Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.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: | \(64.1597980241\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71845 | −1.92223 | −0.961117 | − | 0.276142i | \(-0.910944\pi\) | ||||
−0.961117 | + | 0.276142i | \(0.910944\pi\) | |||||||
\(3\) | −0.706981 | −0.408176 | −0.204088 | − | 0.978953i | \(-0.565423\pi\) | ||||
−0.204088 | + | 0.978953i | \(0.565423\pi\) | |||||||
\(4\) | 5.38997 | 2.69498 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.92189 | 0.784609 | ||||||||
\(7\) | −1.47518 | −0.557567 | −0.278784 | − | 0.960354i | \(-0.589931\pi\) | ||||
−0.278784 | + | 0.960354i | \(0.589931\pi\) | |||||||
\(8\) | −9.21545 | −3.25815 | ||||||||
\(9\) | −2.50018 | −0.833393 | ||||||||
\(10\) | −2.71845 | −0.859649 | ||||||||
\(11\) | −4.87853 | −1.47093 | −0.735466 | − | 0.677562i | \(-0.763037\pi\) | ||||
−0.735466 | + | 0.677562i | \(0.763037\pi\) | |||||||
\(12\) | −3.81061 | −1.10003 | ||||||||
\(13\) | 1.58069 | 0.438404 | 0.219202 | − | 0.975679i | \(-0.429655\pi\) | ||||
0.219202 | + | 0.975679i | \(0.429655\pi\) | |||||||
\(14\) | 4.01021 | 1.07177 | ||||||||
\(15\) | −0.706981 | −0.182542 | ||||||||
\(16\) | 14.2718 | 3.56795 | ||||||||
\(17\) | −5.03382 | −1.22088 | −0.610440 | − | 0.792062i | \(-0.709008\pi\) | ||||
−0.610440 | + | 0.792062i | \(0.709008\pi\) | |||||||
\(18\) | 6.79661 | 1.60198 | ||||||||
\(19\) | 0.358119 | 0.0821581 | 0.0410791 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410791 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(20\) | 5.38997 | 1.20523 | ||||||||
\(21\) | 1.04293 | 0.227585 | ||||||||
\(22\) | 13.2620 | 2.82748 | ||||||||
\(23\) | 5.10498 | 1.06446 | 0.532230 | − | 0.846600i | \(-0.321354\pi\) | ||||
0.532230 | + | 0.846600i | \(0.321354\pi\) | |||||||
\(24\) | 6.51515 | 1.32990 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.29702 | −0.842715 | ||||||||
\(27\) | 3.88852 | 0.748346 | ||||||||
\(28\) | −7.95119 | −1.50263 | ||||||||
\(29\) | −1.87684 | −0.348521 | −0.174261 | − | 0.984700i | \(-0.555753\pi\) | ||||
−0.174261 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(30\) | 1.92189 | 0.350888 | ||||||||
\(31\) | −3.56650 | −0.640563 | −0.320281 | − | 0.947322i | \(-0.603777\pi\) | ||||
−0.320281 | + | 0.947322i | \(0.603777\pi\) | |||||||
\(32\) | −20.3663 | −3.60028 | ||||||||
\(33\) | 3.44903 | 0.600399 | ||||||||
\(34\) | 13.6842 | 2.34682 | ||||||||
\(35\) | −1.47518 | −0.249352 | ||||||||
\(36\) | −13.4759 | −2.24598 | ||||||||
\(37\) | 9.21989 | 1.51574 | 0.757870 | − | 0.652405i | \(-0.226240\pi\) | ||||
0.757870 | + | 0.652405i | \(0.226240\pi\) | |||||||
\(38\) | −0.973528 | −0.157927 | ||||||||
\(39\) | −1.11752 | −0.178946 | ||||||||
\(40\) | −9.21545 | −1.45709 | ||||||||
\(41\) | −7.76168 | −1.21217 | −0.606085 | − | 0.795400i | \(-0.707261\pi\) | ||||
−0.606085 | + | 0.795400i | \(0.707261\pi\) | |||||||
\(42\) | −2.83514 | −0.437472 | ||||||||
\(43\) | 1.91236 | 0.291633 | 0.145816 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145816 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(44\) | −26.2951 | −3.96414 | ||||||||
\(45\) | −2.50018 | −0.372704 | ||||||||
\(46\) | −13.8776 | −2.04614 | ||||||||
\(47\) | −5.66005 | −0.825603 | −0.412801 | − | 0.910821i | \(-0.635450\pi\) | ||||
−0.412801 | + | 0.910821i | \(0.635450\pi\) | |||||||
\(48\) | −10.0899 | −1.45635 | ||||||||
\(49\) | −4.82383 | −0.689119 | ||||||||
\(50\) | −2.71845 | −0.384447 | ||||||||
\(51\) | 3.55882 | 0.498334 | ||||||||
\(52\) | 8.51986 | 1.18149 | ||||||||
\(53\) | 11.8097 | 1.62218 | 0.811092 | − | 0.584919i | \(-0.198874\pi\) | ||||
0.811092 | + | 0.584919i | \(0.198874\pi\) | |||||||
\(54\) | −10.5708 | −1.43850 | ||||||||
\(55\) | −4.87853 | −0.657821 | ||||||||
\(56\) | 13.5945 | 1.81664 | ||||||||
\(57\) | −0.253183 | −0.0335350 | ||||||||
\(58\) | 5.10210 | 0.669939 | ||||||||
\(59\) | 8.68911 | 1.13123 | 0.565613 | − | 0.824671i | \(-0.308640\pi\) | ||||
0.565613 | + | 0.824671i | \(0.308640\pi\) | |||||||
\(60\) | −3.81061 | −0.491947 | ||||||||
\(61\) | 0.0576245 | 0.00737806 | 0.00368903 | − | 0.999993i | \(-0.498826\pi\) | ||||
0.00368903 | + | 0.999993i | \(0.498826\pi\) | |||||||
\(62\) | 9.69536 | 1.23131 | ||||||||
\(63\) | 3.68822 | 0.464672 | ||||||||
\(64\) | 26.8211 | 3.35264 | ||||||||
\(65\) | 1.58069 | 0.196060 | ||||||||
\(66\) | −9.37601 | −1.15411 | ||||||||
\(67\) | 12.8902 | 1.57479 | 0.787397 | − | 0.616447i | \(-0.211428\pi\) | ||||
0.787397 | + | 0.616447i | \(0.211428\pi\) | |||||||
\(68\) | −27.1321 | −3.29025 | ||||||||
\(69\) | −3.60912 | −0.434487 | ||||||||
\(70\) | 4.01021 | 0.479312 | ||||||||
\(71\) | 5.72097 | 0.678955 | 0.339477 | − | 0.940614i | \(-0.389750\pi\) | ||||
0.339477 | + | 0.940614i | \(0.389750\pi\) | |||||||
\(72\) | 23.0403 | 2.71532 | ||||||||
\(73\) | 4.17106 | 0.488186 | 0.244093 | − | 0.969752i | \(-0.421510\pi\) | ||||
0.244093 | + | 0.969752i | \(0.421510\pi\) | |||||||
\(74\) | −25.0638 | −2.91361 | ||||||||
\(75\) | −0.706981 | −0.0816352 | ||||||||
\(76\) | 1.93025 | 0.221415 | ||||||||
\(77\) | 7.19673 | 0.820143 | ||||||||
\(78\) | 3.03791 | 0.343976 | ||||||||
\(79\) | 5.96417 | 0.671021 | 0.335511 | − | 0.942036i | \(-0.391091\pi\) | ||||
0.335511 | + | 0.942036i | \(0.391091\pi\) | |||||||
\(80\) | 14.2718 | 1.59564 | ||||||||
\(81\) | 4.75142 | 0.527936 | ||||||||
\(82\) | 21.0997 | 2.33007 | ||||||||
\(83\) | −6.35712 | −0.697784 | −0.348892 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348892 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(84\) | 5.62134 | 0.613339 | ||||||||
\(85\) | −5.03382 | −0.545995 | ||||||||
\(86\) | −5.19866 | −0.560586 | ||||||||
\(87\) | 1.32689 | 0.142258 | ||||||||
\(88\) | 44.9579 | 4.79252 | ||||||||
\(89\) | 13.2929 | 1.40905 | 0.704524 | − | 0.709680i | \(-0.251161\pi\) | ||||
0.704524 | + | 0.709680i | \(0.251161\pi\) | |||||||
\(90\) | 6.79661 | 0.716425 | ||||||||
\(91\) | −2.33181 | −0.244440 | ||||||||
\(92\) | 27.5156 | 2.86870 | ||||||||
\(93\) | 2.52145 | 0.261462 | ||||||||
\(94\) | 15.3865 | 1.58700 | ||||||||
\(95\) | 0.358119 | 0.0367422 | ||||||||
\(96\) | 14.3986 | 1.46955 | ||||||||
\(97\) | −0.185315 | −0.0188159 | −0.00940795 | − | 0.999956i | \(-0.502995\pi\) | ||||
−0.00940795 | + | 0.999956i | \(0.502995\pi\) | |||||||
\(98\) | 13.1133 | 1.32465 | ||||||||
\(99\) | 12.1972 | 1.22586 | ||||||||
\(100\) | 5.38997 | 0.538997 | ||||||||
\(101\) | −15.8166 | −1.57381 | −0.786906 | − | 0.617072i | \(-0.788319\pi\) | ||||
−0.786906 | + | 0.617072i | \(0.788319\pi\) | |||||||
\(102\) | −9.67446 | −0.957915 | ||||||||
\(103\) | 7.77860 | 0.766449 | 0.383224 | − | 0.923655i | \(-0.374814\pi\) | ||||
0.383224 | + | 0.923655i | \(0.374814\pi\) | |||||||
\(104\) | −14.5668 | −1.42839 | ||||||||
\(105\) | 1.04293 | 0.101779 | ||||||||
\(106\) | −32.1040 | −3.11822 | ||||||||
\(107\) | −9.70917 | −0.938621 | −0.469310 | − | 0.883033i | \(-0.655497\pi\) | ||||
−0.469310 | + | 0.883033i | \(0.655497\pi\) | |||||||
\(108\) | 20.9590 | 2.01678 | ||||||||
