Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1839,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1839");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.m (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1839.18 | ||
Character | \(\chi\) | \(=\) | 1840.1839 |
Dual form | 1840.2.m.g.1839.19 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.924187 | −0.533580 | −0.266790 | − | 0.963755i | \(-0.585963\pi\) | ||||
−0.266790 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.611037 | − | 2.15096i | −0.273264 | − | 0.961939i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.51428i | − | 0.572346i | −0.958178 | − | 0.286173i | \(-0.907617\pi\) | ||
0.958178 | − | 0.286173i | \(-0.0923832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.14588 | −0.715293 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.770524 | 0.232322 | 0.116161 | − | 0.993230i | \(-0.462941\pi\) | ||||
0.116161 | + | 0.993230i | \(0.462941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.68356i | 1.29899i | 0.760367 | + | 0.649493i | \(0.225019\pi\) | ||||
−0.760367 | + | 0.649493i | \(0.774981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.564712 | + | 1.98789i | 0.145808 | + | 0.513271i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00822 | 0.972136 | 0.486068 | − | 0.873921i | \(-0.338431\pi\) | ||||
0.486068 | + | 0.873921i | \(0.338431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.17499 | −1.64606 | −0.823028 | − | 0.568000i | \(-0.807717\pi\) | ||||
−0.823028 | + | 0.568000i | \(0.807717\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.39948i | 0.305392i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.38418 | + | 1.94395i | −0.914166 | + | 0.405341i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.25327 | + | 2.62863i | −0.850654 | + | 0.525726i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.75575 | 0.915245 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.41697 | −0.820211 | −0.410105 | − | 0.912038i | \(-0.634508\pi\) | ||||
−0.410105 | + | 0.912038i | \(0.634508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.07318i | − | 0.551959i | −0.961164 | − | 0.275979i | \(-0.910998\pi\) | ||
0.961164 | − | 0.275979i | \(-0.0890021\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.712108 | −0.123962 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.25717 | + | 0.925283i | −0.550562 | + | 0.156401i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.52910 | 0.908978 | 0.454489 | − | 0.890752i | \(-0.349822\pi\) | ||||
0.454489 | + | 0.890752i | \(0.349822\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.32849i | − | 0.693113i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.75875 | 1.21171 | 0.605856 | − | 0.795574i | \(-0.292831\pi\) | ||||
0.605856 | + | 0.795574i | \(0.292831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.03824i | 0.310829i | 0.987849 | + | 0.155415i | \(0.0496714\pi\) | ||||
−0.987849 | + | 0.155415i | \(0.950329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.31121 | + | 4.61570i | 0.195464 | + | 0.688068i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.08211 | −0.595436 | −0.297718 | − | 0.954654i | \(-0.596226\pi\) | ||||
−0.297718 | + | 0.954654i | \(0.596226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.70694 | 0.672420 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.70434 | −0.518712 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.2815 | 1.41227 | 0.706137 | − | 0.708075i | \(-0.250436\pi\) | ||||
0.706137 | + | 0.708075i | \(0.250436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.470818 | − | 1.65737i | −0.0634851 | − | 0.223479i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.63104 | 0.878302 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.831684i | 0.108276i | 0.998533 | + | 0.0541380i | \(0.0172411\pi\) | ||||
−0.998533 | + | 0.0541380i | \(0.982759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.18803i | 0.920334i | 0.887832 | + | 0.460167i | \(0.152210\pi\) | ||||
−0.887832 | + | 0.460167i | \(0.847790\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.24947i | 0.409395i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.0742 | − | 2.86183i | 1.24955 | − | 0.354966i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6052i | 1.53998i | 0.638058 | + | 0.769988i | \(0.279738\pi\) | ||||
−0.638058 | + | 0.769988i | \(0.720262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.05181 | − | 1.79657i | 0.487780 | − | 0.216282i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.23430i | 0.265162i | 0.991172 | + | 0.132581i | \(0.0423265\pi\) | ||||
−0.991172 | + | 0.132581i | \(0.957673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1803i | 1.30855i | 0.756256 | + | 0.654276i | \(0.227027\pi\) | ||||
−0.756256 | + | 0.654276i | \(0.772973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.93082 | − | 2.42935i | 0.453891 | − | 0.280517i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.16679i | − | 0.132968i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.98050 | 0.447841 | 0.223920 | − | 0.974607i | \(-0.428114\pi\) | ||||
0.223920 | + | 0.974607i | \(0.428114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.04243 | 0.226937 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.33338i | 0.804943i | 0.915432 | + | 0.402472i | \(0.131849\pi\) | ||||
−0.915432 | + | 0.402472i | \(0.868151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.44917 | − | 8.62152i | −0.265650 | − | 0.935135i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.08211 | 0.437648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.08954i | 0.115491i | 0.998331 | + | 0.0577456i | \(0.0183912\pi\) | ||||
−0.998331 | + | 0.0577456i | \(0.981609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.09225 | 0.743470 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.84019i | 0.294514i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.38418 | + | 15.4331i | 0.449808 | + | 1.58341i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74295 | −0.278505 | −0.139252 | − | 0.990257i | \(-0.544470\pi\) | ||||
−0.139252 | + | 0.990257i | \(0.544470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.65345 | −0.166178 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8717 | −1.08177 | −0.540887 | − | 0.841095i | \(-0.681911\pi\) | ||||
−0.540887 | + | 0.841095i | \(0.681911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.7824i | − | 1.65362i | −0.562484 | − | 0.826808i | \(-0.690154\pi\) | ||
0.562484 | − | 0.826808i | \(-0.309846\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.01023 | − | 0.855135i | 0.293769 | − | 0.0834526i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3125i | 1.09363i | 0.837255 | + | 0.546813i | \(0.184159\pi\) | ||||
−0.837255 | + | 0.546813i | \(0.815841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.94861i | 0.186643i | 0.995636 | + | 0.0933217i | \(0.0297485\pi\) | ||||
