Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, 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("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + \cdots + 48312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.2 | ||
Root | \(-2.05018 - 2.44140i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.n.122.11 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.83317i | − | 1.91659i | −0.285787 | − | 0.958293i | \(-0.592255\pi\) | ||
0.285787 | − | 0.958293i | \(-0.407745\pi\) | |||||||
\(3\) | 1.74344 | + | 2.44140i | 0.581147 | + | 0.813799i | ||||
\(4\) | −10.6932 | −2.67330 | ||||||||
\(5\) | 0.620885i | 0.124177i | 0.998071 | + | 0.0620885i | \(0.0197761\pi\) | ||||
−0.998071 | + | 0.0620885i | \(0.980224\pi\) | |||||||
\(6\) | 9.35829 | − | 6.68291i | 1.55972 | − | 1.11382i | ||||
\(7\) | 1.92745 | 0.275350 | 0.137675 | − | 0.990477i | \(-0.456037\pi\) | ||||
0.137675 | + | 0.990477i | \(0.456037\pi\) | |||||||
\(8\) | 25.6562i | 3.20703i | ||||||||
\(9\) | −2.92083 | + | 8.51286i | −0.324536 | + | 0.945873i | ||||
\(10\) | 2.37996 | 0.237996 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −18.6430 | − | 26.1064i | −1.55358 | − | 2.17553i | ||||
\(13\) | 15.9458 | 1.22660 | 0.613301 | − | 0.789849i | \(-0.289841\pi\) | ||||
0.613301 | + | 0.789849i | \(0.289841\pi\) | |||||||
\(14\) | − | 7.38824i | − | 0.527732i | ||||||
\(15\) | −1.51582 | + | 1.08248i | −0.101055 | + | 0.0721650i | ||||
\(16\) | 55.5719 | 3.47325 | ||||||||
\(17\) | 14.4412i | 0.849484i | 0.905315 | + | 0.424742i | \(0.139635\pi\) | ||||
−0.905315 | + | 0.424742i | \(0.860365\pi\) | |||||||
\(18\) | 32.6313 | + | 11.1960i | 1.81285 | + | 0.622002i | ||||
\(19\) | 16.4986 | 0.868348 | 0.434174 | − | 0.900829i | \(-0.357040\pi\) | ||||
0.434174 | + | 0.900829i | \(0.357040\pi\) | |||||||
\(20\) | − | 6.63925i | − | 0.331962i | ||||||
\(21\) | 3.36039 | + | 4.70566i | 0.160019 | + | 0.224079i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.6669i | 0.463776i | 0.972742 | + | 0.231888i | \(0.0744903\pi\) | ||||
−0.972742 | + | 0.231888i | \(0.925510\pi\) | |||||||
\(24\) | −62.6370 | + | 44.7301i | −2.60988 | + | 1.86376i | ||||
\(25\) | 24.6145 | 0.984580 | ||||||||
\(26\) | − | 61.1231i | − | 2.35089i | ||||||
\(27\) | −25.8755 | + | 7.71077i | −0.958354 | + | 0.285584i | ||||
\(28\) | −20.6106 | −0.736093 | ||||||||
\(29\) | − | 19.1659i | − | 0.660892i | −0.943825 | − | 0.330446i | \(-0.892801\pi\) | ||
0.943825 | − | 0.330446i | \(-0.107199\pi\) | |||||||
\(30\) | 4.14932 | + | 5.81042i | 0.138311 | + | 0.193681i | ||||
\(31\) | 22.0054 | 0.709852 | 0.354926 | − | 0.934894i | \(-0.384506\pi\) | ||||
0.354926 | + | 0.934894i | \(0.384506\pi\) | |||||||
\(32\) | − | 110.392i | − | 3.44975i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 55.3557 | 1.62811 | ||||||||
\(35\) | 1.19672i | 0.0341921i | ||||||||
\(36\) | 31.2330 | − | 91.0298i | 0.867584 | − | 2.52861i | ||||
\(37\) | −20.6452 | −0.557979 | −0.278990 | − | 0.960294i | \(-0.589999\pi\) | ||||
−0.278990 | + | 0.960294i | \(0.589999\pi\) | |||||||
\(38\) | − | 63.2420i | − | 1.66426i | ||||||
\(39\) | 27.8006 | + | 38.9301i | 0.712836 | + | 0.998207i | ||||
\(40\) | −15.9296 | −0.398239 | ||||||||
\(41\) | − | 27.0161i | − | 0.658930i | −0.944168 | − | 0.329465i | \(-0.893132\pi\) | ||
0.944168 | − | 0.329465i | \(-0.106868\pi\) | |||||||
\(42\) | 18.0376 | − | 12.8810i | 0.429467 | − | 0.306690i | ||||
\(43\) | 53.1596 | 1.23627 | 0.618134 | − | 0.786072i | \(-0.287889\pi\) | ||||
0.618134 | + | 0.786072i | \(0.287889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.28550 | − | 1.81350i | −0.117456 | − | 0.0402999i | ||||
\(46\) | 40.8879 | 0.888867 | ||||||||
\(47\) | 45.7258i | 0.972888i | 0.873712 | + | 0.486444i | \(0.161706\pi\) | ||||
−0.873712 | + | 0.486444i | \(0.838294\pi\) | |||||||
\(48\) | 96.8864 | + | 135.673i | 2.01847 | + | 2.82652i | ||||
\(49\) | −45.2849 | −0.924183 | ||||||||
\(50\) | − | 94.3516i | − | 1.88703i | ||||||
\(51\) | −35.2567 | + | 25.1774i | −0.691309 | + | 0.493675i | ||||
\(52\) | −170.512 | −3.27908 | ||||||||
\(53\) | 60.4562i | 1.14068i | 0.821408 | + | 0.570341i | \(0.193189\pi\) | ||||
−0.821408 | + | 0.570341i | \(0.806811\pi\) | |||||||
\(54\) | 29.5567 | + | 99.1854i | 0.547346 | + | 1.83677i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 49.4511i | 0.883055i | ||||||||
\(57\) | 28.7643 | + | 40.2796i | 0.504638 | + | 0.706660i | ||||
\(58\) | −73.4661 | −1.26666 | ||||||||
\(59\) | 40.5384i | 0.687092i | 0.939136 | + | 0.343546i | \(0.111628\pi\) | ||||
−0.939136 | + | 0.343546i | \(0.888372\pi\) | |||||||
\(60\) | 16.2090 | − | 11.5751i | 0.270151 | − | 0.192919i | ||||
\(61\) | 64.1073 | 1.05094 | 0.525469 | − | 0.850812i | \(-0.323890\pi\) | ||||
0.525469 | + | 0.850812i | \(0.323890\pi\) | |||||||
\(62\) | − | 84.3505i | − | 1.36049i | ||||||
\(63\) | −5.62974 | + | 16.4081i | −0.0893610 | + | 0.260446i | ||||
\(64\) | −200.863 | −3.13849 | ||||||||
\(65\) | 9.90052i | 0.152316i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25.7214 | −0.383901 | −0.191951 | − | 0.981405i | \(-0.561481\pi\) | ||||
−0.191951 | + | 0.981405i | \(0.561481\pi\) | |||||||
\(68\) | − | 154.423i | − | 2.27093i | ||||||
\(69\) | −26.0420 | + | 18.5970i | −0.377420 | + | 0.269522i | ||||
\(70\) | 4.58724 | 0.0655321 | ||||||||
\(71\) | − | 114.125i | − | 1.60740i | −0.595036 | − | 0.803699i | \(-0.702862\pi\) | ||
0.595036 | − | 0.803699i | \(-0.297138\pi\) | |||||||
\(72\) | −218.408 | − | 74.9374i | −3.03344 | − | 1.04080i | ||||
\(73\) | −84.4359 | −1.15666 | −0.578328 | − | 0.815804i | \(-0.696295\pi\) | ||||
−0.578328 | + | 0.815804i | \(0.696295\pi\) | |||||||
\(74\) | 79.1367i | 1.06942i | ||||||||
\(75\) | 42.9139 | + | 60.0937i | 0.572186 | + | 0.801250i | ||||
\(76\) | −176.423 | −2.32136 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 149.226 | − | 106.565i | 1.91315 | − | 1.36621i | ||||
\(79\) | −65.2788 | −0.826314 | −0.413157 | − | 0.910660i | \(-0.635574\pi\) | ||||
−0.413157 | + | 0.910660i | \(0.635574\pi\) | |||||||
\(80\) | 34.5038i | 0.431297i | ||||||||
\(81\) | −63.9375 | − | 49.7292i | −0.789352 | − | 0.613941i | ||||
\(82\) | −103.558 | −1.26290 | ||||||||
\(83\) | 89.6649i | 1.08030i | 0.841569 | + | 0.540150i | \(0.181633\pi\) | ||||
−0.841569 | + | 0.540150i | \(0.818367\pi\) | |||||||
\(84\) | −35.9334 | − | 50.3187i | −0.427778 | − | 0.599032i | ||||
\(85\) | −8.96633 | −0.105486 | ||||||||
\(86\) | − | 203.770i | − | 2.36942i | ||||||
\(87\) | 46.7915 | − | 33.4145i | 0.537833 | − | 0.384075i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 146.530i | 1.64640i | 0.567750 | + | 0.823201i | \(0.307814\pi\) | ||||
−0.567750 | + | 0.823201i | \(0.692186\pi\) | |||||||
\(90\) | −6.95145 | + | 20.2602i | −0.0772383 | + | 0.225114i | ||||
\(91\) | 30.7348 | 0.337745 | ||||||||
\(92\) | − | 114.063i | − | 1.23981i | ||||||
\(93\) | 38.3651 | + | 53.7239i | 0.412528 | + | 0.577677i | ||||
\(94\) | 175.275 | 1.86462 | ||||||||
\(95\) | 10.2437i | 0.107829i | ||||||||
\(96\) | 269.510 | − | 192.462i | 2.80740 | − | 2.00481i | ||||
\(97\) | 62.3547 | 0.642832 | 0.321416 | − | 0.946938i | \(-0.395841\pi\) | ||||
0.321416 | + | 0.946938i | \(0.395841\pi\) | |||||||
\(98\) | 173.585i | 1.77128i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −263.208 | −2.63208 | ||||||||
\(101\) | 88.2635i | 0.873896i | 0.899487 | + | 0.436948i | \(0.143941\pi\) | ||||
−0.899487 | + | 0.436948i | \(0.856059\pi\) | |||||||
\(102\) | 96.5094 | + | 135.145i | 0.946170 | + | 1.32495i | ||||
\(103\) | −30.0534 | −0.291781 | −0.145890 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145890 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(104\) | 409.110i | 3.93375i | ||||||||
\(105\) | −2.92167 | + | 2.08642i | −0.0278255 | + | 0.0198706i | ||||
\(106\) | 231.739 | 2.18622 | ||||||||
\(107\) | − | 120.202i | − | 1.12338i | −0.827348 | − | 0.561689i | \(-0.810152\pi\) | ||
0.827348 | − | 0.561689i | \(-0.189848\pi\) | |||||||
\(108\) | 276.693 | − | 82.4529i | 2.56197 | − | 0.763453i | ||||
\(109\) | 152.110 | 1.39551 | 0.697753 | − | 0.716338i | \(-0.254183\pi\) | ||||
0.697753 | + | 0.716338i | \(0.254183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.9937 | − | 50.4032i | −0.324268 | − | 0.454083i | ||||
\(112\) | 107.112 | 0.956357 | ||||||||
\(113\) | − | 129.552i | − | 1.14648i | −0.819387 | − | 0.573241i | \(-0.805686\pi\) | ||
