Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.7 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.a.277.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −4.90121 | + | 0.988992i | −0.980243 | + | 0.197798i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 2.14995 | − | 2.14995i | 0.307135 | − | 0.307135i | −0.536662 | − | 0.843797i | \(-0.680315\pi\) |
0.843797 | + | 0.536662i | \(0.180315\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −3.91222 | + | 5.89021i | −0.391222 | + | 0.589021i | ||||
\(11\) | −12.9969 | −1.18154 | −0.590770 | − | 0.806840i | \(-0.701176\pi\) | ||||
−0.590770 | + | 0.806840i | \(0.701176\pi\) | |||||||
\(12\) | −2.44949 | + | 2.44949i | −0.204124 | + | 0.204124i | ||||
\(13\) | 10.2470 | + | 10.2470i | 0.788229 | + | 0.788229i | 0.981204 | − | 0.192975i | \(-0.0618136\pi\) |
−0.192975 | + | 0.981204i | \(0.561814\pi\) | |||||||
\(14\) | − | 4.29989i | − | 0.307135i | ||||||
\(15\) | 7.21400 | + | 4.79147i | 0.480933 | + | 0.319432i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −2.98774 | + | 2.98774i | −0.175749 | + | 0.175749i | −0.789500 | − | 0.613751i | \(-0.789660\pi\) |
0.613751 | + | 0.789500i | \(0.289660\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 26.4014i | 1.38955i | 0.719228 | + | 0.694774i | \(0.244496\pi\) | ||||
−0.719228 | + | 0.694774i | \(0.755504\pi\) | |||||||
\(20\) | 1.97798 | + | 9.80243i | 0.0988992 | + | 0.490121i | ||||
\(21\) | −5.26627 | −0.250775 | ||||||||
\(22\) | −12.9969 | + | 12.9969i | −0.590770 | + | 0.590770i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 23.0438 | − | 9.69452i | 0.921752 | − | 0.387781i | ||||
\(26\) | 20.4940 | 0.788229 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −4.29989 | − | 4.29989i | −0.153568 | − | 0.153568i | ||||
\(29\) | − | 45.6115i | − | 1.57281i | −0.617711 | − | 0.786406i | \(-0.711940\pi\) | ||
0.617711 | − | 0.786406i | \(-0.288060\pi\) | |||||||
\(30\) | 12.0055 | − | 2.42253i | 0.400182 | − | 0.0807509i | ||||
\(31\) | 37.4631 | 1.20849 | 0.604243 | − | 0.796800i | \(-0.293476\pi\) | ||||
0.604243 | + | 0.796800i | \(0.293476\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 15.9179 | + | 15.9179i | 0.482361 | + | 0.482361i | ||||
\(34\) | 5.97547i | 0.175749i | ||||||||
\(35\) | −8.41107 | + | 12.6636i | −0.240316 | + | 0.361818i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −44.9599 | + | 44.9599i | −1.21513 | + | 1.21513i | −0.245815 | + | 0.969317i | \(0.579055\pi\) |
−0.969317 | + | 0.245815i | \(0.920945\pi\) | |||||||
\(38\) | 26.4014 | + | 26.4014i | 0.694774 | + | 0.694774i | ||||
\(39\) | − | 25.0999i | − | 0.643586i | ||||||
\(40\) | 11.7804 | + | 7.82444i | 0.294510 | + | 0.195611i | ||||
\(41\) | 39.3742 | 0.960347 | 0.480173 | − | 0.877174i | \(-0.340574\pi\) | ||||
0.480173 | + | 0.877174i | \(0.340574\pi\) | |||||||
\(42\) | −5.26627 | + | 5.26627i | −0.125387 | + | 0.125387i | ||||
\(43\) | 29.7399 | + | 29.7399i | 0.691627 | + | 0.691627i | 0.962590 | − | 0.270963i | \(-0.0873421\pi\) |
−0.270963 | + | 0.962590i | \(0.587342\pi\) | |||||||
\(44\) | 25.9939i | 0.590770i | ||||||||
\(45\) | −2.96698 | − | 14.7036i | −0.0659328 | − | 0.326748i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −10.2691 | + | 10.2691i | −0.218491 | + | 0.218491i | −0.807862 | − | 0.589371i | \(-0.799376\pi\) |
0.589371 | + | 0.807862i | \(0.299376\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | 39.7555i | 0.811336i | ||||||||
\(50\) | 13.3493 | − | 32.7383i | 0.266985 | − | 0.654766i | ||||
\(51\) | 7.31843 | 0.143499 | ||||||||
\(52\) | 20.4940 | − | 20.4940i | 0.394114 | − | 0.394114i | ||||
\(53\) | 34.6215 | + | 34.6215i | 0.653235 | + | 0.653235i | 0.953771 | − | 0.300535i | \(-0.0971654\pi\) |
−0.300535 | + | 0.953771i | \(0.597165\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 63.7007 | − | 12.8539i | 1.15820 | − | 0.233707i | ||||
\(56\) | −8.59979 | −0.153568 | ||||||||
\(57\) | 32.3350 | − | 32.3350i | 0.567281 | − | 0.567281i | ||||
\(58\) | −45.6115 | − | 45.6115i | −0.786406 | − | 0.786406i | ||||
\(59\) | 22.8736i | 0.387688i | 0.981032 | + | 0.193844i | \(0.0620955\pi\) | ||||
−0.981032 | + | 0.193844i | \(0.937904\pi\) | |||||||
\(60\) | 9.58295 | − | 14.4280i | 0.159716 | − | 0.240467i | ||||
\(61\) | −70.3445 | −1.15319 | −0.576595 | − | 0.817030i | \(-0.695619\pi\) | ||||
−0.576595 | + | 0.817030i | \(0.695619\pi\) | |||||||
\(62\) | 37.4631 | − | 37.4631i | 0.604243 | − | 0.604243i | ||||
\(63\) | 6.44984 | + | 6.44984i | 0.102378 | + | 0.102378i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −60.3568 | − | 40.0884i | −0.928566 | − | 0.616745i | ||||
\(66\) | 31.8358 | 0.482361 | ||||||||
\(67\) | 19.6879 | − | 19.6879i | 0.293849 | − | 0.293849i | −0.544750 | − | 0.838599i | \(-0.683375\pi\) |
0.838599 | + | 0.544750i | \(0.183375\pi\) | |||||||
\(68\) | 5.97547 | + | 5.97547i | 0.0878746 | + | 0.0878746i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | 4.25256 | + | 21.0747i | 0.0607509 | + | 0.301067i | ||||
\(71\) | 131.287 | 1.84911 | 0.924557 | − | 0.381044i | \(-0.124436\pi\) | ||||
0.924557 | + | 0.381044i | \(0.124436\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 49.0534 | + | 49.0534i | 0.671964 | + | 0.671964i | 0.958169 | − | 0.286205i | \(-0.0923937\pi\) |
−0.286205 | + | 0.958169i | \(0.592394\pi\) | |||||||
\(74\) | 89.9197i | 1.21513i | ||||||||
\(75\) | −40.0961 | − | 16.3494i | −0.534614 | − | 0.217993i | ||||
\(76\) | 52.8028 | 0.694774 | ||||||||
\(77\) | −27.9427 | + | 27.9427i | −0.362892 | + | 0.362892i | ||||
\(78\) | −25.0999 | − | 25.0999i | −0.321793 | − | 0.321793i | ||||
\(79\) | 59.2011i | 0.749381i | 0.927150 | + | 0.374691i | \(0.122251\pi\) | ||||
−0.927150 | + | 0.374691i | \(0.877749\pi\) | |||||||
\(80\) | 19.6049 | − | 3.95597i | 0.245061 | − | 0.0494496i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 39.3742 | − | 39.3742i | 0.480173 | − | 0.480173i | ||||
\(83\) | −31.0483 | − | 31.0483i | −0.374076 | − | 0.374076i | 0.494883 | − | 0.868960i | \(-0.335211\pi\) |
−0.868960 | + | 0.494883i | \(0.835211\pi\) | |||||||
\(84\) | 10.5325i | 0.125387i | ||||||||
\(85\) | 11.6887 | − | 17.5984i | 0.137514 | − | 0.207040i | ||||
\(86\) | 59.4799 | 0.691627 | ||||||||
\(87\) | −55.8625 | + | 55.8625i | −0.642097 | + | 0.642097i | ||||
\(88\) | 25.9939 | + | 25.9939i | 0.295385 | + | 0.295385i | ||||
\(89\) | 169.901i | 1.90900i | 0.298219 | + | 0.954498i | \(0.403608\pi\) | ||||
−0.298219 | + | 0.954498i | \(0.596392\pi\) | |||||||
\(90\) | −17.6706 | − | 11.7367i | −0.196340 | − | 0.130407i | ||||
\(91\) | 44.0609 | 0.484186 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | −45.8827 | − | 45.8827i | −0.493362 | − | 0.493362i | ||||
\(94\) | 20.5382i | 0.218491i | ||||||||
\(95\) | −26.1108 | − | 129.399i | −0.274850 | − | 1.36209i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 8.17591 | − | 8.17591i | 0.0842878 | − | 0.0842878i | −0.663706 | − | 0.747994i | \(-0.731017\pi\) |
0.747994 | + | 0.663706i | \(0.231017\pi\) | |||||||
\(98\) | 39.7555 | + | 39.7555i | 0.405668 | + | 0.405668i | ||||
\(99\) | − | 38.9908i | − | 0.393846i | ||||||
\(100\) | −19.3890 | − | 46.0876i | −0.193890 | − | 0.460876i | ||||
\(101\) | −155.093 | −1.53558 | −0.767788 | − | 0.640704i | \(-0.778643\pi\) | ||||
−0.767788 | + | 0.640704i | \(0.778643\pi\) | |||||||
\(102\) | 7.31843 | − | 7.31843i | 0.0717493 | − | 0.0717493i | ||||
\(103\) | −46.5485 | − | 46.5485i | −0.451927 | − | 0.451927i | 0.444067 | − | 0.895994i | \(-0.353535\pi\) |
−0.895994 | + | 0.444067i | \(0.853535\pi\) | |||||||
\(104\) | − | 40.9879i | − | 0.394114i | ||||||
\(105\) | 25.8111 | − | 5.20830i | 0.245820 | − | 0.0496029i | ||||
\(106\) | 69.2429 | 0.653235 | ||||||||
\(107\) | 13.6792 | − | 13.6792i | 0.127843 | − | 0.127843i | −0.640290 | − | 0.768133i | \(-0.721186\pi\) |
0.768133 | + | 0.640290i | \(0.221186\pi\) | |||||||
\(108\) | −7.34847 | − | 7.34847i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 105.153i | − | 0.964702i | −0.875978 | − | 0.482351i | \(-0.839783\pi\) | ||
0.875978 | − | 0.482351i | \(-0.160217\pi\) | |||||||
\(110\) | 50.8469 | − | 76.5546i | 0.462244 | − | 0.695951i | ||||
\(111\) | 110.129 | 0.992151 | ||||||||
\(112\) | −8.59979 | + | 8.59979i | −0.0767838 | + | 0.0767838i | ||||
\(113\) | −140.459 | − | 140.459i | −1.24300 | − | 1.24300i | −0.958749 | − | 0.284254i | \(-0.908254\pi\) |
−0.284254 | − | 0.958749i | \(-0.591746\pi\) | |||||||
\(114\) | − | 64.6700i | − | 0.567281i | ||||||
\(115\) | −19.9747 | − | 13.2670i | −0.173693 | − | 0.115365i | ||||
\(116\) | −91.2230 | −0.786406 | ||||||||
\(117\) | −30.7409 | + | 30.7409i | −0.262743 | + | 0.262743i | ||||
\(118\) | 22.8736 | + | 22.8736i | 0.193844 | + | 0.193844i | ||||
\(119\) | 12.8469i | 0.107958i | ||||||||
\(120\) | −4.84505 | − | 24.0109i | −0.0403754 | − | 0.200091i | ||||
\(121\) | 47.9202 | 0.396035 | ||||||||
\(122\) | −70.3445 | + | 70.3445i | −0.576595 | + | 0.576595i | ||||
\(123\) | −48.2234 | − | 48.2234i | −0.392060 | − | 0.392060i | ||||
\(124\) | − | 74.9261i | − | 0.604243i | ||||||
\(125\) | −103.355 | + | 70.3051i | −0.826838 | + | 0.562441i | ||||
