Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.76808 | −1.59815 | −0.799076 | − | 0.601230i | \(-0.794678\pi\) | ||||
−0.799076 | + | 0.601230i | \(0.794678\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.07666 | 1.82314 | 0.911569 | − | 0.411148i | \(-0.134872\pi\) | ||||
0.911569 | + | 0.411148i | \(0.134872\pi\) | |||||||
\(6\) | −2.76808 | −1.13006 | ||||||||
\(7\) | 2.61903 | 0.989901 | 0.494951 | − | 0.868921i | \(-0.335186\pi\) | ||||
0.494951 | + | 0.868921i | \(0.335186\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.66227 | 1.55409 | ||||||||
\(10\) | 4.07666 | 1.28915 | ||||||||
\(11\) | −4.42706 | −1.33481 | −0.667404 | − | 0.744696i | \(-0.732594\pi\) | ||||
−0.667404 | + | 0.744696i | \(0.732594\pi\) | |||||||
\(12\) | −2.76808 | −0.799076 | ||||||||
\(13\) | −6.42164 | −1.78104 | −0.890522 | − | 0.454941i | \(-0.849660\pi\) | ||||
−0.890522 | + | 0.454941i | \(0.849660\pi\) | |||||||
\(14\) | 2.61903 | 0.699966 | ||||||||
\(15\) | −11.2845 | −2.91365 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.31227 | −1.04588 | −0.522939 | − | 0.852370i | \(-0.675165\pi\) | ||||
−0.522939 | + | 0.852370i | \(0.675165\pi\) | |||||||
\(18\) | 4.66227 | 1.09891 | ||||||||
\(19\) | −3.26346 | −0.748690 | −0.374345 | − | 0.927289i | \(-0.622132\pi\) | ||||
−0.374345 | + | 0.927289i | \(0.622132\pi\) | |||||||
\(20\) | 4.07666 | 0.911569 | ||||||||
\(21\) | −7.24969 | −1.58201 | ||||||||
\(22\) | −4.42706 | −0.943851 | ||||||||
\(23\) | 3.62139 | 0.755113 | 0.377557 | − | 0.925987i | \(-0.376764\pi\) | ||||
0.377557 | + | 0.925987i | \(0.376764\pi\) | |||||||
\(24\) | −2.76808 | −0.565032 | ||||||||
\(25\) | 11.6192 | 2.32383 | ||||||||
\(26\) | −6.42164 | −1.25939 | ||||||||
\(27\) | −4.60130 | −0.885521 | ||||||||
\(28\) | 2.61903 | 0.494951 | ||||||||
\(29\) | −1.10363 | −0.204939 | −0.102470 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102470 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(30\) | −11.2845 | −2.06026 | ||||||||
\(31\) | 10.0846 | 1.81124 | 0.905620 | − | 0.424091i | \(-0.139406\pi\) | ||||
0.905620 | + | 0.424091i | \(0.139406\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 12.2544 | 2.13323 | ||||||||
\(34\) | −4.31227 | −0.739548 | ||||||||
\(35\) | 10.6769 | 1.80473 | ||||||||
\(36\) | 4.66227 | 0.777045 | ||||||||
\(37\) | −1.48795 | −0.244617 | −0.122309 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122309 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(38\) | −3.26346 | −0.529404 | ||||||||
\(39\) | 17.7756 | 2.84638 | ||||||||
\(40\) | 4.07666 | 0.644576 | ||||||||
\(41\) | −2.84887 | −0.444919 | −0.222459 | − | 0.974942i | \(-0.571409\pi\) | ||||
−0.222459 | + | 0.974942i | \(0.571409\pi\) | |||||||
\(42\) | −7.24969 | −1.11865 | ||||||||
\(43\) | −9.08959 | −1.38615 | −0.693075 | − | 0.720866i | \(-0.743744\pi\) | ||||
−0.693075 | + | 0.720866i | \(0.743744\pi\) | |||||||
\(44\) | −4.42706 | −0.667404 | ||||||||
\(45\) | 19.0065 | 2.83332 | ||||||||
\(46\) | 3.62139 | 0.533946 | ||||||||
\(47\) | −5.38514 | −0.785504 | −0.392752 | − | 0.919644i | \(-0.628477\pi\) | ||||
−0.392752 | + | 0.919644i | \(0.628477\pi\) | |||||||
\(48\) | −2.76808 | −0.399538 | ||||||||
\(49\) | −0.140671 | −0.0200958 | ||||||||
\(50\) | 11.6192 | 1.64320 | ||||||||
\(51\) | 11.9367 | 1.67147 | ||||||||
\(52\) | −6.42164 | −0.890522 | ||||||||
\(53\) | −8.55357 | −1.17492 | −0.587461 | − | 0.809252i | \(-0.699873\pi\) | ||||
−0.587461 | + | 0.809252i | \(0.699873\pi\) | |||||||
\(54\) | −4.60130 | −0.626158 | ||||||||
\(55\) | −18.0476 | −2.43354 | ||||||||
\(56\) | 2.61903 | 0.349983 | ||||||||
\(57\) | 9.03353 | 1.19652 | ||||||||
\(58\) | −1.10363 | −0.144914 | ||||||||
\(59\) | 12.1824 | 1.58601 | 0.793006 | − | 0.609214i | \(-0.208515\pi\) | ||||
0.793006 | + | 0.609214i | \(0.208515\pi\) | |||||||
\(60\) | −11.2845 | −1.45683 | ||||||||
\(61\) | −6.07490 | −0.777811 | −0.388906 | − | 0.921278i | \(-0.627147\pi\) | ||||
−0.388906 | + | 0.921278i | \(0.627147\pi\) | |||||||
\(62\) | 10.0846 | 1.28074 | ||||||||
\(63\) | 12.2106 | 1.53840 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −26.1788 | −3.24709 | ||||||||
\(66\) | 12.2544 | 1.50842 | ||||||||
\(67\) | −7.23324 | −0.883681 | −0.441841 | − | 0.897094i | \(-0.645674\pi\) | ||||
−0.441841 | + | 0.897094i | \(0.645674\pi\) | |||||||
\(68\) | −4.31227 | −0.522939 | ||||||||
\(69\) | −10.0243 | −1.20679 | ||||||||
\(70\) | 10.6769 | 1.27613 | ||||||||
\(71\) | 3.42135 | 0.406040 | 0.203020 | − | 0.979175i | \(-0.434924\pi\) | ||||
0.203020 | + | 0.979175i | \(0.434924\pi\) | |||||||
\(72\) | 4.66227 | 0.549454 | ||||||||
\(73\) | −16.3826 | −1.91743 | −0.958717 | − | 0.284362i | \(-0.908218\pi\) | ||||
−0.958717 | + | 0.284362i | \(0.908218\pi\) | |||||||
\(74\) | −1.48795 | −0.172970 | ||||||||
\(75\) | −32.1627 | −3.71383 | ||||||||
\(76\) | −3.26346 | −0.374345 | ||||||||
\(77\) | −11.5946 | −1.32133 | ||||||||
\(78\) | 17.7756 | 2.01269 | ||||||||
\(79\) | 0.250564 | 0.0281906 | 0.0140953 | − | 0.999901i | \(-0.495513\pi\) | ||||
0.0140953 | + | 0.999901i | \(0.495513\pi\) | |||||||
\(80\) | 4.07666 | 0.455784 | ||||||||
\(81\) | −1.25004 | −0.138894 | ||||||||
\(82\) | −2.84887 | −0.314605 | ||||||||
\(83\) | 12.3640 | 1.35713 | 0.678565 | − | 0.734541i | \(-0.262602\pi\) | ||||
0.678565 | + | 0.734541i | \(0.262602\pi\) | |||||||
\(84\) | −7.24969 | −0.791006 | ||||||||
\(85\) | −17.5796 | −1.90678 | ||||||||
\(86\) | −9.08959 | −0.980155 | ||||||||
\(87\) | 3.05494 | 0.327524 | ||||||||
\(88\) | −4.42706 | −0.471926 | ||||||||
\(89\) | −6.26669 | −0.664268 | −0.332134 | − | 0.943232i | \(-0.607769\pi\) | ||||
−0.332134 | + | 0.943232i | \(0.607769\pi\) | |||||||
\(90\) | 19.0065 | 2.00346 | ||||||||
\(91\) | −16.8185 | −1.76306 | ||||||||
\(92\) | 3.62139 | 0.377557 | ||||||||
\(93\) | −27.9149 | −2.89464 | ||||||||
\(94\) | −5.38514 | −0.555435 | ||||||||
\(95\) | −13.3040 | −1.36497 | ||||||||
\(96\) | −2.76808 | −0.282516 | ||||||||
\(97\) | 11.0161 | 1.11852 | 0.559259 | − | 0.828993i | \(-0.311086\pi\) | ||||
0.559259 | + | 0.828993i | \(0.311086\pi\) | |||||||
\(98\) | −0.140671 | −0.0142099 | ||||||||
\(99\) | −20.6401 | −2.07441 | ||||||||
\(100\) | 11.6192 | 1.16192 | ||||||||
\(101\) | 12.9098 | 1.28457 | 0.642285 | − | 0.766466i | \(-0.277987\pi\) | ||||
0.642285 | + | 0.766466i | \(0.277987\pi\) | |||||||
\(102\) | 11.9367 | 1.18191 | ||||||||
\(103\) | 1.88415 | 0.185651 | 0.0928253 | − | 0.995682i | \(-0.470410\pi\) | ||||
0.0928253 | + | 0.995682i | \(0.470410\pi\) | |||||||
\(104\) | −6.42164 | −0.629694 | ||||||||
\(105\) | −29.5545 | −2.88423 | ||||||||
\(106\) | −8.55357 | −0.830796 | ||||||||
\(107\) | −16.7897 | −1.62312 | −0.811559 | − | 0.584271i | \(-0.801381\pi\) | ||||
−0.811559 | + | 0.584271i | \(0.801381\pi\) | |||||||
\(108\) | −4.60130 | −0.442760 | ||||||||
\(109\) | 8.89079 | 0.851583 | 0.425792 | − | 0.904821i | \(-0.359996\pi\) | ||||
0.425792 | + | 0.904821i | \(0.359996\pi\) | |||||||
\(110\) | −18.0476 | −1.72077 | ||||||||
\(111\) | 4.11876 | 0.390935 | ||||||||
\(112\) | 2.61903 | 0.247475 | ||||||||
