Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1121,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.l (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.6 | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.f.1121.5 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45082 | −1.73299 | −0.866494 | − | 0.499187i | \(-0.833632\pi\) | ||||
−0.866494 | + | 0.499187i | \(0.833632\pi\) | |||||||
\(3\) | 0.877309 | − | 1.49343i | 0.506514 | − | 0.862231i | ||||
\(4\) | 4.00650 | 2.00325 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −2.15012 | + | 3.66012i | −0.877784 | + | 1.49424i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −4.91756 | −1.73862 | ||||||||
\(9\) | −1.46066 | − | 2.62040i | −0.486886 | − | 0.873465i | ||||
\(10\) | − | 2.45082i | − | 0.775016i | ||||||
\(11\) | −0.828579 | − | 3.21146i | −0.249826 | − | 0.968291i | ||||
\(12\) | 3.51494 | − | 5.98342i | 1.01468 | − | 1.72727i | ||||
\(13\) | − | 6.76117i | − | 1.87521i | −0.347700 | − | 0.937606i | \(-0.613037\pi\) | ||
0.347700 | − | 0.937606i | \(-0.386963\pi\) | |||||||
\(14\) | − | 2.45082i | − | 0.655008i | ||||||
\(15\) | 1.49343 | + | 0.877309i | 0.385602 | + | 0.226520i | ||||
\(16\) | 4.03905 | 1.00976 | ||||||||
\(17\) | −5.22115 | −1.26631 | −0.633157 | − | 0.774023i | \(-0.718241\pi\) | ||||
−0.633157 | + | 0.774023i | \(0.718241\pi\) | |||||||
\(18\) | 3.57981 | + | 6.42211i | 0.843768 | + | 1.51371i | ||||
\(19\) | 6.21697i | 1.42627i | 0.701026 | + | 0.713136i | \(0.252726\pi\) | ||||
−0.701026 | + | 0.713136i | \(0.747274\pi\) | |||||||
\(20\) | 4.00650i | 0.895881i | ||||||||
\(21\) | 1.49343 | + | 0.877309i | 0.325893 | + | 0.191444i | ||||
\(22\) | 2.03069 | + | 7.87069i | 0.432945 | + | 1.67804i | ||||
\(23\) | 3.22384i | 0.672216i | 0.941823 | + | 0.336108i | \(0.109111\pi\) | ||||
−0.941823 | + | 0.336108i | \(0.890889\pi\) | |||||||
\(24\) | −4.31422 | + | 7.34403i | −0.880637 | + | 1.49909i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 16.5704i | 3.24972i | ||||||||
\(27\) | −5.19482 | − | 0.117506i | −0.999744 | − | 0.0226141i | ||||
\(28\) | 4.00650i | 0.757157i | ||||||||
\(29\) | 4.08004 | 0.757644 | 0.378822 | − | 0.925469i | \(-0.376329\pi\) | ||||
0.378822 | + | 0.925469i | \(0.376329\pi\) | |||||||
\(30\) | −3.66012 | − | 2.15012i | −0.668243 | − | 0.392557i | ||||
\(31\) | 2.16563 | 0.388959 | 0.194479 | − | 0.980907i | \(-0.437698\pi\) | ||||
0.194479 | + | 0.980907i | \(0.437698\pi\) | |||||||
\(32\) | −0.0638312 | −0.0112839 | ||||||||
\(33\) | −5.52300 | − | 1.58002i | −0.961431 | − | 0.275046i | ||||
\(34\) | 12.7961 | 2.19451 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −5.85213 | − | 10.4986i | −0.975355 | − | 1.74977i | ||||
\(37\) | −8.03446 | −1.32086 | −0.660428 | − | 0.750889i | \(-0.729625\pi\) | ||||
−0.660428 | + | 0.750889i | \(0.729625\pi\) | |||||||
\(38\) | − | 15.2367i | − | 2.47171i | ||||||
\(39\) | −10.0973 | − | 5.93164i | −1.61687 | − | 0.949822i | ||||
\(40\) | − | 4.91756i | − | 0.777535i | ||||||
\(41\) | −5.40856 | −0.844675 | −0.422338 | − | 0.906439i | \(-0.638790\pi\) | ||||
−0.422338 | + | 0.906439i | \(0.638790\pi\) | |||||||
\(42\) | −3.66012 | − | 2.15012i | −0.564769 | − | 0.331771i | ||||
\(43\) | − | 6.96368i | − | 1.06195i | −0.847387 | − | 0.530976i | \(-0.821825\pi\) | ||
0.847387 | − | 0.530976i | \(-0.178175\pi\) | |||||||
\(44\) | −3.31970 | − | 12.8667i | −0.500464 | − | 1.93973i | ||||
\(45\) | 2.62040 | − | 1.46066i | 0.390626 | − | 0.217742i | ||||
\(46\) | − | 7.90103i | − | 1.16494i | ||||||
\(47\) | 7.86819i | 1.14769i | 0.818963 | + | 0.573847i | \(0.194549\pi\) | ||||
−0.818963 | + | 0.573847i | \(0.805451\pi\) | |||||||
\(48\) | 3.54349 | − | 6.03203i | 0.511459 | − | 0.870648i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.45082 | 0.346598 | ||||||||
\(51\) | −4.58056 | + | 7.79741i | −0.641407 | + | 1.09186i | ||||
\(52\) | − | 27.0886i | − | 3.75652i | ||||||
\(53\) | − | 7.52801i | − | 1.03405i | −0.855970 | − | 0.517026i | \(-0.827039\pi\) | ||
0.855970 | − | 0.517026i | \(-0.172961\pi\) | |||||||
\(54\) | 12.7316 | + | 0.287987i | 1.73255 | + | 0.0391900i | ||||
\(55\) | 3.21146 | − | 0.828579i | 0.433033 | − | 0.111726i | ||||
\(56\) | − | 4.91756i | − | 0.657137i | ||||||
\(57\) | 9.28461 | + | 5.45421i | 1.22978 | + | 0.722427i | ||||
\(58\) | −9.99943 | −1.31299 | ||||||||
\(59\) | 4.90450i | 0.638512i | 0.947669 | + | 0.319256i | \(0.103433\pi\) | ||||
−0.947669 | + | 0.319256i | \(0.896567\pi\) | |||||||
\(60\) | 5.98342 | + | 3.51494i | 0.772457 | + | 0.453777i | ||||
\(61\) | 5.13402i | 0.657344i | 0.944444 | + | 0.328672i | \(0.106601\pi\) | ||||
−0.944444 | + | 0.328672i | \(0.893399\pi\) | |||||||
\(62\) | −5.30756 | −0.674061 | ||||||||
\(63\) | 2.62040 | − | 1.46066i | 0.330139 | − | 0.184026i | ||||
\(64\) | −7.92165 | −0.990207 | ||||||||
\(65\) | 6.76117 | 0.838620 | ||||||||
\(66\) | 13.5359 | + | 3.87233i | 1.66615 | + | 0.476651i | ||||
\(67\) | −10.7537 | −1.31377 | −0.656886 | − | 0.753990i | \(-0.728127\pi\) | ||||
−0.656886 | + | 0.753990i | \(0.728127\pi\) | |||||||
\(68\) | −20.9185 | −2.53675 | ||||||||
\(69\) | 4.81457 | + | 2.82830i | 0.579606 | + | 0.340487i | ||||
\(70\) | 2.45082 | 0.292929 | ||||||||
\(71\) | 8.09497i | 0.960696i | 0.877078 | + | 0.480348i | \(0.159490\pi\) | ||||
−0.877078 | + | 0.480348i | \(0.840510\pi\) | |||||||
\(72\) | 7.18288 | + | 12.8860i | 0.846511 | + | 1.51863i | ||||
\(73\) | − | 10.2197i | − | 1.19613i | −0.801448 | − | 0.598064i | \(-0.795937\pi\) | ||
0.801448 | − | 0.598064i | \(-0.204063\pi\) | |||||||
\(74\) | 19.6910 | 2.28903 | ||||||||
\(75\) | −0.877309 | + | 1.49343i | −0.101303 | + | 0.172446i | ||||
\(76\) | 24.9083i | 2.85718i | ||||||||
\(77\) | 3.21146 | − | 0.828579i | 0.365980 | − | 0.0944253i | ||||
\(78\) | 24.7467 | + | 14.5373i | 2.80201 | + | 1.64603i | ||||
\(79\) | − | 10.3009i | − | 1.15894i | −0.814992 | − | 0.579472i | \(-0.803259\pi\) | ||
0.814992 | − | 0.579472i | \(-0.196741\pi\) | |||||||
\(80\) | 4.03905i | 0.451579i | ||||||||
\(81\) | −4.73295 | + | 7.65501i | −0.525884 | + | 0.850557i | ||||
\(82\) | 13.2554 | 1.46381 | ||||||||
\(83\) | −4.27488 | −0.469229 | −0.234615 | − | 0.972088i | \(-0.575383\pi\) | ||||
−0.234615 | + | 0.972088i | \(0.575383\pi\) | |||||||
\(84\) | 5.98342 | + | 3.51494i | 0.652845 | + | 0.383511i | ||||
\(85\) | − | 5.22115i | − | 0.566313i | ||||||
\(86\) | 17.0667i | 1.84035i | ||||||||
\(87\) | 3.57945 | − | 6.09325i | 0.383758 | − | 0.653265i | ||||
\(88\) | 4.07459 | + | 15.7925i | 0.434353 | + | 1.68349i | ||||
\(89\) | − | 7.30053i | − | 0.773854i | −0.922110 | − | 0.386927i | \(-0.873536\pi\) | ||
0.922110 | − | 0.386927i | \(-0.126464\pi\) | |||||||
\(90\) | −6.42211 | + | 3.57981i | −0.676950 | + | 0.377345i | ||||
\(91\) | 6.76117 | 0.708763 | ||||||||
\(92\) | 12.9163i | 1.34662i | ||||||||
\(93\) | 1.89993 | − | 3.23421i | 0.197013 | − | 0.335372i | ||||
\(94\) | − | 19.2835i | − | 1.98894i | ||||||
\(95\) | −6.21697 | −0.637848 | ||||||||
\(96\) | −0.0559996 | + | 0.0953273i | −0.00571544 | + | 0.00972930i | ||||
\(97\) | −15.4968 | −1.57347 | −0.786733 | − | 0.617294i | \(-0.788229\pi\) | ||||
−0.786733 | + | 0.617294i | \(0.788229\pi\) | |||||||
\(98\) | 2.45082 | 0.247570 | ||||||||
\(99\) | −7.20502 | + | 6.86205i | −0.724132 | + | 0.689662i | ||||
\(100\) | −4.00650 | −0.400650 | ||||||||
\(101\) | −3.84761 | −0.382851 | −0.191426 | − | 0.981507i | \(-0.561311\pi\) | ||||
−0.191426 | + | 0.981507i | \(0.561311\pi\) | |||||||
\(102\) | 11.2261 | − | 19.1100i | 1.11155 | − | 1.89217i | ||||
\(103\) | 8.87110 | 0.874096 | 0.437048 | − | 0.899438i | \(-0.356024\pi\) | ||||
0.437048 | + | 0.899438i | \(0.356024\pi\) | |||||||
\(104\) | 33.2485i | 3.26028i | ||||||||
\(105\) | −0.877309 | + | 1.49343i | −0.0856166 | + | 0.145744i | ||||
\(106\) | 18.4498i | 1.79200i | ||||||||
\(107\) | −11.0644 | −1.06964 | −0.534820 | − | 0.844966i | \(-0.679621\pi\) | ||||
−0.534820 | + | 0.844966i | \(0.679621\pi\) | |||||||
\(108\) | −20.8131 | − | 0.470790i | −2.00274 | − | 0.0453018i | ||||
\(109\) | 15.3821i | 1.47333i | 0.676256 | + | 0.736667i | \(0.263602\pi\) | ||||
−0.676256 | + | 0.736667i | \(0.736398\pi\) | |||||||
\(110\) | −7.87069 | + | 2.03069i | −0.750441 | + | 0.193619i | ||||
\(111\) | −7.04870 | + | 11.9989i | −0.669033 | + | 1.13888i | ||||
\(112\) | 4.03905i | 0.381654i | ||||||||
\(113\) | 2.90261i | 0.273054i | 0.990636 | + | 0.136527i | \(0.0435941\pi\) | ||||
−0.990636 | + | 0.136527i | \(0.956406\pi\) | |||||||
\(114\) | −22.7549 | − | 13.3673i | −2.13119 | − | 1.25196i | ||||
