Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(0\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.95638 | −1.70687 | −0.853433 | − | 0.521203i | \(-0.825483\pi\) | ||||
−0.853433 | + | 0.521203i | \(0.825483\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.704147 | −0.314904 | −0.157452 | − | 0.987527i | \(-0.550328\pi\) | ||||
−0.157452 | + | 0.987527i | \(0.550328\pi\) | |||||||
\(6\) | −2.95638 | −1.20694 | ||||||||
\(7\) | −0.285333 | −0.107846 | −0.0539228 | − | 0.998545i | \(-0.517172\pi\) | ||||
−0.0539228 | + | 0.998545i | \(0.517172\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.74016 | 1.91339 | ||||||||
\(10\) | −0.704147 | −0.222671 | ||||||||
\(11\) | 2.13212 | 0.642860 | 0.321430 | − | 0.946933i | \(-0.395837\pi\) | ||||
0.321430 | + | 0.946933i | \(0.395837\pi\) | |||||||
\(12\) | −2.95638 | −0.853433 | ||||||||
\(13\) | −0.824474 | −0.228668 | −0.114334 | − | 0.993442i | \(-0.536473\pi\) | ||||
−0.114334 | + | 0.993442i | \(0.536473\pi\) | |||||||
\(14\) | −0.285333 | −0.0762584 | ||||||||
\(15\) | 2.08172 | 0.537499 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.07908 | 0.746787 | 0.373393 | − | 0.927673i | \(-0.378194\pi\) | ||||
0.373393 | + | 0.927673i | \(0.378194\pi\) | |||||||
\(18\) | 5.74016 | 1.35297 | ||||||||
\(19\) | −3.85577 | −0.884574 | −0.442287 | − | 0.896874i | \(-0.645833\pi\) | ||||
−0.442287 | + | 0.896874i | \(0.645833\pi\) | |||||||
\(20\) | −0.704147 | −0.157452 | ||||||||
\(21\) | 0.843551 | 0.184078 | ||||||||
\(22\) | 2.13212 | 0.454570 | ||||||||
\(23\) | 6.98769 | 1.45703 | 0.728517 | − | 0.685028i | \(-0.240210\pi\) | ||||
0.728517 | + | 0.685028i | \(0.240210\pi\) | |||||||
\(24\) | −2.95638 | −0.603468 | ||||||||
\(25\) | −4.50418 | −0.900835 | ||||||||
\(26\) | −0.824474 | −0.161693 | ||||||||
\(27\) | −8.10096 | −1.55903 | ||||||||
\(28\) | −0.285333 | −0.0539228 | ||||||||
\(29\) | 9.72258 | 1.80544 | 0.902719 | − | 0.430230i | \(-0.141568\pi\) | ||||
0.902719 | + | 0.430230i | \(0.141568\pi\) | |||||||
\(30\) | 2.08172 | 0.380069 | ||||||||
\(31\) | −1.99726 | −0.358718 | −0.179359 | − | 0.983784i | \(-0.557402\pi\) | ||||
−0.179359 | + | 0.983784i | \(0.557402\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.30336 | −1.09727 | ||||||||
\(34\) | 3.07908 | 0.528058 | ||||||||
\(35\) | 0.200916 | 0.0339610 | ||||||||
\(36\) | 5.74016 | 0.956694 | ||||||||
\(37\) | 2.22155 | 0.365221 | 0.182611 | − | 0.983185i | \(-0.441545\pi\) | ||||
0.182611 | + | 0.983185i | \(0.441545\pi\) | |||||||
\(38\) | −3.85577 | −0.625488 | ||||||||
\(39\) | 2.43746 | 0.390305 | ||||||||
\(40\) | −0.704147 | −0.111335 | ||||||||
\(41\) | −0.562653 | −0.0878716 | −0.0439358 | − | 0.999034i | \(-0.513990\pi\) | ||||
−0.0439358 | + | 0.999034i | \(0.513990\pi\) | |||||||
\(42\) | 0.843551 | 0.130163 | ||||||||
\(43\) | −7.45494 | −1.13687 | −0.568434 | − | 0.822729i | \(-0.692451\pi\) | ||||
−0.568434 | + | 0.822729i | \(0.692451\pi\) | |||||||
\(44\) | 2.13212 | 0.321430 | ||||||||
\(45\) | −4.04192 | −0.602534 | ||||||||
\(46\) | 6.98769 | 1.03028 | ||||||||
\(47\) | 2.16566 | 0.315894 | 0.157947 | − | 0.987448i | \(-0.449512\pi\) | ||||
0.157947 | + | 0.987448i | \(0.449512\pi\) | |||||||
\(48\) | −2.95638 | −0.426716 | ||||||||
\(49\) | −6.91859 | −0.988369 | ||||||||
\(50\) | −4.50418 | −0.636987 | ||||||||
\(51\) | −9.10292 | −1.27466 | ||||||||
\(52\) | −0.824474 | −0.114334 | ||||||||
\(53\) | −3.81629 | −0.524208 | −0.262104 | − | 0.965040i | \(-0.584416\pi\) | ||||
−0.262104 | + | 0.965040i | \(0.584416\pi\) | |||||||
\(54\) | −8.10096 | −1.10240 | ||||||||
\(55\) | −1.50133 | −0.202439 | ||||||||
\(56\) | −0.285333 | −0.0381292 | ||||||||
\(57\) | 11.3991 | 1.50985 | ||||||||
\(58\) | 9.72258 | 1.27664 | ||||||||
\(59\) | 1.74958 | 0.227776 | 0.113888 | − | 0.993494i | \(-0.463669\pi\) | ||||
0.113888 | + | 0.993494i | \(0.463669\pi\) | |||||||
\(60\) | 2.08172 | 0.268749 | ||||||||
\(61\) | 9.87230 | 1.26402 | 0.632009 | − | 0.774961i | \(-0.282230\pi\) | ||||
0.632009 | + | 0.774961i | \(0.282230\pi\) | |||||||
\(62\) | −1.99726 | −0.253652 | ||||||||
\(63\) | −1.63786 | −0.206351 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.580551 | 0.0720085 | ||||||||
\(66\) | −6.30336 | −0.775890 | ||||||||
\(67\) | −3.32261 | −0.405921 | −0.202961 | − | 0.979187i | \(-0.565056\pi\) | ||||
−0.202961 | + | 0.979187i | \(0.565056\pi\) | |||||||
\(68\) | 3.07908 | 0.373393 | ||||||||
\(69\) | −20.6582 | −2.48696 | ||||||||
\(70\) | 0.200916 | 0.0240141 | ||||||||
\(71\) | −9.11043 | −1.08121 | −0.540604 | − | 0.841277i | \(-0.681804\pi\) | ||||
−0.540604 | + | 0.841277i | \(0.681804\pi\) | |||||||
\(72\) | 5.74016 | 0.676485 | ||||||||
