Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(461,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.461");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.g (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.7 | ||
Character | \(\chi\) | \(=\) | 690.461 |
Dual form | 690.3.g.a.461.8 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.56849 | + | 2.55731i | 0.522831 | + | 0.852436i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 3.61658 | − | 2.21819i | 0.602763 | − | 0.369698i | ||||
\(7\) | −1.76788 | −0.252555 | −0.126277 | − | 0.991995i | \(-0.540303\pi\) | ||||
−0.126277 | + | 0.991995i | \(0.540303\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −4.07965 | + | 8.02225i | −0.453295 | + | 0.891361i | ||||
\(10\) | 3.16228 | 0.316228 | ||||||||
\(11\) | − | 17.7224i | − | 1.61113i | −0.592508 | − | 0.805564i | \(-0.701862\pi\) | ||
0.592508 | − | 0.805564i | \(-0.298138\pi\) | |||||||
\(12\) | −3.13699 | − | 5.11462i | −0.261416 | − | 0.426218i | ||||
\(13\) | −20.6890 | −1.59146 | −0.795730 | − | 0.605652i | \(-0.792913\pi\) | ||||
−0.795730 | + | 0.605652i | \(0.792913\pi\) | |||||||
\(14\) | 2.50016i | 0.178583i | ||||||||
\(15\) | −5.71832 | + | 3.50726i | −0.381221 | + | 0.233817i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 0.0288786i | − | 0.00169874i | −1.00000 | 0.000849371i | \(-0.999730\pi\) | |||
1.00000 | 0.000849371i | \(-0.000270363\pi\) | ||||||||
\(18\) | 11.3452 | + | 5.76950i | 0.630287 | + | 0.320528i | ||||
\(19\) | −5.91750 | −0.311447 | −0.155724 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155724 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | −2.77291 | − | 4.52102i | −0.132043 | − | 0.215287i | ||||
\(22\) | −25.0633 | −1.13924 | ||||||||
\(23\) | − | 4.79583i | − | 0.208514i | ||||||
\(24\) | −7.23316 | + | 4.43637i | −0.301382 | + | 0.184849i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 29.2586i | 1.12533i | ||||||||
\(27\) | −26.9143 | + | 2.14992i | −0.996825 | + | 0.0796268i | ||||
\(28\) | 3.53576 | 0.126277 | ||||||||
\(29\) | − | 45.1942i | − | 1.55842i | −0.626763 | − | 0.779210i | \(-0.715621\pi\) | ||
0.626763 | − | 0.779210i | \(-0.284379\pi\) | |||||||
\(30\) | 4.96001 | + | 8.08692i | 0.165334 | + | 0.269564i | ||||
\(31\) | 41.1755 | 1.32824 | 0.664121 | − | 0.747625i | \(-0.268806\pi\) | ||||
0.664121 | + | 0.747625i | \(0.268806\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 45.3217 | − | 27.7975i | 1.37338 | − | 0.842349i | ||||
\(34\) | −0.0408405 | −0.00120119 | ||||||||
\(35\) | − | 3.95310i | − | 0.112946i | ||||||
\(36\) | 8.15930 | − | 16.0445i | 0.226647 | − | 0.445680i | ||||
\(37\) | −70.8841 | −1.91579 | −0.957893 | − | 0.287125i | \(-0.907300\pi\) | ||||
−0.957893 | + | 0.287125i | \(0.907300\pi\) | |||||||
\(38\) | 8.36861i | 0.220226i | ||||||||
\(39\) | −32.4505 | − | 52.9081i | −0.832065 | − | 1.35662i | ||||
\(40\) | −6.32456 | −0.158114 | ||||||||
\(41\) | − | 18.6543i | − | 0.454982i | −0.973780 | − | 0.227491i | \(-0.926948\pi\) | ||
0.973780 | − | 0.227491i | \(-0.0730522\pi\) | |||||||
\(42\) | −6.39369 | + | 3.92149i | −0.152231 | + | 0.0933688i | ||||
\(43\) | 60.4201 | 1.40512 | 0.702559 | − | 0.711625i | \(-0.252041\pi\) | ||||
0.702559 | + | 0.711625i | \(0.252041\pi\) | |||||||
\(44\) | 35.4448i | 0.805564i | ||||||||
\(45\) | −17.9383 | − | 9.12238i | −0.398629 | − | 0.202719i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | − | 51.6509i | − | 1.09896i | −0.835508 | − | 0.549478i | \(-0.814827\pi\) | ||
0.835508 | − | 0.549478i | \(-0.185173\pi\) | |||||||
\(48\) | 6.27398 | + | 10.2292i | 0.130708 | + | 0.213109i | ||||
\(49\) | −45.8746 | −0.936216 | ||||||||
\(50\) | 7.07107i | 0.141421i | ||||||||
\(51\) | 0.0738515 | − | 0.0452959i | 0.00144807 | − | 0.000888155i | ||||
\(52\) | 41.3780 | 0.795730 | ||||||||
\(53\) | − | 21.7689i | − | 0.410734i | −0.978685 | − | 0.205367i | \(-0.934161\pi\) | ||
0.978685 | − | 0.205367i | \(-0.0658388\pi\) | |||||||
\(54\) | 3.04045 | + | 38.0625i | 0.0563046 | + | 0.704862i | ||||
\(55\) | 39.6285 | 0.720519 | ||||||||
\(56\) | − | 5.00033i | − | 0.0892915i | ||||||
\(57\) | −9.28156 | − | 15.1329i | −0.162834 | − | 0.265489i | ||||
\(58\) | −63.9142 | −1.10197 | ||||||||
\(59\) | 68.2581i | 1.15692i | 0.815712 | + | 0.578458i | \(0.196345\pi\) | ||||
−0.815712 | + | 0.578458i | \(0.803655\pi\) | |||||||
\(60\) | 11.4366 | − | 7.01452i | 0.190611 | − | 0.116909i | ||||
\(61\) | 1.38027 | 0.0226273 | 0.0113136 | − | 0.999936i | \(-0.496399\pi\) | ||||
0.0113136 | + | 0.999936i | \(0.496399\pi\) | |||||||
\(62\) | − | 58.2310i | − | 0.939209i | ||||||
\(63\) | 7.21234 | − | 14.1824i | 0.114482 | − | 0.225117i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 46.2620i | − | 0.711722i | ||||||
\(66\) | −39.3116 | − | 64.0945i | −0.595631 | − | 0.971129i | ||||
\(67\) | −100.715 | −1.50322 | −0.751608 | − | 0.659610i | \(-0.770721\pi\) | ||||
−0.751608 | + | 0.659610i | \(0.770721\pi\) | |||||||
\(68\) | 0.0577572i | 0.000849371i | ||||||||
\(69\) | 12.2644 | − | 7.52223i | 0.177745 | − | 0.109018i | ||||
\(70\) | −5.59053 | −0.0798648 | ||||||||
\(71\) | − | 56.2569i | − | 0.792350i | −0.918175 | − | 0.396175i | \(-0.870337\pi\) | ||
0.918175 | − | 0.396175i | \(-0.129663\pi\) | |||||||
\(72\) | −22.6903 | − | 11.5390i | −0.315144 | − | 0.160264i | ||||
\(73\) | −73.9837 | −1.01348 | −0.506738 | − | 0.862100i | \(-0.669149\pi\) | ||||
−0.506738 | + | 0.862100i | \(0.669149\pi\) | |||||||
\(74\) | 100.245i | 1.35467i | ||||||||
\(75\) | −7.84247 | − | 12.7865i | −0.104566 | − | 0.170487i | ||||
\(76\) | 11.8350 | 0.155724 | ||||||||
\(77\) | 31.3311i | 0.406898i | ||||||||
\(78\) | −74.8233 | + | 45.8920i | −0.959274 | + | 0.588359i | ||||
\(79\) | 4.47024 | 0.0565854 | 0.0282927 | − | 0.999600i | \(-0.490993\pi\) | ||||
0.0282927 | + | 0.999600i | \(0.490993\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | −47.7129 | − | 65.4559i | −0.589048 | − | 0.808098i | ||||
\(82\) | −26.3811 | −0.321721 | ||||||||
\(83\) | − | 21.0356i | − | 0.253441i | −0.991938 | − | 0.126721i | \(-0.959555\pi\) | ||
0.991938 | − | 0.126721i | \(-0.0404451\pi\) | |||||||
\(84\) | 5.54583 | + | 9.04204i | 0.0660217 | + | 0.107643i | ||||
\(85\) | 0.0645745 | 0.000759700 | ||||||||
\(86\) | − | 85.4469i | − | 0.993569i | ||||||
\(87\) | 115.575 | − | 70.8868i | 1.32845 | − | 0.814791i | ||||
\(88\) | 50.1266 | 0.569620 | ||||||||
\(89\) | 28.2078i | 0.316942i | 0.987364 | + | 0.158471i | \(0.0506564\pi\) | ||||
−0.987364 | + | 0.158471i | \(0.949344\pi\) | |||||||
\(90\) | −12.9010 | + | 25.3686i | −0.143344 | + | 0.281873i | ||||
\(91\) | 36.5757 | 0.401930 | ||||||||
\(92\) | 9.59166i | 0.104257i | ||||||||
\(93\) | 64.5835 | + | 105.298i | 0.694447 | + | 1.13224i | ||||
\(94\) | −73.0455 | −0.777079 | ||||||||
\(95\) | − | 13.2319i | − | 0.139283i | ||||||
\(96\) | 14.4663 | − | 8.87274i | 0.150691 | − | 0.0924244i | ||||
\(97\) | 57.7059 | 0.594906 | 0.297453 | − | 0.954736i | \(-0.403863\pi\) | ||||
0.297453 | + | 0.954736i | \(0.403863\pi\) | |||||||
\(98\) | 64.8765i | 0.662005i | ||||||||
\(99\) | 142.174 | + | 72.3013i | 1.43610 | + | 0.730316i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 68.2488i | 0.675730i | 0.941195 | + | 0.337865i | \(0.109705\pi\) | ||||
−0.941195 | + | 0.337865i | \(0.890295\pi\) | |||||||
\(102\) | −0.0640581 | − | 0.104442i | −0.000628021 | − | 0.00102394i | ||||
\(103\) | −61.1415 | −0.593607 | −0.296803 | − | 0.954939i | \(-0.595921\pi\) | ||||
−0.296803 | + | 0.954939i | \(0.595921\pi\) | |||||||
\(104\) | − | 58.5173i | − | 0.562666i | ||||||
\(105\) | 10.1093 | − | 6.20042i | 0.0962791 | − | 0.0590516i | ||||
\(106\) | −30.7859 | −0.290433 | ||||||||
\(107\) | 146.342i | 1.36769i | 0.729629 | + | 0.683843i | \(0.239693\pi\) | ||||
−0.729629 | + | 0.683843i | \(0.760307\pi\) | |||||||
\(108\) | 53.8285 | − | 4.29985i | 0.498412 | − | 0.0398134i | ||||
\(109\) | 48.8918 | 0.448549 | 0.224274 | − | 0.974526i | \(-0.427999\pi\) | ||||
0.224274 | + | 0.974526i | \(0.427999\pi\) | |||||||
\(110\) | − | 56.0432i | − | 0.509484i | ||||||
\(111\) | −111.181 | − | 181.272i | −1.00163 | − | 1.63309i | ||||
\(112\) | −7.07153 | −0.0631386 | ||||||||
\(113\) | − | 127.489i | − | 1.12822i | −0.825698 | − | 0.564112i | \(-0.809219\pi\) | ||
0.825698 | − | 0.564112i | \(-0.190781\pi\) | |||||||
\(114\) | −21.4011 | + | 13.1261i | −0.187729 | + | 0.115141i | ||||
\(115\) | 10.7238 | 0.0932505 | ||||||||