\(126\) | 12.8997 | 0.102378 | ||||||||
\(127\) | −110.338 | + | 110.338i | −0.868803 | + | 0.868803i | −0.992340 | − | 0.123537i | \(-0.960576\pi\) |
0.123537 | + | 0.992340i | \(0.460576\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 72.8477i | − | 0.564711i | ||||||
\(130\) | −100.445 | + | 20.2684i | −0.772656 | + | 0.155910i | ||||
\(131\) | 62.3911 | 0.476268 | 0.238134 | − | 0.971232i | \(-0.423464\pi\) | ||||
0.238134 | + | 0.971232i | \(0.423464\pi\) | |||||||
\(132\) | 31.8358 | − | 31.8358i | 0.241181 | − | 0.241181i | ||||
\(133\) | 56.7616 | + | 56.7616i | 0.426779 | + | 0.426779i | ||||
\(134\) | − | 39.3757i | − | 0.293849i | ||||||
\(135\) | −14.3744 | + | 21.6420i | −0.106477 | + | 0.160311i | ||||
\(136\) | 11.9509 | 0.0878746 | ||||||||
\(137\) | −3.75731 | + | 3.75731i | −0.0274256 | + | 0.0274256i | −0.720687 | − | 0.693261i | \(-0.756173\pi\) |
0.693261 | + | 0.720687i | \(0.256173\pi\) | |||||||
\(138\) | −8.30662 | − | 8.30662i | −0.0601929 | − | 0.0601929i | ||||
\(139\) | 244.157i | 1.75652i | 0.478179 | + | 0.878262i | \(0.341297\pi\) | ||||
−0.478179 | + | 0.878262i | \(0.658703\pi\) | |||||||
\(140\) | 25.3273 | + | 16.8221i | 0.180909 | + | 0.120158i | ||||
\(141\) | 25.1540 | 0.178397 | ||||||||
\(142\) | 131.287 | − | 131.287i | 0.924557 | − | 0.924557i | ||||
\(143\) | −133.179 | − | 133.179i | −0.931323 | − | 0.931323i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 45.1094 | + | 223.552i | 0.311100 | + | 1.54174i | ||||
\(146\) | 98.1067 | 0.671964 | ||||||||
\(147\) | 48.6903 | − | 48.6903i | 0.331226 | − | 0.331226i | ||||
\(148\) | 89.9197 | + | 89.9197i | 0.607566 | + | 0.607566i | ||||
\(149\) | 209.038i | 1.40294i | 0.712699 | + | 0.701470i | \(0.247473\pi\) | ||||
−0.712699 | + | 0.701470i | \(0.752527\pi\) | |||||||
\(150\) | −56.4455 | + | 23.7466i | −0.376303 | + | 0.158311i | ||||
\(151\) | −97.4480 | −0.645351 | −0.322675 | − | 0.946510i | \(-0.604582\pi\) | ||||
−0.322675 | + | 0.946510i | \(0.604582\pi\) | |||||||
\(152\) | 52.8028 | − | 52.8028i | 0.347387 | − | 0.347387i | ||||
\(153\) | −8.96321 | − | 8.96321i | −0.0585830 | − | 0.0585830i | ||||
\(154\) | 55.8854i | 0.362892i | ||||||||
\(155\) | −183.614 | + | 37.0507i | −1.18461 | + | 0.239037i | ||||
\(156\) | −50.1997 | −0.321793 | ||||||||
\(157\) | 142.961 | − | 142.961i | 0.910581 | − | 0.910581i | −0.0857369 | − | 0.996318i | \(-0.527324\pi\) |
0.996318 | + | 0.0857369i | \(0.0273245\pi\) | |||||||
\(158\) | 59.2011 | + | 59.2011i | 0.374691 | + | 0.374691i | ||||
\(159\) | − | 84.8049i | − | 0.533364i | ||||||
\(160\) | 15.6489 | − | 23.5608i | 0.0978055 | − | 0.147255i | ||||
\(161\) | 14.5817 | 0.0905693 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −102.695 | − | 102.695i | −0.630032 | − | 0.630032i | 0.318044 | − | 0.948076i | \(-0.396974\pi\) |
−0.948076 | + | 0.318044i | \(0.896974\pi\) | |||||||
\(164\) | − | 78.7484i | − | 0.480173i | ||||||
\(165\) | −93.7599 | − | 62.2744i | −0.568242 | − | 0.377421i | ||||
\(166\) | −62.0967 | −0.374076 | ||||||||
\(167\) | −169.393 | + | 169.393i | −1.01433 | + | 1.01433i | −0.0144364 | + | 0.999896i | \(0.504595\pi\) |
−0.999896 | + | 0.0144364i | \(0.995405\pi\) | |||||||
\(168\) | 10.5325 | + | 10.5325i | 0.0626937 | + | 0.0626937i | ||||
\(169\) | 41.0011i | 0.242610i | ||||||||
\(170\) | −5.90969 | − | 29.2871i | −0.0347629 | − | 0.172277i | ||||
\(171\) | −79.2042 | −0.463183 | ||||||||
\(172\) | 59.4799 | − | 59.4799i | 0.345813 | − | 0.345813i | ||||
\(173\) | 91.2722 | + | 91.2722i | 0.527585 | + | 0.527585i | 0.919852 | − | 0.392267i | \(-0.128309\pi\) |
−0.392267 | + | 0.919852i | \(0.628309\pi\) | |||||||
\(174\) | 111.725i | 0.642097i | ||||||||
\(175\) | 28.7002 | − | 70.3857i | 0.164001 | − | 0.402204i | ||||
\(176\) | 51.9877 | 0.295385 | ||||||||
\(177\) | 28.0143 | − | 28.0143i | 0.158273 | − | 0.158273i | ||||
\(178\) | 169.901 | + | 169.901i | 0.954498 | + | 0.954498i | ||||
\(179\) | 134.161i | 0.749503i | 0.927125 | + | 0.374752i | \(0.122272\pi\) | ||||
−0.927125 | + | 0.374752i | \(0.877728\pi\) | |||||||
\(180\) | −29.4073 | + | 5.93395i | −0.163374 | + | 0.0329664i | ||||
\(181\) | −102.342 | −0.565424 | −0.282712 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282712 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(182\) | 44.0609 | − | 44.0609i | 0.242093 | − | 0.242093i | ||||
\(183\) | 86.1541 | + | 86.1541i | 0.470787 | + | 0.470787i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 175.893 | − | 264.823i | 0.950773 | − | 1.43148i | ||||
\(186\) | −91.7654 | −0.493362 | ||||||||
\(187\) | 38.8314 | − | 38.8314i | 0.207654 | − | 0.207654i | ||||
\(188\) | 20.5382 | + | 20.5382i | 0.109246 | + | 0.109246i | ||||
\(189\) | − | 15.7988i | − | 0.0835917i | ||||||
\(190\) | −155.510 | − | 103.288i | −0.818472 | − | 0.543622i | ||||
\(191\) | 139.686 | 0.731342 | 0.365671 | − | 0.930744i | \(-0.380840\pi\) | ||||
0.365671 | + | 0.930744i | \(0.380840\pi\) | |||||||
\(192\) | 9.79796 | − | 9.79796i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −103.467 | − | 103.467i | −0.536099 | − | 0.536099i | 0.386282 | − | 0.922381i | \(-0.373759\pi\) |
−0.922381 | + | 0.386282i | \(0.873759\pi\) | |||||||
\(194\) | − | 16.3518i | − | 0.0842878i | ||||||
\(195\) | 24.8236 | + | 123.020i | 0.127300 | + | 0.630871i | ||||
\(196\) | 79.5109 | 0.405668 | ||||||||
\(197\) | −233.769 | + | 233.769i | −1.18664 | + | 1.18664i | −0.208653 | + | 0.977990i | \(0.566908\pi\) |
−0.977990 | + | 0.208653i | \(0.933092\pi\) | |||||||
\(198\) | −38.9908 | − | 38.9908i | −0.196923 | − | 0.196923i | ||||
\(199\) | 164.360i | 0.825929i | 0.910747 | + | 0.412965i | \(0.135507\pi\) | ||||
−0.910747 | + | 0.412965i | \(0.864493\pi\) | |||||||
\(200\) | −65.4766 | − | 26.6985i | −0.327383 | − | 0.133493i | ||||
\(201\) | −48.2252 | −0.239926 | ||||||||
\(202\) | −155.093 | + | 155.093i | −0.767788 | + | 0.767788i | ||||
\(203\) | −98.0624 | − | 98.0624i | −0.483066 | − | 0.483066i | ||||
\(204\) | − | 14.6369i | − | 0.0717493i | ||||||
\(205\) | −192.981 | + | 38.9408i | −0.941373 | + | 0.189955i | ||||
\(206\) | −93.0969 | −0.451927 | ||||||||
\(207\) | −10.1735 | + | 10.1735i | −0.0491473 | + | 0.0491473i | ||||
\(208\) | −40.9879 | − | 40.9879i | −0.197057 | − | 0.197057i | ||||
\(209\) | − | 343.137i | − | 1.64181i | ||||||
\(210\) | 20.6028 | − | 31.0194i | 0.0981087 | − | 0.147712i | ||||
\(211\) | 75.9698 | 0.360047 | 0.180023 | − | 0.983662i | \(-0.442383\pi\) | ||||
0.180023 | + | 0.983662i | \(0.442383\pi\) | |||||||
\(212\) | 69.2429 | − | 69.2429i | 0.326618 | − | 0.326618i | ||||
\(213\) | −160.793 | − | 160.793i | −0.754897 | − | 0.754897i | ||||
\(214\) | − | 27.3584i | − | 0.127843i | ||||||
\(215\) | −175.174 | − | 116.349i | −0.814765 | − | 0.541159i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 80.5436 | − | 80.5436i | 0.371169 | − | 0.371169i | ||||
\(218\) | −105.153 | − | 105.153i | −0.482351 | − | 0.482351i | ||||
\(219\) | − | 120.156i | − | 0.548656i | ||||||
\(220\) | −25.7077 | − | 127.401i | −0.116853 | − | 0.579098i | ||||
\(221\) | −61.2305 | −0.277061 | ||||||||
\(222\) | 110.129 | − | 110.129i | 0.496075 | − | 0.496075i | ||||
\(223\) | 235.175 | + | 235.175i | 1.05460 | + | 1.05460i | 0.998421 | + | 0.0561774i | \(0.0178912\pi\) |
0.0561774 | + | 0.998421i | \(0.482109\pi\) | |||||||
\(224\) | 17.1996i | 0.0767838i | ||||||||
\(225\) | 29.0836 | + | 69.1314i | 0.129260 | + | 0.307251i | ||||
\(226\) | −280.919 | −1.24300 | ||||||||
\(227\) | 22.8432 | − | 22.8432i | 0.100631 | − | 0.100631i | −0.654999 | − | 0.755630i | \(-0.727331\pi\) |
0.755630 | + | 0.654999i | \(0.227331\pi\) | |||||||
\(228\) | −64.6700 | − | 64.6700i | −0.283640 | − | 0.283640i | ||||
\(229\) | 93.3450i | 0.407620i | 0.979010 | + | 0.203810i | \(0.0653325\pi\) | ||||
−0.979010 | + | 0.203810i | \(0.934667\pi\) | |||||||
\(230\) | −33.2416 | + | 6.70767i | −0.144529 | + | 0.0291638i | ||||
\(231\) | 68.4454 | 0.296300 | ||||||||
\(232\) | −91.2230 | + | 91.2230i | −0.393203 | + | 0.393203i | ||||
\(233\) | −154.261 | − | 154.261i | −0.662063 | − | 0.662063i | 0.293803 | − | 0.955866i | \(-0.405079\pi\) |
−0.955866 | + | 0.293803i | \(0.905079\pi\) | |||||||
\(234\) | 61.4819i | 0.262743i | ||||||||
\(235\) | 40.1749 | − | 60.4870i | 0.170957 | − | 0.257391i | ||||
\(236\) | 45.7471 | 0.193844 | ||||||||
\(237\) | 72.5063 | − | 72.5063i | 0.305934 | − | 0.305934i | ||||
\(238\) | 12.8469 | + | 12.8469i | 0.0539788 | + | 0.0539788i | ||||
\(239\) | 9.07323i | 0.0379633i | 0.999820 | + | 0.0189816i | \(0.00604241\pi\) | ||||
−0.999820 | + | 0.0189816i | \(0.993958\pi\) | |||||||
\(240\) | −28.8560 | − | 19.1659i | −0.120233 | − | 0.0798579i | ||||
\(241\) | 253.551 | 1.05208 | 0.526039 | − | 0.850460i | \(-0.323677\pi\) | ||||
0.526039 | + | 0.850460i | \(0.323677\pi\) | |||||||
\(242\) | 47.9202 | − | 47.9202i | 0.198017 | − | 0.198017i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 140.689i | 0.576595i | ||||||||
\(245\) | −39.3178 | − | 194.850i | −0.160481 | − | 0.795306i | ||||
\(246\) | −96.4468 | −0.392060 | ||||||||
\(247\) | −270.535 | + | 270.535i | −1.09528 | + | 1.09528i | ||||
