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: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54273 | −1.79798 | −0.898989 | − | 0.437970i | \(-0.855697\pi\) | ||||
−0.898989 | + | 0.437970i | \(0.855697\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.46545 | 2.23273 | ||||||||
\(5\) | −2.67798 | −1.19763 | −0.598815 | − | 0.800888i | \(-0.704361\pi\) | ||||
−0.598815 | + | 0.800888i | \(0.704361\pi\) | |||||||
\(6\) | 2.54273 | 1.03806 | ||||||||
\(7\) | 2.94599 | 1.11348 | 0.556741 | − | 0.830686i | \(-0.312052\pi\) | ||||
0.556741 | + | 0.830686i | \(0.312052\pi\) | |||||||
\(8\) | −6.26898 | −2.21642 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.80937 | 2.15331 | ||||||||
\(11\) | 1.14862 | 0.346323 | 0.173161 | − | 0.984893i | \(-0.444602\pi\) | ||||
0.173161 | + | 0.984893i | \(0.444602\pi\) | |||||||
\(12\) | −4.46545 | −1.28907 | ||||||||
\(13\) | 5.66604 | 1.57148 | 0.785738 | − | 0.618559i | \(-0.212283\pi\) | ||||
0.785738 | + | 0.618559i | \(0.212283\pi\) | |||||||
\(14\) | −7.49086 | −2.00202 | ||||||||
\(15\) | 2.67798 | 0.691452 | ||||||||
\(16\) | 7.00938 | 1.75234 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.54273 | −0.599326 | ||||||||
\(19\) | 6.65907 | 1.52769 | 0.763847 | − | 0.645397i | \(-0.223308\pi\) | ||||
0.763847 | + | 0.645397i | \(0.223308\pi\) | |||||||
\(20\) | −11.9584 | −2.67398 | ||||||||
\(21\) | −2.94599 | −0.642869 | ||||||||
\(22\) | −2.92063 | −0.622681 | ||||||||
\(23\) | −4.86607 | −1.01465 | −0.507323 | − | 0.861756i | \(-0.669365\pi\) | ||||
−0.507323 | + | 0.861756i | \(0.669365\pi\) | |||||||
\(24\) | 6.26898 | 1.27965 | ||||||||
\(25\) | 2.17158 | 0.434316 | ||||||||
\(26\) | −14.4072 | −2.82548 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 13.1552 | 2.48610 | ||||||||
\(29\) | 7.98328 | 1.48246 | 0.741229 | − | 0.671252i | \(-0.234243\pi\) | ||||
0.741229 | + | 0.671252i | \(0.234243\pi\) | |||||||
\(30\) | −6.80937 | −1.24322 | ||||||||
\(31\) | 8.48950 | 1.52476 | 0.762380 | − | 0.647130i | \(-0.224031\pi\) | ||||
0.762380 | + | 0.647130i | \(0.224031\pi\) | |||||||
\(32\) | −5.28497 | −0.934260 | ||||||||
\(33\) | −1.14862 | −0.199950 | ||||||||
\(34\) | −2.54273 | −0.436074 | ||||||||
\(35\) | −7.88932 | −1.33354 | ||||||||
\(36\) | 4.46545 | 0.744242 | ||||||||
\(37\) | 1.03093 | 0.169485 | 0.0847423 | − | 0.996403i | \(-0.472993\pi\) | ||||
0.0847423 | + | 0.996403i | \(0.472993\pi\) | |||||||
\(38\) | −16.9322 | −2.74676 | ||||||||
\(39\) | −5.66604 | −0.907292 | ||||||||
\(40\) | 16.7882 | 2.65445 | ||||||||
\(41\) | −9.73755 | −1.52075 | −0.760375 | − | 0.649484i | \(-0.774985\pi\) | ||||
−0.760375 | + | 0.649484i | \(0.774985\pi\) | |||||||
\(42\) | 7.49086 | 1.15586 | ||||||||
\(43\) | 3.63622 | 0.554518 | 0.277259 | − | 0.960795i | \(-0.410574\pi\) | ||||
0.277259 | + | 0.960795i | \(0.410574\pi\) | |||||||
\(44\) | 5.12913 | 0.773245 | ||||||||
\(45\) | −2.67798 | −0.399210 | ||||||||
\(46\) | 12.3731 | 1.82431 | ||||||||
\(47\) | 9.61783 | 1.40290 | 0.701452 | − | 0.712717i | \(-0.252535\pi\) | ||||
0.701452 | + | 0.712717i | \(0.252535\pi\) | |||||||
\(48\) | −7.00938 | −1.01172 | ||||||||
\(49\) | 1.67889 | 0.239841 | ||||||||
\(50\) | −5.52174 | −0.780891 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 25.3014 | 3.50868 | ||||||||
\(53\) | 13.7771 | 1.89242 | 0.946212 | − | 0.323546i | \(-0.104875\pi\) | ||||
0.946212 | + | 0.323546i | \(0.104875\pi\) | |||||||
\(54\) | 2.54273 | 0.346021 | ||||||||
\(55\) | −3.07599 | −0.414767 | ||||||||
\(56\) | −18.4684 | −2.46794 | ||||||||
\(57\) | −6.65907 | −0.882015 | ||||||||
\(58\) | −20.2993 | −2.66543 | ||||||||
\(59\) | 14.9266 | 1.94328 | 0.971638 | − | 0.236472i | \(-0.0759911\pi\) | ||||
0.971638 | + | 0.236472i | \(0.0759911\pi\) | |||||||
\(60\) | 11.9584 | 1.54382 | ||||||||
\(61\) | −5.54929 | −0.710514 | −0.355257 | − | 0.934769i | \(-0.615607\pi\) | ||||
−0.355257 | + | 0.934769i | \(0.615607\pi\) | |||||||
\(62\) | −21.5865 | −2.74148 | ||||||||
\(63\) | 2.94599 | 0.371160 | ||||||||
\(64\) | −0.580516 | −0.0725645 | ||||||||
\(65\) | −15.1735 | −1.88205 | ||||||||
\(66\) | 2.92063 | 0.359505 | ||||||||
\(67\) | 10.3001 | 1.25836 | 0.629178 | − | 0.777261i | \(-0.283392\pi\) | ||||
0.629178 | + | 0.777261i | \(0.283392\pi\) | |||||||
\(68\) | 4.46545 | 0.541516 | ||||||||
\(69\) | 4.86607 | 0.585806 | ||||||||
\(70\) | 20.0604 | 2.39767 | ||||||||
\(71\) | 10.3559 | 1.22902 | 0.614510 | − | 0.788909i | \(-0.289354\pi\) | ||||
0.614510 | + | 0.788909i | \(0.289354\pi\) | |||||||
\(72\) | −6.26898 | −0.738806 | ||||||||
\(73\) | 1.44898 | 0.169590 | 0.0847949 | − | 0.996398i | \(-0.472976\pi\) | ||||
0.0847949 | + | 0.996398i | \(0.472976\pi\) | |||||||
\(74\) | −2.62138 | −0.304730 | ||||||||
\(75\) | −2.17158 | −0.250753 | ||||||||
\(76\) | 29.7358 | 3.41093 | ||||||||
\(77\) | 3.38384 | 0.385624 | ||||||||
\(78\) | 14.4072 | 1.63129 | ||||||||
\(79\) | −1.75552 | −0.197512 | −0.0987559 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987559 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(80\) | −18.7710 | −2.09866 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 24.7599 | 2.73428 | ||||||||
\(83\) | 14.2150 | 1.56030 | 0.780149 | − | 0.625593i | \(-0.215143\pi\) | ||||
0.780149 | + | 0.625593i | \(0.215143\pi\) | |||||||
\(84\) | −13.1552 | −1.43535 | ||||||||
\(85\) | −2.67798 | −0.290468 | ||||||||
\(86\) | −9.24590 | −0.997011 | ||||||||
\(87\) | −7.98328 | −0.855898 | ||||||||
\(88\) | −7.20069 | −0.767596 | ||||||||
\(89\) | −4.33431 | −0.459436 | −0.229718 | − | 0.973257i | \(-0.573780\pi\) | ||||
−0.229718 | + | 0.973257i | \(0.573780\pi\) | |||||||
\(90\) | 6.80937 | 0.717771 | ||||||||
\(91\) | 16.6921 | 1.74981 | ||||||||
\(92\) | −21.7292 | −2.26543 | ||||||||
\(93\) | −8.48950 | −0.880320 | ||||||||
\(94\) | −24.4555 | −2.52239 | ||||||||
\(95\) | −17.8329 | −1.82961 | ||||||||
\(96\) | 5.28497 | 0.539395 | ||||||||
\(97\) | −6.00271 | −0.609483 | −0.304742 | − | 0.952435i | \(-0.598570\pi\) | ||||
−0.304742 | + | 0.952435i | \(0.598570\pi\) | |||||||
\(98\) | −4.26895 | −0.431229 | ||||||||
\(99\) | 1.14862 | 0.115441 | ||||||||
\(100\) | 9.69710 | 0.969710 | ||||||||
\(101\) | −3.33028 | −0.331375 | −0.165687 | − | 0.986178i | \(-0.552984\pi\) | ||||
−0.165687 | + | 0.986178i | \(0.552984\pi\) | |||||||
\(102\) | 2.54273 | 0.251767 | ||||||||
\(103\) | −0.902439 | −0.0889199 | −0.0444600 | − | 0.999011i | \(-0.514157\pi\) | ||||
−0.0444600 | + | 0.999011i | \(0.514157\pi\) | |||||||
\(104\) | −35.5203 | −3.48305 | ||||||||
\(105\) | 7.88932 | 0.769919 | ||||||||
\(106\) | −35.0313 | −3.40254 | ||||||||
\(107\) | 10.9399 | 1.05760 | 0.528801 | − | 0.848746i | \(-0.322642\pi\) | ||||
0.528801 | + | 0.848746i | \(0.322642\pi\) | |||||||
\(108\) | −4.46545 | −0.429689 | ||||||||
\(109\) | 14.5605 | 1.39464 | 0.697321 | − | 0.716759i | \(-0.254375\pi\) | ||||
0.697321 | + | 0.716759i | \(0.254375\pi\) | |||||||
\(110\) | 7.82140 | 0.745741 | ||||||||
\(111\) | −1.03093 | −0.0978520 | ||||||||
\(112\) | 20.6496 | 1.95120 | ||||||||
