Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.p.136.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 2.36603i | 0.482963 | + | 0.836516i | 0.999809 | − | 0.0195623i | \(-0.00622726\pi\) |
−0.516846 | + | 0.856079i | \(0.672894\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.267949 | − | 0.464102i | 0.0334936 | − | 0.0580127i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | − | 6.00000i | −0.187044 | − | 0.323970i | 0.757219 | − | 0.653161i | \(-0.226557\pi\) |
−0.944263 | + | 0.329191i | \(0.893224\pi\) | |||||||
\(8\) | 23.3205 | 1.03063 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 13.6603 | 0.431975 | ||||||||
\(11\) | −29.7487 | − | 51.5263i | −0.815416 | − | 1.41234i | −0.909029 | − | 0.416733i | \(-0.863175\pi\) |
0.0936131 | − | 0.995609i | \(-0.470158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.5359 | − | 21.7128i | 0.267449 | − | 0.463235i | −0.700754 | − | 0.713403i | \(-0.747153\pi\) |
0.968202 | + | 0.250169i | \(0.0804861\pi\) | |||||||
\(14\) | 9.46410 | − | 16.3923i | 0.180671 | − | 0.312931i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 29.7128 | + | 51.4641i | 0.464263 | + | 0.804127i | ||||
\(17\) | −112.995 | −1.61208 | −0.806038 | − | 0.591864i | \(-0.798392\pi\) | ||||
−0.806038 | + | 0.591864i | \(0.798392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −122.779 | −1.48250 | −0.741251 | − | 0.671228i | \(-0.765767\pi\) | ||||
−0.741251 | + | 0.671228i | \(0.765767\pi\) | |||||||
\(20\) | −1.33975 | − | 2.32051i | −0.0149788 | − | 0.0259441i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 81.2750 | − | 140.772i | 0.787631 | − | 1.36422i | ||||
\(23\) | −48.7128 | + | 84.3731i | −0.441623 | + | 0.764913i | −0.997810 | − | 0.0661439i | \(-0.978930\pi\) |
0.556187 | + | 0.831057i | \(0.312264\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 68.4974 | 0.516671 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.71281 | −0.0250591 | ||||||||
\(29\) | −63.2846 | − | 109.612i | −0.405230 | − | 0.701878i | 0.589119 | − | 0.808047i | \(-0.299475\pi\) |
−0.994348 | + | 0.106168i | \(0.966142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54.1077 | − | 93.7173i | 0.313485 | − | 0.542972i | −0.665629 | − | 0.746282i | \(-0.731837\pi\) |
0.979114 | + | 0.203311i | \(0.0651702\pi\) | |||||||
\(32\) | 12.1051 | − | 20.9667i | 0.0668720 | − | 0.115826i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −154.354 | − | 267.349i | −0.778572 | − | 1.34853i | ||||
\(35\) | −34.6410 | −0.167297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 294.344 | 1.30783 | 0.653916 | − | 0.756567i | \(-0.273125\pi\) | ||||
0.653916 | + | 0.756567i | \(0.273125\pi\) | |||||||
\(38\) | −167.720 | − | 290.499i | −0.715994 | − | 1.24014i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 58.3013 | − | 100.981i | 0.230456 | − | 0.399162i | ||||
\(41\) | −102.931 | + | 178.281i | −0.392075 | + | 0.679094i | −0.992723 | − | 0.120419i | \(-0.961576\pi\) |
0.600648 | + | 0.799514i | \(0.294909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.1000 | + | 69.4552i | 0.142214 | + | 0.246321i | 0.928330 | − | 0.371757i | \(-0.121245\pi\) |
−0.786116 | + | 0.618079i | \(0.787911\pi\) | |||||||
\(44\) | −31.8846 | −0.109245 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −266.172 | −0.853150 | ||||||||
\(47\) | −134.856 | − | 233.578i | −0.418528 | − | 0.724912i | 0.577263 | − | 0.816558i | \(-0.304121\pi\) |
−0.995792 | + | 0.0916458i | \(0.970787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 147.500 | − | 255.477i | 0.430029 | − | 0.744832i | ||||
\(50\) | 34.1506 | − | 59.1506i | 0.0965926 | − | 0.167303i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.71797 | − | 11.6359i | −0.0179157 | − | 0.0310308i | ||||
\(53\) | 98.7949 | 0.256048 | 0.128024 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128024 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −297.487 | −0.729330 | ||||||||
\(56\) | −80.7846 | − | 139.923i | −0.192773 | − | 0.333893i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 172.897 | − | 299.466i | 0.391422 | − | 0.677962i | ||||
\(59\) | −152.251 | + | 263.707i | −0.335956 | + | 0.581894i | −0.983668 | − | 0.179992i | \(-0.942393\pi\) |
0.647712 | + | 0.761886i | \(0.275726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −333.277 | − | 577.252i | −0.699537 | − | 1.21163i | −0.968627 | − | 0.248518i | \(-0.920056\pi\) |
0.269091 | − | 0.963115i | \(-0.413277\pi\) | |||||||
\(62\) | 295.650 | 0.605606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 541.549 | 1.05771 | ||||||||
\(65\) | −62.6795 | − | 108.564i | −0.119607 | − | 0.207165i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 317.967 | − | 550.734i | 0.579788 | − | 1.00422i | −0.415715 | − | 0.909495i | \(-0.636469\pi\) |
0.995503 | − | 0.0947278i | \(-0.0301981\pi\) | |||||||
\(68\) | −30.2769 | + | 52.4411i | −0.0539943 | + | 0.0935208i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −47.3205 | − | 81.9615i | −0.0807983 | − | 0.139947i | ||||
\(71\) | 826.482 | 1.38148 | 0.690742 | − | 0.723101i | \(-0.257284\pi\) | ||||
0.690742 | + | 0.723101i | \(0.257284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 751.349 | 1.20464 | 0.602320 | − | 0.798255i | \(-0.294243\pi\) | ||||
0.602320 | + | 0.798255i | \(0.294243\pi\) | |||||||
\(74\) | 402.081 | + | 696.424i | 0.631634 | + | 1.09402i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −32.8987 | + | 56.9821i | −0.0496544 | + | 0.0860039i | ||||
\(77\) | −206.105 | + | 356.985i | −0.305037 | + | 0.528340i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9334 | − | 20.6692i | −0.0169950 | − | 0.0294363i | 0.857403 | − | 0.514646i | \(-0.172077\pi\) |
−0.874398 | + | 0.485210i | \(0.838743\pi\) | |||||||
\(80\) | 297.128 | 0.415249 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −562.424 | −0.757431 | ||||||||
\(83\) | 408.615 | + | 707.742i | 0.540378 | + | 0.935962i | 0.998882 | + | 0.0472695i | \(0.0150520\pi\) |
−0.458504 | + | 0.888692i | \(0.651615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −282.487 | + | 489.282i | −0.360471 | + | 0.624354i | ||||
\(86\) | −109.555 | + | 189.755i | −0.137368 | + | 0.237928i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −693.755 | − | 1201.62i | −0.840392 | − | 1.45560i | ||||
\(89\) | 513.000 | 0.610988 | 0.305494 | − | 0.952194i | \(-0.401178\pi\) | ||||
0.305494 | + | 0.952194i | \(0.401178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −173.703 | −0.200099 | ||||||||
\(92\) | 26.1051 | + | 45.2154i | 0.0295831 | + | 0.0512395i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 368.435 | − | 638.147i | 0.404267 | − | 0.700211i | ||||
\(95\) | −306.949 | + | 531.651i | −0.331498 | + | 0.574171i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −214.051 | − | 370.748i | −0.224058 | − | 0.388079i | 0.731979 | − | 0.681328i | \(-0.238597\pi\) |
−0.956036 | + | 0.293248i | \(0.905264\pi\) | |||||||
\(98\) | 805.955 | 0.830753 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3975 | −0.0133975 | ||||||||
\(101\) | −456.043 | − | 789.890i | −0.449287 | − | 0.778188i | 0.549052 | − | 0.835788i | \(-0.314989\pi\) |
−0.998340 | + | 0.0575994i | \(0.981655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −139.249 | + | 241.186i | −0.133210 | + | 0.230726i | −0.924912 | − | 0.380181i | \(-0.875862\pi\) |
0.791703 | + | 0.610907i | \(0.209195\pi\) | |||||||
\(104\) | 292.344 | − | 506.354i | 0.275641 | − | 0.477424i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 134.956 | + | 233.751i | 0.123662 | + | 0.214188i | ||||
\(107\) | −1512.33 | −1.36638 | −0.683191 | − | 0.730240i | \(-0.739408\pi\) | ||||
−0.683191 | + | 0.730240i | \(0.739408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1991.53 | 1.75004 | 0.875020 | − | 0.484087i | \(-0.160848\pi\) | ||||
0.875020 | + | 0.484087i | \(0.160848\pi\) | |||||||
\(110\) | −406.375 | − | 703.862i | −0.352239 | − | 0.610096i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 205.856 | − | 356.554i | 0.173675 | − | 0.300814i | ||||
\(113\) | 253.951 | − | 439.856i | 0.211413 | − | 0.366179i | −0.740744 | − | 0.671788i | \(-0.765527\pi\) |
0.952157 | + | 0.305609i | \(0.0988600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 243.564 | + | 421.865i | 0.197500 | + | 0.342080i | ||||