\(115\) | −3.22384 | −0.300624 | ||||||||
\(116\) | 16.3467 | 1.51775 | ||||||||
\(117\) | −17.7170 | + | 9.87577i | −1.63793 | + | 0.913015i | ||||
\(118\) | − | 12.0200i | − | 1.10653i | ||||||
\(119\) | − | 5.22115i | − | 0.478622i | ||||||
\(120\) | −7.34403 | − | 4.31422i | −0.670415 | − | 0.393833i | ||||
\(121\) | −9.62691 | + | 5.32189i | −0.875174 | + | 0.483808i | ||||
\(122\) | − | 12.5825i | − | 1.13917i | ||||||
\(123\) | −4.74498 | + | 8.07730i | −0.427840 | + | 0.728306i | ||||
\(124\) | 8.67660 | 0.779182 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −6.42211 | + | 3.57981i | −0.572127 | + | 0.318915i | ||||
\(127\) | − | 8.67052i | − | 0.769384i | −0.923045 | − | 0.384692i | \(-0.874308\pi\) | ||
0.923045 | − | 0.384692i | \(-0.125692\pi\) | |||||||
\(128\) | 19.5422 | 1.72730 | ||||||||
\(129\) | −10.3998 | − | 6.10930i | −0.915648 | − | 0.537894i | ||||
\(130\) | −16.5704 | −1.45332 | ||||||||
\(131\) | −1.26696 | −0.110695 | −0.0553476 | − | 0.998467i | \(-0.517627\pi\) | ||||
−0.0553476 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(132\) | −22.1279 | − | 6.33034i | −1.92599 | − | 0.550985i | ||||
\(133\) | −6.21697 | −0.539080 | ||||||||
\(134\) | 26.3553 | 2.27675 | ||||||||
\(135\) | 0.117506 | − | 5.19482i | 0.0101133 | − | 0.447099i | ||||
\(136\) | 25.6753 | 2.20164 | ||||||||
\(137\) | − | 7.91882i | − | 0.676550i | −0.941047 | − | 0.338275i | \(-0.890157\pi\) | ||
0.941047 | − | 0.338275i | \(-0.109843\pi\) | |||||||
\(138\) | −11.7996 | − | 6.93164i | −1.00445 | − | 0.590060i | ||||
\(139\) | 8.44234i | 0.716070i | 0.933708 | + | 0.358035i | \(0.116553\pi\) | ||||
−0.933708 | + | 0.358035i | \(0.883447\pi\) | |||||||
\(140\) | −4.00650 | −0.338611 | ||||||||
\(141\) | 11.7506 | + | 6.90283i | 0.989577 | + | 0.581323i | ||||
\(142\) | − | 19.8393i | − | 1.66488i | ||||||
\(143\) | −21.7132 | + | 5.60216i | −1.81575 | + | 0.468476i | ||||
\(144\) | −5.89967 | − | 10.5839i | −0.491639 | − | 0.881992i | ||||
\(145\) | 4.08004i | 0.338829i | ||||||||
\(146\) | 25.0467i | 2.07288i | ||||||||
\(147\) | −0.877309 | + | 1.49343i | −0.0723592 | + | 0.123176i | ||||
\(148\) | −32.1901 | −2.64601 | ||||||||
\(149\) | 3.70906 | 0.303858 | 0.151929 | − | 0.988391i | \(-0.451452\pi\) | ||||
0.151929 | + | 0.988391i | \(0.451452\pi\) | |||||||
\(150\) | 2.15012 | − | 3.66012i | 0.175557 | − | 0.298848i | ||||
\(151\) | − | 3.84108i | − | 0.312583i | −0.987711 | − | 0.156291i | \(-0.950046\pi\) | ||
0.987711 | − | 0.156291i | \(-0.0499539\pi\) | |||||||
\(152\) | − | 30.5724i | − | 2.47975i | ||||||
\(153\) | 7.62632 | + | 13.6815i | 0.616551 | + | 1.10608i | ||||
\(154\) | −7.87069 | + | 2.03069i | −0.634238 | + | 0.163638i | ||||
\(155\) | 2.16563i | 0.173948i | ||||||||
\(156\) | −40.4550 | − | 23.7651i | −3.23899 | − | 1.90273i | ||||
\(157\) | −4.25023 | −0.339206 | −0.169603 | − | 0.985513i | \(-0.554248\pi\) | ||||
−0.169603 | + | 0.985513i | \(0.554248\pi\) | |||||||
\(158\) | 25.2457i | 2.00844i | ||||||||
\(159\) | −11.2426 | − | 6.60439i | −0.891592 | − | 0.523762i | ||||
\(160\) | − | 0.0638312i | − | 0.00504630i | ||||||
\(161\) | −3.22384 | −0.254074 | ||||||||
\(162\) | 11.5996 | − | 18.7610i | 0.911350 | − | 1.47401i | ||||
\(163\) | 16.3126 | 1.27770 | 0.638850 | − | 0.769331i | \(-0.279410\pi\) | ||||
0.638850 | + | 0.769331i | \(0.279410\pi\) | |||||||
\(164\) | −21.6694 | −1.69210 | ||||||||
\(165\) | 1.58002 | − | 5.52300i | 0.123004 | − | 0.429965i | ||||
\(166\) | 10.4769 | 0.813169 | ||||||||
\(167\) | 1.33486 | 0.103295 | 0.0516474 | − | 0.998665i | \(-0.483553\pi\) | ||||
0.0516474 | + | 0.998665i | \(0.483553\pi\) | |||||||
\(168\) | −7.34403 | − | 4.31422i | −0.566604 | − | 0.332849i | ||||
\(169\) | −32.7135 | −2.51642 | ||||||||
\(170\) | 12.7961i | 0.981414i | ||||||||
\(171\) | 16.2909 | − | 9.08088i | 1.24580 | − | 0.694432i | ||||
\(172\) | − | 27.9000i | − | 2.12736i | ||||||
\(173\) | −12.3959 | −0.942446 | −0.471223 | − | 0.882014i | \(-0.656187\pi\) | ||||
−0.471223 | + | 0.882014i | \(0.656187\pi\) | |||||||
\(174\) | −8.77259 | + | 14.9334i | −0.665048 | + | 1.13210i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | −3.34667 | − | 12.9712i | −0.252265 | − | 0.977743i | ||||
\(177\) | 7.32453 | + | 4.30276i | 0.550545 | + | 0.323415i | ||||
\(178\) | 17.8922i | 1.34108i | ||||||||
\(179\) | − | 21.9783i | − | 1.64274i | −0.570397 | − | 0.821369i | \(-0.693210\pi\) | ||
0.570397 | − | 0.821369i | \(-0.306790\pi\) | |||||||
\(180\) | 10.4986 | − | 5.85213i | 0.782521 | − | 0.436192i | ||||
\(181\) | 20.1572 | 1.49827 | 0.749136 | − | 0.662416i | \(-0.230469\pi\) | ||||
0.749136 | + | 0.662416i | \(0.230469\pi\) | |||||||
\(182\) | −16.5704 | −1.22828 | ||||||||
\(183\) | 7.66729 | + | 4.50412i | 0.566783 | + | 0.332954i | ||||
\(184\) | − | 15.8534i | − | 1.16873i | ||||||
\(185\) | − | 8.03446i | − | 0.590705i | ||||||
\(186\) | −4.65637 | + | 7.92647i | −0.341422 | + | 0.581197i | ||||
\(187\) | 4.32613 | + | 16.7675i | 0.316358 | + | 1.22616i | ||||
\(188\) | 31.5239i | 2.29912i | ||||||||
\(189\) | 0.117506 | − | 5.19482i | 0.00854734 | − | 0.377868i | ||||
\(190\) | 15.2367 | 1.10538 | ||||||||
\(191\) | − | 13.4860i | − | 0.975814i | −0.872896 | − | 0.487907i | \(-0.837761\pi\) | ||
0.872896 | − | 0.487907i | \(-0.162239\pi\) | |||||||
\(192\) | −6.94974 | + | 11.8304i | −0.501554 | + | 0.853787i | ||||
\(193\) | 19.5427i | 1.40671i | 0.710837 | + | 0.703357i | \(0.248316\pi\) | ||||
−0.710837 | + | 0.703357i | \(0.751684\pi\) | |||||||
\(194\) | 37.9799 | 2.72680 | ||||||||
\(195\) | 5.93164 | − | 10.0973i | 0.424773 | − | 0.723085i | ||||
\(196\) | −4.00650 | −0.286179 | ||||||||
\(197\) | −3.89168 | −0.277271 | −0.138635 | − | 0.990343i | \(-0.544272\pi\) | ||||
−0.138635 | + | 0.990343i | \(0.544272\pi\) | |||||||
\(198\) | 17.6582 | − | 16.8176i | 1.25491 | − | 1.19518i | ||||
\(199\) | −15.5753 | −1.10410 | −0.552051 | − | 0.833810i | \(-0.686155\pi\) | ||||
−0.552051 | + | 0.833810i | \(0.686155\pi\) | |||||||
\(200\) | 4.91756 | 0.347724 | ||||||||
\(201\) | −9.43431 | + | 16.0599i | −0.665445 | + | 1.13278i | ||||
\(202\) | 9.42977 | 0.663477 | ||||||||
\(203\) | 4.08004i | 0.286363i | ||||||||
\(204\) | −18.3520 | + | 31.2403i | −1.28490 | + | 2.18726i | ||||
\(205\) | − | 5.40856i | − | 0.377750i | ||||||
\(206\) | −21.7414 | −1.51480 | ||||||||
\(207\) | 8.44772 | − | 4.70892i | 0.587157 | − | 0.327293i | ||||
\(208\) | − | 27.3087i | − | 1.89352i | ||||||
\(209\) | 19.9655 | − | 5.15125i | 1.38105 | − | 0.356320i | ||||
\(210\) | 2.15012 | − | 3.66012i | 0.148373 | − | 0.252572i | ||||
\(211\) | 9.87355i | 0.679723i | 0.940475 | + | 0.339862i | \(0.110380\pi\) | ||||
−0.940475 | + | 0.339862i | \(0.889620\pi\) | |||||||
\(212\) | − | 30.1610i | − | 2.07147i | ||||||
\(213\) | 12.0893 | + | 7.10179i | 0.828343 | + | 0.486606i | ||||
\(214\) | 27.1169 | 1.85367 | ||||||||
\(215\) | 6.96368 | 0.474919 | ||||||||
\(216\) | 25.5459 | + | 0.577846i | 1.73818 | + | 0.0393174i | ||||
\(217\) | 2.16563i | 0.147013i | ||||||||
\(218\) | − | 37.6986i | − | 2.55327i | ||||||
\(219\) | −15.2624 | − | 8.96585i | −1.03134 | − | 0.605856i | ||||
\(220\) | 12.8667 | − | 3.31970i | 0.867473 | − | 0.223814i | ||||
\(221\) | 35.3011i | 2.37461i | ||||||||
\(222\) | 17.2751 | − | 29.4071i | 1.15943 | − | 1.97367i | ||||
\(223\) | −9.08225 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(224\) | − | 0.0638312i | − | 0.00426490i | ||||||
\(225\) | 1.46066 | + | 2.62040i | 0.0973773 | + | 0.174693i | ||||
\(226\) | − | 7.11375i | − | 0.473200i | ||||||
\(227\) | 18.6066 | 1.23496 | 0.617480 | − | 0.786587i | \(-0.288154\pi\) | ||||
0.617480 | + | 0.786587i | \(0.288154\pi\) | |||||||
\(228\) | 37.1988 | + | 21.8523i | 2.46355 | + | 1.44720i | ||||
\(229\) | −0.491124 | −0.0324544 | −0.0162272 | − | 0.999868i | \(-0.505166\pi\) | ||||
−0.0162272 | + | 0.999868i | \(0.505166\pi\) | |||||||
\(230\) | 7.90103 | 0.520978 | ||||||||
\(231\) | 1.58002 | − | 5.52300i | 0.103957 | − | 0.363387i | ||||
\(232\) | −20.0639 | −1.31726 | ||||||||
\(233\) | −4.03019 | −0.264027 | −0.132013 | − | 0.991248i | \(-0.542144\pi\) | ||||
−0.132013 | + | 0.991248i | \(0.542144\pi\) | |||||||
\(234\) | 43.4210 | − | 24.2037i | 2.83852 | − | 1.58224i | ||||
\(235\) | −7.86819 | −0.513264 | ||||||||
\(236\) | 19.6499i | 1.27910i | ||||||||
\(237\) | −15.3837 | − | 9.03708i | −0.999278 | − | 0.587022i | ||||
\(238\) | 12.7961i | 0.829446i | ||||||||
\(239\) | −25.6196 | −1.65719 | −0.828596 | − | 0.559847i | \(-0.810860\pi\) | ||||
−0.828596 | + | 0.559847i | \(0.810860\pi\) | |||||||
