Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04403 | −0.738239 | −0.369119 | − | 0.929382i | \(-0.620341\pi\) | ||||
−0.369119 | + | 0.929382i | \(0.620341\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.910007 | −0.455004 | ||||||||
\(5\) | 3.07941 | 1.37716 | 0.688578 | − | 0.725162i | \(-0.258235\pi\) | ||||
0.688578 | + | 0.725162i | \(0.258235\pi\) | |||||||
\(6\) | −1.04403 | −0.426222 | ||||||||
\(7\) | 2.83741 | 1.07244 | 0.536220 | − | 0.844078i | \(-0.319852\pi\) | ||||
0.536220 | + | 0.844078i | \(0.319852\pi\) | |||||||
\(8\) | 3.03813 | 1.07414 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.21499 | −1.01667 | ||||||||
\(11\) | 6.36912 | 1.92036 | 0.960181 | − | 0.279380i | \(-0.0901290\pi\) | ||||
0.960181 | + | 0.279380i | \(0.0901290\pi\) | |||||||
\(12\) | −0.910007 | −0.262696 | ||||||||
\(13\) | −3.32170 | −0.921274 | −0.460637 | − | 0.887589i | \(-0.652379\pi\) | ||||
−0.460637 | + | 0.887589i | \(0.652379\pi\) | |||||||
\(14\) | −2.96233 | −0.791717 | ||||||||
\(15\) | 3.07941 | 0.795101 | ||||||||
\(16\) | −1.35187 | −0.337968 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.04403 | −0.246080 | ||||||||
\(19\) | −0.177756 | −0.0407801 | −0.0203901 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203901 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(20\) | −2.80229 | −0.626611 | ||||||||
\(21\) | 2.83741 | 0.619173 | ||||||||
\(22\) | −6.64953 | −1.41768 | ||||||||
\(23\) | −8.97949 | −1.87235 | −0.936177 | − | 0.351529i | \(-0.885662\pi\) | ||||
−0.936177 | + | 0.351529i | \(0.885662\pi\) | |||||||
\(24\) | 3.03813 | 0.620155 | ||||||||
\(25\) | 4.48279 | 0.896559 | ||||||||
\(26\) | 3.46795 | 0.680120 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.58206 | −0.487964 | ||||||||
\(29\) | −0.984886 | −0.182889 | −0.0914443 | − | 0.995810i | \(-0.529148\pi\) | ||||
−0.0914443 | + | 0.995810i | \(0.529148\pi\) | |||||||
\(30\) | −3.21499 | −0.586975 | ||||||||
\(31\) | 0.989160 | 0.177658 | 0.0888292 | − | 0.996047i | \(-0.471687\pi\) | ||||
0.0888292 | + | 0.996047i | \(0.471687\pi\) | |||||||
\(32\) | −4.66486 | −0.824639 | ||||||||
\(33\) | 6.36912 | 1.10872 | ||||||||
\(34\) | −1.04403 | −0.179049 | ||||||||
\(35\) | 8.73756 | 1.47692 | ||||||||
\(36\) | −0.910007 | −0.151668 | ||||||||
\(37\) | 2.70995 | 0.445513 | 0.222757 | − | 0.974874i | \(-0.428494\pi\) | ||||
0.222757 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(38\) | 0.185583 | 0.0301055 | ||||||||
\(39\) | −3.32170 | −0.531898 | ||||||||
\(40\) | 9.35565 | 1.47926 | ||||||||
\(41\) | 11.2712 | 1.76026 | 0.880131 | − | 0.474730i | \(-0.157454\pi\) | ||||
0.880131 | + | 0.474730i | \(0.157454\pi\) | |||||||
\(42\) | −2.96233 | −0.457098 | ||||||||
\(43\) | −0.492547 | −0.0751127 | −0.0375563 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375563 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(44\) | −5.79594 | −0.873771 | ||||||||
\(45\) | 3.07941 | 0.459052 | ||||||||
\(46\) | 9.37484 | 1.38224 | ||||||||
\(47\) | −7.56257 | −1.10311 | −0.551557 | − | 0.834137i | \(-0.685966\pi\) | ||||
−0.551557 | + | 0.834137i | \(0.685966\pi\) | |||||||
\(48\) | −1.35187 | −0.195126 | ||||||||
\(49\) | 1.05089 | 0.150127 | ||||||||
\(50\) | −4.68016 | −0.661874 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 3.02277 | 0.419183 | ||||||||
\(53\) | −1.66192 | −0.228282 | −0.114141 | − | 0.993465i | \(-0.536412\pi\) | ||||
−0.114141 | + | 0.993465i | \(0.536412\pi\) | |||||||
\(54\) | −1.04403 | −0.142074 | ||||||||
\(55\) | 19.6132 | 2.64464 | ||||||||
\(56\) | 8.62041 | 1.15195 | ||||||||
\(57\) | −0.177756 | −0.0235444 | ||||||||
\(58\) | 1.02825 | 0.135015 | ||||||||
\(59\) | −5.58915 | −0.727646 | −0.363823 | − | 0.931468i | \(-0.618529\pi\) | ||||
−0.363823 | + | 0.931468i | \(0.618529\pi\) | |||||||
\(60\) | −2.80229 | −0.361774 | ||||||||
\(61\) | 1.79537 | 0.229874 | 0.114937 | − | 0.993373i | \(-0.463333\pi\) | ||||
0.114937 | + | 0.993373i | \(0.463333\pi\) | |||||||
\(62\) | −1.03271 | −0.131154 | ||||||||
\(63\) | 2.83741 | 0.357480 | ||||||||
\(64\) | 7.57399 | 0.946749 | ||||||||
\(65\) | −10.2289 | −1.26874 | ||||||||
\(66\) | −6.64953 | −0.818501 | ||||||||
\(67\) | −2.00950 | −0.245500 | −0.122750 | − | 0.992438i | \(-0.539171\pi\) | ||||
−0.122750 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(68\) | −0.910007 | −0.110355 | ||||||||
\(69\) | −8.97949 | −1.08100 | ||||||||
\(70\) | −9.12225 | −1.09032 | ||||||||
\(71\) | −0.642831 | −0.0762900 | −0.0381450 | − | 0.999272i | \(-0.512145\pi\) | ||||
−0.0381450 | + | 0.999272i | \(0.512145\pi\) | |||||||
\(72\) | 3.03813 | 0.358047 | ||||||||
\(73\) | 6.00518 | 0.702853 | 0.351427 | − | 0.936215i | \(-0.385697\pi\) | ||||
0.351427 | + | 0.936215i | \(0.385697\pi\) | |||||||
\(74\) | −2.82926 | −0.328895 | ||||||||
\(75\) | 4.48279 | 0.517628 | ||||||||
\(76\) | 0.161760 | 0.0185551 | ||||||||
\(77\) | 18.0718 | 2.05947 | ||||||||
\(78\) | 3.46795 | 0.392667 | ||||||||
\(79\) | 5.71140 | 0.642582 | 0.321291 | − | 0.946980i | \(-0.395883\pi\) | ||||
0.321291 | + | 0.946980i | \(0.395883\pi\) | |||||||
\(80\) | −4.16298 | −0.465435 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.7674 | −1.29949 | ||||||||
\(83\) | 10.1735 | 1.11668 | 0.558342 | − | 0.829611i | \(-0.311438\pi\) | ||||
0.558342 | + | 0.829611i | \(0.311438\pi\) | |||||||
\(84\) | −2.58206 | −0.281726 | ||||||||
\(85\) | 3.07941 | 0.334009 | ||||||||
\(86\) | 0.514232 | 0.0554511 | ||||||||
\(87\) | −0.984886 | −0.105591 | ||||||||
\(88\) | 19.3502 | 2.06274 | ||||||||
\(89\) | 12.4747 | 1.32231 | 0.661157 | − | 0.750248i | \(-0.270066\pi\) | ||||
0.661157 | + | 0.750248i | \(0.270066\pi\) | |||||||
\(90\) | −3.21499 | −0.338890 | ||||||||
\(91\) | −9.42502 | −0.988011 | ||||||||
\(92\) | 8.17140 | 0.851928 | ||||||||
\(93\) | 0.989160 | 0.102571 | ||||||||
\(94\) | 7.89553 | 0.814361 | ||||||||
\(95\) | −0.547386 | −0.0561606 | ||||||||
\(96\) | −4.66486 | −0.476105 | ||||||||
\(97\) | 15.3137 | 1.55488 | 0.777438 | − | 0.628960i | \(-0.216519\pi\) | ||||
0.777438 | + | 0.628960i | \(0.216519\pi\) | |||||||
\(98\) | −1.09716 | −0.110830 | ||||||||
\(99\) | 6.36912 | 0.640120 | ||||||||
\(100\) | −4.07937 | −0.407937 | ||||||||
\(101\) | 10.8892 | 1.08351 | 0.541756 | − | 0.840536i | \(-0.317760\pi\) | ||||
0.541756 | + | 0.840536i | \(0.317760\pi\) | |||||||
\(102\) | −1.04403 | −0.103374 | ||||||||
\(103\) | 5.62573 | 0.554319 | 0.277160 | − | 0.960824i | \(-0.410607\pi\) | ||||
0.277160 | + | 0.960824i | \(0.410607\pi\) | |||||||
\(104\) | −10.0917 | −0.989577 | ||||||||
\(105\) | 8.73756 | 0.852698 | ||||||||
\(106\) | 1.73509 | 0.168527 | ||||||||
\(107\) | −5.38419 | −0.520509 | −0.260255 | − | 0.965540i | \(-0.583807\pi\) | ||||
−0.260255 | + | 0.965540i | \(0.583807\pi\) | |||||||
\(108\) | −0.910007 | −0.0875655 | ||||||||
\(109\) | 4.14346 | 0.396871 | 0.198436 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198436 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(110\) | −20.4767 | −1.95237 | ||||||||
\(111\) | 2.70995 | 0.257217 | ||||||||
\(112\) | −3.83582 | −0.362451 | ||||||||
