Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, 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("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(0\) |
Dimension: | \(195\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54911 | −1.80249 | −0.901247 | − | 0.433305i | \(-0.857347\pi\) | ||||
−0.901247 | + | 0.433305i | \(0.857347\pi\) | |||||||
\(3\) | 2.95187 | 1.70427 | 0.852133 | − | 0.523326i | \(-0.175309\pi\) | ||||
0.852133 | + | 0.523326i | \(0.175309\pi\) | |||||||
\(4\) | 4.49797 | 2.24899 | ||||||||
\(5\) | 1.50040 | 0.670997 | 0.335499 | − | 0.942041i | \(-0.391095\pi\) | ||||
0.335499 | + | 0.942041i | \(0.391095\pi\) | |||||||
\(6\) | −7.52466 | −3.07193 | ||||||||
\(7\) | 0.00462218 | 0.00174702 | 0.000873511 | − | 1.00000i | \(-0.499722\pi\) | ||||
0.000873511 | 1.00000i | \(0.499722\pi\) | ||||||||
\(8\) | −6.36761 | −2.25129 | ||||||||
\(9\) | 5.71356 | 1.90452 | ||||||||
\(10\) | −3.82468 | −1.20947 | ||||||||
\(11\) | 0.915110 | 0.275916 | 0.137958 | − | 0.990438i | \(-0.455946\pi\) | ||||
0.137958 | + | 0.990438i | \(0.455946\pi\) | |||||||
\(12\) | 13.2774 | 3.83287 | ||||||||
\(13\) | 3.64298 | 1.01038 | 0.505190 | − | 0.863008i | \(-0.331422\pi\) | ||||
0.505190 | + | 0.863008i | \(0.331422\pi\) | |||||||
\(14\) | −0.0117825 | −0.00314900 | ||||||||
\(15\) | 4.42898 | 1.14356 | ||||||||
\(16\) | 7.23581 | 1.80895 | ||||||||
\(17\) | −5.36049 | −1.30011 | −0.650055 | − | 0.759887i | \(-0.725254\pi\) | ||||
−0.650055 | + | 0.759887i | \(0.725254\pi\) | |||||||
\(18\) | −14.5645 | −3.43289 | ||||||||
\(19\) | 5.52584 | 1.26771 | 0.633857 | − | 0.773450i | \(-0.281471\pi\) | ||||
0.633857 | + | 0.773450i | \(0.281471\pi\) | |||||||
\(20\) | 6.74874 | 1.50906 | ||||||||
\(21\) | 0.0136441 | 0.00297739 | ||||||||
\(22\) | −2.33272 | −0.497337 | ||||||||
\(23\) | 2.61394 | 0.545044 | 0.272522 | − | 0.962150i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(24\) | −18.7964 | −3.83680 | ||||||||
\(25\) | −2.74881 | −0.549763 | ||||||||
\(26\) | −9.28636 | −1.82120 | ||||||||
\(27\) | 8.01009 | 1.54154 | ||||||||
\(28\) | 0.0207905 | 0.00392903 | ||||||||
\(29\) | −3.05203 | −0.566748 | −0.283374 | − | 0.959010i | \(-0.591454\pi\) | ||||
−0.283374 | + | 0.959010i | \(0.591454\pi\) | |||||||
\(30\) | −11.2900 | −2.06126 | ||||||||
\(31\) | 7.05511 | 1.26714 | 0.633568 | − | 0.773687i | \(-0.281590\pi\) | ||||
0.633568 | + | 0.773687i | \(0.281590\pi\) | |||||||
\(32\) | −5.70967 | −1.00934 | ||||||||
\(33\) | 2.70129 | 0.470234 | ||||||||
\(34\) | 13.6645 | 2.34344 | ||||||||
\(35\) | 0.00693510 | 0.00117225 | ||||||||
\(36\) | 25.6994 | 4.28324 | ||||||||
\(37\) | −4.15585 | −0.683217 | −0.341608 | − | 0.939842i | \(-0.610972\pi\) | ||||
−0.341608 | + | 0.939842i | \(0.610972\pi\) | |||||||
\(38\) | −14.0860 | −2.28505 | ||||||||
\(39\) | 10.7536 | 1.72196 | ||||||||
\(40\) | −9.55394 | −1.51061 | ||||||||
\(41\) | 9.94726 | 1.55350 | 0.776750 | − | 0.629809i | \(-0.216867\pi\) | ||||
0.776750 | + | 0.629809i | \(0.216867\pi\) | |||||||
\(42\) | −0.0347803 | −0.00536672 | ||||||||
\(43\) | 10.0386 | 1.53087 | 0.765436 | − | 0.643512i | \(-0.222523\pi\) | ||||
0.765436 | + | 0.643512i | \(0.222523\pi\) | |||||||
\(44\) | 4.11614 | 0.620531 | ||||||||
\(45\) | 8.57260 | 1.27793 | ||||||||
\(46\) | −6.66322 | −0.982438 | ||||||||
\(47\) | 5.72607 | 0.835233 | 0.417616 | − | 0.908623i | \(-0.362866\pi\) | ||||
0.417616 | + | 0.908623i | \(0.362866\pi\) | |||||||
\(48\) | 21.3592 | 3.08294 | ||||||||
\(49\) | −6.99998 | −0.999997 | ||||||||
\(50\) | 7.00703 | 0.990944 | ||||||||
\(51\) | −15.8235 | −2.21573 | ||||||||
\(52\) | 16.3860 | 2.27233 | ||||||||
\(53\) | −8.21492 | −1.12841 | −0.564203 | − | 0.825636i | \(-0.690817\pi\) | ||||
−0.564203 | + | 0.825636i | \(0.690817\pi\) | |||||||
\(54\) | −20.4186 | −2.77862 | ||||||||
\(55\) | 1.37303 | 0.185139 | ||||||||
\(56\) | −0.0294323 | −0.00393305 | ||||||||
\(57\) | 16.3116 | 2.16052 | ||||||||
\(58\) | 7.77997 | 1.02156 | ||||||||
\(59\) | −13.6497 | −1.77704 | −0.888519 | − | 0.458840i | \(-0.848265\pi\) | ||||
−0.888519 | + | 0.458840i | \(0.848265\pi\) | |||||||
\(60\) | 19.9214 | 2.57184 | ||||||||
\(61\) | 11.3779 | 1.45680 | 0.728398 | − | 0.685154i | \(-0.240265\pi\) | ||||
0.728398 | + | 0.685154i | \(0.240265\pi\) | |||||||
\(62\) | −17.9843 | −2.28400 | ||||||||
\(63\) | 0.0264091 | 0.00332724 | ||||||||
\(64\) | 0.0829690 | 0.0103711 | ||||||||
\(65\) | 5.46591 | 0.677962 | ||||||||
\(66\) | −6.88589 | −0.847594 | ||||||||
\(67\) | −11.5822 | −1.41499 | −0.707495 | − | 0.706719i | \(-0.750175\pi\) | ||||
−0.707495 | + | 0.706719i | \(0.750175\pi\) | |||||||
\(68\) | −24.1113 | −2.92393 | ||||||||
\(69\) | 7.71602 | 0.928899 | ||||||||
\(70\) | −0.0176784 | −0.00211297 | ||||||||
\(71\) | −3.36596 | −0.399466 | −0.199733 | − | 0.979850i | \(-0.564007\pi\) | ||||
−0.199733 | + | 0.979850i | \(0.564007\pi\) | |||||||
\(72\) | −36.3817 | −4.28763 | ||||||||
\(73\) | −3.92477 | −0.459359 | −0.229680 | − | 0.973266i | \(-0.573768\pi\) | ||||
−0.229680 | + | 0.973266i | \(0.573768\pi\) | |||||||
\(74\) | 10.5937 | 1.23149 | ||||||||
\(75\) | −8.11415 | −0.936942 | ||||||||
\(76\) | 24.8551 | 2.85107 | ||||||||
\(77\) | 0.00422980 | 0.000482031 0 | ||||||||
\(78\) | −27.4122 | −3.10382 | ||||||||
\(79\) | 10.5215 | 1.18376 | 0.591878 | − | 0.806027i | \(-0.298387\pi\) | ||||
0.591878 | + | 0.806027i | \(0.298387\pi\) | |||||||
\(80\) | 10.8566 | 1.21380 | ||||||||
\(81\) | 6.50409 | 0.722677 | ||||||||
\(82\) | −25.3567 | −2.80018 | ||||||||
\(83\) | 15.7822 | 1.73232 | 0.866159 | − | 0.499768i | \(-0.166581\pi\) | ||||
0.866159 | + | 0.499768i | \(0.166581\pi\) | |||||||
\(84\) | 0.0613708 | 0.00669610 | ||||||||
\(85\) | −8.04285 | −0.872370 | ||||||||
\(86\) | −25.5895 | −2.75939 | ||||||||
\(87\) | −9.00921 | −0.965888 | ||||||||
\(88\) | −5.82706 | −0.621167 | ||||||||
\(89\) | −13.9848 | −1.48239 | −0.741194 | − | 0.671291i | \(-0.765740\pi\) | ||||
−0.741194 | + | 0.671291i | \(0.765740\pi\) | |||||||
\(90\) | −21.8525 | −2.30346 | ||||||||
\(91\) | 0.0168385 | 0.00176516 | ||||||||
\(92\) | 11.7574 | 1.22580 | ||||||||
\(93\) | 20.8258 | 2.15954 | ||||||||
\(94\) | −14.5964 | −1.50550 | ||||||||
\(95\) | 8.29094 | 0.850633 | ||||||||
\(96\) | −16.8542 | −1.72018 | ||||||||
\(97\) | 14.5548 | 1.47782 | 0.738910 | − | 0.673805i | \(-0.235341\pi\) | ||||
0.738910 | + | 0.673805i | \(0.235341\pi\) | |||||||
\(98\) | 17.8437 | 1.80249 | ||||||||
\(99\) | 5.22853 | 0.525487 | ||||||||
\(100\) | −12.3641 | −1.23641 | ||||||||
\(101\) | −15.2426 | −1.51670 | −0.758348 | − | 0.651850i | \(-0.773993\pi\) | ||||
−0.758348 | + | 0.651850i | \(0.773993\pi\) | |||||||
\(102\) | 40.3358 | 3.99384 | ||||||||
\(103\) | 8.46423 | 0.834005 | 0.417003 | − | 0.908905i | \(-0.363081\pi\) | ||||
0.417003 | + | 0.908905i | \(0.363081\pi\) | |||||||
\(104\) | −23.1971 | −2.27466 | ||||||||
\(105\) | 0.0204716 | 0.00199782 | ||||||||
\(106\) | 20.9408 | 2.03395 | ||||||||
\(107\) | 19.5701 | 1.89191 | 0.945957 | − | 0.324291i | \(-0.105126\pi\) | ||||
0.945957 | + | 0.324291i | \(0.105126\pi\) | |||||||
\(108\) | 36.0292 | 3.46691 | ||||||||
\(109\) | −7.54636 | −0.722810 | −0.361405 | − | 0.932409i | \(-0.617703\pi\) | ||||