\(109\) | 4.65543 | 0.445910 | 0.222955 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222955 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(110\) | 13.2620 | 1.26449 | ||||||||
\(111\) | −6.51829 | −0.618689 | ||||||||
\(112\) | −21.0535 | −1.98937 | ||||||||
\(113\) | 6.86268 | 0.645587 | 0.322793 | − | 0.946469i | \(-0.395378\pi\) | ||||
0.322793 | + | 0.946469i | \(0.395378\pi\) | |||||||
\(114\) | 0.688266 | 0.0644620 | ||||||||
\(115\) | 5.10498 | 0.476041 | ||||||||
\(116\) | −10.1161 | −0.939258 | ||||||||
\(117\) | −3.95200 | −0.365363 | ||||||||
\(118\) | −23.6209 | −2.17448 | ||||||||
\(119\) | 7.42581 | 0.680723 | ||||||||
\(120\) | 6.51515 | 0.594749 | ||||||||
\(121\) | 12.8001 | 1.16364 | ||||||||
\(122\) | −0.156649 | −0.0141823 | ||||||||
\(123\) | 5.48736 | 0.494779 | ||||||||
\(124\) | −19.2233 | −1.72631 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −10.0262 | −0.893209 | ||||||||
\(127\) | 3.18545 | 0.282663 | 0.141332 | − | 0.989962i | \(-0.454862\pi\) | ||||
0.141332 | + | 0.989962i | \(0.454862\pi\) | |||||||
\(128\) | −32.1792 | −2.84427 | ||||||||
\(129\) | −1.35201 | −0.119037 | ||||||||
\(130\) | −4.29702 | −0.376874 | ||||||||
\(131\) | 6.42824 | 0.561638 | 0.280819 | − | 0.959761i | \(-0.409394\pi\) | ||||
0.280819 | + | 0.959761i | \(0.409394\pi\) | |||||||
\(132\) | 18.5902 | 1.61807 | ||||||||
\(133\) | −0.528291 | −0.0458087 | ||||||||
\(134\) | −35.0415 | −3.02712 | ||||||||
\(135\) | 3.88852 | 0.334671 | ||||||||
\(136\) | 46.3889 | 3.97782 | ||||||||
\(137\) | 14.1747 | 1.21102 | 0.605512 | − | 0.795836i | \(-0.292968\pi\) | ||||
0.605512 | + | 0.795836i | \(0.292968\pi\) | |||||||
\(138\) | 9.81121 | 0.835186 | ||||||||
\(139\) | 3.84558 | 0.326178 | 0.163089 | − | 0.986611i | \(-0.447854\pi\) | ||||
0.163089 | + | 0.986611i | \(0.447854\pi\) | |||||||
\(140\) | −7.95119 | −0.671998 | ||||||||
\(141\) | 4.00155 | 0.336991 | ||||||||
\(142\) | −15.5522 | −1.30511 | ||||||||
\(143\) | −7.71144 | −0.644863 | ||||||||
\(144\) | −35.6821 | −2.97350 | ||||||||
\(145\) | −1.87684 | −0.155863 | ||||||||
\(146\) | −11.3388 | −0.938407 | ||||||||
\(147\) | 3.41036 | 0.281282 | ||||||||
\(148\) | 49.6949 | 4.08490 | ||||||||
\(149\) | −24.0900 | −1.97353 | −0.986763 | − | 0.162166i | \(-0.948152\pi\) | ||||
−0.986763 | + | 0.162166i | \(0.948152\pi\) | |||||||
\(150\) | 1.92189 | 0.156922 | ||||||||
\(151\) | −3.04298 | −0.247634 | −0.123817 | − | 0.992305i | \(-0.539514\pi\) | ||||
−0.123817 | + | 0.992305i | \(0.539514\pi\) | |||||||
\(152\) | −3.30023 | −0.267684 | ||||||||
\(153\) | 12.5854 | 1.01747 | ||||||||
\(154\) | −19.5639 | −1.57651 | ||||||||
\(155\) | −3.56650 | −0.286468 | ||||||||
\(156\) | −6.02338 | −0.482256 | ||||||||
\(157\) | −23.1326 | −1.84618 | −0.923091 | − | 0.384581i | \(-0.874346\pi\) | ||||
−0.923091 | + | 0.384581i | \(0.874346\pi\) | |||||||
\(158\) | −16.2133 | −1.28986 | ||||||||
\(159\) | −8.34922 | −0.662136 | ||||||||
\(160\) | −20.3663 | −1.61010 | ||||||||
\(161\) | −7.53078 | −0.593508 | ||||||||
\(162\) | −12.9165 | −1.01482 | ||||||||
\(163\) | −8.18237 | −0.640892 | −0.320446 | − | 0.947267i | \(-0.603833\pi\) | ||||
−0.320446 | + | 0.947267i | \(0.603833\pi\) | |||||||
\(164\) | −41.8352 | −3.26678 | ||||||||
\(165\) | 3.44903 | 0.268507 | ||||||||
\(166\) | 17.2815 | 1.34130 | ||||||||
\(167\) | −6.93143 | −0.536370 | −0.268185 | − | 0.963367i | \(-0.586424\pi\) | ||||
−0.268185 | + | 0.963367i | \(0.586424\pi\) | |||||||
\(168\) | −9.61105 | −0.741508 | ||||||||
\(169\) | −10.5014 | −0.807802 | ||||||||
\(170\) | 13.6842 | 1.04953 | ||||||||
\(171\) | −0.895361 | −0.0684700 | ||||||||
\(172\) | 10.3076 | 0.785945 | ||||||||
\(173\) | −1.39886 | −0.106354 | −0.0531768 | − | 0.998585i | \(-0.516935\pi\) | ||||
−0.0531768 | + | 0.998585i | \(0.516935\pi\) | |||||||
\(174\) | −3.60709 | −0.273453 | ||||||||
\(175\) | −1.47518 | −0.111513 | ||||||||
\(176\) | −69.6254 | −5.24822 | ||||||||
\(177\) | −6.14304 | −0.461739 | ||||||||
\(178\) | −36.1362 | −2.70852 | ||||||||
\(179\) | 11.4579 | 0.856407 | 0.428203 | − | 0.903682i | \(-0.359147\pi\) | ||||
0.428203 | + | 0.903682i | \(0.359147\pi\) | |||||||
\(180\) | −13.4759 | −1.00443 | ||||||||
\(181\) | 17.9619 | 1.33510 | 0.667550 | − | 0.744565i | \(-0.267343\pi\) | ||||
0.667550 | + | 0.744565i | \(0.267343\pi\) | |||||||
\(182\) | 6.33890 | 0.469870 | ||||||||
\(183\) | −0.0407394 | −0.00301154 | ||||||||
\(184\) | −47.0447 | −3.46818 | ||||||||
\(185\) | 9.21989 | 0.677860 | ||||||||
\(186\) | −6.85444 | −0.502592 | ||||||||
\(187\) | 24.5576 | 1.79583 | ||||||||
\(188\) | −30.5075 | −2.22499 | ||||||||
\(189\) | −5.73628 | −0.417253 | ||||||||
\(190\) | −0.973528 | −0.0706272 | ||||||||
\(191\) | −23.4796 | −1.69893 | −0.849463 | − | 0.527647i | \(-0.823074\pi\) | ||||
−0.849463 | + | 0.527647i | \(0.823074\pi\) | |||||||
\(192\) | −18.9620 | −1.36846 | ||||||||
\(193\) | 13.9732 | 1.00581 | 0.502906 | − | 0.864341i | \(-0.332264\pi\) | ||||
0.502906 | + | 0.864341i | \(0.332264\pi\) | |||||||
\(194\) | 0.503770 | 0.0361686 | ||||||||
\(195\) | −1.11752 | −0.0800271 | ||||||||
\(196\) | −26.0003 | −1.85716 | ||||||||
\(197\) | 21.7177 | 1.54732 | 0.773659 | − | 0.633602i | \(-0.218424\pi\) | ||||
0.773659 | + | 0.633602i | \(0.218424\pi\) | |||||||
\(198\) | −33.1574 | −2.35640 | ||||||||
\(199\) | −17.7517 | −1.25839 | −0.629194 | − | 0.777248i | \(-0.716615\pi\) | ||||
−0.629194 | + | 0.777248i | \(0.716615\pi\) | |||||||
\(200\) | −9.21545 | −0.651631 | ||||||||
\(201\) | −9.11316 | −0.642792 | ||||||||
\(202\) | 42.9967 | 3.02524 | ||||||||
\(203\) | 2.76869 | 0.194324 | ||||||||
\(204\) | 19.1819 | 1.34300 | ||||||||
\(205\) | −7.76168 | −0.542099 | ||||||||
\(206\) | −21.1457 | −1.47329 | ||||||||
\(207\) | −12.7633 | −0.887114 | ||||||||
\(208\) | 22.5593 | 1.56420 | ||||||||
\(209\) | −1.74709 | −0.120849 | ||||||||
\(210\) | −2.83514 | −0.195644 | ||||||||
\(211\) | −6.92206 | −0.476534 | −0.238267 | − | 0.971200i | \(-0.576579\pi\) | ||||
−0.238267 | + | 0.971200i | \(0.576579\pi\) | |||||||
\(212\) | 63.6538 | 4.37176 | ||||||||
\(213\) | −4.04462 | −0.277133 | ||||||||
\(214\) | 26.3939 | 1.80425 | ||||||||
\(215\) | 1.91236 | 0.130422 | ||||||||
\(216\) | −35.8345 | −2.43823 | ||||||||
\(217\) | 5.26125 | 0.357157 | ||||||||
\(218\) | −12.6556 | −0.857142 | ||||||||
\(219\) | −2.94886 | −0.199266 | ||||||||
\(220\) | −26.2951 | −1.77282 | ||||||||
\(221\) | −7.95690 | −0.535239 | ||||||||
\(222\) | 17.7196 | 1.18926 | ||||||||
\(223\) | 20.7086 | 1.38675 | 0.693376 | − | 0.720576i | \(-0.256123\pi\) | ||||
0.693376 | + | 0.720576i | \(0.256123\pi\) | |||||||
\(224\) | 30.0440 | 2.00740 | ||||||||
\(225\) | −2.50018 | −0.166679 | ||||||||
\(226\) | −18.6559 | −1.24097 | ||||||||
\(227\) | 9.38692 | 0.623032 | 0.311516 | − | 0.950241i | \(-0.399163\pi\) | ||||
0.311516 | + | 0.950241i | \(0.399163\pi\) | |||||||
\(228\) | −1.36465 | −0.0903762 | ||||||||
\(229\) | −17.5332 | −1.15863 | −0.579313 | − | 0.815105i | \(-0.696679\pi\) | ||||
−0.579313 | + | 0.815105i | \(0.696679\pi\) | |||||||
\(230\) | −13.8776 | −0.915063 | ||||||||
\(231\) | −5.08795 | −0.334763 | ||||||||
\(232\) | 17.2960 | 1.13554 | ||||||||