\(113\) | −7.51822 | −0.707254 | −0.353627 | − | 0.935386i | \(-0.615052\pi\) | ||||
−0.353627 | + | 0.935386i | \(0.615052\pi\) | |||||||
\(114\) | 0.185583 | 0.0173814 | ||||||||
\(115\) | −27.6516 | −2.57852 | ||||||||
\(116\) | 0.896253 | 0.0832150 | ||||||||
\(117\) | −3.32170 | −0.307091 | ||||||||
\(118\) | 5.83523 | 0.537176 | ||||||||
\(119\) | 2.83741 | 0.260105 | ||||||||
\(120\) | 9.35565 | 0.854050 | ||||||||
\(121\) | 29.5657 | 2.68779 | ||||||||
\(122\) | −1.87442 | −0.169702 | ||||||||
\(123\) | 11.2712 | 1.01629 | ||||||||
\(124\) | −0.900143 | −0.0808352 | ||||||||
\(125\) | −1.59270 | −0.142455 | ||||||||
\(126\) | −2.96233 | −0.263906 | ||||||||
\(127\) | 17.2157 | 1.52765 | 0.763823 | − | 0.645426i | \(-0.223320\pi\) | ||||
0.763823 | + | 0.645426i | \(0.223320\pi\) | |||||||
\(128\) | 1.42227 | 0.125712 | ||||||||
\(129\) | −0.492547 | −0.0433663 | ||||||||
\(130\) | 10.6792 | 0.936631 | ||||||||
\(131\) | 19.1433 | 1.67255 | 0.836277 | − | 0.548307i | \(-0.184728\pi\) | ||||
0.836277 | + | 0.548307i | \(0.184728\pi\) | |||||||
\(132\) | −5.79594 | −0.504472 | ||||||||
\(133\) | −0.504368 | −0.0437342 | ||||||||
\(134\) | 2.09798 | 0.181237 | ||||||||
\(135\) | 3.07941 | 0.265034 | ||||||||
\(136\) | 3.03813 | 0.260517 | ||||||||
\(137\) | −3.20919 | −0.274180 | −0.137090 | − | 0.990559i | \(-0.543775\pi\) | ||||
−0.137090 | + | 0.990559i | \(0.543775\pi\) | |||||||
\(138\) | 9.37484 | 0.798039 | ||||||||
\(139\) | −2.46969 | −0.209477 | −0.104738 | − | 0.994500i | \(-0.533400\pi\) | ||||
−0.104738 | + | 0.994500i | \(0.533400\pi\) | |||||||
\(140\) | −7.95124 | −0.672002 | ||||||||
\(141\) | −7.56257 | −0.636883 | ||||||||
\(142\) | 0.671133 | 0.0563202 | ||||||||
\(143\) | −21.1563 | −1.76918 | ||||||||
\(144\) | −1.35187 | −0.112656 | ||||||||
\(145\) | −3.03287 | −0.251866 | ||||||||
\(146\) | −6.26957 | −0.518873 | ||||||||
\(147\) | 1.05089 | 0.0866758 | ||||||||
\(148\) | −2.46608 | −0.202710 | ||||||||
\(149\) | −14.4988 | −1.18779 | −0.593894 | − | 0.804543i | \(-0.702410\pi\) | ||||
−0.593894 | + | 0.804543i | \(0.702410\pi\) | |||||||
\(150\) | −4.68016 | −0.382133 | ||||||||
\(151\) | 16.7526 | 1.36331 | 0.681655 | − | 0.731673i | \(-0.261260\pi\) | ||||
0.681655 | + | 0.731673i | \(0.261260\pi\) | |||||||
\(152\) | −0.540047 | −0.0438036 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −18.8674 | −1.52038 | ||||||||
\(155\) | 3.04603 | 0.244663 | ||||||||
\(156\) | 3.02277 | 0.242015 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −5.96285 | −0.474379 | ||||||||
\(159\) | −1.66192 | −0.131799 | ||||||||
\(160\) | −14.3650 | −1.13566 | ||||||||
\(161\) | −25.4785 | −2.00799 | ||||||||
\(162\) | −1.04403 | −0.0820265 | ||||||||
\(163\) | 11.0117 | 0.862502 | 0.431251 | − | 0.902232i | \(-0.358072\pi\) | ||||
0.431251 | + | 0.902232i | \(0.358072\pi\) | |||||||
\(164\) | −10.2569 | −0.800926 | ||||||||
\(165\) | 19.6132 | 1.52688 | ||||||||
\(166\) | −10.6214 | −0.824379 | ||||||||
\(167\) | 2.51155 | 0.194350 | 0.0971749 | − | 0.995267i | \(-0.469019\pi\) | ||||
0.0971749 | + | 0.995267i | \(0.469019\pi\) | |||||||
\(168\) | 8.62041 | 0.665079 | ||||||||
\(169\) | −1.96631 | −0.151255 | ||||||||
\(170\) | −3.21499 | −0.246579 | ||||||||
\(171\) | −0.177756 | −0.0135934 | ||||||||
\(172\) | 0.448221 | 0.0341765 | ||||||||
\(173\) | 4.86909 | 0.370190 | 0.185095 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185095 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(174\) | 1.02825 | 0.0779512 | ||||||||
\(175\) | 12.7195 | 0.961505 | ||||||||
\(176\) | −8.61024 | −0.649021 | ||||||||
\(177\) | −5.58915 | −0.420107 | ||||||||
\(178\) | −13.0239 | −0.976183 | ||||||||
\(179\) | −25.5245 | −1.90779 | −0.953897 | − | 0.300134i | \(-0.902968\pi\) | ||||
−0.953897 | + | 0.300134i | \(0.902968\pi\) | |||||||
\(180\) | −2.80229 | −0.208870 | ||||||||
\(181\) | −14.0676 | −1.04564 | −0.522819 | − | 0.852444i | \(-0.675120\pi\) | ||||
−0.522819 | + | 0.852444i | \(0.675120\pi\) | |||||||
\(182\) | 9.83998 | 0.729388 | ||||||||
\(183\) | 1.79537 | 0.132718 | ||||||||
\(184\) | −27.2808 | −2.01117 | ||||||||
\(185\) | 8.34507 | 0.613542 | ||||||||
\(186\) | −1.03271 | −0.0757220 | ||||||||
\(187\) | 6.36912 | 0.465756 | ||||||||
\(188\) | 6.88199 | 0.501921 | ||||||||
\(189\) | 2.83741 | 0.206391 | ||||||||
\(190\) | 0.571486 | 0.0414599 | ||||||||
\(191\) | 4.50177 | 0.325736 | 0.162868 | − | 0.986648i | \(-0.447925\pi\) | ||||
0.162868 | + | 0.986648i | \(0.447925\pi\) | |||||||
\(192\) | 7.57399 | 0.546606 | ||||||||
\(193\) | 4.00264 | 0.288117 | 0.144058 | − | 0.989569i | \(-0.453985\pi\) | ||||
0.144058 | + | 0.989569i | \(0.453985\pi\) | |||||||
\(194\) | −15.9880 | −1.14787 | ||||||||
\(195\) | −10.2289 | −0.732506 | ||||||||
\(196\) | −0.956316 | −0.0683083 | ||||||||
\(197\) | 16.5345 | 1.17804 | 0.589019 | − | 0.808119i | \(-0.299514\pi\) | ||||
0.589019 | + | 0.808119i | \(0.299514\pi\) | |||||||
\(198\) | −6.64953 | −0.472562 | ||||||||
\(199\) | −14.9570 | −1.06027 | −0.530136 | − | 0.847913i | \(-0.677859\pi\) | ||||
−0.530136 | + | 0.847913i | \(0.677859\pi\) | |||||||
\(200\) | 13.6193 | 0.963029 | ||||||||
\(201\) | −2.00950 | −0.141739 | ||||||||
\(202\) | −11.3686 | −0.799890 | ||||||||
\(203\) | −2.79452 | −0.196137 | ||||||||
\(204\) | −0.910007 | −0.0637132 | ||||||||
\(205\) | 34.7086 | 2.42416 | ||||||||
\(206\) | −5.87341 | −0.409220 | ||||||||
\(207\) | −8.97949 | −0.624118 | ||||||||
\(208\) | 4.49052 | 0.311361 | ||||||||
\(209\) | −1.13215 | −0.0783126 | ||||||||
\(210\) | −9.12225 | −0.629495 | ||||||||
\(211\) | −8.45862 | −0.582316 | −0.291158 | − | 0.956675i | \(-0.594040\pi\) | ||||
−0.291158 | + | 0.956675i | \(0.594040\pi\) | |||||||
\(212\) | 1.51236 | 0.103869 | ||||||||
\(213\) | −0.642831 | −0.0440460 | ||||||||
\(214\) | 5.62124 | 0.384260 | ||||||||
\(215\) | −1.51676 | −0.103442 | ||||||||
\(216\) | 3.03813 | 0.206718 | ||||||||
\(217\) | 2.80665 | 0.190528 | ||||||||
\(218\) | −4.32588 | −0.292986 | ||||||||
\(219\) | 6.00518 | 0.405792 | ||||||||
\(220\) | −17.8481 | −1.20332 | ||||||||
\(221\) | −3.32170 | −0.223442 | ||||||||
\(222\) | −2.82926 | −0.189888 | ||||||||
\(223\) | 8.06220 | 0.539885 | 0.269943 | − | 0.962876i | \(-0.412995\pi\) | ||||
0.269943 | + | 0.962876i | \(0.412995\pi\) | |||||||
\(224\) | −13.2361 | −0.884375 | ||||||||
\(225\) | 4.48279 | 0.298853 | ||||||||
\(226\) | 7.84922 | 0.522123 | ||||||||
\(227\) | 0.655276 | 0.0434922 | 0.0217461 | − | 0.999764i | \(-0.493077\pi\) | ||||
0.0217461 | + | 0.999764i | \(0.493077\pi\) | |||||||
\(228\) | 0.161760 | 0.0107128 | ||||||||
\(229\) | −28.0895 | −1.85621 | −0.928104 | − | 0.372321i | \(-0.878562\pi\) | ||||
−0.928104 | + | 0.372321i | \(0.878562\pi\) | |||||||
\(230\) | 28.8690 | 1.90357 | ||||||||
\(231\) | 18.0718 | 1.18904 | ||||||||
\(232\) | −2.99221 | −0.196448 | ||||||||
\(233\) | 8.81046 | 0.577193 | 0.288596 | − | 0.957451i | \(-0.406811\pi\) | ||||
0.288596 | + | 0.957451i | \(0.406811\pi\) | |||||||
\(234\) | 3.46795 | 0.226707 | ||||||||
\(235\) | −23.2883 | −1.51916 | ||||||||
\(236\) | 5.08617 | 0.331082 | ||||||||
\(237\) | 5.71140 | 0.370995 | ||||||||
