Properties

Level $69$
Weight $0$
Character 69.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 69 = 3 \cdot 23 \)
Weight: \( 0 \)
Character: 69.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.8232157864 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.087794597\) \(a_{3}=-0.577350269\) \(a_{4}=+0.183297085\) \(a_{5}=+0.099912184\)
\(a_{6}=-0.628038503\) \(a_{7}=-1.375544519\) \(a_{8}=-0.888405018\) \(a_{9}=+0.333333333\) \(a_{10}=+0.108683934\)
\(a_{11}=+1.337677226\) \(a_{12}=-0.105826622\) \(a_{13}=-0.865031080\) \(a_{14}=-1.496309896\) \(a_{15}=-0.057684326\)
\(a_{16}=-1.149699264\) \(a_{17}=+0.519817043\) \(a_{18}=+0.362598199\) \(a_{19}=-1.769582554\) \(a_{20}=+0.018313612\)
\(a_{21}=+0.794170998\) \(a_{22}=+1.455118059\) \(a_{23}=+0.208514414\) \(a_{24}=+0.512920876\) \(a_{25}=-0.990017555\)
\(a_{26}=-0.940976135\) \(a_{27}=-0.192450090\) \(a_{28}=-0.252133301\) \(a_{29}=-0.545464064\) \(a_{30}=-0.062748699\)
\(a_{31}=+1.151843358\) \(a_{32}=-0.362231629\) \(a_{33}=-0.772308307\) \(a_{34}=+0.565454171\) \(a_{35}=-0.137433657\)
\(a_{36}=+0.061099028\) \(a_{37}=-0.756234176\) \(a_{38}=-1.924942341\) \(a_{39}=+0.499425927\) \(a_{40}=-0.088762486\)
\(a_{41}=-0.845988626\) \(a_{42}=+0.863894921\) \(a_{43}=+1.685548865\) \(a_{44}=+0.245192337\) \(a_{45}=+0.033304061\)
\(a_{46}=+0.226820853\) \(a_{47}=-0.545687058\) \(a_{48}=+0.663779179\) \(a_{49}=+0.892122724\) \(a_{50}=-1.076935748\)
\(a_{51}=-0.300116510\) \(a_{52}=-0.158557676\) \(a_{53}=+1.683867091\) \(a_{54}=-0.209346168\) \(a_{55}=+0.133650253\)
\(a_{56}=+1.222040653\) \(a_{57}=+1.021668964\) \(a_{58}=-0.593352862\) \(a_{59}=+0.070407498\) \(a_{60}=-0.010573369\)
\(a_{61}=-0.985852958\) \(a_{62}=+1.252968981\) \(a_{63}=-0.458514840\) \(a_{64}=+0.755665655\) \(a_{65}=-0.086427144\)
\(a_{66}=-0.840112803\) \(a_{67}=-0.477734178\) \(a_{68}=+0.095280949\) \(a_{69}=-0.120385853\) \(a_{70}=-0.149499590\)
\(a_{71}=-1.094975299\) \(a_{72}=-0.296135006\) \(a_{73}=+0.396568722\) \(a_{74}=-0.822627451\) \(a_{75}=+0.571586902\)
\(a_{76}=-0.324359324\) \(a_{77}=-1.840034576\) \(a_{78}=+0.543272825\) \(a_{79}=-1.840385746\) \(a_{80}=-0.114868964\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.920261856\) \(a_{83}=+0.240879713\) \(a_{84}=+0.145569229\) \(a_{85}=+0.051936056\)
\(a_{86}=+1.833530948\) \(a_{87}=+0.314923824\) \(a_{88}=-1.188399160\) \(a_{89}=-0.107368299\) \(a_{90}=+0.036227978\)
\(a_{91}=+1.189888760\) \(a_{92}=+0.038220084\) \(a_{93}=-0.665017073\) \(a_{94}=-0.593595434\) \(a_{95}=-0.176802858\)
\(a_{96}=+0.209134529\) \(a_{97}=-0.468690238\) \(a_{98}=+0.970446279\) \(a_{99}=+0.445892409\) \(a_{100}=-0.181467332\)

Showing 100 of 502 available coefficients

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