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 | 277.9 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.9 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 4.95981 | + | 0.632643i | 0.991963 | + | 0.126529i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 3.11187 | + | 3.11187i | 0.444552 | + | 0.444552i | 0.893539 | − | 0.448986i | \(-0.148215\pi\) |
−0.448986 | + | 0.893539i | \(0.648215\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 4.32717 | + | 5.59246i | 0.432717 | + | 0.559246i | ||||
\(11\) | −11.9521 | −1.08656 | −0.543278 | − | 0.839553i | \(-0.682817\pi\) | ||||
−0.543278 | + | 0.839553i | \(0.682817\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | −6.79511 | + | 6.79511i | −0.522701 | + | 0.522701i | −0.918386 | − | 0.395685i | \(-0.870507\pi\) |
0.395685 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(14\) | 6.22373i | 0.444552i | ||||||||
\(15\) | −6.84933 | + | 5.29968i | −0.456622 | + | 0.353312i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −3.44295 | − | 3.44295i | −0.202527 | − | 0.202527i | 0.598555 | − | 0.801082i | \(-0.295742\pi\) |
−0.801082 | + | 0.598555i | \(0.795742\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 27.8436i | 1.46545i | 0.680524 | + | 0.732726i | \(0.261752\pi\) | ||||
−0.680524 | + | 0.732726i | \(0.738248\pi\) | |||||||
\(20\) | −1.26529 | + | 9.91963i | −0.0632643 | + | 0.495981i | ||||
\(21\) | −7.62248 | −0.362975 | ||||||||
\(22\) | −11.9521 | − | 11.9521i | −0.543278 | − | 0.543278i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 24.1995 | + | 6.27559i | 0.967981 | + | 0.251023i | ||||
\(26\) | −13.5902 | −0.522701 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −6.22373 | + | 6.22373i | −0.222276 | + | 0.222276i | ||||
\(29\) | 26.4720i | 0.912829i | 0.889767 | + | 0.456415i | \(0.150867\pi\) | ||||
−0.889767 | + | 0.456415i | \(0.849133\pi\) | |||||||
\(30\) | −12.1490 | − | 1.54965i | −0.404967 | − | 0.0516551i | ||||
\(31\) | −16.0271 | −0.517003 | −0.258501 | − | 0.966011i | \(-0.583229\pi\) | ||||
−0.258501 | + | 0.966011i | \(0.583229\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 14.6383 | − | 14.6383i | 0.443585 | − | 0.443585i | ||||
\(34\) | − | 6.88590i | − | 0.202527i | ||||||
\(35\) | 13.4656 | + | 17.4030i | 0.384731 | + | 0.497228i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 13.6416 | + | 13.6416i | 0.368693 | + | 0.368693i | 0.867000 | − | 0.498307i | \(-0.166045\pi\) |
−0.498307 | + | 0.867000i | \(0.666045\pi\) | |||||||
\(38\) | −27.8436 | + | 27.8436i | −0.732726 | + | 0.732726i | ||||
\(39\) | − | 16.6446i | − | 0.426783i | ||||||
\(40\) | −11.1849 | + | 8.65434i | −0.279623 | + | 0.216359i | ||||
\(41\) | 32.3332 | 0.788615 | 0.394307 | − | 0.918979i | \(-0.370985\pi\) | ||||
0.394307 | + | 0.918979i | \(0.370985\pi\) | |||||||
\(42\) | −7.62248 | − | 7.62248i | −0.181488 | − | 0.181488i | ||||
\(43\) | −22.4332 | + | 22.4332i | −0.521702 | + | 0.521702i | −0.918085 | − | 0.396383i | \(-0.870265\pi\) |
0.396383 | + | 0.918085i | \(0.370265\pi\) | |||||||
\(44\) | − | 23.9043i | − | 0.543278i | ||||||
\(45\) | 1.89793 | − | 14.8794i | 0.0421762 | − | 0.330654i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −35.7929 | − | 35.7929i | −0.761551 | − | 0.761551i | 0.215052 | − | 0.976603i | \(-0.431008\pi\) |
−0.976603 | + | 0.215052i | \(0.931008\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 29.6326i | − | 0.604746i | ||||||
\(50\) | 17.9239 | + | 30.4751i | 0.358479 | + | 0.609502i | ||||
\(51\) | 8.43348 | 0.165362 | ||||||||
\(52\) | −13.5902 | − | 13.5902i | −0.261350 | − | 0.261350i | ||||
\(53\) | −41.6197 | + | 41.6197i | −0.785277 | + | 0.785277i | −0.980716 | − | 0.195439i | \(-0.937387\pi\) |
0.195439 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | −59.2803 | − | 7.56143i | −1.07782 | − | 0.137481i | ||||
\(56\) | −12.4475 | −0.222276 | ||||||||
\(57\) | −34.1013 | − | 34.1013i | −0.598268 | − | 0.598268i | ||||
\(58\) | −26.4720 | + | 26.4720i | −0.456415 | + | 0.456415i | ||||
\(59\) | 59.3699i | 1.00627i | 0.864208 | + | 0.503135i | \(0.167820\pi\) | ||||
−0.864208 | + | 0.503135i | \(0.832180\pi\) | |||||||
\(60\) | −10.5994 | − | 13.6987i | −0.176656 | − | 0.228311i | ||||
\(61\) | 9.79153 | 0.160517 | 0.0802584 | − | 0.996774i | \(-0.474425\pi\) | ||||
0.0802584 | + | 0.996774i | \(0.474425\pi\) | |||||||
\(62\) | −16.0271 | − | 16.0271i | −0.258501 | − | 0.258501i | ||||
\(63\) | 9.33560 | − | 9.33560i | 0.148184 | − | 0.148184i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −38.0014 | + | 29.4036i | −0.584636 | + | 0.452363i | ||||
\(66\) | 29.2766 | 0.443585 | ||||||||
\(67\) | −35.1732 | − | 35.1732i | −0.524972 | − | 0.524972i | 0.394097 | − | 0.919069i | \(-0.371058\pi\) |
−0.919069 | + | 0.394097i | \(0.871058\pi\) | |||||||
\(68\) | 6.88590 | − | 6.88590i | 0.101263 | − | 0.101263i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −3.93740 | + | 30.8686i | −0.0562486 | + | 0.440979i | ||||
\(71\) | 28.4741 | 0.401044 | 0.200522 | − | 0.979689i | \(-0.435736\pi\) | ||||
0.200522 | + | 0.979689i | \(0.435736\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −2.27141 | + | 2.27141i | −0.0311152 | + | 0.0311152i | −0.722493 | − | 0.691378i | \(-0.757004\pi\) |
0.691378 | + | 0.722493i | \(0.257004\pi\) | |||||||
\(74\) | 27.2833i | 0.368693i | ||||||||
\(75\) | −37.3242 | + | 21.9523i | −0.497656 | + | 0.292697i | ||||
\(76\) | −55.6872 | −0.732726 | ||||||||
\(77\) | −37.1934 | − | 37.1934i | −0.483031 | − | 0.483031i | ||||
\(78\) | 16.6446 | − | 16.6446i | 0.213392 | − | 0.213392i | ||||
\(79\) | 21.6053i | 0.273485i | 0.990607 | + | 0.136742i | \(0.0436632\pi\) | ||||
−0.990607 | + | 0.136742i | \(0.956337\pi\) | |||||||
\(80\) | −19.8393 | − | 2.53057i | −0.247991 | − | 0.0316322i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 32.3332 | + | 32.3332i | 0.394307 | + | 0.394307i | ||||
\(83\) | −48.0807 | + | 48.0807i | −0.579286 | + | 0.579286i | −0.934706 | − | 0.355421i | \(-0.884338\pi\) |
0.355421 | + | 0.934706i | \(0.384338\pi\) | |||||||
\(84\) | − | 15.2450i | − | 0.181488i | ||||||
\(85\) | −14.8982 | − | 19.2546i | −0.175273 | − | 0.226524i | ||||
\(86\) | −44.8664 | −0.521702 | ||||||||
\(87\) | −32.4215 | − | 32.4215i | −0.372661 | − | 0.372661i | ||||
\(88\) | 23.9043 | − | 23.9043i | 0.271639 | − | 0.271639i | ||||
\(89\) | − | 113.080i | − | 1.27057i | −0.772279 | − | 0.635283i | \(-0.780883\pi\) | ||
0.772279 | − | 0.635283i | \(-0.219117\pi\) | |||||||
\(90\) | 16.7774 | − | 12.9815i | 0.186415 | − | 0.144239i | ||||
\(91\) | −42.2909 | −0.464736 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 19.6291 | − | 19.6291i | 0.211065 | − | 0.211065i | ||||
\(94\) | − | 71.5858i | − | 0.761551i | ||||||
\(95\) | −17.6151 | + | 138.099i | −0.185422 | + | 1.45367i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 43.1625 | + | 43.1625i | 0.444974 | + | 0.444974i | 0.893680 | − | 0.448705i | \(-0.148115\pi\) |
−0.448705 | + | 0.893680i | \(0.648115\pi\) | |||||||
\(98\) | 29.6326 | − | 29.6326i | 0.302373 | − | 0.302373i | ||||
\(99\) | 35.8564i | 0.362186i | ||||||||
\(100\) | −12.5512 | + | 48.3991i | −0.125512 | + | 0.483991i | ||||
\(101\) | 53.6055 | 0.530747 | 0.265374 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265374 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(102\) | 8.43348 | + | 8.43348i | 0.0826811 | + | 0.0826811i | ||||
\(103\) | −8.64457 | + | 8.64457i | −0.0839279 | + | 0.0839279i | −0.747824 | − | 0.663897i | \(-0.768902\pi\) |
0.663897 | + | 0.747824i | \(0.268902\pi\) | |||||||
\(104\) | − | 27.1804i | − | 0.261350i | ||||||
\(105\) | −37.8061 | − | 4.82231i | −0.360058 | − | 0.0459268i | ||||
\(106\) | −83.2394 | −0.785277 | ||||||||
\(107\) | 39.5516 | + | 39.5516i | 0.369641 | + | 0.369641i | 0.867346 | − | 0.497705i | \(-0.165824\pi\) |
−0.497705 | + | 0.867346i | \(0.665824\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 6.74005i | − | 0.0618353i | −0.999522 | − | 0.0309176i | \(-0.990157\pi\) | ||
0.999522 | − | 0.0309176i | \(-0.00984296\pi\) | |||||||
\(110\) | −51.7189 | − | 66.8418i | −0.470172 | − | 0.607652i | ||||
\(111\) | −33.4151 | −0.301037 | ||||||||
\(112\) | −12.4475 | − | 12.4475i | −0.111138 | − | 0.111138i | ||||
\(113\) | 116.074 | − | 116.074i | 1.02720 | − | 1.02720i | 0.0275812 | − | 0.999620i | \(-0.491220\pi\) |
0.999620 | − | 0.0275812i | \(-0.00878050\pi\) | |||||||
\(114\) | − | 68.2026i | − | 0.598268i | ||||||
\(115\) | 18.9649 | − | 14.6742i | 0.164913 | − | 0.127601i | ||||
\(116\) | −52.9441 | −0.456415 | ||||||||
\(117\) | 20.3853 | + | 20.3853i | 0.174234 | + | 0.174234i | ||||
\(118\) | −59.3699 | + | 59.3699i | −0.503135 | + | 0.503135i | ||||
\(119\) | − | 21.4280i | − | 0.180067i | ||||||
\(120\) | 3.09931 | − | 24.2980i | 0.0258275 | − | 0.202484i | ||||
\(121\) | 21.8533 | 0.180606 | ||||||||
\(122\) | 9.79153 | + | 9.79153i | 0.0802584 | + | 0.0802584i | ||||
\(123\) | −39.5999 | + | 39.5999i | −0.321951 | + | 0.321951i | ||||
\(124\) | − | 32.0542i | − | 0.258501i | ||||||
\(125\) | 116.055 | + | 46.4354i | 0.928440 | + | 0.371483i | ||||