\(248\) | −74.9261 | − | 74.9261i | −0.302121 | − | 0.302121i | ||||
\(249\) | 76.0526i | 0.305432i | ||||||||
\(250\) | −33.0497 | + | 173.660i | −0.132199 | + | 0.694639i | ||||
\(251\) | 139.932 | 0.557498 | 0.278749 | − | 0.960364i | \(-0.410080\pi\) | ||||
0.278749 | + | 0.960364i | \(0.410080\pi\) | |||||||
\(252\) | 12.8997 | − | 12.8997i | 0.0511892 | − | 0.0511892i | ||||
\(253\) | −44.0747 | − | 44.0747i | −0.174208 | − | 0.174208i | ||||
\(254\) | 220.676i | 0.868803i | ||||||||
\(255\) | −35.8692 | + | 7.23787i | −0.140663 | + | 0.0283838i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −27.8299 | + | 27.8299i | −0.108287 | + | 0.108287i | −0.759175 | − | 0.650887i | \(-0.774397\pi\) |
0.650887 | + | 0.759175i | \(0.274397\pi\) | |||||||
\(258\) | −72.8477 | − | 72.8477i | −0.282355 | − | 0.282355i | ||||
\(259\) | 193.323i | 0.746420i | ||||||||
\(260\) | −80.1769 | + | 120.714i | −0.308373 | + | 0.464283i | ||||
\(261\) | 136.835 | 0.524270 | ||||||||
\(262\) | 62.3911 | − | 62.3911i | 0.238134 | − | 0.238134i | ||||
\(263\) | −224.271 | − | 224.271i | −0.852741 | − | 0.852741i | 0.137729 | − | 0.990470i | \(-0.456020\pi\) |
−0.990470 | + | 0.137729i | \(0.956020\pi\) | |||||||
\(264\) | − | 63.6717i | − | 0.241181i | ||||||
\(265\) | −203.928 | − | 135.447i | −0.769538 | − | 0.511120i | ||||
\(266\) | 113.523 | 0.426779 | ||||||||
\(267\) | 208.085 | − | 208.085i | 0.779344 | − | 0.779344i | ||||
\(268\) | −39.3757 | − | 39.3757i | −0.146924 | − | 0.146924i | ||||
\(269\) | − | 458.186i | − | 1.70329i | −0.524117 | − | 0.851646i | \(-0.675605\pi\) | ||
0.524117 | − | 0.851646i | \(-0.324395\pi\) | |||||||
\(270\) | 7.26758 | + | 36.0164i | 0.0269170 | + | 0.133394i | ||||
\(271\) | 334.255 | 1.23341 | 0.616706 | − | 0.787193i | \(-0.288467\pi\) | ||||
0.616706 | + | 0.787193i | \(0.288467\pi\) | |||||||
\(272\) | 11.9509 | − | 11.9509i | 0.0439373 | − | 0.0439373i | ||||
\(273\) | −53.9634 | − | 53.9634i | −0.197668 | − | 0.197668i | ||||
\(274\) | 7.51462i | 0.0274256i | ||||||||
\(275\) | −299.499 | + | 125.999i | −1.08909 | + | 0.458178i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −200.494 | + | 200.494i | −0.723807 | + | 0.723807i | −0.969378 | − | 0.245572i | \(-0.921024\pi\) |
0.245572 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(278\) | 244.157 | + | 244.157i | 0.878262 | + | 0.878262i | ||||
\(279\) | 112.389i | 0.402829i | ||||||||
\(280\) | 42.1494 | − | 8.50513i | 0.150534 | − | 0.0303754i | ||||
\(281\) | 44.8143 | 0.159482 | 0.0797408 | − | 0.996816i | \(-0.474591\pi\) | ||||
0.0797408 | + | 0.996816i | \(0.474591\pi\) | |||||||
\(282\) | 25.1540 | − | 25.1540i | 0.0891986 | − | 0.0891986i | ||||
\(283\) | 76.0560 | + | 76.0560i | 0.268749 | + | 0.268749i | 0.828596 | − | 0.559847i | \(-0.189140\pi\) |
−0.559847 | + | 0.828596i | \(0.689140\pi\) | |||||||
\(284\) | − | 262.574i | − | 0.924557i | ||||||
\(285\) | −126.502 | + | 190.460i | −0.443865 | + | 0.668280i | ||||
\(286\) | −266.358 | −0.931323 | ||||||||
\(287\) | 84.6525 | − | 84.6525i | 0.294956 | − | 0.294956i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 271.147i | 0.938224i | ||||||||
\(290\) | 268.661 | + | 178.442i | 0.926418 | + | 0.615318i | ||||
\(291\) | −20.0268 | −0.0688207 | ||||||||
\(292\) | 98.1067 | − | 98.1067i | 0.335982 | − | 0.335982i | ||||
\(293\) | −144.599 | − | 144.599i | −0.493512 | − | 0.493512i | 0.415899 | − | 0.909411i | \(-0.363467\pi\) |
−0.909411 | + | 0.415899i | \(0.863467\pi\) | |||||||
\(294\) | − | 97.3806i | − | 0.331226i | ||||||
\(295\) | −22.6218 | − | 112.108i | −0.0766840 | − | 0.380028i | ||||
\(296\) | 179.839 | 0.607566 | ||||||||
\(297\) | −47.7538 | + | 47.7538i | −0.160787 | + | 0.160787i | ||||
\(298\) | 209.038 | + | 209.038i | 0.701470 | + | 0.701470i | ||||
\(299\) | 69.4984i | 0.232436i | ||||||||
\(300\) | −32.6989 | + | 80.1922i | −0.108996 | + | 0.267307i | ||||
\(301\) | 127.879 | 0.424846 | ||||||||
\(302\) | −97.4480 | + | 97.4480i | −0.322675 | + | 0.322675i | ||||
\(303\) | 189.950 | + | 189.950i | 0.626896 | + | 0.626896i | ||||
\(304\) | − | 105.606i | − | 0.347387i | ||||||
\(305\) | 344.774 | − | 69.5702i | 1.13041 | − | 0.228099i | ||||
\(306\) | −17.9264 | −0.0585830 | ||||||||
\(307\) | 168.960 | − | 168.960i | 0.550360 | − | 0.550360i | −0.376185 | − | 0.926545i | \(-0.622764\pi\) |
0.926545 | + | 0.376185i | \(0.122764\pi\) | |||||||
\(308\) | 55.8854 | + | 55.8854i | 0.181446 | + | 0.181446i | ||||
\(309\) | 114.020i | 0.368997i | ||||||||
\(310\) | −146.564 | + | 220.665i | −0.472786 | + | 0.711823i | ||||
\(311\) | 527.554 | 1.69631 | 0.848157 | − | 0.529745i | \(-0.177712\pi\) | ||||
0.848157 | + | 0.529745i | \(0.177712\pi\) | |||||||
\(312\) | −50.1997 | + | 50.1997i | −0.160897 | + | 0.160897i | ||||
\(313\) | −385.731 | − | 385.731i | −1.23237 | − | 1.23237i | −0.963052 | − | 0.269316i | \(-0.913202\pi\) |
−0.269316 | − | 0.963052i | \(-0.586798\pi\) | |||||||
\(314\) | − | 285.922i | − | 0.910581i | ||||||
\(315\) | −37.9909 | − | 25.2332i | −0.120606 | − | 0.0801054i | ||||
\(316\) | 118.402 | 0.374691 | ||||||||
\(317\) | 211.055 | − | 211.055i | 0.665788 | − | 0.665788i | −0.290950 | − | 0.956738i | \(-0.593971\pi\) |
0.956738 | + | 0.290950i | \(0.0939714\pi\) | |||||||
\(318\) | −84.8049 | − | 84.8049i | −0.266682 | − | 0.266682i | ||||
\(319\) | 592.810i | 1.85834i | ||||||||
\(320\) | −7.91194 | − | 39.2097i | −0.0247248 | − | 0.122530i | ||||
\(321\) | −33.5070 | −0.104383 | ||||||||
\(322\) | 14.5817 | − | 14.5817i | 0.0452846 | − | 0.0452846i | ||||
\(323\) | −78.8804 | − | 78.8804i | −0.244212 | − | 0.244212i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 335.469 | + | 136.790i | 1.03221 | + | 0.420891i | ||||
\(326\) | −205.390 | −0.630032 | ||||||||
\(327\) | −128.785 | + | 128.785i | −0.393838 | + | 0.393838i | ||||
\(328\) | −78.7484 | − | 78.7484i | −0.240087 | − | 0.240087i | ||||
\(329\) | 44.1560i | 0.134213i | ||||||||
\(330\) | −156.034 | + | 31.4854i | −0.472831 | + | 0.0954103i | ||||
\(331\) | 136.580 | 0.412627 | 0.206313 | − | 0.978486i | \(-0.433853\pi\) | ||||
0.206313 | + | 0.978486i | \(0.433853\pi\) | |||||||
\(332\) | −62.0967 | + | 62.0967i | −0.187038 | + | 0.187038i | ||||
\(333\) | −134.880 | − | 134.880i | −0.405044 | − | 0.405044i | ||||
\(334\) | 338.787i | 1.01433i | ||||||||
\(335\) | −77.0232 | + | 115.966i | −0.229920 | + | 0.346166i | ||||
\(336\) | 21.0651 | 0.0626937 | ||||||||
\(337\) | −77.6053 | + | 77.6053i | −0.230283 | + | 0.230283i | −0.812811 | − | 0.582528i | \(-0.802064\pi\) |
0.582528 | + | 0.812811i | \(0.302064\pi\) | |||||||
\(338\) | 41.0011 | + | 41.0011i | 0.121305 | + | 0.121305i | ||||
\(339\) | 344.054i | 1.01491i | ||||||||
\(340\) | −35.1968 | − | 23.3774i | −0.103520 | − | 0.0687569i | ||||
\(341\) | −486.905 | −1.42787 | ||||||||
\(342\) | −79.2042 | + | 79.2042i | −0.231591 | + | 0.231591i | ||||
\(343\) | 190.820 | + | 190.820i | 0.556325 | + | 0.556325i | ||||
\(344\) | − | 118.960i | − | 0.345813i | ||||||
\(345\) | 8.21519 | + | 40.7125i | 0.0238121 | + | 0.118007i | ||||
\(346\) | 182.544 | 0.527585 | ||||||||
\(347\) | −334.981 | + | 334.981i | −0.965362 | + | 0.965362i | −0.999420 | − | 0.0340576i | \(-0.989157\pi\) |
0.0340576 | + | 0.999420i | \(0.489157\pi\) | |||||||
\(348\) | 111.725 | + | 111.725i | 0.321049 | + | 0.321049i | ||||
\(349\) | − | 462.956i | − | 1.32652i | −0.748389 | − | 0.663261i | \(-0.769172\pi\) | ||
0.748389 | − | 0.663261i | \(-0.230828\pi\) | |||||||
\(350\) | −41.6854 | − | 99.0859i | −0.119101 | − | 0.283102i | ||||
\(351\) | 75.2996 | 0.214529 | ||||||||
\(352\) | 51.9877 | − | 51.9877i | 0.147692 | − | 0.147692i | ||||
\(353\) | −419.637 | − | 419.637i | −1.18877 | − | 1.18877i | −0.977407 | − | 0.211367i | \(-0.932208\pi\) |
−0.211367 | − | 0.977407i | \(-0.567792\pi\) | |||||||
\(354\) | − | 56.0286i | − | 0.158273i | ||||||
\(355\) | −643.466 | + | 129.842i | −1.81258 | + | 0.365752i | ||||
\(356\) | 339.801 | 0.954498 | ||||||||
\(357\) | 15.7342 | − | 15.7342i | 0.0440735 | − | 0.0440735i | ||||
\(358\) | 134.161 | + | 134.161i | 0.374752 | + | 0.374752i | ||||
\(359\) | − | 253.226i | − | 0.705366i | −0.935743 | − | 0.352683i | \(-0.885269\pi\) | ||
0.935743 | − | 0.352683i | \(-0.114731\pi\) | |||||||
\(360\) | −23.4733 | + | 35.3412i | −0.0652037 | + | 0.0981701i | ||||
\(361\) | −336.034 | −0.930843 | ||||||||
\(362\) | −102.342 | + | 102.342i | −0.282712 | + | 0.282712i | ||||
\(363\) | −58.6900 | − | 58.6900i | −0.161681 | − | 0.161681i | ||||
\(364\) | − | 88.1218i | − | 0.242093i | ||||||
\(365\) | −288.934 | − | 191.908i | −0.791601 | − | 0.525774i | ||||
\(366\) | 172.308 | 0.470787 | ||||||||
\(367\) | 133.234 | − | 133.234i | 0.363035 | − | 0.363035i | −0.501894 | − | 0.864929i | \(-0.667363\pi\) |
0.864929 | + | 0.501894i | \(0.167363\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 118.123i | 0.320116i | ||||||||
\(370\) | −88.9299 | − | 440.716i | −0.240351 | − | 1.19112i | ||||
\(371\) | 148.869 | 0.401263 | ||||||||
\(372\) | −91.7654 | + | 91.7654i | −0.246681 | + | 0.246681i | ||||