−0.361405 | + | 0.932409i | \(0.617703\pi\) | |||||||
\(110\) | −3.50000 | −0.333712 | ||||||||
\(111\) | −12.2675 | −1.16438 | ||||||||
\(112\) | 0.0334452 | 0.00316028 | ||||||||
\(113\) | 11.2685 | 1.06005 | 0.530023 | − | 0.847983i | \(-0.322183\pi\) | ||||
0.530023 | + | 0.847983i | \(0.322183\pi\) | |||||||
\(114\) | −41.5801 | −3.89433 | ||||||||
\(115\) | 3.92194 | 0.365723 | ||||||||
\(116\) | −13.7279 | −1.27461 | ||||||||
\(117\) | 20.8144 | 1.92429 | ||||||||
\(118\) | 34.7946 | 3.20310 | ||||||||
\(119\) | −0.0247772 | −0.00227132 | ||||||||
\(120\) | −28.2020 | −2.57448 | ||||||||
\(121\) | −10.1626 | −0.923870 | ||||||||
\(122\) | −29.0036 | −2.62587 | ||||||||
\(123\) | 29.3630 | 2.64758 | ||||||||
\(124\) | 31.7337 | 2.84977 | ||||||||
\(125\) | −11.6263 | −1.03989 | ||||||||
\(126\) | −0.0673198 | −0.00599733 | ||||||||
\(127\) | 1.93886 | 0.172046 | 0.0860230 | − | 0.996293i | \(-0.472584\pi\) | ||||
0.0860230 | + | 0.996293i | \(0.472584\pi\) | |||||||
\(128\) | 11.2078 | 0.990643 | ||||||||
\(129\) | 29.6327 | 2.60901 | ||||||||
\(130\) | −13.9332 | −1.22202 | ||||||||
\(131\) | 0.526451 | 0.0459962 | 0.0229981 | − | 0.999736i | \(-0.492679\pi\) | ||||
0.0229981 | + | 0.999736i | \(0.492679\pi\) | |||||||
\(132\) | 12.1503 | 1.05755 | ||||||||
\(133\) | 0.0255414 | 0.00221472 | ||||||||
\(134\) | 29.5243 | 2.55051 | ||||||||
\(135\) | 12.0183 | 1.03437 | ||||||||
\(136\) | 34.1335 | 2.92692 | ||||||||
\(137\) | 7.77265 | 0.664063 | 0.332031 | − | 0.943268i | \(-0.392266\pi\) | ||||
0.332031 | + | 0.943268i | \(0.392266\pi\) | |||||||
\(138\) | −19.6690 | −1.67434 | ||||||||
\(139\) | −7.75632 | −0.657883 | −0.328941 | − | 0.944350i | \(-0.606692\pi\) | ||||
−0.328941 | + | 0.944350i | \(0.606692\pi\) | |||||||
\(140\) | 0.0311939 | 0.00263637 | ||||||||
\(141\) | 16.9026 | 1.42346 | ||||||||
\(142\) | 8.58020 | 0.720035 | ||||||||
\(143\) | 3.33372 | 0.278780 | ||||||||
\(144\) | 41.3422 | 3.44519 | ||||||||
\(145\) | −4.57925 | −0.380286 | ||||||||
\(146\) | 10.0047 | 0.827993 | ||||||||
\(147\) | −20.6631 | −1.70426 | ||||||||
\(148\) | −18.6929 | −1.53655 | ||||||||
\(149\) | −9.34367 | −0.765463 | −0.382732 | − | 0.923860i | \(-0.625017\pi\) | ||||
−0.382732 | + | 0.923860i | \(0.625017\pi\) | |||||||
\(150\) | 20.6839 | 1.68883 | ||||||||
\(151\) | 2.86280 | 0.232971 | 0.116486 | − | 0.993192i | \(-0.462837\pi\) | ||||
0.116486 | + | 0.993192i | \(0.462837\pi\) | |||||||
\(152\) | −35.1864 | −2.85399 | ||||||||
\(153\) | −30.6275 | −2.47608 | ||||||||
\(154\) | −0.0107822 | −0.000868858 0 | ||||||||
\(155\) | 10.5855 | 0.850244 | ||||||||
\(156\) | 48.3694 | 3.87266 | ||||||||
\(157\) | 10.3224 | 0.823815 | 0.411908 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411908 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(158\) | −26.8204 | −2.13371 | ||||||||
\(159\) | −24.2494 | −1.92310 | ||||||||
\(160\) | −8.56676 | −0.677262 | ||||||||
\(161\) | 0.0120821 | 0.000952203 0 | ||||||||
\(162\) | −16.5797 | −1.30262 | ||||||||
\(163\) | −0.192412 | −0.0150709 | −0.00753545 | − | 0.999972i | \(-0.502399\pi\) | ||||
−0.00753545 | + | 0.999972i | \(0.502399\pi\) | |||||||
\(164\) | 44.7425 | 3.49380 | ||||||||
\(165\) | 4.05300 | 0.315526 | ||||||||
\(166\) | −40.2305 | −3.12249 | ||||||||
\(167\) | 17.6694 | 1.36730 | 0.683651 | − | 0.729809i | \(-0.260391\pi\) | ||||
0.683651 | + | 0.729809i | \(0.260391\pi\) | |||||||
\(168\) | −0.0868804 | −0.00670297 | ||||||||
\(169\) | 0.271286 | 0.0208682 | ||||||||
\(170\) | 20.5021 | 1.57244 | ||||||||
\(171\) | 31.5722 | 2.41439 | ||||||||
\(172\) | 45.1533 | 3.44291 | ||||||||
\(173\) | −18.2056 | −1.38414 | −0.692071 | − | 0.721829i | \(-0.743302\pi\) | ||||
−0.692071 | + | 0.721829i | \(0.743302\pi\) | |||||||
\(174\) | 22.9655 | 1.74101 | ||||||||
\(175\) | −0.0127055 | −0.000960447 0 | ||||||||
\(176\) | 6.62156 | 0.499119 | ||||||||
\(177\) | −40.2922 | −3.02854 | ||||||||
\(178\) | 35.6489 | 2.67200 | ||||||||
\(179\) | 9.83691 | 0.735245 | 0.367623 | − | 0.929975i | \(-0.380172\pi\) | ||||
0.367623 | + | 0.929975i | \(0.380172\pi\) | |||||||
\(180\) | 38.5593 | 2.87404 | ||||||||
\(181\) | −4.34576 | −0.323018 | −0.161509 | − | 0.986871i | \(-0.551636\pi\) | ||||
−0.161509 | + | 0.986871i | \(0.551636\pi\) | |||||||
\(182\) | −0.0429233 | −0.00318168 | ||||||||
\(183\) | 33.5862 | 2.48277 | ||||||||
\(184\) | −16.6445 | −1.22705 | ||||||||
\(185\) | −6.23541 | −0.458437 | ||||||||
\(186\) | −53.0873 | −3.89255 | ||||||||
\(187\) | −4.90544 | −0.358721 | ||||||||
\(188\) | 25.7557 | 1.87843 | ||||||||
\(189\) | 0.0370241 | 0.00269311 | ||||||||
\(190\) | −21.1345 | −1.53326 | ||||||||
\(191\) | 23.3581 | 1.69013 | 0.845065 | − | 0.534663i | \(-0.179561\pi\) | ||||
0.845065 | + | 0.534663i | \(0.179561\pi\) | |||||||
\(192\) | 0.244914 | 0.0176751 | ||||||||
\(193\) | 4.53940 | 0.326753 | 0.163376 | − | 0.986564i | \(-0.447761\pi\) | ||||
0.163376 | + | 0.986564i | \(0.447761\pi\) | |||||||
\(194\) | −37.1019 | −2.66376 | ||||||||
\(195\) | 16.1347 | 1.15543 | ||||||||
\(196\) | −31.4857 | −2.24898 | ||||||||
\(197\) | −24.8451 | −1.77014 | −0.885072 | − | 0.465455i | \(-0.845891\pi\) | ||||
−0.885072 | + | 0.465455i | \(0.845891\pi\) | |||||||
\(198\) | −13.3281 | −0.947188 | ||||||||
\(199\) | 4.05814 | 0.287674 | 0.143837 | − | 0.989601i | \(-0.454056\pi\) | ||||
0.143837 | + | 0.989601i | \(0.454056\pi\) | |||||||
\(200\) | 17.5034 | 1.23768 | ||||||||
\(201\) | −34.1892 | −2.41152 | ||||||||
\(202\) | 38.8551 | 2.73383 | ||||||||
\(203\) | −0.0141070 | −0.000990120 0 | ||||||||
\(204\) | −71.1736 | −4.98315 | ||||||||
\(205\) | 14.9248 | 1.04239 | ||||||||
\(206\) | −21.5763 | −1.50329 | ||||||||
\(207\) | 14.9349 | 1.03805 | ||||||||
\(208\) | 26.3599 | 1.82773 | ||||||||
\(209\) | 5.05675 | 0.349783 | ||||||||
\(210\) | −0.0521843 | −0.00360106 | ||||||||
\(211\) | 23.1060 | 1.59068 | 0.795341 | − | 0.606162i | \(-0.207292\pi\) | ||||
0.795341 | + | 0.606162i | \(0.207292\pi\) | |||||||
\(212\) | −36.9505 | −2.53777 | ||||||||
\(213\) | −9.93588 | −0.680796 | ||||||||
\(214\) | −49.8864 | −3.41017 | ||||||||
\(215\) | 15.0619 | 1.02721 | ||||||||
\(216\) | −51.0051 | −3.47046 | ||||||||
\(217\) | 0.0326100 | 0.00221371 | ||||||||
\(218\) | 19.2365 | 1.30286 | ||||||||
\(219\) | −11.5854 | −0.782870 | ||||||||
\(220\) | 6.17583 | 0.416375 | ||||||||
\(221\) | −19.5281 | −1.31360 | ||||||||
\(222\) | 31.2713 | 2.09879 | ||||||||
\(223\) | −2.62407 | −0.175720 | −0.0878602 | − | 0.996133i | \(-0.528003\pi\) | ||||
−0.0878602 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(224\) | −0.0263911 | −0.00176333 | ||||||||
\(225\) | −15.7055 | −1.04703 | ||||||||
\(226\) | −28.7245 | −1.91073 | ||||||||
\(227\) | −19.3383 | −1.28353 | −0.641764 | − | 0.766903i | \(-0.721797\pi\) | ||||
−0.641764 | + | 0.766903i | \(0.721797\pi\) | |||||||
\(228\) | 73.3691 | 4.85898 | ||||||||
\(229\) | 21.3270 | 1.40933 | 0.704665 | − | 0.709541i | \(-0.251097\pi\) | ||||
0.704665 | + | 0.709541i | \(0.251097\pi\) | |||||||
\(230\) | −9.99747 | −0.659213 | ||||||||
\(231\) | 0.0124859 | 0.000821509 0 | ||||||||
\(232\) | 19.4341 | 1.27591 | ||||||||