\(126\) | 18.6712 | 0.148184 | ||||||||
\(127\) | 2.15703 | + | 2.15703i | 0.0169845 | + | 0.0169845i | 0.715548 | − | 0.698564i | \(-0.246177\pi\) |
−0.698564 | + | 0.715548i | \(0.746177\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 54.9499i | − | 0.425968i | ||||||
\(130\) | −67.4050 | − | 8.59776i | −0.518500 | − | 0.0661366i | ||||
\(131\) | 260.534 | 1.98881 | 0.994404 | − | 0.105640i | \(-0.0336892\pi\) | ||||
0.994404 | + | 0.105640i | \(0.0336892\pi\) | |||||||
\(132\) | 29.2766 | + | 29.2766i | 0.221792 | + | 0.221792i | ||||
\(133\) | −86.6455 | + | 86.6455i | −0.651470 | + | 0.651470i | ||||
\(134\) | − | 70.3463i | − | 0.524972i | ||||||
\(135\) | 15.8990 | + | 20.5480i | 0.117771 | + | 0.152207i | ||||
\(136\) | 13.7718 | 0.101263 | ||||||||
\(137\) | −0.350640 | − | 0.350640i | −0.00255941 | − | 0.00255941i | 0.705826 | − | 0.708385i | \(-0.250576\pi\) |
−0.708385 | + | 0.705826i | \(0.750576\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | 115.396i | 0.830185i | 0.909779 | + | 0.415092i | \(0.136251\pi\) | ||||
−0.909779 | + | 0.415092i | \(0.863749\pi\) | |||||||
\(140\) | −34.8060 | + | 26.9312i | −0.248614 | + | 0.192365i | ||||
\(141\) | 87.6743 | 0.621803 | ||||||||
\(142\) | 28.4741 | + | 28.4741i | 0.200522 | + | 0.200522i | ||||
\(143\) | 81.2160 | − | 81.2160i | 0.567944 | − | 0.567944i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −16.7474 | + | 131.296i | −0.115499 | + | 0.905493i | ||||
\(146\) | −4.54282 | −0.0311152 | ||||||||
\(147\) | 36.2923 | + | 36.2923i | 0.246887 | + | 0.246887i | ||||
\(148\) | −27.2833 | + | 27.2833i | −0.184346 | + | 0.184346i | ||||
\(149\) | − | 276.290i | − | 1.85429i | −0.374699 | − | 0.927146i | \(-0.622254\pi\) | ||
0.374699 | − | 0.927146i | \(-0.377746\pi\) | |||||||
\(150\) | −59.2765 | − | 15.3720i | −0.395177 | − | 0.102480i | ||||
\(151\) | 37.7638 | 0.250091 | 0.125046 | − | 0.992151i | \(-0.460092\pi\) | ||||
0.125046 | + | 0.992151i | \(0.460092\pi\) | |||||||
\(152\) | −55.6872 | − | 55.6872i | −0.366363 | − | 0.366363i | ||||
\(153\) | −10.3289 | + | 10.3289i | −0.0675089 | + | 0.0675089i | ||||
\(154\) | − | 74.3868i | − | 0.483031i | ||||||
\(155\) | −79.4913 | − | 10.1394i | −0.512847 | − | 0.0654156i | ||||
\(156\) | 33.2891 | 0.213392 | ||||||||
\(157\) | 122.971 | + | 122.971i | 0.783253 | + | 0.783253i | 0.980378 | − | 0.197126i | \(-0.0631607\pi\) |
−0.197126 | + | 0.980378i | \(0.563161\pi\) | |||||||
\(158\) | −21.6053 | + | 21.6053i | −0.136742 | + | 0.136742i | ||||
\(159\) | − | 101.947i | − | 0.641176i | ||||||
\(160\) | −17.3087 | − | 22.3698i | −0.108179 | − | 0.139811i | ||||
\(161\) | 21.1057 | 0.131091 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −21.6235 | + | 21.6235i | −0.132659 | + | 0.132659i | −0.770319 | − | 0.637659i | \(-0.779903\pi\) |
0.637659 | + | 0.770319i | \(0.279903\pi\) | |||||||
\(164\) | 64.6664i | 0.394307i | ||||||||
\(165\) | 81.8641 | − | 63.3425i | 0.496146 | − | 0.383894i | ||||
\(166\) | −96.1615 | −0.579286 | ||||||||
\(167\) | 79.3633 | + | 79.3633i | 0.475229 | + | 0.475229i | 0.903602 | − | 0.428373i | \(-0.140913\pi\) |
−0.428373 | + | 0.903602i | \(0.640913\pi\) | |||||||
\(168\) | 15.2450 | − | 15.2450i | 0.0907439 | − | 0.0907439i | ||||
\(169\) | 76.6530i | 0.453568i | ||||||||
\(170\) | 4.35632 | − | 34.1528i | 0.0256254 | − | 0.200899i | ||||
\(171\) | 83.5308 | 0.488484 | ||||||||
\(172\) | −44.8664 | − | 44.8664i | −0.260851 | − | 0.260851i | ||||
\(173\) | 167.187 | − | 167.187i | 0.966399 | − | 0.966399i | −0.0330549 | − | 0.999454i | \(-0.510524\pi\) |
0.999454 | + | 0.0330549i | \(0.0105236\pi\) | |||||||
\(174\) | − | 64.8430i | − | 0.372661i | ||||||
\(175\) | 55.7769 | + | 94.8345i | 0.318725 | + | 0.541911i | ||||
\(176\) | 47.8085 | 0.271639 | ||||||||
\(177\) | −72.7130 | − | 72.7130i | −0.410808 | − | 0.410808i | ||||
\(178\) | 113.080 | − | 113.080i | 0.635283 | − | 0.635283i | ||||
\(179\) | − | 88.2952i | − | 0.493269i | −0.969109 | − | 0.246635i | \(-0.920675\pi\) | ||
0.969109 | − | 0.246635i | \(-0.0793247\pi\) | |||||||
\(180\) | 29.7589 | + | 3.79586i | 0.165327 | + | 0.0210881i | ||||
\(181\) | 275.272 | 1.52084 | 0.760420 | − | 0.649432i | \(-0.224993\pi\) | ||||
0.760420 | + | 0.649432i | \(0.224993\pi\) | |||||||
\(182\) | −42.2909 | − | 42.2909i | −0.232368 | − | 0.232368i | ||||
\(183\) | −11.9921 | + | 11.9921i | −0.0655307 | + | 0.0655307i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | 59.0297 | + | 76.2903i | 0.319080 | + | 0.412380i | ||||
\(186\) | 39.2582 | 0.211065 | ||||||||
\(187\) | 41.1506 | + | 41.1506i | 0.220057 | + | 0.220057i | ||||
\(188\) | 71.5858 | − | 71.5858i | 0.380775 | − | 0.380775i | ||||
\(189\) | 22.8675i | 0.120992i | ||||||||
\(190\) | −155.714 | + | 120.484i | −0.819548 | + | 0.634126i | ||||
\(191\) | 284.801 | 1.49111 | 0.745553 | − | 0.666447i | \(-0.232186\pi\) | ||||
0.745553 | + | 0.666447i | \(0.232186\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −71.5610 | + | 71.5610i | −0.370782 | + | 0.370782i | −0.867762 | − | 0.496980i | \(-0.834442\pi\) |
0.496980 | + | 0.867762i | \(0.334442\pi\) | |||||||
\(194\) | 86.3250i | 0.444974i | ||||||||
\(195\) | 10.5301 | − | 82.5539i | 0.0540003 | − | 0.423353i | ||||
\(196\) | 59.2652 | 0.302373 | ||||||||
\(197\) | 214.648 | + | 214.648i | 1.08958 | + | 1.08958i | 0.995571 | + | 0.0940112i | \(0.0299690\pi\) |
0.0940112 | + | 0.995571i | \(0.470031\pi\) | |||||||
\(198\) | −35.8564 | + | 35.8564i | −0.181093 | + | 0.181093i | ||||
\(199\) | 89.3086i | 0.448787i | 0.974499 | + | 0.224394i | \(0.0720401\pi\) | ||||
−0.974499 | + | 0.224394i | \(0.927960\pi\) | |||||||
\(200\) | −60.9502 | + | 35.8479i | −0.304751 | + | 0.179239i | ||||
\(201\) | 86.1563 | 0.428638 | ||||||||
\(202\) | 53.6055 | + | 53.6055i | 0.265374 | + | 0.265374i | ||||
\(203\) | −82.3775 | + | 82.3775i | −0.405800 | + | 0.405800i | ||||
\(204\) | 16.8670i | 0.0826811i | ||||||||
\(205\) | 160.367 | + | 20.4554i | 0.782277 | + | 0.0997823i | ||||
\(206\) | −17.2891 | −0.0839279 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | 27.1804 | − | 27.1804i | 0.130675 | − | 0.130675i | ||||
\(209\) | − | 332.790i | − | 1.59230i | ||||||
\(210\) | −32.9838 | − | 42.6284i | −0.157066 | − | 0.202992i | ||||
\(211\) | −320.246 | −1.51775 | −0.758876 | − | 0.651235i | \(-0.774251\pi\) | ||||
−0.758876 | + | 0.651235i | \(0.774251\pi\) | |||||||
\(212\) | −83.2394 | − | 83.2394i | −0.392639 | − | 0.392639i | ||||
\(213\) | −34.8735 | + | 34.8735i | −0.163725 | + | 0.163725i | ||||
\(214\) | 79.1032i | 0.369641i | ||||||||
\(215\) | −125.457 | + | 97.0723i | −0.583520 | + | 0.451499i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −49.8741 | − | 49.8741i | −0.229835 | − | 0.229835i | ||||
\(218\) | 6.74005 | − | 6.74005i | 0.0309176 | − | 0.0309176i | ||||
\(219\) | − | 5.56379i | − | 0.0254055i | ||||||
\(220\) | 15.1229 | − | 118.561i | 0.0687403 | − | 0.538912i | ||||
\(221\) | 46.7905 | 0.211722 | ||||||||
\(222\) | −33.4151 | − | 33.4151i | −0.150518 | − | 0.150518i | ||||
\(223\) | −58.8321 | + | 58.8321i | −0.263821 | + | 0.263821i | −0.826604 | − | 0.562783i | \(-0.809731\pi\) |
0.562783 | + | 0.826604i | \(0.309731\pi\) | |||||||
\(224\) | − | 24.8949i | − | 0.111138i | ||||||
\(225\) | 18.8268 | − | 72.5986i | 0.0836745 | − | 0.322660i | ||||
\(226\) | 232.147 | 1.02720 | ||||||||
\(227\) | −80.2967 | − | 80.2967i | −0.353730 | − | 0.353730i | 0.507766 | − | 0.861495i | \(-0.330472\pi\) |
−0.861495 | + | 0.507766i | \(0.830472\pi\) | |||||||
\(228\) | 68.2026 | − | 68.2026i | 0.299134 | − | 0.299134i | ||||
\(229\) | − | 93.0094i | − | 0.406154i | −0.979163 | − | 0.203077i | \(-0.934906\pi\) | ||
0.979163 | − | 0.203077i | \(-0.0650942\pi\) | |||||||
\(230\) | 33.6391 | + | 4.29079i | 0.146257 | + | 0.0186556i | ||||
\(231\) | 91.1049 | 0.394393 | ||||||||
\(232\) | −52.9441 | − | 52.9441i | −0.228207 | − | 0.228207i | ||||
\(233\) | −182.811 | + | 182.811i | −0.784598 | + | 0.784598i | −0.980603 | − | 0.196005i | \(-0.937203\pi\) |
0.196005 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(234\) | 40.7707i | 0.174234i | ||||||||
\(235\) | −154.882 | − | 200.170i | −0.659072 | − | 0.851788i | ||||
\(236\) | −118.740 | −0.503135 | ||||||||
\(237\) | −26.4610 | − | 26.4610i | −0.111650 | − | 0.111650i | ||||
\(238\) | 21.4280 | − | 21.4280i | 0.0900337 | − | 0.0900337i | ||||
\(239\) | 180.221i | 0.754061i | 0.926201 | + | 0.377030i | \(0.123055\pi\) | ||||
−0.926201 | + | 0.377030i | \(0.876945\pi\) | |||||||
\(240\) | 27.3973 | − | 21.1987i | 0.114156 | − | 0.0883280i | ||||
\(241\) | −79.4799 | −0.329792 | −0.164896 | − | 0.986311i | \(-0.552729\pi\) | ||||
−0.164896 | + | 0.986311i | \(0.552729\pi\) | |||||||
\(242\) | 21.8533 | + | 21.8533i | 0.0903029 | + | 0.0903029i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 19.5831i | 0.0802584i | ||||||||
\(245\) | 18.7468 | − | 146.972i | 0.0765177 | − | 0.599886i | ||||
\(246\) | −79.1998 | −0.321951 | ||||||||
\(247\) | −189.200 | − | 189.200i | −0.765993 | − | 0.765993i | ||||
\(248\) | 32.0542 | − | 32.0542i | 0.129251 | − | 0.129251i | ||||
