Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.3 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.d.3599.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.28967 | − | 2.28967i | −1.02397 | − | 1.02397i | −0.999706 | − | 0.0242660i | \(-0.992275\pi\) |
−0.0242660 | − | 0.999706i | \(-0.507725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.92329 | + | 3.92329i | −1.18292 | + | 1.18292i | −0.203932 | + | 0.978985i | \(0.565372\pi\) |
−0.978985 | + | 0.203932i | \(0.934628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38904 | + | 1.38904i | 0.385251 | + | 0.385251i | 0.872990 | − | 0.487739i | \(-0.162178\pi\) |
−0.487739 | + | 0.872990i | \(0.662178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.10467i | − | 0.995528i | −0.867312 | − | 0.497764i | \(-0.834154\pi\) | ||
0.867312 | − | 0.497764i | \(-0.165846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.60592 | + | 3.60592i | −0.827255 | + | 0.827255i | −0.987136 | − | 0.159881i | \(-0.948889\pi\) |
0.159881 | + | 0.987136i | \(0.448889\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.68375i | − | 0.559600i | −0.960058 | − | 0.279800i | \(-0.909732\pi\) | ||
0.960058 | − | 0.279800i | \(-0.0902681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.48518i | 1.09704i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.10020 | − | 6.10020i | 1.13278 | − | 1.13278i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
0.989713 | − | 0.143065i | \(-0.0456957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.45644i | 0.980006i | 0.871721 | + | 0.490003i | \(0.163004\pi\) | ||||
−0.871721 | + | 0.490003i | \(0.836996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.28967 | − | 2.28967i | −0.387025 | − | 0.387025i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.04656 | + | 4.04656i | −0.665250 | + | 0.665250i | −0.956613 | − | 0.291362i | \(-0.905891\pi\) |
0.291362 | + | 0.956613i | \(0.405891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.75676 | 1.21140 | 0.605701 | − | 0.795692i | \(-0.292893\pi\) | ||||
0.605701 | + | 0.795692i | \(0.292893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0577035 | − | 0.0577035i | −0.00879970 | − | 0.00879970i | 0.702693 | − | 0.711493i | \(-0.251981\pi\) |
−0.711493 | + | 0.702693i | \(0.751981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.70367 | 0.248506 | 0.124253 | − | 0.992251i | \(-0.460347\pi\) | ||||
0.124253 | + | 0.992251i | \(0.460347\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.517297 | + | 0.517297i | 0.0710562 | + | 0.0710562i | 0.741742 | − | 0.670686i | \(-0.234000\pi\) |
−0.670686 | + | 0.741742i | \(0.734000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.9661 | 2.42255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.10709 | + | 7.10709i | −0.925265 | + | 0.925265i | −0.997395 | − | 0.0721304i | \(-0.977020\pi\) |
0.0721304 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19652 | + | 2.19652i | 0.281236 | + | 0.281236i | 0.833602 | − | 0.552366i | \(-0.186275\pi\) |
−0.552366 | + | 0.833602i | \(0.686275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.36089i | − | 0.788972i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.98139 | − | 6.98139i | 0.852913 | − | 0.852913i | −0.137578 | − | 0.990491i | \(-0.543932\pi\) |
0.990491 | + | 0.137578i | \(0.0439318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.356496i | − | 0.0423082i | −0.999776 | − | 0.0211541i | \(-0.993266\pi\) | ||
0.999776 | − | 0.0211541i | \(-0.00673407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.05490i | − | 0.825713i | −0.910796 | − | 0.412857i | \(-0.864531\pi\) | ||
0.910796 | − | 0.412857i | \(-0.135469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.92329 | + | 3.92329i | −0.447101 | + | 0.447101i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.163773i | 0.0184259i | 0.999958 | + | 0.00921297i | \(0.00293262\pi\) | ||||
−0.999958 | + | 0.00921297i | \(0.997067\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.33131 | + | 7.33131i | 0.804716 | + | 0.804716i | 0.983829 | − | 0.179112i | \(-0.0573226\pi\) |
−0.179112 | + | 0.983829i | \(0.557323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.39834 | + | 9.39834i | −1.01939 | + | 1.01939i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1465 | −1.71153 | −0.855764 | − | 0.517367i | \(-0.826912\pi\) | ||||
−0.855764 | + | 0.517367i | \(0.826912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.38904 | + | 1.38904i | 0.145611 | + | 0.145611i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.5127 | 1.69417 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.56055 | 0.869192 | 0.434596 | − | 0.900626i | \(-0.356891\pi\) | ||||
0.434596 | + | 0.900626i | \(0.356891\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.02014 | − | 1.02014i | −0.101507 | − | 0.101507i | 0.654529 | − | 0.756037i | \(-0.272867\pi\) |
−0.756037 | + | 0.654529i | \(0.772867\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.7494 | 1.74890 | 0.874451 | − | 0.485113i | \(-0.161222\pi\) | ||||
0.874451 | + | 0.485113i | \(0.161222\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0872 | − | 12.0872i | 1.16851 | − | 1.16851i | 0.185951 | − | 0.982559i | \(-0.440464\pi\) |
0.982559 | − | 0.185951i | \(-0.0595365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8663 | + | 13.8663i | 1.32815 | + | 1.32815i | 0.906986 | + | 0.421160i | \(0.138377\pi\) |
0.421160 | + | 0.906986i | \(0.361623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.0746i | − | 1.41810i | −0.705158 | − | 0.709050i | \(-0.749124\pi\) | ||
