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: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.10 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.10 |
$q$-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 | ||||||||
\(5\) | −4.46596 | − | 2.24837i | −0.893192 | − | 0.449675i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −8.35401 | − | 8.35401i | −1.19343 | − | 1.19343i | −0.976098 | − | 0.217333i | \(-0.930264\pi\) |
−0.217333 | − | 0.976098i | \(-0.569736\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 2.21759 | + | 6.71434i | 0.221759 | + | 0.671434i | ||||
\(11\) | 17.4360 | 1.58509 | 0.792545 | − | 0.609813i | \(-0.208756\pi\) | ||||
0.792545 | + | 0.609813i | \(0.208756\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 11.0505 | − | 11.0505i | 0.850041 | − | 0.850041i | −0.140097 | − | 0.990138i | \(-0.544741\pi\) |
0.990138 | + | 0.140097i | \(0.0447413\pi\) | |||||||
\(14\) | 16.7080i | 1.19343i | ||||||||
\(15\) | 8.22335 | − | 2.71598i | 0.548223 | − | 0.181065i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −14.9996 | − | 14.9996i | −0.882330 | − | 0.882330i | 0.111441 | − | 0.993771i | \(-0.464453\pi\) |
−0.993771 | + | 0.111441i | \(0.964453\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | 2.87824i | 0.151486i | 0.997127 | + | 0.0757431i | \(0.0241329\pi\) | ||||
−0.997127 | + | 0.0757431i | \(0.975867\pi\) | |||||||
\(20\) | 4.49675 | − | 8.93192i | 0.224837 | − | 0.446596i | ||||
\(21\) | 20.4631 | 0.974432 | ||||||||
\(22\) | −17.4360 | − | 17.4360i | −0.792545 | − | 0.792545i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 14.8896 | + | 20.0823i | 0.595585 | + | 0.803292i | ||||
\(26\) | −22.1011 | −0.850041 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 16.7080 | − | 16.7080i | 0.596715 | − | 0.596715i | ||||
\(29\) | − | 3.12728i | − | 0.107837i | −0.998545 | − | 0.0539187i | \(-0.982829\pi\) | ||
0.998545 | − | 0.0539187i | \(-0.0171712\pi\) | |||||||
\(30\) | −10.9393 | − | 5.50737i | −0.364644 | − | 0.183579i | ||||
\(31\) | 18.1414 | 0.585207 | 0.292604 | − | 0.956234i | \(-0.405478\pi\) | ||||
0.292604 | + | 0.956234i | \(0.405478\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −21.3546 | + | 21.3546i | −0.647110 | + | 0.647110i | ||||
\(34\) | 29.9992i | 0.882330i | ||||||||
\(35\) | 18.5258 | + | 56.0917i | 0.529308 | + | 1.60262i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −11.8822 | − | 11.8822i | −0.321139 | − | 0.321139i | 0.528065 | − | 0.849204i | \(-0.322918\pi\) |
−0.849204 | + | 0.528065i | \(0.822918\pi\) | |||||||
\(38\) | 2.87824 | − | 2.87824i | 0.0757431 | − | 0.0757431i | ||||
\(39\) | 27.0682i | 0.694056i | ||||||||
\(40\) | −13.4287 | + | 4.43518i | −0.335717 | + | 0.110879i | ||||
\(41\) | −72.2362 | −1.76186 | −0.880929 | − | 0.473248i | \(-0.843081\pi\) | ||||
−0.880929 | + | 0.473248i | \(0.843081\pi\) | |||||||
\(42\) | −20.4631 | − | 20.4631i | −0.487216 | − | 0.487216i | ||||
\(43\) | −43.7755 | + | 43.7755i | −1.01803 | + | 1.01803i | −0.0181999 | + | 0.999834i | \(0.505794\pi\) |
−0.999834 | + | 0.0181999i | \(0.994206\pi\) | |||||||
\(44\) | 34.8720i | 0.792545i | ||||||||
\(45\) | −6.74512 | + | 13.3979i | −0.149892 | + | 0.297731i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −61.4968 | − | 61.4968i | −1.30844 | − | 1.30844i | −0.922540 | − | 0.385902i | \(-0.873890\pi\) |
−0.385902 | − | 0.922540i | \(-0.626110\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 90.5791i | 1.84855i | ||||||||
\(50\) | 5.19267 | − | 34.9719i | 0.103853 | − | 0.699439i | ||||
\(51\) | 36.7414 | 0.720420 | ||||||||
\(52\) | 22.1011 | + | 22.1011i | 0.425021 | + | 0.425021i | ||||
\(53\) | 43.0455 | − | 43.0455i | 0.812180 | − | 0.812180i | −0.172781 | − | 0.984960i | \(-0.555275\pi\) |
0.984960 | + | 0.172781i | \(0.0552752\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | −77.8685 | − | 39.2026i | −1.41579 | − | 0.712775i | ||||
\(56\) | −33.4161 | −0.596715 | ||||||||
\(57\) | −3.52511 | − | 3.52511i | −0.0618440 | − | 0.0618440i | ||||
\(58\) | −3.12728 | + | 3.12728i | −0.0539187 | + | 0.0539187i | ||||
\(59\) | − | 60.4399i | − | 1.02440i | −0.858865 | − | 0.512202i | \(-0.828830\pi\) | ||
0.858865 | − | 0.512202i | \(-0.171170\pi\) | |||||||
\(60\) | 5.43196 | + | 16.4467i | 0.0905327 | + | 0.274112i | ||||
\(61\) | 1.37448 | 0.0225324 | 0.0112662 | − | 0.999937i | \(-0.496414\pi\) | ||||
0.0112662 | + | 0.999937i | \(0.496414\pi\) | |||||||
\(62\) | −18.1414 | − | 18.1414i | −0.292604 | − | 0.292604i | ||||
\(63\) | −25.0620 | + | 25.0620i | −0.397810 | + | 0.397810i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −74.1970 | + | 24.5055i | −1.14149 | + | 0.377008i | ||||
\(66\) | 42.7093 | 0.647110 | ||||||||
\(67\) | 60.8442 | + | 60.8442i | 0.908123 | + | 0.908123i | 0.996121 | − | 0.0879977i | \(-0.0280468\pi\) |
−0.0879977 | + | 0.996121i | \(0.528047\pi\) | |||||||
\(68\) | 29.9992 | − | 29.9992i | 0.441165 | − | 0.441165i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 37.5659 | − | 74.6174i | 0.536656 | − | 1.06596i | ||||
\(71\) | −89.3191 | −1.25802 | −0.629008 | − | 0.777399i | \(-0.716539\pi\) | ||||
−0.629008 | + | 0.777399i | \(0.716539\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −19.0044 | + | 19.0044i | −0.260334 | + | 0.260334i | −0.825190 | − | 0.564856i | \(-0.808932\pi\) |
0.564856 | + | 0.825190i | \(0.308932\pi\) | |||||||
\(74\) | 23.7643i | 0.321139i | ||||||||
\(75\) | −42.8317 | − | 6.35969i | −0.571089 | − | 0.0847959i | ||||
\(76\) | −5.75648 | −0.0757431 | ||||||||
\(77\) | −145.661 | − | 145.661i | −1.89170 | − | 1.89170i | ||||
\(78\) | 27.0682 | − | 27.0682i | 0.347028 | − | 0.347028i | ||||
\(79\) | − | 44.8163i | − | 0.567294i | −0.958929 | − | 0.283647i | \(-0.908456\pi\) | ||
0.958929 | − | 0.283647i | \(-0.0915445\pi\) | |||||||
\(80\) | 17.8638 | + | 8.99349i | 0.223298 | + | 0.112419i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 72.2362 | + | 72.2362i | 0.880929 | + | 0.880929i | ||||
\(83\) | −1.63595 | + | 1.63595i | −0.0197103 | + | 0.0197103i | −0.716893 | − | 0.697183i | \(-0.754437\pi\) |
0.697183 | + | 0.716893i | \(0.254437\pi\) | |||||||
\(84\) | 40.9261i | 0.487216i | ||||||||
\(85\) | 33.2630 | + | 100.712i | 0.391329 | + | 1.18485i | ||||
\(86\) | 87.5510 | 1.01803 | ||||||||
\(87\) | 3.83012 | + | 3.83012i | 0.0440244 | + | 0.0440244i | ||||
\(88\) | 34.8720 | − | 34.8720i | 0.396273 | − | 0.396273i | ||||
\(89\) | 16.6308i | 0.186863i | 0.995626 | + | 0.0934313i | \(0.0297835\pi\) | ||||
−0.995626 | + | 0.0934313i | \(0.970216\pi\) | |||||||
\(90\) | 20.1430 | − | 6.65277i | 0.223811 | − | 0.0739196i | ||||
\(91\) | −184.633 | −2.02893 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −22.2186 | + | 22.2186i | −0.238910 | + | 0.238910i | ||||
\(94\) | 122.994i | 1.30844i | ||||||||
\(95\) | 6.47135 | − | 12.8541i | 0.0681195 | − | 0.135306i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 53.3660 | + | 53.3660i | 0.550164 | + | 0.550164i | 0.926488 | − | 0.376324i | \(-0.122812\pi\) |
−0.376324 | + | 0.926488i | \(0.622812\pi\) | |||||||
\(98\) | 90.5791 | − | 90.5791i | 0.924276 | − | 0.924276i | ||||
\(99\) | − | 52.3080i | − | 0.528363i | ||||||
\(100\) | −40.1646 | + | 29.7793i | −0.401646 | + | 0.297793i | ||||
\(101\) | −35.9808 | −0.356246 | −0.178123 | − | 0.984008i | \(-0.557002\pi\) | ||||
−0.178123 | + | 0.984008i | \(0.557002\pi\) | |||||||
\(102\) | −36.7414 | − | 36.7414i | −0.360210 | − | 0.360210i | ||||
\(103\) | −76.7772 | + | 76.7772i | −0.745409 | + | 0.745409i | −0.973613 | − | 0.228204i | \(-0.926715\pi\) |
0.228204 | + | 0.973613i | \(0.426715\pi\) | |||||||
\(104\) | − | 44.2021i | − | 0.425021i | ||||||
\(105\) | −91.3873 | − | 46.0086i | −0.870355 | − | 0.438177i | ||||
\(106\) | −86.0910 | −0.812180 | ||||||||
\(107\) | 111.941 | + | 111.941i | 1.04618 | + | 1.04618i | 0.998881 | + | 0.0472976i | \(0.0150609\pi\) |
0.0472976 | + | 0.998881i | \(0.484939\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 207.304i | 1.90187i | 0.309386 | + | 0.950936i | \(0.399876\pi\) | ||||
−0.309386 | + | 0.950936i | \(0.600124\pi\) | |||||||
\(110\) | 38.6659 | + | 117.071i | 0.351508 | + | 1.06428i | ||||
\(111\) | 29.1052 | 0.262209 | ||||||||
\(112\) | 33.4161 | + | 33.4161i | 0.298358 | + | 0.298358i | ||||
\(113\) | −121.606 | + | 121.606i | −1.07616 | + | 1.07616i | −0.0793109 | + | 0.996850i | \(0.525272\pi\) |
−0.996850 | + | 0.0793109i | \(0.974728\pi\) | |||||||
\(114\) | 7.05021i | 0.0618440i | ||||||||
\(115\) | −22.7694 | + | 7.52021i | −0.197995 | + | 0.0653931i | ||||
\(116\) | 6.25456 | 0.0539187 | ||||||||
\(117\) | −33.1516 | − | 33.1516i | −0.283347 | − | 0.283347i | ||||
\(118\) | −60.4399 | + | 60.4399i | −0.512202 | + | 0.512202i | ||||
\(119\) | 250.614i | 2.10600i | ||||||||
\(120\) | 11.0147 | − | 21.8787i | 0.0917895 | − | 0.182322i | ||||
\(121\) | 183.014 | 1.51251 | ||||||||
\(122\) | −1.37448 | − | 1.37448i | −0.0112662 | − | 0.0112662i | ||||
\(123\) | 88.4709 | − | 88.4709i | 0.719276 | − | 0.719276i | ||||
\(124\) | 36.2829i | 0.292604i | ||||||||