\(249\) | − | 117.773i | − | 0.472985i | ||||||
\(250\) | 69.6196 | + | 162.490i | 0.278478 | + | 0.649961i | ||||
\(251\) | 348.706 | 1.38927 | 0.694633 | − | 0.719364i | \(-0.255567\pi\) | ||||
0.694633 | + | 0.719364i | \(0.255567\pi\) | |||||||
\(252\) | 18.6712 | + | 18.6712i | 0.0740921 | + | 0.0740921i | ||||
\(253\) | −40.5316 | + | 40.5316i | −0.160204 | + | 0.160204i | ||||
\(254\) | 4.31405i | 0.0169845i | ||||||||
\(255\) | 41.8285 | + | 5.33538i | 0.164033 | + | 0.0209231i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −170.411 | − | 170.411i | −0.663077 | − | 0.663077i | 0.293027 | − | 0.956104i | \(-0.405337\pi\) |
−0.956104 | + | 0.293027i | \(0.905337\pi\) | |||||||
\(258\) | 54.9499 | − | 54.9499i | 0.212984 | − | 0.212984i | ||||
\(259\) | 84.9019i | 0.327807i | ||||||||
\(260\) | −58.8072 | − | 76.0027i | −0.226182 | − | 0.292318i | ||||
\(261\) | 79.4161 | 0.304276 | ||||||||
\(262\) | 260.534 | + | 260.534i | 0.994404 | + | 0.994404i | ||||
\(263\) | −92.8602 | + | 92.8602i | −0.353081 | + | 0.353081i | −0.861254 | − | 0.508174i | \(-0.830321\pi\) |
0.508174 | + | 0.861254i | \(0.330321\pi\) | |||||||
\(264\) | 58.5532i | 0.221792i | ||||||||
\(265\) | −232.756 | + | 180.096i | −0.878326 | + | 0.679606i | ||||
\(266\) | −173.291 | −0.651470 | ||||||||
\(267\) | 138.495 | + | 138.495i | 0.518707 | + | 0.518707i | ||||
\(268\) | 70.3463 | − | 70.3463i | 0.262486 | − | 0.262486i | ||||
\(269\) | − | 71.4621i | − | 0.265658i | −0.991139 | − | 0.132829i | \(-0.957594\pi\) | ||
0.991139 | − | 0.132829i | \(-0.0424062\pi\) | |||||||
\(270\) | −4.64896 | + | 36.4470i | −0.0172184 | + | 0.134989i | ||||
\(271\) | 115.820 | 0.427380 | 0.213690 | − | 0.976902i | \(-0.431452\pi\) | ||||
0.213690 | + | 0.976902i | \(0.431452\pi\) | |||||||
\(272\) | 13.7718 | + | 13.7718i | 0.0506316 | + | 0.0506316i | ||||
\(273\) | 51.7956 | − | 51.7956i | 0.189728 | − | 0.189728i | ||||
\(274\) | − | 0.701280i | − | 0.00255941i | ||||||
\(275\) | −289.236 | − | 75.0066i | −1.05177 | − | 0.272751i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 252.887 | + | 252.887i | 0.912949 | + | 0.912949i | 0.996503 | − | 0.0835544i | \(-0.0266273\pi\) |
−0.0835544 | + | 0.996503i | \(0.526627\pi\) | |||||||
\(278\) | −115.396 | + | 115.396i | −0.415092 | + | 0.415092i | ||||
\(279\) | 48.0812i | 0.172334i | ||||||||
\(280\) | −61.7371 | − | 7.87480i | −0.220490 | − | 0.0281243i | ||||
\(281\) | 505.455 | 1.79877 | 0.899386 | − | 0.437156i | \(-0.144014\pi\) | ||||
0.899386 | + | 0.437156i | \(0.144014\pi\) | |||||||
\(282\) | 87.6743 | + | 87.6743i | 0.310902 | + | 0.310902i | ||||
\(283\) | −291.311 | + | 291.311i | −1.02937 | + | 1.02937i | −0.0298108 | + | 0.999556i | \(0.509490\pi\) |
−0.999556 | + | 0.0298108i | \(0.990510\pi\) | |||||||
\(284\) | 56.9482i | 0.200522i | ||||||||
\(285\) | −147.562 | − | 190.710i | −0.517762 | − | 0.669158i | ||||
\(286\) | 162.432 | 0.567944 | ||||||||
\(287\) | 100.617 | + | 100.617i | 0.350580 | + | 0.350580i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 265.292i | − | 0.917966i | ||||||
\(290\) | −148.044 | + | 114.549i | −0.510496 | + | 0.394997i | ||||
\(291\) | −105.726 | −0.363320 | ||||||||
\(292\) | −4.54282 | − | 4.54282i | −0.0155576 | − | 0.0155576i | ||||
\(293\) | −155.811 | + | 155.811i | −0.531778 | + | 0.531778i | −0.921101 | − | 0.389323i | \(-0.872709\pi\) |
0.389323 | + | 0.921101i | \(0.372709\pi\) | |||||||
\(294\) | 72.5847i | 0.246887i | ||||||||
\(295\) | −37.5600 | + | 294.464i | −0.127322 | + | 0.998182i | ||||
\(296\) | −54.5666 | −0.184346 | ||||||||
\(297\) | −43.9149 | − | 43.9149i | −0.147862 | − | 0.147862i | ||||
\(298\) | 276.290 | − | 276.290i | 0.927146 | − | 0.927146i | ||||
\(299\) | 46.0867i | 0.154136i | ||||||||
\(300\) | −43.9045 | − | 74.6485i | −0.146348 | − | 0.248828i | ||||
\(301\) | −139.618 | −0.463848 | ||||||||
\(302\) | 37.7638 | + | 37.7638i | 0.125046 | + | 0.125046i | ||||
\(303\) | −65.6530 | + | 65.6530i | −0.216677 | + | 0.216677i | ||||
\(304\) | − | 111.374i | − | 0.366363i | ||||||
\(305\) | 48.5642 | + | 6.19454i | 0.159227 | + | 0.0203100i | ||||
\(306\) | −20.6577 | −0.0675089 | ||||||||
\(307\) | −1.45006 | − | 1.45006i | −0.00472331 | − | 0.00472331i | 0.704741 | − | 0.709464i | \(-0.251063\pi\) |
−0.709464 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(308\) | 74.3868 | − | 74.3868i | 0.241516 | − | 0.241516i | ||||
\(309\) | − | 21.1748i | − | 0.0685268i | ||||||
\(310\) | −69.3519 | − | 89.6308i | −0.223716 | − | 0.289131i | ||||
\(311\) | 421.289 | 1.35463 | 0.677314 | − | 0.735694i | \(-0.263144\pi\) | ||||
0.677314 | + | 0.735694i | \(0.263144\pi\) | |||||||
\(312\) | 33.2891 | + | 33.2891i | 0.106696 | + | 0.106696i | ||||
\(313\) | −97.7145 | + | 97.7145i | −0.312187 | + | 0.312187i | −0.845756 | − | 0.533569i | \(-0.820850\pi\) |
0.533569 | + | 0.845756i | \(0.320850\pi\) | |||||||
\(314\) | 245.941i | 0.783253i | ||||||||
\(315\) | 52.2089 | − | 40.3967i | 0.165743 | − | 0.128244i | ||||
\(316\) | −43.2106 | −0.136742 | ||||||||
\(317\) | −314.471 | − | 314.471i | −0.992023 | − | 0.992023i | 0.00794582 | − | 0.999968i | \(-0.497471\pi\) |
−0.999968 | + | 0.00794582i | \(0.997471\pi\) | |||||||
\(318\) | 101.947 | − | 101.947i | 0.320588 | − | 0.320588i | ||||
\(319\) | − | 316.397i | − | 0.991841i | ||||||
\(320\) | 5.06115 | − | 39.6785i | 0.0158161 | − | 0.123995i | ||||
\(321\) | −96.8812 | −0.301811 | ||||||||
\(322\) | 21.1057 | + | 21.1057i | 0.0655457 | + | 0.0655457i | ||||
\(323\) | 95.8641 | − | 95.8641i | 0.296793 | − | 0.296793i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −207.082 | + | 121.795i | −0.637175 | + | 0.374754i | ||||
\(326\) | −43.2470 | −0.132659 | ||||||||
\(327\) | 8.25484 | + | 8.25484i | 0.0252442 | + | 0.0252442i | ||||
\(328\) | −64.6664 | + | 64.6664i | −0.197154 | + | 0.197154i | ||||
\(329\) | − | 222.765i | − | 0.677098i | ||||||
\(330\) | 145.207 | + | 18.5216i | 0.440020 | + | 0.0561262i | ||||
\(331\) | −49.4958 | −0.149534 | −0.0747670 | − | 0.997201i | \(-0.523821\pi\) | ||||
−0.0747670 | + | 0.997201i | \(0.523821\pi\) | |||||||
\(332\) | −96.1615 | − | 96.1615i | −0.289643 | − | 0.289643i | ||||
\(333\) | 40.9249 | − | 40.9249i | 0.122898 | − | 0.122898i | ||||
\(334\) | 158.727i | 0.475229i | ||||||||
\(335\) | −152.200 | − | 196.704i | −0.454329 | − | 0.587177i | ||||
\(336\) | 30.4899 | 0.0907439 | ||||||||
\(337\) | 278.322 | + | 278.322i | 0.825883 | + | 0.825883i | 0.986944 | − | 0.161062i | \(-0.0514918\pi\) |
−0.161062 | + | 0.986944i | \(0.551492\pi\) | |||||||
\(338\) | −76.6530 | + | 76.6530i | −0.226784 | + | 0.226784i | ||||
\(339\) | 284.321i | 0.838706i | ||||||||
\(340\) | 38.5091 | − | 29.7965i | 0.113262 | − | 0.0876367i | ||||
\(341\) | 191.558 | 0.561753 | ||||||||
\(342\) | 83.5308 | + | 83.5308i | 0.244242 | + | 0.244242i | ||||
\(343\) | 244.694 | − | 244.694i | 0.713394 | − | 0.713394i | ||||
\(344\) | − | 89.7328i | − | 0.260851i | ||||||
\(345\) | −5.25513 | + | 41.1993i | −0.0152323 | + | 0.119418i | ||||
\(346\) | 334.374 | 0.966399 | ||||||||
\(347\) | −169.044 | − | 169.044i | −0.487158 | − | 0.487158i | 0.420250 | − | 0.907408i | \(-0.361942\pi\) |
−0.907408 | + | 0.420250i | \(0.861942\pi\) | |||||||
\(348\) | 64.8430 | − | 64.8430i | 0.186330 | − | 0.186330i | ||||
\(349\) | − | 407.984i | − | 1.16901i | −0.811390 | − | 0.584505i | \(-0.801289\pi\) | ||
0.811390 | − | 0.584505i | \(-0.198711\pi\) | |||||||
\(350\) | −39.0576 | + | 150.611i | −0.111593 | + | 0.430318i | ||||
\(351\) | −49.9337 | −0.142261 | ||||||||
\(352\) | 47.8085 | + | 47.8085i | 0.135820 | + | 0.135820i | ||||
\(353\) | 356.837 | − | 356.837i | 1.01087 | − | 1.01087i | 0.0109302 | − | 0.999940i | \(-0.496521\pi\) |
0.999940 | − | 0.0109302i | \(-0.00347925\pi\) | |||||||
\(354\) | − | 145.426i | − | 0.410808i | ||||||
\(355\) | 141.226 | + | 18.0139i | 0.397821 | + | 0.0507435i | ||||
\(356\) | 226.161 | 0.635283 | ||||||||
\(357\) | 26.2438 | + | 26.2438i | 0.0735122 | + | 0.0735122i | ||||
\(358\) | 88.2952 | − | 88.2952i | 0.246635 | − | 0.246635i | ||||
\(359\) | − | 321.635i | − | 0.895919i | −0.894054 | − | 0.447960i | \(-0.852151\pi\) | ||
0.894054 | − | 0.447960i | \(-0.147849\pi\) | |||||||
\(360\) | 25.9630 | + | 33.5547i | 0.0721195 | + | 0.0932076i | ||||
\(361\) | −414.265 | −1.14755 | ||||||||
\(362\) | 275.272 | + | 275.272i | 0.760420 | + | 0.760420i | ||||
\(363\) | −26.7647 | + | 26.7647i | −0.0737320 | + | 0.0737320i | ||||
\(364\) | − | 84.5819i | − | 0.232368i | ||||||
\(365\) | −12.7028 | + | 9.82878i | −0.0348021 | + | 0.0269282i | ||||
\(366\) | −23.9842 | −0.0655307 | ||||||||
\(367\) | 201.984 | + | 201.984i | 0.550364 | + | 0.550364i | 0.926546 | − | 0.376182i | \(-0.122763\pi\) |
−0.376182 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 96.9996i | − | 0.262872i | ||||||
\(370\) | −17.2606 | + | 135.320i | −0.0466502 | + | 0.365730i | ||||
\(371\) | −259.030 | −0.698194 | ||||||||
\(372\) | 39.2582 | + | 39.2582i | 0.105533 | + | 0.105533i | ||||
\(373\) | 304.698 | − | 304.698i | 0.816884 | − | 0.816884i | −0.168771 | − | 0.985655i | \(-0.553980\pi\) |
