Properties

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

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Maass form invariants

Level: \( 69 = 3 \cdot 23 \)
Weight: \( 0 \)
Character: 69.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.608726470249 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.881835253\) \(a_{3}=+0.577350269\) \(a_{4}=-0.222366586\) \(a_{5}=+1.439310647\)
\(a_{6}=-0.509127821\) \(a_{7}=+0.277006296\) \(a_{8}=+1.077925948\) \(a_{9}=+0.333333333\) \(a_{10}=-1.269234869\)
\(a_{11}=-0.430588395\) \(a_{12}=-0.128383409\) \(a_{13}=+0.141172830\) \(a_{14}=-0.244273917\) \(a_{15}=+0.830986390\)
\(a_{16}=-0.728186515\) \(a_{17}=-1.490558648\) \(a_{18}=-0.293945084\) \(a_{19}=-1.001264936\) \(a_{20}=-0.320054595\)
\(a_{21}=+0.159929659\) \(a_{22}=+0.379708027\) \(a_{23}=-0.208514414\) \(a_{24}=+0.622340836\) \(a_{25}=+1.071615140\)
\(a_{26}=-0.124491178\) \(a_{27}=+0.192450090\) \(a_{28}=-0.061596944\) \(a_{29}=+0.360318949\) \(a_{30}=-0.732793093\)
\(a_{31}=+0.716247261\) \(a_{32}=-0.435785408\) \(a_{33}=-0.248600326\) \(a_{34}=+1.314427163\) \(a_{35}=+0.398698111\)
\(a_{36}=-0.074122195\) \(a_{37}=+0.203751233\) \(a_{38}=+0.882950719\) \(a_{39}=+0.081506171\) \(a_{40}=+1.551470294\)
\(a_{41}=+0.908453505\) \(a_{42}=-0.141031612\) \(a_{43}=-1.335350346\) \(a_{44}=+0.095748472\) \(a_{45}=+0.479770216\)
\(a_{46}=+0.183875361\) \(a_{47}=+0.401382781\) \(a_{48}=-0.420418680\) \(a_{49}=-0.923267512\) \(a_{50}=-0.944988008\)
\(a_{51}=-0.860574437\) \(a_{52}=-0.031392120\) \(a_{53}=-1.898372116\) \(a_{54}=-0.169709274\) \(a_{55}=-0.619750462\)
\(a_{56}=+0.298592274\) \(a_{57}=-0.578080581\) \(a_{58}=-0.317741952\) \(a_{59}=+0.517023610\) \(a_{60}=-0.184783607\)
\(a_{61}=+0.501771110\) \(a_{62}=-0.631612085\) \(a_{63}=+0.092335432\) \(a_{64}=+1.112477451\) \(a_{65}=+0.203191557\)
\(a_{66}=+0.219224531\) \(a_{67}=+0.853316444\) \(a_{68}=+0.331450438\) \(a_{69}=-0.120385853\) \(a_{70}=-0.351586049\)
\(a_{71}=-0.357462549\) \(a_{72}=+0.359308649\) \(a_{73}=-1.007500292\) \(a_{74}=-0.179675020\) \(a_{75}=+0.618697289\)
\(a_{76}=+0.222647866\) \(a_{77}=-0.119275696\) \(a_{78}=-0.071875015\) \(a_{79}=+1.651800316\) \(a_{80}=-1.048086604\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.801106327\) \(a_{83}=+0.301418086\) \(a_{84}=-0.035563012\) \(a_{85}=-2.145376933\)
\(a_{86}=+1.177559010\) \(a_{87}=+0.208030242\) \(a_{88}=-0.464142404\) \(a_{89}=+1.057350664\) \(a_{90}=-0.423078290\)
\(a_{91}=+0.039105763\) \(a_{92}=+0.046366638\) \(a_{93}=+0.413525549\) \(a_{94}=-0.353953486\) \(a_{95}=-1.441131284\)
\(a_{96}=-0.251600823\) \(a_{97}=+0.588286795\) \(a_{98}=+0.814169840\) \(a_{99}=-0.143529465\) \(a_{100}=-0.238291401\)

Showing 100 of 546 available coefficients

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