\(240\) | 6.03203 | + | 3.54349i | 0.389366 | + | 0.228731i | ||||
\(241\) | − | 20.3487i | − | 1.31077i | −0.755293 | − | 0.655387i | \(-0.772506\pi\) | ||
0.755293 | − | 0.655387i | \(-0.227494\pi\) | |||||||
\(242\) | 23.5938 | − | 13.0430i | 1.51667 | − | 0.838434i | ||||
\(243\) | 7.27995 | + | 13.7841i | 0.467009 | + | 0.884253i | ||||
\(244\) | 20.5695i | 1.31682i | ||||||||
\(245\) | − | 1.00000i | − | 0.0638877i | ||||||
\(246\) | 11.6291 | − | 19.7960i | 0.741442 | − | 1.26215i | ||||
\(247\) | 42.0340 | 2.67456 | ||||||||
\(248\) | −10.6496 | −0.676252 | ||||||||
\(249\) | −3.75039 | + | 6.38423i | −0.237671 | + | 0.404584i | ||||
\(250\) | 2.45082i | 0.155003i | ||||||||
\(251\) | − | 20.4591i | − | 1.29137i | −0.763605 | − | 0.645683i | \(-0.776573\pi\) | ||
0.763605 | − | 0.645683i | \(-0.223427\pi\) | |||||||
\(252\) | 10.4986 | − | 5.85213i | 0.661351 | − | 0.368650i | ||||
\(253\) | 10.3532 | − | 2.67120i | 0.650901 | − | 0.167937i | ||||
\(254\) | 21.2499i | 1.33333i | ||||||||
\(255\) | −7.79741 | − | 4.58056i | −0.488293 | − | 0.286846i | ||||
\(256\) | −32.0510 | −2.00319 | ||||||||
\(257\) | 5.12084i | 0.319429i | 0.987163 | + | 0.159715i | \(0.0510574\pi\) | ||||
−0.987163 | + | 0.159715i | \(0.948943\pi\) | |||||||
\(258\) | 25.4879 | + | 14.9728i | 1.58681 | + | 0.932164i | ||||
\(259\) | − | 8.03446i | − | 0.499237i | ||||||
\(260\) | 27.0886 | 1.67997 | ||||||||
\(261\) | −5.95955 | − | 10.6913i | −0.368887 | − | 0.661776i | ||||
\(262\) | 3.10510 | 0.191834 | ||||||||
\(263\) | −17.5580 | −1.08267 | −0.541336 | − | 0.840807i | \(-0.682081\pi\) | ||||
−0.541336 | + | 0.840807i | \(0.682081\pi\) | |||||||
\(264\) | 27.1597 | + | 7.76983i | 1.67157 | + | 0.478200i | ||||
\(265\) | 7.52801 | 0.462442 | ||||||||
\(266\) | 15.2367 | 0.934220 | ||||||||
\(267\) | −10.9028 | − | 6.40482i | −0.667242 | − | 0.391968i | ||||
\(268\) | −43.0847 | −2.63182 | ||||||||
\(269\) | 16.7138i | 1.01906i | 0.860454 | + | 0.509528i | \(0.170180\pi\) | ||||
−0.860454 | + | 0.509528i | \(0.829820\pi\) | |||||||
\(270\) | −0.287987 | + | 12.7316i | −0.0175263 | + | 0.774818i | ||||
\(271\) | − | 29.7002i | − | 1.80416i | −0.431573 | − | 0.902078i | \(-0.642041\pi\) | ||
0.431573 | − | 0.902078i | \(-0.357959\pi\) | |||||||
\(272\) | −21.0885 | −1.27868 | ||||||||
\(273\) | 5.93164 | − | 10.0973i | 0.358999 | − | 0.611118i | ||||
\(274\) | 19.4076i | 1.17245i | ||||||||
\(275\) | 0.828579 | + | 3.21146i | 0.0499652 | + | 0.193658i | ||||
\(276\) | 19.2896 | + | 11.3316i | 1.16110 | + | 0.682081i | ||||
\(277\) | 10.1482i | 0.609748i | 0.952393 | + | 0.304874i | \(0.0986144\pi\) | ||||
−0.952393 | + | 0.304874i | \(0.901386\pi\) | |||||||
\(278\) | − | 20.6906i | − | 1.24094i | ||||||
\(279\) | −3.16325 | − | 5.67481i | −0.189379 | − | 0.339742i | ||||
\(280\) | 4.91756 | 0.293881 | ||||||||
\(281\) | 9.84817 | 0.587492 | 0.293746 | − | 0.955883i | \(-0.405098\pi\) | ||||
0.293746 | + | 0.955883i | \(0.405098\pi\) | |||||||
\(282\) | −28.7985 | − | 16.9176i | −1.71493 | − | 1.00743i | ||||
\(283\) | − | 10.3929i | − | 0.617795i | −0.951095 | − | 0.308897i | \(-0.900040\pi\) | ||
0.951095 | − | 0.308897i | \(-0.0999600\pi\) | |||||||
\(284\) | 32.4325i | 1.92452i | ||||||||
\(285\) | −5.45421 | + | 9.28461i | −0.323079 | + | 0.549973i | ||||
\(286\) | 53.2151 | − | 13.7299i | 3.14668 | − | 0.811865i | ||||
\(287\) | − | 5.40856i | − | 0.319257i | ||||||
\(288\) | 0.0932355 | + | 0.167263i | 0.00549396 | + | 0.00985606i | ||||
\(289\) | 10.2604 | 0.603553 | ||||||||
\(290\) | − | 9.99943i | − | 0.587187i | ||||||
\(291\) | −13.5955 | + | 23.1434i | −0.796983 | + | 1.35669i | ||||
\(292\) | − | 40.9453i | − | 2.39614i | ||||||
\(293\) | 30.1418 | 1.76090 | 0.880450 | − | 0.474139i | \(-0.157240\pi\) | ||||
0.880450 | + | 0.474139i | \(0.157240\pi\) | |||||||
\(294\) | 2.15012 | − | 3.66012i | 0.125398 | − | 0.213463i | ||||
\(295\) | −4.90450 | −0.285551 | ||||||||
\(296\) | 39.5100 | 2.29647 | ||||||||
\(297\) | 3.92695 | + | 16.7803i | 0.227865 | + | 0.973693i | ||||
\(298\) | −9.09022 | −0.526582 | ||||||||
\(299\) | 21.7969 | 1.26055 | ||||||||
\(300\) | −3.51494 | + | 5.98342i | −0.202935 | + | 0.345453i | ||||
\(301\) | 6.96368 | 0.401380 | ||||||||
\(302\) | 9.41378i | 0.541702i | ||||||||
\(303\) | −3.37554 | + | 5.74613i | −0.193920 | + | 0.330106i | ||||
\(304\) | 25.1106i | 1.44019i | ||||||||
\(305\) | −5.13402 | −0.293973 | ||||||||
\(306\) | −18.6907 | − | 33.5308i | −1.06848 | − | 1.91683i | ||||
\(307\) | 4.22373i | 0.241061i | 0.992710 | + | 0.120530i | \(0.0384595\pi\) | ||||
−0.992710 | + | 0.120530i | \(0.961540\pi\) | |||||||
\(308\) | 12.8667 | − | 3.31970i | 0.733149 | − | 0.189158i | ||||
\(309\) | 7.78270 | − | 13.2484i | 0.442742 | − | 0.753673i | ||||
\(310\) | − | 5.30756i | − | 0.301449i | ||||||
\(311\) | − | 9.25912i | − | 0.525036i | −0.964927 | − | 0.262518i | \(-0.915447\pi\) | ||
0.964927 | − | 0.262518i | \(-0.0845530\pi\) | |||||||
\(312\) | 49.6543 | + | 29.1692i | 2.81112 | + | 1.65138i | ||||
\(313\) | −16.1922 | −0.915237 | −0.457618 | − | 0.889149i | \(-0.651297\pi\) | ||||
−0.457618 | + | 0.889149i | \(0.651297\pi\) | |||||||
\(314\) | 10.4165 | 0.587839 | ||||||||
\(315\) | 1.46066 | + | 2.62040i | 0.0822988 | + | 0.147643i | ||||
\(316\) | − | 41.2706i | − | 2.32165i | ||||||
\(317\) | − | 13.6532i | − | 0.766839i | −0.923574 | − | 0.383419i | \(-0.874746\pi\) | ||
0.923574 | − | 0.383419i | \(-0.125254\pi\) | |||||||
\(318\) | 27.5534 | + | 16.1862i | 1.54512 | + | 0.907674i | ||||
\(319\) | −3.38063 | − | 13.1029i | −0.189279 | − | 0.733620i | ||||
\(320\) | − | 7.92165i | − | 0.442834i | ||||||
\(321\) | −9.70693 | + | 16.5240i | −0.541788 | + | 0.922277i | ||||
\(322\) | 7.90103 | 0.440307 | ||||||||
\(323\) | − | 32.4597i | − | 1.80611i | ||||||
\(324\) | −18.9626 | + | 30.6698i | −1.05348 | + | 1.70388i | ||||
\(325\) | 6.76117i | 0.375042i | ||||||||
\(326\) | −39.9792 | −2.21424 | ||||||||
\(327\) | 22.9720 | + | 13.4948i | 1.27036 | + | 0.746265i | ||||
\(328\) | 26.5970 | 1.46857 | ||||||||
\(329\) | −7.86819 | −0.433787 | ||||||||
\(330\) | −3.87233 | + | 13.5359i | −0.213165 | + | 0.745125i | ||||
\(331\) | 15.8005 | 0.868476 | 0.434238 | − | 0.900798i | \(-0.357018\pi\) | ||||
0.434238 | + | 0.900798i | \(0.357018\pi\) | |||||||
\(332\) | −17.1273 | −0.939983 | ||||||||
\(333\) | 11.7356 | + | 21.0535i | 0.643107 | + | 1.15372i | ||||
\(334\) | −3.27151 | −0.179009 | ||||||||
\(335\) | − | 10.7537i | − | 0.587537i | ||||||
\(336\) | 6.03203 | + | 3.54349i | 0.329074 | + | 0.193313i | ||||
\(337\) | 15.4400i | 0.841069i | 0.907277 | + | 0.420534i | \(0.138157\pi\) | ||||
−0.907277 | + | 0.420534i | \(0.861843\pi\) | |||||||
\(338\) | 80.1747 | 4.36093 | ||||||||
\(339\) | 4.33484 | + | 2.54648i | 0.235436 | + | 0.138306i | ||||
\(340\) | − | 20.9185i | − | 1.13447i | ||||||
\(341\) | −1.79440 | − | 6.95483i | −0.0971720 | − | 0.376625i | ||||
\(342\) | −39.9261 | + | 22.2556i | −2.15896 | + | 1.20344i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 34.2444i | 1.84633i | ||||||||
\(345\) | −2.82830 | + | 4.81457i | −0.152270 | + | 0.259208i | ||||
\(346\) | 30.3802 | 1.63325 | ||||||||
\(347\) | 0.952324 | 0.0511234 | 0.0255617 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255617 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(348\) | 14.3411 | − | 24.4126i | 0.768763 | − | 1.30865i | ||||
\(349\) | 10.9106i | 0.584031i | 0.956414 | + | 0.292015i | \(0.0943258\pi\) | ||||
−0.956414 | + | 0.292015i | \(0.905674\pi\) | |||||||
\(350\) | 2.45082i | 0.131002i | ||||||||
\(351\) | −0.794482 | + | 35.1231i | −0.0424063 | + | 1.87473i | ||||
\(352\) | 0.0528891 | + | 0.204991i | 0.00281900 | + | 0.0109261i | ||||
\(353\) | 17.4326i | 0.927846i | 0.885876 | + | 0.463923i | \(0.153558\pi\) | ||||
−0.885876 | + | 0.463923i | \(0.846442\pi\) | |||||||
\(354\) | −17.9511 | − | 10.5453i | −0.954088 | − | 0.560475i | ||||
\(355\) | −8.09497 | −0.429636 | ||||||||
\(356\) | − | 29.2496i | − | 1.55022i | ||||||
\(357\) | −7.79741 | − | 4.58056i | −0.412683 | − | 0.242429i | ||||
\(358\) | 53.8649i | 2.84685i | ||||||||
\(359\) | 4.35980 | 0.230101 | 0.115051 | − | 0.993360i | \(-0.463297\pi\) | ||||
0.115051 | + | 0.993360i | \(0.463297\pi\) | |||||||
\(360\) | −12.8860 | + | 7.18288i | −0.679150 | + | 0.378571i | ||||
\(361\) | −19.6508 | −1.03425 | ||||||||
\(362\) | −49.4016 | −2.59649 | ||||||||
\(363\) | −0.497912 | + | 19.0461i | −0.0261336 | + | 0.999658i | ||||
\(364\) | 27.0886 | 1.41983 | ||||||||
\(365\) | 10.2197 | 0.534925 | ||||||||
\(366\) | −18.7911 | − | 11.0388i | −0.982228 | − | 0.577006i | ||||
