Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45467 | −1.02860 | −0.514302 | − | 0.857609i | \(-0.671949\pi\) | ||||
−0.514302 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(3\) | 0.452328 | 0.261152 | 0.130576 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130576 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(4\) | 0.116052 | 0.0580258 | ||||||||
\(5\) | −2.57197 | −1.15022 | −0.575111 | − | 0.818076i | \(-0.695041\pi\) | ||||
−0.575111 | + | 0.818076i | \(0.695041\pi\) | |||||||
\(6\) | −0.657986 | −0.268622 | ||||||||
\(7\) | 3.66955 | 1.38696 | 0.693481 | − | 0.720475i | \(-0.256076\pi\) | ||||
0.693481 | + | 0.720475i | \(0.256076\pi\) | |||||||
\(8\) | 2.74051 | 0.968918 | ||||||||
\(9\) | −2.79540 | −0.931800 | ||||||||
\(10\) | 3.74136 | 1.18312 | ||||||||
\(11\) | −2.93433 | −0.884733 | −0.442366 | − | 0.896834i | \(-0.645861\pi\) | ||||
−0.442366 | + | 0.896834i | \(0.645861\pi\) | |||||||
\(12\) | 0.0524935 | 0.0151536 | ||||||||
\(13\) | 2.49330 | 0.691518 | 0.345759 | − | 0.938323i | \(-0.387621\pi\) | ||||
0.345759 | + | 0.938323i | \(0.387621\pi\) | |||||||
\(14\) | −5.33797 | −1.42663 | ||||||||
\(15\) | −1.16338 | −0.300382 | ||||||||
\(16\) | −4.21864 | −1.05466 | ||||||||
\(17\) | 6.40808 | 1.55419 | 0.777094 | − | 0.629384i | \(-0.216693\pi\) | ||||
0.777094 | + | 0.629384i | \(0.216693\pi\) | |||||||
\(18\) | 4.06637 | 0.958453 | ||||||||
\(19\) | −3.49802 | −0.802501 | −0.401251 | − | 0.915968i | \(-0.631424\pi\) | ||||
−0.401251 | + | 0.915968i | \(0.631424\pi\) | |||||||
\(20\) | −0.298482 | −0.0667426 | ||||||||
\(21\) | 1.65984 | 0.362208 | ||||||||
\(22\) | 4.26846 | 0.910040 | ||||||||
\(23\) | 1.44313 | 0.300914 | 0.150457 | − | 0.988617i | \(-0.451925\pi\) | ||||
0.150457 | + | 0.988617i | \(0.451925\pi\) | |||||||
\(24\) | 1.23961 | 0.253035 | ||||||||
\(25\) | 1.61505 | 0.323009 | ||||||||
\(26\) | −3.62692 | −0.711298 | ||||||||
\(27\) | −2.62142 | −0.504493 | ||||||||
\(28\) | 0.425858 | 0.0804796 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.69232 | 0.308975 | ||||||||
\(31\) | −8.88131 | −1.59513 | −0.797565 | − | 0.603232i | \(-0.793879\pi\) | ||||
−0.797565 | + | 0.603232i | \(0.793879\pi\) | |||||||
\(32\) | 0.655674 | 0.115908 | ||||||||
\(33\) | −1.32728 | −0.231050 | ||||||||
\(34\) | −9.32162 | −1.59864 | ||||||||
\(35\) | −9.43800 | −1.59531 | ||||||||
\(36\) | −0.324411 | −0.0540685 | ||||||||
\(37\) | −2.73580 | −0.449763 | −0.224882 | − | 0.974386i | \(-0.572200\pi\) | ||||
−0.224882 | + | 0.974386i | \(0.572200\pi\) | |||||||
\(38\) | 5.08845 | 0.825456 | ||||||||
\(39\) | 1.12779 | 0.180591 | ||||||||
\(40\) | −7.04853 | −1.11447 | ||||||||
\(41\) | 0.584181 | 0.0912337 | 0.0456168 | − | 0.998959i | \(-0.485475\pi\) | ||||
0.0456168 | + | 0.998959i | \(0.485475\pi\) | |||||||
\(42\) | −2.41452 | −0.372568 | ||||||||
\(43\) | 0.583716 | 0.0890159 | 0.0445079 | − | 0.999009i | \(-0.485828\pi\) | ||||
0.0445079 | + | 0.999009i | \(0.485828\pi\) | |||||||
\(44\) | −0.340534 | −0.0513374 | ||||||||
\(45\) | 7.18969 | 1.07178 | ||||||||
\(46\) | −2.09928 | −0.309521 | ||||||||
\(47\) | 4.41166 | 0.643506 | 0.321753 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321753 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(48\) | −1.90821 | −0.275426 | ||||||||
\(49\) | 6.46563 | 0.923662 | ||||||||
\(50\) | −2.34935 | −0.332248 | ||||||||
\(51\) | 2.89856 | 0.405879 | ||||||||
\(52\) | 0.289352 | 0.0401259 | ||||||||
\(53\) | 0.988874 | 0.135832 | 0.0679162 | − | 0.997691i | \(-0.478365\pi\) | ||||
0.0679162 | + | 0.997691i | \(0.478365\pi\) | |||||||
\(54\) | 3.81329 | 0.518924 | ||||||||
\(55\) | 7.54701 | 1.01764 | ||||||||
\(56\) | 10.0565 | 1.34385 | ||||||||
\(57\) | −1.58225 | −0.209575 | ||||||||
\(58\) | −1.45467 | −0.191007 | ||||||||
\(59\) | 6.69320 | 0.871380 | 0.435690 | − | 0.900097i | \(-0.356504\pi\) | ||||
0.435690 | + | 0.900097i | \(0.356504\pi\) | |||||||
\(60\) | −0.135012 | −0.0174299 | ||||||||
\(61\) | 5.80854 | 0.743708 | 0.371854 | − | 0.928291i | \(-0.378722\pi\) | ||||
0.371854 | + | 0.928291i | \(0.378722\pi\) | |||||||
\(62\) | 12.9193 | 1.64076 | ||||||||
\(63\) | −10.2579 | −1.29237 | ||||||||
\(64\) | 7.48348 | 0.935436 | ||||||||
\(65\) | −6.41271 | −0.795399 | ||||||||
\(66\) | 1.93075 | 0.237659 | ||||||||
\(67\) | 5.16481 | 0.630982 | 0.315491 | − | 0.948929i | \(-0.397831\pi\) | ||||
0.315491 | + | 0.948929i | \(0.397831\pi\) | |||||||
\(68\) | 0.743669 | 0.0901831 | ||||||||
\(69\) | 0.652770 | 0.0785843 | ||||||||
\(70\) | 13.7291 | 1.64094 | ||||||||
\(71\) | 3.81808 | 0.453123 | 0.226561 | − | 0.973997i | \(-0.427252\pi\) | ||||
0.226561 | + | 0.973997i | \(0.427252\pi\) | |||||||
\(72\) | −7.66083 | −0.902838 | ||||||||
\(73\) | −15.3088 | −1.79176 | −0.895880 | − | 0.444295i | \(-0.853454\pi\) | ||||
−0.895880 | + | 0.444295i | \(0.853454\pi\) | |||||||
\(74\) | 3.97968 | 0.462628 | ||||||||
\(75\) | 0.730531 | 0.0843544 | ||||||||
\(76\) | −0.405951 | −0.0465658 | ||||||||
\(77\) | −10.7677 | −1.22709 | ||||||||
\(78\) | −1.64056 | −0.185757 | ||||||||
\(79\) | −3.65727 | −0.411475 | −0.205738 | − | 0.978607i | \(-0.565959\pi\) | ||||
−0.205738 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(80\) | 10.8502 | 1.21309 | ||||||||
\(81\) | 7.20045 | 0.800050 | ||||||||
\(82\) | −0.849787 | −0.0938433 | ||||||||
\(83\) | 11.4971 | 1.26197 | 0.630985 | − | 0.775795i | \(-0.282651\pi\) | ||||
0.630985 | + | 0.775795i | \(0.282651\pi\) | |||||||
\(84\) | 0.192628 | 0.0210174 | ||||||||
\(85\) | −16.4814 | −1.78766 | ||||||||
\(86\) | −0.849112 | −0.0915621 | ||||||||
\(87\) | 0.452328 | 0.0484947 | ||||||||
\(88\) | −8.04157 | −0.857234 | ||||||||
\(89\) | −15.4764 | −1.64050 | −0.820249 | − | 0.572007i | \(-0.806165\pi\) | ||||
−0.820249 | + | 0.572007i | \(0.806165\pi\) | |||||||
\(90\) | −10.4586 | −1.10243 | ||||||||
\(91\) | 9.14931 | 0.959109 | ||||||||
\(92\) | 0.167478 | 0.0174608 | ||||||||
\(93\) | −4.01727 | −0.416571 | ||||||||
\(94\) | −6.41749 | −0.661913 | ||||||||
\(95\) | 8.99682 | 0.923054 | ||||||||
\(96\) | 0.296580 | 0.0302696 | ||||||||
\(97\) | 7.82262 | 0.794267 | 0.397133 | − | 0.917761i | \(-0.370005\pi\) | ||||
0.397133 | + | 0.917761i | \(0.370005\pi\) | |||||||
\(98\) | −9.40533 | −0.950082 | ||||||||
\(99\) | 8.20261 | 0.824394 | ||||||||
\(100\) | 0.187429 | 0.0187429 | ||||||||
\(101\) | −2.34504 | −0.233340 | −0.116670 | − | 0.993171i | \(-0.537222\pi\) | ||||
−0.116670 | + | 0.993171i | \(0.537222\pi\) | |||||||
\(102\) | −4.21643 | −0.417489 | ||||||||
\(103\) | 1.76883 | 0.174288 | 0.0871440 | − | 0.996196i | \(-0.472226\pi\) | ||||
0.0871440 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(104\) | 6.83293 | 0.670024 | ||||||||
\(105\) | −4.26907 | −0.416619 | ||||||||
\(106\) | −1.43848 | −0.139718 | ||||||||
\(107\) | −17.7276 | −1.71380 | −0.856898 | − | 0.515487i | \(-0.827611\pi\) | ||||
−0.856898 | + | 0.515487i | \(0.827611\pi\) | |||||||
\(108\) | −0.304221 | −0.0292736 | ||||||||
\(109\) | −7.06227 | −0.676443 | −0.338221 | − | 0.941067i | \(-0.609825\pi\) | ||||
−0.338221 | + | 0.941067i | \(0.609825\pi\) | |||||||
\(110\) | −10.9784 | −1.04675 | ||||||||