\(116\) | 90.3884i | 0.779210i | ||||||||
\(117\) | 84.4038 | − | 165.972i | 0.721400 | − | 1.41856i | ||||
\(118\) | 96.5315 | 0.818064 | ||||||||
\(119\) | 0.0510540i | 0.000429025i | ||||||||
\(120\) | −9.92003 | − | 16.1738i | −0.0826669 | − | 0.134782i | ||||
\(121\) | −193.084 | −1.59574 | ||||||||
\(122\) | − | 1.95199i | − | 0.0159999i | ||||||
\(123\) | 47.7047 | − | 29.2591i | 0.387843 | − | 0.237879i | ||||
\(124\) | −82.3510 | −0.664121 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −20.0569 | − | 10.1998i | −0.159182 | − | 0.0809507i | ||||
\(127\) | −230.507 | −1.81501 | −0.907506 | − | 0.420038i | \(-0.862017\pi\) | ||||
−0.907506 | + | 0.420038i | \(0.862017\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 94.7685 | + | 154.513i | 0.734640 | + | 1.19777i | ||||
\(130\) | −65.4243 | −0.503264 | ||||||||
\(131\) | 65.2731i | 0.498268i | 0.968469 | + | 0.249134i | \(0.0801460\pi\) | ||||
−0.968469 | + | 0.249134i | \(0.919854\pi\) | |||||||
\(132\) | −90.6434 | + | 55.5950i | −0.686692 | + | 0.421174i | ||||
\(133\) | 10.4614 | 0.0786574 | ||||||||
\(134\) | 142.433i | 1.06293i | ||||||||
\(135\) | −4.80737 | − | 60.1821i | −0.0356102 | − | 0.445794i | ||||
\(136\) | 0.0816810 | 0.000600596 | ||||||||
\(137\) | 123.243i | 0.899587i | 0.893133 | + | 0.449793i | \(0.148502\pi\) | ||||
−0.893133 | + | 0.449793i | \(0.851498\pi\) | |||||||
\(138\) | −10.6380 | − | 17.3445i | −0.0770873 | − | 0.125685i | ||||
\(139\) | −219.172 | −1.57678 | −0.788389 | − | 0.615177i | \(-0.789085\pi\) | ||||
−0.788389 | + | 0.615177i | \(0.789085\pi\) | |||||||
\(140\) | 7.90621i | 0.0564729i | ||||||||
\(141\) | 132.087 | − | 81.0142i | 0.936790 | − | 0.574569i | ||||
\(142\) | −79.5592 | −0.560276 | ||||||||
\(143\) | 366.659i | 2.56405i | ||||||||
\(144\) | −16.3186 | + | 32.0890i | −0.113324 | + | 0.222840i | ||||
\(145\) | 101.057 | 0.696947 | ||||||||
\(146\) | 104.629i | 0.716635i | ||||||||
\(147\) | −71.9540 | − | 117.315i | −0.489483 | − | 0.798064i | ||||
\(148\) | 141.768 | 0.957893 | ||||||||
\(149\) | 84.6070i | 0.567832i | 0.958849 | + | 0.283916i | \(0.0916337\pi\) | ||||
−0.958849 | + | 0.283916i | \(0.908366\pi\) | |||||||
\(150\) | −18.0829 | + | 11.0909i | −0.120553 | + | 0.0739395i | ||||
\(151\) | −29.2120 | −0.193457 | −0.0967284 | − | 0.995311i | \(-0.530838\pi\) | ||||
−0.0967284 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(152\) | − | 16.7372i | − | 0.110113i | ||||||
\(153\) | 0.231671 | + | 0.117815i | 0.00151419 | + | 0.000770030i | ||||
\(154\) | 44.3089 | 0.287720 | ||||||||
\(155\) | 92.0712i | 0.594008i | ||||||||
\(156\) | 64.9011 | + | 105.816i | 0.416033 | + | 0.678309i | ||||
\(157\) | 269.251 | 1.71498 | 0.857488 | − | 0.514503i | \(-0.172024\pi\) | ||||
0.857488 | + | 0.514503i | \(0.172024\pi\) | |||||||
\(158\) | − | 6.32188i | − | 0.0400119i | ||||||
\(159\) | 55.6698 | − | 34.1444i | 0.350125 | − | 0.214745i | ||||
\(160\) | 12.6491 | 0.0790569 | ||||||||
\(161\) | 8.47846i | 0.0526613i | ||||||||
\(162\) | −92.5687 | + | 67.4762i | −0.571412 | + | 0.416520i | ||||
\(163\) | −296.191 | −1.81712 | −0.908561 | − | 0.417752i | \(-0.862818\pi\) | ||||
−0.908561 | + | 0.417752i | \(0.862818\pi\) | |||||||
\(164\) | 37.3085i | 0.227491i | ||||||||
\(165\) | 62.1571 | + | 101.342i | 0.376710 | + | 0.614196i | ||||
\(166\) | −29.7488 | −0.179210 | ||||||||
\(167\) | 139.977i | 0.838188i | 0.907943 | + | 0.419094i | \(0.137652\pi\) | ||||
−0.907943 | + | 0.419094i | \(0.862348\pi\) | |||||||
\(168\) | 12.7874 | − | 7.84298i | 0.0761153 | − | 0.0466844i | ||||
\(169\) | 259.034 | 1.53274 | ||||||||
\(170\) | − | 0.0913222i | − | 0.000537189i | ||||||
\(171\) | 24.1413 | − | 47.4716i | 0.141177 | − | 0.277612i | ||||
\(172\) | −120.840 | −0.702559 | ||||||||
\(173\) | 2.23761i | 0.0129342i | 0.999979 | + | 0.00646708i | \(0.00205855\pi\) | ||||
−0.999979 | + | 0.00646708i | \(0.997941\pi\) | |||||||
\(174\) | −100.249 | − | 163.448i | −0.576144 | − | 0.939359i | ||||
\(175\) | 8.83941 | 0.0505109 | ||||||||
\(176\) | − | 70.8897i | − | 0.402782i | ||||||
\(177\) | −174.557 | + | 107.062i | −0.986198 | + | 0.604872i | ||||
\(178\) | 39.8919 | 0.224112 | ||||||||
\(179\) | − | 86.0465i | − | 0.480707i | −0.970685 | − | 0.240353i | \(-0.922737\pi\) | ||
0.970685 | − | 0.240353i | \(-0.0772633\pi\) | |||||||
\(180\) | 35.8766 | + | 18.2448i | 0.199314 | + | 0.101360i | ||||
\(181\) | 43.5809 | 0.240778 | 0.120389 | − | 0.992727i | \(-0.461586\pi\) | ||||
0.120389 | + | 0.992727i | \(0.461586\pi\) | |||||||
\(182\) | − | 51.7258i | − | 0.284208i | ||||||
\(183\) | 2.16494 | + | 3.52976i | 0.0118303 | + | 0.0192883i | ||||
\(184\) | 13.5647 | 0.0737210 | ||||||||
\(185\) | − | 158.502i | − | 0.856766i | ||||||
\(186\) | 148.914 | − | 91.3349i | 0.800616 | − | 0.491048i | ||||
\(187\) | −0.511799 | −0.00273689 | ||||||||
\(188\) | 103.302i | 0.549478i | ||||||||
\(189\) | 47.5812 | − | 3.80081i | 0.251753 | − | 0.0201101i | ||||
\(190\) | −18.7128 | −0.0984883 | ||||||||
\(191\) | − | 195.043i | − | 1.02117i | −0.859828 | − | 0.510584i | \(-0.829429\pi\) | ||
0.859828 | − | 0.510584i | \(-0.170571\pi\) | |||||||
\(192\) | −12.5480 | − | 20.4585i | −0.0653539 | − | 0.106555i | ||||
\(193\) | 330.591 | 1.71290 | 0.856452 | − | 0.516226i | \(-0.172664\pi\) | ||||
0.856452 | + | 0.516226i | \(0.172664\pi\) | |||||||
\(194\) | − | 81.6085i | − | 0.420662i | ||||||
\(195\) | 118.306 | − | 72.5616i | 0.606698 | − | 0.372111i | ||||
\(196\) | 91.7492 | 0.468108 | ||||||||
\(197\) | 91.7002i | 0.465483i | 0.972539 | + | 0.232742i | \(0.0747697\pi\) | ||||
−0.972539 | + | 0.232742i | \(0.925230\pi\) | |||||||
\(198\) | 102.249 | − | 201.064i | 0.516411 | − | 1.01547i | ||||
\(199\) | 6.18236 | 0.0310671 | 0.0155336 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155336 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(200\) | − | 14.1421i | − | 0.0707107i | ||||||
\(201\) | −157.972 | − | 257.560i | −0.785928 | − | 1.28140i | ||||
\(202\) | 96.5183 | 0.477813 | ||||||||
\(203\) | 79.8980i | 0.393586i | ||||||||
\(204\) | −0.147703 | + | 0.0905919i | −0.000724034 | + | 0.000444078i | ||||
\(205\) | 41.7122 | 0.203474 | ||||||||
\(206\) | 86.4671i | 0.419743i | ||||||||
\(207\) | 38.4733 | + | 19.5653i | 0.185862 | + | 0.0945185i | ||||
\(208\) | −82.7559 | −0.397865 | ||||||||
\(209\) | 104.872i | 0.501782i | ||||||||
\(210\) | −8.76872 | − | 14.2967i | −0.0417558 | − | 0.0680796i | ||||
\(211\) | 312.639 | 1.48170 | 0.740851 | − | 0.671670i | \(-0.234423\pi\) | ||||
0.740851 | + | 0.671670i | \(0.234423\pi\) | |||||||
\(212\) | 43.5378i | 0.205367i | ||||||||
\(213\) | 143.866 | − | 88.2386i | 0.675428 | − | 0.414266i | ||||
\(214\) | 206.959 | 0.967100 | ||||||||
\(215\) | 135.103i | 0.628388i | ||||||||
\(216\) | −6.08090 | − | 76.1250i | −0.0281523 | − | 0.352431i | ||||
\(217\) | −72.7934 | −0.335454 | ||||||||
\(218\) | − | 69.1435i | − | 0.317172i | ||||||
\(219\) | −116.043 | − | 189.199i | −0.529877 | − | 0.863923i | ||||
\(220\) | −79.2571 | −0.360259 | ||||||||
\(221\) | 0.597469i | 0.00270348i | ||||||||
\(222\) | −256.358 | + | 157.234i | −1.15477 | + | 0.708262i | ||||
\(223\) | 73.3202 | 0.328790 | 0.164395 | − | 0.986395i | \(-0.447433\pi\) | ||||
0.164395 | + | 0.986395i | \(0.447433\pi\) | |||||||
\(224\) | 10.0007i | 0.0446458i | ||||||||
\(225\) | 20.3983 | − | 40.1112i | 0.0906589 | − | 0.178272i | ||||
\(226\) | −180.297 | −0.797775 | ||||||||
\(227\) | − | 54.4085i | − | 0.239685i | −0.992793 | − | 0.119843i | \(-0.961761\pi\) | ||
0.992793 | − | 0.119843i | \(-0.0382390\pi\) | |||||||
\(228\) | 18.5631 | + | 30.2657i | 0.0814172 | + | 0.132744i | ||||
\(229\) | −104.576 | −0.456662 | −0.228331 | − | 0.973584i | \(-0.573327\pi\) | ||||
−0.228331 | + | 0.973584i | \(0.573327\pi\) | |||||||
\(230\) | − | 15.1658i | − | 0.0659380i | ||||||
\(231\) | −80.1234 | + | 49.1427i | −0.346854 | + | 0.212739i | ||||
\(232\) | 127.828 | 0.550985 | ||||||||
\(233\) | 72.9504i | 0.313092i | 0.987671 | + | 0.156546i | \(0.0500359\pi\) | ||||
−0.987671 | + | 0.156546i | \(0.949964\pi\) | |||||||
\(234\) | −234.720 | − | 119.365i | −1.00308 | − | 0.510107i | ||||
\(235\) | 115.495 | 0.491468 | ||||||||
\(236\) | − | 136.516i | − | 0.578458i | ||||||
\(237\) | 7.01155 | + | 11.4318i | 0.0295846 | + | 0.0482354i | ||||
\(238\) | 0.0722012 | 0.000303366 | ||||||||
\(239\) | − | 401.263i | − | 1.67892i | −0.543418 | − | 0.839462i | \(-0.682870\pi\) | ||