0.819387 | − | 0.573241i | \(-0.194314\pi\) | |||||||
\(114\) | 154.399 | − | 110.259i | 1.35437 | − | 0.967181i | ||||
\(115\) | −6.62288 | −0.0575903 | ||||||||
\(116\) | 204.945i | 1.76676i | ||||||||
\(117\) | −46.5750 | + | 135.745i | −0.398077 | + | 1.16021i | ||||
\(118\) | 155.391 | 1.31687 | ||||||||
\(119\) | 27.8347i | 0.233905i | ||||||||
\(120\) | −27.7722 | − | 38.8904i | −0.231435 | − | 0.324086i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 245.734i | − | 2.01422i | ||||||
\(123\) | 65.9571 | − | 47.1011i | 0.536237 | − | 0.382935i | ||||
\(124\) | −235.309 | −1.89765 | ||||||||
\(125\) | 30.8049i | 0.246439i | ||||||||
\(126\) | 62.8951 | + | 21.5798i | 0.499167 | + | 0.171268i | ||||
\(127\) | −63.1439 | −0.497196 | −0.248598 | − | 0.968607i | \(-0.579970\pi\) | ||||
−0.248598 | + | 0.968607i | \(0.579970\pi\) | |||||||
\(128\) | 328.376i | 2.56544i | ||||||||
\(129\) | 92.6805 | + | 129.784i | 0.718454 | + | 1.00607i | ||||
\(130\) | 37.9504 | 0.291926 | ||||||||
\(131\) | − | 79.8306i | − | 0.609394i | −0.952449 | − | 0.304697i | \(-0.901445\pi\) | ||
0.952449 | − | 0.304697i | \(-0.0985552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.8002 | 0.239099 | ||||||||
\(134\) | 98.5945i | 0.735780i | ||||||||
\(135\) | −4.78750 | − | 16.0657i | −0.0354629 | − | 0.119005i | ||||
\(136\) | −370.507 | −2.72432 | ||||||||
\(137\) | − | 83.5542i | − | 0.609885i | −0.952371 | − | 0.304942i | \(-0.901363\pi\) | ||
0.952371 | − | 0.304942i | \(-0.0986372\pi\) | |||||||
\(138\) | 71.2856 | + | 99.8235i | 0.516562 | + | 0.723359i | ||||
\(139\) | 80.8218 | 0.581452 | 0.290726 | − | 0.956806i | \(-0.406103\pi\) | ||||
0.290726 | + | 0.956806i | \(0.406103\pi\) | |||||||
\(140\) | − | 12.7968i | − | 0.0914058i | ||||||
\(141\) | −111.635 | + | 79.7202i | −0.791735 | + | 0.565391i | ||||
\(142\) | −437.462 | −3.08072 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −162.316 | + | 473.076i | −1.12719 | + | 3.28525i | ||||
\(145\) | 11.8998 | 0.0820675 | ||||||||
\(146\) | 323.657i | 2.21683i | ||||||||
\(147\) | −78.9516 | − | 110.558i | −0.537086 | − | 0.752098i | ||||
\(148\) | 220.764 | 1.49165 | ||||||||
\(149\) | − | 273.816i | − | 1.83769i | −0.394613 | − | 0.918847i | \(-0.629121\pi\) | ||
0.394613 | − | 0.918847i | \(-0.370879\pi\) | |||||||
\(150\) | 230.350 | − | 164.496i | 1.53566 | − | 1.09664i | ||||
\(151\) | 4.36383 | 0.0288995 | 0.0144498 | − | 0.999896i | \(-0.495400\pi\) | ||||
0.0144498 | + | 0.999896i | \(0.495400\pi\) | |||||||
\(152\) | 423.292i | 2.78482i | ||||||||
\(153\) | −122.936 | − | 42.1803i | −0.803504 | − | 0.275688i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6628i | 0.0881472i | ||||||||
\(156\) | −297.278 | − | 416.288i | −1.90563 | − | 2.66851i | ||||
\(157\) | 137.724 | 0.877222 | 0.438611 | − | 0.898677i | \(-0.355471\pi\) | ||||
0.438611 | + | 0.898677i | \(0.355471\pi\) | |||||||
\(158\) | 250.225i | 1.58370i | ||||||||
\(159\) | −147.597 | + | 105.402i | −0.928286 | + | 0.662904i | ||||
\(160\) | 68.5406 | 0.428379 | ||||||||
\(161\) | 20.5598i | 0.127701i | ||||||||
\(162\) | −190.621 | + | 245.084i | −1.17667 | + | 1.51286i | ||||
\(163\) | −301.797 | −1.85152 | −0.925759 | − | 0.378115i | \(-0.876573\pi\) | ||||
−0.925759 | + | 0.378115i | \(0.876573\pi\) | |||||||
\(164\) | 288.889i | 1.76152i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 343.701 | 2.07049 | ||||||||
\(167\) | − | 140.149i | − | 0.839213i | −0.907706 | − | 0.419606i | \(-0.862168\pi\) | ||
0.907706 | − | 0.419606i | \(-0.137832\pi\) | |||||||
\(168\) | −120.730 | + | 86.2150i | −0.718629 | + | 0.513185i | ||||
\(169\) | 85.2695 | 0.504553 | ||||||||
\(170\) | 34.3695i | 0.202174i | ||||||||
\(171\) | −48.1896 | + | 140.450i | −0.281810 | + | 0.821347i | ||||
\(172\) | −568.446 | −3.30492 | ||||||||
\(173\) | − | 187.690i | − | 1.08492i | −0.840083 | − | 0.542458i | \(-0.817494\pi\) | ||
0.840083 | − | 0.542458i | \(-0.182506\pi\) | |||||||
\(174\) | −128.084 | − | 179.360i | −0.736113 | − | 1.03080i | ||||
\(175\) | 47.4432 | 0.271104 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −98.9703 | + | 70.6763i | −0.559154 | + | 0.399301i | ||||
\(178\) | 561.674 | 3.15547 | ||||||||
\(179\) | − | 118.994i | − | 0.664771i | −0.943144 | − | 0.332386i | \(-0.892146\pi\) | ||
0.943144 | − | 0.332386i | \(-0.107854\pi\) | |||||||
\(180\) | 56.5190 | + | 19.3921i | 0.313994 | + | 0.107734i | ||||
\(181\) | 207.591 | 1.14691 | 0.573456 | − | 0.819236i | \(-0.305602\pi\) | ||||
0.573456 | + | 0.819236i | \(0.305602\pi\) | |||||||
\(182\) | − | 117.812i | − | 0.647317i | ||||||
\(183\) | 111.767 | + | 156.511i | 0.610750 | + | 0.855253i | ||||
\(184\) | −273.671 | −1.48734 | ||||||||
\(185\) | − | 12.8183i | − | 0.0692881i | ||||||
\(186\) | 205.933 | − | 147.060i | 1.10717 | − | 0.790646i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 488.955i | − | 2.60083i | ||||||
\(189\) | −49.8738 | + | 14.8621i | −0.263882 | + | 0.0786355i | ||||
\(190\) | 39.2660 | 0.206663 | ||||||||
\(191\) | 368.710i | 1.93042i | 0.261480 | + | 0.965209i | \(0.415790\pi\) | ||||
−0.261480 | + | 0.965209i | \(0.584210\pi\) | |||||||
\(192\) | −350.193 | − | 490.387i | −1.82392 | − | 2.55410i | ||||
\(193\) | −204.400 | −1.05907 | −0.529533 | − | 0.848289i | \(-0.677633\pi\) | ||||
−0.529533 | + | 0.848289i | \(0.677633\pi\) | |||||||
\(194\) | − | 239.016i | − | 1.23204i | ||||||
\(195\) | −24.1711 | + | 17.2610i | −0.123954 | + | 0.0885178i | ||||
\(196\) | 484.241 | 2.47062 | ||||||||
\(197\) | 61.4657i | 0.312009i | 0.987756 | + | 0.156004i | \(0.0498614\pi\) | ||||
−0.987756 | + | 0.156004i | \(0.950139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −53.9505 | −0.271108 | −0.135554 | − | 0.990770i | \(-0.543281\pi\) | ||||
−0.135554 | + | 0.990770i | \(0.543281\pi\) | |||||||
\(200\) | 631.515i | 3.15758i | ||||||||
\(201\) | −44.8437 | − | 62.7961i | −0.223103 | − | 0.312418i | ||||
\(202\) | 338.329 | 1.67490 | ||||||||
\(203\) | − | 36.9412i | − | 0.181976i | ||||||
\(204\) | 377.008 | − | 269.227i | 1.84808 | − | 1.31974i | ||||
\(205\) | 16.7739 | 0.0818239 | ||||||||
\(206\) | 115.200i | 0.559223i | ||||||||
\(207\) | −90.8054 | − | 31.1560i | −0.438674 | − | 0.150512i | ||||
\(208\) | 886.141 | 4.26029 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 7.99759 | + | 11.1993i | 0.0380838 | + | 0.0533299i | ||||
\(211\) | −153.970 | −0.729714 | −0.364857 | − | 0.931064i | \(-0.618882\pi\) | ||||
−0.364857 | + | 0.931064i | \(0.618882\pi\) | |||||||
\(212\) | − | 646.470i | − | 3.04939i | ||||||
\(213\) | 278.625 | − | 198.971i | 1.30810 | − | 0.934135i | ||||
\(214\) | −460.753 | −2.15305 | ||||||||
\(215\) | 33.0059i | 0.153516i | ||||||||
\(216\) | −197.829 | − | 663.869i | −0.915876 | − | 3.07347i | ||||
\(217\) | 42.4143 | 0.195458 | ||||||||
\(218\) | − | 583.064i | − | 2.67461i | ||||||
\(219\) | −147.209 | − | 206.141i | −0.672187 | − | 0.941285i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 230.277i | 1.04198i | ||||||||
\(222\) | −193.204 | + | 137.970i | −0.870289 | + | 0.621487i | ||||
\(223\) | −155.734 | −0.698357 | −0.349178 | − | 0.937056i | \(-0.613539\pi\) | ||||
−0.349178 | + | 0.937056i | \(0.613539\pi\) | |||||||
\(224\) | − | 212.775i | − | 0.949886i | ||||||
\(225\) | −71.8947 | + | 209.540i | −0.319532 | + | 0.931288i | ||||
\(226\) | −496.597 | −2.19733 | ||||||||
\(227\) | − | 76.7844i | − | 0.338257i | −0.985594 | − | 0.169129i | \(-0.945905\pi\) | ||
0.985594 | − | 0.169129i | \(-0.0540953\pi\) | |||||||
\(228\) | −307.583 | − | 430.719i | −1.34905 | − | 1.88912i | ||||
\(229\) | −42.1829 | −0.184205 | −0.0921023 | − | 0.995750i | \(-0.529359\pi\) | ||||
−0.0921023 | + | 0.995750i | \(0.529359\pi\) | |||||||
\(230\) | 25.3867i | 0.110377i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 491.724 | 2.11950 | ||||||||
\(233\) | − | 46.7608i | − | 0.200690i | −0.994953 | − | 0.100345i | \(-0.968005\pi\) | ||
0.994953 | − | 0.100345i | \(-0.0319946\pi\) | |||||||
\(234\) | 520.333 | + | 178.530i | 2.22364 | + | 0.762949i | ||||
\(235\) | −28.3904 | −0.120810 | ||||||||
\(236\) | − | 433.486i | − | 1.83680i | ||||||
\(237\) | −113.810 | − | 159.371i | −0.480210 | − | 0.672453i | ||||
\(238\) | 106.695 | 0.448299 | ||||||||
\(239\) | − | 157.528i | − | 0.659114i | −0.944136 | − | 0.329557i | \(-0.893101\pi\) | ||
0.944136 | − | 0.329557i | \(-0.106899\pi\) | |||||||
\(240\) | −84.2373 | + | 60.1553i | −0.350989 | + | 0.250647i | ||||
