Properties

Level $38$
Weight $0$
Character 38.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 38 = 2 \cdot 19 \)
Weight: \( 0 \)
Character: 38.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.97899241306 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.948802152\) \(a_{4}=+0.500000000\) \(a_{5}=-0.263594465\)
\(a_{6}=-1.378011217\) \(a_{7}=-1.095217142\) \(a_{8}=-0.353553391\) \(a_{9}=+2.797829828\) \(a_{10}=+0.186389434\)
\(a_{11}=+0.245893706\) \(a_{12}=+0.974401076\) \(a_{13}=-0.463141470\) \(a_{14}=+0.774435468\) \(a_{15}=-0.513693461\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.174139873\) \(a_{18}=-1.978364444\) \(a_{19}=-0.229415734\) \(a_{20}=-0.131797233\)
\(a_{21}=-2.134361523\) \(a_{22}=-0.173873107\) \(a_{23}=+0.552261853\) \(a_{24}=-0.689005608\) \(a_{25}=-0.930517958\)
\(a_{26}=+0.327490474\) \(a_{27}=+3.503614638\) \(a_{28}=-0.547608571\) \(a_{29}=-0.269249464\) \(a_{30}=+0.363236130\)
\(a_{31}=-0.162349922\) \(a_{32}=-0.176776695\) \(a_{33}=+0.479198182\) \(a_{34}=-0.830242266\) \(a_{35}=+0.288693176\)
\(a_{36}=+1.398914914\) \(a_{37}=-0.171977725\) \(a_{38}=+0.162221422\) \(a_{39}=-0.902571095\) \(a_{40}=+0.093194717\)
\(a_{41}=-0.731248434\) \(a_{42}=+1.509221508\) \(a_{43}=-1.365673952\) \(a_{44}=+0.122946852\) \(a_{45}=-0.737492456\)
\(a_{46}=-0.390508102\) \(a_{47}=+0.545524986\) \(a_{48}=+0.487200543\) \(a_{49}=+0.199500587\) \(a_{50}=+0.657975558\)
\(a_{51}=+2.288166307\) \(a_{52}=-0.231570734\) \(a_{53}=+0.546520135\) \(a_{54}=-2.477429667\) \(a_{55}=-0.064816222\)
\(a_{56}=+0.387217738\) \(a_{57}=-0.447085892\) \(a_{58}=+0.190388130\) \(a_{59}=+0.009077191\) \(a_{60}=-0.256846731\)
\(a_{61}=-0.791354979\) \(a_{62}=+0.114798716\) \(a_{63}=-3.064231189\) \(a_{64}=+0.125000009\) \(a_{65}=+0.122081535\)
\(a_{66}=-0.338844289\) \(a_{67}=+1.814321795\) \(a_{68}=+0.587069950\) \(a_{69}=+1.076249083\) \(a_{70}=-0.204136880\)
\(a_{71}=-1.051430286\) \(a_{72}=-0.989182233\) \(a_{73}=+0.039206578\) \(a_{74}=+0.121606600\) \(a_{75}=-1.813395414\)
\(a_{76}=-0.114707860\) \(a_{77}=-0.269307019\) \(a_{78}=+0.638214238\) \(a_{79}=+1.473454785\) \(a_{80}=-0.065898685\)
\(a_{81}=+4.030021820\) \(a_{82}=+0.517070759\) \(a_{83}=+0.433802911\) \(a_{84}=-1.067180739\) \(a_{85}=-0.309496726\)
\(a_{86}=+0.965677304\) \(a_{87}=-0.524714004\) \(a_{88}=-0.086936516\) \(a_{89}=-1.040932044\) \(a_{90}=+0.521485989\)
\(a_{91}=+0.507240428\) \(a_{92}=+0.276130939\) \(a_{93}=-0.316387943\) \(a_{94}=-0.385744487\) \(a_{95}=+0.060472725\)
\(a_{96}=-0.344502798\) \(a_{97}=-0.513131619\) \(a_{98}=-0.141068146\) \(a_{99}=+0.687968785\) \(a_{100}=-0.465258947\)

Showing 100 of 2000 available coefficients

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