\(238\) | −2.96233 | −0.192019 | ||||||||
\(239\) | −24.9840 | −1.61608 | −0.808042 | − | 0.589125i | \(-0.799472\pi\) | ||||
−0.808042 | + | 0.589125i | \(0.799472\pi\) | |||||||
\(240\) | −4.16298 | −0.268719 | ||||||||
\(241\) | −12.6888 | −0.817355 | −0.408678 | − | 0.912679i | \(-0.634010\pi\) | ||||
−0.408678 | + | 0.912679i | \(0.634010\pi\) | |||||||
\(242\) | −30.8673 | −1.98423 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.63380 | −0.104593 | ||||||||
\(245\) | 3.23612 | 0.206748 | ||||||||
\(246\) | −11.7674 | −0.750263 | ||||||||
\(247\) | 0.590454 | 0.0375697 | ||||||||
\(248\) | 3.00519 | 0.190830 | ||||||||
\(249\) | 10.1735 | 0.644717 | ||||||||
\(250\) | 1.66282 | 0.105166 | ||||||||
\(251\) | 5.91664 | 0.373455 | 0.186727 | − | 0.982412i | \(-0.440212\pi\) | ||||
0.186727 | + | 0.982412i | \(0.440212\pi\) | |||||||
\(252\) | −2.58206 | −0.162655 | ||||||||
\(253\) | −57.1914 | −3.59560 | ||||||||
\(254\) | −17.9737 | −1.12777 | ||||||||
\(255\) | 3.07941 | 0.192840 | ||||||||
\(256\) | −16.6329 | −1.03955 | ||||||||
\(257\) | 24.1193 | 1.50452 | 0.752262 | − | 0.658864i | \(-0.228963\pi\) | ||||
0.752262 | + | 0.658864i | \(0.228963\pi\) | |||||||
\(258\) | 0.514232 | 0.0320147 | ||||||||
\(259\) | 7.68924 | 0.477786 | ||||||||
\(260\) | 9.30836 | 0.577280 | ||||||||
\(261\) | −0.984886 | −0.0609629 | ||||||||
\(262\) | −19.9861 | −1.23474 | ||||||||
\(263\) | 20.1796 | 1.24433 | 0.622164 | − | 0.782887i | \(-0.286254\pi\) | ||||
0.622164 | + | 0.782887i | \(0.286254\pi\) | |||||||
\(264\) | 19.3502 | 1.19092 | ||||||||
\(265\) | −5.11774 | −0.314380 | ||||||||
\(266\) | 0.526574 | 0.0322863 | ||||||||
\(267\) | 12.4747 | 0.763438 | ||||||||
\(268\) | 1.82866 | 0.111703 | ||||||||
\(269\) | 7.78801 | 0.474843 | 0.237422 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237422 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(270\) | −3.21499 | −0.195658 | ||||||||
\(271\) | −3.65833 | −0.222228 | −0.111114 | − | 0.993808i | \(-0.535442\pi\) | ||||
−0.111114 | + | 0.993808i | \(0.535442\pi\) | |||||||
\(272\) | −1.35187 | −0.0819693 | ||||||||
\(273\) | −9.42502 | −0.570428 | ||||||||
\(274\) | 3.35048 | 0.202410 | ||||||||
\(275\) | 28.5514 | 1.72172 | ||||||||
\(276\) | 8.17140 | 0.491861 | ||||||||
\(277\) | 15.7821 | 0.948256 | 0.474128 | − | 0.880456i | \(-0.342763\pi\) | ||||
0.474128 | + | 0.880456i | \(0.342763\pi\) | |||||||
\(278\) | 2.57843 | 0.154644 | ||||||||
\(279\) | 0.989160 | 0.0592195 | ||||||||
\(280\) | 26.5458 | 1.58642 | ||||||||
\(281\) | −11.5636 | −0.689829 | −0.344914 | − | 0.938634i | \(-0.612092\pi\) | ||||
−0.344914 | + | 0.938634i | \(0.612092\pi\) | |||||||
\(282\) | 7.89553 | 0.470172 | ||||||||
\(283\) | −11.5233 | −0.684989 | −0.342495 | − | 0.939520i | \(-0.611272\pi\) | ||||
−0.342495 | + | 0.939520i | \(0.611272\pi\) | |||||||
\(284\) | 0.584981 | 0.0347122 | ||||||||
\(285\) | −0.547386 | −0.0324243 | ||||||||
\(286\) | 22.0877 | 1.30608 | ||||||||
\(287\) | 31.9809 | 1.88778 | ||||||||
\(288\) | −4.66486 | −0.274880 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.16640 | 0.185937 | ||||||||
\(291\) | 15.3137 | 0.897708 | ||||||||
\(292\) | −5.46476 | −0.319801 | ||||||||
\(293\) | −6.67959 | −0.390226 | −0.195113 | − | 0.980781i | \(-0.562507\pi\) | ||||
−0.195113 | + | 0.980781i | \(0.562507\pi\) | |||||||
\(294\) | −1.09716 | −0.0639875 | ||||||||
\(295\) | −17.2113 | −1.00208 | ||||||||
\(296\) | 8.23318 | 0.478544 | ||||||||
\(297\) | 6.36912 | 0.369574 | ||||||||
\(298\) | 15.1371 | 0.876871 | ||||||||
\(299\) | 29.8272 | 1.72495 | ||||||||
\(300\) | −4.07937 | −0.235523 | ||||||||
\(301\) | −1.39756 | −0.0805538 | ||||||||
\(302\) | −17.4902 | −1.00645 | ||||||||
\(303\) | 10.8892 | 0.625566 | ||||||||
\(304\) | 0.240304 | 0.0137824 | ||||||||
\(305\) | 5.52869 | 0.316572 | ||||||||
\(306\) | −1.04403 | −0.0596831 | ||||||||
\(307\) | 15.8173 | 0.902743 | 0.451372 | − | 0.892336i | \(-0.350935\pi\) | ||||
0.451372 | + | 0.892336i | \(0.350935\pi\) | |||||||
\(308\) | −16.4455 | −0.937067 | ||||||||
\(309\) | 5.62573 | 0.320036 | ||||||||
\(310\) | −3.18014 | −0.180620 | ||||||||
\(311\) | −17.2152 | −0.976183 | −0.488091 | − | 0.872793i | \(-0.662307\pi\) | ||||
−0.488091 | + | 0.872793i | \(0.662307\pi\) | |||||||
\(312\) | −10.0917 | −0.571333 | ||||||||
\(313\) | −0.598984 | −0.0338566 | −0.0169283 | − | 0.999857i | \(-0.505389\pi\) | ||||
−0.0169283 | + | 0.999857i | \(0.505389\pi\) | |||||||
\(314\) | −1.04403 | −0.0589179 | ||||||||
\(315\) | 8.73756 | 0.492306 | ||||||||
\(316\) | −5.19741 | −0.292377 | ||||||||
\(317\) | 4.33420 | 0.243433 | 0.121717 | − | 0.992565i | \(-0.461160\pi\) | ||||
0.121717 | + | 0.992565i | \(0.461160\pi\) | |||||||
\(318\) | 1.73509 | 0.0972990 | ||||||||
\(319\) | −6.27285 | −0.351212 | ||||||||
\(320\) | 23.3234 | 1.30382 | ||||||||
\(321\) | −5.38419 | −0.300516 | ||||||||
\(322\) | 26.6002 | 1.48237 | ||||||||
\(323\) | −0.177756 | −0.00989063 | ||||||||
\(324\) | −0.910007 | −0.0505560 | ||||||||
\(325\) | −14.8905 | −0.825976 | ||||||||
\(326\) | −11.4965 | −0.636732 | ||||||||
\(327\) | 4.14346 | 0.229134 | ||||||||
\(328\) | 34.2433 | 1.89077 | ||||||||
\(329\) | −21.4581 | −1.18302 | ||||||||
\(330\) | −20.4767 | −1.12720 | ||||||||
\(331\) | 6.30140 | 0.346356 | 0.173178 | − | 0.984891i | \(-0.444596\pi\) | ||||
0.173178 | + | 0.984891i | \(0.444596\pi\) | |||||||
\(332\) | −9.25793 | −0.508095 | ||||||||
\(333\) | 2.70995 | 0.148504 | ||||||||
\(334\) | −2.62213 | −0.143477 | ||||||||
\(335\) | −6.18809 | −0.338091 | ||||||||
\(336\) | −3.83582 | −0.209261 | ||||||||
\(337\) | −12.7217 | −0.692995 | −0.346497 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346497 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(338\) | 2.05288 | 0.111662 | ||||||||
\(339\) | −7.51822 | −0.408334 | ||||||||
\(340\) | −2.80229 | −0.151975 | ||||||||
\(341\) | 6.30008 | 0.341168 | ||||||||
\(342\) | 0.185583 | 0.0100352 | ||||||||
\(343\) | −16.8801 | −0.911438 | ||||||||
\(344\) | −1.49642 | −0.0806815 | ||||||||
\(345\) | −27.6516 | −1.48871 | ||||||||
\(346\) | −5.08346 | −0.273289 | ||||||||
\(347\) | −32.3010 | −1.73401 | −0.867005 | − | 0.498300i | \(-0.833958\pi\) | ||||
−0.867005 | + | 0.498300i | \(0.833958\pi\) | |||||||
\(348\) | 0.896253 | 0.0480442 | ||||||||
\(349\) | −12.7535 | −0.682677 | −0.341339 | − | 0.939940i | \(-0.610880\pi\) | ||||
−0.341339 | + | 0.939940i | \(0.610880\pi\) | |||||||
\(350\) | −13.2795 | −0.709820 | ||||||||
\(351\) | −3.32170 | −0.177299 | ||||||||
\(352\) | −29.7110 | −1.58360 | ||||||||
\(353\) | 15.6117 | 0.830929 | 0.415465 | − | 0.909609i | \(-0.363619\pi\) | ||||
0.415465 | + | 0.909609i | \(0.363619\pi\) | |||||||
\(354\) | 5.83523 | 0.310139 | ||||||||
\(355\) | −1.97954 | −0.105063 | ||||||||
\(356\) | −11.3521 | −0.601657 | ||||||||
\(357\) | 2.83741 | 0.150172 | ||||||||
\(358\) | 26.6483 | 1.40841 | ||||||||
\(359\) | 15.9703 | 0.842879 | 0.421439 | − | 0.906857i | \(-0.361525\pi\) | ||||
0.421439 | + | 0.906857i | \(0.361525\pi\) | |||||||
\(360\) | 9.35565 | 0.493086 | ||||||||
\(361\) | −18.9684 | −0.998337 | ||||||||