\(73\) | −3.56037 | −0.416710 | −0.208355 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208355 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(74\) | 2.22155 | 0.258250 | ||||||||
\(75\) | 13.3160 | 1.53760 | ||||||||
\(76\) | −3.85577 | −0.442287 | ||||||||
\(77\) | −0.608365 | −0.0693296 | ||||||||
\(78\) | 2.43746 | 0.275988 | ||||||||
\(79\) | 5.23132 | 0.588570 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(80\) | −0.704147 | −0.0787260 | ||||||||
\(81\) | 6.72900 | 0.747666 | ||||||||
\(82\) | −0.562653 | −0.0621346 | ||||||||
\(83\) | 10.1482 | 1.11391 | 0.556955 | − | 0.830543i | \(-0.311970\pi\) | ||||
0.556955 | + | 0.830543i | \(0.311970\pi\) | |||||||
\(84\) | 0.843551 | 0.0920389 | ||||||||
\(85\) | −2.16813 | −0.235166 | ||||||||
\(86\) | −7.45494 | −0.803887 | ||||||||
\(87\) | −28.7436 | −3.08164 | ||||||||
\(88\) | 2.13212 | 0.227285 | ||||||||
\(89\) | 1.32183 | 0.140114 | 0.0700570 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700570 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(90\) | −4.04192 | −0.426056 | ||||||||
\(91\) | 0.235249 | 0.0246608 | ||||||||
\(92\) | 6.98769 | 0.728517 | ||||||||
\(93\) | 5.90464 | 0.612283 | ||||||||
\(94\) | 2.16566 | 0.223371 | ||||||||
\(95\) | 2.71503 | 0.278556 | ||||||||
\(96\) | −2.95638 | −0.301734 | ||||||||
\(97\) | −5.88876 | −0.597913 | −0.298956 | − | 0.954267i | \(-0.596638\pi\) | ||||
−0.298956 | + | 0.954267i | \(0.596638\pi\) | |||||||
\(98\) | −6.91859 | −0.698883 | ||||||||
\(99\) | 12.2387 | 1.23004 | ||||||||
\(100\) | −4.50418 | −0.450418 | ||||||||
\(101\) | 3.20302 | 0.318713 | 0.159356 | − | 0.987221i | \(-0.449058\pi\) | ||||
0.159356 | + | 0.987221i | \(0.449058\pi\) | |||||||
\(102\) | −9.10292 | −0.901324 | ||||||||
\(103\) | −5.94076 | −0.585360 | −0.292680 | − | 0.956210i | \(-0.594547\pi\) | ||||
−0.292680 | + | 0.956210i | \(0.594547\pi\) | |||||||
\(104\) | −0.824474 | −0.0808463 | ||||||||
\(105\) | −0.593984 | −0.0579669 | ||||||||
\(106\) | −3.81629 | −0.370671 | ||||||||
\(107\) | 0.282513 | 0.0273116 | 0.0136558 | − | 0.999907i | \(-0.495653\pi\) | ||||
0.0136558 | + | 0.999907i | \(0.495653\pi\) | |||||||
\(108\) | −8.10096 | −0.779515 | ||||||||
\(109\) | 9.55550 | 0.915251 | 0.457626 | − | 0.889145i | \(-0.348700\pi\) | ||||
0.457626 | + | 0.889145i | \(0.348700\pi\) | |||||||
\(110\) | −1.50133 | −0.143146 | ||||||||
\(111\) | −6.56775 | −0.623383 | ||||||||
\(112\) | −0.285333 | −0.0269614 | ||||||||
\(113\) | 2.37643 | 0.223555 | 0.111778 | − | 0.993733i | \(-0.464346\pi\) | ||||
0.111778 | + | 0.993733i | \(0.464346\pi\) | |||||||
\(114\) | 11.3991 | 1.06762 | ||||||||
\(115\) | −4.92036 | −0.458826 | ||||||||
\(116\) | 9.72258 | 0.902719 | ||||||||
\(117\) | −4.73262 | −0.437531 | ||||||||
\(118\) | 1.74958 | 0.161062 | ||||||||
\(119\) | −0.878562 | −0.0805377 | ||||||||
\(120\) | 2.08172 | 0.190035 | ||||||||
\(121\) | −6.45404 | −0.586731 | ||||||||
\(122\) | 9.87230 | 0.893796 | ||||||||
\(123\) | 1.66341 | 0.149985 | ||||||||
\(124\) | −1.99726 | −0.179359 | ||||||||
\(125\) | 6.69234 | 0.598581 | ||||||||
\(126\) | −1.63786 | −0.145912 | ||||||||
\(127\) | 12.2521 | 1.08720 | 0.543600 | − | 0.839344i | \(-0.317061\pi\) | ||||
0.543600 | + | 0.839344i | \(0.317061\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 22.0396 | 1.94048 | ||||||||
\(130\) | 0.580551 | 0.0509177 | ||||||||
\(131\) | 0.754565 | 0.0659266 | 0.0329633 | − | 0.999457i | \(-0.489506\pi\) | ||||
0.0329633 | + | 0.999457i | \(0.489506\pi\) | |||||||
\(132\) | −6.30336 | −0.548637 | ||||||||
\(133\) | 1.10018 | 0.0953974 | ||||||||
\(134\) | −3.32261 | −0.287030 | ||||||||
\(135\) | 5.70427 | 0.490945 | ||||||||
\(136\) | 3.07908 | 0.264029 | ||||||||
\(137\) | 19.2410 | 1.64387 | 0.821936 | − | 0.569580i | \(-0.192894\pi\) | ||||
0.821936 | + | 0.569580i | \(0.192894\pi\) | |||||||
\(138\) | −20.6582 | −1.75855 | ||||||||
\(139\) | −16.0240 | −1.35914 | −0.679569 | − | 0.733612i | \(-0.737833\pi\) | ||||
−0.679569 | + | 0.733612i | \(0.737833\pi\) | |||||||
\(140\) | 0.200916 | 0.0169805 | ||||||||
\(141\) | −6.40251 | −0.539189 | ||||||||
\(142\) | −9.11043 | −0.764530 | ||||||||
\(143\) | −1.75788 | −0.147001 | ||||||||
\(144\) | 5.74016 | 0.478347 | ||||||||
\(145\) | −6.84613 | −0.568540 | ||||||||
\(146\) | −3.56037 | −0.294658 | ||||||||
\(147\) | 20.4539 | 1.68701 | ||||||||
\(148\) | 2.22155 | 0.182611 | ||||||||
\(149\) | 7.14519 | 0.585357 | 0.292678 | − | 0.956211i | \(-0.405453\pi\) | ||||
0.292678 | + | 0.956211i | \(0.405453\pi\) | |||||||
\(150\) | 13.3160 | 1.08725 | ||||||||
\(151\) | −20.0088 | −1.62829 | −0.814145 | − | 0.580662i | \(-0.802794\pi\) | ||||
−0.814145 | + | 0.580662i | \(0.802794\pi\) | |||||||