\(111\) | −1.23748 | −0.117457 | ||||||||
\(112\) | −15.4805 | −1.46277 | ||||||||
\(113\) | 10.3893 | 0.977345 | 0.488672 | − | 0.872467i | \(-0.337481\pi\) | ||||
0.488672 | + | 0.872467i | \(0.337481\pi\) | |||||||
\(114\) | 2.30165 | 0.215569 | ||||||||
\(115\) | −3.71170 | −0.346118 | ||||||||
\(116\) | 0.116052 | 0.0107751 | ||||||||
\(117\) | −6.96978 | −0.644356 | ||||||||
\(118\) | −9.73636 | −0.896305 | ||||||||
\(119\) | 23.5148 | 2.15560 | ||||||||
\(120\) | −3.18825 | −0.291046 | ||||||||
\(121\) | −2.38973 | −0.217248 | ||||||||
\(122\) | −8.44949 | −0.764981 | ||||||||
\(123\) | 0.264241 | 0.0238259 | ||||||||
\(124\) | −1.03069 | −0.0925588 | ||||||||
\(125\) | 8.70601 | 0.778689 | ||||||||
\(126\) | 14.9218 | 1.32934 | ||||||||
\(127\) | −3.76685 | −0.334254 | −0.167127 | − | 0.985935i | \(-0.553449\pi\) | ||||
−0.167127 | + | 0.985935i | \(0.553449\pi\) | |||||||
\(128\) | −12.1973 | −1.07810 | ||||||||
\(129\) | 0.264031 | 0.0232467 | ||||||||
\(130\) | 9.32835 | 0.818150 | ||||||||
\(131\) | 2.62936 | 0.229728 | 0.114864 | − | 0.993381i | \(-0.463357\pi\) | ||||
0.114864 | + | 0.993381i | \(0.463357\pi\) | |||||||
\(132\) | −0.154033 | −0.0134068 | ||||||||
\(133\) | −12.8362 | −1.11304 | ||||||||
\(134\) | −7.51307 | −0.649030 | ||||||||
\(135\) | 6.74223 | 0.580279 | ||||||||
\(136\) | 17.5614 | 1.50588 | ||||||||
\(137\) | −9.29355 | −0.794002 | −0.397001 | − | 0.917818i | \(-0.629949\pi\) | ||||
−0.397001 | + | 0.917818i | \(0.629949\pi\) | |||||||
\(138\) | −0.949562 | −0.0808321 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | −1.09530 | −0.0925693 | ||||||||
\(141\) | 1.99552 | 0.168053 | ||||||||
\(142\) | −5.55403 | −0.466084 | ||||||||
\(143\) | −7.31617 | −0.611809 | ||||||||
\(144\) | 11.7928 | 0.982731 | ||||||||
\(145\) | −2.57197 | −0.213591 | ||||||||
\(146\) | 22.2692 | 1.84301 | ||||||||
\(147\) | 2.92459 | 0.241216 | ||||||||
\(148\) | −0.317495 | −0.0260979 | ||||||||
\(149\) | 6.72008 | 0.550530 | 0.275265 | − | 0.961368i | \(-0.411234\pi\) | ||||
0.275265 | + | 0.961368i | \(0.411234\pi\) | |||||||
\(150\) | −1.06268 | −0.0867673 | ||||||||
\(151\) | −5.30911 | −0.432049 | −0.216024 | − | 0.976388i | \(-0.569309\pi\) | ||||
−0.216024 | + | 0.976388i | \(0.569309\pi\) | |||||||
\(152\) | −9.58638 | −0.777558 | ||||||||
\(153\) | −17.9132 | −1.44819 | ||||||||
\(154\) | 15.6634 | 1.26219 | ||||||||
\(155\) | 22.8425 | 1.83475 | ||||||||
\(156\) | 0.130882 | 0.0104790 | ||||||||
\(157\) | −1.43271 | −0.114343 | −0.0571713 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571713 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(158\) | 5.32010 | 0.423245 | ||||||||
\(159\) | 0.447296 | 0.0354729 | ||||||||
\(160\) | −1.68638 | −0.133320 | ||||||||
\(161\) | 5.29566 | 0.417356 | ||||||||
\(162\) | −10.4743 | −0.822935 | ||||||||
\(163\) | 0.759060 | 0.0594541 | 0.0297271 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297271 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(164\) | 0.0677951 | 0.00529391 | ||||||||
\(165\) | 3.41373 | 0.265758 | ||||||||
\(166\) | −16.7244 | −1.29807 | ||||||||
\(167\) | 18.4304 | 1.42619 | 0.713095 | − | 0.701067i | \(-0.247293\pi\) | ||||
0.713095 | + | 0.701067i | \(0.247293\pi\) | |||||||
\(168\) | 4.54883 | 0.350950 | ||||||||
\(169\) | −6.78344 | −0.521803 | ||||||||
\(170\) | 23.9750 | 1.83879 | ||||||||
\(171\) | 9.77837 | 0.747770 | ||||||||
\(172\) | 0.0677412 | 0.00516522 | ||||||||
\(173\) | −0.295069 | −0.0224337 | −0.0112168 | − | 0.999937i | \(-0.503571\pi\) | ||||
−0.0112168 | + | 0.999937i | \(0.503571\pi\) | |||||||
\(174\) | −0.657986 | −0.0498818 | ||||||||
\(175\) | 5.92650 | 0.448001 | ||||||||
\(176\) | 12.3789 | 0.933091 | ||||||||
\(177\) | 3.02752 | 0.227563 | ||||||||
\(178\) | 22.5130 | 1.68742 | ||||||||
\(179\) | 10.9862 | 0.821146 | 0.410573 | − | 0.911828i | \(-0.365329\pi\) | ||||
0.410573 | + | 0.911828i | \(0.365329\pi\) | |||||||
\(180\) | 0.834376 | 0.0621907 | ||||||||
\(181\) | −26.3556 | −1.95900 | −0.979498 | − | 0.201453i | \(-0.935434\pi\) | ||||
−0.979498 | + | 0.201453i | \(0.935434\pi\) | |||||||
\(182\) | −13.3092 | −0.986543 | ||||||||
\(183\) | 2.62737 | 0.194221 | ||||||||
\(184\) | 3.95493 | 0.291561 | ||||||||
\(185\) | 7.03641 | 0.517328 | ||||||||
\(186\) | 5.84378 | 0.428487 | ||||||||
\(187\) | −18.8034 | −1.37504 | ||||||||
\(188\) | 0.511980 | 0.0373400 | ||||||||
\(189\) | −9.61946 | −0.699713 | ||||||||
\(190\) | −13.0874 | −0.949457 | ||||||||
\(191\) | −23.0657 | −1.66898 | −0.834489 | − | 0.551025i | \(-0.814237\pi\) | ||||
−0.834489 | + | 0.551025i | \(0.814237\pi\) | |||||||
\(192\) | 3.38499 | 0.244291 | ||||||||
\(193\) | −16.3362 | −1.17591 | −0.587953 | − | 0.808895i | \(-0.700066\pi\) | ||||
−0.587953 | + | 0.808895i | \(0.700066\pi\) | |||||||
\(194\) | −11.3793 | −0.816986 | ||||||||
\(195\) | −2.90065 | −0.207720 | ||||||||
\(196\) | 0.750347 | 0.0535962 | ||||||||
\(197\) | 19.7708 | 1.40861 | 0.704306 | − | 0.709896i | \(-0.251258\pi\) | ||||
0.704306 | + | 0.709896i | \(0.251258\pi\) | |||||||
\(198\) | −11.9321 | −0.847975 | ||||||||
\(199\) | −25.5751 | −1.81297 | −0.906486 | − | 0.422237i | \(-0.861245\pi\) | ||||
−0.906486 | + | 0.422237i | \(0.861245\pi\) | |||||||
\(200\) | 4.42606 | 0.312969 | ||||||||
\(201\) | 2.33619 | 0.164782 | ||||||||
\(202\) | 3.41125 | 0.240015 | ||||||||
\(203\) | 3.66955 | 0.257552 | ||||||||
\(204\) | 0.336383 | 0.0235515 | ||||||||
\(205\) | −1.50250 | −0.104939 | ||||||||
\(206\) | −2.57306 | −0.179273 | ||||||||
\(207\) | −4.03413 | −0.280392 | ||||||||
\(208\) | −10.5183 | −0.729315 | ||||||||
\(209\) | 10.2643 | 0.709999 | ||||||||
\(210\) | 6.21007 | 0.428536 | ||||||||
\(211\) | 17.9825 | 1.23797 | 0.618984 | − | 0.785404i | \(-0.287545\pi\) | ||||
0.618984 | + | 0.785404i | \(0.287545\pi\) | |||||||
\(212\) | 0.114760 | 0.00788178 | ||||||||
\(213\) | 1.72703 | 0.118334 | ||||||||
\(214\) | 25.7878 | 1.76282 | ||||||||
\(215\) | −1.50130 | −0.102388 | ||||||||
\(216\) | −7.18405 | −0.488813 | ||||||||
\(217\) | −32.5905 | −2.21238 | ||||||||
\(218\) | 10.2732 | 0.695792 | ||||||||
\(219\) | −6.92461 | −0.467922 | ||||||||
\(220\) | 0.875843 | 0.0590493 | ||||||||
\(221\) | 15.9773 | 1.07475 | ||||||||
\(222\) | 1.80012 | 0.120816 | ||||||||
\(223\) | −18.3792 | −1.23076 | −0.615380 | − | 0.788231i | \(-0.710997\pi\) | ||||
−0.615380 | + | 0.788231i | \(0.710997\pi\) | |||||||
\(224\) | 2.40603 | 0.160760 | ||||||||
\(225\) | −4.51470 | −0.300980 | ||||||||
\(226\) | −15.1130 | −1.00530 | ||||||||
\(227\) | −21.3280 | −1.41559 | −0.707795 | − | 0.706418i | \(-0.750310\pi\) | ||||
−0.707795 | + | 0.706418i | \(0.750310\pi\) | |||||||
\(228\) | −0.183623 | −0.0121607 | ||||||||
\(229\) | 12.6990 | 0.839176 | 0.419588 | − | 0.907715i | \(-0.362175\pi\) | ||||
0.419588 | + | 0.907715i | \(0.362175\pi\) | |||||||
\(230\) | 5.39928 | 0.356018 | ||||||||
\(231\) | −4.87052 | −0.320457 | ||||||||
\(232\) | 2.74051 | 0.179924 | ||||||||
\(233\) | −13.1917 | −0.864217 | −0.432108 | − | 0.901822i | \(-0.642230\pi\) | ||||
−0.432108 | + | 0.901822i | \(0.642230\pi\) | |||||||
\(234\) | 10.1387 | 0.662787 | ||||||||
\(235\) | −11.3467 | −0.740175 | ||||||||