\(362\) | 14.6870 | 0.771931 | ||||||||
\(363\) | 29.5657 | 1.55179 | ||||||||
\(364\) | 8.57684 | 0.449548 | ||||||||
\(365\) | 18.4924 | 0.967938 | ||||||||
\(366\) | −1.87442 | −0.0979773 | ||||||||
\(367\) | −10.1029 | −0.527366 | −0.263683 | − | 0.964609i | \(-0.584937\pi\) | ||||
−0.263683 | + | 0.964609i | \(0.584937\pi\) | |||||||
\(368\) | 12.1391 | 0.632796 | ||||||||
\(369\) | 11.2712 | 0.586754 | ||||||||
\(370\) | −8.71248 | −0.452940 | ||||||||
\(371\) | −4.71555 | −0.244819 | ||||||||
\(372\) | −0.900143 | −0.0466702 | ||||||||
\(373\) | −6.96565 | −0.360668 | −0.180334 | − | 0.983605i | \(-0.557718\pi\) | ||||
−0.180334 | + | 0.983605i | \(0.557718\pi\) | |||||||
\(374\) | −6.64953 | −0.343839 | ||||||||
\(375\) | −1.59270 | −0.0822465 | ||||||||
\(376\) | −22.9760 | −1.18490 | ||||||||
\(377\) | 3.27149 | 0.168491 | ||||||||
\(378\) | −2.96233 | −0.152366 | ||||||||
\(379\) | −19.4351 | −0.998314 | −0.499157 | − | 0.866512i | \(-0.666357\pi\) | ||||
−0.499157 | + | 0.866512i | \(0.666357\pi\) | |||||||
\(380\) | 0.498125 | 0.0255533 | ||||||||
\(381\) | 17.2157 | 0.881987 | ||||||||
\(382\) | −4.69997 | −0.240471 | ||||||||
\(383\) | −11.5755 | −0.591480 | −0.295740 | − | 0.955268i | \(-0.595566\pi\) | ||||
−0.295740 | + | 0.955268i | \(0.595566\pi\) | |||||||
\(384\) | 1.42227 | 0.0725801 | ||||||||
\(385\) | 55.6505 | 2.83621 | ||||||||
\(386\) | −4.17887 | −0.212699 | ||||||||
\(387\) | −0.492547 | −0.0250376 | ||||||||
\(388\) | −13.9356 | −0.707474 | ||||||||
\(389\) | 22.1538 | 1.12324 | 0.561622 | − | 0.827394i | \(-0.310178\pi\) | ||||
0.561622 | + | 0.827394i | \(0.310178\pi\) | |||||||
\(390\) | 10.6792 | 0.540764 | ||||||||
\(391\) | −8.97949 | −0.454113 | ||||||||
\(392\) | 3.19273 | 0.161257 | ||||||||
\(393\) | 19.1433 | 0.965649 | ||||||||
\(394\) | −17.2625 | −0.869673 | ||||||||
\(395\) | 17.5878 | 0.884936 | ||||||||
\(396\) | −5.79594 | −0.291257 | ||||||||
\(397\) | −11.3932 | −0.571809 | −0.285905 | − | 0.958258i | \(-0.592294\pi\) | ||||
−0.285905 | + | 0.958258i | \(0.592294\pi\) | |||||||
\(398\) | 15.6155 | 0.782734 | ||||||||
\(399\) | −0.504368 | −0.0252500 | ||||||||
\(400\) | −6.06017 | −0.303008 | ||||||||
\(401\) | 21.2219 | 1.05977 | 0.529885 | − | 0.848069i | \(-0.322235\pi\) | ||||
0.529885 | + | 0.848069i | \(0.322235\pi\) | |||||||
\(402\) | 2.09798 | 0.104637 | ||||||||
\(403\) | −3.28569 | −0.163672 | ||||||||
\(404\) | −9.90921 | −0.493002 | ||||||||
\(405\) | 3.07941 | 0.153017 | ||||||||
\(406\) | 2.91756 | 0.144796 | ||||||||
\(407\) | 17.2600 | 0.855547 | ||||||||
\(408\) | 3.03813 | 0.150410 | ||||||||
\(409\) | 17.9507 | 0.887606 | 0.443803 | − | 0.896124i | \(-0.353629\pi\) | ||||
0.443803 | + | 0.896124i | \(0.353629\pi\) | |||||||
\(410\) | −36.2368 | −1.78961 | ||||||||
\(411\) | −3.20919 | −0.158298 | ||||||||
\(412\) | −5.11945 | −0.252217 | ||||||||
\(413\) | −15.8587 | −0.780356 | ||||||||
\(414\) | 9.37484 | 0.460748 | ||||||||
\(415\) | 31.3283 | 1.53785 | ||||||||
\(416\) | 15.4953 | 0.759718 | ||||||||
\(417\) | −2.46969 | −0.120941 | ||||||||
\(418\) | 1.18200 | 0.0578134 | ||||||||
\(419\) | −35.0825 | −1.71389 | −0.856946 | − | 0.515406i | \(-0.827641\pi\) | ||||
−0.856946 | + | 0.515406i | \(0.827641\pi\) | |||||||
\(420\) | −7.95124 | −0.387981 | ||||||||
\(421\) | −31.5413 | −1.53723 | −0.768614 | − | 0.639713i | \(-0.779053\pi\) | ||||
−0.768614 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(422\) | 8.83103 | 0.429888 | ||||||||
\(423\) | −7.56257 | −0.367705 | ||||||||
\(424\) | −5.04912 | −0.245207 | ||||||||
\(425\) | 4.48279 | 0.217447 | ||||||||
\(426\) | 0.671133 | 0.0325165 | ||||||||
\(427\) | 5.09420 | 0.246526 | ||||||||
\(428\) | 4.89965 | 0.236834 | ||||||||
\(429\) | −21.1563 | −1.02144 | ||||||||
\(430\) | 1.58353 | 0.0763648 | ||||||||
\(431\) | 21.6518 | 1.04293 | 0.521466 | − | 0.853272i | \(-0.325385\pi\) | ||||
0.521466 | + | 0.853272i | \(0.325385\pi\) | |||||||
\(432\) | −1.35187 | −0.0650420 | ||||||||
\(433\) | 29.0209 | 1.39466 | 0.697328 | − | 0.716752i | \(-0.254372\pi\) | ||||
0.697328 | + | 0.716752i | \(0.254372\pi\) | |||||||
\(434\) | −2.93022 | −0.140655 | ||||||||
\(435\) | −3.03287 | −0.145415 | ||||||||
\(436\) | −3.77058 | −0.180578 | ||||||||
\(437\) | 1.59616 | 0.0763548 | ||||||||
\(438\) | −6.26957 | −0.299572 | ||||||||
\(439\) | 6.39001 | 0.304978 | 0.152489 | − | 0.988305i | \(-0.451271\pi\) | ||||
0.152489 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(440\) | 59.5872 | 2.84071 | ||||||||
\(441\) | 1.05089 | 0.0500423 | ||||||||
\(442\) | 3.46795 | 0.164953 | ||||||||
\(443\) | −10.5739 | −0.502382 | −0.251191 | − | 0.967937i | \(-0.580822\pi\) | ||||
−0.251191 | + | 0.967937i | \(0.580822\pi\) | |||||||
\(444\) | −2.46608 | −0.117035 | ||||||||
\(445\) | 38.4147 | 1.82103 | ||||||||
\(446\) | −8.41716 | −0.398564 | ||||||||
\(447\) | −14.4988 | −0.685770 | ||||||||
\(448\) | 21.4905 | 1.01533 | ||||||||
\(449\) | −34.0674 | −1.60774 | −0.803869 | − | 0.594806i | \(-0.797229\pi\) | ||||
−0.803869 | + | 0.594806i | \(0.797229\pi\) | |||||||
\(450\) | −4.68016 | −0.220625 | ||||||||
\(451\) | 71.7875 | 3.38034 | ||||||||
\(452\) | 6.84163 | 0.321803 | ||||||||
\(453\) | 16.7526 | 0.787108 | ||||||||
\(454\) | −0.684125 | −0.0321076 | ||||||||
\(455\) | −29.0235 | −1.36064 | ||||||||
\(456\) | −0.540047 | −0.0252900 | ||||||||
\(457\) | −3.66280 | −0.171339 | −0.0856693 | − | 0.996324i | \(-0.527303\pi\) | ||||
−0.0856693 | + | 0.996324i | \(0.527303\pi\) | |||||||
\(458\) | 29.3262 | 1.37032 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 25.1631 | 1.17324 | ||||||||
\(461\) | −29.7615 | −1.38613 | −0.693066 | − | 0.720874i | \(-0.743741\pi\) | ||||
−0.693066 | + | 0.720874i | \(0.743741\pi\) | |||||||
\(462\) | −18.8674 | −0.877793 | ||||||||
\(463\) | 25.3807 | 1.17954 | 0.589771 | − | 0.807571i | \(-0.299218\pi\) | ||||
0.589771 | + | 0.807571i | \(0.299218\pi\) | |||||||
\(464\) | 1.33144 | 0.0618105 | ||||||||
\(465\) | 3.04603 | 0.141256 | ||||||||
\(466\) | −9.19836 | −0.426106 | ||||||||
\(467\) | 21.9413 | 1.01532 | 0.507662 | − | 0.861556i | \(-0.330510\pi\) | ||||
0.507662 | + | 0.861556i | \(0.330510\pi\) | |||||||
\(468\) | 3.02277 | 0.139728 | ||||||||
\(469\) | −5.70178 | −0.263284 | ||||||||
\(470\) | 24.3136 | 1.12150 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −16.9806 | −0.781594 | ||||||||
\(473\) | −3.13709 | −0.144243 | ||||||||
\(474\) | −5.96285 | −0.273883 | ||||||||
\(475\) | −0.796845 | −0.0365618 | ||||||||
\(476\) | −2.58206 | −0.118349 | ||||||||
\(477\) | −1.66192 | −0.0760941 | ||||||||
\(478\) | 26.0840 | 1.19306 | ||||||||
\(479\) | 2.19814 | 0.100436 | 0.0502178 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502178 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(480\) | −14.3650 | −0.655671 | ||||||||
\(481\) | −9.00165 | −0.410440 | ||||||||
\(482\) | 13.2474 | 0.603403 | ||||||||
\(483\) | −25.4785 | −1.15931 | ||||||||
\(484\) | −26.9050 | −1.22295 | ||||||||
\(485\) | 47.1574 | 2.14131 | ||||||||
\(486\) | −1.04403 | −0.0473580 | ||||||||
