Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.a (trivial) |
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: | yes |
Analytic conductor: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3173728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 29x^{2} + 118 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.21254\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.21254 | 0.782249 | 0.391125 | − | 0.920338i | \(-0.372086\pi\) | ||||
0.391125 | + | 0.920338i | \(0.372086\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.10469 | −0.388086 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.1047 | −0.923566 | −0.461783 | − | 0.886993i | \(-0.652790\pi\) | ||||
−0.461783 | + | 0.886993i | \(0.652790\pi\) | |||||||
\(8\) | −24.5695 | −1.08583 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 66.8393 | 1.83207 | 0.916037 | − | 0.401094i | \(-0.131370\pi\) | ||||
0.916037 | + | 0.401094i | \(0.131370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −72.7328 | −1.55173 | −0.775863 | − | 0.630901i | \(-0.782685\pi\) | ||||
−0.775863 | + | 0.630901i | \(0.782685\pi\) | |||||||
\(14\) | −37.8447 | −0.722459 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.5234 | −0.461304 | ||||||||
\(17\) | −40.2889 | −0.574794 | −0.287397 | − | 0.957812i | \(-0.592790\pi\) | ||||
−0.287397 | + | 0.957812i | \(0.592790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.4766 | 0.464586 | 0.232293 | − | 0.972646i | \(-0.425377\pi\) | ||||
0.232293 | + | 0.972646i | \(0.425377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 147.884 | 1.43314 | ||||||||
\(23\) | 204.480 | 1.85378 | 0.926891 | − | 0.375331i | \(-0.122471\pi\) | ||||
0.926891 | + | 0.375331i | \(0.122471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −160.924 | −1.21384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 53.1047 | 0.358423 | ||||||||
\(29\) | −21.6621 | −0.138709 | −0.0693544 | − | 0.997592i | \(-0.522094\pi\) | ||||
−0.0693544 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 128.372 | 0.743751 | 0.371875 | − | 0.928283i | \(-0.378715\pi\) | ||||
0.371875 | + | 0.928283i | \(0.378715\pi\) | |||||||
\(32\) | 131.234 | 0.724975 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −89.1406 | −0.449632 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.4187 | −0.0862817 | −0.0431408 | − | 0.999069i | \(-0.513736\pi\) | ||||
−0.0431408 | + | 0.999069i | \(0.513736\pi\) | |||||||
\(38\) | 85.1308 | 0.363422 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 270.393 | 1.02996 | 0.514978 | − | 0.857203i | \(-0.327800\pi\) | ||||
0.514978 | + | 0.857203i | \(0.327800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −242.884 | −0.861384 | −0.430692 | − | 0.902499i | \(-0.641730\pi\) | ||||
−0.430692 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(44\) | −207.515 | −0.711002 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 452.419 | 1.45012 | ||||||||
\(47\) | 307.646 | 0.954783 | 0.477391 | − | 0.878691i | \(-0.341582\pi\) | ||||
0.477391 | + | 0.878691i | \(0.341582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −50.4297 | −0.147025 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 225.813 | 0.602203 | ||||||||
\(53\) | 289.019 | 0.749054 | 0.374527 | − | 0.927216i | \(-0.377805\pi\) | ||||
0.374527 | + | 0.927216i | \(0.377805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 420.254 | 1.00284 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47.9282 | −0.108505 | ||||||||
\(59\) | 17.7003 | 0.0390573 | 0.0195287 | − | 0.999809i | \(-0.493783\pi\) | ||||
0.0195287 | + | 0.999809i | \(0.493783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 764.851 | 1.60540 | 0.802698 | − | 0.596385i | \(-0.203397\pi\) | ||||
0.802698 | + | 0.596385i | \(0.203397\pi\) | |||||||
\(62\) | 284.027 | 0.581799 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 526.548 | 1.02841 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 532.176 | 0.970384 | 0.485192 | − | 0.874408i | \(-0.338750\pi\) | ||||
0.485192 | + | 0.874408i | \(0.338750\pi\) | |||||||
\(68\) | 125.084 | 0.223069 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 409.886 | 0.685134 | 0.342567 | − | 0.939493i | \(-0.388704\pi\) | ||||
0.342567 | + | 0.939493i | \(0.388704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −220.581 | −0.353659 | −0.176829 | − | 0.984242i | \(-0.556584\pi\) | ||||
−0.176829 | + | 0.984242i | \(0.556584\pi\) | |||||||
\(74\) | −42.9647 | −0.0674938 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −119.458 | −0.180299 | ||||||||
\(77\) | −1143.27 | −1.69204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1133.70 | 1.61457 | 0.807286 | − | 0.590160i | \(-0.200935\pi\) | ||||
0.807286 | + | 0.590160i | \(0.200935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 598.253 | 0.805683 | ||||||||
\(83\) | 253.619 | 0.335401 | 0.167700 | − | 0.985838i | \(-0.446366\pi\) | ||||
0.167700 | + | 0.985838i | \(0.446366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −537.390 | −0.673817 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1642.21 | −1.98932 | ||||||||
\(89\) | −1625.13 | −1.93555 | −0.967775 | − | 0.251816i | \(-0.918972\pi\) | ||||
−0.967775 | + | 0.251816i | \(0.918972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1244.07 | 1.43312 | ||||||||
\(92\) | −634.846 | −0.719426 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 680.678 | 0.746878 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −457.573 | −0.478964 | −0.239482 | − | 0.970901i | \(-0.576978\pi\) | ||||
−0.239482 | + | 0.970901i | \(0.576978\pi\) | |||||||
\(98\) | −111.578 | −0.115011 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1262.95 | −1.24424 | −0.622120 | − | 0.782922i | \(-0.713728\pi\) | ||||
−0.622120 | + | 0.782922i | \(0.713728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −433.419 | −0.414622 | −0.207311 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207311 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(104\) | 1787.01 | 1.68491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 639.466 | 0.585947 | ||||||||