\(113\) | 6.44854 | 0.606628 | 0.303314 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(114\) | 16.9322 | 1.58584 | ||||||||
\(115\) | 13.0312 | 1.21517 | ||||||||
\(116\) | 35.6490 | 3.30992 | ||||||||
\(117\) | 5.66604 | 0.523826 | ||||||||
\(118\) | −37.9542 | −3.49397 | ||||||||
\(119\) | 2.94599 | 0.270059 | ||||||||
\(120\) | −16.7882 | −1.53255 | ||||||||
\(121\) | −9.68066 | −0.880060 | ||||||||
\(122\) | 14.1103 | 1.27749 | ||||||||
\(123\) | 9.73755 | 0.878006 | ||||||||
\(124\) | 37.9095 | 3.40437 | ||||||||
\(125\) | 7.57445 | 0.677480 | ||||||||
\(126\) | −7.49086 | −0.667339 | ||||||||
\(127\) | −8.02012 | −0.711671 | −0.355835 | − | 0.934549i | \(-0.615804\pi\) | ||||
−0.355835 | + | 0.934549i | \(0.615804\pi\) | |||||||
\(128\) | 12.0460 | 1.06473 | ||||||||
\(129\) | −3.63622 | −0.320151 | ||||||||
\(130\) | 38.5822 | 3.38388 | ||||||||
\(131\) | 11.2240 | 0.980648 | 0.490324 | − | 0.871540i | \(-0.336878\pi\) | ||||
0.490324 | + | 0.871540i | \(0.336878\pi\) | |||||||
\(132\) | −5.12913 | −0.446433 | ||||||||
\(133\) | 19.6176 | 1.70106 | ||||||||
\(134\) | −26.1903 | −2.26250 | ||||||||
\(135\) | 2.67798 | 0.230484 | ||||||||
\(136\) | −6.26898 | −0.537560 | ||||||||
\(137\) | 13.1733 | 1.12547 | 0.562734 | − | 0.826638i | \(-0.309749\pi\) | ||||
0.562734 | + | 0.826638i | \(0.309749\pi\) | |||||||
\(138\) | −12.3731 | −1.05327 | ||||||||
\(139\) | −20.3308 | −1.72444 | −0.862218 | − | 0.506537i | \(-0.830925\pi\) | ||||
−0.862218 | + | 0.506537i | \(0.830925\pi\) | |||||||
\(140\) | −35.2294 | −2.97743 | ||||||||
\(141\) | −9.61783 | −0.809967 | ||||||||
\(142\) | −26.3322 | −2.20975 | ||||||||
\(143\) | 6.50814 | 0.544238 | ||||||||
\(144\) | 7.00938 | 0.584115 | ||||||||
\(145\) | −21.3791 | −1.77544 | ||||||||
\(146\) | −3.68435 | −0.304919 | ||||||||
\(147\) | −1.67889 | −0.138472 | ||||||||
\(148\) | 4.60359 | 0.378413 | ||||||||
\(149\) | −4.27599 | −0.350303 | −0.175151 | − | 0.984542i | \(-0.556041\pi\) | ||||
−0.175151 | + | 0.984542i | \(0.556041\pi\) | |||||||
\(150\) | 5.52174 | 0.450848 | ||||||||
\(151\) | −18.5641 | −1.51072 | −0.755361 | − | 0.655309i | \(-0.772538\pi\) | ||||
−0.755361 | + | 0.655309i | \(0.772538\pi\) | |||||||
\(152\) | −41.7455 | −3.38601 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −8.60417 | −0.693344 | ||||||||
\(155\) | −22.7347 | −1.82610 | ||||||||
\(156\) | −25.3014 | −2.02574 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 4.46381 | 0.355122 | ||||||||
\(159\) | −13.7771 | −1.09259 | ||||||||
\(160\) | 14.1531 | 1.11890 | ||||||||
\(161\) | −14.3354 | −1.12979 | ||||||||
\(162\) | −2.54273 | −0.199775 | ||||||||
\(163\) | −11.5849 | −0.907397 | −0.453699 | − | 0.891155i | \(-0.649896\pi\) | ||||
−0.453699 | + | 0.891155i | \(0.649896\pi\) | |||||||
\(164\) | −43.4826 | −3.39542 | ||||||||
\(165\) | 3.07599 | 0.239466 | ||||||||
\(166\) | −36.1448 | −2.80538 | ||||||||
\(167\) | −3.97649 | −0.307710 | −0.153855 | − | 0.988093i | \(-0.549169\pi\) | ||||
−0.153855 | + | 0.988093i | \(0.549169\pi\) | |||||||
\(168\) | 18.4684 | 1.42487 | ||||||||
\(169\) | 19.1040 | 1.46954 | ||||||||
\(170\) | 6.80937 | 0.522255 | ||||||||
\(171\) | 6.65907 | 0.509232 | ||||||||
\(172\) | 16.2374 | 1.23809 | ||||||||
\(173\) | 9.89085 | 0.751987 | 0.375994 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375994 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(174\) | 20.2993 | 1.53889 | ||||||||
\(175\) | 6.39747 | 0.483603 | ||||||||
\(176\) | 8.05113 | 0.606877 | ||||||||
\(177\) | −14.9266 | −1.12195 | ||||||||
\(178\) | 11.0210 | 0.826056 | ||||||||
\(179\) | 3.11527 | 0.232846 | 0.116423 | − | 0.993200i | \(-0.462857\pi\) | ||||
0.116423 | + | 0.993200i | \(0.462857\pi\) | |||||||
\(180\) | −11.9584 | −0.891327 | ||||||||
\(181\) | −13.3295 | −0.990775 | −0.495387 | − | 0.868672i | \(-0.664974\pi\) | ||||
−0.495387 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(182\) | −42.4435 | −3.14612 | ||||||||
\(183\) | 5.54929 | 0.410215 | ||||||||
\(184\) | 30.5053 | 2.24888 | ||||||||
\(185\) | −2.76082 | −0.202980 | ||||||||
\(186\) | 21.5865 | 1.58280 | ||||||||
\(187\) | 1.14862 | 0.0839957 | ||||||||
\(188\) | 42.9480 | 3.13230 | ||||||||
\(189\) | −2.94599 | −0.214290 | ||||||||
\(190\) | 45.3441 | 3.28960 | ||||||||
\(191\) | −8.78858 | −0.635919 | −0.317959 | − | 0.948104i | \(-0.602998\pi\) | ||||
−0.317959 | + | 0.948104i | \(0.602998\pi\) | |||||||
\(192\) | 0.580516 | 0.0418952 | ||||||||
\(193\) | 20.7784 | 1.49566 | 0.747831 | − | 0.663889i | \(-0.231095\pi\) | ||||
0.747831 | + | 0.663889i | \(0.231095\pi\) | |||||||
\(194\) | 15.2633 | 1.09584 | ||||||||
\(195\) | 15.1735 | 1.08660 | ||||||||
\(196\) | 7.49699 | 0.535499 | ||||||||
\(197\) | −23.7695 | −1.69351 | −0.846753 | − | 0.531986i | \(-0.821446\pi\) | ||||
−0.846753 | + | 0.531986i | \(0.821446\pi\) | |||||||
\(198\) | −2.92063 | −0.207560 | ||||||||
\(199\) | 15.2002 | 1.07751 | 0.538756 | − | 0.842462i | \(-0.318894\pi\) | ||||
0.538756 | + | 0.842462i | \(0.318894\pi\) | |||||||
\(200\) | −13.6136 | −0.962626 | ||||||||
\(201\) | −10.3001 | −0.726512 | ||||||||
\(202\) | 8.46798 | 0.595805 | ||||||||
\(203\) | 23.5187 | 1.65069 | ||||||||
\(204\) | −4.46545 | −0.312644 | ||||||||
\(205\) | 26.0770 | 1.82130 | ||||||||
\(206\) | 2.29465 | 0.159876 | ||||||||
\(207\) | −4.86607 | −0.338215 | ||||||||
\(208\) | 39.7154 | 2.75377 | ||||||||
\(209\) | 7.64876 | 0.529076 | ||||||||
\(210\) | −20.0604 | −1.38430 | ||||||||
\(211\) | 15.7713 | 1.08574 | 0.542869 | − | 0.839817i | \(-0.317338\pi\) | ||||
0.542869 | + | 0.839817i | \(0.317338\pi\) | |||||||
\(212\) | 61.5208 | 4.22527 | ||||||||
\(213\) | −10.3559 | −0.709575 | ||||||||
\(214\) | −27.8172 | −1.90154 | ||||||||
\(215\) | −9.73772 | −0.664107 | ||||||||
\(216\) | 6.26898 | 0.426550 | ||||||||
\(217\) | 25.0100 | 1.69779 | ||||||||
\(218\) | −37.0233 | −2.50754 | ||||||||
\(219\) | −1.44898 | −0.0979127 | ||||||||
\(220\) | −13.7357 | −0.926061 | ||||||||
\(221\) | 5.66604 | 0.381139 | ||||||||
\(222\) | 2.62138 | 0.175936 | ||||||||
\(223\) | 9.15149 | 0.612829 | 0.306415 | − | 0.951898i | \(-0.400871\pi\) | ||||
0.306415 | + | 0.951898i | \(0.400871\pi\) | |||||||
\(224\) | −15.5695 | −1.04028 | ||||||||
\(225\) | 2.17158 | 0.144772 | ||||||||
\(226\) | −16.3969 | −1.09070 | ||||||||
\(227\) | −20.5423 | −1.36344 | −0.681720 | − | 0.731613i | \(-0.738768\pi\) | ||||
−0.681720 | + | 0.731613i | \(0.738768\pi\) | |||||||
\(228\) | −29.7358 | −1.96930 | ||||||||
\(229\) | −14.8520 | −0.981448 | −0.490724 | − | 0.871315i | \(-0.663268\pi\) | ||||
−0.490724 | + | 0.871315i | \(0.663268\pi\) | |||||||
\(230\) | −33.1349 | −2.18485 | ||||||||
\(231\) | −3.38384 | −0.222640 | ||||||||
\(232\) | −50.0470 | −3.28575 | ||||||||
\(233\) | −6.18493 | −0.405188 | −0.202594 | − | 0.979263i | \(-0.564937\pi\) | ||||
−0.202594 | + | 0.979263i | \(0.564937\pi\) | |||||||
\(234\) | −14.4072 | −0.941827 | ||||||||
\(235\) | −25.7564 | −1.68016 | ||||||||
\(236\) | 66.6540 | 4.33881 | ||||||||
\(237\) | 1.75552 | 0.114033 | ||||||||
\(238\) | −7.49086 | −0.485560 | ||||||||
