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: \( 0.7559153342 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.765605616\) \(a_{3}=-0.794362927\) \(a_{4}=+2.117362477\) \(a_{5}=-0.698246391\)
\(a_{6}=-1.402531176\) \(a_{7}=-0.993792050\) \(a_{8}=+1.972821103\) \(a_{9}=-0.368987901\) \(a_{10}=-1.232827699\)
\(a_{11}=+0.221277185\) \(a_{12}=-1.681953823\) \(a_{13}=-0.616053857\) \(a_{14}=-1.754644813\) \(a_{15}=+0.554660992\)
\(a_{16}=+1.365861440\) \(a_{17}=-1.246699392\) \(a_{18}=-0.651486870\) \(a_{19}=-0.021189757\) \(a_{20}=-1.478440991\)
\(a_{21}=+0.789431407\) \(a_{22}=+0.390688246\) \(a_{23}=-0.418368791\) \(a_{24}=-1.567135574\) \(a_{25}=-0.512451993\)
\(a_{26}=-1.087708110\) \(a_{27}=+1.087472660\) \(a_{28}=-2.104218168\) \(a_{29}=+1.136857674\) \(a_{30}=+0.979312597\)
\(a_{31}=-0.395368046\) \(a_{32}=+0.438751161\) \(a_{33}=-0.175774429\) \(a_{34}=-2.201178812\) \(a_{35}=+0.693911758\)
\(a_{36}=-0.781280859\) \(a_{37}=-0.023707944\) \(a_{38}=-0.037412482\) \(a_{39}=+0.489370427\) \(a_{40}=-1.377515629\)
\(a_{41}=-0.917676884\) \(a_{42}=+1.393824248\) \(a_{43}=+1.673899242\) \(a_{44}=+0.468524030\) \(a_{45}=+0.257644353\)
\(a_{46}=-0.738674485\) \(a_{47}=-0.836815683\) \(a_{48}=-1.084989352\) \(a_{49}=-0.012377061\) \(a_{50}=-0.904787927\)
\(a_{51}=+0.990331498\) \(a_{52}=-1.304409641\) \(a_{53}=-0.048661474\) \(a_{54}=+1.920047606\) \(a_{55}=-0.154505940\)
\(a_{56}=-1.960574461\) \(a_{57}=+0.016832456\) \(a_{58}=+2.007242074\) \(a_{59}=-0.100641009\) \(a_{60}=+1.174418381\)
\(a_{61}=-0.528478754\) \(a_{62}=-0.698063952\) \(a_{63}=+0.366697522\) \(a_{64}=-0.591199951\) \(a_{65}=+0.430157446\)
\(a_{66}=-0.310348184\) \(a_{67}=-0.190730848\) \(a_{68}=-2.639714008\) \(a_{69}=+0.332336676\) \(a_{70}=+1.225174560\)
\(a_{71}=+1.564172138\) \(a_{72}=-0.727946835\) \(a_{73}=-0.178775613\) \(a_{74}=-0.041858801\) \(a_{75}=+0.407072599\)
\(a_{76}=-0.044865814\) \(a_{77}=-0.219903614\) \(a_{78}=+0.864034985\) \(a_{79}=-1.256700869\) \(a_{80}=-0.953708064\)
\(a_{81}=-0.494859546\) \(a_{82}=-1.620255068\) \(a_{83}=+1.652610449\) \(a_{84}=+1.671512301\) \(a_{85}=+0.870503342\)
\(a_{86}=+2.955445374\) \(a_{87}=-0.903077081\) \(a_{88}=+0.436540389\) \(a_{89}=+0.262092924\) \(a_{90}=+0.454898139\)
\(a_{91}=+0.612229650\) \(a_{92}=-0.885838966\) \(a_{93}=+0.314065936\) \(a_{94}=-1.477486229\) \(a_{95}=+0.014795267\)
\(a_{96}=-0.348527437\) \(a_{97}=+0.645746252\) \(a_{98}=-0.021852865\) \(a_{99}=-0.081648513\) \(a_{100}=-1.085046270\)

Showing 100 of 2110 available coefficients

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