\(487\) | −2.43924 | −0.110533 | −0.0552664 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552664 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(488\) | 5.45457 | 0.246917 | ||||||||
\(489\) | 11.0117 | 0.497966 | ||||||||
\(490\) | −3.37860 | −0.152630 | ||||||||
\(491\) | −17.5849 | −0.793595 | −0.396797 | − | 0.917906i | \(-0.629878\pi\) | ||||
−0.396797 | + | 0.917906i | \(0.629878\pi\) | |||||||
\(492\) | −10.2569 | −0.462415 | ||||||||
\(493\) | −0.984886 | −0.0443570 | ||||||||
\(494\) | −0.616450 | −0.0277354 | ||||||||
\(495\) | 19.6132 | 0.881546 | ||||||||
\(496\) | −1.33722 | −0.0600429 | ||||||||
\(497\) | −1.82397 | −0.0818164 | ||||||||
\(498\) | −10.6214 | −0.475955 | ||||||||
\(499\) | 21.7188 | 0.972265 | 0.486133 | − | 0.873885i | \(-0.338407\pi\) | ||||
0.486133 | + | 0.873885i | \(0.338407\pi\) | |||||||
\(500\) | 1.44936 | 0.0648175 | ||||||||
\(501\) | 2.51155 | 0.112208 | ||||||||
\(502\) | −6.17713 | −0.275699 | ||||||||
\(503\) | 32.3476 | 1.44231 | 0.721155 | − | 0.692774i | \(-0.243612\pi\) | ||||
0.721155 | + | 0.692774i | \(0.243612\pi\) | |||||||
\(504\) | 8.62041 | 0.383983 | ||||||||
\(505\) | 33.5322 | 1.49216 | ||||||||
\(506\) | 59.7094 | 2.65441 | ||||||||
\(507\) | −1.96631 | −0.0873269 | ||||||||
\(508\) | −15.6664 | −0.695085 | ||||||||
\(509\) | 2.98686 | 0.132390 | 0.0661952 | − | 0.997807i | \(-0.478914\pi\) | ||||
0.0661952 | + | 0.997807i | \(0.478914\pi\) | |||||||
\(510\) | −3.21499 | −0.142362 | ||||||||
\(511\) | 17.0391 | 0.753768 | ||||||||
\(512\) | 14.5206 | 0.641727 | ||||||||
\(513\) | −0.177756 | −0.00784814 | ||||||||
\(514\) | −25.1813 | −1.11070 | ||||||||
\(515\) | 17.3239 | 0.763384 | ||||||||
\(516\) | 0.448221 | 0.0197318 | ||||||||
\(517\) | −48.1669 | −2.11838 | ||||||||
\(518\) | −8.02778 | −0.352720 | ||||||||
\(519\) | 4.86909 | 0.213729 | ||||||||
\(520\) | −31.0767 | −1.36280 | ||||||||
\(521\) | 17.2814 | 0.757114 | 0.378557 | − | 0.925578i | \(-0.376420\pi\) | ||||
0.378557 | + | 0.925578i | \(0.376420\pi\) | |||||||
\(522\) | 1.02825 | 0.0450052 | ||||||||
\(523\) | −12.9211 | −0.565000 | −0.282500 | − | 0.959267i | \(-0.591164\pi\) | ||||
−0.282500 | + | 0.959267i | \(0.591164\pi\) | |||||||
\(524\) | −17.4205 | −0.761018 | ||||||||
\(525\) | 12.7195 | 0.555125 | ||||||||
\(526\) | −21.0681 | −0.918611 | ||||||||
\(527\) | 0.989160 | 0.0430885 | ||||||||
\(528\) | −8.61024 | −0.374712 | ||||||||
\(529\) | 57.6313 | 2.50571 | ||||||||
\(530\) | 5.34306 | 0.232088 | ||||||||
\(531\) | −5.58915 | −0.242549 | ||||||||
\(532\) | 0.458978 | 0.0198992 | ||||||||
\(533\) | −37.4395 | −1.62168 | ||||||||
\(534\) | −13.0239 | −0.563600 | ||||||||
\(535\) | −16.5802 | −0.716822 | ||||||||
\(536\) | −6.10512 | −0.263701 | ||||||||
\(537\) | −25.5245 | −1.10147 | ||||||||
\(538\) | −8.13090 | −0.350548 | ||||||||
\(539\) | 6.69323 | 0.288298 | ||||||||
\(540\) | −2.80229 | −0.120591 | ||||||||
\(541\) | −39.3346 | −1.69113 | −0.845563 | − | 0.533875i | \(-0.820735\pi\) | ||||
−0.845563 | + | 0.533875i | \(0.820735\pi\) | |||||||
\(542\) | 3.81940 | 0.164057 | ||||||||
\(543\) | −14.0676 | −0.603699 | ||||||||
\(544\) | −4.66486 | −0.200004 | ||||||||
\(545\) | 12.7594 | 0.546554 | ||||||||
\(546\) | 9.83998 | 0.421112 | ||||||||
\(547\) | 11.0190 | 0.471137 | 0.235568 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235568 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(548\) | 2.92039 | 0.124753 | ||||||||
\(549\) | 1.79537 | 0.0766246 | ||||||||
\(550\) | −29.8085 | −1.27104 | ||||||||
\(551\) | 0.175070 | 0.00745822 | ||||||||
\(552\) | −27.2808 | −1.16115 | ||||||||
\(553\) | 16.2056 | 0.689131 | ||||||||
\(554\) | −16.4770 | −0.700039 | ||||||||
\(555\) | 8.34507 | 0.354228 | ||||||||
\(556\) | 2.24744 | 0.0953126 | ||||||||
\(557\) | 14.1637 | 0.600137 | 0.300068 | − | 0.953918i | \(-0.402990\pi\) | ||||
0.300068 | + | 0.953918i | \(0.402990\pi\) | |||||||
\(558\) | −1.03271 | −0.0437181 | ||||||||
\(559\) | 1.63609 | 0.0691993 | ||||||||
\(560\) | −11.8121 | −0.499151 | ||||||||
\(561\) | 6.36912 | 0.268904 | ||||||||
\(562\) | 12.0727 | 0.509258 | ||||||||
\(563\) | 45.8411 | 1.93197 | 0.965987 | − | 0.258592i | \(-0.0832586\pi\) | ||||
0.965987 | + | 0.258592i | \(0.0832586\pi\) | |||||||
\(564\) | 6.88199 | 0.289784 | ||||||||
\(565\) | −23.1517 | −0.974000 | ||||||||
\(566\) | 12.0306 | 0.505685 | ||||||||
\(567\) | 2.83741 | 0.119160 | ||||||||
\(568\) | −1.95300 | −0.0819461 | ||||||||
\(569\) | −39.9188 | −1.67348 | −0.836741 | − | 0.547598i | \(-0.815542\pi\) | ||||
−0.836741 | + | 0.547598i | \(0.815542\pi\) | |||||||
\(570\) | 0.571486 | 0.0239369 | ||||||||
\(571\) | −40.0366 | −1.67548 | −0.837740 | − | 0.546069i | \(-0.816123\pi\) | ||||
−0.837740 | + | 0.546069i | \(0.816123\pi\) | |||||||
\(572\) | 19.2524 | 0.804982 | ||||||||
\(573\) | 4.50177 | 0.188064 | ||||||||
\(574\) | −33.3890 | −1.39363 | ||||||||
\(575\) | −40.2532 | −1.67867 | ||||||||
\(576\) | 7.57399 | 0.315583 | ||||||||
\(577\) | −43.1834 | −1.79775 | −0.898874 | − | 0.438207i | \(-0.855614\pi\) | ||||
−0.898874 | + | 0.438207i | \(0.855614\pi\) | |||||||
\(578\) | −1.04403 | −0.0434258 | ||||||||
\(579\) | 4.00264 | 0.166344 | ||||||||
\(580\) | 2.75993 | 0.114600 | ||||||||
\(581\) | 28.8663 | 1.19758 | ||||||||
\(582\) | −15.9880 | −0.662723 | ||||||||
\(583\) | −10.5850 | −0.438384 | ||||||||
\(584\) | 18.2445 | 0.754963 | ||||||||
\(585\) | −10.2289 | −0.422913 | ||||||||
\(586\) | 6.97368 | 0.288080 | ||||||||
\(587\) | 17.4060 | 0.718423 | 0.359211 | − | 0.933256i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933256i | \(0.383046\pi\) | |||||||
\(588\) | −0.956316 | −0.0394378 | ||||||||
\(589\) | −0.175830 | −0.00724493 | ||||||||
\(590\) | 17.9691 | 0.739776 | ||||||||
\(591\) | 16.5345 | 0.680140 | ||||||||
\(592\) | −3.66351 | −0.150569 | ||||||||
\(593\) | 26.6552 | 1.09460 | 0.547300 | − | 0.836937i | \(-0.315656\pi\) | ||||
0.547300 | + | 0.836937i | \(0.315656\pi\) | |||||||
\(594\) | −6.64953 | −0.272834 | ||||||||
\(595\) | 8.73756 | 0.358205 | ||||||||
\(596\) | 13.1940 | 0.540448 | ||||||||
\(597\) | −14.9570 | −0.612148 | ||||||||
\(598\) | −31.1404 | −1.27343 | ||||||||
\(599\) | −34.2439 | −1.39917 | −0.699583 | − | 0.714551i | \(-0.746631\pi\) | ||||
−0.699583 | + | 0.714551i | \(0.746631\pi\) | |||||||
\(600\) | 13.6193 | 0.556005 | ||||||||
\(601\) | 15.8430 | 0.646248 | 0.323124 | − | 0.946357i | \(-0.395267\pi\) | ||||
0.323124 | + | 0.946357i | \(0.395267\pi\) | |||||||
\(602\) | 1.45909 | 0.0594680 | ||||||||
\(603\) | −2.00950 | −0.0818333 | ||||||||
\(604\) | −15.2450 | −0.620311 | ||||||||
\(605\) | 91.0449 | 3.70150 | ||||||||
\(606\) | −11.3686 | −0.461817 | ||||||||
\(607\) | −7.83813 | −0.318140 | −0.159070 | − | 0.987267i | \(-0.550850\pi\) | ||||
−0.159070 | + | 0.987267i | \(0.550850\pi\) | |||||||
\(608\) | 0.829209 | 0.0336289 | ||||||||
\(609\) | −2.79452 | −0.113240 | ||||||||
\(610\) | −5.77211 | −0.233706 | ||||||||
\(611\) | 25.1206 | 1.01627 | ||||||||
\(612\) | −0.910007 | −0.0367849 | ||||||||
\(613\) | 9.91693 | 0.400541 | 0.200271 | − | 0.979741i | \(-0.435818\pi\) | ||||
0.200271 | + | 0.979741i | \(0.435818\pi\) | |||||||