\(239\) | −8.90165 | −0.575800 | −0.287900 | − | 0.957660i | \(-0.592957\pi\) | ||||
−0.287900 | + | 0.957660i | \(0.592957\pi\) | |||||||
\(240\) | 18.7710 | 1.21166 | ||||||||
\(241\) | −9.59092 | −0.617805 | −0.308903 | − | 0.951094i | \(-0.599962\pi\) | ||||
−0.308903 | + | 0.951094i | \(0.599962\pi\) | |||||||
\(242\) | 24.6153 | 1.58233 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −24.7801 | −1.58638 | ||||||||
\(245\) | −4.49602 | −0.287240 | ||||||||
\(246\) | −24.7599 | −1.57864 | ||||||||
\(247\) | 37.7305 | 2.40074 | ||||||||
\(248\) | −53.2205 | −3.37950 | ||||||||
\(249\) | −14.2150 | −0.900839 | ||||||||
\(250\) | −19.2598 | −1.21809 | ||||||||
\(251\) | −12.8153 | −0.808898 | −0.404449 | − | 0.914561i | \(-0.632537\pi\) | ||||
−0.404449 | + | 0.914561i | \(0.632537\pi\) | |||||||
\(252\) | 13.1552 | 0.828700 | ||||||||
\(253\) | −5.58928 | −0.351395 | ||||||||
\(254\) | 20.3930 | 1.27957 | ||||||||
\(255\) | 2.67798 | 0.167702 | ||||||||
\(256\) | −29.4687 | −1.84180 | ||||||||
\(257\) | −18.2418 | −1.13789 | −0.568945 | − | 0.822375i | \(-0.692648\pi\) | ||||
−0.568945 | + | 0.822375i | \(0.692648\pi\) | |||||||
\(258\) | 9.24590 | 0.575625 | ||||||||
\(259\) | 3.03713 | 0.188718 | ||||||||
\(260\) | −67.7568 | −4.20210 | ||||||||
\(261\) | 7.98328 | 0.494153 | ||||||||
\(262\) | −28.5396 | −1.76318 | ||||||||
\(263\) | 12.8203 | 0.790531 | 0.395266 | − | 0.918567i | \(-0.370653\pi\) | ||||
0.395266 | + | 0.918567i | \(0.370653\pi\) | |||||||
\(264\) | 7.20069 | 0.443172 | ||||||||
\(265\) | −36.8947 | −2.26642 | ||||||||
\(266\) | −49.8821 | −3.05847 | ||||||||
\(267\) | 4.33431 | 0.265256 | ||||||||
\(268\) | 45.9946 | 2.80957 | ||||||||
\(269\) | 14.0139 | 0.854440 | 0.427220 | − | 0.904148i | \(-0.359493\pi\) | ||||
0.427220 | + | 0.904148i | \(0.359493\pi\) | |||||||
\(270\) | −6.80937 | −0.414405 | ||||||||
\(271\) | 1.72927 | 0.105046 | 0.0525230 | − | 0.998620i | \(-0.483274\pi\) | ||||
0.0525230 | + | 0.998620i | \(0.483274\pi\) | |||||||
\(272\) | 7.00938 | 0.425006 | ||||||||
\(273\) | −16.6921 | −1.01025 | ||||||||
\(274\) | −33.4960 | −2.02357 | ||||||||
\(275\) | 2.49433 | 0.150414 | ||||||||
\(276\) | 21.7292 | 1.30794 | ||||||||
\(277\) | −20.2522 | −1.21684 | −0.608419 | − | 0.793616i | \(-0.708196\pi\) | ||||
−0.608419 | + | 0.793616i | \(0.708196\pi\) | |||||||
\(278\) | 51.6957 | 3.10050 | ||||||||
\(279\) | 8.48950 | 0.508253 | ||||||||
\(280\) | 49.4579 | 2.95568 | ||||||||
\(281\) | 5.78300 | 0.344985 | 0.172492 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172492 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(282\) | 24.4555 | 1.45630 | ||||||||
\(283\) | −11.5004 | −0.683630 | −0.341815 | − | 0.939767i | \(-0.611042\pi\) | ||||
−0.341815 | + | 0.939767i | \(0.611042\pi\) | |||||||
\(284\) | 46.2438 | 2.74407 | ||||||||
\(285\) | 17.8329 | 1.05633 | ||||||||
\(286\) | −16.5484 | −0.978529 | ||||||||
\(287\) | −28.6868 | −1.69333 | ||||||||
\(288\) | −5.28497 | −0.311420 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 54.3611 | 3.19219 | ||||||||
\(291\) | 6.00271 | 0.351885 | ||||||||
\(292\) | 6.47034 | 0.378648 | ||||||||
\(293\) | 5.66538 | 0.330975 | 0.165488 | − | 0.986212i | \(-0.447080\pi\) | ||||
0.165488 | + | 0.986212i | \(0.447080\pi\) | |||||||
\(294\) | 4.26895 | 0.248970 | ||||||||
\(295\) | −39.9731 | −2.32733 | ||||||||
\(296\) | −6.46290 | −0.375649 | ||||||||
\(297\) | −1.14862 | −0.0666499 | ||||||||
\(298\) | 10.8727 | 0.629837 | ||||||||
\(299\) | −27.5713 | −1.59449 | ||||||||
\(300\) | −9.69710 | −0.559862 | ||||||||
\(301\) | 10.7123 | 0.617445 | ||||||||
\(302\) | 47.2033 | 2.71625 | ||||||||
\(303\) | 3.33028 | 0.191319 | ||||||||
\(304\) | 46.6759 | 2.67705 | ||||||||
\(305\) | 14.8609 | 0.850932 | ||||||||
\(306\) | −2.54273 | −0.145358 | ||||||||
\(307\) | 24.2299 | 1.38288 | 0.691438 | − | 0.722436i | \(-0.256978\pi\) | ||||
0.691438 | + | 0.722436i | \(0.256978\pi\) | |||||||
\(308\) | 15.1104 | 0.860994 | ||||||||
\(309\) | 0.902439 | 0.0513379 | ||||||||
\(310\) | 57.8082 | 3.28328 | ||||||||
\(311\) | −1.55255 | −0.0880371 | −0.0440185 | − | 0.999031i | \(-0.514016\pi\) | ||||
−0.0440185 | + | 0.999031i | \(0.514016\pi\) | |||||||
\(312\) | 35.5203 | 2.01094 | ||||||||
\(313\) | −22.4840 | −1.27087 | −0.635436 | − | 0.772153i | \(-0.719180\pi\) | ||||
−0.635436 | + | 0.772153i | \(0.719180\pi\) | |||||||
\(314\) | 2.54273 | 0.143494 | ||||||||
\(315\) | −7.88932 | −0.444513 | ||||||||
\(316\) | −7.83921 | −0.440990 | ||||||||
\(317\) | −24.6033 | −1.38186 | −0.690929 | − | 0.722922i | \(-0.742798\pi\) | ||||
−0.690929 | + | 0.722922i | \(0.742798\pi\) | |||||||
\(318\) | 35.0313 | 1.96446 | ||||||||
\(319\) | 9.16978 | 0.513409 | ||||||||
\(320\) | 1.55461 | 0.0869054 | ||||||||
\(321\) | −10.9399 | −0.610606 | ||||||||
\(322\) | 36.4510 | 2.03134 | ||||||||
\(323\) | 6.65907 | 0.370520 | ||||||||
\(324\) | 4.46545 | 0.248081 | ||||||||
\(325\) | 12.3043 | 0.682518 | ||||||||
\(326\) | 29.4572 | 1.63148 | ||||||||
\(327\) | −14.5605 | −0.805197 | ||||||||
\(328\) | 61.0445 | 3.37062 | ||||||||
\(329\) | 28.3341 | 1.56211 | ||||||||
\(330\) | −7.82140 | −0.430554 | ||||||||
\(331\) | −9.42272 | −0.517920 | −0.258960 | − | 0.965888i | \(-0.583380\pi\) | ||||
−0.258960 | + | 0.965888i | \(0.583380\pi\) | |||||||
\(332\) | 63.4764 | 3.48372 | ||||||||
\(333\) | 1.03093 | 0.0564949 | ||||||||
\(334\) | 10.1111 | 0.553256 | ||||||||
\(335\) | −27.5834 | −1.50704 | ||||||||
\(336\) | −20.6496 | −1.12653 | ||||||||
\(337\) | −9.58223 | −0.521977 | −0.260989 | − | 0.965342i | \(-0.584048\pi\) | ||||
−0.260989 | + | 0.965342i | \(0.584048\pi\) | |||||||
\(338\) | −48.5762 | −2.64220 | ||||||||
\(339\) | −6.44854 | −0.350237 | ||||||||
\(340\) | −11.9584 | −0.648535 | ||||||||
\(341\) | 9.75124 | 0.528059 | ||||||||
\(342\) | −16.9322 | −0.915588 | ||||||||
\(343\) | −15.6760 | −0.846423 | ||||||||
\(344\) | −22.7954 | −1.22904 | ||||||||
\(345\) | −13.0312 | −0.701578 | ||||||||
\(346\) | −25.1497 | −1.35206 | ||||||||
\(347\) | −27.3762 | −1.46963 | −0.734816 | − | 0.678267i | \(-0.762731\pi\) | ||||
−0.734816 | + | 0.678267i | \(0.762731\pi\) | |||||||
\(348\) | −35.6490 | −1.91099 | ||||||||
\(349\) | 17.9630 | 0.961540 | 0.480770 | − | 0.876847i | \(-0.340357\pi\) | ||||
0.480770 | + | 0.876847i | \(0.340357\pi\) | |||||||
\(350\) | −16.2670 | −0.869508 | ||||||||
\(351\) | −5.66604 | −0.302431 | ||||||||
\(352\) | −6.07044 | −0.323556 | ||||||||
\(353\) | −27.5292 | −1.46523 | −0.732615 | − | 0.680644i | \(-0.761700\pi\) | ||||
−0.732615 | + | 0.680644i | \(0.761700\pi\) | |||||||
\(354\) | 37.9542 | 2.01724 | ||||||||
\(355\) | −27.7329 | −1.47191 | ||||||||
\(356\) | −19.3547 | −1.02580 | ||||||||
\(357\) | −2.94599 | −0.155919 | ||||||||
\(358\) | −7.92127 | −0.418652 | ||||||||
\(359\) | 11.4062 | 0.601995 | 0.300998 | − | 0.953625i | \(-0.402680\pi\) | ||||
0.300998 | + | 0.953625i | \(0.402680\pi\) | |||||||
\(360\) | 16.7882 | 0.884816 | ||||||||
\(361\) | 25.3432 | 1.33385 | ||||||||
\(362\) | 33.8933 | 1.78139 | ||||||||