\(373\) | −158.070 | − | 158.070i | −0.423780 | − | 0.423780i | 0.462723 | − | 0.886503i | \(-0.346872\pi\) |
−0.886503 | + | 0.462723i | \(0.846872\pi\) | |||||||
\(374\) | − | 77.6628i | − | 0.207654i | ||||||
\(375\) | 212.689 | + | 40.4774i | 0.567170 | + | 0.107940i | ||||
\(376\) | 41.0763 | 0.109246 | ||||||||
\(377\) | 467.380 | − | 467.380i | 1.23974 | − | 1.23974i | ||||
\(378\) | −15.7988 | − | 15.7988i | −0.0417958 | − | 0.0417958i | ||||
\(379\) | 485.673i | 1.28146i | 0.767766 | + | 0.640730i | \(0.221368\pi\) | ||||
−0.767766 | + | 0.640730i | \(0.778632\pi\) | |||||||
\(380\) | −258.798 | + | 52.2216i | −0.681047 | + | 0.137425i | ||||
\(381\) | 270.272 | 0.709375 | ||||||||
\(382\) | 139.686 | − | 139.686i | 0.365671 | − | 0.365671i | ||||
\(383\) | 447.060 | + | 447.060i | 1.16726 | + | 1.16726i | 0.982849 | + | 0.184410i | \(0.0590375\pi\) |
0.184410 | + | 0.982849i | \(0.440963\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 109.318 | − | 164.588i | 0.283943 | − | 0.427502i | ||||
\(386\) | −206.934 | −0.536099 | ||||||||
\(387\) | −89.2198 | + | 89.2198i | −0.230542 | + | 0.230542i | ||||
\(388\) | −16.3518 | − | 16.3518i | −0.0421439 | − | 0.0421439i | ||||
\(389\) | 252.009i | 0.647837i | 0.946085 | + | 0.323919i | \(0.105000\pi\) | ||||
−0.946085 | + | 0.323919i | \(0.895000\pi\) | |||||||
\(390\) | 147.843 | + | 98.1962i | 0.379086 | + | 0.251785i | ||||
\(391\) | −20.2638 | −0.0518256 | ||||||||
\(392\) | 79.5109 | − | 79.5109i | 0.202834 | − | 0.202834i | ||||
\(393\) | −76.4132 | − | 76.4132i | −0.194436 | − | 0.194436i | ||||
\(394\) | 467.537i | 1.18664i | ||||||||
\(395\) | −58.5494 | − | 290.157i | −0.148226 | − | 0.734575i | ||||
\(396\) | −77.9816 | −0.196923 | ||||||||
\(397\) | 527.251 | − | 527.251i | 1.32809 | − | 1.32809i | 0.421050 | − | 0.907038i | \(-0.361662\pi\) |
0.907038 | − | 0.421050i | \(-0.138338\pi\) | |||||||
\(398\) | 164.360 | + | 164.360i | 0.412965 | + | 0.412965i | ||||
\(399\) | − | 139.037i | − | 0.348464i | ||||||
\(400\) | −92.1752 | + | 38.7781i | −0.230438 | + | 0.0969452i | ||||
\(401\) | 337.961 | 0.842796 | 0.421398 | − | 0.906876i | \(-0.361540\pi\) | ||||
0.421398 | + | 0.906876i | \(0.361540\pi\) | |||||||
\(402\) | −48.2252 | + | 48.2252i | −0.119963 | + | 0.119963i | ||||
\(403\) | 383.883 | + | 383.883i | 0.952563 | + | 0.952563i | ||||
\(404\) | 310.186i | 0.767788i | ||||||||
\(405\) | 44.1109 | − | 8.90093i | 0.108916 | − | 0.0219776i | ||||
\(406\) | −196.125 | −0.483066 | ||||||||
\(407\) | 584.340 | − | 584.340i | 1.43573 | − | 1.43573i | ||||
\(408\) | −14.6369 | − | 14.6369i | −0.0358746 | − | 0.0358746i | ||||
\(409\) | − | 669.062i | − | 1.63585i | −0.575327 | − | 0.817924i | \(-0.695125\pi\) | ||
0.575327 | − | 0.817924i | \(-0.304875\pi\) | |||||||
\(410\) | −154.041 | + | 231.922i | −0.375709 | + | 0.565664i | ||||
\(411\) | 9.20349 | 0.0223929 | ||||||||
\(412\) | −93.0969 | + | 93.0969i | −0.225963 | + | 0.225963i | ||||
\(413\) | 49.1770 | + | 49.1770i | 0.119073 | + | 0.119073i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 182.881 | + | 121.468i | 0.440677 | + | 0.292694i | ||||
\(416\) | −81.9758 | −0.197057 | ||||||||
\(417\) | 299.030 | − | 299.030i | 0.717098 | − | 0.717098i | ||||
\(418\) | −343.137 | − | 343.137i | −0.820903 | − | 0.820903i | ||||
\(419\) | 141.319i | 0.337278i | 0.985678 | + | 0.168639i | \(0.0539372\pi\) | ||||
−0.985678 | + | 0.168639i | \(0.946063\pi\) | |||||||
\(420\) | −10.4166 | − | 51.6223i | −0.0248014 | − | 0.122910i | ||||
\(421\) | 336.422 | 0.799103 | 0.399551 | − | 0.916711i | \(-0.369166\pi\) | ||||
0.399551 | + | 0.916711i | \(0.369166\pi\) | |||||||
\(422\) | 75.9698 | − | 75.9698i | 0.180023 | − | 0.180023i | ||||
\(423\) | −30.8072 | − | 30.8072i | −0.0728303 | − | 0.0728303i | ||||
\(424\) | − | 138.486i | − | 0.326618i | ||||||
\(425\) | −39.8841 | + | 97.8134i | −0.0938449 | + | 0.230149i | ||||
\(426\) | −321.586 | −0.754897 | ||||||||
\(427\) | −151.237 | + | 151.237i | −0.354185 | + | 0.354185i | ||||
\(428\) | −27.3584 | − | 27.3584i | −0.0639214 | − | 0.0639214i | ||||
\(429\) | 326.221i | 0.760422i | ||||||||
\(430\) | −291.524 | + | 58.8252i | −0.677962 | + | 0.136803i | ||||
\(431\) | 568.586 | 1.31922 | 0.659612 | − | 0.751606i | \(-0.270720\pi\) | ||||
0.659612 | + | 0.751606i | \(0.270720\pi\) | |||||||
\(432\) | −14.6969 | + | 14.6969i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 222.386 | + | 222.386i | 0.513593 | + | 0.513593i | 0.915626 | − | 0.402032i | \(-0.131696\pi\) |
−0.402032 | + | 0.915626i | \(0.631696\pi\) | |||||||
\(434\) | − | 161.087i | − | 0.371169i | ||||||
\(435\) | 218.546 | − | 329.041i | 0.502405 | − | 0.756417i | ||||
\(436\) | −210.305 | −0.482351 | ||||||||
\(437\) | −89.5315 | + | 89.5315i | −0.204878 | + | 0.204878i | ||||
\(438\) | −120.156 | − | 120.156i | −0.274328 | − | 0.274328i | ||||
\(439\) | − | 215.602i | − | 0.491121i | −0.969381 | − | 0.245561i | \(-0.921028\pi\) | ||
0.969381 | − | 0.245561i | \(-0.0789720\pi\) | |||||||
\(440\) | −153.109 | − | 101.694i | −0.347975 | − | 0.231122i | ||||
\(441\) | −119.266 | −0.270445 | ||||||||
\(442\) | −61.2305 | + | 61.2305i | −0.138531 | + | 0.138531i | ||||
\(443\) | 282.186 | + | 282.186i | 0.636988 | + | 0.636988i | 0.949811 | − | 0.312823i | \(-0.101275\pi\) |
−0.312823 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(444\) | − | 220.257i | − | 0.496075i | ||||||
\(445\) | −168.030 | − | 832.719i | −0.377596 | − | 1.87128i | ||||
\(446\) | 470.351 | 1.05460 | ||||||||
\(447\) | 256.018 | − | 256.018i | 0.572748 | − | 0.572748i | ||||
\(448\) | 17.1996 | + | 17.1996i | 0.0383919 | + | 0.0383919i | ||||
\(449\) | 761.526i | 1.69605i | 0.529958 | + | 0.848024i | \(0.322208\pi\) | ||||
−0.529958 | + | 0.848024i | \(0.677792\pi\) | |||||||
\(450\) | 98.2149 | + | 40.0478i | 0.218255 | + | 0.0889951i | ||||
\(451\) | −511.744 | −1.13469 | ||||||||
\(452\) | −280.919 | + | 280.919i | −0.621502 | + | 0.621502i | ||||
\(453\) | 119.349 | + | 119.349i | 0.263463 | + | 0.263463i | ||||
\(454\) | − | 45.6864i | − | 0.100631i | ||||||
\(455\) | −215.952 | + | 43.5759i | −0.474620 | + | 0.0957712i | ||||
\(456\) | −129.340 | −0.283640 | ||||||||
\(457\) | 271.064 | − | 271.064i | 0.593138 | − | 0.593138i | −0.345340 | − | 0.938478i | \(-0.612236\pi\) |
0.938478 | + | 0.345340i | \(0.112236\pi\) | |||||||
\(458\) | 93.3450 | + | 93.3450i | 0.203810 | + | 0.203810i | ||||
\(459\) | 21.9553i | 0.0478329i | ||||||||
\(460\) | −26.5340 | + | 39.9493i | −0.0576826 | + | 0.0868463i | ||||
\(461\) | 29.2935 | 0.0635435 | 0.0317717 | − | 0.999495i | \(-0.489885\pi\) | ||||
0.0317717 | + | 0.999495i | \(0.489885\pi\) | |||||||
\(462\) | 68.4454 | − | 68.4454i | 0.148150 | − | 0.148150i | ||||
\(463\) | −233.316 | − | 233.316i | −0.503922 | − | 0.503922i | 0.408733 | − | 0.912654i | \(-0.365971\pi\) |
−0.912654 | + | 0.408733i | \(0.865971\pi\) | |||||||
\(464\) | 182.446i | 0.393203i | ||||||||
\(465\) | 270.258 | + | 179.503i | 0.581201 | + | 0.386028i | ||||
\(466\) | −308.521 | −0.662063 | ||||||||
\(467\) | −407.377 | + | 407.377i | −0.872328 | + | 0.872328i | −0.992726 | − | 0.120398i | \(-0.961583\pi\) |
0.120398 | + | 0.992726i | \(0.461583\pi\) | |||||||
\(468\) | 61.4819 | + | 61.4819i | 0.131371 | + | 0.131371i | ||||
\(469\) | − | 84.6557i | − | 0.180503i | ||||||
\(470\) | −20.3121 | − | 100.662i | −0.0432172 | − | 0.214174i | ||||
\(471\) | −350.182 | −0.743486 | ||||||||
\(472\) | 45.7471 | − | 45.7471i | 0.0969219 | − | 0.0969219i | ||||
\(473\) | −386.528 | − | 386.528i | −0.817184 | − | 0.817184i | ||||
\(474\) | − | 145.013i | − | 0.305934i | ||||||
\(475\) | 255.949 | + | 608.388i | 0.538840 | + | 1.28082i | ||||
\(476\) | 25.6939 | 0.0539788 | ||||||||
\(477\) | −103.864 | + | 103.864i | −0.217745 | + | 0.217745i | ||||
\(478\) | 9.07323 | + | 9.07323i | 0.0189816 | + | 0.0189816i | ||||
\(479\) | − | 703.739i | − | 1.46918i | −0.678509 | − | 0.734592i | \(-0.737374\pi\) | ||
0.678509 | − | 0.734592i | \(-0.262626\pi\) | |||||||
\(480\) | −48.0219 | + | 9.69011i | −0.100046 | + | 0.0201877i | ||||
\(481\) | −921.405 | −1.91560 | ||||||||
\(482\) | 253.551 | − | 253.551i | 0.526039 | − | 0.526039i | ||||
\(483\) | −17.8588 | − | 17.8588i | −0.0369747 | − | 0.0369747i | ||||
\(484\) | − | 95.8404i | − | 0.198017i | ||||||
\(485\) | −31.9860 | + | 48.1578i | −0.0659505 | + | 0.0992944i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 407.800 | − | 407.800i | 0.837372 | − | 0.837372i | −0.151141 | − | 0.988512i | \(-0.548295\pi\) |
0.988512 | + | 0.151141i | \(0.0482946\pi\) | |||||||
\(488\) | 140.689 | + | 140.689i | 0.288297 | + | 0.288297i | ||||
\(489\) | 251.551i | 0.514419i | ||||||||
\(490\) | −234.168 | − | 155.532i | −0.477893 | − | 0.317413i | ||||
\(491\) | −198.942 | −0.405178 | −0.202589 | − | 0.979264i | \(-0.564936\pi\) | ||||
−0.202589 | + | 0.979264i | \(0.564936\pi\) | |||||||
\(492\) | −96.4468 | + | 96.4468i | −0.196030 | + | 0.196030i | ||||
\(493\) | 136.275 | + | 136.275i | 0.276420 | + | 0.276420i | ||||
\(494\) | 541.069i | 1.09528i | ||||||||
\(495\) | 38.5616 | + | 191.102i | 0.0779022 | + | 0.386065i | ||||