\(107\) | 1667.95 | 1.50698 | 0.753489 | − | 0.657461i | \(-0.228370\pi\) | ||||
0.753489 | + | 0.657461i | \(0.228370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1191.98 | −1.04744 | −0.523721 | − | 0.851890i | \(-0.675456\pi\) | ||||
−0.523721 | + | 0.851890i | \(0.675456\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 504.989 | 0.426044 | ||||||||
\(113\) | −506.311 | −0.421502 | −0.210751 | − | 0.977540i | \(-0.567591\pi\) | ||||
−0.210751 | + | 0.977540i | \(0.567591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 67.2541 | 0.0538309 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 39.1625 | 0.0305526 | ||||||||
\(119\) | 689.129 | 0.530860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3136.49 | 2.35649 | ||||||||
\(122\) | 1692.26 | 1.25582 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −398.554 | −0.288639 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2042.84 | 1.42735 | 0.713673 | − | 0.700479i | \(-0.247030\pi\) | ||||
0.713673 | + | 0.700479i | \(0.247030\pi\) | |||||||
\(128\) | 115.131 | 0.0795021 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1854.98 | 1.23718 | 0.618590 | − | 0.785714i | \(-0.287704\pi\) | ||||
0.618590 | + | 0.785714i | \(0.287704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −658.130 | −0.429076 | ||||||||
\(134\) | 1177.46 | 0.759082 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 989.878 | 0.624128 | ||||||||
\(137\) | −1698.04 | −1.05893 | −0.529466 | − | 0.848331i | \(-0.677608\pi\) | ||||
−0.529466 | + | 0.848331i | \(0.677608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2386.02 | 1.45597 | 0.727986 | − | 0.685592i | \(-0.240457\pi\) | ||||
0.727986 | + | 0.685592i | \(0.240457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 906.887 | 0.535946 | ||||||||
\(143\) | −4861.41 | −2.84288 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −488.044 | −0.276649 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 60.2891 | 0.0334847 | ||||||||
\(149\) | 1090.68 | 0.599676 | 0.299838 | − | 0.953990i | \(-0.403067\pi\) | ||||
0.299838 | + | 0.953990i | \(0.403067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2779.07 | −1.49773 | −0.748865 | − | 0.662722i | \(-0.769401\pi\) | ||||
−0.748865 | + | 0.662722i | \(0.769401\pi\) | |||||||
\(152\) | −945.351 | −0.504461 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2529.52 | −1.32360 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1277.14 | 0.649218 | 0.324609 | − | 0.945848i | \(-0.394767\pi\) | ||||
0.324609 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(158\) | 2508.35 | 1.26300 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3497.56 | −1.71209 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1328.05 | 0.638167 | 0.319084 | − | 0.947727i | \(-0.396625\pi\) | ||||
0.319084 | + | 0.947727i | \(0.396625\pi\) | |||||||
\(164\) | −839.484 | −0.399712 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 561.141 | 0.262367 | ||||||||
\(167\) | −3995.28 | −1.85128 | −0.925641 | − | 0.378404i | \(-0.876473\pi\) | ||||
−0.925641 | + | 0.378404i | \(0.876473\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3093.06 | 1.40786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 754.080 | 0.334291 | ||||||||
\(173\) | −807.216 | −0.354748 | −0.177374 | − | 0.984143i | \(-0.556760\pi\) | ||||
−0.177374 | + | 0.984143i | \(0.556760\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1973.33 | −0.845142 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3595.67 | −1.51408 | ||||||||
\(179\) | −1708.08 | −0.713227 | −0.356614 | − | 0.934252i | \(-0.616069\pi\) | ||||
−0.356614 | + | 0.934252i | \(0.616069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1772.50 | 0.727895 | 0.363948 | − | 0.931419i | \(-0.381429\pi\) | ||||
0.363948 | + | 0.931419i | \(0.381429\pi\) | |||||||
\(182\) | 2752.55 | 1.12106 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5023.97 | −2.01289 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2692.88 | −1.05306 | ||||||||
\(188\) | −955.145 | −0.370538 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2644.91 | 1.00199 | 0.500993 | − | 0.865452i | \(-0.332968\pi\) | ||||
0.500993 | + | 0.865452i | \(0.332968\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 531.799 | 0.198340 | 0.0991702 | − | 0.995070i | \(-0.468381\pi\) | ||||
0.0991702 | + | 0.995070i | \(0.468381\pi\) | |||||||
\(194\) | −1012.40 | −0.374670 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 156.568 | 0.0570585 | ||||||||
\(197\) | −1331.90 | −0.481694 | −0.240847 | − | 0.970563i | \(-0.577425\pi\) | ||||
−0.240847 | + | 0.970563i | \(0.577425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1775.44 | 0.632450 | 0.316225 | − | 0.948684i | \(-0.397585\pi\) | ||||
0.316225 | + | 0.948684i | \(0.397585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2794.32 | −0.973306 | ||||||||
\(203\) | 370.524 | 0.128107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −958.954 | −0.324337 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2147.32 | 0.715817 | ||||||||
\(209\) | 2571.75 | 0.851155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3344.62 | −1.09125 | −0.545623 | − | 0.838031i | \(-0.683707\pi\) | ||||
−0.545623 | + | 0.838031i | \(0.683707\pi\) | |||||||
\(212\) | −897.314 | −0.290697 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3690.39 | 1.17883 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2195.76 | −0.686903 | ||||||||
\(218\) | −2637.30 | −0.819360 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2930.32 | 0.891923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4203.68 | −1.26233 | −0.631164 | − | 0.775649i | \(-0.717422\pi\) | ||||
−0.631164 | + | 0.775649i | \(0.717422\pi\) | |||||||
\(224\) | −2244.72 | −0.669562 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1120.23 | −0.329720 | ||||||||
\(227\) | −305.634 | −0.0893641 | −0.0446821 | − | 0.999001i | \(-0.514227\pi\) | ||||
−0.0446821 | + | 0.999001i | \(0.514227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −123.562 | −0.0356560 | −0.0178280 | − | 0.999841i | \(-0.505675\pi\) | ||||