\(367\) | 21.9215 | 1.14429 | 0.572146 | − | 0.820152i | \(-0.306111\pi\) | ||||
0.572146 | + | 0.820152i | \(0.306111\pi\) | |||||||
\(368\) | 13.0212i | 0.678778i | ||||||||
\(369\) | 7.90006 | + | 14.1726i | 0.411261 | + | 0.737795i | ||||
\(370\) | 19.6910i | 1.02369i | ||||||||
\(371\) | 7.52801 | 0.390835 | ||||||||
\(372\) | 7.61206 | − | 12.9579i | 0.394667 | − | 0.671835i | ||||
\(373\) | 5.79535i | 0.300072i | 0.988681 | + | 0.150036i | \(0.0479389\pi\) | ||||
−0.988681 | + | 0.150036i | \(0.952061\pi\) | |||||||
\(374\) | −10.6026 | − | 41.0941i | −0.548245 | − | 2.12492i | ||||
\(375\) | −1.49343 | − | 0.877309i | −0.0771203 | − | 0.0453040i | ||||
\(376\) | − | 38.6923i | − | 1.99540i | ||||||
\(377\) | − | 27.5859i | − | 1.42074i | ||||||
\(378\) | −0.287987 | + | 12.7316i | −0.0148124 | + | 0.654841i | ||||
\(379\) | 25.5329 | 1.31154 | 0.655768 | − | 0.754963i | \(-0.272345\pi\) | ||||
0.655768 | + | 0.754963i | \(0.272345\pi\) | |||||||
\(380\) | −24.9083 | −1.27777 | ||||||||
\(381\) | −12.9488 | − | 7.60672i | −0.663387 | − | 0.389704i | ||||
\(382\) | 33.0518i | 1.69107i | ||||||||
\(383\) | − | 26.6491i | − | 1.36170i | −0.732421 | − | 0.680852i | \(-0.761610\pi\) | ||
0.732421 | − | 0.680852i | \(-0.238390\pi\) | |||||||
\(384\) | 17.1445 | − | 29.1849i | 0.874903 | − | 1.48933i | ||||
\(385\) | 0.828579 | + | 3.21146i | 0.0422283 | + | 0.163671i | ||||
\(386\) | − | 47.8956i | − | 2.43782i | ||||||
\(387\) | −18.2476 | + | 10.1716i | −0.927578 | + | 0.517050i | ||||
\(388\) | −62.0881 | −3.15204 | ||||||||
\(389\) | − | 37.2190i | − | 1.88708i | −0.331260 | − | 0.943540i | \(-0.607474\pi\) | ||
0.331260 | − | 0.943540i | \(-0.392526\pi\) | |||||||
\(390\) | −14.5373 | + | 24.7467i | −0.736127 | + | 1.25310i | ||||
\(391\) | − | 16.8321i | − | 0.851237i | ||||||
\(392\) | 4.91756 | 0.248375 | ||||||||
\(393\) | −1.11152 | + | 1.89212i | −0.0560687 | + | 0.0954449i | ||||
\(394\) | 9.53779 | 0.480507 | ||||||||
\(395\) | 10.3009 | 0.518295 | ||||||||
\(396\) | −28.8669 | + | 27.4928i | −1.45062 | + | 1.38157i | ||||
\(397\) | 6.56168 | 0.329321 | 0.164661 | − | 0.986350i | \(-0.447347\pi\) | ||||
0.164661 | + | 0.986350i | \(0.447347\pi\) | |||||||
\(398\) | 38.1721 | 1.91340 | ||||||||
\(399\) | −5.45421 | + | 9.28461i | −0.273052 | + | 0.464812i | ||||
\(400\) | −4.03905 | −0.201952 | ||||||||
\(401\) | − | 1.69993i | − | 0.0848902i | −0.999099 | − | 0.0424451i | \(-0.986485\pi\) | ||
0.999099 | − | 0.0424451i | \(-0.0135148\pi\) | |||||||
\(402\) | 23.1218 | − | 39.3598i | 1.15321 | − | 1.96309i | ||||
\(403\) | − | 14.6422i | − | 0.729380i | ||||||
\(404\) | −15.4154 | −0.766947 | ||||||||
\(405\) | −7.65501 | − | 4.73295i | −0.380380 | − | 0.235182i | ||||
\(406\) | − | 9.99943i | − | 0.496263i | ||||||
\(407\) | 6.65718 | + | 25.8023i | 0.329984 | + | 1.27897i | ||||
\(408\) | 22.5252 | − | 38.3443i | 1.11516 | − | 1.89833i | ||||
\(409\) | 25.7955i | 1.27551i | 0.770240 | + | 0.637754i | \(0.220136\pi\) | ||||
−0.770240 | + | 0.637754i | \(0.779864\pi\) | |||||||
\(410\) | 13.2554i | 0.654637i | ||||||||
\(411\) | −11.8262 | − | 6.94725i | −0.583343 | − | 0.342682i | ||||
\(412\) | 35.5421 | 1.75103 | ||||||||
\(413\) | −4.90450 | −0.241335 | ||||||||
\(414\) | −20.7038 | + | 11.5407i | −1.01754 | + | 0.567195i | ||||
\(415\) | − | 4.27488i | − | 0.209846i | ||||||
\(416\) | 0.431573i | 0.0211596i | ||||||||
\(417\) | 12.6080 | + | 7.40654i | 0.617418 | + | 0.362700i | ||||
\(418\) | −48.9319 | + | 12.6248i | −2.39334 | + | 0.617498i | ||||
\(419\) | 14.9751i | 0.731579i | 0.930698 | + | 0.365790i | \(0.119201\pi\) | ||||
−0.930698 | + | 0.365790i | \(0.880799\pi\) | |||||||
\(420\) | −3.51494 | + | 5.98342i | −0.171511 | + | 0.291961i | ||||
\(421\) | −33.0972 | −1.61306 | −0.806529 | − | 0.591194i | \(-0.798657\pi\) | ||||
−0.806529 | + | 0.591194i | \(0.798657\pi\) | |||||||
\(422\) | − | 24.1983i | − | 1.17795i | ||||||
\(423\) | 20.6178 | − | 11.4927i | 1.00247 | − | 0.558796i | ||||
\(424\) | 37.0195i | 1.79783i | ||||||||
\(425\) | 5.22115 | 0.253263 | ||||||||
\(426\) | −29.6286 | − | 17.4052i | −1.43551 | − | 0.843284i | ||||
\(427\) | −5.13402 | −0.248453 | ||||||||
\(428\) | −44.3297 | −2.14276 | ||||||||
\(429\) | −10.6828 | + | 37.3420i | −0.515769 | + | 1.80289i | ||||
\(430\) | −17.0667 | −0.823030 | ||||||||
\(431\) | 20.1624 | 0.971191 | 0.485595 | − | 0.874184i | \(-0.338603\pi\) | ||||
0.485595 | + | 0.874184i | \(0.338603\pi\) | |||||||
\(432\) | −20.9821 | − | 0.474614i | −1.00950 | − | 0.0228349i | ||||
\(433\) | 33.9440 | 1.63124 | 0.815622 | − | 0.578585i | \(-0.196395\pi\) | ||||
0.815622 | + | 0.578585i | \(0.196395\pi\) | |||||||
\(434\) | − | 5.30756i | − | 0.254771i | ||||||
\(435\) | 6.09325 | + | 3.57945i | 0.292149 | + | 0.171622i | ||||
\(436\) | 61.6282i | 2.95146i | ||||||||
\(437\) | −20.0425 | −0.958763 | ||||||||
\(438\) | 37.4054 | + | 21.9737i | 1.78730 | + | 1.04994i | ||||
\(439\) | − | 34.0473i | − | 1.62499i | −0.582967 | − | 0.812496i | \(-0.698108\pi\) | ||
0.582967 | − | 0.812496i | \(-0.301892\pi\) | |||||||
\(440\) | −15.7925 | + | 4.07459i | −0.752880 | + | 0.194248i | ||||
\(441\) | 1.46066 | + | 2.62040i | 0.0695552 | + | 0.124781i | ||||
\(442\) | − | 86.5165i | − | 4.11517i | ||||||
\(443\) | 4.14496i | 0.196933i | 0.995140 | + | 0.0984666i | \(0.0313938\pi\) | ||||
−0.995140 | + | 0.0984666i | \(0.968606\pi\) | |||||||
\(444\) | −28.2406 | + | 48.0736i | −1.34024 | + | 2.28147i | ||||
\(445\) | 7.30053 | 0.346078 | ||||||||
\(446\) | 22.2589 | 1.05399 | ||||||||
\(447\) | 3.25399 | − | 5.53921i | 0.153908 | − | 0.261996i | ||||
\(448\) | − | 7.92165i | − | 0.374263i | ||||||
\(449\) | − | 26.1823i | − | 1.23562i | −0.786328 | − | 0.617809i | \(-0.788020\pi\) | ||
0.786328 | − | 0.617809i | \(-0.211980\pi\) | |||||||
\(450\) | −3.57981 | − | 6.42211i | −0.168754 | − | 0.302741i | ||||
\(451\) | 4.48142 | + | 17.3694i | 0.211022 | + | 0.817891i | ||||
\(452\) | 11.6293i | 0.546996i | ||||||||
\(453\) | −5.73638 | − | 3.36981i | −0.269519 | − | 0.158328i | ||||
\(454\) | −45.6012 | −2.14017 | ||||||||
\(455\) | 6.76117i | 0.316969i | ||||||||
\(456\) | −45.6577 | − | 26.8214i | −2.13812 | − | 1.25603i | ||||
\(457\) | − | 12.8229i | − | 0.599831i | −0.953966 | − | 0.299915i | \(-0.903042\pi\) | ||
0.953966 | − | 0.299915i | \(-0.0969584\pi\) | |||||||
\(458\) | 1.20365 | 0.0562431 | ||||||||
\(459\) | 27.1229 | + | 0.613519i | 1.26599 | + | 0.0286366i | ||||
\(460\) | −12.9163 | −0.602225 | ||||||||
\(461\) | −16.4469 | −0.766009 | −0.383005 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383005 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(462\) | −3.87233 | + | 13.5359i | −0.180157 | + | 0.629745i | ||||
\(463\) | −17.2397 | −0.801198 | −0.400599 | − | 0.916254i | \(-0.631198\pi\) | ||||
−0.400599 | + | 0.916254i | \(0.631198\pi\) | |||||||
\(464\) | 16.4795 | 0.765040 | ||||||||
\(465\) | 3.23421 | + | 1.89993i | 0.149983 | + | 0.0881070i | ||||
\(466\) | 9.87726 | 0.457555 | ||||||||
\(467\) | − | 35.6700i | − | 1.65061i | −0.564687 | − | 0.825305i | \(-0.691003\pi\) | ||
0.564687 | − | 0.825305i | \(-0.308997\pi\) | |||||||
\(468\) | −70.9830 | + | 39.5673i | −3.28119 | + | 1.82900i | ||||
\(469\) | − | 10.7537i | − | 0.496559i | ||||||
\(470\) | 19.2835 | 0.889481 | ||||||||
\(471\) | −3.72877 | + | 6.34742i | −0.171812 | + | 0.292474i | ||||
\(472\) | − | 24.1182i | − | 1.11013i | ||||||
\(473\) | −22.3636 | + | 5.76996i | −1.02828 | + | 0.265303i | ||||
\(474\) | 37.7026 | + | 22.1482i | 1.73174 | + | 1.01730i | ||||
\(475\) | − | 6.21697i | − | 0.285254i | ||||||
\(476\) | − | 20.9185i | − | 0.958800i | ||||||
\(477\) | −19.7264 | + | 10.9959i | −0.903209 | + | 0.503466i | ||||
\(478\) | 62.7889 | 2.87190 | ||||||||
\(479\) | 14.7539 | 0.674123 | 0.337061 | − | 0.941483i | \(-0.390567\pi\) | ||||
0.337061 | + | 0.941483i | \(0.390567\pi\) | |||||||
\(480\) | −0.0953273 | − | 0.0559996i | −0.00435108 | − | 0.00255602i | ||||
\(481\) | 54.3224i | 2.47689i | ||||||||
\(482\) | 49.8709i | 2.27156i | ||||||||
\(483\) | −2.82830 | + | 4.81457i | −0.128692 | + | 0.219070i | ||||
\(484\) | −38.5702 | + | 21.3222i | −1.75319 | + | 0.969189i | ||||
\(485\) | − | 15.4968i | − | 0.703675i | ||||||
\(486\) | −17.8418 | − | 33.7824i | −0.809322 | − | 1.53240i | ||||
\(487\) | 35.1791 | 1.59412 | 0.797058 | − | 0.603903i | \(-0.206388\pi\) | ||||
0.797058 | + | 0.603903i | \(0.206388\pi\) | |||||||
\(488\) | − | 25.2469i | − | 1.14287i | ||||||
\(489\) | 14.3112 | − | 24.3617i | 0.647174 | − | 1.10167i | ||||
\(490\) | 2.45082i | 0.110717i | ||||||||
