Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(83,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.b (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: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 83.5 | ||
Character | \(\chi\) | \(=\) | 287.83 |
Dual form | 287.3.b.a.83.6 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.35920 | −1.67960 | −0.839799 | − | 0.542898i | \(-0.817327\pi\) | ||||
−0.839799 | + | 0.542898i | \(0.817327\pi\) | |||||||
\(3\) | − | 4.56039i | − | 1.52013i | −0.649846 | − | 0.760066i | \(-0.725167\pi\) | ||
0.649846 | − | 0.760066i | \(-0.274833\pi\) | |||||||
\(4\) | 7.28419 | 1.82105 | ||||||||
\(5\) | 3.56634i | 0.713269i | 0.934244 | + | 0.356634i | \(0.116076\pi\) | ||||
−0.934244 | + | 0.356634i | \(0.883924\pi\) | |||||||
\(6\) | 15.3193i | 2.55321i | ||||||||
\(7\) | 1.27295 | + | 6.88328i | 0.181850 | + | 0.983326i | ||||
\(8\) | −11.0323 | −1.37903 | ||||||||
\(9\) | −11.7972 | −1.31080 | ||||||||
\(10\) | − | 11.9800i | − | 1.19800i | ||||||
\(11\) | 0.313836 | 0.0285306 | 0.0142653 | − | 0.999898i | \(-0.495459\pi\) | ||||
0.0142653 | + | 0.999898i | \(0.495459\pi\) | |||||||
\(12\) | − | 33.2188i | − | 2.76823i | ||||||
\(13\) | − | 10.3956i | − | 0.799658i | −0.916590 | − | 0.399829i | \(-0.869069\pi\) | ||
0.916590 | − | 0.399829i | \(-0.130931\pi\) | |||||||
\(14\) | −4.27608 | − | 23.1223i | −0.305434 | − | 1.65159i | ||||
\(15\) | 16.2639 | 1.08426 | ||||||||
\(16\) | 7.92271 | 0.495169 | ||||||||
\(17\) | − | 26.5564i | − | 1.56214i | −0.624444 | − | 0.781070i | \(-0.714674\pi\) | ||
0.624444 | − | 0.781070i | \(-0.285326\pi\) | |||||||
\(18\) | 39.6291 | 2.20162 | ||||||||
\(19\) | 4.84799i | 0.255157i | 0.991828 | + | 0.127579i | \(0.0407205\pi\) | ||||
−0.991828 | + | 0.127579i | \(0.959280\pi\) | |||||||
\(20\) | 25.9779i | 1.29890i | ||||||||
\(21\) | 31.3905 | − | 5.80514i | 1.49479 | − | 0.276435i | ||||
\(22\) | −1.05424 | −0.0479199 | ||||||||
\(23\) | −34.6765 | −1.50767 | −0.753836 | − | 0.657063i | \(-0.771799\pi\) | ||||
−0.753836 | + | 0.657063i | \(0.771799\pi\) | |||||||
\(24\) | 50.3114i | 2.09631i | ||||||||
\(25\) | 12.2812 | 0.491248 | ||||||||
\(26\) | 34.9207i | 1.34310i | ||||||||
\(27\) | 12.7563i | 0.472457i | ||||||||
\(28\) | 9.27239 | + | 50.1392i | 0.331157 | + | 1.79069i | ||||
\(29\) | −45.2334 | −1.55977 | −0.779886 | − | 0.625922i | \(-0.784723\pi\) | ||||
−0.779886 | + | 0.625922i | \(0.784723\pi\) | |||||||
\(30\) | −54.6337 | −1.82112 | ||||||||
\(31\) | − | 35.3890i | − | 1.14158i | −0.821096 | − | 0.570790i | \(-0.806637\pi\) | ||
0.821096 | − | 0.570790i | \(-0.193363\pi\) | |||||||
\(32\) | 17.5151 | 0.547346 | ||||||||
\(33\) | − | 1.43122i | − | 0.0433702i | ||||||
\(34\) | 89.2080i | 2.62377i | ||||||||
\(35\) | −24.5482 | + | 4.53977i | −0.701376 | + | 0.129708i | ||||
\(36\) | −85.9331 | −2.38703 | ||||||||
\(37\) | 17.8108 | 0.481373 | 0.240687 | − | 0.970603i | \(-0.422627\pi\) | ||||
0.240687 | + | 0.970603i | \(0.422627\pi\) | |||||||
\(38\) | − | 16.2853i | − | 0.428561i | ||||||
\(39\) | −47.4078 | −1.21559 | ||||||||
\(40\) | − | 39.3448i | − | 0.983620i | ||||||
\(41\) | − | 6.40312i | − | 0.156174i | ||||||
\(42\) | −105.447 | + | 19.5006i | −2.51064 | + | 0.464300i | ||||
\(43\) | −0.974054 | −0.0226524 | −0.0113262 | − | 0.999936i | \(-0.503605\pi\) | ||||
−0.0113262 | + | 0.999936i | \(0.503605\pi\) | |||||||
\(44\) | 2.28604 | 0.0519556 | ||||||||
\(45\) | − | 42.0729i | − | 0.934953i | ||||||
\(46\) | 116.485 | 2.53228 | ||||||||
\(47\) | − | 56.7092i | − | 1.20658i | −0.797522 | − | 0.603290i | \(-0.793856\pi\) | ||
0.797522 | − | 0.603290i | \(-0.206144\pi\) | |||||||
\(48\) | − | 36.1307i | − | 0.752723i | ||||||
\(49\) | −45.7592 | + | 17.5241i | −0.933861 | + | 0.357635i | ||||
\(50\) | −41.2549 | −0.825099 | ||||||||
\(51\) | −121.108 | −2.37466 | ||||||||
\(52\) | − | 75.7233i | − | 1.45622i | ||||||
\(53\) | −87.2889 | −1.64696 | −0.823480 | − | 0.567345i | \(-0.807971\pi\) | ||||
−0.823480 | + | 0.567345i | \(0.807971\pi\) | |||||||
\(54\) | − | 42.8511i | − | 0.793538i | ||||||
\(55\) | 1.11925i | 0.0203500i | ||||||||
\(56\) | −14.0435 | − | 75.9381i | −0.250776 | − | 1.35604i | ||||
\(57\) | 22.1087 | 0.387872 | ||||||||
\(58\) | 151.948 | 2.61979 | ||||||||
\(59\) | 15.1393i | 0.256599i | 0.991735 | + | 0.128299i | \(0.0409518\pi\) | ||||
−0.991735 | + | 0.128299i | \(0.959048\pi\) | |||||||
\(60\) | 118.470 | 1.97449 | ||||||||
\(61\) | 6.27574i | 0.102881i | 0.998676 | + | 0.0514405i | \(0.0163812\pi\) | ||||
−0.998676 | + | 0.0514405i | \(0.983619\pi\) | |||||||
\(62\) | 118.879i | 1.91740i | ||||||||
\(63\) | −15.0172 | − | 81.2035i | −0.238368 | − | 1.28894i | ||||
\(64\) | −90.5274 | −1.41449 | ||||||||
\(65\) | 37.0741 | 0.570371 | ||||||||
\(66\) | 4.80774i | 0.0728445i | ||||||||
\(67\) | 39.9510 | 0.596283 | 0.298141 | − | 0.954522i | \(-0.403633\pi\) | ||||
0.298141 | + | 0.954522i | \(0.403633\pi\) | |||||||
\(68\) | − | 193.442i | − | 2.84473i | ||||||
\(69\) | 158.138i | 2.29186i | ||||||||
\(70\) | 82.4621 | − | 15.2500i | 1.17803 | − | 0.217857i | ||||
\(71\) | −48.0225 | −0.676374 | −0.338187 | − | 0.941079i | \(-0.609814\pi\) | ||||
−0.338187 | + | 0.941079i | \(0.609814\pi\) | |||||||
\(72\) | 130.150 | 1.80763 | ||||||||
\(73\) | 28.6886i | 0.392994i | 0.980504 | + | 0.196497i | \(0.0629566\pi\) | ||||
−0.980504 | + | 0.196497i | \(0.937043\pi\) | |||||||
\(74\) | −59.8300 | −0.808513 | ||||||||
\(75\) | − | 56.0071i | − | 0.746761i | ||||||
\(76\) | 35.3137i | 0.464654i | ||||||||
\(77\) | 0.399497 | + | 2.16022i | 0.00518827 | + | 0.0280549i | ||||
\(78\) | 159.252 | 2.04170 | ||||||||
\(79\) | 38.1014 | 0.482296 | 0.241148 | − | 0.970488i | \(-0.422476\pi\) | ||||
0.241148 | + | 0.970488i | \(0.422476\pi\) | |||||||
\(80\) | 28.2551i | 0.353189i | ||||||||
\(81\) | −48.0008 | −0.592603 | ||||||||
\(82\) | 21.5093i | 0.262309i | ||||||||
\(83\) | − | 73.4375i | − | 0.884790i | −0.896820 | − | 0.442395i | \(-0.854129\pi\) | ||
0.896820 | − | 0.442395i | \(-0.145871\pi\) | |||||||
\(84\) | 228.654 | − | 42.2858i | 2.72208 | − | 0.503402i | ||||
\(85\) | 94.7091 | 1.11423 | ||||||||
\(86\) | 3.27204 | 0.0380469 | ||||||||
\(87\) | 206.282i | 2.37106i | ||||||||
\(88\) | −3.46232 | −0.0393445 | ||||||||
\(89\) | 104.582i | 1.17508i | 0.809196 | + | 0.587539i | \(0.199903\pi\) | ||||
−0.809196 | + | 0.587539i | \(0.800097\pi\) | |||||||
\(90\) | 141.331i | 1.57034i | ||||||||
\(91\) | 71.5556 | − | 13.2330i | 0.786325 | − | 0.145417i | ||||
\(92\) | −252.590 | −2.74554 | ||||||||
\(93\) | −161.388 | −1.73535 | ||||||||
\(94\) | 190.497i | 2.02657i | ||||||||
\(95\) | −17.2896 | −0.181996 | ||||||||
\(96\) | − | 79.8757i | − | 0.832038i | ||||||
\(97\) | − | 65.6700i | − | 0.677010i | −0.940965 | − | 0.338505i | \(-0.890079\pi\) | ||
0.940965 | − | 0.338505i | \(-0.109921\pi\) | |||||||
\(98\) | 153.714 | − | 58.8669i | 1.56851 | − | 0.600683i | ||||
\(99\) | −3.70239 | −0.0373979 | ||||||||
\(100\) | 89.4586 | 0.894586 | ||||||||
\(101\) | − | 21.6084i | − | 0.213944i | −0.994262 | − | 0.106972i | \(-0.965884\pi\) | ||
0.994262 | − | 0.106972i | \(-0.0341155\pi\) | |||||||
\(102\) | 406.824 | 3.98847 | ||||||||
\(103\) | − | 73.2761i | − | 0.711418i | −0.934597 | − | 0.355709i | \(-0.884239\pi\) | ||
0.934597 | − | 0.355709i | \(-0.115761\pi\) | |||||||
\(104\) | 114.686i | 1.10275i | ||||||||
\(105\) | 20.7031 | + | 111.949i | 0.197173 | + | 1.06618i | ||||
\(106\) | 293.220 | 2.76623 | ||||||||
\(107\) | 74.1395 | 0.692892 | 0.346446 | − | 0.938070i | \(-0.387388\pi\) | ||||
0.346446 | + | 0.938070i | \(0.387388\pi\) | |||||||
\(108\) | 92.9197i | 0.860367i | ||||||||
\(109\) | −109.258 | −1.00237 | −0.501184 | − | 0.865341i | \(-0.667102\pi\) | ||||
−0.501184 | + | 0.865341i | \(0.667102\pi\) | |||||||
\(110\) | − | 3.75977i | − | 0.0341797i | ||||||