−0.0178280 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 532.228 | 0.150614 | ||||||||
\(233\) | 5246.76 | 1.47522 | 0.737611 | − | 0.675226i | \(-0.235954\pi\) | ||||
0.737611 | + | 0.675226i | \(0.235954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −54.9538 | −0.0151576 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1524.72 | 0.415265 | ||||||||
\(239\) | 4300.72 | 1.16398 | 0.581988 | − | 0.813197i | \(-0.302275\pi\) | ||||
0.581988 | + | 0.813197i | \(0.302275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5355.47 | −1.43144 | −0.715718 | − | 0.698390i | \(-0.753900\pi\) | ||||
−0.715718 | + | 0.698390i | \(0.753900\pi\) | |||||||
\(242\) | 6939.60 | 1.84337 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2374.62 | −0.623032 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2798.51 | −0.720910 | ||||||||
\(248\) | −3154.03 | −0.807586 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2587.28 | 0.650627 | 0.325314 | − | 0.945606i | \(-0.394530\pi\) | ||||
0.325314 | + | 0.945606i | \(0.394530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13667.3 | 3.39626 | ||||||||
\(254\) | 4519.86 | 1.11654 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3957.65 | −0.966224 | ||||||||
\(257\) | 4909.53 | 1.19163 | 0.595813 | − | 0.803123i | \(-0.296830\pi\) | ||||
0.595813 | + | 0.803123i | \(0.296830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 332.152 | 0.0796868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4104.22 | 0.967783 | ||||||||
\(263\) | 4464.34 | 1.04670 | 0.523351 | − | 0.852117i | \(-0.324682\pi\) | ||||
0.523351 | + | 0.852117i | \(0.324682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1456.14 | −0.335644 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1652.24 | −0.376592 | ||||||||
\(269\) | −5957.80 | −1.35039 | −0.675193 | − | 0.737641i | \(-0.735940\pi\) | ||||
−0.675193 | + | 0.737641i | \(0.735940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4805.80 | 1.07724 | 0.538619 | − | 0.842549i | \(-0.318946\pi\) | ||||
0.538619 | + | 0.842549i | \(0.318946\pi\) | |||||||
\(272\) | 1189.47 | 0.265154 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3756.98 | −0.828349 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3531.98 | −0.766122 | −0.383061 | − | 0.923723i | \(-0.625130\pi\) | ||||
−0.383061 | + | 0.923723i | \(0.625130\pi\) | |||||||
\(278\) | 5279.17 | 1.13893 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 437.107 | 0.0927958 | 0.0463979 | − | 0.998923i | \(-0.485226\pi\) | ||||
0.0463979 | + | 0.998923i | \(0.485226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6278.33 | 1.31876 | 0.659378 | − | 0.751811i | \(-0.270820\pi\) | ||||
0.659378 | + | 0.751811i | \(0.270820\pi\) | |||||||
\(284\) | −1272.57 | −0.265891 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10756.0 | −2.22384 | ||||||||
\(287\) | −4624.98 | −0.951233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3289.81 | −0.669612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 684.836 | 0.137250 | ||||||||
\(293\) | 1065.21 | 0.212390 | 0.106195 | − | 0.994345i | \(-0.466133\pi\) | ||||
0.106195 | + | 0.994345i | \(0.466133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 477.109 | 0.0936872 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2413.16 | 0.469096 | ||||||||
\(299\) | −14872.4 | −2.87656 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4154.46 | 0.795545 | ||||||||
\(302\) | −6148.78 | −1.17160 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1135.96 | −0.214315 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10015.7 | −1.86197 | −0.930986 | − | 0.365055i | \(-0.881050\pi\) | ||||
−0.930986 | + | 0.365055i | \(0.881050\pi\) | |||||||
\(308\) | 3549.48 | 0.656657 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3600.63 | −0.656505 | −0.328253 | − | 0.944590i | \(-0.606460\pi\) | ||||
−0.328253 | + | 0.944590i | \(0.606460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1913.29 | −0.345512 | −0.172756 | − | 0.984965i | \(-0.555267\pi\) | ||||
−0.172756 | + | 0.984965i | \(0.555267\pi\) | |||||||
\(314\) | 2825.73 | 0.507850 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3519.78 | −0.626593 | ||||||||
\(317\) | −4472.16 | −0.792371 | −0.396186 | − | 0.918170i | \(-0.629666\pi\) | ||||
−0.396186 | + | 0.918170i | \(0.629666\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1447.88 | −0.254125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7738.48 | −1.33928 | ||||||||
\(323\) | −1550.18 | −0.267041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2938.37 | 0.499206 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6643.41 | −1.11836 | ||||||||
\(329\) | −5262.19 | −0.881805 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7693.11 | −1.27750 | −0.638748 | − | 0.769416i | \(-0.720547\pi\) | ||||
−0.638748 | + | 0.769416i | \(0.720547\pi\) | |||||||
\(332\) | −787.407 | −0.130164 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8839.70 | −1.44816 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 395.941 | 0.0640009 | 0.0320005 | − | 0.999488i | \(-0.489812\pi\) | ||||
0.0320005 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(338\) | 6843.51 | 1.10130 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8580.29 | 1.36261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6729.49 | 1.05935 | ||||||||
\(344\) | 5967.55 | 0.935316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1785.99 | −0.277502 | ||||||||
\(347\) | 9074.49 | 1.40387 | 0.701937 | − | 0.712239i | \(-0.252319\pi\) | ||||
0.701937 | + | 0.712239i | \(0.252319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8879.84 | 1.36197 | 0.680984 | − | 0.732298i | \(-0.261552\pi\) | ||||
0.680984 | + | 0.732298i | \(0.261552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8771.62 | 1.32821 | ||||||||
\(353\) | −5229.73 | −0.788528 | −0.394264 | − | 0.918997i | \(-0.629000\pi\) | ||||
−0.394264 | + | 0.918997i | \(0.629000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5045.53 | 0.751160 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3779.18 | −0.557922 | ||||||||