0.985655 | + | 0.168771i | \(0.0539800\pi\) | |||||||
\(374\) | 82.3012i | 0.220057i | ||||||||
\(375\) | −199.009 | + | 85.2662i | −0.530691 | + | 0.227377i | ||||
\(376\) | 143.172 | 0.380775 | ||||||||
\(377\) | −179.880 | − | 179.880i | −0.477136 | − | 0.477136i | ||||
\(378\) | −22.8675 | + | 22.8675i | −0.0604959 | + | 0.0604959i | ||||
\(379\) | 665.410i | 1.75570i | 0.478937 | + | 0.877849i | \(0.341022\pi\) | ||||
−0.478937 | + | 0.877849i | \(0.658978\pi\) | |||||||
\(380\) | −276.198 | − | 35.2301i | −0.726837 | − | 0.0927108i | ||||
\(381\) | −5.28361 | −0.0138678 | ||||||||
\(382\) | 284.801 | + | 284.801i | 0.745553 | + | 0.745553i | ||||
\(383\) | −160.655 | + | 160.655i | −0.419466 | + | 0.419466i | −0.885020 | − | 0.465554i | \(-0.845855\pi\) |
0.465554 | + | 0.885020i | \(0.345855\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −160.942 | − | 208.003i | −0.418032 | − | 0.540267i | ||||
\(386\) | −143.122 | −0.370782 | ||||||||
\(387\) | 67.2996 | + | 67.2996i | 0.173901 | + | 0.173901i | ||||
\(388\) | −86.3250 | + | 86.3250i | −0.222487 | + | 0.222487i | ||||
\(389\) | − | 303.465i | − | 0.780117i | −0.920790 | − | 0.390058i | \(-0.872455\pi\) | ||
0.920790 | − | 0.390058i | \(-0.127545\pi\) | |||||||
\(390\) | 93.0840 | − | 72.0238i | 0.238677 | − | 0.184677i | ||||
\(391\) | −23.3512 | −0.0597218 | ||||||||
\(392\) | 59.2652 | + | 59.2652i | 0.151187 | + | 0.151187i | ||||
\(393\) | −319.088 | + | 319.088i | −0.811928 | + | 0.811928i | ||||
\(394\) | 429.295i | 1.08958i | ||||||||
\(395\) | −13.6684 | + | 107.158i | −0.0346036 | + | 0.271287i | ||||
\(396\) | −71.7128 | −0.181093 | ||||||||
\(397\) | 69.7386 | + | 69.7386i | 0.175664 | + | 0.175664i | 0.789463 | − | 0.613799i | \(-0.210359\pi\) |
−0.613799 | + | 0.789463i | \(0.710359\pi\) | |||||||
\(398\) | −89.3086 | + | 89.3086i | −0.224394 | + | 0.224394i | ||||
\(399\) | − | 212.237i | − | 0.531923i | ||||||
\(400\) | −96.7981 | − | 25.1023i | −0.241995 | − | 0.0627559i | ||||
\(401\) | 92.9627 | 0.231827 | 0.115914 | − | 0.993259i | \(-0.463020\pi\) | ||||
0.115914 | + | 0.993259i | \(0.463020\pi\) | |||||||
\(402\) | 86.1563 | + | 86.1563i | 0.214319 | + | 0.214319i | ||||
\(403\) | 108.906 | − | 108.906i | 0.270238 | − | 0.270238i | ||||
\(404\) | 107.211i | 0.265374i | ||||||||
\(405\) | −44.6383 | − | 5.69379i | −0.110218 | − | 0.0140587i | ||||
\(406\) | −164.755 | −0.405800 | ||||||||
\(407\) | −163.047 | − | 163.047i | −0.400606 | − | 0.400606i | ||||
\(408\) | −16.8670 | + | 16.8670i | −0.0413406 | + | 0.0413406i | ||||
\(409\) | − | 302.309i | − | 0.739141i | −0.929203 | − | 0.369571i | \(-0.879505\pi\) | ||
0.929203 | − | 0.369571i | \(-0.120495\pi\) | |||||||
\(410\) | 139.911 | + | 180.822i | 0.341247 | + | 0.441029i | ||||
\(411\) | 0.858889 | 0.00208975 | ||||||||
\(412\) | −17.2891 | − | 17.2891i | −0.0419639 | − | 0.0419639i | ||||
\(413\) | −184.751 | + | 184.751i | −0.447340 | + | 0.447340i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −268.889 | + | 208.054i | −0.647926 | + | 0.501334i | ||||
\(416\) | 54.3609 | 0.130675 | ||||||||
\(417\) | −141.330 | − | 141.330i | −0.338921 | − | 0.338921i | ||||
\(418\) | 332.790 | − | 332.790i | 0.796148 | − | 0.796148i | ||||
\(419\) | − | 654.635i | − | 1.56237i | −0.624297 | − | 0.781187i | \(-0.714615\pi\) | ||
0.624297 | − | 0.781187i | \(-0.285385\pi\) | |||||||
\(420\) | 9.64462 | − | 75.6122i | 0.0229634 | − | 0.180029i | ||||
\(421\) | 77.9606 | 0.185180 | 0.0925898 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925898 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(422\) | −320.246 | − | 320.246i | −0.758876 | − | 0.758876i | ||||
\(423\) | −107.379 | + | 107.379i | −0.253850 | + | 0.253850i | ||||
\(424\) | − | 166.479i | − | 0.392639i | ||||||
\(425\) | −61.7113 | − | 104.924i | −0.145203 | − | 0.246881i | ||||
\(426\) | −69.7470 | −0.163725 | ||||||||
\(427\) | 30.4699 | + | 30.4699i | 0.0713581 | + | 0.0713581i | ||||
\(428\) | −79.1032 | + | 79.1032i | −0.184821 | + | 0.184821i | ||||
\(429\) | 198.938i | 0.463724i | ||||||||
\(430\) | −222.529 | − | 28.3844i | −0.517510 | − | 0.0660103i | ||||
\(431\) | 486.621 | 1.12905 | 0.564526 | − | 0.825415i | \(-0.309059\pi\) | ||||
0.564526 | + | 0.825415i | \(0.309059\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −305.280 | + | 305.280i | −0.705034 | + | 0.705034i | −0.965487 | − | 0.260453i | \(-0.916128\pi\) |
0.260453 | + | 0.965487i | \(0.416128\pi\) | |||||||
\(434\) | − | 99.7482i | − | 0.229835i | ||||||
\(435\) | −140.293 | − | 181.316i | −0.322514 | − | 0.416818i | ||||
\(436\) | 13.4801 | 0.0309176 | ||||||||
\(437\) | 94.4222 | + | 94.4222i | 0.216069 | + | 0.216069i | ||||
\(438\) | 5.56379 | − | 5.56379i | 0.0127027 | − | 0.0127027i | ||||
\(439\) | 12.3810i | 0.0282028i | 0.999901 | + | 0.0141014i | \(0.00448877\pi\) | ||||
−0.999901 | + | 0.0141014i | \(0.995511\pi\) | |||||||
\(440\) | 133.684 | − | 103.438i | 0.303826 | − | 0.235086i | ||||
\(441\) | −88.8977 | −0.201582 | ||||||||
\(442\) | 46.7905 | + | 46.7905i | 0.105861 | + | 0.105861i | ||||
\(443\) | −35.7800 | + | 35.7800i | −0.0807676 | + | 0.0807676i | −0.746336 | − | 0.665569i | \(-0.768189\pi\) |
0.665569 | + | 0.746336i | \(0.268189\pi\) | |||||||
\(444\) | − | 66.8301i | − | 0.150518i | ||||||
\(445\) | 71.5396 | − | 560.858i | 0.160763 | − | 1.26036i | ||||
\(446\) | −117.664 | −0.263821 | ||||||||
\(447\) | 338.384 | + | 338.384i | 0.757012 | + | 0.757012i | ||||
\(448\) | 24.8949 | − | 24.8949i | 0.0555690 | − | 0.0555690i | ||||
\(449\) | 586.729i | 1.30675i | 0.757036 | + | 0.653373i | \(0.226647\pi\) | ||||
−0.757036 | + | 0.653373i | \(0.773353\pi\) | |||||||
\(450\) | 91.4253 | − | 53.7718i | 0.203167 | − | 0.119493i | ||||
\(451\) | −386.450 | −0.856875 | ||||||||
\(452\) | 232.147 | + | 232.147i | 0.513600 | + | 0.513600i | ||||
\(453\) | −46.2510 | + | 46.2510i | −0.102099 | + | 0.102099i | ||||
\(454\) | − | 160.593i | − | 0.353730i | ||||||
\(455\) | −209.755 | − | 26.7551i | −0.461001 | − | 0.0588024i | ||||
\(456\) | 136.405 | 0.299134 | ||||||||
\(457\) | −202.555 | − | 202.555i | −0.443227 | − | 0.443227i | 0.449868 | − | 0.893095i | \(-0.351471\pi\) |
−0.893095 | + | 0.449868i | \(0.851471\pi\) | |||||||
\(458\) | 93.0094 | − | 93.0094i | 0.203077 | − | 0.203077i | ||||
\(459\) | − | 25.3004i | − | 0.0551208i | ||||||
\(460\) | 29.3483 | + | 37.9299i | 0.0638007 | + | 0.0824563i | ||||
\(461\) | −527.587 | −1.14444 | −0.572220 | − | 0.820100i | \(-0.693918\pi\) | ||||
−0.572220 | + | 0.820100i | \(0.693918\pi\) | |||||||
\(462\) | 91.1049 | + | 91.1049i | 0.197197 | + | 0.197197i | ||||
\(463\) | −358.778 | + | 358.778i | −0.774898 | + | 0.774898i | −0.978958 | − | 0.204060i | \(-0.934586\pi\) |
0.204060 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(464\) | − | 105.888i | − | 0.228207i | ||||||
\(465\) | 109.775 | − | 84.9384i | 0.236075 | − | 0.182663i | ||||
\(466\) | −365.623 | −0.784598 | ||||||||
\(467\) | −485.338 | − | 485.338i | −1.03927 | − | 1.03927i | −0.999197 | − | 0.0400718i | \(-0.987241\pi\) |
−0.0400718 | − | 0.999197i | \(-0.512759\pi\) | |||||||
\(468\) | −40.7707 | + | 40.7707i | −0.0871168 | + | 0.0871168i | ||||
\(469\) | − | 218.908i | − | 0.466755i | ||||||
\(470\) | 45.2882 | − | 355.052i | 0.0963579 | − | 0.755430i | ||||
\(471\) | −301.215 | −0.639523 | ||||||||
\(472\) | −118.740 | − | 118.740i | −0.251567 | − | 0.251567i | ||||
\(473\) | 268.124 | − | 268.124i | 0.566859 | − | 0.566859i | ||||
\(474\) | − | 52.9219i | − | 0.111650i | ||||||
\(475\) | −174.735 | + | 673.802i | −0.367863 | + | 1.41853i | ||||
\(476\) | 42.8560 | 0.0900337 | ||||||||
\(477\) | 124.859 | + | 124.859i | 0.261759 | + | 0.261759i | ||||
\(478\) | −180.221 | + | 180.221i | −0.377030 | + | 0.377030i | ||||
\(479\) | − | 319.112i | − | 0.666204i | −0.942891 | − | 0.333102i | \(-0.891905\pi\) | ||
0.942891 | − | 0.333102i | \(-0.108095\pi\) | |||||||
\(480\) | 48.5961 | + | 6.19861i | 0.101242 | + | 0.0129138i | ||||
\(481\) | −185.393 | −0.385432 | ||||||||
\(482\) | −79.4799 | − | 79.4799i | −0.164896 | − | 0.164896i | ||||
\(483\) | −25.8491 | + | 25.8491i | −0.0535178 | + | 0.0535178i | ||||
\(484\) | 43.7066i | 0.0903029i | ||||||||
\(485\) | 186.772 | + | 241.385i | 0.385096 | + | 0.497700i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −394.168 | − | 394.168i | −0.809380 | − | 0.809380i | 0.175160 | − | 0.984540i | \(-0.443956\pi\) |
−0.984540 | + | 0.175160i | \(0.943956\pi\) | |||||||
\(488\) | −19.5831 | + | 19.5831i | −0.0401292 | + | 0.0401292i | ||||
\(489\) | − | 52.9665i | − | 0.108316i | ||||||
\(490\) | 165.719 | − | 128.225i | 0.338202 | − | 0.261684i | ||||
\(491\) | 403.304 | 0.821393 | 0.410696 | − | 0.911772i | \(-0.365286\pi\) | ||||
0.410696 | + | 0.911772i | \(0.365286\pi\) | |||||||
\(492\) | −79.1998 | − | 79.1998i | −0.160975 | − | 0.160975i | ||||
\(493\) | 91.1420 | − | 91.1420i | 0.184872 | − | 0.184872i | ||||
\(494\) | − | 378.400i | − | 0.765993i | ||||||
\(495\) | −22.6843 | + | 177.841i | −0.0458268 | + | 0.359275i | ||||
