Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(671,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.h (of order \(2\), degree \(1\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.9 | ||
Character | \(\chi\) | \(=\) | 2240.671 |
Dual form | 2240.2.h.e.671.10 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.85258i | − | 1.06959i | −0.844982 | − | 0.534794i | \(-0.820389\pi\) | ||
0.844982 | − | 0.534794i | \(-0.179611\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.29892 | + | 2.30495i | 0.490947 | + | 0.871189i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.432061 | −0.144020 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.01905 | −0.608767 | −0.304384 | − | 0.952550i | \(-0.598450\pi\) | ||||
−0.304384 | + | 0.952550i | \(0.598450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82816 | −0.507039 | −0.253519 | − | 0.967330i | \(-0.581588\pi\) | ||||
−0.253519 | + | 0.967330i | \(0.581588\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.85258i | 0.478335i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.64627i | 0.399279i | 0.979869 | + | 0.199640i | \(0.0639772\pi\) | ||||
−0.979869 | + | 0.199640i | \(0.936023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.26022i | − | 0.289113i | −0.989497 | − | 0.144557i | \(-0.953824\pi\) | ||
0.989497 | − | 0.144557i | \(-0.0461756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.27011 | − | 2.40636i | 0.931814 | − | 0.525112i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.19054i | 0.665273i | 0.943055 | + | 0.332636i | \(0.107938\pi\) | ||||
−0.943055 | + | 0.332636i | \(0.892062\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.75732i | − | 0.915546i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.57459i | 0.849480i | 0.905315 | + | 0.424740i | \(0.139635\pi\) | ||||
−0.905315 | + | 0.424740i | \(0.860365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.834131 | −0.149814 | −0.0749072 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749072 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.74046i | 0.651131i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.29892 | − | 2.30495i | −0.219558 | − | 0.389608i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.82567i | 1.28653i | 0.765643 | + | 0.643266i | \(0.222421\pi\) | ||||
−0.765643 | + | 0.643266i | \(0.777579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.38681i | 0.542323i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.75676i | 0.430534i | 0.976555 | + | 0.215267i | \(0.0690622\pi\) | ||||
−0.976555 | + | 0.215267i | \(0.930938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.74801 | −1.02906 | −0.514531 | − | 0.857472i | \(-0.672034\pi\) | ||||
−0.514531 | + | 0.857472i | \(0.672034\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.432061 | 0.0644079 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8378 | 1.58085 | 0.790425 | − | 0.612558i | \(-0.209860\pi\) | ||||
0.790425 | + | 0.612558i | \(0.209860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.62559 | + | 5.98791i | −0.517941 | + | 0.855416i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.04985 | 0.427065 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.65980i | 1.18951i | 0.803905 | + | 0.594757i | \(0.202752\pi\) | ||||
−0.803905 | + | 0.594757i | \(0.797248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.01905 | 0.272249 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.33465 | −0.309233 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.88971i | 0.506397i | 0.967414 | + | 0.253198i | \(0.0814825\pi\) | ||||
−0.967414 | + | 0.253198i | \(0.918517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.285800 | 0.0365929 | 0.0182965 | − | 0.999833i | \(-0.494176\pi\) | ||||
0.0182965 | + | 0.999833i | \(0.494176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.561215 | − | 0.995879i | −0.0707064 | − | 0.125469i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.82816 | 0.226755 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.94648 | 0.482139 | 0.241069 | − | 0.970508i | \(-0.422502\pi\) | ||||
0.241069 | + | 0.970508i | \(0.422502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.91073 | 0.711568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1095i | 1.31846i | 0.751943 | + | 0.659228i | \(0.229117\pi\) | ||||
−0.751943 | + | 0.659228i | \(0.770883\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4725i | 1.57684i | 0.615137 | + | 0.788420i | \(0.289101\pi\) | ||||
−0.615137 | + | 0.788420i | \(0.710899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.85258i | − | 0.213918i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.62260 | − | 4.65382i | −0.298873 | − | 0.530352i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.8586i | − | 1.44670i | −0.690480 | − | 0.723351i | \(-0.742601\pi\) | ||
0.690480 | − | 0.723351i | \(-0.257399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1095 | −1.12328 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.74578i | − | 0.850210i | −0.905144 | − | 0.425105i | \(-0.860237\pi\) | ||
0.905144 | − | 0.425105i | \(-0.139763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.64627i | − | 0.178563i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.47481 | 0.908595 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.39967i | 0.890363i | 0.895440 | + | 0.445182i | \(0.146861\pi\) | ||||
−0.895440 | + | 0.445182i | \(0.853139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.37464 | − | 4.21381i | −0.248929 | − | 0.441727i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.54530i | 0.160240i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.26022i | 0.129295i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.32004i | − | 0.946306i | −0.880980 | − | 0.473153i | \(-0.843116\pi\) | ||
0.880980 | − | 0.473153i | \(-0.156884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.872354 | 0.0876749 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5289 | 1.44568 | 0.722838 | − | 0.691017i | \(-0.242837\pi\) | ||||
0.722838 | + | 0.691017i | \(0.242837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.72895 | −0.465958 | −0.232979 | − | 0.972482i | \(-0.574847\pi\) | ||||
−0.232979 | + | 0.972482i | \(0.574847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.27011 | + | 2.40636i | −0.416720 | + | 0.234837i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4021 | 1.39230 | 0.696152 | − | 0.717894i | \(-0.254894\pi\) | ||||
0.696152 | + | 0.717894i | \(0.254894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.27624i | 0.409590i | 0.978805 | + | 0.204795i | \(0.0656527\pi\) | ||||
−0.978805 | + | 0.204795i | \(0.934347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.4977 | 1.37606 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.66456 | −0.815093 | −0.407547 | − | 0.913184i | \(-0.633616\pi\) | ||||