\(359\) | 13431.1 | 1.97456 | 0.987278 | − | 0.159001i | \(-0.0508272\pi\) | ||||
0.987278 | + | 0.159001i | \(0.0508272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5378.55 | −0.784160 | ||||||||
\(362\) | 3921.72 | 0.569395 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3862.45 | −0.556175 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7283.77 | −1.03599 | −0.517997 | − | 0.855383i | \(-0.673322\pi\) | ||||
−0.517997 | + | 0.855383i | \(0.673322\pi\) | |||||||
\(368\) | −6036.94 | −0.855156 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4943.59 | −0.691801 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7344.75 | 1.01956 | 0.509781 | − | 0.860304i | \(-0.329726\pi\) | ||||
0.509781 | + | 0.860304i | \(0.329726\pi\) | |||||||
\(374\) | −5958.10 | −0.823759 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7558.72 | −1.03673 | ||||||||
\(377\) | 1575.55 | 0.215238 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1553.95 | −0.210610 | −0.105305 | − | 0.994440i | \(-0.533582\pi\) | ||||
−0.105305 | + | 0.994440i | \(0.533582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5851.96 | 0.783802 | ||||||||
\(383\) | −2923.68 | −0.390060 | −0.195030 | − | 0.980797i | \(-0.562480\pi\) | ||||
−0.195030 | + | 0.980797i | \(0.562480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1176.62 | 0.155152 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1420.62 | 0.185879 | ||||||||
\(389\) | 397.904 | 0.0518625 | 0.0259312 | − | 0.999664i | \(-0.491745\pi\) | ||||
0.0259312 | + | 0.999664i | \(0.491745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8238.26 | −1.06554 | ||||||||
\(392\) | 1239.03 | 0.159644 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2946.87 | −0.376805 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1333.10 | 0.168530 | 0.0842649 | − | 0.996443i | \(-0.473146\pi\) | ||||
0.0842649 | + | 0.996443i | \(0.473146\pi\) | |||||||
\(398\) | 3928.22 | 0.494734 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6293.28 | 0.783719 | 0.391860 | − | 0.920025i | \(-0.371832\pi\) | ||||
0.391860 | + | 0.920025i | \(0.371832\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9336.85 | −1.15410 | ||||||||
\(404\) | 3921.06 | 0.482872 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 819.797 | 0.100211 | ||||||||
\(407\) | −1297.94 | −0.158074 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12522.2 | 1.51390 | 0.756948 | − | 0.653475i | \(-0.226690\pi\) | ||||
0.756948 | + | 0.653475i | \(0.226690\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1345.63 | 0.160909 | ||||||||
\(413\) | −302.758 | −0.0360720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9545.05 | −1.12496 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5690.08 | 0.665816 | ||||||||
\(419\) | −5505.42 | −0.641903 | −0.320952 | − | 0.947096i | \(-0.604003\pi\) | ||||
−0.320952 | + | 0.947096i | \(0.604003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5957.76 | 0.689700 | 0.344850 | − | 0.938658i | \(-0.387930\pi\) | ||||
0.344850 | + | 0.938658i | \(0.387930\pi\) | |||||||
\(422\) | −7400.08 | −0.853627 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7101.07 | −0.813345 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13082.5 | −1.48269 | ||||||||
\(428\) | −5178.45 | −0.584836 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12509.3 | −1.39804 | −0.699018 | − | 0.715104i | \(-0.746379\pi\) | ||||
−0.699018 | + | 0.715104i | \(0.746379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4345.52 | −0.482292 | −0.241146 | − | 0.970489i | \(-0.577523\pi\) | ||||
−0.241146 | + | 0.970489i | \(0.577523\pi\) | |||||||
\(434\) | −4858.20 | −0.537330 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3700.73 | 0.406497 | ||||||||
\(437\) | 7867.68 | 0.861241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7014.09 | 0.762561 | 0.381281 | − | 0.924459i | \(-0.375483\pi\) | ||||
0.381281 | + | 0.924459i | \(0.375483\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6483.45 | 0.697706 | ||||||||
\(443\) | 8727.29 | 0.935996 | 0.467998 | − | 0.883730i | \(-0.344975\pi\) | ||||
0.467998 | + | 0.883730i | \(0.344975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9300.79 | −0.987455 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9006.44 | −0.949809 | ||||||||
\(449\) | 13100.4 | 1.37694 | 0.688472 | − | 0.725263i | \(-0.258282\pi\) | ||||
0.688472 | + | 0.725263i | \(0.258282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18072.9 | 1.88696 | ||||||||
\(452\) | 1571.94 | 0.163579 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −676.227 | −0.0699050 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1063.47 | −0.108855 | −0.0544277 | − | 0.998518i | \(-0.517333\pi\) | ||||
−0.0544277 | + | 0.998518i | \(0.517333\pi\) | |||||||
\(458\) | −273.386 | −0.0278919 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8355.46 | −0.844149 | −0.422074 | − | 0.906561i | \(-0.638698\pi\) | ||||
−0.422074 | + | 0.906561i | \(0.638698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11866.0 | 1.19106 | 0.595528 | − | 0.803335i | \(-0.296943\pi\) | ||||
0.595528 | + | 0.803335i | \(0.296943\pi\) | |||||||
\(464\) | 639.540 | 0.0639868 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11608.6 | 1.15399 | ||||||||
\(467\) | −5687.16 | −0.563534 | −0.281767 | − | 0.959483i | \(-0.590920\pi\) | ||||
−0.281767 | + | 0.959483i | \(0.590920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9102.71 | −0.896214 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −434.887 | −0.0424096 | ||||||||
\(473\) | −16234.2 | −1.57812 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2139.53 | −0.206019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9515.49 | 0.910520 | ||||||||
\(479\) | 10556.5 | 1.00697 | 0.503485 | − | 0.864004i | \(-0.332051\pi\) | ||||
0.503485 | + | 0.864004i | \(0.332051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1412.38 | 0.133886 | ||||||||
