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: \( 27.7036935138 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.734820815\) \(a_{3}=+0.577350269\) \(a_{4}=+2.009603262\) \(a_{5}=-1.753332169\)
\(a_{6}=-1.001599265\) \(a_{7}=+1.193985823\) \(a_{8}=-1.751480753\) \(a_{9}=+0.333333333\) \(a_{10}=+3.041717144\)
\(a_{11}=-0.260716224\) \(a_{12}=+1.160244984\) \(a_{13}=-0.601800246\) \(a_{14}=-2.071351460\) \(a_{15}=-1.012286800\)
\(a_{16}=+1.028902007\) \(a_{17}=-0.697523278\) \(a_{18}=-0.578273605\) \(a_{19}=+0.725085893\) \(a_{20}=-3.523502046\)
\(a_{21}=+0.689348036\) \(a_{22}=+0.452295933\) \(a_{23}=-0.034951310\) \(a_{24}=-1.011217884\) \(a_{25}=+2.074173696\)
\(a_{26}=+1.044015594\) \(a_{27}=+0.192450090\) \(a_{28}=+2.399437805\) \(a_{29}=+0.590214857\) \(a_{30}=+1.756136212\)
\(a_{31}=-0.694183663\) \(a_{32}=-0.033479866\) \(a_{33}=-0.150524582\) \(a_{34}=+1.210077901\) \(a_{35}=-2.093453754\)
\(a_{36}=+0.669867754\) \(a_{37}=+0.972008445\) \(a_{38}=-1.257894100\) \(a_{39}=-0.347449534\) \(a_{40}=+3.070927549\)
\(a_{41}=+0.753859155\) \(a_{42}=-1.195895323\) \(a_{43}=+1.031707670\) \(a_{44}=-0.523936175\) \(a_{45}=-0.584444056\)
\(a_{46}=+0.060634260\) \(a_{47}=+0.386129962\) \(a_{48}=+0.594036851\) \(a_{49}=+0.425602146\) \(a_{50}=-3.598319702\)
\(a_{51}=-0.402715252\) \(a_{52}=-1.209379737\) \(a_{53}=+0.489011486\) \(a_{54}=-0.333866422\) \(a_{55}=+0.457122143\)
\(a_{56}=-2.091243189\) \(a_{57}=+0.418628535\) \(a_{58}=-1.023917020\) \(a_{59}=+0.577585178\) \(a_{60}=-2.034294855\)
\(a_{61}=-1.090145463\) \(a_{62}=+1.204284268\) \(a_{63}=+0.397995274\) \(a_{64}=-0.970820439\) \(a_{65}=+1.055155731\)
\(a_{66}=+0.261133179\) \(a_{67}=-1.894094264\) \(a_{68}=-1.401745054\) \(a_{69}=-0.020179148\) \(a_{70}=+3.631767148\)
\(a_{71}=-0.641450818\) \(a_{72}=-0.583826918\) \(a_{73}=-1.589858139\) \(a_{74}=-1.686260483\) \(a_{75}=+1.197524742\)
\(a_{76}=+1.457134975\) \(a_{77}=-0.311291476\) \(a_{78}=+0.602762684\) \(a_{79}=+1.493470709\) \(a_{80}=-1.804006988\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.307810555\) \(a_{83}=-1.095021850\) \(a_{84}=+1.385316062\) \(a_{85}=+1.222990002\)
\(a_{86}=-1.789827941\) \(a_{87}=+0.340760707\) \(a_{88}=+0.456639449\) \(a_{89}=+0.911985964\) \(a_{90}=+1.013905714\)
\(a_{91}=-0.718540962\) \(a_{92}=-0.070238266\) \(a_{93}=-0.400787125\) \(a_{94}=-0.669866296\) \(a_{95}=-1.271316421\)
\(a_{96}=-0.019329610\) \(a_{97}=+0.788093576\) \(a_{98}=-0.738343462\) \(a_{99}=-0.086905408\) \(a_{100}=+4.168266224\)

Showing 100 of 1228 available coefficients

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