−0.407547 | + | 0.913184i | \(0.633616\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.19054i | − | 0.297519i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.789875 | 0.0730240 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.79457 | + | 2.13838i | −0.347848 | + | 0.196025i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.92343 | −0.629402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.10713 | 0.460494 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.61570i | 0.143370i | 0.997427 | + | 0.0716850i | \(0.0228376\pi\) | ||||
−0.997427 | + | 0.0716850i | \(0.977162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5012i | 1.10067i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.173193i | − | 0.0151319i | −0.999971 | − | 0.00756597i | \(-0.997592\pi\) | ||
0.999971 | − | 0.00756597i | \(-0.00240835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.90474 | − | 1.63693i | 0.251873 | − | 0.141939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.75732i | 0.409445i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.7750 | 1.51862 | 0.759312 | − | 0.650727i | \(-0.225536\pi\) | ||||
0.759312 | + | 0.650727i | \(0.225536\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.19653i | 0.525583i | 0.964853 | + | 0.262791i | \(0.0846431\pi\) | ||||
−0.964853 | + | 0.262791i | \(0.915357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.0779i | − | 1.69086i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.69114 | 0.308669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.57459i | − | 0.379899i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0931 | + | 6.71670i | 0.914943 | + | 0.553984i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.49776i | 0.778087i | 0.921219 | + | 0.389043i | \(0.127194\pi\) | ||||
−0.921219 | + | 0.389043i | \(0.872806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.49710i | 0.121832i | 0.998143 | + | 0.0609162i | \(0.0194022\pi\) | ||||
−0.998143 | + | 0.0609162i | \(0.980598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.711290i | − | 0.0575044i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.834131 | 0.0669990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.26866 | −0.580102 | −0.290051 | − | 0.957011i | \(-0.593672\pi\) | ||||
−0.290051 | + | 0.957011i | \(0.593672\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.0430 | 1.27229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.35403 | + | 4.14426i | −0.579578 | + | 0.326614i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2922 | 1.35443 | 0.677215 | − | 0.735785i | \(-0.263187\pi\) | ||||
0.677215 | + | 0.735785i | \(0.263187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 3.74046i | − | 0.291195i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.8910 | 1.61659 | 0.808295 | − | 0.588777i | \(-0.200390\pi\) | ||||
0.808295 | + | 0.588777i | \(0.200390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65785 | −0.742911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.544491i | 0.0416382i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.87701 | −0.142706 | −0.0713532 | − | 0.997451i | \(-0.522732\pi\) | ||||
−0.0713532 | + | 0.997451i | \(0.522732\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.29892 | + | 2.30495i | 0.0981895 | + | 0.174238i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.20600 | 0.541636 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.47135 | 0.408948 | 0.204474 | − | 0.978872i | \(-0.434452\pi\) | ||||
0.204474 | + | 0.978872i | \(0.434452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.67879 | 0.570760 | 0.285380 | − | 0.958414i | \(-0.407880\pi\) | ||||
0.285380 | + | 0.958414i | \(0.407880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.529468i | − | 0.0391394i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 7.82567i | − | 0.575355i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.32391i | − | 0.243068i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.9654 | − | 6.17940i | 0.797614 | − | 0.449485i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.63878i | − | 0.263293i | −0.991297 | − | 0.131646i | \(-0.957974\pi\) | ||
0.991297 | − | 0.131646i | \(-0.0420263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.555242 | −0.0399672 | −0.0199836 | − | 0.999800i | \(-0.506361\pi\) | ||||
−0.0199836 | + | 0.999800i | \(0.506361\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.38681i | − | 0.242534i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.44936i | − | 0.245757i | −0.992422 | − | 0.122878i | \(-0.960787\pi\) | ||
0.992422 | − | 0.122878i | \(-0.0392125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.8014 | −1.68723 | −0.843617 | − | 0.536945i | \(-0.819578\pi\) | ||||
−0.843617 | + | 0.536945i | \(0.819578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.31117i | − | 0.515690i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.5442 | + | 5.94205i | −0.740058 | + | 0.417050i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.75676i | − | 0.192541i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.37851i | − | 0.0958128i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.54444i | 0.176003i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.3284 | −1.74368 | −0.871841 | − | 0.489789i | \(-0.837074\pi\) | ||||
−0.871841 | + | 0.489789i | \(0.837074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.5813 | 1.41021 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.74801 | 0.460210 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.08347 | − | 1.92263i | −0.0735510 | − | 0.130517i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.9590 | 1.68657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.00964i | − | 0.202450i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4743 | 0.902305 | 0.451152 | − | 0.892447i | \(-0.351013\pi\) | ||||
0.451152 | + | 0.892447i | \(0.351013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.432061 | −0.0288041 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.28098i | − | 0.0850218i | −0.999096 | − | 0.0425109i | \(-0.986464\pi\) | ||
0.999096 | − | 0.0425109i | \(-0.0135357\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0084 | 0.793540 | 0.396770 | − | 0.917918i | \(-0.370131\pi\) | ||||
0.396770 | + | 0.917918i | \(0.370131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.62158 | + | 4.85858i | −0.567258 | + | 0.319671i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.35568 | 0.547399 | 0.273699 | − | 0.961815i | \(-0.411753\pi\) | ||||
0.273699 | + | 0.961815i | \(0.411753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8378 | −0.706978 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.8216 | −1.54738 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0313201i | 0.00202593i | 0.999999 | + | 0.00101296i | \(0.000322437\pi\) | ||||