\(233\) | 7.33932 | 0.480815 | 0.240407 | − | 0.970672i | \(-0.422719\pi\) | ||||
0.240407 | + | 0.970672i | \(0.422719\pi\) | |||||||
\(234\) | −53.0582 | −3.46852 | ||||||||
\(235\) | 8.59137 | 0.560439 | ||||||||
\(236\) | −61.3959 | −3.99653 | ||||||||
\(237\) | 31.0580 | 2.01743 | ||||||||
\(238\) | 0.0631598 | 0.00409404 | ||||||||
\(239\) | 0.513609 | 0.0332226 | 0.0166113 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166113 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(240\) | 32.0473 | 2.06864 | ||||||||
\(241\) | −15.1014 | −0.972765 | −0.486382 | − | 0.873746i | \(-0.661684\pi\) | ||||
−0.486382 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(242\) | 25.9055 | 1.66527 | ||||||||
\(243\) | −4.83101 | −0.309909 | ||||||||
\(244\) | 51.1777 | 3.27631 | ||||||||
\(245\) | −10.5027 | −0.670995 | ||||||||
\(246\) | −74.8497 | −4.77224 | ||||||||
\(247\) | 20.1305 | 1.28087 | ||||||||
\(248\) | −44.9242 | −2.85269 | ||||||||
\(249\) | 46.5870 | 2.95233 | ||||||||
\(250\) | 29.6367 | 1.87439 | ||||||||
\(251\) | −27.2410 | −1.71943 | −0.859717 | − | 0.510770i | \(-0.829360\pi\) | ||||
−0.859717 | + | 0.510770i | \(0.829360\pi\) | |||||||
\(252\) | 0.118788 | 0.00748291 | ||||||||
\(253\) | 2.39204 | 0.150386 | ||||||||
\(254\) | −4.94237 | −0.310112 | ||||||||
\(255\) | −23.7415 | −1.48675 | ||||||||
\(256\) | −28.7360 | −1.79600 | ||||||||
\(257\) | −24.9546 | −1.55662 | −0.778312 | − | 0.627878i | \(-0.783924\pi\) | ||||
−0.778312 | + | 0.627878i | \(0.783924\pi\) | |||||||
\(258\) | −75.5370 | −4.70273 | ||||||||
\(259\) | −0.0192091 | −0.00119359 | ||||||||
\(260\) | 24.5855 | 1.52473 | ||||||||
\(261\) | −17.4380 | −1.07938 | ||||||||
\(262\) | −1.34198 | −0.0829080 | ||||||||
\(263\) | 8.68790 | 0.535719 | 0.267859 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267859 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(264\) | −17.2008 | −1.05863 | ||||||||
\(265\) | −12.3256 | −0.757158 | ||||||||
\(266\) | −0.0651080 | −0.00399203 | ||||||||
\(267\) | −41.2814 | −2.52638 | ||||||||
\(268\) | −52.0964 | −3.18229 | ||||||||
\(269\) | −14.2432 | −0.868423 | −0.434211 | − | 0.900811i | \(-0.642973\pi\) | ||||
−0.434211 | + | 0.900811i | \(0.642973\pi\) | |||||||
\(270\) | −30.6360 | −1.86445 | ||||||||
\(271\) | −13.4489 | −0.816961 | −0.408481 | − | 0.912767i | \(-0.633941\pi\) | ||||
−0.408481 | + | 0.912767i | \(0.633941\pi\) | |||||||
\(272\) | −38.7875 | −2.35184 | ||||||||
\(273\) | 0.0497052 | 0.00300829 | ||||||||
\(274\) | −19.8134 | −1.19697 | ||||||||
\(275\) | −2.51547 | −0.151688 | ||||||||
\(276\) | 34.7064 | 2.08908 | ||||||||
\(277\) | −7.90622 | −0.475038 | −0.237519 | − | 0.971383i | \(-0.576334\pi\) | ||||
−0.237519 | + | 0.971383i | \(0.576334\pi\) | |||||||
\(278\) | 19.7717 | 1.18583 | ||||||||
\(279\) | 40.3098 | 2.41329 | ||||||||
\(280\) | −0.0441600 | −0.00263907 | ||||||||
\(281\) | 5.65916 | 0.337597 | 0.168799 | − | 0.985651i | \(-0.446011\pi\) | ||||
0.168799 | + | 0.985651i | \(0.446011\pi\) | |||||||
\(282\) | −43.0867 | −2.56578 | ||||||||
\(283\) | −9.12743 | −0.542570 | −0.271285 | − | 0.962499i | \(-0.587449\pi\) | ||||
−0.271285 | + | 0.962499i | \(0.587449\pi\) | |||||||
\(284\) | −15.1400 | −0.898393 | ||||||||
\(285\) | 24.4738 | 1.44970 | ||||||||
\(286\) | −8.49804 | −0.502499 | ||||||||
\(287\) | 0.0459780 | 0.00271400 | ||||||||
\(288\) | −32.6226 | −1.92230 | ||||||||
\(289\) | 11.7348 | 0.690285 | ||||||||
\(290\) | 11.6730 | 0.685464 | ||||||||
\(291\) | 42.9640 | 2.51860 | ||||||||
\(292\) | −17.6535 | −1.03309 | ||||||||
\(293\) | 9.36213 | 0.546941 | 0.273471 | − | 0.961880i | \(-0.411828\pi\) | ||||
0.273471 | + | 0.961880i | \(0.411828\pi\) | |||||||
\(294\) | 52.6724 | 3.07192 | ||||||||
\(295\) | −20.4799 | −1.19239 | ||||||||
\(296\) | 26.4628 | 1.53812 | ||||||||
\(297\) | 7.33011 | 0.425336 | ||||||||
\(298\) | 23.8181 | 1.37974 | ||||||||
\(299\) | 9.52252 | 0.550701 | ||||||||
\(300\) | −36.4972 | −2.10717 | ||||||||
\(301\) | 0.0464002 | 0.00267447 | ||||||||
\(302\) | −7.29759 | −0.419929 | ||||||||
\(303\) | −44.9942 | −2.58485 | ||||||||
\(304\) | 39.9839 | 2.29324 | ||||||||
\(305\) | 17.0714 | 0.977506 | ||||||||
\(306\) | 78.0729 | 4.46313 | ||||||||
\(307\) | −29.5506 | −1.68654 | −0.843270 | − | 0.537490i | \(-0.819373\pi\) | ||||
−0.843270 | + | 0.537490i | \(0.819373\pi\) | |||||||
\(308\) | 0.0190255 | 0.00108408 | ||||||||
\(309\) | 24.9853 | 1.42137 | ||||||||
\(310\) | −26.9835 | −1.53256 | ||||||||
\(311\) | 5.32872 | 0.302164 | 0.151082 | − | 0.988521i | \(-0.451724\pi\) | ||||
0.151082 | + | 0.988521i | \(0.451724\pi\) | |||||||
\(312\) | −68.4748 | −3.87662 | ||||||||
\(313\) | 13.3000 | 0.751761 | 0.375880 | − | 0.926668i | \(-0.377340\pi\) | ||||
0.375880 | + | 0.926668i | \(0.377340\pi\) | |||||||
\(314\) | −26.3129 | −1.48492 | ||||||||
\(315\) | 0.0396241 | 0.00223257 | ||||||||
\(316\) | 47.3252 | 2.66225 | ||||||||
\(317\) | −24.4974 | −1.37591 | −0.687955 | − | 0.725754i | \(-0.741491\pi\) | ||||
−0.687955 | + | 0.725754i | \(0.741491\pi\) | |||||||
\(318\) | 61.8145 | 3.46638 | ||||||||
\(319\) | −2.79294 | −0.156375 | ||||||||
\(320\) | 0.124486 | 0.00695900 | ||||||||
\(321\) | 57.7685 | 3.22432 | ||||||||
\(322\) | −0.0307986 | −0.00171634 | ||||||||
\(323\) | −29.6212 | −1.64817 | ||||||||
\(324\) | 29.2552 | 1.62529 | ||||||||
\(325\) | −10.0139 | −0.555469 | ||||||||
\(326\) | 0.490481 | 0.0271652 | ||||||||
\(327\) | −22.2759 | −1.23186 | ||||||||
\(328\) | −63.3403 | −3.49738 | ||||||||
\(329\) | 0.0264669 | 0.00145917 | ||||||||
\(330\) | −10.3316 | −0.568733 | ||||||||
\(331\) | −13.0062 | −0.714884 | −0.357442 | − | 0.933935i | \(-0.616351\pi\) | ||||
−0.357442 | + | 0.933935i | \(0.616351\pi\) | |||||||
\(332\) | 70.9878 | 3.89596 | ||||||||
\(333\) | −23.7447 | −1.30120 | ||||||||
\(334\) | −45.0414 | −2.46456 | ||||||||
\(335\) | −17.3779 | −0.949454 | ||||||||
\(336\) | 0.0987262 | 0.00538595 | ||||||||
\(337\) | 31.6916 | 1.72635 | 0.863175 | − | 0.504904i | \(-0.168472\pi\) | ||||
0.863175 | + | 0.504904i | \(0.168472\pi\) | |||||||
\(338\) | −0.691539 | −0.0376148 | ||||||||
\(339\) | 33.2631 | 1.80660 | ||||||||
\(340\) | −36.1765 | −1.96195 | ||||||||
\(341\) | 6.45620 | 0.349623 | ||||||||
\(342\) | −80.4811 | −4.35192 | ||||||||
\(343\) | −0.0647105 | −0.00349404 | ||||||||
\(344\) | −63.9219 | −3.44644 | ||||||||
\(345\) | 11.5771 | 0.623289 | ||||||||
\(346\) | 46.4080 | 2.49491 | ||||||||
\(347\) | −27.7317 | −1.48872 | −0.744358 | − | 0.667781i | \(-0.767244\pi\) | ||||
−0.744358 | + | 0.667781i | \(0.767244\pi\) | |||||||
\(348\) | −40.5232 | −2.17227 | ||||||||
\(349\) | 9.51397 | 0.509271 | 0.254636 | − | 0.967037i | \(-0.418044\pi\) | ||||
0.254636 | + | 0.967037i | \(0.418044\pi\) | |||||||
\(350\) | 0.0323878 | 0.00173120 | ||||||||
\(351\) | 29.1806 | 1.55754 | ||||||||
\(352\) | −5.22498 | −0.278492 | ||||||||
\(353\) | 34.0646 | 1.81308 | 0.906539 | − | 0.422123i | \(-0.138715\pi\) | ||||
0.906539 | + | 0.422123i | \(0.138715\pi\) | |||||||
\(354\) | 102.709 | 5.45893 | ||||||||
\(355\) | −5.05027 | −0.268040 | ||||||||
\(356\) | −62.9033 | −3.33387 | ||||||||
\(357\) | −0.0731391 | −0.00387093 | ||||||||