\(236\) | 0.776756 | 0.0505625 | ||||||||
\(237\) | −1.65429 | −0.107457 | ||||||||
\(238\) | −34.2062 | −2.21726 | ||||||||
\(239\) | −7.10677 | −0.459699 | −0.229849 | − | 0.973226i | \(-0.573823\pi\) | ||||
−0.229849 | + | 0.973226i | \(0.573823\pi\) | |||||||
\(240\) | 4.90786 | 0.316801 | ||||||||
\(241\) | −13.3767 | −0.861667 | −0.430834 | − | 0.902431i | \(-0.641780\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641780\pi\) | |||||||
\(242\) | 3.47625 | 0.223462 | ||||||||
\(243\) | 11.1212 | 0.713428 | ||||||||
\(244\) | 0.674091 | 0.0431543 | ||||||||
\(245\) | −16.6294 | −1.06242 | ||||||||
\(246\) | −0.384383 | −0.0245074 | ||||||||
\(247\) | −8.72163 | −0.554944 | ||||||||
\(248\) | −24.3394 | −1.54555 | ||||||||
\(249\) | 5.20046 | 0.329566 | ||||||||
\(250\) | −12.6643 | −0.800963 | ||||||||
\(251\) | −0.947082 | −0.0597793 | −0.0298896 | − | 0.999553i | \(-0.509516\pi\) | ||||
−0.0298896 | + | 0.999553i | \(0.509516\pi\) | |||||||
\(252\) | −1.19044 | −0.0749909 | ||||||||
\(253\) | −4.23463 | −0.266229 | ||||||||
\(254\) | 5.47950 | 0.343815 | ||||||||
\(255\) | −7.45501 | −0.466851 | ||||||||
\(256\) | 2.77604 | 0.173503 | ||||||||
\(257\) | −4.15862 | −0.259407 | −0.129704 | − | 0.991553i | \(-0.541403\pi\) | ||||
−0.129704 | + | 0.991553i | \(0.541403\pi\) | |||||||
\(258\) | −0.384077 | −0.0239116 | ||||||||
\(259\) | −10.0392 | −0.623804 | ||||||||
\(260\) | −0.744206 | −0.0461537 | ||||||||
\(261\) | −2.79540 | −0.173031 | ||||||||
\(262\) | −3.82484 | −0.236300 | ||||||||
\(263\) | −14.6513 | −0.903436 | −0.451718 | − | 0.892161i | \(-0.649189\pi\) | ||||
−0.451718 | + | 0.892161i | \(0.649189\pi\) | |||||||
\(264\) | −3.63743 | −0.223868 | ||||||||
\(265\) | −2.54336 | −0.156237 | ||||||||
\(266\) | 18.6724 | 1.14488 | ||||||||
\(267\) | −7.00043 | −0.428419 | ||||||||
\(268\) | 0.599384 | 0.0366132 | ||||||||
\(269\) | 4.96083 | 0.302467 | 0.151234 | − | 0.988498i | \(-0.451675\pi\) | ||||
0.151234 | + | 0.988498i | \(0.451675\pi\) | |||||||
\(270\) | −9.80769 | −0.596877 | ||||||||
\(271\) | 12.7684 | 0.775626 | 0.387813 | − | 0.921738i | \(-0.373231\pi\) | ||||
0.387813 | + | 0.921738i | \(0.373231\pi\) | |||||||
\(272\) | −27.0334 | −1.63914 | ||||||||
\(273\) | 4.13849 | 0.250473 | ||||||||
\(274\) | 13.5190 | 0.816713 | ||||||||
\(275\) | −4.73907 | −0.285777 | ||||||||
\(276\) | 0.0757551 | 0.00455992 | ||||||||
\(277\) | −19.1362 | −1.14978 | −0.574892 | − | 0.818229i | \(-0.694956\pi\) | ||||
−0.574892 | + | 0.818229i | \(0.694956\pi\) | |||||||
\(278\) | −1.45467 | −0.0872450 | ||||||||
\(279\) | 24.8268 | 1.48634 | ||||||||
\(280\) | −25.8650 | −1.54573 | ||||||||
\(281\) | 18.7341 | 1.11758 | 0.558790 | − | 0.829309i | \(-0.311266\pi\) | ||||
0.558790 | + | 0.829309i | \(0.311266\pi\) | |||||||
\(282\) | −2.90281 | −0.172860 | ||||||||
\(283\) | −27.5753 | −1.63918 | −0.819590 | − | 0.572951i | \(-0.805799\pi\) | ||||
−0.819590 | + | 0.572951i | \(0.805799\pi\) | |||||||
\(284\) | 0.443095 | 0.0262928 | ||||||||
\(285\) | 4.06952 | 0.241057 | ||||||||
\(286\) | 10.6426 | 0.629309 | ||||||||
\(287\) | 2.14368 | 0.126538 | ||||||||
\(288\) | −1.83287 | −0.108003 | ||||||||
\(289\) | 24.0635 | 1.41550 | ||||||||
\(290\) | 3.74136 | 0.219700 | ||||||||
\(291\) | 3.53839 | 0.207424 | ||||||||
\(292\) | −1.77661 | −0.103968 | ||||||||
\(293\) | −5.89088 | −0.344149 | −0.172074 | − | 0.985084i | \(-0.555047\pi\) | ||||
−0.172074 | + | 0.985084i | \(0.555047\pi\) | |||||||
\(294\) | −4.25430 | −0.248116 | ||||||||
\(295\) | −17.2147 | −1.00228 | ||||||||
\(296\) | −7.49751 | −0.435784 | ||||||||
\(297\) | 7.69211 | 0.446342 | ||||||||
\(298\) | −9.77546 | −0.566277 | ||||||||
\(299\) | 3.59817 | 0.208088 | ||||||||
\(300\) | 0.0847793 | 0.00489474 | ||||||||
\(301\) | 2.14198 | 0.123462 | ||||||||
\(302\) | 7.72297 | 0.444407 | ||||||||
\(303\) | −1.06073 | −0.0609372 | ||||||||
\(304\) | 14.7569 | 0.846365 | ||||||||
\(305\) | −14.9394 | −0.855428 | ||||||||
\(306\) | 26.0576 | 1.48962 | ||||||||
\(307\) | −24.9475 | −1.42383 | −0.711913 | − | 0.702267i | \(-0.752171\pi\) | ||||
−0.711913 | + | 0.702267i | \(0.752171\pi\) | |||||||
\(308\) | −1.24961 | −0.0712029 | ||||||||
\(309\) | 0.800092 | 0.0455156 | ||||||||
\(310\) | −33.2282 | −1.88723 | ||||||||
\(311\) | −16.7694 | −0.950906 | −0.475453 | − | 0.879741i | \(-0.657716\pi\) | ||||
−0.475453 | + | 0.879741i | \(0.657716\pi\) | |||||||
\(312\) | 3.09073 | 0.174978 | ||||||||
\(313\) | 25.9100 | 1.46452 | 0.732260 | − | 0.681026i | \(-0.238466\pi\) | ||||
0.732260 | + | 0.681026i | \(0.238466\pi\) | |||||||
\(314\) | 2.08411 | 0.117613 | ||||||||
\(315\) | 26.3830 | 1.48651 | ||||||||
\(316\) | −0.424432 | −0.0238762 | ||||||||
\(317\) | −27.9231 | −1.56832 | −0.784158 | − | 0.620562i | \(-0.786905\pi\) | ||||
−0.784158 | + | 0.620562i | \(0.786905\pi\) | |||||||
\(318\) | −0.650666 | −0.0364875 | ||||||||
\(319\) | −2.93433 | −0.164291 | ||||||||
\(320\) | −19.2473 | −1.07596 | ||||||||
\(321\) | −8.01871 | −0.447561 | ||||||||
\(322\) | −7.70341 | −0.429294 | ||||||||
\(323\) | −22.4156 | −1.24724 | ||||||||
\(324\) | 0.835625 | 0.0464236 | ||||||||
\(325\) | 4.02680 | 0.223367 | ||||||||
\(326\) | −1.10418 | −0.0611548 | ||||||||
\(327\) | −3.19447 | −0.176654 | ||||||||
\(328\) | 1.60096 | 0.0883980 | ||||||||
\(329\) | 16.1888 | 0.892519 | ||||||||
\(330\) | −4.96583 | −0.273360 | ||||||||
\(331\) | 6.87398 | 0.377828 | 0.188914 | − | 0.981994i | \(-0.439503\pi\) | ||||
0.188914 | + | 0.981994i | \(0.439503\pi\) | |||||||
\(332\) | 1.33426 | 0.0732268 | ||||||||
\(333\) | 7.64766 | 0.419089 | ||||||||
\(334\) | −26.8101 | −1.46699 | ||||||||
\(335\) | −13.2837 | −0.725768 | ||||||||
\(336\) | −7.00228 | −0.382005 | ||||||||
\(337\) | −3.13247 | −0.170636 | −0.0853182 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853182 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(338\) | 9.86763 | 0.536729 | ||||||||
\(339\) | 4.69938 | 0.255235 | ||||||||
\(340\) | −1.91270 | −0.103731 | ||||||||
\(341\) | 26.0607 | 1.41126 | ||||||||
\(342\) | −14.2243 | −0.769159 | ||||||||
\(343\) | −1.96090 | −0.105878 | ||||||||
\(344\) | 1.59968 | 0.0862491 | ||||||||
\(345\) | −1.67891 | −0.0903893 | ||||||||
\(346\) | 0.429226 | 0.0230754 | ||||||||
\(347\) | 21.8717 | 1.17413 | 0.587067 | − | 0.809538i | \(-0.300283\pi\) | ||||
0.587067 | + | 0.809538i | \(0.300283\pi\) | |||||||
\(348\) | 0.0524935 | 0.00281394 | ||||||||
\(349\) | 28.1698 | 1.50789 | 0.753947 | − | 0.656935i | \(-0.228147\pi\) | ||||
0.753947 | + | 0.656935i | \(0.228147\pi\) | |||||||
\(350\) | −8.62107 | −0.460816 | ||||||||
\(351\) | −6.53600 | −0.348866 | ||||||||
\(352\) | −1.92396 | −0.102548 | ||||||||
\(353\) | −21.3897 | −1.13846 | −0.569230 | − | 0.822178i | \(-0.692759\pi\) | ||||
−0.569230 | + | 0.822178i | \(0.692759\pi\) | |||||||
\(354\) | −4.40403 | −0.234072 | ||||||||
\(355\) | −9.82000 | −0.521191 | ||||||||
\(356\) | −1.79607 | −0.0951913 | ||||||||
\(357\) | 10.6364 | 0.562939 | ||||||||
\(358\) | −15.9812 | −0.844634 | ||||||||
\(359\) | 23.4995 | 1.24025 | 0.620127 | − | 0.784502i | \(-0.287081\pi\) | ||||
0.620127 | + | 0.784502i | \(0.287081\pi\) | |||||||