\(363\) | 9.68066 | 0.508103 | ||||||||
\(364\) | 74.5379 | 3.90685 | ||||||||
\(365\) | −3.88033 | −0.203106 | ||||||||
\(366\) | −14.1103 | −0.737559 | ||||||||
\(367\) | 18.3147 | 0.956021 | 0.478010 | − | 0.878354i | \(-0.341358\pi\) | ||||
0.478010 | + | 0.878354i | \(0.341358\pi\) | |||||||
\(368\) | −34.1081 | −1.77801 | ||||||||
\(369\) | −9.73755 | −0.506917 | ||||||||
\(370\) | 7.02001 | 0.364953 | ||||||||
\(371\) | 40.5872 | 2.10718 | ||||||||
\(372\) | −37.9095 | −1.96551 | ||||||||
\(373\) | 20.9121 | 1.08279 | 0.541394 | − | 0.840769i | \(-0.317897\pi\) | ||||
0.541394 | + | 0.840769i | \(0.317897\pi\) | |||||||
\(374\) | −2.92063 | −0.151022 | ||||||||
\(375\) | −7.57445 | −0.391143 | ||||||||
\(376\) | −60.2939 | −3.10942 | ||||||||
\(377\) | 45.2336 | 2.32965 | ||||||||
\(378\) | 7.49086 | 0.385288 | ||||||||
\(379\) | 2.98218 | 0.153184 | 0.0765922 | − | 0.997063i | \(-0.475596\pi\) | ||||
0.0765922 | + | 0.997063i | \(0.475596\pi\) | |||||||
\(380\) | −79.6318 | −4.08503 | ||||||||
\(381\) | 8.02012 | 0.410883 | ||||||||
\(382\) | 22.3469 | 1.14337 | ||||||||
\(383\) | 32.8908 | 1.68064 | 0.840322 | − | 0.542088i | \(-0.182366\pi\) | ||||
0.840322 | + | 0.542088i | \(0.182366\pi\) | |||||||
\(384\) | −12.0460 | −0.614722 | ||||||||
\(385\) | −9.06185 | −0.461835 | ||||||||
\(386\) | −52.8338 | −2.68917 | ||||||||
\(387\) | 3.63622 | 0.184839 | ||||||||
\(388\) | −26.8048 | −1.36081 | ||||||||
\(389\) | −32.0896 | −1.62701 | −0.813505 | − | 0.581558i | \(-0.802443\pi\) | ||||
−0.813505 | + | 0.581558i | \(0.802443\pi\) | |||||||
\(390\) | −38.5822 | −1.95368 | ||||||||
\(391\) | −4.86607 | −0.246088 | ||||||||
\(392\) | −10.5249 | −0.531587 | ||||||||
\(393\) | −11.2240 | −0.566177 | ||||||||
\(394\) | 60.4393 | 3.04489 | ||||||||
\(395\) | 4.70126 | 0.236546 | ||||||||
\(396\) | 5.12913 | 0.257748 | ||||||||
\(397\) | −23.8666 | −1.19783 | −0.598914 | − | 0.800813i | \(-0.704401\pi\) | ||||
−0.598914 | + | 0.800813i | \(0.704401\pi\) | |||||||
\(398\) | −38.6499 | −1.93734 | ||||||||
\(399\) | −19.6176 | −0.982107 | ||||||||
\(400\) | 15.2214 | 0.761072 | ||||||||
\(401\) | −27.9994 | −1.39822 | −0.699112 | − | 0.715012i | \(-0.746421\pi\) | ||||
−0.699112 | + | 0.715012i | \(0.746421\pi\) | |||||||
\(402\) | 26.1903 | 1.30625 | ||||||||
\(403\) | 48.1018 | 2.39612 | ||||||||
\(404\) | −14.8712 | −0.739870 | ||||||||
\(405\) | −2.67798 | −0.133070 | ||||||||
\(406\) | −59.8016 | −2.96790 | ||||||||
\(407\) | 1.18416 | 0.0586964 | ||||||||
\(408\) | 6.26898 | 0.310361 | ||||||||
\(409\) | −9.86637 | −0.487861 | −0.243930 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243930 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(410\) | −66.3066 | −3.27465 | ||||||||
\(411\) | −13.1733 | −0.649790 | ||||||||
\(412\) | −4.02980 | −0.198534 | ||||||||
\(413\) | 43.9737 | 2.16380 | ||||||||
\(414\) | 12.3731 | 0.608104 | ||||||||
\(415\) | −38.0675 | −1.86866 | ||||||||
\(416\) | −29.9449 | −1.46817 | ||||||||
\(417\) | 20.3308 | 0.995604 | ||||||||
\(418\) | −19.4487 | −0.951267 | ||||||||
\(419\) | 10.3559 | 0.505919 | 0.252959 | − | 0.967477i | \(-0.418596\pi\) | ||||
0.252959 | + | 0.967477i | \(0.418596\pi\) | |||||||
\(420\) | 35.2294 | 1.71902 | ||||||||
\(421\) | 17.7266 | 0.863940 | 0.431970 | − | 0.901888i | \(-0.357819\pi\) | ||||
0.431970 | + | 0.901888i | \(0.357819\pi\) | |||||||
\(422\) | −40.1020 | −1.95213 | ||||||||
\(423\) | 9.61783 | 0.467635 | ||||||||
\(424\) | −86.3681 | −4.19440 | ||||||||
\(425\) | 2.17158 | 0.105337 | ||||||||
\(426\) | 26.3322 | 1.27580 | ||||||||
\(427\) | −16.3482 | −0.791144 | ||||||||
\(428\) | 48.8517 | 2.36133 | ||||||||
\(429\) | −6.50814 | −0.314216 | ||||||||
\(430\) | 24.7603 | 1.19405 | ||||||||
\(431\) | 5.07575 | 0.244490 | 0.122245 | − | 0.992500i | \(-0.460991\pi\) | ||||
0.122245 | + | 0.992500i | \(0.460991\pi\) | |||||||
\(432\) | −7.00938 | −0.337239 | ||||||||
\(433\) | −1.50363 | −0.0722599 | −0.0361300 | − | 0.999347i | \(-0.511503\pi\) | ||||
−0.0361300 | + | 0.999347i | \(0.511503\pi\) | |||||||
\(434\) | −63.5936 | −3.05259 | ||||||||
\(435\) | 21.3791 | 1.02505 | ||||||||
\(436\) | 65.0192 | 3.11386 | ||||||||
\(437\) | −32.4035 | −1.55007 | ||||||||
\(438\) | 3.68435 | 0.176045 | ||||||||
\(439\) | −14.2046 | −0.677949 | −0.338975 | − | 0.940796i | \(-0.610080\pi\) | ||||
−0.338975 | + | 0.940796i | \(0.610080\pi\) | |||||||
\(440\) | 19.2833 | 0.919296 | ||||||||
\(441\) | 1.67889 | 0.0799469 | ||||||||
\(442\) | −14.4072 | −0.685280 | ||||||||
\(443\) | −36.1147 | −1.71586 | −0.857932 | − | 0.513764i | \(-0.828251\pi\) | ||||
−0.857932 | + | 0.513764i | \(0.828251\pi\) | |||||||
\(444\) | −4.60359 | −0.218477 | ||||||||
\(445\) | 11.6072 | 0.550234 | ||||||||
\(446\) | −23.2697 | −1.10185 | ||||||||
\(447\) | 4.27599 | 0.202247 | ||||||||
\(448\) | −1.71020 | −0.0807993 | ||||||||
\(449\) | −9.30746 | −0.439246 | −0.219623 | − | 0.975585i | \(-0.570483\pi\) | ||||
−0.219623 | + | 0.975585i | \(0.570483\pi\) | |||||||
\(450\) | −5.52174 | −0.260297 | ||||||||
\(451\) | −11.1848 | −0.526671 | ||||||||
\(452\) | 28.7957 | 1.35444 | ||||||||
\(453\) | 18.5641 | 0.872216 | ||||||||
\(454\) | 52.2334 | 2.45144 | ||||||||
\(455\) | −44.7012 | −2.09562 | ||||||||
\(456\) | 41.7455 | 1.95491 | ||||||||
\(457\) | 22.4678 | 1.05100 | 0.525499 | − | 0.850794i | \(-0.323879\pi\) | ||||
0.525499 | + | 0.850794i | \(0.323879\pi\) | |||||||
\(458\) | 37.7646 | 1.76462 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 58.1904 | 2.71314 | ||||||||
\(461\) | 11.1532 | 0.519457 | 0.259729 | − | 0.965682i | \(-0.416367\pi\) | ||||
0.259729 | + | 0.965682i | \(0.416367\pi\) | |||||||
\(462\) | 8.60417 | 0.400302 | ||||||||
\(463\) | −6.37371 | −0.296211 | −0.148106 | − | 0.988972i | \(-0.547318\pi\) | ||||
−0.148106 | + | 0.988972i | \(0.547318\pi\) | |||||||
\(464\) | 55.9578 | 2.59778 | ||||||||
\(465\) | 22.7347 | 1.05430 | ||||||||
\(466\) | 15.7266 | 0.728520 | ||||||||
\(467\) | −4.10325 | −0.189876 | −0.0949379 | − | 0.995483i | \(-0.530265\pi\) | ||||
−0.0949379 | + | 0.995483i | \(0.530265\pi\) | |||||||
\(468\) | 25.3014 | 1.16956 | ||||||||
\(469\) | 30.3440 | 1.40116 | ||||||||
\(470\) | 65.4914 | 3.02089 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −93.5744 | −4.30711 | ||||||||
\(473\) | 4.17664 | 0.192042 | ||||||||
\(474\) | −4.46381 | −0.205030 | ||||||||
\(475\) | 14.4607 | 0.663503 | ||||||||
\(476\) | 13.1552 | 0.602968 | ||||||||
\(477\) | 13.7771 | 0.630808 | ||||||||
\(478\) | 22.6345 | 1.03528 | ||||||||
\(479\) | −25.2367 | −1.15309 | −0.576547 | − | 0.817064i | \(-0.695600\pi\) | ||||
−0.576547 | + | 0.817064i | \(0.695600\pi\) | |||||||
\(480\) | −14.1531 | −0.645996 | ||||||||
\(481\) | 5.84131 | 0.266341 | ||||||||
\(482\) | 24.3871 | 1.11080 | ||||||||
\(483\) | 14.3354 | 0.652284 | ||||||||
\(484\) | −43.2286 | −1.96494 | ||||||||
\(485\) | 16.0751 | 0.729935 | ||||||||
\(486\) | 2.54273 | 0.115340 | ||||||||
\(487\) | −38.9121 | −1.76328 | −0.881638 | − | 0.471926i | \(-0.843559\pi\) | ||||
−0.881638 | + | 0.471926i | \(0.843559\pi\) | |||||||