\(241\) | −267.401 | −1.10955 | −0.554773 | − | 0.832002i | \(-0.687195\pi\) | ||||
−0.554773 | + | 0.832002i | \(0.687195\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.93733 | − | 242.797i | 0.0408944 | − | 0.999163i | ||||
\(244\) | −685.513 | −2.80948 | ||||||||
\(245\) | − | 28.1167i | − | 0.114762i | ||||||
\(246\) | −180.546 | − | 252.825i | −0.733929 | − | 1.02774i | ||||
\(247\) | 263.084 | 1.06512 | ||||||||
\(248\) | 564.576i | 2.27652i | ||||||||
\(249\) | −218.908 | + | 156.326i | −0.879147 | + | 0.627813i | ||||
\(250\) | 118.080 | 0.472322 | ||||||||
\(251\) | − | 327.642i | − | 1.30535i | −0.757639 | − | 0.652673i | \(-0.773647\pi\) | ||
0.757639 | − | 0.652673i | \(-0.226353\pi\) | |||||||
\(252\) | 60.2000 | − | 175.455i | 0.238889 | − | 0.696251i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 242.042i | 0.952919i | ||||||||
\(255\) | −15.6323 | − | 21.8904i | −0.0613030 | − | 0.0858446i | ||||
\(256\) | 455.270 | 1.77840 | ||||||||
\(257\) | 6.13018i | 0.0238528i | 0.999929 | + | 0.0119264i | \(0.00379639\pi\) | ||||
−0.999929 | + | 0.0119264i | \(0.996204\pi\) | |||||||
\(258\) | 497.483 | − | 355.261i | 1.92823 | − | 1.37698i | ||||
\(259\) | −39.7926 | −0.153639 | ||||||||
\(260\) | − | 105.868i | − | 0.407186i | ||||||
\(261\) | 163.156 | + | 55.9802i | 0.625120 | + | 0.214483i | ||||
\(262\) | −306.004 | −1.16796 | ||||||||
\(263\) | − | 171.833i | − | 0.653356i | −0.945136 | − | 0.326678i | \(-0.894071\pi\) | ||
0.945136 | − | 0.326678i | \(-0.105929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.5363 | −0.141646 | ||||||||
\(266\) | − | 121.896i | − | 0.458254i | ||||||
\(267\) | −357.737 | + | 255.466i | −1.33984 | + | 0.956802i | ||||
\(268\) | 275.044 | 1.02628 | ||||||||
\(269\) | 96.2444i | 0.357786i | 0.983869 | + | 0.178893i | \(0.0572516\pi\) | ||||
−0.983869 | + | 0.178893i | \(0.942748\pi\) | |||||||
\(270\) | −61.5827 | + | 18.3513i | −0.228084 | + | 0.0679678i | ||||
\(271\) | −81.6129 | −0.301155 | −0.150577 | − | 0.988598i | \(-0.548113\pi\) | ||||
−0.150577 | + | 0.988598i | \(0.548113\pi\) | |||||||
\(272\) | 802.527i | 2.95047i | ||||||||
\(273\) | 53.5842 | + | 75.0357i | 0.196279 | + | 0.274856i | ||||
\(274\) | −320.278 | −1.16890 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 278.473 | − | 198.862i | 1.00896 | − | 0.720514i | ||||
\(277\) | −160.351 | −0.578886 | −0.289443 | − | 0.957195i | \(-0.593470\pi\) | ||||
−0.289443 | + | 0.957195i | \(0.593470\pi\) | |||||||
\(278\) | − | 309.804i | − | 1.11440i | ||||||
\(279\) | −64.2740 | + | 187.329i | −0.230373 | + | 0.671430i | ||||
\(280\) | −30.7034 | −0.109655 | ||||||||
\(281\) | − | 342.068i | − | 1.21732i | −0.793430 | − | 0.608662i | \(-0.791707\pi\) | ||
0.793430 | − | 0.608662i | \(-0.208293\pi\) | |||||||
\(282\) | 305.581 | + | 427.915i | 1.08362 | + | 1.51743i | ||||
\(283\) | −291.087 | −1.02858 | −0.514288 | − | 0.857618i | \(-0.671944\pi\) | ||||
−0.514288 | + | 0.857618i | \(0.671944\pi\) | |||||||
\(284\) | 1220.37i | 4.29706i | ||||||||
\(285\) | −25.0090 | + | 17.8593i | −0.0877509 | + | 0.0626643i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 52.0722i | − | 0.181436i | ||||||
\(288\) | 939.750 | + | 322.436i | 3.26302 | + | 1.11957i | ||||
\(289\) | 80.4511 | 0.278377 | ||||||||
\(290\) | − | 45.6139i | − | 0.157289i | ||||||
\(291\) | 108.712 | + | 152.232i | 0.373580 | + | 0.523136i | ||||
\(292\) | 902.890 | 3.09209 | ||||||||
\(293\) | − | 120.198i | − | 0.410233i | −0.978738 | − | 0.205117i | \(-0.934243\pi\) | ||
0.978738 | − | 0.205117i | \(-0.0657574\pi\) | |||||||
\(294\) | −423.790 | + | 302.635i | −1.44146 | + | 1.02937i | ||||
\(295\) | −25.1697 | −0.0853209 | ||||||||
\(296\) | − | 529.679i | − | 1.78946i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1049.59 | −3.52210 | ||||||||
\(299\) | 170.092i | 0.568869i | ||||||||
\(300\) | −458.888 | − | 642.595i | −1.52963 | − | 2.14198i | ||||
\(301\) | 102.462 | 0.340406 | ||||||||
\(302\) | − | 16.7273i | − | 0.0553884i | ||||||
\(303\) | −215.486 | + | 153.882i | −0.711176 | + | 0.507862i | ||||
\(304\) | 916.859 | 3.01598 | ||||||||
\(305\) | 39.8032i | 0.130502i | ||||||||
\(306\) | −161.684 | + | 471.235i | −0.528381 | + | 1.53998i | ||||
\(307\) | 140.853 | 0.458806 | 0.229403 | − | 0.973332i | \(-0.426323\pi\) | ||||
0.229403 | + | 0.973332i | \(0.426323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52.3963 | − | 73.3722i | −0.169567 | − | 0.237451i | ||||
\(310\) | 52.3719 | 0.168942 | ||||||||
\(311\) | 409.326i | 1.31616i | 0.752947 | + | 0.658081i | \(0.228632\pi\) | ||||
−0.752947 | + | 0.658081i | \(0.771368\pi\) | |||||||
\(312\) | −998.799 | + | 713.259i | −3.20128 | + | 2.28609i | ||||
\(313\) | 373.913 | 1.19461 | 0.597305 | − | 0.802014i | \(-0.296238\pi\) | ||||
0.597305 | + | 0.802014i | \(0.296238\pi\) | |||||||
\(314\) | − | 527.919i | − | 1.68127i | ||||||
\(315\) | −10.1875 | − | 3.49542i | −0.0323414 | − | 0.0110966i | ||||
\(316\) | 698.040 | 2.20899 | ||||||||
\(317\) | − | 176.622i | − | 0.557168i | −0.960412 | − | 0.278584i | \(-0.910135\pi\) | ||
0.960412 | − | 0.278584i | \(-0.0898651\pi\) | |||||||
\(318\) | 404.023 | + | 565.766i | 1.27051 | + | 1.77914i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 124.713i | − | 0.389728i | ||||||
\(321\) | 293.460 | − | 209.564i | 0.914204 | − | 0.652848i | ||||
\(322\) | 78.8093 | 0.244749 | ||||||||
\(323\) | 238.260i | 0.737647i | ||||||||
\(324\) | 683.698 | + | 531.765i | 2.11018 | + | 1.64125i | ||||
\(325\) | 392.499 | 1.20769 | ||||||||
\(326\) | 1156.84i | 3.54859i | ||||||||
\(327\) | 265.195 | + | 371.361i | 0.810994 | + | 1.13566i | ||||
\(328\) | 693.133 | 2.11321 | ||||||||
\(329\) | 88.1340i | 0.267885i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 97.5763 | 0.294793 | 0.147396 | − | 0.989078i | \(-0.452911\pi\) | ||||
0.147396 | + | 0.989078i | \(0.452911\pi\) | |||||||
\(332\) | − | 958.806i | − | 2.88797i | ||||||
\(333\) | 60.3011 | − | 175.750i | 0.181085 | − | 0.527777i | ||||
\(334\) | −537.214 | −1.60842 | ||||||||
\(335\) | − | 15.9700i | − | 0.0476717i | ||||||
\(336\) | 186.743 | + | 261.503i | 0.555784 | + | 0.778282i | ||||
\(337\) | 170.086 | 0.504707 | 0.252353 | − | 0.967635i | \(-0.418795\pi\) | ||||
0.252353 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(338\) | − | 326.853i | − | 0.967020i | ||||||
\(339\) | 316.289 | − | 225.867i | 0.933005 | − | 0.666275i | ||||
\(340\) | 95.8789 | 0.281997 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 538.370 | + | 184.719i | 1.57418 | + | 0.540114i | ||||
\(343\) | −181.729 | −0.529823 | ||||||||
\(344\) | 1363.87i | 3.96475i | ||||||||
\(345\) | −11.5466 | − | 16.1691i | −0.0334684 | − | 0.0468669i | ||||
\(346\) | −719.450 | −2.07934 | ||||||||
\(347\) | 433.131i | 1.24822i | 0.781338 | + | 0.624108i | \(0.214537\pi\) | ||||
−0.781338 | + | 0.624108i | \(0.785463\pi\) | |||||||
\(348\) | −500.351 | + | 357.309i | −1.43779 | + | 1.02675i | ||||
\(349\) | −412.379 | −1.18160 | −0.590800 | − | 0.806818i | \(-0.701188\pi\) | ||||
−0.590800 | + | 0.806818i | \(0.701188\pi\) | |||||||
\(350\) | − | 181.858i | − | 0.519594i | ||||||
\(351\) | −412.607 | + | 122.955i | −1.17552 | + | 0.350298i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 116.450i | − | 0.329888i | −0.986303 | − | 0.164944i | \(-0.947256\pi\) | ||
0.986303 | − | 0.164944i | \(-0.0527443\pi\) | |||||||
\(354\) | 270.915 | + | 379.370i | 0.765295 | + | 1.07167i | ||||
\(355\) | 70.8586 | 0.199602 | ||||||||
\(356\) | − | 1566.87i | − | 4.40133i | ||||||
\(357\) | −67.9555 | + | 48.5282i | −0.190352 | + | 0.135933i | ||||
\(358\) | −456.125 | −1.27409 | ||||||||
\(359\) | − | 579.340i | − | 1.61376i | −0.590716 | − | 0.806880i | \(-0.701154\pi\) | ||
0.590716 | − | 0.806880i | \(-0.298846\pi\) | |||||||
\(360\) | 46.5275 | − | 135.606i | 0.129243 | − | 0.376684i | ||||
\(361\) | −88.7961 | −0.245973 | ||||||||
\(362\) | − | 795.733i | − | 2.19816i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −328.653 | −0.902894 | ||||||||
\(365\) | − | 52.4249i | − | 0.143630i | ||||||
\(366\) | 599.935 | − | 428.423i | 1.63917 | − | 1.17056i | ||||
\(367\) | −135.045 | −0.367970 | −0.183985 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183985 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(368\) | 592.778i | 1.61081i | ||||||||
\(369\) | 229.985 | + | 78.9095i | 0.623265 | + | 0.213847i | ||||