\(125\) | −21.3440 | − | 123.164i | −0.170752 | − | 0.985314i | ||||
\(126\) | 50.1241 | 0.397810 | ||||||||
\(127\) | −79.3364 | − | 79.3364i | −0.624696 | − | 0.624696i | 0.322033 | − | 0.946729i | \(-0.395634\pi\) |
−0.946729 | + | 0.322033i | \(0.895634\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 107.228i | − | 0.831222i | ||||||
\(130\) | 98.7025 | + | 49.6915i | 0.759250 | + | 0.382242i | ||||
\(131\) | 77.0233 | 0.587964 | 0.293982 | − | 0.955811i | \(-0.405019\pi\) | ||||
0.293982 | + | 0.955811i | \(0.405019\pi\) | |||||||
\(132\) | −42.7093 | − | 42.7093i | −0.323555 | − | 0.323555i | ||||
\(133\) | 24.0448 | − | 24.0448i | 0.180788 | − | 0.180788i | ||||
\(134\) | − | 121.688i | − | 0.908123i | ||||||
\(135\) | −8.14794 | − | 24.6700i | −0.0603551 | − | 0.182741i | ||||
\(136\) | −59.9985 | −0.441165 | ||||||||
\(137\) | 22.4557 | + | 22.4557i | 0.163910 | + | 0.163910i | 0.784296 | − | 0.620386i | \(-0.213024\pi\) |
−0.620386 | + | 0.784296i | \(0.713024\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | − | 24.4482i | − | 0.175887i | −0.996125 | − | 0.0879433i | \(-0.971971\pi\) | ||
0.996125 | − | 0.0879433i | \(-0.0280294\pi\) | |||||||
\(140\) | −112.183 | + | 37.0515i | −0.801309 | + | 0.264654i | ||||
\(141\) | 150.636 | 1.06834 | ||||||||
\(142\) | 89.3191 | + | 89.3191i | 0.629008 | + | 0.629008i | ||||
\(143\) | 192.677 | − | 192.677i | 1.34739 | − | 1.34739i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −7.03130 | + | 13.9663i | −0.0484917 | + | 0.0963195i | ||||
\(146\) | 38.0087 | 0.260334 | ||||||||
\(147\) | −110.936 | − | 110.936i | −0.754669 | − | 0.754669i | ||||
\(148\) | 23.7643 | − | 23.7643i | 0.160570 | − | 0.160570i | ||||
\(149\) | 188.531i | 1.26531i | 0.774435 | + | 0.632654i | \(0.218034\pi\) | ||||
−0.774435 | + | 0.632654i | \(0.781966\pi\) | |||||||
\(150\) | 36.4720 | + | 49.1914i | 0.243147 | + | 0.327943i | ||||
\(151\) | 176.089 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(152\) | 5.75648 | + | 5.75648i | 0.0378715 | + | 0.0378715i | ||||
\(153\) | −44.9989 | + | 44.9989i | −0.294110 | + | 0.294110i | ||||
\(154\) | 291.321i | 1.89170i | ||||||||
\(155\) | −81.0189 | − | 40.7887i | −0.522703 | − | 0.263153i | ||||
\(156\) | −54.1363 | −0.347028 | ||||||||
\(157\) | −32.4124 | − | 32.4124i | −0.206449 | − | 0.206449i | 0.596308 | − | 0.802756i | \(-0.296634\pi\) |
−0.802756 | + | 0.596308i | \(0.796634\pi\) | |||||||
\(158\) | −44.8163 | + | 44.8163i | −0.283647 | + | 0.283647i | ||||
\(159\) | 105.440i | 0.663142i | ||||||||
\(160\) | −8.87035 | − | 26.8573i | −0.0554397 | − | 0.167858i | ||||
\(161\) | −56.6597 | −0.351923 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 85.5836 | − | 85.5836i | 0.525053 | − | 0.525053i | −0.394041 | − | 0.919093i | \(-0.628923\pi\) |
0.919093 | + | 0.394041i | \(0.128923\pi\) | |||||||
\(164\) | − | 144.472i | − | 0.880929i | ||||||
\(165\) | 143.382 | − | 47.3558i | 0.868983 | − | 0.287005i | ||||
\(166\) | 3.27191 | 0.0197103 | ||||||||
\(167\) | 68.9683 | + | 68.9683i | 0.412984 | + | 0.412984i | 0.882777 | − | 0.469793i | \(-0.155671\pi\) |
−0.469793 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(168\) | 40.9261 | − | 40.9261i | 0.243608 | − | 0.243608i | ||||
\(169\) | − | 75.2287i | − | 0.445140i | ||||||
\(170\) | 67.4495 | − | 133.975i | 0.396762 | − | 0.788091i | ||||
\(171\) | 8.63471 | 0.0504954 | ||||||||
\(172\) | −87.5510 | − | 87.5510i | −0.509017 | − | 0.509017i | ||||
\(173\) | 27.9513 | − | 27.9513i | 0.161568 | − | 0.161568i | −0.621693 | − | 0.783261i | \(-0.713555\pi\) |
0.783261 | + | 0.621693i | \(0.213555\pi\) | |||||||
\(174\) | − | 7.66025i | − | 0.0440244i | ||||||
\(175\) | 43.3796 | − | 292.156i | 0.247884 | − | 1.66946i | ||||
\(176\) | −69.7440 | −0.396273 | ||||||||
\(177\) | 74.0234 | + | 74.0234i | 0.418211 | + | 0.418211i | ||||
\(178\) | 16.6308 | − | 16.6308i | 0.0934313 | − | 0.0934313i | ||||
\(179\) | − | 129.232i | − | 0.721969i | −0.932572 | − | 0.360984i | \(-0.882441\pi\) | ||
0.932572 | − | 0.360984i | \(-0.117559\pi\) | |||||||
\(180\) | −26.7958 | − | 13.4902i | −0.148865 | − | 0.0749458i | ||||
\(181\) | 43.8532 | 0.242283 | 0.121141 | − | 0.992635i | \(-0.461345\pi\) | ||||
0.121141 | + | 0.992635i | \(0.461345\pi\) | |||||||
\(182\) | 184.633 | + | 184.633i | 1.01447 | + | 1.01447i | ||||
\(183\) | −1.68339 | + | 1.68339i | −0.00919883 | + | 0.00919883i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 26.3497 | + | 79.7808i | 0.142431 | + | 0.431248i | ||||
\(186\) | 44.4373 | 0.238910 | ||||||||
\(187\) | −261.533 | − | 261.533i | −1.39857 | − | 1.39857i | ||||
\(188\) | 122.994 | − | 122.994i | 0.654221 | − | 0.654221i | ||||
\(189\) | − | 61.3892i | − | 0.324811i | ||||||
\(190\) | −19.3255 | + | 6.38275i | −0.101713 | + | 0.0335934i | ||||
\(191\) | −371.805 | −1.94662 | −0.973311 | − | 0.229490i | \(-0.926294\pi\) | ||||
−0.973311 | + | 0.229490i | \(0.926294\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −135.050 | + | 135.050i | −0.699740 | + | 0.699740i | −0.964354 | − | 0.264614i | \(-0.914755\pi\) |
0.264614 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(194\) | − | 106.732i | − | 0.550164i | ||||||
\(195\) | 60.8594 | − | 120.885i | 0.312099 | − | 0.619925i | ||||
\(196\) | −181.158 | −0.924276 | ||||||||
\(197\) | −129.928 | − | 129.928i | −0.659534 | − | 0.659534i | 0.295735 | − | 0.955270i | \(-0.404435\pi\) |
−0.955270 | + | 0.295735i | \(0.904435\pi\) | |||||||
\(198\) | −52.3080 | + | 52.3080i | −0.264182 | + | 0.264182i | ||||
\(199\) | − | 191.204i | − | 0.960823i | −0.877043 | − | 0.480411i | \(-0.840487\pi\) | ||
0.877043 | − | 0.480411i | \(-0.159513\pi\) | |||||||
\(200\) | 69.9439 | + | 10.3853i | 0.349719 | + | 0.0519267i | ||||
\(201\) | −149.037 | −0.741479 | ||||||||
\(202\) | 35.9808 | + | 35.9808i | 0.178123 | + | 0.178123i | ||||
\(203\) | −26.1254 | + | 26.1254i | −0.128696 | + | 0.128696i | ||||
\(204\) | 73.4828i | 0.360210i | ||||||||
\(205\) | 322.604 | + | 162.414i | 1.57368 | + | 0.792263i | ||||
\(206\) | 153.554 | 0.745409 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | −44.2021 | + | 44.2021i | −0.212510 | + | 0.212510i | ||||
\(209\) | 50.1849i | 0.240119i | ||||||||
\(210\) | 45.3787 | + | 137.396i | 0.216089 | + | 0.654266i | ||||
\(211\) | −17.0920 | −0.0810047 | −0.0405024 | − | 0.999179i | \(-0.512896\pi\) | ||||
−0.0405024 | + | 0.999179i | \(0.512896\pi\) | |||||||
\(212\) | 86.0910 | + | 86.0910i | 0.406090 | + | 0.406090i | ||||
\(213\) | 109.393 | − | 109.393i | 0.513582 | − | 0.513582i | ||||
\(214\) | − | 223.882i | − | 1.04618i | ||||||
\(215\) | 293.923 | − | 97.0760i | 1.36708 | − | 0.451516i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −151.554 | − | 151.554i | −0.698405 | − | 0.698405i | ||||
\(218\) | 207.304 | − | 207.304i | 0.950936 | − | 0.950936i | ||||
\(219\) | − | 46.5510i | − | 0.212562i | ||||||
\(220\) | 78.4052 | − | 155.737i | 0.356387 | − | 0.707895i | ||||
\(221\) | −331.508 | −1.50003 | ||||||||
\(222\) | −29.1052 | − | 29.1052i | −0.131105 | − | 0.131105i | ||||
\(223\) | −54.8788 | + | 54.8788i | −0.246093 | + | 0.246093i | −0.819365 | − | 0.573272i | \(-0.805674\pi\) |
0.573272 | + | 0.819365i | \(0.305674\pi\) | |||||||
\(224\) | − | 66.8321i | − | 0.298358i | ||||||
\(225\) | 60.2469 | − | 44.6689i | 0.267764 | − | 0.198528i | ||||
\(226\) | 243.212 | 1.07616 | ||||||||
\(227\) | −82.2540 | − | 82.2540i | −0.362352 | − | 0.362352i | 0.502326 | − | 0.864678i | \(-0.332478\pi\) |
−0.864678 | + | 0.502326i | \(0.832478\pi\) | |||||||
\(228\) | 7.05021 | − | 7.05021i | 0.0309220 | − | 0.0309220i | ||||
\(229\) | 429.556i | 1.87579i | 0.346916 | + | 0.937896i | \(0.387229\pi\) | ||||
−0.346916 | + | 0.937896i | \(0.612771\pi\) | |||||||
\(230\) | 30.2896 | + | 15.2492i | 0.131694 | + | 0.0663009i | ||||
\(231\) | 356.794 | 1.54456 | ||||||||
\(232\) | −6.25456 | − | 6.25456i | −0.0269593 | − | 0.0269593i | ||||
\(233\) | −35.0961 | + | 35.0961i | −0.150627 | + | 0.150627i | −0.778398 | − | 0.627771i | \(-0.783967\pi\) |
0.627771 | + | 0.778398i | \(0.283967\pi\) | |||||||
\(234\) | 66.3032i | 0.283347i | ||||||||
\(235\) | 136.375 | + | 412.910i | 0.580317 | + | 1.75706i | ||||
\(236\) | 120.880 | 0.512202 | ||||||||
\(237\) | 54.8885 | + | 54.8885i | 0.231597 | + | 0.231597i | ||||
\(238\) | 250.614 | − | 250.614i | 1.05300 | − | 1.05300i | ||||
\(239\) | − | 108.716i | − | 0.454880i | −0.973792 | − | 0.227440i | \(-0.926965\pi\) | ||
0.973792 | − | 0.227440i | \(-0.0730355\pi\) | |||||||
\(240\) | −32.8934 | + | 10.8639i | −0.137056 | + | 0.0452663i | ||||
\(241\) | −294.692 | −1.22279 | −0.611394 | − | 0.791327i | \(-0.709391\pi\) | ||||
−0.611394 | + | 0.791327i | \(0.709391\pi\) | |||||||
\(242\) | −183.014 | − | 183.014i | −0.756256 | − | 0.756256i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 2.74896i | 0.0112662i | ||||||||
\(245\) | 203.656 | − | 404.523i | 0.831248 | − | 1.65111i | ||||
\(246\) | −176.942 | −0.719276 | ||||||||
\(247\) | 31.8061 | + | 31.8061i | 0.128770 | + | 0.128770i | ||||