\(116\) | −67.8282 | −0.0542905 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −831.917 | −0.649018 | ||||||||
\(119\) | 391.426 | + | 677.969i | 0.301529 | + | 0.522263i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1104.47 | + | 1913.00i | −0.829806 | + | 1.43727i | ||||
\(122\) | 910.529 | − | 1577.08i | 0.675700 | − | 1.17035i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −28.9962 | − | 50.2229i | −0.0209995 | − | 0.0363722i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1845.91 | 1.28975 | 0.644873 | − | 0.764290i | \(-0.276910\pi\) | ||||
0.644873 | + | 0.764290i | \(0.276910\pi\) | |||||||
\(128\) | 642.928 | + | 1113.58i | 0.443964 | + | 0.768968i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 171.244 | − | 296.603i | 0.115531 | − | 0.200106i | ||||
\(131\) | −1282.35 | + | 2221.10i | −0.855265 | + | 1.48136i | 0.0211333 | + | 0.999777i | \(0.493273\pi\) |
−0.876399 | + | 0.481586i | \(0.840061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 425.321 | + | 736.677i | 0.277293 | + | 0.480286i | ||||
\(134\) | 1737.40 | 1.12006 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2635.10 | −1.66145 | ||||||||
\(137\) | −253.390 | − | 438.884i | −0.158019 | − | 0.273696i | 0.776135 | − | 0.630566i | \(-0.217177\pi\) |
−0.934154 | + | 0.356870i | \(0.883844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1111.32 | + | 1924.87i | −0.678138 | + | 1.17457i | 0.297403 | + | 0.954752i | \(0.403880\pi\) |
−0.975541 | + | 0.219818i | \(0.929454\pi\) | |||||||
\(140\) | −9.28203 | + | 16.0770i | −0.00560339 | + | 0.00970536i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1129.00 | + | 1955.48i | 0.667206 | + | 1.15563i | ||||
\(143\) | −1491.71 | −0.872327 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −632.846 | −0.362448 | ||||||||
\(146\) | 1026.36 | + | 1777.71i | 0.581796 | + | 1.00770i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 78.8691 | − | 136.605i | 0.0438041 | − | 0.0758709i | ||||
\(149\) | −255.046 | + | 441.753i | −0.140229 | + | 0.242884i | −0.927583 | − | 0.373617i | \(-0.878117\pi\) |
0.787354 | + | 0.616502i | \(0.211451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −337.631 | − | 584.793i | −0.181960 | − | 0.315164i | 0.760588 | − | 0.649235i | \(-0.224911\pi\) |
−0.942548 | + | 0.334071i | \(0.891578\pi\) | |||||||
\(152\) | −2863.28 | −1.52791 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1126.18 | −0.589286 | ||||||||
\(155\) | −270.538 | − | 468.586i | −0.140195 | − | 0.242824i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1813.99 | − | 3141.92i | 0.922115 | − | 1.59715i | 0.125979 | − | 0.992033i | \(-0.459793\pi\) |
0.796136 | − | 0.605118i | \(-0.206874\pi\) | |||||||
\(158\) | 32.6025 | − | 56.4693i | 0.0164159 | − | 0.0284332i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −60.5256 | − | 104.833i | −0.0299060 | − | 0.0517988i | ||||
\(161\) | 674.985 | 0.330411 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −119.559 | −0.0574514 | −0.0287257 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287257 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(164\) | 55.1604 | + | 95.5407i | 0.0262641 | + | 0.0454907i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1116.36 | + | 1933.59i | −0.521965 | + | 0.904070i | ||||
\(167\) | 1534.49 | − | 2657.82i | 0.711035 | − | 1.23155i | −0.253435 | − | 0.967353i | \(-0.581560\pi\) |
0.964469 | − | 0.264195i | \(-0.0851064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 784.203 | + | 1358.28i | 0.356942 | + | 0.618242i | ||||
\(170\) | −1543.54 | −0.696376 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 42.9790 | 0.0190530 | ||||||||
\(173\) | −1056.30 | − | 1829.57i | −0.464216 | − | 0.804046i | 0.534950 | − | 0.844884i | \(-0.320331\pi\) |
−0.999166 | + | 0.0408382i | \(0.986997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −86.6025 | + | 150.000i | −0.0374088 | + | 0.0647939i | ||||
\(176\) | 1767.84 | − | 3061.98i | 0.757134 | − | 1.31140i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 700.771 | + | 1213.77i | 0.295084 | + | 0.511101i | ||||
\(179\) | −1624.79 | −0.678449 | −0.339225 | − | 0.940705i | \(-0.610165\pi\) | ||||
−0.339225 | + | 0.940705i | \(0.610165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2545.41 | −1.04530 | −0.522649 | − | 0.852548i | \(-0.675056\pi\) | ||||
−0.522649 | + | 0.852548i | \(0.675056\pi\) | |||||||
\(182\) | −237.282 | − | 410.985i | −0.0966402 | − | 0.167386i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1136.01 | + | 1967.62i | −0.455150 | + | 0.788343i | ||||
\(185\) | 735.859 | − | 1274.54i | 0.292440 | − | 0.506521i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3361.45 | + | 5822.20i | 1.31451 | + | 2.27680i | ||||
\(188\) | −144.539 | −0.0560722 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1677.20 | −0.640404 | ||||||||
\(191\) | −2402.83 | − | 4161.82i | −0.910274 | − | 1.57664i | −0.813677 | − | 0.581317i | \(-0.802538\pi\) |
−0.0965970 | − | 0.995324i | \(-0.530796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1788.92 | + | 3098.50i | −0.667198 | + | 1.15562i | 0.311486 | + | 0.950251i | \(0.399173\pi\) |
−0.978684 | + | 0.205371i | \(0.934160\pi\) | |||||||
\(194\) | 584.799 | − | 1012.90i | 0.216423 | − | 0.374856i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −79.0450 | − | 136.910i | −0.0288065 | − | 0.0498943i | ||||
\(197\) | −3788.88 | −1.37029 | −0.685144 | − | 0.728408i | \(-0.740261\pi\) | ||||
−0.685144 | + | 0.728408i | \(0.740261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2048.31 | 0.729652 | 0.364826 | − | 0.931076i | \(-0.381129\pi\) | ||||
0.364826 | + | 0.931076i | \(0.381129\pi\) | |||||||
\(200\) | −291.506 | − | 504.904i | −0.103063 | − | 0.178510i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1245.93 | − | 2158.02i | 0.433978 | − | 0.751672i | ||||
\(203\) | −438.449 | + | 759.415i | −0.151591 | + | 0.262564i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 514.654 | + | 891.407i | 0.175341 | + | 0.303700i | ||||
\(206\) | −760.869 | −0.257341 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1489.91 | 0.496666 | ||||||||
\(209\) | 3652.53 | + | 6326.37i | 1.20886 | + | 2.09380i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1190.90 | + | 2062.69i | −0.388553 | + | 0.672994i | −0.992255 | − | 0.124216i | \(-0.960358\pi\) |
0.603702 | + | 0.797210i | \(0.293692\pi\) | |||||||
\(212\) | 26.4720 | − | 45.8509i | 0.00857597 | − | 0.0148540i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2065.89 | − | 3578.22i | −0.659911 | − | 1.14300i | ||||
\(215\) | 401.000 | 0.127200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −749.738 | −0.234542 | ||||||||
\(218\) | 2720.48 | + | 4712.02i | 0.845204 | + | 1.46394i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −79.7114 | + | 138.064i | −0.0244279 | + | 0.0423104i | ||||
\(221\) | −1416.49 | + | 2453.44i | −0.431147 | + | 0.746769i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 278.577 | + | 482.510i | 0.0836543 | + | 0.144893i | 0.904817 | − | 0.425801i | \(-0.140008\pi\) |
−0.821163 | + | 0.570694i | \(0.806674\pi\) | |||||||
\(224\) | −167.733 | −0.0500320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1387.62 | 0.408419 | ||||||||
\(227\) | −2589.04 | − | 4484.36i | −0.757008 | − | 1.31118i | −0.944370 | − | 0.328886i | \(-0.893327\pi\) |
0.187362 | − | 0.982291i | \(-0.440006\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 459.138 | − | 795.250i | 0.132492 | − | 0.229483i | −0.792145 | − | 0.610334i | \(-0.791035\pi\) |
0.924637 | + | 0.380850i | \(0.124369\pi\) | |||||||
\(230\) | −665.429 | + | 1152.56i | −0.190770 | + | 0.330423i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1475.83 | − | 2556.21i | −0.417642 | − | 0.723377i | ||||
\(233\) | 5896.92 | 1.65803 | 0.829013 | − | 0.559230i | \(-0.188903\pi\) | ||||
0.829013 | + | 0.559230i | \(0.188903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1348.56 | −0.374343 | ||||||||
\(236\) | 81.5912 | + | 141.320i | 0.0225048 | + | 0.0389795i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1069.39 | + | 1852.25i | −0.291254 | + | 0.504468i | ||||
\(239\) | 263.420 | − | 456.257i | 0.0712938 | − | 0.123485i | −0.828175 | − | 0.560470i | \(-0.810621\pi\) |
