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: \( 3.49100447103 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.670364625\) \(a_{3}=+0.520720005\) \(a_{4}=+1.790117721\) \(a_{5}=+0.459190294\)
\(a_{6}=-0.869792139\) \(a_{7}=-0.169656726\) \(a_{8}=-1.319784635\) \(a_{9}=-0.728850762\) \(a_{10}=-0.767015155\)
\(a_{11}=+0.158388456\) \(a_{12}=+0.932150083\) \(a_{13}=-0.003616235\) \(a_{14}=+0.283388708\) \(a_{15}=+0.239109533\)
\(a_{16}=+0.414403718\) \(a_{17}=-1.128768032\) \(a_{18}=+1.217446424\) \(a_{19}=-1.282462017\) \(a_{20}=+0.822004672\)
\(a_{21}=-0.088343714\) \(a_{22}=-0.264566552\) \(a_{23}=-0.089440816\) \(a_{24}=-0.687238200\) \(a_{25}=-0.789144297\)
\(a_{26}=+0.006040424\) \(a_{27}=-0.900247117\) \(a_{28}=-0.303705531\) \(a_{29}=+1.212529937\) \(a_{30}=-0.399400127\)
\(a_{31}=-0.839947571\) \(a_{32}=+0.627579425\) \(a_{33}=+0.082476092\) \(a_{34}=+1.885454108\) \(a_{35}=-0.077904754\)
\(a_{36}=-1.304728625\) \(a_{37}=-0.164398989\) \(a_{38}=+2.142178994\) \(a_{39}=-0.001883052\) \(a_{40}=-0.606032254\)
\(a_{41}=+0.058232296\) \(a_{42}=+0.147566049\) \(a_{43}=-1.664868123\) \(a_{44}=+0.283533987\) \(a_{45}=-0.334681174\)
\(a_{46}=+0.149398891\) \(a_{47}=+0.313878082\) \(a_{48}=+0.215788247\) \(a_{49}=-0.971216655\) \(a_{50}=+1.318158716\)
\(a_{51}=-0.587772028\) \(a_{52}=-0.006473526\) \(a_{53}=-0.193092555\) \(a_{54}=+1.503740849\) \(a_{55}=+0.072730460\)
\(a_{56}=+0.223910417\) \(a_{57}=-0.667803540\) \(a_{58}=-2.025366971\) \(a_{59}=+1.052407882\) \(a_{60}=+0.428034215\)
\(a_{61}=+1.310682482\) \(a_{62}=+1.403018648\) \(a_{63}=+0.123654405\) \(a_{64}=-1.462689975\) \(a_{65}=-0.001660546\)
\(a_{66}=-0.137765023\) \(a_{67}=+0.817112972\) \(a_{68}=-2.020627645\) \(a_{69}=-0.046573647\) \(a_{70}=+0.130129293\)
\(a_{71}=-1.904114477\) \(a_{72}=+0.961926002\) \(a_{73}=-1.277112941\) \(a_{74}=+0.274606238\) \(a_{75}=-0.410923211\)
\(a_{76}=-2.295757951\) \(a_{77}=-0.026871635\) \(a_{78}=+0.003145391\) \(a_{79}=+1.795367509\) \(a_{80}=+0.190290153\)
\(a_{81}=+0.260074118\) \(a_{82}=-0.097269182\) \(a_{83}=+0.179064376\) \(a_{84}=-0.158145620\) \(a_{85}=-0.518319273\)
\(a_{86}=+2.780936683\) \(a_{87}=+0.631388490\) \(a_{88}=-0.209038718\) \(a_{89}=+1.453637095\) \(a_{90}=+0.559039545\)
\(a_{91}=+0.000613583\) \(a_{92}=-0.160109570\) \(a_{93}=-0.437377491\) \(a_{94}=-0.524290742\) \(a_{95}=-0.588894081\)
\(a_{96}=+0.326793075\) \(a_{97}=-0.080410059\) \(a_{98}=+1.622285781\) \(a_{99}=-0.115441545\) \(a_{100}=-1.412661237\)

Showing 100 of 2000 available coefficients

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