\(360\) | 19.7035 | 1.03846 | ||||||||
\(361\) | −6.76384 | −0.355992 | ||||||||
\(362\) | 38.3386 | 2.01503 | ||||||||
\(363\) | −1.08094 | −0.0567347 | ||||||||
\(364\) | 1.06179 | 0.0556531 | ||||||||
\(365\) | 39.3738 | 2.06092 | ||||||||
\(366\) | −3.82194 | −0.199776 | ||||||||
\(367\) | −28.3023 | −1.47737 | −0.738683 | − | 0.674053i | \(-0.764552\pi\) | ||||
−0.738683 | + | 0.674053i | \(0.764552\pi\) | |||||||
\(368\) | −6.08805 | −0.317362 | ||||||||
\(369\) | −1.63302 | −0.0850115 | ||||||||
\(370\) | −10.2356 | −0.532125 | ||||||||
\(371\) | 3.62873 | 0.188394 | ||||||||
\(372\) | −0.466211 | −0.0241719 | ||||||||
\(373\) | −14.8632 | −0.769587 | −0.384793 | − | 0.923003i | \(-0.625727\pi\) | ||||
−0.384793 | + | 0.923003i | \(0.625727\pi\) | |||||||
\(374\) | 27.3527 | 1.41437 | ||||||||
\(375\) | 3.93798 | 0.203356 | ||||||||
\(376\) | 12.0902 | 0.623505 | ||||||||
\(377\) | 2.49330 | 0.128412 | ||||||||
\(378\) | 13.9931 | 0.719727 | ||||||||
\(379\) | 16.0781 | 0.825878 | 0.412939 | − | 0.910759i | \(-0.364502\pi\) | ||||
0.412939 | + | 0.910759i | \(0.364502\pi\) | |||||||
\(380\) | 1.04410 | 0.0535610 | ||||||||
\(381\) | −1.70385 | −0.0872910 | ||||||||
\(382\) | 33.5529 | 1.71672 | ||||||||
\(383\) | −30.7612 | −1.57182 | −0.785912 | − | 0.618338i | \(-0.787806\pi\) | ||||
−0.785912 | + | 0.618338i | \(0.787806\pi\) | |||||||
\(384\) | −5.51719 | −0.281548 | ||||||||
\(385\) | 27.6942 | 1.41143 | ||||||||
\(386\) | 23.7637 | 1.20954 | ||||||||
\(387\) | −1.63172 | −0.0829450 | ||||||||
\(388\) | 0.907828 | 0.0460880 | ||||||||
\(389\) | −27.2329 | −1.38076 | −0.690380 | − | 0.723447i | \(-0.742557\pi\) | ||||
−0.690380 | + | 0.723447i | \(0.742557\pi\) | |||||||
\(390\) | 4.21948 | 0.213661 | ||||||||
\(391\) | 9.24772 | 0.467677 | ||||||||
\(392\) | 17.7192 | 0.894953 | ||||||||
\(393\) | 1.18934 | 0.0599940 | ||||||||
\(394\) | −28.7599 | −1.44890 | ||||||||
\(395\) | 9.40640 | 0.473287 | ||||||||
\(396\) | 0.951927 | 0.0478361 | ||||||||
\(397\) | 9.91379 | 0.497559 | 0.248779 | − | 0.968560i | \(-0.419971\pi\) | ||||
0.248779 | + | 0.968560i | \(0.419971\pi\) | |||||||
\(398\) | 37.2032 | 1.86483 | ||||||||
\(399\) | −5.80617 | −0.290672 | ||||||||
\(400\) | −6.81329 | −0.340664 | ||||||||
\(401\) | 5.23191 | 0.261269 | 0.130635 | − | 0.991431i | \(-0.458299\pi\) | ||||
0.130635 | + | 0.991431i | \(0.458299\pi\) | |||||||
\(402\) | −3.39837 | −0.169495 | ||||||||
\(403\) | −22.1438 | −1.10306 | ||||||||
\(404\) | −0.272146 | −0.0135398 | ||||||||
\(405\) | −18.5194 | −0.920235 | ||||||||
\(406\) | −5.33797 | −0.264919 | ||||||||
\(407\) | 8.02774 | 0.397920 | ||||||||
\(408\) | 7.94354 | 0.393264 | ||||||||
\(409\) | −7.64002 | −0.377775 | −0.188887 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188887 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(410\) | 2.18563 | 0.107941 | ||||||||
\(411\) | −4.20374 | −0.207355 | ||||||||
\(412\) | 0.205276 | 0.0101132 | ||||||||
\(413\) | 24.5610 | 1.20857 | ||||||||
\(414\) | 5.86832 | 0.288412 | ||||||||
\(415\) | −29.5702 | −1.45154 | ||||||||
\(416\) | 1.63479 | 0.0801524 | ||||||||
\(417\) | 0.452328 | 0.0221506 | ||||||||
\(418\) | −14.9312 | −0.730308 | ||||||||
\(419\) | −8.72697 | −0.426340 | −0.213170 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213170 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(420\) | −0.495433 | −0.0241747 | ||||||||
\(421\) | −13.5233 | −0.659085 | −0.329542 | − | 0.944141i | \(-0.606894\pi\) | ||||
−0.329542 | + | 0.944141i | \(0.606894\pi\) | |||||||
\(422\) | −26.1585 | −1.27338 | ||||||||
\(423\) | −12.3323 | −0.599619 | ||||||||
\(424\) | 2.71002 | 0.131610 | ||||||||
\(425\) | 10.3493 | 0.502017 | ||||||||
\(426\) | −2.51225 | −0.121719 | ||||||||
\(427\) | 21.3148 | 1.03149 | ||||||||
\(428\) | −2.05732 | −0.0994444 | ||||||||
\(429\) | −3.30931 | −0.159775 | ||||||||
\(430\) | 2.18389 | 0.105317 | ||||||||
\(431\) | −6.78982 | −0.327054 | −0.163527 | − | 0.986539i | \(-0.552287\pi\) | ||||
−0.163527 | + | 0.986539i | \(0.552287\pi\) | |||||||
\(432\) | 11.0588 | 0.532068 | ||||||||
\(433\) | −30.3466 | −1.45836 | −0.729182 | − | 0.684319i | \(-0.760099\pi\) | ||||
−0.729182 | + | 0.684319i | \(0.760099\pi\) | |||||||
\(434\) | 47.4082 | 2.27567 | ||||||||
\(435\) | −1.16338 | −0.0557796 | ||||||||
\(436\) | −0.819588 | −0.0392512 | ||||||||
\(437\) | −5.04811 | −0.241484 | ||||||||
\(438\) | 10.0730 | 0.481306 | ||||||||
\(439\) | −8.50975 | −0.406148 | −0.203074 | − | 0.979163i | \(-0.565093\pi\) | ||||
−0.203074 | + | 0.979163i | \(0.565093\pi\) | |||||||
\(440\) | 20.6827 | 0.986009 | ||||||||
\(441\) | −18.0740 | −0.860668 | ||||||||
\(442\) | −23.2416 | −1.10549 | ||||||||
\(443\) | −21.2132 | −1.00787 | −0.503936 | − | 0.863741i | \(-0.668115\pi\) | ||||
−0.503936 | + | 0.863741i | \(0.668115\pi\) | |||||||
\(444\) | −0.143612 | −0.00681552 | ||||||||
\(445\) | 39.8050 | 1.88694 | ||||||||
\(446\) | 26.7355 | 1.26596 | ||||||||
\(447\) | 3.03968 | 0.143772 | ||||||||
\(448\) | 27.4611 | 1.29741 | ||||||||
\(449\) | −4.15245 | −0.195966 | −0.0979832 | − | 0.995188i | \(-0.531239\pi\) | ||||
−0.0979832 | + | 0.995188i | \(0.531239\pi\) | |||||||
\(450\) | 6.56737 | 0.309589 | ||||||||
\(451\) | −1.71418 | −0.0807174 | ||||||||
\(452\) | 1.20570 | 0.0567112 | ||||||||
\(453\) | −2.40146 | −0.112830 | ||||||||
\(454\) | 31.0251 | 1.45608 | ||||||||
\(455\) | −23.5318 | −1.10319 | ||||||||
\(456\) | −4.33619 | −0.203061 | ||||||||
\(457\) | 27.0383 | 1.26480 | 0.632400 | − | 0.774642i | \(-0.282070\pi\) | ||||
0.632400 | + | 0.774642i | \(0.282070\pi\) | |||||||
\(458\) | −18.4729 | −0.863180 | ||||||||
\(459\) | −16.7983 | −0.784078 | ||||||||
\(460\) | −0.430749 | −0.0200838 | ||||||||
\(461\) | −16.1662 | −0.752933 | −0.376467 | − | 0.926430i | \(-0.622861\pi\) | ||||
−0.376467 | + | 0.926430i | \(0.622861\pi\) | |||||||
\(462\) | 7.08498 | 0.329623 | ||||||||
\(463\) | −17.2547 | −0.801894 | −0.400947 | − | 0.916101i | \(-0.631319\pi\) | ||||
−0.400947 | + | 0.916101i | \(0.631319\pi\) | |||||||
\(464\) | −4.21864 | −0.195845 | ||||||||
\(465\) | 10.3323 | 0.479149 | ||||||||
\(466\) | 19.1895 | 0.888937 | ||||||||
\(467\) | −30.2582 | −1.40018 | −0.700092 | − | 0.714052i | \(-0.746858\pi\) | ||||
−0.700092 | + | 0.714052i | \(0.746858\pi\) | |||||||
\(468\) | −0.808854 | −0.0373893 | ||||||||
\(469\) | 18.9525 | 0.875147 | ||||||||
\(470\) | 16.5056 | 0.761347 | ||||||||
\(471\) | −0.648055 | −0.0298608 | ||||||||
\(472\) | 18.3428 | 0.844296 | ||||||||
\(473\) | −1.71281 | −0.0787553 | ||||||||
\(474\) | 2.40643 | 0.110531 | ||||||||
\(475\) | −5.64946 | −0.259215 | ||||||||
\(476\) | 2.72893 | 0.125080 | ||||||||
\(477\) | −2.76430 | −0.126569 | ||||||||
\(478\) | 10.3380 | 0.472848 | ||||||||
\(479\) | 6.81778 | 0.311512 | 0.155756 | − | 0.987796i | \(-0.450219\pi\) | ||||
0.155756 | + | 0.987796i | \(0.450219\pi\) | |||||||
\(480\) | −0.762796 | −0.0348167 | ||||||||
\(481\) | −6.82119 | −0.311019 | ||||||||
\(482\) | 19.4586 | 0.886314 | ||||||||
\(483\) | 2.39538 | 0.108993 | ||||||||
\(484\) | −0.277332 | −0.0126060 | ||||||||
\(485\) | −20.1196 | −0.913583 | ||||||||