0.899469 | + | 0.436985i | \(0.143954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2911.60 | + | 5043.03i | 0.778226 | + | 1.34793i | 0.932963 | + | 0.359971i | \(0.117213\pi\) |
−0.154738 | + | 0.987956i | \(0.549453\pi\) | |||||||
\(242\) | −6034.95 | −1.60306 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −357.205 | −0.0937201 | ||||||||
\(245\) | −737.500 | − | 1277.39i | −0.192315 | − | 0.333099i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1539.15 | + | 2665.89i | −0.396493 | + | 0.686746i | ||||
\(248\) | 1261.82 | − | 2185.53i | 0.323087 | − | 0.559603i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −170.753 | − | 295.753i | −0.0431975 | − | 0.0748203i | ||||
\(251\) | 3244.98 | 0.816022 | 0.408011 | − | 0.912977i | \(-0.366222\pi\) | ||||
0.408011 | + | 0.912977i | \(0.366222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5796.57 | 1.44042 | ||||||||
\(254\) | 2521.56 | + | 4367.46i | 0.622900 | + | 1.07889i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 409.682 | − | 709.590i | 0.100020 | − | 0.173240i | ||||
\(257\) | −630.700 | + | 1092.40i | −0.153082 | + | 0.265145i | −0.932359 | − | 0.361534i | \(-0.882253\pi\) |
0.779277 | + | 0.626679i | \(0.215586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1019.64 | − | 1766.06i | −0.244622 | − | 0.423698i | ||||
\(260\) | −67.1797 | −0.0160243 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7006.91 | −1.65225 | ||||||||
\(263\) | 962.141 | + | 1666.48i | 0.225582 | + | 0.390720i | 0.956494 | − | 0.291752i | \(-0.0942382\pi\) |
−0.730912 | + | 0.682472i | \(0.760905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 246.987 | − | 427.795i | 0.0572540 | − | 0.0991668i | ||||
\(266\) | −1162.00 | + | 2012.64i | −0.267844 | + | 0.463920i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −170.398 | − | 295.138i | −0.0388384 | − | 0.0672702i | ||||
\(269\) | 4762.53 | 1.07947 | 0.539733 | − | 0.841836i | \(-0.318525\pi\) | ||||
0.539733 | + | 0.841836i | \(0.318525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1595.10 | 0.357547 | 0.178774 | − | 0.983890i | \(-0.442787\pi\) | ||||
0.178774 | + | 0.983890i | \(0.442787\pi\) | |||||||
\(272\) | −3357.39 | − | 5815.18i | −0.748426 | − | 1.29631i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 692.274 | − | 1199.05i | 0.152634 | − | 0.264370i | ||||
\(275\) | −743.718 | + | 1288.16i | −0.163083 | + | 0.282468i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −524.792 | − | 908.966i | −0.113833 | − | 0.197164i | 0.803480 | − | 0.595332i | \(-0.202979\pi\) |
−0.917313 | + | 0.398168i | \(0.869646\pi\) | |||||||
\(278\) | −6072.38 | −1.31006 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −807.846 | −0.172422 | ||||||||
\(281\) | 3788.02 | + | 6561.04i | 0.804179 | + | 1.39288i | 0.916844 | + | 0.399246i | \(0.130728\pi\) |
−0.112665 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2926.47 | − | 5068.79i | 0.614701 | − | 1.06469i | −0.375736 | − | 0.926727i | \(-0.622610\pi\) |
0.990437 | − | 0.137966i | \(-0.0440566\pi\) | |||||||
\(284\) | 221.455 | − | 383.572i | 0.0462709 | − | 0.0801436i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2037.71 | − | 3529.42i | −0.421302 | − | 0.729716i | ||||
\(287\) | 1426.25 | 0.293341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7854.84 | 1.59879 | ||||||||
\(290\) | −864.484 | − | 1497.33i | −0.175049 | − | 0.303194i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 201.323 | − | 348.702i | 0.0403478 | − | 0.0698844i | ||||
\(293\) | −1769.80 | + | 3065.38i | −0.352876 | + | 0.611199i | −0.986752 | − | 0.162235i | \(-0.948130\pi\) |
0.633876 | + | 0.773435i | \(0.281463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 761.256 | + | 1318.53i | 0.150244 | + | 0.260231i | ||||
\(296\) | 6864.24 | 1.34789 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1393.60 | −0.270902 | ||||||||
\(299\) | 1221.32 | + | 2115.38i | 0.236223 | + | 0.409150i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 277.821 | − | 481.200i | 0.0532004 | − | 0.0921458i | ||||
\(302\) | 922.424 | − | 1597.68i | 0.175760 | − | 0.304425i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3648.12 | − | 6318.73i | −0.688270 | − | 1.19212i | ||||
\(305\) | −3332.77 | −0.625685 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −293.303 | −0.0545267 | −0.0272634 | − | 0.999628i | \(-0.508679\pi\) | ||||
−0.0272634 | + | 0.999628i | \(0.508679\pi\) | |||||||
\(308\) | 110.451 | + | 191.307i | 0.0204336 | + | 0.0353921i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 739.125 | − | 1280.20i | 0.135418 | − | 0.234550i | ||||
\(311\) | 2295.95 | − | 3976.70i | 0.418621 | − | 0.725074i | −0.577180 | − | 0.816617i | \(-0.695847\pi\) |
0.995801 | + | 0.0915436i | \(0.0291801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3870.53 | − | 6703.95i | −0.698962 | − | 1.21064i | −0.968827 | − | 0.247740i | \(-0.920312\pi\) |
0.269864 | − | 0.962898i | \(-0.413021\pi\) | |||||||
\(314\) | 9911.82 | 1.78139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.7901 | −0.00227690 | ||||||||
\(317\) | −958.662 | − | 1660.45i | −0.169854 | − | 0.294196i | 0.768514 | − | 0.639833i | \(-0.220996\pi\) |
−0.938369 | + | 0.345636i | \(0.887663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3765.27 | + | 6521.64i | −0.660861 | + | 1.14465i | ||||
\(320\) | 1353.87 | − | 2344.97i | 0.236512 | − | 0.409650i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 922.046 | + | 1597.03i | 0.159576 | + | 0.276395i | ||||
\(323\) | 13873.4 | 2.38990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −626.795 | −0.106979 | ||||||||
\(326\) | −163.321 | − | 282.879i | −0.0277469 | − | 0.0480590i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2400.40 | + | 4157.61i | −0.404085 | + | 0.699895i | ||||
\(329\) | −934.313 | + | 1618.28i | −0.156566 | + | 0.271181i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4128.27 | − | 7150.37i | −0.685529 | − | 1.18737i | −0.973270 | − | 0.229663i | \(-0.926238\pi\) |
0.287742 | − | 0.957708i | \(-0.407096\pi\) | |||||||
\(332\) | 437.952 | 0.0723969 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8384.63 | 1.37361 | ||||||||
\(335\) | −1589.83 | − | 2753.67i | −0.259289 | − | 0.449102i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4259.34 | − | 7377.40i | 0.688490 | − | 1.19250i | −0.283836 | − | 0.958873i | \(-0.591607\pi\) |
0.972326 | − | 0.233627i | \(-0.0750594\pi\) | |||||||
\(338\) | −2142.48 | + | 3710.89i | −0.344780 | + | 0.597176i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 151.384 | + | 262.205i | 0.0241470 | + | 0.0418238i | ||||
\(341\) | −6438.54 | −1.02248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4420.19 | −0.695825 | ||||||||
\(344\) | 935.152 | + | 1619.73i | 0.146570 | + | 0.253866i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2885.88 | − | 4998.49i | 0.448398 | − | 0.776648i | ||||
\(347\) | −4813.82 | + | 8337.77i | −0.744724 | + | 1.28990i | 0.205600 | + | 0.978636i | \(0.434085\pi\) |
−0.950324 | + | 0.311263i | \(0.899248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3795.89 | + | 6574.68i | 0.582205 | + | 1.00841i | 0.995218 | + | 0.0976832i | \(0.0311432\pi\) |
−0.413013 | + | 0.910725i | \(0.635523\pi\) | |||||||
\(350\) | −473.205 | −0.0722682 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1440.45 | −0.218114 | ||||||||
\(353\) | −693.613 | − | 1201.37i | −0.104582 | − | 0.181141i | 0.808986 | − | 0.587828i | \(-0.200017\pi\) |
−0.913567 | + | 0.406688i | \(0.866684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2066.20 | − | 3578.77i | 0.308909 | − | 0.535046i | ||||
\(356\) | 137.458 | − | 238.084i | 0.0204642 | − | 0.0354450i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2219.50 | − | 3844.29i | −0.327666 | − | 0.567534i | ||||
\(359\) | 6335.93 | 0.931469 | 0.465735 | − | 0.884924i | \(-0.345790\pi\) | ||||
0.465735 | + | 0.884924i | \(0.345790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8215.79 | 1.19781 | ||||||||
\(362\) | −3477.09 | − | 6022.50i | −0.504840 | − | 0.874408i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −46.5434 | + | 80.6156i | −0.00670203 | + | 0.0116083i | ||||
\(365\) | 1878.37 | − | 3253.44i | 0.269366 | − | 0.466555i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4595.14 | + | 7959.01i | 0.653581 | + | 1.13204i | 0.982248 | + | 0.187589i | \(0.0600674\pi\) |