\(152\) | −3.85577 | −0.312744 | ||||||||
\(153\) | 17.6744 | 1.42889 | ||||||||
\(154\) | −0.608365 | −0.0490234 | ||||||||
\(155\) | 1.40636 | 0.112962 | ||||||||
\(156\) | 2.43746 | 0.195153 | ||||||||
\(157\) | 13.1473 | 1.04926 | 0.524632 | − | 0.851329i | \(-0.324203\pi\) | ||||
0.524632 | + | 0.851329i | \(0.324203\pi\) | |||||||
\(158\) | 5.23132 | 0.416182 | ||||||||
\(159\) | 11.2824 | 0.894752 | ||||||||
\(160\) | −0.704147 | −0.0556677 | ||||||||
\(161\) | −1.99382 | −0.157135 | ||||||||
\(162\) | 6.72900 | 0.528680 | ||||||||
\(163\) | 7.81901 | 0.612432 | 0.306216 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306216 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(164\) | −0.562653 | −0.0439358 | ||||||||
\(165\) | 4.43850 | 0.345536 | ||||||||
\(166\) | 10.1482 | 0.787653 | ||||||||
\(167\) | −1.89276 | −0.146466 | −0.0732332 | − | 0.997315i | \(-0.523332\pi\) | ||||
−0.0732332 | + | 0.997315i | \(0.523332\pi\) | |||||||
\(168\) | 0.843551 | 0.0650814 | ||||||||
\(169\) | −12.3202 | −0.947711 | ||||||||
\(170\) | −2.16813 | −0.166288 | ||||||||
\(171\) | −22.1328 | −1.69253 | ||||||||
\(172\) | −7.45494 | −0.568434 | ||||||||
\(173\) | −2.02229 | −0.153752 | −0.0768760 | − | 0.997041i | \(-0.524495\pi\) | ||||
−0.0768760 | + | 0.997041i | \(0.524495\pi\) | |||||||
\(174\) | −28.7436 | −2.17905 | ||||||||
\(175\) | 1.28519 | 0.0971511 | ||||||||
\(176\) | 2.13212 | 0.160715 | ||||||||
\(177\) | −5.17242 | −0.388783 | ||||||||
\(178\) | 1.32183 | 0.0990756 | ||||||||
\(179\) | −12.0044 | −0.897249 | −0.448624 | − | 0.893720i | \(-0.648086\pi\) | ||||
−0.448624 | + | 0.893720i | \(0.648086\pi\) | |||||||
\(180\) | −4.04192 | −0.301267 | ||||||||
\(181\) | 4.31112 | 0.320443 | 0.160221 | − | 0.987081i | \(-0.448779\pi\) | ||||
0.160221 | + | 0.987081i | \(0.448779\pi\) | |||||||
\(182\) | 0.235249 | 0.0174378 | ||||||||
\(183\) | −29.1862 | −2.15751 | ||||||||
\(184\) | 6.98769 | 0.515139 | ||||||||
\(185\) | −1.56430 | −0.115010 | ||||||||
\(186\) | 5.90464 | 0.432949 | ||||||||
\(187\) | 6.56498 | 0.480079 | ||||||||
\(188\) | 2.16566 | 0.157947 | ||||||||
\(189\) | 2.31147 | 0.168135 | ||||||||
\(190\) | 2.71503 | 0.196969 | ||||||||
\(191\) | 24.4644 | 1.77018 | 0.885092 | − | 0.465416i | \(-0.154095\pi\) | ||||
0.885092 | + | 0.465416i | \(0.154095\pi\) | |||||||
\(192\) | −2.95638 | −0.213358 | ||||||||
\(193\) | 16.1289 | 1.16098 | 0.580491 | − | 0.814267i | \(-0.302861\pi\) | ||||
0.580491 | + | 0.814267i | \(0.302861\pi\) | |||||||
\(194\) | −5.88876 | −0.422788 | ||||||||
\(195\) | −1.71633 | −0.122909 | ||||||||
\(196\) | −6.91859 | −0.494185 | ||||||||
\(197\) | 26.6450 | 1.89838 | 0.949191 | − | 0.314702i | \(-0.101905\pi\) | ||||
0.949191 | + | 0.314702i | \(0.101905\pi\) | |||||||
\(198\) | 12.2387 | 0.869770 | ||||||||
\(199\) | −8.63087 | −0.611826 | −0.305913 | − | 0.952059i | \(-0.598962\pi\) | ||||
−0.305913 | + | 0.952059i | \(0.598962\pi\) | |||||||
\(200\) | −4.50418 | −0.318493 | ||||||||
\(201\) | 9.82289 | 0.692853 | ||||||||
\(202\) | 3.20302 | 0.225364 | ||||||||
\(203\) | −2.77417 | −0.194709 | ||||||||
\(204\) | −9.10292 | −0.637332 | ||||||||
\(205\) | 0.396190 | 0.0276711 | ||||||||
\(206\) | −5.94076 | −0.413912 | ||||||||
\(207\) | 40.1105 | 2.78787 | ||||||||
\(208\) | −0.824474 | −0.0571670 | ||||||||
\(209\) | −8.22098 | −0.568657 | ||||||||
\(210\) | −0.593984 | −0.0409888 | ||||||||
\(211\) | 28.0721 | 1.93256 | 0.966282 | − | 0.257486i | \(-0.0828942\pi\) | ||||
0.966282 | + | 0.257486i | \(0.0828942\pi\) | |||||||
\(212\) | −3.81629 | −0.262104 | ||||||||
\(213\) | 26.9339 | 1.84548 | ||||||||
\(214\) | 0.282513 | 0.0193122 | ||||||||
\(215\) | 5.24938 | 0.358005 | ||||||||
\(216\) | −8.10096 | −0.551201 | ||||||||
\(217\) | 0.569882 | 0.0386861 | ||||||||
\(218\) | 9.55550 | 0.647180 | ||||||||
\(219\) | 10.5258 | 0.711267 | ||||||||
\(220\) | −1.50133 | −0.101220 | ||||||||
\(221\) | −2.53862 | −0.170766 | ||||||||
\(222\) | −6.56775 | −0.440799 | ||||||||
\(223\) | −26.0000 | −1.74109 | −0.870543 | − | 0.492093i | \(-0.836232\pi\) | ||||
−0.870543 | + | 0.492093i | \(0.836232\pi\) | |||||||
\(224\) | −0.285333 | −0.0190646 | ||||||||
\(225\) | −25.8547 | −1.72365 | ||||||||
\(226\) | 2.37643 | 0.158077 | ||||||||
\(227\) | 19.7096 | 1.30817 | 0.654084 | − | 0.756422i | \(-0.273054\pi\) | ||||
0.654084 | + | 0.756422i | \(0.273054\pi\) | |||||||
\(228\) | 11.3991 | 0.754924 | ||||||||
\(229\) | 4.04796 | 0.267497 | 0.133748 | − | 0.991015i | \(-0.457299\pi\) | ||||
0.133748 | + | 0.991015i | \(0.457299\pi\) | |||||||
\(230\) | −4.92036 | −0.324439 | ||||||||
\(231\) | 1.79856 | 0.118336 | ||||||||
\(232\) | 9.72258 | 0.638319 | ||||||||