0.543418 | − | 0.839462i | \(-0.317130\pi\) | |||||||
\(240\) | −22.8733 | + | 14.0290i | −0.0953053 | + | 0.0584543i | ||||
\(241\) | −75.2115 | −0.312081 | −0.156041 | − | 0.987751i | \(-0.549873\pi\) | ||||
−0.156041 | + | 0.987751i | \(0.549873\pi\) | |||||||
\(242\) | 273.062i | 1.12836i | ||||||||
\(243\) | 92.5536 | − | 224.684i | 0.380879 | − | 0.924625i | ||||
\(244\) | −2.76053 | −0.0113136 | ||||||||
\(245\) | − | 102.579i | − | 0.418689i | ||||||
\(246\) | −41.3786 | − | 67.4646i | −0.168206 | − | 0.274246i | ||||
\(247\) | 122.427 | 0.495656 | ||||||||
\(248\) | 116.462i | 0.469604i | ||||||||
\(249\) | 53.7945 | − | 32.9942i | 0.216042 | − | 0.132507i | ||||
\(250\) | −15.8114 | −0.0632456 | ||||||||
\(251\) | 95.2872i | 0.379630i | 0.981820 | + | 0.189815i | \(0.0607889\pi\) | ||||
−0.981820 | + | 0.189815i | \(0.939211\pi\) | |||||||
\(252\) | −14.4247 | + | 28.3648i | −0.0572408 | + | 0.112559i | ||||
\(253\) | −84.9937 | −0.335944 | ||||||||
\(254\) | 325.986i | 1.28341i | ||||||||
\(255\) | 0.101285 | + | 0.165137i | 0.000397195 | + | 0.000647596i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 110.044i | − | 0.428188i | −0.976813 | − | 0.214094i | \(-0.931320\pi\) | ||
0.976813 | − | 0.214094i | \(-0.0686799\pi\) | |||||||
\(258\) | 218.514 | − | 134.023i | 0.846954 | − | 0.519469i | ||||
\(259\) | 125.315 | 0.483840 | ||||||||
\(260\) | 92.5239i | 0.355861i | ||||||||
\(261\) | 362.559 | + | 184.377i | 1.38911 | + | 0.706423i | ||||
\(262\) | 92.3101 | 0.352329 | ||||||||
\(263\) | 372.584i | 1.41667i | 0.705876 | + | 0.708335i | \(0.250554\pi\) | ||||
−0.705876 | + | 0.708335i | \(0.749446\pi\) | |||||||
\(264\) | 78.6232 | + | 128.189i | 0.297815 | + | 0.485565i | ||||
\(265\) | 48.6767 | 0.183686 | ||||||||
\(266\) | − | 14.7947i | − | 0.0556192i | ||||||
\(267\) | −72.1361 | + | 44.2438i | −0.270173 | + | 0.165707i | ||||
\(268\) | 201.431 | 0.751608 | ||||||||
\(269\) | − | 61.0243i | − | 0.226856i | −0.993546 | − | 0.113428i | \(-0.963817\pi\) | ||
0.993546 | − | 0.113428i | \(-0.0361831\pi\) | |||||||
\(270\) | −85.1104 | + | 6.79865i | −0.315224 | + | 0.0251802i | ||||
\(271\) | 489.007 | 1.80445 | 0.902227 | − | 0.431262i | \(-0.141932\pi\) | ||||
0.902227 | + | 0.431262i | \(0.141932\pi\) | |||||||
\(272\) | − | 0.115514i | − | 0.000424685i | ||||||
\(273\) | 57.3687 | + | 93.5353i | 0.210142 | + | 0.342620i | ||||
\(274\) | 174.292 | 0.636104 | ||||||||
\(275\) | 88.6121i | 0.322226i | ||||||||
\(276\) | −24.5288 | + | 15.0445i | −0.0888726 | + | 0.0545089i | ||||
\(277\) | 319.748 | 1.15432 | 0.577162 | − | 0.816630i | \(-0.304160\pi\) | ||||
0.577162 | + | 0.816630i | \(0.304160\pi\) | |||||||
\(278\) | 309.956i | 1.11495i | ||||||||
\(279\) | −167.982 | + | 330.320i | −0.602085 | + | 1.18394i | ||||
\(280\) | 11.1811 | 0.0399324 | ||||||||
\(281\) | − | 244.012i | − | 0.868371i | −0.900824 | − | 0.434185i | \(-0.857036\pi\) | ||
0.900824 | − | 0.434185i | \(-0.142964\pi\) | |||||||
\(282\) | −114.571 | − | 186.800i | −0.406282 | − | 0.662410i | ||||
\(283\) | −312.536 | −1.10437 | −0.552183 | − | 0.833723i | \(-0.686205\pi\) | ||||
−0.552183 | + | 0.833723i | \(0.686205\pi\) | |||||||
\(284\) | 112.514i | 0.396175i | ||||||||
\(285\) | 33.8381 | − | 20.7542i | 0.118730 | − | 0.0728218i | ||||
\(286\) | 518.534 | 1.81305 | ||||||||
\(287\) | 32.9785i | 0.114908i | ||||||||
\(288\) | 45.3807 | + | 23.0780i | 0.157572 | + | 0.0801319i | ||||
\(289\) | 288.999 | 0.999997 | ||||||||
\(290\) | − | 142.917i | − | 0.492816i | ||||||
\(291\) | 90.5114 | + | 147.572i | 0.311036 | + | 0.507120i | ||||
\(292\) | 147.967 | 0.506738 | ||||||||
\(293\) | 439.469i | 1.49989i | 0.661498 | + | 0.749947i | \(0.269921\pi\) | ||||
−0.661498 | + | 0.749947i | \(0.730079\pi\) | |||||||
\(294\) | −165.909 | + | 101.758i | −0.564317 | + | 0.346117i | ||||
\(295\) | −152.630 | −0.517389 | ||||||||
\(296\) | − | 200.490i | − | 0.677333i | ||||||
\(297\) | 38.1018 | + | 476.986i | 0.128289 | + | 1.60601i | ||||
\(298\) | 119.652 | 0.401518 | ||||||||
\(299\) | 99.2209i | 0.331842i | ||||||||
\(300\) | 15.6849 | + | 25.5731i | 0.0522831 | + | 0.0852436i | ||||
\(301\) | −106.816 | −0.354869 | ||||||||
\(302\) | 41.3120i | 0.136795i | ||||||||
\(303\) | −174.533 | + | 107.048i | −0.576017 | + | 0.353293i | ||||
\(304\) | −23.6700 | −0.0778618 | ||||||||
\(305\) | 3.08637i | 0.0101192i | ||||||||
\(306\) | 0.166615 | − | 0.327633i | 0.000544494 | − | 0.00107070i | ||||
\(307\) | −147.088 | −0.479115 | −0.239557 | − | 0.970882i | \(-0.577002\pi\) | ||||
−0.239557 | + | 0.970882i | \(0.577002\pi\) | |||||||
\(308\) | − | 62.6623i | − | 0.203449i | ||||||
\(309\) | −95.9001 | − | 156.358i | −0.310356 | − | 0.506012i | ||||
\(310\) | 130.208 | 0.420027 | ||||||||
\(311\) | − | 601.613i | − | 1.93445i | −0.253930 | − | 0.967223i | \(-0.581723\pi\) | ||
0.253930 | − | 0.967223i | \(-0.418277\pi\) | |||||||
\(312\) | 149.647 | − | 91.7840i | 0.479637 | − | 0.294179i | ||||
\(313\) | −88.4556 | −0.282606 | −0.141303 | − | 0.989966i | \(-0.545129\pi\) | ||||
−0.141303 | + | 0.989966i | \(0.545129\pi\) | |||||||
\(314\) | − | 380.779i | − | 1.21267i | ||||||
\(315\) | 31.7128 | + | 16.1273i | 0.100675 | + | 0.0511977i | ||||
\(316\) | −8.94049 | −0.0282927 | ||||||||
\(317\) | − | 435.939i | − | 1.37520i | −0.726089 | − | 0.687601i | \(-0.758664\pi\) | ||
0.726089 | − | 0.687601i | \(-0.241336\pi\) | |||||||
\(318\) | −48.2875 | − | 78.7290i | −0.151847 | − | 0.247575i | ||||
\(319\) | −800.950 | −2.51082 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | −374.243 | + | 229.537i | −1.16586 | + | 0.715069i | ||||
\(322\) | 11.9904 | 0.0372371 | ||||||||
\(323\) | 0.170889i | 0.000529068i | ||||||||
\(324\) | 95.4258 | + | 130.912i | 0.294524 | + | 0.404049i | ||||
\(325\) | 103.445 | 0.318292 | ||||||||
\(326\) | 418.877i | 1.28490i | ||||||||
\(327\) | 76.6865 | + | 125.031i | 0.234515 | + | 0.382359i | ||||
\(328\) | 52.7622 | 0.160860 | ||||||||
\(329\) | 91.3128i | 0.277546i | ||||||||
\(330\) | 143.320 | − | 87.9034i | 0.434302 | − | 0.266374i | ||||
\(331\) | 305.202 | 0.922060 | 0.461030 | − | 0.887384i | \(-0.347480\pi\) | ||||
0.461030 | + | 0.887384i | \(0.347480\pi\) | |||||||
\(332\) | 42.0712i | 0.126721i | ||||||||
\(333\) | 289.182 | − | 568.650i | 0.868415 | − | 1.70766i | ||||
\(334\) | 197.958 | 0.592688 | ||||||||
\(335\) | − | 225.207i | − | 0.672258i | ||||||
\(336\) | −11.0917 | − | 18.0841i | −0.0330109 | − | 0.0538217i | ||||
\(337\) | 222.147 | 0.659189 | 0.329594 | − | 0.944123i | \(-0.393088\pi\) | ||||
0.329594 | + | 0.944123i | \(0.393088\pi\) | |||||||
\(338\) | − | 366.329i | − | 1.08381i | ||||||
\(339\) | 326.029 | − | 199.966i | 0.961739 | − | 0.589871i | ||||
\(340\) | −0.129149 | −0.000379850 | ||||||||
\(341\) | − | 729.729i | − | 2.13997i | ||||||
\(342\) | −67.1350 | − | 34.1410i | −0.196301 | − | 0.0998275i | ||||
\(343\) | 167.727 | 0.489000 | ||||||||
\(344\) | 170.894i | 0.496784i | ||||||||
\(345\) | 16.8202 | + | 27.4241i | 0.0487543 | + | 0.0794901i | ||||
\(346\) | 3.16446 | 0.00914583 | ||||||||
\(347\) | 656.982i | 1.89332i | 0.322235 | + | 0.946660i | \(0.395566\pi\) | ||||
−0.322235 | + | 0.946660i | \(0.604434\pi\) | |||||||
\(348\) | −231.151 | + | 141.774i | −0.664227 | + | 0.407396i | ||||
\(349\) | −409.550 | −1.17350 | −0.586748 | − | 0.809769i | \(-0.699592\pi\) | ||||
−0.586748 | + | 0.809769i | \(0.699592\pi\) | |||||||
\(350\) | − | 12.5008i | − | 0.0357166i | ||||||
\(351\) | 556.829 | − | 44.4797i | 1.58641 | − | 0.126723i | ||||
\(352\) | −100.253 | −0.284810 | ||||||||
\(353\) | 249.433i | 0.706609i | 0.935508 | + | 0.353304i | \(0.114942\pi\) | ||||
−0.935508 | + | 0.353304i | \(0.885058\pi\) | |||||||
\(354\) | 151.409 | + | 246.861i | 0.427709 | + | 0.697347i | ||||
\(355\) | 125.794 | 0.354350 | ||||||||
\(356\) | − | 56.4156i | − | 0.158471i | ||||||
\(357\) | −0.130561 | + | 0.0800778i | −0.000365716 | + | 0.000224308i | ||||
\(358\) | −121.688 | −0.339911 | ||||||||
\(359\) | − | 333.458i | − | 0.928851i | −0.885612 | − | 0.464426i | \(-0.846261\pi\) | ||
0.885612 | − | 0.464426i | \(-0.153739\pi\) | |||||||
\(360\) | 25.8020 | − | 50.7371i | 0.0716722 | − | 0.140937i | ||||
\(361\) | −325.983 | −0.903001 | ||||||||
\(362\) | − | 61.6327i | − | 0.170256i | ||||||
\(363\) | −302.851 | − | 493.775i | −0.834301 | − | 1.36026i | ||||
\(364\) | −73.1513 | −0.200965 | ||||||||
\(365\) | − | 165.433i | − | 0.453240i | ||||||