\(248\) | 36.2829 | − | 36.2829i | 0.146302 | − | 0.146302i | ||||
\(249\) | − | 4.00725i | − | 0.0160934i | ||||||
\(250\) | −101.820 | + | 144.508i | −0.407281 | + | 0.578033i | ||||
\(251\) | 451.400 | 1.79841 | 0.899203 | − | 0.437532i | \(-0.144147\pi\) | ||||
0.899203 | + | 0.437532i | \(0.144147\pi\) | |||||||
\(252\) | −50.1241 | − | 50.1241i | −0.198905 | − | 0.198905i | ||||
\(253\) | 59.1283 | − | 59.1283i | 0.233709 | − | 0.233709i | ||||
\(254\) | 158.673i | 0.624696i | ||||||||
\(255\) | −164.086 | − | 82.6084i | −0.643473 | − | 0.323955i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −185.908 | − | 185.908i | −0.723378 | − | 0.723378i | 0.245914 | − | 0.969292i | \(-0.420912\pi\) |
−0.969292 | + | 0.245914i | \(0.920912\pi\) | |||||||
\(258\) | −107.228 | + | 107.228i | −0.415611 | + | 0.415611i | ||||
\(259\) | 198.527i | 0.766515i | ||||||||
\(260\) | −49.0111 | − | 148.394i | −0.188504 | − | 0.570746i | ||||
\(261\) | −9.38185 | −0.0359458 | ||||||||
\(262\) | −77.0233 | − | 77.0233i | −0.293982 | − | 0.293982i | ||||
\(263\) | 274.719 | − | 274.719i | 1.04456 | − | 1.04456i | 0.0456006 | − | 0.998960i | \(-0.485480\pi\) |
0.998960 | − | 0.0456006i | \(-0.0145202\pi\) | |||||||
\(264\) | 85.4186i | 0.323555i | ||||||||
\(265\) | −289.022 | + | 95.4573i | −1.09065 | + | 0.360216i | ||||
\(266\) | −48.0897 | −0.180788 | ||||||||
\(267\) | −20.3684 | − | 20.3684i | −0.0762863 | − | 0.0762863i | ||||
\(268\) | −121.688 | + | 121.688i | −0.454061 | + | 0.454061i | ||||
\(269\) | − | 427.490i | − | 1.58918i | −0.607146 | − | 0.794591i | \(-0.707686\pi\) | ||
0.607146 | − | 0.794591i | \(-0.292314\pi\) | |||||||
\(270\) | −16.5221 | + | 32.8180i | −0.0611930 | + | 0.121548i | ||||
\(271\) | 101.987 | 0.376334 | 0.188167 | − | 0.982137i | \(-0.439745\pi\) | ||||
0.188167 | + | 0.982137i | \(0.439745\pi\) | |||||||
\(272\) | 59.9985 | + | 59.9985i | 0.220583 | + | 0.220583i | ||||
\(273\) | 226.128 | − | 226.128i | 0.828307 | − | 0.828307i | ||||
\(274\) | − | 44.9114i | − | 0.163910i | ||||||
\(275\) | 259.616 | + | 350.155i | 0.944056 | + | 1.27329i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −254.686 | − | 254.686i | −0.919443 | − | 0.919443i | 0.0775463 | − | 0.996989i | \(-0.475291\pi\) |
−0.996989 | + | 0.0775463i | \(0.975291\pi\) | |||||||
\(278\) | −24.4482 | + | 24.4482i | −0.0879433 | + | 0.0879433i | ||||
\(279\) | − | 54.4243i | − | 0.195069i | ||||||
\(280\) | 149.235 | + | 75.1318i | 0.532982 | + | 0.268328i | ||||
\(281\) | −438.626 | −1.56094 | −0.780472 | − | 0.625190i | \(-0.785021\pi\) | ||||
−0.780472 | + | 0.625190i | \(0.785021\pi\) | |||||||
\(282\) | −150.636 | − | 150.636i | −0.534169 | − | 0.534169i | ||||
\(283\) | 85.3328 | − | 85.3328i | 0.301529 | − | 0.301529i | −0.540083 | − | 0.841612i | \(-0.681607\pi\) |
0.841612 | + | 0.540083i | \(0.181607\pi\) | |||||||
\(284\) | − | 178.638i | − | 0.629008i | ||||||
\(285\) | 7.81724 | + | 23.6688i | 0.0274289 | + | 0.0830482i | ||||
\(286\) | −385.354 | −1.34739 | ||||||||
\(287\) | 603.462 | + | 603.462i | 2.10266 | + | 2.10266i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 160.977i | 0.557014i | ||||||||
\(290\) | 20.9976 | − | 6.93503i | 0.0724056 | − | 0.0239139i | ||||
\(291\) | −130.719 | −0.449207 | ||||||||
\(292\) | −38.0087 | − | 38.0087i | −0.130167 | − | 0.130167i | ||||
\(293\) | −66.5716 | + | 66.5716i | −0.227207 | + | 0.227207i | −0.811525 | − | 0.584318i | \(-0.801362\pi\) |
0.584318 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(294\) | 221.873i | 0.754669i | ||||||||
\(295\) | −135.891 | + | 269.922i | −0.460649 | + | 0.914990i | ||||
\(296\) | −47.5286 | −0.160570 | ||||||||
\(297\) | 64.0639 | + | 64.0639i | 0.215703 | + | 0.215703i | ||||
\(298\) | 188.531 | − | 188.531i | 0.632654 | − | 0.632654i | ||||
\(299\) | − | 74.9484i | − | 0.250663i | ||||||
\(300\) | 12.7194 | − | 85.6634i | 0.0423980 | − | 0.285545i | ||||
\(301\) | 731.402 | 2.42991 | ||||||||
\(302\) | −176.089 | − | 176.089i | −0.583077 | − | 0.583077i | ||||
\(303\) | 44.0673 | − | 44.0673i | 0.145437 | − | 0.145437i | ||||
\(304\) | − | 11.5130i | − | 0.0378715i | ||||||
\(305\) | −6.13837 | − | 3.09034i | −0.0201258 | − | 0.0101323i | ||||
\(306\) | 89.9977 | 0.294110 | ||||||||
\(307\) | −292.269 | − | 292.269i | −0.952015 | − | 0.952015i | 0.0468849 | − | 0.998900i | \(-0.485071\pi\) |
−0.998900 | + | 0.0468849i | \(0.985071\pi\) | |||||||
\(308\) | 291.321 | − | 291.321i | 0.945848 | − | 0.945848i | ||||
\(309\) | − | 188.065i | − | 0.608624i | ||||||
\(310\) | 40.2302 | + | 121.808i | 0.129775 | + | 0.392928i | ||||
\(311\) | −81.4097 | −0.261767 | −0.130884 | − | 0.991398i | \(-0.541781\pi\) | ||||
−0.130884 | + | 0.991398i | \(0.541781\pi\) | |||||||
\(312\) | 54.1363 | + | 54.1363i | 0.173514 | + | 0.173514i | ||||
\(313\) | 147.092 | − | 147.092i | 0.469941 | − | 0.469941i | −0.431954 | − | 0.901895i | \(-0.642176\pi\) |
0.901895 | + | 0.431954i | \(0.142176\pi\) | |||||||
\(314\) | 64.8248i | 0.206449i | ||||||||
\(315\) | 168.275 | − | 55.5773i | 0.534206 | − | 0.176436i | ||||
\(316\) | 89.6325 | 0.283647 | ||||||||
\(317\) | 51.5605 | + | 51.5605i | 0.162651 | + | 0.162651i | 0.783740 | − | 0.621089i | \(-0.213309\pi\) |
−0.621089 | + | 0.783740i | \(0.713309\pi\) | |||||||
\(318\) | 105.440 | − | 105.440i | 0.331571 | − | 0.331571i | ||||
\(319\) | − | 54.5273i | − | 0.170932i | ||||||
\(320\) | −17.9870 | + | 35.7277i | −0.0562093 | + | 0.111649i | ||||
\(321\) | −274.199 | −0.854201 | ||||||||
\(322\) | 56.6597 | + | 56.6597i | 0.175962 | + | 0.175962i | ||||
\(323\) | 43.1725 | − | 43.1725i | 0.133661 | − | 0.133661i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 386.459 | + | 57.3818i | 1.18910 | + | 0.176559i | ||||
\(326\) | −171.167 | −0.525053 | ||||||||
\(327\) | −253.895 | − | 253.895i | −0.776436 | − | 0.776436i | ||||
\(328\) | −144.472 | + | 144.472i | −0.440465 | + | 0.440465i | ||||
\(329\) | 1027.49i | 3.12307i | ||||||||
\(330\) | −190.738 | − | 96.0264i | −0.577994 | − | 0.290989i | ||||
\(331\) | −445.932 | −1.34723 | −0.673614 | − | 0.739084i | \(-0.735259\pi\) | ||||
−0.673614 | + | 0.739084i | \(0.735259\pi\) | |||||||
\(332\) | −3.27191 | − | 3.27191i | −0.00985515 | − | 0.00985515i | ||||
\(333\) | −35.6465 | + | 35.6465i | −0.107046 | + | 0.107046i | ||||
\(334\) | − | 137.937i | − | 0.412984i | ||||||
\(335\) | −134.927 | − | 408.529i | −0.402769 | − | 1.21949i | ||||
\(336\) | −81.8523 | −0.243608 | ||||||||
\(337\) | −178.974 | − | 178.974i | −0.531081 | − | 0.531081i | 0.389813 | − | 0.920894i | \(-0.372540\pi\) |
−0.920894 | + | 0.389813i | \(0.872540\pi\) | |||||||
\(338\) | −75.2287 | + | 75.2287i | −0.222570 | + | 0.222570i | ||||
\(339\) | − | 297.873i | − | 0.878682i | ||||||
\(340\) | −201.425 | + | 66.5260i | −0.592426 | + | 0.195665i | ||||
\(341\) | 316.314 | 0.927607 | ||||||||
\(342\) | −8.63471 | − | 8.63471i | −0.0252477 | − | 0.0252477i | ||||
\(343\) | 347.352 | − | 347.352i | 1.01269 | − | 1.01269i | ||||
\(344\) | 175.102i | 0.509017i | ||||||||
\(345\) | 18.6764 | − | 37.0971i | 0.0541345 | − | 0.107528i | ||||
\(346\) | −55.9026 | −0.161568 | ||||||||
\(347\) | −195.326 | − | 195.326i | −0.562898 | − | 0.562898i | 0.367232 | − | 0.930130i | \(-0.380306\pi\) |
−0.930130 | + | 0.367232i | \(0.880306\pi\) | |||||||
\(348\) | −7.66025 | + | 7.66025i | −0.0220122 | + | 0.0220122i | ||||
\(349\) | 616.027i | 1.76512i | 0.470200 | + | 0.882560i | \(0.344182\pi\) | ||||
−0.470200 | + | 0.882560i | \(0.655818\pi\) | |||||||
\(350\) | −335.536 | + | 248.776i | −0.958673 | + | 0.710790i | ||||
\(351\) | 81.2045 | 0.231352 | ||||||||
\(352\) | 69.7440 | + | 69.7440i | 0.198136 | + | 0.198136i | ||||
\(353\) | −242.640 | + | 242.640i | −0.687366 | + | 0.687366i | −0.961649 | − | 0.274283i | \(-0.911560\pi\) |
0.274283 | + | 0.961649i | \(0.411560\pi\) | |||||||
\(354\) | − | 148.047i | − | 0.418211i | ||||||
\(355\) | 398.896 | + | 200.823i | 1.12365 | + | 0.565698i | ||||
\(356\) | −33.2615 | −0.0934313 | ||||||||
\(357\) | −306.938 | − | 306.938i | −0.859771 | − | 0.859771i | ||||
\(358\) | −129.232 | + | 129.232i | −0.360984 | + | 0.360984i | ||||
\(359\) | − | 309.086i | − | 0.860963i | −0.902599 | − | 0.430482i | \(-0.858344\pi\) | ||
0.902599 | − | 0.430482i | \(-0.141656\pi\) | |||||||
\(360\) | 13.3055 | + | 40.2860i | 0.0369598 | + | 0.111906i | ||||
\(361\) | 352.716 | 0.977052 | ||||||||
\(362\) | −43.8532 | − | 43.8532i | −0.121141 | − | 0.121141i | ||||
\(363\) | −224.145 | + | 224.145i | −0.617480 | + | 0.617480i | ||||
\(364\) | − | 369.265i | − | 1.01447i | ||||||
\(365\) | 127.602 | − | 42.1439i | 0.349594 | − | 0.115463i | ||||
\(366\) | 3.36677 | 0.00919883 | ||||||||
\(367\) | 320.182 | + | 320.182i | 0.872429 | + | 0.872429i | 0.992737 | − | 0.120307i | \(-0.0383880\pi\) |
−0.120307 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 216.709i | 0.587286i | ||||||||
\(370\) | 53.4311 | − | 106.131i | 0.144408 | − | 0.286839i | ||||
\(371\) | −719.206 | −1.93856 | ||||||||
\(372\) | −44.4373 | − | 44.4373i | −0.119455 | − | 0.119455i | ||||