\(496\) | 64.1083 | 0.129251 | ||||||||
\(497\) | 88.6076 | + | 88.6076i | 0.178285 | + | 0.178285i | ||||
\(498\) | 117.773 | − | 117.773i | 0.236492 | − | 0.236492i | ||||
\(499\) | − | 970.563i | − | 1.94502i | −0.232868 | − | 0.972508i | \(-0.574811\pi\) | ||
0.232868 | − | 0.972508i | \(-0.425189\pi\) | |||||||
\(500\) | −92.8708 | + | 232.110i | −0.185742 | + | 0.464220i | ||||
\(501\) | −194.400 | −0.388023 | ||||||||
\(502\) | 348.706 | + | 348.706i | 0.694633 | + | 0.694633i | ||||
\(503\) | −526.039 | + | 526.039i | −1.04580 | + | 1.04580i | −0.0469034 | + | 0.998899i | \(0.514935\pi\) |
−0.998899 | + | 0.0469034i | \(0.985065\pi\) | |||||||
\(504\) | 37.3424i | 0.0740921i | ||||||||
\(505\) | 265.873 | + | 33.9131i | 0.526481 | + | 0.0671547i | ||||
\(506\) | −81.0633 | −0.160204 | ||||||||
\(507\) | −93.8803 | − | 93.8803i | −0.185168 | − | 0.185168i | ||||
\(508\) | −4.31405 | + | 4.31405i | −0.00849223 | + | 0.00849223i | ||||
\(509\) | 928.920i | 1.82499i | 0.409088 | + | 0.912495i | \(0.365847\pi\) | ||||
−0.409088 | + | 0.912495i | \(0.634153\pi\) | |||||||
\(510\) | 36.4931 | + | 47.1639i | 0.0715551 | + | 0.0924782i | ||||
\(511\) | −14.1366 | −0.0276647 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −102.304 | + | 102.304i | −0.199423 | + | 0.199423i | ||||
\(514\) | − | 340.822i | − | 0.663077i | ||||||
\(515\) | −48.3444 | + | 37.4065i | −0.0938726 | + | 0.0726341i | ||||
\(516\) | 109.900 | 0.212984 | ||||||||
\(517\) | 427.801 | + | 427.801i | 0.827468 | + | 0.827468i | ||||
\(518\) | −84.9019 | + | 84.9019i | −0.163903 | + | 0.163903i | ||||
\(519\) | 409.523i | 0.789061i | ||||||||
\(520\) | 17.1955 | − | 134.810i | 0.0330683 | − | 0.259250i | ||||
\(521\) | −299.847 | −0.575522 | −0.287761 | − | 0.957702i | \(-0.592911\pi\) | ||||
−0.287761 | + | 0.957702i | \(0.592911\pi\) | |||||||
\(522\) | 79.4161 | + | 79.4161i | 0.152138 | + | 0.152138i | ||||
\(523\) | −421.509 | + | 421.509i | −0.805944 | + | 0.805944i | −0.984017 | − | 0.178073i | \(-0.943014\pi\) |
0.178073 | + | 0.984017i | \(0.443014\pi\) | |||||||
\(524\) | 521.068i | 0.994404i | ||||||||
\(525\) | −184.460 | − | 47.8356i | −0.351353 | − | 0.0911153i | ||||
\(526\) | −185.720 | −0.353081 | ||||||||
\(527\) | 55.1805 | + | 55.1805i | 0.104707 | + | 0.104707i | ||||
\(528\) | −58.5532 | + | 58.5532i | −0.110896 | + | 0.110896i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −412.852 | − | 52.6608i | −0.778966 | − | 0.0993601i | ||||
\(531\) | 178.110 | 0.335423 | ||||||||
\(532\) | −173.291 | − | 173.291i | −0.325735 | − | 0.325735i | ||||
\(533\) | −219.708 | + | 219.708i | −0.412210 | + | 0.412210i | ||||
\(534\) | 276.989i | 0.518707i | ||||||||
\(535\) | 171.147 | + | 221.191i | 0.319900 | + | 0.413440i | ||||
\(536\) | 140.693 | 0.262486 | ||||||||
\(537\) | 108.139 | + | 108.139i | 0.201376 | + | 0.201376i | ||||
\(538\) | 71.4621 | − | 71.4621i | 0.132829 | − | 0.132829i | ||||
\(539\) | 354.172i | 0.657091i | ||||||||
\(540\) | −41.0960 | + | 31.7981i | −0.0761037 | + | 0.0588853i | ||||
\(541\) | −437.815 | −0.809270 | −0.404635 | − | 0.914478i | \(-0.632601\pi\) | ||||
−0.404635 | + | 0.914478i | \(0.632601\pi\) | |||||||
\(542\) | 115.820 | + | 115.820i | 0.213690 | + | 0.213690i | ||||
\(543\) | −337.138 | + | 337.138i | −0.620880 | + | 0.620880i | ||||
\(544\) | 27.5436i | 0.0506316i | ||||||||
\(545\) | 4.26404 | − | 33.4294i | 0.00782394 | − | 0.0613383i | ||||
\(546\) | 103.591 | 0.189728 | ||||||||
\(547\) | 194.907 | + | 194.907i | 0.356321 | + | 0.356321i | 0.862455 | − | 0.506134i | \(-0.168926\pi\) |
−0.506134 | + | 0.862455i | \(0.668926\pi\) | |||||||
\(548\) | 0.701280 | − | 0.701280i | 0.00127971 | − | 0.00127971i | ||||
\(549\) | − | 29.3746i | − | 0.0535056i | ||||||
\(550\) | −214.229 | − | 364.242i | −0.389508 | − | 0.662259i | ||||
\(551\) | −737.077 | −1.33771 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −67.2328 | + | 67.2328i | −0.121578 | + | 0.121578i | ||||
\(554\) | 505.774i | 0.912949i | ||||||||
\(555\) | −165.733 | − | 21.1398i | −0.298617 | − | 0.0380897i | ||||
\(556\) | −230.791 | −0.415092 | ||||||||
\(557\) | 496.792 | + | 496.792i | 0.891907 | + | 0.891907i | 0.994703 | − | 0.102795i | \(-0.0327786\pi\) |
−0.102795 | + | 0.994703i | \(0.532779\pi\) | |||||||
\(558\) | −48.0812 | + | 48.0812i | −0.0861671 | + | 0.0861671i | ||||
\(559\) | − | 304.872i | − | 0.545389i | ||||||
\(560\) | −53.8623 | − | 69.6119i | −0.0961827 | − | 0.124307i | ||||
\(561\) | −100.798 | −0.179676 | ||||||||
\(562\) | 505.455 | + | 505.455i | 0.899386 | + | 0.899386i | ||||
\(563\) | −165.676 | + | 165.676i | −0.294273 | + | 0.294273i | −0.838766 | − | 0.544493i | \(-0.816722\pi\) |
0.544493 | + | 0.838766i | \(0.316722\pi\) | |||||||
\(564\) | 175.349i | 0.310902i | ||||||||
\(565\) | 649.137 | − | 502.271i | 1.14892 | − | 0.888975i | ||||
\(566\) | −582.621 | −1.02937 | ||||||||
\(567\) | −28.0068 | − | 28.0068i | −0.0493947 | − | 0.0493947i | ||||
\(568\) | −56.9482 | + | 56.9482i | −0.100261 | + | 0.100261i | ||||
\(569\) | 1045.26i | 1.83702i | 0.395397 | + | 0.918510i | \(0.370607\pi\) | ||||
−0.395397 | + | 0.918510i | \(0.629393\pi\) | |||||||
\(570\) | 43.1479 | − | 338.272i | 0.0756981 | − | 0.593460i | ||||
\(571\) | 76.1504 | 0.133363 | 0.0666816 | − | 0.997774i | \(-0.478759\pi\) | ||||
0.0666816 | + | 0.997774i | \(0.478759\pi\) | |||||||
\(572\) | 162.432 | + | 162.432i | 0.283972 | + | 0.283972i | ||||
\(573\) | −348.809 | + | 348.809i | −0.608741 | + | 0.608741i | ||||
\(574\) | 201.233i | 0.350580i | ||||||||
\(575\) | 103.346 | − | 60.7830i | 0.179732 | − | 0.105710i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −356.490 | − | 356.490i | −0.617833 | − | 0.617833i | 0.327142 | − | 0.944975i | \(-0.393914\pi\) |
−0.944975 | + | 0.327142i | \(0.893914\pi\) | |||||||
\(578\) | 265.292 | − | 265.292i | 0.458983 | − | 0.458983i | ||||
\(579\) | − | 175.288i | − | 0.302743i | ||||||
\(580\) | −262.593 | − | 33.4947i | −0.452746 | − | 0.0577495i | ||||
\(581\) | −299.242 | −0.515046 | ||||||||
\(582\) | −105.726 | − | 105.726i | −0.181660 | − | 0.181660i | ||||
\(583\) | 497.444 | − | 497.444i | 0.853248 | − | 0.853248i | ||||
\(584\) | − | 9.08564i | − | 0.0155576i | ||||||
\(585\) | 88.2108 | + | 114.004i | 0.150788 | + | 0.194879i | ||||
\(586\) | −311.622 | −0.531778 | ||||||||
\(587\) | −82.5345 | − | 82.5345i | −0.140604 | − | 0.140604i | 0.633301 | − | 0.773905i | \(-0.281699\pi\) |
−0.773905 | + | 0.633301i | \(0.781699\pi\) | |||||||
\(588\) | −72.5847 | + | 72.5847i | −0.123443 | + | 0.123443i | ||||
\(589\) | − | 446.251i | − | 0.757642i | ||||||
\(590\) | −332.024 | + | 256.904i | −0.562752 | + | 0.435430i | ||||
\(591\) | −525.777 | −0.889640 | ||||||||
\(592\) | −54.5666 | − | 54.5666i | −0.0921732 | − | 0.0921732i | ||||
\(593\) | 542.153 | − | 542.153i | 0.914255 | − | 0.914255i | −0.0823485 | − | 0.996604i | \(-0.526242\pi\) |
0.996604 | + | 0.0823485i | \(0.0262420\pi\) | |||||||
\(594\) | − | 87.8298i | − | 0.147862i | ||||||
\(595\) | 13.5563 | − | 106.279i | 0.0227837 | − | 0.178620i | ||||
\(596\) | 552.579 | 0.927146 | ||||||||
\(597\) | −109.380 | − | 109.380i | −0.183217 | − | 0.183217i | ||||
\(598\) | −46.0867 | + | 46.0867i | −0.0770680 | + | 0.0770680i | ||||
\(599\) | − | 846.862i | − | 1.41379i | −0.707317 | − | 0.706896i | \(-0.750095\pi\) | ||
0.707317 | − | 0.706896i | \(-0.249905\pi\) | |||||||
\(600\) | 30.7440 | − | 118.553i | 0.0512399 | − | 0.197588i | ||||
\(601\) | −768.954 | −1.27946 | −0.639729 | − | 0.768600i | \(-0.720953\pi\) | ||||
−0.639729 | + | 0.768600i | \(0.720953\pi\) | |||||||
\(602\) | −139.618 | − | 139.618i | −0.231924 | − | 0.231924i | ||||
\(603\) | −105.519 | + | 105.519i | −0.174991 | + | 0.174991i | ||||
\(604\) | 75.5275i | 0.125046i | ||||||||
\(605\) | 108.388 | + | 13.8253i | 0.179154 | + | 0.0228518i | ||||
\(606\) | −131.306 | −0.216677 | ||||||||
\(607\) | 203.884 | + | 203.884i | 0.335889 | + | 0.335889i | 0.854818 | − | 0.518929i | \(-0.173669\pi\) |
−0.518929 | + | 0.854818i | \(0.673669\pi\) | |||||||
\(608\) | 111.374 | − | 111.374i | 0.183181 | − | 0.183181i | ||||
\(609\) | − | 201.783i | − | 0.331335i | ||||||
\(610\) | 42.3696 | + | 54.7587i | 0.0694584 | + | 0.0897684i | ||||
\(611\) | 486.433 | 0.796126 | ||||||||
\(612\) | −20.6577 | − | 20.6577i | −0.0337544 | − | 0.0337544i | ||||
\(613\) | −68.5345 | + | 68.5345i | −0.111802 | + | 0.111802i | −0.760795 | − | 0.648993i | \(-0.775191\pi\) |
0.648993 | + | 0.760795i | \(0.275191\pi\) | |||||||
\(614\) | − | 2.90011i | − | 0.00472331i | ||||||
\(615\) | −221.461 | + | 171.356i | −0.360099 | + | 0.278627i | ||||
\(616\) | 148.774 | 0.241516 | ||||||||
\(617\) | −150.157 | − | 150.157i | −0.243366 | − | 0.243366i | 0.574875 | − | 0.818241i | \(-0.305051\pi\) |
−0.818241 | + | 0.574875i | \(0.805051\pi\) | |||||||
\(618\) | 21.1748 | − | 21.1748i | 0.0342634 | − | 0.0342634i | ||||
\(619\) | − | 457.106i | − | 0.738459i | −0.929338 | − | 0.369230i | \(-0.879622\pi\) | ||
0.929338 | − | 0.369230i | \(-0.120378\pi\) | |||||||