\(491\) | −5.41086 | −0.244189 | −0.122094 | − | 0.992519i | \(-0.538961\pi\) | ||||
−0.122094 | + | 0.992519i | \(0.538961\pi\) | |||||||
\(492\) | −19.0108 | + | 32.3617i | −0.857071 | + | 1.45898i | ||||
\(493\) | −21.3025 | −0.959416 | ||||||||
\(494\) | −103.018 | −4.63499 | ||||||||
\(495\) | −6.86205 | − | 7.20502i | −0.308426 | − | 0.323842i | ||||
\(496\) | 8.74708 | 0.392756 | ||||||||
\(497\) | −8.09497 | −0.363109 | ||||||||
\(498\) | 9.19152 | − | 15.6466i | 0.411882 | − | 0.701140i | ||||
\(499\) | −33.6639 | −1.50700 | −0.753501 | − | 0.657447i | \(-0.771636\pi\) | ||||
−0.753501 | + | 0.657447i | \(0.771636\pi\) | |||||||
\(500\) | − | 4.00650i | − | 0.179176i | ||||||
\(501\) | 1.17109 | − | 1.99352i | 0.0523203 | − | 0.0890641i | ||||
\(502\) | 50.1415i | 2.23792i | ||||||||
\(503\) | −6.76013 | −0.301419 | −0.150710 | − | 0.988578i | \(-0.548156\pi\) | ||||
−0.150710 | + | 0.988578i | \(0.548156\pi\) | |||||||
\(504\) | −12.8860 | + | 7.18288i | −0.573987 | + | 0.319951i | ||||
\(505\) | − | 3.84761i | − | 0.171216i | ||||||
\(506\) | −25.3738 | + | 6.54662i | −1.12800 | + | 0.291033i | ||||
\(507\) | −28.6998 | + | 48.8552i | −1.27460 | + | 2.16974i | ||||
\(508\) | − | 34.7385i | − | 1.54127i | ||||||
\(509\) | − | 15.9644i | − | 0.707612i | −0.935319 | − | 0.353806i | \(-0.884887\pi\) | ||
0.935319 | − | 0.353806i | \(-0.115113\pi\) | |||||||
\(510\) | 19.1100 | + | 11.2261i | 0.846206 | + | 0.497101i | ||||
\(511\) | 10.2197 | 0.452094 | ||||||||
\(512\) | 39.4667 | 1.74420 | ||||||||
\(513\) | 0.730535 | − | 32.2961i | 0.0322539 | − | 1.42591i | ||||
\(514\) | − | 12.5502i | − | 0.553567i | ||||||
\(515\) | 8.87110i | 0.390908i | ||||||||
\(516\) | −41.6667 | − | 24.4769i | −1.83427 | − | 1.07754i | ||||
\(517\) | 25.2684 | − | 6.51941i | 1.11130 | − | 0.286723i | ||||
\(518\) | 19.6910i | 0.865172i | ||||||||
\(519\) | −10.8751 | + | 18.5125i | −0.477363 | + | 0.812607i | ||||
\(520\) | −33.2485 | −1.45804 | ||||||||
\(521\) | − | 8.99231i | − | 0.393960i | −0.980407 | − | 0.196980i | \(-0.936887\pi\) | ||
0.980407 | − | 0.196980i | \(-0.0631134\pi\) | |||||||
\(522\) | 14.6058 | + | 26.2025i | 0.639277 | + | 1.14685i | ||||
\(523\) | 16.4392i | 0.718838i | 0.933176 | + | 0.359419i | \(0.117025\pi\) | ||||
−0.933176 | + | 0.359419i | \(0.882975\pi\) | |||||||
\(524\) | −5.07609 | −0.221750 | ||||||||
\(525\) | −1.49343 | − | 0.877309i | −0.0651786 | − | 0.0382889i | ||||
\(526\) | 43.0314 | 1.87626 | ||||||||
\(527\) | −11.3071 | −0.492544 | ||||||||
\(528\) | −22.3077 | − | 6.38176i | −0.970816 | − | 0.277730i | ||||
\(529\) | 12.6069 | 0.548126 | ||||||||
\(530\) | −18.4498 | −0.801407 | ||||||||
\(531\) | 12.8517 | − | 7.16381i | 0.557718 | − | 0.310883i | ||||
\(532\) | −24.9083 | −1.07991 | ||||||||
\(533\) | 36.5682i | 1.58395i | ||||||||
\(534\) | 26.7208 | + | 15.6970i | 1.15632 | + | 0.679277i | ||||
\(535\) | − | 11.0644i | − | 0.478358i | ||||||
\(536\) | 52.8820 | 2.28415 | ||||||||
\(537\) | −32.8231 | − | 19.2818i | −1.41642 | − | 0.832071i | ||||
\(538\) | − | 40.9624i | − | 1.76601i | ||||||
\(539\) | 0.828579 | + | 3.21146i | 0.0356894 | + | 0.138327i | ||||
\(540\) | 0.470790 | − | 20.8131i | 0.0202596 | − | 0.895652i | ||||
\(541\) | − | 7.78365i | − | 0.334645i | −0.985902 | − | 0.167323i | \(-0.946488\pi\) | ||
0.985902 | − | 0.167323i | \(-0.0535121\pi\) | |||||||
\(542\) | 72.7896i | 3.12658i | ||||||||
\(543\) | 17.6841 | − | 30.1033i | 0.758896 | − | 1.29186i | ||||
\(544\) | 0.333272 | 0.0142889 | ||||||||
\(545\) | −15.3821 | −0.658895 | ||||||||
\(546\) | −14.5373 | + | 24.7467i | −0.622141 | + | 1.05906i | ||||
\(547\) | − | 3.68679i | − | 0.157636i | −0.996889 | − | 0.0788179i | \(-0.974885\pi\) | ||
0.996889 | − | 0.0788179i | \(-0.0251146\pi\) | |||||||
\(548\) | − | 31.7267i | − | 1.35530i | ||||||
\(549\) | 13.4532 | − | 7.49905i | 0.574167 | − | 0.320052i | ||||
\(550\) | −2.03069 | − | 7.87069i | −0.0865891 | − | 0.335607i | ||||
\(551\) | 25.3655i | 1.08061i | ||||||||
\(552\) | −23.6759 | − | 13.9083i | −1.00772 | − | 0.591978i | ||||
\(553\) | 10.3009 | 0.438040 | ||||||||
\(554\) | − | 24.8715i | − | 1.05669i | ||||||
\(555\) | −11.9989 | − | 7.04870i | −0.509325 | − | 0.299201i | ||||
\(556\) | 33.8243i | 1.43447i | ||||||||
\(557\) | −17.6433 | −0.747572 | −0.373786 | − | 0.927515i | \(-0.621941\pi\) | ||||
−0.373786 | + | 0.927515i | \(0.621941\pi\) | |||||||
\(558\) | 7.75254 | + | 13.9079i | 0.328191 | + | 0.588769i | ||||
\(559\) | −47.0827 | −1.99138 | ||||||||
\(560\) | −4.03905 | −0.170681 | ||||||||
\(561\) | 28.8364 | + | 8.24950i | 1.21747 | + | 0.348294i | ||||
\(562\) | −24.1360 | −1.01812 | ||||||||
\(563\) | −23.7291 | −1.00006 | −0.500031 | − | 0.866007i | \(-0.666678\pi\) | ||||
−0.500031 | + | 0.866007i | \(0.666678\pi\) | |||||||
\(564\) | 47.0787 | + | 27.6562i | 1.98237 | + | 1.16454i | ||||
\(565\) | −2.90261 | −0.122114 | ||||||||
\(566\) | 25.4711i | 1.07063i | ||||||||
\(567\) | −7.65501 | − | 4.73295i | −0.321480 | − | 0.198765i | ||||
\(568\) | − | 39.8075i | − | 1.67029i | ||||||
\(569\) | 9.02479 | 0.378339 | 0.189169 | − | 0.981944i | \(-0.439420\pi\) | ||||
0.189169 | + | 0.981944i | \(0.439420\pi\) | |||||||
\(570\) | 13.3673 | − | 22.7549i | 0.559893 | − | 0.953097i | ||||
\(571\) | − | 46.3533i | − | 1.93983i | −0.243451 | − | 0.969913i | \(-0.578279\pi\) | ||
0.243451 | − | 0.969913i | \(-0.421721\pi\) | |||||||
\(572\) | −86.9940 | + | 22.4451i | −3.63740 | + | 0.938476i | ||||
\(573\) | −20.1404 | − | 11.8314i | −0.841378 | − | 0.494264i | ||||
\(574\) | 13.2554i | 0.553269i | ||||||||
\(575\) | − | 3.22384i | − | 0.134443i | ||||||
\(576\) | 11.5708 | + | 20.7579i | 0.482118 | + | 0.864911i | ||||
\(577\) | 11.5321 | 0.480087 | 0.240044 | − | 0.970762i | \(-0.422838\pi\) | ||||
0.240044 | + | 0.970762i | \(0.422838\pi\) | |||||||
\(578\) | −25.1463 | −1.04595 | ||||||||
\(579\) | 29.1856 | + | 17.1450i | 1.21291 | + | 0.712521i | ||||
\(580\) | 16.3467i | 0.678759i | ||||||||
\(581\) | − | 4.27488i | − | 0.177352i | ||||||
\(582\) | 33.3201 | − | 56.7203i | 1.38116 | − | 2.35113i | ||||
\(583\) | −24.1759 | + | 6.23755i | −1.00126 | + | 0.258333i | ||||
\(584\) | 50.2561i | 2.07961i | ||||||||
\(585\) | −9.87577 | − | 17.7170i | −0.408313 | − | 0.732506i | ||||
\(586\) | −73.8719 | −3.05162 | ||||||||
\(587\) | 37.9265i | 1.56540i | 0.622402 | + | 0.782698i | \(0.286157\pi\) | ||||
−0.622402 | + | 0.782698i | \(0.713843\pi\) | |||||||
\(588\) | −3.51494 | + | 5.98342i | −0.144954 | + | 0.246752i | ||||
\(589\) | 13.4637i | 0.554761i | ||||||||
\(590\) | 12.0200 | 0.494857 | ||||||||
\(591\) | −3.41420 | + | 5.81195i | −0.140442 | + | 0.239071i | ||||
\(592\) | −32.4515 | −1.33375 | ||||||||
\(593\) | 38.3152 | 1.57342 | 0.786708 | − | 0.617326i | \(-0.211784\pi\) | ||||
0.786708 | + | 0.617326i | \(0.211784\pi\) | |||||||
\(594\) | −9.62424 | − | 41.1255i | −0.394887 | − | 1.68740i | ||||
\(595\) | 5.22115 | 0.214046 | ||||||||
\(596\) | 14.8603 | 0.608703 | ||||||||
\(597\) | −13.6643 | + | 23.2606i | −0.559243 | + | 0.951991i | ||||
\(598\) | −53.4202 | −2.18451 | ||||||||
\(599\) | − | 30.0699i | − | 1.22862i | −0.789064 | − | 0.614311i | \(-0.789434\pi\) | ||
0.789064 | − | 0.614311i | \(-0.210566\pi\) | |||||||
\(600\) | 4.31422 | − | 7.34403i | 0.176127 | − | 0.299819i | ||||
\(601\) | − | 5.54057i | − | 0.226004i | −0.993595 | − | 0.113002i | \(-0.963953\pi\) | ||
0.993595 | − | 0.113002i | \(-0.0360467\pi\) | |||||||
\(602\) | −17.0667 | −0.695587 | ||||||||
\(603\) | 15.7075 | + | 28.1789i | 0.639658 | + | 1.14753i | ||||
\(604\) | − | 15.3893i | − | 0.626181i | ||||||
\(605\) | −5.32189 | − | 9.62691i | −0.216366 | − | 0.391390i | ||||
\(606\) | 8.27282 | − | 14.0827i | 0.336060 | − | 0.572070i | ||||
\(607\) | 21.8600i | 0.887270i | 0.896208 | + | 0.443635i | \(0.146311\pi\) | ||||
−0.896208 | + | 0.443635i | \(0.853689\pi\) | |||||||
\(608\) | − | 0.396837i | − | 0.0160939i | ||||||
\(609\) | 6.09325 | + | 3.57945i | 0.246911 | + | 0.145047i | ||||
\(610\) | 12.5825 | 0.509452 | ||||||||
\(611\) | 53.1982 | 2.15217 | ||||||||
\(612\) | 30.5548 | + | 54.8149i | 1.23511 | + | 2.21576i | ||||
\(613\) | − | 18.7017i | − | 0.755353i | −0.925938 | − | 0.377677i | \(-0.876723\pi\) | ||
0.925938 | − | 0.377677i | \(-0.123277\pi\) | |||||||
\(614\) | − | 10.3516i | − | 0.417756i | ||||||
\(615\) | −8.07730 | − | 4.74498i | −0.325708 | − | 0.191336i | ||||
\(616\) | −15.7925 | + | 4.07459i | −0.636300 | + | 0.164170i | ||||
\(617\) | − | 26.5714i | − | 1.06973i | −0.844939 | − | 0.534863i | \(-0.820363\pi\) | ||
0.844939 | − | 0.534863i | \(-0.179637\pi\) | |||||||
