Properties

Level $37$
Weight $0$
Character 37.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 37 \)
Weight: \( 0 \)
Character: 37.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.6423059582 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.260973420\) \(a_{3}=-1.092287908\) \(a_{4}=+0.590053966\) \(a_{5}=-0.229523059\)
\(a_{6}=-1.377346019\) \(a_{7}=+0.451609744\) \(a_{8}=-0.516931053\) \(a_{9}=+0.193092875\) \(a_{10}=-0.289422476\)
\(a_{11}=+0.560170056\) \(a_{12}=-0.644508812\) \(a_{13}=+1.613925863\) \(a_{14}=+0.569467883\) \(a_{15}=+0.250705262\)
\(a_{16}=-1.241890283\) \(a_{17}=-0.997990675\) \(a_{18}=+0.243484983\) \(a_{19}=-0.011648336\) \(a_{20}=-0.135430991\)
\(a_{21}=-0.493287862\) \(a_{22}=+0.706359551\) \(a_{23}=+0.665221333\) \(a_{24}=+0.564637538\) \(a_{25}=-0.947319165\)
\(a_{26}=+2.035117616\) \(a_{27}=+0.881374896\) \(a_{28}=+0.266474120\) \(a_{29}=+0.005083362\) \(a_{30}=+0.316132671\)
\(a_{31}=-1.192814280\) \(a_{32}=-1.049059585\) \(a_{33}=-0.611866979\) \(a_{34}=-1.258439715\) \(a_{35}=-0.103654850\)
\(a_{36}=+0.113935217\) \(a_{37}=+0.164398987\) \(a_{38}=-0.014688242\) \(a_{39}=-1.762871706\) \(a_{40}=+0.118647596\)
\(a_{41}=+0.276660174\) \(a_{42}=-0.622022883\) \(a_{43}=-0.409438645\) \(a_{44}=+0.330530563\) \(a_{45}=-0.044319267\)
\(a_{46}=+0.838826420\) \(a_{47}=+0.707574028\) \(a_{48}=+1.356501740\) \(a_{49}=-0.796048639\) \(a_{50}=-1.194544288\)
\(a_{51}=+1.090093147\) \(a_{52}=+0.952303356\) \(a_{53}=+1.484895570\) \(a_{54}=+1.111390317\) \(a_{55}=-0.128571945\)
\(a_{56}=-0.233451100\) \(a_{57}=+0.012723336\) \(a_{58}=+0.006409984\) \(a_{59}=-0.375707089\) \(a_{60}=+0.147929634\)
\(a_{61}=+1.051263094\) \(a_{62}=-1.504107102\) \(a_{63}=+0.087202624\) \(a_{64}=-0.080945970\) \(a_{65}=-0.370433201\)
\(a_{66}=-0.771547997\) \(a_{67}=+0.442625167\) \(a_{68}=-0.588868356\) \(a_{69}=-0.726613219\) \(a_{70}=-0.130706010\)
\(a_{71}=+0.157019706\) \(a_{72}=-0.099815703\) \(a_{73}=+0.501855252\) \(a_{74}=+0.207302753\) \(a_{75}=+1.034745270\)
\(a_{76}=-0.006873147\) \(a_{77}=+0.252978255\) \(a_{78}=-2.222934364\) \(a_{79}=+0.371187076\) \(a_{80}=+0.285042456\)
\(a_{81}=-1.155808017\) \(a_{82}=+0.348861126\) \(a_{83}=-1.553768003\) \(a_{84}=-0.291066459\) \(a_{85}=+0.229061872\)
\(a_{86}=-0.516291249\) \(a_{87}=-0.005552495\) \(a_{88}=-0.289569297\) \(a_{89}=-0.161052733\) \(a_{90}=-0.055885418\)
\(a_{91}=+0.728864645\) \(a_{92}=+0.392516486\) \(a_{93}=+1.302896615\) \(a_{94}=+0.892232042\) \(a_{95}=+0.002673562\)
\(a_{96}=+1.145875100\) \(a_{97}=+1.325077248\) \(a_{98}=-1.003796175\) \(a_{99}=+0.108164847\) \(a_{100}=-0.558969431\)

Showing 100 of 546 available coefficients

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