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: \( 3.42597313676 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.838005942\) \(a_{3}=-1.767585257\) \(a_{4}=-0.297746041\) \(a_{5}=+0.913126845\)
\(a_{6}=-1.481246949\) \(a_{7}=-0.772916008\) \(a_{8}=-1.087518894\) \(a_{9}=+2.124357642\) \(a_{10}=+0.765205722\)
\(a_{11}=-1.331809436\) \(a_{12}=+0.526291512\) \(a_{13}=+0.439175091\) \(a_{14}=-0.647708207\) \(a_{15}=-1.614029550\)
\(a_{16}=-0.613601255\) \(a_{17}=-0.614292978\) \(a_{18}=+1.780224328\) \(a_{19}=-0.229415734\) \(a_{20}=-0.271879903\)
\(a_{21}=+1.366194940\) \(a_{22}=-1.116064221\) \(a_{23}=+1.089760689\) \(a_{24}=+1.922282364\) \(a_{25}=-0.166199365\)
\(a_{26}=+0.368031336\) \(a_{27}=-1.987397994\) \(a_{28}=+0.230132682\) \(a_{29}=-1.266271850\) \(a_{30}=-1.352566355\)
\(a_{31}=-0.061879239\) \(a_{32}=+0.573317394\) \(a_{33}=+2.354086726\) \(a_{34}=-0.514781165\) \(a_{35}=-0.705770359\)
\(a_{36}=-0.632519072\) \(a_{37}=+0.992668601\) \(a_{38}=-0.192251738\) \(a_{39}=-0.776279413\) \(a_{40}=-0.993042718\)
\(a_{41}=-0.200935960\) \(a_{42}=+1.144879458\) \(a_{43}=-0.496362713\) \(a_{44}=+0.396540975\) \(a_{45}=+1.939807895\)
\(a_{46}=+0.913225933\) \(a_{47}=-1.526367877\) \(a_{48}=+1.084592532\) \(a_{49}=-0.402600846\) \(a_{50}=-0.139276055\)
\(a_{51}=+1.085815210\) \(a_{52}=-0.130762644\) \(a_{53}=+0.134025536\) \(a_{54}=-1.665451326\) \(a_{55}=-1.216110948\)
\(a_{56}=+0.840560749\) \(a_{57}=+0.405511872\) \(a_{58}=-1.061143323\) \(a_{59}=+0.136633894\) \(a_{60}=+0.480570901\)
\(a_{61}=-0.829271698\) \(a_{62}=-0.051855153\) \(a_{63}=-1.641950025\) \(a_{64}=+1.094044643\) \(a_{65}=+0.401022577\)
\(a_{66}=+1.972738618\) \(a_{67}=+0.033915854\) \(a_{68}=+0.182903323\) \(a_{69}=-1.926244926\) \(a_{70}=-0.591439751\)
\(a_{71}=+1.774494853\) \(a_{72}=-2.310279083\) \(a_{73}=+0.667630147\) \(a_{74}=+0.831862209\) \(a_{75}=+0.293771560\)
\(a_{76}=+0.068307616\) \(a_{77}=+1.029376803\) \(a_{78}=-0.650526763\) \(a_{79}=-0.859541724\) \(a_{80}=-0.560295763\)
\(a_{81}=+1.388537761\) \(a_{82}=-0.168385644\) \(a_{83}=-0.207499146\) \(a_{84}=-0.406779129\) \(a_{85}=-0.560927404\)
\(a_{86}=-0.415954951\) \(a_{87}=+2.238243512\) \(a_{88}=+1.448367880\) \(a_{89}=+0.426930972\) \(a_{90}=+1.625570650\)
\(a_{91}=-0.339445500\) \(a_{92}=-0.324471955\) \(a_{93}=+0.109376913\) \(a_{94}=-1.279105274\) \(a_{95}=-0.209485746\)
\(a_{96}=-1.013387371\) \(a_{97}=-0.600690040\) \(a_{98}=-0.337381871\) \(a_{99}=-2.829239542\) \(a_{100}=+0.049485212\)

Showing 100 of 1500 available coefficients

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