−0.995636 | + | 0.0933217i | \(0.970251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.10992 | −0.485012 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41749 | 0.133346 | 0.0666731 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666731 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.86025 | + | 8.24239i | 0.639722 | + | 0.768607i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.0504i | − | 0.929156i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.06958i | − | 0.556398i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4063 | −0.946027 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.17053 | −0.646545 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.25299 | + | 7.54243i | 0.738170 | + | 0.674615i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.9437 | −1.05984 | −0.529918 | − | 0.848049i | \(-0.677777\pi\) | ||||
−0.529918 | + | 0.848049i | \(0.677777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.88372i | − | 0.165852i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.39358i | − | 0.820721i | −0.911923 | − | 0.410360i | \(-0.865403\pi\) | ||
0.911923 | − | 0.410360i | \(-0.134597\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8650i | 0.942114i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.90594 | − | 10.2294i | −0.250103 | − | 0.880410i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8161 | 1.18039 | 0.590194 | − | 0.807261i | \(-0.299051\pi\) | ||||
0.590194 | + | 0.807261i | \(0.299051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0085i | 1.69710i | 0.529114 | + | 0.848551i | \(0.322524\pi\) | ||||
−0.529114 | + | 0.848551i | \(0.677476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.77263 | 0.317713 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.60880i | 0.301783i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.69893 | + | 9.50073i | 0.224134 | + | 0.788993i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.35009 | −0.358790 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.70733i | 0.467563i | 0.972289 | + | 0.233781i | \(0.0751100\pi\) | ||||
−0.972289 | + | 0.233781i | \(0.924890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.03536i | − | 0.735287i | −0.929967 | − | 0.367643i | \(-0.880165\pi\) | ||
0.929967 | − | 0.367643i | \(-0.119835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.60115 | −0.695362 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.61028 | + | 1.87782i | −0.530951 | + | 0.150830i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.88848 | −0.310335 | −0.155167 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155167 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.50204 | −0.753561 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.94369 | + | 6.63890i | 0.231995 | + | 0.523219i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.1380 | −1.89064 | −0.945318 | − | 0.326151i | \(-0.894248\pi\) | ||||
−0.945318 | + | 0.326151i | \(0.894248\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.435124 | + | 1.53172i | 0.0338744 | + | 0.119244i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.51434 | 0.504094 | 0.252047 | − | 0.967715i | \(-0.418896\pi\) | ||||
0.252047 | + | 0.967715i | \(0.418896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.93577 | −0.687367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.3967 | 1.17741 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8909i | 1.28419i | 0.766625 | + | 0.642095i | \(0.221934\pi\) | ||||
−0.766625 | + | 0.642095i | \(0.778066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.98050 | + | 6.44066i | 0.300897 | + | 0.486868i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.768632i | − | 0.0577739i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.50098i | 0.710137i | 0.934840 | + | 0.355068i | \(0.115542\pi\) | ||||
−0.934840 | + | 0.355068i | \(0.884458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.90483i | − | 0.290244i | −0.989414 | − | 0.145122i | \(-0.953643\pi\) | ||
0.989414 | − | 0.145122i | \(-0.0463575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.64309i | − | 0.491071i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.37848 | − | 11.8929i | −0.248391 | − | 0.874382i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.08843 | 0.225848 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 7.20156i | − | 0.523837i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2206 | 0.956607 | 0.478303 | − | 0.878195i | \(-0.341252\pi\) | ||||
0.478303 | + | 0.878195i | \(0.341252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1726i | 0.732242i | 0.930567 | + | 0.366121i | \(0.119314\pi\) | ||||
−0.930567 | + | 0.366121i | \(0.880686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.31041 | + | 2.64486i | −0.666732 | + | 0.189403i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2809i | 1.30246i | 0.758880 | + | 0.651231i | \(0.225747\pi\) | ||||
−0.758880 | + | 0.651231i | \(0.774253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.9189 | 1.27023 | 0.635117 | − | 0.772416i | \(-0.280952\pi\) | ||||
0.635117 | + | 0.772416i | \(0.280952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.6496i | − | 0.821700i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.68855i | 0.469444i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.74088 | − | 16.6888i | −0.331117 | − | 1.16559i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.40793 | − | 4.17147i | 0.653896 | − | 0.289937i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.52850 | −0.382415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.8222i | − | 1.08925i | −0.838681 | − | 0.544623i | \(-0.816673\pi\) | ||
0.838681 | − | 0.544623i | \(-0.183327\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.06491i | − | 0.141485i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.38418 | − | 1.24544i | 0.298999 | − | 0.0849384i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.65366 | −0.315911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 10.3327i | − | 0.698217i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.7727i | 1.26279i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4686 | 1.16978 | 0.584891 | − | 0.811112i | \(-0.301137\pi\) | ||||
0.584891 | + | 0.811112i | \(0.301137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.12700 | − | 5.64072i | 0.608467 | − | 0.376048i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.56046i | 0.568178i | 0.958798 | + | 0.284089i | \(0.0916910\pi\) | ||||
−0.958798 | + | 0.284089i | \(0.908309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.96756i | 0.526511i | 0.964726 | + | 0.263256i | \(0.0847963\pi\) | ||||
−0.964726 | + | 0.263256i | \(0.915204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07833i | 0.0709492i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.20846i | 0.472242i | 0.971724 | + | 0.236121i | \(0.0758761\pi\) | ||||