\(496\) | −149.852 | −0.302121 | ||||||||
\(497\) | 282.260 | − | 282.260i | 0.567928 | − | 0.567928i | ||||
\(498\) | 76.0526 | + | 76.0526i | 0.152716 | + | 0.152716i | ||||
\(499\) | 460.033i | 0.921910i | 0.887424 | + | 0.460955i | \(0.152493\pi\) | ||||
−0.887424 | + | 0.460955i | \(0.847507\pi\) | |||||||
\(500\) | 140.610 | + | 206.709i | 0.281220 | + | 0.413419i | ||||
\(501\) | 414.928 | 0.828199 | ||||||||
\(502\) | 139.932 | − | 139.932i | 0.278749 | − | 0.278749i | ||||
\(503\) | −7.49816 | − | 7.49816i | −0.0149069 | − | 0.0149069i | 0.699614 | − | 0.714521i | \(-0.253355\pi\) |
−0.714521 | + | 0.699614i | \(0.753355\pi\) | |||||||
\(504\) | − | 25.7994i | − | 0.0511892i | ||||||
\(505\) | 760.145 | − | 153.386i | 1.50524 | − | 0.303735i | ||||
\(506\) | −88.1495 | −0.174208 | ||||||||
\(507\) | 50.2158 | − | 50.2158i | 0.0990450 | − | 0.0990450i | ||||
\(508\) | 220.676 | + | 220.676i | 0.434402 | + | 0.434402i | ||||
\(509\) | 485.709i | 0.954241i | 0.878838 | + | 0.477120i | \(0.158319\pi\) | ||||
−0.878838 | + | 0.477120i | \(0.841681\pi\) | |||||||
\(510\) | −28.6313 | + | 43.1070i | −0.0561398 | + | 0.0845236i | ||||
\(511\) | 210.924 | 0.412768 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 97.0050 | + | 97.0050i | 0.189094 | + | 0.189094i | ||||
\(514\) | 55.6598i | 0.108287i | ||||||||
\(515\) | 274.180 | + | 182.108i | 0.532388 | + | 0.353607i | ||||
\(516\) | −145.695 | −0.282355 | ||||||||
\(517\) | 133.466 | − | 133.466i | 0.258156 | − | 0.258156i | ||||
\(518\) | 193.323 | + | 193.323i | 0.373210 | + | 0.373210i | ||||
\(519\) | − | 223.570i | − | 0.430771i | ||||||
\(520\) | 40.5367 | + | 200.890i | 0.0779552 | + | 0.386328i | ||||
\(521\) | −125.674 | −0.241217 | −0.120609 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120609 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(522\) | 136.835 | − | 136.835i | 0.262135 | − | 0.262135i | ||||
\(523\) | 378.858 | + | 378.858i | 0.724393 | + | 0.724393i | 0.969497 | − | 0.245103i | \(-0.0788219\pi\) |
−0.245103 | + | 0.969497i | \(0.578822\pi\) | |||||||
\(524\) | − | 124.782i | − | 0.238134i | ||||||
\(525\) | −121.355 | + | 51.0540i | −0.231152 | + | 0.0972458i | ||||
\(526\) | −448.542 | −0.852741 | ||||||||
\(527\) | −111.930 | + | 111.930i | −0.212390 | + | 0.212390i | ||||
\(528\) | −63.6717 | − | 63.6717i | −0.120590 | − | 0.120590i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −339.374 | + | 68.4807i | −0.640329 | + | 0.129209i | ||||
\(531\) | −68.6207 | −0.129229 | ||||||||
\(532\) | 113.523 | − | 113.523i | 0.213390 | − | 0.213390i | ||||
\(533\) | 403.467 | + | 403.467i | 0.756973 | + | 0.756973i | ||||
\(534\) | − | 416.170i | − | 0.779344i | ||||||
\(535\) | −53.5160 | + | 80.5732i | −0.100030 | + | 0.150604i | ||||
\(536\) | −78.7514 | −0.146924 | ||||||||
\(537\) | 164.313 | − | 164.313i | 0.305983 | − | 0.305983i | ||||
\(538\) | −458.186 | − | 458.186i | −0.851646 | − | 0.851646i | ||||
\(539\) | − | 516.699i | − | 0.958625i | ||||||
\(540\) | 43.2840 | + | 28.7488i | 0.0801555 | + | 0.0532386i | ||||
\(541\) | 377.104 | 0.697050 | 0.348525 | − | 0.937300i | \(-0.386683\pi\) | ||||
0.348525 | + | 0.937300i | \(0.386683\pi\) | |||||||
\(542\) | 334.255 | − | 334.255i | 0.616706 | − | 0.616706i | ||||
\(543\) | 125.343 | + | 125.343i | 0.230833 | + | 0.230833i | ||||
\(544\) | − | 23.9019i | − | 0.0439373i | ||||||
\(545\) | 103.995 | + | 515.375i | 0.190817 | + | 0.945643i | ||||
\(546\) | −107.927 | −0.197668 | ||||||||
\(547\) | 444.740 | − | 444.740i | 0.813052 | − | 0.813052i | −0.172038 | − | 0.985090i | \(-0.555035\pi\) |
0.985090 | + | 0.172038i | \(0.0550352\pi\) | |||||||
\(548\) | 7.51462 | + | 7.51462i | 0.0137128 | + | 0.0137128i | ||||
\(549\) | − | 211.034i | − | 0.384396i | ||||||
\(550\) | −173.499 | + | 425.498i | −0.315454 | + | 0.773632i | ||||
\(551\) | 1204.21 | 2.18550 | ||||||||
\(552\) | −16.6132 | + | 16.6132i | −0.0300965 | + | 0.0300965i | ||||
\(553\) | 127.279 | + | 127.279i | 0.230161 | + | 0.230161i | ||||
\(554\) | 400.989i | 0.723807i | ||||||||
\(555\) | −539.764 | + | 108.916i | −0.972549 | + | 0.196246i | ||||
\(556\) | 488.314 | 0.878262 | ||||||||
\(557\) | −583.468 | + | 583.468i | −1.04752 | + | 1.04752i | −0.0487058 | + | 0.998813i | \(0.515510\pi\) |
−0.998813 | + | 0.0487058i | \(0.984490\pi\) | |||||||
\(558\) | 112.389 | + | 112.389i | 0.201414 | + | 0.201414i | ||||
\(559\) | 609.489i | 1.09032i | ||||||||
\(560\) | 33.6443 | − | 50.6545i | 0.0600791 | − | 0.0904545i | ||||
\(561\) | −95.1171 | −0.169549 | ||||||||
\(562\) | 44.8143 | − | 44.8143i | 0.0797408 | − | 0.0797408i | ||||
\(563\) | −38.5193 | − | 38.5193i | −0.0684179 | − | 0.0684179i | 0.672070 | − | 0.740488i | \(-0.265405\pi\) |
−0.740488 | + | 0.672070i | \(0.765405\pi\) | |||||||
\(564\) | − | 50.3080i | − | 0.0891986i | ||||||
\(565\) | 827.335 | + | 549.508i | 1.46431 | + | 0.972581i | ||||
\(566\) | 152.112 | 0.268749 | ||||||||
\(567\) | −19.3495 | + | 19.3495i | −0.0341261 | + | 0.0341261i | ||||
\(568\) | −262.574 | − | 262.574i | −0.462278 | − | 0.462278i | ||||
\(569\) | − | 72.1680i | − | 0.126833i | −0.997987 | − | 0.0634165i | \(-0.979800\pi\) | ||
0.997987 | − | 0.0634165i | \(-0.0201997\pi\) | |||||||
\(570\) | 63.9581 | + | 316.961i | 0.112207 | + | 0.556073i | ||||
\(571\) | −653.227 | −1.14401 | −0.572003 | − | 0.820252i | \(-0.693833\pi\) | ||||
−0.572003 | + | 0.820252i | \(0.693833\pi\) | |||||||
\(572\) | −266.358 | + | 266.358i | −0.465662 | + | 0.465662i | ||||
\(573\) | −171.080 | − | 171.080i | −0.298569 | − | 0.298569i | ||||
\(574\) | − | 169.305i | − | 0.294956i | ||||||
\(575\) | 111.021 | + | 45.2696i | 0.193080 | + | 0.0787297i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 401.108 | − | 401.108i | 0.695161 | − | 0.695161i | −0.268202 | − | 0.963363i | \(-0.586429\pi\) |
0.963363 | + | 0.268202i | \(0.0864293\pi\) | |||||||
\(578\) | 271.147 | + | 271.147i | 0.469112 | + | 0.469112i | ||||
\(579\) | 253.442i | 0.437723i | ||||||||
\(580\) | 447.104 | − | 90.2189i | 0.770868 | − | 0.155550i | ||||
\(581\) | −133.505 | −0.229784 | ||||||||
\(582\) | −20.0268 | + | 20.0268i | −0.0344103 | + | 0.0344103i | ||||
\(583\) | −449.973 | − | 449.973i | −0.771823 | − | 0.771823i | ||||
\(584\) | − | 196.213i | − | 0.335982i | ||||||
\(585\) | 120.265 | − | 181.070i | 0.205582 | − | 0.309522i | ||||
\(586\) | −289.198 | −0.493512 | ||||||||
\(587\) | −341.521 | + | 341.521i | −0.581807 | + | 0.581807i | −0.935400 | − | 0.353593i | \(-0.884960\pi\) |
0.353593 | + | 0.935400i | \(0.384960\pi\) | |||||||
\(588\) | −97.3806 | − | 97.3806i | −0.165613 | − | 0.165613i | ||||
\(589\) | 989.077i | 1.67925i | ||||||||
\(590\) | −134.730 | − | 89.4865i | −0.228356 | − | 0.151672i | ||||
\(591\) | 572.614 | 0.968890 | ||||||||
\(592\) | 179.839 | − | 179.839i | 0.303783 | − | 0.303783i | ||||
\(593\) | −4.85045 | − | 4.85045i | −0.00817952 | − | 0.00817952i | 0.703005 | − | 0.711185i | \(-0.251841\pi\) |
−0.711185 | + | 0.703005i | \(0.751841\pi\) | |||||||
\(594\) | 95.5075i | 0.160787i | ||||||||
\(595\) | −12.7055 | − | 62.9656i | −0.0213538 | − | 0.105825i | ||||
\(596\) | 418.076 | 0.701470 | ||||||||
\(597\) | 201.299 | − | 201.299i | 0.337184 | − | 0.337184i | ||||
\(598\) | 69.4984 | + | 69.4984i | 0.116218 | + | 0.116218i | ||||
\(599\) | 555.468i | 0.927326i | 0.886012 | + | 0.463663i | \(0.153465\pi\) | ||||
−0.886012 | + | 0.463663i | \(0.846535\pi\) | |||||||
\(600\) | 47.4933 | + | 112.891i | 0.0791555 | + | 0.188152i | ||||
\(601\) | 705.957 | 1.17464 | 0.587319 | − | 0.809356i | \(-0.300183\pi\) | ||||
0.587319 | + | 0.809356i | \(0.300183\pi\) | |||||||
\(602\) | 127.879 | − | 127.879i | 0.212423 | − | 0.212423i | ||||
\(603\) | 59.0636 | + | 59.0636i | 0.0979495 | + | 0.0979495i | ||||
\(604\) | 194.896i | 0.322675i | ||||||||
\(605\) | −234.867 | + | 47.3927i | −0.388210 | + | 0.0783351i | ||||
\(606\) | 379.899 | 0.626896 | ||||||||
\(607\) | 429.607 | − | 429.607i | 0.707755 | − | 0.707755i | −0.258308 | − | 0.966063i | \(-0.583165\pi\) |
0.966063 | + | 0.258308i | \(0.0831648\pi\) | |||||||
\(608\) | −105.606 | − | 105.606i | −0.173693 | − | 0.173693i | ||||
\(609\) | 240.203i | 0.394422i | ||||||||
\(610\) | 275.203 | − | 414.344i | 0.451153 | − | 0.679252i | ||||
\(611\) | −210.454 | −0.344442 | ||||||||
\(612\) | −17.9264 | + | 17.9264i | −0.0292915 | + | 0.0292915i | ||||
\(613\) | 396.285 | + | 396.285i | 0.646468 | + | 0.646468i | 0.952138 | − | 0.305670i | \(-0.0988803\pi\) |
−0.305670 | + | 0.952138i | \(0.598880\pi\) | |||||||
\(614\) | − | 337.921i | − | 0.550360i | ||||||
\(615\) | 284.046 | + | 188.661i | 0.461863 | + | 0.306765i | ||||
\(616\) | 111.771 | 0.181446 | ||||||||
\(617\) | −800.870 | + | 800.870i | −1.29801 | + | 1.29801i | −0.368299 | + | 0.929707i | \(0.620060\pi\) |
−0.929707 | + | 0.368299i | \(0.879940\pi\) | |||||||
\(618\) | 114.020 | + | 114.020i | 0.184498 | + | 0.184498i | ||||
\(619\) | − | 480.925i | − | 0.776939i | −0.921462 | − | 0.388469i | \(-0.873004\pi\) | ||
0.921462 | − | 0.388469i | \(-0.126996\pi\) | |||||||