0.705158 | − | 0.709050i | \(-0.250876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.14490 | + | 6.14490i | −0.573014 | + | 0.573014i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.10467i | − | 0.376274i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.7845i | − | 1.79859i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.11090 | − | 1.11090i | 0.0993617 | − | 0.0993617i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.9384i | − | 1.41430i | −0.707063 | − | 0.707151i | \(-0.749980\pi\) | ||
0.707063 | − | 0.707151i | \(-0.250020\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.98295 | + | 1.98295i | 0.173251 | + | 0.173251i | 0.788406 | − | 0.615155i | \(-0.210907\pi\) |
−0.615155 | + | 0.788406i | \(0.710907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.60592 | + | 3.60592i | −0.312673 | + | 0.312673i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.97010 | 0.424624 | 0.212312 | − | 0.977202i | \(-0.431901\pi\) | ||||
0.212312 | + | 0.977202i | \(0.431901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.20608 | − | 6.20608i | −0.526393 | − | 0.526393i | 0.393102 | − | 0.919495i | \(-0.371402\pi\) |
−0.919495 | + | 0.393102i | \(0.871402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.8992 | −0.911440 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.9349 | −2.31987 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6879 | + | 10.6879i | 0.875585 | + | 0.875585i | 0.993074 | − | 0.117489i | \(-0.0374846\pi\) |
−0.117489 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12562 | −0.417117 | −0.208559 | − | 0.978010i | \(-0.566877\pi\) | ||||
−0.208559 | + | 0.978010i | \(0.566877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4935 | − | 12.4935i | 1.00350 | − | 1.00350i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.50142 | + | 8.50142i | 0.678487 | + | 0.678487i | 0.959658 | − | 0.281170i | \(-0.0907226\pi\) |
−0.281170 | + | 0.959658i | \(0.590723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.68375i | − | 0.211509i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.05470 | − | 1.05470i | 0.0826108 | − | 0.0826108i | −0.664594 | − | 0.747205i | \(-0.731395\pi\) |
0.747205 | + | 0.664594i | \(0.231395\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.59381i | 0.432862i | 0.976298 | + | 0.216431i | \(0.0694417\pi\) | ||||
−0.976298 | + | 0.216431i | \(0.930558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.14113i | − | 0.703164i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4457 | − | 14.4457i | 1.09829 | − | 1.09829i | 0.103678 | − | 0.994611i | \(-0.466939\pi\) |
0.994611 | − | 0.103678i | \(-0.0330611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.48518i | 0.414640i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8918 | − | 18.8918i | −1.41204 | − | 1.41204i | −0.745197 | − | 0.666845i | \(-0.767644\pi\) |
−0.666845 | − | 0.745197i | \(-0.732356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.04746 | − | 6.04746i | 0.449504 | − | 0.449504i | −0.445686 | − | 0.895190i | \(-0.647040\pi\) |
0.895190 | + | 0.445686i | \(0.147040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.5306 | 1.36239 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1038 | + | 16.1038i | 1.17763 | + | 1.17763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.1862 | 1.53298 | 0.766490 | − | 0.642256i | \(-0.222001\pi\) | ||||
0.766490 | + | 0.642256i | \(0.222001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.51759 | 0.181220 | 0.0906100 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906100 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.3329 | − | 15.3329i | −1.09242 | − | 1.09242i | −0.995269 | − | 0.0971552i | \(-0.969026\pi\) |
−0.0971552 | − | 0.995269i | \(-0.530974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9712 | 0.919505 | 0.459752 | − | 0.888047i | \(-0.347938\pi\) | ||||
0.459752 | + | 0.888047i | \(0.347938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.10020 | − | 6.10020i | 0.428150 | − | 0.428150i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.7604 | − | 17.7604i | −1.24044 | − | 1.24044i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 28.2942i | − | 1.95715i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.79983 | + | 9.79983i | −0.674648 | + | 0.674648i | −0.958784 | − | 0.284136i | \(-0.908293\pi\) |
0.284136 | + | 0.958784i | \(0.408293\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.264244i | 0.0180213i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.45644i | 0.370407i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70155 | − | 5.70155i | 0.383528 | − | 0.383528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.2225i | − | 1.15330i | −0.816991 | − | 0.576651i | \(-0.804359\pi\) | ||
0.816991 | − | 0.576651i | \(-0.195641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.18661 | − | 7.18661i | −0.476992 | − | 0.476992i | 0.427176 | − | 0.904168i | \(-0.359508\pi\) |
−0.904168 | + | 0.427176i | \(0.859508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.85424 | + | 4.85424i | −0.320778 | + | 0.320778i | −0.849065 | − | 0.528288i | \(-0.822834\pi\) |
0.528288 | + | 0.849065i | \(0.322834\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1752 | 0.994163 | 0.497081 | − | 0.867704i | \(-0.334405\pi\) | ||||
0.497081 | + | 0.867704i | \(0.334405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.90085 | − | 3.90085i | −0.254463 | − | 0.254463i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.48591 | 0.290169 | 0.145085 | − | 0.989419i | \(-0.453655\pi\) | ||||