\(370\) | −49.1348 | −0.132797 | ||||||||
\(371\) | 116.526i | 0.314087i | ||||||||
\(372\) | −410.247 | − | 574.481i | −1.10281 | − | 1.54430i | ||||
\(373\) | −125.984 | −0.337760 | −0.168880 | − | 0.985637i | \(-0.554015\pi\) | ||||
−0.168880 | + | 0.985637i | \(0.554015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −75.2069 | + | 53.7065i | −0.200552 | + | 0.143217i | ||||
\(376\) | −1173.15 | −3.12008 | ||||||||
\(377\) | − | 305.616i | − | 0.810651i | ||||||
\(378\) | 56.9690 | + | 191.175i | 0.150712 | + | 0.505753i | ||||
\(379\) | −402.169 | −1.06113 | −0.530565 | − | 0.847644i | \(-0.678020\pi\) | ||||
−0.530565 | + | 0.847644i | \(0.678020\pi\) | |||||||
\(380\) | − | 109.538i | − | 0.288259i | ||||||
\(381\) | −110.088 | − | 154.159i | −0.288944 | − | 0.404618i | ||||
\(382\) | 1413.33 | 3.69981 | ||||||||
\(383\) | 417.205i | 1.08931i | 0.838661 | + | 0.544653i | \(0.183339\pi\) | ||||
−0.838661 | + | 0.544653i | \(0.816661\pi\) | |||||||
\(384\) | −801.697 | + | 572.505i | −2.08775 | + | 1.49090i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 783.499i | 2.02979i | ||||||||
\(387\) | −155.270 | + | 452.540i | −0.401214 | + | 1.16935i | ||||
\(388\) | −666.772 | −1.71848 | ||||||||
\(389\) | − | 423.279i | − | 1.08812i | −0.839046 | − | 0.544061i | \(-0.816886\pi\) | ||
0.839046 | − | 0.544061i | \(-0.183114\pi\) | |||||||
\(390\) | 66.1643 | + | 92.6520i | 0.169652 | + | 0.237569i | ||||
\(391\) | −154.042 | −0.393970 | ||||||||
\(392\) | − | 1161.84i | − | 2.96388i | ||||||
\(393\) | 194.898 | − | 139.180i | 0.495924 | − | 0.354147i | ||||
\(394\) | 235.609 | 0.597992 | ||||||||
\(395\) | − | 40.5306i | − | 0.102609i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 230.173 | 0.579781 | 0.289891 | − | 0.957060i | \(-0.406381\pi\) | ||||
0.289891 | + | 0.957060i | \(0.406381\pi\) | |||||||
\(398\) | 206.802i | 0.519602i | ||||||||
\(399\) | 55.4418 | + | 77.6369i | 0.138952 | + | 0.194579i | ||||
\(400\) | 1367.88 | 3.41969 | ||||||||
\(401\) | − | 420.358i | − | 1.04827i | −0.851634 | − | 0.524137i | \(-0.824388\pi\) | ||
0.851634 | − | 0.524137i | \(-0.175612\pi\) | |||||||
\(402\) | −240.708 | + | 171.894i | −0.598777 | + | 0.427596i | ||||
\(403\) | 350.895 | 0.870706 | ||||||||
\(404\) | − | 943.821i | − | 2.33619i | ||||||
\(405\) | 30.8761 | − | 39.6978i | 0.0762372 | − | 0.0980193i | ||||
\(406\) | −141.602 | −0.348773 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −645.958 | − | 904.555i | −1.58323 | − | 2.21705i | ||||
\(409\) | 432.898 | 1.05843 | 0.529215 | − | 0.848488i | \(-0.322486\pi\) | ||||
0.529215 | + | 0.848488i | \(0.322486\pi\) | |||||||
\(410\) | − | 64.2973i | − | 0.156823i | ||||||
\(411\) | 203.989 | − | 145.672i | 0.496323 | − | 0.354433i | ||||
\(412\) | 321.367 | 0.780018 | ||||||||
\(413\) | 78.1357i | 0.189190i | ||||||||
\(414\) | −119.426 | + | 348.073i | −0.288470 | + | 0.840756i | ||||
\(415\) | −55.6716 | −0.134148 | ||||||||
\(416\) | − | 1760.29i | − | 4.23147i | ||||||
\(417\) | 140.908 | + | 197.318i | 0.337909 | + | 0.473185i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 258.662i | − | 0.617331i | −0.951171 | − | 0.308665i | \(-0.900118\pi\) | ||
0.951171 | − | 0.308665i | \(-0.0998823\pi\) | |||||||
\(420\) | 31.2421 | − | 22.3105i | 0.0743859 | − | 0.0531202i | ||||
\(421\) | 559.980 | 1.33012 | 0.665060 | − | 0.746790i | \(-0.268406\pi\) | ||||
0.665060 | + | 0.746790i | \(0.268406\pi\) | |||||||
\(422\) | 590.192i | 1.39856i | ||||||||
\(423\) | −389.257 | − | 133.557i | −0.920229 | − | 0.315738i | ||||
\(424\) | −1551.08 | −3.65820 | ||||||||
\(425\) | 355.464i | 0.836385i | ||||||||
\(426\) | −762.689 | − | 1068.02i | −1.79035 | − | 2.50708i | ||||
\(427\) | 123.563 | 0.289376 | ||||||||
\(428\) | 1285.34i | 3.00313i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 126.517 | 0.294227 | ||||||||
\(431\) | − | 137.319i | − | 0.318606i | −0.987230 | − | 0.159303i | \(-0.949075\pi\) | ||
0.987230 | − | 0.159303i | \(-0.0509247\pi\) | |||||||
\(432\) | −1437.95 | + | 428.502i | −3.32860 | + | 0.991904i | ||||
\(433\) | 443.788 | 1.02491 | 0.512457 | − | 0.858713i | \(-0.328735\pi\) | ||||
0.512457 | + | 0.858713i | \(0.328735\pi\) | |||||||
\(434\) | − | 162.581i | − | 0.374611i | ||||||
\(435\) | 20.7466 | + | 29.0521i | 0.0476933 | + | 0.0667864i | ||||
\(436\) | −1626.55 | −3.73061 | ||||||||
\(437\) | 175.988i | 0.402719i | ||||||||
\(438\) | −790.175 | + | 564.277i | −1.80405 | + | 1.28830i | ||||
\(439\) | 850.056 | 1.93635 | 0.968173 | − | 0.250281i | \(-0.0805230\pi\) | ||||
0.968173 | + | 0.250281i | \(0.0805230\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 132.270 | − | 385.504i | 0.299931 | − | 0.874159i | ||||
\(442\) | 882.693 | 1.99704 | ||||||||
\(443\) | 300.820i | 0.679052i | 0.940597 | + | 0.339526i | \(0.110267\pi\) | ||||
−0.940597 | + | 0.339526i | \(0.889733\pi\) | |||||||
\(444\) | 384.889 | + | 538.972i | 0.866866 | + | 1.21390i | ||||
\(445\) | −90.9781 | −0.204445 | ||||||||
\(446\) | 596.954i | 1.33846i | ||||||||
\(447\) | 668.494 | − | 477.383i | 1.49551 | − | 1.06797i | ||||
\(448\) | −387.154 | −0.864182 | ||||||||
\(449\) | − | 242.612i | − | 0.540339i | −0.962813 | − | 0.270170i | \(-0.912920\pi\) | ||
0.962813 | − | 0.270170i | \(-0.0870798\pi\) | |||||||
\(450\) | 803.202 | + | 275.585i | 1.78489 | + | 0.612411i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1385.33i | 3.06489i | ||||||||
\(453\) | 7.60808 | + | 10.6538i | 0.0167949 | + | 0.0235184i | ||||
\(454\) | −294.328 | −0.648299 | ||||||||
\(455\) | 19.0827i | 0.0419401i | ||||||||
\(456\) | −1033.42 | + | 737.985i | −2.26628 | + | 1.61839i | ||||
\(457\) | 643.634 | 1.40839 | 0.704194 | − | 0.710007i | \(-0.251308\pi\) | ||||
0.704194 | + | 0.710007i | \(0.251308\pi\) | |||||||
\(458\) | 161.694i | 0.353044i | ||||||||
\(459\) | −111.353 | − | 373.675i | −0.242599 | − | 0.814106i | ||||
\(460\) | 70.8199 | 0.153956 | ||||||||
\(461\) | 526.878i | 1.14290i | 0.820636 | + | 0.571451i | \(0.193619\pi\) | ||||
−0.820636 | + | 0.571451i | \(0.806381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 487.010 | 1.05186 | 0.525928 | − | 0.850529i | \(-0.323718\pi\) | ||||
0.525928 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(464\) | − | 1065.08i | − | 2.29544i | ||||||
\(465\) | −33.3564 | + | 23.8203i | −0.0717341 | + | 0.0512265i | ||||
\(466\) | −179.242 | −0.384640 | ||||||||
\(467\) | 395.720i | 0.847367i | 0.905810 | + | 0.423683i | \(0.139263\pi\) | ||||
−0.905810 | + | 0.423683i | \(0.860737\pi\) | |||||||
\(468\) | 498.037 | − | 1451.55i | 1.06418 | − | 3.10159i | ||||
\(469\) | −49.5767 | −0.105707 | ||||||||
\(470\) | 108.825i | 0.231543i | ||||||||
\(471\) | 240.113 | + | 336.238i | 0.509795 | + | 0.713882i | ||||
\(472\) | −1040.06 | −2.20352 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −610.898 | + | 436.252i | −1.28881 | + | 0.920363i | ||||
\(475\) | 406.105 | 0.854958 | ||||||||
\(476\) | − | 297.642i | − | 0.625299i | ||||||
\(477\) | −514.655 | − | 176.582i | −1.07894 | − | 0.370193i | ||||
\(478\) | −603.833 | −1.26325 | ||||||||
\(479\) | − | 283.860i | − | 0.592610i | −0.955093 | − | 0.296305i | \(-0.904246\pi\) | ||
0.955093 | − | 0.296305i | \(-0.0957545\pi\) | |||||||
\(480\) | 119.496 | + | 167.335i | 0.248951 | + | 0.348614i | ||||
\(481\) | −329.205 | −0.684418 | ||||||||
\(482\) | 1024.99i | 2.12654i | ||||||||
\(483\) | −50.1946 | + | 35.8448i | −0.103923 | + | 0.0742129i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 38.7151i | 0.0798249i | ||||||||
\(486\) | −930.682 | − | 38.0915i | −1.91498 | − | 0.0783776i | ||||
\(487\) | 185.942 | 0.381811 | 0.190906 | − | 0.981608i | \(-0.438858\pi\) | ||||
0.190906 | + | 0.981608i | \(0.438858\pi\) | |||||||
\(488\) | 1644.75i | 3.37039i | ||||||||
\(489\) | −526.166 | − | 736.807i | −1.07600 | − | 1.50676i | ||||
\(490\) | −107.776 | −0.219952 | ||||||||
\(491\) | − | 603.898i | − | 1.22993i | −0.788553 | − | 0.614967i | \(-0.789169\pi\) | ||
0.788553 | − | 0.614967i | \(-0.210831\pi\) | |||||||
\(492\) | −705.293 | + | 503.662i | −1.43352 | + | 1.02370i | ||||
\(493\) | 276.778 | 0.561417 | ||||||||
\(494\) | − | 1008.45i | − | 2.04139i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1222.88 | 2.46549 | ||||||||
\(497\) | − | 219.971i | − | 0.442597i | ||||||
\(498\) | 599.223 | + | 839.111i | 1.20326 | + | 1.68496i | ||||
\(499\) | −831.869 | −1.66707 | −0.833536 | − | 0.552465i | \(-0.813687\pi\) | ||||