\(620\) | 74.1013 | + | 367.229i | 0.119518 | + | 0.592305i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 527.554 | − | 527.554i | 0.848157 | − | 0.848157i | ||||
\(623\) | 365.277 | + | 365.277i | 0.586320 | + | 0.586320i | ||||
\(624\) | 100.399i | 0.160897i | ||||||||
\(625\) | 437.032 | − | 446.797i | 0.699252 | − | 0.714875i | ||||
\(626\) | −771.462 | −1.23237 | ||||||||
\(627\) | −420.256 | + | 420.256i | −0.670264 | + | 0.670264i | ||||
\(628\) | −285.922 | − | 285.922i | −0.455290 | − | 0.455290i | ||||
\(629\) | − | 268.656i | − | 0.427117i | ||||||
\(630\) | −63.2241 | + | 12.7577i | −0.100356 | + | 0.0202503i | ||||
\(631\) | −205.865 | −0.326251 | −0.163126 | − | 0.986605i | \(-0.552158\pi\) | ||||
−0.163126 | + | 0.986605i | \(0.552158\pi\) | |||||||
\(632\) | 118.402 | − | 118.402i | 0.187345 | − | 0.187345i | ||||
\(633\) | −93.0437 | − | 93.0437i | −0.146988 | − | 0.146988i | ||||
\(634\) | − | 422.110i | − | 0.665788i | ||||||
\(635\) | 431.667 | − | 649.913i | 0.679790 | − | 1.02349i | ||||
\(636\) | −169.610 | −0.266682 | ||||||||
\(637\) | −407.373 | + | 407.373i | −0.639518 | + | 0.639518i | ||||
\(638\) | 592.810 | + | 592.810i | 0.929169 | + | 0.929169i | ||||
\(639\) | 393.861i | 0.616371i | ||||||||
\(640\) | −47.1216 | − | 31.2978i | −0.0736276 | − | 0.0489028i | ||||
\(641\) | 652.976 | 1.01868 | 0.509342 | − | 0.860564i | \(-0.329889\pi\) | ||||
0.509342 | + | 0.860564i | \(0.329889\pi\) | |||||||
\(642\) | −33.5070 | + | 33.5070i | −0.0521916 | + | 0.0521916i | ||||
\(643\) | −702.135 | − | 702.135i | −1.09197 | − | 1.09197i | −0.995319 | − | 0.0966483i | \(-0.969188\pi\) |
−0.0966483 | − | 0.995319i | \(-0.530812\pi\) | |||||||
\(644\) | − | 29.1633i | − | 0.0452846i | ||||||
\(645\) | 72.0458 | + | 357.042i | 0.111699 | + | 0.553554i | ||||
\(646\) | −157.761 | −0.244212 | ||||||||
\(647\) | −575.223 | + | 575.223i | −0.889062 | + | 0.889062i | −0.994433 | − | 0.105371i | \(-0.966397\pi\) |
0.105371 | + | 0.994433i | \(0.466397\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 297.286i | − | 0.458068i | ||||||
\(650\) | 472.258 | − | 198.679i | 0.726551 | − | 0.305660i | ||||
\(651\) | −197.291 | −0.303058 | ||||||||
\(652\) | −205.390 | + | 205.390i | −0.315016 | + | 0.315016i | ||||
\(653\) | −260.357 | − | 260.357i | −0.398708 | − | 0.398708i | 0.479069 | − | 0.877777i | \(-0.340974\pi\) |
−0.877777 | + | 0.479069i | \(0.840974\pi\) | |||||||
\(654\) | 257.570i | 0.393838i | ||||||||
\(655\) | −305.792 | + | 61.7043i | −0.466858 | + | 0.0942050i | ||||
\(656\) | −157.497 | −0.240087 | ||||||||
\(657\) | −147.160 | + | 147.160i | −0.223988 | + | 0.223988i | ||||
\(658\) | 44.1560 | + | 44.1560i | 0.0671063 | + | 0.0671063i | ||||
\(659\) | 421.514i | 0.639626i | 0.947481 | + | 0.319813i | \(0.103620\pi\) | ||||
−0.947481 | + | 0.319813i | \(0.896380\pi\) | |||||||
\(660\) | −124.549 | + | 187.520i | −0.188710 | + | 0.284121i | ||||
\(661\) | −190.516 | −0.288224 | −0.144112 | − | 0.989561i | \(-0.546033\pi\) | ||||
−0.144112 | + | 0.989561i | \(0.546033\pi\) | |||||||
\(662\) | 136.580 | − | 136.580i | 0.206313 | − | 0.206313i | ||||
\(663\) | 74.9917 | + | 74.9917i | 0.113110 | + | 0.113110i | ||||
\(664\) | 124.193i | 0.187038i | ||||||||
\(665\) | −334.338 | − | 222.064i | −0.502764 | − | 0.333931i | ||||
\(666\) | −269.759 | −0.405044 | ||||||||
\(667\) | 154.676 | − | 154.676i | 0.231898 | − | 0.231898i | ||||
\(668\) | 338.787 | + | 338.787i | 0.507166 | + | 0.507166i | ||||
\(669\) | − | 576.060i | − | 0.861076i | ||||||
\(670\) | 38.9423 | + | 192.989i | 0.0581228 | + | 0.288043i | ||||
\(671\) | 914.263 | 1.36254 | ||||||||
\(672\) | 21.0651 | − | 21.0651i | 0.0313469 | − | 0.0313469i | ||||
\(673\) | −268.061 | − | 268.061i | −0.398308 | − | 0.398308i | 0.479328 | − | 0.877636i | \(-0.340880\pi\) |
−0.877636 | + | 0.479328i | \(0.840880\pi\) | |||||||
\(674\) | 155.211i | 0.230283i | ||||||||
\(675\) | 49.0483 | − | 120.288i | 0.0726642 | − | 0.178205i | ||||
\(676\) | 82.0021 | 0.121305 | ||||||||
\(677\) | 242.456 | − | 242.456i | 0.358133 | − | 0.358133i | −0.504991 | − | 0.863124i | \(-0.668504\pi\) |
0.863124 | + | 0.504991i | \(0.168504\pi\) | |||||||
\(678\) | 344.054 | + | 344.054i | 0.507454 | + | 0.507454i | ||||
\(679\) | − | 35.1556i | − | 0.0517755i | ||||||
\(680\) | −58.5741 | + | 11.8194i | −0.0861384 | + | 0.0173815i | ||||
\(681\) | −55.9541 | −0.0821647 | ||||||||
\(682\) | −486.905 | + | 486.905i | −0.713937 | + | 0.713937i | ||||
\(683\) | −636.304 | − | 636.304i | −0.931630 | − | 0.931630i | 0.0661774 | − | 0.997808i | \(-0.478920\pi\) |
−0.997808 | + | 0.0661774i | \(0.978920\pi\) | |||||||
\(684\) | 158.408i | 0.231591i | ||||||||
\(685\) | 14.6994 | − | 22.1313i | 0.0214590 | − | 0.0323085i | ||||
\(686\) | 381.639 | 0.556325 | ||||||||
\(687\) | 114.324 | − | 114.324i | 0.166410 | − | 0.166410i | ||||
\(688\) | −118.960 | − | 118.960i | −0.172907 | − | 0.172907i | ||||
\(689\) | 709.531i | 1.02980i | ||||||||
\(690\) | 48.9277 | + | 32.4974i | 0.0709097 | + | 0.0470976i | ||||
\(691\) | −761.609 | −1.10218 | −0.551092 | − | 0.834445i | \(-0.685789\pi\) | ||||
−0.551092 | + | 0.834445i | \(0.685789\pi\) | |||||||
\(692\) | 182.544 | − | 182.544i | 0.263792 | − | 0.263792i | ||||
\(693\) | −83.8282 | − | 83.8282i | −0.120964 | − | 0.120964i | ||||
\(694\) | 669.961i | 0.965362i | ||||||||
\(695\) | −241.469 | − | 1196.67i | −0.347438 | − | 1.72182i | ||||
\(696\) | 223.450 | 0.321049 | ||||||||
\(697\) | −117.640 | + | 117.640i | −0.168780 | + | 0.168780i | ||||
\(698\) | −462.956 | − | 462.956i | −0.663261 | − | 0.663261i | ||||
\(699\) | 377.860i | 0.540572i | ||||||||
\(700\) | −140.771 | − | 57.4004i | −0.201102 | − | 0.0820006i | ||||
\(701\) | −752.904 | −1.07404 | −0.537022 | − | 0.843569i | \(-0.680451\pi\) | ||||
−0.537022 | + | 0.843569i | \(0.680451\pi\) | |||||||
\(702\) | 75.2996 | − | 75.2996i | 0.107264 | − | 0.107264i | ||||
\(703\) | −1187.00 | − | 1187.00i | −1.68848 | − | 1.68848i | ||||
\(704\) | − | 103.975i | − | 0.147692i | ||||||
\(705\) | −123.285 | + | 24.8771i | −0.174873 | + | 0.0352867i | ||||
\(706\) | −839.274 | −1.18877 | ||||||||
\(707\) | −333.442 | + | 333.442i | −0.471630 | + | 0.471630i | ||||
\(708\) | −56.0286 | − | 56.0286i | −0.0791364 | − | 0.0791364i | ||||
\(709\) | − | 492.812i | − | 0.695080i | −0.937665 | − | 0.347540i | \(-0.887017\pi\) | ||
0.937665 | − | 0.347540i | \(-0.112983\pi\) | |||||||
\(710\) | −513.624 | + | 773.308i | −0.723414 | + | 1.08917i | ||||
\(711\) | −177.603 | −0.249794 | ||||||||
\(712\) | 339.801 | − | 339.801i | 0.477249 | − | 0.477249i | ||||
\(713\) | 127.043 | + | 127.043i | 0.178181 | + | 0.178181i | ||||
\(714\) | − | 31.4685i | − | 0.0440735i | ||||||
\(715\) | 784.453 | + | 521.027i | 1.09714 | + | 0.728709i | ||||
\(716\) | 268.322 | 0.374752 | ||||||||
\(717\) | 11.1124 | − | 11.1124i | 0.0154984 | − | 0.0154984i | ||||
\(718\) | −253.226 | − | 253.226i | −0.352683 | − | 0.352683i | ||||
\(719\) | 66.9427i | 0.0931052i | 0.998916 | + | 0.0465526i | \(0.0148235\pi\) | ||||
−0.998916 | + | 0.0465526i | \(0.985176\pi\) | |||||||
\(720\) | 11.8679 | + | 58.8146i | 0.0164832 | + | 0.0816869i | ||||
\(721\) | −200.153 | −0.277605 | ||||||||
\(722\) | −336.034 | + | 336.034i | −0.465422 | + | 0.465422i | ||||
\(723\) | −310.535 | − | 310.535i | −0.429509 | − | 0.429509i | ||||
\(724\) | 204.684i | 0.282712i | ||||||||
\(725\) | −442.182 | − | 1051.06i | −0.609906 | − | 1.44974i | ||||
\(726\) | −117.380 | −0.161681 | ||||||||
\(727\) | −264.488 | + | 264.488i | −0.363807 | + | 0.363807i | −0.865212 | − | 0.501406i | \(-0.832816\pi\) |
0.501406 | + | 0.865212i | \(0.332816\pi\) | |||||||
\(728\) | −88.1218 | − | 88.1218i | −0.121046 | − | 0.121046i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −480.842 | + | 97.0268i | −0.658688 | + | 0.132913i | ||||
\(731\) | −177.710 | −0.243106 | ||||||||
\(732\) | 172.308 | − | 172.308i | 0.235394 | − | 0.235394i | ||||
\(733\) | 0.545555 | + | 0.545555i | 0.000744277 | + | 0.000744277i | 0.707479 | − | 0.706735i | \(-0.249832\pi\) |
−0.706735 | + | 0.707479i | \(0.749832\pi\) | |||||||
\(734\) | − | 266.467i | − | 0.363035i | ||||||
\(735\) | −190.487 | + | 286.796i | −0.259166 | + | 0.390198i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −255.882 | + | 255.882i | −0.347194 | + | 0.347194i | ||||
\(738\) | 118.123 | + | 118.123i | 0.160058 | + | 0.160058i | ||||
\(739\) | 682.594i | 0.923673i | 0.886965 | + | 0.461836i | \(0.152809\pi\) | ||||
−0.886965 | + | 0.461836i | \(0.847191\pi\) | |||||||
\(740\) | −529.646 | − | 351.786i | −0.715738 | − | 0.475386i | ||||
\(741\) | 662.672 | 0.894294 | ||||||||
\(742\) | 148.869 | − | 148.869i | 0.200632 | − | 0.200632i | ||||
\(743\) | −390.572 | − | 390.572i | −0.525670 | − | 0.525670i | 0.393609 | − | 0.919278i | \(-0.371227\pi\) |
−0.919278 | + | 0.393609i | \(0.871227\pi\) | |||||||
\(744\) | 183.531i | 0.246681i | ||||||||
\(745\) | −206.737 | − | 1024.54i | −0.277499 | − | 1.37522i | ||||
\(746\) | −316.140 | −0.423780 | ||||||||
\(747\) | 93.1450 | − | 93.1450i | 0.124692 | − | 0.124692i | ||||
\(748\) | −77.6628 | − | 77.6628i | −0.103827 | − | 0.103827i | ||||