\(358\) | −25.0754 | −1.32528 | ||||||||
\(359\) | 3.16457 | 0.167020 | 0.0835098 | − | 0.996507i | \(-0.473387\pi\) | ||||
0.0835098 | + | 0.996507i | \(0.473387\pi\) | |||||||
\(360\) | −54.5870 | −2.87699 | ||||||||
\(361\) | 11.5349 | 0.607100 | ||||||||
\(362\) | 11.0778 | 0.582238 | ||||||||
\(363\) | −29.9986 | −1.57452 | ||||||||
\(364\) | 0.0757392 | 0.00396981 | ||||||||
\(365\) | −5.88870 | −0.308229 | ||||||||
\(366\) | −85.6151 | −4.47517 | ||||||||
\(367\) | −5.00040 | −0.261019 | −0.130509 | − | 0.991447i | \(-0.541661\pi\) | ||||
−0.130509 | + | 0.991447i | \(0.541661\pi\) | |||||||
\(368\) | 18.9140 | 0.985959 | ||||||||
\(369\) | 56.8342 | 2.95867 | ||||||||
\(370\) | 15.8948 | 0.826330 | ||||||||
\(371\) | −0.0379709 | −0.00197135 | ||||||||
\(372\) | 93.6739 | 4.85676 | ||||||||
\(373\) | 37.1857 | 1.92540 | 0.962702 | − | 0.270565i | \(-0.0872104\pi\) | ||||
0.962702 | + | 0.270565i | \(0.0872104\pi\) | |||||||
\(374\) | 12.5045 | 0.646593 | ||||||||
\(375\) | −34.3193 | −1.77224 | ||||||||
\(376\) | −36.4614 | −1.88035 | ||||||||
\(377\) | −11.1185 | −0.572631 | ||||||||
\(378\) | −0.0943786 | −0.00485431 | ||||||||
\(379\) | 8.28572 | 0.425609 | 0.212805 | − | 0.977095i | \(-0.431740\pi\) | ||||
0.212805 | + | 0.977095i | \(0.431740\pi\) | |||||||
\(380\) | 37.2924 | 1.91306 | ||||||||
\(381\) | 5.72327 | 0.293212 | ||||||||
\(382\) | −59.5424 | −3.04645 | ||||||||
\(383\) | −32.2768 | −1.64927 | −0.824633 | − | 0.565667i | \(-0.808619\pi\) | ||||
−0.824633 | + | 0.565667i | \(0.808619\pi\) | |||||||
\(384\) | 33.0841 | 1.68832 | ||||||||
\(385\) | 0.00634638 | 0.000323441 0 | ||||||||
\(386\) | −11.5714 | −0.588970 | ||||||||
\(387\) | 57.3561 | 2.91558 | ||||||||
\(388\) | 65.4672 | 3.32360 | ||||||||
\(389\) | −19.7935 | −1.00357 | −0.501786 | − | 0.864992i | \(-0.667324\pi\) | ||||
−0.501786 | + | 0.864992i | \(0.667324\pi\) | |||||||
\(390\) | −41.1291 | −2.08265 | ||||||||
\(391\) | −14.0120 | −0.708617 | ||||||||
\(392\) | 44.5731 | 2.25128 | ||||||||
\(393\) | 1.55402 | 0.0783898 | ||||||||
\(394\) | 63.3331 | 3.19067 | ||||||||
\(395\) | 15.7863 | 0.794297 | ||||||||
\(396\) | 23.5178 | 1.18181 | ||||||||
\(397\) | −5.23152 | −0.262563 | −0.131281 | − | 0.991345i | \(-0.541909\pi\) | ||||
−0.131281 | + | 0.991345i | \(0.541909\pi\) | |||||||
\(398\) | −10.3447 | −0.518531 | ||||||||
\(399\) | 0.0753951 | 0.00377448 | ||||||||
\(400\) | −19.8899 | −0.994495 | ||||||||
\(401\) | −4.10787 | −0.205137 | −0.102569 | − | 0.994726i | \(-0.532706\pi\) | ||||
−0.102569 | + | 0.994726i | \(0.532706\pi\) | |||||||
\(402\) | 87.1520 | 4.34675 | ||||||||
\(403\) | 25.7016 | 1.28029 | ||||||||
\(404\) | −68.5608 | −3.41103 | ||||||||
\(405\) | 9.75871 | 0.484914 | ||||||||
\(406\) | 0.0359604 | 0.00178469 | ||||||||
\(407\) | −3.80306 | −0.188510 | ||||||||
\(408\) | 100.758 | 4.98826 | ||||||||
\(409\) | 1.33455 | 0.0659893 | 0.0329947 | − | 0.999456i | \(-0.489496\pi\) | ||||
0.0329947 | + | 0.999456i | \(0.489496\pi\) | |||||||
\(410\) | −38.0450 | −1.87891 | ||||||||
\(411\) | 22.9439 | 1.13174 | ||||||||
\(412\) | 38.0719 | 1.87567 | ||||||||
\(413\) | −0.0630914 | −0.00310452 | ||||||||
\(414\) | −38.0707 | −1.87107 | ||||||||
\(415\) | 23.6795 | 1.16238 | ||||||||
\(416\) | −20.8002 | −1.01981 | ||||||||
\(417\) | −22.8957 | −1.12121 | ||||||||
\(418\) | −12.8902 | −0.630481 | ||||||||
\(419\) | −16.9558 | −0.828343 | −0.414171 | − | 0.910199i | \(-0.635929\pi\) | ||||
−0.414171 | + | 0.910199i | \(0.635929\pi\) | |||||||
\(420\) | 0.0920805 | 0.00449307 | ||||||||
\(421\) | −40.4275 | −1.97032 | −0.985159 | − | 0.171644i | \(-0.945092\pi\) | ||||
−0.985159 | + | 0.171644i | \(0.945092\pi\) | |||||||
\(422\) | −58.8998 | −2.86720 | ||||||||
\(423\) | 32.7162 | 1.59072 | ||||||||
\(424\) | 52.3094 | 2.54037 | ||||||||
\(425\) | 14.7350 | 0.714752 | ||||||||
\(426\) | 25.3277 | 1.22713 | ||||||||
\(427\) | 0.0525909 | 0.00254505 | ||||||||
\(428\) | 88.0258 | 4.25489 | ||||||||
\(429\) | 9.84073 | 0.475115 | ||||||||
\(430\) | −38.3944 | −1.85154 | ||||||||
\(431\) | −13.0345 | −0.627849 | −0.313924 | − | 0.949448i | \(-0.601644\pi\) | ||||
−0.313924 | + | 0.949448i | \(0.601644\pi\) | |||||||
\(432\) | 57.9595 | 2.78858 | ||||||||
\(433\) | 5.87320 | 0.282248 | 0.141124 | − | 0.989992i | \(-0.454928\pi\) | ||||
0.141124 | + | 0.989992i | \(0.454928\pi\) | |||||||
\(434\) | −0.0831266 | −0.00399020 | ||||||||
\(435\) | −13.5174 | −0.648108 | ||||||||
\(436\) | −33.9433 | −1.62559 | ||||||||
\(437\) | 14.4442 | 0.690960 | ||||||||
\(438\) | 29.5325 | 1.41112 | ||||||||
\(439\) | 20.3681 | 0.972117 | 0.486059 | − | 0.873926i | \(-0.338434\pi\) | ||||
0.486059 | + | 0.873926i | \(0.338434\pi\) | |||||||
\(440\) | −8.74290 | −0.416801 | ||||||||
\(441\) | −39.9948 | −1.90451 | ||||||||
\(442\) | 49.7794 | 2.36777 | ||||||||
\(443\) | 4.33123 | 0.205783 | 0.102891 | − | 0.994693i | \(-0.467191\pi\) | ||||
0.102891 | + | 0.994693i | \(0.467191\pi\) | |||||||
\(444\) | −55.1790 | −2.61868 | ||||||||
\(445\) | −20.9828 | −0.994678 | ||||||||
\(446\) | 6.68904 | 0.316735 | ||||||||
\(447\) | −27.5813 | −1.30455 | ||||||||
\(448\) | 0.000383498 0 | 1.81186e−5 0 | ||||||||
\(449\) | −1.05155 | −0.0496258 | −0.0248129 | − | 0.999692i | \(-0.507899\pi\) | ||||
−0.0248129 | + | 0.999692i | \(0.507899\pi\) | |||||||
\(450\) | 40.0351 | 1.88727 | ||||||||
\(451\) | 9.10283 | 0.428635 | ||||||||
\(452\) | 50.6852 | 2.38403 | ||||||||
\(453\) | 8.45062 | 0.397045 | ||||||||
\(454\) | 49.2955 | 2.31355 | ||||||||
\(455\) | 0.0252644 | 0.00118441 | ||||||||
\(456\) | −103.866 | −4.86396 | ||||||||
\(457\) | −29.4666 | −1.37839 | −0.689195 | − | 0.724576i | \(-0.742036\pi\) | ||||
−0.689195 | + | 0.724576i | \(0.742036\pi\) | |||||||
\(458\) | −54.3650 | −2.54031 | ||||||||
\(459\) | −42.9380 | −2.00417 | ||||||||
\(460\) | 17.6408 | 0.822506 | ||||||||
\(461\) | −15.9660 | −0.743609 | −0.371804 | − | 0.928311i | \(-0.621261\pi\) | ||||
−0.371804 | + | 0.928311i | \(0.621261\pi\) | |||||||
\(462\) | −0.0318278 | −0.00148076 | ||||||||
\(463\) | 28.6875 | 1.33322 | 0.666611 | − | 0.745406i | \(-0.267744\pi\) | ||||
0.666611 | + | 0.745406i | \(0.267744\pi\) | |||||||
\(464\) | −22.0839 | −1.02522 | ||||||||
\(465\) | 31.2469 | 1.44904 | ||||||||
\(466\) | −18.7088 | −0.866666 | ||||||||
\(467\) | 31.6695 | 1.46549 | 0.732744 | − | 0.680504i | \(-0.238239\pi\) | ||||
0.732744 | + | 0.680504i | \(0.238239\pi\) | |||||||
\(468\) | 93.6225 | 4.32770 | ||||||||
\(469\) | −0.0535350 | −0.00247202 | ||||||||
\(470\) | −21.9004 | −1.01019 | ||||||||
\(471\) | 30.4704 | 1.40400 | ||||||||
\(472\) | 86.9159 | 4.00063 | ||||||||
\(473\) | 9.18642 | 0.422392 | ||||||||
\(474\) | −79.1704 | −3.63641 | ||||||||
\(475\) | −15.1895 | −0.696942 | ||||||||
\(476\) | −0.111447 | −0.00510816 | ||||||||
\(477\) | −46.9365 | −2.14907 | ||||||||
\(478\) | −1.30925 | −0.0598835 | ||||||||
\(479\) | 14.5936 | 0.666800 | 0.333400 | − | 0.942786i | \(-0.391804\pi\) | ||||
0.333400 | + | 0.942786i | \(0.391804\pi\) | |||||||
\(480\) | −25.2880 | −1.15423 | ||||||||
\(481\) | −15.1397 | −0.690309 | ||||||||
\(482\) | 38.4951 | 1.75340 | ||||||||
\(483\) | 0.0356648 | 0.00162281 | ||||||||