−0.328667 | + | 0.944446i | \(0.606599\pi\) | |||||||
\(368\) | −5789.58 | −0.820116 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4020.81 | 0.564951 | ||||||||
\(371\) | −342.236 | − | 592.770i | −0.0478922 | − | 0.0829516i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6342.70 | − | 10985.9i | 0.880462 | − | 1.52501i | 0.0296342 | − | 0.999561i | \(-0.490566\pi\) |
0.850828 | − | 0.525444i | \(-0.176101\pi\) | |||||||
\(374\) | −9183.66 | + | 15906.6i | −1.26972 | + | 2.19922i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3144.92 | − | 5447.16i | −0.431348 | − | 0.747117i | ||||
\(377\) | −3173.32 | −0.433512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13119.0 | −1.77804 | −0.889022 | − | 0.457865i | \(-0.848614\pi\) | ||||
−0.889022 | + | 0.457865i | \(0.848614\pi\) | |||||||
\(380\) | 164.493 | + | 284.911i | 0.0222061 | + | 0.0384621i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6564.64 | − | 11370.3i | 0.879257 | − | 1.52292i | ||||
\(383\) | 867.126 | − | 1501.91i | 0.115687 | − | 0.200376i | −0.802367 | − | 0.596831i | \(-0.796426\pi\) |
0.918054 | + | 0.396455i | \(0.129760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1030.53 | + | 1784.92i | 0.136417 | + | 0.236281i | ||||
\(386\) | −9774.84 | −1.28893 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −229.419 | −0.0300181 | ||||||||
\(389\) | −4681.99 | − | 8109.45i | −0.610248 | − | 1.05698i | −0.991198 | − | 0.132385i | \(-0.957736\pi\) |
0.380950 | − | 0.924596i | \(-0.375597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5504.30 | − | 9533.72i | 0.711929 | − | 1.23310i | ||||
\(392\) | 3439.77 | − | 5957.86i | 0.443201 | − | 0.767647i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5175.71 | − | 8964.59i | −0.661798 | − | 1.14627i | ||||
\(395\) | −119.334 | −0.0152008 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7661.94 | −0.968619 | −0.484309 | − | 0.874897i | \(-0.660929\pi\) | ||||
−0.484309 | + | 0.874897i | \(0.660929\pi\) | |||||||
\(398\) | 2798.04 | + | 4846.35i | 0.352395 | + | 0.610366i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 742.820 | − | 1286.60i | 0.0928525 | − | 0.160825i | ||||
\(401\) | 72.8247 | − | 126.136i | 0.00906906 | − | 0.0157081i | −0.861455 | − | 0.507833i | \(-0.830447\pi\) |
0.870524 | + | 0.492125i | \(0.163780\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1356.58 | − | 2349.66i | −0.167682 | − | 0.290434i | ||||
\(404\) | −488.786 | −0.0601931 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2395.73 | −0.292852 | ||||||||
\(407\) | −8756.34 | − | 15166.4i | −1.06643 | − | 1.84711i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4445.36 | + | 7699.59i | −0.537430 | + | 0.930856i | 0.461612 | + | 0.887082i | \(0.347271\pi\) |
−0.999041 | + | 0.0437736i | \(0.986062\pi\) | |||||||
\(410\) | −1406.06 | + | 2435.37i | −0.169367 | + | 0.293352i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 74.6232 | + | 129.251i | 0.00892335 | + | 0.0154557i | ||||
\(413\) | 2109.66 | 0.251354 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4086.15 | 0.483329 | ||||||||
\(416\) | −303.497 | − | 525.672i | −0.0357696 | − | 0.0619548i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9978.90 | + | 17284.0i | −1.16766 | + | 2.02245i | ||||
\(419\) | 1584.20 | − | 2743.91i | 0.184709 | − | 0.319926i | −0.758769 | − | 0.651360i | \(-0.774199\pi\) |
0.943479 | + | 0.331434i | \(0.107532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4247.51 | + | 7356.91i | 0.491713 | + | 0.851672i | 0.999954 | − | 0.00954269i | \(-0.00303758\pi\) |
−0.508241 | + | 0.861215i | \(0.669704\pi\) | |||||||
\(422\) | −6507.18 | −0.750627 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2303.95 | 0.263891 | ||||||||
\(425\) | 1412.44 | + | 2446.41i | 0.161208 | + | 0.279220i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2309.01 | + | 3999.32i | −0.261688 | + | 0.453257i | ||||
\(428\) | −405.228 | + | 701.876i | −0.0457651 | + | 0.0792675i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 547.776 | + | 948.775i | 0.0614328 | + | 0.106405i | ||||
\(431\) | 2072.30 | 0.231599 | 0.115799 | − | 0.993273i | \(-0.463057\pi\) | ||||
0.115799 | + | 0.993273i | \(0.463057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2906.44 | 0.322574 | 0.161287 | − | 0.986908i | \(-0.448435\pi\) | ||||
0.161287 | + | 0.986908i | \(0.448435\pi\) | |||||||
\(434\) | −1024.16 | − | 1773.90i | −0.113275 | − | 0.196198i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 533.630 | − | 924.274i | 0.0586152 | − | 0.101525i | ||||
\(437\) | 5980.93 | − | 10359.3i | 0.654707 | − | 1.13399i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −965.538 | − | 1672.36i | −0.104972 | − | 0.181817i | 0.808755 | − | 0.588146i | \(-0.200142\pi\) |
−0.913727 | + | 0.406329i | \(0.866809\pi\) | |||||||
\(440\) | −6937.55 | −0.751670 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7739.86 | −0.832913 | ||||||||
\(443\) | 122.312 | + | 211.851i | 0.0131179 | + | 0.0227209i | 0.872510 | − | 0.488597i | \(-0.162491\pi\) |
−0.859392 | + | 0.511317i | \(0.829158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1282.50 | − | 2221.36i | 0.136621 | − | 0.236634i | ||||
\(446\) | −761.087 | + | 1318.24i | −0.0808038 | + | 0.139956i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1875.98 | − | 3249.29i | −0.197839 | − | 0.342667i | ||||
\(449\) | 13276.7 | 1.39547 | 0.697734 | − | 0.716357i | \(-0.254192\pi\) | ||||
0.697734 | + | 0.716357i | \(0.254192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12248.2 | 1.27882 | ||||||||
\(452\) | −136.092 | − | 235.718i | −0.0141620 | − | 0.0245293i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7073.40 | − | 12251.5i | 0.731214 | − | 1.26650i | ||||
\(455\) | −434.256 | + | 752.154i | −0.0447434 | + | 0.0774978i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6257.10 | − | 10837.6i | −0.640470 | − | 1.10933i | −0.985328 | − | 0.170671i | \(-0.945406\pi\) |
0.344859 | − | 0.938655i | \(-0.387927\pi\) | |||||||
\(458\) | 2508.78 | 0.255955 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 261.051 | 0.0264599 | ||||||||
\(461\) | −2245.44 | − | 3889.22i | −0.226856 | − | 0.392926i | 0.730019 | − | 0.683427i | \(-0.239511\pi\) |
−0.956875 | + | 0.290501i | \(0.906178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3046.44 | − | 5276.60i | 0.305789 | − | 0.529642i | −0.671648 | − | 0.740871i | \(-0.734413\pi\) |
0.977437 | + | 0.211229i | \(0.0677465\pi\) | |||||||
\(464\) | 3760.73 | − | 6513.77i | 0.376266 | − | 0.651712i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8055.34 | + | 13952.3i | 0.800765 | + | 1.38697i | ||||
\(467\) | −5193.68 | −0.514635 | −0.257318 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257318 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4405.88 | −0.433783 | ||||||||
\(470\) | −1842.17 | − | 3190.74i | −0.180794 | − | 0.313144i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3550.58 | + | 6149.78i | −0.346247 | + | 0.599717i | ||||
\(473\) | 2385.84 | − | 4132.40i | 0.231927 | − | 0.401709i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1534.74 | + | 2658.25i | 0.148250 | + | 0.256777i | ||||
\(476\) | 419.529 | 0.0403972 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1439.35 | 0.137729 | ||||||||
\(479\) | 9441.27 | + | 16352.8i | 0.900590 | + | 1.55987i | 0.826730 | + | 0.562599i | \(0.190199\pi\) |
0.0738604 | + | 0.997269i | \(0.476468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3689.86 | − | 6391.03i | 0.349778 | − | 0.605833i | ||||
\(482\) | −7954.63 | + | 13777.8i | −0.751708 | + | 1.30200i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 591.885 | + | 1025.17i | 0.0555865 | + | 0.0962786i | ||||
\(485\) | −2140.51 | −0.200403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17619.1 | −1.63942 | −0.819708 | − | 0.572781i | \(-0.805864\pi\) | ||||
−0.819708 | + | 0.572781i | \(0.805864\pi\) | |||||||
\(488\) | −7772.19 | − | 13461.8i | −0.720964 | − | 1.24875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2014.89 | − | 3489.89i | 0.185762 | − | 0.321749i | ||||
\(491\) | 458.133 | − | 793.510i | 0.0421085 | − | 0.0729341i | −0.844203 | − | 0.536024i | \(-0.819926\pi\) |