\(618\) | −19.0740 | + | 32.4693i | −0.767267 | + | 1.30611i | ||||
\(619\) | 44.2269 | 1.77763 | 0.888815 | − | 0.458266i | \(-0.151529\pi\) | ||||
0.888815 | + | 0.458266i | \(0.151529\pi\) | |||||||
\(620\) | 8.67660i | 0.348461i | ||||||||
\(621\) | 0.378822 | − | 16.7473i | 0.0152016 | − | 0.672044i | ||||
\(622\) | 22.6924i | 0.909882i | ||||||||
\(623\) | 7.30053 | 0.292489 | ||||||||
\(624\) | −40.7836 | − | 23.9582i | −1.63265 | − | 0.959094i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 39.6841 | 1.58609 | ||||||||
\(627\) | 9.82292 | − | 34.3364i | 0.392290 | − | 1.37126i | ||||
\(628\) | −17.0286 | −0.679514 | ||||||||
\(629\) | 41.9491 | 1.67262 | ||||||||
\(630\) | −3.57981 | − | 6.42211i | −0.142623 | − | 0.255863i | ||||
\(631\) | −10.4485 | −0.415947 | −0.207974 | − | 0.978134i | \(-0.566687\pi\) | ||||
−0.207974 | + | 0.978134i | \(0.566687\pi\) | |||||||
\(632\) | 50.6554i | 2.01496i | ||||||||
\(633\) | 14.7454 | + | 8.66215i | 0.586079 | + | 0.344290i | ||||
\(634\) | 33.4614i | 1.32892i | ||||||||
\(635\) | 8.67052 | 0.344079 | ||||||||
\(636\) | −45.0433 | − | 26.4605i | −1.78608 | − | 1.04923i | ||||
\(637\) | 6.76117i | 0.267887i | ||||||||
\(638\) | 8.28531 | + | 32.1127i | 0.328019 | + | 1.27136i | ||||
\(639\) | 21.2120 | − | 11.8240i | 0.839135 | − | 0.467750i | ||||
\(640\) | 19.5422i | 0.772473i | ||||||||
\(641\) | − | 11.1207i | − | 0.439241i | −0.975585 | − | 0.219620i | \(-0.929518\pi\) | ||
0.975585 | − | 0.219620i | \(-0.0704819\pi\) | |||||||
\(642\) | 23.7899 | − | 40.4972i | 0.938913 | − | 1.59830i | ||||
\(643\) | 16.6563 | 0.656859 | 0.328430 | − | 0.944528i | \(-0.393481\pi\) | ||||
0.328430 | + | 0.944528i | \(0.393481\pi\) | |||||||
\(644\) | −12.9163 | −0.508973 | ||||||||
\(645\) | 6.10930 | − | 10.3998i | 0.240553 | − | 0.409490i | ||||
\(646\) | 79.5529i | 3.12997i | ||||||||
\(647\) | − | 11.5359i | − | 0.453521i | −0.973951 | − | 0.226761i | \(-0.927186\pi\) | ||
0.973951 | − | 0.226761i | \(-0.0728135\pi\) | |||||||
\(648\) | 23.2746 | − | 37.6440i | 0.914312 | − | 1.47880i | ||||
\(649\) | 15.7506 | − | 4.06377i | 0.618265 | − | 0.159517i | ||||
\(650\) | − | 16.5704i | − | 0.649944i | ||||||
\(651\) | 3.23421 | + | 1.89993i | 0.126759 | + | 0.0744640i | ||||
\(652\) | 65.3564 | 2.55955 | ||||||||
\(653\) | 42.2616i | 1.65383i | 0.562330 | + | 0.826913i | \(0.309905\pi\) | ||||
−0.562330 | + | 0.826913i | \(0.690095\pi\) | |||||||
\(654\) | −56.3002 | − | 33.0733i | −2.20151 | − | 1.29327i | ||||
\(655\) | − | 1.26696i | − | 0.0495044i | ||||||
\(656\) | −21.8454 | −0.852921 | ||||||||
\(657\) | −26.7797 | + | 14.9275i | −1.04478 | + | 0.582378i | ||||
\(658\) | 19.2835 | 0.751749 | ||||||||
\(659\) | 9.42440 | 0.367122 | 0.183561 | − | 0.983008i | \(-0.441237\pi\) | ||||
0.183561 | + | 0.983008i | \(0.441237\pi\) | |||||||
\(660\) | 6.33034 | − | 22.1279i | 0.246408 | − | 0.861328i | ||||
\(661\) | 41.7218 | 1.62279 | 0.811395 | − | 0.584498i | \(-0.198709\pi\) | ||||
0.811395 | + | 0.584498i | \(0.198709\pi\) | |||||||
\(662\) | −38.7242 | −1.50506 | ||||||||
\(663\) | 52.7197 | + | 30.9700i | 2.04746 | + | 1.20277i | ||||
\(664\) | 21.0220 | 0.815812 | ||||||||
\(665\) | − | 6.21697i | − | 0.241084i | ||||||
\(666\) | −28.7618 | − | 51.5982i | −1.11450 | − | 1.99939i | ||||
\(667\) | 13.1534i | 0.509301i | ||||||||
\(668\) | 5.34813 | 0.206925 | ||||||||
\(669\) | −7.96794 | + | 13.5637i | −0.308058 | + | 0.524403i | ||||
\(670\) | 26.3553i | 1.01820i | ||||||||
\(671\) | 16.4877 | − | 4.25394i | 0.636500 | − | 0.164222i | ||||
\(672\) | −0.0953273 | − | 0.0559996i | −0.00367733 | − | 0.00216023i | ||||
\(673\) | − | 18.4153i | − | 0.709858i | −0.934893 | − | 0.354929i | \(-0.884505\pi\) | ||
0.934893 | − | 0.354929i | \(-0.115495\pi\) | |||||||
\(674\) | − | 37.8405i | − | 1.45756i | ||||||
\(675\) | 5.19482 | + | 0.117506i | 0.199949 | + | 0.00452283i | ||||
\(676\) | −131.066 | −5.04102 | ||||||||
\(677\) | 7.40444 | 0.284576 | 0.142288 | − | 0.989825i | \(-0.454554\pi\) | ||||
0.142288 | + | 0.989825i | \(0.454554\pi\) | |||||||
\(678\) | −10.6239 | − | 6.24096i | −0.408008 | − | 0.239683i | ||||
\(679\) | − | 15.4968i | − | 0.594714i | ||||||
\(680\) | 25.6753i | 0.984604i | ||||||||
\(681\) | 16.3237 | − | 27.7876i | 0.625525 | − | 1.06482i | ||||
\(682\) | 4.39773 | + | 17.0450i | 0.168398 | + | 0.652687i | ||||
\(683\) | 24.9152i | 0.953352i | 0.879079 | + | 0.476676i | \(0.158159\pi\) | ||||
−0.879079 | + | 0.476676i | \(0.841841\pi\) | |||||||
\(684\) | 65.2696 | − | 36.3825i | 2.49565 | − | 1.39112i | ||||
\(685\) | 7.91882 | 0.302562 | ||||||||
\(686\) | 2.45082i | 0.0935726i | ||||||||
\(687\) | −0.430867 | + | 0.733459i | −0.0164386 | + | 0.0279832i | ||||
\(688\) | − | 28.1266i | − | 1.07232i | ||||||
\(689\) | −50.8982 | −1.93907 | ||||||||
\(690\) | 6.93164 | − | 11.7996i | 0.263883 | − | 0.449204i | ||||
\(691\) | 41.5886 | 1.58210 | 0.791052 | − | 0.611749i | \(-0.209534\pi\) | ||||
0.791052 | + | 0.611749i | \(0.209534\pi\) | |||||||
\(692\) | −49.6644 | −1.88796 | ||||||||
\(693\) | −6.86205 | − | 7.20502i | −0.260668 | − | 0.273696i | ||||
\(694\) | −2.33397 | −0.0885964 | ||||||||
\(695\) | −8.44234 | −0.320236 | ||||||||
\(696\) | −17.6022 | + | 29.9639i | −0.667210 | + | 1.13578i | ||||
\(697\) | 28.2389 | 1.06962 | ||||||||
\(698\) | − | 26.7399i | − | 1.01212i | ||||||
\(699\) | −3.53572 | + | 6.01880i | −0.133733 | + | 0.227652i | ||||
\(700\) | − | 4.00650i | − | 0.151431i | ||||||
\(701\) | −14.5839 | −0.550825 | −0.275412 | − | 0.961326i | \(-0.588814\pi\) | ||||
−0.275412 | + | 0.961326i | \(0.588814\pi\) | |||||||
\(702\) | 1.94713 | − | 86.0803i | 0.0734896 | − | 3.24889i | ||||
\(703\) | − | 49.9500i | − | 1.88390i | ||||||
\(704\) | 6.56371 | + | 25.4401i | 0.247379 | + | 0.958808i | ||||
\(705\) | −6.90283 | + | 11.7506i | −0.259976 | + | 0.442552i | ||||
\(706\) | − | 42.7242i | − | 1.60795i | ||||||
\(707\) | − | 3.84761i | − | 0.144704i | ||||||
\(708\) | 29.3457 | + | 17.2390i | 1.10288 | + | 0.647882i | ||||
\(709\) | −18.9610 | −0.712096 | −0.356048 | − | 0.934468i | \(-0.615876\pi\) | ||||
−0.356048 | + | 0.934468i | \(0.615876\pi\) | |||||||
\(710\) | 19.8393 | 0.744555 | ||||||||
\(711\) | −26.9925 | + | 15.0461i | −1.01230 | + | 0.564274i | ||||
\(712\) | 35.9008i | 1.34544i | ||||||||
\(713\) | 6.98164i | 0.261464i | ||||||||
\(714\) | 19.1100 | + | 11.2261i | 0.715175 | + | 0.420127i | ||||
\(715\) | −5.60216 | − | 21.7132i | −0.209509 | − | 0.812028i | ||||
\(716\) | − | 88.0563i | − | 3.29082i | ||||||
\(717\) | −22.4763 | + | 38.2610i | −0.839392 | + | 1.42888i | ||||
\(718\) | −10.6851 | −0.398763 | ||||||||
\(719\) | 14.9636i | 0.558049i | 0.960284 | + | 0.279025i | \(0.0900111\pi\) | ||||
−0.960284 | + | 0.279025i | \(0.909989\pi\) | |||||||
\(720\) | 10.5839 | − | 5.89967i | 0.394439 | − | 0.219868i | ||||
\(721\) | 8.87110i | 0.330377i | ||||||||
\(722\) | 48.1604 | 1.79235 | ||||||||
\(723\) | −30.3893 | − | 17.8521i | −1.13019 | − | 0.663926i | ||||
\(724\) | 80.7598 | 3.00141 | ||||||||
\(725\) | −4.08004 | −0.151529 | ||||||||
\(726\) | 1.22029 | − | 46.6784i | 0.0452893 | − | 1.73240i | ||||
\(727\) | −31.8033 | −1.17952 | −0.589760 | − | 0.807579i | \(-0.700778\pi\) | ||||
−0.589760 | + | 0.807579i | \(0.700778\pi\) | |||||||
\(728\) | −33.2485 | −1.23227 | ||||||||
\(729\) | 26.9724 | + | 1.22085i | 0.998977 | + | 0.0452167i | ||||
\(730\) | −25.0467 | −0.927019 | ||||||||
\(731\) | 36.3584i | 1.34476i | ||||||||
\(732\) | 30.7190 | + | 18.0458i | 1.13541 | + | 0.666991i | ||||
\(733\) | 4.15219i | 0.153364i | 0.997056 | + | 0.0766822i | \(0.0244327\pi\) | ||||
−0.997056 | + | 0.0766822i | \(0.975567\pi\) | |||||||
\(734\) | −53.7256 | −1.98305 | ||||||||
\(735\) | −1.49343 | − | 0.877309i | −0.0550859 | − | 0.0323600i | ||||
\(736\) | − | 0.205781i | − | 0.00758519i | ||||||
\(737\) | 8.91028 | + | 34.5350i | 0.328214 | + | 1.27211i | ||||
\(738\) | −19.3616 | − | 34.7344i | −0.712711 | − | 1.27859i | ||||
\(739\) | − | 18.8605i | − | 0.693796i | −0.937903 | − | 0.346898i | \(-0.887235\pi\) | ||
0.937903 | − | 0.346898i | \(-0.112765\pi\) | |||||||
\(740\) | − | 32.1901i | − | 1.18333i | ||||||
\(741\) | 36.8768 | − | 62.7748i | 1.35470 | − | 2.30609i | ||||
\(742\) | −18.4498 | −0.677313 | ||||||||
\(743\) | −29.8260 | −1.09421 | −0.547105 | − | 0.837064i | \(-0.684270\pi\) | ||||
−0.547105 | + | 0.837064i | \(0.684270\pi\) | |||||||
\(744\) | −9.34301 | + | 15.9045i | −0.342531 | + | 0.583086i | ||||
\(745\) | 3.70906i | 0.135889i | ||||||||
\(746\) | − | 14.2033i | − | 0.520021i | ||||||