−0.999999 | + | 0.00101296i | \(0.999678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.13884i | 0.395437i | 0.980259 | + | 0.197719i | \(0.0633533\pi\) | ||||
−0.980259 | + | 0.197719i | \(0.936647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.45674i | 0.285900i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.62559 | − | 5.98791i | 0.231630 | − | 0.382554i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.30387i | 0.146592i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3497 | −0.909375 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 29.7162i | − | 1.87567i | −0.347084 | − | 0.937834i | \(-0.612828\pi\) | ||
0.347084 | − | 0.937834i | \(-0.387172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.44186i | − | 0.404996i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.04985 | −0.190989 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.91131i | − | 0.243981i | −0.992531 | − | 0.121991i | \(-0.961072\pi\) | ||
0.992531 | − | 0.121991i | \(-0.0389277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0378 | + | 10.1650i | −1.12081 | + | 0.631619i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.97650i | − | 0.122343i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.11255i | 0.253591i | 0.991929 | + | 0.126795i | \(0.0404691\pi\) | ||||
−0.991929 | + | 0.126795i | \(0.959531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.65980i | − | 0.531967i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5611 | 0.952323 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2052 | −0.622223 | −0.311111 | − | 0.950373i | \(-0.600701\pi\) | ||||
−0.311111 | + | 0.950373i | \(0.600701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2208 | −1.41056 | −0.705282 | − | 0.708926i | \(-0.749180\pi\) | ||||
−0.705282 | + | 0.708926i | \(0.749180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.80642 | + | 4.39921i | −0.472466 | + | 0.266252i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.01905 | −0.121753 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.5201i | 1.11277i | 0.830925 | + | 0.556384i | \(0.187812\pi\) | ||||
−0.830925 | + | 0.556384i | \(0.812188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.360396 | 0.0215763 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0391 | −1.19543 | −0.597717 | − | 0.801707i | \(-0.703925\pi\) | ||||
−0.597717 | + | 0.801707i | \(0.703925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0081i | 0.832693i | 0.909206 | + | 0.416346i | \(0.136690\pi\) | ||||
−0.909206 | + | 0.416346i | \(0.863310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.33465 | 0.138293 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.35420 | + | 3.58083i | −0.375077 | + | 0.211369i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2898 | 0.840576 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2661 | −1.01216 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.98711 | −0.525033 | −0.262516 | − | 0.964928i | \(-0.584552\pi\) | ||||
−0.262516 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.88971i | − | 0.226467i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.60528i | 0.557355i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 5.83279i | − | 0.337319i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.76515 | − | 15.5538i | −0.505215 | − | 0.896507i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26.9159i | − | 1.54628i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.285800 | −0.0163649 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00496i | 0.0573559i | 0.999589 | + | 0.0286779i | \(0.00912972\pi\) | ||||
−0.999589 | + | 0.0286779i | \(0.990870\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.76077i | 0.498383i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9507 | −0.677663 | −0.338831 | − | 0.940847i | \(-0.610032\pi\) | ||||
−0.338831 | + | 0.940847i | \(0.610032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.4336i | − | 0.589745i | −0.955537 | − | 0.294872i | \(-0.904723\pi\) | ||
0.955537 | − | 0.294872i | \(-0.0952771\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.561215 | + | 0.995879i | 0.0316209 | + | 0.0561115i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.6214i | 1.77604i | 0.459809 | + | 0.888018i | \(0.347918\pi\) | ||||
−0.459809 | + | 0.888018i | \(0.652082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.23634i | − | 0.517136i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 26.6811i | − | 1.48919i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.07466 | 0.115437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.82816 | −0.101408 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.92209 | 0.438093 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0774 | + | 24.9805i | 0.776114 | + | 1.37722i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5944 | −1.02204 | −0.511020 | − | 0.859569i | \(-0.670732\pi\) | ||||
−0.511020 | + | 0.859569i | \(0.670732\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.38117i | − | 0.185287i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.94648 | −0.215619 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9730 | 1.30589 | 0.652947 | − | 0.757403i | \(-0.273532\pi\) | ||||
0.652947 | + | 0.757403i | \(0.273532\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0518i | 0.871815i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.68415 | 0.0912021 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5112 | − | 0.578959i | −0.999511 | − | 0.0312609i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.91073 | −0.318223 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.56248 | 0.405975 | 0.202988 | − | 0.979181i | \(-0.434935\pi\) | ||||
0.202988 | + | 0.979181i | \(0.434935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.5581 | −1.79633 | −0.898163 | − | 0.439662i | \(-0.855098\pi\) | ||||
−0.898163 | + | 0.439662i | \(0.855098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.69712i | 0.464218i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1431i | 0.752763i | 0.926465 | + | 0.376382i | \(0.122832\pi\) | ||||
−0.926465 | + | 0.376382i | \(0.877168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.1095i | − | 0.589631i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.96153 | + | 7.02976i | 0.209666 | + | 0.372054i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10.5868i | − | 0.558748i | −0.960182 | − | 0.279374i | \(-0.909873\pi\) | ||
0.960182 | − | 0.279374i | \(-0.0901269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4119 | 0.916413 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.8262i | 0.673202i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.4725i | − | 0.705184i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.2730 | −1.11044 | −0.555222 | − | 0.831703i | \(-0.687367\pi\) | ||||
