Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,4,Mod(19,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.e (of order \(9\), degree \(6\), not 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: | \(9.55830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Character | \(\chi\) | \(=\) | 162.19 |
Dual form | 162.4.e.b.145.3 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87939 | + | 0.684040i | −0.664463 | + | 0.241845i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.06418 | − | 2.57115i | 0.383022 | − | 0.321394i | ||||
\(5\) | −0.127307 | − | 0.721992i | −0.0113867 | − | 0.0645769i | 0.978585 | − | 0.205843i | \(-0.0659937\pi\) |
−0.989972 | + | 0.141266i | \(0.954883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.18538 | + | 0.994655i | 0.0640047 | + | 0.0537063i | 0.674229 | − | 0.738523i | \(-0.264476\pi\) |
−0.610224 | + | 0.792229i | \(0.708921\pi\) | |||||||
\(8\) | −4.00000 | + | 6.92820i | −0.176777 | + | 0.306186i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.733130 | + | 1.26982i | 0.0231836 | + | 0.0401552i | ||||
\(11\) | 4.18063 | − | 23.7095i | 0.114592 | − | 0.649881i | −0.872360 | − | 0.488864i | \(-0.837411\pi\) |
0.986952 | − | 0.161017i | \(-0.0514775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.9008 | + | 9.79111i | 0.573919 | + | 0.208890i | 0.612642 | − | 0.790360i | \(-0.290107\pi\) |
−0.0387227 | + | 0.999250i | \(0.512329\pi\) | |||||||
\(14\) | −2.90818 | − | 1.05849i | −0.0555173 | − | 0.0202067i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.77837 | − | 15.7569i | 0.0434120 | − | 0.246202i | ||||
\(17\) | −34.8695 | − | 60.3957i | −0.497476 | − | 0.861654i | 0.502519 | − | 0.864566i | \(-0.332407\pi\) |
−0.999996 | + | 0.00291171i | \(0.999073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.7514 | + | 25.5501i | −0.178116 | + | 0.308505i | −0.941235 | − | 0.337752i | \(-0.890333\pi\) |
0.763119 | + | 0.646257i | \(0.223667\pi\) | |||||||
\(20\) | −2.24644 | − | 1.88499i | −0.0251160 | − | 0.0210748i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.36126 | + | 47.4191i | 0.0810285 | + | 0.459536i | ||||
\(23\) | 125.729 | − | 105.499i | 1.13984 | − | 0.956441i | 0.140409 | − | 0.990094i | \(-0.455158\pi\) |
0.999434 | + | 0.0336525i | \(0.0107139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 116.957 | − | 42.5687i | 0.935652 | − | 0.340550i | ||||
\(26\) | −57.2546 | −0.431867 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.18963 | 0.0417761 | ||||||||
\(29\) | 197.138 | − | 71.7522i | 1.26233 | − | 0.459450i | 0.377779 | − | 0.925896i | \(-0.376688\pi\) |
0.884550 | + | 0.466446i | \(0.154466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 83.3328 | − | 69.9245i | 0.482807 | − | 0.405123i | −0.368633 | − | 0.929575i | \(-0.620174\pi\) |
0.851440 | + | 0.524452i | \(0.175730\pi\) | |||||||
\(32\) | 5.55674 | + | 31.5138i | 0.0306970 | + | 0.174091i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 106.846 | + | 89.6547i | 0.538941 | + | 0.452225i | ||||
\(35\) | 0.567225 | − | 0.982463i | 0.00273939 | − | 0.00474476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63.3079 | + | 109.652i | 0.281291 | + | 0.487210i | 0.971703 | − | 0.236206i | \(-0.0759042\pi\) |
−0.690412 | + | 0.723416i | \(0.742571\pi\) | |||||||
\(38\) | 10.2462 | − | 58.1091i | 0.0437409 | − | 0.248067i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.51133 | + | 2.00596i | 0.0217855 | + | 0.00792926i | ||||
\(41\) | 95.0553 | + | 34.5973i | 0.362077 | + | 0.131785i | 0.516651 | − | 0.856196i | \(-0.327178\pi\) |
−0.154574 | + | 0.987981i | \(0.549401\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 85.0002 | − | 482.060i | 0.301451 | − | 1.70962i | −0.338304 | − | 0.941037i | \(-0.609853\pi\) |
0.639755 | − | 0.768579i | \(-0.279036\pi\) | |||||||
\(44\) | −48.1506 | − | 83.3993i | −0.164977 | − | 0.285748i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −164.128 | + | 284.278i | −0.526073 | + | 0.911185i | ||||
\(47\) | 223.532 | + | 187.565i | 0.693733 | + | 0.582111i | 0.919983 | − | 0.391958i | \(-0.128202\pi\) |
−0.226250 | + | 0.974069i | \(0.572647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −59.1455 | − | 335.431i | −0.172436 | − | 0.977933i | ||||
\(50\) | −190.688 | + | 160.006i | −0.539346 | + | 0.452565i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 107.603 | − | 39.1644i | 0.286960 | − | 0.104445i | ||||
\(53\) | −523.625 | −1.35708 | −0.678542 | − | 0.734562i | \(-0.737388\pi\) | ||||
−0.678542 | + | 0.734562i | \(0.737388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.6503 | −0.0432722 | ||||||||
\(56\) | −11.6327 | + | 4.23396i | −0.0277587 | + | 0.0101033i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −321.416 | + | 269.700i | −0.727655 | + | 0.610575i | ||||
\(59\) | 100.933 | + | 572.420i | 0.222718 | + | 1.26310i | 0.867000 | + | 0.498309i | \(0.166045\pi\) |
−0.644282 | + | 0.764788i | \(0.722843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 104.632 | + | 87.7968i | 0.219619 | + | 0.184282i | 0.745959 | − | 0.665992i | \(-0.231992\pi\) |
−0.526340 | + | 0.850274i | \(0.676436\pi\) | |||||||
\(62\) | −108.783 | + | 188.418i | −0.222830 | + | 0.385954i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32.0000 | − | 55.4256i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 3.64444 | − | 20.6687i | 0.00695442 | − | 0.0394405i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −822.330 | − | 299.304i | −1.49946 | − | 0.545758i | −0.543537 | − | 0.839385i | \(-0.682915\pi\) |
−0.955920 | + | 0.293627i | \(0.905138\pi\) | |||||||
\(68\) | −262.133 | − | 95.4086i | −0.467475 | − | 0.170147i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.393991 | + | 2.23443i | −0.000672727 | + | 0.00381522i | ||||
\(71\) | −265.726 | − | 460.252i | −0.444168 | − | 0.769322i | 0.553826 | − | 0.832633i | \(-0.313167\pi\) |
−0.997994 | + | 0.0633110i | \(0.979834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −593.378 | + | 1027.76i | −0.951364 | + | 1.64781i | −0.208888 | + | 0.977940i | \(0.566984\pi\) |
−0.742477 | + | 0.669872i | \(0.766349\pi\) | |||||||
\(74\) | −193.987 | − | 162.774i | −0.304736 | − | 0.255704i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.4924 | + | 116.218i | 0.0309295 | + | 0.175410i | ||||
\(77\) | 28.5385 | − | 23.9466i | 0.0422371 | − | 0.0354412i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −200.068 | + | 72.8188i | −0.284929 | + | 0.103706i | −0.480531 | − | 0.876978i | \(-0.659556\pi\) |
0.195602 | + | 0.980683i | \(0.437334\pi\) | |||||||
\(80\) | −11.7301 | −0.0163933 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −202.311 | −0.272458 | ||||||||
\(83\) | 506.381 | − | 184.308i | 0.669670 | − | 0.243740i | 0.0152640 | − | 0.999883i | \(-0.495141\pi\) |
0.654406 | + | 0.756144i | \(0.272919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −39.1661 | + | 32.8643i | −0.0499784 | + | 0.0419368i | ||||
\(86\) | 170.000 | + | 964.120i | 0.213158 | + | 1.20888i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 147.542 | + | 123.802i | 0.178728 | + | 0.149970i | ||||
\(89\) | −173.475 | + | 300.468i | −0.206611 | + | 0.357860i | −0.950645 | − | 0.310282i | \(-0.899577\pi\) |
0.744034 | + | 0.668142i | \(0.232910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.1490 | + | 38.3633i | 0.0255148 | + | 0.0441930i | ||||
\(92\) | 114.002 | − | 646.538i | 0.129191 | − | 0.732676i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −548.405 | − | 199.603i | −0.601741 | − | 0.219016i | ||||
\(95\) | 20.3249 | + | 7.39767i | 0.0219505 | + | 0.00798932i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −83.7836 | + | 475.160i | −0.0877004 | + | 0.497373i | 0.909041 | + | 0.416707i | \(0.136816\pi\) |
−0.996741 | + | 0.0806663i | \(0.974295\pi\) | |||||||
\(98\) | 340.606 | + | 589.946i | 0.351085 | + | 0.608097i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 248.925 | − | 431.151i | 0.248925 | − | 0.431151i | ||||
\(101\) | −279.180 | − | 234.260i | −0.275044 | − | 0.230789i | 0.494823 | − | 0.868994i | \(-0.335233\pi\) |
−0.769867 | + | 0.638205i | \(0.779677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −212.306 | − | 1204.05i | −0.203099 | − | 1.15183i | −0.900404 | − | 0.435055i | \(-0.856729\pi\) |
0.697305 | − | 0.716775i | \(-0.254382\pi\) | |||||||
\(104\) | −175.438 | + | 147.210i | −0.165415 | + | 0.138799i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 984.093 | − | 358.181i | 0.901732 | − | 0.328203i | ||||
\(107\) | −762.846 | −0.689226 | −0.344613 | − | 0.938745i | \(-0.611990\pi\) | ||||
−0.344613 | + | 0.938745i | \(0.611990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2087.75 | 1.83459 | 0.917296 | − | 0.398206i | \(-0.130367\pi\) | ||||
0.917296 | + | 0.398206i | \(0.130367\pi\) | |||||||
\(110\) | 33.1718 | − | 12.0735i | 0.0287527 | − | 0.0104651i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.9661 | − | 15.9145i | 0.0160012 | − | 0.0134266i | ||||