\(233\) | 30.1140 | 1.97283 | 0.986417 | − | 0.164259i | \(-0.0525232\pi\) | ||||
0.986417 | + | 0.164259i | \(0.0525232\pi\) | |||||||
\(234\) | −4.73262 | −0.309381 | ||||||||
\(235\) | −1.52494 | −0.0994764 | ||||||||
\(236\) | 1.74958 | 0.113888 | ||||||||
\(237\) | −15.4658 | −1.00461 | ||||||||
\(238\) | −0.878562 | −0.0569487 | ||||||||
\(239\) | 16.1795 | 1.04657 | 0.523284 | − | 0.852158i | \(-0.324707\pi\) | ||||
0.523284 | + | 0.852158i | \(0.324707\pi\) | |||||||
\(240\) | 2.08172 | 0.134375 | ||||||||
\(241\) | −28.0150 | −1.80460 | −0.902301 | − | 0.431106i | \(-0.858123\pi\) | ||||
−0.902301 | + | 0.431106i | \(0.858123\pi\) | |||||||
\(242\) | −6.45404 | −0.414882 | ||||||||
\(243\) | 4.40943 | 0.282865 | ||||||||
\(244\) | 9.87230 | 0.632009 | ||||||||
\(245\) | 4.87170 | 0.311242 | ||||||||
\(246\) | 1.66341 | 0.106055 | ||||||||
\(247\) | 3.17898 | 0.202274 | ||||||||
\(248\) | −1.99726 | −0.126826 | ||||||||
\(249\) | −30.0019 | −1.90129 | ||||||||
\(250\) | 6.69234 | 0.423261 | ||||||||
\(251\) | −15.5728 | −0.982943 | −0.491472 | − | 0.870894i | \(-0.663541\pi\) | ||||
−0.491472 | + | 0.870894i | \(0.663541\pi\) | |||||||
\(252\) | −1.63786 | −0.103175 | ||||||||
\(253\) | 14.8986 | 0.936669 | ||||||||
\(254\) | 12.2521 | 0.768767 | ||||||||
\(255\) | 6.40980 | 0.401397 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.3394 | 1.83014 | 0.915072 | − | 0.403290i | \(-0.132134\pi\) | ||||
0.915072 | + | 0.403290i | \(0.132134\pi\) | |||||||
\(258\) | 22.0396 | 1.37213 | ||||||||
\(259\) | −0.633882 | −0.0393875 | ||||||||
\(260\) | 0.580551 | 0.0360042 | ||||||||
\(261\) | 55.8092 | 3.45450 | ||||||||
\(262\) | 0.754565 | 0.0466172 | ||||||||
\(263\) | −7.17445 | −0.442396 | −0.221198 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221198 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(264\) | −6.30336 | −0.387945 | ||||||||
\(265\) | 2.68723 | 0.165075 | ||||||||
\(266\) | 1.10018 | 0.0674562 | ||||||||
\(267\) | −3.90784 | −0.239156 | ||||||||
\(268\) | −3.32261 | −0.202961 | ||||||||
\(269\) | 11.3203 | 0.690213 | 0.345107 | − | 0.938564i | \(-0.387843\pi\) | ||||
0.345107 | + | 0.938564i | \(0.387843\pi\) | |||||||
\(270\) | 5.70427 | 0.347151 | ||||||||
\(271\) | −19.7521 | −1.19985 | −0.599927 | − | 0.800055i | \(-0.704804\pi\) | ||||
−0.599927 | + | 0.800055i | \(0.704804\pi\) | |||||||
\(272\) | 3.07908 | 0.186697 | ||||||||
\(273\) | −0.695486 | −0.0420927 | ||||||||
\(274\) | 19.2410 | 1.16239 | ||||||||
\(275\) | −9.60347 | −0.579111 | ||||||||
\(276\) | −20.6582 | −1.24348 | ||||||||
\(277\) | 19.7273 | 1.18530 | 0.592649 | − | 0.805461i | \(-0.298082\pi\) | ||||
0.592649 | + | 0.805461i | \(0.298082\pi\) | |||||||
\(278\) | −16.0240 | −0.961055 | ||||||||
\(279\) | −11.4646 | −0.686366 | ||||||||
\(280\) | 0.200916 | 0.0120070 | ||||||||
\(281\) | 10.7098 | 0.638892 | 0.319446 | − | 0.947604i | \(-0.396503\pi\) | ||||
0.319446 | + | 0.947604i | \(0.396503\pi\) | |||||||
\(282\) | −6.40251 | −0.381264 | ||||||||
\(283\) | −5.28438 | −0.314124 | −0.157062 | − | 0.987589i | \(-0.550202\pi\) | ||||
−0.157062 | + | 0.987589i | \(0.550202\pi\) | |||||||
\(284\) | −9.11043 | −0.540604 | ||||||||
\(285\) | −8.02665 | −0.475458 | ||||||||
\(286\) | −1.75788 | −0.103946 | ||||||||
\(287\) | 0.160543 | 0.00947657 | ||||||||
\(288\) | 5.74016 | 0.338242 | ||||||||
\(289\) | −7.51927 | −0.442310 | ||||||||
\(290\) | −6.84613 | −0.402019 | ||||||||
\(291\) | 17.4094 | 1.02056 | ||||||||
\(292\) | −3.56037 | −0.208355 | ||||||||
\(293\) | 31.5082 | 1.84073 | 0.920364 | − | 0.391063i | \(-0.127893\pi\) | ||||
0.920364 | + | 0.391063i | \(0.127893\pi\) | |||||||
\(294\) | 20.4539 | 1.19290 | ||||||||
\(295\) | −1.23196 | −0.0717277 | ||||||||
\(296\) | 2.22155 | 0.129125 | ||||||||
\(297\) | −17.2723 | −1.00224 | ||||||||
\(298\) | 7.14519 | 0.413910 | ||||||||
\(299\) | −5.76117 | −0.333177 | ||||||||
\(300\) | 13.3160 | 0.768802 | ||||||||
\(301\) | 2.12714 | 0.122606 | ||||||||
\(302\) | −20.0088 | −1.15137 | ||||||||
\(303\) | −9.46935 | −0.544000 | ||||||||
\(304\) | −3.85577 | −0.221144 | ||||||||
\(305\) | −6.95155 | −0.398045 | ||||||||
\(306\) | 17.6744 | 1.01038 | ||||||||
\(307\) | 12.6660 | 0.722889 | 0.361444 | − | 0.932394i | \(-0.382284\pi\) | ||||
0.361444 | + | 0.932394i | \(0.382284\pi\) | |||||||
\(308\) | −0.608365 | −0.0346648 | ||||||||
\(309\) | 17.5631 | 0.999131 | ||||||||
\(310\) | 1.40636 | 0.0798760 | ||||||||
\(311\) | 25.2909 | 1.43412 | 0.717058 | − | 0.697013i | \(-0.245488\pi\) | ||||
0.717058 | + | 0.697013i | \(0.245488\pi\) | |||||||
\(312\) | 2.43746 | 0.137994 | ||||||||
\(313\) | −2.81859 | −0.159316 | −0.0796582 | − | 0.996822i | \(-0.525383\pi\) | ||||