\(111\) | − | 81.2243i | − | 0.731751i | ||||||
\(112\) | 10.0852 | + | 54.5343i | 0.0900463 | + | 0.486913i | ||||
\(113\) | 126.959 | 1.12353 | 0.561764 | − | 0.827297i | \(-0.310123\pi\) | ||||
0.561764 | + | 0.827297i | \(0.310123\pi\) | |||||||
\(114\) | −74.2675 | −0.651470 | ||||||||
\(115\) | − | 123.668i | − | 1.07538i | ||||||
\(116\) | −329.489 | −2.84042 | ||||||||
\(117\) | 122.638i | 1.04819i | ||||||||
\(118\) | − | 50.8560i | − | 0.430983i | ||||||
\(119\) | 182.795 | − | 33.8048i | 1.53609 | − | 0.284074i | ||||
\(120\) | −179.428 | −1.49523 | ||||||||
\(121\) | −120.902 | −0.999186 | ||||||||
\(122\) | − | 21.0814i | − | 0.172799i | ||||||
\(123\) | −29.2008 | −0.237405 | ||||||||
\(124\) | − | 257.780i | − | 2.07887i | ||||||
\(125\) | 132.958i | 1.06366i | ||||||||
\(126\) | 50.4457 | + | 272.778i | 0.400363 | + | 2.16491i | ||||
\(127\) | 120.508 | 0.948880 | 0.474440 | − | 0.880288i | \(-0.342651\pi\) | ||||
0.474440 | + | 0.880288i | \(0.342651\pi\) | |||||||
\(128\) | 234.039 | 1.82843 | ||||||||
\(129\) | 4.44207i | 0.0344346i | ||||||||
\(130\) | −124.539 | −0.957994 | ||||||||
\(131\) | − | 214.162i | − | 1.63482i | −0.576054 | − | 0.817412i | \(-0.695408\pi\) | ||
0.576054 | − | 0.817412i | \(-0.304592\pi\) | |||||||
\(132\) | − | 10.4253i | − | 0.0789793i | ||||||
\(133\) | −33.3701 | + | 6.17123i | −0.250903 | + | 0.0464002i | ||||
\(134\) | −134.203 | −1.00152 | ||||||||
\(135\) | −45.4935 | −0.336989 | ||||||||
\(136\) | 292.977i | 2.15424i | ||||||||
\(137\) | −146.468 | −1.06911 | −0.534556 | − | 0.845133i | \(-0.679521\pi\) | ||||
−0.534556 | + | 0.845133i | \(0.679521\pi\) | |||||||
\(138\) | − | 531.217i | − | 3.84940i | ||||||
\(139\) | − | 226.849i | − | 1.63200i | −0.578049 | − | 0.816002i | \(-0.696186\pi\) | ||
0.578049 | − | 0.816002i | \(-0.303814\pi\) | |||||||
\(140\) | −178.814 | + | 33.0685i | −1.27724 | + | 0.236204i | ||||
\(141\) | −258.617 | −1.83416 | ||||||||
\(142\) | 161.317 | 1.13604 | ||||||||
\(143\) | − | 3.26250i | − | 0.0228147i | ||||||
\(144\) | −93.4658 | −0.649068 | ||||||||
\(145\) | − | 161.318i | − | 1.11254i | ||||||
\(146\) | − | 96.3705i | − | 0.660072i | ||||||
\(147\) | 79.9169 | + | 208.680i | 0.543652 | + | 1.41959i | ||||
\(148\) | 129.737 | 0.876604 | ||||||||
\(149\) | −151.441 | −1.01638 | −0.508192 | − | 0.861244i | \(-0.669686\pi\) | ||||
−0.508192 | + | 0.861244i | \(0.669686\pi\) | |||||||
\(150\) | 188.139i | 1.25426i | ||||||||
\(151\) | −264.889 | −1.75423 | −0.877117 | − | 0.480277i | \(-0.840536\pi\) | ||||
−0.877117 | + | 0.480277i | \(0.840536\pi\) | |||||||
\(152\) | − | 53.4842i | − | 0.351870i | ||||||
\(153\) | 313.291i | 2.04765i | ||||||||
\(154\) | −1.34199 | − | 7.25662i | −0.00871421 | − | 0.0471209i | ||||
\(155\) | 126.209 | 0.814254 | ||||||||
\(156\) | −345.328 | −2.21364 | ||||||||
\(157\) | − | 120.013i | − | 0.764417i | −0.924076 | − | 0.382209i | \(-0.875164\pi\) | ||
0.924076 | − | 0.382209i | \(-0.124836\pi\) | |||||||
\(158\) | −127.990 | −0.810063 | ||||||||
\(159\) | 398.072i | 2.50360i | ||||||||
\(160\) | 62.4648i | 0.390405i | ||||||||
\(161\) | −44.1413 | − | 238.688i | −0.274169 | − | 1.48253i | ||||
\(162\) | 161.244 | 0.995335 | ||||||||
\(163\) | 57.9974 | 0.355812 | 0.177906 | − | 0.984047i | \(-0.443068\pi\) | ||||
0.177906 | + | 0.984047i | \(0.443068\pi\) | |||||||
\(164\) | − | 46.6416i | − | 0.284400i | ||||||
\(165\) | 5.10421 | 0.0309346 | ||||||||
\(166\) | 246.691i | 1.48609i | ||||||||
\(167\) | 109.476i | 0.655547i | 0.944756 | + | 0.327773i | \(0.106298\pi\) | ||||
−0.944756 | + | 0.327773i | \(0.893702\pi\) | |||||||
\(168\) | −346.308 | + | 64.0438i | −2.06136 | + | 0.381213i | ||||
\(169\) | 60.9324 | 0.360547 | ||||||||
\(170\) | −318.147 | −1.87145 | ||||||||
\(171\) | − | 57.1927i | − | 0.334460i | ||||||
\(172\) | −7.09519 | −0.0412511 | ||||||||
\(173\) | − | 172.305i | − | 0.995981i | −0.867182 | − | 0.497991i | \(-0.834071\pi\) | ||
0.867182 | − | 0.497991i | \(-0.165929\pi\) | |||||||
\(174\) | − | 692.942i | − | 3.98242i | ||||||
\(175\) | 15.6333 | + | 84.5350i | 0.0893332 | + | 0.483057i | ||||
\(176\) | 2.48643 | 0.0141275 | ||||||||
\(177\) | 69.0413 | 0.390064 | ||||||||
\(178\) | − | 351.311i | − | 1.97366i | ||||||
\(179\) | 308.450 | 1.72319 | 0.861593 | − | 0.507599i | \(-0.169467\pi\) | ||||
0.861593 | + | 0.507599i | \(0.169467\pi\) | |||||||
\(180\) | − | 306.467i | − | 1.70259i | ||||||
\(181\) | 310.847i | 1.71739i | 0.512490 | + | 0.858693i | \(0.328723\pi\) | ||||
−0.512490 | + | 0.858693i | \(0.671277\pi\) | |||||||
\(182\) | −240.369 | + | 44.4522i | −1.32071 | + | 0.244243i | ||||
\(183\) | 28.6198 | 0.156393 | ||||||||
\(184\) | 382.559 | 2.07913 | ||||||||
\(185\) | 63.5195i | 0.343348i | ||||||||
\(186\) | 542.133 | 2.91469 | ||||||||
\(187\) | − | 8.33435i | − | 0.0445687i | ||||||
\(188\) | − | 413.081i | − | 2.19724i | ||||||
\(189\) | −87.8055 | + | 16.2381i | −0.464580 | + | 0.0859161i | ||||
\(190\) | 58.0791 | 0.305679 | ||||||||
\(191\) | 100.425 | 0.525787 | 0.262894 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262894 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(192\) | 412.841i | 2.15021i | ||||||||
\(193\) | −35.3561 | −0.183192 | −0.0915960 | − | 0.995796i | \(-0.529197\pi\) | ||||
−0.0915960 | + | 0.995796i | \(0.529197\pi\) | |||||||
\(194\) | 220.598i | 1.13710i | ||||||||
\(195\) | − | 169.073i | − | 0.867039i | ||||||
\(196\) | −333.319 | + | 127.649i | −1.70061 | + | 0.651271i | ||||
\(197\) | 169.453 | 0.860170 | 0.430085 | − | 0.902788i | \(-0.358484\pi\) | ||||
0.430085 | + | 0.902788i | \(0.358484\pi\) | |||||||
\(198\) | 12.4371 | 0.0628134 | ||||||||
\(199\) | − | 26.0523i | − | 0.130916i | −0.997855 | − | 0.0654581i | \(-0.979149\pi\) | ||
0.997855 | − | 0.0654581i | \(-0.0208509\pi\) | |||||||
\(200\) | −135.489 | −0.677446 | ||||||||
\(201\) | − | 182.192i | − | 0.906429i | ||||||
\(202\) | 72.5867i | 0.359340i | ||||||||
\(203\) | −57.5797 | − | 311.354i | −0.283644 | − | 1.53376i | ||||
\(204\) | −882.171 | −4.32437 | ||||||||
\(205\) | 22.8357 | 0.111394 | ||||||||
\(206\) | 246.149i | 1.19490i | ||||||||
\(207\) | 409.085 | 1.97626 | ||||||||
\(208\) | − | 82.3610i | − | 0.395966i | ||||||
\(209\) | 1.52147i | 0.00727978i | ||||||||
\(210\) | −69.5458 | − | 376.060i | −0.331171 | − | 1.79076i | ||||
\(211\) | −42.6517 | −0.202141 | −0.101070 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101070 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(212\) | −635.829 | −2.99919 | ||||||||
\(213\) | 219.002i | 1.02818i | ||||||||
\(214\) | −249.049 | −1.16378 | ||||||||
\(215\) | − | 3.47381i | − | 0.0161573i | ||||||
\(216\) | − | 140.731i | − | 0.651533i | ||||||
\(217\) | 243.593 | − | 45.0483i | 1.12255 | − | 0.207596i | ||||
\(218\) | 367.019 | 1.68357 | ||||||||
\(219\) | 130.831 | 0.597403 | ||||||||
\(220\) | 8.15282i | 0.0370583i | ||||||||
\(221\) | −276.068 | −1.24918 | ||||||||
\(222\) | 272.848i | 1.22905i | ||||||||
\(223\) | 292.007i | 1.30945i | 0.755868 | + | 0.654724i | \(0.227215\pi\) | ||||
−0.755868 | + | 0.654724i | \(0.772785\pi\) | |||||||
\(224\) | 22.2958 | + | 120.561i | 0.0995346 | + | 0.538220i | ||||
\(225\) | −144.884 | −0.643928 | ||||||||
\(226\) | −426.479 | −1.88708 | ||||||||
\(227\) | − | 55.3238i | − | 0.243717i | −0.992547 | − | 0.121859i | \(-0.961115\pi\) | ||
0.992547 | − | 0.121859i | \(-0.0388854\pi\) | |||||||
\(228\) | 161.044 | 0.706335 | ||||||||
\(229\) | 78.9671i | 0.344835i | 0.985024 | + | 0.172417i | \(0.0551577\pi\) | ||||
−0.985024 | + | 0.172417i | \(0.944842\pi\) | |||||||
\(230\) | 415.425i | 1.80620i | ||||||||
\(231\) | 9.85148 | − | 1.82186i | 0.0426471 | − | 0.00788685i | ||||
\(232\) | 499.026 | 2.15097 | ||||||||
\(233\) | 357.687 | 1.53514 | 0.767569 | − | 0.640967i | \(-0.221466\pi\) | ||||