\(113\) | 234.912 | + | 1332.25i | 0.195563 | + | 1.10909i | 0.911614 | + | 0.411046i | \(0.134837\pi\) |
−0.716051 | + | 0.698048i | \(0.754052\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −92.1759 | − | 77.3448i | −0.0747430 | − | 0.0627168i | ||||
\(116\) | 419.579 | − | 726.732i | 0.335836 | − | 0.581684i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −581.250 | − | 1006.76i | −0.453461 | − | 0.785418i | ||||
\(119\) | 18.7392 | − | 106.275i | 0.0144355 | − | 0.0818675i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 706.066 | + | 256.987i | 0.530478 | + | 0.193078i | ||||
\(122\) | −256.701 | − | 93.4314i | −0.190497 | − | 0.0693351i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 75.5600 | − | 428.522i | 0.0547217 | − | 0.310342i | ||||
\(125\) | −91.4442 | − | 158.386i | −0.0654321 | − | 0.113332i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −500.766 | + | 867.353i | −0.349888 | + | 0.606025i | −0.986229 | − | 0.165383i | \(-0.947114\pi\) |
0.636341 | + | 0.771408i | \(0.280447\pi\) | |||||||
\(128\) | 98.0537 | + | 82.2768i | 0.0677094 | + | 0.0568149i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.28889 | + | 41.3373i | 0.00491752 | + | 0.0278886i | ||||
\(131\) | 1481.61 | − | 1243.22i | 0.988157 | − | 0.829162i | 0.00285684 | − | 0.999996i | \(-0.499091\pi\) |
0.985300 | + | 0.170834i | \(0.0546462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −42.8996 | + | 15.6142i | −0.0279689 | + | 0.0101799i | ||||
\(134\) | 1750.21 | 1.12832 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 557.912 | 0.351769 | ||||||||
\(137\) | −208.769 | + | 75.9858i | −0.130192 | + | 0.0473862i | −0.406295 | − | 0.913742i | \(-0.633179\pi\) |
0.276102 | + | 0.961128i | \(0.410957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 741.480 | − | 622.175i | 0.452457 | − | 0.379656i | −0.387890 | − | 0.921706i | \(-0.626796\pi\) |
0.840347 | + | 0.542049i | \(0.182351\pi\) | |||||||
\(140\) | −0.787981 | − | 4.46886i | −0.000475690 | − | 0.00269777i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 814.233 | + | 683.223i | 0.481190 | + | 0.403766i | ||||
\(143\) | 344.605 | − | 596.874i | 0.201520 | − | 0.349043i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −76.9015 | − | 133.197i | −0.0440436 | − | 0.0762857i | ||||
\(146\) | 412.156 | − | 2337.45i | 0.233632 | − | 1.32499i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 475.920 | + | 173.221i | 0.264327 | + | 0.0962071i | ||||
\(149\) | −1418.44 | − | 516.269i | −0.779886 | − | 0.283855i | −0.0787607 | − | 0.996894i | \(-0.525096\pi\) |
−0.701125 | + | 0.713038i | \(0.747319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −272.728 | + | 1546.72i | −0.146982 | + | 0.833578i | 0.818772 | + | 0.574119i | \(0.194655\pi\) |
−0.965754 | + | 0.259459i | \(0.916456\pi\) | |||||||
\(152\) | −118.011 | − | 204.401i | −0.0629734 | − | 0.109073i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −37.2543 | + | 64.5264i | −0.0194938 | + | 0.0337642i | ||||
\(155\) | −61.0938 | − | 51.2638i | −0.0316592 | − | 0.0265652i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 234.882 | + | 1332.08i | 0.119399 | + | 0.677145i | 0.984478 | + | 0.175509i | \(0.0561571\pi\) |
−0.865079 | + | 0.501636i | \(0.832732\pi\) | |||||||
\(158\) | 326.194 | − | 273.709i | 0.164244 | − | 0.137817i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 22.0453 | − | 8.02385i | 0.0108927 | − | 0.00396463i | ||||
\(161\) | 253.973 | 0.124322 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2676.86 | 1.28630 | 0.643152 | − | 0.765739i | \(-0.277626\pi\) | ||||
0.643152 | + | 0.765739i | \(0.277626\pi\) | |||||||
\(164\) | 380.221 | − | 138.389i | 0.181038 | − | 0.0658926i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −825.612 | + | 692.771i | −0.386024 | + | 0.323912i | ||||
\(167\) | −494.206 | − | 2802.78i | −0.228999 | − | 1.29872i | −0.854891 | − | 0.518807i | \(-0.826376\pi\) |
0.625893 | − | 0.779909i | \(-0.284735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1055.21 | − | 885.426i | −0.480296 | − | 0.403016i | ||||
\(170\) | 51.1277 | − | 88.5558i | 0.0230666 | − | 0.0399525i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −978.993 | − | 1695.67i | −0.433997 | − | 0.751705i | ||||
\(173\) | −740.549 | + | 4199.86i | −0.325450 | + | 1.84572i | 0.181042 | + | 0.983475i | \(0.442053\pi\) |
−0.506493 | + | 0.862244i | \(0.669058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 180.979 | + | 65.8711i | 0.0781758 | + | 0.0284537i | ||||
\(176\) | −361.974 | − | 131.748i | −0.155027 | − | 0.0564254i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 120.495 | − | 683.359i | 0.0507385 | − | 0.287752i | ||||
\(179\) | −771.476 | − | 1336.24i | −0.322139 | − | 0.557960i | 0.658791 | − | 0.752326i | \(-0.271068\pi\) |
−0.980929 | + | 0.194366i | \(0.937735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1650.55 | + | 2858.83i | −0.677814 | + | 1.17401i | 0.297824 | + | 0.954621i | \(0.403739\pi\) |
−0.975638 | + | 0.219387i | \(0.929594\pi\) | |||||||
\(182\) | −67.8686 | − | 56.9485i | −0.0276415 | − | 0.0231940i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 228.004 | + | 1293.08i | 0.0913516 | + | 0.518080i | ||||
\(185\) | 71.1087 | − | 59.6673i | 0.0282595 | − | 0.0237126i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1577.73 | + | 574.248i | −0.616980 | + | 0.224562i | ||||
\(188\) | 1167.20 | 0.452802 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −43.2587 | −0.0165175 | ||||||||
\(191\) | −987.903 | + | 359.567i | −0.374252 | + | 0.136217i | −0.522296 | − | 0.852764i | \(-0.674924\pi\) |
0.148044 | + | 0.988981i | \(0.452702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 999.507 | − | 838.686i | 0.372778 | − | 0.312798i | −0.437082 | − | 0.899422i | \(-0.643988\pi\) |
0.809859 | + | 0.586624i | \(0.199543\pi\) | |||||||
\(194\) | −167.567 | − | 950.321i | −0.0620135 | − | 0.351696i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1043.68 | − | 875.748i | −0.380348 | − | 0.319150i | ||||
\(197\) | −1223.38 | + | 2118.95i | −0.442447 | + | 0.766341i | −0.997870 | − | 0.0652268i | \(-0.979223\pi\) |
0.555423 | + | 0.831568i | \(0.312556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2315.78 | − | 4011.05i | −0.824931 | − | 1.42882i | −0.901972 | − | 0.431794i | \(-0.857881\pi\) |
0.0770413 | − | 0.997028i | \(-0.475453\pi\) | |||||||
\(200\) | −172.902 | + | 980.573i | −0.0611299 | + | 0.346685i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 684.929 | + | 249.294i | 0.238572 | + | 0.0868329i | ||||
\(203\) | 305.052 | + | 111.030i | 0.105470 | + | 0.0383881i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.8778 | − | 73.0336i | 0.00438744 | − | 0.0248824i | ||||
\(206\) | 1222.62 | + | 2117.65i | 0.413516 | + | 0.716230i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 229.018 | − | 396.671i | 0.0763440 | − | 0.132232i | ||||
\(209\) | 544.112 | + | 456.564i | 0.180081 | + | 0.151106i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 214.649 | + | 1217.34i | 0.0700335 | + | 0.397180i | 0.999594 | + | 0.0285090i | \(0.00907592\pi\) |
−0.929560 | + | 0.368671i | \(0.879813\pi\) | |||||||
\(212\) | −1604.48 | + | 1346.32i | −0.519793 | + | 0.436158i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1433.68 | − | 521.818i | 0.457965 | − | 0.166686i | ||||
\(215\) | −358.865 | −0.113834 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 168.332 | 0.0526596 | ||||||||
\(218\) | −3923.69 | + | 1428.11i | −1.21902 | + | 0.443687i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −54.0837 | + | 45.3816i | −0.0165742 | + | 0.0139074i | ||||
\(221\) | −346.678 | − | 1966.11i | −0.105521 | − | 0.598438i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3019.42 | − | 2533.59i | −0.906705 | − | 0.760816i | 0.0647843 | − | 0.997899i | \(-0.479364\pi\) |
−0.971489 | + | 0.237083i | \(0.923809\pi\) | |||||||
\(224\) | −24.7585 | + | 42.8830i | −0.00738504 | + | 0.0127913i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1352.80 | − | 2343.12i | −0.398173 | − | 0.689656i | ||||
\(227\) | −712.882 | + | 4042.96i | −0.208439 | + | 1.18212i | 0.683496 | + | 0.729954i | \(0.260458\pi\) |
−0.891935 | + | 0.452163i | \(0.850653\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4707.41 | + | 1713.36i | 1.35840 | + | 0.494419i | 0.915560 | − | 0.402180i | \(-0.131748\pi\) |
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(230\) | 226.141 | + | 82.3086i | 0.0648317 | + | 0.0235968i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −291.436 | + | 1652.82i | −0.0824730 | + | 0.467728i | ||||
\(233\) | 2225.37 | + | 3854.45i | 0.625703 | + | 1.08375i | 0.988405 | + | 0.151843i | \(0.0485210\pi\) |
−0.362702 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 106.964 | − | 185.266i | 0.0296917 | − | 0.0514275i | ||||