\(747\) | 6.24414 | + | 11.2019i | 0.228461 | + | 0.409855i | ||||
\(748\) | 17.3327 | + | 67.1790i | 0.633745 | + | 2.45631i | ||||
\(749\) | − | 11.0644i | − | 0.404286i | ||||||
\(750\) | 3.66012 | + | 2.15012i | 0.133649 | + | 0.0785114i | ||||
\(751\) | 0.946690 | 0.0345452 | 0.0172726 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172726 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(752\) | 31.7800i | 1.15890i | ||||||||
\(753\) | −30.5542 | − | 17.9489i | −1.11346 | − | 0.654096i | ||||
\(754\) | 67.6079i | 2.46213i | ||||||||
\(755\) | 3.84108 | 0.139791 | ||||||||
\(756\) | 0.470790 | − | 20.8131i | 0.0171225 | − | 0.756964i | ||||
\(757\) | −14.6974 | −0.534188 | −0.267094 | − | 0.963671i | \(-0.586063\pi\) | ||||
−0.267094 | + | 0.963671i | \(0.586063\pi\) | |||||||
\(758\) | −62.5764 | −2.27288 | ||||||||
\(759\) | 5.09371 | − | 17.8052i | 0.184890 | − | 0.646290i | ||||
\(760\) | 30.5724 | 1.10898 | ||||||||
\(761\) | 51.7603 | 1.87631 | 0.938155 | − | 0.346215i | \(-0.112533\pi\) | ||||
0.938155 | + | 0.346215i | \(0.112533\pi\) | |||||||
\(762\) | 31.7351 | + | 18.6427i | 1.14964 | + | 0.675353i | ||||
\(763\) | −15.3821 | −0.556868 | ||||||||
\(764\) | − | 54.0317i | − | 1.95480i | ||||||
\(765\) | −13.6815 | + | 7.62632i | −0.494655 | + | 0.275730i | ||||
\(766\) | 65.3120i | 2.35982i | ||||||||
\(767\) | 33.1602 | 1.19735 | ||||||||
\(768\) | −28.1186 | + | 47.8659i | −1.01464 | + | 1.72721i | ||||
\(769\) | 13.4546i | 0.485186i | 0.970128 | + | 0.242593i | \(0.0779980\pi\) | ||||
−0.970128 | + | 0.242593i | \(0.922002\pi\) | |||||||
\(770\) | −2.03069 | − | 7.87069i | −0.0731811 | − | 0.283640i | ||||
\(771\) | 7.64761 | + | 4.49256i | 0.275422 | + | 0.161795i | ||||
\(772\) | 78.2978i | 2.81800i | ||||||||
\(773\) | 11.4201i | 0.410753i | 0.978683 | + | 0.205376i | \(0.0658418\pi\) | ||||
−0.978683 | + | 0.205376i | \(0.934158\pi\) | |||||||
\(774\) | 44.7215 | − | 24.9286i | 1.60748 | − | 0.896041i | ||||
\(775\) | −2.16563 | −0.0777917 | ||||||||
\(776\) | 76.2067 | 2.73566 | ||||||||
\(777\) | −11.9989 | − | 7.04870i | −0.430458 | − | 0.252871i | ||||
\(778\) | 91.2170i | 3.27029i | ||||||||
\(779\) | − | 33.6249i | − | 1.20474i | ||||||
\(780\) | 23.7651 | − | 40.4550i | 0.850927 | − | 1.44852i | ||||
\(781\) | 25.9967 | − | 6.70732i | 0.930233 | − | 0.240007i | ||||
\(782\) | 41.2524i | 1.47518i | ||||||||
\(783\) | −21.1951 | − | 0.479431i | −0.757451 | − | 0.0171335i | ||||
\(784\) | −4.03905 | −0.144252 | ||||||||
\(785\) | − | 4.25023i | − | 0.151697i | ||||||
\(786\) | 2.72413 | − | 4.63724i | 0.0971664 | − | 0.165405i | ||||
\(787\) | 18.4375i | 0.657226i | 0.944465 | + | 0.328613i | \(0.106581\pi\) | ||||
−0.944465 | + | 0.328613i | \(0.893419\pi\) | |||||||
\(788\) | −15.5920 | −0.555443 | ||||||||
\(789\) | −15.4038 | + | 26.2216i | −0.548389 | + | 0.933513i | ||||
\(790\) | −25.2457 | −0.898200 | ||||||||
\(791\) | −2.90261 | −0.103205 | ||||||||
\(792\) | 35.4311 | − | 33.7446i | 1.25899 | − | 1.19906i | ||||
\(793\) | 34.7120 | 1.23266 | ||||||||
\(794\) | −16.0815 | −0.570710 | ||||||||
\(795\) | 6.60439 | − | 11.2426i | 0.234234 | − | 0.398732i | ||||
\(796\) | −62.4023 | −2.21179 | ||||||||
\(797\) | 10.8354i | 0.383810i | 0.981414 | + | 0.191905i | \(0.0614666\pi\) | ||||
−0.981414 | + | 0.191905i | \(0.938533\pi\) | |||||||
\(798\) | 13.3673 | − | 22.7549i | 0.473196 | − | 0.805514i | ||||
\(799\) | − | 41.0810i | − | 1.45334i | ||||||
\(800\) | 0.0638312 | 0.00225677 | ||||||||
\(801\) | −19.1303 | + | 10.6636i | −0.675935 | + | 0.376779i | ||||
\(802\) | 4.16620i | 0.147114i | ||||||||
\(803\) | −32.8202 | + | 8.46784i | −1.15820 | + | 0.298824i | ||||
\(804\) | −37.7986 | + | 64.3439i | −1.33305 | + | 2.26923i | ||||
\(805\) | − | 3.22384i | − | 0.113625i | ||||||
\(806\) | 35.8853i | 1.26401i | ||||||||
\(807\) | 24.9608 | + | 14.6631i | 0.878662 | + | 0.516167i | ||||
\(808\) | 18.9208 | 0.665633 | ||||||||
\(809\) | 5.97274 | 0.209990 | 0.104995 | − | 0.994473i | \(-0.466517\pi\) | ||||
0.104995 | + | 0.994473i | \(0.466517\pi\) | |||||||
\(810\) | 18.7610 | + | 11.5996i | 0.659195 | + | 0.407568i | ||||
\(811\) | 29.1820i | 1.02472i | 0.858772 | + | 0.512359i | \(0.171228\pi\) | ||||
−0.858772 | + | 0.512359i | \(0.828772\pi\) | |||||||
\(812\) | 16.3467i | 0.573656i | ||||||||
\(813\) | −44.3551 | − | 26.0562i | −1.55560 | − | 0.913831i | ||||
\(814\) | −16.3155 | − | 63.2367i | −0.571859 | − | 2.21645i | ||||
\(815\) | 16.3126i | 0.571405i | ||||||||
\(816\) | −18.5011 | + | 31.4941i | −0.647668 | + | 1.10251i | ||||
\(817\) | 43.2930 | 1.51463 | ||||||||
\(818\) | − | 63.2201i | − | 2.21044i | ||||||
\(819\) | −9.87577 | − | 17.7170i | −0.345087 | − | 0.619080i | ||||
\(820\) | − | 21.6694i | − | 0.756729i | ||||||
\(821\) | 6.98359 | 0.243729 | 0.121865 | − | 0.992547i | \(-0.461113\pi\) | ||||
0.121865 | + | 0.992547i | \(0.461113\pi\) | |||||||
\(822\) | 28.9838 | + | 17.0264i | 1.01093 | + | 0.593865i | ||||
\(823\) | −37.2635 | −1.29892 | −0.649461 | − | 0.760395i | \(-0.725006\pi\) | ||||
−0.649461 | + | 0.760395i | \(0.725006\pi\) | |||||||
\(824\) | −43.6242 | −1.51972 | ||||||||
\(825\) | 5.52300 | + | 1.58002i | 0.192286 | + | 0.0550091i | ||||
\(826\) | 12.0200 | 0.418231 | ||||||||
\(827\) | 30.8523 | 1.07284 | 0.536421 | − | 0.843951i | \(-0.319776\pi\) | ||||
0.536421 | + | 0.843951i | \(0.319776\pi\) | |||||||
\(828\) | 33.8458 | − | 18.8663i | 1.17622 | − | 0.655649i | ||||
\(829\) | −45.1467 | −1.56801 | −0.784005 | − | 0.620754i | \(-0.786826\pi\) | ||||
−0.784005 | + | 0.620754i | \(0.786826\pi\) | |||||||
\(830\) | 10.4769i | 0.363660i | ||||||||
\(831\) | 15.1557 | + | 8.90313i | 0.525744 | + | 0.308846i | ||||
\(832\) | 53.5597i | 1.85685i | ||||||||
\(833\) | 5.22115 | 0.180902 | ||||||||
\(834\) | −30.9000 | − | 18.1521i | −1.06998 | − | 0.628555i | ||||
\(835\) | 1.33486i | 0.0461949i | ||||||||
\(836\) | 79.9920 | − | 20.6385i | 2.76658 | − | 0.713797i | ||||
\(837\) | −11.2501 | − | 0.254476i | −0.388859 | − | 0.00879596i | ||||
\(838\) | − | 36.7011i | − | 1.26782i | ||||||
\(839\) | 32.7880i | 1.13197i | 0.824417 | + | 0.565983i | \(0.191503\pi\) | ||||
−0.824417 | + | 0.565983i | \(0.808497\pi\) | |||||||
\(840\) | 4.31422 | − | 7.34403i | 0.148855 | − | 0.253393i | ||||
\(841\) | −12.3533 | −0.425975 | ||||||||
\(842\) | 81.1152 | 2.79541 | ||||||||
\(843\) | 8.63988 | − | 14.7075i | 0.297573 | − | 0.506554i | ||||
\(844\) | 39.5584i | 1.36166i | ||||||||
\(845\) | − | 32.7135i | − | 1.12538i | ||||||
\(846\) | −50.5304 | + | 28.1666i | −1.73727 | + | 0.968387i | ||||
\(847\) | −5.32189 | − | 9.62691i | −0.182862 | − | 0.330785i | ||||
\(848\) | − | 30.4060i | − | 1.04415i | ||||||
\(849\) | −15.5211 | − | 9.11780i | −0.532682 | − | 0.312922i | ||||
\(850\) | −12.7961 | −0.438902 | ||||||||
\(851\) | − | 25.9018i | − | 0.887901i | ||||||
\(852\) | 48.4356 | + | 28.4533i | 1.65938 | + | 0.974795i | ||||
\(853\) | − | 5.83489i | − | 0.199783i | −0.994998 | − | 0.0998914i | \(-0.968150\pi\) | ||
0.994998 | − | 0.0998914i | \(-0.0318495\pi\) | |||||||
\(854\) | 12.5825 | 0.430566 | ||||||||
\(855\) | 9.08088 | + | 16.2909i | 0.310559 | + | 0.557138i | ||||
\(856\) | 54.4101 | 1.85970 | ||||||||
\(857\) | 9.05521 | 0.309320 | 0.154660 | − | 0.987968i | \(-0.450572\pi\) | ||||
0.154660 | + | 0.987968i | \(0.450572\pi\) | |||||||
\(858\) | 26.1815 | − | 91.5183i | 0.893821 | − | 3.12438i | ||||
\(859\) | 21.7802 | 0.743131 | 0.371566 | − | 0.928407i | \(-0.378821\pi\) | ||||
0.371566 | + | 0.928407i | \(0.378821\pi\) | |||||||
\(860\) | 27.9000 | 0.951382 | ||||||||
\(861\) | −8.07730 | − | 4.74498i | −0.275274 | − | 0.161708i | ||||
\(862\) | −49.4145 | −1.68306 | ||||||||
\(863\) | − | 18.0628i | − | 0.614866i | −0.951570 | − | 0.307433i | \(-0.900530\pi\) | ||
0.951570 | − | 0.307433i | \(-0.0994701\pi\) | |||||||
\(864\) | 0.331592 | + | 0.00750057i | 0.0112810 | + | 0.000255175i | ||||
\(865\) | − | 12.3959i | − | 0.421475i | ||||||
\(866\) | −83.1905 | −2.82693 | ||||||||
\(867\) | 9.00154 | − | 15.3232i | 0.305708 | − | 0.520402i | ||||
\(868\) | 8.67660i | 0.294503i | ||||||||
\(869\) | −33.0810 | + | 8.53512i | −1.12219 | + | 0.289534i | ||||
\(870\) | −14.9334 | − | 8.77259i | −0.506291 | − | 0.297419i | ||||
\(871\) | 72.7076i | 2.46360i | ||||||||
\(872\) | − | 75.6423i | − | 2.56157i | ||||||
\(873\) | 22.6356 | + | 40.6078i | 0.766099 | + | 1.37437i | ||||
\(874\) | 49.1205 | 1.66153 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −61.1489 | − | 35.9217i | −2.06603 | − | 1.21368i | ||||
\(877\) | − | 31.8025i | − | 1.07389i | −0.843616 | − | 0.536947i | \(-0.819578\pi\) | ||