0.767569 | + | 0.640967i | \(0.221466\pi\) | |||||||
\(234\) | − | 411.967i | − | 1.76054i | ||||||
\(235\) | 202.245 | 0.860616 | ||||||||
\(236\) | 110.278i | 0.467279i | ||||||||
\(237\) | − | 173.757i | − | 0.733153i | ||||||
\(238\) | −614.044 | + | 113.557i | −2.58002 | + | 0.477131i | ||||
\(239\) | −342.471 | −1.43293 | −0.716466 | − | 0.697622i | \(-0.754241\pi\) | ||||
−0.716466 | + | 0.697622i | \(0.754241\pi\) | |||||||
\(240\) | 128.854 | 0.536893 | ||||||||
\(241\) | 316.926i | 1.31505i | 0.753435 | + | 0.657523i | \(0.228396\pi\) | ||||
−0.753435 | + | 0.657523i | \(0.771604\pi\) | |||||||
\(242\) | 406.132 | 1.67823 | ||||||||
\(243\) | 333.710i | 1.37329i | ||||||||
\(244\) | 45.7137i | 0.187351i | ||||||||
\(245\) | −62.4970 | − | 163.193i | −0.255090 | − | 0.666094i | ||||
\(246\) | 98.0911 | 0.398744 | ||||||||
\(247\) | 50.3975 | 0.204039 | ||||||||
\(248\) | 390.420i | 1.57428i | ||||||||
\(249\) | −334.904 | −1.34500 | ||||||||
\(250\) | − | 446.630i | − | 1.78652i | ||||||
\(251\) | − | 55.4944i | − | 0.221093i | −0.993871 | − | 0.110547i | \(-0.964740\pi\) | ||
0.993871 | − | 0.110547i | \(-0.0352601\pi\) | |||||||
\(252\) | −109.388 | − | 591.502i | −0.434080 | − | 2.34723i | ||||
\(253\) | −10.8827 | −0.0430147 | ||||||||
\(254\) | −404.809 | −1.59374 | ||||||||
\(255\) | − | 431.911i | − | 1.69377i | ||||||
\(256\) | −424.073 | −1.65653 | ||||||||
\(257\) | 470.721i | 1.83160i | 0.401636 | + | 0.915799i | \(0.368442\pi\) | ||||
−0.401636 | + | 0.915799i | \(0.631558\pi\) | |||||||
\(258\) | − | 14.9218i | − | 0.0578363i | ||||||
\(259\) | 22.6722 | + | 122.597i | 0.0875375 | + | 0.473347i | ||||
\(260\) | 270.055 | 1.03867 | ||||||||
\(261\) | 533.627 | 2.04455 | ||||||||
\(262\) | 719.412i | 2.74585i | ||||||||
\(263\) | −461.940 | −1.75643 | −0.878213 | − | 0.478271i | \(-0.841264\pi\) | ||||
−0.878213 | + | 0.478271i | \(0.841264\pi\) | |||||||
\(264\) | 15.7895i | 0.0598089i | ||||||||
\(265\) | − | 311.302i | − | 1.17473i | ||||||
\(266\) | 112.097 | − | 20.7304i | 0.421416 | − | 0.0779337i | ||||
\(267\) | 476.935 | 1.78627 | ||||||||
\(268\) | 291.011 | 1.08586 | ||||||||
\(269\) | 96.5332i | 0.358859i | 0.983771 | + | 0.179430i | \(0.0574252\pi\) | ||||
−0.983771 | + | 0.179430i | \(0.942575\pi\) | |||||||
\(270\) | 152.822 | 0.566006 | ||||||||
\(271\) | − | 281.587i | − | 1.03907i | −0.854450 | − | 0.519533i | \(-0.826106\pi\) | ||
0.854450 | − | 0.519533i | \(-0.173894\pi\) | |||||||
\(272\) | − | 210.398i | − | 0.773524i | ||||||
\(273\) | −60.3477 | − | 326.322i | −0.221054 | − | 1.19532i | ||||
\(274\) | 492.016 | 1.79568 | ||||||||
\(275\) | 3.85428 | 0.0140156 | ||||||||
\(276\) | 1151.91i | 4.17359i | ||||||||
\(277\) | 295.004 | 1.06500 | 0.532498 | − | 0.846431i | \(-0.321253\pi\) | ||||
0.532498 | + | 0.846431i | \(0.321253\pi\) | |||||||
\(278\) | 762.029i | 2.74111i | ||||||||
\(279\) | 417.491i | 1.49638i | ||||||||
\(280\) | 270.821 | − | 50.0838i | 0.967219 | − | 0.178871i | ||||
\(281\) | 433.500 | 1.54270 | 0.771352 | − | 0.636409i | \(-0.219581\pi\) | ||||
0.771352 | + | 0.636409i | \(0.219581\pi\) | |||||||
\(282\) | 868.744 | 3.08065 | ||||||||
\(283\) | − | 453.321i | − | 1.60184i | −0.598770 | − | 0.800921i | \(-0.704344\pi\) | ||
0.598770 | − | 0.800921i | \(-0.295656\pi\) | |||||||
\(284\) | −349.805 | −1.23171 | ||||||||
\(285\) | 78.8473i | 0.276657i | ||||||||
\(286\) | 10.9594i | 0.0383195i | ||||||||
\(287\) | 44.0745 | − | 8.15084i | 0.153570 | − | 0.0284001i | ||||
\(288\) | −206.629 | −0.717461 | ||||||||
\(289\) | −416.241 | −1.44028 | ||||||||
\(290\) | 541.898i | 1.86861i | ||||||||
\(291\) | −299.481 | −1.02914 | ||||||||
\(292\) | 208.973i | 0.715661i | ||||||||
\(293\) | − | 287.106i | − | 0.979882i | −0.871756 | − | 0.489941i | \(-0.837018\pi\) | ||
0.871756 | − | 0.489941i | \(-0.162982\pi\) | |||||||
\(294\) | −268.456 | − | 700.997i | −0.913117 | − | 2.38434i | ||||
\(295\) | −53.9920 | −0.183024 | ||||||||
\(296\) | −196.493 | −0.663829 | ||||||||
\(297\) | 4.00340i | 0.0134795i | ||||||||
\(298\) | 508.720 | 1.70711 | ||||||||
\(299\) | 360.481i | 1.20562i | ||||||||
\(300\) | − | 407.967i | − | 1.35989i | ||||||
\(301\) | −1.23992 | − | 6.70469i | −0.00411933 | − | 0.0222747i | ||||
\(302\) | 889.815 | 2.94641 | ||||||||
\(303\) | −98.5427 | −0.325223 | ||||||||
\(304\) | 38.4092i | 0.126346i | ||||||||
\(305\) | −22.3814 | −0.0733818 | ||||||||
\(306\) | − | 1052.41i | − | 3.43923i | ||||||
\(307\) | − | 455.564i | − | 1.48392i | −0.670443 | − | 0.741961i | \(-0.733896\pi\) | ||
0.670443 | − | 0.741961i | \(-0.266104\pi\) | |||||||
\(308\) | 2.91001 | + | 15.7355i | 0.00944809 | + | 0.0510893i | ||||
\(309\) | −334.168 | −1.08145 | ||||||||
\(310\) | −423.962 | −1.36762 | ||||||||
\(311\) | 164.684i | 0.529531i | 0.964313 | + | 0.264766i | \(0.0852946\pi\) | ||||
−0.964313 | + | 0.264766i | \(0.914705\pi\) | |||||||
\(312\) | 523.015 | 1.67633 | ||||||||
\(313\) | 79.6054i | 0.254330i | 0.991882 | + | 0.127165i | \(0.0405878\pi\) | ||||
−0.991882 | + | 0.127165i | \(0.959412\pi\) | |||||||
\(314\) | 403.149i | 1.28391i | ||||||||
\(315\) | 289.600 | − | 53.5565i | 0.919364 | − | 0.170021i | ||||
\(316\) | 277.538 | 0.878284 | ||||||||
\(317\) | 309.299 | 0.975705 | 0.487853 | − | 0.872926i | \(-0.337780\pi\) | ||||
0.487853 | + | 0.872926i | \(0.337780\pi\) | |||||||
\(318\) | − | 1337.20i | − | 4.20504i | ||||||
\(319\) | −14.1959 | −0.0445012 | ||||||||
\(320\) | − | 322.852i | − | 1.00891i | ||||||
\(321\) | − | 338.105i | − | 1.05329i | ||||||
\(322\) | 148.279 | + | 801.799i | 0.460494 | + | 2.49006i | ||||
\(323\) | 128.745 | 0.398591 | ||||||||
\(324\) | −349.648 | −1.07916 | ||||||||
\(325\) | − | 127.670i | − | 0.392830i | ||||||
\(326\) | −194.825 | −0.597622 | ||||||||
\(327\) | 498.260i | 1.52373i | ||||||||
\(328\) | 70.6409i | 0.215369i | ||||||||
\(329\) | 390.346 | − | 72.1879i | 1.18646 | − | 0.219416i | ||||
\(330\) | −17.1460 | −0.0519577 | ||||||||
\(331\) | 382.963 | 1.15699 | 0.578495 | − | 0.815686i | \(-0.303640\pi\) | ||||
0.578495 | + | 0.815686i | \(0.303640\pi\) | |||||||
\(332\) | − | 534.933i | − | 1.61124i | ||||||
\(333\) | −210.118 | −0.630984 | ||||||||
\(334\) | − | 367.752i | − | 1.10106i | ||||||
\(335\) | 142.479i | 0.425310i | ||||||||
\(336\) | 248.698 | − | 45.9924i | 0.740172 | − | 0.136882i | ||||
\(337\) | −524.806 | −1.55729 | −0.778644 | − | 0.627466i | \(-0.784092\pi\) | ||||
−0.778644 | + | 0.627466i | \(0.784092\pi\) | |||||||
\(338\) | −204.684 | −0.605573 | ||||||||
\(339\) | − | 578.982i | − | 1.70791i | ||||||
\(340\) | 689.880 | 2.02906 | ||||||||
\(341\) | − | 11.1064i | − | 0.0325699i | ||||||
\(342\) | 192.121i | 0.561758i | ||||||||
\(343\) | −178.872 | − | 292.666i | −0.521494 | − | 0.853255i | ||||
\(344\) | 10.7460 | 0.0312384 | ||||||||
\(345\) | −563.976 | −1.63471 | ||||||||
\(346\) | 578.805i | 1.67285i | ||||||||
\(347\) | −198.980 | −0.573430 | −0.286715 | − | 0.958016i | \(-0.592563\pi\) | ||||
−0.286715 | + | 0.958016i | \(0.592563\pi\) | |||||||
\(348\) | 1502.60i | 4.31781i | ||||||||
\(349\) | 520.274i | 1.49076i | 0.666642 | + | 0.745378i | \(0.267731\pi\) | ||||
−0.666642 | + | 0.745378i | \(0.732269\pi\) | |||||||
\(350\) | −52.5153 | − | 283.969i | −0.150044 | − | 0.811341i | ||||
\(351\) | 132.609 | 0.377804 | ||||||||
\(352\) | 5.49687 | 0.0156161 | ||||||||
\(353\) | − | 357.173i | − | 1.01182i | −0.862586 | − | 0.505911i | \(-0.831156\pi\) | ||
0.862586 | − | 0.505911i | \(-0.168844\pi\) | |||||||
\(354\) | −231.923 | −0.655150 | ||||||||
\(355\) | − | 171.265i | − | 0.482436i | ||||||
\(356\) | 761.796i | 2.13988i | ||||||||
\(357\) | −154.163 | − | 833.618i | −0.431830 | − | 2.33506i | ||||
\(358\) | −1036.15 | −2.89426 | ||||||||
\(359\) | 706.755 | 1.96868 | 0.984338 | − | 0.176293i | \(-0.0564105\pi\) | ||||