\(236\) | 1781.05 | + | 1494.48i | 0.491258 | + | 0.412214i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 37.4784 | + | 212.550i | 0.0102074 | + | 0.0578891i | ||||
\(239\) | 3305.93 | − | 2774.01i | 0.894740 | − | 0.750776i | −0.0744150 | − | 0.997227i | \(-0.523709\pi\) |
0.969155 | + | 0.246451i | \(0.0792645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4277.35 | + | 1556.83i | −1.14327 | + | 0.416117i | −0.843094 | − | 0.537766i | \(-0.819268\pi\) |
−0.300178 | + | 0.953883i | \(0.597046\pi\) | |||||||
\(242\) | −1502.76 | −0.399178 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 546.350 | 0.143346 | ||||||||
\(245\) | −234.649 | + | 85.4052i | −0.0611884 | + | 0.0222708i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −646.989 | + | 542.888i | −0.166668 | + | 0.139851i | ||||
\(248\) | 151.120 | + | 857.045i | 0.0386941 | + | 0.219445i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 280.201 | + | 235.117i | 0.0708859 | + | 0.0594804i | ||||
\(251\) | 1279.99 | − | 2217.00i | 0.321880 | − | 0.557513i | −0.658996 | − | 0.752147i | \(-0.729018\pi\) |
0.980876 | + | 0.194634i | \(0.0623518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1975.71 | − | 3422.04i | −0.490957 | − | 0.850362i | ||||
\(254\) | 347.829 | − | 1972.63i | 0.0859241 | − | 0.487300i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −240.561 | − | 87.5572i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | 664.783 | + | 241.961i | 0.161354 | + | 0.0587281i | 0.421434 | − | 0.906859i | \(-0.361527\pi\) |
−0.260080 | + | 0.965587i | \(0.583749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.0222 | + | 192.950i | −0.00816231 | + | 0.0462908i | ||||
\(260\) | −41.9750 | − | 72.7029i | −0.0100122 | − | 0.0173417i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1934.10 | + | 3349.96i | −0.456065 | + | 0.789928i | ||||
\(263\) | −1392.56 | − | 1168.50i | −0.326498 | − | 0.273965i | 0.464773 | − | 0.885430i | \(-0.346136\pi\) |
−0.791271 | + | 0.611465i | \(0.790580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 66.6609 | + | 378.053i | 0.0154526 | + | 0.0876363i | ||||
\(266\) | 69.9442 | − | 58.6901i | 0.0161224 | − | 0.0135283i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3289.32 | + | 1197.22i | −0.749729 | + | 0.272879i | ||||
\(269\) | 2704.39 | 0.612972 | 0.306486 | − | 0.951875i | \(-0.400847\pi\) | ||||
0.306486 | + | 0.951875i | \(0.400847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3407.25 | 0.763747 | 0.381874 | − | 0.924215i | \(-0.375279\pi\) | ||||
0.381874 | + | 0.924215i | \(0.375279\pi\) | |||||||
\(272\) | −1048.53 | + | 381.634i | −0.233737 | + | 0.0850735i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 340.381 | − | 285.613i | 0.0750480 | − | 0.0629727i | ||||
\(275\) | −520.332 | − | 2950.95i | −0.114099 | − | 0.647087i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1318.55 | + | 1106.40i | 0.286008 | + | 0.239989i | 0.774492 | − | 0.632584i | \(-0.218006\pi\) |
−0.488484 | + | 0.872573i | \(0.662450\pi\) | |||||||
\(278\) | −967.933 | + | 1676.51i | −0.208823 | + | 0.361692i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.53780 | + | 7.85971i | 0.000968520 | + | 0.00167753i | ||||
\(281\) | 32.4048 | − | 183.777i | 0.00687939 | − | 0.0390149i | −0.981175 | − | 0.193122i | \(-0.938139\pi\) |
0.988054 | + | 0.154107i | \(0.0492499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2224.17 | − | 809.532i | −0.467184 | − | 0.170041i | 0.0976921 | − | 0.995217i | \(-0.468854\pi\) |
−0.564876 | + | 0.825175i | \(0.691076\pi\) | |||||||
\(284\) | −1997.61 | − | 727.070i | −0.417381 | − | 0.151914i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −239.360 | + | 1357.48i | −0.0494884 | + | 0.280662i | ||||
\(287\) | 78.2646 | + | 135.558i | 0.0160969 | + | 0.0278807i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.7357 | − | 42.8434i | 0.00503474 | − | 0.00872042i | ||||
\(290\) | 235.640 | + | 197.725i | 0.0477146 | + | 0.0400373i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 824.312 | + | 4674.90i | 0.165203 | + | 0.936911i | ||||
\(293\) | −4350.54 | + | 3650.54i | −0.867445 | + | 0.727873i | −0.963558 | − | 0.267498i | \(-0.913803\pi\) |
0.0961136 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 400.433 | − | 145.746i | 0.0790309 | − | 0.0287649i | ||||
\(296\) | −1012.93 | −0.198903 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3018.94 | 0.586854 | ||||||||
\(299\) | 4415.18 | − | 1606.99i | 0.853968 | − | 0.310819i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 580.241 | − | 486.880i | 0.111111 | − | 0.0932336i | ||||
\(302\) | −545.457 | − | 3093.44i | −0.103932 | − | 0.589428i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 361.607 | + | 303.424i | 0.0682223 | + | 0.0572453i | ||||
\(305\) | 50.0682 | − | 86.7206i | 0.00939966 | − | 0.0162807i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2881.18 | − | 4990.36i | −0.535628 | − | 0.927735i | −0.999133 | − | 0.0416406i | \(-0.986742\pi\) |
0.463505 | − | 0.886095i | \(-0.346592\pi\) | |||||||
\(308\) | 25.8766 | − | 146.753i | 0.00478719 | − | 0.0271495i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 149.885 | + | 54.5537i | 0.0274610 | + | 0.00999498i | ||||
\(311\) | 3837.77 | + | 1396.84i | 0.699743 | + | 0.254686i | 0.667301 | − | 0.744788i | \(-0.267449\pi\) |
0.0324420 | + | 0.999474i | \(0.489672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 742.685 | − | 4211.98i | 0.134118 | − | 0.760623i | −0.841351 | − | 0.540489i | \(-0.818239\pi\) |
0.975470 | − | 0.220134i | \(-0.0706495\pi\) | |||||||
\(314\) | −1352.63 | − | 2342.83i | −0.243100 | − | 0.421062i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −425.816 | + | 737.534i | −0.0758038 | + | 0.131296i | ||||
\(317\) | −5951.52 | − | 4993.92i | −1.05448 | − | 0.884816i | −0.0609245 | − | 0.998142i | \(-0.519405\pi\) |
−0.993558 | + | 0.113327i | \(0.963849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −877.053 | − | 4974.01i | −0.153936 | − | 0.873013i | ||||
\(320\) | −35.9430 | + | 30.1598i | −0.00627899 | + | 0.00526870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −477.313 | + | 173.728i | −0.0826075 | + | 0.0300667i | ||||
\(323\) | 2057.49 | 0.354433 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3563.02 | 0.608126 | ||||||||
\(326\) | −5030.84 | + | 1831.08i | −0.854701 | + | 0.311086i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −619.918 | + | 520.173i | −0.104358 | + | 0.0875664i | ||||
\(329\) | 78.4080 | + | 444.674i | 0.0131391 | + | 0.0745157i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5920.82 | + | 4968.15i | 0.983195 | + | 0.824998i | 0.984568 | − | 0.175001i | \(-0.0559928\pi\) |
−0.00137364 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(332\) | 1077.76 | − | 1866.73i | 0.178162 | − | 0.308585i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2846.02 | + | 4929.45i | 0.466249 | + | 0.807567i | ||||
\(335\) | −111.407 | + | 631.819i | −0.0181696 | + | 0.103045i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −336.804 | − | 122.587i | −0.0544418 | − | 0.0198152i | 0.314656 | − | 0.949206i | \(-0.398111\pi\) |
−0.369097 | + | 0.929391i | \(0.620333\pi\) | |||||||
\(338\) | 2588.81 | + | 942.251i | 0.416606 | + | 0.151632i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −35.5130 | + | 201.404i | −0.00566459 | + | 0.0321255i | ||||
\(341\) | −1309.49 | − | 2268.11i | −0.207956 | − | 0.360191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 528.908 | − | 916.096i | 0.0832605 | − | 0.144211i | ||||
\(344\) | 2999.81 | + | 2517.14i | 0.470171 | + | 0.394521i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1481.10 | − | 8399.72i | −0.230128 | − | 1.30512i | ||||
\(347\) | −4662.23 | + | 3912.07i | −0.721272 | + | 0.605219i | −0.927737 | − | 0.373235i | \(-0.878249\pi\) |
0.206465 | + | 0.978454i | \(0.433804\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8660.80 | − | 3152.27i | 1.32837 | − | 0.483488i | 0.422241 | − | 0.906484i | \(-0.361244\pi\) |
0.906132 | + | 0.422995i | \(0.139021\pi\) | |||||||
\(350\) | −385.189 | −0.0588263 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 770.410 | 0.116656 | ||||||||
\(353\) | 8601.41 | − | 3130.66i | 1.29690 | − | 0.472034i | 0.400916 | − | 0.916115i | \(-0.368692\pi\) |
0.895987 | + | 0.444081i | \(0.146470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −298.469 | + | 250.445i | −0.0446228 | + | 0.0374430i | ||||
\(356\) | 240.989 | + | 1366.72i | 0.0358776 | + | 0.203472i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2363.94 | + | 1983.58i | 0.348989 | + | 0.292836i | ||||
\(359\) | 2699.19 | − | 4675.13i | 0.396818 | − | 0.687309i | −0.596514 | − | 0.802603i | \(-0.703448\pi\) |
0.993331 | + | 0.115294i | \(0.0367812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2994.29 | + | 5186.27i | 0.436550 | + | 0.756126i | ||||
\(362\) | 1146.46 | − | 6501.89i | 0.166455 | − | 0.944011i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 166.506 | + | 60.6034i | 0.0239761 | + | 0.00872659i | ||||
