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: \( 15.4831618965 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.163070576\) \(a_{3}=-0.577350269\) \(a_{4}=+0.352733164\) \(a_{5}=-0.560023889\)
\(a_{6}=+0.671499110\) \(a_{7}=+0.546256127\) \(a_{8}=+0.752817011\) \(a_{9}=+0.333333333\) \(a_{10}=+0.651347307\)
\(a_{11}=+1.568237573\) \(a_{12}=-0.203650587\) \(a_{13}=-0.656973137\) \(a_{14}=-0.635334428\) \(a_{15}=+0.323329943\)
\(a_{16}=-1.228312479\) \(a_{17}=-1.615691063\) \(a_{18}=-0.387690192\) \(a_{19}=+0.485148064\) \(a_{20}=-0.197538998\)
\(a_{21}=-0.315381122\) \(a_{22}=-1.823970977\) \(a_{23}=+1.645499328\) \(a_{24}=-0.434639104\) \(a_{25}=-0.686373244\)
\(a_{26}=+0.764106125\) \(a_{27}=-0.192450090\) \(a_{28}=+0.192682652\) \(a_{29}=-0.143680452\) \(a_{30}=-0.376055543\)
\(a_{31}=-0.483386875\) \(a_{32}=+0.675797091\) \(a_{33}=-0.905422385\) \(a_{34}=+1.879162735\) \(a_{35}=-0.305916480\)
\(a_{36}=+0.117577721\) \(a_{37}=-1.092843959\) \(a_{38}=-0.564261438\) \(a_{39}=+0.379303618\) \(a_{40}=-0.421595510\)
\(a_{41}=+1.046667270\) \(a_{42}=+0.366810503\) \(a_{43}=+0.001299238\) \(a_{44}=+0.553169401\) \(a_{45}=-0.186674630\)
\(a_{46}=-1.913831851\) \(a_{47}=+0.095863903\) \(a_{48}=+0.709166540\) \(a_{49}=-0.701604244\) \(a_{50}=+0.798300524\)
\(a_{51}=+0.932819670\) \(a_{52}=-0.231736214\) \(a_{53}=-0.300875817\) \(a_{54}=+0.223833037\) \(a_{55}=-0.878250504\)
\(a_{56}=+0.411230905\) \(a_{57}=-0.280100365\) \(a_{58}=+0.167110506\) \(a_{59}=+0.388525845\) \(a_{60}=+0.114049194\)
\(a_{61}=-1.648602557\) \(a_{62}=+0.562213051\) \(a_{63}=+0.182085376\) \(a_{64}=+0.442312767\) \(a_{65}=+0.367920651\)
\(a_{66}=+1.053070134\) \(a_{67}=-0.089404910\) \(a_{68}=-0.569907821\) \(a_{69}=-0.950029480\) \(a_{70}=+0.355802457\)
\(a_{71}=-1.464415740\) \(a_{72}=+0.250939004\) \(a_{73}=-0.453725560\) \(a_{74}=+1.271054653\) \(a_{75}=+0.396277777\)
\(a_{76}=+0.171127812\) \(a_{77}=+0.856659382\) \(a_{78}=-0.441156877\) \(a_{79}=-0.294929152\) \(a_{80}=+0.687884331\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.217347904\) \(a_{83}=-1.413727176\) \(a_{84}=-0.111245381\) \(a_{85}=+0.904825592\)
\(a_{86}=-0.001511105\) \(a_{87}=+0.082953948\) \(a_{88}=+1.180595922\) \(a_{89}=-0.551081298\) \(a_{90}=+0.217115769\)
\(a_{91}=-0.358875601\) \(a_{92}=+0.580422185\) \(a_{93}=+0.279083542\) \(a_{94}=-0.111496484\) \(a_{95}=-0.271694505\)
\(a_{96}=-0.390171633\) \(a_{97}=-1.049442987\) \(a_{98}=+0.816015252\) \(a_{99}=+0.522745858\) \(a_{100}=-0.242106606\)

Showing 100 of 1228 available coefficients

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