\(749\) | − | 58.8190i | − | 0.0785301i | ||||||
\(750\) | 253.166 | − | 172.212i | 0.337555 | − | 0.229615i | ||||
\(751\) | −39.5226 | −0.0526266 | −0.0263133 | − | 0.999654i | \(-0.508377\pi\) | ||||
−0.0263133 | + | 0.999654i | \(0.508377\pi\) | |||||||
\(752\) | 41.0763 | − | 41.0763i | 0.0546228 | − | 0.0546228i | ||||
\(753\) | −171.381 | − | 171.381i | −0.227598 | − | 0.227598i | ||||
\(754\) | − | 934.760i | − | 1.23974i | ||||||
\(755\) | 477.613 | − | 96.3753i | 0.632601 | − | 0.127649i | ||||
\(756\) | −31.5976 | −0.0417958 | ||||||||
\(757\) | 775.732 | − | 775.732i | 1.02474 | − | 1.02474i | 0.0250588 | − | 0.999686i | \(-0.492023\pi\) |
0.999686 | − | 0.0250588i | \(-0.00797731\pi\) | |||||||
\(758\) | 485.673 | + | 485.673i | 0.640730 | + | 0.640730i | ||||
\(759\) | 107.961i | 0.142241i | ||||||||
\(760\) | −206.576 | + | 311.019i | −0.271811 | + | 0.409236i | ||||
\(761\) | −993.258 | −1.30520 | −0.652600 | − | 0.757702i | \(-0.726322\pi\) | ||||
−0.652600 | + | 0.757702i | \(0.726322\pi\) | |||||||
\(762\) | 270.272 | − | 270.272i | 0.354687 | − | 0.354687i | ||||
\(763\) | −226.072 | − | 226.072i | −0.296294 | − | 0.296294i | ||||
\(764\) | − | 279.373i | − | 0.365671i | ||||||
\(765\) | 52.7951 | + | 35.0660i | 0.0690132 | + | 0.0458380i | ||||
\(766\) | 894.121 | 1.16726 | ||||||||
\(767\) | −234.385 | + | 234.385i | −0.305587 | + | 0.305587i | ||||
\(768\) | −19.5959 | − | 19.5959i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 938.784i | − | 1.22079i | −0.792099 | − | 0.610393i | \(-0.791012\pi\) | ||
0.792099 | − | 0.610393i | \(-0.208988\pi\) | |||||||
\(770\) | −55.2703 | − | 273.906i | −0.0717796 | − | 0.355723i | ||||
\(771\) | 68.1690 | 0.0884163 | ||||||||
\(772\) | −206.934 | + | 206.934i | −0.268049 | + | 0.268049i | ||||
\(773\) | 709.202 | + | 709.202i | 0.917467 | + | 0.917467i | 0.996845 | − | 0.0793776i | \(-0.0252933\pi\) |
−0.0793776 | + | 0.996845i | \(0.525293\pi\) | |||||||
\(774\) | 178.440i | 0.230542i | ||||||||
\(775\) | 863.291 | − | 363.187i | 1.11392 | − | 0.468628i | ||||
\(776\) | −32.7036 | −0.0421439 | ||||||||
\(777\) | 236.771 | − | 236.771i | 0.304725 | − | 0.304725i | ||||
\(778\) | 252.009 | + | 252.009i | 0.323919 | + | 0.323919i | ||||
\(779\) | 1039.53i | 1.33445i | ||||||||
\(780\) | 246.040 | − | 49.6471i | 0.315435 | − | 0.0636502i | ||||
\(781\) | −1706.33 | −2.18480 | ||||||||
\(782\) | −20.2638 | + | 20.2638i | −0.0259128 | + | 0.0259128i | ||||
\(783\) | −167.587 | − | 167.587i | −0.214032 | − | 0.214032i | ||||
\(784\) | − | 159.022i | − | 0.202834i | ||||||
\(785\) | −559.296 | + | 842.071i | −0.712479 | + | 1.07270i | ||||
\(786\) | −152.826 | −0.194436 | ||||||||
\(787\) | −13.9567 | + | 13.9567i | −0.0177341 | + | 0.0177341i | −0.715918 | − | 0.698184i | \(-0.753992\pi\) |
0.698184 | + | 0.715918i | \(0.253992\pi\) | |||||||
\(788\) | 467.537 | + | 467.537i | 0.593321 | + | 0.593321i | ||||
\(789\) | 549.349i | 0.696260i | ||||||||
\(790\) | −348.707 | − | 231.608i | −0.441401 | − | 0.293174i | ||||
\(791\) | −603.961 | −0.763540 | ||||||||
\(792\) | −77.9816 | + | 77.9816i | −0.0984616 | + | 0.0984616i | ||||
\(793\) | −720.819 | − | 720.819i | −0.908977 | − | 0.908977i | ||||
\(794\) | − | 1054.50i | − | 1.32809i | ||||||
\(795\) | 83.8714 | + | 415.647i | 0.105499 | + | 0.522826i | ||||
\(796\) | 328.720 | 0.412965 | ||||||||
\(797\) | −495.513 | + | 495.513i | −0.621723 | + | 0.621723i | −0.945972 | − | 0.324249i | \(-0.894888\pi\) |
0.324249 | + | 0.945972i | \(0.394888\pi\) | |||||||
\(798\) | −139.037 | − | 139.037i | −0.174232 | − | 0.174232i | ||||
\(799\) | − | 61.3626i | − | 0.0767992i | ||||||
\(800\) | −53.3971 | + | 130.953i | −0.0667463 | + | 0.163692i | ||||
\(801\) | −509.702 | −0.636332 | ||||||||
\(802\) | 337.961 | − | 337.961i | 0.421398 | − | 0.421398i | ||||
\(803\) | −637.543 | − | 637.543i | −0.793952 | − | 0.793952i | ||||
\(804\) | 96.4504i | 0.119963i | ||||||||
\(805\) | −71.4678 | + | 14.4211i | −0.0887799 | + | 0.0179145i | ||||
\(806\) | 767.766 | 0.952563 | ||||||||
\(807\) | −561.161 | + | 561.161i | −0.695366 | + | 0.695366i | ||||
\(808\) | 310.186 | + | 310.186i | 0.383894 | + | 0.383894i | ||||
\(809\) | 417.197i | 0.515694i | 0.966186 | + | 0.257847i | \(0.0830131\pi\) | ||||
−0.966186 | + | 0.257847i | \(0.916987\pi\) | |||||||
\(810\) | 35.2100 | − | 53.0119i | 0.0434691 | − | 0.0654467i | ||||
\(811\) | −3.41357 | −0.00420909 | −0.00210454 | − | 0.999998i | \(-0.500670\pi\) | ||||
−0.00210454 | + | 0.999998i | \(0.500670\pi\) | |||||||
\(812\) | −196.125 | + | 196.125i | −0.241533 | + | 0.241533i | ||||
\(813\) | −409.377 | − | 409.377i | −0.503539 | − | 0.503539i | ||||
\(814\) | − | 1168.68i | − | 1.43573i | ||||||
\(815\) | 604.896 | + | 401.767i | 0.742204 | + | 0.492965i | ||||
\(816\) | −29.2737 | −0.0358746 | ||||||||
\(817\) | −785.176 | + | 785.176i | −0.961048 | + | 0.961048i | ||||
\(818\) | −669.062 | − | 669.062i | −0.817924 | − | 0.817924i | ||||
\(819\) | 132.183i | 0.161395i | ||||||||
\(820\) | 77.8816 | + | 385.963i | 0.0949776 | + | 0.470687i | ||||
\(821\) | 1209.69 | 1.47344 | 0.736718 | − | 0.676200i | \(-0.236375\pi\) | ||||
0.736718 | + | 0.676200i | \(0.236375\pi\) | |||||||
\(822\) | 9.20349 | − | 9.20349i | 0.0111965 | − | 0.0111965i | ||||
\(823\) | 326.244 | + | 326.244i | 0.396409 | + | 0.396409i | 0.876964 | − | 0.480556i | \(-0.159565\pi\) |
−0.480556 | + | 0.876964i | \(0.659565\pi\) | |||||||
\(824\) | 186.194i | 0.225963i | ||||||||
\(825\) | 521.126 | + | 212.493i | 0.631668 | + | 0.257567i | ||||
\(826\) | 98.3540 | 0.119073 | ||||||||
\(827\) | −195.429 | + | 195.429i | −0.236311 | + | 0.236311i | −0.815321 | − | 0.579009i | \(-0.803439\pi\) |
0.579009 | + | 0.815321i | \(0.303439\pi\) | |||||||
\(828\) | 20.3470 | + | 20.3470i | 0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 1340.21i | − | 1.61666i | −0.588733 | − | 0.808328i | \(-0.700373\pi\) | ||
0.588733 | − | 0.808328i | \(-0.299627\pi\) | |||||||
\(830\) | 304.349 | − | 61.4131i | 0.366686 | − | 0.0739917i | ||||
\(831\) | 491.109 | 0.590986 | ||||||||
\(832\) | −81.9758 | + | 81.9758i | −0.0985286 | + | 0.0985286i | ||||
\(833\) | −118.779 | − | 118.779i | −0.142592 | − | 0.142592i | ||||
\(834\) | − | 598.060i | − | 0.717098i | ||||||
\(835\) | 662.705 | − | 997.762i | 0.793658 | − | 1.19493i | ||||
\(836\) | −686.275 | −0.820903 | ||||||||
\(837\) | 137.648 | − | 137.648i | 0.164454 | − | 0.164454i | ||||
\(838\) | 141.319 | + | 141.319i | 0.168639 | + | 0.168639i | ||||
\(839\) | − | 649.331i | − | 0.773934i | −0.922094 | − | 0.386967i | \(-0.873523\pi\) | ||
0.922094 | − | 0.386967i | \(-0.126477\pi\) | |||||||
\(840\) | −62.0389 | − | 41.2057i | −0.0738558 | − | 0.0490544i | ||||
\(841\) | −1239.41 | −1.47373 | ||||||||
\(842\) | 336.422 | − | 336.422i | 0.399551 | − | 0.399551i | ||||
\(843\) | −54.8861 | − | 54.8861i | −0.0651081 | − | 0.0651081i | ||||
\(844\) | − | 151.940i | − | 0.180023i | ||||||
\(845\) | −40.5497 | − | 200.955i | −0.0479878 | − | 0.237816i | ||||
\(846\) | −61.6145 | −0.0728303 | ||||||||
\(847\) | 103.026 | − | 103.026i | 0.121636 | − | 0.121636i | ||||
\(848\) | −138.486 | − | 138.486i | −0.163309 | − | 0.163309i | ||||
\(849\) | − | 186.298i | − | 0.219433i | ||||||
\(850\) | 57.9293 | + | 137.697i | 0.0681522 | + | 0.161997i | ||||
\(851\) | −304.933 | −0.358323 | ||||||||
\(852\) | −321.586 | + | 321.586i | −0.377449 | + | 0.377449i | ||||
\(853\) | −708.610 | − | 708.610i | −0.830726 | − | 0.830726i | 0.156890 | − | 0.987616i | \(-0.449853\pi\) |
−0.987616 | + | 0.156890i | \(0.949853\pi\) | |||||||
\(854\) | 302.474i | 0.354185i | ||||||||
\(855\) | 388.197 | − | 78.3324i | 0.454031 | − | 0.0916168i | ||||
\(856\) | −54.7167 | −0.0639214 | ||||||||
\(857\) | −846.209 | + | 846.209i | −0.987409 | + | 0.987409i | −0.999922 | − | 0.0125131i | \(-0.996017\pi\) |
0.0125131 | + | 0.999922i | \(0.496017\pi\) | |||||||
\(858\) | 326.221 | + | 326.221i | 0.380211 | + | 0.380211i | ||||
\(859\) | 97.8764i | 0.113942i | 0.998376 | + | 0.0569711i | \(0.0181443\pi\) | ||||
−0.998376 | + | 0.0569711i | \(0.981856\pi\) | |||||||
\(860\) | −232.699 | + | 350.349i | −0.270580 | + | 0.407382i | ||||
\(861\) | −207.355 | −0.240831 | ||||||||
\(862\) | 568.586 | − | 568.586i | 0.659612 | − | 0.659612i | ||||
\(863\) | 126.219 | + | 126.219i | 0.146256 | + | 0.146256i | 0.776443 | − | 0.630187i | \(-0.217022\pi\) |
−0.630187 | + | 0.776443i | \(0.717022\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −537.612 | − | 357.077i | −0.621517 | − | 0.412806i | ||||
\(866\) | 444.772 | 0.513593 | ||||||||
\(867\) | 332.086 | − | 332.086i | 0.383029 | − | 0.383029i | ||||
\(868\) | −161.087 | − | 161.087i | −0.185584 | − | 0.185584i | ||||
\(869\) | − | 769.433i | − | 0.885423i | ||||||
\(870\) | −110.495 | − | 547.588i | −0.127006 | − | 0.629411i | ||||
\(871\) | 403.482 | 0.463240 | ||||||||
\(872\) | −210.305 | + | 210.305i | −0.241176 | + | 0.241176i | ||||
\(873\) | 24.5277 | + | 24.5277i | 0.0280959 | + | 0.0280959i | ||||
\(874\) | 179.063i | 0.204878i | ||||||||
\(875\) | −71.0550 | + | 373.359i | −0.0812057 | + | 0.426696i | ||||