0.984338 | + | 0.176293i | \(0.0564105\pi\) | |||||||
\(360\) | 464.158i | 1.28933i | ||||||||
\(361\) | 337.497 | 0.934895 | ||||||||
\(362\) | − | 1044.20i | − | 2.88452i | ||||||
\(363\) | 551.359i | 1.51889i | ||||||||
\(364\) | 521.225 | − | 96.3917i | 1.43194 | − | 0.264812i | ||||
\(365\) | −102.313 | −0.280310 | ||||||||
\(366\) | −96.1396 | −0.262677 | ||||||||
\(367\) | − | 197.305i | − | 0.537616i | −0.963194 | − | 0.268808i | \(-0.913370\pi\) | ||
0.963194 | − | 0.268808i | \(-0.0866296\pi\) | |||||||
\(368\) | −274.731 | −0.746553 | ||||||||
\(369\) | 75.5389i | 0.204713i | ||||||||
\(370\) | − | 213.374i | − | 0.576687i | ||||||
\(371\) | −111.114 | − | 600.834i | −0.299499 | − | 1.61950i | ||||
\(372\) | −1175.58 | −3.16016 | ||||||||
\(373\) | −4.03029 | −0.0108051 | −0.00540253 | − | 0.999985i | \(-0.501720\pi\) | ||||
−0.00540253 | + | 0.999985i | \(0.501720\pi\) | |||||||
\(374\) | 27.9967i | 0.0748575i | ||||||||
\(375\) | 606.339 | 1.61690 | ||||||||
\(376\) | 625.631i | 1.66391i | ||||||||
\(377\) | 470.226i | 1.24728i | ||||||||
\(378\) | 294.956 | − | 54.5471i | 0.780307 | − | 0.144305i | ||||
\(379\) | −322.599 | −0.851183 | −0.425592 | − | 0.904915i | \(-0.639934\pi\) | ||||
−0.425592 | + | 0.904915i | \(0.639934\pi\) | |||||||
\(380\) | −125.941 | −0.331423 | ||||||||
\(381\) | − | 549.563i | − | 1.44242i | ||||||
\(382\) | −337.349 | −0.883111 | ||||||||
\(383\) | 623.478i | 1.62788i | 0.580948 | + | 0.813941i | \(0.302682\pi\) | ||||
−0.580948 | + | 0.813941i | \(0.697318\pi\) | |||||||
\(384\) | − | 1067.31i | − | 2.77945i | ||||||
\(385\) | −7.70410 | + | 1.42474i | −0.0200107 | + | 0.00370063i | ||||
\(386\) | 118.768 | 0.307689 | ||||||||
\(387\) | 11.4911 | 0.0296928 | ||||||||
\(388\) | − | 478.353i | − | 1.23287i | ||||||
\(389\) | −346.644 | −0.891115 | −0.445557 | − | 0.895253i | \(-0.646994\pi\) | ||||
−0.445557 | + | 0.895253i | \(0.646994\pi\) | |||||||
\(390\) | 567.948i | 1.45628i | ||||||||
\(391\) | 920.881i | 2.35519i | ||||||||
\(392\) | 504.827 | − | 193.330i | 1.28782 | − | 0.493190i | ||||
\(393\) | −976.663 | −2.48515 | ||||||||
\(394\) | −569.227 | −1.44474 | ||||||||
\(395\) | 135.883i | 0.344007i | ||||||||
\(396\) | −26.9689 | −0.0681033 | ||||||||
\(397\) | 97.5499i | 0.245718i | 0.992424 | + | 0.122859i | \(0.0392062\pi\) | ||||
−0.992424 | + | 0.122859i | \(0.960794\pi\) | |||||||
\(398\) | 87.5148i | 0.219887i | ||||||||
\(399\) | 28.1432 | + | 152.181i | 0.0705344 | + | 0.381405i | ||||
\(400\) | 97.3003 | 0.243251 | ||||||||
\(401\) | 375.671 | 0.936836 | 0.468418 | − | 0.883507i | \(-0.344824\pi\) | ||||
0.468418 | + | 0.883507i | \(0.344824\pi\) | |||||||
\(402\) | 612.019i | 1.52244i | ||||||||
\(403\) | −367.888 | −0.912874 | ||||||||
\(404\) | − | 157.400i | − | 0.389603i | ||||||
\(405\) | − | 171.188i | − | 0.422685i | ||||||
\(406\) | 193.421 | + | 1045.90i | 0.476407 | + | 2.57611i | ||||
\(407\) | 5.58968 | 0.0137339 | ||||||||
\(408\) | 1336.09 | 3.27473 | ||||||||
\(409\) | − | 13.2401i | − | 0.0323719i | −0.999869 | − | 0.0161859i | \(-0.994848\pi\) | ||
0.999869 | − | 0.0161859i | \(-0.00515237\pi\) | |||||||
\(410\) | −76.7097 | −0.187097 | ||||||||
\(411\) | 667.953i | 1.62519i | ||||||||
\(412\) | − | 533.757i | − | 1.29553i | ||||||
\(413\) | −104.208 | + | 19.2716i | −0.252320 | + | 0.0466624i | ||||
\(414\) | −1374.20 | −3.31932 | ||||||||
\(415\) | 261.903 | 0.631093 | ||||||||
\(416\) | − | 182.079i | − | 0.437690i | ||||||
\(417\) | −1034.52 | −2.48086 | ||||||||
\(418\) | − | 5.11093i | − | 0.0122271i | ||||||
\(419\) | − | 275.854i | − | 0.658363i | −0.944267 | − | 0.329182i | \(-0.893227\pi\) | ||
0.944267 | − | 0.329182i | \(-0.106773\pi\) | |||||||
\(420\) | 150.806 | + | 815.460i | 0.359061 | + | 1.94157i | ||||
\(421\) | 284.626 | 0.676072 | 0.338036 | − | 0.941133i | \(-0.390237\pi\) | ||||
0.338036 | + | 0.941133i | \(0.390237\pi\) | |||||||
\(422\) | 143.276 | 0.339516 | ||||||||
\(423\) | 669.010i | 1.58158i | ||||||||
\(424\) | 962.993 | 2.27121 | ||||||||
\(425\) | − | 326.144i | − | 0.767398i | ||||||
\(426\) | − | 735.669i | − | 1.72692i | ||||||
\(427\) | −43.1977 | + | 7.98868i | −0.101166 | + | 0.0187089i | ||||
\(428\) | 540.046 | 1.26179 | ||||||||
\(429\) | −14.8783 | −0.0346814 | ||||||||
\(430\) | 11.6692i | 0.0271377i | ||||||||
\(431\) | 312.665 | 0.725441 | 0.362721 | − | 0.931898i | \(-0.381848\pi\) | ||||
0.362721 | + | 0.931898i | \(0.381848\pi\) | |||||||
\(432\) | 101.065i | 0.233946i | ||||||||
\(433\) | − | 345.940i | − | 0.798937i | −0.916747 | − | 0.399468i | \(-0.869195\pi\) | ||
0.916747 | − | 0.399468i | \(-0.130805\pi\) | |||||||
\(434\) | −818.275 | + | 151.326i | −1.88543 | + | 0.348678i | ||||
\(435\) | −735.673 | −1.69120 | ||||||||
\(436\) | −795.857 | −1.82536 | ||||||||
\(437\) | − | 168.111i | − | 0.384693i | ||||||
\(438\) | −439.488 | −1.00340 | ||||||||
\(439\) | 52.2923i | 0.119117i | 0.998225 | + | 0.0595585i | \(0.0189693\pi\) | ||||
−0.998225 | + | 0.0595585i | \(0.981031\pi\) | |||||||
\(440\) | − | 12.3478i | − | 0.0280632i | ||||||
\(441\) | 539.831 | − | 206.735i | 1.22411 | − | 0.468788i | ||||
\(442\) | 927.367 | 2.09812 | ||||||||
\(443\) | 552.013 | 1.24608 | 0.623039 | − | 0.782191i | \(-0.285898\pi\) | ||||
0.623039 | + | 0.782191i | \(0.285898\pi\) | |||||||
\(444\) | − | 591.654i | − | 1.33255i | ||||||
\(445\) | −372.975 | −0.838147 | ||||||||
\(446\) | − | 980.909i | − | 2.19935i | ||||||
\(447\) | 690.631i | 1.54504i | ||||||||
\(448\) | −115.237 | − | 623.126i | −0.257224 | − | 1.39091i | ||||
\(449\) | 226.412 | 0.504259 | 0.252129 | − | 0.967694i | \(-0.418869\pi\) | ||||
0.252129 | + | 0.967694i | \(0.418869\pi\) | |||||||
\(450\) | 486.693 | 1.08154 | ||||||||
\(451\) | − | 2.00953i | − | 0.00445573i | ||||||
\(452\) | 924.792 | 2.04600 | ||||||||
\(453\) | 1208.00i | 2.66667i | ||||||||
\(454\) | 185.843i | 0.409347i | ||||||||
\(455\) | 47.1934 | + | 255.192i | 0.103722 | + | 0.560861i | ||||
\(456\) | −243.909 | −0.534888 | ||||||||
\(457\) | −434.321 | −0.950375 | −0.475188 | − | 0.879884i | \(-0.657620\pi\) | ||||
−0.475188 | + | 0.879884i | \(0.657620\pi\) | |||||||
\(458\) | − | 265.266i | − | 0.579183i | ||||||
\(459\) | 338.762 | 0.738044 | ||||||||
\(460\) | − | 900.823i | − | 1.95831i | ||||||
\(461\) | − | 254.309i | − | 0.551646i | −0.961208 | − | 0.275823i | \(-0.911050\pi\) | ||
0.961208 | − | 0.275823i | \(-0.0889504\pi\) | |||||||
\(462\) | −33.0930 | + | 6.12000i | −0.0716299 | + | 0.0132467i | ||||
\(463\) | 152.748 | 0.329908 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(464\) | −358.371 | −0.772351 | ||||||||
\(465\) | − | 575.564i | − | 1.23777i | ||||||
\(466\) | −1201.54 | −2.57841 | ||||||||
\(467\) | 224.444i | 0.480608i | 0.970698 | + | 0.240304i | \(0.0772472\pi\) | ||||
−0.970698 | + | 0.240304i | \(0.922753\pi\) | |||||||
\(468\) | 893.323i | 1.90881i | ||||||||
\(469\) | 50.8554 | + | 274.994i | 0.108434 | + | 0.586341i | ||||
\(470\) | −679.379 | −1.44549 | ||||||||
\(471\) | −547.309 | −1.16201 | ||||||||
\(472\) | − | 167.021i | − | 0.353858i | ||||||
\(473\) | −0.305693 | −0.000646286 | ||||||||
\(474\) | 583.685i | 1.23140i | ||||||||
\(475\) | 59.5391i | 0.125345i | ||||||||
\(476\) | 1331.51 | − | 246.241i | 2.79730 | − | 0.517313i | ||||
\(477\) | 1029.76 | 2.15884 | ||||||||
\(478\) | 1150.43 | 2.40675 | ||||||||
\(479\) | 198.911i | 0.415263i | 0.978207 | + | 0.207632i | \(0.0665755\pi\) | ||||
−0.978207 | + | 0.207632i | \(0.933424\pi\) | |||||||
\(480\) | 284.864 | 0.593467 | ||||||||
\(481\) | − | 185.153i | − | 0.384934i | ||||||
\(482\) | − | 1064.62i | − | 2.20875i | ||||||
\(483\) | −1088.51 | + | 201.302i | −2.25365 | + | 0.416774i | ||||
\(484\) | −880.670 | −1.81957 | ||||||||
\(485\) | 234.202 | 0.482890 | ||||||||
\(486\) | − | 1121.00i | − | 2.30658i | ||||||
\(487\) | 431.443 | 0.885919 | 0.442960 | − | 0.896542i | \(-0.353928\pi\) | ||||
