Properties

Level $74$
Weight $0$
Character 74.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 74 = 2 \cdot 37 \)
Weight: \( 0 \)
Character: 74.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.90777111141 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.187553382\) \(a_{4}=+0.500000000\) \(a_{5}=-0.358229666\)
\(a_{6}=-0.132620268\) \(a_{7}=+0.593902617\) \(a_{8}=+0.353553391\) \(a_{9}=-0.964823729\) \(a_{10}=-0.253306626\)
\(a_{11}=+0.523180757\) \(a_{12}=-0.093776691\) \(a_{13}=-1.000656193\) \(a_{14}=+0.419952568\) \(a_{15}=+0.067187185\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.673264013\) \(a_{18}=-0.682233401\) \(a_{19}=-0.803196337\) \(a_{20}=-0.179114833\)
\(a_{21}=-0.111388444\) \(a_{22}=+0.369944661\) \(a_{23}=-0.377064695\) \(a_{24}=-0.066310134\) \(a_{25}=-0.871671506\)
\(a_{26}=-0.707570780\) \(a_{27}=+0.368509335\) \(a_{28}=+0.296951308\) \(a_{29}=-1.147426221\) \(a_{30}=+0.047508514\)
\(a_{31}=+0.303992788\) \(a_{32}=+0.176776695\) \(a_{33}=-0.098124320\) \(a_{34}=-1.183176330\) \(a_{35}=-0.212753536\)
\(a_{36}=-0.482411864\) \(a_{37}=+0.164398987\) \(a_{38}=-0.567945577\) \(a_{39}=+0.187676453\) \(a_{40}=-0.126653313\)
\(a_{41}=+1.018980278\) \(a_{42}=-0.078763524\) \(a_{43}=+1.766525263\) \(a_{44}=+0.261590378\) \(a_{45}=+0.345628482\)
\(a_{46}=-0.266625002\) \(a_{47}=+1.265409630\) \(a_{48}=-0.046888345\) \(a_{49}=-0.647279682\) \(a_{50}=-0.616364833\)
\(a_{51}=+0.313826325\) \(a_{52}=-0.500328097\) \(a_{53}=-1.855698462\) \(a_{54}=+0.260575450\) \(a_{55}=-0.187418868\)
\(a_{56}=+0.209976284\) \(a_{57}=+0.150642189\) \(a_{58}=-0.811352862\) \(a_{59}=+0.046783972\) \(a_{60}=+0.033593593\)
\(a_{61}=-0.461916903\) \(a_{62}=+0.214955362\) \(a_{63}=-0.573011337\) \(a_{64}=+0.125000000\) \(a_{65}=+0.358464734\)
\(a_{66}=-0.069384372\) \(a_{67}=-1.029956387\) \(a_{68}=-0.836632007\) \(a_{69}=+0.070719759\) \(a_{70}=-0.150439468\)
\(a_{71}=+0.187580680\) \(a_{72}=-0.341116701\) \(a_{73}=-0.542823467\) \(a_{74}=+0.116247639\) \(a_{75}=+0.163484939\)
\(a_{76}=-0.401598169\) \(a_{77}=+0.310718421\) \(a_{78}=+0.132707293\) \(a_{79}=-0.022824066\) \(a_{80}=-0.089557416\)
\(a_{81}=+0.895708557\) \(a_{82}=+0.720527864\) \(a_{83}=+0.444496699\) \(a_{84}=-0.055694222\) \(a_{85}=+0.599412808\)
\(a_{86}=+1.249121992\) \(a_{87}=+0.215203668\) \(a_{88}=+0.184972330\) \(a_{89}=-1.197592677\) \(a_{90}=+0.244396243\)
\(a_{91}=-0.594292332\) \(a_{92}=-0.188532347\) \(a_{93}=-0.057014875\) \(a_{94}=+0.894779730\) \(a_{95}=+0.287728755\)
\(a_{96}=-0.033155067\) \(a_{97}=+1.605634249\) \(a_{98}=-0.457695852\) \(a_{99}=-0.504777209\) \(a_{100}=-0.435835753\)

Showing 100 of 726 available coefficients

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