\(488\) | 34.7884 | 1.57480 | ||||||||
\(489\) | 11.5849 | 0.523886 | ||||||||
\(490\) | 11.4322 | 0.516452 | ||||||||
\(491\) | −29.8868 | −1.34877 | −0.674387 | − | 0.738378i | \(-0.735592\pi\) | ||||
−0.674387 | + | 0.738378i | \(0.735592\pi\) | |||||||
\(492\) | 43.4826 | 1.96035 | ||||||||
\(493\) | 7.98328 | 0.359549 | ||||||||
\(494\) | −95.9384 | −4.31647 | ||||||||
\(495\) | −3.07599 | −0.138256 | ||||||||
\(496\) | 59.5061 | 2.67190 | ||||||||
\(497\) | 30.5085 | 1.36849 | ||||||||
\(498\) | 36.1448 | 1.61969 | ||||||||
\(499\) | −33.6178 | −1.50494 | −0.752469 | − | 0.658628i | \(-0.771137\pi\) | ||||
−0.752469 | + | 0.658628i | \(0.771137\pi\) | |||||||
\(500\) | 33.8234 | 1.51263 | ||||||||
\(501\) | 3.97649 | 0.177657 | ||||||||
\(502\) | 32.5859 | 1.45438 | ||||||||
\(503\) | −21.6655 | −0.966018 | −0.483009 | − | 0.875616i | \(-0.660456\pi\) | ||||
−0.483009 | + | 0.875616i | \(0.660456\pi\) | |||||||
\(504\) | −18.4684 | −0.822647 | ||||||||
\(505\) | 8.91842 | 0.396864 | ||||||||
\(506\) | 14.2120 | 0.631801 | ||||||||
\(507\) | −19.1040 | −0.848438 | ||||||||
\(508\) | −35.8135 | −1.58897 | ||||||||
\(509\) | −30.7088 | −1.36114 | −0.680571 | − | 0.732682i | \(-0.738268\pi\) | ||||
−0.680571 | + | 0.732682i | \(0.738268\pi\) | |||||||
\(510\) | −6.80937 | −0.301524 | ||||||||
\(511\) | 4.26868 | 0.188835 | ||||||||
\(512\) | 50.8389 | 2.24678 | ||||||||
\(513\) | −6.65907 | −0.294005 | ||||||||
\(514\) | 46.3838 | 2.04590 | ||||||||
\(515\) | 2.41671 | 0.106493 | ||||||||
\(516\) | −16.2374 | −0.714810 | ||||||||
\(517\) | 11.0473 | 0.485858 | ||||||||
\(518\) | −7.72258 | −0.339311 | ||||||||
\(519\) | −9.89085 | −0.434160 | ||||||||
\(520\) | 95.1226 | 4.17140 | ||||||||
\(521\) | −21.0919 | −0.924052 | −0.462026 | − | 0.886866i | \(-0.652877\pi\) | ||||
−0.462026 | + | 0.886866i | \(0.652877\pi\) | |||||||
\(522\) | −20.2993 | −0.888476 | ||||||||
\(523\) | 28.9815 | 1.26727 | 0.633637 | − | 0.773631i | \(-0.281561\pi\) | ||||
0.633637 | + | 0.773631i | \(0.281561\pi\) | |||||||
\(524\) | 50.1204 | 2.18952 | ||||||||
\(525\) | −6.39747 | −0.279208 | ||||||||
\(526\) | −32.5984 | −1.42136 | ||||||||
\(527\) | 8.48950 | 0.369808 | ||||||||
\(528\) | −8.05113 | −0.350381 | ||||||||
\(529\) | 0.678634 | 0.0295058 | ||||||||
\(530\) | 93.8131 | 4.07498 | ||||||||
\(531\) | 14.9266 | 0.647759 | ||||||||
\(532\) | 87.6014 | 3.79800 | ||||||||
\(533\) | −55.1734 | −2.38982 | ||||||||
\(534\) | −11.0210 | −0.476924 | ||||||||
\(535\) | −29.2969 | −1.26661 | ||||||||
\(536\) | −64.5710 | −2.78904 | ||||||||
\(537\) | −3.11527 | −0.134434 | ||||||||
\(538\) | −35.6334 | −1.53626 | ||||||||
\(539\) | 1.92841 | 0.0830624 | ||||||||
\(540\) | 11.9584 | 0.514608 | ||||||||
\(541\) | −39.1386 | −1.68270 | −0.841351 | − | 0.540490i | \(-0.818239\pi\) | ||||
−0.841351 | + | 0.540490i | \(0.818239\pi\) | |||||||
\(542\) | −4.39707 | −0.188870 | ||||||||
\(543\) | 13.3295 | 0.572024 | ||||||||
\(544\) | −5.28497 | −0.226591 | ||||||||
\(545\) | −38.9927 | −1.67026 | ||||||||
\(546\) | 42.4435 | 1.81641 | ||||||||
\(547\) | 13.0844 | 0.559450 | 0.279725 | − | 0.960080i | \(-0.409757\pi\) | ||||
0.279725 | + | 0.960080i | \(0.409757\pi\) | |||||||
\(548\) | 58.8247 | 2.51286 | ||||||||
\(549\) | −5.54929 | −0.236838 | ||||||||
\(550\) | −6.34239 | −0.270441 | ||||||||
\(551\) | 53.1612 | 2.26474 | ||||||||
\(552\) | −30.5053 | −1.29839 | ||||||||
\(553\) | −5.17176 | −0.219926 | ||||||||
\(554\) | 51.4958 | 2.18785 | ||||||||
\(555\) | 2.76082 | 0.117190 | ||||||||
\(556\) | −90.7863 | −3.85020 | ||||||||
\(557\) | 1.86466 | 0.0790082 | 0.0395041 | − | 0.999219i | \(-0.487422\pi\) | ||||
0.0395041 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(558\) | −21.5865 | −0.913828 | ||||||||
\(559\) | 20.6029 | 0.871412 | ||||||||
\(560\) | −55.2992 | −2.33682 | ||||||||
\(561\) | −1.14862 | −0.0484949 | ||||||||
\(562\) | −14.7046 | −0.620275 | ||||||||
\(563\) | −37.2297 | −1.56905 | −0.784523 | − | 0.620099i | \(-0.787092\pi\) | ||||
−0.784523 | + | 0.620099i | \(0.787092\pi\) | |||||||
\(564\) | −42.9480 | −1.80844 | ||||||||
\(565\) | −17.2691 | −0.726516 | ||||||||
\(566\) | 29.2425 | 1.22915 | ||||||||
\(567\) | 2.94599 | 0.123720 | ||||||||
\(568\) | −64.9209 | −2.72402 | ||||||||
\(569\) | −13.1522 | −0.551367 | −0.275683 | − | 0.961248i | \(-0.588904\pi\) | ||||
−0.275683 | + | 0.961248i | \(0.588904\pi\) | |||||||
\(570\) | −45.3441 | −1.89925 | ||||||||
\(571\) | 6.97925 | 0.292073 | 0.146036 | − | 0.989279i | \(-0.453348\pi\) | ||||
0.146036 | + | 0.989279i | \(0.453348\pi\) | |||||||
\(572\) | 29.0618 | 1.21514 | ||||||||
\(573\) | 8.78858 | 0.367148 | ||||||||
\(574\) | 72.9426 | 3.04457 | ||||||||
\(575\) | −10.5671 | −0.440677 | ||||||||
\(576\) | −0.580516 | −0.0241882 | ||||||||
\(577\) | 31.6789 | 1.31881 | 0.659405 | − | 0.751788i | \(-0.270808\pi\) | ||||
0.659405 | + | 0.751788i | \(0.270808\pi\) | |||||||
\(578\) | −2.54273 | −0.105763 | ||||||||
\(579\) | −20.7784 | −0.863521 | ||||||||
\(580\) | −95.4673 | −3.96406 | ||||||||
\(581\) | 41.8773 | 1.73736 | ||||||||
\(582\) | −15.2633 | −0.632682 | ||||||||
\(583\) | 15.8247 | 0.655390 | ||||||||
\(584\) | −9.08359 | −0.375882 | ||||||||
\(585\) | −15.1735 | −0.627349 | ||||||||
\(586\) | −14.4055 | −0.595086 | ||||||||
\(587\) | 4.00509 | 0.165308 | 0.0826538 | − | 0.996578i | \(-0.473660\pi\) | ||||
0.0826538 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(588\) | −7.49699 | −0.309171 | ||||||||
\(589\) | 56.5322 | 2.32937 | ||||||||
\(590\) | 101.641 | 4.18448 | ||||||||
\(591\) | 23.7695 | 0.977746 | ||||||||
\(592\) | 7.22621 | 0.296995 | ||||||||
\(593\) | −0.572225 | −0.0234985 | −0.0117492 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117492 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(594\) | 2.92063 | 0.119835 | ||||||||
\(595\) | −7.88932 | −0.323430 | ||||||||
\(596\) | −19.0942 | −0.782131 | ||||||||
\(597\) | −15.2002 | −0.622102 | ||||||||
\(598\) | 70.1064 | 2.86686 | ||||||||
\(599\) | 6.26893 | 0.256141 | 0.128071 | − | 0.991765i | \(-0.459122\pi\) | ||||
0.128071 | + | 0.991765i | \(0.459122\pi\) | |||||||
\(600\) | 13.6136 | 0.555772 | ||||||||
\(601\) | 3.24638 | 0.132422 | 0.0662112 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662112 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(602\) | −27.2384 | −1.11015 | ||||||||
\(603\) | 10.3001 | 0.419452 | ||||||||
\(604\) | −82.8970 | −3.37303 | ||||||||
\(605\) | 25.9246 | 1.05399 | ||||||||
\(606\) | −8.46798 | −0.343988 | ||||||||
\(607\) | 15.5336 | 0.630489 | 0.315245 | − | 0.949010i | \(-0.397913\pi\) | ||||
0.315245 | + | 0.949010i | \(0.397913\pi\) | |||||||
\(608\) | −35.1930 | −1.42726 | ||||||||
\(609\) | −23.5187 | −0.953026 | ||||||||
\(610\) | −37.7872 | −1.52996 | ||||||||
\(611\) | 54.4950 | 2.20463 | ||||||||
\(612\) | 4.46545 | 0.180505 | ||||||||
\(613\) | −8.94320 | −0.361212 | −0.180606 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180606 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(614\) | −61.6101 | −2.48638 | ||||||||