\(233\) | −6.11022 | −0.400294 | −0.200147 | − | 0.979766i | \(-0.564142\pi\) | ||||
−0.200147 | + | 0.979766i | \(0.564142\pi\) | |||||||
\(234\) | 10.7433 | 0.702313 | ||||||||
\(235\) | −5.66005 | −0.369221 | ||||||||
\(236\) | 46.8340 | 3.04864 | ||||||||
\(237\) | −4.21656 | −0.273895 | ||||||||
\(238\) | −20.1867 | −1.30851 | ||||||||
\(239\) | −6.07982 | −0.393271 | −0.196635 | − | 0.980477i | \(-0.563001\pi\) | ||||
−0.196635 | + | 0.980477i | \(0.563001\pi\) | |||||||
\(240\) | −10.0899 | −0.651300 | ||||||||
\(241\) | 10.0879 | 0.649818 | 0.324909 | − | 0.945745i | \(-0.394666\pi\) | ||||
0.324909 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(242\) | −34.7963 | −2.23679 | ||||||||
\(243\) | −15.0247 | −0.963837 | ||||||||
\(244\) | 0.310594 | 0.0198837 | ||||||||
\(245\) | −4.82383 | −0.308183 | ||||||||
\(246\) | −14.9171 | −0.951080 | ||||||||
\(247\) | 0.566074 | 0.0360185 | ||||||||
\(248\) | 32.8669 | 2.08705 | ||||||||
\(249\) | 4.49436 | 0.284819 | ||||||||
\(250\) | −2.71845 | −0.171930 | ||||||||
\(251\) | −13.7874 | −0.870250 | −0.435125 | − | 0.900370i | \(-0.643296\pi\) | ||||
−0.435125 | + | 0.900370i | \(0.643296\pi\) | |||||||
\(252\) | 19.8794 | 1.25228 | ||||||||
\(253\) | −24.9048 | −1.56575 | ||||||||
\(254\) | −8.65949 | −0.543345 | ||||||||
\(255\) | 3.55882 | 0.222862 | ||||||||
\(256\) | 33.8354 | 2.11471 | ||||||||
\(257\) | −10.7739 | −0.672060 | −0.336030 | − | 0.941851i | \(-0.609084\pi\) | ||||
−0.336030 | + | 0.941851i | \(0.609084\pi\) | |||||||
\(258\) | 3.67536 | 0.228818 | ||||||||
\(259\) | −13.6010 | −0.845127 | ||||||||
\(260\) | 8.51986 | 0.528379 | ||||||||
\(261\) | 4.69244 | 0.290455 | ||||||||
\(262\) | −17.4749 | −1.07960 | ||||||||
\(263\) | −4.40182 | −0.271428 | −0.135714 | − | 0.990748i | \(-0.543333\pi\) | ||||
−0.135714 | + | 0.990748i | \(0.543333\pi\) | |||||||
\(264\) | −31.7844 | −1.95619 | ||||||||
\(265\) | 11.8097 | 0.725463 | ||||||||
\(266\) | 1.43613 | 0.0880550 | ||||||||
\(267\) | −9.39785 | −0.575139 | ||||||||
\(268\) | 69.4780 | 4.24404 | ||||||||
\(269\) | 25.1991 | 1.53642 | 0.768209 | − | 0.640200i | \(-0.221148\pi\) | ||||
0.768209 | + | 0.640200i | \(0.221148\pi\) | |||||||
\(270\) | −10.5708 | −0.643315 | ||||||||
\(271\) | −15.3734 | −0.933867 | −0.466933 | − | 0.884292i | \(-0.654641\pi\) | ||||
−0.466933 | + | 0.884292i | \(0.654641\pi\) | |||||||
\(272\) | −71.8417 | −4.35604 | ||||||||
\(273\) | 1.64854 | 0.0997744 | ||||||||
\(274\) | −38.5331 | −2.32787 | ||||||||
\(275\) | −4.87853 | −0.294186 | ||||||||
\(276\) | −19.4530 | −1.17094 | ||||||||
\(277\) | −7.92769 | −0.476329 | −0.238164 | − | 0.971225i | \(-0.576546\pi\) | ||||
−0.238164 | + | 0.971225i | \(0.576546\pi\) | |||||||
\(278\) | −10.4540 | −0.626990 | ||||||||
\(279\) | 8.91689 | 0.533840 | ||||||||
\(280\) | 13.5945 | 0.812426 | ||||||||
\(281\) | −19.7785 | −1.17989 | −0.589943 | − | 0.807445i | \(-0.700850\pi\) | ||||
−0.589943 | + | 0.807445i | \(0.700850\pi\) | |||||||
\(282\) | −10.8780 | −0.647775 | ||||||||
\(283\) | 22.0446 | 1.31042 | 0.655209 | − | 0.755448i | \(-0.272581\pi\) | ||||
0.655209 | + | 0.755448i | \(0.272581\pi\) | |||||||
\(284\) | 30.8359 | 1.82977 | ||||||||
\(285\) | −0.253183 | −0.0149973 | ||||||||
\(286\) | 20.9631 | 1.23958 | ||||||||
\(287\) | 11.4499 | 0.675866 | ||||||||
\(288\) | 50.9193 | 3.00045 | ||||||||
\(289\) | 8.33935 | 0.490550 | ||||||||
\(290\) | 5.10210 | 0.299606 | ||||||||
\(291\) | 0.131014 | 0.00768020 | ||||||||
\(292\) | 22.4819 | 1.31565 | ||||||||
\(293\) | −11.6646 | −0.681455 | −0.340728 | − | 0.940162i | \(-0.610673\pi\) | ||||
−0.340728 | + | 0.940162i | \(0.610673\pi\) | |||||||
\(294\) | −9.27089 | −0.540689 | ||||||||
\(295\) | 8.68911 | 0.505900 | ||||||||
\(296\) | −84.9655 | −4.93852 | ||||||||
\(297\) | −18.9703 | −1.10077 | ||||||||
\(298\) | 65.4874 | 3.79358 | ||||||||
\(299\) | 8.06938 | 0.466664 | ||||||||
\(300\) | −3.81061 | −0.220005 | ||||||||
\(301\) | −2.82109 | −0.162605 | ||||||||
\(302\) | 8.27219 | 0.476011 | ||||||||
\(303\) | 11.1821 | 0.642392 | ||||||||
\(304\) | 5.11100 | 0.293136 | ||||||||
\(305\) | 0.0576245 | 0.00329957 | ||||||||
\(306\) | −34.2129 | −1.95582 | ||||||||
\(307\) | −8.49400 | −0.484778 | −0.242389 | − | 0.970179i | \(-0.577931\pi\) | ||||
−0.242389 | + | 0.970179i | \(0.577931\pi\) | |||||||
\(308\) | 38.7901 | 2.21027 | ||||||||
\(309\) | −5.49933 | −0.312846 | ||||||||
\(310\) | 9.69536 | 0.550659 | ||||||||
\(311\) | −8.53645 | −0.484058 | −0.242029 | − | 0.970269i | \(-0.577813\pi\) | ||||
−0.242029 | + | 0.970269i | \(0.577813\pi\) | |||||||
\(312\) | 10.2984 | 0.583034 | ||||||||
\(313\) | −22.9002 | −1.29440 | −0.647198 | − | 0.762322i | \(-0.724059\pi\) | ||||
−0.647198 | + | 0.762322i | \(0.724059\pi\) | |||||||
\(314\) | 62.8848 | 3.54879 | ||||||||
\(315\) | 3.68822 | 0.207808 | ||||||||
\(316\) | 32.1467 | 1.80839 | ||||||||
\(317\) | −17.8009 | −0.999797 | −0.499898 | − | 0.866084i | \(-0.666629\pi\) | ||||
−0.499898 | + | 0.866084i | \(0.666629\pi\) | |||||||
\(318\) | 22.6969 | 1.27278 | ||||||||
\(319\) | 9.15624 | 0.512651 | ||||||||
\(320\) | 26.8211 | 1.49934 | ||||||||
\(321\) | 6.86420 | 0.383122 | ||||||||
\(322\) | 20.4720 | 1.14086 | ||||||||
\(323\) | −1.80271 | −0.100305 | ||||||||
\(324\) | 25.6100 | 1.42278 | ||||||||
\(325\) | 1.58069 | 0.0876808 | ||||||||
\(326\) | 22.2433 | 1.23195 | ||||||||
\(327\) | −3.29130 | −0.182009 | ||||||||
\(328\) | 71.5274 | 3.94944 | ||||||||
\(329\) | 8.34961 | 0.460329 | ||||||||
\(330\) | −9.37601 | −0.516132 | ||||||||
\(331\) | 19.1065 | 1.05019 | 0.525094 | − | 0.851044i | \(-0.324030\pi\) | ||||
0.525094 | + | 0.851044i | \(0.324030\pi\) | |||||||
\(332\) | −34.2646 | −1.88052 | ||||||||
\(333\) | −23.0514 | −1.26321 | ||||||||
\(334\) | 18.8427 | 1.03103 | ||||||||
\(335\) | 12.8902 | 0.704269 | ||||||||
\(336\) | 14.8845 | 0.812014 | ||||||||
\(337\) | −31.4061 | −1.71080 | −0.855400 | − | 0.517968i | \(-0.826689\pi\) | ||||
−0.855400 | + | 0.517968i | \(0.826689\pi\) | |||||||
\(338\) | 28.5476 | 1.55278 | ||||||||
\(339\) | −4.85179 | −0.263513 | ||||||||
\(340\) | −27.1321 | −1.47145 | ||||||||
\(341\) | 17.3993 | 0.942225 | ||||||||
\(342\) | 2.43399 | 0.131615 | ||||||||
\(343\) | 17.4423 | 0.941797 | ||||||||
\(344\) | −17.6233 | −0.950184 | ||||||||
\(345\) | −3.60912 | −0.194309 | ||||||||
\(346\) | 3.80274 | 0.204437 | ||||||||
\(347\) | 25.2009 | 1.35286 | 0.676429 | − | 0.736508i | \(-0.263527\pi\) | ||||
0.676429 | + | 0.736508i | \(0.263527\pi\) | |||||||
\(348\) | 7.15191 | 0.383383 | ||||||||
\(349\) | 28.5847 | 1.53010 | 0.765051 | − | 0.643970i | \(-0.222714\pi\) | ||||
0.765051 | + | 0.643970i | \(0.222714\pi\) | |||||||
\(350\) | 4.01021 | 0.214355 | ||||||||
\(351\) | 6.14654 | 0.328078 | ||||||||
\(352\) | 99.3575 | 5.29577 | ||||||||
\(353\) | −18.5979 | −0.989868 | −0.494934 | − | 0.868931i | \(-0.664808\pi\) | ||||
−0.494934 | + | 0.868931i | \(0.664808\pi\) | |||||||
\(354\) | 16.6995 | 0.887571 | ||||||||
\(355\) | 5.72097 | 0.303638 | ||||||||
\(356\) | 71.6484 | 3.79736 | ||||||||
\(357\) | −5.24991 | −0.277855 | ||||||||
\(358\) | −31.1478 | −1.64621 | ||||||||