\(113\) | −3.81909 | −0.359270 | −0.179635 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179635 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(114\) | 9.03353 | 0.846068 | ||||||||
\(115\) | 14.7632 | 1.37667 | ||||||||
\(116\) | −1.10363 | −0.102470 | ||||||||
\(117\) | −29.9394 | −2.76790 | ||||||||
\(118\) | 12.1824 | 1.12148 | ||||||||
\(119\) | −11.2940 | −1.03532 | ||||||||
\(120\) | −11.2845 | −1.03013 | ||||||||
\(121\) | 8.59882 | 0.781711 | ||||||||
\(122\) | −6.07490 | −0.549996 | ||||||||
\(123\) | 7.88591 | 0.711048 | ||||||||
\(124\) | 10.0846 | 0.905620 | ||||||||
\(125\) | 26.9840 | 2.41352 | ||||||||
\(126\) | 12.2106 | 1.08781 | ||||||||
\(127\) | −14.8373 | −1.31660 | −0.658299 | − | 0.752756i | \(-0.728724\pi\) | ||||
−0.658299 | + | 0.752756i | \(0.728724\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 25.1607 | 2.21528 | ||||||||
\(130\) | −26.1788 | −2.29604 | ||||||||
\(131\) | −12.5690 | −1.09816 | −0.549081 | − | 0.835769i | \(-0.685022\pi\) | ||||
−0.549081 | + | 0.835769i | \(0.685022\pi\) | |||||||
\(132\) | 12.2544 | 1.06661 | ||||||||
\(133\) | −8.54712 | −0.741129 | ||||||||
\(134\) | −7.23324 | −0.624857 | ||||||||
\(135\) | −18.7579 | −1.61443 | ||||||||
\(136\) | −4.31227 | −0.369774 | ||||||||
\(137\) | −10.5628 | −0.902442 | −0.451221 | − | 0.892412i | \(-0.649011\pi\) | ||||
−0.451221 | + | 0.892412i | \(0.649011\pi\) | |||||||
\(138\) | −10.0243 | −0.853326 | ||||||||
\(139\) | −1.94959 | −0.165362 | −0.0826812 | − | 0.996576i | \(-0.526348\pi\) | ||||
−0.0826812 | + | 0.996576i | \(0.526348\pi\) | |||||||
\(140\) | 10.6769 | 0.902363 | ||||||||
\(141\) | 14.9065 | 1.25535 | ||||||||
\(142\) | 3.42135 | 0.287114 | ||||||||
\(143\) | 28.4290 | 2.37735 | ||||||||
\(144\) | 4.66227 | 0.388523 | ||||||||
\(145\) | −4.49913 | −0.373632 | ||||||||
\(146\) | −16.3826 | −1.35583 | ||||||||
\(147\) | 0.389388 | 0.0321162 | ||||||||
\(148\) | −1.48795 | −0.122309 | ||||||||
\(149\) | −4.53225 | −0.371296 | −0.185648 | − | 0.982616i | \(-0.559438\pi\) | ||||
−0.185648 | + | 0.982616i | \(0.559438\pi\) | |||||||
\(150\) | −32.1627 | −2.62608 | ||||||||
\(151\) | 8.66262 | 0.704954 | 0.352477 | − | 0.935820i | \(-0.385339\pi\) | ||||
0.352477 | + | 0.935820i | \(0.385339\pi\) | |||||||
\(152\) | −3.26346 | −0.264702 | ||||||||
\(153\) | −20.1050 | −1.62539 | ||||||||
\(154\) | −11.5946 | −0.934319 | ||||||||
\(155\) | 41.1113 | 3.30214 | ||||||||
\(156\) | 17.7756 | 1.42319 | ||||||||
\(157\) | −23.2800 | −1.85794 | −0.928972 | − | 0.370150i | \(-0.879306\pi\) | ||||
−0.928972 | + | 0.370150i | \(0.879306\pi\) | |||||||
\(158\) | 0.250564 | 0.0199338 | ||||||||
\(159\) | 23.6770 | 1.87771 | ||||||||
\(160\) | 4.07666 | 0.322288 | ||||||||
\(161\) | 9.48455 | 0.747487 | ||||||||
\(162\) | −1.25004 | −0.0982126 | ||||||||
\(163\) | −2.91089 | −0.227999 | −0.113999 | − | 0.993481i | \(-0.536366\pi\) | ||||
−0.113999 | + | 0.993481i | \(0.536366\pi\) | |||||||
\(164\) | −2.84887 | −0.222459 | ||||||||
\(165\) | 49.9572 | 3.88916 | ||||||||
\(166\) | 12.3640 | 0.959635 | ||||||||
\(167\) | −18.5603 | −1.43624 | −0.718118 | − | 0.695921i | \(-0.754996\pi\) | ||||
−0.718118 | + | 0.695921i | \(0.754996\pi\) | |||||||
\(168\) | −7.24969 | −0.559326 | ||||||||
\(169\) | 28.2375 | 2.17211 | ||||||||
\(170\) | −17.5796 | −1.34830 | ||||||||
\(171\) | −15.2152 | −1.16353 | ||||||||
\(172\) | −9.08959 | −0.693075 | ||||||||
\(173\) | −9.08924 | −0.691042 | −0.345521 | − | 0.938411i | \(-0.612298\pi\) | ||||
−0.345521 | + | 0.938411i | \(0.612298\pi\) | |||||||
\(174\) | 3.05494 | 0.231594 | ||||||||
\(175\) | 30.4309 | 2.30036 | ||||||||
\(176\) | −4.42706 | −0.333702 | ||||||||
\(177\) | −33.7218 | −2.53469 | ||||||||
\(178\) | −6.26669 | −0.469708 | ||||||||
\(179\) | 12.1436 | 0.907659 | 0.453829 | − | 0.891089i | \(-0.350058\pi\) | ||||
0.453829 | + | 0.891089i | \(0.350058\pi\) | |||||||
\(180\) | 19.0065 | 1.41666 | ||||||||
\(181\) | −6.12127 | −0.454990 | −0.227495 | − | 0.973779i | \(-0.573054\pi\) | ||||
−0.227495 | + | 0.973779i | \(0.573054\pi\) | |||||||
\(182\) | −16.8185 | −1.24667 | ||||||||
\(183\) | 16.8158 | 1.24306 | ||||||||
\(184\) | 3.62139 | 0.266973 | ||||||||
\(185\) | −6.06586 | −0.445971 | ||||||||
\(186\) | −27.9149 | −2.04682 | ||||||||
\(187\) | 19.0906 | 1.39605 | ||||||||
\(188\) | −5.38514 | −0.392752 | ||||||||
\(189\) | −12.0510 | −0.876578 | ||||||||
\(190\) | −13.3040 | −0.965176 | ||||||||
\(191\) | −13.8874 | −1.00486 | −0.502428 | − | 0.864619i | \(-0.667560\pi\) | ||||
−0.502428 | + | 0.864619i | \(0.667560\pi\) | |||||||
\(192\) | −2.76808 | −0.199769 | ||||||||
\(193\) | −8.86002 | −0.637758 | −0.318879 | − | 0.947795i | \(-0.603306\pi\) | ||||
−0.318879 | + | 0.947795i | \(0.603306\pi\) | |||||||
\(194\) | 11.0161 | 0.790912 | ||||||||
\(195\) | 72.4652 | 5.18934 | ||||||||
\(196\) | −0.140671 | −0.0100479 | ||||||||
\(197\) | −0.0391097 | −0.00278645 | −0.00139323 | − | 0.999999i | \(-0.500443\pi\) | ||||
−0.00139323 | + | 0.999999i | \(0.500443\pi\) | |||||||
\(198\) | −20.6401 | −1.46683 | ||||||||
\(199\) | 14.8184 | 1.05045 | 0.525224 | − | 0.850964i | \(-0.323981\pi\) | ||||
0.525224 | + | 0.850964i | \(0.323981\pi\) | |||||||
\(200\) | 11.6192 | 0.821598 | ||||||||
\(201\) | 20.0222 | 1.41226 | ||||||||
\(202\) | 12.9098 | 0.908328 | ||||||||
\(203\) | −2.89044 | −0.202869 | ||||||||
\(204\) | 11.9367 | 0.835736 | ||||||||
\(205\) | −11.6139 | −0.811148 | ||||||||
\(206\) | 1.88415 | 0.131275 | ||||||||
\(207\) | 16.8839 | 1.17351 | ||||||||
\(208\) | −6.42164 | −0.445261 | ||||||||
\(209\) | 14.4475 | 0.999357 | ||||||||
\(210\) | −29.5545 | −2.03946 | ||||||||
\(211\) | −13.3946 | −0.922125 | −0.461062 | − | 0.887368i | \(-0.652532\pi\) | ||||
−0.461062 | + | 0.887368i | \(0.652532\pi\) | |||||||
\(212\) | −8.55357 | −0.587461 | ||||||||
\(213\) | −9.47058 | −0.648914 | ||||||||
\(214\) | −16.7897 | −1.14772 | ||||||||
\(215\) | −37.0552 | −2.52714 | ||||||||
\(216\) | −4.60130 | −0.313079 | ||||||||
\(217\) | 26.4118 | 1.79295 | ||||||||
\(218\) | 8.89079 | 0.602160 | ||||||||
\(219\) | 45.3483 | 3.06435 | ||||||||
\(220\) | −18.0476 | −1.21677 | ||||||||
\(221\) | 27.6918 | 1.86275 | ||||||||
\(222\) | 4.11876 | 0.276433 | ||||||||
\(223\) | 20.0938 | 1.34558 | 0.672789 | − | 0.739834i | \(-0.265096\pi\) | ||||
0.672789 | + | 0.739834i | \(0.265096\pi\) | |||||||
\(224\) | 2.61903 | 0.174991 | ||||||||
\(225\) | 54.1716 | 3.61144 | ||||||||
\(226\) | −3.81909 | −0.254042 | ||||||||
\(227\) | −13.8976 | −0.922416 | −0.461208 | − | 0.887292i | \(-0.652584\pi\) | ||||
−0.461208 | + | 0.887292i | \(0.652584\pi\) | |||||||
\(228\) | 9.03353 | 0.598260 | ||||||||
\(229\) | −18.1092 | −1.19669 | −0.598345 | − | 0.801239i | \(-0.704175\pi\) | ||||
−0.598345 | + | 0.801239i | \(0.704175\pi\) | |||||||
\(230\) | 14.7632 | 0.973456 | ||||||||
\(231\) | 32.0948 | 2.11168 | ||||||||
\(232\) | −1.10363 | −0.0724569 | ||||||||
\(233\) | −0.852296 | −0.0558358 | −0.0279179 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279179 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(234\) | −29.9394 | −1.95720 | ||||||||