0.442960 | + | 0.896542i | \(0.353928\pi\) | |||||||
\(488\) | − | 69.2355i | − | 0.141876i | ||||||
\(489\) | − | 264.491i | − | 0.540882i | ||||||
\(490\) | 209.940 | + | 548.197i | 0.428448 | + | 1.11877i | ||||
\(491\) | 746.425 | 1.52021 | 0.760107 | − | 0.649798i | \(-0.225147\pi\) | ||||
0.760107 | + | 0.649798i | \(0.225147\pi\) | |||||||
\(492\) | −212.704 | −0.432325 | ||||||||
\(493\) | 1201.23i | 2.43658i | ||||||||
\(494\) | −169.295 | −0.342703 | ||||||||
\(495\) | − | 13.2040i | − | 0.0266747i | ||||||
\(496\) | − | 280.377i | − | 0.565276i | ||||||
\(497\) | −61.1301 | − | 330.553i | −0.122998 | − | 0.665096i | ||||
\(498\) | 1125.01 | 2.25905 | ||||||||
\(499\) | 726.174 | 1.45526 | 0.727629 | − | 0.685971i | \(-0.240622\pi\) | ||||
0.727629 | + | 0.685971i | \(0.240622\pi\) | |||||||
\(500\) | 968.489i | 1.93698i | ||||||||
\(501\) | 499.255 | 0.996518 | ||||||||
\(502\) | 186.416i | 0.371348i | ||||||||
\(503\) | − | 84.2302i | − | 0.167456i | −0.996489 | − | 0.0837278i | \(-0.973317\pi\) | ||
0.996489 | − | 0.0837278i | \(-0.0266826\pi\) | |||||||
\(504\) | 165.674 | + | 895.857i | 0.328717 | + | 1.77749i | ||||
\(505\) | 77.0628 | 0.152600 | ||||||||
\(506\) | 36.5572 | 0.0722474 | ||||||||
\(507\) | − | 277.876i | − | 0.548078i | ||||||
\(508\) | 877.802 | 1.72796 | ||||||||
\(509\) | − | 183.067i | − | 0.359659i | −0.983698 | − | 0.179830i | \(-0.942445\pi\) | ||
0.983698 | − | 0.179830i | \(-0.0575546\pi\) | |||||||
\(510\) | 1450.87i | 2.84485i | ||||||||
\(511\) | −197.472 | + | 36.5190i | −0.386442 | + | 0.0714658i | ||||
\(512\) | 488.388 | 0.953883 | ||||||||
\(513\) | −61.8426 | −0.120551 | ||||||||
\(514\) | − | 1581.24i | − | 3.07635i | ||||||
\(515\) | 261.328 | 0.507432 | ||||||||
\(516\) | 32.3569i | 0.0627072i | ||||||||
\(517\) | − | 17.7974i | − | 0.0344244i | ||||||
\(518\) | −76.1604 | − | 411.827i | −0.147028 | − | 0.795032i | ||||
\(519\) | −785.778 | −1.51402 | ||||||||
\(520\) | −409.011 | −0.786560 | ||||||||
\(521\) | 1012.94i | 1.94421i | 0.234539 | + | 0.972107i | \(0.424642\pi\) | ||||
−0.234539 | + | 0.972107i | \(0.575358\pi\) | |||||||
\(522\) | −1792.56 | −3.43402 | ||||||||
\(523\) | 183.566i | 0.350987i | 0.984481 | + | 0.175493i | \(0.0561521\pi\) | ||||
−0.984481 | + | 0.175493i | \(0.943848\pi\) | |||||||
\(524\) | − | 1560.00i | − | 2.97709i | ||||||
\(525\) | 385.513 | − | 71.2941i | 0.734310 | − | 0.135798i | ||||
\(526\) | 1551.75 | 2.95009 | ||||||||
\(527\) | −939.803 | −1.78331 | ||||||||
\(528\) | − | 11.3391i | − | 0.0214756i | ||||||
\(529\) | 673.456 | 1.27307 | ||||||||
\(530\) | 1045.72i | 1.97307i | ||||||||
\(531\) | − | 178.602i | − | 0.336350i | ||||||
\(532\) | −243.074 | + | 44.9524i | −0.456906 | + | 0.0844970i | ||||
\(533\) | −66.5640 | −0.124886 | ||||||||
\(534\) | −1602.12 | −3.00022 | ||||||||
\(535\) | 264.407i | 0.494218i | ||||||||
\(536\) | −440.749 | −0.822293 | ||||||||
\(537\) | − | 1406.66i | − | 2.61947i | ||||||
\(538\) | − | 324.274i | − | 0.602739i | ||||||
\(539\) | −14.3609 | + | 5.49970i | −0.0266436 | + | 0.0102035i | ||||
\(540\) | −331.383 | −0.613673 | ||||||||
\(541\) | −361.613 | −0.668417 | −0.334208 | − | 0.942499i | \(-0.608469\pi\) | ||||
−0.334208 | + | 0.942499i | \(0.608469\pi\) | |||||||
\(542\) | 945.906i | 1.74521i | ||||||||
\(543\) | 1417.58 | 2.61065 | ||||||||
\(544\) | − | 465.137i | − | 0.855031i | ||||||
\(545\) | − | 389.652i | − | 0.714957i | ||||||
\(546\) | 202.720 | + | 1096.18i | 0.371281 | + | 2.00765i | ||||
\(547\) | −811.077 | −1.48277 | −0.741386 | − | 0.671079i | \(-0.765831\pi\) | ||||
−0.741386 | + | 0.671079i | \(0.765831\pi\) | |||||||
\(548\) | −1066.90 | −1.94690 | ||||||||
\(549\) | − | 74.0361i | − | 0.134856i | ||||||
\(550\) | −12.9473 | −0.0235405 | ||||||||
\(551\) | − | 219.291i | − | 0.397987i | ||||||
\(552\) | − | 1744.62i | − | 3.16055i | ||||||
\(553\) | 48.5010 | + | 262.263i | 0.0877053 | + | 0.474254i | ||||
\(554\) | −990.976 | −1.78877 | ||||||||
\(555\) | 289.674 | 0.521935 | ||||||||
\(556\) | − | 1652.41i | − | 2.97196i | ||||||
\(557\) | 144.121 | 0.258745 | 0.129373 | − | 0.991596i | \(-0.458704\pi\) | ||||
0.129373 | + | 0.991596i | \(0.458704\pi\) | |||||||
\(558\) | − | 1402.43i | − | 2.51332i | ||||||
\(559\) | 10.1258i | 0.0181142i | ||||||||
\(560\) | −194.488 | + | 35.9672i | −0.347300 | + | 0.0642272i | ||||
\(561\) | −38.0079 | −0.0677503 | ||||||||
\(562\) | −1456.21 | −2.59112 | ||||||||
\(563\) | 310.122i | 0.550838i | 0.961324 | + | 0.275419i | \(0.0888166\pi\) | ||||
−0.961324 | + | 0.275419i | \(0.911183\pi\) | |||||||
\(564\) | −1883.81 | −3.34009 | ||||||||
\(565\) | 452.778i | 0.801378i | ||||||||
\(566\) | 1522.79i | 2.69045i | ||||||||
\(567\) | −61.1025 | − | 330.404i | −0.107765 | − | 0.582722i | ||||
\(568\) | 529.796 | 0.932740 | ||||||||
\(569\) | −411.027 | −0.722367 | −0.361183 | − | 0.932495i | \(-0.617627\pi\) | ||||
−0.361183 | + | 0.932495i | \(0.617627\pi\) | |||||||
\(570\) | − | 264.864i | − | 0.464673i | ||||||
\(571\) | −356.814 | −0.624893 | −0.312447 | − | 0.949935i | \(-0.601149\pi\) | ||||
−0.312447 | + | 0.949935i | \(0.601149\pi\) | |||||||
\(572\) | − | 23.7647i | − | 0.0415467i | ||||||
\(573\) | − | 457.979i | − | 0.799266i | ||||||
\(574\) | −148.055 | + | 27.3803i | −0.257935 | + | 0.0477008i | ||||
\(575\) | −425.868 | −0.740640 | ||||||||
\(576\) | 1067.97 | 1.85411 | ||||||||
\(577\) | 391.139i | 0.677884i | 0.940807 | + | 0.338942i | \(0.110069\pi\) | ||||
−0.940807 | + | 0.338942i | \(0.889931\pi\) | |||||||
\(578\) | 1398.23 | 2.41909 | ||||||||
\(579\) | 161.238i | 0.278476i | ||||||||
\(580\) | − | 1175.07i | − | 2.02598i | ||||||
\(581\) | 505.491 | − | 93.4821i | 0.870037 | − | 0.160899i | ||||
\(582\) | 1006.02 | 1.72855 | ||||||||
\(583\) | −27.3944 | −0.0469887 | ||||||||
\(584\) | − | 316.500i | − | 0.541951i | ||||||
\(585\) | −437.371 | −0.747643 | ||||||||
\(586\) | 964.443i | 1.64581i | ||||||||
\(587\) | 513.174i | 0.874231i | 0.899405 | + | 0.437116i | \(0.144000\pi\) | ||||
−0.899405 | + | 0.437116i | \(0.856000\pi\) | |||||||
\(588\) | 582.130 | + | 1520.07i | 0.990017 | + | 2.58515i | ||||
\(589\) | 171.565 | 0.291282 | ||||||||
\(590\) | 181.370 | 0.307406 | ||||||||
\(591\) | − | 772.775i | − | 1.30757i | ||||||
\(592\) | 141.110 | 0.238361 | ||||||||
\(593\) | − | 1140.99i | − | 1.92410i | −0.272874 | − | 0.962050i | \(-0.587974\pi\) | ||
0.272874 | − | 0.962050i | \(-0.412026\pi\) | |||||||
\(594\) | − | 13.4482i | − | 0.0226401i | ||||||
\(595\) | 120.560 | + | 651.910i | 0.202621 | + | 1.09565i | ||||
\(596\) | −1103.13 | −1.85088 | ||||||||
\(597\) | −118.809 | −0.199010 | ||||||||
\(598\) | − | 1210.93i | − | 2.02496i | ||||||
\(599\) | 863.757 | 1.44200 | 0.720999 | − | 0.692936i | \(-0.243683\pi\) | ||||
0.720999 | + | 0.692936i | \(0.243683\pi\) | |||||||
\(600\) | 617.884i | 1.02981i | ||||||||
\(601\) | 263.404i | 0.438276i | 0.975694 | + | 0.219138i | \(0.0703245\pi\) | ||||
−0.975694 | + | 0.219138i | \(0.929676\pi\) | |||||||
\(602\) | 4.16513 | + | 22.5224i | 0.00691882 | + | 0.0374126i | ||||
\(603\) | −471.310 | −0.781608 | ||||||||
\(604\) | −1929.50 | −3.19454 | ||||||||
\(605\) | − | 431.176i | − | 0.712688i | ||||||
\(606\) | 331.024 | 0.546244 | ||||||||
\(607\) | − | 468.563i | − | 0.771932i | −0.922513 | − | 0.385966i | \(-0.873868\pi\) | ||
0.922513 | − | 0.385966i | \(-0.126132\pi\) | |||||||
\(608\) | 84.9128i | 0.139659i | ||||||||
\(609\) | −1419.90 | + | 262.586i | −2.33152 | + | 0.431176i | ||||
\(610\) | 75.1836 | 0.123252 | ||||||||
\(611\) | −589.524 | −0.964851 | ||||||||
\(612\) | 2282.07i | 3.72888i | ||||||||
\(613\) | −285.996 | −0.466551 | −0.233275 | − | 0.972411i | \(-0.574944\pi\) | ||||
−0.233275 | + | 0.972411i | \(0.574944\pi\) | |||||||
\(614\) | 1530.33i | 2.49239i | ||||||||
