Properties

Level $37$
Weight $0$
Character 37.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 37 \)
Weight: \( 0 \)
Character: 37.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.3832468962 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.662047111\) \(a_{3}=-0.631737838\) \(a_{4}=+1.762400599\) \(a_{5}=-1.572005536\)
\(a_{6}=+1.049978048\) \(a_{7}=-0.914981173\) \(a_{8}=-1.267145712\) \(a_{9}=-0.600907305\) \(a_{10}=+2.612747259\)
\(a_{11}=-0.574956227\) \(a_{12}=-1.113375143\) \(a_{13}=+1.234038949\) \(a_{14}=+1.520741815\) \(a_{15}=+0.993095378\)
\(a_{16}=+0.343655271\) \(a_{17}=-1.180645928\) \(a_{18}=+0.998736249\) \(a_{19}=-0.529931903\) \(a_{20}=-2.770503498\)
\(a_{21}=+0.578028227\) \(a_{22}=+0.955604336\) \(a_{23}=+0.781724470\) \(a_{24}=+0.800503892\) \(a_{25}=+1.471201405\)
\(a_{26}=-2.051030870\) \(a_{27}=+1.011353719\) \(a_{28}=-1.612563366\) \(a_{29}=-1.960167987\) \(a_{30}=-1.650571304\)
\(a_{31}=+0.209453860\) \(a_{32}=+0.695974462\) \(a_{33}=+0.363221604\) \(a_{34}=+1.962289153\) \(a_{35}=+1.438355469\)
\(a_{36}=-1.059039393\) \(a_{37}=-0.164398987\) \(a_{38}=+0.880771788\) \(a_{39}=-0.779589097\) \(a_{40}=+1.991960074\)
\(a_{41}=+1.072742317\) \(a_{42}=-0.960710145\) \(a_{43}=+0.230039885\) \(a_{44}=-1.013303199\) \(a_{45}=+0.944629609\)
\(a_{46}=-1.299262897\) \(a_{47}=-1.342257468\) \(a_{48}=-0.217100038\) \(a_{49}=-0.162809454\) \(a_{50}=-2.445206045\)
\(a_{51}=+0.745858705\) \(a_{52}=+2.174870982\) \(a_{53}=-0.475451467\) \(a_{54}=-1.680917526\) \(a_{55}=+0.903834372\)
\(a_{56}=+1.159414470\) \(a_{57}=+0.334778034\) \(a_{58}=+3.257891540\) \(a_{59}=-1.174372156\) \(a_{60}=+1.750231889\)
\(a_{61}=+0.551358680\) \(a_{62}=-0.348122183\) \(a_{63}=+0.549818870\) \(a_{64}=-1.500397614\) \(a_{65}=-1.939916060\)
\(a_{66}=-0.603691417\) \(a_{67}=+0.597421415\) \(a_{68}=-2.080771090\) \(a_{69}=-0.493844926\) \(a_{70}=-2.390614551\)
\(a_{71}=+0.667105014\) \(a_{72}=+0.761437114\) \(a_{73}=+1.657305777\) \(a_{74}=+0.273238862\) \(a_{75}=-0.929413594\)
\(a_{76}=-0.933952302\) \(a_{77}=+0.526074123\) \(a_{78}=+1.295713807\) \(a_{79}=-1.086435695\) \(a_{80}=-0.540227989\)
\(a_{81}=-0.038003107\) \(a_{82}=-1.782948269\) \(a_{83}=+1.260565322\) \(a_{84}=+1.018717294\) \(a_{85}=+1.855981934\)
\(a_{86}=-0.382337126\) \(a_{87}=+1.238312286\) \(a_{88}=+0.728553318\) \(a_{89}=-0.766532379\) \(a_{90}=-1.570018913\)
\(a_{91}=-1.129122405\) \(a_{92}=+1.377711674\) \(a_{93}=-0.132319929\) \(a_{94}=+2.230895147\) \(a_{95}=+0.833055885\)
\(a_{96}=-0.439673401\) \(a_{97}=-0.010254085\) \(a_{98}=+0.270596982\) \(a_{99}=+0.345495397\) \(a_{100}=+2.592846237\)

Showing 100 of 546 available coefficients

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