\(359\) | 7.82272 | 0.412868 | 0.206434 | − | 0.978461i | \(-0.433814\pi\) | ||||
0.206434 | + | 0.978461i | \(0.433814\pi\) | |||||||
\(360\) | 23.0403 | 1.21433 | ||||||||
\(361\) | −18.8718 | −0.993250 | ||||||||
\(362\) | −48.8286 | −2.56638 | ||||||||
\(363\) | −9.04940 | −0.474970 | ||||||||
\(364\) | −12.5684 | −0.658761 | ||||||||
\(365\) | 4.17106 | 0.218323 | ||||||||
\(366\) | 0.110748 | 0.00578889 | ||||||||
\(367\) | −14.3950 | −0.751415 | −0.375708 | − | 0.926738i | \(-0.622600\pi\) | ||||
−0.375708 | + | 0.926738i | \(0.622600\pi\) | |||||||
\(368\) | 72.8572 | 3.79795 | ||||||||
\(369\) | 19.4056 | 1.01021 | ||||||||
\(370\) | −25.0638 | −1.30300 | ||||||||
\(371\) | −17.4214 | −0.904476 | ||||||||
\(372\) | 13.5905 | 0.704636 | ||||||||
\(373\) | −33.1214 | −1.71496 | −0.857480 | − | 0.514517i | \(-0.827971\pi\) | ||||
−0.857480 | + | 0.514517i | \(0.827971\pi\) | |||||||
\(374\) | −66.7587 | −3.45201 | ||||||||
\(375\) | −0.706981 | −0.0365084 | ||||||||
\(376\) | 52.1599 | 2.68994 | ||||||||
\(377\) | −2.96670 | −0.152793 | ||||||||
\(378\) | 15.5938 | 0.802058 | ||||||||
\(379\) | −3.04761 | −0.156545 | −0.0782725 | − | 0.996932i | \(-0.524940\pi\) | ||||
−0.0782725 | + | 0.996932i | \(0.524940\pi\) | |||||||
\(380\) | 1.93025 | 0.0990197 | ||||||||
\(381\) | −2.25206 | −0.115376 | ||||||||
\(382\) | 63.8282 | 3.26574 | ||||||||
\(383\) | −16.8503 | −0.861010 | −0.430505 | − | 0.902588i | \(-0.641664\pi\) | ||||
−0.430505 | + | 0.902588i | \(0.641664\pi\) | |||||||
\(384\) | 22.7501 | 1.16096 | ||||||||
\(385\) | 7.19673 | 0.366779 | ||||||||
\(386\) | −37.9854 | −1.93341 | ||||||||
\(387\) | −4.78125 | −0.243044 | ||||||||
\(388\) | −0.998842 | −0.0507085 | ||||||||
\(389\) | 30.5264 | 1.54775 | 0.773876 | − | 0.633337i | \(-0.218315\pi\) | ||||
0.773876 | + | 0.633337i | \(0.218315\pi\) | |||||||
\(390\) | 3.03791 | 0.153831 | ||||||||
\(391\) | −25.6975 | −1.29958 | ||||||||
\(392\) | 44.4538 | 2.24526 | ||||||||
\(393\) | −4.54465 | −0.229247 | ||||||||
\(394\) | −59.0383 | −2.97431 | ||||||||
\(395\) | 5.96417 | 0.300090 | ||||||||
\(396\) | 65.7425 | 3.30368 | ||||||||
\(397\) | 23.0646 | 1.15758 | 0.578790 | − | 0.815476i | \(-0.303525\pi\) | ||||
0.578790 | + | 0.815476i | \(0.303525\pi\) | |||||||
\(398\) | 48.2572 | 2.41892 | ||||||||
\(399\) | 0.373492 | 0.0186980 | ||||||||
\(400\) | 14.2718 | 0.713590 | ||||||||
\(401\) | −1.86876 | −0.0933216 | −0.0466608 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466608 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(402\) | 24.7737 | 1.23560 | ||||||||
\(403\) | −5.63753 | −0.280825 | ||||||||
\(404\) | −85.2511 | −4.24140 | ||||||||
\(405\) | 4.75142 | 0.236100 | ||||||||
\(406\) | −7.52654 | −0.373536 | ||||||||
\(407\) | −44.9795 | −2.22955 | ||||||||
\(408\) | −32.7961 | −1.62365 | ||||||||
\(409\) | −23.0063 | −1.13759 | −0.568795 | − | 0.822479i | \(-0.692590\pi\) | ||||
−0.568795 | + | 0.822479i | \(0.692590\pi\) | |||||||
\(410\) | 21.0997 | 1.04204 | ||||||||
\(411\) | −10.0212 | −0.494311 | ||||||||
\(412\) | 41.9264 | 2.06557 | ||||||||
\(413\) | −12.8180 | −0.630734 | ||||||||
\(414\) | 34.6965 | 1.70524 | ||||||||
\(415\) | −6.35712 | −0.312059 | ||||||||
\(416\) | −32.1927 | −1.57838 | ||||||||
\(417\) | −2.71875 | −0.133138 | ||||||||
\(418\) | 4.74939 | 0.232300 | ||||||||
\(419\) | 8.45864 | 0.413231 | 0.206616 | − | 0.978422i | \(-0.433755\pi\) | ||||
0.206616 | + | 0.978422i | \(0.433755\pi\) | |||||||
\(420\) | 5.62134 | 0.274293 | ||||||||
\(421\) | 13.2311 | 0.644846 | 0.322423 | − | 0.946596i | \(-0.395503\pi\) | ||||
0.322423 | + | 0.946596i | \(0.395503\pi\) | |||||||
\(422\) | 18.8173 | 0.916010 | ||||||||
\(423\) | 14.1511 | 0.688051 | ||||||||
\(424\) | −108.832 | −5.28533 | ||||||||
\(425\) | −5.03382 | −0.244176 | ||||||||
\(426\) | 10.9951 | 0.532714 | ||||||||
\(427\) | −0.0850067 | −0.00411376 | ||||||||
\(428\) | −52.3321 | −2.52957 | ||||||||
\(429\) | 5.45184 | 0.263217 | ||||||||
\(430\) | −5.19866 | −0.250702 | ||||||||
\(431\) | −24.5279 | −1.18147 | −0.590733 | − | 0.806867i | \(-0.701161\pi\) | ||||
−0.590733 | + | 0.806867i | \(0.701161\pi\) | |||||||
\(432\) | 55.4962 | 2.67006 | ||||||||
\(433\) | −6.48827 | −0.311806 | −0.155903 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155903 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(434\) | −14.3024 | −0.686539 | ||||||||
\(435\) | 1.32689 | 0.0636197 | ||||||||
\(436\) | 25.0926 | 1.20172 | ||||||||
\(437\) | 1.82819 | 0.0874541 | ||||||||
\(438\) | 8.01633 | 0.383035 | ||||||||
\(439\) | 19.5977 | 0.935347 | 0.467673 | − | 0.883901i | \(-0.345092\pi\) | ||||
0.467673 | + | 0.883901i | \(0.345092\pi\) | |||||||
\(440\) | 44.9579 | 2.14328 | ||||||||
\(441\) | 12.0604 | 0.574307 | ||||||||
\(442\) | 21.6304 | 1.02885 | ||||||||
\(443\) | −0.134618 | −0.00639588 | −0.00319794 | − | 0.999995i | \(-0.501018\pi\) | ||||
−0.00319794 | + | 0.999995i | \(0.501018\pi\) | |||||||
\(444\) | −35.1334 | −1.66736 | ||||||||
\(445\) | 13.2929 | 0.630145 | ||||||||
\(446\) | −56.2953 | −2.66566 | ||||||||
\(447\) | 17.0312 | 0.805546 | ||||||||
\(448\) | −39.5660 | −1.86932 | ||||||||
\(449\) | −13.1854 | −0.622256 | −0.311128 | − | 0.950368i | \(-0.600707\pi\) | ||||
−0.311128 | + | 0.950368i | \(0.600707\pi\) | |||||||
\(450\) | 6.79661 | 0.320395 | ||||||||
\(451\) | 37.8656 | 1.78302 | ||||||||
\(452\) | 36.9896 | 1.73985 | ||||||||
\(453\) | 2.15133 | 0.101078 | ||||||||
\(454\) | −25.5179 | −1.19761 | ||||||||
\(455\) | −2.33181 | −0.109317 | ||||||||
\(456\) | 2.33320 | 0.109262 | ||||||||
\(457\) | −28.4708 | −1.33181 | −0.665904 | − | 0.746038i | \(-0.731954\pi\) | ||||
−0.665904 | + | 0.746038i | \(0.731954\pi\) | |||||||
\(458\) | 47.6631 | 2.22715 | ||||||||
\(459\) | −19.5741 | −0.913642 | ||||||||
\(460\) | 27.5156 | 1.28292 | ||||||||
\(461\) | 3.73462 | 0.173939 | 0.0869693 | − | 0.996211i | \(-0.472282\pi\) | ||||
0.0869693 | + | 0.996211i | \(0.472282\pi\) | |||||||
\(462\) | 13.8313 | 0.643492 | ||||||||
\(463\) | 26.0760 | 1.21185 | 0.605927 | − | 0.795520i | \(-0.292802\pi\) | ||||
0.605927 | + | 0.795520i | \(0.292802\pi\) | |||||||
\(464\) | −26.7859 | −1.24351 | ||||||||
\(465\) | 2.52145 | 0.116929 | ||||||||
\(466\) | 16.6103 | 0.769458 | ||||||||
\(467\) | 13.1441 | 0.608237 | 0.304118 | − | 0.952634i | \(-0.401638\pi\) | ||||
0.304118 | + | 0.952634i | \(0.401638\pi\) | |||||||
\(468\) | −21.3012 | −0.984646 | ||||||||
\(469\) | −19.0155 | −0.878053 | ||||||||
\(470\) | 15.3865 | 0.709729 | ||||||||
\(471\) | 16.3543 | 0.753567 | ||||||||
\(472\) | −80.0741 | −3.68571 | ||||||||
\(473\) | −9.32952 | −0.428972 | ||||||||
\(474\) | 11.4625 | 0.526490 | ||||||||
\(475\) | 0.358119 | 0.0164316 | ||||||||
\(476\) | 40.0249 | 1.83454 | ||||||||
\(477\) | −29.5263 | −1.35192 | ||||||||
\(478\) | 16.5277 | 0.755958 | ||||||||
\(479\) | 35.2113 | 1.60885 | 0.804423 | − | 0.594056i | \(-0.202474\pi\) | ||||
0.804423 | + | 0.594056i | \(0.202474\pi\) | |||||||
\(480\) | 14.3986 | 0.657202 | ||||||||
\(481\) | 14.5738 | 0.664507 | ||||||||
\(482\) | −27.4234 | −1.24910 | ||||||||
\(483\) | 5.32412 | 0.242256 | ||||||||