−0.971724 | + | 0.236121i | \(0.924124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.49432 | + | 8.78045i | 0.162711 | + | 0.572774i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.67872 | −0.238959 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.76559i | 0.631683i | 0.948812 | + | 0.315842i | \(0.102287\pi\) | ||||
−0.948812 | + | 0.315842i | \(0.897713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.8111i | − | 1.72706i | −0.504300 | − | 0.863528i | \(-0.668250\pi\) | ||
0.504300 | − | 0.863528i | \(-0.331750\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1548 | −1.03633 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.87611 | − | 10.1245i | −0.183748 | − | 0.646827i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.6045i | − | 2.13821i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.77742i | − | 0.429501i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.6349 | −1.68118 | −0.840590 | − | 0.541672i | \(-0.817792\pi\) | ||||
−0.840590 | + | 0.541672i | \(0.817792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.37812 | + | 1.49786i | −0.212380 | + | 0.0941695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.26349 | + | 7.96790i | 0.141745 | + | 0.498969i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.102882i | 0.00641757i | 0.999995 | + | 0.00320879i | \(0.00102139\pi\) | ||||
−0.999995 | + | 0.00320879i | \(0.998979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.37263i | − | 0.520250i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.47828 | 0.586691 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.710540i | − | 0.0438138i | −0.999760 | − | 0.0219069i | \(-0.993026\pi\) | ||
0.999760 | − | 0.0219069i | \(-0.00697373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.28238 | − | 22.1151i | −0.385924 | − | 1.35852i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.00694i | − | 0.0616238i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.62225 | 0.464736 | 0.232368 | − | 0.972628i | \(-0.425353\pi\) | ||||
0.232368 | + | 0.972628i | \(0.425353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.3110i | − | 1.17306i | −0.809928 | − | 0.586530i | \(-0.800494\pi\) | ||
0.809928 | − | 0.586530i | \(-0.199506\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.55456 | −0.396700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.27724 | + | 2.02542i | −0.197625 | + | 0.122138i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.30436i | − | 0.198540i | −0.995061 | − | 0.0992698i | \(-0.968349\pi\) | ||
0.995061 | − | 0.0992698i | \(-0.0316507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.59466i | 0.394812i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8091i | 1.30102i | 0.759496 | + | 0.650512i | \(0.225446\pi\) | ||||
−0.759496 | + | 0.650512i | \(0.774554\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.5316i | − | 1.04215i | −0.853512 | − | 0.521073i | \(-0.825532\pi\) | ||
0.853512 | − | 0.521073i | \(-0.174468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.05181 | − | 14.2631i | −0.240008 | − | 0.844873i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.7490i | − | 0.693519i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.934184 | −0.0549520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.53500 | 0.148604 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.9898 | −1.40150 | −0.700751 | − | 0.713406i | \(-0.747152\pi\) | ||||
−0.700751 | + | 0.713406i | \(0.747152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.78892 | − | 0.508189i | 0.104155 | − | 0.0295879i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.66442 | 0.212631 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.10460 | − | 20.5336i | −0.526533 | − | 1.18749i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.08648 | 0.177902 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.0475 | 0.577213 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.4612 | − | 4.39215i | 0.885305 | − | 0.251494i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.35359 | 0.362618 | 0.181309 | − | 0.983426i | \(-0.441967\pi\) | ||||
0.181309 | + | 0.983426i | \(0.441967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5100i | 0.882336i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.3653i | 1.21151i | 0.795650 | + | 0.605757i | \(0.207130\pi\) | ||||
−0.795650 | + | 0.605757i | \(0.792870\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.9033 | −0.785860 | −0.392930 | − | 0.919568i | \(-0.628538\pi\) | ||||
−0.392930 | + | 0.919568i | \(0.628538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.98949 | − | 1.98555i | 0.393813 | − | 0.111873i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 32.1985i | − | 1.80845i | −0.427058 | − | 0.904224i | \(-0.640450\pi\) | ||
0.427058 | − | 0.904224i | \(-0.359550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.40338 | −0.190553 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.4549i | − | 0.583536i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.7589 | −1.60019 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.3114 | − | 19.9205i | −0.682912 | − | 1.10499i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.80088i | − | 0.0995891i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.18147i | 0.340795i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1630i | 1.60294i | 0.598032 | + | 0.801472i | \(0.295949\pi\) | ||||
−0.598032 | + | 0.801472i | \(0.704051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8648 | −0.650186 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.1134 | − | 7.70227i | 1.48136 | − | 0.420820i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.6280 | −1.50499 | −0.752495 | − | 0.658598i | \(-0.771150\pi\) | ||||
−0.752495 | + | 0.658598i | \(0.771150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.31003 | −0.0711508 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.36796i | − | 0.128232i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.7276i | − | 0.957203i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.34015 | − | 7.61751i | −0.341342 | − | 0.410113i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.3319 | 0.662014 | 0.331007 | − | 0.943628i | \(-0.392612\pi\) | ||||
0.331007 | + | 0.943628i | \(0.392612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.3284 | 1.19521 | 0.597605 | − | 0.801790i | \(-0.296119\pi\) | ||||
0.597605 | + | 0.801790i | \(0.296119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.2739i | 1.18889i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.1661i | 1.23300i | 0.787353 | + | 0.616502i | \(0.211451\pi\) | ||||
−0.787353 | + | 0.616502i | \(0.788549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.80589 | − | 1.36524i | 0.255070 | − | 0.0724593i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.60943i | 0.296883i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1784 | 1.22331 | 0.611655 | − | 0.791124i | \(-0.290504\pi\) | ||||