0.886312 | + | 0.463089i | \(0.153259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7150.83 | + | 12385.6i | 0.653260 | + | 1.13148i | ||||
\(494\) | −8410.08 | −0.765966 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6430.77 | 0.582157 | ||||||||
\(497\) | −2863.02 | − | 4958.89i | −0.258398 | − | 0.447559i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6231.71 | + | 10793.6i | −0.559058 | + | 0.968316i | 0.438518 | + | 0.898723i | \(0.355504\pi\) |
−0.997575 | + | 0.0695938i | \(0.977830\pi\) | |||||||
\(500\) | −33.4936 | + | 58.0127i | −0.00299576 | + | 0.00518881i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4432.73 | + | 7677.71i | 0.394108 | + | 0.682616i | ||||
\(503\) | 49.4842 | 0.00438646 | 0.00219323 | − | 0.999998i | \(-0.499302\pi\) | ||||
0.00219323 | + | 0.999998i | \(0.499302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4560.43 | −0.401855 | ||||||||
\(506\) | 7918.27 | + | 13714.8i | 0.695672 | + | 1.20494i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 494.609 | − | 856.689i | 0.0431983 | − | 0.0748217i | ||||
\(509\) | 3077.51 | − | 5330.40i | 0.267992 | − | 0.464176i | −0.700351 | − | 0.713799i | \(-0.746973\pi\) |
0.968343 | + | 0.249622i | \(0.0803065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2602.75 | − | 4508.09i | −0.225321 | − | 0.390267i | ||||
\(512\) | 12525.4 | 1.08115 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3446.21 | −0.295731 | ||||||||
\(515\) | 696.244 | + | 1205.93i | 0.0595731 | + | 0.103184i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8023.61 | + | 13897.3i | −0.682549 | + | 1.18221i | ||||
\(518\) | 2785.70 | − | 4824.97i | 0.236287 | − | 0.409261i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1461.72 | − | 2531.77i | −0.123270 | − | 0.213510i | ||||
\(521\) | −14718.1 | −1.23764 | −0.618821 | − | 0.785532i | \(-0.712390\pi\) | ||||
−0.618821 | + | 0.785532i | \(0.712390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8318.46 | −0.695489 | −0.347744 | − | 0.937589i | \(-0.613052\pi\) | ||||
−0.347744 | + | 0.937589i | \(0.613052\pi\) | |||||||
\(524\) | 687.211 | + | 1190.28i | 0.0572919 | + | 0.0992325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2628.62 | + | 4552.90i | −0.217896 | + | 0.377407i | ||||
\(527\) | −6113.89 | + | 10589.6i | −0.505361 | + | 0.875311i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1337.62 | + | 2316.83i | 0.109939 | + | 0.190419i | ||||
\(530\) | 1349.56 | 0.110606 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 455.857 | 0.0371502 | ||||||||
\(533\) | 2580.66 | + | 4469.83i | 0.209720 | + | 0.363246i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3780.83 | + | 6548.59i | −0.305532 | + | 0.529197i | ||||
\(536\) | 7415.14 | − | 12843.4i | 0.597548 | − | 1.03498i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6505.74 | + | 11268.3i | 0.521342 | + | 0.902991i | ||||
\(539\) | −17551.7 | −1.40261 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19372.0 | 1.53949 | 0.769746 | − | 0.638350i | \(-0.220383\pi\) | ||||
0.769746 | + | 0.638350i | \(0.220383\pi\) | |||||||
\(542\) | 2178.94 | + | 3774.04i | 0.172682 | + | 0.299094i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1367.82 | + | 2369.13i | −0.107803 | + | 0.186720i | ||||
\(545\) | 4978.83 | − | 8623.59i | 0.391321 | − | 0.677787i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 494.864 | + | 857.129i | 0.0386816 | + | 0.0669985i | 0.884718 | − | 0.466127i | \(-0.154351\pi\) |
−0.846036 | + | 0.533125i | \(0.821018\pi\) | |||||||
\(548\) | −271.582 | −0.0211705 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4063.75 | −0.315052 | ||||||||
\(551\) | 7770.05 | + | 13458.1i | 0.600754 | + | 1.04054i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −82.6767 | + | 143.200i | −0.00635764 | + | 0.0110117i | ||||
\(554\) | 1433.76 | − | 2483.34i | 0.109954 | − | 0.190446i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 595.556 | + | 1031.53i | 0.0454266 | + | 0.0786812i | ||||
\(557\) | 4616.60 | 0.351188 | 0.175594 | − | 0.984463i | \(-0.443815\pi\) | ||||
0.175594 | + | 0.984463i | \(0.443815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2010.76 | 0.152139 | ||||||||
\(560\) | −1029.28 | − | 1782.77i | −0.0776698 | − | 0.134528i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10349.1 | + | 17925.1i | −0.776777 | + | 1.34542i | ||||
\(563\) | −6754.79 | + | 11699.6i | −0.505649 | + | 0.875809i | 0.494330 | + | 0.869274i | \(0.335414\pi\) |
−0.999979 | + | 0.00653505i | \(0.997920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1269.76 | − | 2199.28i | −0.0945470 | − | 0.163760i | ||||
\(566\) | 15990.5 | 1.18751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19274.0 | 1.42380 | ||||||||
\(569\) | 5694.04 | + | 9862.37i | 0.419520 | + | 0.726629i | 0.995891 | − | 0.0905585i | \(-0.0288652\pi\) |
−0.576372 | + | 0.817188i | \(0.695532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4708.69 | + | 8155.70i | −0.345101 | + | 0.597732i | −0.985372 | − | 0.170417i | \(-0.945489\pi\) |
0.640271 | + | 0.768149i | \(0.278822\pi\) | |||||||
\(572\) | −399.702 | + | 692.304i | −0.0292174 | + | 0.0506061i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1948.29 | + | 3374.55i | 0.141673 | + | 0.245385i | ||||
\(575\) | 2435.64 | 0.176649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3751.39 | −0.270663 | −0.135332 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135332 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(578\) | 10729.9 | + | 18584.7i | 0.772154 | + | 1.33741i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −169.571 | + | 293.705i | −0.0121397 | + | 0.0210266i | ||||
\(581\) | 2830.97 | − | 4903.38i | 0.202149 | − | 0.350132i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2939.02 | − | 5090.53i | −0.208785 | − | 0.361627i | ||||
\(584\) | 17521.8 | 1.24154 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9670.35 | −0.681704 | ||||||||
\(587\) | 4646.77 | + | 8048.45i | 0.326734 | + | 0.565920i | 0.981862 | − | 0.189598i | \(-0.0607186\pi\) |
−0.655128 | + | 0.755518i | \(0.727385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6643.31 | + | 11506.6i | −0.464742 | + | 0.804957i | ||||
\(590\) | −2079.79 | + | 3602.30i | −0.145125 | + | 0.251364i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8745.77 | + | 15148.1i | 0.607178 | + | 1.05166i | ||||
\(593\) | 1527.88 | 0.105805 | 0.0529027 | − | 0.998600i | \(-0.483153\pi\) | ||||
0.0529027 | + | 0.998600i | \(0.483153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3914.26 | 0.269696 | ||||||||
\(596\) | 136.679 | + | 236.735i | 0.00939359 | + | 0.0162702i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3336.70 | + | 5779.34i | −0.228174 | + | 0.395209i | ||||
\(599\) | −835.199 | + | 1446.61i | −0.0569704 | + | 0.0986757i | −0.893104 | − | 0.449850i | \(-0.851477\pi\) |
0.836134 | + | 0.548526i | \(0.184811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8696.95 | − | 15063.6i | −0.590276 | − | 1.02239i | −0.994195 | − | 0.107593i | \(-0.965686\pi\) |
0.403919 | − | 0.914795i | \(-0.367648\pi\) | |||||||
\(602\) | 1518.04 | 0.102775 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −361.871 | −0.0243780 | ||||||||
\(605\) | 5522.36 | + | 9565.01i | 0.371100 | + | 0.642765i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2040.68 | + | 3534.56i | −0.136456 | + | 0.236348i | −0.926153 | − | 0.377149i | \(-0.876904\pi\) |
0.789697 | + | 0.613497i | \(0.210238\pi\) | |||||||
\(608\) | −1486.26 | + | 2574.28i | −0.0991378 | + | 0.171712i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4552.65 | − | 7885.42i | −0.302182 | − | 0.523395i | ||||
\(611\) | −6762.18 | −0.447739 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2300.45 | 0.151573 | 0.0757866 | − | 0.997124i | \(-0.475853\pi\) | ||||
0.0757866 | + | 0.997124i | \(0.475853\pi\) | |||||||
\(614\) | −400.660 | − | 693.963i | −0.0263344 | − | 0.0456125i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4806.48 | + | 8325.06i | −0.314381 | + | 0.544523i | ||||
\(617\) | 1452.92 | − | 2516.53i | 0.0948012 | − | 0.164201i | −0.814724 | − | 0.579848i | \(-0.803112\pi\) |
0.909526 | + | 0.415648i | \(0.136445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8927.74 | − | 15463.3i | −0.579703 | − | 1.00408i | −0.995513 | − | 0.0946238i | \(-0.969835\pi\) |