\(373\) | 40.8847 | − | 40.8847i | 0.109610 | − | 0.109610i | −0.650175 | − | 0.759785i | \(-0.725304\pi\) |
0.759785 | + | 0.650175i | \(0.225304\pi\) | |||||||
\(374\) | 523.066i | 1.39857i | ||||||||
\(375\) | 176.986 | + | 124.704i | 0.471962 | + | 0.332543i | ||||
\(376\) | −245.987 | −0.654221 | ||||||||
\(377\) | −34.5581 | − | 34.5581i | −0.0916662 | − | 0.0916662i | ||||
\(378\) | −61.3892 | + | 61.3892i | −0.162405 | + | 0.162405i | ||||
\(379\) | 235.010i | 0.620079i | 0.950724 | + | 0.310040i | \(0.100342\pi\) | ||||
−0.950724 | + | 0.310040i | \(0.899658\pi\) | |||||||
\(380\) | 25.7082 | + | 12.9427i | 0.0676532 | + | 0.0340598i | ||||
\(381\) | 194.334 | 0.510062 | ||||||||
\(382\) | 371.805 | + | 371.805i | 0.973311 | + | 0.973311i | ||||
\(383\) | −344.365 | + | 344.365i | −0.899125 | + | 0.899125i | −0.995359 | − | 0.0962334i | \(-0.969320\pi\) |
0.0962334 | + | 0.995359i | \(0.469320\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 323.015 | + | 978.014i | 0.839000 | + | 2.54030i | ||||
\(386\) | 270.100 | 0.699740 | ||||||||
\(387\) | 131.326 | + | 131.326i | 0.339345 | + | 0.339345i | ||||
\(388\) | −106.732 | + | 106.732i | −0.275082 | + | 0.275082i | ||||
\(389\) | 522.732i | 1.34378i | 0.740649 | + | 0.671892i | \(0.234518\pi\) | ||||
−0.740649 | + | 0.671892i | \(0.765482\pi\) | |||||||
\(390\) | −181.745 | + | 60.0261i | −0.466012 | + | 0.153913i | ||||
\(391\) | −101.732 | −0.260185 | ||||||||
\(392\) | 181.158 | + | 181.158i | 0.462138 | + | 0.462138i | ||||
\(393\) | −94.3339 | + | 94.3339i | −0.240035 | + | 0.240035i | ||||
\(394\) | 259.857i | 0.659534i | ||||||||
\(395\) | −100.764 | + | 200.148i | −0.255098 | + | 0.506703i | ||||
\(396\) | 104.616 | 0.264182 | ||||||||
\(397\) | −130.039 | − | 130.039i | −0.327554 | − | 0.327554i | 0.524101 | − | 0.851656i | \(-0.324401\pi\) |
−0.851656 | + | 0.524101i | \(0.824401\pi\) | |||||||
\(398\) | −191.204 | + | 191.204i | −0.480411 | + | 0.480411i | ||||
\(399\) | 58.8976i | 0.147613i | ||||||||
\(400\) | −59.5585 | − | 80.3292i | −0.148896 | − | 0.200823i | ||||
\(401\) | 711.927 | 1.77538 | 0.887690 | − | 0.460442i | \(-0.152309\pi\) | ||||
0.887690 | + | 0.460442i | \(0.152309\pi\) | |||||||
\(402\) | 149.037 | + | 149.037i | 0.370740 | + | 0.370740i | ||||
\(403\) | 200.473 | − | 200.473i | 0.497450 | − | 0.497450i | ||||
\(404\) | − | 71.9617i | − | 0.178123i | ||||||
\(405\) | 40.1937 | + | 20.2354i | 0.0992436 | + | 0.0499639i | ||||
\(406\) | 52.2507 | 0.128696 | ||||||||
\(407\) | −207.177 | − | 207.177i | −0.509035 | − | 0.509035i | ||||
\(408\) | 73.4828 | − | 73.4828i | 0.180105 | − | 0.180105i | ||||
\(409\) | 225.265i | 0.550770i | 0.961334 | + | 0.275385i | \(0.0888054\pi\) | ||||
−0.961334 | + | 0.275385i | \(0.911195\pi\) | |||||||
\(410\) | −160.190 | − | 485.018i | −0.390708 | − | 1.18297i | ||||
\(411\) | −55.0050 | −0.133832 | ||||||||
\(412\) | −153.554 | − | 153.554i | −0.372705 | − | 0.372705i | ||||
\(413\) | −504.916 | + | 504.916i | −1.22256 | + | 1.22256i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 10.9843 | − | 3.62787i | 0.0264683 | − | 0.00874187i | ||||
\(416\) | 88.4043 | 0.212510 | ||||||||
\(417\) | 29.9428 | + | 29.9428i | 0.0718054 | + | 0.0718054i | ||||
\(418\) | 50.1849 | − | 50.1849i | 0.120060 | − | 0.120060i | ||||
\(419\) | − | 727.460i | − | 1.73618i | −0.496406 | − | 0.868090i | \(-0.665347\pi\) | ||
0.496406 | − | 0.868090i | \(-0.334653\pi\) | |||||||
\(420\) | 92.0173 | − | 182.775i | 0.219089 | − | 0.435178i | ||||
\(421\) | 188.423 | 0.447562 | 0.223781 | − | 0.974640i | \(-0.428160\pi\) | ||||
0.223781 | + | 0.974640i | \(0.428160\pi\) | |||||||
\(422\) | 17.0920 | + | 17.0920i | 0.0405024 | + | 0.0405024i | ||||
\(423\) | −184.490 | + | 184.490i | −0.436147 | + | 0.436147i | ||||
\(424\) | − | 172.182i | − | 0.406090i | ||||||
\(425\) | 77.8880 | − | 524.566i | 0.183266 | − | 1.23427i | ||||
\(426\) | −218.786 | −0.513582 | ||||||||
\(427\) | −11.4824 | − | 11.4824i | −0.0268909 | − | 0.0268909i | ||||
\(428\) | −223.882 | + | 223.882i | −0.523089 | + | 0.523089i | ||||
\(429\) | 471.960i | 1.10014i | ||||||||
\(430\) | −390.999 | − | 196.847i | −0.909301 | − | 0.457784i | ||||
\(431\) | 624.307 | 1.44851 | 0.724254 | − | 0.689534i | \(-0.242185\pi\) | ||||
0.724254 | + | 0.689534i | \(0.242185\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 208.628 | − | 208.628i | 0.481821 | − | 0.481821i | −0.423892 | − | 0.905713i | \(-0.639336\pi\) |
0.905713 | + | 0.423892i | \(0.139336\pi\) | |||||||
\(434\) | 303.108i | 0.698405i | ||||||||
\(435\) | −8.49364 | − | 25.7167i | −0.0195256 | − | 0.0591189i | ||||
\(436\) | −414.608 | −0.950936 | ||||||||
\(437\) | 9.76058 | + | 9.76058i | 0.0223354 | + | 0.0223354i | ||||
\(438\) | −46.5510 | + | 46.5510i | −0.106281 | + | 0.106281i | ||||
\(439\) | − | 555.867i | − | 1.26621i | −0.774065 | − | 0.633106i | \(-0.781780\pi\) | ||
0.774065 | − | 0.633106i | \(-0.218220\pi\) | |||||||
\(440\) | −234.142 | + | 77.3317i | −0.532141 | + | 0.175754i | ||||
\(441\) | 271.737 | 0.616184 | ||||||||
\(442\) | 331.508 | + | 331.508i | 0.750017 | + | 0.750017i | ||||
\(443\) | −479.179 | + | 479.179i | −1.08167 | + | 1.08167i | −0.0853137 | + | 0.996354i | \(0.527189\pi\) |
−0.996354 | + | 0.0853137i | \(0.972811\pi\) | |||||||
\(444\) | 58.2104i | 0.131105i | ||||||||
\(445\) | 37.3922 | − | 74.2724i | 0.0840273 | − | 0.166904i | ||||
\(446\) | 109.758 | 0.246093 | ||||||||
\(447\) | −230.902 | − | 230.902i | −0.516560 | − | 0.516560i | ||||
\(448\) | −66.8321 | + | 66.8321i | −0.149179 | + | 0.149179i | ||||
\(449\) | 526.390i | 1.17236i | 0.810180 | + | 0.586181i | \(0.199369\pi\) | ||||
−0.810180 | + | 0.586181i | \(0.800631\pi\) | |||||||
\(450\) | −104.916 | − | 15.5780i | −0.233146 | − | 0.0346178i | ||||
\(451\) | −1259.51 | −2.79270 | ||||||||
\(452\) | −243.212 | − | 243.212i | −0.538080 | − | 0.538080i | ||||
\(453\) | −215.664 | + | 215.664i | −0.476080 | + | 0.476080i | ||||
\(454\) | 164.508i | 0.362352i | ||||||||
\(455\) | 824.562 | + | 415.123i | 1.81223 | + | 0.912359i | ||||
\(456\) | −14.1004 | −0.0309220 | ||||||||
\(457\) | 190.661 | + | 190.661i | 0.417201 | + | 0.417201i | 0.884238 | − | 0.467037i | \(-0.154678\pi\) |
−0.467037 | + | 0.884238i | \(0.654678\pi\) | |||||||
\(458\) | 429.556 | − | 429.556i | 0.937896 | − | 0.937896i | ||||
\(459\) | − | 110.224i | − | 0.240140i | ||||||
\(460\) | −15.0404 | − | 45.5388i | −0.0326966 | − | 0.0989975i | ||||
\(461\) | −138.301 | −0.300003 | −0.150001 | − | 0.988686i | \(-0.547928\pi\) | ||||
−0.150001 | + | 0.988686i | \(0.547928\pi\) | |||||||
\(462\) | −356.794 | − | 356.794i | −0.772281 | − | 0.772281i | ||||
\(463\) | 377.857 | − | 377.857i | 0.816106 | − | 0.816106i | −0.169435 | − | 0.985541i | \(-0.554194\pi\) |
0.985541 | + | 0.169435i | \(0.0541943\pi\) | |||||||
\(464\) | 12.5091i | 0.0269593i | ||||||||
\(465\) | 149.183 | − | 49.2718i | 0.320824 | − | 0.105961i | ||||
\(466\) | 70.1921 | 0.150627 | ||||||||
\(467\) | −121.247 | − | 121.247i | −0.259629 | − | 0.259629i | 0.565274 | − | 0.824903i | \(-0.308770\pi\) |
−0.824903 | + | 0.565274i | \(0.808770\pi\) | |||||||
\(468\) | 66.3032 | − | 66.3032i | 0.141674 | − | 0.141674i | ||||
\(469\) | − | 1016.59i | − | 2.16756i | ||||||
\(470\) | 276.535 | − | 549.284i | 0.588373 | − | 1.16869i | ||||
\(471\) | 79.3939 | 0.168565 | ||||||||
\(472\) | −120.880 | − | 120.880i | −0.256101 | − | 0.256101i | ||||
\(473\) | −763.269 | + | 763.269i | −1.61368 | + | 1.61368i | ||||
\(474\) | − | 109.777i | − | 0.231597i | ||||||
\(475\) | −57.8016 | + | 42.8559i | −0.121688 | + | 0.0902230i | ||||
\(476\) | −501.228 | −1.05300 | ||||||||
\(477\) | −129.137 | − | 129.137i | −0.270727 | − | 0.270727i | ||||
\(478\) | −108.716 | + | 108.716i | −0.227440 | + | 0.227440i | ||||
\(479\) | − | 687.235i | − | 1.43473i | −0.696698 | − | 0.717364i | \(-0.745348\pi\) | ||
0.696698 | − | 0.717364i | \(-0.254652\pi\) | |||||||
\(480\) | 43.7573 | + | 22.0295i | 0.0911611 | + | 0.0458947i | ||||
\(481\) | −262.608 | −0.545963 | ||||||||
\(482\) | 294.692 | + | 294.692i | 0.611394 | + | 0.611394i | ||||
\(483\) | 69.3937 | − | 69.3937i | 0.143672 | − | 0.143672i | ||||
\(484\) | 366.028i | 0.756256i | ||||||||
\(485\) | −118.344 | − | 358.317i | −0.244008 | − | 0.738798i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 437.113 | + | 437.113i | 0.897563 | + | 0.897563i | 0.995220 | − | 0.0976574i | \(-0.0311349\pi\) |
−0.0976574 | + | 0.995220i | \(0.531135\pi\) | |||||||
\(488\) | 2.74896 | − | 2.74896i | 0.00563311 | − | 0.00563311i | ||||
\(489\) | 209.636i | 0.428704i | ||||||||
\(490\) | −608.178 | + | 200.867i | −1.24118 | + | 0.409933i | ||||
\(491\) | −129.408 | −0.263559 | −0.131780 | − | 0.991279i | \(-0.542069\pi\) | ||||
−0.131780 | + | 0.991279i | \(0.542069\pi\) | |||||||
\(492\) | 176.942 | + | 176.942i | 0.359638 | + | 0.359638i | ||||
\(493\) | −46.9080 | + | 46.9080i | −0.0951482 | + | 0.0951482i | ||||
\(494\) | − | 63.6121i | − | 0.128770i | ||||||
\(495\) | −117.608 | + | 233.605i | −0.237592 | + | 0.471930i | ||||