−0.0796582 | + | 0.996822i | \(0.525383\pi\) | |||||||
\(314\) | 13.1473 | 0.741942 | ||||||||
\(315\) | 1.15329 | 0.0649806 | ||||||||
\(316\) | 5.23132 | 0.294285 | ||||||||
\(317\) | −9.50407 | −0.533802 | −0.266901 | − | 0.963724i | \(-0.586000\pi\) | ||||
−0.266901 | + | 0.963724i | \(0.586000\pi\) | |||||||
\(318\) | 11.2824 | 0.632685 | ||||||||
\(319\) | 20.7298 | 1.16064 | ||||||||
\(320\) | −0.704147 | −0.0393630 | ||||||||
\(321\) | −0.835216 | −0.0466172 | ||||||||
\(322\) | −1.99382 | −0.111111 | ||||||||
\(323\) | −11.8722 | −0.660588 | ||||||||
\(324\) | 6.72900 | 0.373833 | ||||||||
\(325\) | 3.71358 | 0.205992 | ||||||||
\(326\) | 7.81901 | 0.433055 | ||||||||
\(327\) | −28.2497 | −1.56221 | ||||||||
\(328\) | −0.562653 | −0.0310673 | ||||||||
\(329\) | −0.617934 | −0.0340678 | ||||||||
\(330\) | 4.43850 | 0.244331 | ||||||||
\(331\) | 19.0048 | 1.04460 | 0.522298 | − | 0.852763i | \(-0.325075\pi\) | ||||
0.522298 | + | 0.852763i | \(0.325075\pi\) | |||||||
\(332\) | 10.1482 | 0.556955 | ||||||||
\(333\) | 12.7521 | 0.698810 | ||||||||
\(334\) | −1.89276 | −0.103567 | ||||||||
\(335\) | 2.33961 | 0.127826 | ||||||||
\(336\) | 0.843551 | 0.0460195 | ||||||||
\(337\) | −9.92416 | −0.540604 | −0.270302 | − | 0.962776i | \(-0.587123\pi\) | ||||
−0.270302 | + | 0.962776i | \(0.587123\pi\) | |||||||
\(338\) | −12.3202 | −0.670133 | ||||||||
\(339\) | −7.02561 | −0.381579 | ||||||||
\(340\) | −2.16813 | −0.117583 | ||||||||
\(341\) | −4.25840 | −0.230605 | ||||||||
\(342\) | −22.1328 | −1.19680 | ||||||||
\(343\) | 3.97143 | 0.214437 | ||||||||
\(344\) | −7.45494 | −0.401944 | ||||||||
\(345\) | 14.5464 | 0.783154 | ||||||||
\(346\) | −2.02229 | −0.108719 | ||||||||
\(347\) | −12.7437 | −0.684116 | −0.342058 | − | 0.939679i | \(-0.611124\pi\) | ||||
−0.342058 | + | 0.939679i | \(0.611124\pi\) | |||||||
\(348\) | −28.7436 | −1.54082 | ||||||||
\(349\) | −12.7200 | −0.680886 | −0.340443 | − | 0.940265i | \(-0.610577\pi\) | ||||
−0.340443 | + | 0.940265i | \(0.610577\pi\) | |||||||
\(350\) | 1.28519 | 0.0686962 | ||||||||
\(351\) | 6.67903 | 0.356500 | ||||||||
\(352\) | 2.13212 | 0.113643 | ||||||||
\(353\) | −15.5391 | −0.827064 | −0.413532 | − | 0.910490i | \(-0.635705\pi\) | ||||
−0.413532 | + | 0.910490i | \(0.635705\pi\) | |||||||
\(354\) | −5.17242 | −0.274911 | ||||||||
\(355\) | 6.41508 | 0.340477 | ||||||||
\(356\) | 1.32183 | 0.0700570 | ||||||||
\(357\) | 2.59736 | 0.137467 | ||||||||
\(358\) | −12.0044 | −0.634451 | ||||||||
\(359\) | 23.8705 | 1.25984 | 0.629920 | − | 0.776660i | \(-0.283088\pi\) | ||||
0.629920 | + | 0.776660i | \(0.283088\pi\) | |||||||
\(360\) | −4.04192 | −0.213028 | ||||||||
\(361\) | −4.13304 | −0.217529 | ||||||||
\(362\) | 4.31112 | 0.226587 | ||||||||
\(363\) | 19.0806 | 1.00147 | ||||||||
\(364\) | 0.235249 | 0.0123304 | ||||||||
\(365\) | 2.50702 | 0.131224 | ||||||||
\(366\) | −29.1862 | −1.52559 | ||||||||
\(367\) | 28.9891 | 1.51322 | 0.756610 | − | 0.653866i | \(-0.226854\pi\) | ||||
0.756610 | + | 0.653866i | \(0.226854\pi\) | |||||||
\(368\) | 6.98769 | 0.364259 | ||||||||
\(369\) | −3.22972 | −0.168133 | ||||||||
\(370\) | −1.56430 | −0.0813241 | ||||||||
\(371\) | 1.08891 | 0.0565335 | ||||||||
\(372\) | 5.90464 | 0.306141 | ||||||||
\(373\) | 10.7208 | 0.555101 | 0.277551 | − | 0.960711i | \(-0.410477\pi\) | ||||
0.277551 | + | 0.960711i | \(0.410477\pi\) | |||||||
\(374\) | 6.56498 | 0.339467 | ||||||||
\(375\) | −19.7851 | −1.02170 | ||||||||
\(376\) | 2.16566 | 0.111685 | ||||||||
\(377\) | −8.01602 | −0.412846 | ||||||||
\(378\) | 2.31147 | 0.118889 | ||||||||
\(379\) | 26.4805 | 1.36021 | 0.680106 | − | 0.733114i | \(-0.261934\pi\) | ||||
0.680106 | + | 0.733114i | \(0.261934\pi\) | |||||||
\(380\) | 2.71503 | 0.139278 | ||||||||
\(381\) | −36.2219 | −1.85570 | ||||||||
\(382\) | 24.4644 | 1.25171 | ||||||||
\(383\) | 12.9398 | 0.661195 | 0.330597 | − | 0.943772i | \(-0.392750\pi\) | ||||
0.330597 | + | 0.943772i | \(0.392750\pi\) | |||||||
\(384\) | −2.95638 | −0.150867 | ||||||||
\(385\) | 0.428378 | 0.0218322 | ||||||||
\(386\) | 16.1289 | 0.820938 | ||||||||
\(387\) | −42.7926 | −2.17527 | ||||||||
\(388\) | −5.88876 | −0.298956 | ||||||||
\(389\) | 5.05213 | 0.256153 | 0.128077 | − | 0.991764i | \(-0.459120\pi\) | ||||
0.128077 | + | 0.991764i | \(0.459120\pi\) | |||||||
\(390\) | −1.71633 | −0.0869096 | ||||||||
\(391\) | 21.5157 | 1.08809 | ||||||||
\(392\) | −6.91859 | −0.349441 | ||||||||
\(393\) | −2.23078 | −0.112528 | ||||||||
\(394\) | 26.6450 | 1.34236 | ||||||||
\(395\) | −3.68362 | −0.185343 | ||||||||
\(396\) | 12.2387 | 0.615020 | ||||||||
\(397\) | 29.8019 | 1.49571 | 0.747856 | − | 0.663860i | \(-0.231083\pi\) | ||||