−0.555222 | + | 0.831703i | \(0.687367\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.19109i | − | 0.0620057i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.9604 | + | 11.2484i | −1.03629 | + | 0.583989i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.97368i | 0.464639i | 0.972639 | + | 0.232320i | \(0.0746315\pi\) | ||||
−0.972639 | + | 0.232320i | \(0.925368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.85258i | 0.0956669i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.36306i | − | 0.430720i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1082 | −0.878789 | −0.439394 | − | 0.898294i | \(-0.644807\pi\) | ||||
−0.439394 | + | 0.898294i | \(0.644807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.99321 | 0.153347 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0052 | −0.766729 | −0.383364 | − | 0.923597i | \(-0.625235\pi\) | ||||
−0.383364 | + | 0.923597i | \(0.625235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.62260 | + | 4.65382i | 0.133660 | + | 0.237180i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.91555 | 0.148206 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.1486i | 1.12298i | 0.827485 | + | 0.561488i | \(0.189771\pi\) | ||||
−0.827485 | + | 0.561488i | \(0.810229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.25249 | −0.265630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.320854 | −0.0161850 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.8586i | 0.646985i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.6284 | −1.63757 | −0.818787 | − | 0.574097i | \(-0.805353\pi\) | ||||
−0.818787 | + | 0.574097i | \(0.805353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.03254 | − | 5.38126i | −0.151817 | − | 0.269400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.98039 | 0.248709 | 0.124354 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124354 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52492 | 0.0759617 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.1095 | 0.502345 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.8004i | − | 0.783199i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.0802i | − | 1.83350i | −0.399467 | − | 0.916748i | \(-0.630805\pi\) | ||
0.399467 | − | 0.916748i | \(-0.369195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 32.9297i | − | 1.62430i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.96558 | + | 5.05243i | −0.441167 | + | 0.248614i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.74578i | 0.380225i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.4796 | 0.562158 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.49215i | − | 0.268309i | −0.990960 | − | 0.134155i | \(-0.957168\pi\) | ||
0.990960 | − | 0.134155i | \(-0.0428319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.32022i | 0.210555i | 0.994443 | + | 0.105277i | \(0.0335731\pi\) | ||||
−0.994443 | + | 0.105277i | \(0.966427\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.68258 | −0.227675 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.64627i | 0.0798559i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.371233 | + | 0.658755i | 0.0179652 | + | 0.0318794i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.83814i | − | 0.330149i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.2143i | 0.925518i | 0.886484 | + | 0.462759i | \(0.153140\pi\) | ||||
−0.886484 | + | 0.462759i | \(0.846860\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 38.8480i | − | 1.86691i | −0.358689 | − | 0.933457i | \(-0.616776\pi\) | ||
0.358689 | − | 0.933457i | \(-0.383224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.47481 | −0.406336 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.02077 | 0.192339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.10197 | 0.243504 | 0.121752 | − | 0.992561i | \(-0.461149\pi\) | ||||
0.121752 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.56648 | − | 2.58714i | 0.0745941 | − | 0.123197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.06583 | −0.335708 | −0.167854 | − | 0.985812i | \(-0.553684\pi\) | ||||
−0.167854 | + | 0.985812i | \(0.553684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.39967i | − | 0.398183i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.5954 | 0.832233 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.3486 | 1.80978 | 0.904892 | − | 0.425641i | \(-0.139952\pi\) | ||||
0.904892 | + | 0.425641i | \(0.139952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.56605i | − | 0.262095i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.77350 | 0.130311 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.37464 | + | 4.21381i | 0.111325 | + | 0.197546i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.1807 | 1.55213 | 0.776064 | − | 0.630654i | \(-0.217213\pi\) | ||||
0.776064 | + | 0.630654i | \(0.217213\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.83184 | 0.365559 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.2266 | −0.476299 | −0.238150 | − | 0.971228i | \(-0.576541\pi\) | ||||
−0.238150 | + | 0.971228i | \(0.576541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6829i | 0.821793i | 0.911682 | + | 0.410897i | \(0.134784\pi\) | ||||
−0.911682 | + | 0.410897i | \(0.865216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.54530i | − | 0.0716614i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6870i | 1.04983i | 0.851154 | + | 0.524916i | \(0.175903\pi\) | ||||
−0.851154 | + | 0.524916i | \(0.824097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.12617 | + | 9.09643i | 0.236705 | + | 0.420034i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4658i | 0.620470i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.6246 | 0.626459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.26022i | − | 0.0578227i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.74156i | − | 0.171314i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2749 | −1.47468 | −0.737338 | − | 0.675524i | \(-0.763918\pi\) | ||||
−0.737338 | + | 0.675524i | \(0.763918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.3065i | − | 0.652322i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.67759 | + | 13.6239i | 0.349343 | + | 0.619911i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.32004i | 0.423201i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 41.7770i | − | 1.89309i | −0.322565 | − | 0.946547i | \(-0.604545\pi\) | ||
0.322565 | − | 0.946547i | \(-0.395455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 32.0352i | − | 1.44868i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2165 | −0.957488 | −0.478744 | − | 0.877955i | \(-0.658908\pi\) | ||||