0.145085 | + | 0.989419i | \(0.453655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2916 | 0.985018 | 0.492509 | − | 0.870307i | \(-0.336080\pi\) | ||||
0.492509 | + | 0.870307i | \(0.336080\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.28967 | − | 2.28967i | −0.146282 | − | 0.146282i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0175 | −0.637401 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8987 | − | 21.8987i | 1.38223 | − | 1.38223i | 0.541588 | − | 0.840644i | \(-0.317823\pi\) |
0.840644 | − | 0.541588i | \(-0.182177\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5291 | + | 10.5291i | 0.661960 | + | 0.661960i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.1240i | 1.94146i | 0.240165 | + | 0.970732i | \(0.422798\pi\) | ||||
−0.240165 | + | 0.970732i | \(0.577202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.04656 | + | 4.04656i | −0.251441 | + | 0.251441i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.83612i | 0.606521i | 0.952908 | + | 0.303261i | \(0.0980753\pi\) | ||||
−0.952908 | + | 0.303261i | \(0.901925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.36888i | − | 0.145519i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.7767 | + | 22.7767i | −1.38872 | + | 1.38872i | −0.560701 | + | 0.828018i | \(0.689468\pi\) |
−0.828018 | + | 0.560701i | \(0.810532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.28014i | 0.381492i | 0.981639 | + | 0.190746i | \(0.0610906\pi\) | ||||
−0.981639 | + | 0.190746i | \(0.938909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.5200 | − | 21.5200i | −1.29770 | − | 1.29770i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4973 | − | 14.4973i | 0.871058 | − | 0.871058i | −0.121530 | − | 0.992588i | \(-0.538780\pi\) |
0.992588 | + | 0.121530i | \(0.0387801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.0904 | 1.37746 | 0.688728 | − | 0.725020i | \(-0.258170\pi\) | ||||
0.688728 | + | 0.725020i | \(0.258170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.37723 | − | 4.37723i | −0.260199 | − | 0.260199i | 0.564936 | − | 0.825135i | \(-0.308901\pi\) |
−0.825135 | + | 0.564936i | \(0.808901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.75676 | 0.457867 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.151693 | 0.00892312 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.34166 | + | 3.34166i | 0.195222 | + | 0.195222i | 0.797948 | − | 0.602726i | \(-0.205919\pi\) |
−0.602726 | + | 0.797948i | \(0.705919\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.5458 | 1.89489 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.72784 | − | 3.72784i | 0.215586 | − | 0.215586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0577035 | − | 0.0577035i | −0.00332597 | − | 0.00332597i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 10.0586i | − | 0.575955i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.119162 | − | 0.119162i | 0.00680096 | − | 0.00680096i | −0.703698 | − | 0.710499i | \(-0.748469\pi\) |
0.710499 | + | 0.703698i | \(0.248469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6414i | 1.05706i | 0.848915 | + | 0.528529i | \(0.177256\pi\) | ||||
−0.848915 | + | 0.528529i | \(0.822744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.35618i | − | 0.0766556i | −0.999265 | − | 0.0383278i | \(-0.987797\pi\) | ||
0.999265 | − | 0.0383278i | \(-0.0122031\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2596 | + | 12.2596i | −0.688566 | + | 0.688566i | −0.961915 | − | 0.273349i | \(-0.911869\pi\) |
0.273349 | + | 0.961915i | \(0.411869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.8657i | 2.67997i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.8011 | + | 14.8011i | 0.823556 | + | 0.823556i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.61914 | + | 7.61914i | −0.422634 | + | 0.422634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.70367 | 0.0939265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1478 | − | 11.1478i | −0.612741 | − | 0.612741i | 0.330918 | − | 0.943659i | \(-0.392642\pi\) |
−0.943659 | + | 0.330918i | \(0.892642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.9702 | −1.74672 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.47574 | 0.0803886 | 0.0401943 | − | 0.999192i | \(-0.487202\pi\) | ||||
0.0401943 | + | 0.999192i | \(0.487202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.4072 | − | 21.4072i | −1.15927 | − | 1.15927i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.38522 | − | 6.38522i | 0.342776 | − | 0.342776i | −0.514634 | − | 0.857410i | \(-0.672072\pi\) |
0.857410 | + | 0.514634i | \(0.172072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1578 | + | 17.1578i | 0.918435 | + | 0.918435i | 0.996916 | − | 0.0784806i | \(-0.0250069\pi\) |
−0.0784806 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.07308i | 0.270013i | 0.990845 | + | 0.135007i | \(0.0431055\pi\) | ||||
−0.990845 | + | 0.135007i | \(0.956894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.816257 | + | 0.816257i | −0.0433224 | + | 0.0433224i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.13760i | 0.0600402i | 0.999549 | + | 0.0300201i | \(0.00955712\pi\) | ||||
−0.999549 | + | 0.0300201i | \(0.990443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 7.00533i | − | 0.368701i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.1534 | + | 16.1534i | −0.845507 | + | 0.845507i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.78975i | − | 0.145624i | −0.997346 | − | 0.0728119i | \(-0.976803\pi\) | ||