0.611655 | + | 0.791124i | \(0.290504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.4805 | 1.70950 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.61736 | 0.504781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0483 | − | 6.83156i | 1.25875 | − | 0.357580i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5956i | 0.709683i | 0.934926 | + | 0.354842i | \(0.115465\pi\) | ||||
−0.934926 | + | 0.354842i | \(0.884535\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.6493 | −0.866730 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 15.5691i | − | 0.808309i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2567 | −1.46307 | −0.731537 | − | 0.681802i | \(-0.761197\pi\) | ||||
−0.731537 | + | 0.681802i | \(0.761197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.62730 | − | 6.97061i | −0.393872 | − | 0.359961i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.6872i | − | 1.06544i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0649 | −1.03067 | −0.515333 | − | 0.856990i | \(-0.672332\pi\) | ||||
−0.515333 | + | 0.856990i | \(0.672332\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0382 | 0.565506 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11.3479i | − | 0.579850i | −0.957049 | − | 0.289925i | \(-0.906370\pi\) | ||
0.957049 | − | 0.289925i | \(-0.0936303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.50972 | + | 0.712953i | −0.127907 | + | 0.0363354i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.37382i | − | 0.222334i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 22.6863i | − | 1.15024i | −0.818069 | − | 0.575121i | \(-0.804955\pi\) | ||
0.818069 | − | 0.575121i | \(-0.195045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.5728 | + | 7.79176i | −0.888693 | + | 0.394046i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.68142i | 0.437920i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.43223 | − | 8.56189i | −0.122379 | − | 0.430796i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.68242i | − | 0.485947i | −0.970033 | − | 0.242973i | \(-0.921877\pi\) | ||
0.970033 | − | 0.242973i | \(-0.0781228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 10.0413i | − | 0.502693i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.3976i | − | 0.519232i | −0.965712 | − | 0.259616i | \(-0.916404\pi\) | ||
0.965712 | − | 0.259616i | \(-0.0835960\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.3934 | 0.716987 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.24800 | − | 4.39319i | −0.0620136 | − | 0.218299i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.26030 | 0.211175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.1286 | −0.748060 | −0.374030 | − | 0.927417i | \(-0.622024\pi\) | ||||
−0.374030 | + | 0.927417i | \(0.622024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.7687 | −0.629831 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.25941 | 0.0619713 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7738 | − | 4.48097i | 0.774307 | − | 0.219962i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 18.4916i | − | 0.905538i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.5455 | 1.49224 | 0.746122 | − | 0.665810i | \(-0.231914\pi\) | ||||
0.746122 | + | 0.665810i | \(0.231914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.6570i | − | 1.59160i | −0.605557 | − | 0.795802i | \(-0.707050\pi\) | ||
0.605557 | − | 0.795802i | \(-0.292950\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.75970 | 0.425911 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.0480 | + | 10.5361i | −0.826951 | + | 0.511077i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8847 | 0.526749 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 3.33520i | − | 0.161025i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.72165 | −0.0829289 | −0.0414645 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414645 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1333 | 0.535034 | 0.267517 | − | 0.963553i | \(-0.413797\pi\) | ||||
0.267517 | + | 0.963553i | \(0.413797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.49432 | − | 8.78045i | −0.119593 | − | 0.420990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.4565 | − | 13.9478i | 1.50477 | − | 0.667214i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9505i | 1.57264i | 0.617818 | + | 0.786321i | \(0.288017\pi\) | ||||
−0.617818 | + | 0.786321i | \(0.711983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.1005 | −0.480977 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.3281 | −1.72600 | −0.863001 | − | 0.505203i | \(-0.831418\pi\) | ||||
−0.863001 | + | 0.505203i | \(0.831418\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.34356 | − | 0.665750i | 0.111096 | − | 0.0315596i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.27464i | − | 0.249482i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.5895 | −0.641327 | −0.320664 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320664 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.97830 | 0.281507 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.35036i | 0.392334i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.33362 | − | 15.2552i | −0.203163 | − | 0.715172i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.4328 | −1.42359 | −0.711794 | − | 0.702389i | \(-0.752117\pi\) | ||||
−0.711794 | + | 0.702389i | \(0.752117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.0621 | 0.889743 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.1419 | −0.984674 | −0.492337 | − | 0.870405i | \(-0.663857\pi\) | ||||
−0.492337 | + | 0.870405i | \(0.663857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4326 | −1.36785 | −0.683924 | − | 0.729553i | \(-0.739728\pi\) | ||||
−0.683924 | + | 0.729553i | \(0.739728\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.10914 | − | 1.73546i | 0.283304 | − | 0.0804800i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.4494i | 1.91805i | 0.283321 | + | 0.959025i | \(0.408564\pi\) | ||||
−0.283321 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0879 | 0.881399 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.59368 | 0.165588 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.57052i | 0.0722124i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.5172 | − | 18.8604i | 1.40022 | − | 0.865375i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.0629 | −1.01019 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.2206 | −1.19805 | −0.599025 | − | 0.800730i | \(-0.704445\pi\) | ||||
−0.599025 | + | 0.800730i | \(0.704445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.8959i | 1.18075i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.72052 | − | 6.13559i | −0.123788 | − | 0.279179i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.67604 | + | 5.89999i | 0.0761053 | + | 0.267905i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.75788 | −0.442172 | −0.221086 | − | 0.975254i | \(-0.570960\pi\) | ||||
−0.221086 | + | 0.975254i | \(0.570960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3080 | 1.00880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.43561i | 0.335564i | 0.985824 | + | 0.167782i | \(0.0536605\pi\) | ||||