−0.833536 | + | 0.552465i | \(0.813687\pi\) | |||||||
\(500\) | − | 329.403i | − | 0.658806i | ||||||
\(501\) | 342.158 | − | 244.341i | 0.682950 | − | 0.487706i | ||||
\(502\) | −1255.91 | −2.50181 | ||||||||
\(503\) | 865.650i | 1.72097i | 0.509472 | + | 0.860487i | \(0.329841\pi\) | ||||
−0.509472 | + | 0.860487i | \(0.670159\pi\) | |||||||
\(504\) | −420.970 | − | 144.438i | −0.835258 | − | 0.286583i | ||||
\(505\) | −54.8015 | −0.108518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 148.662 | + | 208.177i | 0.293220 | + | 0.410605i | ||||
\(508\) | 675.211 | 1.32916 | ||||||||
\(509\) | − | 224.906i | − | 0.441859i | −0.975290 | − | 0.220930i | \(-0.929091\pi\) | ||
0.975290 | − | 0.220930i | \(-0.0709091\pi\) | |||||||
\(510\) | −83.9095 | + | 59.9212i | −0.164529 | + | 0.117493i | ||||
\(511\) | −162.746 | −0.318485 | ||||||||
\(512\) | − | 431.622i | − | 0.843012i | ||||||
\(513\) | −426.910 | + | 127.217i | −0.832184 | + | 0.247986i | ||||
\(514\) | 23.4980 | 0.0457160 | ||||||||
\(515\) | − | 18.6597i | − | 0.0362324i | ||||||
\(516\) | −991.053 | − | 1387.80i | −1.92064 | − | 2.68954i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 152.532i | 0.294463i | ||||||||
\(519\) | 458.227 | − | 327.227i | 0.882903 | − | 0.630496i | ||||
\(520\) | −254.010 | −0.488481 | ||||||||
\(521\) | − | 685.513i | − | 1.31576i | −0.753121 | − | 0.657882i | \(-0.771453\pi\) | ||
0.753121 | − | 0.657882i | \(-0.228547\pi\) | |||||||
\(522\) | 214.582 | − | 625.406i | 0.411076 | − | 1.19810i | ||||
\(523\) | −144.428 | −0.276153 | −0.138076 | − | 0.990422i | \(-0.544092\pi\) | ||||
−0.138076 | + | 0.990422i | \(0.544092\pi\) | |||||||
\(524\) | 853.645i | 1.62909i | ||||||||
\(525\) | 82.7144 | + | 115.828i | 0.157551 | + | 0.220624i | ||||
\(526\) | −658.664 | −1.25221 | ||||||||
\(527\) | 317.785i | 0.603008i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 415.218 | 0.784912 | ||||||||
\(530\) | 143.883i | 0.271478i | ||||||||
\(531\) | −345.098 | − | 118.406i | −0.649902 | − | 0.222986i | ||||
\(532\) | −340.046 | −0.639185 | ||||||||
\(533\) | − | 430.795i | − | 0.808246i | ||||||
\(534\) | 979.246 | + | 1371.27i | 1.83379 | + | 2.56792i | ||||
\(535\) | 74.6313 | 0.139498 | ||||||||
\(536\) | − | 659.914i | − | 1.23118i | ||||||
\(537\) | 290.512 | − | 207.459i | 0.540990 | − | 0.386330i | ||||
\(538\) | 368.921 | 0.685727 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 51.1937 | + | 171.794i | 0.0948032 | + | 0.318137i | ||||
\(541\) | −175.837 | −0.325023 | −0.162511 | − | 0.986707i | \(-0.551959\pi\) | ||||
−0.162511 | + | 0.986707i | \(0.551959\pi\) | |||||||
\(542\) | 312.836i | 0.577189i | ||||||||
\(543\) | 361.923 | + | 506.812i | 0.666525 | + | 0.933356i | ||||
\(544\) | 1594.19 | 2.93050 | ||||||||
\(545\) | 94.4428i | 0.173290i | ||||||||
\(546\) | 287.625 | − | 205.398i | 0.526785 | − | 0.376186i | ||||
\(547\) | 257.468 | 0.470691 | 0.235345 | − | 0.971912i | \(-0.424378\pi\) | ||||
0.235345 | + | 0.971912i | \(0.424378\pi\) | |||||||
\(548\) | 893.463i | 1.63041i | ||||||||
\(549\) | −187.246 | + | 545.736i | −0.341068 | + | 0.994055i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 316.210i | − | 0.573884i | ||||||
\(552\) | −477.130 | − | 668.140i | −0.864366 | − | 1.21040i | ||||
\(553\) | −125.821 | −0.227525 | ||||||||
\(554\) | 614.655i | 1.10949i | ||||||||
\(555\) | 31.2945 | − | 22.3480i | 0.0563866 | − | 0.0402666i | ||||
\(556\) | −864.245 | −1.55440 | ||||||||
\(557\) | 702.773i | 1.26171i | 0.775901 | + | 0.630855i | \(0.217296\pi\) | ||||
−0.775901 | + | 0.630855i | \(0.782704\pi\) | |||||||
\(558\) | 718.064 | + | 246.373i | 1.28685 | + | 0.441529i | ||||
\(559\) | 847.673 | 1.51641 | ||||||||
\(560\) | 66.5042i | 0.118757i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1311.21 | −2.33311 | ||||||||
\(563\) | 791.940i | 1.40664i | 0.710872 | + | 0.703322i | \(0.248301\pi\) | ||||
−0.710872 | + | 0.703322i | \(0.751699\pi\) | |||||||
\(564\) | 1193.73 | − | 852.464i | 2.11655 | − | 1.51146i | ||||
\(565\) | 80.4371 | 0.142367 | ||||||||
\(566\) | 1115.79i | 1.97135i | ||||||||
\(567\) | −123.236 | − | 95.8504i | −0.217348 | − | 0.169048i | ||||
\(568\) | 2928.03 | 5.15497 | ||||||||
\(569\) | − | 422.423i | − | 0.742395i | −0.928554 | − | 0.371197i | \(-0.878947\pi\) | ||
0.928554 | − | 0.371197i | \(-0.121053\pi\) | |||||||
\(570\) | 68.4579 | + | 95.8638i | 0.120102 | + | 0.168182i | ||||
\(571\) | 637.530 | 1.11652 | 0.558258 | − | 0.829668i | \(-0.311470\pi\) | ||||
0.558258 | + | 0.829668i | \(0.311470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −900.167 | + | 642.824i | −1.57097 | + | 1.12186i | ||||
\(574\) | −199.602 | −0.347738 | ||||||||
\(575\) | 262.559i | 0.456625i | ||||||||
\(576\) | 586.687 | − | 1709.92i | 1.01855 | − | 2.96861i | ||||
\(577\) | 606.711 | 1.05149 | 0.525746 | − | 0.850641i | \(-0.323786\pi\) | ||||
0.525746 | + | 0.850641i | \(0.323786\pi\) | |||||||
\(578\) | − | 308.383i | − | 0.533534i | ||||||
\(579\) | −356.359 | − | 499.021i | −0.615473 | − | 0.861866i | ||||
\(580\) | −127.247 | −0.219391 | ||||||||
\(581\) | 172.825i | 0.297460i | ||||||||
\(582\) | 583.533 | − | 416.711i | 1.00263 | − | 0.715998i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 2166.31i | − | 3.70943i | ||||||
\(585\) | −84.2817 | − | 28.9177i | −0.144071 | − | 0.0494320i | ||||
\(586\) | −460.741 | −0.786248 | ||||||||
\(587\) | − | 950.811i | − | 1.61978i | −0.586582 | − | 0.809890i | \(-0.699527\pi\) | ||
0.586582 | − | 0.809890i | \(-0.300473\pi\) | |||||||
\(588\) | 844.246 | + | 1182.23i | 1.43579 | + | 2.01059i | ||||
\(589\) | 363.059 | 0.616398 | ||||||||
\(590\) | 96.4797i | 0.163525i | ||||||||
\(591\) | −150.062 | + | 107.162i | −0.253912 | + | 0.181323i | ||||
\(592\) | −1147.30 | −1.93800 | ||||||||
\(593\) | 590.217i | 0.995307i | 0.867376 | + | 0.497654i | \(0.165805\pi\) | ||||
−0.867376 | + | 0.497654i | \(0.834195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.2821 | −0.0290456 | ||||||||
\(596\) | 2927.98i | 4.91271i | ||||||||
\(597\) | −94.0595 | − | 131.715i | −0.157554 | − | 0.220627i | ||||
\(598\) | 651.991 | 1.09029 | ||||||||
\(599\) | 567.280i | 0.947045i | 0.880782 | + | 0.473522i | \(0.157018\pi\) | ||||
−0.880782 | + | 0.473522i | \(0.842982\pi\) | |||||||
\(600\) | −1541.78 | + | 1101.01i | −2.56963 | + | 1.83502i | ||||
\(601\) | 13.6571 | 0.0227239 | 0.0113620 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113620 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(602\) | − | 392.756i | − | 0.652418i | ||||||
\(603\) | 75.1278 | − | 218.963i | 0.124590 | − | 0.363122i | ||||
\(604\) | −46.6633 | −0.0772572 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 589.857 | + | 825.996i | 0.973362 | + | 1.36303i | ||||
\(607\) | −683.261 | −1.12564 | −0.562818 | − | 0.826581i | \(-0.690283\pi\) | ||||
−0.562818 | + | 0.826581i | \(0.690283\pi\) | |||||||
\(608\) | − | 1821.31i | − | 2.99558i | ||||||
\(609\) | 90.1881 | − | 64.4048i | 0.148092 | − | 0.105755i | ||||
\(610\) | 152.573 | 0.250119 | ||||||||
\(611\) | 729.135i | 1.19335i | ||||||||
\(612\) | 1314.58 | + | 451.043i | 2.14801 | + | 0.736999i | ||||
\(613\) | −284.867 | −0.464710 | −0.232355 | − | 0.972631i | \(-0.574643\pi\) | ||||
−0.232355 | + | 0.972631i | \(0.574643\pi\) | |||||||
\(614\) | − | 539.916i | − | 0.879341i | ||||||
\(615\) | 29.2443 | + | 40.9517i | 0.0475517 | + | 0.0665882i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1136.28i | − | 1.84162i | −0.390010 | − | 0.920811i | \(-0.627528\pi\) | ||
0.390010 | − | 0.920811i | \(-0.372472\pi\) | |||||||
\(618\) | −281.248 | + | 200.844i | −0.455095 | + | 0.324991i | ||||
\(619\) | −318.917 | −0.515213 | −0.257606 | − | 0.966250i | \(-0.582934\pi\) | ||||
−0.257606 | + | 0.966250i | \(0.582934\pi\) | |||||||
\(620\) | − | 146.099i | − | 0.235644i | ||||||
\(621\) | −82.2497 | − | 276.011i | −0.132447 | − | 0.444462i | ||||
\(622\) | 1569.02 | 2.52254 | ||||||||
\(623\) | 282.429i | 0.453337i | ||||||||
\(624\) | 1544.93 | + | 2163.42i | 2.47586 | + | 3.46702i | ||||
\(625\) | 596.236 | 0.953978 | ||||||||
\(626\) | − | 1433.27i | − | 2.28957i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1472.71 | −2.34508 | ||||||||
\(629\) | − | 298.142i | − | 0.473994i | ||||||
\(630\) | −13.3986 | + | 39.0506i | −0.0212675 | + | 0.0619850i | ||||
\(631\) | −204.174 | −0.323572 | −0.161786 | − | 0.986826i | \(-0.551725\pi\) | ||||