\(486\) | −16.1777 | −0.733835 | ||||||||
\(487\) | 13.4922 | 0.611389 | 0.305694 | − | 0.952130i | \(-0.401111\pi\) | ||||
0.305694 | + | 0.952130i | \(0.401111\pi\) | |||||||
\(488\) | 15.9184 | 0.720592 | ||||||||
\(489\) | 0.343344 | 0.0155266 | ||||||||
\(490\) | 24.1903 | 1.09280 | ||||||||
\(491\) | −13.9827 | −0.631031 | −0.315515 | − | 0.948920i | \(-0.602177\pi\) | ||||
−0.315515 | + | 0.948920i | \(0.602177\pi\) | |||||||
\(492\) | 0.0306657 | 0.00138251 | ||||||||
\(493\) | 6.40808 | 0.288606 | ||||||||
\(494\) | 12.6871 | 0.570817 | ||||||||
\(495\) | −21.0969 | −0.948235 | ||||||||
\(496\) | 37.4670 | 1.68232 | ||||||||
\(497\) | 14.0107 | 0.628464 | ||||||||
\(498\) | −7.56493 | −0.338993 | ||||||||
\(499\) | −36.6499 | −1.64068 | −0.820338 | − | 0.571878i | \(-0.806215\pi\) | ||||
−0.820338 | + | 0.571878i | \(0.806215\pi\) | |||||||
\(500\) | 1.01035 | 0.0451841 | ||||||||
\(501\) | 8.33661 | 0.372452 | ||||||||
\(502\) | 1.37769 | 0.0614892 | ||||||||
\(503\) | 8.23735 | 0.367285 | 0.183643 | − | 0.982993i | \(-0.441211\pi\) | ||||
0.183643 | + | 0.982993i | \(0.441211\pi\) | |||||||
\(504\) | −28.1118 | −1.25220 | ||||||||
\(505\) | 6.03138 | 0.268393 | ||||||||
\(506\) | 6.15996 | 0.273844 | ||||||||
\(507\) | −3.06834 | −0.136270 | ||||||||
\(508\) | −0.437149 | −0.0193953 | ||||||||
\(509\) | −4.35286 | −0.192937 | −0.0964686 | − | 0.995336i | \(-0.530755\pi\) | ||||
−0.0964686 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(510\) | 10.8446 | 0.480205 | ||||||||
\(511\) | −56.1765 | −2.48510 | ||||||||
\(512\) | 20.3564 | 0.899635 | ||||||||
\(513\) | 9.16980 | 0.404856 | ||||||||
\(514\) | 6.04940 | 0.266827 | ||||||||
\(515\) | −4.54938 | −0.200470 | ||||||||
\(516\) | 0.0306413 | 0.00134891 | ||||||||
\(517\) | −12.9452 | −0.569331 | ||||||||
\(518\) | 14.6037 | 0.641648 | ||||||||
\(519\) | −0.133468 | −0.00585859 | ||||||||
\(520\) | −17.5741 | −0.770676 | ||||||||
\(521\) | −14.7970 | −0.648270 | −0.324135 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324135 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(522\) | 4.06637 | 0.177980 | ||||||||
\(523\) | 30.3359 | 1.32650 | 0.663248 | − | 0.748400i | \(-0.269178\pi\) | ||||
0.663248 | + | 0.748400i | \(0.269178\pi\) | |||||||
\(524\) | 0.305142 | 0.0133302 | ||||||||
\(525\) | 2.68072 | 0.116996 | ||||||||
\(526\) | 21.3127 | 0.929278 | ||||||||
\(527\) | −56.9122 | −2.47913 | ||||||||
\(528\) | 5.59931 | 0.243679 | ||||||||
\(529\) | −20.9174 | −0.909451 | ||||||||
\(530\) | 3.69973 | 0.160706 | ||||||||
\(531\) | −18.7102 | −0.811951 | ||||||||
\(532\) | −1.48966 | −0.0645850 | ||||||||
\(533\) | 1.45654 | 0.0630897 | ||||||||
\(534\) | 10.1833 | 0.440674 | ||||||||
\(535\) | 45.5950 | 1.97124 | ||||||||
\(536\) | 14.1542 | 0.611370 | ||||||||
\(537\) | 4.96936 | 0.214444 | ||||||||
\(538\) | −7.21635 | −0.311119 | ||||||||
\(539\) | −18.9723 | −0.817194 | ||||||||
\(540\) | 0.782447 | 0.0336712 | ||||||||
\(541\) | −24.6002 | −1.05765 | −0.528823 | − | 0.848732i | \(-0.677366\pi\) | ||||
−0.528823 | + | 0.848732i | \(0.677366\pi\) | |||||||
\(542\) | −18.5738 | −0.797812 | ||||||||
\(543\) | −11.9214 | −0.511596 | ||||||||
\(544\) | 4.20161 | 0.180143 | ||||||||
\(545\) | 18.1640 | 0.778059 | ||||||||
\(546\) | −6.02012 | −0.257638 | ||||||||
\(547\) | 8.49200 | 0.363092 | 0.181546 | − | 0.983382i | \(-0.441890\pi\) | ||||
0.181546 | + | 0.983382i | \(0.441890\pi\) | |||||||
\(548\) | −1.07853 | −0.0460726 | ||||||||
\(549\) | −16.2372 | −0.692987 | ||||||||
\(550\) | 6.89376 | 0.293951 | ||||||||
\(551\) | −3.49802 | −0.149021 | ||||||||
\(552\) | 1.78893 | 0.0761418 | ||||||||
\(553\) | −13.4206 | −0.570700 | ||||||||
\(554\) | 27.8368 | 1.18267 | ||||||||
\(555\) | 3.18277 | 0.135101 | ||||||||
\(556\) | 0.116052 | 0.00492169 | ||||||||
\(557\) | 11.7983 | 0.499910 | 0.249955 | − | 0.968258i | \(-0.419584\pi\) | ||||
0.249955 | + | 0.968258i | \(0.419584\pi\) | |||||||
\(558\) | −36.1147 | −1.52886 | ||||||||
\(559\) | 1.45538 | 0.0615561 | ||||||||
\(560\) | 39.8155 | 1.68251 | ||||||||
\(561\) | −8.50532 | −0.359095 | ||||||||
\(562\) | −27.2518 | −1.14955 | ||||||||
\(563\) | 34.0787 | 1.43625 | 0.718123 | − | 0.695916i | \(-0.245002\pi\) | ||||
0.718123 | + | 0.695916i | \(0.245002\pi\) | |||||||
\(564\) | 0.231583 | 0.00975141 | ||||||||
\(565\) | −26.7210 | −1.12416 | ||||||||
\(566\) | 40.1128 | 1.68607 | ||||||||
\(567\) | 26.4225 | 1.10964 | ||||||||
\(568\) | 10.4635 | 0.439039 | ||||||||
\(569\) | 1.18453 | 0.0496582 | 0.0248291 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248291 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(570\) | −5.91978 | −0.247952 | ||||||||
\(571\) | 18.1572 | 0.759855 | 0.379928 | − | 0.925016i | \(-0.375949\pi\) | ||||
0.379928 | + | 0.925016i | \(0.375949\pi\) | |||||||
\(572\) | −0.849053 | −0.0355007 | ||||||||
\(573\) | −10.4333 | −0.435857 | ||||||||
\(574\) | −3.11834 | −0.130157 | ||||||||
\(575\) | 2.33073 | 0.0971980 | ||||||||
\(576\) | −20.9193 | −0.871639 | ||||||||
\(577\) | 29.9164 | 1.24544 | 0.622718 | − | 0.782446i | \(-0.286028\pi\) | ||||
0.622718 | + | 0.782446i | \(0.286028\pi\) | |||||||
\(578\) | −35.0044 | −1.45599 | ||||||||
\(579\) | −7.38933 | −0.307090 | ||||||||
\(580\) | −0.298482 | −0.0123938 | ||||||||
\(581\) | 42.1892 | 1.75030 | ||||||||
\(582\) | −5.14718 | −0.213357 | ||||||||
\(583\) | −2.90168 | −0.120175 | ||||||||
\(584\) | −41.9540 | −1.73607 | ||||||||
\(585\) | 17.9261 | 0.741152 | ||||||||
\(586\) | 8.56926 | 0.353993 | ||||||||
\(587\) | 20.2725 | 0.836736 | 0.418368 | − | 0.908278i | \(-0.362602\pi\) | ||||
0.418368 | + | 0.908278i | \(0.362602\pi\) | |||||||
\(588\) | 0.339403 | 0.0139968 | ||||||||
\(589\) | 31.0670 | 1.28009 | ||||||||
\(590\) | 25.0417 | 1.03095 | ||||||||
\(591\) | 8.94290 | 0.367862 | ||||||||
\(592\) | 11.5414 | 0.474347 | ||||||||
\(593\) | 14.9642 | 0.614506 | 0.307253 | − | 0.951628i | \(-0.400590\pi\) | ||||
0.307253 | + | 0.951628i | \(0.400590\pi\) | |||||||
\(594\) | −11.1895 | −0.459109 | ||||||||
\(595\) | −60.4795 | −2.47942 | ||||||||
\(596\) | 0.779876 | 0.0319450 | ||||||||
\(597\) | −11.5683 | −0.473461 | ||||||||
\(598\) | −5.23413 | −0.214040 | ||||||||
\(599\) | −41.7091 | −1.70419 | −0.852095 | − | 0.523388i | \(-0.824668\pi\) | ||||
−0.852095 | + | 0.523388i | \(0.824668\pi\) | |||||||
\(600\) | 2.00203 | 0.0817326 | ||||||||
\(601\) | −15.8339 | −0.645877 | −0.322939 | − | 0.946420i | \(-0.604671\pi\) | ||||
−0.322939 | + | 0.946420i | \(0.604671\pi\) | |||||||
\(602\) | −3.11586 | −0.126993 | ||||||||
\(603\) | −14.4377 | −0.587948 | ||||||||
\(604\) | −0.616131 | −0.0250700 | ||||||||
\(605\) | 6.14631 | 0.249883 | ||||||||
\(606\) | 1.54300 | 0.0626802 | ||||||||
\(607\) | 25.4985 | 1.03495 | 0.517476 | − | 0.855698i | \(-0.326872\pi\) | ||||
0.517476 | + | 0.855698i | \(0.326872\pi\) | |||||||
\(608\) | −2.29356 | −0.0930162 | ||||||||
\(609\) | 1.65984 | 0.0672603 | ||||||||
\(610\) | 21.7318 | 0.879897 | ||||||||
\(611\) | 10.9996 | 0.444996 | ||||||||
\(612\) | −2.07885 | −0.0840326 | ||||||||
\(613\) | 16.2613 | 0.656787 | 0.328393 | − | 0.944541i | \(-0.393493\pi\) | ||||