\(614\) | −16.5137 | −0.666440 | ||||||||
\(615\) | 34.7086 | 1.39959 | ||||||||
\(616\) | 54.9044 | 2.21216 | ||||||||
\(617\) | −5.64089 | −0.227094 | −0.113547 | − | 0.993533i | \(-0.536221\pi\) | ||||
−0.113547 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(618\) | −5.87341 | −0.236263 | ||||||||
\(619\) | 2.78449 | 0.111918 | 0.0559590 | − | 0.998433i | \(-0.482178\pi\) | ||||
0.0559590 | + | 0.998433i | \(0.482178\pi\) | |||||||
\(620\) | −2.77191 | −0.111323 | ||||||||
\(621\) | −8.97949 | −0.360335 | ||||||||
\(622\) | 17.9731 | 0.720656 | ||||||||
\(623\) | 35.3958 | 1.41810 | ||||||||
\(624\) | 4.49052 | 0.179764 | ||||||||
\(625\) | −27.3185 | −1.09274 | ||||||||
\(626\) | 0.625356 | 0.0249942 | ||||||||
\(627\) | −1.13215 | −0.0452138 | ||||||||
\(628\) | −0.910007 | −0.0363132 | ||||||||
\(629\) | 2.70995 | 0.108053 | ||||||||
\(630\) | −9.12225 | −0.363439 | ||||||||
\(631\) | −43.4932 | −1.73144 | −0.865719 | − | 0.500530i | \(-0.833139\pi\) | ||||
−0.865719 | + | 0.500530i | \(0.833139\pi\) | |||||||
\(632\) | 17.3519 | 0.690223 | ||||||||
\(633\) | −8.45862 | −0.336200 | ||||||||
\(634\) | −4.52503 | −0.179712 | ||||||||
\(635\) | 53.0143 | 2.10381 | ||||||||
\(636\) | 1.51236 | 0.0599689 | ||||||||
\(637\) | −3.49074 | −0.138308 | ||||||||
\(638\) | 6.54903 | 0.259278 | ||||||||
\(639\) | −0.642831 | −0.0254300 | ||||||||
\(640\) | 4.37977 | 0.173125 | ||||||||
\(641\) | 12.2069 | 0.482142 | 0.241071 | − | 0.970507i | \(-0.422501\pi\) | ||||
0.241071 | + | 0.970507i | \(0.422501\pi\) | |||||||
\(642\) | 5.62124 | 0.221853 | ||||||||
\(643\) | 38.0757 | 1.50156 | 0.750779 | − | 0.660554i | \(-0.229678\pi\) | ||||
0.750779 | + | 0.660554i | \(0.229678\pi\) | |||||||
\(644\) | 23.1856 | 0.913641 | ||||||||
\(645\) | −1.51676 | −0.0597222 | ||||||||
\(646\) | 0.185583 | 0.00730165 | ||||||||
\(647\) | −5.76736 | −0.226739 | −0.113369 | − | 0.993553i | \(-0.536164\pi\) | ||||
−0.113369 | + | 0.993553i | \(0.536164\pi\) | |||||||
\(648\) | 3.03813 | 0.119349 | ||||||||
\(649\) | −35.5980 | −1.39734 | ||||||||
\(650\) | 15.5461 | 0.609767 | ||||||||
\(651\) | 2.80665 | 0.110001 | ||||||||
\(652\) | −10.0207 | −0.392441 | ||||||||
\(653\) | −19.2745 | −0.754270 | −0.377135 | − | 0.926158i | \(-0.623091\pi\) | ||||
−0.377135 | + | 0.926158i | \(0.623091\pi\) | |||||||
\(654\) | −4.32588 | −0.169155 | ||||||||
\(655\) | 58.9500 | 2.30337 | ||||||||
\(656\) | −15.2372 | −0.594913 | ||||||||
\(657\) | 6.00518 | 0.234284 | ||||||||
\(658\) | 22.4028 | 0.873354 | ||||||||
\(659\) | −38.0098 | −1.48065 | −0.740325 | − | 0.672249i | \(-0.765328\pi\) | ||||
−0.740325 | + | 0.672249i | \(0.765328\pi\) | |||||||
\(660\) | −17.8481 | −0.694737 | ||||||||
\(661\) | 10.3938 | 0.404274 | 0.202137 | − | 0.979357i | \(-0.435211\pi\) | ||||
0.202137 | + | 0.979357i | \(0.435211\pi\) | |||||||
\(662\) | −6.57883 | −0.255694 | ||||||||
\(663\) | −3.32170 | −0.129004 | ||||||||
\(664\) | 30.9083 | 1.19947 | ||||||||
\(665\) | −1.55316 | −0.0602288 | ||||||||
\(666\) | −2.82926 | −0.109632 | ||||||||
\(667\) | 8.84377 | 0.342432 | ||||||||
\(668\) | −2.28553 | −0.0884298 | ||||||||
\(669\) | 8.06220 | 0.311703 | ||||||||
\(670\) | 6.46053 | 0.249592 | ||||||||
\(671\) | 11.4349 | 0.441441 | ||||||||
\(672\) | −13.2361 | −0.510594 | ||||||||
\(673\) | 35.1915 | 1.35653 | 0.678267 | − | 0.734816i | \(-0.262731\pi\) | ||||
0.678267 | + | 0.734816i | \(0.262731\pi\) | |||||||
\(674\) | 13.2818 | 0.511596 | ||||||||
\(675\) | 4.48279 | 0.172543 | ||||||||
\(676\) | 1.78936 | 0.0688214 | ||||||||
\(677\) | 25.9083 | 0.995736 | 0.497868 | − | 0.867253i | \(-0.334116\pi\) | ||||
0.497868 | + | 0.867253i | \(0.334116\pi\) | |||||||
\(678\) | 7.84922 | 0.301448 | ||||||||
\(679\) | 43.4514 | 1.66751 | ||||||||
\(680\) | 9.35565 | 0.358773 | ||||||||
\(681\) | 0.655276 | 0.0251102 | ||||||||
\(682\) | −6.57745 | −0.251864 | ||||||||
\(683\) | −24.7682 | −0.947728 | −0.473864 | − | 0.880598i | \(-0.657141\pi\) | ||||
−0.473864 | + | 0.880598i | \(0.657141\pi\) | |||||||
\(684\) | 0.161760 | 0.00618503 | ||||||||
\(685\) | −9.88242 | −0.377588 | ||||||||
\(686\) | 17.6232 | 0.672859 | ||||||||
\(687\) | −28.0895 | −1.07168 | ||||||||
\(688\) | 0.665861 | 0.0253857 | ||||||||
\(689\) | 5.52040 | 0.210310 | ||||||||
\(690\) | 28.8690 | 1.09902 | ||||||||
\(691\) | 8.20165 | 0.312006 | 0.156003 | − | 0.987757i | \(-0.450139\pi\) | ||||
0.156003 | + | 0.987757i | \(0.450139\pi\) | |||||||
\(692\) | −4.43091 | −0.168438 | ||||||||
\(693\) | 18.0718 | 0.686491 | ||||||||
\(694\) | 33.7231 | 1.28011 | ||||||||
\(695\) | −7.60520 | −0.288482 | ||||||||
\(696\) | −2.99221 | −0.113419 | ||||||||
\(697\) | 11.2712 | 0.426926 | ||||||||
\(698\) | 13.3150 | 0.503979 | ||||||||
\(699\) | 8.81046 | 0.333242 | ||||||||
\(700\) | −11.5748 | −0.437488 | ||||||||
\(701\) | 29.4275 | 1.11146 | 0.555731 | − | 0.831362i | \(-0.312438\pi\) | ||||
0.555731 | + | 0.831362i | \(0.312438\pi\) | |||||||
\(702\) | 3.46795 | 0.130889 | ||||||||
\(703\) | −0.481712 | −0.0181681 | ||||||||
\(704\) | 48.2396 | 1.81810 | ||||||||
\(705\) | −23.2883 | −0.877087 | ||||||||
\(706\) | −16.2991 | −0.613424 | ||||||||
\(707\) | 30.8970 | 1.16200 | ||||||||
\(708\) | 5.08617 | 0.191150 | ||||||||
\(709\) | −42.8891 | −1.61073 | −0.805366 | − | 0.592777i | \(-0.798031\pi\) | ||||
−0.805366 | + | 0.592777i | \(0.798031\pi\) | |||||||
\(710\) | 2.06670 | 0.0775617 | ||||||||
\(711\) | 5.71140 | 0.214194 | ||||||||
\(712\) | 37.8997 | 1.42035 | ||||||||
\(713\) | −8.88216 | −0.332639 | ||||||||
\(714\) | −2.96233 | −0.110862 | ||||||||
\(715\) | −65.1490 | −2.43643 | ||||||||
\(716\) | 23.2275 | 0.868053 | ||||||||
\(717\) | −24.9840 | −0.933046 | ||||||||
\(718\) | −16.6734 | −0.622246 | ||||||||
\(719\) | 37.2264 | 1.38831 | 0.694155 | − | 0.719826i | \(-0.255778\pi\) | ||||
0.694155 | + | 0.719826i | \(0.255778\pi\) | |||||||
\(720\) | −4.16298 | −0.155145 | ||||||||
\(721\) | 15.9625 | 0.594474 | ||||||||
\(722\) | 19.8035 | 0.737011 | ||||||||
\(723\) | −12.6888 | −0.471900 | ||||||||
\(724\) | 12.8016 | 0.475769 | ||||||||
\(725\) | −4.41504 | −0.163970 | ||||||||
\(726\) | −30.8673 | −1.14559 | ||||||||
\(727\) | −23.6237 | −0.876155 | −0.438078 | − | 0.898937i | \(-0.644340\pi\) | ||||
−0.438078 | + | 0.898937i | \(0.644340\pi\) | |||||||
\(728\) | −28.6344 | −1.06126 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.3066 | −0.714570 | ||||||||
\(731\) | −0.492547 | −0.0182175 | ||||||||
\(732\) | −1.63380 | −0.0603870 | ||||||||
\(733\) | −43.7858 | −1.61727 | −0.808633 | − | 0.588313i | \(-0.799792\pi\) | ||||
−0.808633 | + | 0.588313i | \(0.799792\pi\) | |||||||
\(734\) | 10.5477 | 0.389322 | ||||||||
\(735\) | 3.23612 | 0.119366 | ||||||||
\(736\) | 41.8881 | 1.54402 | ||||||||
\(737\) | −12.7988 | −0.471448 | ||||||||
\(738\) | −11.7674 | −0.433165 | ||||||||
\(739\) | −12.0386 | −0.442847 | −0.221424 | − | 0.975178i | \(-0.571070\pi\) | ||||
−0.221424 | + | 0.975178i | \(0.571070\pi\) | |||||||
\(740\) | −7.59407 | −0.279164 | ||||||||
\(741\) | 0.590454 | 0.0216909 | ||||||||
\(742\) | 4.92316 | 0.180735 | ||||||||