\(482\) | −11849.2 | −1.11974 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9737.83 | −0.914522 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 962.879 | 0.0895938 | 0.0447969 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447969 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(488\) | −18792.0 | −1.74319 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7787.16 | −0.715743 | −0.357871 | − | 0.933771i | \(-0.616497\pi\) | ||||
−0.357871 | + | 0.933771i | \(0.616497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 872.742 | 0.0797289 | ||||||||
\(494\) | −6191.80 | −0.563932 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3789.98 | −0.343095 | ||||||||
\(497\) | −7010.97 | −0.632767 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4036.80 | 0.362148 | 0.181074 | − | 0.983469i | \(-0.442043\pi\) | ||||
0.181074 | + | 0.983469i | \(0.442043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5724.44 | 0.508953 | ||||||||
\(503\) | 13228.9 | 1.17266 | 0.586329 | − | 0.810073i | \(-0.300573\pi\) | ||||
0.586329 | + | 0.810073i | \(0.300573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30239.4 | 2.65673 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6342.39 | −0.553933 | ||||||||
\(509\) | 5516.83 | 0.480411 | 0.240206 | − | 0.970722i | \(-0.422785\pi\) | ||||
0.240206 | + | 0.970722i | \(0.422785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3772.97 | 0.326627 | ||||||||
\(512\) | −9677.50 | −0.835331 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10862.5 | 0.932149 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20562.9 | 1.74923 | ||||||||
\(518\) | 734.897 | 0.0623350 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12832.4 | 1.07908 | 0.539538 | − | 0.841961i | \(-0.318599\pi\) | ||||
0.539538 | + | 0.841961i | \(0.318599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1005.75 | −0.0840888 | −0.0420444 | − | 0.999116i | \(-0.513387\pi\) | ||||
−0.0420444 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(524\) | −5759.14 | −0.480132 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9877.50 | 0.818783 | ||||||||
\(527\) | −5171.96 | −0.427503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29645.0 | 2.43651 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2043.29 | 0.166518 | ||||||||
\(533\) | −19666.4 | −1.59821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13075.3 | −1.05367 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13181.9 | −1.05634 | ||||||||
\(539\) | −3370.69 | −0.269361 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15446.1 | 1.22750 | 0.613751 | − | 0.789500i | \(-0.289660\pi\) | ||||
0.613751 | + | 0.789500i | \(0.289660\pi\) | |||||||
\(542\) | 10633.0 | 0.842669 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5287.29 | −0.416711 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3115.98 | 0.243564 | 0.121782 | − | 0.992557i | \(-0.461139\pi\) | ||||
0.121782 | + | 0.992557i | \(0.461139\pi\) | |||||||
\(548\) | 5271.90 | 0.410957 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −833.484 | −0.0644421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19391.6 | −1.49116 | ||||||||
\(554\) | −7814.62 | −0.599299 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7407.86 | −0.565042 | ||||||||
\(557\) | 1843.45 | 0.140232 | 0.0701162 | − | 0.997539i | \(-0.477663\pi\) | ||||
0.0701162 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17665.7 | 1.33663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 967.115 | 0.0725895 | ||||||||
\(563\) | −13957.3 | −1.04481 | −0.522407 | − | 0.852696i | \(-0.674966\pi\) | ||||
−0.522407 | + | 0.852696i | \(0.674966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13891.0 | 1.03160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10070.7 | −0.743939 | ||||||||
\(569\) | 20049.7 | 1.47720 | 0.738601 | − | 0.674143i | \(-0.235487\pi\) | ||||
0.738601 | + | 0.674143i | \(0.235487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1270.87 | −0.0931421 | −0.0465711 | − | 0.998915i | \(-0.514829\pi\) | ||||
−0.0465711 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(572\) | 15093.2 | 1.10328 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10232.9 | −0.744102 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 211.623 | 0.0152686 | 0.00763431 | − | 0.999971i | \(-0.497570\pi\) | ||||
0.00763431 | + | 0.999971i | \(0.497570\pi\) | |||||||
\(578\) | −7278.81 | −0.523804 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4338.07 | −0.309765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19317.9 | 1.37232 | ||||||||
\(584\) | 5419.57 | 0.384013 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2356.82 | 0.166142 | ||||||||
\(587\) | 11135.1 | 0.782956 | 0.391478 | − | 0.920188i | \(-0.371964\pi\) | ||||
0.391478 | + | 0.920188i | \(0.371964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4939.31 | 0.345536 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 573.308 | 0.0398021 | ||||||||
\(593\) | 20593.7 | 1.42611 | 0.713054 | − | 0.701109i | \(-0.247311\pi\) | ||||
0.713054 | + | 0.701109i | \(0.247311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3386.21 | −0.232726 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −32905.7 | −2.25019 | ||||||||
\(599\) | 2510.98 | 0.171278 | 0.0856392 | − | 0.996326i | \(-0.472707\pi\) | ||||
0.0856392 | + | 0.996326i | \(0.472707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21276.4 | 1.44406 | 0.722031 | − | 0.691861i | \(-0.243209\pi\) | ||||
0.722031 | + | 0.691861i | \(0.243209\pi\) | |||||||
\(602\) | 9191.89 | 0.622315 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8628.13 | 0.581248 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21993.1 | 1.47063 | 0.735316 | − | 0.677725i | \(-0.237034\pi\) | ||||
0.735316 | + | 0.677725i | \(0.237034\pi\) | |||||||
\(608\) | 5049.45 | 0.336813 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22376.0 | −1.48156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13319.8 | −0.877622 | −0.438811 | − | 0.898579i | \(-0.644600\pi\) | ||||
−0.438811 | + | 0.898579i | \(0.644600\pi\) | |||||||
\(614\) | −22160.1 | −1.45653 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28089.5 | 1.83727 | ||||||||