\(235\) | −21.9534 | −1.43208 | ||||||||
\(236\) | 12.1824 | 0.793006 | ||||||||
\(237\) | −0.693581 | −0.0450529 | ||||||||
\(238\) | −11.2940 | −0.732079 | ||||||||
\(239\) | 12.4646 | 0.806271 | 0.403135 | − | 0.915140i | \(-0.367920\pi\) | ||||
0.403135 | + | 0.915140i | \(0.367920\pi\) | |||||||
\(240\) | −11.2845 | −0.728413 | ||||||||
\(241\) | 1.75884 | 0.113297 | 0.0566484 | − | 0.998394i | \(-0.481959\pi\) | ||||
0.0566484 | + | 0.998394i | \(0.481959\pi\) | |||||||
\(242\) | 8.59882 | 0.552753 | ||||||||
\(243\) | 17.2641 | 1.10749 | ||||||||
\(244\) | −6.07490 | −0.388906 | ||||||||
\(245\) | −0.573466 | −0.0366374 | ||||||||
\(246\) | 7.88591 | 0.502787 | ||||||||
\(247\) | 20.9568 | 1.33345 | ||||||||
\(248\) | 10.0846 | 0.640370 | ||||||||
\(249\) | −34.2246 | −2.16890 | ||||||||
\(250\) | 26.9840 | 1.70662 | ||||||||
\(251\) | −17.6318 | −1.11291 | −0.556454 | − | 0.830879i | \(-0.687838\pi\) | ||||
−0.556454 | + | 0.830879i | \(0.687838\pi\) | |||||||
\(252\) | 12.2106 | 0.769198 | ||||||||
\(253\) | −16.0321 | −1.00793 | ||||||||
\(254\) | −14.8373 | −0.930976 | ||||||||
\(255\) | 48.6619 | 3.04732 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5580 | −0.720970 | −0.360485 | − | 0.932765i | \(-0.617389\pi\) | ||||
−0.360485 | + | 0.932765i | \(0.617389\pi\) | |||||||
\(258\) | 25.1607 | 1.56644 | ||||||||
\(259\) | −3.89698 | −0.242147 | ||||||||
\(260\) | −26.1788 | −1.62354 | ||||||||
\(261\) | −5.14543 | −0.318494 | ||||||||
\(262\) | −12.5690 | −0.776518 | ||||||||
\(263\) | 24.5521 | 1.51395 | 0.756975 | − | 0.653444i | \(-0.226677\pi\) | ||||
0.756975 | + | 0.653444i | \(0.226677\pi\) | |||||||
\(264\) | 12.2544 | 0.754209 | ||||||||
\(265\) | −34.8700 | −2.14205 | ||||||||
\(266\) | −8.54712 | −0.524057 | ||||||||
\(267\) | 17.3467 | 1.06160 | ||||||||
\(268\) | −7.23324 | −0.441841 | ||||||||
\(269\) | −16.4425 | −1.00252 | −0.501258 | − | 0.865298i | \(-0.667129\pi\) | ||||
−0.501258 | + | 0.865298i | \(0.667129\pi\) | |||||||
\(270\) | −18.7579 | −1.14157 | ||||||||
\(271\) | −27.0026 | −1.64029 | −0.820146 | − | 0.572155i | \(-0.806108\pi\) | ||||
−0.820146 | + | 0.572155i | \(0.806108\pi\) | |||||||
\(272\) | −4.31227 | −0.261470 | ||||||||
\(273\) | 46.5549 | 2.81763 | ||||||||
\(274\) | −10.5628 | −0.638123 | ||||||||
\(275\) | −51.4386 | −3.10187 | ||||||||
\(276\) | −10.0243 | −0.603393 | ||||||||
\(277\) | 20.4994 | 1.23169 | 0.615843 | − | 0.787869i | \(-0.288815\pi\) | ||||
0.615843 | + | 0.787869i | \(0.288815\pi\) | |||||||
\(278\) | −1.94959 | −0.116929 | ||||||||
\(279\) | 47.0169 | 2.81483 | ||||||||
\(280\) | 10.6769 | 0.638067 | ||||||||
\(281\) | −11.4124 | −0.680807 | −0.340404 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340404 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(282\) | 14.9065 | 0.887670 | ||||||||
\(283\) | 27.2109 | 1.61752 | 0.808760 | − | 0.588139i | \(-0.200139\pi\) | ||||
0.808760 | + | 0.588139i | \(0.200139\pi\) | |||||||
\(284\) | 3.42135 | 0.203020 | ||||||||
\(285\) | 36.8266 | 2.18142 | ||||||||
\(286\) | 28.4290 | 1.68104 | ||||||||
\(287\) | −7.46129 | −0.440426 | ||||||||
\(288\) | 4.66227 | 0.274727 | ||||||||
\(289\) | 1.59565 | 0.0938618 | ||||||||
\(290\) | −4.49913 | −0.264198 | ||||||||
\(291\) | −30.4935 | −1.78756 | ||||||||
\(292\) | −16.3826 | −0.958717 | ||||||||
\(293\) | −17.6980 | −1.03393 | −0.516964 | − | 0.856007i | \(-0.672938\pi\) | ||||
−0.516964 | + | 0.856007i | \(0.672938\pi\) | |||||||
\(294\) | 0.389388 | 0.0227096 | ||||||||
\(295\) | 49.6634 | 2.89152 | ||||||||
\(296\) | −1.48795 | −0.0864852 | ||||||||
\(297\) | 20.3702 | 1.18200 | ||||||||
\(298\) | −4.53225 | −0.262546 | ||||||||
\(299\) | −23.2553 | −1.34489 | ||||||||
\(300\) | −32.1627 | −1.85692 | ||||||||
\(301\) | −23.8059 | −1.37215 | ||||||||
\(302\) | 8.66262 | 0.498478 | ||||||||
\(303\) | −35.7353 | −2.05294 | ||||||||
\(304\) | −3.26346 | −0.187173 | ||||||||
\(305\) | −24.7653 | −1.41806 | ||||||||
\(306\) | −20.1050 | −1.14932 | ||||||||
\(307\) | 1.99344 | 0.113772 | 0.0568858 | − | 0.998381i | \(-0.481883\pi\) | ||||
0.0568858 | + | 0.998381i | \(0.481883\pi\) | |||||||
\(308\) | −11.5946 | −0.660664 | ||||||||
\(309\) | −5.21547 | −0.296698 | ||||||||
\(310\) | 41.1113 | 2.33496 | ||||||||
\(311\) | 8.59382 | 0.487311 | 0.243655 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243655 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(312\) | 17.7756 | 1.00635 | ||||||||
\(313\) | −6.30633 | −0.356455 | −0.178228 | − | 0.983989i | \(-0.557036\pi\) | ||||
−0.178228 | + | 0.983989i | \(0.557036\pi\) | |||||||
\(314\) | −23.2800 | −1.31376 | ||||||||
\(315\) | 49.7786 | 2.80471 | ||||||||
\(316\) | 0.250564 | 0.0140953 | ||||||||
\(317\) | 21.9281 | 1.23160 | 0.615802 | − | 0.787901i | \(-0.288832\pi\) | ||||
0.615802 | + | 0.787901i | \(0.288832\pi\) | |||||||
\(318\) | 23.6770 | 1.32774 | ||||||||
\(319\) | 4.88583 | 0.273554 | ||||||||
\(320\) | 4.07666 | 0.227892 | ||||||||
\(321\) | 46.4751 | 2.59399 | ||||||||
\(322\) | 9.48455 | 0.528553 | ||||||||
\(323\) | 14.0729 | 0.783039 | ||||||||
\(324\) | −1.25004 | −0.0694468 | ||||||||
\(325\) | −74.6140 | −4.13884 | ||||||||
\(326\) | −2.91089 | −0.161219 | ||||||||
\(327\) | −24.6104 | −1.36096 | ||||||||
\(328\) | −2.84887 | −0.157303 | ||||||||
\(329\) | −14.1039 | −0.777571 | ||||||||
\(330\) | 49.9572 | 2.75005 | ||||||||
\(331\) | 16.8527 | 0.926308 | 0.463154 | − | 0.886278i | \(-0.346718\pi\) | ||||
0.463154 | + | 0.886278i | \(0.346718\pi\) | |||||||
\(332\) | 12.3640 | 0.678565 | ||||||||
\(333\) | −6.93721 | −0.380157 | ||||||||
\(334\) | −18.5603 | −1.01557 | ||||||||
\(335\) | −29.4875 | −1.61107 | ||||||||
\(336\) | −7.24969 | −0.395503 | ||||||||
\(337\) | 0.979731 | 0.0533693 | 0.0266847 | − | 0.999644i | \(-0.491505\pi\) | ||||
0.0266847 | + | 0.999644i | \(0.491505\pi\) | |||||||
\(338\) | 28.2375 | 1.53592 | ||||||||
\(339\) | 10.5716 | 0.574168 | ||||||||
\(340\) | −17.5796 | −0.953390 | ||||||||
\(341\) | −44.6449 | −2.41766 | ||||||||
\(342\) | −15.2152 | −0.822741 | ||||||||
\(343\) | −18.7016 | −1.00979 | ||||||||
\(344\) | −9.08959 | −0.490078 | ||||||||
\(345\) | −40.8657 | −2.20014 | ||||||||
\(346\) | −9.08924 | −0.488640 | ||||||||
\(347\) | 31.1263 | 1.67095 | 0.835474 | − | 0.549530i | \(-0.185193\pi\) | ||||
0.835474 | + | 0.549530i | \(0.185193\pi\) | |||||||
\(348\) | 3.05494 | 0.163762 | ||||||||
\(349\) | −15.6169 | −0.835953 | −0.417977 | − | 0.908458i | \(-0.637261\pi\) | ||||
−0.417977 | + | 0.908458i | \(0.637261\pi\) | |||||||
\(350\) | 30.4309 | 1.62660 | ||||||||
\(351\) | 29.5479 | 1.57715 | ||||||||
\(352\) | −4.42706 | −0.235963 | ||||||||
\(353\) | 0.904647 | 0.0481495 | 0.0240748 | − | 0.999710i | \(-0.492336\pi\) | ||||
0.0240748 | + | 0.999710i | \(0.492336\pi\) | |||||||
\(354\) | −33.7218 | −1.79230 | ||||||||
\(355\) | 13.9477 | 0.740267 | ||||||||
\(356\) | −6.26669 | −0.332134 | ||||||||
\(357\) | 31.2626 | 1.65459 | ||||||||
\(358\) | 12.1436 | 0.641812 | ||||||||
\(359\) | 14.0762 | 0.742914 | 0.371457 | − | 0.928450i | \(-0.378858\pi\) | ||||
0.371457 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(360\) | 19.0065 | 1.00173 | ||||||||