−0.478744 | + | 0.877955i | \(0.658908\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.53102 | −0.339180 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.872354 | −0.0392094 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.6069 | + | 14.4304i | −1.14862 | + | 0.647292i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0845 | 0.451443 | 0.225722 | − | 0.974192i | \(-0.427526\pi\) | ||||
0.225722 | + | 0.974192i | \(0.427526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 38.7022i | − | 1.72909i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7345 | 1.23662 | 0.618311 | − | 0.785933i | \(-0.287817\pi\) | ||||
0.618311 | + | 0.785933i | \(0.287817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.5289 | −0.646526 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8920i | 0.794610i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4848 | −1.35121 | −0.675607 | − | 0.737262i | \(-0.736118\pi\) | ||||
−0.675607 | + | 0.737262i | \(0.736118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.0535 | + | 17.4998i | −1.37373 | + | 0.774145i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.99525 | −0.264697 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.72895 | 0.208383 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8820 | −0.962370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.47731i | 0.152637i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7727i | 1.12912i | 0.825391 | + | 0.564562i | \(0.190955\pi\) | ||||
−0.825391 | + | 0.564562i | \(0.809045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.7050i | 1.47382i | 0.675992 | + | 0.736909i | \(0.263715\pi\) | ||||
−0.675992 | + | 0.736909i | \(0.736285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.27011 | − | 2.40636i | 0.186363 | − | 0.105022i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.37321i | − | 0.0598178i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.8205 | 0.557412 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.68059i | − | 0.0729314i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.03979i | − | 0.218297i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4021 | −0.622658 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10.1361i | − | 0.437406i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.32026 | − | 12.0899i | 0.315306 | − | 0.520749i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.0220i | − | 1.29075i | −0.763867 | − | 0.645374i | \(-0.776702\pi\) | ||
0.763867 | − | 0.645374i | \(-0.223298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14.2256i | − | 0.610479i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.27624i | − | 0.183174i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6879 | 0.542493 | 0.271247 | − | 0.962510i | \(-0.412564\pi\) | ||||
0.271247 | + | 0.962510i | \(0.412564\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.123483 | −0.00527013 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.76498 | 0.245596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.6384 | − | 16.7023i | 1.26035 | − | 0.710255i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.4977 | −0.615393 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.08838i | 0.215602i | 0.994173 | + | 0.107801i | \(0.0343809\pi\) | ||||
−0.994173 | + | 0.107801i | \(0.965619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3364 | 0.521774 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.15781 | −0.259983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 40.0160i | − | 1.68647i | −0.537544 | − | 0.843236i | \(-0.680648\pi\) | ||
0.537544 | − | 0.843236i | \(-0.319352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.66456 | 0.364521 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.1315 | − | 23.3019i | −0.551471 | − | 0.978588i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.9994 | −0.922263 | −0.461131 | − | 0.887332i | \(-0.652556\pi\) | ||||
−0.461131 | + | 0.887332i | \(0.652556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.72411 | 0.323244 | 0.161622 | − | 0.986853i | \(-0.448327\pi\) | ||||
0.161622 | + | 0.986853i | \(0.448327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.74113 | −0.281615 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.19054i | 0.133055i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.0415i | 0.875969i | 0.898983 | + | 0.437984i | \(0.144307\pi\) | ||||
−0.898983 | + | 0.437984i | \(0.855693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.02863i | 0.0427485i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.8536 | − | 10.0612i | 0.740693 | − | 0.417408i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.4846i | − | 0.724138i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.789875 | −0.0326573 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.5780i | 0.601700i | 0.953671 | + | 0.300850i | \(0.0972704\pi\) | ||||
−0.953671 | + | 0.300850i | \(0.902730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05119i | 0.0433134i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.39022 | −0.262859 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 40.6323i | − | 1.66857i | −0.551335 | − | 0.834284i | \(-0.685881\pi\) | ||
0.551335 | − | 0.834284i | \(-0.314119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.79457 | − | 2.13838i | 0.155562 | − | 0.0876651i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.0940i | 1.80465i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.14993i | − | 0.251279i | −0.992076 | − | 0.125640i | \(-0.959902\pi\) | ||
0.992076 | − | 0.125640i | \(-0.0400983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.5665i | − | 1.69553i | −0.530370 | − | 0.847766i | \(-0.677947\pi\) | ||
0.530370 | − | 0.847766i | \(-0.322053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.70512 | −0.0694378 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.92343 | 0.281477 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.7351 | −1.36927 | −0.684633 | − | 0.728888i | \(-0.740038\pi\) | ||||
−0.684633 | + | 0.728888i | \(0.740038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.0081 | + | 19.5340i | 0.446072 | + | 0.791558i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.8131 | −0.801553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.12505i | − | 0.166609i | −0.996524 | − | 0.0833045i | \(-0.973453\pi\) | ||
0.996524 | − | 0.0833045i | \(-0.0265474\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.10713 | −0.205939 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2572 | −0.936298 | −0.468149 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468149 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.3241i | 1.98250i | 0.131981 | + | 0.991252i | \(0.457866\pi\) | ||||