\(365\) | 817.575 | + | 297.573i | 0.117243 | + | 0.0426731i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −83.3632 | + | 472.776i | −0.0118570 | + | 0.0672445i | −0.990162 | − | 0.139925i | \(-0.955314\pi\) |
0.978305 | + | 0.207169i | \(0.0664251\pi\) | |||||||
\(368\) | −1313.02 | − | 2274.22i | −0.185995 | − | 0.322152i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −92.8258 | + | 160.779i | −0.0130427 | + | 0.0225905i | ||||
\(371\) | −620.696 | − | 520.826i | −0.0868597 | − | 0.0728839i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 580.895 | + | 3294.42i | 0.0806369 | + | 0.457315i | 0.998213 | + | 0.0597548i | \(0.0190319\pi\) |
−0.917576 | + | 0.397560i | \(0.869857\pi\) | |||||||
\(374\) | 2572.36 | − | 2158.46i | 0.355651 | − | 0.298427i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2193.62 | + | 798.412i | −0.300870 | + | 0.109508i | ||||
\(377\) | 6005.70 | 0.820449 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6504.31 | 0.881541 | 0.440770 | − | 0.897620i | \(-0.354705\pi\) | ||||
0.440770 | + | 0.897620i | \(0.354705\pi\) | |||||||
\(380\) | 81.2998 | − | 29.5907i | 0.0109752 | − | 0.00399466i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1610.69 | − | 1351.53i | 0.215733 | − | 0.181022i | ||||
\(383\) | 484.154 | + | 2745.77i | 0.0645930 | + | 0.366325i | 0.999921 | + | 0.0125441i | \(0.00399302\pi\) |
−0.935328 | + | 0.353781i | \(0.884896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.9224 | − | 17.5560i | −0.00276962 | − | 0.00232399i | ||||
\(386\) | −1304.76 | + | 2259.92i | −0.172049 | + | 0.297997i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 964.981 | + | 1671.40i | 0.126262 | + | 0.218691i | ||||
\(389\) | 2374.56 | − | 13466.8i | 0.309498 | − | 1.75525i | −0.292039 | − | 0.956407i | \(-0.594334\pi\) |
0.601537 | − | 0.798845i | \(-0.294555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10755.8 | − | 3914.80i | −1.39117 | − | 0.506343i | ||||
\(392\) | 2560.52 | + | 931.952i | 0.329912 | + | 0.120078i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 849.750 | − | 4819.17i | 0.108654 | − | 0.616209i | ||||
\(395\) | 78.0445 | + | 135.177i | 0.00994138 | + | 0.0172190i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5323.27 | + | 9220.17i | −0.672965 | + | 1.16561i | 0.304094 | + | 0.952642i | \(0.401646\pi\) |
−0.977059 | + | 0.212968i | \(0.931687\pi\) | |||||||
\(398\) | 7095.96 | + | 5954.22i | 0.893689 | + | 0.749894i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −345.803 | − | 1961.15i | −0.0432254 | − | 0.245143i | ||||
\(401\) | −7854.20 | + | 6590.46i | −0.978105 | + | 0.820728i | −0.983802 | − | 0.179256i | \(-0.942631\pi\) |
0.00569738 | + | 0.999984i | \(0.498186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2926.36 | − | 1065.11i | 0.361718 | − | 0.131655i | ||||
\(404\) | −1457.77 | −0.179522 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −649.260 | −0.0793651 | ||||||||
\(407\) | 2864.48 | − | 1042.58i | 0.348862 | − | 0.126975i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2748.25 | + | 2306.06i | −0.332255 | + | 0.278795i | −0.793618 | − | 0.608416i | \(-0.791805\pi\) |
0.461363 | + | 0.887212i | \(0.347361\pi\) | |||||||
\(410\) | 25.7556 | + | 146.067i | 0.00310239 | + | 0.0175945i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3746.34 | − | 3143.55i | −0.447982 | − | 0.375902i | ||||
\(413\) | −449.716 | + | 778.931i | −0.0535813 | + | 0.0928055i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −197.534 | − | 342.140i | −0.0233653 | − | 0.0404698i | ||||
\(416\) | −159.074 | + | 902.156i | −0.0187482 | + | 0.106327i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1334.90 | − | 485.865i | −0.156202 | − | 0.0568528i | ||||
\(419\) | 7085.05 | + | 2578.75i | 0.826079 | + | 0.300668i | 0.720249 | − | 0.693716i | \(-0.244028\pi\) |
0.105830 | + | 0.994384i | \(0.466250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −64.4943 | + | 365.765i | −0.00746617 | + | 0.0423428i | −0.988313 | − | 0.152437i | \(-0.951288\pi\) |
0.980847 | + | 0.194779i | \(0.0623991\pi\) | |||||||
\(422\) | −1236.12 | − | 2141.02i | −0.142591 | − | 0.246974i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2094.50 | − | 3627.78i | 0.239901 | − | 0.415520i | ||||
\(425\) | −6649.18 | − | 5579.33i | −0.758901 | − | 0.636793i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.7017 | + | 208.146i | 0.00415953 | + | 0.0235899i | ||||
\(428\) | −2337.50 | + | 1961.39i | −0.263989 | + | 0.221513i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 674.445 | − | 245.478i | 0.0756387 | − | 0.0275302i | ||||
\(431\) | −15830.9 | −1.76925 | −0.884624 | − | 0.466306i | \(-0.845585\pi\) | ||||
−0.884624 | + | 0.466306i | \(0.845585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15832.0 | −1.75714 | −0.878568 | − | 0.477618i | \(-0.841500\pi\) | ||||
−0.878568 | + | 0.477618i | \(0.841500\pi\) | |||||||
\(434\) | −316.361 | + | 115.146i | −0.0349903 | + | 0.0127354i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6397.25 | − | 5367.93i | 0.702690 | − | 0.589627i | ||||
\(437\) | 840.844 | + | 4768.66i | 0.0920435 | + | 0.522005i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7191.57 | + | 6034.45i | 0.781857 | + | 0.656056i | 0.943715 | − | 0.330758i | \(-0.107305\pi\) |
−0.161859 | + | 0.986814i | \(0.551749\pi\) | |||||||
\(440\) | 70.6013 | − | 122.285i | 0.00764951 | − | 0.0132493i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1996.44 | + | 3457.93i | 0.214844 | + | 0.372120i | ||||
\(443\) | −2408.55 | + | 13659.5i | −0.258315 | + | 1.46498i | 0.529104 | + | 0.848557i | \(0.322528\pi\) |
−0.787418 | + | 0.616419i | \(0.788583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 239.020 | + | 86.9962i | 0.0254621 | + | 0.00926745i | ||||
\(446\) | 7407.73 | + | 2696.19i | 0.786471 | + | 0.286252i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.1971 | − | 97.5296i | 0.00181359 | − | 0.0102854i | ||||
\(449\) | 813.413 | + | 1408.87i | 0.0854952 | + | 0.148082i | 0.905602 | − | 0.424128i | \(-0.139419\pi\) |
−0.820107 | + | 0.572210i | \(0.806086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1217.68 | − | 2109.08i | 0.127136 | − | 0.220205i | ||||
\(452\) | 4145.23 | + | 3478.26i | 0.431361 | + | 0.361955i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1425.76 | − | 8085.91i | −0.147389 | − | 0.835883i | ||||
\(455\) | 24.8783 | − | 20.8753i | 0.00256332 | − | 0.00215088i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7249.59 | − | 2638.63i | 0.742060 | − | 0.270088i | 0.0567993 | − | 0.998386i | \(-0.481910\pi\) |
0.685261 | + | 0.728298i | \(0.259688\pi\) | |||||||
\(458\) | −10019.0 | −1.02218 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −481.308 | −0.0487850 | ||||||||
\(461\) | 4106.01 | − | 1494.47i | 0.414828 | − | 0.150985i | −0.126170 | − | 0.992009i | \(-0.540269\pi\) |
0.540999 | + | 0.841023i | \(0.318046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13494.6 | + | 11323.3i | −1.35453 | + | 1.13658i | −0.376896 | + | 0.926256i | \(0.623009\pi\) |
−0.977631 | + | 0.210327i | \(0.932547\pi\) | |||||||
\(464\) | −582.873 | − | 3305.64i | −0.0583172 | − | 0.330733i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6818.92 | − | 5721.76i | −0.677855 | − | 0.568788i | ||||
\(467\) | −8580.50 | + | 14861.9i | −0.850232 | + | 1.47264i | 0.0307675 | + | 0.999527i | \(0.490205\pi\) |
−0.880999 | + | 0.473118i | \(0.843128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −677.073 | − | 1172.72i | −0.0666617 | − | 0.115461i | ||||
\(470\) | −74.2962 | + | 421.355i | −0.00729155 | + | 0.0413524i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4369.57 | − | 1590.39i | −0.426114 | − | 0.155093i | ||||
\(473\) | −11074.1 | − | 4030.63i | −1.07650 | − | 0.391815i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −637.634 | + | 3616.20i | −0.0615930 | + | 0.349311i | ||||
\(476\) | −215.829 | − | 373.827i | −0.0207826 | − | 0.0359965i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4315.59 | + | 7474.82i | −0.412950 | + | 0.715251i | ||||
\(479\) | −4996.09 | − | 4192.22i | −0.476570 | − | 0.399890i | 0.372614 | − | 0.927986i | \(-0.378462\pi\) |
−0.849184 | + | 0.528096i | \(0.822906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 629.417 | + | 3569.60i | 0.0596651 | + | 0.338378i | ||||
\(482\) | 6973.86 | − | 5851.76i | 0.659026 | − | 0.552989i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2824.26 | − | 1027.95i | 0.265239 | − | 0.0965391i | ||||
\(485\) | 353.728 | 0.0331175 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10552.3 | −0.981868 | −0.490934 | − | 0.871197i | \(-0.663344\pi\) | ||||
−0.490934 | + | 0.871197i | \(0.663344\pi\) | |||||||
\(488\) | −1026.80 | + | 373.725i | −0.0952483 | + | 0.0346675i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 382.575 | − | 321.019i | 0.0352714 | − | 0.0295962i | ||||
