Properties

Level $829$
Weight $0$
Character 829.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 829 \)
Weight: \( 0 \)
Character: 829.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.9416580027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.896745837\) \(a_{3}=+1.366178615\) \(a_{4}=+2.597645467\) \(a_{5}=-1.440282313\)
\(a_{6}=+2.591293231\) \(a_{7}=+0.435612084\) \(a_{8}=+3.030328930\) \(a_{9}=+0.866441638\) \(a_{10}=-2.731850213\)
\(a_{11}=-0.193665203\) \(a_{12}=+3.548845865\) \(a_{13}=+1.905356229\) \(a_{14}=+0.826246377\) \(a_{15}=-1.967682525\)
\(a_{16}=+3.150117558\) \(a_{17}=-1.643899708\) \(a_{18}=+1.643420317\) \(a_{19}=+0.955035357\) \(a_{20}=-3.741344990\)
\(a_{21}=+0.595124560\) \(a_{22}=-0.367333657\) \(a_{23}=-0.762921840\) \(a_{24}=+4.139966983\) \(a_{25}=+1.074413934\)
\(a_{26}=+3.613977304\) \(a_{27}=-0.182465302\) \(a_{28}=+1.131567759\) \(a_{29}=-1.908592217\) \(a_{30}=-3.732193609\)
\(a_{31}=+0.554535030\) \(a_{32}=+2.944644331\) \(a_{33}=-0.264580636\) \(a_{34}=-3.118060648\) \(a_{35}=-0.627404393\)
\(a_{36}=+2.250707770\) \(a_{37}=-0.781391078\) \(a_{38}=+1.811460089\) \(a_{39}=+2.603055449\) \(a_{40}=-4.364530855\)
\(a_{41}=+0.491673565\) \(a_{42}=+1.128799950\) \(a_{43}=-0.011091703\) \(a_{44}=-0.503073352\) \(a_{45}=-1.247921112\)
\(a_{46}=-1.447069289\) \(a_{47}=+0.864161236\) \(a_{48}=+4.303620513\) \(a_{49}=-0.810242645\) \(a_{50}=+2.037890702\)
\(a_{51}=-2.245858931\) \(a_{52}=+4.949440366\) \(a_{53}=-0.371875057\) \(a_{54}=-0.346089635\) \(a_{55}=+0.278933108\)
\(a_{56}=+1.320050033\) \(a_{57}=+1.304748865\) \(a_{58}=-3.620113538\) \(a_{59}=+0.980434071\) \(a_{60}=-5.111341022\)
\(a_{61}=+0.151580658\) \(a_{62}=+1.051812630\) \(a_{63}=+0.377433417\) \(a_{64}=+2.435125840\) \(a_{65}=-2.744251621\)
\(a_{66}=-0.501843154\) \(a_{67}=-1.525012460\) \(a_{68}=-4.270270138\) \(a_{69}=-1.042287004\) \(a_{70}=-1.190027868\)
\(a_{71}=+0.406037662\) \(a_{72}=+2.625602065\) \(a_{73}=-0.395107637\) \(a_{74}=-1.482101266\) \(a_{75}=+1.467841555\)
\(a_{76}=+2.480844240\) \(a_{77}=-0.084363269\) \(a_{78}=+4.937335278\) \(a_{79}=+1.512756156\) \(a_{80}=-4.537061284\)
\(a_{81}=-1.115721095\) \(a_{82}=+0.932580384\) \(a_{83}=+0.410639244\) \(a_{84}=+1.545922081\) \(a_{85}=+2.367680351\)
\(a_{86}=-0.021038886\) \(a_{87}=-2.607474775\) \(a_{88}=-0.586869260\) \(a_{89}=+0.268205093\) \(a_{90}=-2.366989311\)
\(a_{91}=+0.829997521\) \(a_{92}=-1.981801617\) \(a_{93}=+0.757594809\) \(a_{94}=+1.639094721\) \(a_{95}=-1.375520570\)
\(a_{96}=+4.022908747\) \(a_{97}=-1.854667229\) \(a_{98}=-1.536822888\) \(a_{99}=-0.167799188\) \(a_{100}=+2.790947969\)

Showing 100 of 2016 available coefficients

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