\(496\) | −72.5657 | −0.146302 | ||||||||
\(497\) | 746.173 | + | 746.173i | 1.50135 | + | 1.50135i | ||||
\(498\) | −4.00725 | + | 4.00725i | −0.00804670 | + | 0.00804670i | ||||
\(499\) | − | 958.920i | − | 1.92168i | −0.277098 | − | 0.960842i | \(-0.589373\pi\) | ||
0.277098 | − | 0.960842i | \(-0.410627\pi\) | |||||||
\(500\) | 246.329 | − | 42.6880i | 0.492657 | − | 0.0853761i | ||||
\(501\) | −168.937 | −0.337200 | ||||||||
\(502\) | −451.400 | − | 451.400i | −0.899203 | − | 0.899203i | ||||
\(503\) | −135.406 | + | 135.406i | −0.269197 | + | 0.269197i | −0.828777 | − | 0.559580i | \(-0.810963\pi\) |
0.559580 | + | 0.828777i | \(0.310963\pi\) | |||||||
\(504\) | 100.248i | 0.198905i | ||||||||
\(505\) | 160.689 | + | 80.8984i | 0.318196 | + | 0.160195i | ||||
\(506\) | −118.257 | −0.233709 | ||||||||
\(507\) | 92.1359 | + | 92.1359i | 0.181728 | + | 0.181728i | ||||
\(508\) | 158.673 | − | 158.673i | 0.312348 | − | 0.312348i | ||||
\(509\) | 642.984i | 1.26323i | 0.775282 | + | 0.631615i | \(0.217608\pi\) | ||||
−0.775282 | + | 0.631615i | \(0.782392\pi\) | |||||||
\(510\) | 81.4773 | + | 246.694i | 0.159759 | + | 0.483714i | ||||
\(511\) | 317.526 | 0.621381 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −10.5753 | + | 10.5753i | −0.0206147 | + | 0.0206147i | ||||
\(514\) | 371.816i | 0.723378i | ||||||||
\(515\) | 515.508 | − | 170.260i | 1.00099 | − | 0.330602i | ||||
\(516\) | 214.455 | 0.415611 | ||||||||
\(517\) | −1072.26 | − | 1072.26i | −2.07400 | − | 2.07400i | ||||
\(518\) | 198.527 | − | 198.527i | 0.383258 | − | 0.383258i | ||||
\(519\) | 68.4664i | 0.131920i | ||||||||
\(520\) | −99.3829 | + | 197.405i | −0.191121 | + | 0.379625i | ||||
\(521\) | 343.522 | 0.659351 | 0.329676 | − | 0.944094i | \(-0.393061\pi\) | ||||
0.329676 | + | 0.944094i | \(0.393061\pi\) | |||||||
\(522\) | 9.38185 | + | 9.38185i | 0.0179729 | + | 0.0179729i | ||||
\(523\) | −44.8371 | + | 44.8371i | −0.0857306 | + | 0.0857306i | −0.748672 | − | 0.662941i | \(-0.769308\pi\) |
0.662941 | + | 0.748672i | \(0.269308\pi\) | |||||||
\(524\) | 154.047i | 0.293982i | ||||||||
\(525\) | 304.688 | + | 410.946i | 0.580357 | + | 0.782753i | ||||
\(526\) | −549.439 | −1.04456 | ||||||||
\(527\) | −272.115 | − | 272.115i | −0.516346 | − | 0.516346i | ||||
\(528\) | 85.4186 | − | 85.4186i | 0.161778 | − | 0.161778i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 384.479 | + | 193.565i | 0.725433 | + | 0.365217i | ||||
\(531\) | −181.320 | −0.341468 | ||||||||
\(532\) | 48.0897 | + | 48.0897i | 0.0903941 | + | 0.0903941i | ||||
\(533\) | −798.249 | + | 798.249i | −1.49765 | + | 1.49765i | ||||
\(534\) | 40.7369i | 0.0762863i | ||||||||
\(535\) | −248.239 | − | 751.610i | −0.463999 | − | 1.40488i | ||||
\(536\) | 243.377 | 0.454061 | ||||||||
\(537\) | 158.277 | + | 158.277i | 0.294742 | + | 0.294742i | ||||
\(538\) | −427.490 | + | 427.490i | −0.794591 | + | 0.794591i | ||||
\(539\) | 1579.34i | 2.93012i | ||||||||
\(540\) | 49.3401 | − | 16.2959i | 0.0913705 | − | 0.0301776i | ||||
\(541\) | −425.664 | −0.786809 | −0.393404 | − | 0.919366i | \(-0.628703\pi\) | ||||
−0.393404 | + | 0.919366i | \(0.628703\pi\) | |||||||
\(542\) | −101.987 | − | 101.987i | −0.188167 | − | 0.188167i | ||||
\(543\) | −53.7089 | + | 53.7089i | −0.0989115 | + | 0.0989115i | ||||
\(544\) | − | 119.997i | − | 0.220583i | ||||||
\(545\) | 466.097 | − | 925.812i | 0.855224 | − | 1.69874i | ||||
\(546\) | −452.256 | −0.828307 | ||||||||
\(547\) | −561.015 | − | 561.015i | −1.02562 | − | 1.02562i | −0.999663 | − | 0.0259585i | \(-0.991736\pi\) |
−0.0259585 | − | 0.999663i | \(-0.508264\pi\) | |||||||
\(548\) | −44.9114 | + | 44.9114i | −0.0819551 | + | 0.0819551i | ||||
\(549\) | − | 4.12344i | − | 0.00751082i | ||||||
\(550\) | 90.5393 | − | 609.770i | 0.164617 | − | 1.10867i | ||||
\(551\) | 9.00106 | 0.0163359 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | −374.396 | + | 374.396i | −0.677026 | + | 0.677026i | ||||
\(554\) | 509.371i | 0.919443i | ||||||||
\(555\) | −129.983 | − | 65.4394i | −0.234203 | − | 0.117909i | ||||
\(556\) | 48.8964 | 0.0879433 | ||||||||
\(557\) | 567.369 | + | 567.369i | 1.01862 | + | 1.01862i | 0.999823 | + | 0.0187923i | \(0.00598211\pi\) |
0.0187923 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(558\) | −54.4243 | + | 54.4243i | −0.0975346 | + | 0.0975346i | ||||
\(559\) | 967.485i | 1.73074i | ||||||||
\(560\) | −74.1031 | − | 224.367i | −0.132327 | − | 0.400655i | ||||
\(561\) | 640.623 | 1.14193 | ||||||||
\(562\) | 438.626 | + | 438.626i | 0.780472 | + | 0.780472i | ||||
\(563\) | −156.606 | + | 156.606i | −0.278164 | + | 0.278164i | −0.832376 | − | 0.554212i | \(-0.813020\pi\) |
0.554212 | + | 0.832376i | \(0.313020\pi\) | |||||||
\(564\) | 301.271i | 0.534169i | ||||||||
\(565\) | 816.505 | − | 269.672i | 1.44514 | − | 0.477296i | ||||
\(566\) | −170.666 | −0.301529 | ||||||||
\(567\) | 75.1861 | + | 75.1861i | 0.132603 | + | 0.132603i | ||||
\(568\) | −178.638 | + | 178.638i | −0.314504 | + | 0.314504i | ||||
\(569\) | − | 331.356i | − | 0.582347i | −0.956670 | − | 0.291174i | \(-0.905954\pi\) | ||
0.956670 | − | 0.291174i | \(-0.0940458\pi\) | |||||||
\(570\) | 15.8515 | − | 31.4860i | 0.0278097 | − | 0.0552386i | ||||
\(571\) | −859.490 | −1.50524 | −0.752618 | − | 0.658457i | \(-0.771209\pi\) | ||||
−0.752618 | + | 0.658457i | \(0.771209\pi\) | |||||||
\(572\) | 385.354 | + | 385.354i | 0.673696 | + | 0.673696i | ||||
\(573\) | 455.366 | − | 455.366i | 0.794705 | − | 0.794705i | ||||
\(574\) | − | 1206.92i | − | 2.10266i | ||||||
\(575\) | 118.596 | + | 17.6092i | 0.206253 | + | 0.0306247i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 20.7204 | + | 20.7204i | 0.0359106 | + | 0.0359106i | 0.724834 | − | 0.688923i | \(-0.241916\pi\) |
−0.688923 | + | 0.724834i | \(0.741916\pi\) | |||||||
\(578\) | 160.977 | − | 160.977i | 0.278507 | − | 0.278507i | ||||
\(579\) | − | 330.803i | − | 0.571336i | ||||||
\(580\) | −27.9326 | − | 14.0626i | −0.0481597 | − | 0.0242459i | ||||
\(581\) | 27.3336 | 0.0470457 | ||||||||
\(582\) | 130.719 | + | 130.719i | 0.224604 | + | 0.224604i | ||||
\(583\) | 750.541 | − | 750.541i | 1.28738 | − | 1.28738i | ||||
\(584\) | 76.0175i | 0.130167i | ||||||||
\(585\) | 73.5166 | + | 222.591i | 0.125669 | + | 0.380497i | ||||
\(586\) | 133.143 | 0.227207 | ||||||||
\(587\) | −103.084 | − | 103.084i | −0.175612 | − | 0.175612i | 0.613828 | − | 0.789440i | \(-0.289629\pi\) |
−0.789440 | + | 0.613828i | \(0.789629\pi\) | |||||||
\(588\) | 221.873 | − | 221.873i | 0.377334 | − | 0.377334i | ||||
\(589\) | 52.2154i | 0.0886509i | ||||||||
\(590\) | 405.814 | − | 134.031i | 0.687820 | − | 0.227171i | ||||
\(591\) | 318.258 | 0.538508 | ||||||||
\(592\) | 47.5286 | + | 47.5286i | 0.0802849 | + | 0.0802849i | ||||
\(593\) | 489.343 | − | 489.343i | 0.825199 | − | 0.825199i | −0.161649 | − | 0.986848i | \(-0.551681\pi\) |
0.986848 | + | 0.161649i | \(0.0516814\pi\) | |||||||
\(594\) | − | 128.128i | − | 0.215703i | ||||||
\(595\) | 563.474 | − | 1119.23i | 0.947015 | − | 1.88106i | ||||
\(596\) | −377.062 | −0.632654 | ||||||||
\(597\) | 234.176 | + | 234.176i | 0.392254 | + | 0.392254i | ||||
\(598\) | −74.9484 | + | 74.9484i | −0.125332 | + | 0.125332i | ||||
\(599\) | − | 351.503i | − | 0.586816i | −0.955987 | − | 0.293408i | \(-0.905211\pi\) | ||
0.955987 | − | 0.293408i | \(-0.0947894\pi\) | |||||||
\(600\) | −98.3828 | + | 72.9440i | −0.163971 | + | 0.121573i | ||||
\(601\) | −985.264 | −1.63937 | −0.819687 | − | 0.572811i | \(-0.805853\pi\) | ||||
−0.819687 | + | 0.572811i | \(0.805853\pi\) | |||||||
\(602\) | −731.402 | − | 731.402i | −1.21495 | − | 1.21495i | ||||
\(603\) | 182.533 | − | 182.533i | 0.302708 | − | 0.302708i | ||||
\(604\) | 352.178i | 0.583077i | ||||||||
\(605\) | −817.333 | − | 411.483i | −1.35096 | − | 0.680138i | ||||
\(606\) | −88.1347 | −0.145437 | ||||||||
\(607\) | 167.150 | + | 167.150i | 0.275371 | + | 0.275371i | 0.831258 | − | 0.555887i | \(-0.187621\pi\) |
−0.555887 | + | 0.831258i | \(0.687621\pi\) | |||||||
\(608\) | −11.5130 | + | 11.5130i | −0.0189358 | + | 0.0189358i | ||||
\(609\) | − | 63.9938i | − | 0.105080i | ||||||
\(610\) | 3.04803 | + | 9.22871i | 0.00499677 | + | 0.0151290i | ||||
\(611\) | −1359.14 | −2.22446 | ||||||||
\(612\) | −89.9977 | − | 89.9977i | −0.147055 | − | 0.147055i | ||||
\(613\) | 50.3714 | − | 50.3714i | 0.0821719 | − | 0.0821719i | −0.664826 | − | 0.746998i | \(-0.731494\pi\) |
0.746998 | + | 0.664826i | \(0.231494\pi\) | |||||||
\(614\) | 584.537i | 0.952015i | ||||||||
\(615\) | −594.023 | + | 196.192i | −0.965892 | + | 0.319012i | ||||
\(616\) | −582.642 | −0.945848 | ||||||||
\(617\) | −318.895 | − | 318.895i | −0.516848 | − | 0.516848i | 0.399768 | − | 0.916616i | \(-0.369091\pi\) |
−0.916616 | + | 0.399768i | \(0.869091\pi\) | |||||||
\(618\) | −188.065 | + | 188.065i | −0.304312 | + | 0.304312i | ||||
\(619\) | 316.148i | 0.510741i | 0.966843 | + | 0.255370i | \(0.0821974\pi\) | ||||
−0.966843 | + | 0.255370i | \(0.917803\pi\) | |||||||