\(484\) | 68.9919 | 3.13599 | ||||||||
\(485\) | −0.185315 | −0.00841473 | ||||||||
\(486\) | 40.8440 | 1.85272 | ||||||||
\(487\) | −31.7568 | −1.43904 | −0.719520 | − | 0.694472i | \(-0.755638\pi\) | ||||
−0.719520 | + | 0.694472i | \(0.755638\pi\) | |||||||
\(488\) | −0.531035 | −0.0240388 | ||||||||
\(489\) | 5.78478 | 0.261597 | ||||||||
\(490\) | 13.1133 | 0.592401 | ||||||||
\(491\) | −40.2572 | −1.81678 | −0.908392 | − | 0.418120i | \(-0.862689\pi\) | ||||
−0.908392 | + | 0.418120i | \(0.862689\pi\) | |||||||
\(492\) | 29.5767 | 1.33342 | ||||||||
\(493\) | 9.44769 | 0.425503 | ||||||||
\(494\) | −1.53884 | −0.0692359 | ||||||||
\(495\) | 12.1972 | 0.548223 | ||||||||
\(496\) | −50.9004 | −2.28550 | ||||||||
\(497\) | −8.43949 | −0.378563 | ||||||||
\(498\) | −12.2177 | −0.547488 | ||||||||
\(499\) | 10.2506 | 0.458881 | 0.229441 | − | 0.973323i | \(-0.426310\pi\) | ||||
0.229441 | + | 0.973323i | \(0.426310\pi\) | |||||||
\(500\) | 5.38997 | 0.241047 | ||||||||
\(501\) | 4.90039 | 0.218933 | ||||||||
\(502\) | 37.4802 | 1.67282 | ||||||||
\(503\) | 40.3892 | 1.80086 | 0.900432 | − | 0.434996i | \(-0.143250\pi\) | ||||
0.900432 | + | 0.434996i | \(0.143250\pi\) | |||||||
\(504\) | −33.9886 | −1.51397 | ||||||||
\(505\) | −15.8166 | −0.703830 | ||||||||
\(506\) | 67.7024 | 3.00974 | ||||||||
\(507\) | 7.42431 | 0.329725 | ||||||||
\(508\) | 17.1695 | 0.761773 | ||||||||
\(509\) | 27.9511 | 1.23891 | 0.619456 | − | 0.785031i | \(-0.287353\pi\) | ||||
0.619456 | + | 0.785031i | \(0.287353\pi\) | |||||||
\(510\) | −9.67446 | −0.428392 | ||||||||
\(511\) | −6.15308 | −0.272196 | ||||||||
\(512\) | −27.6213 | −1.22070 | ||||||||
\(513\) | 1.39255 | 0.0614827 | ||||||||
\(514\) | 29.2884 | 1.29186 | ||||||||
\(515\) | 7.77860 | 0.342766 | ||||||||
\(516\) | −7.28726 | −0.320804 | ||||||||
\(517\) | 27.6127 | 1.21441 | ||||||||
\(518\) | 36.9737 | 1.62453 | ||||||||
\(519\) | 0.988971 | 0.0434110 | ||||||||
\(520\) | −14.5668 | −0.638795 | ||||||||
\(521\) | 16.4776 | 0.721895 | 0.360947 | − | 0.932586i | \(-0.382453\pi\) | ||||
0.360947 | + | 0.932586i | \(0.382453\pi\) | |||||||
\(522\) | −12.7562 | −0.558322 | ||||||||
\(523\) | −18.3490 | −0.802347 | −0.401174 | − | 0.916002i | \(-0.631398\pi\) | ||||
−0.401174 | + | 0.916002i | \(0.631398\pi\) | |||||||
\(524\) | 34.6480 | 1.51361 | ||||||||
\(525\) | 1.04293 | 0.0455171 | ||||||||
\(526\) | 11.9661 | 0.521748 | ||||||||
\(527\) | 17.9531 | 0.782051 | ||||||||
\(528\) | 49.2239 | 2.14219 | ||||||||
\(529\) | 3.06077 | 0.133077 | ||||||||
\(530\) | −32.1040 | −1.39451 | ||||||||
\(531\) | −21.7243 | −0.942756 | ||||||||
\(532\) | −2.84747 | −0.123454 | ||||||||
\(533\) | −12.2688 | −0.531420 | ||||||||
\(534\) | 25.5476 | 1.10555 | ||||||||
\(535\) | −9.70917 | −0.419764 | ||||||||
\(536\) | −118.789 | −5.13092 | ||||||||
\(537\) | −8.10055 | −0.349565 | ||||||||
\(538\) | −68.5025 | −2.95335 | ||||||||
\(539\) | 23.5332 | 1.01365 | ||||||||
\(540\) | 20.9590 | 0.901932 | ||||||||
\(541\) | −6.12390 | −0.263287 | −0.131644 | − | 0.991297i | \(-0.542025\pi\) | ||||
−0.131644 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(542\) | 41.7918 | 1.79511 | ||||||||
\(543\) | −12.6988 | −0.544956 | ||||||||
\(544\) | 102.520 | 4.39552 | ||||||||
\(545\) | 4.65543 | 0.199417 | ||||||||
\(546\) | −4.48148 | −0.191790 | ||||||||
\(547\) | 39.2464 | 1.67806 | 0.839028 | − | 0.544088i | \(-0.183124\pi\) | ||||
0.839028 | + | 0.544088i | \(0.183124\pi\) | |||||||
\(548\) | 76.4010 | 3.26369 | ||||||||
\(549\) | −0.144071 | −0.00614882 | ||||||||
\(550\) | 13.2620 | 0.565495 | ||||||||
\(551\) | −0.672133 | −0.0286338 | ||||||||
\(552\) | 33.2597 | 1.41563 | ||||||||
\(553\) | −8.79824 | −0.374139 | ||||||||
\(554\) | 21.5510 | 0.915616 | ||||||||
\(555\) | −6.51829 | −0.276686 | ||||||||
\(556\) | 20.7275 | 0.879044 | ||||||||
\(557\) | 32.3225 | 1.36955 | 0.684775 | − | 0.728755i | \(-0.259901\pi\) | ||||
0.684775 | + | 0.728755i | \(0.259901\pi\) | |||||||
\(558\) | −24.2401 | −1.02617 | ||||||||
\(559\) | 3.02285 | 0.127853 | ||||||||
\(560\) | −21.0535 | −0.889674 | ||||||||
\(561\) | −17.3618 | −0.733016 | ||||||||
\(562\) | 53.7669 | 2.26802 | ||||||||
\(563\) | 35.2490 | 1.48557 | 0.742784 | − | 0.669531i | \(-0.233505\pi\) | ||||
0.742784 | + | 0.669531i | \(0.233505\pi\) | |||||||
\(564\) | 21.5682 | 0.908185 | ||||||||
\(565\) | 6.86268 | 0.288715 | ||||||||
\(566\) | −59.9272 | −2.51893 | ||||||||
\(567\) | −7.00922 | −0.294359 | ||||||||
\(568\) | −52.7214 | −2.21214 | ||||||||
\(569\) | −15.7040 | −0.658347 | −0.329174 | − | 0.944269i | \(-0.606770\pi\) | ||||
−0.329174 | + | 0.944269i | \(0.606770\pi\) | |||||||
\(570\) | 0.688266 | 0.0288283 | ||||||||
\(571\) | 0.859042 | 0.0359498 | 0.0179749 | − | 0.999838i | \(-0.494278\pi\) | ||||
0.0179749 | + | 0.999838i | \(0.494278\pi\) | |||||||
\(572\) | −41.5644 | −1.73789 | ||||||||
\(573\) | 16.5997 | 0.693461 | ||||||||
\(574\) | −31.1260 | −1.29917 | ||||||||
\(575\) | 5.10498 | 0.212892 | ||||||||
\(576\) | −67.0575 | −2.79406 | ||||||||
\(577\) | −32.2001 | −1.34051 | −0.670253 | − | 0.742132i | \(-0.733815\pi\) | ||||
−0.670253 | + | 0.742132i | \(0.733815\pi\) | |||||||
\(578\) | −22.6701 | −0.942952 | ||||||||
\(579\) | −9.87878 | −0.410548 | ||||||||
\(580\) | −10.1161 | −0.420049 | ||||||||
\(581\) | 9.37791 | 0.389061 | ||||||||
\(582\) | −0.356156 | −0.0147631 | ||||||||
\(583\) | −57.6139 | −2.38612 | ||||||||
\(584\) | −38.4382 | −1.59058 | ||||||||
\(585\) | −3.95200 | −0.163395 | ||||||||
\(586\) | 31.7097 | 1.30992 | ||||||||
\(587\) | −14.7665 | −0.609477 | −0.304739 | − | 0.952436i | \(-0.598569\pi\) | ||||
−0.304739 | + | 0.952436i | \(0.598569\pi\) | |||||||
\(588\) | 18.3817 | 0.758050 | ||||||||
\(589\) | −1.27723 | −0.0526274 | ||||||||
\(590\) | −23.6209 | −0.972458 | ||||||||
\(591\) | −15.3540 | −0.631578 | ||||||||
\(592\) | 131.584 | 5.40809 | ||||||||
\(593\) | −33.1269 | −1.36036 | −0.680178 | − | 0.733047i | \(-0.738098\pi\) | ||||
−0.680178 | + | 0.733047i | \(0.738098\pi\) | |||||||
\(594\) | 51.5697 | 2.11593 | ||||||||
\(595\) | 7.42581 | 0.304429 | ||||||||
\(596\) | −129.844 | −5.31862 | ||||||||
\(597\) | 12.5502 | 0.513643 | ||||||||
\(598\) | −21.9362 | −0.897037 | ||||||||
\(599\) | −6.82450 | −0.278841 | −0.139421 | − | 0.990233i | \(-0.544524\pi\) | ||||
−0.139421 | + | 0.990233i | \(0.544524\pi\) | |||||||
\(600\) | 6.51515 | 0.265980 | ||||||||
\(601\) | 10.5329 | 0.429645 | 0.214822 | − | 0.976653i | \(-0.431083\pi\) | ||||
0.214822 | + | 0.976653i | \(0.431083\pi\) | |||||||
\(602\) | 7.66898 | 0.312564 | ||||||||
\(603\) | −32.2279 | −1.31242 | ||||||||
\(604\) | −16.4016 | −0.667371 | ||||||||
\(605\) | 12.8001 | 0.520396 | ||||||||
\(606\) | −30.3979 | −1.23483 | ||||||||
\(607\) | 36.6944 | 1.48938 | 0.744690 | − | 0.667410i | \(-0.232597\pi\) | ||||
0.744690 | + | 0.667410i | \(0.232597\pi\) | |||||||
\(608\) | −7.29355 | −0.295793 | ||||||||
\(609\) | −1.95741 | −0.0793183 | ||||||||
\(610\) | −0.156649 | −0.00634254 | ||||||||
\(611\) | −8.94677 | −0.361948 | ||||||||
\(612\) | 67.8351 | 2.74207 | ||||||||
\(613\) | 23.9037 | 0.965460 | 0.482730 | − | 0.875769i | \(-0.339645\pi\) | ||||