0.328393 | + | 0.944541i | \(0.393493\pi\) | |||||||
\(614\) | 36.2902 | 1.46455 | ||||||||
\(615\) | −0.679622 | −0.0274050 | ||||||||
\(616\) | −29.5090 | −1.18895 | ||||||||
\(617\) | 9.28613 | 0.373845 | 0.186923 | − | 0.982375i | \(-0.440149\pi\) | ||||
0.186923 | + | 0.982375i | \(0.440149\pi\) | |||||||
\(618\) | −1.16387 | −0.0468176 | ||||||||
\(619\) | −2.38713 | −0.0959467 | −0.0479733 | − | 0.998849i | \(-0.515276\pi\) | ||||
−0.0479733 | + | 0.998849i | \(0.515276\pi\) | |||||||
\(620\) | 2.65091 | 0.106463 | ||||||||
\(621\) | −3.78306 | −0.151809 | ||||||||
\(622\) | 24.3939 | 0.978106 | ||||||||
\(623\) | −56.7916 | −2.27531 | ||||||||
\(624\) | −4.75774 | −0.190462 | ||||||||
\(625\) | −30.4669 | −1.21867 | ||||||||
\(626\) | −37.6904 | −1.50641 | ||||||||
\(627\) | 4.64285 | 0.185418 | ||||||||
\(628\) | −0.166268 | −0.00663482 | ||||||||
\(629\) | −17.5313 | −0.699017 | ||||||||
\(630\) | −38.3784 | −1.52903 | ||||||||
\(631\) | −45.3824 | −1.80664 | −0.903321 | − | 0.428964i | \(-0.858879\pi\) | ||||
−0.903321 | + | 0.428964i | \(0.858879\pi\) | |||||||
\(632\) | −10.0228 | −0.398686 | ||||||||
\(633\) | 8.13400 | 0.323298 | ||||||||
\(634\) | 40.6187 | 1.61318 | ||||||||
\(635\) | 9.68823 | 0.384466 | ||||||||
\(636\) | 0.0519094 | 0.00205834 | ||||||||
\(637\) | 16.1208 | 0.638729 | ||||||||
\(638\) | 4.26846 | 0.168990 | ||||||||
\(639\) | −10.6731 | −0.422220 | ||||||||
\(640\) | 31.3712 | 1.24005 | ||||||||
\(641\) | 12.4448 | 0.491541 | 0.245771 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245771 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(642\) | 11.6645 | 0.460363 | ||||||||
\(643\) | 14.9156 | 0.588213 | 0.294106 | − | 0.955773i | \(-0.404978\pi\) | ||||
0.294106 | + | 0.955773i | \(0.404978\pi\) | |||||||
\(644\) | 0.614570 | 0.0242174 | ||||||||
\(645\) | −0.679082 | −0.0267388 | ||||||||
\(646\) | 32.6072 | 1.28291 | ||||||||
\(647\) | −32.8140 | −1.29005 | −0.645025 | − | 0.764162i | \(-0.723153\pi\) | ||||
−0.645025 | + | 0.764162i | \(0.723153\pi\) | |||||||
\(648\) | 19.7329 | 0.775183 | ||||||||
\(649\) | −19.6400 | −0.770938 | ||||||||
\(650\) | −5.85764 | −0.229756 | ||||||||
\(651\) | −14.7416 | −0.577768 | ||||||||
\(652\) | 0.0880901 | 0.00344988 | ||||||||
\(653\) | −20.9996 | −0.821778 | −0.410889 | − | 0.911685i | \(-0.634782\pi\) | ||||
−0.410889 | + | 0.911685i | \(0.634782\pi\) | |||||||
\(654\) | 4.64688 | 0.181707 | ||||||||
\(655\) | −6.76265 | −0.264239 | ||||||||
\(656\) | −2.46444 | −0.0962204 | ||||||||
\(657\) | 42.7942 | 1.66956 | ||||||||
\(658\) | −23.5493 | −0.918048 | ||||||||
\(659\) | 17.7959 | 0.693231 | 0.346616 | − | 0.938007i | \(-0.387331\pi\) | ||||
0.346616 | + | 0.938007i | \(0.387331\pi\) | |||||||
\(660\) | 0.396169 | 0.0154208 | ||||||||
\(661\) | 28.9288 | 1.12520 | 0.562600 | − | 0.826729i | \(-0.309801\pi\) | ||||
0.562600 | + | 0.826729i | \(0.309801\pi\) | |||||||
\(662\) | −9.99934 | −0.388635 | ||||||||
\(663\) | 7.22699 | 0.280673 | ||||||||
\(664\) | 31.5079 | 1.22275 | ||||||||
\(665\) | 33.0143 | 1.28024 | ||||||||
\(666\) | −11.1248 | −0.431077 | ||||||||
\(667\) | 1.44313 | 0.0558784 | ||||||||
\(668\) | 2.13888 | 0.0827559 | ||||||||
\(669\) | −8.31342 | −0.321415 | ||||||||
\(670\) | 19.3234 | 0.746528 | ||||||||
\(671\) | −17.0442 | −0.657983 | ||||||||
\(672\) | 1.08832 | 0.0419827 | ||||||||
\(673\) | −27.1240 | −1.04555 | −0.522776 | − | 0.852470i | \(-0.675104\pi\) | ||||
−0.522776 | + | 0.852470i | \(0.675104\pi\) | |||||||
\(674\) | 4.55669 | 0.175517 | ||||||||
\(675\) | −4.23372 | −0.162956 | ||||||||
\(676\) | −0.787229 | −0.0302781 | ||||||||
\(677\) | 0.243947 | 0.00937564 | 0.00468782 | − | 0.999989i | \(-0.498508\pi\) | ||||
0.00468782 | + | 0.999989i | \(0.498508\pi\) | |||||||
\(678\) | −6.83603 | −0.262536 | ||||||||
\(679\) | 28.7055 | 1.10162 | ||||||||
\(680\) | −45.1676 | −1.73210 | ||||||||
\(681\) | −9.64727 | −0.369684 | ||||||||
\(682\) | −37.9096 | −1.45163 | ||||||||
\(683\) | 48.0076 | 1.83696 | 0.918479 | − | 0.395470i | \(-0.129418\pi\) | ||||
0.918479 | + | 0.395470i | \(0.129418\pi\) | |||||||
\(684\) | 1.13480 | 0.0433900 | ||||||||
\(685\) | 23.9028 | 0.913278 | ||||||||
\(686\) | 2.85245 | 0.108907 | ||||||||
\(687\) | 5.74414 | 0.219152 | ||||||||
\(688\) | −2.46249 | −0.0938814 | ||||||||
\(689\) | 2.46556 | 0.0939305 | ||||||||
\(690\) | 2.44225 | 0.0929748 | ||||||||
\(691\) | −9.97504 | −0.379468 | −0.189734 | − | 0.981835i | \(-0.560763\pi\) | ||||
−0.189734 | + | 0.981835i | \(0.560763\pi\) | |||||||
\(692\) | −0.0342432 | −0.00130173 | ||||||||
\(693\) | 30.0999 | 1.14340 | ||||||||
\(694\) | −31.8160 | −1.20772 | ||||||||
\(695\) | −2.57197 | −0.0975605 | ||||||||
\(696\) | 1.23961 | 0.0469874 | ||||||||
\(697\) | 3.74348 | 0.141794 | ||||||||
\(698\) | −40.9776 | −1.55103 | ||||||||
\(699\) | −5.96698 | −0.225692 | ||||||||
\(700\) | 0.687780 | 0.0259956 | ||||||||
\(701\) | 5.36105 | 0.202484 | 0.101242 | − | 0.994862i | \(-0.467718\pi\) | ||||
0.101242 | + | 0.994862i | \(0.467718\pi\) | |||||||
\(702\) | 9.50770 | 0.358845 | ||||||||
\(703\) | 9.56990 | 0.360936 | ||||||||
\(704\) | −21.9590 | −0.827611 | ||||||||
\(705\) | −5.13242 | −0.193298 | ||||||||
\(706\) | 31.1149 | 1.17103 | ||||||||
\(707\) | −8.60525 | −0.323634 | ||||||||
\(708\) | 0.351349 | 0.0132045 | ||||||||
\(709\) | −21.8751 | −0.821536 | −0.410768 | − | 0.911740i | \(-0.634739\pi\) | ||||
−0.410768 | + | 0.911740i | \(0.634739\pi\) | |||||||
\(710\) | 14.2848 | 0.536100 | ||||||||
\(711\) | 10.2235 | 0.383412 | ||||||||
\(712\) | −42.4134 | −1.58951 | ||||||||
\(713\) | −12.8169 | −0.479997 | ||||||||
\(714\) | −15.4724 | −0.579041 | ||||||||
\(715\) | 18.8170 | 0.703715 | ||||||||
\(716\) | 1.27497 | 0.0476477 | ||||||||
\(717\) | −3.21459 | −0.120051 | ||||||||
\(718\) | −34.1838 | −1.27573 | ||||||||
\(719\) | 8.20170 | 0.305872 | 0.152936 | − | 0.988236i | \(-0.451127\pi\) | ||||
0.152936 | + | 0.988236i | \(0.451127\pi\) | |||||||
\(720\) | −30.3307 | −1.13036 | ||||||||
\(721\) | 6.49082 | 0.241731 | ||||||||
\(722\) | 9.83913 | 0.366175 | ||||||||
\(723\) | −6.05065 | −0.225026 | ||||||||
\(724\) | −3.05861 | −0.113672 | ||||||||
\(725\) | 1.61505 | 0.0599813 | ||||||||
\(726\) | 1.57241 | 0.0583575 | ||||||||
\(727\) | 11.3264 | 0.420072 | 0.210036 | − | 0.977694i | \(-0.432642\pi\) | ||||
0.210036 | + | 0.977694i | \(0.432642\pi\) | |||||||
\(728\) | 25.0738 | 0.929298 | ||||||||
\(729\) | −16.5709 | −0.613737 | ||||||||
\(730\) | −57.2758 | −2.11987 | ||||||||
\(731\) | 3.74050 | 0.138347 | ||||||||
\(732\) | 0.304910 | 0.0112698 | ||||||||
\(733\) | −10.6872 | −0.394740 | −0.197370 | − | 0.980329i | \(-0.563240\pi\) | ||||
−0.197370 | + | 0.980329i | \(0.563240\pi\) | |||||||
\(734\) | 41.1703 | 1.51962 | ||||||||
\(735\) | −7.52196 | −0.277452 | ||||||||
\(736\) | 0.946225 | 0.0348783 | ||||||||
\(737\) | −15.1552 | −0.558250 | ||||||||
\(738\) | 2.37549 | 0.0874432 | ||||||||
\(739\) | 29.0316 | 1.06795 | 0.533973 | − | 0.845502i | \(-0.320698\pi\) | ||||
0.533973 | + | 0.845502i | \(0.320698\pi\) | |||||||
\(740\) | 0.816588 | 0.0300184 | ||||||||
\(741\) | −3.94504 | −0.144925 | ||||||||