\(620\) | 20.2788 | − | 158.983i | 0.0327078 | − | 0.256424i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 421.289 | + | 421.289i | 0.677314 | + | 0.677314i | ||||
\(623\) | 351.891 | − | 351.891i | 0.564833 | − | 0.564833i | ||||
\(624\) | 66.5782i | 0.106696i | ||||||||
\(625\) | 546.234 | + | 303.732i | 0.873974 | + | 0.485972i | ||||
\(626\) | −195.429 | −0.312187 | ||||||||
\(627\) | 407.583 | + | 407.583i | 0.650052 | + | 0.650052i | ||||
\(628\) | −245.941 | + | 245.941i | −0.391626 | + | 0.391626i | ||||
\(629\) | − | 93.9350i | − | 0.149340i | ||||||
\(630\) | 92.6057 | + | 11.8122i | 0.146993 | + | 0.0187495i | ||||
\(631\) | −305.258 | −0.483768 | −0.241884 | − | 0.970305i | \(-0.577765\pi\) | ||||
−0.241884 | + | 0.970305i | \(0.577765\pi\) | |||||||
\(632\) | −43.2106 | − | 43.2106i | −0.0683712 | − | 0.0683712i | ||||
\(633\) | 392.219 | − | 392.219i | 0.619620 | − | 0.619620i | ||||
\(634\) | − | 628.942i | − | 0.992023i | ||||||
\(635\) | 9.33382 | + | 12.0631i | 0.0146989 | + | 0.0189970i | ||||
\(636\) | 203.894 | 0.320588 | ||||||||
\(637\) | 201.357 | + | 201.357i | 0.316101 | + | 0.316101i | ||||
\(638\) | 316.397 | − | 316.397i | 0.495920 | − | 0.495920i | ||||
\(639\) | − | 85.4223i | − | 0.133681i | ||||||
\(640\) | 44.7397 | − | 34.6174i | 0.0699057 | − | 0.0540896i | ||||
\(641\) | 280.793 | 0.438055 | 0.219028 | − | 0.975719i | \(-0.429711\pi\) | ||||
0.219028 | + | 0.975719i | \(0.429711\pi\) | |||||||
\(642\) | −96.8812 | − | 96.8812i | −0.150905 | − | 0.150905i | ||||
\(643\) | −713.836 | + | 713.836i | −1.11017 | + | 1.11017i | −0.117038 | + | 0.993127i | \(0.537340\pi\) |
−0.993127 | + | 0.117038i | \(0.962660\pi\) | |||||||
\(644\) | 42.2114i | 0.0655457i | ||||||||
\(645\) | 34.7637 | − | 272.541i | 0.0538972 | − | 0.422545i | ||||
\(646\) | 191.728 | 0.296793 | ||||||||
\(647\) | 397.749 | + | 397.749i | 0.614759 | + | 0.614759i | 0.944182 | − | 0.329424i | \(-0.106854\pi\) |
−0.329424 | + | 0.944182i | \(0.606854\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 709.597i | − | 1.09337i | ||||||
\(650\) | −328.877 | − | 85.2866i | −0.505964 | − | 0.131210i | ||||
\(651\) | 122.166 | 0.187659 | ||||||||
\(652\) | −43.2470 | − | 43.2470i | −0.0663297 | − | 0.0663297i | ||||
\(653\) | −217.770 | + | 217.770i | −0.333491 | + | 0.333491i | −0.853911 | − | 0.520419i | \(-0.825776\pi\) |
0.520419 | + | 0.853911i | \(0.325776\pi\) | |||||||
\(654\) | 16.5097i | 0.0252442i | ||||||||
\(655\) | 1292.20 | + | 164.825i | 1.97282 | + | 0.251641i | ||||
\(656\) | −129.333 | −0.197154 | ||||||||
\(657\) | 6.81423 | + | 6.81423i | 0.0103717 | + | 0.0103717i | ||||
\(658\) | 222.765 | − | 222.765i | 0.338549 | − | 0.338549i | ||||
\(659\) | 1073.09i | 1.62836i | 0.580610 | + | 0.814182i | \(0.302814\pi\) | ||||
−0.580610 | + | 0.814182i | \(0.697186\pi\) | |||||||
\(660\) | 126.685 | + | 163.728i | 0.191947 | + | 0.248073i | ||||
\(661\) | −326.114 | −0.493365 | −0.246683 | − | 0.969096i | \(-0.579340\pi\) | ||||
−0.246683 | + | 0.969096i | \(0.579340\pi\) | |||||||
\(662\) | −49.4958 | − | 49.4958i | −0.0747670 | − | 0.0747670i | ||||
\(663\) | −57.3064 | + | 57.3064i | −0.0864350 | + | 0.0864350i | ||||
\(664\) | − | 192.323i | − | 0.289643i | ||||||
\(665\) | −484.561 | + | 374.930i | −0.728664 | + | 0.563804i | ||||
\(666\) | 81.8498 | 0.122898 | ||||||||
\(667\) | 89.7711 | + | 89.7711i | 0.134589 | + | 0.134589i | ||||
\(668\) | −158.727 | + | 158.727i | −0.237615 | + | 0.237615i | ||||
\(669\) | − | 144.109i | − | 0.215409i | ||||||
\(670\) | 44.5041 | − | 348.905i | 0.0664240 | − | 0.520753i | ||||
\(671\) | −117.030 | −0.174411 | ||||||||
\(672\) | 30.4899 | + | 30.4899i | 0.0453719 | + | 0.0453719i | ||||
\(673\) | 557.149 | − | 557.149i | 0.827859 | − | 0.827859i | −0.159361 | − | 0.987220i | \(-0.550943\pi\) |
0.987220 | + | 0.159361i | \(0.0509435\pi\) | |||||||
\(674\) | 556.645i | 0.825883i | ||||||||
\(675\) | 65.8568 | + | 111.973i | 0.0975656 | + | 0.165885i | ||||
\(676\) | −153.306 | −0.226784 | ||||||||
\(677\) | −819.127 | − | 819.127i | −1.20994 | − | 1.20994i | −0.971047 | − | 0.238890i | \(-0.923216\pi\) |
−0.238890 | − | 0.971047i | \(-0.576784\pi\) | |||||||
\(678\) | −284.321 | + | 284.321i | −0.419353 | + | 0.419353i | ||||
\(679\) | 268.632i | 0.395629i | ||||||||
\(680\) | 68.3056 | + | 8.71264i | 0.100449 | + | 0.0128127i | ||||
\(681\) | 196.686 | 0.288819 | ||||||||
\(682\) | 191.558 | + | 191.558i | 0.280876 | + | 0.280876i | ||||
\(683\) | 220.351 | − | 220.351i | 0.322622 | − | 0.322622i | −0.527150 | − | 0.849772i | \(-0.676739\pi\) |
0.849772 | + | 0.527150i | \(0.176739\pi\) | |||||||
\(684\) | 167.062i | 0.244242i | ||||||||
\(685\) | −1.51728 | − | 1.96094i | −0.00221501 | − | 0.00286268i | ||||
\(686\) | 489.388 | 0.713394 | ||||||||
\(687\) | 113.913 | + | 113.913i | 0.165812 | + | 0.165812i | ||||
\(688\) | 89.7328 | − | 89.7328i | 0.130426 | − | 0.130426i | ||||
\(689\) | − | 565.621i | − | 0.820930i | ||||||
\(690\) | −46.4544 | + | 35.9442i | −0.0673253 | + | 0.0520930i | ||||
\(691\) | −256.102 | −0.370626 | −0.185313 | − | 0.982680i | \(-0.559330\pi\) | ||||
−0.185313 | + | 0.982680i | \(0.559330\pi\) | |||||||
\(692\) | 334.374 | + | 334.374i | 0.483199 | + | 0.483199i | ||||
\(693\) | −111.580 | + | 111.580i | −0.161010 | + | 0.161010i | ||||
\(694\) | − | 338.088i | − | 0.487158i | ||||||
\(695\) | −73.0043 | + | 572.341i | −0.105042 | + | 0.823512i | ||||
\(696\) | 129.686 | 0.186330 | ||||||||
\(697\) | −111.322 | − | 111.322i | −0.159715 | − | 0.159715i | ||||
\(698\) | 407.984 | − | 407.984i | 0.584505 | − | 0.584505i | ||||
\(699\) | − | 447.794i | − | 0.640622i | ||||||
\(700\) | −189.669 | + | 111.554i | −0.270956 | + | 0.159363i | ||||
\(701\) | −58.5051 | −0.0834595 | −0.0417297 | − | 0.999129i | \(-0.513287\pi\) | ||||
−0.0417297 | + | 0.999129i | \(0.513287\pi\) | |||||||
\(702\) | −49.9337 | − | 49.9337i | −0.0711306 | − | 0.0711306i | ||||
\(703\) | −379.832 | + | 379.832i | −0.540302 | + | 0.540302i | ||||
\(704\) | 95.6170i | 0.135820i | ||||||||
\(705\) | 434.848 | + | 55.4665i | 0.616806 | + | 0.0786759i | ||||
\(706\) | 713.675 | 1.01087 | ||||||||
\(707\) | 166.813 | + | 166.813i | 0.235945 | + | 0.235945i | ||||
\(708\) | 145.426 | − | 145.426i | 0.205404 | − | 0.205404i | ||||
\(709\) | − | 775.572i | − | 1.09390i | −0.837167 | − | 0.546948i | \(-0.815789\pi\) | ||
0.837167 | − | 0.546948i | \(-0.184211\pi\) | |||||||
\(710\) | 123.212 | + | 159.240i | 0.173539 | + | 0.224282i | ||||
\(711\) | 64.8159 | 0.0911615 | ||||||||
\(712\) | 226.161 | + | 226.161i | 0.317642 | + | 0.317642i | ||||
\(713\) | −54.3505 | + | 54.3505i | −0.0762279 | + | 0.0762279i | ||||
\(714\) | 52.4877i | 0.0735122i | ||||||||
\(715\) | 454.197 | − | 351.436i | 0.635241 | − | 0.491518i | ||||
\(716\) | 176.590 | 0.246635 | ||||||||
\(717\) | −220.724 | − | 220.724i | −0.307844 | − | 0.307844i | ||||
\(718\) | 321.635 | − | 321.635i | 0.447960 | − | 0.447960i | ||||
\(719\) | 434.665i | 0.604541i | 0.953222 | + | 0.302271i | \(0.0977446\pi\) | ||||
−0.953222 | + | 0.302271i | \(0.902255\pi\) | |||||||
\(720\) | −7.59172 | + | 59.5178i | −0.0105441 | + | 0.0826636i | ||||
\(721\) | −53.8015 | −0.0746207 | ||||||||
\(722\) | −414.265 | − | 414.265i | −0.573775 | − | 0.573775i | ||||
\(723\) | 97.3426 | − | 97.3426i | 0.134637 | − | 0.134637i | ||||
\(724\) | 550.544i | 0.760420i | ||||||||
\(725\) | −166.128 | + | 640.611i | −0.229141 | + | 0.883601i | ||||
\(726\) | −53.5294 | −0.0737320 | ||||||||
\(727\) | −495.930 | − | 495.930i | −0.682159 | − | 0.682159i | 0.278327 | − | 0.960486i | \(-0.410220\pi\) |
−0.960486 | + | 0.278327i | \(0.910220\pi\) | |||||||
\(728\) | 84.5819 | − | 84.5819i | 0.116184 | − | 0.116184i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −22.5315 | − | 2.87398i | −0.0308651 | − | 0.00393696i | ||||
\(731\) | 154.473 | 0.211317 | ||||||||
\(732\) | −23.9842 | − | 23.9842i | −0.0327654 | − | 0.0327654i | ||||
\(733\) | 2.73615 | − | 2.73615i | 0.00373282 | − | 0.00373282i | −0.705238 | − | 0.708971i | \(-0.749160\pi\) |
0.708971 | + | 0.705238i | \(0.249160\pi\) | |||||||
\(734\) | 403.967i | 0.550364i | ||||||||
\(735\) | 157.043 | + | 202.963i | 0.213664 | + | 0.276141i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 420.394 | + | 420.394i | 0.570412 | + | 0.570412i | ||||
\(738\) | 96.9996 | − | 96.9996i | 0.131436 | − | 0.131436i | ||||
\(739\) | − | 850.579i | − | 1.15099i | −0.817807 | − | 0.575493i | \(-0.804810\pi\) | ||
0.817807 | − | 0.575493i | \(-0.195190\pi\) | |||||||
\(740\) | −152.581 | + | 118.059i | −0.206190 | + | 0.159540i | ||||
\(741\) | 463.444 | 0.625431 | ||||||||
\(742\) | −259.030 | − | 259.030i | −0.349097 | − | 0.349097i | ||||
\(743\) | −946.760 | + | 946.760i | −1.27424 | + | 1.27424i | −0.330397 | + | 0.943842i | \(0.607183\pi\) |
−0.943842 | + | 0.330397i | \(0.892817\pi\) | |||||||
\(744\) | 78.5163i | 0.105533i | ||||||||
\(745\) | 174.793 | − | 1370.35i | 0.234621 | − | 1.83939i | ||||
\(746\) | 609.395 | 0.816884 | ||||||||
\(747\) | 144.242 | + | 144.242i | 0.193095 | + | 0.193095i | ||||
\(748\) | −82.3012 | + | 82.3012i | −0.110028 | + | 0.110028i | ||||