0.482730 | + | 0.875769i | \(0.339645\pi\) | |||||||
\(614\) | 23.0905 | 0.931858 | ||||||||
\(615\) | 5.48736 | 0.221272 | ||||||||
\(616\) | −66.3211 | −2.67215 | ||||||||
\(617\) | 18.4538 | 0.742923 | 0.371461 | − | 0.928448i | \(-0.378857\pi\) | ||||
0.371461 | + | 0.928448i | \(0.378857\pi\) | |||||||
\(618\) | 14.9496 | 0.601363 | ||||||||
\(619\) | −6.70657 | −0.269560 | −0.134780 | − | 0.990876i | \(-0.543033\pi\) | ||||
−0.134780 | + | 0.990876i | \(0.543033\pi\) | |||||||
\(620\) | −19.2233 | −0.772028 | ||||||||
\(621\) | 19.8508 | 0.796586 | ||||||||
\(622\) | 23.2059 | 0.930472 | ||||||||
\(623\) | −19.6095 | −0.785638 | ||||||||
\(624\) | −15.9490 | −0.638471 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 62.2530 | 2.48813 | ||||||||
\(627\) | 1.23516 | 0.0493276 | ||||||||
\(628\) | −124.684 | −4.97543 | ||||||||
\(629\) | −46.4113 | −1.85054 | ||||||||
\(630\) | −10.0262 | −0.399455 | ||||||||
\(631\) | 8.09212 | 0.322142 | 0.161071 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161071 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(632\) | −54.9625 | −2.18629 | ||||||||
\(633\) | 4.89377 | 0.194510 | ||||||||
\(634\) | 48.3908 | 1.92184 | ||||||||
\(635\) | 3.18545 | 0.126411 | ||||||||
\(636\) | −45.0020 | −1.78445 | ||||||||
\(637\) | −7.62498 | −0.302113 | ||||||||
\(638\) | −24.8908 | −0.985435 | ||||||||
\(639\) | −14.3035 | −0.565836 | ||||||||
\(640\) | −32.1792 | −1.27199 | ||||||||
\(641\) | −37.2110 | −1.46975 | −0.734874 | − | 0.678204i | \(-0.762759\pi\) | ||||
−0.734874 | + | 0.678204i | \(0.762759\pi\) | |||||||
\(642\) | −18.6600 | −0.736451 | ||||||||
\(643\) | −5.32766 | −0.210102 | −0.105051 | − | 0.994467i | \(-0.533501\pi\) | ||||
−0.105051 | + | 0.994467i | \(0.533501\pi\) | |||||||
\(644\) | −40.5906 | −1.59949 | ||||||||
\(645\) | −1.35201 | −0.0532351 | ||||||||
\(646\) | 4.90057 | 0.192810 | ||||||||
\(647\) | −9.45277 | −0.371627 | −0.185813 | − | 0.982585i | \(-0.559492\pi\) | ||||
−0.185813 | + | 0.982585i | \(0.559492\pi\) | |||||||
\(648\) | −43.7865 | −1.72010 | ||||||||
\(649\) | −42.3901 | −1.66396 | ||||||||
\(650\) | −4.29702 | −0.168543 | ||||||||
\(651\) | −3.71960 | −0.145783 | ||||||||
\(652\) | −44.1027 | −1.72719 | ||||||||
\(653\) | −12.7928 | −0.500620 | −0.250310 | − | 0.968166i | \(-0.580533\pi\) | ||||
−0.250310 | + | 0.968166i | \(0.580533\pi\) | |||||||
\(654\) | 8.94724 | 0.349865 | ||||||||
\(655\) | 6.42824 | 0.251172 | ||||||||
\(656\) | −110.773 | −4.32497 | ||||||||
\(657\) | −10.4284 | −0.406850 | ||||||||
\(658\) | −22.6980 | −0.884859 | ||||||||
\(659\) | −47.1291 | −1.83589 | −0.917945 | − | 0.396707i | \(-0.870153\pi\) | ||||
−0.917945 | + | 0.396707i | \(0.870153\pi\) | |||||||
\(660\) | 18.5902 | 0.723621 | ||||||||
\(661\) | 46.0404 | 1.79077 | 0.895383 | − | 0.445298i | \(-0.146902\pi\) | ||||
0.895383 | + | 0.445298i | \(0.146902\pi\) | |||||||
\(662\) | −51.9400 | −2.01871 | ||||||||
\(663\) | 5.62538 | 0.218472 | ||||||||
\(664\) | 58.5837 | 2.27349 | ||||||||
\(665\) | −0.528291 | −0.0204863 | ||||||||
\(666\) | 62.6640 | 2.42818 | ||||||||
\(667\) | −9.58124 | −0.370987 | ||||||||
\(668\) | −37.3602 | −1.44551 | ||||||||
\(669\) | −14.6406 | −0.566038 | ||||||||
\(670\) | −35.0415 | −1.35377 | ||||||||
\(671\) | −0.281123 | −0.0108526 | ||||||||
\(672\) | −21.2405 | −0.819372 | ||||||||
\(673\) | −36.9987 | −1.42620 | −0.713098 | − | 0.701064i | \(-0.752709\pi\) | ||||
−0.713098 | + | 0.701064i | \(0.752709\pi\) | |||||||
\(674\) | 85.3759 | 3.28856 | ||||||||
\(675\) | 3.88852 | 0.149669 | ||||||||
\(676\) | −56.6023 | −2.17701 | ||||||||
\(677\) | −30.5930 | −1.17578 | −0.587892 | − | 0.808939i | \(-0.700042\pi\) | ||||
−0.587892 | + | 0.808939i | \(0.700042\pi\) | |||||||
\(678\) | 13.1893 | 0.506534 | ||||||||
\(679\) | 0.273374 | 0.0104911 | ||||||||
\(680\) | 46.3889 | 1.77893 | ||||||||
\(681\) | −6.63637 | −0.254306 | ||||||||
\(682\) | −47.2991 | −1.81118 | ||||||||
\(683\) | −12.3008 | −0.470675 | −0.235338 | − | 0.971914i | \(-0.575620\pi\) | ||||
−0.235338 | + | 0.971914i | \(0.575620\pi\) | |||||||
\(684\) | −4.82597 | −0.184525 | ||||||||
\(685\) | 14.1747 | 0.541587 | ||||||||
\(686\) | −47.4161 | −1.81035 | ||||||||
\(687\) | 12.3956 | 0.472923 | ||||||||
\(688\) | 27.2929 | 1.04053 | ||||||||
\(689\) | 18.6674 | 0.711172 | ||||||||
\(690\) | 9.81121 | 0.373507 | ||||||||
\(691\) | −8.52828 | −0.324431 | −0.162216 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162216 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(692\) | −7.53983 | −0.286621 | ||||||||
\(693\) | −17.9931 | −0.683501 | ||||||||
\(694\) | −68.5075 | −2.60051 | ||||||||
\(695\) | 3.84558 | 0.145871 | ||||||||
\(696\) | −12.2279 | −0.463498 | ||||||||
\(697\) | 39.0709 | 1.47992 | ||||||||
\(698\) | −77.7060 | −2.94121 | ||||||||
\(699\) | 4.31981 | 0.163390 | ||||||||
\(700\) | −7.95119 | −0.300527 | ||||||||
\(701\) | −29.6545 | −1.12004 | −0.560018 | − | 0.828480i | \(-0.689206\pi\) | ||||
−0.560018 | + | 0.828480i | \(0.689206\pi\) | |||||||
\(702\) | −16.7091 | −0.630643 | ||||||||
\(703\) | 3.30182 | 0.124530 | ||||||||
\(704\) | −130.847 | −4.93150 | ||||||||
\(705\) | 4.00155 | 0.150707 | ||||||||
\(706\) | 50.5575 | 1.90276 | ||||||||
\(707\) | 23.3324 | 0.877506 | ||||||||
\(708\) | −33.1108 | −1.24438 | ||||||||
\(709\) | 24.2556 | 0.910939 | 0.455470 | − | 0.890251i | \(-0.349471\pi\) | ||||
0.455470 | + | 0.890251i | \(0.349471\pi\) | |||||||
\(710\) | −15.5522 | −0.583663 | ||||||||
\(711\) | −14.9115 | −0.559224 | ||||||||
\(712\) | −122.500 | −4.59089 | ||||||||
\(713\) | −18.2069 | −0.681854 | ||||||||
\(714\) | 14.2716 | 0.534102 | ||||||||
\(715\) | −7.71144 | −0.288391 | ||||||||
\(716\) | 61.7579 | 2.30800 | ||||||||
\(717\) | 4.29832 | 0.160524 | ||||||||
\(718\) | −21.2657 | −0.793628 | ||||||||
\(719\) | −7.50727 | −0.279974 | −0.139987 | − | 0.990153i | \(-0.544706\pi\) | ||||
−0.139987 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(720\) | −35.6821 | −1.32979 | ||||||||
\(721\) | −11.4749 | −0.427346 | ||||||||
\(722\) | 51.3019 | 1.90926 | ||||||||
\(723\) | −7.13195 | −0.265240 | ||||||||
\(724\) | 96.8143 | 3.59807 | ||||||||
\(725\) | −1.87684 | −0.0697042 | ||||||||
\(726\) | 24.6003 | 0.913004 | ||||||||
\(727\) | −42.2766 | −1.56795 | −0.783976 | − | 0.620792i | \(-0.786811\pi\) | ||||
−0.783976 | + | 0.620792i | \(0.786811\pi\) | |||||||
\(728\) | 21.4886 | 0.796422 | ||||||||
\(729\) | −3.63206 | −0.134521 | ||||||||
\(730\) | −11.3388 | −0.419668 | ||||||||
\(731\) | −9.62649 | −0.356049 | ||||||||
\(732\) | −0.219584 | −0.00811606 | ||||||||
\(733\) | 23.7618 | 0.877661 | 0.438830 | − | 0.898570i | \(-0.355393\pi\) | ||||
0.438830 | + | 0.898570i | \(0.355393\pi\) | |||||||
\(734\) | 39.1322 | 1.44440 | ||||||||
\(735\) | 3.41036 | 0.125793 | ||||||||
\(736\) | −103.969 | −3.83236 | ||||||||
\(737\) | −62.8854 | −2.31641 | ||||||||
\(738\) | −52.7531 | −1.94187 | ||||||||
\(739\) | −35.8335 | −1.31816 | −0.659079 | − | 0.752074i | \(-0.729054\pi\) | ||||
−0.659079 | + | 0.752074i | \(0.729054\pi\) | |||||||
\(740\) | 49.6949 | 1.82682 | ||||||||