\(361\) | −8.34980 | −0.439463 | ||||||||
\(362\) | −6.12127 | −0.321727 | ||||||||
\(363\) | −23.8022 | −1.24929 | ||||||||
\(364\) | −16.8185 | −0.881528 | ||||||||
\(365\) | −66.7861 | −3.49575 | ||||||||
\(366\) | 16.8158 | 0.878977 | ||||||||
\(367\) | 24.3904 | 1.27317 | 0.636584 | − | 0.771208i | \(-0.280347\pi\) | ||||
0.636584 | + | 0.771208i | \(0.280347\pi\) | |||||||
\(368\) | 3.62139 | 0.188778 | ||||||||
\(369\) | −13.2822 | −0.691444 | ||||||||
\(370\) | −6.06586 | −0.315349 | ||||||||
\(371\) | −22.4021 | −1.16306 | ||||||||
\(372\) | −27.9149 | −1.44732 | ||||||||
\(373\) | 17.3071 | 0.896130 | 0.448065 | − | 0.894001i | \(-0.352113\pi\) | ||||
0.448065 | + | 0.894001i | \(0.352113\pi\) | |||||||
\(374\) | 19.0906 | 0.987154 | ||||||||
\(375\) | −74.6939 | −3.85718 | ||||||||
\(376\) | −5.38514 | −0.277717 | ||||||||
\(377\) | 7.08712 | 0.365005 | ||||||||
\(378\) | −12.0510 | −0.619834 | ||||||||
\(379\) | −1.53442 | −0.0788181 | −0.0394090 | − | 0.999223i | \(-0.512548\pi\) | ||||
−0.0394090 | + | 0.999223i | \(0.512548\pi\) | |||||||
\(380\) | −13.3040 | −0.682483 | ||||||||
\(381\) | 41.0709 | 2.10412 | ||||||||
\(382\) | −13.8874 | −0.710540 | ||||||||
\(383\) | 15.2502 | 0.779250 | 0.389625 | − | 0.920974i | \(-0.372605\pi\) | ||||
0.389625 | + | 0.920974i | \(0.372605\pi\) | |||||||
\(384\) | −2.76808 | −0.141258 | ||||||||
\(385\) | −47.2672 | −2.40896 | ||||||||
\(386\) | −8.86002 | −0.450963 | ||||||||
\(387\) | −42.3781 | −2.15420 | ||||||||
\(388\) | 11.0161 | 0.559259 | ||||||||
\(389\) | 9.01331 | 0.456993 | 0.228497 | − | 0.973545i | \(-0.426619\pi\) | ||||
0.228497 | + | 0.973545i | \(0.426619\pi\) | |||||||
\(390\) | 72.4652 | 3.66942 | ||||||||
\(391\) | −15.6164 | −0.789756 | ||||||||
\(392\) | −0.140671 | −0.00710494 | ||||||||
\(393\) | 34.7921 | 1.75503 | ||||||||
\(394\) | −0.0391097 | −0.00197032 | ||||||||
\(395\) | 1.02146 | 0.0513954 | ||||||||
\(396\) | −20.6401 | −1.03721 | ||||||||
\(397\) | 13.3055 | 0.667786 | 0.333893 | − | 0.942611i | \(-0.391638\pi\) | ||||
0.333893 | + | 0.942611i | \(0.391638\pi\) | |||||||
\(398\) | 14.8184 | 0.742779 | ||||||||
\(399\) | 23.6591 | 1.18444 | ||||||||
\(400\) | 11.6192 | 0.580958 | ||||||||
\(401\) | 21.7260 | 1.08495 | 0.542473 | − | 0.840073i | \(-0.317488\pi\) | ||||
0.542473 | + | 0.840073i | \(0.317488\pi\) | |||||||
\(402\) | 20.0222 | 0.998616 | ||||||||
\(403\) | −64.7594 | −3.22589 | ||||||||
\(404\) | 12.9098 | 0.642285 | ||||||||
\(405\) | −5.09600 | −0.253222 | ||||||||
\(406\) | −2.89044 | −0.143450 | ||||||||
\(407\) | 6.58723 | 0.326517 | ||||||||
\(408\) | 11.9367 | 0.590955 | ||||||||
\(409\) | −18.7793 | −0.928576 | −0.464288 | − | 0.885684i | \(-0.653690\pi\) | ||||
−0.464288 | + | 0.885684i | \(0.653690\pi\) | |||||||
\(410\) | −11.6139 | −0.573569 | ||||||||
\(411\) | 29.2387 | 1.44224 | ||||||||
\(412\) | 1.88415 | 0.0928253 | ||||||||
\(413\) | 31.9061 | 1.56999 | ||||||||
\(414\) | 16.8839 | 0.829800 | ||||||||
\(415\) | 50.4040 | 2.47423 | ||||||||
\(416\) | −6.42164 | −0.314847 | ||||||||
\(417\) | 5.39663 | 0.264274 | ||||||||
\(418\) | 14.4475 | 0.706652 | ||||||||
\(419\) | −31.9674 | −1.56171 | −0.780855 | − | 0.624712i | \(-0.785216\pi\) | ||||
−0.780855 | + | 0.624712i | \(0.785216\pi\) | |||||||
\(420\) | −29.5545 | −1.44211 | ||||||||
\(421\) | −0.152108 | −0.00741329 | −0.00370664 | − | 0.999993i | \(-0.501180\pi\) | ||||
−0.00370664 | + | 0.999993i | \(0.501180\pi\) | |||||||
\(422\) | −13.3946 | −0.652040 | ||||||||
\(423\) | −25.1070 | −1.22074 | ||||||||
\(424\) | −8.55357 | −0.415398 | ||||||||
\(425\) | −50.1049 | −2.43044 | ||||||||
\(426\) | −9.47058 | −0.458851 | ||||||||
\(427\) | −15.9104 | −0.769956 | ||||||||
\(428\) | −16.7897 | −0.811559 | ||||||||
\(429\) | −78.6937 | −3.79937 | ||||||||
\(430\) | −37.0552 | −1.78696 | ||||||||
\(431\) | 20.7945 | 1.00164 | 0.500819 | − | 0.865552i | \(-0.333032\pi\) | ||||
0.500819 | + | 0.865552i | \(0.333032\pi\) | |||||||
\(432\) | −4.60130 | −0.221380 | ||||||||
\(433\) | 16.8286 | 0.808731 | 0.404365 | − | 0.914598i | \(-0.367492\pi\) | ||||
0.404365 | + | 0.914598i | \(0.367492\pi\) | |||||||
\(434\) | 26.4118 | 1.26781 | ||||||||
\(435\) | 12.4539 | 0.597121 | ||||||||
\(436\) | 8.89079 | 0.425792 | ||||||||
\(437\) | −11.8183 | −0.565346 | ||||||||
\(438\) | 45.3483 | 2.16682 | ||||||||
\(439\) | 9.79890 | 0.467676 | 0.233838 | − | 0.972276i | \(-0.424871\pi\) | ||||
0.233838 | + | 0.972276i | \(0.424871\pi\) | |||||||
\(440\) | −18.0476 | −0.860385 | ||||||||
\(441\) | −0.655845 | −0.0312307 | ||||||||
\(442\) | 27.6918 | 1.31717 | ||||||||
\(443\) | −14.8303 | −0.704610 | −0.352305 | − | 0.935885i | \(-0.614602\pi\) | ||||
−0.352305 | + | 0.935885i | \(0.614602\pi\) | |||||||
\(444\) | 4.11876 | 0.195468 | ||||||||
\(445\) | −25.5472 | −1.21105 | ||||||||
\(446\) | 20.0938 | 0.951467 | ||||||||
\(447\) | 12.5456 | 0.593388 | ||||||||
\(448\) | 2.61903 | 0.123738 | ||||||||
\(449\) | 16.6571 | 0.786098 | 0.393049 | − | 0.919518i | \(-0.371420\pi\) | ||||
0.393049 | + | 0.919518i | \(0.371420\pi\) | |||||||
\(450\) | 54.1716 | 2.55368 | ||||||||
\(451\) | 12.6121 | 0.593881 | ||||||||
\(452\) | −3.81909 | −0.179635 | ||||||||
\(453\) | −23.9788 | −1.12662 | ||||||||
\(454\) | −13.8976 | −0.652247 | ||||||||
\(455\) | −68.5632 | −3.21429 | ||||||||
\(456\) | 9.03353 | 0.423034 | ||||||||
\(457\) | −4.84273 | −0.226533 | −0.113267 | − | 0.993565i | \(-0.536131\pi\) | ||||
−0.113267 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(458\) | −18.1092 | −0.846187 | ||||||||
\(459\) | 19.8420 | 0.926147 | ||||||||
\(460\) | 14.7632 | 0.688337 | ||||||||
\(461\) | −12.0470 | −0.561083 | −0.280541 | − | 0.959842i | \(-0.590514\pi\) | ||||
−0.280541 | + | 0.959842i | \(0.590514\pi\) | |||||||
\(462\) | 32.0948 | 1.49318 | ||||||||
\(463\) | 29.5573 | 1.37364 | 0.686821 | − | 0.726827i | \(-0.259006\pi\) | ||||
0.686821 | + | 0.726827i | \(0.259006\pi\) | |||||||
\(464\) | −1.10363 | −0.0512348 | ||||||||
\(465\) | −113.799 | −5.27732 | ||||||||
\(466\) | −0.852296 | −0.0394819 | ||||||||
\(467\) | −26.9216 | −1.24578 | −0.622891 | − | 0.782309i | \(-0.714042\pi\) | ||||
−0.622891 | + | 0.782309i | \(0.714042\pi\) | |||||||
\(468\) | −29.9394 | −1.38395 | ||||||||
\(469\) | −18.9441 | −0.874757 | ||||||||
\(470\) | −21.9534 | −1.01263 | ||||||||
\(471\) | 64.4408 | 2.96928 | ||||||||
\(472\) | 12.1824 | 0.560740 | ||||||||
\(473\) | 40.2401 | 1.85024 | ||||||||
\(474\) | −0.693581 | −0.0318572 | ||||||||
\(475\) | −37.9187 | −1.73983 | ||||||||
\(476\) | −11.2940 | −0.517658 | ||||||||
\(477\) | −39.8790 | −1.82594 | ||||||||
\(478\) | 12.4646 | 0.570120 | ||||||||
\(479\) | −4.54626 | −0.207724 | −0.103862 | − | 0.994592i | \(-0.533120\pi\) | ||||
−0.103862 | + | 0.994592i | \(0.533120\pi\) | |||||||
\(480\) | −11.2845 | −0.515066 | ||||||||
\(481\) | 9.55507 | 0.435674 | ||||||||
\(482\) | 1.75884 | 0.0801129 | ||||||||
\(483\) | −26.2540 | −1.19460 | ||||||||
\(484\) | 8.59882 | 0.390855 | ||||||||
\(485\) | 44.9090 | 2.03921 | ||||||||
\(486\) | 17.2641 | 0.783116 | ||||||||