\(617\) | 7815.28 | 0.509938 | 0.254969 | − | 0.966949i | \(-0.417935\pi\) | ||||
0.254969 | + | 0.966949i | \(0.417935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18163.9 | −1.17943 | −0.589716 | − | 0.807611i | \(-0.700760\pi\) | ||||
−0.589716 | + | 0.807611i | \(0.700760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7966.53 | −0.513551 | ||||||||
\(623\) | 27797.4 | 1.78761 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4233.21 | −0.270277 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3965.13 | −0.251952 | ||||||||
\(629\) | 782.360 | 0.0495941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2884.98 | 0.182011 | 0.0910057 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910057 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(632\) | −27854.5 | −1.75315 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9894.82 | −0.619832 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3667.89 | 0.228143 | ||||||||
\(638\) | −3203.49 | −0.198789 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26713.6 | −1.64606 | −0.823029 | − | 0.567999i | \(-0.807718\pi\) | ||||
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11316.8 | 0.694079 | 0.347039 | − | 0.937851i | \(-0.387187\pi\) | ||||
0.347039 | + | 0.937851i | \(0.387187\pi\) | |||||||
\(644\) | 10858.8 | 0.664438 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3429.82 | −0.208893 | ||||||||
\(647\) | −11244.8 | −0.683272 | −0.341636 | − | 0.939832i | \(-0.610981\pi\) | ||||
−0.341636 | + | 0.939832i | \(0.610981\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1183.07 | 0.0715559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4123.19 | −0.247664 | ||||||||
\(653\) | 19898.7 | 1.19249 | 0.596244 | − | 0.802803i | \(-0.296659\pi\) | ||||
0.596244 | + | 0.802803i | \(0.296659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7982.92 | −0.475123 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11642.8 | −0.689792 | ||||||||
\(659\) | −21502.2 | −1.27103 | −0.635514 | − | 0.772089i | \(-0.719212\pi\) | ||||
−0.635514 | + | 0.772089i | \(0.719212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11903.3 | 0.700434 | 0.350217 | − | 0.936669i | \(-0.386108\pi\) | ||||
0.350217 | + | 0.936669i | \(0.386108\pi\) | |||||||
\(662\) | −17021.3 | −0.999321 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6231.29 | −0.364188 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4429.46 | −0.257136 | ||||||||
\(668\) | 12404.1 | 0.718456 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51122.1 | 2.94121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11771.3 | −0.674221 | −0.337110 | − | 0.941465i | \(-0.609450\pi\) | ||||
−0.337110 | + | 0.941465i | \(0.609450\pi\) | |||||||
\(674\) | 876.035 | 0.0500647 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9602.98 | −0.546369 | ||||||||
\(677\) | 25739.9 | 1.46125 | 0.730624 | − | 0.682780i | \(-0.239229\pi\) | ||||
0.730624 | + | 0.682780i | \(0.239229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7826.65 | 0.442355 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18984.2 | 1.06590 | ||||||||
\(683\) | −29200.8 | −1.63592 | −0.817962 | − | 0.575272i | \(-0.804896\pi\) | ||||
−0.817962 | + | 0.575272i | \(0.804896\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14889.2 | 0.828679 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7170.78 | 0.397360 | ||||||||
\(689\) | −21021.2 | −1.16233 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5160.72 | 0.284114 | 0.142057 | − | 0.989858i | \(-0.454628\pi\) | ||||
0.142057 | + | 0.989858i | \(0.454628\pi\) | |||||||
\(692\) | 2506.15 | 0.137673 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20077.6 | 1.09818 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10893.8 | −0.592012 | ||||||||
\(698\) | 19647.0 | 1.06540 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11437.2 | 0.616229 | 0.308115 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308115 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −747.167 | −0.0400852 | ||||||||
\(704\) | 35194.1 | 1.88413 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11571.0 | −0.616826 | ||||||||
\(707\) | 21602.4 | 1.14914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 726.443 | 0.0384797 | 0.0192399 | − | 0.999815i | \(-0.493875\pi\) | ||||
0.0192399 | + | 0.999815i | \(0.493875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 39928.8 | 2.10168 | ||||||||
\(713\) | 26249.5 | 1.37875 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5303.04 | 0.276793 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29716.8 | 1.54460 | ||||||||
\(719\) | −2949.11 | −0.152967 | −0.0764835 | − | 0.997071i | \(-0.524369\pi\) | ||||
−0.0764835 | + | 0.997071i | \(0.524369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7413.49 | 0.382930 | ||||||||
\(722\) | −11900.2 | −0.613409 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5503.06 | −0.282486 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34433.2 | 1.75661 | 0.878306 | − | 0.478100i | \(-0.158674\pi\) | ||||
0.878306 | + | 0.478100i | \(0.158674\pi\) | |||||||
\(728\) | −30566.2 | −1.55613 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9785.54 | 0.495118 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1382.56 | 0.0696670 | 0.0348335 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348335 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(734\) | −16115.6 | −0.810406 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26834.8 | 1.34395 | ||||||||
\(737\) | 35570.3 | 1.77781 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10335.3 | −0.514466 | −0.257233 | − | 0.966349i | \(-0.582811\pi\) | ||||
−0.257233 | + | 0.966349i | \(0.582811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10937.9 | −0.541161 | ||||||||
\(743\) | 4880.52 | 0.240981 | 0.120491 | − | 0.992714i | \(-0.461553\pi\) | ||||
0.120491 | + | 0.992714i | \(0.461553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16250.5 | 0.797552 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8360.55 | 0.408679 | ||||||||