0.747856 | + | 0.663860i | \(0.231083\pi\) | |||||||
\(398\) | −8.63087 | −0.432626 | ||||||||
\(399\) | −3.25254 | −0.162831 | ||||||||
\(400\) | −4.50418 | −0.225209 | ||||||||
\(401\) | −13.1336 | −0.655863 | −0.327931 | − | 0.944702i | \(-0.606351\pi\) | ||||
−0.327931 | + | 0.944702i | \(0.606351\pi\) | |||||||
\(402\) | 9.82289 | 0.489921 | ||||||||
\(403\) | 1.64669 | 0.0820273 | ||||||||
\(404\) | 3.20302 | 0.159356 | ||||||||
\(405\) | −4.73820 | −0.235443 | ||||||||
\(406\) | −2.77417 | −0.137680 | ||||||||
\(407\) | 4.73663 | 0.234786 | ||||||||
\(408\) | −9.10292 | −0.450662 | ||||||||
\(409\) | −2.53363 | −0.125280 | −0.0626399 | − | 0.998036i | \(-0.519952\pi\) | ||||
−0.0626399 | + | 0.998036i | \(0.519952\pi\) | |||||||
\(410\) | 0.396190 | 0.0195665 | ||||||||
\(411\) | −56.8837 | −2.80587 | ||||||||
\(412\) | −5.94076 | −0.292680 | ||||||||
\(413\) | −0.499213 | −0.0245647 | ||||||||
\(414\) | 40.1105 | 1.97132 | ||||||||
\(415\) | −7.14583 | −0.350775 | ||||||||
\(416\) | −0.824474 | −0.0404232 | ||||||||
\(417\) | 47.3730 | 2.31986 | ||||||||
\(418\) | −8.22098 | −0.402101 | ||||||||
\(419\) | −38.1765 | −1.86504 | −0.932521 | − | 0.361116i | \(-0.882396\pi\) | ||||
−0.932521 | + | 0.361116i | \(0.882396\pi\) | |||||||
\(420\) | −0.593984 | −0.0289834 | ||||||||
\(421\) | 33.4945 | 1.63242 | 0.816211 | − | 0.577754i | \(-0.196071\pi\) | ||||
0.816211 | + | 0.577754i | \(0.196071\pi\) | |||||||
\(422\) | 28.0721 | 1.36653 | ||||||||
\(423\) | 12.4313 | 0.604428 | ||||||||
\(424\) | −3.81629 | −0.185335 | ||||||||
\(425\) | −13.8687 | −0.672732 | ||||||||
\(426\) | 26.9339 | 1.30495 | ||||||||
\(427\) | −2.81689 | −0.136319 | ||||||||
\(428\) | 0.282513 | 0.0136558 | ||||||||
\(429\) | 5.19696 | 0.250912 | ||||||||
\(430\) | 5.24938 | 0.253147 | ||||||||
\(431\) | 30.0466 | 1.44730 | 0.723648 | − | 0.690170i | \(-0.242464\pi\) | ||||
0.723648 | + | 0.690170i | \(0.242464\pi\) | |||||||
\(432\) | −8.10096 | −0.389758 | ||||||||
\(433\) | 34.8119 | 1.67295 | 0.836476 | − | 0.548004i | \(-0.184612\pi\) | ||||
0.836476 | + | 0.548004i | \(0.184612\pi\) | |||||||
\(434\) | 0.569882 | 0.0273552 | ||||||||
\(435\) | 20.2397 | 0.970421 | ||||||||
\(436\) | 9.55550 | 0.457626 | ||||||||
\(437\) | −26.9429 | −1.28885 | ||||||||
\(438\) | 10.5258 | 0.502942 | ||||||||
\(439\) | −1.05540 | −0.0503716 | −0.0251858 | − | 0.999683i | \(-0.508018\pi\) | ||||
−0.0251858 | + | 0.999683i | \(0.508018\pi\) | |||||||
\(440\) | −1.50133 | −0.0715731 | ||||||||
\(441\) | −39.7138 | −1.89113 | ||||||||
\(442\) | −2.53862 | −0.120750 | ||||||||
\(443\) | −30.0688 | −1.42861 | −0.714306 | − | 0.699834i | \(-0.753257\pi\) | ||||
−0.714306 | + | 0.699834i | \(0.753257\pi\) | |||||||
\(444\) | −6.56775 | −0.311692 | ||||||||
\(445\) | −0.930765 | −0.0441225 | ||||||||
\(446\) | −26.0000 | −1.23113 | ||||||||
\(447\) | −21.1239 | −0.999125 | ||||||||
\(448\) | −0.285333 | −0.0134807 | ||||||||
\(449\) | 20.0551 | 0.946457 | 0.473229 | − | 0.880940i | \(-0.343088\pi\) | ||||
0.473229 | + | 0.880940i | \(0.343088\pi\) | |||||||
\(450\) | −25.8547 | −1.21880 | ||||||||
\(451\) | −1.19965 | −0.0564891 | ||||||||
\(452\) | 2.37643 | 0.111778 | ||||||||
\(453\) | 59.1534 | 2.77927 | ||||||||
\(454\) | 19.7096 | 0.925015 | ||||||||
\(455\) | −0.165650 | −0.00776580 | ||||||||
\(456\) | 11.3991 | 0.533812 | ||||||||
\(457\) | −19.1140 | −0.894117 | −0.447058 | − | 0.894505i | \(-0.647528\pi\) | ||||
−0.447058 | + | 0.894505i | \(0.647528\pi\) | |||||||
\(458\) | 4.04796 | 0.189149 | ||||||||
\(459\) | −24.9435 | −1.16426 | ||||||||
\(460\) | −4.92036 | −0.229413 | ||||||||
\(461\) | 11.4975 | 0.535492 | 0.267746 | − | 0.963489i | \(-0.413721\pi\) | ||||
0.267746 | + | 0.963489i | \(0.413721\pi\) | |||||||
\(462\) | 1.79856 | 0.0836764 | ||||||||
\(463\) | −12.4145 | −0.576949 | −0.288475 | − | 0.957488i | \(-0.593148\pi\) | ||||
−0.288475 | + | 0.957488i | \(0.593148\pi\) | |||||||
\(464\) | 9.72258 | 0.451360 | ||||||||
\(465\) | −4.15774 | −0.192810 | ||||||||
\(466\) | 30.1140 | 1.39500 | ||||||||
\(467\) | −9.23241 | −0.427225 | −0.213613 | − | 0.976918i | \(-0.568523\pi\) | ||||
−0.213613 | + | 0.976918i | \(0.568523\pi\) | |||||||
\(468\) | −4.73262 | −0.218765 | ||||||||
\(469\) | 0.948049 | 0.0437768 | ||||||||
\(470\) | −1.52494 | −0.0703404 | ||||||||
\(471\) | −38.8682 | −1.79095 | ||||||||
\(472\) | 1.74958 | 0.0805310 | ||||||||
\(473\) | −15.8949 | −0.730847 | ||||||||
\(474\) | −15.4658 | −0.710366 | ||||||||
\(475\) | 17.3671 | 0.796856 | ||||||||
\(476\) | −0.878562 | −0.0402688 | ||||||||
\(477\) | −21.9061 | −1.00301 | ||||||||
\(478\) | 16.1795 | 0.740035 | ||||||||
\(479\) | −22.6355 | −1.03424 | −0.517121 | − | 0.855912i | \(-0.672996\pi\) | ||||