\(620\) | 81.5774 | − | 162.038i | 0.131577 | − | 0.261351i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 81.4097 | + | 81.4097i | 0.130884 | + | 0.130884i | ||||
\(623\) | 138.934 | − | 138.934i | 0.223007 | − | 0.223007i | ||||
\(624\) | − | 108.273i | − | 0.173514i | ||||||
\(625\) | −181.598 | + | 598.036i | −0.290556 | + | 0.956858i | ||||
\(626\) | −294.183 | −0.469941 | ||||||||
\(627\) | −61.4637 | − | 61.4637i | −0.0980283 | − | 0.0980283i | ||||
\(628\) | 64.8248 | − | 64.8248i | 0.103224 | − | 0.103224i | ||||
\(629\) | 356.456i | 0.566702i | ||||||||
\(630\) | −223.852 | − | 112.698i | −0.355321 | − | 0.178885i | ||||
\(631\) | 605.041 | 0.958861 | 0.479430 | − | 0.877580i | \(-0.340843\pi\) | ||||
0.479430 | + | 0.877580i | \(0.340843\pi\) | |||||||
\(632\) | −89.6325 | − | 89.6325i | −0.141824 | − | 0.141824i | ||||
\(633\) | 20.9333 | − | 20.9333i | 0.0330700 | − | 0.0330700i | ||||
\(634\) | − | 103.121i | − | 0.162651i | ||||||
\(635\) | 175.935 | + | 532.691i | 0.277064 | + | 0.838884i | ||||
\(636\) | −210.879 | −0.331571 | ||||||||
\(637\) | 1000.95 | + | 1000.95i | 1.57135 | + | 1.57135i | ||||
\(638\) | −54.5273 | + | 54.5273i | −0.0854659 | + | 0.0854659i | ||||
\(639\) | 267.957i | 0.419338i | ||||||||
\(640\) | 53.7147 | − | 17.7407i | 0.0839292 | − | 0.0277199i | ||||
\(641\) | −465.040 | −0.725491 | −0.362745 | − | 0.931888i | \(-0.618161\pi\) | ||||
−0.362745 | + | 0.931888i | \(0.618161\pi\) | |||||||
\(642\) | 274.199 | + | 274.199i | 0.427101 | + | 0.427101i | ||||
\(643\) | −348.885 | + | 348.885i | −0.542590 | + | 0.542590i | −0.924287 | − | 0.381697i | \(-0.875340\pi\) |
0.381697 | + | 0.924287i | \(0.375340\pi\) | |||||||
\(644\) | − | 113.319i | − | 0.175962i | ||||||
\(645\) | −241.088 | + | 478.874i | −0.373779 | + | 0.742441i | ||||
\(646\) | −86.3449 | −0.133661 | ||||||||
\(647\) | −190.931 | − | 190.931i | −0.295102 | − | 0.295102i | 0.543990 | − | 0.839092i | \(-0.316913\pi\) |
−0.839092 | + | 0.543990i | \(0.816913\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 1053.83i | − | 1.62377i | ||||||
\(650\) | −329.077 | − | 443.840i | −0.506272 | − | 0.682831i | ||||
\(651\) | 371.229 | 0.570245 | ||||||||
\(652\) | 171.167 | + | 171.167i | 0.262526 | + | 0.262526i | ||||
\(653\) | −149.378 | + | 149.378i | −0.228756 | + | 0.228756i | −0.812173 | − | 0.583417i | \(-0.801715\pi\) |
0.583417 | + | 0.812173i | \(0.301715\pi\) | |||||||
\(654\) | 507.789i | 0.776436i | ||||||||
\(655\) | −343.983 | − | 173.177i | −0.525165 | − | 0.264393i | ||||
\(656\) | 288.945 | 0.440465 | ||||||||
\(657\) | 57.0131 | + | 57.0131i | 0.0867780 | + | 0.0867780i | ||||
\(658\) | 1027.49 | − | 1027.49i | 1.56153 | − | 1.56153i | ||||
\(659\) | − | 577.391i | − | 0.876163i | −0.898935 | − | 0.438081i | \(-0.855658\pi\) | ||
0.898935 | − | 0.438081i | \(-0.144342\pi\) | |||||||
\(660\) | 94.7116 | + | 286.764i | 0.143502 | + | 0.434492i | ||||
\(661\) | 734.430 | 1.11109 | 0.555545 | − | 0.831487i | \(-0.312510\pi\) | ||||
0.555545 | + | 0.831487i | \(0.312510\pi\) | |||||||
\(662\) | 445.932 | + | 445.932i | 0.673614 | + | 0.673614i | ||||
\(663\) | 406.012 | − | 406.012i | 0.612386 | − | 0.612386i | ||||
\(664\) | 6.54382i | 0.00985515i | ||||||||
\(665\) | −161.445 | + | 53.3216i | −0.242775 | + | 0.0801828i | ||||
\(666\) | 71.2929 | 0.107046 | ||||||||
\(667\) | −10.6051 | − | 10.6051i | −0.0158997 | − | 0.0158997i | ||||
\(668\) | −137.937 | + | 137.937i | −0.206492 | + | 0.206492i | ||||
\(669\) | − | 134.425i | − | 0.200934i | ||||||
\(670\) | −273.601 | + | 543.456i | −0.408360 | + | 0.811129i | ||||
\(671\) | 23.9654 | 0.0357160 | ||||||||
\(672\) | 81.8523 | + | 81.8523i | 0.121804 | + | 0.121804i | ||||
\(673\) | −310.291 | + | 310.291i | −0.461057 | + | 0.461057i | −0.899002 | − | 0.437945i | \(-0.855706\pi\) |
0.437945 | + | 0.899002i | \(0.355706\pi\) | |||||||
\(674\) | 357.949i | 0.531081i | ||||||||
\(675\) | −19.0791 | + | 128.495i | −0.0282653 | + | 0.190363i | ||||
\(676\) | 150.457 | 0.222570 | ||||||||
\(677\) | 474.216 | + | 474.216i | 0.700467 | + | 0.700467i | 0.964511 | − | 0.264044i | \(-0.0850564\pi\) |
−0.264044 | + | 0.964511i | \(0.585056\pi\) | |||||||
\(678\) | −297.873 | + | 297.873i | −0.439341 | + | 0.439341i | ||||
\(679\) | − | 891.640i | − | 1.31317i | ||||||
\(680\) | 267.951 | + | 134.899i | 0.394045 | + | 0.198381i | ||||
\(681\) | 201.480 | 0.295860 | ||||||||
\(682\) | −316.314 | − | 316.314i | −0.463803 | − | 0.463803i | ||||
\(683\) | −640.291 | + | 640.291i | −0.937469 | + | 0.937469i | −0.998157 | − | 0.0606878i | \(-0.980671\pi\) |
0.0606878 | + | 0.998157i | \(0.480671\pi\) | |||||||
\(684\) | 17.2694i | 0.0252477i | ||||||||
\(685\) | −49.7975 | − | 150.775i | −0.0726971 | − | 0.220110i | ||||
\(686\) | −694.705 | −1.01269 | ||||||||
\(687\) | −526.097 | − | 526.097i | −0.765789 | − | 0.765789i | ||||
\(688\) | 175.102 | − | 175.102i | 0.254509 | − | 0.254509i | ||||
\(689\) | − | 951.352i | − | 1.38077i | ||||||
\(690\) | −55.7735 | + | 18.4207i | −0.0808311 | + | 0.0266966i | ||||
\(691\) | 270.091 | 0.390870 | 0.195435 | − | 0.980717i | \(-0.437388\pi\) | ||||
0.195435 | + | 0.980717i | \(0.437388\pi\) | |||||||
\(692\) | 55.9026 | + | 55.9026i | 0.0807841 | + | 0.0807841i | ||||
\(693\) | −436.982 | + | 436.982i | −0.630565 | + | 0.630565i | ||||
\(694\) | 390.651i | 0.562898i | ||||||||
\(695\) | −54.9687 | + | 109.185i | −0.0790917 | + | 0.157100i | ||||
\(696\) | 15.3205 | 0.0220122 | ||||||||
\(697\) | 1083.52 | + | 1083.52i | 1.55454 | + | 1.55454i | ||||
\(698\) | 616.027 | − | 616.027i | 0.882560 | − | 0.882560i | ||||
\(699\) | − | 85.9674i | − | 0.122986i | ||||||
\(700\) | 584.312 | + | 86.7593i | 0.834732 | + | 0.123942i | ||||
\(701\) | −713.112 | −1.01728 | −0.508639 | − | 0.860980i | \(-0.669851\pi\) | ||||
−0.508639 | + | 0.860980i | \(0.669851\pi\) | |||||||
\(702\) | −81.2045 | − | 81.2045i | −0.115676 | − | 0.115676i | ||||
\(703\) | 34.1997 | − | 34.1997i | 0.0486482 | − | 0.0486482i | ||||
\(704\) | − | 139.488i | − | 0.198136i | ||||||
\(705\) | −672.733 | − | 338.685i | −0.954232 | − | 0.480405i | ||||
\(706\) | 485.281 | 0.687366 | ||||||||
\(707\) | 300.584 | + | 300.584i | 0.425155 | + | 0.425155i | ||||
\(708\) | −148.047 | + | 148.047i | −0.209106 | + | 0.209106i | ||||
\(709\) | − | 1353.88i | − | 1.90956i | −0.297314 | − | 0.954780i | \(-0.596091\pi\) | ||
0.297314 | − | 0.954780i | \(-0.403909\pi\) | |||||||
\(710\) | −198.073 | − | 599.718i | −0.278976 | − | 0.844674i | ||||
\(711\) | −134.449 | −0.189098 | ||||||||
\(712\) | 33.2615 | + | 33.2615i | 0.0467156 | + | 0.0467156i | ||||
\(713\) | 61.5206 | − | 61.5206i | 0.0862841 | − | 0.0862841i | ||||
\(714\) | 613.876i | 0.859771i | ||||||||
\(715\) | −1293.70 | + | 427.278i | −1.80937 | + | 0.597592i | ||||
\(716\) | 258.465 | 0.360984 | ||||||||
\(717\) | 133.150 | + | 133.150i | 0.185704 | + | 0.185704i | ||||
\(718\) | −309.086 | + | 309.086i | −0.430482 | + | 0.430482i | ||||
\(719\) | − | 652.637i | − | 0.907701i | −0.891078 | − | 0.453850i | \(-0.850050\pi\) | ||
0.891078 | − | 0.453850i | \(-0.149950\pi\) | |||||||
\(720\) | 26.9805 | − | 53.5915i | 0.0374729 | − | 0.0744327i | ||||
\(721\) | 1282.79 | 1.77919 | ||||||||
\(722\) | −352.716 | − | 352.716i | −0.488526 | − | 0.488526i | ||||
\(723\) | 360.922 | − | 360.922i | 0.499201 | − | 0.499201i | ||||
\(724\) | 87.7063i | 0.121141i | ||||||||
\(725\) | 62.8030 | − | 46.5641i | 0.0866249 | − | 0.0642263i | ||||
\(726\) | 448.291 | 0.617480 | ||||||||
\(727\) | 532.109 | + | 532.109i | 0.731924 | + | 0.731924i | 0.971001 | − | 0.239076i | \(-0.0768446\pi\) |
−0.239076 | + | 0.971001i | \(0.576845\pi\) | |||||||
\(728\) | −369.265 | + | 369.265i | −0.507233 | + | 0.507233i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −169.746 | − | 85.4579i | −0.232528 | − | 0.117066i | ||||
\(731\) | 1313.23 | 1.79649 | ||||||||
\(732\) | −3.36677 | − | 3.36677i | −0.00459942 | − | 0.00459942i | ||||
\(733\) | −486.414 | + | 486.414i | −0.663594 | + | 0.663594i | −0.956225 | − | 0.292631i | \(-0.905469\pi\) |
0.292631 | + | 0.956225i | \(0.405469\pi\) | |||||||
\(734\) | − | 640.363i | − | 0.872429i | ||||||
\(735\) | 246.011 | + | 744.863i | 0.334709 | + | 1.01342i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 1060.88 | + | 1060.88i | 1.43946 | + | 1.43946i | ||||
\(738\) | 216.709 | − | 216.709i | 0.293643 | − | 0.293643i | ||||
\(739\) | − | 161.727i | − | 0.218846i | −0.993995 | − | 0.109423i | \(-0.965100\pi\) | ||
0.993995 | − | 0.109423i | \(-0.0349003\pi\) | |||||||
\(740\) | −159.562 | + | 52.6995i | −0.215624 | + | 0.0712155i | ||||
\(741\) | −77.9086 | −0.105140 | ||||||||
\(742\) | 719.206 | + | 719.206i | 0.969280 | + | 0.969280i | ||||
\(743\) | −993.064 | + | 993.064i | −1.33656 | + | 1.33656i | −0.437192 | + | 0.899368i | \(0.644027\pi\) |
−0.899368 | + | 0.437192i | \(0.855973\pi\) | |||||||
\(744\) | 88.8745i | 0.119455i | ||||||||
\(745\) | 423.888 | − | 841.971i | 0.568977 | − | 1.13016i | ||||
\(746\) | −81.7694 | −0.109610 | ||||||||
\(747\) | 4.90786 | + | 4.90786i | 0.00657010 | + | 0.00657010i | ||||