−0.161786 | + | 0.986826i | \(0.551725\pi\) | |||||||
\(632\) | − | 1674.81i | − | 2.65001i | ||||||
\(633\) | −268.437 | − | 375.901i | −0.424071 | − | 0.593840i | ||||
\(634\) | −677.024 | −1.06786 | ||||||||
\(635\) | − | 39.2051i | − | 0.0617403i | ||||||
\(636\) | 1578.29 | − | 1127.08i | 2.48159 | − | 1.77214i | ||||
\(637\) | −722.106 | −1.13360 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 971.533 | + | 333.340i | 1.52040 | + | 0.521659i | ||||
\(640\) | −203.884 | −0.318568 | ||||||||
\(641\) | 167.647i | 0.261540i | 0.991413 | + | 0.130770i | \(0.0417450\pi\) | ||||
−0.991413 | + | 0.130770i | \(0.958255\pi\) | |||||||
\(642\) | −803.296 | − | 1124.88i | −1.25124 | − | 1.75215i | ||||
\(643\) | 194.763 | 0.302897 | 0.151449 | − | 0.988465i | \(-0.451606\pi\) | ||||
0.151449 | + | 0.988465i | \(0.451606\pi\) | |||||||
\(644\) | − | 219.850i | − | 0.341383i | ||||||
\(645\) | −80.5806 | + | 57.5439i | −0.124931 | + | 0.0892154i | ||||
\(646\) | 913.292 | 1.41376 | ||||||||
\(647\) | 133.888i | 0.206937i | 0.994633 | + | 0.103469i | \(0.0329941\pi\) | ||||
−0.994633 | + | 0.103469i | \(0.967006\pi\) | |||||||
\(648\) | 1275.86 | − | 1640.40i | 1.96893 | − | 2.53148i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 1504.52i | − | 2.31464i | ||||||
\(651\) | 73.9468 | + | 103.550i | 0.113590 | + | 0.159063i | ||||
\(652\) | 3227.18 | 4.94967 | ||||||||
\(653\) | − | 360.838i | − | 0.552585i | −0.961074 | − | 0.276293i | \(-0.910894\pi\) | ||
0.961074 | − | 0.276293i | \(-0.0891059\pi\) | |||||||
\(654\) | 1423.49 | − | 1016.54i | 2.17659 | − | 1.55434i | ||||
\(655\) | 49.5656 | 0.0756726 | ||||||||
\(656\) | − | 1501.34i | − | 2.28863i | ||||||
\(657\) | 246.623 | − | 718.791i | 0.375377 | − | 1.09405i | ||||
\(658\) | 337.833 | 0.513424 | ||||||||
\(659\) | − | 281.019i | − | 0.426433i | −0.977005 | − | 0.213216i | \(-0.931606\pi\) | ||
0.977005 | − | 0.213216i | \(-0.0683939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −301.249 | −0.455748 | −0.227874 | − | 0.973691i | \(-0.573177\pi\) | ||||
−0.227874 | + | 0.973691i | \(0.573177\pi\) | |||||||
\(662\) | − | 374.027i | − | 0.564995i | ||||||
\(663\) | −562.198 | + | 401.475i | −0.847961 | + | 0.605543i | ||||
\(664\) | −2300.46 | −3.46456 | ||||||||
\(665\) | 19.7443i | 0.0296906i | ||||||||
\(666\) | −673.680 | − | 231.145i | −1.01153 | − | 0.347064i | ||||
\(667\) | 204.439 | 0.306506 | ||||||||
\(668\) | 1498.64i | 2.24347i | ||||||||
\(669\) | −271.512 | − | 380.207i | −0.405848 | − | 0.568322i | ||||
\(670\) | −61.2158 | −0.0913669 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 519.467 | − | 370.960i | 0.773016 | − | 0.552024i | ||||
\(673\) | −469.517 | −0.697648 | −0.348824 | − | 0.937188i | \(-0.613419\pi\) | ||||
−0.348824 | + | 0.937188i | \(0.613419\pi\) | |||||||
\(674\) | − | 651.970i | − | 0.967314i | ||||||
\(675\) | −636.914 | + | 189.797i | −0.943576 | + | 0.281180i | ||||
\(676\) | −911.805 | −1.34882 | ||||||||
\(677\) | − | 437.913i | − | 0.646843i | −0.946255 | − | 0.323421i | \(-0.895167\pi\) | ||
0.946255 | − | 0.323421i | \(-0.104833\pi\) | |||||||
\(678\) | −865.787 | − | 1212.39i | −1.27697 | − | 1.78819i | ||||
\(679\) | 120.185 | 0.177004 | ||||||||
\(680\) | − | 230.042i | − | 0.338298i | ||||||
\(681\) | 187.461 | − | 133.869i | 0.275273 | − | 0.196577i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 848.684i | 1.24258i | 0.783580 | + | 0.621291i | \(0.213392\pi\) | ||||
−0.783580 | + | 0.621291i | \(0.786608\pi\) | |||||||
\(684\) | 515.301 | − | 1501.86i | 0.753365 | − | 2.19571i | ||||
\(685\) | 51.8775 | 0.0757336 | ||||||||
\(686\) | 696.600i | 1.01545i | ||||||||
\(687\) | −73.5433 | − | 102.985i | −0.107050 | − | 0.149906i | ||||
\(688\) | 2954.18 | 4.29387 | ||||||||
\(689\) | 964.024i | 1.39916i | ||||||||
\(690\) | −61.9789 | + | 44.2601i | −0.0898245 | + | 0.0641451i | ||||
\(691\) | −1104.18 | −1.59794 | −0.798970 | − | 0.601370i | \(-0.794622\pi\) | ||||
−0.798970 | + | 0.601370i | \(0.794622\pi\) | |||||||
\(692\) | 2007.01i | 2.90031i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1660.27 | 2.39231 | ||||||||
\(695\) | 50.1810i | 0.0722029i | ||||||||
\(696\) | 857.292 | + | 1200.49i | 1.23174 | + | 1.72485i | ||||
\(697\) | 390.146 | 0.559751 | ||||||||
\(698\) | 1580.72i | 2.26464i | ||||||||
\(699\) | 114.162 | − | 81.5246i | 0.163321 | − | 0.116630i | ||||
\(700\) | −507.320 | −0.724743 | ||||||||
\(701\) | 950.887i | 1.35647i | 0.734844 | + | 0.678236i | \(0.237255\pi\) | ||||
−0.734844 | + | 0.678236i | \(0.762745\pi\) | |||||||
\(702\) | 471.306 | + | 1581.59i | 0.671376 | + | 2.25298i | ||||
\(703\) | −340.617 | −0.484520 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −49.4970 | − | 69.3122i | −0.0702085 | − | 0.0983152i | ||||
\(706\) | −446.374 | −0.632258 | ||||||||
\(707\) | 170.123i | 0.240627i | ||||||||
\(708\) | 1058.31 | − | 755.757i | 1.49479 | − | 1.06745i | ||||
\(709\) | −995.240 | −1.40372 | −0.701862 | − | 0.712313i | \(-0.747648\pi\) | ||||
−0.701862 | + | 0.712313i | \(0.747648\pi\) | |||||||
\(710\) | − | 271.613i | − | 0.382554i | ||||||
\(711\) | 190.668 | − | 555.709i | 0.268169 | − | 0.781588i | ||||
\(712\) | −3759.40 | −5.28006 | ||||||||
\(713\) | 234.729i | 0.329213i | ||||||||
\(714\) | 186.017 | + | 260.485i | 0.260528 | + | 0.364825i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1272.43i | 1.77714i | ||||||||
\(717\) | 384.589 | − | 274.641i | 0.536386 | − | 0.383042i | ||||
\(718\) | −2220.71 | −3.09291 | ||||||||
\(719\) | 1099.64i | 1.52940i | 0.644386 | + | 0.764701i | \(0.277113\pi\) | ||||
−0.644386 | + | 0.764701i | \(0.722887\pi\) | |||||||
\(720\) | −293.726 | − | 100.780i | −0.407952 | − | 0.139972i | ||||
\(721\) | −57.9264 | −0.0803417 | ||||||||
\(722\) | 340.371i | 0.471428i | ||||||||
\(723\) | −466.197 | − | 652.831i | −0.644809 | − | 0.902947i | ||||
\(724\) | −2219.82 | −3.06604 | ||||||||
\(725\) | − | 471.758i | − | 0.650701i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1427.40 | −1.96342 | −0.981708 | − | 0.190395i | \(-0.939023\pi\) | ||||
−0.981708 | + | 0.190395i | \(0.939023\pi\) | |||||||
\(728\) | 788.538i | 1.08316i | ||||||||
\(729\) | 610.088 | − | 399.041i | 0.836883 | − | 0.547381i | ||||
\(730\) | −200.954 | −0.275279 | ||||||||
\(731\) | 767.689i | 1.05019i | ||||||||
\(732\) | −1195.15 | − | 1673.61i | −1.63272 | − | 2.28635i | ||||
\(733\) | 324.830 | 0.443151 | 0.221576 | − | 0.975143i | \(-0.428880\pi\) | ||||
0.221576 | + | 0.975143i | \(0.428880\pi\) | |||||||
\(734\) | 517.651i | 0.705247i | ||||||||
\(735\) | 68.6440 | − | 49.0198i | 0.0933933 | − | 0.0666937i | ||||
\(736\) | 1177.53 | 1.59991 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 302.474 | − | 881.571i | 0.409856 | − | 1.19454i | ||||
\(739\) | 344.719 | 0.466467 | 0.233233 | − | 0.972421i | \(-0.425069\pi\) | ||||
0.233233 | + | 0.972421i | \(0.425069\pi\) | |||||||
\(740\) | 137.069i | 0.185228i | ||||||||
\(741\) | 458.671 | + | 642.292i | 0.618990 | + | 0.866791i | ||||
\(742\) | 446.665 | 0.601974 | ||||||||
\(743\) | − | 236.630i | − | 0.318479i | −0.987240 | − | 0.159239i | \(-0.949096\pi\) | ||
0.987240 | − | 0.159239i | \(-0.0509041\pi\) | |||||||
\(744\) | −1378.35 | + | 984.305i | −1.85263 | + | 1.32299i | ||||
\(745\) | 170.008 | 0.228199 | ||||||||
\(746\) | 482.920i | 0.647346i | ||||||||
\(747\) | −763.305 | − | 261.896i | −1.02183 | − | 0.350597i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 231.682i | − | 0.309322i | ||||||
\(750\) | 205.866 | + | 288.281i | 0.274488 | + | 0.384375i | ||||
\(751\) | −251.272 | −0.334583 | −0.167292 | − | 0.985907i | \(-0.553502\pi\) | ||||
−0.167292 | + | 0.985907i | \(0.553502\pi\) | |||||||
\(752\) | 2541.07i | 3.37908i | ||||||||
\(753\) | 799.904 | − | 571.225i | 1.06229 | − | 0.758598i | ||||
\(754\) | −1171.48 | −1.55368 | ||||||||
\(755\) | 2.70943i | 0.00358865i | ||||||||
\(756\) | 533.311 | − | 158.924i | 0.705438 | − | 0.210216i | ||||
\(757\) | −33.2746 | −0.0439559 | −0.0219779 | − | 0.999758i | \(-0.506996\pi\) | ||||
−0.0219779 | + | 0.999758i | \(0.506996\pi\) | |||||||
\(758\) | 1541.58i | 2.03375i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −262.815 | −0.345810 | ||||||||
\(761\) | − | 1143.98i | − | 1.50326i | −0.659586 | − | 0.751629i | \(-0.729268\pi\) | ||
0.659586 | − | 0.751629i | \(-0.270732\pi\) | |||||||
\(762\) | −590.919 | + | 421.985i | −0.775485 | + | 0.553786i | ||||