0.415810 | − | 0.909452i | \(-0.363498\pi\) | |||||||
\(620\) | −289.962 | −0.0187825 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12545.3 | 0.808714 | ||||||||
\(623\) | −1777.08 | − | 3078.00i | −0.114281 | − | 0.197941i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 10574.5 | − | 18315.5i | 0.675146 | − | 1.16939i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −972.114 | − | 1683.75i | −0.0617700 | − | 0.106989i | ||||
\(629\) | −33259.3 | −2.10832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24250.9 | −1.52998 | −0.764988 | − | 0.644045i | \(-0.777255\pi\) | ||||
−0.764988 | + | 0.644045i | \(0.777255\pi\) | |||||||
\(632\) | −278.292 | − | 482.016i | −0.0175156 | − | 0.0303379i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2619.11 | − | 4536.44i | 0.164067 | − | 0.284172i | ||||
\(635\) | 4614.77 | − | 7993.01i | 0.288396 | − | 0.499517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3698.09 | − | 6405.28i | −0.230021 | − | 0.398409i | ||||
\(638\) | −20573.8 | −1.27669 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6429.28 | 0.397093 | ||||||||
\(641\) | −749.919 | − | 1298.90i | −0.0462091 | − | 0.0800364i | 0.841996 | − | 0.539484i | \(-0.181381\pi\) |
−0.888205 | + | 0.459448i | \(0.848047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11560.1 | + | 20022.6i | −0.708996 | + | 1.22802i | 0.256234 | + | 0.966615i | \(0.417518\pi\) |
−0.965230 | + | 0.261402i | \(0.915815\pi\) | |||||||
\(644\) | 180.862 | − | 313.261i | 0.0110667 | − | 0.0191681i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18951.5 | + | 32824.9i | 1.15424 | + | 1.99919i | ||||
\(647\) | 10703.6 | 0.650391 | 0.325195 | − | 0.945647i | \(-0.394570\pi\) | ||||
0.325195 | + | 0.945647i | \(0.394570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18117.1 | 1.09578 | ||||||||
\(650\) | −856.218 | − | 1483.01i | −0.0516671 | − | 0.0894901i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −32.0357 | + | 55.4875i | −0.00192426 | + | 0.00333291i | ||||
\(653\) | 9054.57 | − | 15683.0i | 0.542623 | − | 0.939850i | −0.456129 | − | 0.889913i | \(-0.650765\pi\) |
0.998752 | − | 0.0499370i | \(-0.0159021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6411.77 | + | 11105.5i | 0.382486 | + | 0.662486i | ||||
\(656\) | −12233.5 | −0.728104 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5105.18 | −0.302463 | ||||||||
\(659\) | −12556.7 | − | 21748.8i | −0.742244 | − | 1.28560i | −0.951471 | − | 0.307737i | \(-0.900428\pi\) |
0.209227 | − | 0.977867i | \(-0.432905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9296.80 | − | 16102.5i | 0.547055 | − | 0.947528i | −0.451419 | − | 0.892312i | \(-0.649082\pi\) |
0.998474 | − | 0.0552157i | \(-0.0175847\pi\) | |||||||
\(662\) | 11278.6 | − | 19535.2i | 0.662170 | − | 1.14691i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9529.12 | + | 16504.9i | 0.556930 | + | 0.964631i | ||||
\(665\) | 4253.21 | 0.248018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12331.1 | 0.715834 | ||||||||
\(668\) | −822.333 | − | 1424.32i | −0.0476303 | − | 0.0824981i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4343.51 | − | 7523.17i | 0.250454 | − | 0.433799i | ||||
\(671\) | −19829.1 | + | 34345.0i | −1.14083 | + | 1.97597i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2145.19 | − | 3715.58i | −0.122869 | − | 0.212816i | 0.798029 | − | 0.602619i | \(-0.205876\pi\) |
−0.920898 | + | 0.389803i | \(0.872543\pi\) | |||||||
\(674\) | 23273.5 | 1.33006 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 840.506 | 0.0478212 | ||||||||
\(677\) | 13475.3 | + | 23339.8i | 0.764988 | + | 1.32500i | 0.940253 | + | 0.340476i | \(0.110588\pi\) |
−0.175266 | + | 0.984521i | \(0.556078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1482.99 | + | 2568.61i | −0.0838173 | + | 0.145176i | ||||
\(680\) | −6587.74 | + | 11410.3i | −0.371512 | + | 0.643478i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8795.20 | − | 15233.7i | −0.493821 | − | 0.855323i | ||||
\(683\) | 18870.9 | 1.05721 | 0.528607 | − | 0.848867i | \(-0.322715\pi\) | ||||
0.528607 | + | 0.848867i | \(0.322715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2533.90 | −0.141336 | ||||||||
\(686\) | −6038.10 | − | 10458.3i | −0.336058 | − | 0.582069i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2382.97 | + | 4127.42i | −0.132049 | + | 0.228716i | ||||
\(689\) | 1238.48 | − | 2145.12i | 0.0684796 | − | 0.118610i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1848.03 | − | 3200.88i | −0.101740 | − | 0.176219i | 0.810662 | − | 0.585515i | \(-0.199108\pi\) |
−0.912402 | + | 0.409296i | \(0.865774\pi\) | |||||||
\(692\) | −1132.14 | −0.0621931 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26303.2 | −1.43870 | ||||||||
\(695\) | 5556.62 | + | 9624.34i | 0.303273 | + | 0.525284i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11630.6 | − | 20144.9i | 0.632055 | − | 1.09475i | ||||
\(698\) | −10370.6 | + | 17962.4i | −0.562367 | + | 0.974048i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 46.4102 | + | 80.3848i | 0.00250591 | + | 0.00434037i | ||||
\(701\) | −1123.53 | −0.0605349 | −0.0302674 | − | 0.999542i | \(-0.509636\pi\) | ||||
−0.0302674 | + | 0.999542i | \(0.509636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36139.3 | −1.93886 | ||||||||
\(704\) | −16110.4 | − | 27904.0i | −0.862475 | − | 1.49385i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1894.99 | − | 3282.21i | 0.101018 | − | 0.174968i | ||||
\(707\) | −3159.56 | + | 5472.52i | −0.168073 | + | 0.291111i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13233.8 | + | 22921.7i | 0.700998 | + | 1.21416i | 0.968116 | + | 0.250501i | \(0.0805952\pi\) |
−0.267118 | + | 0.963664i | \(0.586071\pi\) | |||||||
\(710\) | 11290.0 | 0.596767 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11963.4 | 0.629702 | ||||||||
\(713\) | 5271.48 | + | 9130.46i | 0.276884 | + | 0.479577i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3729.27 | + | 6459.28i | −0.195058 | + | 0.337851i | ||||
\(716\) | −435.361 | + | 754.067i | −0.0227237 | + | 0.0393587i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8655.04 | + | 14991.0i | 0.449865 | + | 0.779189i | ||||
\(719\) | −7882.34 | −0.408848 | −0.204424 | − | 0.978882i | \(-0.565532\pi\) | ||||
−0.204424 | + | 0.978882i | \(0.565532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1929.49 | 0.0996641 | ||||||||
\(722\) | 11223.0 | + | 19438.8i | 0.578499 | + | 1.00199i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −682.040 | + | 1181.33i | −0.0350108 | + | 0.0606405i | ||||
\(725\) | −1582.12 | + | 2740.30i | −0.0810459 | + | 0.140376i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10004.5 | − | 17328.2i | −0.510379 | − | 0.884002i | −0.999928 | − | 0.0120259i | \(-0.996172\pi\) |
0.489549 | − | 0.871976i | \(-0.337161\pi\) | |||||||
\(728\) | −4050.83 | −0.206228 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10263.6 | 0.520375 | ||||||||
\(731\) | −4531.09 | − | 7848.08i | −0.229259 | − | 0.397088i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18146.7 | − | 31431.1i | 0.914414 | − | 1.58381i | 0.106657 | − | 0.994296i | \(-0.465985\pi\) |
0.807757 | − | 0.589515i | \(-0.200681\pi\) | |||||||
\(734\) | −12554.1 | + | 21744.4i | −0.631311 | + | 1.09346i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1179.35 | + | 2042.69i | 0.0590644 | + | 0.102302i | ||||
\(737\) | −37836.4 | −1.89107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27475.5 | −1.36766 | −0.683832 | − | 0.729639i | \(-0.739688\pi\) | ||||
−0.683832 | + | 0.729639i | \(0.739688\pi\) | |||||||
\(740\) | −394.346 | − | 683.027i | −0.0195898 | − | 0.0339305i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 935.005 | − | 1619.48i | 0.0462603 | − | 0.0801251i | ||||
\(743\) | 19074.4 | − | 33037.9i | 0.941822 | − | 1.63128i | 0.179829 | − | 0.983698i | \(-0.442446\pi\) |
0.761993 | − | 0.647585i | \(-0.224221\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1275.23 | + | 2208.76i | 0.0627125 | + | 0.108621i | ||||
\(746\) | 34657.1 | 1.70092 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3602.79 | 0.176111 | ||||||||
\(749\) | 5238.88 | + | 9074.00i | 0.255573 | + | 0.442666i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14111.5 | + | 24441.9i | −0.685669 | + | 1.18761i | 0.287557 | + | 0.957763i | \(0.407157\pi\) |