\(615\) | −26.0770 | −1.05153 | ||||||||
\(616\) | −21.2132 | −0.854704 | ||||||||
\(617\) | 42.5049 | 1.71118 | 0.855592 | − | 0.517651i | \(-0.173193\pi\) | ||||
0.855592 | + | 0.517651i | \(0.173193\pi\) | |||||||
\(618\) | −2.29465 | −0.0923045 | ||||||||
\(619\) | 29.8724 | 1.20067 | 0.600337 | − | 0.799747i | \(-0.295033\pi\) | ||||
0.600337 | + | 0.799747i | \(0.295033\pi\) | |||||||
\(620\) | −101.521 | −4.07718 | ||||||||
\(621\) | 4.86607 | 0.195269 | ||||||||
\(622\) | 3.94771 | 0.158289 | ||||||||
\(623\) | −12.7689 | −0.511573 | ||||||||
\(624\) | −39.7154 | −1.58989 | ||||||||
\(625\) | −31.1421 | −1.24569 | ||||||||
\(626\) | 57.1707 | 2.28500 | ||||||||
\(627\) | −7.64876 | −0.305462 | ||||||||
\(628\) | −4.46545 | −0.178191 | ||||||||
\(629\) | 1.03093 | 0.0411060 | ||||||||
\(630\) | 20.0604 | 0.799224 | ||||||||
\(631\) | 37.2974 | 1.48479 | 0.742394 | − | 0.669964i | \(-0.233690\pi\) | ||||
0.742394 | + | 0.669964i | \(0.233690\pi\) | |||||||
\(632\) | 11.0053 | 0.437768 | ||||||||
\(633\) | −15.7713 | −0.626851 | ||||||||
\(634\) | 62.5594 | 2.48455 | ||||||||
\(635\) | 21.4777 | 0.852318 | ||||||||
\(636\) | −61.5208 | −2.43946 | ||||||||
\(637\) | 9.51263 | 0.376904 | ||||||||
\(638\) | −23.3162 | −0.923099 | ||||||||
\(639\) | 10.3559 | 0.409673 | ||||||||
\(640\) | −32.2591 | −1.27515 | ||||||||
\(641\) | −45.8235 | −1.80992 | −0.904959 | − | 0.425498i | \(-0.860099\pi\) | ||||
−0.904959 | + | 0.425498i | \(0.860099\pi\) | |||||||
\(642\) | 27.8172 | 1.09786 | ||||||||
\(643\) | −40.5538 | −1.59928 | −0.799642 | − | 0.600477i | \(-0.794977\pi\) | ||||
−0.799642 | + | 0.600477i | \(0.794977\pi\) | |||||||
\(644\) | −64.0142 | −2.52251 | ||||||||
\(645\) | 9.73772 | 0.383422 | ||||||||
\(646\) | −16.9322 | −0.666188 | ||||||||
\(647\) | 40.4860 | 1.59167 | 0.795834 | − | 0.605514i | \(-0.207033\pi\) | ||||
0.795834 | + | 0.605514i | \(0.207033\pi\) | |||||||
\(648\) | −6.26898 | −0.246269 | ||||||||
\(649\) | 17.1450 | 0.673001 | ||||||||
\(650\) | −31.2864 | −1.22715 | ||||||||
\(651\) | −25.0100 | −0.980220 | ||||||||
\(652\) | −51.7317 | −2.02597 | ||||||||
\(653\) | −14.6748 | −0.574270 | −0.287135 | − | 0.957890i | \(-0.592703\pi\) | ||||
−0.287135 | + | 0.957890i | \(0.592703\pi\) | |||||||
\(654\) | 37.0233 | 1.44773 | ||||||||
\(655\) | −30.0577 | −1.17445 | ||||||||
\(656\) | −68.2542 | −2.66488 | ||||||||
\(657\) | 1.44898 | 0.0565299 | ||||||||
\(658\) | −72.0458 | −2.80864 | ||||||||
\(659\) | −33.7038 | −1.31291 | −0.656457 | − | 0.754363i | \(-0.727946\pi\) | ||||
−0.656457 | + | 0.754363i | \(0.727946\pi\) | |||||||
\(660\) | 13.7357 | 0.534661 | ||||||||
\(661\) | −13.3403 | −0.518876 | −0.259438 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259438 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(662\) | 23.9594 | 0.931209 | ||||||||
\(663\) | −5.66604 | −0.220051 | ||||||||
\(664\) | −89.1135 | −3.45827 | ||||||||
\(665\) | −52.5355 | −2.03724 | ||||||||
\(666\) | −2.62138 | −0.101577 | ||||||||
\(667\) | −38.8472 | −1.50417 | ||||||||
\(668\) | −17.7568 | −0.687033 | ||||||||
\(669\) | −9.15149 | −0.353817 | ||||||||
\(670\) | 70.1371 | 2.70963 | ||||||||
\(671\) | −6.37405 | −0.246067 | ||||||||
\(672\) | 15.5695 | 0.600607 | ||||||||
\(673\) | 15.8351 | 0.610397 | 0.305198 | − | 0.952289i | \(-0.401277\pi\) | ||||
0.305198 | + | 0.952289i | \(0.401277\pi\) | |||||||
\(674\) | 24.3650 | 0.938504 | ||||||||
\(675\) | −2.17158 | −0.0835842 | ||||||||
\(676\) | 85.3080 | 3.28108 | ||||||||
\(677\) | 48.2236 | 1.85338 | 0.926692 | − | 0.375821i | \(-0.122639\pi\) | ||||
0.926692 | + | 0.375821i | \(0.122639\pi\) | |||||||
\(678\) | 16.3969 | 0.629718 | ||||||||
\(679\) | −17.6840 | −0.678648 | ||||||||
\(680\) | 16.7882 | 0.643798 | ||||||||
\(681\) | 20.5423 | 0.787183 | ||||||||
\(682\) | −24.7947 | −0.949439 | ||||||||
\(683\) | 46.9093 | 1.79493 | 0.897467 | − | 0.441082i | \(-0.145405\pi\) | ||||
0.897467 | + | 0.441082i | \(0.145405\pi\) | |||||||
\(684\) | 29.7358 | 1.13698 | ||||||||
\(685\) | −35.2778 | −1.34789 | ||||||||
\(686\) | 39.8597 | 1.52185 | ||||||||
\(687\) | 14.8520 | 0.566639 | ||||||||
\(688\) | 25.4876 | 0.971706 | ||||||||
\(689\) | 78.0614 | 2.97390 | ||||||||
\(690\) | 33.1349 | 1.26142 | ||||||||
\(691\) | 40.8271 | 1.55314 | 0.776569 | − | 0.630033i | \(-0.216959\pi\) | ||||
0.776569 | + | 0.630033i | \(0.216959\pi\) | |||||||
\(692\) | 44.1671 | 1.67898 | ||||||||
\(693\) | 3.38384 | 0.128541 | ||||||||
\(694\) | 69.6102 | 2.64237 | ||||||||
\(695\) | 54.4455 | 2.06524 | ||||||||
\(696\) | 50.0470 | 1.89703 | ||||||||
\(697\) | −9.73755 | −0.368836 | ||||||||
\(698\) | −45.6751 | −1.72883 | ||||||||
\(699\) | 6.18493 | 0.233936 | ||||||||
\(700\) | 28.5676 | 1.07975 | ||||||||
\(701\) | −32.2668 | −1.21870 | −0.609351 | − | 0.792901i | \(-0.708570\pi\) | ||||
−0.609351 | + | 0.792901i | \(0.708570\pi\) | |||||||
\(702\) | 14.4072 | 0.543764 | ||||||||
\(703\) | 6.86506 | 0.258921 | ||||||||
\(704\) | −0.666794 | −0.0251308 | ||||||||
\(705\) | 25.7564 | 0.970041 | ||||||||
\(706\) | 69.9991 | 2.63445 | ||||||||
\(707\) | −9.81098 | −0.368980 | ||||||||
\(708\) | −66.6540 | −2.50501 | ||||||||
\(709\) | −10.9244 | −0.410276 | −0.205138 | − | 0.978733i | \(-0.565764\pi\) | ||||
−0.205138 | + | 0.978733i | \(0.565764\pi\) | |||||||
\(710\) | 70.5172 | 2.64646 | ||||||||
\(711\) | −1.75552 | −0.0658372 | ||||||||
\(712\) | 27.1717 | 1.01830 | ||||||||
\(713\) | −41.3105 | −1.54709 | ||||||||
\(714\) | 7.49086 | 0.280338 | ||||||||
\(715\) | −17.4287 | −0.651796 | ||||||||
\(716\) | 13.9111 | 0.519882 | ||||||||
\(717\) | 8.90165 | 0.332438 | ||||||||
\(718\) | −29.0028 | −1.08237 | ||||||||
\(719\) | 2.81368 | 0.104933 | 0.0524663 | − | 0.998623i | \(-0.483292\pi\) | ||||
0.0524663 | + | 0.998623i | \(0.483292\pi\) | |||||||
\(720\) | −18.7710 | −0.699553 | ||||||||
\(721\) | −2.65858 | −0.0990107 | ||||||||
\(722\) | −64.4407 | −2.39824 | ||||||||
\(723\) | 9.59092 | 0.356690 | ||||||||
\(724\) | −59.5223 | −2.21213 | ||||||||
\(725\) | 17.3363 | 0.643856 | ||||||||
\(726\) | −24.6153 | −0.913559 | ||||||||
\(727\) | −11.0598 | −0.410185 | −0.205092 | − | 0.978743i | \(-0.565749\pi\) | ||||
−0.205092 | + | 0.978743i | \(0.565749\pi\) | |||||||
\(728\) | −104.643 | −3.87831 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.86661 | 0.365180 | ||||||||
\(731\) | 3.63622 | 0.134490 | ||||||||
\(732\) | 24.7801 | 0.915899 | ||||||||
\(733\) | 21.0413 | 0.777178 | 0.388589 | − | 0.921411i | \(-0.372963\pi\) | ||||
0.388589 | + | 0.921411i | \(0.372963\pi\) | |||||||
\(734\) | −46.5693 | −1.71890 | ||||||||
\(735\) | 4.49602 | 0.165838 | ||||||||
\(736\) | 25.7170 | 0.947943 | ||||||||
\(737\) | 11.8309 | 0.435797 | ||||||||
\(738\) | 24.7599 | 0.911426 | ||||||||
\(739\) | −3.50290 | −0.128856 | −0.0644281 | − | 0.997922i | \(-0.520522\pi\) | ||||
−0.0644281 | + | 0.997922i | \(0.520522\pi\) | |||||||
\(740\) | −12.3283 | −0.453198 | ||||||||
\(741\) | −37.7305 | −1.38607 | ||||||||
\(742\) | −103.202 | −3.78866 | ||||||||
