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: \( 18.9626422396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.600831769\) \(a_{3}=-0.577350269\) \(a_{4}=-0.639001185\) \(a_{5}=-1.639628840\)
\(a_{6}=-0.346890384\) \(a_{7}=-0.662239952\) \(a_{8}=-0.984763982\) \(a_{9}=+0.333333333\) \(a_{10}=-0.985141097\)
\(a_{11}=+0.266071556\) \(a_{12}=+0.368927506\) \(a_{13}=+1.327581178\) \(a_{14}=-0.397894802\) \(a_{15}=+0.946640152\)
\(a_{16}=+0.047323700\) \(a_{17}=-1.709360565\) \(a_{18}=+0.200277256\) \(a_{19}=-0.633531114\) \(a_{20}=+1.047724772\)
\(a_{21}=+0.382344415\) \(a_{22}=+0.159864244\) \(a_{23}=+0.458778997\) \(a_{24}=+0.568553750\) \(a_{25}=+1.688382734\)
\(a_{26}=+0.797652948\) \(a_{27}=-0.192450090\) \(a_{28}=+0.423172114\) \(a_{29}=-0.109828907\) \(a_{30}=+0.568771477\)
\(a_{31}=+0.238328027\) \(a_{32}=+1.013197564\) \(a_{33}=-0.153616484\) \(a_{34}=-1.027038132\) \(a_{35}=+1.085827725\)
\(a_{36}=-0.213000395\) \(a_{37}=-0.031606789\) \(a_{38}=-0.380645620\) \(a_{39}=-0.766479351\) \(a_{40}=+1.614647425\)
\(a_{41}=+0.420613705\) \(a_{42}=+0.229724671\) \(a_{43}=-1.180849881\) \(a_{44}=-0.170020040\) \(a_{45}=-0.546542947\)
\(a_{46}=+0.275648996\) \(a_{47}=+0.659001782\) \(a_{48}=-0.027322351\) \(a_{49}=-0.561438246\) \(a_{50}=+1.014433985\)
\(a_{51}=+0.986899782\) \(a_{52}=-0.848325947\) \(a_{53}=-1.148533690\) \(a_{54}=-0.115630128\) \(a_{55}=-0.436258597\)
\(a_{56}=+0.652150052\) \(a_{57}=+0.365769359\) \(a_{58}=-0.065988696\) \(a_{59}=+0.738474595\) \(a_{60}=-0.604904179\)
\(a_{61}=+0.405295011\) \(a_{62}=+0.143195050\) \(a_{63}=-0.220746651\) \(a_{64}=+0.561437585\) \(a_{65}=-2.176740388\)
\(a_{66}=-0.092297664\) \(a_{67}=+0.656200122\) \(a_{68}=+1.092283427\) \(a_{69}=-0.264876177\) \(a_{70}=+0.652399793\)
\(a_{71}=-1.333879592\) \(a_{72}=-0.328254661\) \(a_{73}=+1.897359314\) \(a_{74}=-0.018990363\) \(a_{75}=-0.974788226\)
\(a_{76}=+0.404827133\) \(a_{77}=-0.176203214\) \(a_{78}=-0.460525144\) \(a_{79}=-0.514234238\) \(a_{80}=-0.077593303\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.252718076\) \(a_{83}=-0.305618707\) \(a_{84}=-0.244318534\) \(a_{85}=+2.802716880\)
\(a_{86}=-0.709492123\) \(a_{87}=+0.063409749\) \(a_{88}=-0.262017685\) \(a_{89}=-0.554561699\) \(a_{90}=-0.328380366\)
\(a_{91}=-0.879177296\) \(a_{92}=-0.293160323\) \(a_{93}=-0.137598751\) \(a_{94}=+0.395949206\) \(a_{95}=+1.038755886\)
\(a_{96}=-0.584969886\) \(a_{97}=+1.086037182\) \(a_{98}=-0.337329934\) \(a_{99}=+0.088690519\) \(a_{100}=-1.078878568\)

Showing 100 of 1228 available coefficients

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