0.997346 | − | 0.0728119i | \(-0.0231973\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.517297 | + | 0.517297i | 0.0268567 | + | 0.0268567i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7939 | − | 20.7939i | 1.07667 | − | 1.07667i | 0.0798639 | − | 0.996806i | \(-0.474551\pi\) |
0.996806 | − | 0.0798639i | \(-0.0254486\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9469 | 0.872807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7712 | + | 23.7712i | 1.22105 | + | 1.22105i | 0.967261 | + | 0.253785i | \(0.0816756\pi\) |
0.253785 | + | 0.967261i | \(0.418324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.74341 | −0.395670 | −0.197835 | − | 0.980235i | \(-0.563391\pi\) | ||||
−0.197835 | + | 0.980235i | \(0.563391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9661 | 0.915637 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.2477 | − | 14.2477i | −0.722385 | − | 0.722385i | 0.246705 | − | 0.969091i | \(-0.420652\pi\) |
−0.969091 | + | 0.246705i | \(0.920652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0159 | −0.557098 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.374987 | − | 0.374987i | 0.0188676 | − | 0.0188676i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6073 | + | 21.6073i | 1.08444 | + | 1.08444i | 0.996089 | + | 0.0883525i | \(0.0281602\pi\) |
0.0883525 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.1405i | 1.60502i | 0.596638 | + | 0.802510i | \(0.296503\pi\) | ||||
−0.596638 | + | 0.802510i | \(0.703497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.57922 | + | 7.57922i | −0.377548 | + | 0.377548i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 31.7517i | − | 1.57387i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.4416i | 1.25801i | 0.777402 | + | 0.629004i | \(0.216537\pi\) | ||||
−0.777402 | + | 0.629004i | \(0.783463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.10709 | + | 7.10709i | −0.349717 | + | 0.349717i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 33.5726i | − | 1.64801i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.68536 | + | 5.68536i | 0.277748 | + | 0.277748i | 0.832209 | − | 0.554461i | \(-0.187076\pi\) |
−0.554461 | + | 0.832209i | \(0.687076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.82028 | − | 1.82028i | 0.0887151 | − | 0.0887151i | −0.661357 | − | 0.750072i | \(-0.730019\pi\) |
0.750072 | + | 0.661357i | \(0.230019\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.5148 | 1.09213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19652 | + | 2.19652i | 0.106297 | + | 0.106297i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7699 | 0.807779 | 0.403889 | − | 0.914808i | \(-0.367658\pi\) | ||||
0.403889 | + | 0.914808i | \(0.367658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.6891 | −1.37871 | −0.689355 | − | 0.724424i | \(-0.742106\pi\) | ||||
−0.689355 | + | 0.724424i | \(0.742106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.67738 | + | 9.67738i | 0.462932 | + | 0.462932i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4747 | 1.21584 | 0.607920 | − | 0.793998i | \(-0.292004\pi\) | ||||
0.607920 | + | 0.793998i | \(0.292004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0293 | + | 11.0293i | −0.524020 | + | 0.524020i | −0.918783 | − | 0.394763i | \(-0.870827\pi\) |
0.394763 | + | 0.918783i | \(0.370827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.9702 | + | 36.9702i | 1.75256 | + | 1.75256i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9697i | 1.22558i | 0.790244 | + | 0.612792i | \(0.209954\pi\) | ||||
−0.790244 | + | 0.612792i | \(0.790046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.4320 | + | 30.4320i | −1.43299 | + | 1.43299i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.36089i | − | 0.298203i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.9383i | − | 1.02623i | −0.858320 | − | 0.513115i | \(-0.828492\pi\) | ||
0.858320 | − | 0.513115i | \(-0.171508\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.54081 | − | 5.54081i | 0.258061 | − | 0.258061i | −0.566204 | − | 0.824265i | \(-0.691589\pi\) |
0.824265 | + | 0.566204i | \(0.191589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.14263i | − | 0.146050i | −0.997330 | − | 0.0730252i | \(-0.976735\pi\) | ||
0.997330 | − | 0.0730252i | \(-0.0232653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0517 | − | 11.0517i | −0.511411 | − | 0.511411i | 0.403548 | − | 0.914959i | \(-0.367777\pi\) |
−0.914959 | + | 0.403548i | \(0.867777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.98139 | − | 6.98139i | 0.322371 | − | 0.322371i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.452775 | 0.0208186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.7791 | − | 19.7791i | −0.907528 | − | 0.907528i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.5140 | −1.34853 | −0.674264 | − | 0.738490i | \(-0.735539\pi\) | ||||
−0.674264 | + | 0.738490i | \(0.735539\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.2417 | −0.512576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.6008 | − | 19.6008i | −0.890028 | − | 0.890028i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.24906 | −0.419115 | −0.209557 | − | 0.977796i | \(-0.567202\pi\) | ||||
−0.209557 | + | 0.977796i | \(0.567202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.07931 | + | 1.07931i | −0.0487085 | + | 0.0487085i | −0.731042 | − | 0.682333i | \(-0.760965\pi\) |