\(366\) | 4.99184 | − | 3.06168i | 0.0136389 | − | 0.00836526i | ||||
\(367\) | −144.077 | −0.392581 | −0.196290 | − | 0.980546i | \(-0.562889\pi\) | ||||
−0.196290 | + | 0.980546i | \(0.562889\pi\) | |||||||
\(368\) | − | 19.1833i | − | 0.0521286i | ||||||
\(369\) | 149.649 | + | 76.1029i | 0.405553 | + | 0.206241i | ||||
\(370\) | −224.155 | −0.605825 | ||||||||
\(371\) | 38.4849i | 0.103733i | ||||||||
\(372\) | −129.167 | − | 210.597i | −0.347223 | − | 0.566121i | ||||
\(373\) | −494.074 | −1.32459 | −0.662297 | − | 0.749241i | \(-0.730418\pi\) | ||||
−0.662297 | + | 0.749241i | \(0.730418\pi\) | |||||||
\(374\) | 0.723793i | 0.00193527i | ||||||||
\(375\) | 28.5916 | − | 17.5363i | 0.0762442 | − | 0.0467635i | ||||
\(376\) | 146.091 | 0.388540 | ||||||||
\(377\) | 935.021i | 2.48016i | ||||||||
\(378\) | −5.37516 | − | 67.2900i | −0.0142200 | − | 0.178016i | ||||
\(379\) | −533.662 | −1.40808 | −0.704040 | − | 0.710160i | \(-0.748622\pi\) | ||||
−0.704040 | + | 0.710160i | \(0.748622\pi\) | |||||||
\(380\) | 26.4639i | 0.0696417i | ||||||||
\(381\) | −361.548 | − | 589.476i | −0.948946 | − | 1.54718i | ||||
\(382\) | −275.833 | −0.722075 | ||||||||
\(383\) | 245.335i | 0.640563i | 0.947322 | + | 0.320281i | \(0.103777\pi\) | ||||
−0.947322 | + | 0.320281i | \(0.896223\pi\) | |||||||
\(384\) | −28.9326 | + | 17.7455i | −0.0753454 | + | 0.0462122i | ||||
\(385\) | −70.0586 | −0.181970 | ||||||||
\(386\) | − | 467.526i | − | 1.21121i | ||||||
\(387\) | −246.493 | + | 484.705i | −0.636932 | + | 1.25247i | ||||
\(388\) | −115.412 | −0.297453 | ||||||||
\(389\) | − | 119.365i | − | 0.306852i | −0.988160 | − | 0.153426i | \(-0.950969\pi\) | ||
0.988160 | − | 0.153426i | \(-0.0490306\pi\) | |||||||
\(390\) | −102.618 | − | 167.310i | −0.263122 | − | 0.429000i | ||||
\(391\) | −0.138497 | −0.000354212 | ||||||||
\(392\) | − | 129.753i | − | 0.331002i | ||||||
\(393\) | −166.923 | + | 102.380i | −0.424742 | + | 0.260510i | ||||
\(394\) | 129.684 | 0.329147 | ||||||||
\(395\) | 9.99577i | 0.0253057i | ||||||||
\(396\) | −284.347 | − | 144.603i | −0.718049 | − | 0.365158i | ||||
\(397\) | 424.026 | 1.06808 | 0.534038 | − | 0.845461i | \(-0.320674\pi\) | ||||
0.534038 | + | 0.845461i | \(0.320674\pi\) | |||||||
\(398\) | − | 8.74317i | − | 0.0219678i | ||||||
\(399\) | 16.4087 | + | 26.7531i | 0.0411246 | + | 0.0670504i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 787.894i | 1.96482i | 0.186731 | + | 0.982411i | \(0.440211\pi\) | ||||
−0.186731 | + | 0.982411i | \(0.559789\pi\) | |||||||
\(402\) | −364.245 | + | 223.406i | −0.906083 | + | 0.555735i | ||||
\(403\) | −851.879 | −2.11384 | ||||||||
\(404\) | − | 136.498i | − | 0.337865i | ||||||
\(405\) | 146.364 | − | 106.689i | 0.361392 | − | 0.263430i | ||||
\(406\) | 112.993 | 0.278307 | ||||||||
\(407\) | 1256.24i | 3.08658i | ||||||||
\(408\) | 0.128116 | + | 0.208884i | 0.000314010 | + | 0.000511970i | ||||
\(409\) | −9.78449 | −0.0239230 | −0.0119615 | − | 0.999928i | \(-0.503808\pi\) | ||||
−0.0119615 | + | 0.999928i | \(0.503808\pi\) | |||||||
\(410\) | − | 58.9900i | − | 0.143878i | ||||||
\(411\) | −315.171 | + | 193.307i | −0.766840 | + | 0.470332i | ||||
\(412\) | 122.283 | 0.296803 | ||||||||
\(413\) | − | 120.672i | − | 0.292185i | ||||||
\(414\) | 27.6695 | − | 54.4095i | 0.0668346 | − | 0.131424i | ||||
\(415\) | 47.0371 | 0.113342 | ||||||||
\(416\) | 117.035i | 0.281333i | ||||||||
\(417\) | −343.770 | − | 560.491i | −0.824389 | − | 1.34410i | ||||
\(418\) | 148.312 | 0.354813 | ||||||||
\(419\) | 542.817i | 1.29551i | 0.761850 | + | 0.647753i | \(0.224291\pi\) | ||||
−0.761850 | + | 0.647753i | \(0.775709\pi\) | |||||||
\(420\) | −20.2186 | + | 12.4008i | −0.0481396 | + | 0.0295258i | ||||
\(421\) | −675.751 | −1.60511 | −0.802555 | − | 0.596578i | \(-0.796527\pi\) | ||||
−0.802555 | + | 0.596578i | \(0.796527\pi\) | |||||||
\(422\) | − | 442.138i | − | 1.04772i | ||||||
\(423\) | 414.357 | + | 210.718i | 0.979566 | + | 0.498151i | ||||
\(424\) | 61.5718 | 0.145216 | ||||||||
\(425\) | 0.144393i | 0.000339748i | ||||||||
\(426\) | −124.788 | − | 203.457i | −0.292930 | − | 0.477600i | ||||
\(427\) | −2.44015 | −0.00571463 | ||||||||
\(428\) | − | 292.685i | − | 0.683843i | ||||||
\(429\) | −937.659 | + | 575.102i | −2.18569 | + | 1.34056i | ||||
\(430\) | 191.065 | 0.444337 | ||||||||
\(431\) | − | 357.378i | − | 0.829184i | −0.910007 | − | 0.414592i | \(-0.863924\pi\) | ||
0.910007 | − | 0.414592i | \(-0.136076\pi\) | |||||||
\(432\) | −107.657 | + | 8.59969i | −0.249206 | + | 0.0199067i | ||||
\(433\) | −59.5104 | −0.137437 | −0.0687187 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687187 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(434\) | 102.945i | 0.237201i | ||||||||
\(435\) | 158.508 | + | 258.435i | 0.364386 | + | 0.594102i | ||||
\(436\) | −97.7836 | −0.224274 | ||||||||
\(437\) | 28.3793i | 0.0649412i | ||||||||
\(438\) | −267.568 | + | 164.110i | −0.610886 | + | 0.374679i | ||||
\(439\) | 292.816 | 0.667006 | 0.333503 | − | 0.942749i | \(-0.391769\pi\) | ||||
0.333503 | + | 0.942749i | \(0.391769\pi\) | |||||||
\(440\) | 112.086i | 0.254742i | ||||||||
\(441\) | 187.152 | − | 368.017i | 0.424382 | − | 0.834506i | ||||
\(442\) | 0.844948 | 0.00191165 | ||||||||
\(443\) | 70.1379i | 0.158325i | 0.996862 | + | 0.0791624i | \(0.0252246\pi\) | ||||
−0.996862 | + | 0.0791624i | \(0.974775\pi\) | |||||||
\(444\) | 222.363 | + | 362.545i | 0.500817 | + | 0.816543i | ||||
\(445\) | −63.0746 | −0.141741 | ||||||||
\(446\) | − | 103.690i | − | 0.232490i | ||||||
\(447\) | −216.366 | + | 132.706i | −0.484040 | + | 0.296880i | ||||
\(448\) | 14.1431 | 0.0315693 | ||||||||
\(449\) | − | 751.278i | − | 1.67323i | −0.547795 | − | 0.836613i | \(-0.684532\pi\) | ||
0.547795 | − | 0.836613i | \(-0.315468\pi\) | |||||||
\(450\) | −56.7259 | − | 28.8475i | −0.126057 | − | 0.0641055i | ||||
\(451\) | −330.599 | −0.733035 | ||||||||
\(452\) | 254.979i | 0.564112i | ||||||||
\(453\) | −45.8188 | − | 74.7040i | −0.101145 | − | 0.164910i | ||||
\(454\) | −76.9453 | −0.169483 | ||||||||
\(455\) | 81.7857i | 0.179749i | ||||||||
\(456\) | 42.8022 | − | 26.2522i | 0.0938645 | − | 0.0575707i | ||||
\(457\) | −296.898 | −0.649666 | −0.324833 | − | 0.945771i | \(-0.605308\pi\) | ||||
−0.324833 | + | 0.945771i | \(0.605308\pi\) | |||||||
\(458\) | 147.892i | 0.322909i | ||||||||
\(459\) | 0.0620868 | + | 0.777247i | 0.000135265 | + | 0.00169335i | ||||
\(460\) | −21.4476 | −0.0466252 | ||||||||
\(461\) | − | 44.6191i | − | 0.0967875i | −0.998828 | − | 0.0483938i | \(-0.984590\pi\) | ||
0.998828 | − | 0.0483938i | \(-0.0154102\pi\) | |||||||
\(462\) | 69.4983 | + | 113.312i | 0.150429 | + | 0.245263i | ||||
\(463\) | −652.545 | −1.40938 | −0.704692 | − | 0.709513i | \(-0.748915\pi\) | ||||
−0.704692 | + | 0.709513i | \(0.748915\pi\) | |||||||
\(464\) | − | 180.777i | − | 0.389605i | ||||||
\(465\) | −235.454 | + | 144.413i | −0.506354 | + | 0.310566i | ||||
\(466\) | 103.167 | 0.221389 | ||||||||
\(467\) | 614.730i | 1.31634i | 0.752870 | + | 0.658169i | \(0.228669\pi\) | ||||
−0.752870 | + | 0.658169i | \(0.771331\pi\) | |||||||
\(468\) | −168.808 | + | 331.944i | −0.360700 | + | 0.709282i | ||||
\(469\) | 178.053 | 0.379644 | ||||||||
\(470\) | − | 163.335i | − | 0.347520i | ||||||
\(471\) | 422.319 | + | 688.559i | 0.896644 | + | 1.46191i | ||||
\(472\) | −193.063 | −0.409032 | ||||||||
\(473\) | − | 1070.79i | − | 2.26383i | ||||||
\(474\) | 16.1670 | − | 9.91583i | 0.0341076 | − | 0.0209195i | ||||
\(475\) | 29.5875 | 0.0622895 | ||||||||
\(476\) | − | 0.102108i | − | 0.000214512i | ||||||
\(477\) | 174.636 | + | 88.8095i | 0.366112 | + | 0.186184i | ||||
\(478\) | −567.471 | −1.18718 | ||||||||
\(479\) | − | 633.184i | − | 1.32189i | −0.750436 | − | 0.660944i | \(-0.770156\pi\) | ||
0.750436 | − | 0.660944i | \(-0.229844\pi\) | |||||||
\(480\) | 19.8401 | + | 32.3477i | 0.0413335 | + | 0.0673910i | ||||
\(481\) | 1466.52 | 3.04890 | ||||||||
\(482\) | 106.365i | 0.220675i | ||||||||
\(483\) | −21.6820 | + | 13.2984i | −0.0448904 | + | 0.0275330i | ||||
\(484\) | 386.168 | 0.797868 | ||||||||
\(485\) | 129.034i | 0.266050i | ||||||||
\(486\) | −317.751 | − | 130.891i | −0.653809 | − | 0.269322i | ||||
\(487\) | −169.555 | −0.348163 | −0.174081 | − | 0.984731i | \(-0.555696\pi\) | ||||
−0.174081 | + | 0.984731i | \(0.555696\pi\) | |||||||
\(488\) | 3.90398i | 0.00799996i | ||||||||
\(489\) | −464.574 | − | 757.451i | −0.950049 | − | 1.54898i | ||||