\(749\) | −28529.7 | −1.39179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21584.1 | −1.04875 | −0.524377 | − | 0.851486i | \(-0.675702\pi\) | ||||
−0.524377 | + | 0.851486i | \(0.675702\pi\) | |||||||
\(752\) | −9082.77 | −0.440445 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3485.95 | 0.168370 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39391.6 | −1.89130 | −0.945648 | − | 0.325191i | \(-0.894571\pi\) | ||||
−0.945648 | + | 0.325191i | \(0.894571\pi\) | |||||||
\(758\) | −3438.17 | −0.164749 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 256.813 | 0.0122332 | 0.00611660 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611660 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20388.5 | 0.967381 | ||||||||
\(764\) | −8211.63 | −0.388856 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6468.74 | −0.305124 | ||||||||
\(767\) | −1287.39 | −0.0606063 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2034.58 | 0.0954081 | 0.0477041 | − | 0.998862i | \(-0.484810\pi\) | ||||
0.0477041 | + | 0.998862i | \(0.484810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1651.07 | −0.0769731 | ||||||||
\(773\) | −2737.54 | −0.127377 | −0.0636884 | − | 0.997970i | \(-0.520286\pi\) | ||||
−0.0636884 | + | 0.997970i | \(0.520286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11242.4 | 0.520073 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 880.376 | 0.0405694 | ||||||||
\(779\) | 10403.8 | 0.478503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27396.5 | 1.25522 | ||||||||
\(782\) | −18227.4 | −0.833519 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1488.86 | 0.0678233 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18449.1 | −0.835629 | −0.417814 | − | 0.908532i | \(-0.637204\pi\) | ||||
−0.417814 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(788\) | 4135.13 | 0.186939 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8660.29 | 0.389285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55629.8 | −2.49114 | ||||||||
\(794\) | 2949.53 | 0.131832 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5512.18 | −0.245445 | ||||||||
\(797\) | −35731.8 | −1.58806 | −0.794031 | − | 0.607878i | \(-0.792021\pi\) | ||||
−0.794031 | + | 0.607878i | \(0.792021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12394.7 | −0.548803 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13924.1 | 0.613064 | ||||||||
\(803\) | −14743.5 | −0.647929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20658.1 | −0.902792 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31030.1 | 1.35103 | ||||||||
\(809\) | −21421.1 | −0.930933 | −0.465467 | − | 0.885065i | \(-0.654113\pi\) | ||||
−0.465467 | + | 0.885065i | \(0.654113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27879.1 | −1.20711 | −0.603555 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603555 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(812\) | −1150.36 | −0.0497164 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2871.73 | −0.123654 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9345.36 | −0.400187 | ||||||||
\(818\) | 27705.8 | 1.18424 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26618.4 | −1.13153 | −0.565767 | − | 0.824565i | \(-0.691420\pi\) | ||||
−0.565767 | + | 0.824565i | \(0.691420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9804.65 | −0.415272 | −0.207636 | − | 0.978206i | \(-0.566577\pi\) | ||||
−0.207636 | + | 0.978206i | \(0.566577\pi\) | |||||||
\(824\) | 10648.9 | 0.450208 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −669.862 | −0.0282173 | ||||||||
\(827\) | 21534.9 | 0.905491 | 0.452745 | − | 0.891640i | \(-0.350445\pi\) | ||||
0.452745 | + | 0.891640i | \(0.350445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2671.33 | −0.111917 | −0.0559585 | − | 0.998433i | \(-0.517821\pi\) | ||||
−0.0559585 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38297.3 | −1.59582 | ||||||||
\(833\) | 2031.76 | 0.0845092 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7984.47 | −0.330321 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12180.9 | −0.502129 | ||||||||
\(839\) | 20755.8 | 0.854076 | 0.427038 | − | 0.904234i | \(-0.359557\pi\) | ||||
0.427038 | + | 0.904234i | \(0.359557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23919.8 | −0.980760 | ||||||||
\(842\) | 13181.8 | 0.539517 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10384.0 | 0.423497 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53648.7 | −2.17638 | ||||||||
\(848\) | −8532.84 | −0.345541 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3970.74 | −0.159947 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15242.4 | 0.611831 | 0.305915 | − | 0.952059i | \(-0.401038\pi\) | ||||
0.305915 | + | 0.952059i | \(0.401038\pi\) | |||||||
\(854\) | −28945.6 | −1.15983 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40980.7 | −1.63632 | ||||||||
\(857\) | −30965.0 | −1.23424 | −0.617121 | − | 0.786868i | \(-0.711701\pi\) | ||||
−0.617121 | + | 0.786868i | \(0.711701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15617.3 | 0.620320 | 0.310160 | − | 0.950684i | \(-0.399617\pi\) | ||||
0.310160 | + | 0.950684i | \(0.399617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27677.4 | −1.09361 | ||||||||
\(863\) | 17853.6 | 0.704223 | 0.352112 | − | 0.935958i | \(-0.385464\pi\) | ||||
0.352112 | + | 0.935958i | \(0.385464\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9614.63 | −0.377273 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6817.15 | 0.266577 | ||||||||
\(869\) | 75775.7 | 2.95802 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38706.7 | −1.50577 | ||||||||
\(872\) | 29286.4 | 1.13734 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17407.5 | 0.673705 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31782.1 | 1.22372 | 0.611862 | − | 0.790965i | \(-0.290421\pi\) | ||||
0.611862 | + | 0.790965i | \(0.290421\pi\) | |||||||
\(878\) | 15518.9 | 0.596513 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51478.0 | −1.96860 | −0.984301 | − | 0.176496i | \(-0.943524\pi\) | ||||