\(749\) | 246.159i | 0.328650i | ||||||||
\(750\) | −284.275 | − | 113.743i | −0.379034 | − | 0.151657i | ||||
\(751\) | 1016.35 | 1.35333 | 0.676666 | − | 0.736290i | \(-0.263424\pi\) | ||||
0.676666 | + | 0.736290i | \(0.263424\pi\) | |||||||
\(752\) | 143.172 | + | 143.172i | 0.190388 | + | 0.190388i | ||||
\(753\) | −427.075 | + | 427.075i | −0.567165 | + | 0.567165i | ||||
\(754\) | − | 359.761i | − | 0.477136i | ||||||
\(755\) | 187.301 | + | 23.8910i | 0.248081 | + | 0.0316437i | ||||
\(756\) | −45.7349 | −0.0604959 | ||||||||
\(757\) | −286.507 | − | 286.507i | −0.378477 | − | 0.378477i | 0.492075 | − | 0.870553i | \(-0.336238\pi\) |
−0.870553 | + | 0.492075i | \(0.836238\pi\) | |||||||
\(758\) | −665.410 | + | 665.410i | −0.877849 | + | 0.877849i | ||||
\(759\) | − | 99.2818i | − | 0.130806i | ||||||
\(760\) | −240.968 | − | 311.428i | −0.317063 | − | 0.409774i | ||||
\(761\) | 1051.65 | 1.38193 | 0.690964 | − | 0.722889i | \(-0.257186\pi\) | ||||
0.690964 | + | 0.722889i | \(0.257186\pi\) | |||||||
\(762\) | −5.28361 | − | 5.28361i | −0.00693388 | − | 0.00693388i | ||||
\(763\) | 20.9741 | − | 20.9741i | 0.0274890 | − | 0.0274890i | ||||
\(764\) | 569.602i | 0.745553i | ||||||||
\(765\) | −57.7637 | + | 44.6947i | −0.0755081 | + | 0.0584245i | ||||
\(766\) | −321.311 | −0.419466 | ||||||||
\(767\) | −403.425 | − | 403.425i | −0.525978 | − | 0.525978i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 1147.01i | − | 1.49155i | −0.666195 | − | 0.745777i | \(-0.732078\pi\) | ||
0.666195 | − | 0.745777i | \(-0.267922\pi\) | |||||||
\(770\) | 47.0603 | − | 368.945i | 0.0611173 | − | 0.479149i | ||||
\(771\) | 417.420 | 0.541400 | ||||||||
\(772\) | −143.122 | − | 143.122i | −0.185391 | − | 0.185391i | ||||
\(773\) | 535.350 | − | 535.350i | 0.692561 | − | 0.692561i | −0.270234 | − | 0.962795i | \(-0.587101\pi\) |
0.962795 | + | 0.270234i | \(0.0871009\pi\) | |||||||
\(774\) | 134.599i | 0.173901i | ||||||||
\(775\) | −387.848 | − | 100.579i | −0.500449 | − | 0.129780i | ||||
\(776\) | −172.650 | −0.222487 | ||||||||
\(777\) | −103.983 | − | 103.983i | −0.133826 | − | 0.133826i | ||||
\(778\) | 303.465 | − | 303.465i | 0.390058 | − | 0.390058i | ||||
\(779\) | 900.272i | 1.15568i | ||||||||
\(780\) | 165.108 | + | 21.0601i | 0.211677 | + | 0.0270002i | ||||
\(781\) | −340.326 | −0.435757 | ||||||||
\(782\) | −23.3512 | − | 23.3512i | −0.0298609 | − | 0.0298609i | ||||
\(783\) | −97.2645 | + | 97.2645i | −0.124220 | + | 0.124220i | ||||
\(784\) | 118.530i | 0.151187i | ||||||||
\(785\) | 532.115 | + | 687.708i | 0.677854 | + | 0.876061i | ||||
\(786\) | −638.175 | −0.811928 | ||||||||
\(787\) | 396.325 | + | 396.325i | 0.503590 | + | 0.503590i | 0.912551 | − | 0.408962i | \(-0.134109\pi\) |
−0.408962 | + | 0.912551i | \(0.634109\pi\) | |||||||
\(788\) | −429.295 | + | 429.295i | −0.544791 | + | 0.544791i | ||||
\(789\) | − | 227.460i | − | 0.288289i | ||||||
\(790\) | −120.827 | + | 93.4898i | −0.152945 | + | 0.118341i | ||||
\(791\) | 722.412 | 0.913289 | ||||||||
\(792\) | −71.7128 | − | 71.7128i | −0.0905464 | − | 0.0905464i | ||||
\(793\) | −66.5345 | + | 66.5345i | −0.0839023 | + | 0.0839023i | ||||
\(794\) | 139.477i | 0.175664i | ||||||||
\(795\) | 64.4961 | − | 505.638i | 0.0811271 | − | 0.636023i | ||||
\(796\) | −178.617 | −0.224394 | ||||||||
\(797\) | −44.5321 | − | 44.5321i | −0.0558746 | − | 0.0558746i | 0.678617 | − | 0.734492i | \(-0.262579\pi\) |
−0.734492 | + | 0.678617i | \(0.762579\pi\) | |||||||
\(798\) | 212.237 | − | 212.237i | 0.265962 | − | 0.265962i | ||||
\(799\) | 246.466i | 0.308468i | ||||||||
\(800\) | −71.6958 | − | 121.900i | −0.0896197 | − | 0.152376i | ||||
\(801\) | −339.241 | −0.423522 | ||||||||
\(802\) | 92.9627 | + | 92.9627i | 0.115914 | + | 0.115914i | ||||
\(803\) | 27.1482 | − | 27.1482i | 0.0338084 | − | 0.0338084i | ||||
\(804\) | 172.313i | 0.214319i | ||||||||
\(805\) | 104.680 | + | 13.3524i | 0.130038 | + | 0.0165868i | ||||
\(806\) | 217.812 | 0.270238 | ||||||||
\(807\) | 87.5228 | + | 87.5228i | 0.108455 | + | 0.108455i | ||||
\(808\) | −107.211 | + | 107.211i | −0.132687 | + | 0.132687i | ||||
\(809\) | 553.522i | 0.684205i | 0.939663 | + | 0.342102i | \(0.111139\pi\) | ||||
−0.939663 | + | 0.342102i | \(0.888861\pi\) | |||||||
\(810\) | −38.9445 | − | 50.3321i | −0.0480797 | − | 0.0621384i | ||||
\(811\) | 1146.25 | 1.41337 | 0.706687 | − | 0.707527i | \(-0.250189\pi\) | ||||
0.706687 | + | 0.707527i | \(0.250189\pi\) | |||||||
\(812\) | −164.755 | − | 164.755i | −0.202900 | − | 0.202900i | ||||
\(813\) | −141.850 | + | 141.850i | −0.174477 | + | 0.174477i | ||||
\(814\) | − | 326.093i | − | 0.400606i | ||||||
\(815\) | −120.928 | + | 93.5685i | −0.148378 | + | 0.114808i | ||||
\(816\) | −33.7339 | −0.0413406 | ||||||||
\(817\) | −624.621 | − | 624.621i | −0.764530 | − | 0.764530i | ||||
\(818\) | 302.309 | − | 302.309i | 0.369571 | − | 0.369571i | ||||
\(819\) | 126.873i | 0.154912i | ||||||||
\(820\) | −40.9108 | + | 320.733i | −0.0498912 | + | 0.391138i | ||||
\(821\) | −245.778 | −0.299365 | −0.149682 | − | 0.988734i | \(-0.547825\pi\) | ||||
−0.149682 | + | 0.988734i | \(0.547825\pi\) | |||||||
\(822\) | 0.858889 | + | 0.858889i | 0.00104488 | + | 0.00104488i | ||||
\(823\) | 287.937 | − | 287.937i | 0.349863 | − | 0.349863i | −0.510196 | − | 0.860058i | \(-0.670427\pi\) |
0.860058 | + | 0.510196i | \(0.170427\pi\) | |||||||
\(824\) | − | 34.5783i | − | 0.0419639i | ||||||
\(825\) | 446.104 | − | 262.376i | 0.540732 | − | 0.318032i | ||||
\(826\) | −369.502 | −0.447340 | ||||||||
\(827\) | 620.763 | + | 620.763i | 0.750621 | + | 0.750621i | 0.974595 | − | 0.223974i | \(-0.0719032\pi\) |
−0.223974 | + | 0.974595i | \(0.571903\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | 1370.82i | 1.65358i | 0.562510 | + | 0.826790i | \(0.309836\pi\) | ||||
−0.562510 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(830\) | −476.943 | − | 60.8359i | −0.574630 | − | 0.0732963i | ||||
\(831\) | −619.444 | −0.745420 | ||||||||
\(832\) | 54.3609 | + | 54.3609i | 0.0653376 | + | 0.0653376i | ||||
\(833\) | −102.024 | + | 102.024i | −0.122477 | + | 0.122477i | ||||
\(834\) | − | 282.661i | − | 0.338921i | ||||||
\(835\) | 343.419 | + | 443.836i | 0.411280 | + | 0.531540i | ||||
\(836\) | 665.580 | 0.796148 | ||||||||
\(837\) | −58.8872 | − | 58.8872i | −0.0703551 | − | 0.0703551i | ||||
\(838\) | 654.635 | − | 654.635i | 0.781187 | − | 0.781187i | ||||
\(839\) | − | 170.012i | − | 0.202637i | −0.994854 | − | 0.101318i | \(-0.967694\pi\) | ||
0.994854 | − | 0.101318i | \(-0.0323061\pi\) | |||||||
\(840\) | 85.2568 | − | 65.9676i | 0.101496 | − | 0.0785329i | ||||
\(841\) | 140.231 | 0.166743 | ||||||||
\(842\) | 77.9606 | + | 77.9606i | 0.0925898 | + | 0.0925898i | ||||
\(843\) | −619.053 | + | 619.053i | −0.734345 | + | 0.734345i | ||||
\(844\) | − | 640.491i | − | 0.758876i | ||||||
\(845\) | −48.4940 | + | 380.184i | −0.0573893 | + | 0.449922i | ||||
\(846\) | −214.757 | −0.253850 | ||||||||
\(847\) | 68.0046 | + | 68.0046i | 0.0802887 | + | 0.0802887i | ||||
\(848\) | 166.479 | − | 166.479i | 0.196319 | − | 0.196319i | ||||
\(849\) | − | 713.562i | − | 0.840474i | ||||||
\(850\) | 43.2131 | − | 166.636i | 0.0508389 | − | 0.196042i | ||||
\(851\) | 92.5221 | 0.108722 | ||||||||
\(852\) | −69.7470 | − | 69.7470i | −0.0818627 | − | 0.0818627i | ||||
\(853\) | 783.069 | − | 783.069i | 0.918018 | − | 0.918018i | −0.0788675 | − | 0.996885i | \(-0.525130\pi\) |
0.996885 | + | 0.0788675i | \(0.0251304\pi\) | |||||||
\(854\) | 60.9398i | 0.0713581i | ||||||||
\(855\) | 414.297 | + | 52.8452i | 0.484558 | + | 0.0618072i | ||||
\(856\) | −158.206 | −0.184821 | ||||||||
\(857\) | −733.197 | − | 733.197i | −0.855540 | − | 0.855540i | 0.135269 | − | 0.990809i | \(-0.456810\pi\) |
−0.990809 | + | 0.135269i | \(0.956810\pi\) | |||||||
\(858\) | −198.938 | + | 198.938i | −0.231862 | + | 0.231862i | ||||
\(859\) | − | 646.644i | − | 0.752787i | −0.926460 | − | 0.376393i | \(-0.877164\pi\) | ||
0.926460 | − | 0.376393i | \(-0.122836\pi\) | |||||||
\(860\) | −194.145 | − | 250.914i | −0.225750 | − | 0.291760i | ||||
\(861\) | −246.459 | −0.286248 | ||||||||
\(862\) | 486.621 | + | 486.621i | 0.564526 | + | 0.564526i | ||||
\(863\) | 246.220 | − | 246.220i | 0.285307 | − | 0.285307i | −0.549914 | − | 0.835221i | \(-0.685340\pi\) |
0.835221 | + | 0.549914i | \(0.185340\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 934.986 | − | 723.447i | 1.08091 | − | 0.836355i | ||||
\(866\) | −610.559 | −0.705034 | ||||||||
\(867\) | 324.915 | + | 324.915i | 0.374758 | + | 0.374758i | ||||
\(868\) | 99.7482 | − | 99.7482i | 0.114917 | − | 0.114917i | ||||
\(869\) | − | 258.229i | − | 0.297157i | ||||||
\(870\) | 41.0225 | − | 321.609i | 0.0471523 | − | 0.369666i | ||||
\(871\) | 478.011 | 0.548807 | ||||||||
\(872\) | 13.4801 | + | 13.4801i | 0.0154588 | + | 0.0154588i | ||||
\(873\) | 129.488 | − | 129.488i | 0.148325 | − | 0.148325i | ||||
\(874\) | 188.844i | 0.216069i | ||||||||
\(875\) | 216.647 | + | 505.648i | 0.247596 | + | 0.577884i | ||||
\(876\) | 11.1276 | 0.0127027 | ||||||||