\(484\) | −45.7110 | −2.07777 | ||||||||
\(485\) | 21.8380 | 0.991613 | ||||||||
\(486\) | 12.3148 | 0.558610 | ||||||||
\(487\) | 15.9608 | 0.723253 | 0.361627 | − | 0.932323i | \(-0.382222\pi\) | ||||
0.361627 | + | 0.932323i | \(0.382222\pi\) | |||||||
\(488\) | −72.4503 | −3.27967 | ||||||||
\(489\) | −0.567977 | −0.0256848 | ||||||||
\(490\) | 26.7727 | 1.20947 | ||||||||
\(491\) | −1.62149 | −0.0731767 | −0.0365883 | − | 0.999330i | \(-0.511649\pi\) | ||||
−0.0365883 | + | 0.999330i | \(0.511649\pi\) | |||||||
\(492\) | 132.074 | 5.95436 | ||||||||
\(493\) | 16.3604 | 0.736834 | ||||||||
\(494\) | −51.3149 | −2.30877 | ||||||||
\(495\) | 7.84487 | 0.352601 | ||||||||
\(496\) | 51.0495 | 2.29219 | ||||||||
\(497\) | −0.0155581 | −0.000697875 0 | ||||||||
\(498\) | −118.755 | −5.32156 | ||||||||
\(499\) | 24.3963 | 1.09213 | 0.546065 | − | 0.837743i | \(-0.316125\pi\) | ||||
0.546065 | + | 0.837743i | \(0.316125\pi\) | |||||||
\(500\) | −52.2947 | −2.33869 | ||||||||
\(501\) | 52.1580 | 2.33025 | ||||||||
\(502\) | 69.4403 | 3.09927 | ||||||||
\(503\) | 17.5035 | 0.780441 | 0.390220 | − | 0.920722i | \(-0.372399\pi\) | ||||
0.390220 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(504\) | −0.168163 | −0.00749058 | ||||||||
\(505\) | −22.8699 | −1.01770 | ||||||||
\(506\) | −6.09758 | −0.271070 | ||||||||
\(507\) | 0.800803 | 0.0355649 | ||||||||
\(508\) | 8.72094 | 0.386929 | ||||||||
\(509\) | −13.5323 | −0.599808 | −0.299904 | − | 0.953969i | \(-0.596955\pi\) | ||||
−0.299904 | + | 0.953969i | \(0.596955\pi\) | |||||||
\(510\) | 60.5197 | 2.67986 | ||||||||
\(511\) | −0.0181410 | −0.000802510 0 | ||||||||
\(512\) | 50.8356 | 2.24664 | ||||||||
\(513\) | 44.2625 | 1.95424 | ||||||||
\(514\) | 63.6120 | 2.80581 | ||||||||
\(515\) | 12.6997 | 0.559615 | ||||||||
\(516\) | 133.287 | 5.86763 | ||||||||
\(517\) | 5.23998 | 0.230454 | ||||||||
\(518\) | 0.0489661 | 0.00215145 | ||||||||
\(519\) | −53.7405 | −2.35895 | ||||||||
\(520\) | −34.8048 | −1.52629 | ||||||||
\(521\) | 27.0095 | 1.18331 | 0.591655 | − | 0.806191i | \(-0.298475\pi\) | ||||
0.591655 | + | 0.806191i | \(0.298475\pi\) | |||||||
\(522\) | 44.4513 | 1.94558 | ||||||||
\(523\) | −25.7344 | −1.12529 | −0.562643 | − | 0.826700i | \(-0.690216\pi\) | ||||
−0.562643 | + | 0.826700i | \(0.690216\pi\) | |||||||
\(524\) | 2.36796 | 0.103445 | ||||||||
\(525\) | −0.0375051 | −0.00163686 | ||||||||
\(526\) | −22.1464 | −0.965630 | ||||||||
\(527\) | −37.8188 | −1.64741 | ||||||||
\(528\) | 19.5460 | 0.850631 | ||||||||
\(529\) | −16.1673 | −0.702927 | ||||||||
\(530\) | 31.4194 | 1.36477 | ||||||||
\(531\) | −77.9883 | −3.38440 | ||||||||
\(532\) | 0.114885 | 0.00498088 | ||||||||
\(533\) | 36.2376 | 1.56963 | ||||||||
\(534\) | 105.231 | 4.55379 | ||||||||
\(535\) | 29.3629 | 1.26947 | ||||||||
\(536\) | 73.7509 | 3.18555 | ||||||||
\(537\) | 29.0373 | 1.25305 | ||||||||
\(538\) | 36.3075 | 1.56533 | ||||||||
\(539\) | −6.40575 | −0.275915 | ||||||||
\(540\) | 54.0580 | 2.32629 | ||||||||
\(541\) | −33.8268 | −1.45433 | −0.727164 | − | 0.686464i | \(-0.759162\pi\) | ||||
−0.727164 | + | 0.686464i | \(0.759162\pi\) | |||||||
\(542\) | 34.2827 | 1.47257 | ||||||||
\(543\) | −12.8281 | −0.550508 | ||||||||
\(544\) | 30.6066 | 1.31225 | ||||||||
\(545\) | −11.3225 | −0.485003 | ||||||||
\(546\) | −0.126704 | −0.00542243 | ||||||||
\(547\) | 11.9447 | 0.510720 | 0.255360 | − | 0.966846i | \(-0.417806\pi\) | ||||
0.255360 | + | 0.966846i | \(0.417806\pi\) | |||||||
\(548\) | 34.9612 | 1.49347 | ||||||||
\(549\) | 65.0085 | 2.77450 | ||||||||
\(550\) | 6.41220 | 0.273417 | ||||||||
\(551\) | −16.8650 | −0.718474 | ||||||||
\(552\) | −49.1326 | −2.09122 | ||||||||
\(553\) | 0.0486321 | 0.00206805 | ||||||||
\(554\) | 20.1538 | 0.856254 | ||||||||
\(555\) | −18.4062 | −0.781298 | ||||||||
\(556\) | −34.8877 | −1.47957 | ||||||||
\(557\) | 35.8936 | 1.52086 | 0.760429 | − | 0.649421i | \(-0.224989\pi\) | ||||
0.760429 | + | 0.649421i | \(0.224989\pi\) | |||||||
\(558\) | −102.754 | −4.34993 | ||||||||
\(559\) | 36.5704 | 1.54676 | ||||||||
\(560\) | 0.0501811 | 0.00212054 | ||||||||
\(561\) | −14.4802 | −0.611356 | ||||||||
\(562\) | −14.4258 | −0.608517 | ||||||||
\(563\) | −40.3092 | −1.69883 | −0.849415 | − | 0.527725i | \(-0.823045\pi\) | ||||
−0.849415 | + | 0.527725i | \(0.823045\pi\) | |||||||
\(564\) | 76.0276 | 3.20134 | ||||||||
\(565\) | 16.9071 | 0.711288 | ||||||||
\(566\) | 23.2668 | 0.977979 | ||||||||
\(567\) | 0.0300631 | 0.00126253 | ||||||||
\(568\) | 21.4331 | 0.899314 | ||||||||
\(569\) | 33.1670 | 1.39043 | 0.695217 | − | 0.718800i | \(-0.255308\pi\) | ||||
0.695217 | + | 0.718800i | \(0.255308\pi\) | |||||||
\(570\) | −62.3865 | −2.61308 | ||||||||
\(571\) | −2.25230 | −0.0942560 | −0.0471280 | − | 0.998889i | \(-0.515007\pi\) | ||||
−0.0471280 | + | 0.998889i | \(0.515007\pi\) | |||||||
\(572\) | 14.9950 | 0.626972 | ||||||||
\(573\) | 68.9501 | 2.88043 | ||||||||
\(574\) | −0.117203 | −0.00489197 | ||||||||
\(575\) | −7.18523 | −0.299645 | ||||||||
\(576\) | 0.474048 | 0.0197520 | ||||||||
\(577\) | −8.30809 | −0.345870 | −0.172935 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172935 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(578\) | −29.9134 | −1.24423 | ||||||||
\(579\) | 13.3997 | 0.556874 | ||||||||
\(580\) | −20.5973 | −0.855258 | ||||||||
\(581\) | 0.0729481 | 0.00302640 | ||||||||
\(582\) | −109.520 | −4.53976 | ||||||||
\(583\) | −7.51756 | −0.311345 | ||||||||
\(584\) | 24.9914 | 1.03415 | ||||||||
\(585\) | 31.2298 | 1.29119 | ||||||||
\(586\) | −23.8651 | −0.985859 | ||||||||
\(587\) | −1.82503 | −0.0753272 | −0.0376636 | − | 0.999290i | \(-0.511992\pi\) | ||||
−0.0376636 | + | 0.999290i | \(0.511992\pi\) | |||||||
\(588\) | −92.9419 | −3.83286 | ||||||||
\(589\) | 38.9854 | 1.60637 | ||||||||
\(590\) | 52.2056 | 2.14927 | ||||||||
\(591\) | −73.3397 | −3.01679 | ||||||||
\(592\) | −30.0709 | −1.23591 | ||||||||
\(593\) | 33.7979 | 1.38792 | 0.693958 | − | 0.720016i | \(-0.255866\pi\) | ||||
0.693958 | + | 0.720016i | \(0.255866\pi\) | |||||||
\(594\) | −18.6853 | −0.766666 | ||||||||
\(595\) | −0.0371755 | −0.00152405 | ||||||||
\(596\) | −42.0276 | −1.72152 | ||||||||
\(597\) | 11.9791 | 0.490273 | ||||||||
\(598\) | −24.2740 | −0.992636 | ||||||||
\(599\) | 1.51681 | 0.0619750 | 0.0309875 | − | 0.999520i | \(-0.490135\pi\) | ||||
0.0309875 | + | 0.999520i | \(0.490135\pi\) | |||||||
\(600\) | 51.6678 | 2.10933 | ||||||||
\(601\) | −2.02529 | −0.0826132 | −0.0413066 | − | 0.999147i | \(-0.513152\pi\) | ||||
−0.0413066 | + | 0.999147i | \(0.513152\pi\) | |||||||
\(602\) | −0.118279 | −0.00482071 | ||||||||
\(603\) | −66.1755 | −2.69488 | ||||||||
\(604\) | 12.8768 | 0.523949 | ||||||||
\(605\) | −15.2479 | −0.619914 | ||||||||
\(606\) | 114.695 | 4.65918 | ||||||||
\(607\) | 44.6349 | 1.81168 | 0.905838 | − | 0.423625i | \(-0.139243\pi\) | ||||
0.905838 | + | 0.423625i | \(0.139243\pi\) | |||||||
\(608\) | −31.5507 | −1.27955 | ||||||||
\(609\) | −0.0416422 | −0.00168743 | ||||||||
\(610\) | −43.5169 | −1.76195 | ||||||||
\(611\) | 20.8599 | 0.843903 | ||||||||
\(612\) | −137.762 | −5.56868 | ||||||||
\(613\) | −9.40983 | −0.380060 | −0.190030 | − | 0.981778i | \(-0.560858\pi\) | ||||