\(490\) | −145.068 | −0.296058 | ||||||||
\(491\) | − | 694.164i | − | 1.41378i | −0.707325 | − | 0.706888i | \(-0.750098\pi\) | ||
0.707325 | − | 0.706888i | \(-0.249902\pi\) | |||||||
\(492\) | −95.4094 | + | 58.5182i | −0.193922 | + | 0.118939i | ||||
\(493\) | −1.30514 | −0.00264735 | ||||||||
\(494\) | − | 173.138i | − | 0.350482i | ||||||
\(495\) | −161.671 | + | 317.910i | −0.326607 | + | 0.642242i | ||||
\(496\) | 164.702 | 0.332060 | ||||||||
\(497\) | 99.4555i | 0.200112i | ||||||||
\(498\) | −46.6609 | − | 76.0770i | −0.0936966 | − | 0.152765i | ||||
\(499\) | 155.122 | 0.310865 | 0.155433 | − | 0.987847i | \(-0.450323\pi\) | ||||
0.155433 | + | 0.987847i | \(0.450323\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −357.965 | + | 219.554i | −0.714502 | + | 0.438231i | ||||
\(502\) | 134.756 | 0.268439 | ||||||||
\(503\) | − | 460.543i | − | 0.915593i | −0.889057 | − | 0.457796i | \(-0.848639\pi\) | ||
0.889057 | − | 0.457796i | \(-0.151361\pi\) | |||||||
\(504\) | 40.1138 | + | 20.3996i | 0.0795910 | + | 0.0404754i | ||||
\(505\) | −152.609 | −0.302196 | ||||||||
\(506\) | 120.199i | 0.237548i | ||||||||
\(507\) | 406.293 | + | 662.429i | 0.801367 | + | 1.30657i | ||||
\(508\) | 461.013 | 0.907506 | ||||||||
\(509\) | − | 720.090i | − | 1.41472i | −0.706856 | − | 0.707358i | \(-0.749887\pi\) | ||
0.706856 | − | 0.707358i | \(-0.250113\pi\) | |||||||
\(510\) | 0.233539 | − | 0.143238i | 0.000457919 | − | 0.000280859i | ||||
\(511\) | 130.794 | 0.255958 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 159.265 | − | 12.7222i | 0.310458 | − | 0.0247995i | ||||
\(514\) | −155.626 | −0.302775 | ||||||||
\(515\) | − | 136.717i | − | 0.265469i | ||||||
\(516\) | −189.537 | − | 309.026i | −0.367320 | − | 0.598887i | ||||
\(517\) | −915.379 | −1.77056 | ||||||||
\(518\) | − | 177.222i | − | 0.342127i | ||||||
\(519\) | −5.72226 | + | 3.50968i | −0.0110255 | + | 0.00676238i | ||||
\(520\) | 130.849 | 0.251632 | ||||||||
\(521\) | 139.098i | 0.266983i | 0.991050 | + | 0.133491i | \(0.0426188\pi\) | ||||
−0.991050 | + | 0.133491i | \(0.957381\pi\) | |||||||
\(522\) | 260.748 | − | 512.736i | 0.499517 | − | 0.982252i | ||||
\(523\) | −665.486 | −1.27244 | −0.636220 | − | 0.771508i | \(-0.719503\pi\) | ||||
−0.636220 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(524\) | − | 130.546i | − | 0.249134i | ||||||
\(525\) | 13.8646 | + | 22.6051i | 0.0264087 | + | 0.0430573i | ||||
\(526\) | 526.914 | 1.00174 | ||||||||
\(527\) | − | 1.18909i | − | 0.00225634i | ||||||
\(528\) | 181.287 | − | 111.190i | 0.343346 | − | 0.210587i | ||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | − | 68.8393i | − | 0.129886i | ||||||
\(531\) | −547.583 | − | 278.469i | −1.03123 | − | 0.524424i | ||||
\(532\) | −20.9229 | −0.0393287 | ||||||||
\(533\) | 385.938i | 0.724086i | ||||||||
\(534\) | 62.5702 | + | 102.016i | 0.117173 | + | 0.191041i | ||||
\(535\) | −327.232 | −0.611648 | ||||||||
\(536\) | − | 284.866i | − | 0.531467i | ||||||
\(537\) | 220.048 | − | 134.963i | 0.409772 | − | 0.251329i | ||||
\(538\) | −86.3014 | −0.160412 | ||||||||
\(539\) | 813.009i | 1.50836i | ||||||||
\(540\) | 9.61475 | + | 120.364i | 0.0178051 | + | 0.222897i | ||||
\(541\) | 673.074 | 1.24413 | 0.622065 | − | 0.782966i | \(-0.286294\pi\) | ||||
0.622065 | + | 0.782966i | \(0.286294\pi\) | |||||||
\(542\) | − | 691.560i | − | 1.27594i | ||||||
\(543\) | 68.3564 | + | 111.450i | 0.125887 | + | 0.205248i | ||||
\(544\) | −0.163362 | −0.000300298 | ||||||||
\(545\) | 109.325i | 0.200597i | ||||||||
\(546\) | 132.279 | − | 81.1316i | 0.242269 | − | 0.148593i | ||||
\(547\) | −298.530 | −0.545759 | −0.272880 | − | 0.962048i | \(-0.587976\pi\) | ||||
−0.272880 | + | 0.962048i | \(0.587976\pi\) | |||||||
\(548\) | − | 246.487i | − | 0.449793i | ||||||
\(549\) | −5.63100 | + | 11.0728i | −0.0102568 | + | 0.0201691i | ||||
\(550\) | 125.316 | 0.227848 | ||||||||
\(551\) | 267.437i | 0.485366i | ||||||||
\(552\) | 21.2761 | + | 34.6890i | 0.0385436 | + | 0.0628424i | ||||
\(553\) | −7.90286 | −0.0142909 | ||||||||
\(554\) | − | 452.191i | − | 0.816230i | ||||||
\(555\) | 405.338 | − | 248.609i | 0.730338 | − | 0.447944i | ||||
\(556\) | 438.344 | 0.788389 | ||||||||
\(557\) | − | 152.164i | − | 0.273185i | −0.990627 | − | 0.136592i | \(-0.956385\pi\) | ||
0.990627 | − | 0.136592i | \(-0.0436150\pi\) | |||||||
\(558\) | 467.143 | + | 237.562i | 0.837174 | + | 0.425738i | ||||
\(559\) | −1250.03 | −2.23619 | ||||||||
\(560\) | − | 15.8124i | − | 0.0282365i | ||||||
\(561\) | −0.802753 | − | 1.30883i | −0.00143093 | − | 0.00233302i | ||||
\(562\) | −345.085 | −0.614031 | ||||||||
\(563\) | − | 216.421i | − | 0.384407i | −0.981355 | − | 0.192203i | \(-0.938437\pi\) | ||
0.981355 | − | 0.192203i | \(-0.0615633\pi\) | |||||||
\(564\) | −264.175 | + | 162.028i | −0.468395 | + | 0.287284i | ||||
\(565\) | 285.075 | 0.504557 | ||||||||
\(566\) | 441.992i | 0.780905i | ||||||||
\(567\) | 84.3508 | + | 115.718i | 0.148767 | + | 0.204089i | ||||
\(568\) | 159.118 | 0.280138 | ||||||||
\(569\) | 168.117i | 0.295460i | 0.989028 | + | 0.147730i | \(0.0471966\pi\) | ||||
−0.989028 | + | 0.147730i | \(0.952803\pi\) | |||||||
\(570\) | −29.3509 | − | 47.8543i | −0.0514928 | − | 0.0839550i | ||||
\(571\) | 17.0074 | 0.0297853 | 0.0148926 | − | 0.999889i | \(-0.495259\pi\) | ||||
0.0148926 | + | 0.999889i | \(0.495259\pi\) | |||||||
\(572\) | − | 733.317i | − | 1.28202i | ||||||
\(573\) | 498.785 | − | 305.924i | 0.870480 | − | 0.533899i | ||||
\(574\) | 46.6387 | 0.0812521 | ||||||||
\(575\) | 23.9792i | 0.0417029i | ||||||||
\(576\) | 32.6372 | − | 64.1780i | 0.0566618 | − | 0.111420i | ||||
\(577\) | 955.512 | 1.65600 | 0.828000 | − | 0.560728i | \(-0.189478\pi\) | ||||
0.828000 | + | 0.560728i | \(0.189478\pi\) | |||||||
\(578\) | − | 408.707i | − | 0.707105i | ||||||
\(579\) | 518.530 | + | 845.422i | 0.895560 | + | 1.46014i | ||||
\(580\) | −202.115 | −0.348473 | ||||||||
\(581\) | 37.1885i | 0.0640077i | ||||||||
\(582\) | 208.698 | − | 128.002i | 0.358588 | − | 0.219935i | ||||
\(583\) | −385.798 | −0.661745 | ||||||||
\(584\) | − | 209.257i | − | 0.358318i | ||||||
\(585\) | 371.125 | + | 188.733i | 0.634401 | + | 0.322620i | ||||
\(586\) | 621.503 | 1.06059 | ||||||||
\(587\) | − | 727.196i | − | 1.23883i | −0.785062 | − | 0.619417i | \(-0.787369\pi\) | ||
0.785062 | − | 0.619417i | \(-0.212631\pi\) | |||||||
\(588\) | 143.908 | + | 234.631i | 0.244742 | + | 0.399032i | ||||
\(589\) | −243.656 | −0.413677 | ||||||||
\(590\) | 215.851i | 0.365849i | ||||||||
\(591\) | −234.506 | + | 143.831i | −0.396795 | + | 0.243369i | ||||
\(592\) | −283.536 | −0.478947 | ||||||||
\(593\) | − | 335.046i | − | 0.565002i | −0.959267 | − | 0.282501i | \(-0.908836\pi\) | ||
0.959267 | − | 0.282501i | \(-0.0911641\pi\) | |||||||
\(594\) | 674.560 | − | 53.8841i | 1.13562 | − | 0.0907140i | ||||
\(595\) | −0.114160 | −0.000191866 | ||||||||
\(596\) | − | 169.214i | − | 0.283916i | ||||||
\(597\) | 9.69699 | + | 15.8102i | 0.0162429 | + | 0.0264827i | ||||
\(598\) | 140.319 | 0.234648 | ||||||||
\(599\) | 228.357i | 0.381230i | 0.981665 | + | 0.190615i | \(0.0610482\pi\) | ||||
−0.981665 | + | 0.190615i | \(0.938952\pi\) | |||||||
\(600\) | 36.1658 | − | 22.1819i | 0.0602763 | − | 0.0369698i | ||||
\(601\) | 710.722 | 1.18257 | 0.591283 | − | 0.806464i | \(-0.298622\pi\) | ||||
0.591283 | + | 0.806464i | \(0.298622\pi\) | |||||||
\(602\) | 151.060i | 0.250930i | ||||||||
\(603\) | 410.884 | − | 807.964i | 0.681399 | − | 1.33991i | ||||
\(604\) | 58.4239 | 0.0967284 | ||||||||
\(605\) | − | 431.749i | − | 0.713635i | ||||||
\(606\) | 151.388 | + | 246.827i | 0.249816 | + | 0.407305i | ||||
\(607\) | 690.106 | 1.13691 | 0.568456 | − | 0.822713i | \(-0.307541\pi\) | ||||
0.568456 | + | 0.822713i | \(0.307541\pi\) | |||||||
\(608\) | 33.4744i | 0.0550566i | ||||||||
\(609\) | −204.324 | + | 125.320i | −0.335507 | + | 0.205779i | ||||
\(610\) | 4.36478 | 0.00715538 | ||||||||
\(611\) | 1068.61i | 1.74894i | ||||||||
\(612\) | −0.463343 | − | 0.235629i | −0.000757096 | − | 0.000385015i | ||||
\(613\) | −812.071 | −1.32475 | −0.662374 | − | 0.749173i | \(-0.730451\pi\) | ||||
−0.662374 | + | 0.749173i | \(0.730451\pi\) | |||||||
\(614\) | 208.014i | 0.338785i | ||||||||
\(615\) | 65.4253 | + | 106.671i | 0.106383 | + | 0.173449i | ||||
\(616\) | −88.6178 | −0.143860 | ||||||||
\(617\) | − | 1026.40i | − | 1.66354i | −0.555120 | − | 0.831770i | \(-0.687328\pi\) | ||