−0.984301 | + | 0.176496i | \(0.943524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5259.06 | 0.200432 | 0.100216 | − | 0.994966i | \(-0.468047\pi\) | ||||
0.100216 | + | 0.994966i | \(0.468047\pi\) | |||||||
\(884\) | −9097.74 | −0.346142 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19309.4 | 0.732182 | ||||||||
\(887\) | 12791.9 | 0.484229 | 0.242114 | − | 0.970248i | \(-0.422159\pi\) | ||||
0.242114 | + | 0.970248i | \(0.422159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34942.2 | −1.31825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13051.1 | 0.489891 | ||||||||
\(893\) | 11837.2 | 0.443579 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1969.28 | −0.0734254 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28985.2 | 1.07711 | ||||||||
\(899\) | −2780.81 | −0.103165 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11644.3 | −0.430551 | ||||||||
\(902\) | 39986.8 | 1.47607 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12439.8 | 0.457679 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19969.8 | 0.731076 | 0.365538 | − | 0.930796i | \(-0.380885\pi\) | ||||
0.365538 | + | 0.930796i | \(0.380885\pi\) | |||||||
\(908\) | 948.899 | 0.0346810 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10692.5 | 0.388868 | 0.194434 | − | 0.980916i | \(-0.437713\pi\) | ||||
0.194434 | + | 0.980916i | \(0.437713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16951.7 | 0.614479 | ||||||||
\(914\) | −2352.96 | −0.0851521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 383.622 | 0.0138376 | ||||||||
\(917\) | −31728.9 | −1.14262 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14818.3 | −0.531895 | −0.265947 | − | 0.963988i | \(-0.585685\pi\) | ||||
−0.265947 | + | 0.963988i | \(0.585685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18486.8 | −0.660335 | ||||||||
\(923\) | −29812.2 | −1.06314 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26253.9 | 0.931702 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2842.82 | −0.100560 | ||||||||
\(929\) | 2229.09 | 0.0787234 | 0.0393617 | − | 0.999225i | \(-0.487468\pi\) | ||||
0.0393617 | + | 0.999225i | \(0.487468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1940.36 | −0.0683059 | ||||||||
\(932\) | −16289.5 | −0.572512 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12583.0 | −0.440824 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17737.2 | 0.618408 | 0.309204 | − | 0.950996i | \(-0.399937\pi\) | ||||
0.309204 | + | 0.950996i | \(0.399937\pi\) | |||||||
\(938\) | −20140.1 | −0.701063 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4291.21 | 0.148660 | 0.0743302 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743302 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55289.8 | 1.90931 | ||||||||
\(944\) | −522.573 | −0.0180173 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35918.8 | −1.23448 | ||||||||
\(947\) | −17768.1 | −0.609700 | −0.304850 | − | 0.952400i | \(-0.598606\pi\) | ||||
−0.304850 | + | 0.952400i | \(0.598606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16043.5 | 0.548782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16931.6 | −0.576423 | ||||||||
\(953\) | −48689.0 | −1.65497 | −0.827487 | − | 0.561485i | \(-0.810230\pi\) | ||||
−0.827487 | + | 0.561485i | \(0.810230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13352.4 | −0.451723 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23356.6 | 0.787701 | ||||||||
\(959\) | 29044.5 | 0.977994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13311.7 | −0.446835 | ||||||||
\(962\) | 3124.94 | 0.104732 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16627.0 | 0.555520 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25690.1 | 0.854330 | 0.427165 | − | 0.904174i | \(-0.359512\pi\) | ||||
0.427165 | + | 0.904174i | \(0.359512\pi\) | |||||||
\(968\) | −77062.1 | −2.55875 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9697.83 | 0.320513 | 0.160257 | − | 0.987075i | \(-0.448768\pi\) | ||||
0.160257 | + | 0.987075i | \(0.448768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40812.2 | −1.34469 | ||||||||
\(974\) | 2130.40 | 0.0700847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22581.0 | −0.740575 | ||||||||
\(977\) | −32608.3 | −1.06779 | −0.533896 | − | 0.845550i | \(-0.679273\pi\) | ||||
−0.533896 | + | 0.845550i | \(0.679273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −108623. | −3.54607 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17229.4 | −0.559890 | ||||||||
\(983\) | −29544.1 | −0.958606 | −0.479303 | − | 0.877649i | \(-0.659111\pi\) | ||||
−0.479303 | + | 0.877649i | \(0.659111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1930.97 | 0.0623679 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8688.49 | 0.279775 | ||||||||
\(989\) | −49664.9 | −1.59682 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51930.3 | −1.66460 | −0.832301 | − | 0.554324i | \(-0.812977\pi\) | ||||
−0.832301 | + | 0.554324i | \(0.812977\pi\) | |||||||
\(992\) | 16846.8 | 0.539201 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15512.0 | −0.494981 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7361.72 | −0.233849 | −0.116925 | − | 0.993141i | \(-0.537304\pi\) | ||||
−0.116925 | + | 0.993141i | \(0.537304\pi\) | |||||||
\(998\) | 8931.56 | 0.283290 | ||||||||
\(999\) | 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 | 675.4.a.w.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 675.4.a.w.1.2 | ✓ | 4 | |
5.2 | odd | 4 | 675.4.b.o.649.5 | 8 | |||
5.3 | odd | 4 | 675.4.b.o.649.4 | 8 | |||
5.4 | even | 2 | 675.4.a.x.1.2 | yes | 4 | ||
15.2 | even | 4 | 675.4.b.o.649.3 | 8 | |||
15.8 | even | 4 | 675.4.b.o.649.6 | 8 | |||
15.14 | odd | 2 | 675.4.a.x.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.w.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
675.4.a.w.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
675.4.a.x.1.2 | yes | 4 | 5.4 | even | 2 | ||
675.4.a.x.1.3 | yes | 4 | 15.14 | odd | 2 | ||
675.4.b.o.649.3 | 8 | 15.2 | even | 4 | |||
675.4.b.o.649.4 | 8 | 5.3 | odd | 4 | |||
675.4.b.o.649.5 | 8 | 5.2 | odd | 4 | |||
675.4.b.o.649.6 | 8 | 15.8 | even | 4 |