\(491\) | 3078.62 | + | 17459.7i | 0.282965 | + | 1.60478i | 0.712464 | + | 0.701708i | \(0.247579\pi\) |
−0.429499 | + | 0.903067i | \(0.641310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11207.6 | − | 9404.31i | −1.02387 | − | 0.859125i | ||||
\(494\) | 844.584 | − | 1462.86i | 0.0769223 | − | 0.133233i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −870.266 | − | 1507.34i | −0.0787824 | − | 0.136455i | ||||
\(497\) | 142.804 | − | 809.881i | 0.0128886 | − | 0.0730948i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1748.04 | + | 636.234i | 0.156819 | + | 0.0570776i | 0.419237 | − | 0.907877i | \(-0.362298\pi\) |
−0.262418 | + | 0.964954i | \(0.584520\pi\) | |||||||
\(500\) | −687.436 | − | 250.206i | −0.0614861 | − | 0.0223791i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −889.068 | + | 5042.16i | −0.0790459 | + | 0.448292i | ||||
\(503\) | −3332.34 | − | 5771.79i | −0.295391 | − | 0.511633i | 0.679684 | − | 0.733505i | \(-0.262117\pi\) |
−0.975076 | + | 0.221872i | \(0.928783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −133.592 | + | 231.388i | −0.0117718 | + | 0.0203894i | ||||
\(506\) | 6053.94 | + | 5079.86i | 0.531878 | + | 0.446299i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 695.657 | + | 3945.27i | 0.0607575 | + | 0.344573i | ||||
\(509\) | −3833.32 | + | 3216.53i | −0.333809 | + | 0.280099i | −0.794250 | − | 0.607591i | \(-0.792136\pi\) |
0.460441 | + | 0.887690i | \(0.347691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1725.65 | + | 628.084i | −0.149390 | + | 0.0543734i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1414.90 | −0.121417 | ||||||||
\(515\) | −842.286 | + | 306.567i | −0.0720690 | + | 0.0262310i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5381.59 | − | 4515.69i | 0.457799 | − | 0.384139i | ||||
\(518\) | −68.0445 | − | 385.899i | −0.00577163 | − | 0.0327325i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 128.619 | + | 107.924i | 0.0108468 | + | 0.00910151i | ||||
\(521\) | −1193.72 | + | 2067.58i | −0.100380 | + | 0.173863i | −0.911841 | − | 0.410543i | \(-0.865339\pi\) |
0.811461 | + | 0.584406i | \(0.198672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9418.72 | + | 16313.7i | 0.787479 | + | 1.36395i | 0.927507 | + | 0.373807i | \(0.121948\pi\) |
−0.140027 | + | 0.990148i | \(0.544719\pi\) | |||||||
\(524\) | 1343.41 | − | 7618.86i | 0.111998 | − | 0.635175i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3416.46 | + | 1243.49i | 0.283203 | + | 0.103077i | ||||
\(527\) | −7128.92 | − | 2594.71i | −0.589261 | − | 0.214473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2564.95 | − | 14546.6i | 0.210812 | − | 1.19558i | ||||
\(530\) | −383.885 | − | 664.908i | −0.0314621 | − | 0.0544939i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −91.3056 | + | 158.146i | −0.00744098 | + | 0.0128882i | ||||
\(533\) | 2218.32 | + | 1861.39i | 0.180274 | + | 0.151268i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 97.1154 | + | 550.769i | 0.00784797 | + | 0.0445081i | ||||
\(536\) | 5362.96 | − | 4500.06i | 0.432173 | − | 0.362636i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5082.59 | + | 1849.91i | −0.407297 | + | 0.148244i | ||||
\(539\) | −8200.18 | −0.655300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17185.2 | −1.36571 | −0.682854 | − | 0.730555i | \(-0.739262\pi\) | ||||
−0.682854 | + | 0.730555i | \(0.739262\pi\) | |||||||
\(542\) | −6403.53 | + | 2330.69i | −0.507482 | + | 0.184708i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1709.54 | − | 1434.48i | 0.134735 | − | 0.113056i | ||||
\(545\) | −265.785 | − | 1507.34i | −0.0208899 | − | 0.118472i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9869.20 | + | 8281.24i | 0.771438 | + | 0.647313i | 0.941077 | − | 0.338193i | \(-0.109816\pi\) |
−0.169639 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(548\) | −444.335 | + | 769.611i | −0.0346370 | + | 0.0599930i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2996.47 | + | 5190.04i | 0.232309 | + | 0.402371i | ||||
\(551\) | −1074.77 | + | 6095.34i | −0.0830977 | + | 0.471271i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −309.587 | − | 112.680i | −0.0238064 | − | 0.00866484i | ||||
\(554\) | −3234.89 | − | 1177.40i | −0.248082 | − | 0.0902943i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 672.319 | − | 3812.91i | 0.0512818 | − | 0.290834i | ||||
\(557\) | 3360.10 | + | 5819.87i | 0.255605 | + | 0.442721i | 0.965060 | − | 0.262030i | \(-0.0843919\pi\) |
−0.709455 | + | 0.704751i | \(0.751059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7006.48 | − | 12135.6i | 0.530130 | − | 0.918212i | ||||
\(560\) | −13.9046 | − | 11.6674i | −0.00104925 | − | 0.000880423i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 64.8096 | + | 367.553i | 0.00486446 | + | 0.0275877i | ||||
\(563\) | 11598.0 | − | 9731.85i | 0.868199 | − | 0.728505i | −0.0955194 | − | 0.995428i | \(-0.530451\pi\) |
0.963718 | + | 0.266922i | \(0.0860067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 931.969 | − | 339.209i | 0.0693951 | − | 0.0252577i | ||||
\(566\) | 4733.82 | 0.351550 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4251.62 | 0.314074 | ||||||||
\(569\) | 11394.8 | − | 4147.37i | 0.839534 | − | 0.305565i | 0.113768 | − | 0.993507i | \(-0.463708\pi\) |
0.725766 | + | 0.687942i | \(0.241486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1326.70 | − | 1113.23i | 0.0972341 | − | 0.0815891i | −0.592875 | − | 0.805295i | \(-0.702007\pi\) |
0.690109 | + | 0.723706i | \(0.257563\pi\) | |||||||
\(572\) | −478.721 | − | 2714.96i | −0.0349936 | − | 0.198458i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −239.817 | − | 201.230i | −0.0174386 | − | 0.0146327i | ||||
\(575\) | 10213.9 | − | 17691.0i | 0.740780 | − | 1.28307i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −887.429 | − | 1537.07i | −0.0640280 | − | 0.110900i | 0.832234 | − | 0.554424i | \(-0.187061\pi\) |
−0.896262 | + | 0.443524i | \(0.853728\pi\) | |||||||
\(578\) | −17.1812 | + | 97.4395i | −0.00123641 | + | 0.00701202i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −578.110 | − | 210.415i | −0.0413874 | − | 0.0150638i | ||||
\(581\) | 783.579 | + | 285.199i | 0.0559524 | + | 0.0203650i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2189.08 | + | 12414.9i | −0.155510 | + | 0.881943i | ||||
\(584\) | −4747.02 | − | 8222.08i | −0.336358 | − | 0.582589i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5679.23 | − | 9836.71i | 0.400353 | − | 0.693431i | ||||
\(587\) | 1355.86 | + | 1137.70i | 0.0953359 | + | 0.0799963i | 0.689210 | − | 0.724562i | \(-0.257958\pi\) |
−0.593874 | + | 0.804558i | \(0.702402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 557.307 | + | 3160.65i | 0.0389872 | + | 0.221107i | ||||
\(590\) | −652.872 | + | 547.825i | −0.0455565 | + | 0.0382264i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1903.68 | − | 692.882i | 0.132163 | − | 0.0481035i | ||||
\(593\) | 23108.7 | 1.60027 | 0.800137 | − | 0.599818i | \(-0.204760\pi\) | ||||
0.800137 | + | 0.599818i | \(0.204760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −79.1155 | −0.00545112 | ||||||||
\(596\) | −5673.75 | + | 2065.08i | −0.389943 | + | 0.141928i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7198.58 | + | 6040.32i | −0.492260 | + | 0.413055i | ||||
\(599\) | −3108.53 | − | 17629.3i | −0.212038 | − | 1.20253i | −0.885973 | − | 0.463738i | \(-0.846508\pi\) |
0.673934 | − | 0.738791i | \(-0.264603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5028.11 | − | 4219.09i | −0.341266 | − | 0.286356i | 0.456005 | − | 0.889977i | \(-0.349280\pi\) |
−0.797272 | + | 0.603621i | \(0.793724\pi\) | |||||||
\(602\) | −757.451 | + | 1311.94i | −0.0512814 | + | 0.0888220i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3141.16 | + | 5440.65i | 0.211609 | + | 0.366518i | ||||
\(605\) | 95.6557 | − | 542.490i | 0.00642803 | − | 0.0364551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12464.6 | + | 4536.76i | 0.833483 | + | 0.303363i | 0.723288 | − | 0.690547i | \(-0.242630\pi\) |
0.110195 | + | 0.993910i | \(0.464852\pi\) | |||||||
\(608\) | −887.153 | − | 322.897i | −0.0591756 | − | 0.0215382i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.7770 | + | 197.230i | −0.00230833 | + | 0.0130912i | ||||
\(611\) | 4176.72 | + | 7234.29i | 0.276550 | + | 0.478999i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10092.8 | − | 17481.3i | 0.665001 | − | 1.15182i | −0.314284 | − | 0.949329i | \(-0.601765\pi\) |
0.979285 | − | 0.202486i | \(-0.0649021\pi\) | |||||||
\(614\) | 8828.46 | + | 7407.96i | 0.580273 | + | 0.486907i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 51.7532 | + | 293.507i | 0.00338505 | + | 0.0191976i | ||||
\(617\) | 7820.48 | − | 6562.17i | 0.510277 | − | 0.428173i | −0.350950 | − | 0.936394i | \(-0.614141\pi\) |