\(876\) | −240.311 | −0.274328 | ||||||||
\(877\) | −374.235 | + | 374.235i | −0.426722 | + | 0.426722i | −0.887510 | − | 0.460788i | \(-0.847567\pi\) |
0.460788 | + | 0.887510i | \(0.347567\pi\) | |||||||
\(878\) | −215.602 | − | 215.602i | −0.245561 | − | 0.245561i | ||||
\(879\) | 354.194i | 0.402951i | ||||||||
\(880\) | −254.803 | + | 51.4155i | −0.289549 | + | 0.0584267i | ||||
\(881\) | 473.542 | 0.537506 | 0.268753 | − | 0.963209i | \(-0.413389\pi\) | ||||
0.268753 | + | 0.963209i | \(0.413389\pi\) | |||||||
\(882\) | −119.266 | + | 119.266i | −0.135223 | + | 0.135223i | ||||
\(883\) | 28.7262 | + | 28.7262i | 0.0325325 | + | 0.0325325i | 0.723186 | − | 0.690653i | \(-0.242677\pi\) |
−0.690653 | + | 0.723186i | \(0.742677\pi\) | |||||||
\(884\) | 122.461i | 0.138531i | ||||||||
\(885\) | −109.598 | + | 165.010i | −0.123840 | + | 0.186452i | ||||
\(886\) | 564.371 | 0.636988 | ||||||||
\(887\) | 819.582 | − | 819.582i | 0.923993 | − | 0.923993i | −0.0733156 | − | 0.997309i | \(-0.523358\pi\) |
0.997309 | + | 0.0733156i | \(0.0233581\pi\) | |||||||
\(888\) | −220.257 | − | 220.257i | −0.248038 | − | 0.248038i | ||||
\(889\) | 474.442i | 0.533680i | ||||||||
\(890\) | −1000.75 | − | 664.689i | −1.12444 | − | 0.746841i | ||||
\(891\) | 116.972 | 0.131282 | ||||||||
\(892\) | 470.351 | − | 470.351i | 0.527299 | − | 0.527299i | ||||
\(893\) | −271.118 | − | 271.118i | −0.303604 | − | 0.303604i | ||||
\(894\) | − | 512.037i | − | 0.572748i | ||||||
\(895\) | −132.684 | − | 657.552i | −0.148251 | − | 0.734695i | ||||
\(896\) | 34.3992 | 0.0383919 | ||||||||
\(897\) | 85.1178 | − | 85.1178i | 0.0948916 | − | 0.0948916i | ||||
\(898\) | 761.526 | + | 761.526i | 0.848024 | + | 0.848024i | ||||
\(899\) | − | 1708.75i | − | 1.90072i | ||||||
\(900\) | 138.263 | − | 58.1671i | 0.153625 | − | 0.0646302i | ||||
\(901\) | −206.880 | −0.229611 | ||||||||
\(902\) | −511.744 | + | 511.744i | −0.567344 | + | 0.567344i | ||||
\(903\) | −156.619 | − | 156.619i | −0.173443 | − | 0.173443i | ||||
\(904\) | 561.837i | 0.621502i | ||||||||
\(905\) | 501.599 | − | 101.215i | 0.554253 | − | 0.111840i | ||||
\(906\) | 238.698 | 0.263463 | ||||||||
\(907\) | −668.812 | + | 668.812i | −0.737389 | + | 0.737389i | −0.972072 | − | 0.234683i | \(-0.924595\pi\) |
0.234683 | + | 0.972072i | \(0.424595\pi\) | |||||||
\(908\) | −45.6864 | − | 45.6864i | −0.0503154 | − | 0.0503154i | ||||
\(909\) | − | 465.280i | − | 0.511859i | ||||||
\(910\) | −172.376 | + | 259.528i | −0.189424 | + | 0.285195i | ||||
\(911\) | −1115.81 | −1.22482 | −0.612410 | − | 0.790540i | \(-0.709800\pi\) | ||||
−0.612410 | + | 0.790540i | \(0.709800\pi\) | |||||||
\(912\) | −129.340 | + | 129.340i | −0.141820 | + | 0.141820i | ||||
\(913\) | 403.533 | + | 403.533i | 0.441986 | + | 0.441986i | ||||
\(914\) | − | 542.128i | − | 0.593138i | ||||||
\(915\) | −507.465 | − | 337.054i | −0.554607 | − | 0.368365i | ||||
\(916\) | 186.690 | 0.203810 | ||||||||
\(917\) | 134.138 | − | 134.138i | 0.146279 | − | 0.146279i | ||||
\(918\) | 21.9553 | + | 21.9553i | 0.0239164 | + | 0.0239164i | ||||
\(919\) | 1390.15i | 1.51268i | 0.654181 | + | 0.756338i | \(0.273014\pi\) | ||||
−0.654181 | + | 0.756338i | \(0.726986\pi\) | |||||||
\(920\) | 13.4153 | + | 66.4833i | 0.0145819 | + | 0.0722645i | ||||
\(921\) | −413.867 | −0.449367 | ||||||||
\(922\) | 29.2935 | − | 29.2935i | 0.0317717 | − | 0.0317717i | ||||
\(923\) | 1345.30 | + | 1345.30i | 1.45752 | + | 1.45752i | ||||
\(924\) | − | 136.891i | − | 0.148150i | ||||||
\(925\) | −600.181 | + | 1471.91i | −0.648844 | + | 1.59125i | ||||
\(926\) | −466.631 | −0.503922 | ||||||||
\(927\) | 139.645 | − | 139.645i | 0.150642 | − | 0.150642i | ||||
\(928\) | 182.446 | + | 182.446i | 0.196601 | + | 0.196601i | ||||
\(929\) | − | 1037.21i | − | 1.11648i | −0.829680 | − | 0.558239i | \(-0.811477\pi\) | ||
0.829680 | − | 0.558239i | \(-0.188523\pi\) | |||||||
\(930\) | 449.762 | − | 90.7552i | 0.483615 | − | 0.0975863i | ||||
\(931\) | −1049.60 | −1.12739 | ||||||||
\(932\) | −308.521 | + | 308.521i | −0.331031 | + | 0.331031i | ||||
\(933\) | −646.119 | − | 646.119i | −0.692517 | − | 0.692517i | ||||
\(934\) | 814.754i | 0.872328i | ||||||||
\(935\) | −151.917 | + | 228.725i | −0.162478 | + | 0.244626i | ||||
\(936\) | 122.964 | 0.131371 | ||||||||
\(937\) | −581.404 | + | 581.404i | −0.620496 | + | 0.620496i | −0.945658 | − | 0.325163i | \(-0.894581\pi\) |
0.325163 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(938\) | −84.6557 | − | 84.6557i | −0.0902513 | − | 0.0902513i | ||||
\(939\) | 944.845i | 1.00622i | ||||||||
\(940\) | −120.974 | − | 80.3498i | −0.128696 | − | 0.0854785i | ||||
\(941\) | 1214.11 | 1.29024 | 0.645118 | − | 0.764083i | \(-0.276808\pi\) | ||||
0.645118 | + | 0.764083i | \(0.276808\pi\) | |||||||
\(942\) | −350.182 | + | 350.182i | −0.371743 | + | 0.371743i | ||||
\(943\) | 133.524 | + | 133.524i | 0.141595 | + | 0.141595i | ||||
\(944\) | − | 91.4943i | − | 0.0969219i | ||||||
\(945\) | 15.6249 | + | 77.4334i | 0.0165343 | + | 0.0819401i | ||||
\(946\) | −773.056 | −0.817184 | ||||||||
\(947\) | −307.946 | + | 307.946i | −0.325181 | + | 0.325181i | −0.850750 | − | 0.525570i | \(-0.823852\pi\) |
0.525570 | + | 0.850750i | \(0.323852\pi\) | |||||||
\(948\) | −145.013 | − | 145.013i | −0.152967 | − | 0.152967i | ||||
\(949\) | 1005.30i | 1.05932i | ||||||||
\(950\) | 864.338 | + | 352.439i | 0.909829 | + | 0.370989i | ||||
\(951\) | −516.977 | −0.543614 | ||||||||
\(952\) | 25.6939 | − | 25.6939i | 0.0269894 | − | 0.0269894i | ||||
\(953\) | 318.991 | + | 318.991i | 0.334723 | + | 0.334723i | 0.854377 | − | 0.519654i | \(-0.173939\pi\) |
−0.519654 | + | 0.854377i | \(0.673939\pi\) | |||||||
\(954\) | 207.729i | 0.217745i | ||||||||
\(955\) | −684.632 | + | 138.149i | −0.716892 | + | 0.144658i | ||||
\(956\) | 18.1465 | 0.0189816 | ||||||||
\(957\) | 726.041 | − | 726.041i | 0.758663 | − | 0.758663i | ||||
\(958\) | −703.739 | − | 703.739i | −0.734592 | − | 0.734592i | ||||
\(959\) | 16.1560i | 0.0168467i | ||||||||
\(960\) | −38.3318 | + | 57.7120i | −0.0399289 | + | 0.0601167i | ||||
\(961\) | 442.480 | 0.460437 | ||||||||
\(962\) | −921.405 | + | 921.405i | −0.957802 | + | 0.957802i | ||||
\(963\) | 41.0375 | + | 41.0375i | 0.0426143 | + | 0.0426143i | ||||
\(964\) | − | 507.102i | − | 0.526039i | ||||||
\(965\) | 609.443 | + | 404.786i | 0.631547 | + | 0.419468i | ||||
\(966\) | −35.7176 | −0.0369747 | ||||||||
\(967\) | −186.468 | + | 186.468i | −0.192831 | + | 0.192831i | −0.796918 | − | 0.604087i | \(-0.793538\pi\) |
0.604087 | + | 0.796918i | \(0.293538\pi\) | |||||||
\(968\) | −95.8404 | − | 95.8404i | −0.0990087 | − | 0.0990087i | ||||
\(969\) | 193.217i | 0.199398i | ||||||||
\(970\) | 16.1718 | + | 80.1438i | 0.0166720 | + | 0.0826225i | ||||
\(971\) | −1246.50 | −1.28373 | −0.641864 | − | 0.766819i | \(-0.721839\pi\) | ||||
−0.641864 | + | 0.766819i | \(0.721839\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 524.925 | + | 524.925i | 0.539491 | + | 0.539491i | ||||
\(974\) | − | 815.600i | − | 0.837372i | ||||||
\(975\) | −243.331 | − | 578.396i | −0.249571 | − | 0.593227i | ||||
\(976\) | 281.378 | 0.288297 | ||||||||
\(977\) | 389.022 | − | 389.022i | 0.398181 | − | 0.398181i | −0.479410 | − | 0.877591i | \(-0.659149\pi\) |
0.877591 | + | 0.479410i | \(0.159149\pi\) | |||||||
\(978\) | 251.551 | + | 251.551i | 0.257210 | + | 0.257210i | ||||
\(979\) | − | 2208.19i | − | 2.25555i | ||||||
\(980\) | −389.700 | + | 78.6357i | −0.397653 | + | 0.0802405i | ||||
\(981\) | 315.458 | 0.321567 | ||||||||
\(982\) | −198.942 | + | 198.942i | −0.202589 | + | 0.202589i | ||||
\(983\) | 552.321 | + | 552.321i | 0.561873 | + | 0.561873i | 0.929839 | − | 0.367966i | \(-0.119946\pi\) |
−0.367966 | + | 0.929839i | \(0.619946\pi\) | |||||||
\(984\) | 192.894i | 0.196030i | ||||||||
\(985\) | 914.555 | − | 1376.95i | 0.928482 | − | 1.39791i | ||||
\(986\) | 272.550 | 0.276420 | ||||||||
\(987\) | 54.0798 | − | 54.0798i | 0.0547921 | − | 0.0547921i | ||||
\(988\) | 541.069 | + | 541.069i | 0.547641 | + | 0.547641i | ||||
\(989\) | 201.706i | 0.203950i | ||||||||
\(990\) | 229.664 | + | 152.541i | 0.231984 | + | 0.154081i | ||||
\(991\) | −1165.66 | −1.17625 | −0.588125 | − | 0.808770i | \(-0.700134\pi\) | ||||
−0.588125 | + | 0.808770i | \(0.700134\pi\) | |||||||
\(992\) | −149.852 | + | 149.852i | −0.151061 | + | 0.151061i | ||||
\(993\) | −167.275 | − | 167.275i | −0.168454 | − | 0.168454i | ||||
\(994\) | − | 564.521i | − | 0.567928i | ||||||
\(995\) | −162.551 | − | 805.563i | −0.163368 | − | 0.809611i | ||||
\(996\) | 152.105 | 0.152716 | ||||||||
\(997\) | 246.119 | − | 246.119i | 0.246860 | − | 0.246860i | −0.572821 | − | 0.819681i | \(-0.694151\pi\) |
0.819681 | + | 0.572821i | \(0.194151\pi\) | |||||||
\(998\) | 460.033 | + | 460.033i | 0.460955 | + | 0.460955i | ||||
\(999\) | 330.386i | 0.330717i |
(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 | 690.3.k.a.553.7 | yes | 40 | |
5.2 | odd | 4 | inner | 690.3.k.a.277.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.7 | ✓ | 40 | 5.2 | odd | 4 | inner | |
690.3.k.a.553.7 | yes | 40 | 1.1 | even | 1 | trivial |