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: \( 3.84044805112 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.973747726\) \(a_{3}=-0.177068661\) \(a_{4}=-0.051815367\) \(a_{5}=+1.505211482\)
\(a_{6}=+0.172420206\) \(a_{7}=-0.169092480\) \(a_{8}=+1.024202821\) \(a_{9}=-0.968646689\) \(a_{10}=-1.465696257\)
\(a_{11}=+1.545394149\) \(a_{12}=+0.009174878\) \(a_{13}=+1.329829331\) \(a_{14}=+0.164653418\) \(a_{15}=-0.266525782\)
\(a_{16}=-0.945499801\) \(a_{17}=+0.062314566\) \(a_{18}=+0.943217511\) \(a_{19}=+0.229415734\) \(a_{20}=-0.077993085\)
\(a_{21}=+0.029940979\) \(a_{22}=-1.504824038\) \(a_{23}=+0.376961711\) \(a_{24}=-0.181354222\) \(a_{25}=+1.265661606\)
\(a_{26}=-1.294918286\) \(a_{27}=+0.348585633\) \(a_{28}=+0.008761589\) \(a_{29}=-1.164010098\) \(a_{30}=+0.259528873\)
\(a_{31}=+1.442841612\) \(a_{32}=-0.103524540\) \(a_{33}=-0.273640873\) \(a_{34}=-0.060678666\) \(a_{35}=-0.254519944\)
\(a_{36}=+0.050190783\) \(a_{37}=+0.753743617\) \(a_{38}=-0.223393051\) \(a_{39}=-0.235471098\) \(a_{40}=+1.541641845\)
\(a_{41}=+0.963091636\) \(a_{42}=-0.029154951\) \(a_{43}=-0.634146669\) \(a_{44}=-0.080075163\) \(a_{45}=-1.458018113\)
\(a_{46}=-0.367065613\) \(a_{47}=-0.058090164\) \(a_{48}=+0.167418333\) \(a_{49}=-0.971407708\) \(a_{50}=-1.232435081\)
\(a_{51}=-0.011034010\) \(a_{52}=-0.068905595\) \(a_{53}=-0.098579589\) \(a_{54}=-0.339434466\) \(a_{55}=+2.326145019\)
\(a_{56}=-0.173184996\) \(a_{57}=-0.040622340\) \(a_{58}=+1.133452184\) \(a_{59}=+0.341807508\) \(a_{60}=+0.013810135\)
\(a_{61}=-0.588580016\) \(a_{62}=-1.404963747\) \(a_{63}=+0.163790866\) \(a_{64}=+1.046306595\) \(a_{65}=+2.001674394\)
\(a_{66}=+0.266457180\) \(a_{67}=-0.096651525\) \(a_{68}=-0.003228867\) \(a_{69}=-0.066748090\) \(a_{70}=+0.247838246\)
\(a_{71}=+0.316160975\) \(a_{72}=-0.992090702\) \(a_{73}=-1.789021340\) \(a_{74}=-0.733956164\) \(a_{75}=-0.224108969\)
\(a_{76}=-0.011887234\) \(a_{77}=-0.261314528\) \(a_{78}=+0.229289450\) \(a_{79}=+1.406314771\) \(a_{80}=-1.423177158\)
\(a_{81}=+0.906923088\) \(a_{82}=-0.937808275\) \(a_{83}=-1.120233600\) \(a_{84}=-0.001551420\) \(a_{85}=+0.093796589\)
\(a_{86}=+0.617498847\) \(a_{87}=+0.206109748\) \(a_{88}=+1.582797066\) \(a_{89}=-1.050989781\) \(a_{90}=+1.419741841\)
\(a_{91}=-0.224864208\) \(a_{92}=-0.019532382\) \(a_{93}=-0.255482050\) \(a_{94}=+0.056565329\) \(a_{95}=+0.345319288\)
\(a_{96}=+0.018330947\) \(a_{97}=-1.097901148\) \(a_{98}=+0.945906072\) \(a_{99}=-1.496940908\) \(a_{100}=-0.065580724\)

Showing 100 of 1500 available coefficients

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