\(487\) | −18.4525 | −0.836165 | −0.418082 | − | 0.908409i | \(-0.637298\pi\) | ||||
−0.418082 | + | 0.908409i | \(0.637298\pi\) | |||||||
\(488\) | −6.07490 | −0.274998 | ||||||||
\(489\) | 8.05759 | 0.364377 | ||||||||
\(490\) | −0.573466 | −0.0259066 | ||||||||
\(491\) | 24.6500 | 1.11244 | 0.556220 | − | 0.831035i | \(-0.312251\pi\) | ||||
0.556220 | + | 0.831035i | \(0.312251\pi\) | |||||||
\(492\) | 7.88591 | 0.355524 | ||||||||
\(493\) | 4.75915 | 0.214341 | ||||||||
\(494\) | 20.9568 | 0.942891 | ||||||||
\(495\) | −84.1428 | −3.78194 | ||||||||
\(496\) | 10.0846 | 0.452810 | ||||||||
\(497\) | 8.96063 | 0.401939 | ||||||||
\(498\) | −34.2246 | −1.53364 | ||||||||
\(499\) | −40.5470 | −1.81513 | −0.907566 | − | 0.419910i | \(-0.862062\pi\) | ||||
−0.907566 | + | 0.419910i | \(0.862062\pi\) | |||||||
\(500\) | 26.9840 | 1.20676 | ||||||||
\(501\) | 51.3763 | 2.29532 | ||||||||
\(502\) | −17.6318 | −0.786945 | ||||||||
\(503\) | 5.55903 | 0.247865 | 0.123932 | − | 0.992291i | \(-0.460449\pi\) | ||||
0.123932 | + | 0.992291i | \(0.460449\pi\) | |||||||
\(504\) | 12.2106 | 0.543905 | ||||||||
\(505\) | 52.6287 | 2.34195 | ||||||||
\(506\) | −16.0321 | −0.712714 | ||||||||
\(507\) | −78.1636 | −3.47137 | ||||||||
\(508\) | −14.8373 | −0.658299 | ||||||||
\(509\) | −42.5344 | −1.88530 | −0.942651 | − | 0.333779i | \(-0.891676\pi\) | ||||
−0.942651 | + | 0.333779i | \(0.891676\pi\) | |||||||
\(510\) | 48.6619 | 2.15478 | ||||||||
\(511\) | −42.9065 | −1.89807 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.0162 | 0.662981 | ||||||||
\(514\) | −11.5580 | −0.509803 | ||||||||
\(515\) | 7.68103 | 0.338467 | ||||||||
\(516\) | 25.1607 | 1.10764 | ||||||||
\(517\) | 23.8403 | 1.04850 | ||||||||
\(518\) | −3.89698 | −0.171224 | ||||||||
\(519\) | 25.1597 | 1.10439 | ||||||||
\(520\) | −26.1788 | −1.14802 | ||||||||
\(521\) | 6.56873 | 0.287781 | 0.143891 | − | 0.989594i | \(-0.454039\pi\) | ||||
0.143891 | + | 0.989594i | \(0.454039\pi\) | |||||||
\(522\) | −5.14543 | −0.225209 | ||||||||
\(523\) | 5.40387 | 0.236295 | 0.118147 | − | 0.992996i | \(-0.462304\pi\) | ||||
0.118147 | + | 0.992996i | \(0.462304\pi\) | |||||||
\(524\) | −12.5690 | −0.549081 | ||||||||
\(525\) | −84.2353 | −3.67633 | ||||||||
\(526\) | 24.5521 | 1.07052 | ||||||||
\(527\) | −43.4873 | −1.89434 | ||||||||
\(528\) | 12.2544 | 0.533306 | ||||||||
\(529\) | −9.88550 | −0.429804 | ||||||||
\(530\) | −34.8700 | −1.51465 | ||||||||
\(531\) | 56.7976 | 2.46481 | ||||||||
\(532\) | −8.54712 | −0.370565 | ||||||||
\(533\) | 18.2944 | 0.792420 | ||||||||
\(534\) | 17.3467 | 0.750665 | ||||||||
\(535\) | −68.4457 | −2.95917 | ||||||||
\(536\) | −7.23324 | −0.312428 | ||||||||
\(537\) | −33.6146 | −1.45058 | ||||||||
\(538\) | −16.4425 | −0.708886 | ||||||||
\(539\) | 0.622757 | 0.0268240 | ||||||||
\(540\) | −18.7579 | −0.807213 | ||||||||
\(541\) | −2.60376 | −0.111944 | −0.0559721 | − | 0.998432i | \(-0.517826\pi\) | ||||
−0.0559721 | + | 0.998432i | \(0.517826\pi\) | |||||||
\(542\) | −27.0026 | −1.15986 | ||||||||
\(543\) | 16.9442 | 0.727144 | ||||||||
\(544\) | −4.31227 | −0.184887 | ||||||||
\(545\) | 36.2447 | 1.55255 | ||||||||
\(546\) | 46.5549 | 1.99237 | ||||||||
\(547\) | −19.5946 | −0.837807 | −0.418903 | − | 0.908031i | \(-0.637585\pi\) | ||||
−0.418903 | + | 0.908031i | \(0.637585\pi\) | |||||||
\(548\) | −10.5628 | −0.451221 | ||||||||
\(549\) | −28.3228 | −1.20879 | ||||||||
\(550\) | −51.4386 | −2.19335 | ||||||||
\(551\) | 3.60166 | 0.153436 | ||||||||
\(552\) | −10.0243 | −0.426663 | ||||||||
\(553\) | 0.656235 | 0.0279059 | ||||||||
\(554\) | 20.4994 | 0.870934 | ||||||||
\(555\) | 16.7908 | 0.712729 | ||||||||
\(556\) | −1.94959 | −0.0826812 | ||||||||
\(557\) | −13.7897 | −0.584289 | −0.292144 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292144 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(558\) | 47.0169 | 1.99038 | ||||||||
\(559\) | 58.3701 | 2.46879 | ||||||||
\(560\) | 10.6769 | 0.451181 | ||||||||
\(561\) | −52.8444 | −2.23109 | ||||||||
\(562\) | −11.4124 | −0.481404 | ||||||||
\(563\) | −28.1674 | −1.18712 | −0.593558 | − | 0.804791i | \(-0.702277\pi\) | ||||
−0.593558 | + | 0.804791i | \(0.702277\pi\) | |||||||
\(564\) | 14.9065 | 0.627677 | ||||||||
\(565\) | −15.5691 | −0.654998 | ||||||||
\(566\) | 27.2109 | 1.14376 | ||||||||
\(567\) | −3.27390 | −0.137491 | ||||||||
\(568\) | 3.42135 | 0.143557 | ||||||||
\(569\) | 26.6749 | 1.11827 | 0.559135 | − | 0.829077i | \(-0.311133\pi\) | ||||
0.559135 | + | 0.829077i | \(0.311133\pi\) | |||||||
\(570\) | 36.8266 | 1.54250 | ||||||||
\(571\) | −21.2917 | −0.891031 | −0.445516 | − | 0.895274i | \(-0.646980\pi\) | ||||
−0.445516 | + | 0.895274i | \(0.646980\pi\) | |||||||
\(572\) | 28.4290 | 1.18867 | ||||||||
\(573\) | 38.4414 | 1.60591 | ||||||||
\(574\) | −7.46129 | −0.311428 | ||||||||
\(575\) | 42.0775 | 1.75475 | ||||||||
\(576\) | 4.66227 | 0.194261 | ||||||||
\(577\) | −28.7089 | −1.19517 | −0.597584 | − | 0.801806i | \(-0.703873\pi\) | ||||
−0.597584 | + | 0.801806i | \(0.703873\pi\) | |||||||
\(578\) | 1.59565 | 0.0663703 | ||||||||
\(579\) | 24.5252 | 1.01923 | ||||||||
\(580\) | −4.49913 | −0.186816 | ||||||||
\(581\) | 32.3818 | 1.34342 | ||||||||
\(582\) | −30.4935 | −1.26400 | ||||||||
\(583\) | 37.8671 | 1.56830 | ||||||||
\(584\) | −16.3826 | −0.677915 | ||||||||
\(585\) | −122.053 | −5.04627 | ||||||||
\(586\) | −17.6980 | −0.731098 | ||||||||
\(587\) | −4.92944 | −0.203460 | −0.101730 | − | 0.994812i | \(-0.532438\pi\) | ||||
−0.101730 | + | 0.994812i | \(0.532438\pi\) | |||||||
\(588\) | 0.389388 | 0.0160581 | ||||||||
\(589\) | −32.9106 | −1.35606 | ||||||||
\(590\) | 49.6634 | 2.04461 | ||||||||
\(591\) | 0.108259 | 0.00445317 | ||||||||
\(592\) | −1.48795 | −0.0611543 | ||||||||
\(593\) | −8.14147 | −0.334330 | −0.167165 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167165 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(594\) | 20.3702 | 0.835800 | ||||||||
\(595\) | −46.0417 | −1.88752 | ||||||||
\(596\) | −4.53225 | −0.185648 | ||||||||
\(597\) | −41.0185 | −1.67878 | ||||||||
\(598\) | −23.2553 | −0.950980 | ||||||||
\(599\) | −5.47770 | −0.223813 | −0.111906 | − | 0.993719i | \(-0.535696\pi\) | ||||
−0.111906 | + | 0.993719i | \(0.535696\pi\) | |||||||
\(600\) | −32.1627 | −1.31304 | ||||||||
\(601\) | −11.2020 | −0.456938 | −0.228469 | − | 0.973551i | \(-0.573372\pi\) | ||||
−0.228469 | + | 0.973551i | \(0.573372\pi\) | |||||||
\(602\) | −23.8059 | −0.970257 | ||||||||
\(603\) | −33.7233 | −1.37332 | ||||||||
\(604\) | 8.66262 | 0.352477 | ||||||||
\(605\) | 35.0544 | 1.42517 | ||||||||
\(606\) | −35.7353 | −1.45165 | ||||||||
\(607\) | 44.3486 | 1.80005 | 0.900027 | − | 0.435834i | \(-0.143547\pi\) | ||||
0.900027 | + | 0.435834i | \(0.143547\pi\) | |||||||
\(608\) | −3.26346 | −0.132351 | ||||||||
\(609\) | 8.00098 | 0.324216 | ||||||||
\(610\) | −24.7653 | −1.00272 | ||||||||
\(611\) | 34.5815 | 1.39902 | ||||||||
\(612\) | −20.1050 | −0.812695 | ||||||||
\(613\) | 5.82769 | 0.235378 | 0.117689 | − | 0.993050i | \(-0.462451\pi\) | ||||
0.117689 | + | 0.993050i | \(0.462451\pi\) | |||||||