\(748\) | 523.066 | − | 523.066i | 0.699287 | − | 0.699287i | ||||
\(749\) | − | 1870.31i | − | 2.49708i | ||||||
\(750\) | −52.2820 | − | 301.690i | −0.0697093 | − | 0.402253i | ||||
\(751\) | 158.149 | 0.210585 | 0.105292 | − | 0.994441i | \(-0.466422\pi\) | ||||
0.105292 | + | 0.994441i | \(0.466422\pi\) | |||||||
\(752\) | 245.987 | + | 245.987i | 0.327110 | + | 0.327110i | ||||
\(753\) | −552.850 | + | 552.850i | −0.734196 | + | 0.734196i | ||||
\(754\) | 69.1163i | 0.0916662i | ||||||||
\(755\) | −786.408 | − | 395.914i | −1.04160 | − | 0.524390i | ||||
\(756\) | 122.778 | 0.162405 | ||||||||
\(757\) | −121.557 | − | 121.557i | −0.160577 | − | 0.160577i | 0.622245 | − | 0.782822i | \(-0.286221\pi\) |
−0.782822 | + | 0.622245i | \(0.786221\pi\) | |||||||
\(758\) | 235.010 | − | 235.010i | 0.310040 | − | 0.310040i | ||||
\(759\) | 144.834i | 0.190822i | ||||||||
\(760\) | −12.7655 | − | 38.6509i | −0.0167967 | − | 0.0508565i | ||||
\(761\) | −15.5981 | −0.0204969 | −0.0102484 | − | 0.999947i | \(-0.503262\pi\) | ||||
−0.0102484 | + | 0.999947i | \(0.503262\pi\) | |||||||
\(762\) | −194.334 | − | 194.334i | −0.255031 | − | 0.255031i | ||||
\(763\) | 1731.82 | − | 1731.82i | 2.26975 | − | 2.26975i | ||||
\(764\) | − | 743.610i | − | 0.973311i | ||||||
\(765\) | 302.137 | − | 99.7889i | 0.394951 | − | 0.130443i | ||||
\(766\) | 688.730 | 0.899125 | ||||||||
\(767\) | −667.893 | − | 667.893i | −0.870786 | − | 0.870786i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 744.420i | − | 0.968037i | −0.875058 | − | 0.484018i | \(-0.839177\pi\) | ||
0.875058 | − | 0.484018i | \(-0.160823\pi\) | |||||||
\(770\) | 654.999 | − | 1301.03i | 0.850647 | − | 1.68965i | ||||
\(771\) | 455.380 | 0.590635 | ||||||||
\(772\) | −270.100 | − | 270.100i | −0.349870 | − | 0.349870i | ||||
\(773\) | 157.930 | − | 157.930i | 0.204308 | − | 0.204308i | −0.597535 | − | 0.801843i | \(-0.703853\pi\) |
0.801843 | + | 0.597535i | \(0.203853\pi\) | |||||||
\(774\) | − | 262.653i | − | 0.339345i | ||||||
\(775\) | 270.119 | + | 364.322i | 0.348541 | + | 0.470093i | ||||
\(776\) | 213.464 | 0.275082 | ||||||||
\(777\) | −243.145 | − | 243.145i | −0.312929 | − | 0.312929i | ||||
\(778\) | 522.732 | − | 522.732i | 0.671892 | − | 0.671892i | ||||
\(779\) | − | 207.913i | − | 0.266897i | ||||||
\(780\) | 241.771 | + | 121.719i | 0.309963 | + | 0.156050i | ||||
\(781\) | −1557.37 | −1.99407 | ||||||||
\(782\) | 101.732 | + | 101.732i | 0.130093 | + | 0.130093i | ||||
\(783\) | 11.4904 | − | 11.4904i | 0.0146748 | − | 0.0146748i | ||||
\(784\) | − | 362.316i | − | 0.462138i | ||||||
\(785\) | 71.8774 | + | 217.628i | 0.0915636 | + | 0.277233i | ||||
\(786\) | 188.668 | 0.240035 | ||||||||
\(787\) | −828.951 | − | 828.951i | −1.05330 | − | 1.05330i | −0.998497 | − | 0.0548078i | \(-0.982545\pi\) |
−0.0548078 | − | 0.998497i | \(-0.517455\pi\) | |||||||
\(788\) | 259.857 | − | 259.857i | 0.329767 | − | 0.329767i | ||||
\(789\) | 672.922i | 0.852880i | ||||||||
\(790\) | 300.911 | − | 99.3840i | 0.380900 | − | 0.125803i | ||||
\(791\) | 2031.80 | 2.56865 | ||||||||
\(792\) | −104.616 | − | 104.616i | −0.132091 | − | 0.132091i | ||||
\(793\) | 15.1887 | − | 15.1887i | 0.0191535 | − | 0.0191535i | ||||
\(794\) | 260.078i | 0.327554i | ||||||||
\(795\) | 237.068 | − | 470.889i | 0.298198 | − | 0.592313i | ||||
\(796\) | 382.407 | 0.480411 | ||||||||
\(797\) | −727.382 | − | 727.382i | −0.912650 | − | 0.912650i | 0.0838299 | − | 0.996480i | \(-0.473285\pi\) |
−0.996480 | + | 0.0838299i | \(0.973285\pi\) | |||||||
\(798\) | 58.8976 | − | 58.8976i | 0.0738065 | − | 0.0738065i | ||||
\(799\) | 1844.86i | 2.30896i | ||||||||
\(800\) | −20.7707 | + | 139.888i | −0.0259633 | + | 0.174860i | ||||
\(801\) | 49.8923 | 0.0622875 | ||||||||
\(802\) | −711.927 | − | 711.927i | −0.887690 | − | 0.887690i | ||||
\(803\) | −331.360 | + | 331.360i | −0.412653 | + | 0.412653i | ||||
\(804\) | − | 298.075i | − | 0.370740i | ||||||
\(805\) | 253.040 | + | 127.392i | 0.314335 | + | 0.158251i | ||||
\(806\) | −400.945 | −0.497450 | ||||||||
\(807\) | 523.566 | + | 523.566i | 0.648780 | + | 0.648780i | ||||
\(808\) | −71.9617 | + | 71.9617i | −0.0890615 | + | 0.0890615i | ||||
\(809\) | − | 864.574i | − | 1.06870i | −0.845265 | − | 0.534348i | \(-0.820557\pi\) | ||
0.845265 | − | 0.534348i | \(-0.179443\pi\) | |||||||
\(810\) | −19.9583 | − | 60.4290i | −0.0246399 | − | 0.0746037i | ||||
\(811\) | 840.459 | 1.03632 | 0.518162 | − | 0.855282i | \(-0.326616\pi\) | ||||
0.518162 | + | 0.855282i | \(0.326616\pi\) | |||||||
\(812\) | −52.2507 | − | 52.2507i | −0.0643482 | − | 0.0643482i | ||||
\(813\) | −124.908 | + | 124.908i | −0.153638 | + | 0.153638i | ||||
\(814\) | 414.354i | 0.509035i | ||||||||
\(815\) | −574.637 | + | 189.789i | −0.705076 | + | 0.232870i | ||||
\(816\) | −146.966 | −0.180105 | ||||||||
\(817\) | −125.996 | − | 125.996i | −0.154218 | − | 0.154218i | ||||
\(818\) | 225.265 | − | 225.265i | 0.275385 | − | 0.275385i | ||||
\(819\) | 553.898i | 0.676310i | ||||||||
\(820\) | −324.828 | + | 645.208i | −0.396132 | + | 0.786839i | ||||
\(821\) | −451.960 | −0.550499 | −0.275250 | − | 0.961373i | \(-0.588761\pi\) | ||||
−0.275250 | + | 0.961373i | \(0.588761\pi\) | |||||||
\(822\) | 55.0050 | + | 55.0050i | 0.0669160 | + | 0.0669160i | ||||
\(823\) | 216.013 | − | 216.013i | 0.262470 | − | 0.262470i | −0.563587 | − | 0.826057i | \(-0.690579\pi\) |
0.826057 | + | 0.563587i | \(0.190579\pi\) | |||||||
\(824\) | 307.109i | 0.372705i | ||||||||
\(825\) | −746.813 | − | 110.888i | −0.905228 | − | 0.134409i | ||||
\(826\) | 1009.83 | 1.22256 | ||||||||
\(827\) | 1019.71 | + | 1019.71i | 1.23303 | + | 1.23303i | 0.962795 | + | 0.270232i | \(0.0871004\pi\) |
0.270232 | + | 0.962795i | \(0.412900\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | 306.072i | 0.369206i | 0.982813 | + | 0.184603i | \(0.0590999\pi\) | ||||
−0.982813 | + | 0.184603i | \(0.940900\pi\) | |||||||
\(830\) | −14.6122 | − | 7.35648i | −0.0176051 | − | 0.00886322i | ||||
\(831\) | 623.850 | 0.750722 | ||||||||
\(832\) | −88.4043 | − | 88.4043i | −0.106255 | − | 0.106255i | ||||
\(833\) | 1358.65 | − | 1358.65i | 1.63103 | − | 1.63103i | ||||
\(834\) | − | 59.8857i | − | 0.0718054i | ||||||
\(835\) | −152.943 | − | 463.076i | −0.183166 | − | 0.554582i | ||||
\(836\) | −100.370 | −0.120060 | ||||||||
\(837\) | 66.6559 | + | 66.6559i | 0.0796367 | + | 0.0796367i | ||||
\(838\) | −727.460 | + | 727.460i | −0.868090 | + | 0.868090i | ||||
\(839\) | − | 827.673i | − | 0.986499i | −0.869888 | − | 0.493250i | \(-0.835809\pi\) | ||
0.869888 | − | 0.493250i | \(-0.164191\pi\) | |||||||
\(840\) | −274.792 | + | 90.7573i | −0.327133 | + | 0.108044i | ||||
\(841\) | 831.220 | 0.988371 | ||||||||
\(842\) | −188.423 | − | 188.423i | −0.223781 | − | 0.223781i | ||||
\(843\) | 537.204 | − | 537.204i | 0.637253 | − | 0.637253i | ||||
\(844\) | − | 34.1840i | − | 0.0405024i | ||||||
\(845\) | −169.142 | + | 335.968i | −0.200168 | + | 0.397596i | ||||
\(846\) | 368.981 | 0.436147 | ||||||||
\(847\) | −1528.90 | − | 1528.90i | −1.80508 | − | 1.80508i | ||||
\(848\) | −172.182 | + | 172.182i | −0.203045 | + | 0.203045i | ||||
\(849\) | 209.022i | 0.246198i | ||||||||
\(850\) | −602.454 | + | 446.678i | −0.708769 | + | 0.525503i | ||||
\(851\) | −80.5887 | −0.0946988 | ||||||||
\(852\) | 218.786 | + | 218.786i | 0.256791 | + | 0.256791i | ||||
\(853\) | −438.820 | + | 438.820i | −0.514443 | + | 0.514443i | −0.915885 | − | 0.401442i | \(-0.868509\pi\) |
0.401442 | + | 0.915885i | \(0.368509\pi\) | |||||||
\(854\) | 22.9648i | 0.0268909i | ||||||||
\(855\) | −38.5623 | − | 19.4141i | −0.0451021 | − | 0.0227065i | ||||
\(856\) | 447.764 | 0.523089 | ||||||||
\(857\) | 940.789 | + | 940.789i | 1.09777 | + | 1.09777i | 0.994671 | + | 0.103098i | \(0.0328757\pi\) |
0.103098 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(858\) | 471.960 | − | 471.960i | 0.550070 | − | 0.550070i | ||||
\(859\) | − | 37.9823i | − | 0.0442169i | −0.999756 | − | 0.0221084i | \(-0.992962\pi\) | ||
0.999756 | − | 0.0221084i | \(-0.00703790\pi\) | |||||||
\(860\) | 194.152 | + | 587.846i | 0.225758 | + | 0.683542i | ||||
\(861\) | −1478.17 | −1.71681 | ||||||||
\(862\) | −624.307 | − | 624.307i | −0.724254 | − | 0.724254i | ||||
\(863\) | 995.920 | − | 995.920i | 1.15402 | − | 1.15402i | 0.168282 | − | 0.985739i | \(-0.446178\pi\) |
0.985739 | − | 0.168282i | \(-0.0538221\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −187.674 | + | 61.9844i | −0.216965 | + | 0.0716583i | ||||
\(866\) | −417.257 | −0.481821 | ||||||||
\(867\) | −197.156 | − | 197.156i | −0.227400 | − | 0.227400i | ||||
\(868\) | 303.108 | − | 303.108i | 0.349202 | − | 0.349202i | ||||
\(869\) | − | 781.416i | − | 0.899213i | ||||||
\(870\) | −17.2231 | + | 34.2104i | −0.0197967 | + | 0.0393223i | ||||
\(871\) | 1344.72 | 1.54388 | ||||||||
\(872\) | 414.608 | + | 414.608i | 0.475468 | + | 0.475468i | ||||
\(873\) | 160.098 | − | 160.098i | 0.183388 | − | 0.183388i | ||||
\(874\) | − | 19.5212i | − | 0.0223354i | ||||||
\(875\) | −850.608 | + | 1207.22i | −0.972123 | + | 1.37968i | ||||