−0.985824 | + | 0.167782i | \(0.946339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.7042 | −0.797356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.01032 | + | 3.55651i | 0.0454104 | + | 0.159853i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.38336 | 0.151765 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.46322i | 0.334100i | 0.985948 | + | 0.167050i | \(0.0534241\pi\) | ||||
−0.985948 | + | 0.167050i | \(0.946576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.02046 | −0.268974 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 28.7105i | − | 1.28014i | −0.768318 | − | 0.640068i | \(-0.778906\pi\) | ||
0.768318 | − | 0.640068i | \(-0.221094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.64301 | + | 23.3846i | 0.295610 | + | 1.04060i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.25832 | 0.366765 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.9943 | −1.01920 | −0.509602 | − | 0.860410i | \(-0.670208\pi\) | ||||
−0.509602 | + | 0.860410i | \(0.670208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.9301 | 0.748945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.1225 | −1.50655 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.0982 | + | 10.2546i | −1.59068 | + | 0.451873i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.14536 | −0.138333 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.6103i | − | 0.685217i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.5570i | 1.51397i | 0.653432 | + | 0.756985i | \(0.273329\pi\) | ||||
−0.653432 | + | 0.756985i | \(0.726671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.88910i | − | 0.432420i | −0.976347 | − | 0.216210i | \(-0.930630\pi\) | ||
0.976347 | − | 0.216210i | \(-0.0693696\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.67872 | − | 5.95237i | −0.160553 | − | 0.259783i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.3180i | − | 0.536579i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4421 | − | 17.0452i | 0.671397 | − | 0.741097i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.78469i | − | 0.0774491i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.3386i | 1.57400i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.3328 | − | 6.91238i | 1.05200 | − | 0.298848i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.78068i | − | 0.378914i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.62681 | 0.156218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9611 | −0.686221 | −0.343111 | − | 0.939295i | \(-0.611481\pi\) | ||||
−0.343111 | + | 0.939295i | \(0.611481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.60880i | 0.154868i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.19139 | − | 1.19067i | 0.179540 | − | 0.0510029i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3204 | 0.911596 | 0.455798 | − | 0.890083i | \(-0.349354\pi\) | ||||
0.455798 | + | 0.890083i | \(0.349354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 15.4246i | − | 0.658308i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.6917 | 1.35011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.02761i | − | 0.256320i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.12235 | + | 10.9912i | 0.132536 | + | 0.466552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.24545 | −0.264628 | −0.132314 | − | 0.991208i | \(-0.542241\pi\) | ||||
−0.132314 | + | 0.991208i | \(0.542241\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.54625 | −0.403763 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.85428 | −0.120508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4311i | 0.734632i | 0.930096 | + | 0.367316i | \(0.119723\pi\) | ||||
−0.930096 | + | 0.367316i | \(0.880277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.866138 | − | 3.04897i | −0.0364387 | − | 0.128271i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.09282i | − | 0.129886i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.7081i | − | 0.993894i | −0.867781 | − | 0.496947i | \(-0.834454\pi\) | ||
0.867781 | − | 0.496947i | \(-0.165546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.0536 | −1.04846 | −0.524230 | − | 0.851577i | \(-0.675647\pi\) | ||||
−0.524230 | + | 0.851577i | \(0.675647\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2183 | −0.510426 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5372 | − | 19.7925i | 0.564540 | − | 0.825406i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.58387i | − | 0.149198i | −0.997214 | − | 0.0745992i | \(-0.976232\pi\) | ||
0.997214 | − | 0.0745992i | \(-0.0237677\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 9.40141i | − | 0.390709i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1048 | 0.460706 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.92215 | 0.328102 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.6179 | + | 6.14114i | −0.893791 | + | 0.253905i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.59996 | 0.272410 | 0.136205 | − | 0.990681i | \(-0.456509\pi\) | ||||
0.136205 | + | 0.990681i | \(0.456509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.0500i | 0.908555i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 16.8950i | − | 0.694967i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.6733i | 1.83451i | 0.398295 | + | 0.917257i | \(0.369602\pi\) | ||||
−0.398295 | + | 0.917257i | \(0.630398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.0554 | + | 3.70874i | −0.535221 | + | 0.152043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.5604 | −0.677771 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.33216i | − | 0.217866i | −0.994049 | − | 0.108933i | \(-0.965257\pi\) | ||
0.994049 | − | 0.108933i | \(-0.0347434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8384 | −0.646064 | −0.323032 | − | 0.946388i | \(-0.604702\pi\) | ||||
−0.323032 | + | 0.946388i | \(0.604702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 27.0493i | − | 1.10153i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.35863 | + | 22.3835i | 0.258515 | + | 0.910020i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3267 | −0.825037 | −0.412519 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412519 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 6.18147i | − | 0.250486i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 19.1188i | − | 0.773464i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.72981 | −0.352594 | −0.176297 | − | 0.984337i | \(-0.556412\pi\) | ||||
−0.176297 | + | 0.984337i | \(0.556412\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.38146 | + | 15.4235i | 0.176677 | + | 0.621937i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7292 | 0.955300 | 0.477650 | − | 0.878550i | \(-0.341489\pi\) | ||||
0.477650 | + | 0.878550i | \(0.341489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6943 | 0.912162 | 0.456081 | − | 0.889938i | \(-0.349253\pi\) | ||||