\(614\) | 1.99344 | 0.0804487 | ||||||||
\(615\) | 32.1481 | 1.29634 | ||||||||
\(616\) | −11.5946 | −0.467160 | ||||||||
\(617\) | −9.86089 | −0.396985 | −0.198492 | − | 0.980102i | \(-0.563604\pi\) | ||||
−0.198492 | + | 0.980102i | \(0.563604\pi\) | |||||||
\(618\) | −5.21547 | −0.209797 | ||||||||
\(619\) | −11.7007 | −0.470289 | −0.235144 | − | 0.971960i | \(-0.575556\pi\) | ||||
−0.235144 | + | 0.971960i | \(0.575556\pi\) | |||||||
\(620\) | 41.1113 | 1.65107 | ||||||||
\(621\) | −16.6631 | −0.668668 | ||||||||
\(622\) | 8.59382 | 0.344581 | ||||||||
\(623\) | −16.4127 | −0.657560 | ||||||||
\(624\) | 17.7756 | 0.711594 | ||||||||
\(625\) | 51.9089 | 2.07636 | ||||||||
\(626\) | −6.30633 | −0.252052 | ||||||||
\(627\) | −39.9920 | −1.59712 | ||||||||
\(628\) | −23.2800 | −0.928972 | ||||||||
\(629\) | 6.41643 | 0.255840 | ||||||||
\(630\) | 49.7786 | 1.98323 | ||||||||
\(631\) | 28.9703 | 1.15329 | 0.576644 | − | 0.816996i | \(-0.304362\pi\) | ||||
0.576644 | + | 0.816996i | \(0.304362\pi\) | |||||||
\(632\) | 0.250564 | 0.00996689 | ||||||||
\(633\) | 37.0774 | 1.47370 | ||||||||
\(634\) | 21.9281 | 0.870875 | ||||||||
\(635\) | −60.4866 | −2.40034 | ||||||||
\(636\) | 23.6770 | 0.938853 | ||||||||
\(637\) | 0.903337 | 0.0357915 | ||||||||
\(638\) | 4.88583 | 0.193432 | ||||||||
\(639\) | 15.9513 | 0.631023 | ||||||||
\(640\) | 4.07666 | 0.161144 | ||||||||
\(641\) | 0.106120 | 0.00419148 | 0.00209574 | − | 0.999998i | \(-0.499333\pi\) | ||||
0.00209574 | + | 0.999998i | \(0.499333\pi\) | |||||||
\(642\) | 46.4751 | 1.83423 | ||||||||
\(643\) | −1.78669 | −0.0704604 | −0.0352302 | − | 0.999379i | \(-0.511216\pi\) | ||||
−0.0352302 | + | 0.999379i | \(0.511216\pi\) | |||||||
\(644\) | 9.48455 | 0.373744 | ||||||||
\(645\) | 102.572 | 4.03875 | ||||||||
\(646\) | 14.0729 | 0.553692 | ||||||||
\(647\) | −19.6340 | −0.771892 | −0.385946 | − | 0.922521i | \(-0.626125\pi\) | ||||
−0.385946 | + | 0.922521i | \(0.626125\pi\) | |||||||
\(648\) | −1.25004 | −0.0491063 | ||||||||
\(649\) | −53.9321 | −2.11702 | ||||||||
\(650\) | −74.6140 | −2.92660 | ||||||||
\(651\) | −73.1099 | −2.86540 | ||||||||
\(652\) | −2.91089 | −0.113999 | ||||||||
\(653\) | −6.77993 | −0.265319 | −0.132660 | − | 0.991162i | \(-0.542352\pi\) | ||||
−0.132660 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(654\) | −24.6104 | −0.962344 | ||||||||
\(655\) | −51.2397 | −2.00210 | ||||||||
\(656\) | −2.84887 | −0.111230 | ||||||||
\(657\) | −76.3799 | −2.97987 | ||||||||
\(658\) | −14.1039 | −0.549826 | ||||||||
\(659\) | −21.2496 | −0.827767 | −0.413884 | − | 0.910330i | \(-0.635828\pi\) | ||||
−0.413884 | + | 0.910330i | \(0.635828\pi\) | |||||||
\(660\) | 49.9572 | 1.94458 | ||||||||
\(661\) | −21.5810 | −0.839402 | −0.419701 | − | 0.907662i | \(-0.637865\pi\) | ||||
−0.419701 | + | 0.907662i | \(0.637865\pi\) | |||||||
\(662\) | 16.8527 | 0.654999 | ||||||||
\(663\) | −76.6532 | −2.97697 | ||||||||
\(664\) | 12.3640 | 0.479818 | ||||||||
\(665\) | −34.8437 | −1.35118 | ||||||||
\(666\) | −6.93721 | −0.268812 | ||||||||
\(667\) | −3.99668 | −0.154752 | ||||||||
\(668\) | −18.5603 | −0.718118 | ||||||||
\(669\) | −55.6212 | −2.15044 | ||||||||
\(670\) | −29.4875 | −1.13920 | ||||||||
\(671\) | 26.8939 | 1.03823 | ||||||||
\(672\) | −7.24969 | −0.279663 | ||||||||
\(673\) | −41.7443 | −1.60912 | −0.804562 | − | 0.593869i | \(-0.797600\pi\) | ||||
−0.804562 | + | 0.593869i | \(0.797600\pi\) | |||||||
\(674\) | 0.979731 | 0.0377378 | ||||||||
\(675\) | −53.4632 | −2.05780 | ||||||||
\(676\) | 28.2375 | 1.08606 | ||||||||
\(677\) | 1.35759 | 0.0521765 | 0.0260882 | − | 0.999660i | \(-0.491695\pi\) | ||||
0.0260882 | + | 0.999660i | \(0.491695\pi\) | |||||||
\(678\) | 10.5716 | 0.405998 | ||||||||
\(679\) | 28.8516 | 1.10722 | ||||||||
\(680\) | −17.5796 | −0.674149 | ||||||||
\(681\) | 38.4697 | 1.47416 | ||||||||
\(682\) | −44.6449 | −1.70954 | ||||||||
\(683\) | 12.0638 | 0.461607 | 0.230803 | − | 0.973000i | \(-0.425865\pi\) | ||||
0.230803 | + | 0.973000i | \(0.425865\pi\) | |||||||
\(684\) | −15.2152 | −0.581766 | ||||||||
\(685\) | −43.0610 | −1.64528 | ||||||||
\(686\) | −18.7016 | −0.714032 | ||||||||
\(687\) | 50.1277 | 1.91249 | ||||||||
\(688\) | −9.08959 | −0.346537 | ||||||||
\(689\) | 54.9279 | 2.09259 | ||||||||
\(690\) | −40.8657 | −1.55573 | ||||||||
\(691\) | 47.8693 | 1.82103 | 0.910517 | − | 0.413472i | \(-0.135684\pi\) | ||||
0.910517 | + | 0.413472i | \(0.135684\pi\) | |||||||
\(692\) | −9.08924 | −0.345521 | ||||||||
\(693\) | −54.0572 | −2.05346 | ||||||||
\(694\) | 31.1263 | 1.18154 | ||||||||
\(695\) | −7.94783 | −0.301478 | ||||||||
\(696\) | 3.05494 | 0.115797 | ||||||||
\(697\) | 12.2851 | 0.465331 | ||||||||
\(698\) | −15.6169 | −0.591108 | ||||||||
\(699\) | 2.35923 | 0.0892341 | ||||||||
\(700\) | 30.4309 | 1.15018 | ||||||||
\(701\) | 14.1512 | 0.534485 | 0.267242 | − | 0.963629i | \(-0.413888\pi\) | ||||
0.267242 | + | 0.963629i | \(0.413888\pi\) | |||||||
\(702\) | 29.5479 | 1.11521 | ||||||||
\(703\) | 4.85586 | 0.183142 | ||||||||
\(704\) | −4.42706 | −0.166851 | ||||||||
\(705\) | 60.7688 | 2.28868 | ||||||||
\(706\) | 0.904647 | 0.0340469 | ||||||||
\(707\) | 33.8111 | 1.27160 | ||||||||
\(708\) | −33.7218 | −1.26734 | ||||||||
\(709\) | −17.5721 | −0.659934 | −0.329967 | − | 0.943992i | \(-0.607038\pi\) | ||||
−0.329967 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(710\) | 13.9477 | 0.523447 | ||||||||
\(711\) | 1.16820 | 0.0438108 | ||||||||
\(712\) | −6.26669 | −0.234854 | ||||||||
\(713\) | 36.5201 | 1.36769 | ||||||||
\(714\) | 31.2626 | 1.16997 | ||||||||
\(715\) | 115.895 | 4.33423 | ||||||||
\(716\) | 12.1436 | 0.453829 | ||||||||
\(717\) | −34.5031 | −1.28854 | ||||||||
\(718\) | 14.0762 | 0.525320 | ||||||||
\(719\) | 48.9097 | 1.82402 | 0.912012 | − | 0.410164i | \(-0.134529\pi\) | ||||
0.912012 | + | 0.410164i | \(0.134529\pi\) | |||||||
\(720\) | 19.0065 | 0.708330 | ||||||||
\(721\) | 4.93464 | 0.183776 | ||||||||
\(722\) | −8.34980 | −0.310747 | ||||||||
\(723\) | −4.86861 | −0.181065 | ||||||||
\(724\) | −6.12127 | −0.227495 | ||||||||
\(725\) | −12.8233 | −0.476244 | ||||||||
\(726\) | −23.8022 | −0.883383 | ||||||||
\(727\) | −48.5496 | −1.80060 | −0.900302 | − | 0.435266i | \(-0.856654\pi\) | ||||
−0.900302 | + | 0.435266i | \(0.856654\pi\) | |||||||
\(728\) | −16.8185 | −0.623335 | ||||||||
\(729\) | −44.0383 | −1.63105 | ||||||||
\(730\) | −66.7861 | −2.47187 | ||||||||
\(731\) | 39.1967 | 1.44974 | ||||||||
\(732\) | 16.8158 | 0.621530 | ||||||||
\(733\) | 35.8106 | 1.32270 | 0.661348 | − | 0.750079i | \(-0.269985\pi\) | ||||
0.661348 | + | 0.750079i | \(0.269985\pi\) | |||||||
\(734\) | 24.3904 | 0.900265 | ||||||||
\(735\) | 1.58740 | 0.0585522 | ||||||||
\(736\) | 3.62139 | 0.133486 | ||||||||
\(737\) | 32.0220 | 1.17954 | ||||||||
\(738\) | −13.2822 | −0.488925 | ||||||||
\(739\) | −17.7784 | −0.653989 | −0.326995 | − | 0.945026i | \(-0.606036\pi\) | ||||
−0.326995 | + | 0.945026i | \(0.606036\pi\) | |||||||
\(740\) | −6.06586 | −0.222985 | ||||||||
\(741\) | −58.0101 | −2.13105 | ||||||||
\(742\) | −22.4021 | −0.822406 | ||||||||