0.843616 | − | 0.536947i | \(-0.180422\pi\) | |||||||
\(878\) | 83.4438i | 2.81609i | ||||||||
\(879\) | 26.4436 | − | 45.0146i | 0.891921 | − | 1.51830i | ||||
\(880\) | 12.9712 | − | 3.34667i | 0.437260 | − | 0.112816i | ||||
\(881\) | − | 4.72317i | − | 0.159128i | −0.996830 | − | 0.0795639i | \(-0.974647\pi\) | ||
0.996830 | − | 0.0795639i | \(-0.0253528\pi\) | |||||||
\(882\) | −3.57981 | − | 6.42211i | −0.120538 | − | 0.216244i | ||||
\(883\) | 3.61235 | 0.121565 | 0.0607826 | − | 0.998151i | \(-0.480640\pi\) | ||||
0.0607826 | + | 0.998151i | \(0.480640\pi\) | |||||||
\(884\) | 141.434i | 4.75693i | ||||||||
\(885\) | −4.30276 | + | 7.32453i | −0.144636 | + | 0.246211i | ||||
\(886\) | − | 10.1585i | − | 0.341283i | ||||||
\(887\) | −21.2949 | −0.715013 | −0.357507 | − | 0.933911i | \(-0.616373\pi\) | ||||
−0.357507 | + | 0.933911i | \(0.616373\pi\) | |||||||
\(888\) | 34.6624 | − | 59.0053i | 1.16320 | − | 1.98009i | ||||
\(889\) | 8.67052 | 0.290800 | ||||||||
\(890\) | −17.8922 | −0.599750 | ||||||||
\(891\) | 28.5054 | + | 8.85689i | 0.954965 | + | 0.296717i | ||||
\(892\) | −36.3880 | −1.21836 | ||||||||
\(893\) | −48.9163 | −1.63692 | ||||||||
\(894\) | −7.97493 | + | 13.5756i | −0.266721 | + | 0.454036i | ||||
\(895\) | 21.9783 | 0.734655 | ||||||||
\(896\) | 19.5422i | 0.652858i | ||||||||
\(897\) | 19.1226 | − | 32.5521i | 0.638486 | − | 1.08688i | ||||
\(898\) | 64.1680i | 2.14131i | ||||||||
\(899\) | 8.83586 | 0.294692 | ||||||||
\(900\) | 5.85213 | + | 10.4986i | 0.195071 | + | 0.349954i | ||||
\(901\) | 39.3049i | 1.30944i | ||||||||
\(902\) | −10.9831 | − | 42.5691i | −0.365698 | − | 1.41740i | ||||
\(903\) | 6.10930 | − | 10.3998i | 0.203305 | − | 0.346082i | ||||
\(904\) | − | 14.2738i | − | 0.474738i | ||||||
\(905\) | 20.1572i | 0.670048i | ||||||||
\(906\) | 14.0588 | + | 8.25879i | 0.467073 | + | 0.274380i | ||||
\(907\) | 47.1038 | 1.56406 | 0.782028 | − | 0.623243i | \(-0.214185\pi\) | ||||
0.782028 | + | 0.623243i | \(0.214185\pi\) | |||||||
\(908\) | 74.5472 | 2.47393 | ||||||||
\(909\) | 5.62004 | + | 10.0823i | 0.186405 | + | 0.334407i | ||||
\(910\) | − | 16.5704i | − | 0.549303i | ||||||
\(911\) | − | 11.6892i | − | 0.387280i | −0.981073 | − | 0.193640i | \(-0.937971\pi\) | ||
0.981073 | − | 0.193640i | \(-0.0620293\pi\) | |||||||
\(912\) | 37.5010 | + | 22.0298i | 1.24178 | + | 0.729479i | ||||
\(913\) | 3.54207 | + | 13.7286i | 0.117226 | + | 0.454350i | ||||
\(914\) | 31.4266i | 1.03950i | ||||||||
\(915\) | −4.50412 | + | 7.66729i | −0.148902 | + | 0.253473i | ||||
\(916\) | −1.96769 | −0.0650143 | ||||||||
\(917\) | − | 1.26696i | − | 0.0418388i | ||||||
\(918\) | −66.4734 | − | 1.50362i | −2.19395 | − | 0.0496269i | ||||
\(919\) | − | 31.1086i | − | 1.02618i | −0.858335 | − | 0.513090i | \(-0.828501\pi\) | ||
0.858335 | − | 0.513090i | \(-0.171499\pi\) | |||||||
\(920\) | 15.8534 | 0.522672 | ||||||||
\(921\) | 6.30783 | + | 3.70551i | 0.207850 | + | 0.122101i | ||||
\(922\) | 40.3084 | 1.32749 | ||||||||
\(923\) | 54.7315 | 1.80151 | ||||||||
\(924\) | 6.33034 | − | 22.1279i | 0.208253 | − | 0.727955i | ||||
\(925\) | 8.03446 | 0.264171 | ||||||||
\(926\) | 42.2514 | 1.38847 | ||||||||
\(927\) | −12.9577 | − | 23.2458i | −0.425585 | − | 0.763492i | ||||
\(928\) | −0.260434 | −0.00854915 | ||||||||
\(929\) | 30.9160i | 1.01432i | 0.861852 | + | 0.507160i | \(0.169305\pi\) | ||||
−0.861852 | + | 0.507160i | \(0.830695\pi\) | |||||||
\(930\) | −7.92647 | − | 4.65637i | −0.259919 | − | 0.152688i | ||||
\(931\) | − | 6.21697i | − | 0.203753i | ||||||
\(932\) | −16.1470 | −0.528911 | ||||||||
\(933\) | −13.8278 | − | 8.12311i | −0.452703 | − | 0.265939i | ||||
\(934\) | 87.4206i | 2.86049i | ||||||||
\(935\) | −16.7675 | + | 4.32613i | −0.548356 | + | 0.141480i | ||||
\(936\) | 87.1242 | − | 48.5647i | 2.84775 | − | 1.58739i | ||||
\(937\) | 12.3089i | 0.402115i | 0.979579 | + | 0.201057i | \(0.0644378\pi\) | ||||
−0.979579 | + | 0.201057i | \(0.935562\pi\) | |||||||
\(938\) | 26.3553i | 0.860532i | ||||||||
\(939\) | −14.2055 | + | 24.1819i | −0.463580 | + | 0.789146i | ||||
\(940\) | −31.5239 | −1.02820 | ||||||||
\(941\) | −42.6841 | −1.39146 | −0.695731 | − | 0.718303i | \(-0.744919\pi\) | ||||
−0.695731 | + | 0.718303i | \(0.744919\pi\) | |||||||
\(942\) | 9.13852 | − | 15.5564i | 0.297749 | − | 0.506854i | ||||
\(943\) | − | 17.4363i | − | 0.567804i | ||||||
\(944\) | 19.8095i | 0.644745i | ||||||||
\(945\) | 5.19482 | + | 0.117506i | 0.168988 | + | 0.00382249i | ||||
\(946\) | 54.8090 | − | 14.1411i | 1.78199 | − | 0.459767i | ||||
\(947\) | − | 19.7327i | − | 0.641228i | −0.947210 | − | 0.320614i | \(-0.896111\pi\) | ||
0.947210 | − | 0.320614i | \(-0.103889\pi\) | |||||||
\(948\) | −61.6347 | − | 36.2071i | −2.00180 | − | 1.17595i | ||||
\(949\) | −69.0973 | −2.24299 | ||||||||
\(950\) | 15.2367i | 0.494343i | ||||||||
\(951\) | −20.3900 | − | 11.9780i | −0.661192 | − | 0.388415i | ||||
\(952\) | 25.6753i | 0.832142i | ||||||||
\(953\) | −1.70876 | −0.0553521 | −0.0276761 | − | 0.999617i | \(-0.508811\pi\) | ||||
−0.0276761 | + | 0.999617i | \(0.508811\pi\) | |||||||
\(954\) | 48.3457 | − | 26.9488i | 1.56525 | − | 0.872501i | ||||
\(955\) | 13.4860 | 0.436397 | ||||||||
\(956\) | −102.645 | −3.31977 | ||||||||
\(957\) | −22.5341 | − | 6.44653i | −0.728423 | − | 0.208387i | ||||
\(958\) | −36.1591 | −1.16825 | ||||||||
\(959\) | 7.91882 | 0.255712 | ||||||||
\(960\) | −11.8304 | − | 6.94974i | −0.381825 | − | 0.224302i | ||||
\(961\) | −26.3100 | −0.848711 | ||||||||
\(962\) | − | 133.134i | − | 4.29242i | ||||||
\(963\) | 16.1614 | + | 28.9932i | 0.520793 | + | 0.934294i | ||||
\(964\) | − | 81.5270i | − | 2.62581i | ||||||
\(965\) | −19.5427 | −0.629102 | ||||||||
\(966\) | 6.93164 | − | 11.7996i | 0.223022 | − | 0.379647i | ||||
\(967\) | 26.7536i | 0.860338i | 0.902748 | + | 0.430169i | \(0.141546\pi\) | ||||
−0.902748 | + | 0.430169i | \(0.858454\pi\) | |||||||
\(968\) | 47.3410 | − | 26.1707i | 1.52160 | − | 0.841159i | ||||
\(969\) | −48.4763 | − | 28.4772i | −1.55728 | − | 0.914820i | ||||
\(970\) | 37.9799i | 1.21946i | ||||||||
\(971\) | 36.5926i | 1.17431i | 0.809474 | + | 0.587156i | \(0.199753\pi\) | ||||
−0.809474 | + | 0.587156i | \(0.800247\pi\) | |||||||
\(972\) | 29.1671 | + | 55.2261i | 0.935536 | + | 1.77138i | ||||
\(973\) | −8.44234 | −0.270649 | ||||||||
\(974\) | −86.2174 | −2.76259 | ||||||||
\(975\) | 10.0973 | + | 5.93164i | 0.323373 | + | 0.189964i | ||||
\(976\) | 20.7365i | 0.663761i | ||||||||
\(977\) | 17.3345i | 0.554581i | 0.960786 | + | 0.277291i | \(0.0894364\pi\) | ||||
−0.960786 | + | 0.277291i | \(0.910564\pi\) | |||||||
\(978\) | −35.0741 | + | 59.7060i | −1.12154 | + | 1.90919i | ||||
\(979\) | −23.4453 | + | 6.04906i | −0.749316 | + | 0.193329i | ||||
\(980\) | − | 4.00650i | − | 0.127983i | ||||||
\(981\) | 40.3071 | − | 22.4679i | 1.28691 | − | 0.717346i | ||||
\(982\) | 13.2610 | 0.423176 | ||||||||
\(983\) | − | 24.9667i | − | 0.796313i | −0.917317 | − | 0.398157i | \(-0.869650\pi\) | ||
0.917317 | − | 0.398157i | \(-0.130350\pi\) | |||||||
\(984\) | 23.3337 | − | 39.7207i | 0.743852 | − | 1.26625i | ||||
\(985\) | − | 3.89168i | − | 0.123999i | ||||||
\(986\) | 52.2085 | 1.66266 | ||||||||
\(987\) | −6.90283 | + | 11.7506i | −0.219720 | + | 0.374025i | ||||
\(988\) | 168.409 | 5.35782 | ||||||||
\(989\) | 22.4498 | 0.713861 | ||||||||
\(990\) | 16.8176 | + | 17.6582i | 0.534499 | + | 0.561214i | ||||
\(991\) | −11.2435 | −0.357162 | −0.178581 | − | 0.983925i | \(-0.557151\pi\) | ||||
−0.178581 | + | 0.983925i | \(0.557151\pi\) | |||||||
\(992\) | −0.138235 | −0.00438896 | ||||||||
\(993\) | 13.8619 | − | 23.5970i | 0.439895 | − | 0.748827i | ||||
\(994\) | 19.8393 | 0.629264 | ||||||||
\(995\) | − | 15.5753i | − | 0.493769i | ||||||
\(996\) | −15.0259 | + | 25.5784i | −0.476115 | + | 0.810483i | ||||
\(997\) | − | 50.2675i | − | 1.59199i | −0.605305 | − | 0.795994i | \(-0.706949\pi\) | ||
0.605305 | − | 0.795994i | \(-0.293051\pi\) | |||||||
\(998\) | 82.5040 | 2.61162 | ||||||||
\(999\) | 41.7376 | + | 0.944101i | 1.32052 | + | 0.0298700i |
(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 | 1155.2.l.f.1121.6 | yes | 40 | |
3.2 | odd | 2 | 1155.2.l.e.1121.35 | ✓ | 40 | ||
11.10 | odd | 2 | 1155.2.l.e.1121.36 | yes | 40 | ||
33.32 | even | 2 | inner | 1155.2.l.f.1121.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.e.1121.35 | ✓ | 40 | 3.2 | odd | 2 | ||
1155.2.l.e.1121.36 | yes | 40 | 11.10 | odd | 2 | ||
1155.2.l.f.1121.5 | yes | 40 | 33.32 | even | 2 | inner | |
1155.2.l.f.1121.6 | yes | 40 | 1.1 | even | 1 | trivial |