\(876\) | 93.1020 | 0.106281 | ||||||||
\(877\) | 475.448 | + | 475.448i | 0.542130 | + | 0.542130i | 0.924153 | − | 0.382023i | \(-0.124773\pi\) |
−0.382023 | + | 0.924153i | \(0.624773\pi\) | |||||||
\(878\) | −555.867 | + | 555.867i | −0.633106 | + | 0.633106i | ||||
\(879\) | − | 163.066i | − | 0.185514i | ||||||
\(880\) | 311.474 | + | 156.810i | 0.353948 | + | 0.178194i | ||||
\(881\) | 1268.64 | 1.44001 | 0.720003 | − | 0.693971i | \(-0.244141\pi\) | ||||
0.720003 | + | 0.693971i | \(0.244141\pi\) | |||||||
\(882\) | −271.737 | − | 271.737i | −0.308092 | − | 0.308092i | ||||
\(883\) | −336.031 | + | 336.031i | −0.380556 | + | 0.380556i | −0.871302 | − | 0.490746i | \(-0.836724\pi\) |
0.490746 | + | 0.871302i | \(0.336724\pi\) | |||||||
\(884\) | − | 663.015i | − | 0.750017i | ||||||
\(885\) | −164.153 | − | 497.018i | −0.185484 | − | 0.561602i | ||||
\(886\) | 958.358 | 1.08167 | ||||||||
\(887\) | −222.340 | − | 222.340i | −0.250665 | − | 0.250665i | 0.570578 | − | 0.821243i | \(-0.306719\pi\) |
−0.821243 | + | 0.570578i | \(0.806719\pi\) | |||||||
\(888\) | 58.2104 | − | 58.2104i | 0.0655523 | − | 0.0655523i | ||||
\(889\) | 1325.55i | 1.49106i | ||||||||
\(890\) | −111.665 | + | 36.8802i | −0.125466 | + | 0.0414384i | ||||
\(891\) | −156.924 | −0.176121 | ||||||||
\(892\) | −109.758 | − | 109.758i | −0.123047 | − | 0.123047i | ||||
\(893\) | 177.002 | − | 177.002i | 0.198211 | − | 0.198211i | ||||
\(894\) | 461.804i | 0.516560i | ||||||||
\(895\) | −290.563 | + | 577.147i | −0.324651 | + | 0.644857i | ||||
\(896\) | 133.664 | 0.149179 | ||||||||
\(897\) | 91.7926 | + | 91.7926i | 0.102333 | + | 0.102333i | ||||
\(898\) | 526.390 | − | 526.390i | 0.586181 | − | 0.586181i | ||||
\(899\) | − | 56.7334i | − | 0.0631072i | ||||||
\(900\) | 89.3378 | + | 120.494i | 0.0992642 | + | 0.133882i | ||||
\(901\) | −1291.33 | −1.43322 | ||||||||
\(902\) | 1259.51 | + | 1259.51i | 1.39635 | + | 1.39635i | ||||
\(903\) | −895.781 | + | 895.781i | −0.992005 | + | 0.992005i | ||||
\(904\) | 486.425i | 0.538080i | ||||||||
\(905\) | −195.847 | − | 98.5983i | −0.216405 | − | 0.108948i | ||||
\(906\) | 431.329 | 0.476080 | ||||||||
\(907\) | 194.442 | + | 194.442i | 0.214379 | + | 0.214379i | 0.806125 | − | 0.591746i | \(-0.201561\pi\) |
−0.591746 | + | 0.806125i | \(0.701561\pi\) | |||||||
\(908\) | 164.508 | − | 164.508i | 0.181176 | − | 0.181176i | ||||
\(909\) | 107.943i | 0.118749i | ||||||||
\(910\) | −409.439 | − | 1239.69i | −0.449933 | − | 1.36229i | ||||
\(911\) | −822.549 | −0.902908 | −0.451454 | − | 0.892294i | \(-0.649094\pi\) | ||||
−0.451454 | + | 0.892294i | \(0.649094\pi\) | |||||||
\(912\) | 14.1004 | + | 14.1004i | 0.0154610 | + | 0.0154610i | ||||
\(913\) | −28.5245 | + | 28.5245i | −0.0312426 | + | 0.0312426i | ||||
\(914\) | − | 381.322i | − | 0.417201i | ||||||
\(915\) | 11.3028 | − | 3.73306i | 0.0123528 | − | 0.00407984i | ||||
\(916\) | −859.113 | −0.937896 | ||||||||
\(917\) | −643.454 | − | 643.454i | −0.701695 | − | 0.701695i | ||||
\(918\) | −110.224 | + | 110.224i | −0.120070 | + | 0.120070i | ||||
\(919\) | 107.710i | 0.117204i | 0.998281 | + | 0.0586020i | \(0.0186643\pi\) | ||||
−0.998281 | + | 0.0586020i | \(0.981336\pi\) | |||||||
\(920\) | −30.4984 | + | 60.5793i | −0.0331505 | + | 0.0658470i | ||||
\(921\) | 715.909 | 0.777317 | ||||||||
\(922\) | 138.301 | + | 138.301i | 0.150001 | + | 0.150001i | ||||
\(923\) | −987.024 | + | 987.024i | −1.06936 | + | 1.06936i | ||||
\(924\) | 713.588i | 0.772281i | ||||||||
\(925\) | 61.7001 | − | 415.542i | 0.0667028 | − | 0.449235i | ||||
\(926\) | −755.714 | −0.816106 | ||||||||
\(927\) | 230.331 | + | 230.331i | 0.248470 | + | 0.248470i | ||||
\(928\) | 12.5091 | − | 12.5091i | 0.0134797 | − | 0.0134797i | ||||
\(929\) | 1205.01i | 1.29710i | 0.761172 | + | 0.648550i | \(0.224624\pi\) | ||||
−0.761172 | + | 0.648550i | \(0.775376\pi\) | |||||||
\(930\) | −198.455 | − | 99.9115i | −0.213393 | − | 0.107432i | ||||
\(931\) | −260.708 | −0.280030 | ||||||||
\(932\) | −70.1921 | − | 70.1921i | −0.0753134 | − | 0.0753134i | ||||
\(933\) | 99.7061 | − | 99.7061i | 0.106866 | − | 0.106866i | ||||
\(934\) | 242.494i | 0.259629i | ||||||||
\(935\) | 579.973 | + | 1756.02i | 0.620292 | + | 1.87810i | ||||
\(936\) | −132.606 | −0.141674 | ||||||||
\(937\) | −71.0492 | − | 71.0492i | −0.0758263 | − | 0.0758263i | 0.668177 | − | 0.744003i | \(-0.267075\pi\) |
−0.744003 | + | 0.668177i | \(0.767075\pi\) | |||||||
\(938\) | −1016.59 | + | 1016.59i | −1.08378 | + | 1.08378i | ||||
\(939\) | 360.299i | 0.383705i | ||||||||
\(940\) | −825.820 | + | 272.749i | −0.878532 | + | 0.290159i | ||||
\(941\) | −163.158 | −0.173387 | −0.0866937 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866937 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(942\) | −79.3939 | − | 79.3939i | −0.0842823 | − | 0.0842823i | ||||
\(943\) | −244.965 | + | 244.965i | −0.259772 | + | 0.259772i | ||||
\(944\) | 241.759i | 0.256101i | ||||||||
\(945\) | −138.026 | + | 274.162i | −0.146059 | + | 0.290118i | ||||
\(946\) | 1526.54 | 1.61368 | ||||||||
\(947\) | 1019.92 | + | 1019.92i | 1.07700 | + | 1.07700i | 0.996777 | + | 0.0802243i | \(0.0255636\pi\) |
0.0802243 | + | 0.996777i | \(0.474436\pi\) | |||||||
\(948\) | −109.777 | + | 109.777i | −0.115798 | + | 0.115798i | ||||
\(949\) | 420.017i | 0.442589i | ||||||||
\(950\) | 100.658 | + | 14.9457i | 0.105955 | + | 0.0157324i | ||||
\(951\) | −126.297 | −0.132804 | ||||||||
\(952\) | 501.228 | + | 501.228i | 0.526500 | + | 0.526500i | ||||
\(953\) | −369.650 | + | 369.650i | −0.387880 | + | 0.387880i | −0.873931 | − | 0.486050i | \(-0.838437\pi\) |
0.486050 | + | 0.873931i | \(0.338437\pi\) | |||||||
\(954\) | 258.273i | 0.270727i | ||||||||
\(955\) | 1660.47 | + | 835.956i | 1.73871 | + | 0.875347i | ||||
\(956\) | 217.432 | 0.227440 | ||||||||
\(957\) | 66.7820 | + | 66.7820i | 0.0697827 | + | 0.0697827i | ||||
\(958\) | −687.235 | + | 687.235i | −0.717364 | + | 0.717364i | ||||
\(959\) | − | 375.190i | − | 0.391231i | ||||||
\(960\) | −21.7278 | − | 65.7868i | −0.0226332 | − | 0.0685279i | ||||
\(961\) | −631.888 | −0.657532 | ||||||||
\(962\) | 262.608 | + | 262.608i | 0.272982 | + | 0.272982i | ||||
\(963\) | 335.823 | − | 335.823i | 0.348726 | − | 0.348726i | ||||
\(964\) | − | 589.383i | − | 0.611394i | ||||||
\(965\) | 906.770 | − | 299.485i | 0.939658 | − | 0.310347i | ||||
\(966\) | −138.787 | −0.143672 | ||||||||
\(967\) | 281.202 | + | 281.202i | 0.290799 | + | 0.290799i | 0.837396 | − | 0.546597i | \(-0.184077\pi\) |
−0.546597 | + | 0.837396i | \(0.684077\pi\) | |||||||
\(968\) | 366.028 | − | 366.028i | 0.378128 | − | 0.378128i | ||||
\(969\) | 105.751i | 0.109134i | ||||||||
\(970\) | −239.973 | + | 476.661i | −0.247395 | + | 0.491403i | ||||
\(971\) | −1264.29 | −1.30205 | −0.651023 | − | 0.759058i | \(-0.725660\pi\) | ||||
−0.651023 | + | 0.759058i | \(0.725660\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −204.241 | + | 204.241i | −0.209908 | + | 0.209908i | ||||
\(974\) | − | 874.226i | − | 0.897563i | ||||||
\(975\) | −543.591 | + | 403.035i | −0.557529 | + | 0.413369i | ||||
\(976\) | −5.49792 | −0.00563311 | ||||||||
\(977\) | −396.137 | − | 396.137i | −0.405463 | − | 0.405463i | 0.474690 | − | 0.880153i | \(-0.342560\pi\) |
−0.880153 | + | 0.474690i | \(0.842560\pi\) | |||||||
\(978\) | 209.636 | − | 209.636i | 0.214352 | − | 0.214352i | ||||
\(979\) | 289.974i | 0.296194i | ||||||||
\(980\) | 809.046 | + | 407.311i | 0.825557 | + | 0.415624i | ||||
\(981\) | 621.912 | 0.633958 | ||||||||
\(982\) | 129.408 | + | 129.408i | 0.131780 | + | 0.131780i | ||||
\(983\) | −1050.18 | + | 1050.18i | −1.06834 | + | 1.06834i | −0.0708503 | + | 0.997487i | \(0.522571\pi\) |
−0.997487 | + | 0.0708503i | \(0.977429\pi\) | |||||||
\(984\) | − | 353.884i | − | 0.359638i | ||||||
\(985\) | 288.127 | + | 872.382i | 0.292515 | + | 0.885667i | ||||
\(986\) | 93.8161 | 0.0951482 | ||||||||
\(987\) | −1258.41 | − | 1258.41i | −1.27499 | − | 1.27499i | ||||
\(988\) | −63.6121 | + | 63.6121i | −0.0643848 | + | 0.0643848i | ||||
\(989\) | 296.900i | 0.300202i | ||||||||
\(990\) | 351.213 | − | 115.998i | 0.354761 | − | 0.117169i | ||||
\(991\) | 291.520 | 0.294167 | 0.147084 | − | 0.989124i | \(-0.453011\pi\) | ||||
0.147084 | + | 0.989124i | \(0.453011\pi\) | |||||||
\(992\) | 72.5657 | + | 72.5657i | 0.0731509 | + | 0.0731509i | ||||
\(993\) | 546.153 | − | 546.153i | 0.550003 | − | 0.550003i | ||||
\(994\) | − | 1492.35i | − | 1.50135i | ||||||
\(995\) | −429.897 | + | 853.909i | −0.432058 | + | 0.858200i | ||||
\(996\) | 8.01451 | 0.00804670 | ||||||||
\(997\) | −1233.91 | − | 1233.91i | −1.23762 | − | 1.23762i | −0.960969 | − | 0.276655i | \(-0.910774\pi\) |
−0.276655 | − | 0.960969i | \(-0.589226\pi\) | |||||||
\(998\) | −958.920 | + | 958.920i | −0.960842 | + | 0.960842i | ||||
\(999\) | − | 87.3157i | − | 0.0874031i |
(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.b.277.10 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.10 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.10 | yes | 48 | 5.3 | odd | 4 | inner |