\(743\) | −52.5632 | −1.92836 | −0.964178 | − | 0.265255i | \(-0.914544\pi\) | ||||
−0.964178 | + | 0.265255i | \(0.914544\pi\) | |||||||
\(744\) | 3.00519 | 0.110176 | ||||||||
\(745\) | −44.6478 | −1.63577 | ||||||||
\(746\) | 7.27233 | 0.266259 | ||||||||
\(747\) | 10.1735 | 0.372228 | ||||||||
\(748\) | −5.79594 | −0.211921 | ||||||||
\(749\) | −15.2771 | −0.558215 | ||||||||
\(750\) | 1.66282 | 0.0607175 | ||||||||
\(751\) | −39.2979 | −1.43400 | −0.717000 | − | 0.697073i | \(-0.754485\pi\) | ||||
−0.717000 | + | 0.697073i | \(0.754485\pi\) | |||||||
\(752\) | 10.2236 | 0.372817 | ||||||||
\(753\) | 5.91664 | 0.215614 | ||||||||
\(754\) | −3.41553 | −0.124386 | ||||||||
\(755\) | 51.5883 | 1.87749 | ||||||||
\(756\) | −2.58206 | −0.0939087 | ||||||||
\(757\) | −24.4219 | −0.887628 | −0.443814 | − | 0.896119i | \(-0.646375\pi\) | ||||
−0.443814 | + | 0.896119i | \(0.646375\pi\) | |||||||
\(758\) | 20.2908 | 0.736994 | ||||||||
\(759\) | −57.1914 | −2.07592 | ||||||||
\(760\) | −1.66303 | −0.0603243 | ||||||||
\(761\) | −18.6490 | −0.676027 | −0.338014 | − | 0.941141i | \(-0.609755\pi\) | ||||
−0.338014 | + | 0.941141i | \(0.609755\pi\) | |||||||
\(762\) | −17.9737 | −0.651117 | ||||||||
\(763\) | 11.7567 | 0.425621 | ||||||||
\(764\) | −4.09664 | −0.148211 | ||||||||
\(765\) | 3.07941 | 0.111336 | ||||||||
\(766\) | 12.0851 | 0.436654 | ||||||||
\(767\) | 18.5655 | 0.670361 | ||||||||
\(768\) | −16.6329 | −0.600187 | ||||||||
\(769\) | 46.4660 | 1.67561 | 0.837803 | − | 0.545972i | \(-0.183840\pi\) | ||||
0.837803 | + | 0.545972i | \(0.183840\pi\) | |||||||
\(770\) | −58.1007 | −2.09380 | ||||||||
\(771\) | 24.1193 | 0.868637 | ||||||||
\(772\) | −3.64243 | −0.131094 | ||||||||
\(773\) | −8.99077 | −0.323376 | −0.161688 | − | 0.986842i | \(-0.551694\pi\) | ||||
−0.161688 | + | 0.986842i | \(0.551694\pi\) | |||||||
\(774\) | 0.514232 | 0.0184837 | ||||||||
\(775\) | 4.43420 | 0.159281 | ||||||||
\(776\) | 46.5251 | 1.67015 | ||||||||
\(777\) | 7.68924 | 0.275850 | ||||||||
\(778\) | −23.1292 | −0.829222 | ||||||||
\(779\) | −2.00352 | −0.0717837 | ||||||||
\(780\) | 9.30836 | 0.333293 | ||||||||
\(781\) | −4.09426 | −0.146504 | ||||||||
\(782\) | 9.37484 | 0.335243 | ||||||||
\(783\) | −0.984886 | −0.0351969 | ||||||||
\(784\) | −1.42067 | −0.0507381 | ||||||||
\(785\) | 3.07941 | 0.109909 | ||||||||
\(786\) | −19.9861 | −0.712880 | ||||||||
\(787\) | 36.0781 | 1.28604 | 0.643022 | − | 0.765847i | \(-0.277680\pi\) | ||||
0.643022 | + | 0.765847i | \(0.277680\pi\) | |||||||
\(788\) | −15.0465 | −0.536011 | ||||||||
\(789\) | 20.1796 | 0.718413 | ||||||||
\(790\) | −18.3621 | −0.653294 | ||||||||
\(791\) | −21.3323 | −0.758488 | ||||||||
\(792\) | 19.3502 | 0.687579 | ||||||||
\(793\) | −5.96368 | −0.211777 | ||||||||
\(794\) | 11.8948 | 0.422132 | ||||||||
\(795\) | −5.11774 | −0.181507 | ||||||||
\(796\) | 13.6110 | 0.482427 | ||||||||
\(797\) | 31.7292 | 1.12390 | 0.561952 | − | 0.827170i | \(-0.310050\pi\) | ||||
0.561952 | + | 0.827170i | \(0.310050\pi\) | |||||||
\(798\) | 0.526574 | 0.0186405 | ||||||||
\(799\) | −7.56257 | −0.267544 | ||||||||
\(800\) | −20.9116 | −0.739337 | ||||||||
\(801\) | 12.4747 | 0.440771 | ||||||||
\(802\) | −22.1562 | −0.782364 | ||||||||
\(803\) | 38.2477 | 1.34973 | ||||||||
\(804\) | 1.82866 | 0.0644919 | ||||||||
\(805\) | −78.4588 | −2.76531 | ||||||||
\(806\) | 3.43035 | 0.120829 | ||||||||
\(807\) | 7.78801 | 0.274151 | ||||||||
\(808\) | 33.0826 | 1.16384 | ||||||||
\(809\) | 50.5510 | 1.77728 | 0.888640 | − | 0.458606i | \(-0.151651\pi\) | ||||
0.888640 | + | 0.458606i | \(0.151651\pi\) | |||||||
\(810\) | −3.21499 | −0.112963 | ||||||||
\(811\) | −9.72705 | −0.341563 | −0.170781 | − | 0.985309i | \(-0.554629\pi\) | ||||
−0.170781 | + | 0.985309i | \(0.554629\pi\) | |||||||
\(812\) | 2.54304 | 0.0892431 | ||||||||
\(813\) | −3.65833 | −0.128303 | ||||||||
\(814\) | −18.0199 | −0.631598 | ||||||||
\(815\) | 33.9095 | 1.18780 | ||||||||
\(816\) | −1.35187 | −0.0473250 | ||||||||
\(817\) | 0.0875534 | 0.00306310 | ||||||||
\(818\) | −18.7410 | −0.655265 | ||||||||
\(819\) | −9.42502 | −0.329337 | ||||||||
\(820\) | −31.5851 | −1.10300 | ||||||||
\(821\) | −38.4514 | −1.34196 | −0.670982 | − | 0.741474i | \(-0.734127\pi\) | ||||
−0.670982 | + | 0.741474i | \(0.734127\pi\) | |||||||
\(822\) | 3.35048 | 0.116861 | ||||||||
\(823\) | −4.41750 | −0.153984 | −0.0769922 | − | 0.997032i | \(-0.524532\pi\) | ||||
−0.0769922 | + | 0.997032i | \(0.524532\pi\) | |||||||
\(824\) | 17.0917 | 0.595416 | ||||||||
\(825\) | 28.5514 | 0.994033 | ||||||||
\(826\) | 16.5569 | 0.576089 | ||||||||
\(827\) | 0.545895 | 0.0189826 | 0.00949131 | − | 0.999955i | \(-0.496979\pi\) | ||||
0.00949131 | + | 0.999955i | \(0.496979\pi\) | |||||||
\(828\) | 8.17140 | 0.283976 | ||||||||
\(829\) | −14.4719 | −0.502631 | −0.251316 | − | 0.967905i | \(-0.580863\pi\) | ||||
−0.251316 | + | 0.967905i | \(0.580863\pi\) | |||||||
\(830\) | −32.7076 | −1.13530 | ||||||||
\(831\) | 15.7821 | 0.547476 | ||||||||
\(832\) | −25.1585 | −0.872215 | ||||||||
\(833\) | 1.05089 | 0.0364111 | ||||||||
\(834\) | 2.57843 | 0.0892836 | ||||||||
\(835\) | 7.73411 | 0.267650 | ||||||||
\(836\) | 1.03027 | 0.0356325 | ||||||||
\(837\) | 0.989160 | 0.0341904 | ||||||||
\(838\) | 36.6271 | 1.26526 | ||||||||
\(839\) | −44.7265 | −1.54413 | −0.772065 | − | 0.635544i | \(-0.780776\pi\) | ||||
−0.772065 | + | 0.635544i | \(0.780776\pi\) | |||||||
\(840\) | 26.5458 | 0.915917 | ||||||||
\(841\) | −28.0300 | −0.966552 | ||||||||
\(842\) | 32.9300 | 1.13484 | ||||||||
\(843\) | −11.5636 | −0.398273 | ||||||||
\(844\) | 7.69741 | 0.264956 | ||||||||
\(845\) | −6.05509 | −0.208301 | ||||||||
\(846\) | 7.89553 | 0.271454 | ||||||||
\(847\) | 83.8899 | 2.88249 | ||||||||
\(848\) | 2.24670 | 0.0771521 | ||||||||
\(849\) | −11.5233 | −0.395479 | ||||||||
\(850\) | −4.68016 | −0.160528 | ||||||||
\(851\) | −24.3340 | −0.834159 | ||||||||
\(852\) | 0.584981 | 0.0200411 | ||||||||
\(853\) | 30.8098 | 1.05491 | 0.527453 | − | 0.849584i | \(-0.323147\pi\) | ||||
0.527453 | + | 0.849584i | \(0.323147\pi\) | |||||||
\(854\) | −5.31849 | −0.181995 | ||||||||
\(855\) | −0.547386 | −0.0187202 | ||||||||
\(856\) | −16.3579 | −0.559100 | ||||||||
\(857\) | −51.5296 | −1.76022 | −0.880110 | − | 0.474771i | \(-0.842531\pi\) | ||||
−0.880110 | + | 0.474771i | \(0.842531\pi\) | |||||||
\(858\) | 22.0877 | 0.754063 | ||||||||
\(859\) | −11.4675 | −0.391265 | −0.195633 | − | 0.980677i | \(-0.562676\pi\) | ||||
−0.195633 | + | 0.980677i | \(0.562676\pi\) | |||||||
\(860\) | 1.38026 | 0.0470664 | ||||||||
\(861\) | 31.9809 | 1.08991 | ||||||||
\(862\) | −22.6051 | −0.769932 | ||||||||
\(863\) | −11.3027 | −0.384748 | −0.192374 | − | 0.981322i | \(-0.561619\pi\) | ||||
−0.192374 | + | 0.981322i | \(0.561619\pi\) | |||||||
\(864\) | −4.66486 | −0.158702 | ||||||||
\(865\) | 14.9940 | 0.509810 | ||||||||
\(866\) | −30.2986 | −1.02959 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −2.55407 | −0.0866909 | ||||||||
\(869\) | 36.3765 | 1.23399 | ||||||||
\(870\) | 3.16640 | 0.107351 | ||||||||
\(871\) | 6.67496 | 0.226172 | ||||||||
\(872\) | 12.5884 | 0.426295 | ||||||||