−0.131981 | + | 0.991252i | \(0.542134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.1784 | 0.609088 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.3608 | + | 10.9105i | −0.775675 | + | 0.437122i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.71379 | 0.188251 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.8832 | −0.513686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.0133i | − | 0.717097i | −0.933511 | − | 0.358548i | \(-0.883272\pi\) | ||
0.933511 | − | 0.358548i | \(-0.116728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 46.9230i | 1.86502i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.61570i | − | 0.0641170i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.62814 | − | 10.9468i | 0.262617 | − | 0.433729i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.79999i | − | 0.189885i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.4333 | −1.55752 | −0.778761 | − | 0.627320i | \(-0.784152\pi\) | ||||
−0.778761 | + | 0.627320i | \(0.784152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.7995i | − | 1.56954i | −0.619789 | − | 0.784769i | \(-0.712782\pi\) | ||
0.619789 | − | 0.784769i | \(-0.287218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12.5012i | − | 0.492236i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.70931 | −0.381712 | −0.190856 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190856 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.85352i | − | 0.308278i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.56183 | + | 2.00722i | −0.139599 | + | 0.0786693i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 29.6501i | − | 1.16030i | −0.814511 | − | 0.580148i | \(-0.802995\pi\) | ||
0.814511 | − | 0.580148i | \(-0.197005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.173193i | 0.00676721i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.82096i | − | 0.227097i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.5744 | 0.606692 | 0.303346 | − | 0.952880i | \(-0.401896\pi\) | ||||
0.303346 | + | 0.952880i | \(0.401896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0366 | 0.973811 | 0.486905 | − | 0.873455i | \(-0.338126\pi\) | ||||
0.486905 | + | 0.873455i | \(0.338126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.57560 | −0.216539 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.90474 | + | 1.63693i | −0.112641 | + | 0.0634773i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.5954 | −0.565136 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 24.9622i | − | 0.965095i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.577045 | −0.0222766 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.5600 | 1.29364 | 0.646821 | − | 0.762642i | \(-0.276098\pi\) | ||||
0.646821 | + | 0.762642i | \(0.276098\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 4.75732i | − | 0.183109i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.9868 | 0.614424 | 0.307212 | − | 0.951641i | \(-0.400604\pi\) | ||||
0.307212 | + | 0.951641i | \(0.400604\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.4822 | − | 12.1060i | 0.824412 | − | 0.464587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.37313 | −0.0909384 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.96348 | −0.113395 | −0.0566973 | − | 0.998391i | \(-0.518057\pi\) | ||||
−0.0566973 | + | 0.998391i | \(0.518057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.7750 | −0.679149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.2466i | − | 0.848762i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.8315i | − | 0.603130i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.5268i | 1.54171i | 0.637009 | + | 0.770856i | \(0.280171\pi\) | ||||
−0.637009 | + | 0.770856i | \(0.719829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.13312 | + | 2.01073i | 0.0430438 | + | 0.0763814i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.19653i | − | 0.235048i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.53838 | −0.171903 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 15.4796i | − | 0.585492i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.5734i | − | 0.550431i | −0.961383 | − | 0.275216i | \(-0.911251\pi\) | ||
0.961383 | − | 0.275216i | \(-0.0887492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.86203 | 0.371954 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.0779i | 0.756176i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.8719 | + | 33.4883i | 0.709751 | + | 1.25946i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 32.4879i | − | 1.22011i | −0.792360 | − | 0.610054i | \(-0.791148\pi\) | ||
0.792360 | − | 0.610054i | \(-0.208852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.55569i | 0.208355i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.66133i | − | 0.0996674i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.69114 | −0.138041 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0580231 | 0.00216691 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.7021 | 1.77899 | 0.889494 | − | 0.456946i | \(-0.151057\pi\) | ||||
0.889494 | + | 0.456946i | \(0.151057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.14255 | − | 10.9000i | −0.228761 | − | 0.405937i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.3727 | 0.422955 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.57459i | 0.169896i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.196227 | −0.00727767 | −0.00363883 | − | 0.999993i | \(-0.501158\pi\) | ||||
−0.00363883 | + | 0.999993i | \(0.501158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0720 | −0.817483 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.1090i | − | 0.410883i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.2927 | −1.59905 | −0.799527 | − | 0.600630i | \(-0.794916\pi\) | ||||
−0.799527 | + | 0.600630i | \(0.794916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.0931 | − | 6.71670i | −0.409175 | − | 0.247749i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.96814 | −0.293510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.7629 | 1.46270 | 0.731350 | − | 0.682002i | \(-0.238890\pi\) | ||||
0.731350 | + | 0.682002i | \(0.238890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.26811 | 0.156793 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 19.0536i | − | 0.699009i | −0.936935 | − | 0.349505i | \(-0.886350\pi\) | ||
0.936935 | − | 0.349505i | \(-0.113650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.49776i | − | 0.347971i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.34665i | 0.122448i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.7073 | + | 33.1962i | 0.683548 | + | 1.21296i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.3244i | 0.376741i | 0.982098 | + | 0.188371i | \(0.0603206\pi\) | ||||