0.456081 | + | 0.889938i | \(0.349253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.8501 | + | 9.24493i | −0.836686 | + | 0.370986i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.64988 | 0.0661009 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1806 | − | 22.3606i | 0.447224 | − | 0.894422i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.10937 | 0.204049 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.1618 | 0.883650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7307 | 0.944706 | 0.472353 | − | 0.881409i | \(-0.343405\pi\) | ||||
0.472353 | + | 0.881409i | \(0.343405\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6227i | 0.581199i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.29806 | + | 25.6905i | 0.289615 | + | 1.01950i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.0453i | 0.873465i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.79453i | − | 0.189669i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.7220i | − | 0.976460i | −0.872715 | − | 0.488230i | \(-0.837643\pi\) | ||
0.872715 | − | 0.488230i | \(-0.162357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.7604i | 1.48913i | 0.667553 | + | 0.744563i | \(0.267342\pi\) | ||||
−0.667553 | + | 0.744563i | \(0.732658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.05181 | + | 1.15102i | −0.159540 | + | 0.0453214i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.8197 | −0.543308 | −0.271654 | − | 0.962395i | \(-0.587571\pi\) | ||||
−0.271654 | + | 0.962395i | \(0.587571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.640832i | 0.0251549i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.30085 | 0.168564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.1266i | 0.396286i | 0.980173 | + | 0.198143i | \(0.0634910\pi\) | ||||
−0.980173 | + | 0.198143i | \(0.936509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.2052 | + | 5.73982i | −0.789483 | + | 0.224273i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.9915i | − | 0.935998i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.08769 | −0.159234 | −0.0796168 | − | 0.996826i | \(-0.525370\pi\) | ||||
−0.0796168 | + | 0.996826i | \(0.525370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.20605i | − | 0.163596i | −0.996649 | − | 0.0817982i | \(-0.973934\pi\) | ||
0.996649 | − | 0.0817982i | \(-0.0260663\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 17.3495i | − | 0.673800i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.3702 | − | 6.63890i | 0.906256 | − | 0.257446i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.3648 | − | 8.58635i | 0.749808 | − | 0.332465i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.1442 | −0.624171 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.53855i | 0.213813i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.1518i | − | 1.16227i | −0.813808 | − | 0.581134i | \(-0.802609\pi\) | ||
0.813808 | − | 0.581134i | \(-0.197391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.2275 | + | 12.5011i | −0.778557 | + | 0.481169i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4970 | 0.403434 | 0.201717 | − | 0.979444i | \(-0.435348\pi\) | ||||
0.201717 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.15361i | 0.159401i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.91146i | − | 0.303168i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.19811 | −0.275428 | −0.137714 | − | 0.990472i | \(-0.543975\pi\) | ||||
−0.137714 | + | 0.990472i | \(0.543975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.44214 | − | 29.7179i | −0.322558 | − | 1.13546i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.36352i | − | 0.280936i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.1541i | 1.83453i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.4264i | 1.69006i | 0.534718 | + | 0.845030i | \(0.320418\pi\) | ||||
−0.534718 | + | 0.845030i | \(0.679582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.50379i | 0.0951113i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.0376 | − | 12.2259i | 1.63251 | − | 0.463756i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.0988 | 1.17795 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 6.66196i | − | 0.251979i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 51.4682i | − | 1.94393i | −0.235129 | − | 0.971964i | \(-0.575551\pi\) | ||
0.235129 | − | 0.971964i | \(-0.424449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6713 | −1.49623 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.30521 | − | 8.11478i | −0.0868194 | − | 0.305620i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.4629i | 0.619149i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.106530i | 0.00400082i | 0.999998 | + | 0.00200041i | \(0.000636750\pi\) | ||||
−0.999998 | + | 0.00200041i | \(0.999363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.54166 | −0.320337 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.97409 | + | 13.4734i | 0.223731 | + | 0.504582i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.76238 | − | 2.20511i | 0.290297 | − | 0.0824663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 9.02523i | − | 0.337053i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5519i | 0.468108i | 0.972224 | + | 0.234054i | \(0.0751993\pi\) | ||||
−0.972224 | + | 0.234054i | \(0.924801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.4133 | −0.946440 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.7785i | 0.921522i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.7866 | − | 11.6106i | 0.697715 | − | 0.431206i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.4070i | − | 1.53570i | −0.640630 | − | 0.767850i | \(-0.721327\pi\) | ||
0.640630 | − | 0.767850i | \(-0.278673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.80281 | 0.326030 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.16973i | 0.302168i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.31345 | 0.307064 | 0.153532 | − | 0.988144i | \(-0.450935\pi\) | ||||
0.153532 | + | 0.988144i | \(0.450935\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.65807 | + | 9.35688i | 0.0980443 | + | 0.345134i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.71264i | 0.357770i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13.6173i | − | 0.500921i | −0.968127 | − | 0.250460i | \(-0.919418\pi\) | ||
0.968127 | − | 0.250460i | \(-0.0805820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.0569i | 1.14090i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.0822i | 0.956864i | 0.878125 | + | 0.478432i | \(0.158795\pi\) | ||||
−0.878125 | + | 0.478432i | \(0.841205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2762 | − | 3.48739i | 0.449767 | − | 0.127768i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 15.7365i | − | 0.575770i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.1304 | 0.625932 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.61490 | 0.277872 | 0.138936 | − | 0.990301i | \(-0.455632\pi\) | ||||