0.555120 | − | 0.831770i | \(-0.312672\pi\) | |||||||
\(618\) | −221.123 | + | 135.623i | −0.357804 | + | 0.219455i | ||||
\(619\) | −682.233 | −1.10215 | −0.551077 | − | 0.834455i | \(-0.685783\pi\) | ||||
−0.551077 | + | 0.834455i | \(0.685783\pi\) | |||||||
\(620\) | − | 184.142i | − | 0.297004i | ||||||
\(621\) | 10.3107 | + | 129.076i | 0.0166033 | + | 0.207852i | ||||
\(622\) | −850.809 | −1.36786 | ||||||||
\(623\) | − | 49.8681i | − | 0.0800451i | ||||||
\(624\) | −129.802 | − | 211.632i | −0.208016 | − | 0.339154i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 125.095i | 0.199833i | ||||||||
\(627\) | −268.191 | + | 164.492i | −0.427737 | + | 0.262347i | ||||
\(628\) | −538.503 | −0.857488 | ||||||||
\(629\) | 2.04703i | 0.00325443i | ||||||||
\(630\) | 22.8074 | − | 44.8486i | 0.0362023 | − | 0.0711883i | ||||
\(631\) | 19.9854 | 0.0316726 | 0.0158363 | − | 0.999875i | \(-0.494959\pi\) | ||||
0.0158363 | + | 0.999875i | \(0.494959\pi\) | |||||||
\(632\) | 12.6438i | 0.0200059i | ||||||||
\(633\) | 490.373 | + | 799.514i | 0.774680 | + | 1.26306i | ||||
\(634\) | −616.511 | −0.972415 | ||||||||
\(635\) | − | 515.428i | − | 0.811698i | ||||||
\(636\) | −111.340 | + | 68.2888i | −0.175062 | + | 0.107372i | ||||
\(637\) | 949.098 | 1.48995 | ||||||||
\(638\) | 1132.71i | 1.77541i | ||||||||
\(639\) | 451.306 | + | 229.508i | 0.706270 | + | 0.359168i | ||||
\(640\) | −25.2982 | −0.0395285 | ||||||||
\(641\) | − | 78.5394i | − | 0.122526i | −0.998122 | − | 0.0612632i | \(-0.980487\pi\) | ||
0.998122 | − | 0.0612632i | \(-0.0195129\pi\) | |||||||
\(642\) | 324.615 | + | 529.259i | 0.505630 | + | 0.824391i | ||||
\(643\) | 947.424 | 1.47344 | 0.736722 | − | 0.676196i | \(-0.236373\pi\) | ||||
0.736722 | + | 0.676196i | \(0.236373\pi\) | |||||||
\(644\) | − | 16.9569i | − | 0.0263306i | ||||||
\(645\) | −345.501 | + | 211.909i | −0.535661 | + | 0.328541i | ||||
\(646\) | 0.241674 | 0.000374108 | ||||||||
\(647\) | 405.423i | 0.626619i | 0.949651 | + | 0.313310i | \(0.101438\pi\) | ||||
−0.949651 | + | 0.313310i | \(0.898562\pi\) | |||||||
\(648\) | 185.137 | − | 134.952i | 0.285706 | − | 0.208260i | ||||
\(649\) | 1209.70 | 1.86394 | ||||||||
\(650\) | − | 146.293i | − | 0.225066i | ||||||
\(651\) | −114.176 | − | 186.155i | −0.175386 | − | 0.285953i | ||||
\(652\) | 592.382 | 0.908561 | ||||||||
\(653\) | − | 953.530i | − | 1.46023i | −0.683325 | − | 0.730115i | \(-0.739467\pi\) | ||
0.683325 | − | 0.730115i | \(-0.260533\pi\) | |||||||
\(654\) | 176.821 | − | 108.451i | 0.270369 | − | 0.165827i | ||||
\(655\) | −145.955 | −0.222832 | ||||||||
\(656\) | − | 74.6170i | − | 0.113746i | ||||||
\(657\) | 301.828 | − | 593.515i | 0.459403 | − | 0.903372i | ||||
\(658\) | 129.136 | 0.196255 | ||||||||
\(659\) | 784.567i | 1.19054i | 0.803525 | + | 0.595271i | \(0.202955\pi\) | ||||
−0.803525 | + | 0.595271i | \(0.797045\pi\) | |||||||
\(660\) | −124.314 | − | 202.685i | −0.188355 | − | 0.307098i | ||||
\(661\) | −525.618 | −0.795186 | −0.397593 | − | 0.917562i | \(-0.630154\pi\) | ||||
−0.397593 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(662\) | − | 431.621i | − | 0.651995i | ||||||
\(663\) | −1.52791 | + | 0.937126i | −0.00230454 | + | 0.00141346i | ||||
\(664\) | 59.4977 | 0.0896050 | ||||||||
\(665\) | 23.3925i | 0.0351767i | ||||||||
\(666\) | −804.192 | − | 408.966i | −1.20750 | − | 0.614062i | ||||
\(667\) | −216.744 | −0.324953 | ||||||||
\(668\) | − | 279.955i | − | 0.419094i | ||||||
\(669\) | 115.002 | + | 187.502i | 0.171902 | + | 0.280273i | ||||
\(670\) | −318.490 | −0.475358 | ||||||||
\(671\) | − | 24.4616i | − | 0.0364555i | ||||||
\(672\) | −25.5747 | + | 15.6860i | −0.0380577 | + | 0.0233422i | ||||
\(673\) | 124.971 | 0.185693 | 0.0928465 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928465 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(674\) | − | 314.163i | − | 0.466117i | ||||||
\(675\) | 134.571 | − | 10.7496i | 0.199365 | − | 0.0159254i | ||||
\(676\) | −518.068 | −0.766372 | ||||||||
\(677\) | − | 867.241i | − | 1.28101i | −0.767956 | − | 0.640503i | \(-0.778726\pi\) | ||
0.767956 | − | 0.640503i | \(-0.221274\pi\) | |||||||
\(678\) | −282.795 | − | 461.075i | −0.417102 | − | 0.680052i | ||||
\(679\) | −102.017 | −0.150246 | ||||||||
\(680\) | 0.182644i | 0.000268595i | ||||||||
\(681\) | 139.139 | − | 85.3395i | 0.204316 | − | 0.125315i | ||||
\(682\) | −1031.99 | −1.51319 | ||||||||
\(683\) | − | 765.086i | − | 1.12018i | −0.828430 | − | 0.560092i | \(-0.810766\pi\) | ||
0.828430 | − | 0.560092i | \(-0.189234\pi\) | |||||||
\(684\) | −48.2827 | + | 94.9433i | −0.0705887 | + | 0.138806i | ||||
\(685\) | −275.581 | −0.402307 | ||||||||
\(686\) | − | 237.202i | − | 0.345775i | ||||||
\(687\) | −164.026 | − | 267.432i | −0.238757 | − | 0.389275i | ||||
\(688\) | 241.680 | 0.351280 | ||||||||
\(689\) | 450.376i | 0.653667i | ||||||||
\(690\) | 38.7835 | − | 23.7874i | 0.0562080 | − | 0.0344745i | ||||
\(691\) | 896.181 | 1.29693 | 0.648467 | − | 0.761243i | \(-0.275411\pi\) | ||||
0.648467 | + | 0.761243i | \(0.275411\pi\) | |||||||
\(692\) | − | 4.47522i | − | 0.00646708i | ||||||
\(693\) | −251.346 | − | 127.820i | −0.362693 | − | 0.184445i | ||||
\(694\) | 929.113 | 1.33878 | ||||||||
\(695\) | − | 490.084i | − | 0.705157i | ||||||
\(696\) | 200.498 | + | 326.897i | 0.288072 | + | 0.469679i | ||||
\(697\) | −0.538709 | −0.000772897 | ||||||||
\(698\) | 579.191i | 0.829787i | ||||||||
\(699\) | −186.557 | + | 114.422i | −0.266891 | + | 0.163694i | ||||
\(700\) | −17.6788 | −0.0252555 | ||||||||
\(701\) | 90.6113i | 0.129260i | 0.997909 | + | 0.0646300i | \(0.0205867\pi\) | ||||
−0.997909 | + | 0.0646300i | \(0.979413\pi\) | |||||||
\(702\) | −62.9038 | − | 787.475i | −0.0896066 | − | 1.12176i | ||||
\(703\) | 419.456 | 0.596666 | ||||||||
\(704\) | 141.779i | 0.201391i | ||||||||
\(705\) | 181.153 | + | 295.356i | 0.256955 | + | 0.418945i | ||||
\(706\) | 352.751 | 0.499648 | ||||||||
\(707\) | − | 120.656i | − | 0.170659i | ||||||
\(708\) | 349.114 | − | 214.125i | 0.493099 | − | 0.302436i | ||||
\(709\) | −393.144 | −0.554505 | −0.277253 | − | 0.960797i | \(-0.589424\pi\) | ||||
−0.277253 | + | 0.960797i | \(0.589424\pi\) | |||||||
\(710\) | − | 177.900i | − | 0.250563i | ||||||
\(711\) | −18.2370 | + | 35.8614i | −0.0256498 | + | 0.0504380i | ||||
\(712\) | −79.7838 | −0.112056 | ||||||||
\(713\) | − | 197.471i | − | 0.276958i | ||||||
\(714\) | 0.113247 | + | 0.184641i | 0.000158609 | + | 0.000258600i | ||||
\(715\) | −819.874 | −1.14668 | ||||||||
\(716\) | 172.093i | 0.240353i | ||||||||
\(717\) | 1026.15 | − | 629.379i | 1.43118 | − | 0.877794i | ||||
\(718\) | −471.580 | −0.656797 | ||||||||
\(719\) | 924.192i | 1.28539i | 0.766124 | + | 0.642693i | \(0.222183\pi\) | ||||
−0.766124 | + | 0.642693i | \(0.777817\pi\) | |||||||
\(720\) | −71.7532 | − | 36.4895i | −0.0996572 | − | 0.0506799i | ||||
\(721\) | 108.091 | 0.149918 | ||||||||
\(722\) | 461.010i | 0.638518i | ||||||||
\(723\) | −117.969 | − | 192.339i | −0.163166 | − | 0.266029i | ||||
\(724\) | −87.1618 | −0.120389 | ||||||||
\(725\) | 225.971i | 0.311684i | ||||||||
\(726\) | −698.304 | + | 428.296i | −0.961851 | + | 0.589940i | ||||
\(727\) | 1152.02 | 1.58463 | 0.792314 | − | 0.610114i | \(-0.208876\pi\) | ||||
0.792314 | + | 0.610114i | \(0.208876\pi\) | |||||||
\(728\) | 103.452i | 0.142104i | ||||||||
\(729\) | 719.756 | − | 115.727i | 0.987319 | − | 0.158748i | ||||
\(730\) | −233.957 | −0.320489 | ||||||||
\(731\) | − | 1.74485i | − | 0.00238693i | ||||||
\(732\) | −4.32988 | − | 7.05953i | −0.00591513 | − | 0.00964416i | ||||
\(733\) | −624.542 | −0.852035 | −0.426017 | − | 0.904715i | \(-0.640084\pi\) | ||||
−0.426017 | + | 0.904715i | \(0.640084\pi\) | |||||||
\(734\) | 203.756i | 0.277596i | ||||||||
\(735\) | 262.325 | − | 160.894i | 0.356905 | − | 0.218904i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 1784.92i | 2.42187i | ||||||||
\(738\) | 107.626 | − | 211.636i | 0.145834 | − | 0.286769i | ||||
\(739\) | −858.733 | −1.16202 | −0.581010 | − | 0.813896i | \(-0.697342\pi\) | ||||
−0.581010 | + | 0.813896i | \(0.697342\pi\) | |||||||
\(740\) | 317.003i | 0.428383i | ||||||||
\(741\) | 192.026 | + | 313.084i | 0.259144 | + | 0.422515i | ||||
\(742\) | 54.4258 | 0.0733501 | ||||||||
\(743\) | 1376.70i | 1.85289i | 0.376429 | + | 0.926445i | \(0.377152\pi\) | ||||
−0.376429 | + | 0.926445i | \(0.622848\pi\) | |||||||
\(744\) | −297.829 | + | 182.670i | −0.400308 | + | 0.245524i | ||||