−0.982098 | + | 0.188371i | \(0.939679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −55.0517 | −2.00619 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.49710i | − | 0.0544851i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2488i | 0.408846i | 0.978883 | + | 0.204423i | \(0.0655317\pi\) | ||||
−0.978883 | + | 0.204423i | \(0.934468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.9341 | −0.433179 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.7291i | − | 0.570180i | −0.958501 | − | 0.285090i | \(-0.907977\pi\) | ||
0.958501 | − | 0.285090i | \(-0.0920235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.85652 | + | 5.55452i | −0.356830 | + | 0.201087i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.711290i | 0.0257167i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.11099i | − | 0.256763i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36.5658i | − | 1.31860i | −0.751881 | − | 0.659299i | \(-0.770853\pi\) | ||
0.751881 | − | 0.659299i | \(-0.229147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.24603 | −0.260959 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.4432 | 0.987063 | 0.493532 | − | 0.869728i | \(-0.335706\pi\) | ||||
0.493532 | + | 0.869728i | \(0.335706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.834131 | −0.0299629 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.8314 | + | 33.4165i | 0.675573 | + | 1.19881i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.47412 | 0.124473 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22.4307i | − | 0.802633i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.7628 | 0.777739 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.26866 | 0.259429 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.2718i | 1.57812i | 0.614316 | + | 0.789060i | \(0.289432\pi\) | ||||
−0.614316 | + | 0.789060i | \(0.710568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.61883 | 0.271238 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2546 | − | 19.9714i | −0.400168 | − | 0.710100i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.522487 | −0.0185540 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.0430 | −0.568986 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.7235 | 1.44250 | 0.721249 | − | 0.692675i | \(-0.243568\pi\) | ||||
0.721249 | + | 0.692675i | \(0.243568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.8419i | 0.631201i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.62917i | − | 0.128230i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 27.2017i | − | 0.959929i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.35403 | − | 4.14426i | 0.259195 | − | 0.146066i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.9060i | 0.665523i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.7995 | 0.450007 | 0.225004 | − | 0.974358i | \(-0.427761\pi\) | ||||
0.225004 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.24848i | − | 0.254529i | −0.991869 | − | 0.127264i | \(-0.959380\pi\) | ||
0.991869 | − | 0.127264i | \(-0.0406197\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.0185i | 1.50872i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.2922 | −0.605720 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.50395i | 0.297515i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.02599 | + | 1.82062i | 0.0358509 | + | 0.0636177i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 42.0607i | − | 1.46793i | −0.679188 | − | 0.733964i | \(-0.737668\pi\) | ||
0.679188 | − | 0.733964i | \(-0.262332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.64831i | 0.266603i | 0.991076 | + | 0.133302i | \(0.0425579\pi\) | ||||
−0.991076 | + | 0.133302i | \(0.957442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.74046i | 0.130226i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.3388 | 1.82000 | 0.909999 | − | 0.414611i | \(-0.136082\pi\) | ||||
0.909999 | + | 0.414611i | \(0.136082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.8432 | −0.828109 | −0.414054 | − | 0.910252i | \(-0.635888\pi\) | ||||
−0.414054 | + | 0.910252i | \(0.635888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.3101 | 1.19020 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.85773 | − | 5.96871i | −0.341550 | − | 0.206803i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.8910 | −0.722961 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.96823i | 0.137162i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.3951 | 1.29102 | 0.645510 | − | 0.763751i | \(-0.276645\pi\) | ||||
0.645510 | + | 0.763751i | \(0.276645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.07310 | 0.278383 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.1241i | 1.27862i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.65785 | 0.332240 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.99301 | − | 15.9582i | −0.309003 | − | 0.548329i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9511 | 0.890639 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.9681 | −0.855895 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.61196 | −0.329107 | −0.164554 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164554 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.544491i | − | 0.0186212i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.6718i | 1.18437i | 0.805804 | + | 0.592183i | \(0.201734\pi\) | ||||
−0.805804 | + | 0.592183i | \(0.798266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 42.4621i | − | 1.44879i | −0.689386 | − | 0.724394i | \(-0.742120\pi\) | ||
0.689386 | − | 0.724394i | \(-0.257880\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.63377 | + | 11.7717i | 0.226078 | + | 0.401178i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.8661i | 1.83362i | 0.399319 | + | 0.916812i | \(0.369247\pi\) | ||||
−0.399319 | + | 0.916812i | \(0.630753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.87701 | 0.0638202 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 26.4730i | − | 0.899071i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9621i | 0.880705i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.21477 | −0.244463 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.02683i | 0.136287i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.29892 | − | 2.30495i | −0.0439117 | − | 0.0779215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.8357i | 0.399665i | 0.979830 | + | 0.199832i | \(0.0640398\pi\) | ||||
−0.979830 | + | 0.199832i | \(0.935960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6494i | 0.561569i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.53888i | − | 0.152919i | −0.997073 | − | 0.0764595i | \(-0.975638\pi\) | ||
0.997073 | − | 0.0764595i | \(-0.0243616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.4525 | 0.991156 | 0.495578 | − | 0.868563i | \(-0.334956\pi\) | ||||