−0.190030 | + | 0.981778i | \(0.560858\pi\) | |||||||
\(614\) | 75.3277 | 3.03998 | ||||||||
\(615\) | 44.0562 | 1.77652 | ||||||||
\(616\) | −0.0269338 | −0.00108519 | ||||||||
\(617\) | −7.61987 | −0.306765 | −0.153382 | − | 0.988167i | \(-0.549017\pi\) | ||||
−0.153382 | + | 0.988167i | \(0.549017\pi\) | |||||||
\(618\) | −63.6904 | −2.56200 | ||||||||
\(619\) | 14.9861 | 0.602340 | 0.301170 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301170 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(620\) | 47.6131 | 1.91219 | ||||||||
\(621\) | 20.9379 | 0.840208 | ||||||||
\(622\) | −13.5835 | −0.544649 | ||||||||
\(623\) | −0.0646404 | −0.00258976 | ||||||||
\(624\) | 77.8111 | 3.11494 | ||||||||
\(625\) | −3.69996 | −0.147998 | ||||||||
\(626\) | −33.9032 | −1.35504 | ||||||||
\(627\) | 14.9269 | 0.596122 | ||||||||
\(628\) | 46.4298 | 1.85275 | ||||||||
\(629\) | 22.2774 | 0.888257 | ||||||||
\(630\) | −0.101006 | −0.00402419 | ||||||||
\(631\) | −19.7105 | −0.784661 | −0.392330 | − | 0.919824i | \(-0.628331\pi\) | ||||
−0.392330 | + | 0.919824i | \(0.628331\pi\) | |||||||
\(632\) | −66.9965 | −2.66498 | ||||||||
\(633\) | 68.2060 | 2.71095 | ||||||||
\(634\) | 62.4465 | 2.48007 | ||||||||
\(635\) | 2.90906 | 0.115442 | ||||||||
\(636\) | −109.073 | −4.32503 | ||||||||
\(637\) | −25.5008 | −1.01038 | ||||||||
\(638\) | 7.11952 | 0.281865 | ||||||||
\(639\) | −19.2316 | −0.760791 | ||||||||
\(640\) | 16.8162 | 0.664719 | ||||||||
\(641\) | 10.0432 | 0.396683 | 0.198342 | − | 0.980133i | \(-0.436444\pi\) | ||||
0.198342 | + | 0.980133i | \(0.436444\pi\) | |||||||
\(642\) | −147.258 | −5.81183 | ||||||||
\(643\) | 38.9922 | 1.53770 | 0.768852 | − | 0.639427i | \(-0.220828\pi\) | ||||
0.768852 | + | 0.639427i | \(0.220828\pi\) | |||||||
\(644\) | 0.0543450 | 0.00214149 | ||||||||
\(645\) | 44.4607 | 1.75064 | ||||||||
\(646\) | 75.5078 | 2.97081 | ||||||||
\(647\) | 2.04625 | 0.0804465 | 0.0402233 | − | 0.999191i | \(-0.487193\pi\) | ||||
0.0402233 | + | 0.999191i | \(0.487193\pi\) | |||||||
\(648\) | −41.4155 | −1.62696 | ||||||||
\(649\) | −12.4910 | −0.490313 | ||||||||
\(650\) | 25.5265 | 1.00123 | ||||||||
\(651\) | 0.0962607 | 0.00377275 | ||||||||
\(652\) | −0.865466 | −0.0338943 | ||||||||
\(653\) | 21.1787 | 0.828786 | 0.414393 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414393 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(654\) | 56.7837 | 2.22042 | ||||||||
\(655\) | 0.789885 | 0.0308634 | ||||||||
\(656\) | 71.9765 | 2.81021 | ||||||||
\(657\) | −22.4244 | −0.874859 | ||||||||
\(658\) | −0.0674672 | −0.00263015 | ||||||||
\(659\) | 2.78147 | 0.108351 | 0.0541754 | − | 0.998531i | \(-0.482747\pi\) | ||||
0.0541754 | + | 0.998531i | \(0.482747\pi\) | |||||||
\(660\) | 18.2303 | 0.709613 | ||||||||
\(661\) | −16.9081 | −0.657650 | −0.328825 | − | 0.944391i | \(-0.606653\pi\) | ||||
−0.328825 | + | 0.944391i | \(0.606653\pi\) | |||||||
\(662\) | 33.1542 | 1.28857 | ||||||||
\(663\) | −57.6446 | −2.23873 | ||||||||
\(664\) | −100.495 | −3.89995 | ||||||||
\(665\) | 0.0383223 | 0.00148607 | ||||||||
\(666\) | 60.5279 | 2.34541 | ||||||||
\(667\) | −7.97782 | −0.308902 | ||||||||
\(668\) | 79.4767 | 3.07505 | ||||||||
\(669\) | −7.74591 | −0.299474 | ||||||||
\(670\) | 44.2981 | 1.71139 | ||||||||
\(671\) | 10.4121 | 0.401953 | ||||||||
\(672\) | −0.0779033 | −0.00300519 | ||||||||
\(673\) | −25.3185 | −0.975957 | −0.487978 | − | 0.872856i | \(-0.662266\pi\) | ||||
−0.487978 | + | 0.872856i | \(0.662266\pi\) | |||||||
\(674\) | −80.7854 | −3.11174 | ||||||||
\(675\) | −22.0182 | −0.847483 | ||||||||
\(676\) | 1.22024 | 0.0469322 | ||||||||
\(677\) | −17.5217 | −0.673412 | −0.336706 | − | 0.941610i | \(-0.609313\pi\) | ||||
−0.336706 | + | 0.941610i | \(0.609313\pi\) | |||||||
\(678\) | −84.7912 | −3.25639 | ||||||||
\(679\) | 0.0672751 | 0.00258178 | ||||||||
\(680\) | 51.2138 | 1.96396 | ||||||||
\(681\) | −57.0842 | −2.18747 | ||||||||
\(682\) | −16.4576 | −0.630193 | ||||||||
\(683\) | −39.1442 | −1.49781 | −0.748905 | − | 0.662678i | \(-0.769420\pi\) | ||||
−0.748905 | + | 0.662678i | \(0.769420\pi\) | |||||||
\(684\) | 142.011 | 5.42993 | ||||||||
\(685\) | 11.6621 | 0.445584 | ||||||||
\(686\) | 0.164954 | 0.00629798 | ||||||||
\(687\) | 62.9547 | 2.40187 | ||||||||
\(688\) | 72.6374 | 2.76928 | ||||||||
\(689\) | −29.9268 | −1.14012 | ||||||||
\(690\) | −29.5113 | −1.12347 | ||||||||
\(691\) | −10.7767 | −0.409963 | −0.204982 | − | 0.978766i | \(-0.565713\pi\) | ||||
−0.204982 | + | 0.978766i | \(0.565713\pi\) | |||||||
\(692\) | −81.8881 | −3.11292 | ||||||||
\(693\) | 0.0241672 | 0.000918038 0 | ||||||||
\(694\) | 70.6912 | 2.68340 | ||||||||
\(695\) | −11.6376 | −0.441438 | ||||||||
\(696\) | 57.3671 | 2.17450 | ||||||||
\(697\) | −53.3222 | −2.01972 | ||||||||
\(698\) | −24.2522 | −0.917958 | ||||||||
\(699\) | 21.6648 | 0.819436 | ||||||||
\(700\) | −0.0571491 | −0.00216003 | ||||||||
\(701\) | −36.6735 | −1.38514 | −0.692569 | − | 0.721351i | \(-0.743521\pi\) | ||||
−0.692569 | + | 0.721351i | \(0.743521\pi\) | |||||||
\(702\) | −74.3846 | −2.80746 | ||||||||
\(703\) | −22.9645 | −0.866124 | ||||||||
\(704\) | 0.0759257 | 0.00286156 | ||||||||
\(705\) | 25.3606 | 0.955137 | ||||||||
\(706\) | −86.8346 | −3.26806 | ||||||||
\(707\) | −0.0704541 | −0.00264970 | ||||||||
\(708\) | −181.233 | −6.81115 | ||||||||
\(709\) | 28.6805 | 1.07712 | 0.538560 | − | 0.842587i | \(-0.318969\pi\) | ||||
0.538560 | + | 0.842587i | \(0.318969\pi\) | |||||||
\(710\) | 12.8737 | 0.483141 | ||||||||
\(711\) | 60.1150 | 2.25449 | ||||||||
\(712\) | 89.0499 | 3.33729 | ||||||||
\(713\) | 18.4416 | 0.690644 | ||||||||
\(714\) | 0.186440 | 0.00697733 | ||||||||
\(715\) | 5.00190 | 0.187061 | ||||||||
\(716\) | 44.2461 | 1.65356 | ||||||||
\(717\) | 1.51611 | 0.0566201 | ||||||||
\(718\) | −8.06685 | −0.301052 | ||||||||
\(719\) | −27.3469 | −1.01987 | −0.509933 | − | 0.860214i | \(-0.670330\pi\) | ||||
−0.509933 | + | 0.860214i | \(0.670330\pi\) | |||||||
\(720\) | 62.0297 | 2.31171 | ||||||||
\(721\) | 0.0391232 | 0.00145702 | ||||||||
\(722\) | −29.4038 | −1.09429 | ||||||||
\(723\) | −44.5773 | −1.65785 | ||||||||
\(724\) | −19.5471 | −0.726462 | ||||||||
\(725\) | 8.38946 | 0.311577 | ||||||||
\(726\) | 76.4699 | 2.83806 | ||||||||
\(727\) | −19.8403 | −0.735836 | −0.367918 | − | 0.929858i | \(-0.619929\pi\) | ||||
−0.367918 | + | 0.929858i | \(0.619929\pi\) | |||||||
\(728\) | −0.107221 | −0.00397388 | ||||||||
\(729\) | −33.7728 | −1.25084 | ||||||||
\(730\) | 15.0110 | 0.555581 | ||||||||
\(731\) | −53.8118 | −1.99030 | ||||||||
\(732\) | 151.070 | 5.58371 | ||||||||
\(733\) | 1.22594 | 0.0452811 | 0.0226405 | − | 0.999744i | \(-0.492793\pi\) | ||||
0.0226405 | + | 0.999744i | \(0.492793\pi\) | |||||||
\(734\) | 12.7466 | 0.470484 | ||||||||
\(735\) | −31.0028 | −1.14355 | ||||||||
\(736\) | −14.9247 | −0.550133 | ||||||||
\(737\) | −10.5990 | −0.390418 | ||||||||
\(738\) | −144.877 | −5.33299 | ||||||||
\(739\) | −15.8595 | −0.583401 | −0.291701 | − | 0.956510i | \(-0.594221\pi\) | ||||
−0.291701 | + | 0.956510i | \(0.594221\pi\) | |||||||
\(740\) | −28.0467 | −1.03102 | ||||||||
\(741\) | 59.4227 | 2.18295 | ||||||||