\(763\) | 293.184 | 0.384252 | ||||||||
\(764\) | − | 3942.69i | − | 5.16059i | ||||||
\(765\) | 26.1891 | − | 76.3291i | 0.0342341 | − | 0.0997766i | ||||
\(766\) | 1599.22 | 2.08775 | ||||||||
\(767\) | 646.419i | 0.842788i | ||||||||
\(768\) | 793.736 | + | 1111.49i | 1.03351 | + | 1.44726i | ||||
\(769\) | 344.520 | 0.448010 | 0.224005 | − | 0.974588i | \(-0.428087\pi\) | ||||
0.224005 | + | 0.974588i | \(0.428087\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9662 | + | 10.6876i | −0.0194114 | + | 0.0138620i | ||||
\(772\) | 2185.69 | 2.83120 | ||||||||
\(773\) | − | 1184.63i | − | 1.53250i | −0.642541 | − | 0.766252i | \(-0.722120\pi\) | ||
0.642541 | − | 0.766252i | \(-0.277880\pi\) | |||||||
\(774\) | 1734.66 | + | 595.176i | 2.24117 | + | 0.768962i | ||||
\(775\) | 541.652 | 0.698906 | ||||||||
\(776\) | 1599.79i | 2.06158i | ||||||||
\(777\) | −69.3761 | − | 97.1495i | −0.0892871 | − | 0.125032i | ||||
\(778\) | −1622.50 | −2.08548 | ||||||||
\(779\) | − | 445.729i | − | 0.572181i | ||||||
\(780\) | 258.467 | − | 184.575i | 0.331367 | − | 0.236635i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 590.471i | 0.755078i | ||||||||
\(783\) | 147.784 | + | 495.927i | 0.188740 | + | 0.633368i | ||||
\(784\) | −2516.57 | −3.20991 | ||||||||
\(785\) | 85.5106i | 0.108931i | ||||||||
\(786\) | −533.501 | − | 747.078i | −0.678754 | − | 0.950481i | ||||
\(787\) | −1199.85 | −1.52458 | −0.762292 | − | 0.647233i | \(-0.775926\pi\) | ||||
−0.762292 | + | 0.647233i | \(0.775926\pi\) | |||||||
\(788\) | − | 657.266i | − | 0.834094i | ||||||
\(789\) | 419.511 | − | 299.580i | 0.531700 | − | 0.379696i | ||||
\(790\) | −155.361 | −0.196659 | ||||||||
\(791\) | − | 249.706i | − | 0.315684i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1022.24 | 1.28908 | ||||||||
\(794\) | − | 882.294i | − | 1.11120i | ||||||
\(795\) | −65.4423 | − | 91.6409i | −0.0823174 | − | 0.115272i | ||||
\(796\) | 576.904 | 0.724754 | ||||||||
\(797\) | 1221.08i | 1.53210i | 0.642783 | + | 0.766048i | \(0.277780\pi\) | ||||
−0.642783 | + | 0.766048i | \(0.722220\pi\) | |||||||
\(798\) | 297.596 | − | 212.518i | 0.372927 | − | 0.266313i | ||||
\(799\) | −660.336 | −0.826453 | ||||||||
\(800\) | − | 2717.24i | − | 3.39655i | ||||||
\(801\) | −1247.39 | − | 427.988i | −1.55729 | − | 0.534318i | ||||
\(802\) | −1611.30 | −2.00911 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 479.524 | + | 671.492i | 0.596422 | + | 0.835189i | ||||
\(805\) | −12.7653 | −0.0158575 | ||||||||
\(806\) | − | 1345.04i | − | 1.66878i | ||||||
\(807\) | −234.971 | + | 167.796i | −0.291166 | + | 0.207926i | ||||
\(808\) | −2264.51 | −2.80261 | ||||||||
\(809\) | 985.567i | 1.21825i | 0.793073 | + | 0.609127i | \(0.208480\pi\) | ||||
−0.793073 | + | 0.609127i | \(0.791520\pi\) | |||||||
\(810\) | −152.169 | − | 118.353i | −0.187862 | − | 0.146115i | ||||
\(811\) | −312.547 | −0.385385 | −0.192692 | − | 0.981259i | \(-0.561722\pi\) | ||||
−0.192692 | + | 0.981259i | \(0.561722\pi\) | |||||||
\(812\) | 395.020i | 0.486478i | ||||||||
\(813\) | −142.287 | − | 199.249i | −0.175015 | − | 0.245079i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 187.381i | − | 0.229916i | ||||||
\(816\) | −1959.29 | + | 1399.16i | −2.40108 | + | 1.71465i | ||||
\(817\) | 877.058 | 1.07351 | ||||||||
\(818\) | − | 1659.37i | − | 2.02857i | ||||||
\(819\) | −89.7709 | + | 261.641i | −0.109610 | + | 0.319464i | ||||
\(820\) | −179.367 | −0.218740 | ||||||||
\(821\) | − | 376.986i | − | 0.459178i | −0.973288 | − | 0.229589i | \(-0.926262\pi\) | ||
0.973288 | − | 0.229589i | \(-0.0737383\pi\) | |||||||
\(822\) | −558.385 | − | 781.925i | −0.679301 | − | 0.951246i | ||||
\(823\) | −1435.09 | −1.74373 | −0.871864 | − | 0.489748i | \(-0.837089\pi\) | ||||
−0.871864 | + | 0.489748i | \(0.837089\pi\) | |||||||
\(824\) | − | 771.057i | − | 0.935749i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 299.508 | 0.362600 | ||||||||
\(827\) | 711.817i | 0.860722i | 0.902657 | + | 0.430361i | \(0.141614\pi\) | ||||
−0.902657 | + | 0.430361i | \(0.858386\pi\) | |||||||
\(828\) | 971.002 | + | 333.158i | 1.17271 | + | 0.402365i | ||||
\(829\) | 1313.36 | 1.58428 | 0.792138 | − | 0.610342i | \(-0.208968\pi\) | ||||
0.792138 | + | 0.610342i | \(0.208968\pi\) | |||||||
\(830\) | 213.399i | 0.257107i | ||||||||
\(831\) | −279.563 | − | 391.481i | −0.336418 | − | 0.471097i | ||||
\(832\) | −3202.93 | −3.84968 | ||||||||
\(833\) | − | 653.970i | − | 0.785078i | ||||||
\(834\) | 756.354 | − | 540.125i | 0.906899 | − | 0.647632i | ||||
\(835\) | 87.0161 | 0.104211 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −569.402 | + | 169.679i | −0.680289 | + | 0.202722i | ||||
\(838\) | −991.495 | −1.18317 | ||||||||
\(839\) | 1195.33i | 1.42470i | 0.701823 | + | 0.712351i | \(0.252370\pi\) | ||||
−0.701823 | + | 0.712351i | \(0.747630\pi\) | |||||||
\(840\) | −53.5296 | − | 74.9592i | −0.0637257 | − | 0.0892371i | ||||
\(841\) | 473.670 | 0.563222 | ||||||||
\(842\) | − | 2146.50i | − | 2.54929i | ||||||
\(843\) | 835.124 | − | 596.376i | 0.990657 | − | 0.707444i | ||||
\(844\) | 1646.43 | 1.95075 | ||||||||
\(845\) | 52.9425i | 0.0626539i | ||||||||
\(846\) | −511.947 | + | 1492.09i | −0.605139 | + | 1.76370i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3359.67i | 3.96187i | ||||||||
\(849\) | −507.493 | − | 710.659i | −0.597754 | − | 0.837054i | ||||
\(850\) | 1362.55 | 1.60300 | ||||||||
\(851\) | − | 220.220i | − | 0.258777i | ||||||
\(852\) | −2979.40 | + | 2127.64i | −3.49694 | + | 2.49723i | ||||
\(853\) | −280.038 | −0.328298 | −0.164149 | − | 0.986436i | \(-0.552488\pi\) | ||||
−0.164149 | + | 0.986436i | \(0.552488\pi\) | |||||||
\(854\) | − | 473.640i | − | 0.554614i | ||||||
\(855\) | −87.2034 | − | 29.9202i | −0.101992 | − | 0.0349943i | ||||
\(856\) | 3083.92 | 3.60271 | ||||||||
\(857\) | − | 1450.04i | − | 1.69200i | −0.533184 | − | 0.845999i | \(-0.679005\pi\) | ||
0.533184 | − | 0.845999i | \(-0.320995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 451.309 | 0.525389 | 0.262694 | − | 0.964879i | \(-0.415389\pi\) | ||||
0.262694 | + | 0.964879i | \(0.415389\pi\) | |||||||
\(860\) | − | 352.940i | − | 0.410395i | ||||||
\(861\) | 127.129 | − | 90.7848i | 0.147653 | − | 0.105441i | ||||
\(862\) | −526.368 | −0.610636 | ||||||||
\(863\) | 443.496i | 0.513900i | 0.966425 | + | 0.256950i | \(0.0827176\pi\) | ||||
−0.966425 | + | 0.256950i | \(0.917282\pi\) | |||||||
\(864\) | 851.206 | + | 2856.45i | 0.985192 | + | 3.30608i | ||||
\(865\) | 116.534 | 0.134722 | ||||||||
\(866\) | − | 1701.12i | − | 1.96434i | ||||||
\(867\) | 140.262 | + | 196.413i | 0.161778 | + | 0.226543i | ||||
\(868\) | −453.545 | −0.522517 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 111.362 | − | 79.5252i | 0.128002 | − | 0.0914083i | ||||
\(871\) | −410.149 | −0.470894 | ||||||||
\(872\) | 3902.57i | 4.47543i | ||||||||
\(873\) | −182.127 | + | 530.817i | −0.208622 | + | 0.608037i | ||||
\(874\) | 674.593 | 0.771846 | ||||||||
\(875\) | 59.3748i | 0.0678569i | ||||||||
\(876\) | 1574.14 | + | 2204.31i | 1.79696 | + | 2.51634i | ||||
\(877\) | 1013.08 | 1.15516 | 0.577582 | − | 0.816332i | \(-0.303996\pi\) | ||||
0.577582 | + | 0.816332i | \(0.303996\pi\) | |||||||
\(878\) | − | 3258.41i | − | 3.71118i | ||||||
\(879\) | 293.452 | − | 209.559i | 0.333847 | − | 0.238406i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 213.844i | 0.242729i | 0.992608 | + | 0.121364i | \(0.0387269\pi\) | ||||
−0.992608 | + | 0.121364i | \(0.961273\pi\) | |||||||
\(882\) | −1477.70 | − | 507.012i | −1.67540 | − | 0.574843i | ||||
\(883\) | 405.012 | 0.458678 | 0.229339 | − | 0.973347i | \(-0.426344\pi\) | ||||
0.229339 | + | 0.973347i | \(0.426344\pi\) | |||||||
\(884\) | − | 2462.40i | − | 2.78552i | ||||||
\(885\) | −43.8818 | − | 61.4491i | −0.0495840 | − | 0.0694340i | ||||
\(886\) | 1153.09 | 1.30146 | ||||||||
\(887\) | 703.939i | 0.793617i | 0.917901 | + | 0.396809i | \(0.129882\pi\) | ||||
−0.917901 | + | 0.396809i | \(0.870118\pi\) | |||||||
\(888\) | 1293.16 | − | 923.464i | 1.45626 | − | 1.03994i | ||||
\(889\) | −121.707 | −0.136903 | ||||||||
\(890\) | 348.735i | 0.391837i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1665.29 | 1.86692 | ||||||||
\(893\) | 754.411i | 0.844805i | ||||||||
\(894\) | −1829.89 | − | 2562.45i | −2.04686 | − | 2.86628i | ||||
\(895\) | 73.8816 | 0.0825492 | ||||||||
\(896\) | 632.928i | 0.706393i | ||||||||