\(743\) | −43.6704 | −1.60211 | −0.801056 | − | 0.598589i | \(-0.795728\pi\) | ||||
−0.801056 | + | 0.598589i | \(0.795728\pi\) | |||||||
\(744\) | −27.9149 | −1.02341 | ||||||||
\(745\) | −18.4764 | −0.676924 | ||||||||
\(746\) | 17.3071 | 0.633659 | ||||||||
\(747\) | 57.6445 | 2.10910 | ||||||||
\(748\) | 19.0906 | 0.698023 | ||||||||
\(749\) | −43.9727 | −1.60673 | ||||||||
\(750\) | −74.6939 | −2.72744 | ||||||||
\(751\) | 25.9057 | 0.945312 | 0.472656 | − | 0.881247i | \(-0.343295\pi\) | ||||
0.472656 | + | 0.881247i | \(0.343295\pi\) | |||||||
\(752\) | −5.38514 | −0.196376 | ||||||||
\(753\) | 48.8062 | 1.77860 | ||||||||
\(754\) | 7.08712 | 0.258098 | ||||||||
\(755\) | 35.3145 | 1.28523 | ||||||||
\(756\) | −12.0510 | −0.438289 | ||||||||
\(757\) | 23.7023 | 0.861476 | 0.430738 | − | 0.902477i | \(-0.358253\pi\) | ||||
0.430738 | + | 0.902477i | \(0.358253\pi\) | |||||||
\(758\) | −1.53442 | −0.0557328 | ||||||||
\(759\) | 44.3782 | 1.61083 | ||||||||
\(760\) | −13.3040 | −0.482588 | ||||||||
\(761\) | −11.5547 | −0.418858 | −0.209429 | − | 0.977824i | \(-0.567160\pi\) | ||||
−0.209429 | + | 0.977824i | \(0.567160\pi\) | |||||||
\(762\) | 41.0709 | 1.48784 | ||||||||
\(763\) | 23.2853 | 0.842983 | ||||||||
\(764\) | −13.8874 | −0.502428 | ||||||||
\(765\) | −81.9611 | −2.96331 | ||||||||
\(766\) | 15.2502 | 0.551013 | ||||||||
\(767\) | −78.2309 | −2.82476 | ||||||||
\(768\) | −2.76808 | −0.0998845 | ||||||||
\(769\) | −32.2203 | −1.16189 | −0.580946 | − | 0.813942i | \(-0.697317\pi\) | ||||
−0.580946 | + | 0.813942i | \(0.697317\pi\) | |||||||
\(770\) | −47.2672 | −1.70339 | ||||||||
\(771\) | 31.9936 | 1.15222 | ||||||||
\(772\) | −8.86002 | −0.318879 | ||||||||
\(773\) | 43.7149 | 1.57231 | 0.786157 | − | 0.618026i | \(-0.212068\pi\) | ||||
0.786157 | + | 0.618026i | \(0.212068\pi\) | |||||||
\(774\) | −42.3781 | −1.52325 | ||||||||
\(775\) | 117.174 | 4.20901 | ||||||||
\(776\) | 11.0161 | 0.395456 | ||||||||
\(777\) | 10.7872 | 0.386987 | ||||||||
\(778\) | 9.01331 | 0.323143 | ||||||||
\(779\) | 9.29719 | 0.333106 | ||||||||
\(780\) | 72.4652 | 2.59467 | ||||||||
\(781\) | −15.1465 | −0.541985 | ||||||||
\(782\) | −15.6164 | −0.558442 | ||||||||
\(783\) | 5.07814 | 0.181478 | ||||||||
\(784\) | −0.140671 | −0.00502395 | ||||||||
\(785\) | −94.9045 | −3.38729 | ||||||||
\(786\) | 34.7921 | 1.24099 | ||||||||
\(787\) | 20.3664 | 0.725984 | 0.362992 | − | 0.931792i | \(-0.381755\pi\) | ||||
0.362992 | + | 0.931792i | \(0.381755\pi\) | |||||||
\(788\) | −0.0391097 | −0.00139323 | ||||||||
\(789\) | −67.9623 | −2.41952 | ||||||||
\(790\) | 1.02146 | 0.0363420 | ||||||||
\(791\) | −10.0023 | −0.355642 | ||||||||
\(792\) | −20.6401 | −0.733415 | ||||||||
\(793\) | 39.0108 | 1.38532 | ||||||||
\(794\) | 13.3055 | 0.472196 | ||||||||
\(795\) | 96.5229 | 3.42331 | ||||||||
\(796\) | 14.8184 | 0.525224 | ||||||||
\(797\) | 21.6137 | 0.765597 | 0.382798 | − | 0.923832i | \(-0.374960\pi\) | ||||
0.382798 | + | 0.923832i | \(0.374960\pi\) | |||||||
\(798\) | 23.6591 | 0.837524 | ||||||||
\(799\) | 23.2222 | 0.821541 | ||||||||
\(800\) | 11.6192 | 0.410799 | ||||||||
\(801\) | −29.2170 | −1.03233 | ||||||||
\(802\) | 21.7260 | 0.767173 | ||||||||
\(803\) | 72.5265 | 2.55940 | ||||||||
\(804\) | 20.0222 | 0.706128 | ||||||||
\(805\) | 38.6653 | 1.36277 | ||||||||
\(806\) | −64.7594 | −2.28105 | ||||||||
\(807\) | 45.5141 | 1.60217 | ||||||||
\(808\) | 12.9098 | 0.454164 | ||||||||
\(809\) | 3.17882 | 0.111761 | 0.0558806 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558806 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(810\) | −5.09600 | −0.179055 | ||||||||
\(811\) | 15.0015 | 0.526775 | 0.263388 | − | 0.964690i | \(-0.415160\pi\) | ||||
0.263388 | + | 0.964690i | \(0.415160\pi\) | |||||||
\(812\) | −2.89044 | −0.101435 | ||||||||
\(813\) | 74.7454 | 2.62144 | ||||||||
\(814\) | 6.58723 | 0.230882 | ||||||||
\(815\) | −11.8667 | −0.415673 | ||||||||
\(816\) | 11.9367 | 0.417868 | ||||||||
\(817\) | 29.6635 | 1.03780 | ||||||||
\(818\) | −18.7793 | −0.656602 | ||||||||
\(819\) | −78.4123 | −2.73995 | ||||||||
\(820\) | −11.6139 | −0.405574 | ||||||||
\(821\) | 42.0632 | 1.46802 | 0.734008 | − | 0.679141i | \(-0.237648\pi\) | ||||
0.734008 | + | 0.679141i | \(0.237648\pi\) | |||||||
\(822\) | 29.2387 | 1.01982 | ||||||||
\(823\) | 25.1776 | 0.877636 | 0.438818 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438818 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(824\) | 1.88415 | 0.0656374 | ||||||||
\(825\) | 142.386 | 4.95725 | ||||||||
\(826\) | 31.9061 | 1.11015 | ||||||||
\(827\) | 25.7884 | 0.896751 | 0.448375 | − | 0.893845i | \(-0.352003\pi\) | ||||
0.448375 | + | 0.893845i | \(0.352003\pi\) | |||||||
\(828\) | 16.8839 | 0.586757 | ||||||||
\(829\) | −46.5701 | −1.61745 | −0.808723 | − | 0.588190i | \(-0.799841\pi\) | ||||
−0.808723 | + | 0.588190i | \(0.799841\pi\) | |||||||
\(830\) | 50.4040 | 1.74955 | ||||||||
\(831\) | −56.7439 | −1.96842 | ||||||||
\(832\) | −6.42164 | −0.222630 | ||||||||
\(833\) | 0.606609 | 0.0210178 | ||||||||
\(834\) | 5.39663 | 0.186870 | ||||||||
\(835\) | −75.6638 | −2.61846 | ||||||||
\(836\) | 14.4475 | 0.499679 | ||||||||
\(837\) | −46.4021 | −1.60389 | ||||||||
\(838\) | −31.9674 | −1.10430 | ||||||||
\(839\) | 27.1817 | 0.938417 | 0.469208 | − | 0.883088i | \(-0.344539\pi\) | ||||
0.469208 | + | 0.883088i | \(0.344539\pi\) | |||||||
\(840\) | −29.5545 | −1.01973 | ||||||||
\(841\) | −27.7820 | −0.958000 | ||||||||
\(842\) | −0.152108 | −0.00524199 | ||||||||
\(843\) | 31.5905 | 1.08803 | ||||||||
\(844\) | −13.3946 | −0.461062 | ||||||||
\(845\) | 115.115 | 3.96006 | ||||||||
\(846\) | −25.1070 | −0.863196 | ||||||||
\(847\) | 22.5206 | 0.773816 | ||||||||
\(848\) | −8.55357 | −0.293731 | ||||||||
\(849\) | −75.3220 | −2.58504 | ||||||||
\(850\) | −50.1049 | −1.71858 | ||||||||
\(851\) | −5.38845 | −0.184714 | ||||||||
\(852\) | −9.47058 | −0.324457 | ||||||||
\(853\) | 43.4306 | 1.48704 | 0.743518 | − | 0.668716i | \(-0.233156\pi\) | ||||
0.743518 | + | 0.668716i | \(0.233156\pi\) | |||||||
\(854\) | −15.9104 | −0.544441 | ||||||||
\(855\) | −62.0270 | −2.12128 | ||||||||
\(856\) | −16.7897 | −0.573859 | ||||||||
\(857\) | 13.6322 | 0.465667 | 0.232833 | − | 0.972517i | \(-0.425200\pi\) | ||||
0.232833 | + | 0.972517i | \(0.425200\pi\) | |||||||
\(858\) | −78.6937 | −2.68656 | ||||||||
\(859\) | 2.83685 | 0.0967921 | 0.0483960 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483960 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(860\) | −37.0552 | −1.26357 | ||||||||
\(861\) | 20.6534 | 0.703867 | ||||||||
\(862\) | 20.7945 | 0.708264 | ||||||||
\(863\) | 2.18430 | 0.0743546 | 0.0371773 | − | 0.999309i | \(-0.488163\pi\) | ||||
0.0371773 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(864\) | −4.60130 | −0.156539 | ||||||||
\(865\) | −37.0537 | −1.25986 | ||||||||
\(866\) | 16.8286 | 0.571859 | ||||||||
\(867\) | −4.41689 | −0.150005 | ||||||||
\(868\) | 26.4118 | 0.896474 | ||||||||
\(869\) | −1.10926 | −0.0376291 | ||||||||
\(870\) | 12.4539 | 0.422228 | ||||||||
\(871\) | 46.4493 | 1.57387 | ||||||||
