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: \( 5.19216949822 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.029728000\) \(a_{3}=+1.297531706\) \(a_{4}=-0.999116246\) \(a_{5}=-0.149265852\)
\(a_{6}=+0.038573022\) \(a_{7}=+1.614159326\) \(a_{8}=-0.059429728\) \(a_{9}=+0.683588529\) \(a_{10}=-0.004437375\)
\(a_{11}=+1.241449061\) \(a_{12}=-1.296385008\) \(a_{13}=+1.552303471\) \(a_{14}=+0.047985728\) \(a_{15}=-0.193677176\)
\(a_{16}=+0.997349519\) \(a_{17}=-1.360180752\) \(a_{18}=+0.020321720\) \(a_{19}=+0.229415734\) \(a_{20}=+0.149133938\)
\(a_{21}=+2.094422905\) \(a_{22}=+0.036905798\) \(a_{23}=+0.518899210\) \(a_{24}=-0.077111956\) \(a_{25}=-0.977719705\)
\(a_{26}=+0.046146878\) \(a_{27}=-0.410553916\) \(a_{28}=-1.612732807\) \(a_{29}=+0.195908419\) \(a_{30}=-0.005757635\)
\(a_{31}=-0.157995363\) \(a_{32}=+0.089078934\) \(a_{33}=+1.610819519\) \(a_{34}=-0.040435453\) \(a_{35}=-0.240938867\)
\(a_{36}=-0.682984405\) \(a_{37}=-0.008947604\) \(a_{38}=+0.006820071\) \(a_{39}=+2.014162972\) \(a_{40}=+0.008870829\)
\(a_{41}=+0.397652690\) \(a_{42}=+0.062263004\) \(a_{43}=-1.209127714\) \(a_{44}=-1.240351926\) \(a_{45}=-0.102036424\)
\(a_{46}=+0.015425836\) \(a_{47}=+0.347318719\) \(a_{48}=+1.294092623\) \(a_{49}=+1.605510331\) \(a_{50}=-0.029065651\)
\(a_{51}=-1.764877652\) \(a_{52}=-1.550931617\) \(a_{53}=+0.039201122\) \(a_{54}=-0.012204947\) \(a_{55}=-0.185305952\)
\(a_{56}=-0.095929049\) \(a_{57}=+0.297674189\) \(a_{58}=+0.005823965\) \(a_{59}=-1.119949859\) \(a_{60}=+0.193506013\)
\(a_{61}=+1.055899789\) \(a_{62}=-0.004696886\) \(a_{63}=+1.103420800\) \(a_{64}=-0.994701381\) \(a_{65}=-0.231705900\)
\(a_{66}=+0.047886443\) \(a_{67}=+0.282202413\) \(a_{68}=+1.358978687\) \(a_{69}=+0.673288178\) \(a_{70}=-0.007162631\)
\(a_{71}=-1.146528736\) \(a_{72}=-0.040625480\) \(a_{73}=+1.406051697\) \(a_{74}=-0.000265994\) \(a_{75}=-1.268622318\)
\(a_{76}=-0.229212987\) \(a_{77}=+2.003896580\) \(a_{78}=+0.059877037\) \(a_{79}=-0.190569043\) \(a_{80}=-0.148870226\)
\(a_{81}=-1.216295252\) \(a_{82}=+0.011821419\) \(a_{83}=-1.017980408\) \(a_{84}=-2.092571951\) \(a_{85}=+0.203028539\)
\(a_{86}=-0.035944949\) \(a_{87}=+0.254197386\) \(a_{88}=-0.073778980\) \(a_{89}=-0.142232779\) \(a_{90}=-0.003033339\)
\(a_{91}=+2.505665125\) \(a_{92}=-0.518440631\) \(a_{93}=-0.205003993\) \(a_{94}=+0.010325091\) \(a_{95}=-0.034243935\)
\(a_{96}=+0.115582741\) \(a_{97}=-1.104774367\) \(a_{98}=+0.047728611\) \(a_{99}=+0.848640338\) \(a_{100}=+0.976855642\)

Showing 100 of 546 available coefficients

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