0.138936 | + | 0.990301i | \(0.455632\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.6156 | 0.897043 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.4347 | + | 5.52093i | −0.707301 | + | 0.200927i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.9893 | 1.05363 | 0.526817 | − | 0.849979i | \(-0.323385\pi\) | ||||
0.526817 | + | 0.849979i | \(0.323385\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.12201 | − | 1.38430i | 0.113322 | − | 0.0502469i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4769 | 0.561035 | 0.280518 | − | 0.959849i | \(-0.409494\pi\) | ||||
0.280518 | + | 0.959849i | \(0.409494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.95076 | 0.106825 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.25562 | + | 18.5007i | 0.190017 | + | 0.668896i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.89524 | −0.140649 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1918i | 0.403586i | 0.979428 | + | 0.201793i | \(0.0646769\pi\) | ||||
−0.979428 | + | 0.201793i | \(0.935323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 0.0950817i | − | 0.00342429i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 55.2126 | 1.98586 | 0.992930 | − | 0.118698i | \(-0.0378721\pi\) | ||||
0.992930 | + | 0.118698i | \(0.0378721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.07825 | + | 13.0710i | 0.290179 | + | 0.469526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.73787i | 0.277595i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.6690 | −1.99455 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.72158i | 0.0616029i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.0060 | −0.750694 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.37600 | + | 8.36397i | 0.0848032 | + | 0.298523i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2547i | 0.436833i | 0.975856 | + | 0.218417i | \(0.0700892\pi\) | ||||
−0.975856 | + | 0.218417i | \(0.929911\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.656672i | 0.0233781i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.14648i | − | 0.0763201i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.6656 | −1.19550 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.80609 | + | 20.4385i | 0.205921 | + | 0.724880i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.1677 | 1.38739 | 0.693695 | − | 0.720268i | \(-0.255981\pi\) | ||||
0.693695 | + | 0.720268i | \(0.255981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3620 | −0.578845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.33802i | − | 0.0826100i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.61467i | 0.304005i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.4813 | − | 10.3884i | 0.439909 | − | 0.366142i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.04438 | −0.247974 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.3097 | −1.10079 | −0.550395 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550395 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.77263i | 0.308049i | 0.988067 | + | 0.154024i | \(0.0492234\pi\) | ||||
−0.988067 | + | 0.154024i | \(0.950777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8470i | 0.625921i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.7492 | + | 51.9199i | 0.516642 | + | 1.81868i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.6244i | − | 0.511643i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.2191 | −0.531798 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.0728 | −1.15425 | −0.577124 | − | 0.816657i | \(-0.695825\pi\) | ||||
−0.577124 | + | 0.816657i | \(0.695825\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5269 | 0.924668 | 0.462334 | − | 0.886706i | \(-0.347012\pi\) | ||||
0.462334 | + | 0.886706i | \(0.347012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.02879 | − | 1.87187i | 0.105449 | − | 0.0651701i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.7494i | 1.62564i | 0.582517 | + | 0.812819i | \(0.302068\pi\) | ||||
−0.582517 | + | 0.812819i | \(0.697932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.9349 | 0.796564 | 0.398282 | − | 0.917263i | \(-0.369607\pi\) | ||||
0.398282 | + | 0.917263i | \(0.369607\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.05385i | 0.105937i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8665 | 0.653684 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.98050 | − | 14.0121i | −0.137751 | − | 0.484908i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 14.6153i | − | 0.505178i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.2879 | −1.59803 | −0.799017 | − | 0.601308i | \(-0.794646\pi\) | ||||
−0.799017 | + | 0.601308i | \(0.794646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.49038 | −0.327254 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 20.1557i | − | 0.694200i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.46008 | + | 19.2205i | 0.187832 | + | 0.661205i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.7581i | 0.541454i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.2025i | 0.556068i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.2406 | + | 10.7483i | −0.830957 | + | 0.368446i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.9817i | − | 0.752640i | −0.926490 | − | 0.376320i | \(-0.877189\pi\) | ||
0.926490 | − | 0.376320i | \(-0.122811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.40793 | − | 33.1176i | −0.321744 | − | 1.13260i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.3790i | 1.72091i | 0.509523 | + | 0.860457i | \(0.329822\pi\) | ||||
−0.509523 | + | 0.860457i | \(0.670178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 38.4290i | − | 1.31118i | −0.755116 | − | 0.655591i | \(-0.772420\pi\) | ||
0.755116 | − | 0.655591i | \(-0.227580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8582i | 0.370047i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65548 | 0.192515 | 0.0962573 | − | 0.995356i | \(-0.469313\pi\) | ||||
0.0962573 | + | 0.995356i | \(0.469313\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.3316 | − | 10.3209i | 1.23531 | − | 0.350923i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.863361 | 0.0293213 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.06707 | 0.104043 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.0375 | −2.00041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.88604 | 0.199212 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.4214 | − | 12.4974i | 0.386113 | − | 0.422488i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7077i | 0.631712i | 0.948807 | + | 0.315856i | \(0.102292\pi\) | ||||
−0.948807 | + | 0.315856i | \(0.897708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1711 | 0.747813 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.1580i | 0.544377i | 0.962244 | + | 0.272188i | \(0.0877474\pi\) | ||||
−0.962244 | + | 0.272188i | \(0.912253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.4724 | 1.56392 | 0.781961 | − | 0.623328i | \(-0.214220\pi\) | ||||