0.682333 | + | 0.731042i | \(0.260965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.0393 | − | 25.0393i | −1.12771 | − | 1.12771i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.356496i | − | 0.0159910i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5136 | + | 20.5136i | −0.918314 | + | 0.918314i | −0.996907 | − | 0.0785932i | \(-0.974957\pi\) |
0.0785932 | + | 0.996907i | \(0.474957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.4273i | 0.598694i | 0.954144 | + | 0.299347i | \(0.0967689\pi\) | ||||
−0.954144 | + | 0.299347i | \(0.903231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67155i | 0.207881i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.73152 | + | 4.73152i | −0.209721 | + | 0.209721i | −0.804149 | − | 0.594428i | \(-0.797379\pi\) |
0.594428 | + | 0.804149i | \(0.297379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.05490i | − | 0.312090i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.6403 | − | 40.6403i | −1.79083 | − | 1.79083i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.68401 | + | 6.68401i | −0.293962 | + | 0.293962i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7681 | −1.17273 | −0.586365 | − | 0.810047i | \(-0.699442\pi\) | ||||
−0.586365 | + | 0.810047i | \(0.699442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3476 | − | 11.3476i | −0.496194 | − | 0.496194i | 0.414057 | − | 0.910251i | \(-0.364112\pi\) |
−0.910251 | + | 0.414057i | \(0.864112\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.3969 | 0.975624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7975 | 0.686848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7745 | + | 10.7745i | 0.466694 | + | 0.466694i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.3512 | −2.39304 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.92329 | + | 3.92329i | −0.168988 | + | 0.168988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3649 | + | 23.3649i | 1.00454 | + | 1.00454i | 0.999990 | + | 0.00454629i | \(0.00144714\pi\) |
0.00454629 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 63.4983i | − | 2.71997i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0340 | − | 15.0340i | 0.642807 | − | 0.642807i | −0.308438 | − | 0.951245i | \(-0.599806\pi\) |
0.951245 | + | 0.308438i | \(0.0998061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.9937i | 1.87419i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.163773i | 0.00696435i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.5441 | − | 28.5441i | 1.20945 | − | 1.20945i | 0.238246 | − | 0.971205i | \(-0.423427\pi\) |
0.971205 | − | 0.238246i | \(-0.0765726\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.160305i | − | 0.00678018i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.1713 | + | 12.1713i | 0.512959 | + | 0.512959i | 0.915432 | − | 0.402473i | \(-0.131849\pi\) |
−0.402473 | + | 0.915432i | \(0.631849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5159 | + | 34.5159i | −1.45209 | + | 1.45209i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.31985 | −0.0553309 | −0.0276654 | − | 0.999617i | \(-0.508807\pi\) | ||||
−0.0276654 | + | 0.999617i | \(0.508807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4342 | − | 20.4342i | −0.855143 | − | 0.855143i | 0.135618 | − | 0.990761i | \(-0.456698\pi\) |
−0.990761 | + | 0.135618i | \(0.956698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.7208 | 0.613901 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0034 | −0.458076 | −0.229038 | − | 0.973417i | \(-0.573558\pi\) | ||||
−0.229038 | + | 0.973417i | \(0.573558\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.33131 | + | 7.33131i | 0.304154 | + | 0.304154i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.05902 | −0.168107 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6048 | + | 11.6048i | −0.478983 | + | 0.478983i | −0.904806 | − | 0.425824i | \(-0.859984\pi\) |
0.425824 | + | 0.904806i | \(0.359984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.6755 | − | 19.6755i | −0.810715 | − | 0.810715i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 29.8971i | − | 1.22773i | −0.789412 | − | 0.613863i | \(-0.789615\pi\) | ||
0.789412 | − | 0.613863i | \(-0.210385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.39834 | + | 9.39834i | −0.385294 | + | 0.385294i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.3069i | 0.707142i | 0.935408 | + | 0.353571i | \(0.115033\pi\) | ||||
−0.935408 | + | 0.353571i | \(0.884967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4350i | 0.833561i | 0.909007 | + | 0.416781i | \(0.136842\pi\) | ||||
−0.909007 | + | 0.416781i | \(0.863158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45.2999 | + | 45.2999i | −1.84170 | + | 1.84170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.2358i | − | 1.06488i | −0.846468 | − | 0.532440i | \(-0.821275\pi\) | ||
0.846468 | − | 0.532440i | \(-0.178725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.36647 | + | 2.36647i | 0.0957372 | + | 0.0957372i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.40107 | + | 2.40107i | −0.0969784 | + | 0.0969784i | −0.753931 | − | 0.656953i | \(-0.771845\pi\) |
0.656953 | + | 0.753931i | \(0.271845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.65661 | −0.267985 | −0.133992 | − | 0.990982i | \(-0.542780\pi\) | ||||
−0.133992 | + | 0.990982i | \(0.542780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.6833 | − | 18.6833i | −0.750946 | − | 0.750946i | 0.223710 | − | 0.974656i | \(-0.428183\pi\) |
