-0.498021785\) \(a_{17}=-0.106298968\) \(a_{18}=+0.760959280\) \(a_{19}=-0.229415734\) \(a_{20}=-0.041291608\)
\(a_{21}=+0.240987013\) \(a_{22}=-0.215033365\) \(a_{23}=-0.517034722\) \(a_{24}=-0.401604811\) \(a_{25}=-0.999087820\)
\(a_{26}=+2.324807495\) \(a_{27}=-1.062536175\) \(a_{28}=+0.463440550\) \(a_{29}=-0.562503020\) \(a_{30}=+0.033035115\)
\(a_{31}=+0.850017180\) \(a_{32}=+1.331144483\) \(a_{33}=+0.099360216\) \(a_{34}=+0.163547336\) \(a_{35}=-0.010237946\)
\(a_{36}=-0.676189597\) \(a_{37}=-1.849555965\) \(a_{38}=+0.352969864\) \(a_{39}=-1.074221086\) \(a_{40}=+0.017061535\)
\(a_{41}=-0.350841372\) \(a_{42}=-0.370772971\) \(a_{43}=+0.279266130\) \(a_{44}=+0.191078981\) \(a_{45}=+0.014937822\)
\(a_{46}=+0.795488925\) \(a_{47}=+1.378159614\) \(a_{48}=-0.354053952\) \(a_{49}=-0.885093374\) \(a_{50}=+1.537156526\)
\(a_{51}=-0.075570131\) \(a_{52}=-2.065827542\) \(a_{53}=+0.940334806\) \(a_{54}=+1.634775624\) \(a_{55}=-0.004221154\)
\(a_{56}=-0.191491869\) \(a_{57}=-0.163096373\) \(a_{58}=+0.865444628\) \(a_{59}=+1.604113494\) \(a_{60}=-0.029355055\)
\(a_{61}=-1.679610213\) \(a_{62}=-1.307802405\) \(a_{63}=-0.167656164\) \(a_{64}=-1.550023827\) \(a_{65}=+0.045636556\)
\(a_{66}=-0.152871649\) \(a_{67}=-0.498623699\) \(a_{68}=-0.145328418\) \(a_{69}=-0.367570638\) \(a_{70}=+0.015751694\)
\(a_{71}=-1.099416036\) \(a_{72}=+0.279398963\) \(a_{73}=+0.340794606\) \(a_{74}=+2.845652769\) \(a_{75}=-0.710272126\)
\(a_{76}=-0.313649567\) \(a_{77}=+0.047376614\) \(a_{78}=+1.652753558\) \(a_{79}=+1.569579880\) \(a_{80}=+0.015041418\)
\(a_{81}=-0.260786960\) \(a_{82}=+0.539790486\) \(a_{83}=-1.406813347\) \(a_{84}=+0.329469446\) \(a_{85}=+0.003210490\)
\(a_{86}=-0.429667641\) \(a_{87}=-0.399895011\) \(a_{88}=-0.078953102\) \(a_{89}=+0.100309049\) \(a_{90}=-0.022982636\)
\(a_{91}=-0.512206523\) \(a_{92}=-0.706872693\) \(a_{93}=+0.604294730\) \(a_{94}=-2.120381210\) \(a_{95}=+0.006928888\)
\(a_{96}=+0.946338050\) \(a_{97}=+0.700823220\) \(a_{98}=+1.361769229\) \(a_{99}=-0.069125516\) \(a_{100}=-1.365919672\)

Showing 100 of 1500 available coefficients

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