0.781961 | + | 0.623328i | \(0.214220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.65330 | + | 0.469662i | −0.0555750 | + | 0.0157875i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.8088 | 0.832998 | 0.416499 | − | 0.909136i | \(-0.363257\pi\) | ||||
0.416499 | + | 0.909136i | \(0.363257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0862i | 0.606592i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.57374 | 0.0527223 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.2891 | 0.980122 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.4362 | − | 5.80545i | 0.683108 | − | 0.194055i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.41435 | + | 18.9769i | 0.280947 | + | 0.633620i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.5741i | 0.452722i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.2106 | 1.37292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.85249 | −0.0949248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.39915 | + | 2.38600i | −0.279197 | + | 0.0793132i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 6.67649i | − | 0.221689i | −0.993838 | − | 0.110845i | \(-0.964644\pi\) | ||
0.993838 | − | 0.110845i | \(-0.0353556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.3294 | 0.773786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7872 | −0.887500 | −0.443750 | − | 0.896151i | \(-0.646352\pi\) | ||||
−0.443750 | + | 0.896151i | \(0.646352\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.65055i | 0.187006i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.2890 | + | 4.05917i | −0.472381 | + | 0.134192i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.2246 | −0.469736 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.3148 | 1.32986 | 0.664931 | − | 0.746905i | \(-0.268461\pi\) | ||||
0.664931 | + | 0.746905i | \(0.268461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.87190 | −0.193486 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4645 | −0.344442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.5167 | + | 14.5340i | −0.773226 | + | 0.477874i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.0129i | 1.18282i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.8831 | −0.882007 | −0.441004 | − | 0.897505i | \(-0.645377\pi\) | ||||
−0.441004 | + | 0.897505i | \(0.645377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.7723 | −1.10684 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 19.7455i | − | 0.646439i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.88714 | − | 6.64309i | −0.0617161 | − | 0.217252i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.0010 | −0.751410 | −0.375705 | − | 0.926739i | \(-0.622599\pi\) | ||||
−0.375705 | + | 0.926739i | \(0.622599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8492 | 0.419319 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.60800i | 0.215415i | 0.994183 | + | 0.107707i | \(0.0343509\pi\) | ||||
−0.994183 | + | 0.107707i | \(0.965649\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.0158 | + | 15.0826i | −1.10771 | + | 0.491157i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.4903 | + | 4.40042i | −0.503899 | + | 0.143146i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.7062 | 0.380400 | 0.190200 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190200 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.3635 | −1.69979 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7574i | 0.964951i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.14979 | −0.102032 | −0.0510158 | − | 0.998698i | \(-0.516246\pi\) | ||||
−0.0510158 | + | 0.998698i | \(0.516246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.07825 | − | 28.4369i | −0.261406 | − | 0.920197i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.14536 | 0.101675 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 20.9215i | − | 0.675591i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.5556 | 0.695342 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 24.2753i | − | 0.782262i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.8809 | − | 6.21585i | 0.704372 | − | 0.200095i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5256 | −0.724374 | −0.362187 | − | 0.932105i | \(-0.617970\pi\) | ||||
−0.362187 | + | 0.932105i | \(0.617970\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.5786 | 0.853829 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.9870 | 1.57207 | 0.786033 | − | 0.618184i | \(-0.212131\pi\) | ||||
0.786033 | + | 0.618184i | \(0.212131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.2986 | 0.971329 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.3780 | + | 18.4102i | 0.364388 | + | 0.589599i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.8557 | 1.30709 | 0.653544 | − | 0.756888i | \(-0.273281\pi\) | ||||
0.653544 | + | 0.756888i | \(0.273281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.839518i | 0.0268311i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.18149i | − | 0.133505i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.78502i | − | 0.184513i | −0.995735 | − | 0.0922567i | \(-0.970592\pi\) | ||
0.995735 | − | 0.0922567i | \(-0.0294080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.3215 | − | 11.1703i | 1.25289 | − | 0.355916i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.71283i | − | 0.181842i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.96224 | − | 8.93604i | −0.125992 | − | 0.284149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.0084i | − | 1.49327i | −0.665233 | − | 0.746636i | \(-0.731668\pi\) | ||
0.665233 | − | 0.746636i | \(-0.268332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 26.9521i | − | 0.855298i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.9491 | − | 38.5428i | −0.347109 | − | 1.22189i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.74045i | − | 0.150132i | −0.997179 | − | 0.0750658i | \(-0.976083\pi\) | ||
0.997179 | − | 0.0750658i | \(-0.0239167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.2950 | 0.831938 |
(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 | 1840.2.m.g.1839.18 | yes | 40 | |
4.3 | odd | 2 | inner | 1840.2.m.g.1839.23 | yes | 40 | |
5.4 | even | 2 | inner | 1840.2.m.g.1839.24 | yes | 40 | |
20.19 | odd | 2 | inner | 1840.2.m.g.1839.17 | ✓ | 40 | |
23.22 | odd | 2 | inner | 1840.2.m.g.1839.20 | yes | 40 | |
92.91 | even | 2 | inner | 1840.2.m.g.1839.21 | yes | 40 | |
115.114 | odd | 2 | inner | 1840.2.m.g.1839.22 | yes | 40 | |
460.459 | even | 2 | inner | 1840.2.m.g.1839.19 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.m.g.1839.17 | ✓ | 40 | 20.19 | odd | 2 | inner | |
1840.2.m.g.1839.18 | yes | 40 | 1.1 | even | 1 | trivial | |
1840.2.m.g.1839.19 | yes | 40 | 460.459 | even | 2 | inner | |
1840.2.m.g.1839.20 | yes | 40 | 23.22 | odd | 2 | inner | |
1840.2.m.g.1839.21 | yes | 40 | 92.91 | even | 2 | inner | |
1840.2.m.g.1839.22 | yes | 40 | 115.114 | odd | 2 | inner | |
1840.2.m.g.1839.23 | yes | 40 | 4.3 | odd | 2 | inner | |
1840.2.m.g.1839.24 | yes | 40 | 5.4 | even | 2 | inner |