\(615\) | − | 104.140i | − | 0.169333i | ||||||
\(616\) | −4.40735 | − | 23.8321i | −0.00715479 | − | 0.0386885i | ||||
\(617\) | −793.126 | −1.28546 | −0.642728 | − | 0.766095i | \(-0.722197\pi\) | ||||
−0.642728 | + | 0.766095i | \(0.722197\pi\) | |||||||
\(618\) | 1122.54 | 1.81640 | ||||||||
\(619\) | − | 1010.76i | − | 1.63290i | −0.577419 | − | 0.816448i | \(-0.695940\pi\) | ||
0.577419 | − | 0.816448i | \(-0.304060\pi\) | |||||||
\(620\) | 919.333 | 1.48280 | ||||||||
\(621\) | − | 442.345i | − | 0.712310i | ||||||
\(622\) | − | 553.206i | − | 0.889399i | ||||||
\(623\) | −719.868 | + | 133.127i | −1.15549 | + | 0.213688i | ||||
\(624\) | −375.599 | −0.601921 | ||||||||
\(625\) | −167.142 | −0.267428 | ||||||||
\(626\) | − | 267.410i | − | 0.427173i | ||||||
\(627\) | 6.93852 | 0.0110662 | ||||||||
\(628\) | − | 874.202i | − | 1.39204i | ||||||
\(629\) | − | 472.990i | − | 0.751972i | ||||||
\(630\) | −972.821 | + | 179.907i | −1.54416 | + | 0.285566i | ||||
\(631\) | 322.792 | 0.511556 | 0.255778 | − | 0.966736i | \(-0.417668\pi\) | ||||
0.255778 | + | 0.966736i | \(0.417668\pi\) | |||||||
\(632\) | −420.344 | −0.665101 | ||||||||
\(633\) | 194.509i | 0.307281i | ||||||||
\(634\) | −1038.99 | −1.63879 | ||||||||
\(635\) | 429.772i | 0.676807i | ||||||||
\(636\) | 2899.63i | 4.55917i | ||||||||
\(637\) | 182.173 | + | 475.693i | 0.285986 | + | 0.746770i | ||||
\(638\) | 47.6867 | 0.0747441 | ||||||||
\(639\) | 566.531 | 0.886591 | ||||||||
\(640\) | 834.663i | 1.30416i | ||||||||
\(641\) | −322.875 | −0.503706 | −0.251853 | − | 0.967766i | \(-0.581040\pi\) | ||||
−0.251853 | + | 0.967766i | \(0.581040\pi\) | |||||||
\(642\) | 1135.76i | 1.76910i | ||||||||
\(643\) | − | 576.809i | − | 0.897059i | −0.893768 | − | 0.448530i | \(-0.851948\pi\) | ||
0.893768 | − | 0.448530i | \(-0.148052\pi\) | |||||||
\(644\) | −321.534 | − | 1738.65i | −0.499276 | − | 2.69977i | ||||
\(645\) | −15.8419 | −0.0245612 | ||||||||
\(646\) | −432.479 | −0.669473 | ||||||||
\(647\) | 1110.71i | 1.71670i | 0.513061 | + | 0.858352i | \(0.328511\pi\) | ||||
−0.513061 | + | 0.858352i | \(0.671489\pi\) | |||||||
\(648\) | 529.557 | 0.817218 | ||||||||
\(649\) | 4.75127i | 0.00732091i | ||||||||
\(650\) | 428.868i | 0.659797i | ||||||||
\(651\) | −205.438 | − | 1110.88i | −0.315573 | − | 1.70642i | ||||
\(652\) | 422.464 | 0.647952 | ||||||||
\(653\) | −1043.70 | −1.59831 | −0.799157 | − | 0.601123i | \(-0.794720\pi\) | ||||
−0.799157 | + | 0.601123i | \(0.794720\pi\) | |||||||
\(654\) | − | 1673.75i | − | 2.55925i | ||||||
\(655\) | 763.775 | 1.16607 | ||||||||
\(656\) | − | 50.7301i | − | 0.0773325i | ||||||
\(657\) | − | 338.445i | − | 0.515137i | ||||||
\(658\) | −1311.25 | + | 242.493i | −1.99278 | + | 0.368531i | ||||
\(659\) | 644.973 | 0.978715 | 0.489358 | − | 0.872083i | \(-0.337231\pi\) | ||||
0.489358 | + | 0.872083i | \(0.337231\pi\) | |||||||
\(660\) | 37.1801 | 0.0563334 | ||||||||
\(661\) | − | 985.098i | − | 1.49031i | −0.666889 | − | 0.745157i | \(-0.732374\pi\) | ||
0.666889 | − | 0.745157i | \(-0.267626\pi\) | |||||||
\(662\) | −1286.45 | −1.94328 | ||||||||
\(663\) | 1258.98i | 1.89891i | ||||||||
\(664\) | 810.181i | 1.22015i | ||||||||
\(665\) | −22.0087 | − | 119.009i | −0.0330958 | − | 0.178961i | ||||
\(666\) | 705.826 | 1.05980 | ||||||||
\(667\) | 1568.53 | 2.35162 | ||||||||
\(668\) | 797.447i | 1.19378i | ||||||||
\(669\) | 1331.67 | 1.99053 | ||||||||
\(670\) | − | 478.614i | − | 0.714350i | ||||||
\(671\) | 1.96955i | 0.00293525i | ||||||||
\(672\) | 549.807 | − | 101.677i | 0.818165 | − | 0.151306i | ||||
\(673\) | −505.650 | −0.751337 | −0.375668 | − | 0.926754i | \(-0.622587\pi\) | ||||
−0.375668 | + | 0.926754i | \(0.622587\pi\) | |||||||
\(674\) | 1762.93 | 2.61562 | ||||||||
\(675\) | 156.663i | 0.232094i | ||||||||
\(676\) | 443.843 | 0.656573 | ||||||||
\(677\) | − | 330.539i | − | 0.488241i | −0.969745 | − | 0.244120i | \(-0.921501\pi\) | ||
0.969745 | − | 0.244120i | \(-0.0784992\pi\) | |||||||
\(678\) | 1944.91i | 2.86860i | ||||||||
\(679\) | 452.025 | − | 83.5944i | 0.665722 | − | 0.123114i | ||||
\(680\) | −1044.85 | −1.53655 | ||||||||
\(681\) | −252.298 | −0.370482 | ||||||||
\(682\) | 37.3084i | 0.0547044i | ||||||||
\(683\) | 1198.70 | 1.75506 | 0.877529 | − | 0.479523i | \(-0.159190\pi\) | ||||
0.877529 | + | 0.479523i | \(0.159190\pi\) | |||||||
\(684\) | − | 416.602i | − | 0.609068i | ||||||
\(685\) | − | 522.356i | − | 0.762564i | ||||||
\(686\) | 600.868 | + | 983.124i | 0.875900 | + | 1.43312i | ||||
\(687\) | 360.121 | 0.524194 | ||||||||
\(688\) | −7.71714 | −0.0112168 | ||||||||
\(689\) | 907.417i | 1.31701i | ||||||||
\(690\) | 1894.50 | 2.74566 | ||||||||
\(691\) | − | 41.6454i | − | 0.0602683i | −0.999546 | − | 0.0301342i | \(-0.990407\pi\) | ||
0.999546 | − | 0.0301342i | \(-0.00959345\pi\) | |||||||
\(692\) | − | 1255.10i | − | 1.81373i | ||||||
\(693\) | −4.71294 | − | 25.4846i | −0.00680079 | − | 0.0367743i | ||||
\(694\) | 668.414 | 0.963132 | ||||||||
\(695\) | 809.020 | 1.16406 | ||||||||
\(696\) | − | 2275.76i | − | 3.26976i | ||||||
\(697\) | −170.044 | −0.243965 | ||||||||
\(698\) | − | 1747.70i | − | 2.50387i | ||||||
\(699\) | − | 1631.19i | − | 2.33361i | ||||||
\(700\) | 113.876 | + | 615.769i | 0.162680 | + | 0.879670i | ||||
\(701\) | 1216.91 | 1.73597 | 0.867984 | − | 0.496592i | \(-0.165415\pi\) | ||||
0.867984 | + | 0.496592i | \(0.165415\pi\) | |||||||
\(702\) | −445.461 | −0.634559 | ||||||||
\(703\) | 86.3465i | 0.122826i | ||||||||
\(704\) | −28.4108 | −0.0403562 | ||||||||
\(705\) | − | 922.315i | − | 1.30825i | ||||||
\(706\) | 1199.81i | 1.69945i | ||||||||
\(707\) | 148.736 | − | 27.5063i | 0.210377 | − | 0.0389056i | ||||
\(708\) | 502.910 | 0.710325 | ||||||||
\(709\) | −1040.79 | −1.46797 | −0.733985 | − | 0.679166i | \(-0.762342\pi\) | ||||
−0.733985 | + | 0.679166i | \(0.762342\pi\) | |||||||
\(710\) | 575.312i | 0.810298i | ||||||||
\(711\) | −449.490 | −0.632194 | ||||||||
\(712\) | − | 1153.78i | − | 1.62047i | ||||||
\(713\) | 1227.16i | 1.72113i | ||||||||
\(714\) | 517.865 | + | 2800.28i | 0.725301 | + | 3.92197i | ||||
\(715\) | 11.6352 | 0.0162730 | ||||||||
\(716\) | 2246.81 | 3.13801 | ||||||||
\(717\) | 1561.80i | 2.17824i | ||||||||
\(718\) | −2374.13 | −3.30658 | ||||||||
\(719\) | − | 1297.76i | − | 1.80496i | −0.430735 | − | 0.902479i | \(-0.641746\pi\) | ||
0.430735 | − | 0.902479i | \(-0.358254\pi\) | |||||||
\(720\) | − | 333.331i | − | 0.462960i | ||||||
\(721\) | 504.380 | − | 93.2766i | 0.699556 | − | 0.129371i | ||||
\(722\) | −1133.72 | −1.57025 | ||||||||
\(723\) | 1445.31 | 1.99904 | ||||||||
\(724\) | 2264.27i | 3.12744i | ||||||||
\(725\) | −555.520 | −0.766234 | ||||||||
\(726\) | − | 1852.12i | − | 2.55113i | ||||||
\(727\) | 193.812i | 0.266592i | 0.991076 | + | 0.133296i | \(0.0425561\pi\) | ||||
−0.991076 | + | 0.133296i | \(0.957444\pi\) | |||||||
\(728\) | −789.419 | + | 145.990i | −1.08437 | + | 0.200535i | ||||
\(729\) | 1089.84 | 1.49498 | ||||||||
\(730\) | 343.690 | 0.470809 | ||||||||
\(731\) | 25.8673i | 0.0353862i | ||||||||
\(732\) | 208.472 | 0.284798 | ||||||||
\(733\) | 206.817i | 0.282152i | 0.989999 | + | 0.141076i | \(0.0450562\pi\) | ||||
−0.989999 | + | 0.141076i | \(0.954944\pi\) | |||||||
\(734\) | 662.786i | 0.902978i | ||||||||
\(735\) | −744.225 | + | 285.011i | −1.01255 | + | 0.387770i | ||||
\(736\) | −607.361 | −0.825218 | ||||||||
\(737\) | 12.5381 | 0.0170123 | ||||||||
\(738\) | − | 253.750i | − | 0.343835i | ||||||
\(739\) | 226.483 | 0.306473 | 0.153236 | − | 0.988190i | \(-0.451030\pi\) | ||||
0.153236 | + | 0.988190i | \(0.451030\pi\) | |||||||
\(740\) | 462.688i | 0.625254i | ||||||||
\(741\) | − | 229.833i | − | 0.310165i | ||||||
\(742\) | 373.254 | + | 2018.32i | 0.503038 | + | 2.72011i | ||||