\(743\) | 17.3606 | 0.636899 | 0.318450 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318450 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(744\) | 53.2205 | 1.95116 | ||||||||
\(745\) | 11.4510 | 0.419533 | ||||||||
\(746\) | −53.1738 | −1.94683 | ||||||||
\(747\) | 14.2150 | 0.520100 | ||||||||
\(748\) | 5.12913 | 0.187539 | ||||||||
\(749\) | 32.2289 | 1.17762 | ||||||||
\(750\) | 19.2598 | 0.703267 | ||||||||
\(751\) | −3.73919 | −0.136445 | −0.0682225 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682225 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(752\) | 67.4150 | 2.45837 | ||||||||
\(753\) | 12.8153 | 0.467017 | ||||||||
\(754\) | −115.017 | −4.18866 | ||||||||
\(755\) | 49.7142 | 1.80928 | ||||||||
\(756\) | −13.1552 | −0.478450 | ||||||||
\(757\) | −1.88287 | −0.0684341 | −0.0342170 | − | 0.999414i | \(-0.510894\pi\) | ||||
−0.0342170 | + | 0.999414i | \(0.510894\pi\) | |||||||
\(758\) | −7.58287 | −0.275422 | ||||||||
\(759\) | 5.58928 | 0.202878 | ||||||||
\(760\) | 111.794 | 4.05518 | ||||||||
\(761\) | 47.0097 | 1.70410 | 0.852050 | − | 0.523460i | \(-0.175359\pi\) | ||||
0.852050 | + | 0.523460i | \(0.175359\pi\) | |||||||
\(762\) | −20.3930 | −0.738760 | ||||||||
\(763\) | 42.8951 | 1.55291 | ||||||||
\(764\) | −39.2450 | −1.41983 | ||||||||
\(765\) | −2.67798 | −0.0968226 | ||||||||
\(766\) | −83.6324 | −3.02176 | ||||||||
\(767\) | 84.5747 | 3.05381 | ||||||||
\(768\) | 29.4687 | 1.06336 | ||||||||
\(769\) | 3.99993 | 0.144241 | 0.0721205 | − | 0.997396i | \(-0.477023\pi\) | ||||
0.0721205 | + | 0.997396i | \(0.477023\pi\) | |||||||
\(770\) | 23.0418 | 0.830369 | ||||||||
\(771\) | 18.2418 | 0.656961 | ||||||||
\(772\) | 92.7850 | 3.33941 | ||||||||
\(773\) | 45.8037 | 1.64745 | 0.823723 | − | 0.566992i | \(-0.191893\pi\) | ||||
0.823723 | + | 0.566992i | \(0.191893\pi\) | |||||||
\(774\) | −9.24590 | −0.332337 | ||||||||
\(775\) | 18.4356 | 0.662228 | ||||||||
\(776\) | 37.6309 | 1.35087 | ||||||||
\(777\) | −3.03713 | −0.108956 | ||||||||
\(778\) | 81.5952 | 2.92533 | ||||||||
\(779\) | −64.8430 | −2.32324 | ||||||||
\(780\) | 67.7568 | 2.42608 | ||||||||
\(781\) | 11.8950 | 0.425638 | ||||||||
\(782\) | 12.3731 | 0.442460 | ||||||||
\(783\) | −7.98328 | −0.285299 | ||||||||
\(784\) | 11.7679 | 0.420284 | ||||||||
\(785\) | 2.67798 | 0.0955812 | ||||||||
\(786\) | 28.5396 | 1.01797 | ||||||||
\(787\) | −37.0113 | −1.31931 | −0.659655 | − | 0.751568i | \(-0.729298\pi\) | ||||
−0.659655 | + | 0.751568i | \(0.729298\pi\) | |||||||
\(788\) | −106.142 | −3.78114 | ||||||||
\(789\) | −12.8203 | −0.456413 | ||||||||
\(790\) | −11.9540 | −0.425304 | ||||||||
\(791\) | 18.9974 | 0.675469 | ||||||||
\(792\) | −7.20069 | −0.255865 | ||||||||
\(793\) | −31.4425 | −1.11656 | ||||||||
\(794\) | 60.6862 | 2.15367 | ||||||||
\(795\) | 36.8947 | 1.30852 | ||||||||
\(796\) | 67.8757 | 2.40579 | ||||||||
\(797\) | −31.2415 | −1.10663 | −0.553315 | − | 0.832972i | \(-0.686637\pi\) | ||||
−0.553315 | + | 0.832972i | \(0.686637\pi\) | |||||||
\(798\) | 49.8821 | 1.76581 | ||||||||
\(799\) | 9.61783 | 0.340254 | ||||||||
\(800\) | −11.4767 | −0.405764 | ||||||||
\(801\) | −4.33431 | −0.153145 | ||||||||
\(802\) | 71.1948 | 2.51398 | ||||||||
\(803\) | 1.66433 | 0.0587328 | ||||||||
\(804\) | −45.9946 | −1.62210 | ||||||||
\(805\) | 38.3900 | 1.35307 | ||||||||
\(806\) | −122.310 | −4.30818 | ||||||||
\(807\) | −14.0139 | −0.493311 | ||||||||
\(808\) | 20.8774 | 0.734465 | ||||||||
\(809\) | −9.29265 | −0.326712 | −0.163356 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163356 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(810\) | 6.80937 | 0.239257 | ||||||||
\(811\) | −21.9752 | −0.771654 | −0.385827 | − | 0.922571i | \(-0.626084\pi\) | ||||
−0.385827 | + | 0.922571i | \(0.626084\pi\) | |||||||
\(812\) | 105.022 | 3.68554 | ||||||||
\(813\) | −1.72927 | −0.0606483 | ||||||||
\(814\) | −3.01098 | −0.105535 | ||||||||
\(815\) | 31.0241 | 1.08673 | ||||||||
\(816\) | −7.00938 | −0.245377 | ||||||||
\(817\) | 24.2138 | 0.847134 | ||||||||
\(818\) | 25.0875 | 0.877163 | ||||||||
\(819\) | 16.6921 | 0.583270 | ||||||||
\(820\) | 116.446 | 4.06646 | ||||||||
\(821\) | 1.19974 | 0.0418710 | 0.0209355 | − | 0.999781i | \(-0.493336\pi\) | ||||
0.0209355 | + | 0.999781i | \(0.493336\pi\) | |||||||
\(822\) | 33.4960 | 1.16831 | ||||||||
\(823\) | 41.0775 | 1.43187 | 0.715936 | − | 0.698166i | \(-0.246000\pi\) | ||||
0.715936 | + | 0.698166i | \(0.246000\pi\) | |||||||
\(824\) | 5.65737 | 0.197084 | ||||||||
\(825\) | −2.49433 | −0.0868414 | ||||||||
\(826\) | −111.813 | −3.89047 | ||||||||
\(827\) | 7.45083 | 0.259091 | 0.129545 | − | 0.991573i | \(-0.458648\pi\) | ||||
0.129545 | + | 0.991573i | \(0.458648\pi\) | |||||||
\(828\) | −21.7292 | −0.755142 | ||||||||
\(829\) | 7.04979 | 0.244849 | 0.122425 | − | 0.992478i | \(-0.460933\pi\) | ||||
0.122425 | + | 0.992478i | \(0.460933\pi\) | |||||||
\(830\) | 96.7952 | 3.35981 | ||||||||
\(831\) | 20.2522 | 0.702542 | ||||||||
\(832\) | −3.28923 | −0.114033 | ||||||||
\(833\) | 1.67889 | 0.0581699 | ||||||||
\(834\) | −51.6957 | −1.79007 | ||||||||
\(835\) | 10.6490 | 0.368523 | ||||||||
\(836\) | 34.1552 | 1.18128 | ||||||||
\(837\) | −8.48950 | −0.293440 | ||||||||
\(838\) | −26.3322 | −0.909631 | ||||||||
\(839\) | 15.2193 | 0.525428 | 0.262714 | − | 0.964874i | \(-0.415382\pi\) | ||||
0.262714 | + | 0.964874i | \(0.415382\pi\) | |||||||
\(840\) | −49.4579 | −1.70646 | ||||||||
\(841\) | 34.7328 | 1.19768 | ||||||||
\(842\) | −45.0738 | −1.55335 | ||||||||
\(843\) | −5.78300 | −0.199177 | ||||||||
\(844\) | 70.4259 | 2.42416 | ||||||||
\(845\) | −51.1601 | −1.75996 | ||||||||
\(846\) | −24.4555 | −0.840797 | ||||||||
\(847\) | −28.5192 | −0.979931 | ||||||||
\(848\) | 96.5686 | 3.31618 | ||||||||
\(849\) | 11.5004 | 0.394694 | ||||||||
\(850\) | −5.52174 | −0.189394 | ||||||||
\(851\) | −5.01660 | −0.171967 | ||||||||
\(852\) | −46.2438 | −1.58429 | ||||||||
\(853\) | 44.8014 | 1.53397 | 0.766985 | − | 0.641665i | \(-0.221756\pi\) | ||||
0.766985 | + | 0.641665i | \(0.221756\pi\) | |||||||
\(854\) | 41.5690 | 1.42246 | ||||||||
\(855\) | −17.8329 | −0.609871 | ||||||||
\(856\) | −68.5820 | −2.34409 | ||||||||
\(857\) | 8.04126 | 0.274684 | 0.137342 | − | 0.990524i | \(-0.456144\pi\) | ||||
0.137342 | + | 0.990524i | \(0.456144\pi\) | |||||||
\(858\) | 16.5484 | 0.564954 | ||||||||
\(859\) | 18.6670 | 0.636910 | 0.318455 | − | 0.947938i | \(-0.396836\pi\) | ||||
0.318455 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(860\) | −43.4833 | −1.48277 | ||||||||
\(861\) | 28.6868 | 0.977643 | ||||||||
\(862\) | −12.9062 | −0.439588 | ||||||||
\(863\) | −23.4954 | −0.799794 | −0.399897 | − | 0.916560i | \(-0.630954\pi\) | ||||
−0.399897 | + | 0.916560i | \(0.630954\pi\) | |||||||
\(864\) | 5.28497 | 0.179798 | ||||||||
\(865\) | −26.4875 | −0.900602 | ||||||||
\(866\) | 3.82332 | 0.129922 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 111.681 | 3.79070 | ||||||||
\(869\) | −2.01643 | −0.0684028 | ||||||||
\(870\) | −54.3611 | −1.84301 | ||||||||
\(871\) | 58.3607 | 1.97748 | ||||||||
\(872\) | −91.2794 | −3.09111 | ||||||||