\(742\) | −5.27858 | −0.193783 | ||||||||
\(743\) | 10.5164 | 0.385810 | 0.192905 | − | 0.981217i | \(-0.438209\pi\) | ||||
0.192905 | + | 0.981217i | \(0.438209\pi\) | |||||||
\(744\) | −11.0094 | −0.403624 | ||||||||
\(745\) | −17.2839 | −0.633231 | ||||||||
\(746\) | 21.6210 | 0.791600 | ||||||||
\(747\) | −32.1389 | −1.17590 | ||||||||
\(748\) | −2.18217 | −0.0797879 | ||||||||
\(749\) | −65.0525 | −2.37697 | ||||||||
\(750\) | −5.72844 | −0.209173 | ||||||||
\(751\) | 23.5188 | 0.858212 | 0.429106 | − | 0.903254i | \(-0.358829\pi\) | ||||
0.429106 | + | 0.903254i | \(0.358829\pi\) | |||||||
\(752\) | −18.6112 | −0.678680 | ||||||||
\(753\) | −0.428392 | −0.0156115 | ||||||||
\(754\) | −3.62692 | −0.132085 | ||||||||
\(755\) | 13.6549 | 0.496952 | ||||||||
\(756\) | −1.11635 | −0.0406014 | ||||||||
\(757\) | 9.24881 | 0.336154 | 0.168077 | − | 0.985774i | \(-0.446244\pi\) | ||||
0.168077 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(758\) | −23.3883 | −0.849501 | ||||||||
\(759\) | −1.91544 | −0.0695261 | ||||||||
\(760\) | 24.6559 | 0.894364 | ||||||||
\(761\) | −21.0001 | −0.761251 | −0.380626 | − | 0.924729i | \(-0.624291\pi\) | ||||
−0.380626 | + | 0.924729i | \(0.624291\pi\) | |||||||
\(762\) | 2.47853 | 0.0897878 | ||||||||
\(763\) | −25.9154 | −0.938200 | ||||||||
\(764\) | −2.67682 | −0.0968438 | ||||||||
\(765\) | 46.0721 | 1.66574 | ||||||||
\(766\) | 44.7473 | 1.61678 | ||||||||
\(767\) | 16.6882 | 0.602575 | ||||||||
\(768\) | 1.25568 | 0.0453106 | ||||||||
\(769\) | −15.8639 | −0.572065 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(770\) | −40.2857 | −1.45180 | ||||||||
\(771\) | −1.88106 | −0.0677447 | ||||||||
\(772\) | −1.89584 | −0.0682329 | ||||||||
\(773\) | 21.7936 | 0.783861 | 0.391930 | − | 0.919995i | \(-0.371807\pi\) | ||||
0.391930 | + | 0.919995i | \(0.371807\pi\) | |||||||
\(774\) | 2.37361 | 0.0853175 | ||||||||
\(775\) | −14.3437 | −0.515242 | ||||||||
\(776\) | 21.4380 | 0.769580 | ||||||||
\(777\) | −4.54101 | −0.162908 | ||||||||
\(778\) | 39.6147 | 1.42026 | ||||||||
\(779\) | −2.04348 | −0.0732151 | ||||||||
\(780\) | −0.336625 | −0.0120531 | ||||||||
\(781\) | −11.2035 | −0.400893 | ||||||||
\(782\) | −13.4523 | −0.481055 | ||||||||
\(783\) | −2.62142 | −0.0936820 | ||||||||
\(784\) | −27.2761 | −0.974148 | ||||||||
\(785\) | 3.68489 | 0.131519 | ||||||||
\(786\) | −1.73008 | −0.0617101 | ||||||||
\(787\) | −31.4728 | −1.12188 | −0.560942 | − | 0.827855i | \(-0.689561\pi\) | ||||
−0.560942 | + | 0.827855i | \(0.689561\pi\) | |||||||
\(788\) | 2.29444 | 0.0817359 | ||||||||
\(789\) | −6.62719 | −0.235934 | ||||||||
\(790\) | −13.6832 | −0.486825 | ||||||||
\(791\) | 38.1242 | 1.35554 | ||||||||
\(792\) | 22.4794 | 0.798770 | ||||||||
\(793\) | 14.4825 | 0.514287 | ||||||||
\(794\) | −14.4213 | −0.511791 | ||||||||
\(795\) | −1.15043 | −0.0408016 | ||||||||
\(796\) | −2.96803 | −0.105199 | ||||||||
\(797\) | −7.66543 | −0.271523 | −0.135762 | − | 0.990742i | \(-0.543348\pi\) | ||||
−0.135762 | + | 0.990742i | \(0.543348\pi\) | |||||||
\(798\) | 8.44603 | 0.298986 | ||||||||
\(799\) | 28.2703 | 1.00013 | ||||||||
\(800\) | 1.05894 | 0.0374393 | ||||||||
\(801\) | 43.2628 | 1.52862 | ||||||||
\(802\) | −7.61068 | −0.268743 | ||||||||
\(803\) | 44.9211 | 1.58523 | ||||||||
\(804\) | 0.271119 | 0.00956162 | ||||||||
\(805\) | −13.6203 | −0.480052 | ||||||||
\(806\) | 32.2118 | 1.13461 | ||||||||
\(807\) | 2.24393 | 0.0789899 | ||||||||
\(808\) | −6.42661 | −0.226087 | ||||||||
\(809\) | 25.1641 | 0.884724 | 0.442362 | − | 0.896837i | \(-0.354141\pi\) | ||||
0.442362 | + | 0.896837i | \(0.354141\pi\) | |||||||
\(810\) | 26.9395 | 0.946557 | ||||||||
\(811\) | 12.5757 | 0.441593 | 0.220797 | − | 0.975320i | \(-0.429134\pi\) | ||||
0.220797 | + | 0.975320i | \(0.429134\pi\) | |||||||
\(812\) | 0.425858 | 0.0149447 | ||||||||
\(813\) | 5.77552 | 0.202556 | ||||||||
\(814\) | −11.6777 | −0.409303 | ||||||||
\(815\) | −1.95228 | −0.0683854 | ||||||||
\(816\) | −12.2280 | −0.428064 | ||||||||
\(817\) | −2.04185 | −0.0714353 | ||||||||
\(818\) | 11.1137 | 0.388581 | ||||||||
\(819\) | −25.5760 | −0.893697 | ||||||||
\(820\) | −0.174367 | −0.00608917 | ||||||||
\(821\) | 5.56714 | 0.194295 | 0.0971473 | − | 0.995270i | \(-0.469028\pi\) | ||||
0.0971473 | + | 0.995270i | \(0.469028\pi\) | |||||||
\(822\) | 6.11503 | 0.213286 | ||||||||
\(823\) | 39.5808 | 1.37970 | 0.689849 | − | 0.723953i | \(-0.257677\pi\) | ||||
0.689849 | + | 0.723953i | \(0.257677\pi\) | |||||||
\(824\) | 4.84750 | 0.168871 | ||||||||
\(825\) | −2.14362 | −0.0746311 | ||||||||
\(826\) | −35.7281 | −1.24314 | ||||||||
\(827\) | 40.0374 | 1.39224 | 0.696118 | − | 0.717927i | \(-0.254909\pi\) | ||||
0.696118 | + | 0.717927i | \(0.254909\pi\) | |||||||
\(828\) | −0.468168 | −0.0162700 | ||||||||
\(829\) | 42.4014 | 1.47266 | 0.736331 | − | 0.676622i | \(-0.236557\pi\) | ||||
0.736331 | + | 0.676622i | \(0.236557\pi\) | |||||||
\(830\) | 43.0147 | 1.49306 | ||||||||
\(831\) | −8.65585 | −0.300268 | ||||||||
\(832\) | 18.6586 | 0.646870 | ||||||||
\(833\) | 41.4323 | 1.43554 | ||||||||
\(834\) | −0.657986 | −0.0227842 | ||||||||
\(835\) | −47.4026 | −1.64043 | ||||||||
\(836\) | 1.19119 | 0.0411983 | ||||||||
\(837\) | 23.2817 | 0.804733 | ||||||||
\(838\) | 12.6948 | 0.438535 | ||||||||
\(839\) | 5.58659 | 0.192871 | 0.0964353 | − | 0.995339i | \(-0.469256\pi\) | ||||
0.0964353 | + | 0.995339i | \(0.469256\pi\) | |||||||
\(840\) | −11.6995 | −0.403670 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 19.6719 | 0.677937 | ||||||||
\(843\) | 8.47395 | 0.291858 | ||||||||
\(844\) | 2.08690 | 0.0718341 | ||||||||
\(845\) | 17.4468 | 0.600189 | ||||||||
\(846\) | 17.9394 | 0.616771 | ||||||||
\(847\) | −8.76923 | −0.301314 | ||||||||
\(848\) | −4.17170 | −0.143257 | ||||||||
\(849\) | −12.4731 | −0.428075 | ||||||||
\(850\) | −15.0548 | −0.516377 | ||||||||
\(851\) | −3.94813 | −0.135340 | ||||||||
\(852\) | 0.200424 | 0.00686642 | ||||||||
\(853\) | −53.3606 | −1.82703 | −0.913515 | − | 0.406804i | \(-0.866643\pi\) | ||||
−0.913515 | + | 0.406804i | \(0.866643\pi\) | |||||||
\(854\) | −31.0058 | −1.06100 | ||||||||
\(855\) | −25.1497 | −0.860101 | ||||||||
\(856\) | −48.5828 | −1.66053 | ||||||||
\(857\) | −27.2601 | −0.931186 | −0.465593 | − | 0.884999i | \(-0.654159\pi\) | ||||
−0.465593 | + | 0.884999i | \(0.654159\pi\) | |||||||
\(858\) | 4.81394 | 0.164345 | ||||||||
\(859\) | 57.3332 | 1.95618 | 0.978091 | − | 0.208177i | \(-0.0667531\pi\) | ||||
0.978091 | + | 0.208177i | \(0.0667531\pi\) | |||||||
\(860\) | −0.174229 | −0.00594115 | ||||||||
\(861\) | 0.969648 | 0.0330455 | ||||||||
\(862\) | 9.87692 | 0.336409 | ||||||||
\(863\) | −18.3434 | −0.624417 | −0.312209 | − | 0.950014i | \(-0.601069\pi\) | ||||
−0.312209 | + | 0.950014i | \(0.601069\pi\) | |||||||
\(864\) | −1.71880 | −0.0584747 | ||||||||
\(865\) | 0.758909 | 0.0258037 | ||||||||
\(866\) | 44.1442 | 1.50008 | ||||||||
\(867\) | 10.8846 | 0.369661 | ||||||||
\(868\) | −3.78218 | −0.128375 | ||||||||
\(869\) | 10.7316 | 0.364045 | ||||||||
\(870\) | 1.69232 | 0.0573751 | ||||||||
\(871\) | 12.8774 | 0.436335 | ||||||||
\(872\) | −19.3543 | −0.655418 | ||||||||