−0.517121 | + | 0.855912i | \(0.672996\pi\) | |||||||
\(480\) | 2.08172 | 0.0950173 | ||||||||
\(481\) | −1.83161 | −0.0835144 | ||||||||
\(482\) | −28.0150 | −1.27605 | ||||||||
\(483\) | 5.89447 | 0.268208 | ||||||||
\(484\) | −6.45404 | −0.293366 | ||||||||
\(485\) | 4.14655 | 0.188285 | ||||||||
\(486\) | 4.40943 | 0.200016 | ||||||||
\(487\) | 12.0008 | 0.543807 | 0.271904 | − | 0.962324i | \(-0.412347\pi\) | ||||
0.271904 | + | 0.962324i | \(0.412347\pi\) | |||||||
\(488\) | 9.87230 | 0.446898 | ||||||||
\(489\) | −23.1160 | −1.04534 | ||||||||
\(490\) | 4.87170 | 0.220081 | ||||||||
\(491\) | 37.5969 | 1.69672 | 0.848361 | − | 0.529418i | \(-0.177590\pi\) | ||||
0.848361 | + | 0.529418i | \(0.177590\pi\) | |||||||
\(492\) | 1.66341 | 0.0749925 | ||||||||
\(493\) | 29.9366 | 1.34828 | ||||||||
\(494\) | 3.17898 | 0.143029 | ||||||||
\(495\) | −8.61788 | −0.387345 | ||||||||
\(496\) | −1.99726 | −0.0896794 | ||||||||
\(497\) | 2.59950 | 0.116604 | ||||||||
\(498\) | −30.0019 | −1.34442 | ||||||||
\(499\) | −5.33365 | −0.238767 | −0.119384 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119384 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(500\) | 6.69234 | 0.299290 | ||||||||
\(501\) | 5.59572 | 0.249998 | ||||||||
\(502\) | −15.5728 | −0.695046 | ||||||||
\(503\) | 1.73557 | 0.0773852 | 0.0386926 | − | 0.999251i | \(-0.487681\pi\) | ||||
0.0386926 | + | 0.999251i | \(0.487681\pi\) | |||||||
\(504\) | −1.63786 | −0.0729559 | ||||||||
\(505\) | −2.25540 | −0.100364 | ||||||||
\(506\) | 14.8986 | 0.662325 | ||||||||
\(507\) | 36.4233 | 1.61761 | ||||||||
\(508\) | 12.2521 | 0.543600 | ||||||||
\(509\) | 12.6870 | 0.562341 | 0.281170 | − | 0.959658i | \(-0.409277\pi\) | ||||
0.281170 | + | 0.959658i | \(0.409277\pi\) | |||||||
\(510\) | 6.40980 | 0.283831 | ||||||||
\(511\) | 1.01589 | 0.0449403 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 31.2354 | 1.37908 | ||||||||
\(514\) | 29.3394 | 1.29411 | ||||||||
\(515\) | 4.18317 | 0.184332 | ||||||||
\(516\) | 22.0396 | 0.970240 | ||||||||
\(517\) | 4.61746 | 0.203076 | ||||||||
\(518\) | −0.633882 | −0.0278512 | ||||||||
\(519\) | 5.97866 | 0.262434 | ||||||||
\(520\) | 0.580551 | 0.0254588 | ||||||||
\(521\) | 11.3962 | 0.499275 | 0.249638 | − | 0.968339i | \(-0.419688\pi\) | ||||
0.249638 | + | 0.968339i | \(0.419688\pi\) | |||||||
\(522\) | 55.8092 | 2.44270 | ||||||||
\(523\) | 13.9379 | 0.609462 | 0.304731 | − | 0.952439i | \(-0.401434\pi\) | ||||
0.304731 | + | 0.952439i | \(0.401434\pi\) | |||||||
\(524\) | 0.754565 | 0.0329633 | ||||||||
\(525\) | −3.79950 | −0.165824 | ||||||||
\(526\) | −7.17445 | −0.312821 | ||||||||
\(527\) | −6.14971 | −0.267886 | ||||||||
\(528\) | −6.30336 | −0.274319 | ||||||||
\(529\) | 25.8278 | 1.12295 | ||||||||
\(530\) | 2.68723 | 0.116726 | ||||||||
\(531\) | 10.0429 | 0.435824 | ||||||||
\(532\) | 1.10018 | 0.0476987 | ||||||||
\(533\) | 0.463893 | 0.0200934 | ||||||||
\(534\) | −3.90784 | −0.169109 | ||||||||
\(535\) | −0.198931 | −0.00860054 | ||||||||
\(536\) | −3.32261 | −0.143515 | ||||||||
\(537\) | 35.4895 | 1.53148 | ||||||||
\(538\) | 11.3203 | 0.488054 | ||||||||
\(539\) | −14.7513 | −0.635383 | ||||||||
\(540\) | 5.70427 | 0.245473 | ||||||||
\(541\) | −3.69759 | −0.158972 | −0.0794858 | − | 0.996836i | \(-0.525328\pi\) | ||||
−0.0794858 | + | 0.996836i | \(0.525328\pi\) | |||||||
\(542\) | −19.7521 | −0.848425 | ||||||||
\(543\) | −12.7453 | −0.546953 | ||||||||
\(544\) | 3.07908 | 0.132014 | ||||||||
\(545\) | −6.72848 | −0.288216 | ||||||||
\(546\) | −0.695486 | −0.0297640 | ||||||||
\(547\) | −3.52377 | −0.150666 | −0.0753329 | − | 0.997158i | \(-0.524002\pi\) | ||||
−0.0753329 | + | 0.997158i | \(0.524002\pi\) | |||||||
\(548\) | 19.2410 | 0.821936 | ||||||||
\(549\) | 56.6686 | 2.41856 | ||||||||
\(550\) | −9.60347 | −0.409493 | ||||||||
\(551\) | −37.4880 | −1.59704 | ||||||||
\(552\) | −20.6582 | −0.879273 | ||||||||
\(553\) | −1.49267 | −0.0634747 | ||||||||
\(554\) | 19.7273 | 0.838133 | ||||||||
\(555\) | 4.62466 | 0.196306 | ||||||||
\(556\) | −16.0240 | −0.679569 | ||||||||
\(557\) | 13.6072 | 0.576554 | 0.288277 | − | 0.957547i | \(-0.406918\pi\) | ||||
0.288277 | + | 0.957547i | \(0.406918\pi\) | |||||||
\(558\) | −11.4646 | −0.485334 | ||||||||
\(559\) | 6.14641 | 0.259965 | ||||||||
\(560\) | 0.200916 | 0.00849026 | ||||||||
\(561\) | −19.4086 | −0.819430 | ||||||||
\(562\) | 10.7098 | 0.451765 | ||||||||
\(563\) | −5.31204 | −0.223876 | −0.111938 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111938 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(564\) | −6.40251 | −0.269594 | ||||||||
\(565\) | −1.67335 | −0.0703985 | ||||||||