−0.974656 | + | 0.223710i | \(0.928183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1465 | −0.646897 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.3387 | 0.893549 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.6098 | + | 16.6098i | 0.662276 | + | 0.662276i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4855 | 0.616468 | 0.308234 | − | 0.951311i | \(-0.400262\pi\) | ||||
0.308234 | + | 0.951311i | \(0.400262\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.4936 | + | 36.4936i | −1.44820 | + | 1.44820i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.38904 | + | 1.38904i | 0.0550358 | + | 0.0550358i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.4867i | 1.91511i | 0.288248 | + | 0.957556i | \(0.406927\pi\) | ||||
−0.288248 | + | 0.957556i | \(0.593073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.0610 | + | 35.0610i | −1.38267 | + | 1.38267i | −0.542829 | + | 0.839843i | \(0.682647\pi\) |
−0.839843 | + | 0.542829i | \(0.817353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4142i | 0.684625i | 0.939586 | + | 0.342312i | \(0.111210\pi\) | ||||
−0.939586 | + | 0.342312i | \(0.888790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 55.7664i | − | 2.18902i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.53254 | + | 3.53254i | −0.138239 | + | 0.138239i | −0.772840 | − | 0.634601i | \(-0.781164\pi\) |
0.634601 | + | 0.772840i | \(0.281164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.08060i | − | 0.354809i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8364 | − | 11.8364i | −0.461080 | − | 0.461080i | 0.437929 | − | 0.899010i | \(-0.355712\pi\) |
−0.899010 | + | 0.437929i | \(0.855712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.27298 | − | 5.27298i | 0.205095 | − | 0.205095i | −0.597084 | − | 0.802179i | \(-0.703674\pi\) |
0.802179 | + | 0.597084i | \(0.203674\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.5127 | 0.640336 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.3714 | − | 16.3714i | −0.633903 | − | 0.633903i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.2352 | −0.665357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3408 | 0.437154 | 0.218577 | − | 0.975820i | \(-0.429858\pi\) | ||||
0.218577 | + | 0.975820i | \(0.429858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.5290 | − | 10.5290i | −0.404664 | − | 0.404664i | 0.475209 | − | 0.879873i | \(-0.342372\pi\) |
−0.879873 | + | 0.475209i | \(0.842372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.56055 | 0.328524 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.4933 | − | 33.4933i | 1.28159 | − | 1.28159i | 0.341821 | − | 0.939765i | \(-0.388956\pi\) |
0.939765 | − | 0.341821i | \(-0.111044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3799 | − | 11.3799i | −0.434803 | − | 0.434803i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.43709i | 0.0547489i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1173 | − | 34.1173i | 1.29788 | − | 1.29788i | 0.368094 | − | 0.929789i | \(-0.380010\pi\) |
0.929789 | − | 0.368094i | \(-0.119990\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.4197i | 1.07802i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 31.8389i | − | 1.20599i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.5268 | − | 18.5268i | 0.699746 | − | 0.699746i | −0.264610 | − | 0.964356i | \(-0.585243\pi\) |
0.964356 | + | 0.264610i | \(0.0852431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 29.1831i | − | 1.10066i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.02014 | − | 1.02014i | −0.0383662 | − | 0.0383662i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.9116 | + | 13.9116i | −0.522462 | + | 0.522462i | −0.918314 | − | 0.395852i | \(-0.870449\pi\) |
0.395852 | + | 0.918314i | \(0.370449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6437 | 0.548411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.9556 | + | 24.9556i | 0.933288 | + | 0.933288i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.8916 | 1.11477 | 0.557384 | − | 0.830255i | \(-0.311805\pi\) | ||||
0.557384 | + | 0.830255i | \(0.311805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.7494 | 0.661023 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.4607 | + | 33.4607i | 1.24270 | + | 1.24270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.42362 | 0.349503 | 0.174751 | − | 0.984613i | \(-0.444088\pi\) | ||||
0.174751 | + | 0.984613i | \(0.444088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.236854 | + | 0.236854i | −0.00876035 | + | 0.00876035i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.8531 | − | 31.8531i | −1.17652 | − | 1.17652i | −0.980624 | − | 0.195897i | \(-0.937238\pi\) |
−0.195897 | − | 0.980624i | \(-0.562762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.7801i | 2.01785i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.55441 | − | 1.55441i | 0.0571797 | − | 0.0571797i | −0.677939 | − | 0.735118i | \(-0.737127\pi\) |
0.735118 | + | 0.677939i | \(0.237127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.57392i | 0.204487i | 0.994759 | + | 0.102244i | \(0.0326021\pi\) | ||||
−0.994759 | + | 0.102244i | \(0.967398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 48.9434i | − | 1.79315i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0872 | − | 12.0872i | 0.441655 | − | 0.441655i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0891i | 0.806043i | 0.915190 | + | 0.403022i | \(0.132040\pi\) | ||||