\(743\) | 485.772 | 0.653798 | 0.326899 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326899 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(744\) | 1780.47 | 2.39311 | ||||||||
\(745\) | − | 540.091i | − | 0.724954i | ||||||
\(746\) | 13.5385 | 0.0181482 | ||||||||
\(747\) | 866.357i | 1.15978i | ||||||||
\(748\) | − | 60.7090i | − | 0.0811618i | ||||||
\(749\) | 94.3756 | + | 510.323i | 0.126002 | + | 0.681339i | ||||
\(750\) | −2036.81 | −2.71575 | ||||||||
\(751\) | −1070.91 | −1.42598 | −0.712990 | − | 0.701175i | \(-0.752659\pi\) | ||||
−0.712990 | + | 0.701175i | \(0.752659\pi\) | |||||||
\(752\) | − | 449.291i | − | 0.597461i | ||||||
\(753\) | −253.076 | −0.336091 | ||||||||
\(754\) | − | 1579.58i | − | 2.09494i | ||||||
\(755\) | − | 944.686i | − | 1.25124i | ||||||
\(756\) | −639.593 | + | 118.282i | −0.846022 | + | 0.156457i | ||||
\(757\) | −685.121 | −0.905047 | −0.452524 | − | 0.891752i | \(-0.649476\pi\) | ||||
−0.452524 | + | 0.891752i | \(0.649476\pi\) | |||||||
\(758\) | 1083.67 | 1.42965 | ||||||||
\(759\) | 49.6295i | 0.0653881i | ||||||||
\(760\) | 190.743 | 0.250978 | ||||||||
\(761\) | 630.601i | 0.828648i | 0.910129 | + | 0.414324i | \(0.135982\pi\) | ||||
−0.910129 | + | 0.414324i | \(0.864018\pi\) | |||||||
\(762\) | 1846.09i | 2.42269i | ||||||||
\(763\) | −139.080 | − | 752.054i | −0.182280 | − | 0.985654i | ||||
\(764\) | 731.518 | 0.957484 | ||||||||
\(765\) | −1117.30 | −1.46053 | ||||||||
\(766\) | − | 2094.39i | − | 2.73419i | ||||||
\(767\) | 157.382 | 0.205191 | ||||||||
\(768\) | 1933.94i | 2.51815i | ||||||||
\(769\) | 253.107i | 0.329138i | 0.986366 | + | 0.164569i | \(0.0526233\pi\) | ||||
−0.986366 | + | 0.164569i | \(0.947377\pi\) | |||||||
\(770\) | 25.8796 | − | 4.78599i | 0.0336098 | − | 0.00621557i | ||||
\(771\) | 2146.67 | 2.78427 | ||||||||
\(772\) | −257.540 | −0.333602 | ||||||||
\(773\) | − | 719.710i | − | 0.931060i | −0.885032 | − | 0.465530i | \(-0.845864\pi\) | ||
0.885032 | − | 0.465530i | \(-0.154136\pi\) | |||||||
\(774\) | −38.6009 | −0.0498719 | ||||||||
\(775\) | − | 434.619i | − | 0.560799i | ||||||
\(776\) | 724.488i | 0.933618i | ||||||||
\(777\) | 559.090 | − | 103.394i | 0.719550 | − | 0.133069i | ||||
\(778\) | 1164.44 | 1.49671 | ||||||||
\(779\) | 31.0423 | 0.0398489 | ||||||||
\(780\) | − | 1231.56i | − | 1.57892i | ||||||
\(781\) | −15.0712 | −0.0192973 | ||||||||
\(782\) | − | 3093.42i | − | 3.95578i | ||||||
\(783\) | − | 577.012i | − | 0.736925i | ||||||
\(784\) | −362.537 | + | 138.838i | −0.462420 | + | 0.177090i | ||||
\(785\) | 428.009 | 0.545235 | ||||||||
\(786\) | 3280.80 | 4.17405 | ||||||||
\(787\) | − | 1179.98i | − | 1.49934i | −0.661812 | − | 0.749670i | \(-0.730212\pi\) | ||
0.661812 | − | 0.749670i | \(-0.269788\pi\) | |||||||
\(788\) | 1234.33 | 1.56641 | ||||||||
\(789\) | 2106.63i | 2.67000i | ||||||||
\(790\) | − | 456.456i | − | 0.577793i | ||||||
\(791\) | 161.612 | + | 873.893i | 0.204313 | + | 1.10479i | ||||
\(792\) | 40.8457 | 0.0515728 | ||||||||
\(793\) | 65.2398 | 0.0822696 | ||||||||
\(794\) | − | 327.689i | − | 0.412707i | ||||||
\(795\) | −1419.66 | −1.78574 | ||||||||
\(796\) | − | 189.770i | − | 0.238405i | ||||||
\(797\) | − | 667.758i | − | 0.837840i | −0.908023 | − | 0.418920i | \(-0.862409\pi\) | ||
0.908023 | − | 0.418920i | \(-0.137591\pi\) | |||||||
\(798\) | −94.5386 | − | 511.205i | −0.118469 | − | 0.640607i | ||||
\(799\) | −1505.99 | −1.88485 | ||||||||
\(800\) | 215.106 | 0.268883 | ||||||||
\(801\) | − | 1233.78i | − | 1.54029i | ||||||
\(802\) | −1261.95 | −1.57351 | ||||||||
\(803\) | 9.00351i | 0.0112123i | ||||||||
\(804\) | − | 1327.12i | − | 1.65065i | ||||||
\(805\) | 851.243 | − | 157.423i | 1.05744 | − | 0.195556i | ||||
\(806\) | 1235.81 | 1.53326 | ||||||||
\(807\) | 440.229 | 0.545513 | ||||||||
\(808\) | 238.389i | 0.295036i | ||||||||
\(809\) | −1168.53 | −1.44441 | −0.722204 | − | 0.691681i | \(-0.756871\pi\) | ||||
−0.722204 | + | 0.691681i | \(0.756871\pi\) | |||||||
\(810\) | 575.052i | 0.709941i | ||||||||
\(811\) | 59.9705i | 0.0739464i | 0.999316 | + | 0.0369732i | \(0.0117716\pi\) | ||||
−0.999316 | + | 0.0369732i | \(0.988228\pi\) | |||||||
\(812\) | −419.422 | − | 2267.96i | −0.516529 | − | 2.79306i | ||||
\(813\) | −1284.15 | −1.57952 | ||||||||
\(814\) | −18.7768 | −0.0230673 | ||||||||
\(815\) | 206.839i | 0.253790i | ||||||||
\(816\) | −959.500 | −1.17586 | ||||||||
\(817\) | − | 4.72220i | − | 0.00577992i | ||||||
\(818\) | 44.4761i | 0.0543717i | ||||||||
\(819\) | −844.156 | + | 156.112i | −1.03072 | + | 0.190613i | ||||
\(820\) | 166.340 | 0.202854 | ||||||||
\(821\) | −286.648 | −0.349145 | −0.174573 | − | 0.984644i | \(-0.555854\pi\) | ||||
−0.174573 | + | 0.984644i | \(0.555854\pi\) | |||||||
\(822\) | − | 2243.79i | − | 2.72967i | ||||||
\(823\) | −114.212 | −0.138776 | −0.0693879 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693879 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(824\) | 808.400i | 0.981068i | ||||||||
\(825\) | − | 17.5771i | − | 0.0213055i | ||||||
\(826\) | 350.056 | − | 64.7369i | 0.423797 | − | 0.0783740i | ||||
\(827\) | −911.840 | −1.10259 | −0.551294 | − | 0.834311i | \(-0.685866\pi\) | ||||
−0.551294 | + | 0.834311i | \(0.685866\pi\) | |||||||
\(828\) | 2979.86 | 3.59886 | ||||||||
\(829\) | 371.561i | 0.448204i | 0.974566 | + | 0.224102i | \(0.0719449\pi\) | ||||
−0.974566 | + | 0.224102i | \(0.928055\pi\) | |||||||
\(830\) | −879.785 | −1.05998 | ||||||||
\(831\) | − | 1345.33i | − | 1.61893i | ||||||
\(832\) | 941.083i | 1.13111i | ||||||||
\(833\) | 465.377 | + | 1215.20i | 0.558676 | + | 1.45882i | ||||
\(834\) | 3475.15 | 4.16685 | ||||||||
\(835\) | −390.430 | −0.467581 | ||||||||
\(836\) | 11.0827i | 0.0132568i | ||||||||
\(837\) | 451.434 | 0.539348 | ||||||||
\(838\) | 926.648i | 1.10579i | ||||||||
\(839\) | 1373.24i | 1.63676i | 0.574676 | + | 0.818381i | \(0.305128\pi\) | ||||
−0.574676 | + | 0.818381i | \(0.694872\pi\) | |||||||
\(840\) | −228.402 | − | 1235.05i | −0.271907 | − | 1.47030i | ||||
\(841\) | 1205.06 | 1.43289 | ||||||||
\(842\) | −956.115 | −1.13553 | ||||||||
\(843\) | − | 1976.93i | − | 2.34511i | ||||||
\(844\) | −310.684 | −0.368109 | ||||||||
\(845\) | 217.306i | 0.257167i | ||||||||
\(846\) | − | 2247.34i | − | 2.65643i | ||||||
\(847\) | −153.901 | − | 832.199i | −0.181702 | − | 0.982526i | ||||
\(848\) | −691.565 | −0.815524 | ||||||||
\(849\) | −2067.32 | −2.43501 | ||||||||
\(850\) | 1095.58i | 1.28892i | ||||||||
\(851\) | −617.616 | −0.725753 | ||||||||
\(852\) | 1595.25i | 1.87236i | ||||||||
\(853\) | 207.974i | 0.243814i | 0.992542 | + | 0.121907i | \(0.0389010\pi\) | ||||
−0.992542 | + | 0.121907i | \(0.961099\pi\) | |||||||
\(854\) | 145.109 | − | 26.8355i | 0.169917 | − | 0.0314233i | ||||
\(855\) | 203.969 | 0.238560 | ||||||||
\(856\) | −817.925 | −0.955520 | ||||||||
\(857\) | − | 348.844i | − | 0.407053i | −0.979069 | − | 0.203526i | \(-0.934760\pi\) | ||
0.979069 | − | 0.203526i | \(-0.0652403\pi\) | |||||||
\(858\) | 49.9791 | 0.0582507 | ||||||||
\(859\) | 1250.96i | 1.45630i | 0.685417 | + | 0.728150i | \(0.259620\pi\) | ||||
−0.685417 | + | 0.728150i | \(0.740380\pi\) | |||||||
\(860\) | − | 25.3039i | − | 0.0294231i | ||||||
\(861\) | −37.1710 | − | 200.997i | −0.0431719 | − | 0.233446i | ||||
\(862\) | −1050.30 | −1.21845 | ||||||||
\(863\) | −816.828 | −0.946498 | −0.473249 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473249 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(864\) | 223.428i | 0.258598i | ||||||||
\(865\) | 614.498 | 0.710402 | ||||||||
\(866\) | 1162.08i | 1.34189i | ||||||||
\(867\) | 1898.22i | 2.18942i | ||||||||
\(868\) | 1774.38 | − | 328.141i | 2.04421 | − | 0.378042i | ||||
\(869\) | 11.9576 | 0.0137602 | ||||||||
\(870\) | 2471.27 | 2.84054 | ||||||||
\(871\) | − | 415.313i | − | 0.476823i | ||||||
\(872\) | 1205.36 | 1.38230 | ||||||||
\(873\) | 774.722i | 0.887425i | ||||||||
