Properties

Level $829$
Weight $0$
Character 829.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 829 \)
Weight: \( 0 \)
Character: 829.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.9316469568 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.760601964\) \(a_{3}=-1.565899356\) \(a_{4}=+2.099695504\) \(a_{5}=-1.577238270\)
\(a_{6}=+2.756928468\) \(a_{7}=-1.886653415\) \(a_{8}=-1.936147449\) \(a_{9}=+1.452052857\) \(a_{10}=+2.776892351\)
\(a_{11}=-1.569207231\) \(a_{12}=-3.287926044\) \(a_{13}=+0.752301965\) \(a_{14}=+3.321629927\) \(a_{15}=+2.469812133\)
\(a_{16}=+1.309049875\) \(a_{17}=-1.270391659\) \(a_{18}=-2.556465875\) \(a_{19}=-0.090977458\) \(a_{20}=-3.311744722\)
\(a_{21}=+2.954314085\) \(a_{22}=+2.762742188\) \(a_{23}=-0.852418786\) \(a_{24}=+3.031801083\) \(a_{25}=+1.487699992\)
\(a_{26}=-1.324509156\) \(a_{27}=-0.707864982\) \(a_{28}=-3.961417283\) \(a_{29}=+0.701272268\) \(a_{30}=-4.348334605\)
\(a_{31}=-1.009426407\) \(a_{32}=-0.368582466\) \(a_{33}=+2.457212220\) \(a_{34}=+2.236646193\) \(a_{35}=+2.975711007\)
\(a_{36}=+3.048864881\) \(a_{37}=+0.202505534\) \(a_{38}=+0.160166855\) \(a_{39}=-1.178040263\) \(a_{40}=+3.053756521\)
\(a_{41}=+0.261611407\) \(a_{42}=-5.201341864\) \(a_{43}=-0.221664495\) \(a_{44}=-3.294859784\) \(a_{45}=-2.290225665\)
\(a_{46}=+1.500762443\) \(a_{47}=+0.079582883\) \(a_{48}=-2.049841608\) \(a_{49}=+2.559446985\) \(a_{50}=-2.619223384\)
\(a_{51}=+1.989293100\) \(a_{52}=+1.579626280\) \(a_{53}=-1.297890514\) \(a_{54}=+1.246249557\) \(a_{55}=+2.475009090\)
\(a_{56}=+3.652802574\) \(a_{57}=+0.142454863\) \(a_{58}=-1.234653010\) \(a_{59}=-0.341632115\) \(a_{60}=+5.185855767\)
\(a_{61}=+0.675072272\) \(a_{62}=+1.777202399\) \(a_{63}=-2.739501723\) \(a_{64}=-0.660140367\) \(a_{65}=-1.186573579\)
\(a_{66}=-4.326180191\) \(a_{67}=-0.200071755\) \(a_{68}=-2.667433739\) \(a_{69}=+1.334809113\) \(a_{70}=-5.239016757\)
\(a_{71}=-1.523207744\) \(a_{72}=-2.811355197\) \(a_{73}=-1.174482520\) \(a_{74}=-0.356510486\) \(a_{75}=-2.329573988\)
\(a_{76}=-0.191026340\) \(a_{77}=+2.960539696\) \(a_{78}=+2.074050518\) \(a_{79}=-0.873730557\) \(a_{80}=-2.064690684\)
\(a_{81}=-0.343610344\) \(a_{82}=-0.460588825\) \(a_{83}=+0.472191202\) \(a_{84}=+6.203171652\) \(a_{85}=+2.003702591\)
\(a_{86}=+0.390262877\) \(a_{87}=-1.098127731\) \(a_{88}=+3.038204664\) \(a_{89}=-1.858693709\) \(a_{90}=+4.032170437\)
\(a_{91}=-1.419341516\) \(a_{92}=-1.789834412\) \(a_{93}=+1.580676059\) \(a_{94}=-0.140120883\) \(a_{95}=+0.143487514\)
\(a_{96}=+0.577163825\) \(a_{97}=+0.362731676\) \(a_{98}=-4.506159523\) \(a_{99}=-2.278557310\) \(a_{100}=+3.123718821\)

Showing 100 of 1948 available coefficients

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