−0.915190 | + | 0.403022i | \(0.867960\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.7360 | + | 11.7360i | 0.427116 | + | 0.427116i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9027 | + | 11.9027i | −0.432612 | + | 0.432612i | −0.889516 | − | 0.456904i | \(-0.848958\pi\) |
0.456904 | + | 0.889516i | \(0.348958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6151 | −0.964798 | −0.482399 | − | 0.875952i | \(-0.660234\pi\) | ||||
−0.482399 | + | 0.875952i | \(0.660234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8663 | + | 13.8663i | 0.501992 | + | 0.501992i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.7441 | −0.712918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.30839 | −0.227486 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5947 | + | 22.5947i | 0.812676 | + | 0.812676i | 0.985034 | − | 0.172359i | \(-0.0551388\pi\) |
−0.172359 | + | 0.985034i | \(0.555139\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.9296 | −1.07510 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.9703 | + | 27.9703i | −1.00214 | + | 1.00214i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.39864 | + | 1.39864i | 0.0500472 | + | 0.0500472i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 38.9309i | − | 1.38950i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1599 | − | 15.1599i | 0.540393 | − | 0.540393i | −0.383251 | − | 0.923644i | \(-0.625196\pi\) |
0.923644 | + | 0.383251i | \(0.125196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 15.0746i | − | 0.535991i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.10212i | 0.216692i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.154906 | − | 0.154906i | 0.00548705 | − | 0.00548705i | −0.704358 | − | 0.709845i | \(-0.748765\pi\) |
0.709845 | + | 0.704358i | \(0.248765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.99301i | − | 0.247395i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.6784 | + | 27.6784i | 0.976751 | + | 0.976751i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.14490 | + | 6.14490i | −0.216579 | + | 0.216579i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.6800 | −0.727071 | −0.363536 | − | 0.931580i | \(-0.618430\pi\) | ||||
−0.363536 | + | 0.931580i | \(0.618430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.15298 | + | 8.15298i | 0.286290 | + | 0.286290i | 0.835611 | − | 0.549321i | \(-0.185114\pi\) |
−0.549321 | + | 0.835611i | \(0.685114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.82985 | −0.169182 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.416148 | 0.0145592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.36475 | + | 7.36475i | 0.257031 | + | 0.257031i | 0.823846 | − | 0.566814i | \(-0.191824\pi\) |
−0.566814 | + | 0.823846i | \(0.691824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.9745 | 1.14942 | 0.574710 | − | 0.818357i | \(-0.305115\pi\) | ||||
0.574710 | + | 0.818357i | \(0.305115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.7733 | − | 10.7733i | 0.374623 | − | 0.374623i | −0.494535 | − | 0.869158i | \(-0.664661\pi\) |
0.869158 | + | 0.494535i | \(0.164661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.50209 | + | 2.50209i | 0.0869011 | + | 0.0869011i | 0.749221 | − | 0.662320i | \(-0.230428\pi\) |
−0.662320 | + | 0.749221i | \(0.730428\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.10467i | − | 0.142218i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.8080 | − | 12.8080i | 0.443239 | − | 0.443239i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40.5205i | − | 1.39892i | −0.714671 | − | 0.699461i | \(-0.753423\pi\) | ||
0.714671 | − | 0.699461i | \(-0.246577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 45.4248i | − | 1.56637i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.9302 | + | 20.9302i | −0.720020 | + | 0.720020i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.7845i | − | 0.679802i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8599 | + | 10.8599i | 0.372274 | + | 0.372274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2785 | − | 20.2785i | 0.694323 | − | 0.694323i | −0.268857 | − | 0.963180i | \(-0.586646\pi\) |
0.963180 | + | 0.268857i | \(0.0866460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.6034 | −1.28451 | −0.642253 | − | 0.766492i | \(-0.722000\pi\) | ||||
−0.642253 | + | 0.766492i | \(0.722000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7814 | + | 10.7814i | 0.367856 | + | 0.367856i | 0.866695 | − | 0.498839i | \(-0.166240\pi\) |
−0.498839 | + | 0.866695i | \(0.666240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.09947 | 0.0374264 | 0.0187132 | − | 0.999825i | \(-0.494043\pi\) | ||||
0.0187132 | + | 0.999825i | \(0.494043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.1519 | −2.24923 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.642531 | − | 0.642531i | −0.0217964 | − | 0.0217964i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3949 | 0.657171 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.11090 | − | 1.11090i | 0.0375552 | − | 0.0375552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.46654 | − | 2.46654i | −0.0832892 | − | 0.0832892i | 0.664235 | − | 0.747524i | \(-0.268758\pi\) |
−0.747524 | + | 0.664235i | \(0.768758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.16526i | − | 0.106640i | −0.998577 | − | 0.0533201i | \(-0.983020\pi\) | ||
0.998577 | − | 0.0533201i | \(-0.0169804\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.5299 | + | 24.5299i | −0.825498 | + | 0.825498i | −0.986890 | − | 0.161392i | \(-0.948402\pi\) |