\(873\) | 15.3137 | 0.518292 | ||||||||
\(874\) | −1.66644 | −0.0563681 | ||||||||
\(875\) | −4.51913 | −0.152774 | ||||||||
\(876\) | −5.46476 | −0.184637 | ||||||||
\(877\) | −34.6496 | −1.17003 | −0.585017 | − | 0.811021i | \(-0.698912\pi\) | ||||
−0.585017 | + | 0.811021i | \(0.698912\pi\) | |||||||
\(878\) | −6.67134 | −0.225147 | ||||||||
\(879\) | −6.67959 | −0.225297 | ||||||||
\(880\) | −26.5145 | −0.893803 | ||||||||
\(881\) | −12.8387 | −0.432546 | −0.216273 | − | 0.976333i | \(-0.569390\pi\) | ||||
−0.216273 | + | 0.976333i | \(0.569390\pi\) | |||||||
\(882\) | −1.09716 | −0.0369432 | ||||||||
\(883\) | 15.0352 | 0.505975 | 0.252987 | − | 0.967470i | \(-0.418587\pi\) | ||||
0.252987 | + | 0.967470i | \(0.418587\pi\) | |||||||
\(884\) | 3.02277 | 0.101667 | ||||||||
\(885\) | −17.2113 | −0.578552 | ||||||||
\(886\) | 11.0395 | 0.370878 | ||||||||
\(887\) | −9.63987 | −0.323675 | −0.161838 | − | 0.986817i | \(-0.551742\pi\) | ||||
−0.161838 | + | 0.986817i | \(0.551742\pi\) | |||||||
\(888\) | 8.23318 | 0.276287 | ||||||||
\(889\) | 48.8480 | 1.63831 | ||||||||
\(890\) | −40.1060 | −1.34436 | ||||||||
\(891\) | 6.36912 | 0.213373 | ||||||||
\(892\) | −7.33666 | −0.245650 | ||||||||
\(893\) | 1.34430 | 0.0449851 | ||||||||
\(894\) | 15.1371 | 0.506262 | ||||||||
\(895\) | −78.6006 | −2.62733 | ||||||||
\(896\) | 4.03557 | 0.134819 | ||||||||
\(897\) | 29.8272 | 0.995901 | ||||||||
\(898\) | 35.5673 | 1.18690 | ||||||||
\(899\) | −0.974209 | −0.0324917 | ||||||||
\(900\) | −4.07937 | −0.135979 | ||||||||
\(901\) | −1.66192 | −0.0553666 | ||||||||
\(902\) | −74.9481 | −2.49550 | ||||||||
\(903\) | −1.39756 | −0.0465078 | ||||||||
\(904\) | −22.8413 | −0.759690 | ||||||||
\(905\) | −43.3200 | −1.44001 | ||||||||
\(906\) | −17.4902 | −0.581073 | ||||||||
\(907\) | 21.4999 | 0.713894 | 0.356947 | − | 0.934125i | \(-0.383818\pi\) | ||||
0.356947 | + | 0.934125i | \(0.383818\pi\) | |||||||
\(908\) | −0.596305 | −0.0197891 | ||||||||
\(909\) | 10.8892 | 0.361171 | ||||||||
\(910\) | 30.3014 | 1.00448 | ||||||||
\(911\) | −13.6656 | −0.452763 | −0.226381 | − | 0.974039i | \(-0.572690\pi\) | ||||
−0.226381 | + | 0.974039i | \(0.572690\pi\) | |||||||
\(912\) | 0.240304 | 0.00795726 | ||||||||
\(913\) | 64.7960 | 2.14443 | ||||||||
\(914\) | 3.82406 | 0.126489 | ||||||||
\(915\) | 5.52869 | 0.182773 | ||||||||
\(916\) | 25.5617 | 0.844581 | ||||||||
\(917\) | 54.3172 | 1.79371 | ||||||||
\(918\) | −1.04403 | −0.0344580 | ||||||||
\(919\) | 21.9653 | 0.724568 | 0.362284 | − | 0.932068i | \(-0.381997\pi\) | ||||
0.362284 | + | 0.932068i | \(0.381997\pi\) | |||||||
\(920\) | −84.0090 | −2.76969 | ||||||||
\(921\) | 15.8173 | 0.521199 | ||||||||
\(922\) | 31.0718 | 1.02330 | ||||||||
\(923\) | 2.13529 | 0.0702839 | ||||||||
\(924\) | −16.4455 | −0.541016 | ||||||||
\(925\) | 12.1482 | 0.399429 | ||||||||
\(926\) | −26.4981 | −0.870783 | ||||||||
\(927\) | 5.62573 | 0.184773 | ||||||||
\(928\) | 4.59435 | 0.150817 | ||||||||
\(929\) | −18.0163 | −0.591097 | −0.295548 | − | 0.955328i | \(-0.595502\pi\) | ||||
−0.295548 | + | 0.955328i | \(0.595502\pi\) | |||||||
\(930\) | −3.18014 | −0.104281 | ||||||||
\(931\) | −0.186802 | −0.00612220 | ||||||||
\(932\) | −8.01759 | −0.262625 | ||||||||
\(933\) | −17.2152 | −0.563599 | ||||||||
\(934\) | −22.9073 | −0.749551 | ||||||||
\(935\) | 19.6132 | 0.641419 | ||||||||
\(936\) | −10.0917 | −0.329859 | ||||||||
\(937\) | −20.8859 | −0.682312 | −0.341156 | − | 0.940007i | \(-0.610818\pi\) | ||||
−0.341156 | + | 0.940007i | \(0.610818\pi\) | |||||||
\(938\) | 5.95281 | 0.194366 | ||||||||
\(939\) | −0.598984 | −0.0195471 | ||||||||
\(940\) | 21.1925 | 0.691223 | ||||||||
\(941\) | −31.6289 | −1.03107 | −0.515536 | − | 0.856868i | \(-0.672407\pi\) | ||||
−0.515536 | + | 0.856868i | \(0.672407\pi\) | |||||||
\(942\) | −1.04403 | −0.0340162 | ||||||||
\(943\) | −101.209 | −3.29583 | ||||||||
\(944\) | 7.55583 | 0.245921 | ||||||||
\(945\) | 8.73756 | 0.284233 | ||||||||
\(946\) | 3.27521 | 0.106486 | ||||||||
\(947\) | 47.7715 | 1.55237 | 0.776183 | − | 0.630507i | \(-0.217153\pi\) | ||||
0.776183 | + | 0.630507i | \(0.217153\pi\) | |||||||
\(948\) | −5.19741 | −0.168804 | ||||||||
\(949\) | −19.9474 | −0.647520 | ||||||||
\(950\) | 0.831928 | 0.0269913 | ||||||||
\(951\) | 4.33420 | 0.140546 | ||||||||
\(952\) | 8.62041 | 0.279389 | ||||||||
\(953\) | 29.5766 | 0.958081 | 0.479040 | − | 0.877793i | \(-0.340985\pi\) | ||||
0.479040 | + | 0.877793i | \(0.340985\pi\) | |||||||
\(954\) | 1.73509 | 0.0561756 | ||||||||
\(955\) | 13.8628 | 0.448590 | ||||||||
\(956\) | 22.7357 | 0.735324 | ||||||||
\(957\) | −6.27285 | −0.202772 | ||||||||
\(958\) | −2.29492 | −0.0741454 | ||||||||
\(959\) | −9.10578 | −0.294041 | ||||||||
\(960\) | 23.3234 | 0.752761 | ||||||||
\(961\) | −30.0216 | −0.968437 | ||||||||
\(962\) | 9.39797 | 0.303003 | ||||||||
\(963\) | −5.38419 | −0.173503 | ||||||||
\(964\) | 11.5469 | 0.371900 | ||||||||
\(965\) | 12.3258 | 0.396781 | ||||||||
\(966\) | 26.6002 | 0.855849 | ||||||||
\(967\) | −33.9793 | −1.09270 | −0.546350 | − | 0.837557i | \(-0.683983\pi\) | ||||
−0.546350 | + | 0.837557i | \(0.683983\pi\) | |||||||
\(968\) | 89.8242 | 2.88706 | ||||||||
\(969\) | −0.177756 | −0.00571036 | ||||||||
\(970\) | −49.2336 | −1.58079 | ||||||||
\(971\) | −42.2017 | −1.35432 | −0.677158 | − | 0.735838i | \(-0.736789\pi\) | ||||
−0.677158 | + | 0.735838i | \(0.736789\pi\) | |||||||
\(972\) | −0.910007 | −0.0291885 | ||||||||
\(973\) | −7.00753 | −0.224651 | ||||||||
\(974\) | 2.54664 | 0.0815996 | ||||||||
\(975\) | −14.8905 | −0.476877 | ||||||||
\(976\) | −2.42711 | −0.0776900 | ||||||||
\(977\) | −33.9587 | −1.08643 | −0.543217 | − | 0.839592i | \(-0.682794\pi\) | ||||
−0.543217 | + | 0.839592i | \(0.682794\pi\) | |||||||
\(978\) | −11.4965 | −0.367617 | ||||||||
\(979\) | 79.4527 | 2.53932 | ||||||||
\(980\) | −2.94489 | −0.0940712 | ||||||||
\(981\) | 4.14346 | 0.132290 | ||||||||
\(982\) | 18.3591 | 0.585862 | ||||||||
\(983\) | −6.24025 | −0.199033 | −0.0995166 | − | 0.995036i | \(-0.531730\pi\) | ||||
−0.0995166 | + | 0.995036i | \(0.531730\pi\) | |||||||
\(984\) | 34.2433 | 1.09164 | ||||||||
\(985\) | 50.9167 | 1.62234 | ||||||||
\(986\) | 1.02825 | 0.0327461 | ||||||||
\(987\) | −21.4581 | −0.683019 | ||||||||
\(988\) | −0.537317 | −0.0170943 | ||||||||
\(989\) | 4.42282 | 0.140638 | ||||||||
\(990\) | −20.4767 | −0.650791 | ||||||||
\(991\) | 16.8706 | 0.535911 | 0.267955 | − | 0.963431i | \(-0.413652\pi\) | ||||
0.267955 | + | 0.963431i | \(0.413652\pi\) | |||||||
\(992\) | −4.61429 | −0.146504 | ||||||||
\(993\) | 6.30140 | 0.199969 | ||||||||
\(994\) | 1.90428 | 0.0604000 | ||||||||
\(995\) | −46.0587 | −1.46016 | ||||||||
\(996\) | −9.25793 | −0.293349 | ||||||||
\(997\) | −7.79332 | −0.246817 | −0.123408 | − | 0.992356i | \(-0.539383\pi\) | ||||
−0.123408 | + | 0.992356i | \(0.539383\pi\) | |||||||
\(998\) | −22.6750 | −0.717764 | ||||||||
\(999\) | 2.70995 | 0.0857391 |
(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 | 8007.2.a.i.1.20 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.i.1.20 | ✓ | 63 | 1.1 | even | 1 | trivial |