\(742\) | 0.0967920 | 0.00355335 | ||||||||
\(743\) | −21.2965 | −0.781291 | −0.390646 | − | 0.920541i | \(-0.627748\pi\) | ||||
−0.390646 | + | 0.920541i | \(0.627748\pi\) | |||||||
\(744\) | −132.611 | −4.86174 | ||||||||
\(745\) | −14.0192 | −0.513624 | ||||||||
\(746\) | −94.7906 | −3.47053 | ||||||||
\(747\) | 90.1724 | 3.29924 | ||||||||
\(748\) | −22.0645 | −0.806758 | ||||||||
\(749\) | 0.0904567 | 0.00330521 | ||||||||
\(750\) | 87.4838 | 3.19446 | ||||||||
\(751\) | 15.1655 | 0.553397 | 0.276698 | − | 0.960957i | \(-0.410760\pi\) | ||||
0.276698 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(752\) | 41.4328 | 1.51090 | ||||||||
\(753\) | −80.4119 | −2.93037 | ||||||||
\(754\) | 28.3422 | 1.03216 | ||||||||
\(755\) | 4.29533 | 0.156323 | ||||||||
\(756\) | 0.166533 | 0.00605676 | ||||||||
\(757\) | 9.74316 | 0.354121 | 0.177061 | − | 0.984200i | \(-0.443341\pi\) | ||||
0.177061 | + | 0.984200i | \(0.443341\pi\) | |||||||
\(758\) | −21.1212 | −0.767158 | ||||||||
\(759\) | 7.06100 | 0.256298 | ||||||||
\(760\) | −52.7935 | −1.91502 | ||||||||
\(761\) | 3.05868 | 0.110877 | 0.0554386 | − | 0.998462i | \(-0.482344\pi\) | ||||
0.0554386 | + | 0.998462i | \(0.482344\pi\) | |||||||
\(762\) | −14.5893 | −0.528513 | ||||||||
\(763\) | −0.0348806 | −0.00126276 | ||||||||
\(764\) | 105.064 | 3.80108 | ||||||||
\(765\) | −45.9533 | −1.66145 | ||||||||
\(766\) | 82.2772 | 2.97279 | ||||||||
\(767\) | −49.7255 | −1.79548 | ||||||||
\(768\) | −84.8250 | −3.06086 | ||||||||
\(769\) | 27.8547 | 1.00447 | 0.502233 | − | 0.864733i | \(-0.332512\pi\) | ||||
0.502233 | + | 0.864733i | \(0.332512\pi\) | |||||||
\(770\) | −0.0161776 | −0.000583001 0 | ||||||||
\(771\) | −73.6628 | −2.65290 | ||||||||
\(772\) | 20.4181 | 0.734863 | ||||||||
\(773\) | −37.0410 | −1.33227 | −0.666135 | − | 0.745831i | \(-0.732053\pi\) | ||||
−0.666135 | + | 0.745831i | \(0.732053\pi\) | |||||||
\(774\) | −146.207 | −5.25531 | ||||||||
\(775\) | −19.3932 | −0.696624 | ||||||||
\(776\) | −92.6795 | −3.32700 | ||||||||
\(777\) | −0.0567028 | −0.00203420 | ||||||||
\(778\) | 50.4560 | 1.80893 | ||||||||
\(779\) | 54.9669 | 1.96939 | ||||||||
\(780\) | 72.5733 | 2.59854 | ||||||||
\(781\) | −3.08022 | −0.110219 | ||||||||
\(782\) | 35.7181 | 1.27728 | ||||||||
\(783\) | −24.4470 | −0.873665 | ||||||||
\(784\) | −50.6505 | −1.80895 | ||||||||
\(785\) | 15.4876 | 0.552778 | ||||||||
\(786\) | −3.96136 | −0.141297 | ||||||||
\(787\) | 34.7310 | 1.23803 | 0.619013 | − | 0.785380i | \(-0.287533\pi\) | ||||
0.619013 | + | 0.785380i | \(0.287533\pi\) | |||||||
\(788\) | −111.753 | −3.98103 | ||||||||
\(789\) | 25.6456 | 0.913007 | ||||||||
\(790\) | −40.2412 | −1.43172 | ||||||||
\(791\) | 0.0520849 | 0.00185192 | ||||||||
\(792\) | −33.2933 | −1.18303 | ||||||||
\(793\) | 41.4496 | 1.47192 | ||||||||
\(794\) | 13.3357 | 0.473268 | ||||||||
\(795\) | −36.3837 | −1.29040 | ||||||||
\(796\) | 18.2534 | 0.646975 | ||||||||
\(797\) | −35.0369 | −1.24107 | −0.620536 | − | 0.784178i | \(-0.713085\pi\) | ||||
−0.620536 | + | 0.784178i | \(0.713085\pi\) | |||||||
\(798\) | −0.192191 | −0.00680347 | ||||||||
\(799\) | −30.6945 | −1.08589 | ||||||||
\(800\) | 15.6948 | 0.554896 | ||||||||
\(801\) | −79.9031 | −2.82324 | ||||||||
\(802\) | 10.4714 | 0.369759 | ||||||||
\(803\) | −3.59159 | −0.126745 | ||||||||
\(804\) | −153.782 | −5.42347 | ||||||||
\(805\) | 0.0181279 | 0.000638926 0 | ||||||||
\(806\) | −65.5163 | −2.30771 | ||||||||
\(807\) | −42.0441 | −1.48002 | ||||||||
\(808\) | 97.0590 | 3.41452 | ||||||||
\(809\) | −27.7118 | −0.974297 | −0.487148 | − | 0.873319i | \(-0.661963\pi\) | ||||
−0.487148 | + | 0.873319i | \(0.661963\pi\) | |||||||
\(810\) | −24.8760 | −0.874055 | ||||||||
\(811\) | 43.6525 | 1.53284 | 0.766422 | − | 0.642337i | \(-0.222035\pi\) | ||||
0.766422 | + | 0.642337i | \(0.222035\pi\) | |||||||
\(812\) | −0.0634531 | −0.00222677 | ||||||||
\(813\) | −39.6994 | −1.39232 | ||||||||
\(814\) | 9.69441 | 0.339789 | ||||||||
\(815\) | −0.288695 | −0.0101125 | ||||||||
\(816\) | −114.496 | −4.00815 | ||||||||
\(817\) | 55.4717 | 1.94071 | ||||||||
\(818\) | −3.40192 | −0.118945 | ||||||||
\(819\) | 0.0962079 | 0.00336177 | ||||||||
\(820\) | 67.1314 | 2.34433 | ||||||||
\(821\) | −15.0462 | −0.525117 | −0.262558 | − | 0.964916i | \(-0.584566\pi\) | ||||
−0.262558 | + | 0.964916i | \(0.584566\pi\) | |||||||
\(822\) | −58.4866 | −2.03995 | ||||||||
\(823\) | −43.6192 | −1.52047 | −0.760236 | − | 0.649647i | \(-0.774917\pi\) | ||||
−0.760236 | + | 0.649647i | \(0.774917\pi\) | |||||||
\(824\) | −53.8969 | −1.87759 | ||||||||
\(825\) | −7.42534 | −0.258517 | ||||||||
\(826\) | 0.160827 | 0.00559588 | ||||||||
\(827\) | −39.7957 | −1.38383 | −0.691916 | − | 0.721978i | \(-0.743233\pi\) | ||||
−0.691916 | + | 0.721978i | \(0.743233\pi\) | |||||||
\(828\) | 67.1767 | 2.33455 | ||||||||
\(829\) | 21.1635 | 0.735039 | 0.367519 | − | 0.930016i | \(-0.380207\pi\) | ||||
0.367519 | + | 0.930016i | \(0.380207\pi\) | |||||||
\(830\) | −60.3617 | −2.09519 | ||||||||
\(831\) | −23.3382 | −0.809592 | ||||||||
\(832\) | 0.302254 | 0.0104788 | ||||||||
\(833\) | 37.5233 | 1.30011 | ||||||||
\(834\) | 58.3637 | 2.02097 | ||||||||
\(835\) | 26.5112 | 0.917456 | ||||||||
\(836\) | 22.7451 | 0.786656 | ||||||||
\(837\) | 56.5121 | 1.95334 | ||||||||
\(838\) | 43.2221 | 1.49308 | ||||||||
\(839\) | −41.8523 | −1.44490 | −0.722452 | − | 0.691421i | \(-0.756985\pi\) | ||||
−0.722452 | + | 0.691421i | \(0.756985\pi\) | |||||||
\(840\) | −0.130355 | −0.00449767 | ||||||||
\(841\) | −19.6851 | −0.678797 | ||||||||
\(842\) | 103.054 | 3.55149 | ||||||||
\(843\) | 16.7051 | 0.575355 | ||||||||
\(844\) | 103.930 | 3.57742 | ||||||||
\(845\) | 0.407037 | 0.0140025 | ||||||||
\(846\) | −83.3974 | −2.86726 | ||||||||
\(847\) | −0.0469733 | −0.00161402 | ||||||||
\(848\) | −59.4416 | −2.04123 | ||||||||
\(849\) | −26.9430 | −0.924682 | ||||||||
\(850\) | −37.5611 | −1.28834 | ||||||||
\(851\) | −10.8631 | −0.372383 | ||||||||
\(852\) | −44.6913 | −1.53110 | ||||||||
\(853\) | −14.7527 | −0.505122 | −0.252561 | − | 0.967581i | \(-0.581273\pi\) | ||||
−0.252561 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(854\) | −0.134060 | −0.00458744 | ||||||||
\(855\) | 47.3708 | 1.62005 | ||||||||
\(856\) | −124.615 | −4.25925 | ||||||||
\(857\) | −21.2950 | −0.727424 | −0.363712 | − | 0.931511i | \(-0.618491\pi\) | ||||
−0.363712 | + | 0.931511i | \(0.618491\pi\) | |||||||
\(858\) | −25.0851 | −0.856392 | ||||||||
\(859\) | 12.0927 | 0.412597 | 0.206298 | − | 0.978489i | \(-0.433858\pi\) | ||||
0.206298 | + | 0.978489i | \(0.433858\pi\) | |||||||
\(860\) | 67.7479 | 2.31018 | ||||||||
\(861\) | 0.135721 | 0.00462537 | ||||||||
\(862\) | 33.2263 | 1.13169 | ||||||||
\(863\) | 52.4326 | 1.78483 | 0.892413 | − | 0.451219i | \(-0.149011\pi\) | ||||
0.892413 | + | 0.451219i | \(0.149011\pi\) | |||||||
\(864\) | −45.7350 | −1.55594 | ||||||||
\(865\) | −27.3155 | −0.928756 | ||||||||
\(866\) | −14.9714 | −0.508750 | ||||||||
\(867\) | 34.6398 | 1.17643 | ||||||||
\(868\) | 0.146679 | 0.00497861 | ||||||||
\(869\) | 9.62829 | 0.326617 | ||||||||
\(870\) | 34.4573 | 1.16821 | ||||||||
\(871\) | −42.1936 | −1.42968 | ||||||||