0.861227 | + | 0.508221i | \(0.169697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15688.1 | − | 5710.00i | 1.01867 | − | 0.370767i | 0.221915 | − | 0.975066i | \(-0.428769\pi\) |
0.796757 | + | 0.604299i | \(0.206547\pi\) | |||||||
\(620\) | −319.009 | −0.0206640 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8168.15 | −0.526548 | ||||||||
\(623\) | −504.497 | + | 183.622i | −0.0324434 | + | 0.0118084i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11815.3 | − | 9914.19i | 0.756177 | − | 0.634508i | ||||
\(626\) | 1485.37 | + | 8423.95i | 0.0948360 | + | 0.537842i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4144.70 | + | 3477.82i | 0.263363 | + | 0.220987i | ||||
\(629\) | 4415.03 | − | 7647.05i | 0.279871 | − | 0.484750i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3922.35 | + | 6793.72i | 0.247459 | + | 0.428611i | 0.962820 | − | 0.270144i | \(-0.0870712\pi\) |
−0.715361 | + | 0.698755i | \(0.753738\pi\) | |||||||
\(632\) | 295.768 | − | 1677.39i | 0.0186156 | − | 0.105574i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14601.2 | + | 5314.42i | 0.914652 | + | 0.332906i | ||||
\(635\) | 689.973 | + | 251.129i | 0.0431193 | + | 0.0156941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1693.18 | − | 9602.48i | 0.105316 | − | 0.597275i | ||||
\(638\) | 5050.74 | + | 8748.15i | 0.313418 | + | 0.542856i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 46.9203 | − | 81.2684i | 0.00289795 | − | 0.00501940i | ||||
\(641\) | −13949.6 | − | 11705.1i | −0.859560 | − | 0.721256i | 0.102313 | − | 0.994752i | \(-0.467376\pi\) |
−0.961873 | + | 0.273496i | \(0.911820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1619.12 | + | 9182.50i | 0.0993032 | + | 0.563177i | 0.993343 | + | 0.115190i | \(0.0367477\pi\) |
−0.894040 | + | 0.447987i | \(0.852141\pi\) | |||||||
\(644\) | 778.218 | − | 653.003i | 0.0476182 | − | 0.0399564i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3866.82 | + | 1407.41i | −0.235508 | + | 0.0857178i | ||||
\(647\) | 657.535 | 0.0399542 | 0.0199771 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199771 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13993.8 | 0.846385 | ||||||||
\(650\) | −6696.29 | + | 2437.25i | −0.404077 | + | 0.147072i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8202.36 | − | 6882.60i | 0.492683 | − | 0.413410i | ||||
\(653\) | −383.096 | − | 2172.65i | −0.0229582 | − | 0.130203i | 0.971175 | − | 0.238370i | \(-0.0766130\pi\) |
−0.994133 | + | 0.108167i | \(0.965502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1086.21 | − | 911.438i | −0.0647965 | − | 0.0543707i | ||||
\(656\) | 809.246 | − | 1401.66i | 0.0481642 | − | 0.0834229i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −451.534 | − | 782.079i | −0.0267517 | − | 0.0463353i | ||||
\(659\) | −3376.22 | + | 19147.5i | −0.199573 | + | 1.13184i | 0.706180 | + | 0.708032i | \(0.250417\pi\) |
−0.905754 | + | 0.423805i | \(0.860694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −413.572 | − | 150.528i | −0.0243360 | − | 0.00885757i | 0.329823 | − | 0.944043i | \(-0.393011\pi\) |
−0.354159 | + | 0.935185i | \(0.615233\pi\) | |||||||
\(662\) | −14525.9 | − | 5287.00i | −0.852818 | − | 0.310400i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −748.604 | + | 4245.54i | −0.0437522 | + | 0.248131i | ||||
\(665\) | 16.7347 | + | 28.9854i | 0.000975856 | + | 0.00169023i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17216.2 | − | 29819.3i | 0.999419 | − | 1.73104i | ||||
\(668\) | −8720.70 | − | 7317.54i | −0.505111 | − | 0.423838i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −222.814 | − | 1263.64i | −0.0128478 | − | 0.0728636i | ||||
\(671\) | 2519.05 | − | 2113.73i | 0.144928 | − | 0.121609i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22211.4 | + | 8084.29i | −1.27219 | + | 0.463041i | −0.887843 | − | 0.460146i | \(-0.847797\pi\) |
−0.384351 | + | 0.923187i | \(0.625575\pi\) | |||||||
\(674\) | 716.838 | 0.0409667 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5509.91 | −0.313491 | ||||||||
\(677\) | 4570.60 | − | 1663.56i | 0.259472 | − | 0.0944400i | −0.209009 | − | 0.977914i | \(-0.567024\pi\) |
0.468481 | + | 0.883474i | \(0.344802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −571.936 | + | 479.911i | −0.0323253 | + | 0.0271242i | ||||
\(680\) | −71.0259 | − | 402.808i | −0.00400547 | − | 0.0227161i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4012.52 | + | 3366.91i | 0.225290 | + | 0.189040i | ||||
\(683\) | 1470.06 | − | 2546.21i | 0.0823575 | − | 0.142647i | −0.821905 | − | 0.569625i | \(-0.807088\pi\) |
0.904262 | + | 0.426978i | \(0.140422\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 81.4389 | + | 141.056i | 0.00454251 | + | 0.00786786i | ||||
\(686\) | −367.376 | + | 2083.49i | −0.0204468 | + | 0.115959i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7359.62 | − | 2678.68i | −0.407824 | − | 0.148436i | ||||
\(689\) | −14086.0 | − | 5126.87i | −0.778857 | − | 0.283481i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5409.49 | + | 30678.7i | −0.297810 | + | 1.68896i | 0.357748 | + | 0.933818i | \(0.383545\pi\) |
−0.655558 | + | 0.755145i | \(0.727567\pi\) | |||||||
\(692\) | 8529.30 | + | 14773.2i | 0.468548 | + | 0.811549i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6086.11 | − | 10541.4i | 0.332890 | − | 0.576582i | ||||
\(695\) | −543.601 | − | 456.135i | −0.0296690 | − | 0.0248953i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1225.00 | − | 6947.33i | −0.0665713 | − | 0.377545i | ||||
\(698\) | −14120.7 | + | 11848.7i | −0.765725 | + | 0.642520i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 723.918 | − | 263.485i | 0.0390879 | − | 0.0142268i | ||||
\(701\) | 28257.6 | 1.52250 | 0.761252 | − | 0.648456i | \(-0.224585\pi\) | ||||
0.761252 | + | 0.648456i | \(0.224585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3735.51 | −0.200409 | ||||||||
\(704\) | −1447.90 | + | 526.991i | −0.0775137 | + | 0.0282127i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14023.9 | + | 11767.4i | −0.747585 | + | 0.627298i | ||||
\(707\) | −97.9276 | − | 555.375i | −0.00520926 | − | 0.0295432i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14734.3 | − | 12363.6i | −0.780479 | − | 0.654899i | 0.162891 | − | 0.986644i | \(-0.447918\pi\) |
−0.943369 | + | 0.331745i | \(0.892363\pi\) | |||||||
\(710\) | 389.624 | − | 674.849i | 0.0205948 | − | 0.0356713i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1387.80 | − | 2403.74i | −0.0730479 | − | 0.126523i | ||||
\(713\) | 3100.38 | − | 17583.1i | 0.162847 | − | 0.923553i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −474.809 | − | 172.816i | −0.0248347 | − | 0.00903910i | ||||
\(716\) | −5799.60 | − | 2110.88i | −0.302711 | − | 0.110178i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1874.83 | + | 10632.7i | −0.0974488 | + | 0.552659i | ||||
\(719\) | −3841.21 | − | 6653.16i | −0.199239 | − | 0.345092i | 0.749043 | − | 0.662521i | \(-0.230514\pi\) |
−0.948282 | + | 0.317429i | \(0.897180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 945.949 | − | 1638.43i | 0.0488613 | − | 0.0846302i | ||||
\(722\) | −9175.05 | − | 7698.78i | −0.472936 | − | 0.396841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2292.92 | + | 13003.8i | 0.117701 | + | 0.667516i | ||||
\(725\) | 20002.1 | − | 16783.8i | 1.02464 | − | 0.859771i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33936.8 | + | 12352.0i | −1.73129 | + | 0.630137i | −0.998721 | − | 0.0505574i | \(-0.983900\pi\) |
−0.732567 | + | 0.680695i | \(0.761678\pi\) | |||||||
\(728\) | −354.385 | −0.0180417 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1740.09 | −0.0882242 | ||||||||
\(731\) | −32078.3 | + | 11675.5i | −1.62306 | + | 0.590746i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3422.22 | + | 2871.58i | −0.172446 | + | 0.144699i | −0.724926 | − | 0.688827i | \(-0.758126\pi\) |
0.552480 | + | 0.833526i | \(0.313682\pi\) | |||||||
\(734\) | −166.726 | − | 945.553i | −0.00838418 | − | 0.0475490i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4023.34 | + | 3375.98i | 0.201498 | + | 0.169077i | ||||
\(737\) | −10534.2 | + | 18245.8i | −0.526503 | + | 0.911930i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4318.02 | + | 7479.04i | 0.214941 | + | 0.372288i | 0.953254 | − | 0.302170i | \(-0.0977109\pi\) |
−0.738314 | + | 0.674458i | \(0.764378\pi\) | |||||||
\(740\) | 64.4761 | − | 365.662i | 0.00320296 | − | 0.0181649i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1522.79 | + | 554.251i | 0.0753417 | + | 0.0274221i | ||||
\(743\) | 3771.96 | + | 1372.88i | 0.186245 | + | 0.0677876i | 0.433459 | − | 0.901173i | \(-0.357293\pi\) |
−0.247214 | + | 0.968961i | \(0.579515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −192.166 | + | 1089.83i | −0.00945021 | + | 0.0535948i | ||||
\(746\) | −3345.24 | − | 5794.12i | −0.164179 | − | 0.284367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3357.97 | + | 5816.18i | −0.164144 | + | 0.284306i | ||||