\(897\) | −415.262 | + | 296.545i | −0.462945 | + | 0.330597i | ||||
\(898\) | −929.975 | −1.03561 | ||||||||
\(899\) | − | 421.753i | − | 0.469135i | ||||||
\(900\) | 768.785 | − | 2240.65i | 0.854206 | − | 2.48961i | ||||
\(901\) | −873.061 | −0.968991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 178.637 | + | 250.151i | 0.197826 | + | 0.277022i | ||||
\(904\) | 3323.83 | 3.67680 | ||||||||
\(905\) | 128.890i | 0.142420i | ||||||||
\(906\) | 40.8380 | − | 29.1631i | 0.0450750 | − | 0.0321888i | ||||
\(907\) | 884.283 | 0.974953 | 0.487477 | − | 0.873136i | \(-0.337917\pi\) | ||||
0.487477 | + | 0.873136i | \(0.337917\pi\) | |||||||
\(908\) | 821.072i | 0.904264i | ||||||||
\(909\) | −751.375 | − | 257.803i | −0.826595 | − | 0.283611i | ||||
\(910\) | 73.1474 | 0.0803818 | ||||||||
\(911\) | 849.732i | 0.932747i | 0.884588 | + | 0.466373i | \(0.154440\pi\) | ||||
−0.884588 | + | 0.466373i | \(0.845560\pi\) | |||||||
\(912\) | 1598.49 | + | 2238.42i | 1.75273 | + | 2.45440i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 2467.16i | − | 2.69930i | ||||||
\(915\) | −97.1754 | + | 69.3946i | −0.106203 | + | 0.0758410i | ||||
\(916\) | 451.070 | 0.492435 | ||||||||
\(917\) | − | 153.869i | − | 0.167796i | ||||||
\(918\) | −1432.36 | + | 426.835i | −1.56030 | + | 0.464962i | ||||
\(919\) | −1026.78 | −1.11728 | −0.558640 | − | 0.829410i | \(-0.688677\pi\) | ||||
−0.558640 | + | 0.829410i | \(0.688677\pi\) | |||||||
\(920\) | − | 169.918i | − | 0.184694i | ||||||
\(921\) | 245.570 | + | 343.879i | 0.266634 | + | 0.373376i | ||||
\(922\) | 2019.61 | 2.19047 | ||||||||
\(923\) | − | 1819.82i | − | 1.97164i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −508.172 | −0.549375 | ||||||||
\(926\) | − | 1866.79i | − | 2.01597i | ||||||
\(927\) | 87.7808 | − | 255.840i | 0.0946934 | − | 0.275987i | ||||
\(928\) | −2115.76 | −2.27991 | ||||||||
\(929\) | − | 322.042i | − | 0.346654i | −0.984864 | − | 0.173327i | \(-0.944548\pi\) | ||
0.984864 | − | 0.173327i | \(-0.0554518\pi\) | |||||||
\(930\) | 91.3074 | + | 127.861i | 0.0981800 | + | 0.137485i | ||||
\(931\) | −747.138 | −0.802512 | ||||||||
\(932\) | 500.023i | 0.536505i | ||||||||
\(933\) | −999.327 | + | 713.636i | −1.07109 | + | 0.764883i | ||||
\(934\) | 1516.86 | 1.62405 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3482.70 | − | 1194.94i | −3.72083 | − | 1.27665i | ||||
\(937\) | 952.845 | 1.01691 | 0.508455 | − | 0.861088i | \(-0.330217\pi\) | ||||
0.508455 | + | 0.861088i | \(0.330217\pi\) | |||||||
\(938\) | 190.036i | 0.202597i | ||||||||
\(939\) | 651.895 | + | 912.869i | 0.694244 | + | 0.972172i | ||||
\(940\) | 303.585 | 0.322962 | ||||||||
\(941\) | − | 1291.41i | − | 1.37238i | −0.727422 | − | 0.686190i | \(-0.759282\pi\) | ||
0.727422 | − | 0.686190i | \(-0.240718\pi\) | |||||||
\(942\) | 1288.86 | − | 920.396i | 1.36822 | − | 0.977066i | ||||
\(943\) | 288.177 | 0.305596 | ||||||||
\(944\) | 2252.80i | 2.38644i | ||||||||
\(945\) | −9.22765 | − | 30.9659i | −0.00976471 | − | 0.0327681i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1080.15i | − | 1.14060i | −0.821435 | − | 0.570302i | \(-0.806826\pi\) | ||
0.821435 | − | 0.570302i | \(-0.193174\pi\) | |||||||
\(948\) | 1216.99 | + | 1704.19i | 1.28375 | + | 1.79767i | ||||
\(949\) | −1346.40 | −1.41876 | ||||||||
\(950\) | − | 1556.67i | − | 1.63860i | ||||||
\(951\) | 431.205 | − | 307.931i | 0.453423 | − | 0.323797i | ||||
\(952\) | −714.134 | −0.750141 | ||||||||
\(953\) | 647.480i | 0.679412i | 0.940532 | + | 0.339706i | \(0.110328\pi\) | ||||
−0.940532 | + | 0.339706i | \(0.889672\pi\) | |||||||
\(954\) | −676.869 | + | 1972.76i | −0.709507 | + | 2.06788i | ||||
\(955\) | −228.926 | −0.239713 | ||||||||
\(956\) | 1684.48i | 1.76201i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1088.09 | −1.13579 | ||||||||
\(959\) | − | 161.046i | − | 0.167932i | ||||||
\(960\) | 304.474 | − | 217.430i | 0.317160 | − | 0.226489i | ||||
\(961\) | −476.762 | −0.496110 | ||||||||
\(962\) | 1261.90i | 1.31175i | ||||||||
\(963\) | 1023.26 | + | 351.088i | 1.06257 | + | 0.364577i | ||||
\(964\) | 2859.37 | 2.96615 | ||||||||
\(965\) | − | 126.909i | − | 0.131512i | ||||||
\(966\) | 137.399 | + | 192.405i | 0.142235 | + | 0.199177i | ||||
\(967\) | 4.41092 | 0.00456145 | 0.00228072 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228072 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −581.687 | + | 415.392i | −0.600296 | + | 0.428681i | ||||
\(970\) | 148.401 | 0.152991 | ||||||||
\(971\) | − | 1112.88i | − | 1.14612i | −0.819515 | − | 0.573058i | \(-0.805757\pi\) | ||
0.819515 | − | 0.573058i | \(-0.194243\pi\) | |||||||
\(972\) | −106.262 | + | 2596.28i | −0.109323 | + | 2.67107i | ||||
\(973\) | 155.780 | 0.160103 | ||||||||
\(974\) | − | 712.748i | − | 0.731775i | ||||||
\(975\) | 684.298 | + | 958.245i | 0.701844 | + | 0.982815i | ||||
\(976\) | 3562.57 | 3.65017 | ||||||||
\(977\) | − | 205.544i | − | 0.210383i | −0.994452 | − | 0.105191i | \(-0.966454\pi\) | ||
0.994452 | − | 0.105191i | \(-0.0335456\pi\) | |||||||
\(978\) | −2824.31 | + | 2016.88i | −2.88784 | + | 2.06225i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 300.658i | 0.306794i | ||||||||
\(981\) | −444.288 | + | 1294.89i | −0.452892 | + | 1.31997i | ||||
\(982\) | −2314.84 | −2.35728 | ||||||||
\(983\) | 578.012i | 0.588009i | 0.955804 | + | 0.294004i | \(0.0949880\pi\) | ||||
−0.955804 | + | 0.294004i | \(0.905012\pi\) | |||||||
\(984\) | 1208.44 | + | 1692.21i | 1.22809 | + | 1.71973i | ||||
\(985\) | −38.1631 | −0.0387443 | ||||||||
\(986\) | − | 1060.94i | − | 1.07600i | ||||||
\(987\) | −215.170 | + | 153.656i | −0.218004 | + | 0.155680i | ||||
\(988\) | −2813.21 | −2.84738 | ||||||||
\(989\) | 567.045i | 0.573352i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −576.755 | −0.581993 | −0.290997 | − | 0.956724i | \(-0.593987\pi\) | ||||
−0.290997 | + | 0.956724i | \(0.593987\pi\) | |||||||
\(992\) | − | 2429.22i | − | 2.44881i | ||||||
\(993\) | 170.119 | + | 238.222i | 0.171318 | + | 0.239902i | ||||
\(994\) | −843.185 | −0.848275 | ||||||||
\(995\) | − | 33.4970i | − | 0.0336654i | ||||||
\(996\) | 2340.83 | − | 1671.62i | 2.35023 | − | 1.67834i | ||||
\(997\) | 576.276 | 0.578010 | 0.289005 | − | 0.957328i | \(-0.406676\pi\) | ||||
0.289005 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(998\) | 3188.70i | 3.19509i | ||||||||
\(999\) | 534.207 | − | 159.191i | 0.534741 | − | 0.159350i |
(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 | 363.3.b.n.122.2 | yes | 12 | |
3.2 | odd | 2 | inner | 363.3.b.n.122.11 | yes | 12 | |
11.2 | odd | 10 | 363.3.h.r.323.12 | 48 | |||
11.3 | even | 5 | 363.3.h.r.251.1 | 48 | |||
11.4 | even | 5 | 363.3.h.r.269.12 | 48 | |||
11.5 | even | 5 | 363.3.h.r.245.11 | 48 | |||
11.6 | odd | 10 | 363.3.h.r.245.1 | 48 | |||
11.7 | odd | 10 | 363.3.h.r.269.2 | 48 | |||
11.8 | odd | 10 | 363.3.h.r.251.11 | 48 | |||
11.9 | even | 5 | 363.3.h.r.323.2 | 48 | |||
11.10 | odd | 2 | inner | 363.3.b.n.122.12 | yes | 12 | |
33.2 | even | 10 | 363.3.h.r.323.1 | 48 | |||
33.5 | odd | 10 | 363.3.h.r.245.2 | 48 | |||
33.8 | even | 10 | 363.3.h.r.251.2 | 48 | |||
33.14 | odd | 10 | 363.3.h.r.251.12 | 48 | |||
33.17 | even | 10 | 363.3.h.r.245.12 | 48 | |||
33.20 | odd | 10 | 363.3.h.r.323.11 | 48 | |||
33.26 | odd | 10 | 363.3.h.r.269.1 | 48 | |||
33.29 | even | 10 | 363.3.h.r.269.11 | 48 | |||
33.32 | even | 2 | inner | 363.3.b.n.122.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.n.122.1 | ✓ | 12 | 33.32 | even | 2 | inner | |
363.3.b.n.122.2 | yes | 12 | 1.1 | even | 1 | trivial | |
363.3.b.n.122.11 | yes | 12 | 3.2 | odd | 2 | inner | |
363.3.b.n.122.12 | yes | 12 | 11.10 | odd | 2 | inner | |
363.3.h.r.245.1 | 48 | 11.6 | odd | 10 | |||
363.3.h.r.245.2 | 48 | 33.5 | odd | 10 | |||
363.3.h.r.245.11 | 48 | 11.5 | even | 5 | |||
363.3.h.r.245.12 | 48 | 33.17 | even | 10 | |||
363.3.h.r.251.1 | 48 | 11.3 | even | 5 | |||
363.3.h.r.251.2 | 48 | 33.8 | even | 10 | |||
363.3.h.r.251.11 | 48 | 11.8 | odd | 10 | |||
363.3.h.r.251.12 | 48 | 33.14 | odd | 10 | |||
363.3.h.r.269.1 | 48 | 33.26 | odd | 10 | |||
363.3.h.r.269.2 | 48 | 11.7 | odd | 10 | |||
363.3.h.r.269.11 | 48 | 33.29 | even | 10 | |||
363.3.h.r.269.12 | 48 | 11.4 | even | 5 | |||
363.3.h.r.323.1 | 48 | 33.2 | even | 10 | |||
363.3.h.r.323.2 | 48 | 11.9 | even | 5 | |||
363.3.h.r.323.11 | 48 | 33.20 | odd | 10 | |||
363.3.h.r.323.12 | 48 | 11.2 | odd | 10 |