\(877\) | 231.081 | + | 231.081i | 0.263490 | + | 0.263490i | 0.826471 | − | 0.562980i | \(-0.190345\pi\) |
−0.562980 | + | 0.826471i | \(0.690345\pi\) | |||||||
\(878\) | −12.3810 | + | 12.3810i | −0.0141014 | + | 0.0141014i | ||||
\(879\) | − | 381.657i | − | 0.434195i | ||||||
\(880\) | 237.121 | + | 30.2457i | 0.269456 | + | 0.0343701i | ||||
\(881\) | 1750.71 | 1.98718 | 0.993592 | − | 0.113024i | \(-0.0360535\pi\) | ||||
0.993592 | + | 0.113024i | \(0.0360535\pi\) | |||||||
\(882\) | −88.8977 | − | 88.8977i | −0.100791 | − | 0.100791i | ||||
\(883\) | 855.096 | − | 855.096i | 0.968399 | − | 0.968399i | −0.0311167 | − | 0.999516i | \(-0.509906\pi\) |
0.999516 | + | 0.0311167i | \(0.00990635\pi\) | |||||||
\(884\) | 93.5810i | 0.105861i | ||||||||
\(885\) | −314.642 | − | 406.644i | −0.355527 | − | 0.459485i | ||||
\(886\) | −71.5601 | −0.0807676 | ||||||||
\(887\) | −1120.79 | − | 1120.79i | −1.26357 | − | 1.26357i | −0.949350 | − | 0.314219i | \(-0.898257\pi\) |
−0.314219 | − | 0.949350i | \(-0.601743\pi\) | |||||||
\(888\) | 66.8301 | − | 66.8301i | 0.0752591 | − | 0.0752591i | ||||
\(889\) | 13.4248i | 0.0151010i | ||||||||
\(890\) | 632.398 | − | 489.319i | 0.710559 | − | 0.549796i | ||||
\(891\) | 107.569 | 0.120729 | ||||||||
\(892\) | −117.664 | − | 117.664i | −0.131910 | − | 0.131910i | ||||
\(893\) | 996.602 | − | 996.602i | 1.11602 | − | 1.11602i | ||||
\(894\) | 676.769i | 0.757012i | ||||||||
\(895\) | 55.8593 | − | 437.928i | 0.0624127 | − | 0.489305i | ||||
\(896\) | 49.7899 | 0.0555690 | ||||||||
\(897\) | −56.4444 | − | 56.4444i | −0.0629258 | − | 0.0629258i | ||||
\(898\) | −586.729 | + | 586.729i | −0.653373 | + | 0.653373i | ||||
\(899\) | − | 424.270i | − | 0.471935i | ||||||
\(900\) | 145.197 | + | 37.6535i | 0.161330 | + | 0.0418372i | ||||
\(901\) | 286.589 | 0.318079 | ||||||||
\(902\) | −386.450 | − | 386.450i | −0.428437 | − | 0.428437i | ||||
\(903\) | 170.997 | − | 170.997i | 0.189365 | − | 0.189365i | ||||
\(904\) | 464.295i | 0.513600i | ||||||||
\(905\) | 1365.30 | + | 174.149i | 1.50862 | + | 0.192430i | ||||
\(906\) | −92.5019 | −0.102099 | ||||||||
\(907\) | 352.078 | + | 352.078i | 0.388179 | + | 0.388179i | 0.874038 | − | 0.485858i | \(-0.161493\pi\) |
−0.485858 | + | 0.874038i | \(0.661493\pi\) | |||||||
\(908\) | 160.593 | − | 160.593i | 0.176865 | − | 0.176865i | ||||
\(909\) | − | 160.816i | − | 0.176916i | ||||||
\(910\) | −183.000 | − | 236.510i | −0.201099 | − | 0.259901i | ||||
\(911\) | −530.824 | −0.582682 | −0.291341 | − | 0.956619i | \(-0.594101\pi\) | ||||
−0.291341 | + | 0.956619i | \(0.594101\pi\) | |||||||
\(912\) | 136.405 | + | 136.405i | 0.149567 | + | 0.149567i | ||||
\(913\) | 574.667 | − | 574.667i | 0.629427 | − | 0.629427i | ||||
\(914\) | − | 405.110i | − | 0.443227i | ||||||
\(915\) | −67.0654 | + | 51.8920i | −0.0732956 | + | 0.0567125i | ||||
\(916\) | 186.019 | 0.203077 | ||||||||
\(917\) | 810.747 | + | 810.747i | 0.884130 | + | 0.884130i | ||||
\(918\) | 25.3004 | − | 25.3004i | 0.0275604 | − | 0.0275604i | ||||
\(919\) | 1607.34i | 1.74901i | 0.485012 | + | 0.874507i | \(0.338815\pi\) | ||||
−0.485012 | + | 0.874507i | \(0.661185\pi\) | |||||||
\(920\) | −8.58159 | + | 67.2782i | −0.00932781 | + | 0.0731285i | ||||
\(921\) | 3.55190 | 0.00385657 | ||||||||
\(922\) | −527.587 | − | 527.587i | −0.572220 | − | 0.572220i | ||||
\(923\) | −193.485 | + | 193.485i | −0.209626 | + | 0.209626i | ||||
\(924\) | 182.210i | 0.197197i | ||||||||
\(925\) | 244.512 | + | 415.731i | 0.264337 | + | 0.449438i | ||||
\(926\) | −717.555 | −0.774898 | ||||||||
\(927\) | 25.9337 | + | 25.9337i | 0.0279760 | + | 0.0279760i | ||||
\(928\) | 105.888 | − | 105.888i | 0.114104 | − | 0.114104i | ||||
\(929\) | − | 1628.88i | − | 1.75337i | −0.481069 | − | 0.876683i | \(-0.659751\pi\) | ||
0.481069 | − | 0.876683i | \(-0.340249\pi\) | |||||||
\(930\) | 194.713 | + | 24.8364i | 0.209369 | + | 0.0267058i | ||||
\(931\) | 825.077 | 0.886227 | ||||||||
\(932\) | −365.623 | − | 365.623i | −0.392299 | − | 0.392299i | ||||
\(933\) | −515.972 | + | 515.972i | −0.553024 | + | 0.553024i | ||||
\(934\) | − | 970.677i | − | 1.03927i | ||||||
\(935\) | 178.066 | + | 230.133i | 0.190445 | + | 0.246132i | ||||
\(936\) | −81.5413 | −0.0871168 | ||||||||
\(937\) | −767.187 | − | 767.187i | −0.818769 | − | 0.818769i | 0.167161 | − | 0.985930i | \(-0.446540\pi\) |
−0.985930 | + | 0.167161i | \(0.946540\pi\) | |||||||
\(938\) | 218.908 | − | 218.908i | 0.233378 | − | 0.233378i | ||||
\(939\) | − | 239.351i | − | 0.254900i | ||||||
\(940\) | 400.340 | − | 309.764i | 0.425894 | − | 0.329536i | ||||
\(941\) | 1024.42 | 1.08865 | 0.544326 | − | 0.838874i | \(-0.316785\pi\) | ||||
0.544326 | + | 0.838874i | \(0.316785\pi\) | |||||||
\(942\) | −301.215 | − | 301.215i | −0.319762 | − | 0.319762i | ||||
\(943\) | 109.647 | − | 109.647i | 0.116275 | − | 0.116275i | ||||
\(944\) | − | 237.480i | − | 0.251567i | ||||||
\(945\) | −14.4669 | + | 113.418i | −0.0153089 | + | 0.120019i | ||||
\(946\) | 536.249 | 0.566859 | ||||||||
\(947\) | −929.596 | − | 929.596i | −0.981622 | − | 0.981622i | 0.0182120 | − | 0.999834i | \(-0.494203\pi\) |
−0.999834 | + | 0.0182120i | \(0.994203\pi\) | |||||||
\(948\) | 52.9219 | − | 52.9219i | 0.0558248 | − | 0.0558248i | ||||
\(949\) | − | 30.8690i | − | 0.0325279i | ||||||
\(950\) | −848.536 | + | 499.067i | −0.893196 | + | 0.525333i | ||||
\(951\) | 770.294 | 0.809983 | ||||||||
\(952\) | 42.8560 | + | 42.8560i | 0.0450168 | + | 0.0450168i | ||||
\(953\) | −426.370 | + | 426.370i | −0.447398 | + | 0.447398i | −0.894489 | − | 0.447091i | \(-0.852460\pi\) |
0.447091 | + | 0.894489i | \(0.352460\pi\) | |||||||
\(954\) | 249.718i | 0.261759i | ||||||||
\(955\) | 1412.56 | + | 180.178i | 1.47912 | + | 0.188668i | ||||
\(956\) | −360.441 | −0.377030 | ||||||||
\(957\) | 387.506 | + | 387.506i | 0.404917 | + | 0.404917i | ||||
\(958\) | 319.112 | − | 319.112i | 0.333102 | − | 0.333102i | ||||
\(959\) | − | 2.18229i | − | 0.00227559i | ||||||
\(960\) | 42.3975 | + | 54.7947i | 0.0441640 | + | 0.0570778i | ||||
\(961\) | −704.133 | −0.732708 | ||||||||
\(962\) | −185.393 | − | 185.393i | −0.192716 | − | 0.192716i | ||||
\(963\) | 118.655 | − | 118.655i | 0.123214 | − | 0.123214i | ||||
\(964\) | − | 158.960i | − | 0.164896i | ||||||
\(965\) | −400.202 | + | 309.657i | −0.414717 | + | 0.320888i | ||||
\(966\) | −51.6982 | −0.0535178 | ||||||||
\(967\) | 471.074 | + | 471.074i | 0.487150 | + | 0.487150i | 0.907406 | − | 0.420256i | \(-0.138060\pi\) |
−0.420256 | + | 0.907406i | \(0.638060\pi\) | |||||||
\(968\) | −43.7066 | + | 43.7066i | −0.0451515 | + | 0.0451515i | ||||
\(969\) | 234.818i | 0.242330i | ||||||||
\(970\) | −54.6129 | + | 428.156i | −0.0563020 | + | 0.441398i | ||||
\(971\) | −155.753 | −0.160405 | −0.0802024 | − | 0.996779i | \(-0.525557\pi\) | ||||
−0.0802024 | + | 0.996779i | \(0.525557\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −359.096 | + | 359.096i | −0.369061 | + | 0.369061i | ||||
\(974\) | − | 788.337i | − | 0.809380i | ||||||
\(975\) | 104.454 | − | 402.790i | 0.107133 | − | 0.413118i | ||||
\(976\) | −39.1661 | −0.0401292 | ||||||||
\(977\) | 319.809 | + | 319.809i | 0.327338 | + | 0.327338i | 0.851573 | − | 0.524235i | \(-0.175649\pi\) |
−0.524235 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(978\) | 52.9665 | − | 52.9665i | 0.0541580 | − | 0.0541580i | ||||
\(979\) | 1351.55i | 1.38054i | ||||||||
\(980\) | 293.944 | + | 37.4937i | 0.299943 | + | 0.0382589i | ||||
\(981\) | −20.2201 | −0.0206118 | ||||||||
\(982\) | 403.304 | + | 403.304i | 0.410696 | + | 0.410696i | ||||
\(983\) | 831.017 | − | 831.017i | 0.845388 | − | 0.845388i | −0.144165 | − | 0.989554i | \(-0.546050\pi\) |
0.989554 | + | 0.144165i | \(0.0460497\pi\) | |||||||
\(984\) | − | 158.400i | − | 0.160975i | ||||||
\(985\) | 928.818 | + | 1200.41i | 0.942962 | + | 1.21869i | ||||
\(986\) | 182.284 | 0.184872 | ||||||||
\(987\) | 272.831 | + | 272.831i | 0.276424 | + | 0.276424i | ||||
\(988\) | 378.400 | − | 378.400i | 0.382996 | − | 0.382996i | ||||
\(989\) | 152.149i | 0.153842i | ||||||||
\(990\) | −200.525 | + | 155.157i | −0.202551 | + | 0.156724i | ||||
\(991\) | −1917.18 | −1.93459 | −0.967297 | − | 0.253648i | \(-0.918370\pi\) | ||||
−0.967297 | + | 0.253648i | \(0.918370\pi\) | |||||||
\(992\) | 64.1083 | + | 64.1083i | 0.0646253 | + | 0.0646253i | ||||
\(993\) | 60.6197 | − | 60.6197i | 0.0610470 | − | 0.0610470i | ||||
\(994\) | 177.215i | 0.178285i | ||||||||
\(995\) | −56.5005 | + | 442.954i | −0.0567844 | + | 0.445180i | ||||
\(996\) | 235.547 | 0.236492 | ||||||||
\(997\) | −1169.64 | − | 1169.64i | −1.17316 | − | 1.17316i | −0.981453 | − | 0.191702i | \(-0.938599\pi\) |
−0.191702 | − | 0.981453i | \(-0.561401\pi\) | |||||||
\(998\) | 970.563 | − | 970.563i | 0.972508 | − | 0.972508i | ||||
\(999\) | 100.245i | 0.100346i |
(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.277.9 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.9 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.9 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.9 | yes | 40 | 5.3 | odd | 4 | inner |