\(741\) | −0.400204 | −0.0147019 | ||||||||
\(742\) | 47.3593 | 1.73861 | ||||||||
\(743\) | −14.3278 | −0.525636 | −0.262818 | − | 0.964845i | \(-0.584652\pi\) | ||||
−0.262818 | + | 0.964845i | \(0.584652\pi\) | |||||||
\(744\) | −23.2363 | −0.851884 | ||||||||
\(745\) | −24.0900 | −0.882588 | ||||||||
\(746\) | 90.0388 | 3.29655 | ||||||||
\(747\) | 15.8939 | 0.581528 | ||||||||
\(748\) | 132.365 | 4.83974 | ||||||||
\(749\) | 14.3228 | 0.523344 | ||||||||
\(750\) | 1.92189 | 0.0701776 | ||||||||
\(751\) | 33.8135 | 1.23387 | 0.616937 | − | 0.787013i | \(-0.288374\pi\) | ||||
0.616937 | + | 0.787013i | \(0.288374\pi\) | |||||||
\(752\) | −80.7791 | −2.94571 | ||||||||
\(753\) | 9.74740 | 0.355215 | ||||||||
\(754\) | 8.06484 | 0.293704 | ||||||||
\(755\) | −3.04298 | −0.110745 | ||||||||
\(756\) | −30.9184 | −1.12449 | ||||||||
\(757\) | 26.3668 | 0.958317 | 0.479159 | − | 0.877728i | \(-0.340942\pi\) | ||||
0.479159 | + | 0.877728i | \(0.340942\pi\) | |||||||
\(758\) | 8.28477 | 0.300916 | ||||||||
\(759\) | 17.6072 | 0.639101 | ||||||||
\(760\) | −3.30023 | −0.119712 | ||||||||
\(761\) | 28.8032 | 1.04411 | 0.522057 | − | 0.852910i | \(-0.325165\pi\) | ||||
0.522057 | + | 0.852910i | \(0.325165\pi\) | |||||||
\(762\) | 6.12210 | 0.221780 | ||||||||
\(763\) | −6.86762 | −0.248624 | ||||||||
\(764\) | −126.554 | −4.57858 | ||||||||
\(765\) | 12.5854 | 0.455028 | ||||||||
\(766\) | 45.8067 | 1.65506 | ||||||||
\(767\) | 13.7348 | 0.495934 | ||||||||
\(768\) | −23.9210 | −0.863173 | ||||||||
\(769\) | −6.25033 | −0.225393 | −0.112696 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(770\) | −19.5639 | −0.705035 | ||||||||
\(771\) | 7.61698 | 0.274319 | ||||||||
\(772\) | 75.3150 | 2.71065 | ||||||||
\(773\) | −31.4722 | −1.13198 | −0.565988 | − | 0.824414i | \(-0.691505\pi\) | ||||
−0.565988 | + | 0.824414i | \(0.691505\pi\) | |||||||
\(774\) | 12.9976 | 0.467188 | ||||||||
\(775\) | −3.56650 | −0.128113 | ||||||||
\(776\) | 1.70776 | 0.0613051 | ||||||||
\(777\) | 9.61567 | 0.344960 | ||||||||
\(778\) | −82.9846 | −2.97514 | ||||||||
\(779\) | −2.77960 | −0.0995896 | ||||||||
\(780\) | −6.02338 | −0.215672 | ||||||||
\(781\) | −27.9099 | −0.998696 | ||||||||
\(782\) | 69.8574 | 2.49810 | ||||||||
\(783\) | −7.29815 | −0.260814 | ||||||||
\(784\) | −68.8448 | −2.45874 | ||||||||
\(785\) | −23.1326 | −0.825638 | ||||||||
\(786\) | 12.3544 | 0.440667 | ||||||||
\(787\) | 10.8632 | 0.387231 | 0.193615 | − | 0.981077i | \(-0.437979\pi\) | ||||
0.193615 | + | 0.981077i | \(0.437979\pi\) | |||||||
\(788\) | 117.057 | 4.17000 | ||||||||
\(789\) | 3.11200 | 0.110790 | ||||||||
\(790\) | −16.2133 | −0.576843 | ||||||||
\(791\) | −10.1237 | −0.359958 | ||||||||
\(792\) | −112.403 | −3.99405 | ||||||||
\(793\) | 0.0910863 | 0.00323457 | ||||||||
\(794\) | −62.7000 | −2.22514 | ||||||||
\(795\) | −8.34922 | −0.296116 | ||||||||
\(796\) | −95.6813 | −3.39133 | ||||||||
\(797\) | 42.4536 | 1.50378 | 0.751892 | − | 0.659286i | \(-0.229141\pi\) | ||||
0.751892 | + | 0.659286i | \(0.229141\pi\) | |||||||
\(798\) | −1.01532 | −0.0359419 | ||||||||
\(799\) | 28.4917 | 1.00796 | ||||||||
\(800\) | −20.3663 | −0.720057 | ||||||||
\(801\) | −33.2347 | −1.17429 | ||||||||
\(802\) | 5.08014 | 0.179386 | ||||||||
\(803\) | −20.3486 | −0.718088 | ||||||||
\(804\) | −49.1196 | −1.73232 | ||||||||
\(805\) | −7.53078 | −0.265425 | ||||||||
\(806\) | 15.3253 | 0.539812 | ||||||||
\(807\) | −17.8153 | −0.627128 | ||||||||
\(808\) | 145.757 | 5.12773 | ||||||||
\(809\) | −46.7224 | −1.64267 | −0.821336 | − | 0.570445i | \(-0.806771\pi\) | ||||
−0.821336 | + | 0.570445i | \(0.806771\pi\) | |||||||
\(810\) | −12.9165 | −0.453839 | ||||||||
\(811\) | 14.2149 | 0.499151 | 0.249576 | − | 0.968355i | \(-0.419709\pi\) | ||||
0.249576 | + | 0.968355i | \(0.419709\pi\) | |||||||
\(812\) | 14.9231 | 0.523700 | ||||||||
\(813\) | 10.8687 | 0.381182 | ||||||||
\(814\) | 122.275 | 4.28572 | ||||||||
\(815\) | −8.18237 | −0.286616 | ||||||||
\(816\) | 50.7907 | 1.77803 | ||||||||
\(817\) | 0.684854 | 0.0239600 | ||||||||
\(818\) | 62.5416 | 2.18671 | ||||||||
\(819\) | 5.82993 | 0.203714 | ||||||||
\(820\) | −41.8352 | −1.46095 | ||||||||
\(821\) | −32.8769 | −1.14741 | −0.573705 | − | 0.819062i | \(-0.694494\pi\) | ||||
−0.573705 | + | 0.819062i | \(0.694494\pi\) | |||||||
\(822\) | 27.2422 | 0.950181 | ||||||||
\(823\) | −26.8886 | −0.937279 | −0.468639 | − | 0.883390i | \(-0.655256\pi\) | ||||
−0.468639 | + | 0.883390i | \(0.655256\pi\) | |||||||
\(824\) | −71.6834 | −2.49721 | ||||||||
\(825\) | 3.44903 | 0.120080 | ||||||||
\(826\) | 34.8452 | 1.21242 | ||||||||
\(827\) | 18.4689 | 0.642227 | 0.321114 | − | 0.947041i | \(-0.395943\pi\) | ||||
0.321114 | + | 0.947041i | \(0.395943\pi\) | |||||||
\(828\) | −68.7940 | −2.39076 | ||||||||
\(829\) | −34.0982 | −1.18428 | −0.592139 | − | 0.805836i | \(-0.701716\pi\) | ||||
−0.592139 | + | 0.805836i | \(0.701716\pi\) | |||||||
\(830\) | 17.2815 | 0.599850 | ||||||||
\(831\) | 5.60473 | 0.194426 | ||||||||
\(832\) | 42.3958 | 1.46981 | ||||||||
\(833\) | 24.2823 | 0.841332 | ||||||||
\(834\) | 7.39079 | 0.255922 | ||||||||
\(835\) | −6.93143 | −0.239872 | ||||||||
\(836\) | −9.41678 | −0.325686 | ||||||||
\(837\) | −13.8684 | −0.479363 | ||||||||
\(838\) | −22.9944 | −0.794327 | ||||||||
\(839\) | 11.5564 | 0.398971 | 0.199485 | − | 0.979901i | \(-0.436073\pi\) | ||||
0.199485 | + | 0.979901i | \(0.436073\pi\) | |||||||
\(840\) | −9.61105 | −0.331613 | ||||||||
\(841\) | −25.4775 | −0.878533 | ||||||||
\(842\) | −35.9682 | −1.23955 | ||||||||
\(843\) | 13.9830 | 0.481601 | ||||||||
\(844\) | −37.3097 | −1.28425 | ||||||||
\(845\) | −10.5014 | −0.361260 | ||||||||
\(846\) | −38.4691 | −1.32259 | ||||||||
\(847\) | −18.8824 | −0.648808 | ||||||||
\(848\) | 168.545 | 5.78787 | ||||||||
\(849\) | −15.5851 | −0.534881 | ||||||||
\(850\) | 13.6842 | 0.469364 | ||||||||
\(851\) | 47.0673 | 1.61345 | ||||||||
\(852\) | −21.8004 | −0.746869 | ||||||||
\(853\) | −8.33383 | −0.285345 | −0.142672 | − | 0.989770i | \(-0.545570\pi\) | ||||
−0.142672 | + | 0.989770i | \(0.545570\pi\) | |||||||
\(854\) | 0.231086 | 0.00790761 | ||||||||
\(855\) | −0.895361 | −0.0306207 | ||||||||
\(856\) | 89.4744 | 3.05817 | ||||||||
\(857\) | −34.9653 | −1.19439 | −0.597196 | − | 0.802095i | \(-0.703719\pi\) | ||||
−0.597196 | + | 0.802095i | \(0.703719\pi\) | |||||||
\(858\) | −14.8206 | −0.505965 | ||||||||
\(859\) | 1.90243 | 0.0649101 | 0.0324551 | − | 0.999473i | \(-0.489667\pi\) | ||||
0.0324551 | + | 0.999473i | \(0.489667\pi\) | |||||||
\(860\) | 10.3076 | 0.351485 | ||||||||
\(861\) | −8.09486 | −0.275872 | ||||||||
\(862\) | 66.6778 | 2.27105 | ||||||||
\(863\) | −43.2298 | −1.47156 | −0.735779 | − | 0.677222i | \(-0.763184\pi\) | ||||
−0.735779 | + | 0.677222i | \(0.763184\pi\) | |||||||
\(864\) | −79.1947 | −2.69426 | ||||||||
\(865\) | −1.39886 | −0.0475628 | ||||||||
\(866\) | 17.6380 | 0.599365 | ||||||||
\(867\) | −5.89576 | −0.200231 | ||||||||
\(868\) | 28.3579 | 0.962531 | ||||||||
\(869\) | −29.0964 | −0.987027 | ||||||||
\(870\) | −3.60709 | −0.122292 | ||||||||
\(871\) | 20.3754 | 0.690396 | ||||||||