\(749\) | −904.265 | − | 758.769i | −0.0441137 | − | 0.0370158i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3272.96 | − | 18561.9i | −0.159030 | − | 0.901906i | −0.955008 | − | 0.296580i | \(-0.904154\pi\) |
0.795978 | − | 0.605326i | \(-0.206957\pi\) | |||||||
\(752\) | 3576.51 | − | 3001.05i | 0.173433 | − | 0.145528i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11287.0 | + | 4108.14i | −0.545158 | + | 0.198421i | ||||
\(755\) | 1151.44 | 0.0555035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40760.5 | −1.95702 | −0.978511 | − | 0.206195i | \(-0.933892\pi\) | ||||
−0.978511 | + | 0.206195i | \(0.933892\pi\) | |||||||
\(758\) | −12224.1 | + | 4449.21i | −0.585751 | + | 0.213196i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −132.552 | + | 111.225i | −0.00632655 | + | 0.00530861i | ||||
\(761\) | 907.661 | + | 5147.60i | 0.0432361 | + | 0.245204i | 0.998764 | − | 0.0496952i | \(-0.0158250\pi\) |
−0.955528 | + | 0.294899i | \(0.904714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2474.79 | + | 2076.59i | 0.117423 | + | 0.0985292i | ||||
\(764\) | −2102.61 | + | 3641.83i | −0.0995677 | + | 0.172456i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2788.13 | − | 4829.19i | −0.131513 | − | 0.227788i | ||||
\(767\) | −2889.44 | + | 16386.8i | −0.136026 | + | 0.771440i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26469.7 | + | 9634.18i | 1.24125 | + | 0.451778i | 0.877436 | − | 0.479693i | \(-0.159252\pi\) |
0.363814 | + | 0.931472i | \(0.381474\pi\) | |||||||
\(770\) | 51.3302 | + | 18.6827i | 0.00240235 | + | 0.000874386i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 906.279 | − | 5139.77i | 0.0422509 | − | 0.239617i | ||||
\(773\) | 4978.93 | + | 8623.75i | 0.231668 | + | 0.401261i | 0.958299 | − | 0.285767i | \(-0.0922483\pi\) |
−0.726631 | + | 0.687028i | \(0.758915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6769.72 | − | 11725.5i | 0.313775 | − | 0.543474i | ||||
\(776\) | −2956.87 | − | 2481.11i | −0.136786 | − | 0.114777i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4749.11 | + | 26933.6i | 0.218848 | + | 1.24115i | ||||
\(779\) | −2286.16 | + | 1918.32i | −0.105148 | + | 0.0882296i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12023.3 | + | 4376.11i | −0.550866 | + | 0.200499i | ||||
\(782\) | 22892.2 | 1.04683 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5449.69 | −0.248255 | ||||||||
\(785\) | 931.850 | − | 339.166i | 0.0423684 | − | 0.0154208i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4270.10 | − | 3583.04i | 0.193409 | − | 0.162289i | −0.540941 | − | 0.841061i | \(-0.681932\pi\) |
0.734350 | + | 0.678771i | \(0.237487\pi\) | |||||||
\(788\) | 1699.50 | + | 9638.34i | 0.0768301 | + | 0.435725i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −239.142 | − | 200.664i | −0.0107700 | − | 0.00903710i | ||||
\(791\) | −1046.67 | + | 1812.88i | −0.0470484 | + | 0.0814902i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1955.06 | + | 3386.27i | 0.0875490 | + | 0.151639i | ||||
\(794\) | 3697.50 | − | 20969.6i | 0.165264 | − | 0.937258i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17409.0 | − | 6336.35i | −0.775181 | − | 0.282143i | ||||
\(797\) | −11821.7 | − | 4302.75i | −0.525403 | − | 0.191231i | 0.0656815 | − | 0.997841i | \(-0.479078\pi\) |
−0.591085 | + | 0.806610i | \(0.701300\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3533.71 | − | 20040.7i | 0.156463 | − | 0.887345i | ||||
\(800\) | 1991.40 | + | 3449.21i | 0.0880083 | + | 0.152435i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10252.9 | − | 17758.6i | 0.451426 | − | 0.781893i | ||||
\(803\) | 21887.0 | + | 18365.4i | 0.961864 | + | 0.807099i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.3324 | − | 183.366i | −0.00141561 | − | 0.00802834i | ||||
\(806\) | −4771.18 | + | 4003.50i | −0.208508 | + | 0.174959i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2739.72 | − | 997.175i | 0.119286 | − | 0.0434165i | ||||
\(809\) | −17237.7 | −0.749129 | −0.374564 | − | 0.927201i | \(-0.622208\pi\) | ||||
−0.374564 | + | 0.927201i | \(0.622208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22420.5 | 0.970763 | 0.485382 | − | 0.874302i | \(-0.338681\pi\) | ||||
0.485382 | + | 0.874302i | \(0.338681\pi\) | |||||||
\(812\) | 1220.21 | − | 444.120i | 0.0527352 | − | 0.0191940i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4670.29 | + | 3918.84i | −0.201098 | + | 0.168741i | ||||
\(815\) | −340.782 | − | 1932.67i | −0.0146467 | − | 0.0830655i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11062.8 | + | 9282.82i | 0.473733 | + | 0.397509i | ||||
\(818\) | 3587.59 | − | 6213.89i | 0.153346 | − | 0.265603i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −148.321 | − | 256.899i | −0.00631656 | − | 0.0109406i | ||||
\(821\) | −6480.94 | + | 36755.2i | −0.275501 | + | 1.56244i | 0.461865 | + | 0.886950i | \(0.347181\pi\) |
−0.737366 | + | 0.675494i | \(0.763931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40979.0 | − | 14915.1i | −1.73565 | − | 0.631724i | −0.736640 | − | 0.676285i | \(-0.763589\pi\) |
−0.999007 | + | 0.0445610i | \(0.985811\pi\) | |||||||
\(824\) | 9191.12 | + | 3345.29i | 0.388578 | + | 0.141431i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 312.369 | − | 1771.53i | 0.0131583 | − | 0.0746242i | ||||
\(827\) | 8190.08 | + | 14185.6i | 0.344374 | + | 0.596473i | 0.985240 | − | 0.171180i | \(-0.0547579\pi\) |
−0.640866 | + | 0.767653i | \(0.721425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1459.28 | + | 2527.55i | −0.0611375 | + | 0.105893i | −0.894974 | − | 0.446118i | \(-0.852806\pi\) |
0.833837 | + | 0.552011i | \(0.186139\pi\) | |||||||
\(830\) | 605.281 | + | 507.891i | 0.0253128 | + | 0.0212399i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −318.149 | − | 1804.31i | −0.0132570 | − | 0.0751842i | ||||
\(833\) | −18196.2 | + | 15268.4i | −0.756857 | + | 0.635079i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1960.67 | + | 713.625i | −0.0812596 | + | 0.0295761i | ||||
\(836\) | 2841.15 | 0.117540 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15079.5 | −0.621614 | ||||||||
\(839\) | 5190.18 | − | 1889.07i | 0.213570 | − | 0.0777330i | −0.233020 | − | 0.972472i | \(-0.574861\pi\) |
0.446589 | + | 0.894739i | \(0.352638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15031.8 | − | 12613.2i | 0.616335 | − | 0.517167i | ||||
\(842\) | −128.989 | − | 731.531i | −0.00527938 | − | 0.0299409i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3787.68 | + | 3178.24i | 0.154476 | + | 0.129620i | ||||
\(845\) | −504.935 | + | 874.574i | −0.0205566 | + | 0.0356050i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 581.346 | + | 1006.92i | 0.0235836 | + | 0.0408479i | ||||
\(848\) | −1454.82 | + | 8250.72i | −0.0589138 | + | 0.334117i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16312.9 | + | 5937.40i | 0.658267 | + | 0.239589i | ||||
\(851\) | 19527.9 | + | 7107.58i | 0.786614 | + | 0.286304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3389.52 | − | 19223.0i | 0.136055 | − | 0.771608i | −0.838064 | − | 0.545572i | \(-0.816312\pi\) |
0.974119 | − | 0.226035i | \(-0.0725765\pi\) | |||||||
\(854\) | −211.357 | − | 366.080i | −0.00846894 | − | 0.0146686i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3051.39 | − | 5285.15i | 0.121839 | − | 0.211031i | ||||
\(857\) | 3314.13 | + | 2780.89i | 0.132099 | + | 0.110844i | 0.706443 | − | 0.707770i | \(-0.250299\pi\) |
−0.574345 | + | 0.818614i | \(0.694743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2186.38 | + | 12399.6i | 0.0868433 | + | 0.492513i | 0.996944 | + | 0.0781247i | \(0.0248932\pi\) |
−0.910100 | + | 0.414388i | \(0.863996\pi\) | |||||||
\(860\) | −1099.63 | + | 922.695i | −0.0436010 | + | 0.0365856i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29752.3 | − | 10828.9i | 1.17560 | − | 0.427883i | ||||
\(863\) | −47955.5 | −1.89157 | −0.945785 | − | 0.324794i | \(-0.894705\pi\) | ||||
−0.945785 | + | 0.324794i | \(0.894705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3126.54 | 0.122897 | ||||||||
\(866\) | 29754.5 | − | 10829.8i | 1.16755 | − | 0.424954i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 515.799 | − | 432.807i | 0.0201698 | − | 0.0169245i | ||||
\(869\) | 890.089 | + | 5047.95i | 0.0347459 | + | 0.197054i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19190.9 | − | 16103.1i | −0.746565 | − | 0.626442i | ||||
\(872\) | −8351.02 | + | 14464.4i | −0.324313 | + | 0.561727i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4842.23 | − | 8386.98i | −0.187404 | − | 0.324593i | ||||
\(875\) | 49.1430 | − | 278.704i | 0.00189867 | − | 0.0107679i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16259.6 | + | 5918.02i | 0.626053 | + | 0.227865i | 0.635513 | − | 0.772091i | \(-0.280789\pi\) |
−0.00945936 | + | 0.999955i | \(0.503011\pi\) | |||||||