\(872\) | 8.89079 | 0.301080 | ||||||||
\(873\) | 51.3602 | 1.73828 | ||||||||
\(874\) | −11.8183 | −0.399760 | ||||||||
\(875\) | 70.6720 | 2.38915 | ||||||||
\(876\) | 45.3483 | 1.53218 | ||||||||
\(877\) | 56.1083 | 1.89464 | 0.947321 | − | 0.320285i | \(-0.103779\pi\) | ||||
0.947321 | + | 0.320285i | \(0.103779\pi\) | |||||||
\(878\) | 9.79890 | 0.330697 | ||||||||
\(879\) | 48.9895 | 1.65237 | ||||||||
\(880\) | −18.0476 | −0.608384 | ||||||||
\(881\) | 23.8877 | 0.804798 | 0.402399 | − | 0.915464i | \(-0.368177\pi\) | ||||
0.402399 | + | 0.915464i | \(0.368177\pi\) | |||||||
\(882\) | −0.655845 | −0.0220834 | ||||||||
\(883\) | −58.3397 | −1.96329 | −0.981644 | − | 0.190721i | \(-0.938917\pi\) | ||||
−0.981644 | + | 0.190721i | \(0.938917\pi\) | |||||||
\(884\) | 27.6918 | 0.931377 | ||||||||
\(885\) | −137.472 | −4.62108 | ||||||||
\(886\) | −14.8303 | −0.498234 | ||||||||
\(887\) | −40.1668 | −1.34867 | −0.674334 | − | 0.738426i | \(-0.735569\pi\) | ||||
−0.674334 | + | 0.738426i | \(0.735569\pi\) | |||||||
\(888\) | 4.11876 | 0.138217 | ||||||||
\(889\) | −38.8594 | −1.30330 | ||||||||
\(890\) | −25.5472 | −0.856343 | ||||||||
\(891\) | 5.53401 | 0.185396 | ||||||||
\(892\) | 20.0938 | 0.672789 | ||||||||
\(893\) | 17.5742 | 0.588099 | ||||||||
\(894\) | 12.5456 | 0.419589 | ||||||||
\(895\) | 49.5055 | 1.65479 | ||||||||
\(896\) | 2.61903 | 0.0874957 | ||||||||
\(897\) | 64.3725 | 2.14934 | ||||||||
\(898\) | 16.6571 | 0.555855 | ||||||||
\(899\) | −11.1296 | −0.371194 | ||||||||
\(900\) | 54.1716 | 1.80572 | ||||||||
\(901\) | 36.8853 | 1.22883 | ||||||||
\(902\) | 12.6121 | 0.419937 | ||||||||
\(903\) | 65.8967 | 2.19291 | ||||||||
\(904\) | −3.81909 | −0.127021 | ||||||||
\(905\) | −24.9543 | −0.829510 | ||||||||
\(906\) | −23.9788 | −0.796643 | ||||||||
\(907\) | 43.4544 | 1.44288 | 0.721439 | − | 0.692478i | \(-0.243481\pi\) | ||||
0.721439 | + | 0.692478i | \(0.243481\pi\) | |||||||
\(908\) | −13.8976 | −0.461208 | ||||||||
\(909\) | 60.1888 | 1.99634 | ||||||||
\(910\) | −68.5632 | −2.27285 | ||||||||
\(911\) | −7.91301 | −0.262170 | −0.131085 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131085 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(912\) | 9.03353 | 0.299130 | ||||||||
\(913\) | −54.7363 | −1.81151 | ||||||||
\(914\) | −4.84273 | −0.160183 | ||||||||
\(915\) | 68.5524 | 2.26627 | ||||||||
\(916\) | −18.1092 | −0.598345 | ||||||||
\(917\) | −32.9187 | −1.08707 | ||||||||
\(918\) | 19.8420 | 0.654885 | ||||||||
\(919\) | −17.1197 | −0.564727 | −0.282363 | − | 0.959308i | \(-0.591118\pi\) | ||||
−0.282363 | + | 0.959308i | \(0.591118\pi\) | |||||||
\(920\) | 14.7632 | 0.486728 | ||||||||
\(921\) | −5.51800 | −0.181824 | ||||||||
\(922\) | −12.0470 | −0.396745 | ||||||||
\(923\) | −21.9707 | −0.723175 | ||||||||
\(924\) | 32.0948 | 1.05584 | ||||||||
\(925\) | −17.2887 | −0.568449 | ||||||||
\(926\) | 29.5573 | 0.971312 | ||||||||
\(927\) | 8.78441 | 0.288518 | ||||||||
\(928\) | −1.10363 | −0.0362285 | ||||||||
\(929\) | 15.9814 | 0.524334 | 0.262167 | − | 0.965023i | \(-0.415563\pi\) | ||||
0.262167 | + | 0.965023i | \(0.415563\pi\) | |||||||
\(930\) | −113.799 | −3.73163 | ||||||||
\(931\) | 0.459074 | 0.0150455 | ||||||||
\(932\) | −0.852296 | −0.0279179 | ||||||||
\(933\) | −23.7884 | −0.778797 | ||||||||
\(934\) | −26.9216 | −0.880901 | ||||||||
\(935\) | 77.8261 | 2.54518 | ||||||||
\(936\) | −29.9394 | −0.978601 | ||||||||
\(937\) | 1.31248 | 0.0428770 | 0.0214385 | − | 0.999770i | \(-0.493175\pi\) | ||||
0.0214385 | + | 0.999770i | \(0.493175\pi\) | |||||||
\(938\) | −18.9441 | −0.618546 | ||||||||
\(939\) | 17.4564 | 0.569669 | ||||||||
\(940\) | −21.9534 | −0.716041 | ||||||||
\(941\) | −13.7344 | −0.447728 | −0.223864 | − | 0.974620i | \(-0.571867\pi\) | ||||
−0.223864 | + | 0.974620i | \(0.571867\pi\) | |||||||
\(942\) | 64.4408 | 2.09960 | ||||||||
\(943\) | −10.3169 | −0.335964 | ||||||||
\(944\) | 12.1824 | 0.396503 | ||||||||
\(945\) | −49.1276 | −1.59812 | ||||||||
\(946\) | 40.2401 | 1.30832 | ||||||||
\(947\) | −50.6953 | −1.64738 | −0.823689 | − | 0.567042i | \(-0.808088\pi\) | ||||
−0.823689 | + | 0.567042i | \(0.808088\pi\) | |||||||
\(948\) | −0.693581 | −0.0225265 | ||||||||
\(949\) | 105.203 | 3.41503 | ||||||||
\(950\) | −37.9187 | −1.23024 | ||||||||
\(951\) | −60.6987 | −1.96829 | ||||||||
\(952\) | −11.2940 | −0.366040 | ||||||||
\(953\) | 29.9770 | 0.971051 | 0.485525 | − | 0.874223i | \(-0.338628\pi\) | ||||
0.485525 | + | 0.874223i | \(0.338628\pi\) | |||||||
\(954\) | −39.8790 | −1.29113 | ||||||||
\(955\) | −56.6141 | −1.83199 | ||||||||
\(956\) | 12.4646 | 0.403135 | ||||||||
\(957\) | −13.5244 | −0.437181 | ||||||||
\(958\) | −4.54626 | −0.146883 | ||||||||
\(959\) | −27.6643 | −0.893328 | ||||||||
\(960\) | −11.2845 | −0.364206 | ||||||||
\(961\) | 70.6982 | 2.28059 | ||||||||
\(962\) | 9.55507 | 0.308068 | ||||||||
\(963\) | −78.2779 | −2.52247 | ||||||||
\(964\) | 1.75884 | 0.0566484 | ||||||||
\(965\) | −36.1193 | −1.16272 | ||||||||
\(966\) | −26.2540 | −0.844709 | ||||||||
\(967\) | −47.2758 | −1.52029 | −0.760143 | − | 0.649756i | \(-0.774871\pi\) | ||||
−0.760143 | + | 0.649756i | \(0.774871\pi\) | |||||||
\(968\) | 8.59882 | 0.276376 | ||||||||
\(969\) | −38.9550 | −1.25142 | ||||||||
\(970\) | 44.9090 | 1.44194 | ||||||||
\(971\) | 57.2167 | 1.83617 | 0.918086 | − | 0.396382i | \(-0.129734\pi\) | ||||
0.918086 | + | 0.396382i | \(0.129734\pi\) | |||||||
\(972\) | 17.2641 | 0.553747 | ||||||||
\(973\) | −5.10605 | −0.163692 | ||||||||
\(974\) | −18.4525 | −0.591258 | ||||||||
\(975\) | 206.538 | 6.61450 | ||||||||
\(976\) | −6.07490 | −0.194453 | ||||||||
\(977\) | −17.2206 | −0.550935 | −0.275468 | − | 0.961310i | \(-0.588833\pi\) | ||||
−0.275468 | + | 0.961310i | \(0.588833\pi\) | |||||||
\(978\) | 8.05759 | 0.257653 | ||||||||
\(979\) | 27.7430 | 0.886670 | ||||||||
\(980\) | −0.573466 | −0.0183187 | ||||||||
\(981\) | 41.4513 | 1.32344 | ||||||||
\(982\) | 24.6500 | 0.786614 | ||||||||
\(983\) | −15.4510 | −0.492810 | −0.246405 | − | 0.969167i | \(-0.579249\pi\) | ||||
−0.246405 | + | 0.969167i | \(0.579249\pi\) | |||||||
\(984\) | 7.88591 | 0.251393 | ||||||||
\(985\) | −0.159437 | −0.00508008 | ||||||||
\(986\) | 4.75915 | 0.151562 | ||||||||
\(987\) | 39.0406 | 1.24268 | ||||||||
\(988\) | 20.9568 | 0.666725 | ||||||||
\(989\) | −32.9170 | −1.04670 | ||||||||
\(990\) | −84.1428 | −2.67423 | ||||||||
\(991\) | 59.2672 | 1.88269 | 0.941343 | − | 0.337452i | \(-0.109565\pi\) | ||||
0.941343 | + | 0.337452i | \(0.109565\pi\) | |||||||
\(992\) | 10.0846 | 0.320185 | ||||||||
\(993\) | −46.6496 | −1.48038 | ||||||||
\(994\) | 8.96063 | 0.284214 | ||||||||
\(995\) | 60.4096 | 1.91511 | ||||||||
\(996\) | −34.2246 | −1.08445 | ||||||||
\(997\) | −32.8228 | −1.03951 | −0.519754 | − | 0.854316i | \(-0.673976\pi\) | ||||
−0.519754 | + | 0.854316i | \(0.673976\pi\) | |||||||
\(998\) | −40.5470 | −1.28349 | ||||||||
\(999\) | 6.84649 | 0.216613 |
(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 | 8002.2.a.d.1.9 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.9 | ✓ | 69 | 1.1 | even | 1 | trivial |