\(873\) | −21.8673 | −0.740098 | ||||||||
\(874\) | 7.34331 | 0.248391 | ||||||||
\(875\) | 31.9472 | 1.08001 | ||||||||
\(876\) | −0.803612 | −0.0271515 | ||||||||
\(877\) | 40.9857 | 1.38399 | 0.691995 | − | 0.721902i | \(-0.256732\pi\) | ||||
0.691995 | + | 0.721902i | \(0.256732\pi\) | |||||||
\(878\) | 12.3788 | 0.417766 | ||||||||
\(879\) | −2.66461 | −0.0898751 | ||||||||
\(880\) | −31.8381 | −1.07326 | ||||||||
\(881\) | −41.2195 | −1.38872 | −0.694361 | − | 0.719627i | \(-0.744313\pi\) | ||||
−0.694361 | + | 0.719627i | \(0.744313\pi\) | |||||||
\(882\) | 26.2917 | 0.885286 | ||||||||
\(883\) | −15.6951 | −0.528182 | −0.264091 | − | 0.964498i | \(-0.585072\pi\) | ||||
−0.264091 | + | 0.964498i | \(0.585072\pi\) | |||||||
\(884\) | 1.85419 | 0.0623632 | ||||||||
\(885\) | −7.78671 | −0.261747 | ||||||||
\(886\) | 30.8582 | 1.03670 | ||||||||
\(887\) | −21.2244 | −0.712645 | −0.356323 | − | 0.934363i | \(-0.615970\pi\) | ||||
−0.356323 | + | 0.934363i | \(0.615970\pi\) | |||||||
\(888\) | −3.39134 | −0.113806 | ||||||||
\(889\) | −13.8227 | −0.463597 | ||||||||
\(890\) | −57.9029 | −1.94091 | ||||||||
\(891\) | −21.1285 | −0.707831 | ||||||||
\(892\) | −2.13293 | −0.0714159 | ||||||||
\(893\) | −15.4321 | −0.516415 | ||||||||
\(894\) | −4.42172 | −0.147884 | ||||||||
\(895\) | −28.2562 | −0.944500 | ||||||||
\(896\) | −44.7587 | −1.49528 | ||||||||
\(897\) | 1.62755 | 0.0543425 | ||||||||
\(898\) | 6.04043 | 0.201572 | ||||||||
\(899\) | −8.88131 | −0.296208 | ||||||||
\(900\) | −0.523938 | −0.0174646 | ||||||||
\(901\) | 6.33679 | 0.211109 | ||||||||
\(902\) | 2.49355 | 0.0830263 | ||||||||
\(903\) | 0.968878 | 0.0322422 | ||||||||
\(904\) | 28.4721 | 0.946967 | ||||||||
\(905\) | 67.7859 | 2.25328 | ||||||||
\(906\) | 3.49332 | 0.116058 | ||||||||
\(907\) | −26.0532 | −0.865081 | −0.432541 | − | 0.901614i | \(-0.642383\pi\) | ||||
−0.432541 | + | 0.901614i | \(0.642383\pi\) | |||||||
\(908\) | −2.47515 | −0.0821408 | ||||||||
\(909\) | 6.55532 | 0.217426 | ||||||||
\(910\) | 34.2309 | 1.13474 | ||||||||
\(911\) | 13.3378 | 0.441900 | 0.220950 | − | 0.975285i | \(-0.429084\pi\) | ||||
0.220950 | + | 0.975285i | \(0.429084\pi\) | |||||||
\(912\) | 6.67495 | 0.221030 | ||||||||
\(913\) | −33.7362 | −1.11651 | ||||||||
\(914\) | −39.3317 | −1.30098 | ||||||||
\(915\) | −6.75752 | −0.223397 | ||||||||
\(916\) | 1.47374 | 0.0486939 | ||||||||
\(917\) | 9.64859 | 0.318624 | ||||||||
\(918\) | 24.4359 | 0.806505 | ||||||||
\(919\) | −0.475423 | −0.0156828 | −0.00784138 | − | 0.999969i | \(-0.502496\pi\) | ||||
−0.00784138 | + | 0.999969i | \(0.502496\pi\) | |||||||
\(920\) | −10.1720 | −0.335360 | ||||||||
\(921\) | −11.2844 | −0.371835 | ||||||||
\(922\) | 23.5164 | 0.774470 | ||||||||
\(923\) | 9.51963 | 0.313343 | ||||||||
\(924\) | −0.565232 | −0.0185948 | ||||||||
\(925\) | −4.41845 | −0.145278 | ||||||||
\(926\) | 25.0998 | 0.824831 | ||||||||
\(927\) | −4.94458 | −0.162401 | ||||||||
\(928\) | 0.655674 | 0.0215236 | ||||||||
\(929\) | 30.3197 | 0.994758 | 0.497379 | − | 0.867533i | \(-0.334296\pi\) | ||||
0.497379 | + | 0.867533i | \(0.334296\pi\) | |||||||
\(930\) | −15.0301 | −0.492855 | ||||||||
\(931\) | −22.6169 | −0.741240 | ||||||||
\(932\) | −1.53092 | −0.0501469 | ||||||||
\(933\) | −7.58528 | −0.248331 | ||||||||
\(934\) | 44.0156 | 1.44024 | ||||||||
\(935\) | 48.3619 | 1.58160 | ||||||||
\(936\) | −19.1008 | −0.624328 | ||||||||
\(937\) | 0.0853592 | 0.00278856 | 0.00139428 | − | 0.999999i | \(-0.499556\pi\) | ||||
0.00139428 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(938\) | −27.5696 | −0.900180 | ||||||||
\(939\) | 11.7198 | 0.382462 | ||||||||
\(940\) | −1.31680 | −0.0429493 | ||||||||
\(941\) | −27.7946 | −0.906079 | −0.453039 | − | 0.891491i | \(-0.649660\pi\) | ||||
−0.453039 | + | 0.891491i | \(0.649660\pi\) | |||||||
\(942\) | 0.942703 | 0.0307149 | ||||||||
\(943\) | 0.843051 | 0.0274535 | ||||||||
\(944\) | −28.2362 | −0.919008 | ||||||||
\(945\) | 24.7410 | 0.804824 | ||||||||
\(946\) | 2.49157 | 0.0810080 | ||||||||
\(947\) | 31.4047 | 1.02052 | 0.510258 | − | 0.860021i | \(-0.329550\pi\) | ||||
0.510258 | + | 0.860021i | \(0.329550\pi\) | |||||||
\(948\) | −0.191983 | −0.00623531 | ||||||||
\(949\) | −38.1695 | −1.23903 | ||||||||
\(950\) | 8.21808 | 0.266630 | ||||||||
\(951\) | −12.6304 | −0.409569 | ||||||||
\(952\) | 64.4427 | 2.08860 | ||||||||
\(953\) | −5.72063 | −0.185309 | −0.0926546 | − | 0.995698i | \(-0.529535\pi\) | ||||
−0.0926546 | + | 0.995698i | \(0.529535\pi\) | |||||||
\(954\) | 4.02113 | 0.130189 | ||||||||
\(955\) | 59.3244 | 1.91969 | ||||||||
\(956\) | −0.824752 | −0.0266744 | ||||||||
\(957\) | −1.32728 | −0.0429048 | ||||||||
\(958\) | −9.91758 | −0.320423 | ||||||||
\(959\) | −34.1032 | −1.10125 | ||||||||
\(960\) | −8.70611 | −0.280988 | ||||||||
\(961\) | 47.8777 | 1.54444 | ||||||||
\(962\) | 9.92255 | 0.319916 | ||||||||
\(963\) | 49.5558 | 1.59691 | ||||||||
\(964\) | −1.55239 | −0.0499990 | ||||||||
\(965\) | 42.0163 | 1.35255 | ||||||||
\(966\) | −3.48447 | −0.112111 | ||||||||
\(967\) | −29.7803 | −0.957671 | −0.478835 | − | 0.877905i | \(-0.658941\pi\) | ||||
−0.478835 | + | 0.877905i | \(0.658941\pi\) | |||||||
\(968\) | −6.54908 | −0.210495 | ||||||||
\(969\) | −10.1392 | −0.325719 | ||||||||
\(970\) | 29.2672 | 0.939715 | ||||||||
\(971\) | −5.97181 | −0.191645 | −0.0958223 | − | 0.995398i | \(-0.530548\pi\) | ||||
−0.0958223 | + | 0.995398i | \(0.530548\pi\) | |||||||
\(972\) | 1.29064 | 0.0413972 | ||||||||
\(973\) | 3.66955 | 0.117641 | ||||||||
\(974\) | −19.6266 | −0.628877 | ||||||||
\(975\) | 1.82144 | 0.0583326 | ||||||||
\(976\) | −24.5041 | −0.784358 | ||||||||
\(977\) | 51.5863 | 1.65039 | 0.825196 | − | 0.564846i | \(-0.191065\pi\) | ||||
0.825196 | + | 0.564846i | \(0.191065\pi\) | |||||||
\(978\) | −0.499451 | −0.0159707 | ||||||||
\(979\) | 45.4129 | 1.45140 | ||||||||
\(980\) | −1.92987 | −0.0616475 | ||||||||
\(981\) | 19.7419 | 0.630309 | ||||||||
\(982\) | 20.3402 | 0.649080 | ||||||||
\(983\) | −20.9291 | −0.667535 | −0.333768 | − | 0.942655i | \(-0.608320\pi\) | ||||
−0.333768 | + | 0.942655i | \(0.608320\pi\) | |||||||
\(984\) | 0.724158 | 0.0230853 | ||||||||
\(985\) | −50.8500 | −1.62022 | ||||||||
\(986\) | −9.32162 | −0.296861 | ||||||||
\(987\) | 7.32266 | 0.233083 | ||||||||
\(988\) | −1.01216 | −0.0322011 | ||||||||
\(989\) | 0.842380 | 0.0267861 | ||||||||
\(990\) | 30.6889 | 0.975358 | ||||||||
\(991\) | −5.93374 | −0.188491 | −0.0942457 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942457 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(992\) | −5.82325 | −0.184888 | ||||||||
\(993\) | 3.10929 | 0.0986705 | ||||||||
\(994\) | −20.3808 | −0.646440 | ||||||||
\(995\) | 65.7785 | 2.08532 | ||||||||
\(996\) | 0.603522 | 0.0191233 | ||||||||
\(997\) | −10.2541 | −0.324752 | −0.162376 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162376 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(998\) | 53.3134 | 1.68761 | ||||||||
\(999\) | 7.17170 | 0.226903 |
(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 | 4031.2.a.b.1.16 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.b.1.16 | ✓ | 59 | 1.1 | even | 1 | trivial |