Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 19.0267767277 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.086138979\) \(a_{3}=-0.577350269\) \(a_{4}=-0.992580076\) \(a_{5}=+0.100788559\)
\(a_{6}=+0.049732363\) \(a_{7}=+1.227824621\) \(a_{8}=+0.171638814\) \(a_{9}=+0.333333333\) \(a_{10}=-0.008681824\)
\(a_{11}=+0.680504243\) \(a_{12}=+0.573066374\) \(a_{13}=-1.180039307\) \(a_{14}=-0.105763560\) \(a_{15}=-0.058190302\)
\(a_{16}=+0.977795284\) \(a_{17}=+0.157530266\) \(a_{18}=-0.028712993\) \(a_{19}=+0.925777354\) \(a_{20}=-0.100040716\)
\(a_{21}=-0.708884875\) \(a_{22}=-0.058617941\) \(a_{23}=-1.857477947\) \(a_{24}=-0.099095716\) \(a_{25}=-0.989841666\)
\(a_{26}=+0.101647382\) \(a_{27}=-0.192450090\) \(a_{28}=-1.218714256\) \(a_{29}=-1.132353227\) \(a_{30}=+0.005012453\)
\(a_{31}=+0.736628082\) \(a_{32}=-0.255865102\) \(a_{33}=-0.392889308\) \(a_{34}=-0.013569496\) \(a_{35}=+0.123750675\)
\(a_{36}=-0.330860025\) \(a_{37}=-0.690303419\) \(a_{38}=-0.079745516\) \(a_{39}=+0.681296012\) \(a_{40}=+0.017299229\)
\(a_{41}=+0.730785522\) \(a_{42}=+0.061062620\) \(a_{43}=-0.832014771\) \(a_{44}=-0.675454953\) \(a_{45}=+0.033596186\)
\(a_{46}=+0.160001255\) \(a_{47}=+0.702113624\) \(a_{48}=-0.564530370\) \(a_{49}=+0.507553300\) \(a_{50}=+0.085263951\)
\(a_{51}=-0.090950142\) \(a_{52}=+1.171283505\) \(a_{53}=-1.843330981\) \(a_{54}=+0.016577454\) \(a_{55}=+0.068587042\)
\(a_{56}=+0.210742362\) \(a_{57}=-0.534497804\) \(a_{58}=+0.097539751\) \(a_{59}=+1.079352125\) \(a_{60}=+0.057758534\)
\(a_{61}=-0.034361690\) \(a_{62}=-0.063452391\) \(a_{63}=+0.409274874\) \(a_{64}=-0.955755325\) \(a_{65}=-0.118934462\)
\(a_{66}=+0.033843084\) \(a_{67}=-0.849228818\) \(a_{68}=-0.156361404\) \(a_{69}=+1.072415393\) \(a_{70}=-0.010659757\)
\(a_{71}=+1.227901406\) \(a_{72}=+0.057212938\) \(a_{73}=-1.196137042\) \(a_{74}=+0.059462032\) \(a_{75}=+0.571485352\)
\(a_{76}=-0.918908156\) \(a_{77}=+0.835539864\) \(a_{78}=-0.058686143\) \(a_{79}=-1.409050362\) \(a_{80}=+0.098550578\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.062949119\) \(a_{83}=+0.662315625\) \(a_{84}=+0.703625004\) \(a_{85}=+0.015877249\)
\(a_{86}=+0.071668903\) \(a_{87}=+0.653764440\) \(a_{88}=+0.116800941\) \(a_{89}=-1.641140053\) \(a_{90}=-0.002893941\)
\(a_{91}=-1.448881315\) \(a_{92}=+1.843695602\) \(a_{93}=-0.425292421\) \(a_{94}=-0.060479351\) \(a_{95}=+0.093307766\)
\(a_{96}=+0.147723786\) \(a_{97}=-0.459169418\) \(a_{98}=-0.043720123\) \(a_{99}=+0.226834748\) \(a_{100}=+0.982497117\)

Showing 100 of 1228 available coefficients

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