\(872\) | −42.9019 | −1.45284 | ||||||||
\(873\) | 0.463321 | 0.0156810 | ||||||||
\(874\) | −4.96984 | −0.168107 | ||||||||
\(875\) | −1.47518 | −0.0498703 | ||||||||
\(876\) | −15.8943 | −0.537017 | ||||||||
\(877\) | 46.0424 | 1.55474 | 0.777370 | − | 0.629043i | \(-0.216553\pi\) | ||||
0.777370 | + | 0.629043i | \(0.216553\pi\) | |||||||
\(878\) | −53.2753 | −1.79796 | ||||||||
\(879\) | 8.24668 | 0.278154 | ||||||||
\(880\) | −69.6254 | −2.34707 | ||||||||
\(881\) | 9.58560 | 0.322947 | 0.161473 | − | 0.986877i | \(-0.448375\pi\) | ||||
0.161473 | + | 0.986877i | \(0.448375\pi\) | |||||||
\(882\) | −32.7857 | −1.10395 | ||||||||
\(883\) | −41.2914 | −1.38956 | −0.694782 | − | 0.719220i | \(-0.744499\pi\) | ||||
−0.694782 | + | 0.719220i | \(0.744499\pi\) | |||||||
\(884\) | −42.8874 | −1.44246 | ||||||||
\(885\) | −6.14304 | −0.206496 | ||||||||
\(886\) | 0.365951 | 0.0122944 | ||||||||
\(887\) | 52.1774 | 1.75195 | 0.875973 | − | 0.482360i | \(-0.160220\pi\) | ||||
0.875973 | + | 0.482360i | \(0.160220\pi\) | |||||||
\(888\) | 60.0690 | 2.01578 | ||||||||
\(889\) | −4.69913 | −0.157604 | ||||||||
\(890\) | −36.1362 | −1.21129 | ||||||||
\(891\) | −23.1799 | −0.776557 | ||||||||
\(892\) | 111.619 | 3.73727 | ||||||||
\(893\) | −2.02697 | −0.0678300 | ||||||||
\(894\) | −46.2983 | −1.54845 | ||||||||
\(895\) | 11.4579 | 0.382997 | ||||||||
\(896\) | 47.4702 | 1.58587 | ||||||||
\(897\) | −5.70490 | −0.190481 | ||||||||
\(898\) | 35.8438 | 1.19612 | ||||||||
\(899\) | 6.69377 | 0.223250 | ||||||||
\(900\) | −13.4759 | −0.449196 | ||||||||
\(901\) | −59.4478 | −1.98049 | ||||||||
\(902\) | −102.936 | −3.42738 | ||||||||
\(903\) | 1.99446 | 0.0663713 | ||||||||
\(904\) | −63.2427 | −2.10342 | ||||||||
\(905\) | 17.9619 | 0.597075 | ||||||||
\(906\) | −5.84829 | −0.194296 | ||||||||
\(907\) | −18.5303 | −0.615287 | −0.307644 | − | 0.951502i | \(-0.599540\pi\) | ||||
−0.307644 | + | 0.951502i | \(0.599540\pi\) | |||||||
\(908\) | 50.5952 | 1.67906 | ||||||||
\(909\) | 39.5444 | 1.31160 | ||||||||
\(910\) | 6.33890 | 0.210132 | ||||||||
\(911\) | −34.2834 | −1.13586 | −0.567930 | − | 0.823077i | \(-0.692255\pi\) | ||||
−0.567930 | + | 0.823077i | \(0.692255\pi\) | |||||||
\(912\) | −3.61338 | −0.119651 | ||||||||
\(913\) | 31.0134 | 1.02639 | ||||||||
\(914\) | 77.3964 | 2.56004 | ||||||||
\(915\) | −0.0407394 | −0.00134680 | ||||||||
\(916\) | −94.5033 | −3.12248 | ||||||||
\(917\) | −9.48284 | −0.313151 | ||||||||
\(918\) | 53.2113 | 1.75623 | ||||||||
\(919\) | −12.2345 | −0.403579 | −0.201789 | − | 0.979429i | \(-0.564676\pi\) | ||||
−0.201789 | + | 0.979429i | \(0.564676\pi\) | |||||||
\(920\) | −47.0447 | −1.55102 | ||||||||
\(921\) | 6.00510 | 0.197875 | ||||||||
\(922\) | −10.1524 | −0.334351 | ||||||||
\(923\) | 9.04308 | 0.297657 | ||||||||
\(924\) | −27.4239 | −0.902180 | ||||||||
\(925\) | 9.21989 | 0.303148 | ||||||||
\(926\) | −70.8863 | −2.32947 | ||||||||
\(927\) | −19.4479 | −0.638753 | ||||||||
\(928\) | 38.2243 | 1.25477 | ||||||||
\(929\) | −40.6051 | −1.33221 | −0.666105 | − | 0.745858i | \(-0.732040\pi\) | ||||
−0.666105 | + | 0.745858i | \(0.732040\pi\) | |||||||
\(930\) | −6.85444 | −0.224766 | ||||||||
\(931\) | −1.72751 | −0.0566167 | ||||||||
\(932\) | −32.9339 | −1.07879 | ||||||||
\(933\) | 6.03511 | 0.197581 | ||||||||
\(934\) | −35.7316 | −1.16917 | ||||||||
\(935\) | 24.5576 | 0.803121 | ||||||||
\(936\) | 36.4195 | 1.19041 | ||||||||
\(937\) | −24.9618 | −0.815468 | −0.407734 | − | 0.913101i | \(-0.633681\pi\) | ||||
−0.407734 | + | 0.913101i | \(0.633681\pi\) | |||||||
\(938\) | 51.6926 | 1.68782 | ||||||||
\(939\) | 16.1900 | 0.528341 | ||||||||
\(940\) | −30.5075 | −0.995044 | ||||||||
\(941\) | 31.8445 | 1.03810 | 0.519050 | − | 0.854744i | \(-0.326286\pi\) | ||||
0.519050 | + | 0.854744i | \(0.326286\pi\) | |||||||
\(942\) | −44.4584 | −1.44853 | ||||||||
\(943\) | −39.6232 | −1.29031 | ||||||||
\(944\) | 124.009 | 4.03616 | ||||||||
\(945\) | −5.73628 | −0.186601 | ||||||||
\(946\) | 25.3618 | 0.824584 | ||||||||
\(947\) | 44.3075 | 1.43980 | 0.719900 | − | 0.694078i | \(-0.244188\pi\) | ||||
0.719900 | + | 0.694078i | \(0.244188\pi\) | |||||||
\(948\) | −22.7271 | −0.738142 | ||||||||
\(949\) | 6.59315 | 0.214023 | ||||||||
\(950\) | −0.973528 | −0.0315854 | ||||||||
\(951\) | 12.5849 | 0.408093 | ||||||||
\(952\) | −68.4322 | −2.21790 | ||||||||
\(953\) | −18.9388 | −0.613488 | −0.306744 | − | 0.951792i | \(-0.599240\pi\) | ||||
−0.306744 | + | 0.951792i | \(0.599240\pi\) | |||||||
\(954\) | 80.2657 | 2.59870 | ||||||||
\(955\) | −23.4796 | −0.759783 | ||||||||
\(956\) | −32.7700 | −1.05986 | ||||||||
\(957\) | −6.47329 | −0.209252 | ||||||||
\(958\) | −95.7202 | −3.09258 | ||||||||
\(959\) | −20.9103 | −0.675227 | ||||||||
\(960\) | −18.9620 | −0.611996 | ||||||||
\(961\) | −18.2801 | −0.589679 | ||||||||
\(962\) | −39.6181 | −1.27734 | ||||||||
\(963\) | 24.2746 | 0.782239 | ||||||||
\(964\) | 54.3734 | 1.75125 | ||||||||
\(965\) | 13.9732 | 0.449813 | ||||||||
\(966\) | −14.4733 | −0.465672 | ||||||||
\(967\) | 54.2348 | 1.74408 | 0.872038 | − | 0.489439i | \(-0.162798\pi\) | ||||
0.872038 | + | 0.489439i | \(0.162798\pi\) | |||||||
\(968\) | −117.958 | −3.79132 | ||||||||
\(969\) | 1.27448 | 0.0409422 | ||||||||
\(970\) | 0.503770 | 0.0161751 | ||||||||
\(971\) | −16.6494 | −0.534303 | −0.267152 | − | 0.963654i | \(-0.586082\pi\) | ||||
−0.267152 | + | 0.963654i | \(0.586082\pi\) | |||||||
\(972\) | −80.9828 | −2.59752 | ||||||||
\(973\) | −5.67293 | −0.181866 | ||||||||
\(974\) | 86.3293 | 2.76617 | ||||||||
\(975\) | −1.11752 | −0.0357892 | ||||||||
\(976\) | 0.822405 | 0.0263245 | ||||||||
\(977\) | −34.0104 | −1.08809 | −0.544044 | − | 0.839057i | \(-0.683108\pi\) | ||||
−0.544044 | + | 0.839057i | \(0.683108\pi\) | |||||||
\(978\) | −15.7256 | −0.502850 | ||||||||
\(979\) | −64.8500 | −2.07261 | ||||||||
\(980\) | −26.0003 | −0.830549 | ||||||||
\(981\) | −11.6394 | −0.371618 | ||||||||
\(982\) | 109.437 | 3.49228 | ||||||||
\(983\) | 61.7051 | 1.96809 | 0.984044 | − | 0.177926i | \(-0.0569387\pi\) | ||||
0.984044 | + | 0.177926i | \(0.0569387\pi\) | |||||||
\(984\) | −50.5685 | −1.61207 | ||||||||
\(985\) | 21.7177 | 0.691982 | ||||||||
\(986\) | −25.6831 | −0.817916 | ||||||||
\(987\) | −5.90302 | −0.187895 | ||||||||
\(988\) | 3.05112 | 0.0970691 | ||||||||
\(989\) | 9.76257 | 0.310432 | ||||||||
\(990\) | −33.1574 | −1.05381 | ||||||||
\(991\) | 52.0963 | 1.65489 | 0.827447 | − | 0.561544i | \(-0.189792\pi\) | ||||
0.827447 | + | 0.561544i | \(0.189792\pi\) | |||||||
\(992\) | 72.6364 | 2.30621 | ||||||||
\(993\) | −13.5079 | −0.428661 | ||||||||
\(994\) | 22.9423 | 0.727686 | ||||||||
\(995\) | −17.7517 | −0.562768 | ||||||||
\(996\) | 24.2245 | 0.767581 | ||||||||
\(997\) | −26.8236 | −0.849512 | −0.424756 | − | 0.905308i | \(-0.639640\pi\) | ||||
−0.424756 | + | 0.905308i | \(0.639640\pi\) | |||||||
\(998\) | −27.8658 | −0.882077 | ||||||||
\(999\) | 35.8517 | 1.13430 |
(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 | 8035.2.a.b.1.3 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.b.1.3 | ✓ | 114 | 1.1 | even | 1 | trivial |