\(873\) | −6.00271 | −0.203161 | ||||||||
\(874\) | 82.3932 | 2.78699 | ||||||||
\(875\) | 22.3143 | 0.754361 | ||||||||
\(876\) | −6.47034 | −0.218612 | ||||||||
\(877\) | 2.98976 | 0.100957 | 0.0504786 | − | 0.998725i | \(-0.483925\pi\) | ||||
0.0504786 | + | 0.998725i | \(0.483925\pi\) | |||||||
\(878\) | 36.1184 | 1.21894 | ||||||||
\(879\) | −5.66538 | −0.191089 | ||||||||
\(880\) | −21.5608 | −0.726814 | ||||||||
\(881\) | −44.9227 | −1.51348 | −0.756742 | − | 0.653714i | \(-0.773210\pi\) | ||||
−0.756742 | + | 0.653714i | \(0.773210\pi\) | |||||||
\(882\) | −4.26895 | −0.143743 | ||||||||
\(883\) | 6.73305 | 0.226585 | 0.113293 | − | 0.993562i | \(-0.463860\pi\) | ||||
0.113293 | + | 0.993562i | \(0.463860\pi\) | |||||||
\(884\) | 25.3014 | 0.850980 | ||||||||
\(885\) | 39.9731 | 1.34368 | ||||||||
\(886\) | 91.8299 | 3.08509 | ||||||||
\(887\) | 8.95244 | 0.300594 | 0.150297 | − | 0.988641i | \(-0.451977\pi\) | ||||
0.150297 | + | 0.988641i | \(0.451977\pi\) | |||||||
\(888\) | 6.46290 | 0.216881 | ||||||||
\(889\) | −23.6272 | −0.792432 | ||||||||
\(890\) | −29.5139 | −0.989309 | ||||||||
\(891\) | 1.14862 | 0.0384803 | ||||||||
\(892\) | 40.8656 | 1.36828 | ||||||||
\(893\) | 64.0458 | 2.14321 | ||||||||
\(894\) | −10.8727 | −0.363637 | ||||||||
\(895\) | −8.34263 | −0.278863 | ||||||||
\(896\) | 35.4876 | 1.18556 | ||||||||
\(897\) | 27.5713 | 0.920580 | ||||||||
\(898\) | 23.6663 | 0.789755 | ||||||||
\(899\) | 67.7741 | 2.26039 | ||||||||
\(900\) | 9.69710 | 0.323237 | ||||||||
\(901\) | 13.7771 | 0.458980 | ||||||||
\(902\) | 28.4398 | 0.946943 | ||||||||
\(903\) | −10.7123 | −0.356482 | ||||||||
\(904\) | −40.4258 | −1.34454 | ||||||||
\(905\) | 35.6962 | 1.18658 | ||||||||
\(906\) | −47.2033 | −1.56822 | ||||||||
\(907\) | 7.36387 | 0.244513 | 0.122257 | − | 0.992499i | \(-0.460987\pi\) | ||||
0.122257 | + | 0.992499i | \(0.460987\pi\) | |||||||
\(908\) | −91.7307 | −3.04419 | ||||||||
\(909\) | −3.33028 | −0.110458 | ||||||||
\(910\) | 113.663 | 3.76789 | ||||||||
\(911\) | 3.85375 | 0.127680 | 0.0638402 | − | 0.997960i | \(-0.479665\pi\) | ||||
0.0638402 | + | 0.997960i | \(0.479665\pi\) | |||||||
\(912\) | −46.6759 | −1.54559 | ||||||||
\(913\) | 16.3277 | 0.540367 | ||||||||
\(914\) | −57.1294 | −1.88967 | ||||||||
\(915\) | −14.8609 | −0.491286 | ||||||||
\(916\) | −66.3210 | −2.19131 | ||||||||
\(917\) | 33.0659 | 1.09193 | ||||||||
\(918\) | 2.54273 | 0.0839225 | ||||||||
\(919\) | 15.5684 | 0.513553 | 0.256777 | − | 0.966471i | \(-0.417340\pi\) | ||||
0.256777 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(920\) | −81.6925 | −2.69332 | ||||||||
\(921\) | −24.2299 | −0.798403 | ||||||||
\(922\) | −28.3596 | −0.933973 | ||||||||
\(923\) | 58.6770 | 1.93138 | ||||||||
\(924\) | −15.1104 | −0.497095 | ||||||||
\(925\) | 2.23876 | 0.0736099 | ||||||||
\(926\) | 16.2066 | 0.532582 | ||||||||
\(927\) | −0.902439 | −0.0296400 | ||||||||
\(928\) | −42.1914 | −1.38500 | ||||||||
\(929\) | −19.5795 | −0.642382 | −0.321191 | − | 0.947014i | \(-0.604083\pi\) | ||||
−0.321191 | + | 0.947014i | \(0.604083\pi\) | |||||||
\(930\) | −57.8082 | −1.89560 | ||||||||
\(931\) | 11.1798 | 0.366404 | ||||||||
\(932\) | −27.6185 | −0.904675 | ||||||||
\(933\) | 1.55255 | 0.0508282 | ||||||||
\(934\) | 10.4334 | 0.341392 | ||||||||
\(935\) | −3.07599 | −0.100596 | ||||||||
\(936\) | −35.5203 | −1.16102 | ||||||||
\(937\) | −46.2258 | −1.51013 | −0.755066 | − | 0.655649i | \(-0.772395\pi\) | ||||
−0.755066 | + | 0.655649i | \(0.772395\pi\) | |||||||
\(938\) | −77.1565 | −2.51925 | ||||||||
\(939\) | 22.4840 | 0.733739 | ||||||||
\(940\) | −115.014 | −3.75134 | ||||||||
\(941\) | 15.7648 | 0.513917 | 0.256958 | − | 0.966422i | \(-0.417280\pi\) | ||||
0.256958 | + | 0.966422i | \(0.417280\pi\) | |||||||
\(942\) | −2.54273 | −0.0828465 | ||||||||
\(943\) | 47.3836 | 1.54302 | ||||||||
\(944\) | 104.626 | 3.40529 | ||||||||
\(945\) | 7.88932 | 0.256640 | ||||||||
\(946\) | −10.6201 | −0.345288 | ||||||||
\(947\) | 37.4702 | 1.21762 | 0.608809 | − | 0.793317i | \(-0.291648\pi\) | ||||
0.608809 | + | 0.793317i | \(0.291648\pi\) | |||||||
\(948\) | 7.83921 | 0.254606 | ||||||||
\(949\) | 8.20995 | 0.266506 | ||||||||
\(950\) | −36.7696 | −1.19296 | ||||||||
\(951\) | 24.6033 | 0.797816 | ||||||||
\(952\) | −18.4684 | −0.598563 | ||||||||
\(953\) | −13.1411 | −0.425683 | −0.212842 | − | 0.977087i | \(-0.568272\pi\) | ||||
−0.212842 | + | 0.977087i | \(0.568272\pi\) | |||||||
\(954\) | −35.0313 | −1.13418 | ||||||||
\(955\) | 23.5356 | 0.761595 | ||||||||
\(956\) | −39.7499 | −1.28560 | ||||||||
\(957\) | −9.16978 | −0.296417 | ||||||||
\(958\) | 64.1700 | 2.07324 | ||||||||
\(959\) | 38.8084 | 1.25319 | ||||||||
\(960\) | −1.55461 | −0.0501749 | ||||||||
\(961\) | 41.0716 | 1.32489 | ||||||||
\(962\) | −14.8529 | −0.478875 | ||||||||
\(963\) | 10.9399 | 0.352534 | ||||||||
\(964\) | −42.8278 | −1.37939 | ||||||||
\(965\) | −55.6442 | −1.79125 | ||||||||
\(966\) | −36.4510 | −1.17279 | ||||||||
\(967\) | 38.3319 | 1.23267 | 0.616335 | − | 0.787484i | \(-0.288617\pi\) | ||||
0.616335 | + | 0.787484i | \(0.288617\pi\) | |||||||
\(968\) | 60.6879 | 1.95058 | ||||||||
\(969\) | −6.65907 | −0.213920 | ||||||||
\(970\) | −40.8747 | −1.31241 | ||||||||
\(971\) | −36.8988 | −1.18414 | −0.592070 | − | 0.805886i | \(-0.701689\pi\) | ||||
−0.592070 | + | 0.805886i | \(0.701689\pi\) | |||||||
\(972\) | −4.46545 | −0.143230 | ||||||||
\(973\) | −59.8944 | −1.92013 | ||||||||
\(974\) | 98.9429 | 3.17033 | ||||||||
\(975\) | −12.3043 | −0.394052 | ||||||||
\(976\) | −38.8971 | −1.24507 | ||||||||
\(977\) | −25.1925 | −0.805981 | −0.402990 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402990 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(978\) | −29.4572 | −0.941936 | ||||||||
\(979\) | −4.97849 | −0.159113 | ||||||||
\(980\) | −20.0768 | −0.641330 | ||||||||
\(981\) | 14.5605 | 0.464881 | ||||||||
\(982\) | 75.9941 | 2.42507 | ||||||||
\(983\) | 37.1597 | 1.18521 | 0.592606 | − | 0.805493i | \(-0.298099\pi\) | ||||
0.592606 | + | 0.805493i | \(0.298099\pi\) | |||||||
\(984\) | −61.0445 | −1.94603 | ||||||||
\(985\) | 63.6542 | 2.02819 | ||||||||
\(986\) | −20.2993 | −0.646461 | ||||||||
\(987\) | −28.3341 | −0.901883 | ||||||||
\(988\) | 168.484 | 5.36019 | ||||||||
\(989\) | −17.6941 | −0.562639 | ||||||||
\(990\) | 7.82140 | 0.248580 | ||||||||
\(991\) | −41.6746 | −1.32384 | −0.661919 | − | 0.749576i | \(-0.730258\pi\) | ||||
−0.661919 | + | 0.749576i | \(0.730258\pi\) | |||||||
\(992\) | −44.8668 | −1.42452 | ||||||||
\(993\) | 9.42272 | 0.299021 | ||||||||
\(994\) | −77.5746 | −2.46052 | ||||||||
\(995\) | −40.7058 | −1.29046 | ||||||||
\(996\) | −63.4764 | −2.01133 | ||||||||
\(997\) | −21.4095 | −0.678045 | −0.339022 | − | 0.940778i | \(-0.610096\pi\) | ||||
−0.339022 | + | 0.940778i | \(0.610096\pi\) | |||||||
\(998\) | 85.4807 | 2.70585 | ||||||||
\(999\) | −1.03093 | −0.0326173 |
(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.j.1.4 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.4 | ✓ | 64 | 1.1 | even | 1 | trivial |