\(745\) | −189.187 | −0.253942 | ||||||||
\(746\) | 698.726i | 0.936630i | ||||||||
\(747\) | 168.753 | + | 85.8180i | 0.225907 | + | 0.114883i | ||||
\(748\) | 1.02360 | 0.00136845 | ||||||||
\(749\) | − | 258.716i | − | 0.345415i | ||||||
\(750\) | −24.8001 | − | 40.4346i | −0.0330668 | − | 0.0539128i | ||||
\(751\) | −841.206 | −1.12011 | −0.560057 | − | 0.828454i | \(-0.689221\pi\) | ||||
−0.560057 | + | 0.828454i | \(0.689221\pi\) | |||||||
\(752\) | − | 206.604i | − | 0.274739i | ||||||
\(753\) | −243.679 | + | 149.457i | −0.323610 | + | 0.198483i | ||||
\(754\) | 1322.32 | 1.75374 | ||||||||
\(755\) | − | 65.3199i | − | 0.0865165i | ||||||
\(756\) | −95.1625 | + | 7.60162i | −0.125876 | + | 0.0100551i | ||||
\(757\) | 21.0572 | 0.0278167 | 0.0139083 | − | 0.999903i | \(-0.495573\pi\) | ||||
0.0139083 | + | 0.999903i | \(0.495573\pi\) | |||||||
\(758\) | 754.713i | 0.995663i | ||||||||
\(759\) | −133.312 | − | 217.355i | −0.175642 | − | 0.286370i | ||||
\(760\) | 37.4255 | 0.0492441 | ||||||||
\(761\) | − | 209.778i | − | 0.275661i | −0.990456 | − | 0.137830i | \(-0.955987\pi\) | ||
0.990456 | − | 0.137830i | \(-0.0440129\pi\) | |||||||
\(762\) | −833.646 | + | 511.307i | −1.09402 | + | 0.671006i | ||||
\(763\) | −86.4350 | −0.113283 | ||||||||
\(764\) | 390.086i | 0.510584i | ||||||||
\(765\) | −0.263442 | + | 0.518033i | −0.000344368 | + | 0.000677167i | ||||
\(766\) | 346.957 | 0.452946 | ||||||||
\(767\) | − | 1412.19i | − | 1.84119i | ||||||
\(768\) | 25.0959 | + | 40.9169i | 0.0326770 | + | 0.0532773i | ||||
\(769\) | −217.912 | −0.283370 | −0.141685 | − | 0.989912i | \(-0.545252\pi\) | ||||
−0.141685 | + | 0.989912i | \(0.545252\pi\) | |||||||
\(770\) | 99.0778i | 0.128672i | ||||||||
\(771\) | 281.417 | − | 172.604i | 0.365003 | − | 0.223870i | ||||
\(772\) | −661.181 | −0.856452 | ||||||||
\(773\) | − | 1256.63i | − | 1.62565i | −0.582507 | − | 0.812826i | \(-0.697928\pi\) | ||
0.582507 | − | 0.812826i | \(-0.302072\pi\) | |||||||
\(774\) | 685.476 | + | 348.594i | 0.885628 | + | 0.450379i | ||||
\(775\) | −205.878 | −0.265648 | ||||||||
\(776\) | 163.217i | 0.210331i | ||||||||
\(777\) | 196.555 | + | 320.468i | 0.252967 | + | 0.412443i | ||||
\(778\) | −168.808 | −0.216977 | ||||||||
\(779\) | 110.387i | 0.141703i | ||||||||
\(780\) | −236.612 | + | 145.123i | −0.303349 | + | 0.186055i | ||||
\(781\) | −997.007 | −1.27658 | ||||||||
\(782\) | 0.195864i | 0.000250466i | ||||||||
\(783\) | 97.1640 | + | 1216.37i | 0.124092 | + | 1.55347i | ||||
\(784\) | −183.498 | −0.234054 | ||||||||
\(785\) | 602.064i | 0.766961i | ||||||||
\(786\) | 144.788 | + | 236.065i | 0.184208 | + | 0.300338i | ||||
\(787\) | 1236.33 | 1.57094 | 0.785471 | − | 0.618898i | \(-0.212421\pi\) | ||||
0.785471 | + | 0.618898i | \(0.212421\pi\) | |||||||
\(788\) | − | 183.400i | − | 0.232742i | ||||||
\(789\) | −952.813 | + | 584.397i | −1.20762 | + | 0.740680i | ||||
\(790\) | 14.1362 | 0.0178939 | ||||||||
\(791\) | 225.386i | 0.284938i | ||||||||
\(792\) | −204.499 | + | 402.128i | −0.258206 | + | 0.507737i | ||||
\(793\) | −28.5563 | −0.0360104 | ||||||||
\(794\) | − | 599.663i | − | 0.755244i | ||||||
\(795\) | 76.3492 | + | 124.481i | 0.0960367 | + | 0.156580i | ||||
\(796\) | −12.3647 | −0.0155336 | ||||||||
\(797\) | − | 1091.81i | − | 1.36990i | −0.728592 | − | 0.684948i | \(-0.759825\pi\) | ||
0.728592 | − | 0.684948i | \(-0.240175\pi\) | |||||||
\(798\) | 37.8346 | − | 23.2054i | 0.0474118 | − | 0.0290795i | ||||
\(799\) | −1.49161 | −0.00186684 | ||||||||
\(800\) | 28.2843i | 0.0353553i | ||||||||
\(801\) | −226.290 | − | 115.078i | −0.282510 | − | 0.143668i | ||||
\(802\) | 1114.25 | 1.38934 | ||||||||
\(803\) | 1311.17i | 1.63284i | ||||||||
\(804\) | 315.943 | + | 515.121i | 0.392964 | + | 0.640698i | ||||
\(805\) | −18.9584 | −0.0235508 | ||||||||
\(806\) | 1204.74i | 1.49471i | ||||||||
\(807\) | 156.058 | − | 95.7163i | 0.193380 | − | 0.118608i | ||||
\(808\) | −193.037 | −0.238907 | ||||||||
\(809\) | − | 264.512i | − | 0.326962i | −0.986547 | − | 0.163481i | \(-0.947728\pi\) | ||
0.986547 | − | 0.163481i | \(-0.0522722\pi\) | |||||||
\(810\) | −150.881 | − | 206.990i | −0.186273 | − | 0.255543i | ||||
\(811\) | −868.374 | −1.07074 | −0.535372 | − | 0.844616i | \(-0.679829\pi\) | ||||
−0.535372 | + | 0.844616i | \(0.679829\pi\) | |||||||
\(812\) | − | 159.796i | − | 0.196793i | ||||||
\(813\) | 767.004 | + | 1250.54i | 0.943425 | + | 1.53818i | ||||
\(814\) | 1776.59 | 2.18254 | ||||||||
\(815\) | − | 662.303i | − | 0.812642i | ||||||
\(816\) | 0.295406 | − | 0.181184i | 0.000362017 | − | 0.000222039i | ||||
\(817\) | −357.536 | −0.437620 | ||||||||
\(818\) | 13.8374i | 0.0169161i | ||||||||
\(819\) | −149.216 | + | 293.419i | −0.182193 | + | 0.358265i | ||||
\(820\) | −83.4244 | −0.101737 | ||||||||
\(821\) | − | 769.647i | − | 0.937451i | −0.883344 | − | 0.468726i | \(-0.844713\pi\) | ||
0.883344 | − | 0.468726i | \(-0.155287\pi\) | |||||||
\(822\) | 273.377 | + | 445.719i | 0.332575 | + | 0.542238i | ||||
\(823\) | 685.803 | 0.833296 | 0.416648 | − | 0.909068i | \(-0.363205\pi\) | ||||
0.416648 | + | 0.909068i | \(0.363205\pi\) | |||||||
\(824\) | − | 172.934i | − | 0.209872i | ||||||
\(825\) | −226.608 | + | 138.988i | −0.274677 | + | 0.168470i | ||||
\(826\) | −170.656 | −0.206606 | ||||||||
\(827\) | − | 123.844i | − | 0.149751i | −0.997193 | − | 0.0748754i | \(-0.976144\pi\) | ||
0.997193 | − | 0.0748754i | \(-0.0238559\pi\) | |||||||
\(828\) | −76.9467 | − | 39.1306i | −0.0929308 | − | 0.0472592i | ||||
\(829\) | 927.381 | 1.11867 | 0.559337 | − | 0.828940i | \(-0.311056\pi\) | ||||
0.559337 | + | 0.828940i | \(0.311056\pi\) | |||||||
\(830\) | − | 66.5204i | − | 0.0801451i | ||||||
\(831\) | 501.522 | + | 817.693i | 0.603516 | + | 0.983987i | ||||
\(832\) | 165.512 | 0.198932 | ||||||||
\(833\) | 1.32479i | 0.00159039i | ||||||||
\(834\) | −792.654 | + | 486.165i | −0.950424 | + | 0.582931i | ||||
\(835\) | −312.999 | −0.374849 | ||||||||
\(836\) | − | 209.745i | − | 0.250891i | ||||||
\(837\) | −1108.21 | + | 88.5242i | −1.32402 | + | 0.105764i | ||||
\(838\) | 767.660 | 0.916062 | ||||||||
\(839\) | − | 819.716i | − | 0.977015i | −0.872560 | − | 0.488508i | \(-0.837541\pi\) | ||
0.872560 | − | 0.488508i | \(-0.162459\pi\) | |||||||
\(840\) | 17.5374 | + | 28.5934i | 0.0208779 | + | 0.0340398i | ||||
\(841\) | −1201.51 | −1.42867 | ||||||||
\(842\) | 955.657i | 1.13498i | ||||||||
\(843\) | 624.014 | − | 382.732i | 0.740230 | − | 0.454011i | ||||
\(844\) | −625.278 | −0.740851 | ||||||||
\(845\) | 579.217i | 0.685464i | ||||||||
\(846\) | 298.000 | − | 585.989i | 0.352246 | − | 0.692658i | ||||
\(847\) | 341.350 | 0.403010 | ||||||||
\(848\) | − | 87.0756i | − | 0.102684i | ||||||
\(849\) | −490.210 | − | 799.250i | −0.577397 | − | 0.941402i | ||||
\(850\) | 0.204203 | 0.000240238 | ||||||||
\(851\) | 339.948i | 0.399469i | ||||||||
\(852\) | −287.732 | + | 176.477i | −0.337714 | + | 0.207133i | ||||
\(853\) | 603.555 | 0.707568 | 0.353784 | − | 0.935327i | \(-0.384895\pi\) | ||||
0.353784 | + | 0.935327i | \(0.384895\pi\) | |||||||
\(854\) | 3.45089i | 0.00404085i | ||||||||
\(855\) | 106.150 | + | 53.9817i | 0.124152 | + | 0.0631364i | ||||
\(856\) | −413.919 | −0.483550 | ||||||||
\(857\) | − | 67.4048i | − | 0.0786521i | −0.999226 | − | 0.0393260i | \(-0.987479\pi\) | ||
0.999226 | − | 0.0393260i | \(-0.0125211\pi\) | |||||||
\(858\) | 813.317 | + | 1326.05i | 0.947922 | + | 1.54551i | ||||
\(859\) | 626.026 | 0.728784 | 0.364392 | − | 0.931246i | \(-0.381277\pi\) | ||||
0.364392 | + | 0.931246i | \(0.381277\pi\) | |||||||
\(860\) | − | 270.207i | − | 0.314194i | ||||||
\(861\) | −84.3363 | + | 51.7266i | −0.0979515 | + | 0.0600774i | ||||
\(862\) | −505.409 | −0.586322 | ||||||||
\(863\) | − | 528.419i | − | 0.612304i | −0.951983 | − | 0.306152i | \(-0.900958\pi\) | ||
0.951983 | − | 0.306152i | \(-0.0990416\pi\) | |||||||
\(864\) | 12.1618 | + | 152.250i | 0.0140762 | + | 0.176215i | ||||
\(865\) | −5.00345 | −0.00578433 | ||||||||
\(866\) | 84.1604i | 0.0971829i | ||||||||
\(867\) | 453.294 | + | 739.060i | 0.522830 | + | 0.852434i | ||||
\(868\) | 145.587 | 0.167727 | ||||||||
\(869\) | − | 79.2235i | − | 0.0911663i | ||||||
\(870\) | 365.482 | − | 224.164i | 0.420094 | − | 0.257660i | ||||
\(871\) | 2083.70 | 2.39231 | ||||||||
\(872\) | 138.287i | 0.158586i | ||||||||
\(873\) | −235.420 | + | 462.931i | −0.269668 | + | 0.530276i | ||||
\(874\) | 40.1344 | 0.0459204 | ||||||||
