Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 27.7011997464 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.389389108\) \(a_{3}=-0.577350269\) \(a_{4}=+0.930402094\) \(a_{5}=-1.718740588\)
\(a_{6}=-0.802164176\) \(a_{7}=-0.302434379\) \(a_{8}=-0.096698572\) \(a_{9}=+0.333333333\) \(a_{10}=-2.387999453\)
\(a_{11}=-1.085495284\) \(a_{12}=-0.537167900\) \(a_{13}=+1.253851807\) \(a_{14}=-0.420199032\) \(a_{15}=+0.992315341\)
\(a_{16}=-1.064754037\) \(a_{17}=+0.827535085\) \(a_{18}=+0.463129703\) \(a_{19}=-0.776223043\) \(a_{20}=-1.599119843\)
\(a_{21}=+0.174610570\) \(a_{22}=-1.508175324\) \(a_{23}=+0.880720483\) \(a_{24}=+0.055828947\) \(a_{25}=+1.954069208\)
\(a_{26}=+1.742088044\) \(a_{27}=-0.192450090\) \(a_{28}=-0.281385579\) \(a_{29}=+0.039366352\) \(a_{30}=+1.378712127\)
\(a_{31}=+1.416547095\) \(a_{32}=-1.382659090\) \(a_{33}=+0.626710994\) \(a_{34}=+1.149768234\) \(a_{35}=+0.519806242\)
\(a_{36}=+0.310134031\) \(a_{37}=+0.450567694\) \(a_{38}=-1.078475841\) \(a_{39}=-0.723911678\) \(a_{40}=+0.166199760\)
\(a_{41}=-1.445479919\) \(a_{42}=+0.242602024\) \(a_{43}=+0.625752111\) \(a_{44}=-1.009947086\) \(a_{45}=-0.572913529\)
\(a_{46}=+1.223663447\) \(a_{47}=-0.130467504\) \(a_{48}=+0.614736030\) \(a_{49}=-0.908533447\) \(a_{50}=+2.714962474\)
\(a_{51}=-0.477777604\) \(a_{52}=+1.166586347\) \(a_{53}=+0.716773531\) \(a_{54}=-0.267388059\) \(a_{55}=+1.865684802\)
\(a_{56}=+0.029244973\) \(a_{57}=+0.448152583\) \(a_{58}=+0.054695181\) \(a_{59}=-0.921446779\) \(a_{60}=+0.923252272\)
\(a_{61}=+1.502921412\) \(a_{62}=+1.968135106\) \(a_{63}=-0.100811460\) \(a_{64}=-0.856297444\) \(a_{65}=-2.155045992\)
\(a_{66}=+0.870745430\) \(a_{67}=+0.463211182\) \(a_{68}=+0.769940377\) \(a_{69}=-0.508484208\) \(a_{70}=+0.722213131\)
\(a_{71}=+0.951329848\) \(a_{72}=-0.032232857\) \(a_{73}=-0.608991151\) \(a_{74}=+0.626013846\) \(a_{75}=-1.128182383\)
\(a_{76}=-0.722199545\) \(a_{77}=+0.328291092\) \(a_{78}=-1.005795001\) \(a_{79}=+1.289662837\) \(a_{80}=+1.830035979\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.008334056\) \(a_{83}=+0.911486876\) \(a_{84}=+0.162458040\) \(a_{85}=-1.422318139\)
\(a_{86}=+0.869413168\) \(a_{87}=-0.022728174\) \(a_{88}=+0.104965844\) \(a_{89}=+0.418029863\) \(a_{90}=-0.795999818\)
\(a_{91}=-0.379207892\) \(a_{92}=+0.819424182\) \(a_{93}=-0.817843847\) \(a_{94}=-0.181270129\) \(a_{95}=+1.334126049\)
\(a_{96}=+0.798278598\) \(a_{97}=-0.394980849\) \(a_{98}=-1.262306475\) \(a_{99}=-0.361831761\) \(a_{100}=+1.818070083\)

Showing 100 of 1228 available coefficients

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