0.161392 | + | 0.986890i | \(0.448402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.9642i | 0.972521i | 0.873814 | + | 0.486260i | \(0.161639\pi\) | ||||
−0.873814 | + | 0.486260i | \(0.838361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.9384i | − | 0.534556i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.14331 | + | 6.14331i | −0.205578 | + | 0.205578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 86.5121i | 2.89178i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.2854 | + | 33.2854i | 1.11013 | + | 1.11013i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.12333 | − | 2.12333i | 0.0707385 | − | 0.0707385i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.6934 | −0.920558 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.1593 | − | 32.1593i | −1.06783 | − | 1.06783i | −0.997525 | − | 0.0703065i | \(-0.977602\pi\) |
−0.0703065 | − | 0.997525i | \(-0.522398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.3226 | 0.838974 | 0.419487 | − | 0.907761i | \(-0.362210\pi\) | ||||
0.419487 | + | 0.907761i | \(0.362210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57.5258 | −1.90383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.98295 | + | 1.98295i | 0.0654828 | + | 0.0654828i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.44624 | −0.0477071 | −0.0238535 | − | 0.999715i | \(-0.507594\pi\) | ||||
−0.0238535 | + | 0.999715i | \(0.507594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.495187 | − | 0.495187i | 0.0162993 | − | 0.0162993i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.1961 | − | 22.1961i | −0.729803 | − | 0.729803i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.88117i | 0.324191i | 0.986775 | + | 0.162095i | \(0.0518252\pi\) | ||||
−0.986775 | + | 0.162095i | \(0.948175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.60592 | + | 3.60592i | −0.118179 | + | 0.118179i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 73.7449i | − | 2.41171i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.0952i | 0.525807i | 0.964822 | + | 0.262904i | \(0.0846801\pi\) | ||||
−0.964822 | + | 0.262904i | \(0.915320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7553 | + | 15.7553i | −0.513608 | + | 0.513608i | −0.915630 | − | 0.402022i | \(-0.868307\pi\) |
0.402022 | + | 0.915630i | \(0.368307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20.8172i | − | 0.677901i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.07070 | + | 9.07070i | 0.294758 | + | 0.294758i | 0.838957 | − | 0.544198i | \(-0.183166\pi\) |
−0.544198 | + | 0.838957i | \(0.683166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.79954 | − | 9.79954i | 0.318107 | − | 0.318107i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.94742 | −0.257442 | −0.128721 | − | 0.991681i | \(-0.541087\pi\) | ||||
−0.128721 | + | 0.991681i | \(0.541087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.5094 | − | 48.5094i | −1.56973 | − | 1.56973i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.97010 | 0.160493 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.22724 | 0.0395883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.76445 | − | 5.76445i | −0.185564 | − | 0.185564i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3273 | 0.525051 | 0.262525 | − | 0.964925i | \(-0.415445\pi\) | ||||
0.262525 | + | 0.964925i | \(0.415445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.6065 | + | 18.6065i | −0.597111 | + | 0.597111i | −0.939543 | − | 0.342432i | \(-0.888749\pi\) |
0.342432 | + | 0.939543i | \(0.388749\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.20608 | − | 6.20608i | −0.198958 | − | 0.198958i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.8881i | − | 0.668271i | −0.942525 | − | 0.334135i | \(-0.891556\pi\) | ||
0.942525 | − | 0.334135i | \(-0.108444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.3475 | − | 63.3475i | 2.02460 | − | 2.02460i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 0.996126i | − | 0.0317715i | −0.999874 | − | 0.0158857i | \(-0.994943\pi\) | ||
0.999874 | − | 0.0158857i | \(-0.00505680\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.2146i | 2.23722i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.154862 | + | 0.154862i | −0.00492431 | + | 0.00492431i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.3570i | 1.12315i | 0.827425 | + | 0.561576i | \(0.189805\pi\) | ||||
−0.827425 | + | 0.561576i | \(0.810195\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6998 | − | 29.6998i | −0.941546 | − | 0.941546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7796 | − | 10.7796i | 0.341392 | − | 0.341392i | −0.515498 | − | 0.856891i | \(-0.672393\pi\) |
0.856891 | + | 0.515498i | \(0.172393\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.d.1583.3 | 36 | ||
3.2 | odd | 2 | inner | 4032.2.v.d.1583.16 | 36 | ||
4.3 | odd | 2 | 1008.2.v.d.323.14 | yes | 36 | ||
12.11 | even | 2 | 1008.2.v.d.323.5 | ✓ | 36 | ||
16.5 | even | 4 | 1008.2.v.d.827.5 | yes | 36 | ||
16.11 | odd | 4 | inner | 4032.2.v.d.3599.16 | 36 | ||
48.5 | odd | 4 | 1008.2.v.d.827.14 | yes | 36 | ||
48.11 | even | 4 | inner | 4032.2.v.d.3599.3 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.d.323.5 | ✓ | 36 | 12.11 | even | 2 | ||
1008.2.v.d.323.14 | yes | 36 | 4.3 | odd | 2 | ||
1008.2.v.d.827.5 | yes | 36 | 16.5 | even | 4 | ||
1008.2.v.d.827.14 | yes | 36 | 48.5 | odd | 4 | ||
4032.2.v.d.1583.3 | 36 | 1.1 | even | 1 | trivial | ||
4032.2.v.d.1583.16 | 36 | 3.2 | odd | 2 | inner | ||
4032.2.v.d.3599.3 | 36 | 48.11 | even | 4 | inner | ||
4032.2.v.d.3599.16 | 36 | 16.11 | odd | 4 | inner |