\(875\) | 19.7655i | 0.0225892i | ||||||||
\(876\) | 232.086 | + | 378.398i | 0.264938 | + | 0.431961i | ||||
\(877\) | −331.804 | −0.378340 | −0.189170 | − | 0.981944i | \(-0.560580\pi\) | ||||
−0.189170 | + | 0.981944i | \(0.560580\pi\) | |||||||
\(878\) | − | 414.104i | − | 0.471644i | ||||||
\(879\) | −1123.86 | + | 689.305i | −1.27856 | + | 0.784192i | ||||
\(880\) | 158.514 | 0.180130 | ||||||||
\(881\) | 962.030i | 1.09198i | 0.837793 | + | 0.545988i | \(0.183845\pi\) | ||||
−0.837793 | + | 0.545988i | \(0.816155\pi\) | |||||||
\(882\) | −520.455 | − | 264.673i | −0.590085 | − | 0.300083i | ||||
\(883\) | −1140.11 | −1.29118 | −0.645589 | − | 0.763685i | \(-0.723388\pi\) | ||||
−0.645589 | + | 0.763685i | \(0.723388\pi\) | |||||||
\(884\) | − | 1.19494i | − | 0.00135174i | ||||||
\(885\) | −239.399 | − | 390.321i | −0.270507 | − | 0.441041i | ||||
\(886\) | 99.1899 | 0.111953 | ||||||||
\(887\) | 9.87436i | 0.0111323i | 0.999985 | + | 0.00556615i | \(0.00177177\pi\) | ||||
−0.999985 | + | 0.00556615i | \(0.998228\pi\) | |||||||
\(888\) | 512.716 | − | 314.468i | 0.577383 | − | 0.354131i | ||||
\(889\) | 407.508 | 0.458390 | ||||||||
\(890\) | 89.2010i | 0.100226i | ||||||||
\(891\) | −1160.04 | + | 845.588i | −1.30195 | + | 0.949032i | ||||
\(892\) | −146.640 | −0.164395 | ||||||||
\(893\) | 305.644i | 0.342267i | ||||||||
\(894\) | 187.674 | + | 305.988i | 0.209926 | + | 0.342268i | ||||
\(895\) | 192.406 | 0.214979 | ||||||||
\(896\) | − | 20.0013i | − | 0.0223229i | ||||||
\(897\) | −253.738 | + | 155.627i | −0.282874 | + | 0.173498i | ||||
\(898\) | −1062.47 | −1.18315 | ||||||||
\(899\) | − | 1860.89i | − | 2.06996i | ||||||
\(900\) | −40.7965 | + | 80.2225i | −0.0453295 | + | 0.0891361i | ||||
\(901\) | −0.628656 | −0.000697731 | ||||||||
\(902\) | 467.537i | 0.518334i | ||||||||
\(903\) | −167.540 | − | 273.160i | −0.185537 | − | 0.302503i | ||||
\(904\) | 360.594 | 0.398887 | ||||||||
\(905\) | 97.4498i | 0.107679i | ||||||||
\(906\) | −105.647 | + | 64.7976i | −0.116609 | + | 0.0715205i | ||||
\(907\) | 556.047 | 0.613062 | 0.306531 | − | 0.951861i | \(-0.400832\pi\) | ||||
0.306531 | + | 0.951861i | \(0.400832\pi\) | |||||||
\(908\) | 108.817i | 0.119843i | ||||||||
\(909\) | −547.508 | − | 278.431i | −0.602319 | − | 0.306305i | ||||
\(910\) | 115.662 | 0.127102 | ||||||||
\(911\) | − | 408.279i | − | 0.448166i | −0.974570 | − | 0.224083i | \(-0.928061\pi\) | ||
0.974570 | − | 0.224083i | \(-0.0719387\pi\) | |||||||
\(912\) | −37.1263 | − | 60.5315i | −0.0407086 | − | 0.0663722i | ||||
\(913\) | −372.802 | −0.408326 | ||||||||
\(914\) | 419.877i | 0.459384i | ||||||||
\(915\) | −7.89279 | + | 4.84095i | −0.00862600 | + | 0.00529065i | ||||
\(916\) | 209.151 | 0.228331 | ||||||||
\(917\) | − | 115.395i | − | 0.125840i | ||||||
\(918\) | 1.09919 | − | 0.0878040i | 0.00119738 | − | 9.56470e-5i | ||||
\(919\) | 937.096 | 1.01969 | 0.509845 | − | 0.860266i | \(-0.329703\pi\) | ||||
0.509845 | + | 0.860266i | \(0.329703\pi\) | |||||||
\(920\) | 30.3315i | 0.0329690i | ||||||||
\(921\) | −230.707 | − | 376.150i | −0.250496 | − | 0.408415i | ||||
\(922\) | −63.1009 | −0.0684391 | ||||||||
\(923\) | 1163.90i | 1.26099i | ||||||||
\(924\) | 160.247 | − | 98.2854i | 0.173427 | − | 0.106370i | ||||
\(925\) | 354.420 | 0.383157 | ||||||||
\(926\) | 922.838i | 0.996585i | ||||||||
\(927\) | 249.436 | − | 490.492i | 0.269079 | − | 0.529118i | ||||
\(928\) | −255.657 | −0.275492 | ||||||||
\(929\) | − | 666.172i | − | 0.717085i | −0.933513 | − | 0.358543i | \(-0.883274\pi\) | ||
0.933513 | − | 0.358543i | \(-0.116726\pi\) | |||||||
\(930\) | 204.231 | + | 332.983i | 0.219603 | + | 0.358046i | ||||
\(931\) | 271.463 | 0.291582 | ||||||||
\(932\) | − | 145.901i | − | 0.156546i | ||||||
\(933\) | 1538.51 | − | 943.626i | 1.64899 | − | 1.01139i | ||||
\(934\) | 869.360 | 0.930792 | ||||||||
\(935\) | − | 1.14442i | − | 0.00122397i | ||||||
\(936\) | 469.440 | + | 238.730i | 0.501538 | + | 0.255053i | ||||
\(937\) | 316.459 | 0.337736 | 0.168868 | − | 0.985639i | \(-0.445989\pi\) | ||||
0.168868 | + | 0.985639i | \(0.445989\pi\) | |||||||
\(938\) | − | 251.805i | − | 0.268449i | ||||||
\(939\) | −138.742 | − | 226.208i | −0.147755 | − | 0.240903i | ||||
\(940\) | −230.990 | −0.245734 | ||||||||
\(941\) | − | 1775.79i | − | 1.88713i | −0.331189 | − | 0.943565i | \(-0.607450\pi\) | ||
0.331189 | − | 0.943565i | \(-0.392550\pi\) | |||||||
\(942\) | 973.769 | − | 597.250i | 1.03373 | − | 0.634023i | ||||
\(943\) | −89.4627 | −0.0948703 | ||||||||
\(944\) | 273.032i | 0.289229i | ||||||||
\(945\) | 8.49887 | + | 106.395i | 0.00899351 | + | 0.112587i | ||||
\(946\) | −1514.33 | −1.60077 | ||||||||
\(947\) | − | 216.023i | − | 0.228113i | −0.993474 | − | 0.114057i | \(-0.963615\pi\) | ||
0.993474 | − | 0.114057i | \(-0.0363845\pi\) | |||||||
\(948\) | −14.0231 | − | 22.8636i | −0.0147923 | − | 0.0241177i | ||||
\(949\) | 1530.65 | 1.61290 | ||||||||
\(950\) | − | 41.8430i | − | 0.0440453i | ||||||
\(951\) | 1114.83 | − | 683.768i | 1.17227 | − | 0.718999i | ||||
\(952\) | −0.144402 | −0.000151683 | ||||||||
\(953\) | 453.018i | 0.475360i | 0.971344 | + | 0.237680i | \(0.0763869\pi\) | ||||
−0.971344 | + | 0.237680i | \(0.923613\pi\) | |||||||
\(954\) | 125.596 | − | 246.972i | 0.131652 | − | 0.258880i | ||||
\(955\) | 436.130 | 0.456680 | ||||||||
\(956\) | 802.526i | 0.839462i | ||||||||
\(957\) | −1256.29 | − | 2048.28i | −1.31273 | − | 2.14031i | ||||
\(958\) | −895.457 | −0.934716 | ||||||||
\(959\) | − | 217.880i | − | 0.227195i | ||||||
\(960\) | 45.7465 | − | 28.0581i | 0.0476526 | − | 0.0292272i | ||||
\(961\) | 734.422 | 0.764227 | ||||||||
\(962\) | − | 2073.97i | − | 2.15590i | ||||||
\(963\) | −1173.99 | − | 597.026i | −1.21910 | − | 0.619965i | ||||
\(964\) | 150.423 | 0.156041 | ||||||||
\(965\) | 739.223i | 0.766034i | ||||||||
\(966\) | 18.8068 | + | 30.6630i | 0.0194687 | + | 0.0317423i | ||||
\(967\) | −806.223 | −0.833736 | −0.416868 | − | 0.908967i | \(-0.636872\pi\) | ||||
−0.416868 | + | 0.908967i | \(0.636872\pi\) | |||||||
\(968\) | − | 546.124i | − | 0.564178i | ||||||
\(969\) | −0.437016 | + | 0.268039i | −0.000450997 | + | 0.000276614i | ||||
\(970\) | 182.482 | 0.188126 | ||||||||
\(971\) | 786.444i | 0.809932i | 0.914332 | + | 0.404966i | \(0.132717\pi\) | ||||
−0.914332 | + | 0.404966i | \(0.867283\pi\) | |||||||
\(972\) | −185.107 | + | 449.368i | −0.190440 | + | 0.462312i | ||||
\(973\) | 387.471 | 0.398223 | ||||||||
\(974\) | 239.787i | 0.246188i | ||||||||
\(975\) | 162.253 | + | 264.540i | 0.166413 | + | 0.271324i | ||||
\(976\) | 5.52106 | 0.00565682 | ||||||||
\(977\) | 210.878i | 0.215842i | 0.994159 | + | 0.107921i | \(0.0344194\pi\) | ||||
−0.994159 | + | 0.107921i | \(0.965581\pi\) | |||||||
\(978\) | −1071.20 | + | 657.006i | −1.09529 | + | 0.671786i | ||||
\(979\) | 499.911 | 0.510634 | ||||||||
\(980\) | 205.157i | 0.209344i | ||||||||
\(981\) | −199.462 | + | 392.222i | −0.203325 | + | 0.399819i | ||||
\(982\) | −981.697 | −0.999691 | ||||||||
\(983\) | − | 1221.83i | − | 1.24296i | −0.783430 | − | 0.621480i | \(-0.786532\pi\) | ||
0.783430 | − | 0.621480i | \(-0.213468\pi\) | |||||||
\(984\) | 82.7572 | + | 134.929i | 0.0841029 | + | 0.137123i | ||||
\(985\) | −205.048 | −0.208171 | ||||||||
\(986\) | 1.84575i | 0.00187196i | ||||||||
\(987\) | −233.515 | + | 143.224i | −0.236591 | + | 0.145110i | ||||
\(988\) | −244.854 | −0.247828 | ||||||||
\(989\) | − | 289.765i | − | 0.292987i | ||||||
\(990\) | 449.592 | + | 228.637i | 0.454134 | + | 0.230946i | ||||
\(991\) | −348.803 | −0.351971 | −0.175985 | − | 0.984393i | \(-0.556311\pi\) | ||||
−0.175985 | + | 0.984393i | \(0.556311\pi\) | |||||||
\(992\) | − | 232.924i | − | 0.234802i | ||||||
\(993\) | 478.708 | + | 780.496i | 0.482082 | + | 0.785998i | ||||
\(994\) | 140.651 | 0.141500 | ||||||||
\(995\) | 13.8242i | 0.0138936i | ||||||||
\(996\) | −107.589 | + | 65.9885i | −0.108021 | + | 0.0662535i | ||||
\(997\) | 264.703 | 0.265499 | 0.132750 | − | 0.991150i | \(-0.457619\pi\) | ||||
0.132750 | + | 0.991150i | \(0.457619\pi\) | |||||||
\(998\) | − | 219.375i | − | 0.219815i | ||||||
\(999\) | 1907.79 | − | 152.395i | 1.90970 | − | 0.152548i |
(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 | 690.3.g.a.461.7 | ✓ | 56 | |
3.2 | odd | 2 | inner | 690.3.g.a.461.8 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.g.a.461.7 | ✓ | 56 | 1.1 | even | 1 | trivial | |
690.3.g.a.461.8 | yes | 56 | 3.2 | odd | 2 | inner |