\(878\) | −17643.5 | − | 6421.72i | −0.678178 | − | 0.246837i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −49.0391 | + | 278.115i | −0.00187853 | + | 0.0106537i | ||||
\(881\) | −13900.2 | − | 24075.9i | −0.531567 | − | 0.920701i | −0.999321 | − | 0.0368423i | \(-0.988270\pi\) |
0.467754 | − | 0.883859i | \(-0.345063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13801.9 | + | 23905.6i | −0.526014 | + | 0.911083i | 0.473527 | + | 0.880779i | \(0.342981\pi\) |
−0.999541 | + | 0.0303037i | \(0.990353\pi\) | |||||||
\(884\) | −6117.44 | − | 5133.14i | −0.232751 | − | 0.195301i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4817.09 | − | 27319.1i | −0.182656 | − | 1.03589i | ||||
\(887\) | 26155.1 | − | 21946.7i | 0.990080 | − | 0.830776i | 0.00450057 | − | 0.999990i | \(-0.498567\pi\) |
0.985579 | + | 0.169214i | \(0.0541230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1456.32 | + | 530.056i | −0.0549418 | + | 0.0199972i | ||||
\(890\) | −508.720 | −0.0191599 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15766.3 | −0.591810 | ||||||||
\(893\) | −8089.72 | + | 2944.42i | −0.303149 | + | 0.110337i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −866.537 | + | 727.111i | −0.0323633 | + | 0.0271560i | ||||
\(896\) | 34.3942 | + | 195.059i | 0.00128240 | + | 0.00727284i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2492.44 | − | 2091.41i | −0.0926213 | − | 0.0777185i | ||||
\(899\) | 11410.8 | − | 19764.1i | 0.423327 | − | 0.733224i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18258.5 | + | 31624.7i | 0.675117 | + | 1.16934i | ||||
\(902\) | −845.790 | + | 4796.71i | −0.0312214 | + | 0.177065i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10169.8 | − | 3701.49i | −0.374160 | − | 0.136183i | ||||
\(905\) | 2274.18 | + | 827.734i | 0.0835319 | + | 0.0304031i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1190.68 | + | 6752.68i | −0.0435897 | + | 0.247209i | −0.998815 | − | 0.0486702i | \(-0.984502\pi\) |
0.955225 | + | 0.295880i | \(0.0956128\pi\) | |||||||
\(908\) | 8210.65 | + | 14221.3i | 0.300088 | + | 0.519768i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −32.4763 | + | 56.2505i | −0.00118305 | + | 0.00204911i | ||||
\(911\) | 7563.92 | + | 6346.88i | 0.275086 | + | 0.230825i | 0.769885 | − | 0.638183i | \(-0.220314\pi\) |
−0.494798 | + | 0.869008i | \(0.664758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2252.86 | − | 12776.6i | −0.0816635 | − | 0.463136i | ||||
\(914\) | −11819.8 | + | 9918.02i | −0.427752 | + | 0.358927i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18829.6 | − | 6853.43i | 0.679202 | − | 0.247209i | ||||
\(917\) | 2992.84 | 0.107778 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4520.13 | −0.162247 | −0.0811237 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811237 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(920\) | 904.564 | − | 329.234i | 0.0324159 | − | 0.0117984i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6694.50 | + | 5617.35i | −0.239123 | + | 0.200648i | ||||
\(923\) | −2641.89 | − | 14982.9i | −0.0942134 | − | 0.534311i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12072.0 | + | 10129.6i | 0.429109 | + | 0.360065i | ||||
\(926\) | 17615.9 | − | 30511.7i | 0.625156 | − | 1.08280i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3356.63 | + | 5813.86i | 0.118736 | + | 0.205656i | ||||
\(929\) | 4600.64 | − | 26091.5i | 0.162478 | − | 0.921458i | −0.789149 | − | 0.614202i | \(-0.789478\pi\) |
0.951627 | − | 0.307256i | \(-0.0994109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9442.79 | + | 3436.89i | 0.332411 | + | 0.120988i | ||||
\(932\) | 16729.3 | + | 6088.97i | 0.587968 | + | 0.214003i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5959.95 | − | 33800.6i | 0.208796 | − | 1.18414i | ||||
\(935\) | 615.458 | + | 1066.00i | 0.0215269 | + | 0.0372856i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20545.5 | + | 35585.8i | −0.716320 | + | 1.24070i | 0.246129 | + | 0.969237i | \(0.420841\pi\) |
−0.962448 | + | 0.271465i | \(0.912492\pi\) | |||||||
\(938\) | 2074.67 | + | 1740.86i | 0.0722179 | + | 0.0605981i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −148.592 | − | 842.709i | −0.00515590 | − | 0.0292406i | ||||
\(941\) | −10086.2 | + | 8463.31i | −0.349416 | + | 0.293195i | −0.800555 | − | 0.599259i | \(-0.795462\pi\) |
0.451140 | + | 0.892453i | \(0.351018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15601.2 | − | 5678.38i | 0.538755 | − | 0.196091i | ||||
\(944\) | 9300.01 | 0.320646 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23569.6 | 0.810056 | ||||||||
\(947\) | 16313.0 | − | 5937.44i | 0.559768 | − | 0.203739i | −0.0466129 | − | 0.998913i | \(-0.514843\pi\) |
0.606381 | + | 0.795174i | \(0.292620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26025.3 | + | 21837.8i | −0.890217 | + | 0.746981i | ||||
\(950\) | −1275.27 | − | 7232.40i | −0.0435528 | − | 0.247000i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 661.340 | + | 554.930i | 0.0225149 | + | 0.0188922i | ||||
\(953\) | −15169.6 | + | 26274.6i | −0.515628 | + | 0.893093i | 0.484208 | + | 0.874953i | \(0.339108\pi\) |
−0.999835 | + | 0.0181401i | \(0.994226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 385.371 | + | 667.483i | 0.0130579 | + | 0.0226170i | ||||
\(956\) | 2997.57 | − | 17000.1i | 0.101411 | − | 0.575128i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12257.2 | + | 4461.27i | 0.413375 | + | 0.150456i | ||||
\(959\) | −323.051 | − | 117.581i | −0.0108779 | − | 0.00395922i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3118.24 | + | 17684.4i | −0.104670 | + | 0.593615i | ||||
\(962\) | −3624.67 | − | 6278.11i | −0.121480 | − | 0.210410i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9103.73 | + | 15768.1i | −0.304161 | + | 0.526823i | ||||
\(965\) | −732.768 | − | 614.866i | −0.0244442 | − | 0.0205111i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 282.202 | + | 1600.45i | 0.00938470 | + | 0.0532233i | 0.989140 | − | 0.146973i | \(-0.0469531\pi\) |
−0.979756 | + | 0.200196i | \(0.935842\pi\) | |||||||
\(968\) | −4604.72 | + | 3863.82i | −0.152894 | + | 0.128293i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −664.791 | + | 241.964i | −0.0220053 | + | 0.00800928i | ||||
\(971\) | −48316.1 | −1.59684 | −0.798422 | − | 0.602098i | \(-0.794332\pi\) | ||||
−0.798422 | + | 0.602098i | \(0.794332\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1497.79 | 0.0493493 | ||||||||
\(974\) | 19831.8 | − | 7218.19i | 0.652415 | − | 0.237460i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1674.11 | − | 1404.75i | 0.0549048 | − | 0.0460706i | ||||
\(977\) | −5343.32 | − | 30303.5i | −0.174972 | − | 0.992318i | −0.938176 | − | 0.346159i | \(-0.887486\pi\) |
0.763203 | − | 0.646158i | \(-0.223625\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6398.72 | + | 5369.17i | 0.208891 | + | 0.175280i | ||||
\(980\) | −499.416 | + | 865.014i | −0.0162788 | + | 0.0281958i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17729.0 | − | 30707.6i | −0.576127 | − | 0.997881i | ||||
\(983\) | 5884.20 | − | 33371.0i | 0.190923 | − | 1.08278i | −0.727184 | − | 0.686442i | \(-0.759171\pi\) |
0.918107 | − | 0.396333i | \(-0.129717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1685.61 | + | 613.512i | 0.0545259 | + | 0.0198458i | ||||
\(986\) | 27496.4 | + | 10007.9i | 0.888096 | + | 0.323240i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −586.642 | + | 3327.01i | −0.0188902 | + | 0.107132i | ||||
\(989\) | −40170.0 | − | 69576.6i | −1.29154 | − | 2.23701i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10533.8 | + | 18245.0i | −0.337656 | + | 0.584837i | −0.983991 | − | 0.178217i | \(-0.942967\pi\) |
0.646336 | + | 0.763053i | \(0.276301\pi\) | |||||||
\(992\) | 2666.65 | + | 2237.58i | 0.0853490 | + | 0.0716163i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 285.608 | + | 1619.76i | 0.00911361 | + | 0.0516858i | ||||
\(995\) | −2601.13 | + | 2182.61i | −0.0828757 | + | 0.0695410i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52839.6 | − | 19232.0i | 1.67848 | − | 0.610917i | 0.685381 | − | 0.728185i | \(-0.259636\pi\) |
0.993100 | + | 0.117267i | \(0.0374134\pi\) | |||||||
\(998\) | −3720.45 | −0.118005 | ||||||||
\(999\) | 0 | 0 |
(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 | 162.4.e.b.19.3 | 30 | ||
3.2 | odd | 2 | 54.4.e.b.7.3 | ✓ | 30 | ||
27.2 | odd | 18 | 1458.4.a.i.1.8 | 15 | |||
27.4 | even | 9 | inner | 162.4.e.b.145.3 | 30 | ||
27.23 | odd | 18 | 54.4.e.b.31.3 | yes | 30 | ||
27.25 | even | 9 | 1458.4.a.j.1.8 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.4.e.b.7.3 | ✓ | 30 | 3.2 | odd | 2 | ||
54.4.e.b.31.3 | yes | 30 | 27.23 | odd | 18 | ||
162.4.e.b.19.3 | 30 | 1.1 | even | 1 | trivial | ||
162.4.e.b.145.3 | 30 | 27.4 | even | 9 | inner | ||
1458.4.a.i.1.8 | 15 | 27.2 | odd | 18 | |||
1458.4.a.j.1.8 | 15 | 27.25 | even | 9 |