\(872\) | 48.0523 | 1.62725 | ||||||||
\(873\) | 83.1599 | 2.81454 | ||||||||
\(874\) | −36.8199 | −1.24545 | ||||||||
\(875\) | −0.0537388 | −0.00181670 | ||||||||
\(876\) | −52.1109 | −1.76066 | ||||||||
\(877\) | 22.4194 | 0.757048 | 0.378524 | − | 0.925591i | \(-0.376432\pi\) | ||||
0.378524 | + | 0.925591i | \(0.376432\pi\) | |||||||
\(878\) | −51.9206 | −1.75224 | ||||||||
\(879\) | 27.6358 | 0.932133 | ||||||||
\(880\) | 9.93496 | 0.334907 | ||||||||
\(881\) | 34.5366 | 1.16357 | 0.581784 | − | 0.813344i | \(-0.302355\pi\) | ||||
0.581784 | + | 0.813344i | \(0.302355\pi\) | |||||||
\(882\) | 101.951 | 3.43288 | ||||||||
\(883\) | 21.5274 | 0.724454 | 0.362227 | − | 0.932090i | \(-0.382016\pi\) | ||||
0.362227 | + | 0.932090i | \(0.382016\pi\) | |||||||
\(884\) | −87.8370 | −2.95428 | ||||||||
\(885\) | −60.4542 | −2.03214 | ||||||||
\(886\) | −11.0408 | −0.370923 | ||||||||
\(887\) | 45.7201 | 1.53513 | 0.767566 | − | 0.640970i | \(-0.221468\pi\) | ||||
0.767566 | + | 0.640970i | \(0.221468\pi\) | |||||||
\(888\) | 78.1149 | 2.62136 | ||||||||
\(889\) | 0.00896177 | 0.000300568 0 | ||||||||
\(890\) | 53.4874 | 1.79290 | ||||||||
\(891\) | 5.95196 | 0.199398 | ||||||||
\(892\) | −11.8030 | −0.395193 | ||||||||
\(893\) | 31.6413 | 1.05884 | ||||||||
\(894\) | 70.3079 | 2.35145 | ||||||||
\(895\) | 14.7593 | 0.493347 | ||||||||
\(896\) | 0.0518047 | 0.00173067 | ||||||||
\(897\) | 28.1093 | 0.938541 | ||||||||
\(898\) | 2.68053 | 0.0894503 | ||||||||
\(899\) | −21.5324 | −0.718146 | ||||||||
\(900\) | −70.6430 | −2.35477 | ||||||||
\(901\) | 44.0360 | 1.46705 | ||||||||
\(902\) | −23.2041 | −0.772613 | ||||||||
\(903\) | 0.136968 | 0.00455800 | ||||||||
\(904\) | −71.7531 | −2.38647 | ||||||||
\(905\) | −6.52036 | −0.216744 | ||||||||
\(906\) | −21.5416 | −0.715671 | ||||||||
\(907\) | −24.7848 | −0.822966 | −0.411483 | − | 0.911417i | \(-0.634989\pi\) | ||||
−0.411483 | + | 0.911417i | \(0.634989\pi\) | |||||||
\(908\) | −86.9831 | −2.88663 | ||||||||
\(909\) | −87.0895 | −2.88858 | ||||||||
\(910\) | −0.0644019 | −0.00213490 | ||||||||
\(911\) | 30.7110 | 1.01750 | 0.508751 | − | 0.860914i | \(-0.330107\pi\) | ||||
0.508751 | + | 0.860914i | \(0.330107\pi\) | |||||||
\(912\) | 118.028 | 3.90828 | ||||||||
\(913\) | 14.4424 | 0.477974 | ||||||||
\(914\) | 75.1137 | 2.48454 | ||||||||
\(915\) | 50.3926 | 1.66593 | ||||||||
\(916\) | 95.9283 | 3.16956 | ||||||||
\(917\) | 0.00243335 | 8.03564e−5 0 | ||||||||
\(918\) | 109.454 | 3.61251 | ||||||||
\(919\) | −15.4383 | −0.509264 | −0.254632 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254632 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(920\) | −24.9734 | −0.823349 | ||||||||
\(921\) | −87.2296 | −2.87431 | ||||||||
\(922\) | 40.6990 | 1.34035 | ||||||||
\(923\) | −12.2621 | −0.403612 | ||||||||
\(924\) | 0.0561610 | 0.00184756 | ||||||||
\(925\) | 11.4236 | 0.375607 | ||||||||
\(926\) | −73.1277 | −2.40312 | ||||||||
\(927\) | 48.3609 | 1.58838 | ||||||||
\(928\) | 17.4261 | 0.572039 | ||||||||
\(929\) | 12.3132 | 0.403983 | 0.201991 | − | 0.979387i | \(-0.435259\pi\) | ||||
0.201991 | + | 0.979387i | \(0.435259\pi\) | |||||||
\(930\) | −79.6519 | −2.61189 | ||||||||
\(931\) | −38.6808 | −1.26771 | ||||||||
\(932\) | 33.0121 | 1.08135 | ||||||||
\(933\) | 15.7297 | 0.514968 | ||||||||
\(934\) | −80.7290 | −2.64153 | ||||||||
\(935\) | −7.36009 | −0.240701 | ||||||||
\(936\) | −132.538 | −4.33214 | ||||||||
\(937\) | 10.4048 | 0.339910 | 0.169955 | − | 0.985452i | \(-0.445638\pi\) | ||||
0.169955 | + | 0.985452i | \(0.445638\pi\) | |||||||
\(938\) | 0.136467 | 0.00445580 | ||||||||
\(939\) | 39.2599 | 1.28120 | ||||||||
\(940\) | 38.6437 | 1.26042 | ||||||||
\(941\) | −25.2153 | −0.821994 | −0.410997 | − | 0.911637i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911637i | \(0.634819\pi\) | |||||||
\(942\) | −77.6724 | −2.53070 | ||||||||
\(943\) | 26.0015 | 0.846726 | ||||||||
\(944\) | −98.7666 | −3.21458 | ||||||||
\(945\) | 0.0555508 | 0.00180707 | ||||||||
\(946\) | −23.4172 | −0.761359 | ||||||||
\(947\) | 35.0036 | 1.13746 | 0.568732 | − | 0.822523i | \(-0.307434\pi\) | ||||
0.568732 | + | 0.822523i | \(0.307434\pi\) | |||||||
\(948\) | 139.698 | 4.53718 | ||||||||
\(949\) | −14.2978 | −0.464128 | ||||||||
\(950\) | 38.7197 | 1.25623 | ||||||||
\(951\) | −72.3131 | −2.34491 | ||||||||
\(952\) | 0.157771 | 0.00511340 | ||||||||
\(953\) | 12.3899 | 0.401348 | 0.200674 | − | 0.979658i | \(-0.435687\pi\) | ||||
0.200674 | + | 0.979658i | \(0.435687\pi\) | |||||||
\(954\) | 119.646 | 3.87369 | ||||||||
\(955\) | 35.0463 | 1.13407 | ||||||||
\(956\) | 2.31020 | 0.0747172 | ||||||||
\(957\) | −8.24441 | −0.266504 | ||||||||
\(958\) | −37.2008 | −1.20190 | ||||||||
\(959\) | 0.0359266 | 0.00116013 | ||||||||
\(960\) | 0.367468 | 0.0118600 | ||||||||
\(961\) | 18.7746 | 0.605632 | ||||||||
\(962\) | 38.5927 | 1.24428 | ||||||||
\(963\) | 111.815 | 3.60319 | ||||||||
\(964\) | −67.9255 | −2.18773 | ||||||||
\(965\) | 6.81089 | 0.219250 | ||||||||
\(966\) | −0.0909137 | −0.00292510 | ||||||||
\(967\) | −31.0616 | −0.998872 | −0.499436 | − | 0.866351i | \(-0.666459\pi\) | ||||
−0.499436 | + | 0.866351i | \(0.666459\pi\) | |||||||
\(968\) | 64.7113 | 2.07990 | ||||||||
\(969\) | −87.4381 | −2.80892 | ||||||||
\(970\) | −55.6675 | −1.78738 | ||||||||
\(971\) | 57.2817 | 1.83826 | 0.919128 | − | 0.393959i | \(-0.128895\pi\) | ||||
0.919128 | + | 0.393959i | \(0.128895\pi\) | |||||||
\(972\) | −21.7297 | −0.696981 | ||||||||
\(973\) | −0.0358512 | −0.00114934 | ||||||||
\(974\) | −40.6859 | −1.30366 | ||||||||
\(975\) | −29.5597 | −0.946667 | ||||||||
\(976\) | 82.3286 | 2.63527 | ||||||||
\(977\) | −2.29819 | −0.0735257 | −0.0367629 | − | 0.999324i | \(-0.511705\pi\) | ||||
−0.0367629 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(978\) | 1.44784 | 0.0462967 | ||||||||
\(979\) | −12.7976 | −0.409014 | ||||||||
\(980\) | −47.2410 | −1.50906 | ||||||||
\(981\) | −43.1166 | −1.37661 | ||||||||
\(982\) | 4.13335 | 0.131901 | ||||||||
\(983\) | −10.3094 | −0.328819 | −0.164409 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164409 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(984\) | −186.972 | −5.96046 | ||||||||
\(985\) | −37.2775 | −1.18776 | ||||||||
\(986\) | −41.7044 | −1.32814 | ||||||||
\(987\) | 0.0781271 | 0.00248681 | ||||||||
\(988\) | 90.5465 | 2.88067 | ||||||||
\(989\) | 26.2403 | 0.834392 | ||||||||
\(990\) | −19.9975 | −0.635561 | ||||||||
\(991\) | −25.5949 | −0.813049 | −0.406525 | − | 0.913640i | \(-0.633259\pi\) | ||||
−0.406525 | + | 0.913640i | \(0.633259\pi\) | |||||||
\(992\) | −40.2824 | −1.27897 | ||||||||
\(993\) | −38.3926 | −1.21835 | ||||||||
\(994\) | 0.0396593 | 0.00125792 | ||||||||
\(995\) | 6.08882 | 0.193029 | ||||||||
\(996\) | 209.547 | 6.63975 | ||||||||
\(997\) | −1.19929 | −0.0379818 | −0.0189909 | − | 0.999820i | \(-0.506045\pi\) | ||||
−0.0189909 | + | 0.999820i | \(0.506045\pi\) | |||||||
\(998\) | −62.1890 | −1.96856 | ||||||||
\(999\) | −33.2887 | −1.05321 |
(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 | 4007.2.a.b.1.14 | ✓ | 195 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.b.1.14 | ✓ | 195 | 1.1 | even | 1 | trivial |