Properties

Level $991$
Weight $0$
Character 991.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 991 \)
Weight: \( 0 \)
Character: 991.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.9165186608 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.731802783\) \(a_{3}=+1.667372831\) \(a_{4}=+1.999138987\) \(a_{5}=-1.832271127\)
\(a_{6}=-2.887563113\) \(a_{7}=+1.139219781\) \(a_{8}=-1.730310953\) \(a_{9}=+1.780136488\) \(a_{10}=+3.173126868\)
\(a_{11}=-0.659995112\) \(a_{12}=+3.333313206\) \(a_{13}=+1.078246290\) \(a_{14}=-1.972901260\) \(a_{15}=-3.055076339\)
\(a_{16}=+0.997421938\) \(a_{17}=+1.215479649\) \(a_{18}=-3.082843169\) \(a_{19}=+1.299054930\) \(a_{20}=-3.662965149\)
\(a_{21}=+1.899505934\) \(a_{22}=+1.142984625\) \(a_{23}=+1.238530611\) \(a_{24}=-2.885080145\) \(a_{25}=+2.357209184\)
\(a_{26}=-1.867308024\) \(a_{27}=+1.300777648\) \(a_{28}=+2.277460765\) \(a_{29}=+0.014732914\) \(a_{30}=+5.290787520\)
\(a_{31}=+0.481608877\) \(a_{32}=+0.002977849\) \(a_{33}=-1.100457808\) \(a_{34}=-2.104968266\) \(a_{35}=-2.087356806\)
\(a_{36}=+3.558739017\) \(a_{37}=-1.828532946\) \(a_{38}=-2.249702658\) \(a_{39}=+1.797840376\) \(a_{40}=+3.170400734\)
\(a_{41}=-0.228309588\) \(a_{42}=-3.289568642\) \(a_{43}=-0.564465997\) \(a_{44}=-1.319423665\) \(a_{45}=-3.261683373\)
\(a_{46}=-2.144898618\) \(a_{47}=+0.931565897\) \(a_{48}=+1.663075976\) \(a_{49}=+0.297822164\) \(a_{50}=-4.082226404\)
\(a_{51}=+2.026656314\) \(a_{52}=+2.155566095\) \(a_{53}=-1.248139685\) \(a_{54}=-2.252686396\) \(a_{55}=+1.209289541\)
\(a_{56}=-1.971206529\) \(a_{57}=+2.166010686\) \(a_{58}=-0.025516856\) \(a_{59}=-0.732269823\) \(a_{60}=-6.107529065\)
\(a_{61}=+1.708997494\) \(a_{62}=-0.834055819\) \(a_{63}=+2.027964404\) \(a_{64}=-1.002576825\) \(a_{65}=-1.975636064\)
\(a_{66}=+1.905777392\) \(a_{67}=-1.301328652\) \(a_{68}=+2.429914620\) \(a_{69}=+2.065095260\) \(a_{70}=+3.614891555\)
\(a_{71}=+1.301425162\) \(a_{72}=-3.080193152\) \(a_{73}=-0.077140319\) \(a_{74}=+3.166650751\) \(a_{75}=+3.930346006\)
\(a_{76}=+2.596991879\) \(a_{77}=-0.751881383\) \(a_{78}=-3.113503044\) \(a_{79}=+0.220517155\) \(a_{80}=-1.827542390\)
\(a_{81}=+0.388745714\) \(a_{82}=+0.395381542\) \(a_{83}=-0.507723992\) \(a_{84}=+3.797378273\) \(a_{85}=-2.227083733\)
\(a_{86}=+0.977539843\) \(a_{87}=+0.024564100\) \(a_{88}=+1.142000970\) \(a_{89}=-1.014300544\) \(a_{90}=+5.648596320\)
\(a_{91}=+1.228360912\) \(a_{92}=+2.475998900\) \(a_{93}=+0.803022716\) \(a_{94}=-1.613296021\) \(a_{95}=-2.380215339\)
\(a_{96}=+0.004964495\) \(a_{97}=-0.605197191\) \(a_{98}=-0.515766794\) \(a_{99}=-1.174879841\) \(a_{100}=+4.712390163\)

Showing 100 of 2332 available coefficients

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