0.495578 | + | 0.868563i | \(0.334956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.20600 | −0.242227 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.42071 | −0.0812795 | −0.0406398 | − | 0.999174i | \(-0.512940\pi\) | ||||
−0.0406398 | + | 0.999174i | \(0.512940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.72410 | + | 2.09867i | −0.124902 | + | 0.0703871i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.4116 | 0.683815 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13.6579i | − | 0.457045i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.47135 | −0.182887 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.8057 | −0.360793 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 3.81581i | − | 0.127264i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2564 | −0.474949 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.8147 | + | 16.2382i | −0.958894 | + | 0.540372i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.67879 | −0.255252 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.19443 | −0.238887 | −0.119444 | − | 0.992841i | \(-0.538111\pi\) | ||||
−0.119444 | + | 0.992841i | \(0.538111\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.27736 | −0.208207 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.87733i | 0.294119i | 0.989128 | + | 0.147059i | \(0.0469809\pi\) | ||||
−0.989128 | + | 0.147059i | \(0.953019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.6391i | 0.517580i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.529468i | 0.0175037i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.399201 | − | 0.224965i | 0.0131828 | − | 0.00742899i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.15534i | − | 0.170059i | −0.996378 | − | 0.0850295i | \(-0.972902\pi\) | ||
0.996378 | − | 0.0850295i | \(-0.0270985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.86176 | 0.0613472 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.3099i | − | 0.668509i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.82567i | 0.257306i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.04320 | 0.0671074 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.1036i | 1.77508i | 0.460729 | + | 0.887541i | \(0.347588\pi\) | ||||
−0.460729 | + | 0.887541i | \(0.652412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.54606 | + | 4.56903i | 0.247312 | + | 0.149744i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.1397i | 0.724821i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.32391i | 0.108703i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.66847i | − | 0.0545064i | −0.999629 | − | 0.0272532i | \(-0.991324\pi\) | ||
0.999629 | − | 0.0272532i | \(-0.00867603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.3292 | −0.630784 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.0397 | 1.56605 | 0.783025 | − | 0.621990i | \(-0.213675\pi\) | ||||
0.783025 | + | 0.621990i | \(0.213675\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.79555 | −0.286422 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.9654 | + | 6.17940i | −0.356704 | + | 0.201016i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.8737 | −1.71816 | −0.859081 | − | 0.511839i | \(-0.828964\pi\) | ||||
−0.859081 | + | 0.511839i | \(0.828964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 24.6299i | − | 0.799519i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 58.5813 | 1.89963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4029 | 0.369376 | 0.184688 | − | 0.982797i | \(-0.440873\pi\) | ||||
0.184688 | + | 0.982797i | \(0.440873\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.63878i | 0.117748i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.1111 | −0.553123 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.0884 | + | 40.9706i | 0.745565 | + | 1.32301i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3042 | −0.977556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.22259 | −0.200520 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.555242 | 0.0178739 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.8940i | − | 1.12212i | −0.827776 | − | 0.561058i | \(-0.810394\pi\) | ||
0.827776 | − | 0.561058i | \(-0.189606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 3.84347i | − | 0.123470i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 27.3230i | − | 0.876837i | −0.898771 | − | 0.438418i | \(-0.855539\pi\) | ||
0.898771 | − | 0.438418i | \(-0.144461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.2827 | + | 8.04882i | −0.457882 | + | 0.258033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.38681i | 0.108465i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.876235 | −0.0280332 | −0.0140166 | − | 0.999902i | \(-0.504462\pi\) | ||||
−0.0140166 | + | 0.999902i | \(0.504462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.9594i | − | 0.542024i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.84760i | − | 0.0589893i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.4686 | 1.38643 | 0.693216 | − | 0.720730i | \(-0.256193\pi\) | ||||
0.693216 | + | 0.720730i | \(0.256193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.44936i | 0.109906i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.2784 | − | 26.0796i | 1.47306 | − | 0.830123i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 21.5298i | − | 0.684606i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.8129i | − | 0.597610i | −0.954314 | − | 0.298805i | \(-0.903412\pi\) | ||
0.954314 | − | 0.298805i | \(-0.0965880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.4477i | 1.09316i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.8014 | 0.754554 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3046 | 0.706394 | 0.353197 | − | 0.935549i | \(-0.385094\pi\) | ||||
0.353197 | + | 0.935549i | \(0.385094\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.2292 | 1.17788 |
(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 | 2240.2.h.e.671.9 | ✓ | 24 | |
4.3 | odd | 2 | inner | 2240.2.h.e.671.16 | yes | 24 | |
7.6 | odd | 2 | 2240.2.h.f.671.16 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.h.f.671.15 | yes | 24 | ||
8.5 | even | 2 | 2240.2.h.f.671.10 | yes | 24 | ||
28.27 | even | 2 | 2240.2.h.f.671.9 | yes | 24 | ||
56.13 | odd | 2 | inner | 2240.2.h.e.671.15 | yes | 24 | |
56.27 | even | 2 | inner | 2240.2.h.e.671.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.h.e.671.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2240.2.h.e.671.10 | yes | 24 | 56.27 | even | 2 | inner | |
2240.2.h.e.671.15 | yes | 24 | 56.13 | odd | 2 | inner | |
2240.2.h.e.671.16 | yes | 24 | 4.3 | odd | 2 | inner | |
2240.2.h.f.671.9 | yes | 24 | 28.27 | even | 2 | ||
2240.2.h.f.671.10 | yes | 24 | 8.5 | even | 2 | ||
2240.2.h.f.671.15 | yes | 24 | 8.3 | odd | 2 | ||
2240.2.h.f.671.16 | yes | 24 | 7.6 | odd | 2 |