−0.973226 | + | 0.229850i | \(0.926177\pi\) | |||||||
\(752\) | 8013.93 | − | 13880.5i | 0.388614 | − | 0.673099i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4334.83 | − | 7508.15i | −0.209370 | − | 0.362640i | ||||
\(755\) | −3376.31 | −0.162750 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34786.4 | 1.67019 | 0.835095 | − | 0.550106i | \(-0.185413\pi\) | ||||
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(758\) | −17920.9 | − | 31039.9i | −0.858729 | − | 1.48736i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7158.20 | + | 12398.4i | −0.341651 | + | 0.591758i | ||||
\(761\) | 582.982 | − | 1009.76i | 0.0277702 | − | 0.0480993i | −0.851806 | − | 0.523857i | \(-0.824493\pi\) |
0.879576 | + | 0.475758i | \(0.157826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6898.87 | − | 11949.2i | −0.327334 | − | 0.566959i | ||||
\(764\) | −2575.34 | −0.121954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4738.07 | 0.223490 | ||||||||
\(767\) | 3817.21 | + | 6611.61i | 0.179702 | + | 0.311253i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13172.7 | − | 22815.7i | 0.617710 | − | 1.06990i | −0.372193 | − | 0.928155i | \(-0.621394\pi\) |
0.989903 | − | 0.141749i | \(-0.0452727\pi\) | |||||||
\(770\) | −2815.45 | + | 4876.50i | −0.131768 | + | 0.228230i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 958.679 | + | 1660.48i | 0.0446938 | + | 0.0774120i | ||||
\(773\) | −25867.0 | −1.20358 | −0.601792 | − | 0.798653i | \(-0.705546\pi\) | ||||
−0.601792 | + | 0.798653i | \(0.705546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2705.38 | −0.125394 | ||||||||
\(776\) | −4991.78 | − | 8646.02i | −0.230921 | − | 0.399967i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12791.4 | − | 22155.4i | 0.589454 | − | 1.02096i | ||||
\(779\) | 12637.8 | − | 21889.3i | 0.581252 | − | 1.00676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24586.8 | − | 42585.5i | −1.12648 | − | 1.95113i | ||||
\(782\) | 30076.0 | 1.37534 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17530.6 | 0.798586 | ||||||||
\(785\) | −9069.95 | − | 15709.6i | −0.412383 | − | 0.714267i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4035.49 | − | 6989.67i | 0.182782 | − | 0.316588i | −0.760045 | − | 0.649871i | \(-0.774823\pi\) |
0.942827 | + | 0.333283i | \(0.108156\pi\) | |||||||
\(788\) | −1015.23 | + | 1758.43i | −0.0458959 | + | 0.0794941i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −163.013 | − | 282.346i | −0.00734143 | − | 0.0127157i | ||||
\(791\) | −3518.85 | −0.158174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16711.7 | −0.748361 | ||||||||
\(794\) | −10466.4 | − | 18128.3i | −0.467807 | − | 0.810265i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 548.842 | − | 950.623i | 0.0244387 | − | 0.0423291i | ||||
\(797\) | −6450.54 | + | 11172.7i | −0.286688 | + | 0.496557i | −0.973017 | − | 0.230733i | \(-0.925888\pi\) |
0.686329 | + | 0.727291i | \(0.259221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15238.1 | + | 26393.1i | 0.674699 | + | 1.16861i | ||||
\(800\) | −605.256 | −0.0267488 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 397.922 | 0.0175201 | ||||||||
\(803\) | −22351.7 | − | 38714.2i | −0.982282 | − | 1.70136i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1687.46 | − | 2922.77i | 0.0738822 | − | 0.127968i | ||||
\(806\) | 3706.24 | − | 6419.39i | 0.161969 | − | 0.280538i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10635.2 | − | 18420.6i | −0.463049 | − | 0.802025i | ||||
\(809\) | −26916.2 | −1.16974 | −0.584872 | − | 0.811126i | \(-0.698855\pi\) | ||||
−0.584872 | + | 0.811126i | \(0.698855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28082.5 | −1.21592 | −0.607959 | − | 0.793969i | \(-0.708011\pi\) | ||||
−0.607959 | + | 0.793969i | \(0.708011\pi\) | |||||||
\(812\) | 234.964 | + | 406.969i | 0.0101547 | + | 0.0175885i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23922.8 | − | 41435.4i | 1.03009 | − | 1.78417i | ||||
\(815\) | −298.897 | + | 517.705i | −0.0128465 | + | 0.0222508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4923.45 | − | 8527.67i | −0.210832 | − | 0.365172i | ||||
\(818\) | −24289.9 | −1.03823 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 551.604 | 0.0234913 | ||||||||
\(821\) | −23186.8 | − | 40160.8i | −0.985659 | − | 1.70721i | −0.638971 | − | 0.769231i | \(-0.720640\pi\) |
−0.346688 | − | 0.937981i | \(-0.612694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3902.27 | − | 6758.94i | 0.165279 | − | 0.286272i | −0.771475 | − | 0.636259i | \(-0.780481\pi\) |
0.936754 | + | 0.349988i | \(0.113814\pi\) | |||||||
\(824\) | −3247.35 | + | 5624.58i | −0.137290 | + | 0.237793i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2881.84 | + | 4991.50i | 0.121395 | + | 0.210262i | ||||
\(827\) | 23964.1 | 1.00764 | 0.503818 | − | 0.863810i | \(-0.331928\pi\) | ||||
0.503818 | + | 0.863810i | \(0.331928\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4583.86 | −0.192044 | −0.0960218 | − | 0.995379i | \(-0.530612\pi\) | ||||
−0.0960218 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(830\) | 5581.79 | + | 9667.94i | 0.233430 | + | 0.404312i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6788.80 | − | 11758.5i | 0.282884 | − | 0.489969i | ||||
\(833\) | −16666.7 | + | 28867.6i | −0.693239 | + | 1.20073i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7672.47 | − | 13289.1i | −0.317984 | − | 0.550765i | ||||
\(836\) | 3914.77 | 0.161956 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8656.23 | 0.356831 | ||||||||
\(839\) | −13464.2 | − | 23320.6i | −0.554034 | − | 0.959614i | −0.997978 | − | 0.0635601i | \(-0.979755\pi\) |
0.443944 | − | 0.896054i | \(-0.353579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4184.62 | − | 7247.97i | 0.171578 | − | 0.297182i | ||||
\(842\) | −11604.4 | + | 20099.5i | −0.474958 | + | 0.822652i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 638.200 | + | 1105.39i | 0.0260281 | + | 0.0450821i | ||||
\(845\) | 7842.03 | 0.319259 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15304.0 | 0.620841 | ||||||||
\(848\) | 2935.47 | + | 5084.39i | 0.118873 | + | 0.205895i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3858.85 | + | 6683.72i | −0.155714 | + | 0.269705i | ||||
\(851\) | −14338.3 | + | 24834.7i | −0.577568 | + | 1.00038i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3506.70 | + | 6073.78i | 0.140759 | + | 0.243801i | 0.927782 | − | 0.373122i | \(-0.121713\pi\) |
−0.787024 | + | 0.616922i | \(0.788379\pi\) | |||||||
\(854\) | −12616.7 | −0.505543 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35268.4 | −1.40823 | ||||||||
\(857\) | 10332.5 | + | 17896.4i | 0.411846 | + | 0.713338i | 0.995092 | − | 0.0989575i | \(-0.0315508\pi\) |
−0.583246 | + | 0.812296i | \(0.698217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10127.9 | − | 17542.1i | 0.402283 | − | 0.696774i | −0.591718 | − | 0.806145i | \(-0.701550\pi\) |
0.994001 | + | 0.109371i | \(0.0348836\pi\) | |||||||
\(860\) | 107.448 | − | 186.105i | 0.00426038 | − | 0.00737920i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2830.81 | + | 4903.11i | 0.111854 | + | 0.193736i | ||||
\(863\) | 16293.0 | 0.642666 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10563.0 | −0.415207 | ||||||||
\(866\) | 3970.27 | + | 6876.71i | 0.155791 | + | 0.269839i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −200.892 | + | 347.955i | −0.00785566 | + | 0.0136064i | ||||
\(869\) | −710.004 | + | 1229.76i | −0.0277160 | + | 0.0480056i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7972.00 | − | 13807.9i | −0.310127 | − | 0.537156i | ||||
\(872\) | 46443.6 | 1.80364 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32680.4 | 1.26480 | ||||||||
\(875\) | 433.013 | + | 750.000i | 0.0167297 | + | 0.0289767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14132.1 | + | 24477.4i | −0.544134 | + | 0.942468i | 0.454527 | + | 0.890733i | \(0.349808\pi\) |
−0.998661 | + | 0.0517347i | \(0.983525\pi\) | |||||||
\(878\) | 2637.90 | − | 4568.98i | 0.101395 | − | 0.175621i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8839.18 | − | 15309.9i | −0.338601 | − | 0.586474i | ||||