\(874\) | 564.718i | 0.646130i | ||||||||
\(875\) | −915.185 | + | 169.248i | −1.04593 | + | 0.193426i | ||||
\(876\) | 953.000 | 1.08790 | ||||||||
\(877\) | 961.635 | 1.09650 | 0.548252 | − | 0.836313i | \(-0.315293\pi\) | ||||
0.548252 | + | 0.836313i | \(0.315293\pi\) | |||||||
\(878\) | − | 175.660i | − | 0.200069i | ||||||
\(879\) | −1309.31 | −1.48955 | ||||||||
\(880\) | 8.86747i | 0.0100767i | ||||||||
\(881\) | 1434.50i | 1.62826i | 0.580684 | + | 0.814129i | \(0.302785\pi\) | ||||
−0.580684 | + | 0.814129i | \(0.697215\pi\) | |||||||
\(882\) | −1813.40 | + | 694.465i | −2.05601 | + | 0.787375i | ||||
\(883\) | −455.276 | −0.515602 | −0.257801 | − | 0.966198i | \(-0.582998\pi\) | ||||
−0.257801 | + | 0.966198i | \(0.582998\pi\) | |||||||
\(884\) | −2010.94 | −2.27481 | ||||||||
\(885\) | 246.225i | 0.278220i | ||||||||
\(886\) | −1854.32 | −2.09291 | ||||||||
\(887\) | 644.091i | 0.726146i | 0.931761 | + | 0.363073i | \(0.118272\pi\) | ||||
−0.931761 | + | 0.363073i | \(0.881728\pi\) | |||||||
\(888\) | 896.087i | 1.00911i | ||||||||
\(889\) | 153.400 | + | 829.490i | 0.172553 | + | 0.933059i | ||||
\(890\) | 1252.90 | 1.40775 | ||||||||
\(891\) | −15.0644 | −0.0169073 | ||||||||
\(892\) | 2127.04i | 2.38457i | ||||||||
\(893\) | 274.926 | 0.307867 | ||||||||
\(894\) | − | 2319.97i | − | 2.59504i | ||||||
\(895\) | 1100.04i | 1.22910i | ||||||||
\(896\) | 297.919 | + | 1610.96i | 0.332499 | + | 1.79794i | ||||
\(897\) | 1643.94 | 1.83270 | ||||||||
\(898\) | −760.563 | −0.846952 | ||||||||
\(899\) | 1600.76i | 1.78060i | ||||||||
\(900\) | −1055.36 | −1.17262 | ||||||||
\(901\) | 2318.08i | 2.57278i | ||||||||
\(902\) | 6.75041i | 0.00748383i | ||||||||
\(903\) | −30.5760 | + | 5.65452i | −0.0338605 | + | 0.00626192i | ||||
\(904\) | −1400.64 | −1.54938 | ||||||||
\(905\) | −1108.59 | −1.22496 | ||||||||
\(906\) | − | 4057.91i | − | 4.47893i | ||||||
\(907\) | −925.902 | −1.02084 | −0.510420 | − | 0.859925i | \(-0.670510\pi\) | ||||
−0.510420 | + | 0.859925i | \(0.670510\pi\) | |||||||
\(908\) | − | 402.989i | − | 0.443821i | ||||||
\(909\) | 254.918i | 0.280438i | ||||||||
\(910\) | −158.532 | − | 857.239i | −0.174211 | − | 0.942021i | ||||
\(911\) | −1443.40 | −1.58441 | −0.792205 | − | 0.610254i | \(-0.791067\pi\) | ||||
−0.792205 | + | 0.610254i | \(0.791067\pi\) | |||||||
\(912\) | 175.161 | 0.192063 | ||||||||
\(913\) | − | 23.0474i | − | 0.0252435i | ||||||
\(914\) | 1458.97 | 1.59625 | ||||||||
\(915\) | 102.068i | 0.111550i | ||||||||
\(916\) | 575.212i | 0.627960i | ||||||||
\(917\) | 1474.14 | − | 272.617i | 1.60757 | − | 0.297292i | ||||
\(918\) | −1137.97 | −1.23962 | ||||||||
\(919\) | 306.624 | 0.333650 | 0.166825 | − | 0.985987i | \(-0.446649\pi\) | ||||
0.166825 | + | 0.985987i | \(0.446649\pi\) | |||||||
\(920\) | 1364.34i | 1.48298i | ||||||||
\(921\) | −2077.55 | −2.25576 | ||||||||
\(922\) | 854.273i | 0.926544i | ||||||||
\(923\) | 499.221i | 0.540868i | ||||||||
\(924\) | 71.7601 | − | 13.2708i | 0.0776624 | − | 0.0143623i | ||||
\(925\) | 218.738 | 0.236474 | ||||||||
\(926\) | −513.109 | −0.554113 | ||||||||
\(927\) | 864.453i | 0.932527i | ||||||||
\(928\) | −792.266 | −0.853735 | ||||||||
\(929\) | − | 253.479i | − | 0.272852i | −0.990650 | − | 0.136426i | \(-0.956438\pi\) | ||
0.990650 | − | 0.136426i | \(-0.0435616\pi\) | |||||||
\(930\) | 1933.43i | 2.07896i | ||||||||
\(931\) | −84.9566 | − | 221.840i | −0.0912531 | − | 0.238281i | ||||
\(932\) | 2605.46 | 2.79556 | ||||||||
\(933\) | 751.025 | 0.804957 | ||||||||
\(934\) | − | 753.951i | − | 0.807229i | ||||||
\(935\) | 29.7232 | 0.0317895 | ||||||||
\(936\) | − | 1352.98i | − | 1.44549i | ||||||
\(937\) | − | 604.636i | − | 0.645289i | −0.946520 | − | 0.322645i | \(-0.895428\pi\) | ||
0.946520 | − | 0.322645i | \(-0.104572\pi\) | |||||||
\(938\) | −170.833 | − | 923.758i | −0.182125 | − | 0.984817i | ||||
\(939\) | 363.032 | 0.386616 | ||||||||
\(940\) | 1473.19 | 1.56722 | ||||||||
\(941\) | − | 114.537i | − | 0.121719i | −0.998146 | − | 0.0608593i | \(-0.980616\pi\) | ||
0.998146 | − | 0.0608593i | \(-0.0193841\pi\) | |||||||
\(942\) | 1838.52 | 1.95172 | ||||||||
\(943\) | 222.038i | 0.235459i | ||||||||
\(944\) | 119.944i | 0.127060i | ||||||||
\(945\) | −57.9108 | − | 313.145i | −0.0612813 | − | 0.331370i | ||||
\(946\) | 1.02688 | 0.00108550 | ||||||||
\(947\) | 110.502 | 0.116686 | 0.0583431 | − | 0.998297i | \(-0.481418\pi\) | ||||
0.0583431 | + | 0.998297i | \(0.481418\pi\) | |||||||
\(948\) | − | 1265.68i | − | 1.33511i | ||||||
\(949\) | 298.234 | 0.314261 | ||||||||
\(950\) | − | 200.003i | − | 0.210530i | ||||||
\(951\) | − | 1410.52i | − | 1.48320i | ||||||
\(952\) | −2016.64 | + | 372.944i | −2.11832 | + | 0.391747i | ||||
\(953\) | −954.457 | −1.00153 | −0.500764 | − | 0.865584i | \(-0.666948\pi\) | ||||
−0.500764 | + | 0.865584i | \(0.666948\pi\) | |||||||
\(954\) | −3459.18 | −3.62598 | ||||||||
\(955\) | 358.151i | 0.375028i | ||||||||
\(956\) | −2494.62 | −2.60944 | ||||||||
\(957\) | 64.7388i | 0.0676476i | ||||||||
\(958\) | − | 668.181i | − | 0.697475i | ||||||
\(959\) | −186.446 | − | 1008.18i | −0.194417 | − | 1.05129i | ||||
\(960\) | −1472.33 | −1.53368 | ||||||||
\(961\) | −291.381 | −0.303206 | ||||||||
\(962\) | 621.966i | 0.646534i | ||||||||
\(963\) | −874.638 | −0.908243 | ||||||||
\(964\) | 2308.55i | 2.39476i | ||||||||
\(965\) | − | 126.092i | − | 0.130665i | ||||||
\(966\) | 3656.52 | − | 676.212i | 3.78522 | − | 0.700012i | ||||
\(967\) | −175.233 | −0.181213 | −0.0906063 | − | 0.995887i | \(-0.528880\pi\) | ||||
−0.0906063 | + | 0.995887i | \(0.528880\pi\) | |||||||
\(968\) | 1333.82 | 1.37791 | ||||||||
\(969\) | − | 587.128i | − | 0.605911i | ||||||
\(970\) | −786.729 | −0.811061 | ||||||||
\(971\) | − | 1515.13i | − | 1.56039i | −0.625539 | − | 0.780193i | \(-0.715121\pi\) | ||
0.625539 | − | 0.780193i | \(-0.284879\pi\) | |||||||
\(972\) | 2430.81i | 2.50083i | ||||||||
\(973\) | 1561.46 | − | 288.766i | 1.60479 | − | 0.296779i | ||||
\(974\) | −1449.30 | −1.48799 | ||||||||
\(975\) | −582.225 | −0.597154 | ||||||||
\(976\) | 49.7208i | 0.0509435i | ||||||||
\(977\) | −1089.12 | −1.11476 | −0.557381 | − | 0.830257i | \(-0.688194\pi\) | ||||
−0.557381 | + | 0.830257i | \(0.688194\pi\) | |||||||
\(978\) | 888.477i | 0.908464i | ||||||||
\(979\) | 32.8216i | 0.0335257i | ||||||||
\(980\) | −455.240 | − | 1188.73i | −0.464531 | − | 1.21299i | ||||
\(981\) | 1288.94 | 1.31390 | ||||||||
\(982\) | −2507.39 | −2.55335 | ||||||||
\(983\) | − | 1353.41i | − | 1.37682i | −0.725323 | − | 0.688409i | \(-0.758309\pi\) | ||
0.725323 | − | 0.688409i | \(-0.241691\pi\) | |||||||
\(984\) | 322.150 | 0.327388 | ||||||||
\(985\) | 604.329i | 0.613532i | ||||||||
\(986\) | − | 4035.18i | − | 4.09248i | ||||||
\(987\) | −329.205 | − | 1780.13i | −0.333541 | − | 1.80358i | ||||
\(988\) | 367.105 | 0.371564 | ||||||||
\(989\) | 33.7767 | 0.0341524 | ||||||||
\(990\) | 44.3548i | 0.0448028i | ||||||||
\(991\) | 529.599 | 0.534409 | 0.267204 | − | 0.963640i | \(-0.413900\pi\) | ||||
0.267204 | + | 0.963640i | \(0.413900\pi\) | |||||||
\(992\) | − | 619.841i | − | 0.624840i | ||||||
\(993\) | − | 1746.46i | − | 1.75878i | ||||||
\(994\) | 205.348 | + | 1110.39i | 0.206588 | + | 1.11709i | ||||
\(995\) | 92.9115 | 0.0933784 | ||||||||
\(996\) | −2439.51 | −2.44930 | ||||||||
\(997\) | − | 113.108i | − | 0.113448i | −0.998390 | − | 0.0567241i | \(-0.981934\pi\) | ||
0.998390 | − | 0.0567241i | \(-0.0180656\pi\) | |||||||
\(998\) | −2439.36 | −2.44425 | ||||||||
\(999\) | 227.201i | 0.227428i |
(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 | 287.3.b.a.83.5 | ✓ | 52 | |
7.6 | odd | 2 | inner | 287.3.b.a.83.6 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.b.a.83.5 | ✓ | 52 | 1.1 | even | 1 | trivial | |
287.3.b.a.83.6 | yes | 52 | 7.6 | odd | 2 | inner |