\(881\) | −24644.6 | −0.942447 | −0.471224 | − | 0.882014i | \(-0.656188\pi\) | ||||
−0.471224 | + | 0.882014i | \(0.656188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36026.4 | 1.37303 | 0.686515 | − | 0.727116i | \(-0.259140\pi\) | ||||
0.686515 | + | 0.727116i | \(0.259140\pi\) | |||||||
\(884\) | 759.096 | + | 1314.79i | 0.0288814 | + | 0.0500240i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −334.163 | + | 578.788i | −0.0126709 | + | 0.0219467i | ||||
\(887\) | −7087.35 | + | 12275.6i | −0.268286 | + | 0.464685i | −0.968419 | − | 0.249327i | \(-0.919791\pi\) |
0.700133 | + | 0.714012i | \(0.253124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6394.41 | − | 11075.4i | −0.241239 | − | 0.417839i | ||||
\(890\) | 7007.71 | 0.263931 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 298.578 | 0.0112075 | ||||||||
\(893\) | 16557.6 | + | 28678.6i | 0.620469 | + | 1.07468i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4061.97 | + | 7035.54i | −0.151706 | + | 0.262762i | ||||
\(896\) | 4454.34 | − | 7715.14i | 0.166081 | − | 0.287661i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18136.3 | + | 31412.9i | 0.673959 | + | 1.16733i | ||||
\(899\) | −13696.7 | −0.508133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11163.3 | −0.412768 | ||||||||
\(902\) | 16731.4 | + | 28979.6i | 0.617621 | + | 1.06975i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5922.27 | − | 10257.7i | 0.217889 | − | 0.377395i | ||||
\(905\) | −6363.52 | + | 11021.9i | −0.233736 | + | 0.404842i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18002.6 | − | 31181.4i | −0.659058 | − | 1.14152i | −0.980860 | − | 0.194714i | \(-0.937622\pi\) |
0.321802 | − | 0.946807i | \(-0.395711\pi\) | |||||||
\(908\) | −2774.93 | −0.101420 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2372.82 | −0.0864376 | ||||||||
\(911\) | 601.245 | + | 1041.39i | 0.0218662 | + | 0.0378734i | 0.876751 | − | 0.480944i | \(-0.159706\pi\) |
−0.854885 | + | 0.518817i | \(0.826373\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24311.6 | − | 42108.8i | 0.881265 | − | 1.52640i | ||||
\(914\) | 17094.7 | − | 29608.9i | 0.618646 | − | 1.07153i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −246.051 | − | 426.173i | −0.00887529 | − | 0.0153725i | ||||
\(917\) | 17768.8 | 0.639889 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1151.63 | 0.0413370 | 0.0206685 | − | 0.999786i | \(-0.493421\pi\) | ||||
0.0206685 | + | 0.999786i | \(0.493421\pi\) | |||||||
\(920\) | 5680.04 | + | 9838.11i | 0.203549 | + | 0.352558i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6134.66 | − | 10625.6i | 0.219126 | − | 0.379538i | ||||
\(923\) | 10360.7 | − | 17945.2i | 0.369476 | − | 0.639951i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3679.29 | − | 6372.72i | −0.130783 | − | 0.226523i | ||||
\(926\) | 16646.1 | 0.590739 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3064.27 | −0.108394 | ||||||||
\(929\) | 2698.53 | + | 4673.99i | 0.0953023 | + | 0.165068i | 0.909735 | − | 0.415190i | \(-0.136285\pi\) |
−0.814432 | + | 0.580258i | \(0.802952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18110.0 | + | 31367.4i | −0.637519 | + | 1.10422i | ||||
\(932\) | 1580.07 | − | 2736.77i | 0.0555333 | − | 0.0961865i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7094.70 | − | 12288.4i | −0.248550 | − | 0.430501i | ||||
\(935\) | 33614.5 | 1.17573 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45594.6 | 1.58966 | 0.794830 | − | 0.606832i | \(-0.207560\pi\) | ||||
0.794830 | + | 0.606832i | \(0.207560\pi\) | |||||||
\(938\) | −6018.54 | − | 10424.4i | −0.209501 | − | 0.362867i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −361.347 | + | 625.871i | −0.0125381 | + | 0.0217167i | ||||
\(941\) | −18622.8 | + | 32255.6i | −0.645149 | + | 1.11743i | 0.339119 | + | 0.940744i | \(0.389871\pi\) |
−0.984267 | + | 0.176687i | \(0.943462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10028.1 | − | 17369.2i | −0.346299 | − | 0.599807i | ||||
\(944\) | −18095.3 | −0.623888 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13036.5 | 0.448048 | ||||||||
\(947\) | 2388.77 | + | 4137.47i | 0.0819689 | + | 0.141974i | 0.904096 | − | 0.427330i | \(-0.140546\pi\) |
−0.822127 | + | 0.569305i | \(0.807213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9418.83 | − | 16313.9i | 0.322179 | − | 0.558031i | ||||
\(950\) | −4193.00 | + | 7262.48i | −0.143199 | + | 0.248027i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9128.24 | + | 15810.6i | 0.310765 | + | 0.538260i | ||||
\(953\) | 56883.2 | 1.93350 | 0.966752 | − | 0.255717i | \(-0.0823114\pi\) | ||||
0.966752 | + | 0.255717i | \(0.0823114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24028.3 | −0.814174 | ||||||||
\(956\) | −141.166 | − | 244.507i | −0.00477578 | − | 0.00827190i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25794.0 | + | 44676.6i | −0.869903 | + | 1.50672i | ||||
\(959\) | −1755.54 | + | 3040.68i | −0.0591129 | + | 0.102386i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9040.21 | + | 15658.1i | 0.303455 | + | 0.525599i | ||||
\(962\) | 20161.8 | 0.675719 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3120.64 | 0.104262 | ||||||||
\(965\) | 8944.60 | + | 15492.5i | 0.298380 | + | 0.516810i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7024.99 | + | 12167.6i | −0.233618 | + | 0.404638i | −0.958870 | − | 0.283845i | \(-0.908390\pi\) |
0.725252 | + | 0.688483i | \(0.241723\pi\) | |||||||
\(968\) | −25756.8 | + | 44612.2i | −0.855223 | + | 1.48129i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2923.99 | − | 5064.51i | −0.0967874 | − | 0.167641i | ||||
\(971\) | −779.492 | −0.0257622 | −0.0128811 | − | 0.999917i | \(-0.504100\pi\) | ||||
−0.0128811 | + | 0.999917i | \(0.504100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15398.9 | 0.507366 | ||||||||
\(974\) | −24068.1 | − | 41687.1i | −0.791777 | − | 1.37140i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19805.2 | − | 34303.6i | 0.649537 | − | 1.12503i | ||||
\(977\) | 23377.4 | − | 40490.9i | 0.765517 | − | 1.32592i | −0.174455 | − | 0.984665i | \(-0.555816\pi\) |
0.939973 | − | 0.341250i | \(-0.110850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15261.1 | − | 26433.0i | −0.498209 | − | 0.862923i | ||||
\(980\) | −790.450 | −0.0257653 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2503.29 | 0.0813474 | ||||||||
\(983\) | −1798.05 | − | 3114.31i | −0.0583406 | − | 0.101049i | 0.835380 | − | 0.549673i | \(-0.185248\pi\) |
−0.893721 | + | 0.448624i | \(0.851914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9472.21 | + | 16406.3i | −0.306406 | + | 0.530710i | ||||
\(986\) | −19536.4 | + | 33838.1i | −0.631001 | + | 1.09293i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 824.828 | + | 1428.64i | 0.0265600 | + | 0.0460033i | ||||
\(989\) | −7813.53 | −0.251219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15143.8 | −0.485427 | −0.242713 | − | 0.970098i | \(-0.578037\pi\) | ||||
−0.242713 | + | 0.970098i | \(0.578037\pi\) | |||||||
\(992\) | −1309.96 | − | 2268.92i | −0.0419267 | − | 0.0726192i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7821.91 | − | 13547.9i | 0.249593 | − | 0.432309i | ||||
\(995\) | 5120.77 | − | 8869.43i | 0.163155 | − | 0.282593i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11004.4 | − | 19060.3i | −0.349563 | − | 0.605461i | 0.636609 | − | 0.771187i | \(-0.280337\pi\) |
−0.986172 | + | 0.165726i | \(0.947003\pi\) | |||||||
\(998\) | −34050.7 | −1.08002 | ||||||||
\(999\) | 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 | 405.4.e.p.271.2 | 4 | ||
3.2 | odd | 2 | 405.4.e.o.271.1 | 4 | |||
9.2 | odd | 6 | 405.4.e.o.136.1 | 4 | |||
9.4 | even | 3 | 405.4.a.c.1.1 | ✓ | 2 | ||
9.5 | odd | 6 | 405.4.a.f.1.2 | yes | 2 | ||
9.7 | even | 3 | inner | 405.4.e.p.136.2 | 4 | ||
45.4 | even | 6 | 2025.4.a.m.1.2 | 2 | |||
45.14 | odd | 6 | 2025.4.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.c.1.1 | ✓ | 2 | 9.4 | even | 3 | ||
405.4.a.f.1.2 | yes | 2 | 9.5 | odd | 6 | ||
405.4.e.o.136.1 | 4 | 9.2 | odd | 6 | |||
405.4.e.o.271.1 | 4 | 3.2 | odd | 2 | |||
405.4.e.p.136.2 | 4 | 9.7 | even | 3 | inner | ||
405.4.e.p.271.2 | 4 | 1.1 | even | 1 | trivial | ||
2025.4.a.i.1.1 | 2 | 45.14 | odd | 6 | |||
2025.4.a.m.1.2 | 2 | 45.4 | even | 6 |