\(566\) | −5.28438 | −0.222119 | ||||||||
\(567\) | −1.92000 | −0.0806325 | ||||||||
\(568\) | −9.11043 | −0.382265 | ||||||||
\(569\) | −0.806131 | −0.0337948 | −0.0168974 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168974 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(570\) | −8.02665 | −0.336199 | ||||||||
\(571\) | −37.5543 | −1.57160 | −0.785800 | − | 0.618480i | \(-0.787749\pi\) | ||||
−0.785800 | + | 0.618480i | \(0.787749\pi\) | |||||||
\(572\) | −1.75788 | −0.0735007 | ||||||||
\(573\) | −72.3261 | −3.02147 | ||||||||
\(574\) | 0.160543 | 0.00670095 | ||||||||
\(575\) | −31.4738 | −1.31255 | ||||||||
\(576\) | 5.74016 | 0.239174 | ||||||||
\(577\) | −26.4069 | −1.09933 | −0.549667 | − | 0.835384i | \(-0.685246\pi\) | ||||
−0.549667 | + | 0.835384i | \(0.685246\pi\) | |||||||
\(578\) | −7.51927 | −0.312760 | ||||||||
\(579\) | −47.6830 | −1.98164 | ||||||||
\(580\) | −6.84613 | −0.284270 | ||||||||
\(581\) | −2.89561 | −0.120130 | ||||||||
\(582\) | 17.4094 | 0.721642 | ||||||||
\(583\) | −8.13681 | −0.336992 | ||||||||
\(584\) | −3.56037 | −0.147329 | ||||||||
\(585\) | 3.33246 | 0.137780 | ||||||||
\(586\) | 31.5082 | 1.30159 | ||||||||
\(587\) | −39.4487 | −1.62822 | −0.814110 | − | 0.580711i | \(-0.802775\pi\) | ||||
−0.814110 | + | 0.580711i | \(0.802775\pi\) | |||||||
\(588\) | 20.4539 | 0.843507 | ||||||||
\(589\) | 7.70096 | 0.317312 | ||||||||
\(590\) | −1.23196 | −0.0507191 | ||||||||
\(591\) | −78.7728 | −3.24028 | ||||||||
\(592\) | 2.22155 | 0.0913053 | ||||||||
\(593\) | −33.5736 | −1.37870 | −0.689350 | − | 0.724428i | \(-0.742104\pi\) | ||||
−0.689350 | + | 0.724428i | \(0.742104\pi\) | |||||||
\(594\) | −17.2723 | −0.708689 | ||||||||
\(595\) | 0.618637 | 0.0253616 | ||||||||
\(596\) | 7.14519 | 0.292678 | ||||||||
\(597\) | 25.5161 | 1.04430 | ||||||||
\(598\) | −5.76117 | −0.235592 | ||||||||
\(599\) | 13.8852 | 0.567333 | 0.283666 | − | 0.958923i | \(-0.408449\pi\) | ||||
0.283666 | + | 0.958923i | \(0.408449\pi\) | |||||||
\(600\) | 13.3160 | 0.543625 | ||||||||
\(601\) | −36.4806 | −1.48807 | −0.744036 | − | 0.668139i | \(-0.767091\pi\) | ||||
−0.744036 | + | 0.668139i | \(0.767091\pi\) | |||||||
\(602\) | 2.12714 | 0.0866957 | ||||||||
\(603\) | −19.0723 | −0.776685 | ||||||||
\(604\) | −20.0088 | −0.814145 | ||||||||
\(605\) | 4.54460 | 0.184764 | ||||||||
\(606\) | −9.46935 | −0.384666 | ||||||||
\(607\) | 10.0795 | 0.409116 | 0.204558 | − | 0.978854i | \(-0.434424\pi\) | ||||
0.204558 | + | 0.978854i | \(0.434424\pi\) | |||||||
\(608\) | −3.85577 | −0.156372 | ||||||||
\(609\) | 8.20149 | 0.332341 | ||||||||
\(610\) | −6.95155 | −0.281460 | ||||||||
\(611\) | −1.78553 | −0.0722349 | ||||||||
\(612\) | 17.6744 | 0.714446 | ||||||||
\(613\) | −7.67662 | −0.310056 | −0.155028 | − | 0.987910i | \(-0.549547\pi\) | ||||
−0.155028 | + | 0.987910i | \(0.549547\pi\) | |||||||
\(614\) | 12.6660 | 0.511160 | ||||||||
\(615\) | −1.17129 | −0.0472309 | ||||||||
\(616\) | −0.608365 | −0.0245117 | ||||||||
\(617\) | −13.0932 | −0.527111 | −0.263556 | − | 0.964644i | \(-0.584895\pi\) | ||||
−0.263556 | + | 0.964644i | \(0.584895\pi\) | |||||||
\(618\) | 17.5631 | 0.706492 | ||||||||
\(619\) | 17.9421 | 0.721155 | 0.360577 | − | 0.932729i | \(-0.382580\pi\) | ||||
0.360577 | + | 0.932729i | \(0.382580\pi\) | |||||||
\(620\) | 1.40636 | 0.0564809 | ||||||||
\(621\) | −56.6070 | −2.27156 | ||||||||
\(622\) | 25.2909 | 1.01407 | ||||||||
\(623\) | −0.377162 | −0.0151107 | ||||||||
\(624\) | 2.43746 | 0.0975763 | ||||||||
\(625\) | 17.8085 | 0.712340 | ||||||||
\(626\) | −2.81859 | −0.112654 | ||||||||
\(627\) | 24.3043 | 0.970621 | ||||||||
\(628\) | 13.1473 | 0.524632 | ||||||||
\(629\) | 6.84034 | 0.272742 | ||||||||
\(630\) | 1.15329 | 0.0459483 | ||||||||
\(631\) | −31.4797 | −1.25319 | −0.626594 | − | 0.779345i | \(-0.715552\pi\) | ||||
−0.626594 | + | 0.779345i | \(0.715552\pi\) | |||||||
\(632\) | 5.23132 | 0.208091 | ||||||||
\(633\) | −82.9917 | −3.29863 | ||||||||
\(634\) | −9.50407 | −0.377455 | ||||||||
\(635\) | −8.62730 | −0.342364 | ||||||||
\(636\) | 11.2824 | 0.447376 | ||||||||
\(637\) | 5.70419 | 0.226008 | ||||||||
\(638\) | 20.7298 | 0.820699 | ||||||||
\(639\) | −52.2954 | −2.06877 | ||||||||
\(640\) | −0.704147 | −0.0278339 | ||||||||
\(641\) | −8.32710 | −0.328901 | −0.164450 | − | 0.986385i | \(-0.552585\pi\) | ||||
−0.164450 | + | 0.986385i | \(0.552585\pi\) | |||||||
\(642\) | −0.835216 | −0.0329633 | ||||||||
\(643\) | −36.2734 | −1.43048 | −0.715242 | − | 0.698876i | \(-0.753684\pi\) | ||||
−0.715242 | + | 0.698876i | \(0.753684\pi\) | |||||||
\(644\) | −1.99382 | −0.0785674 | ||||||||
\(645\) | −15.5191 | −0.611065 | ||||||||
\(646\) | −11.8722 | −0.467106 | ||||||||
\(647\) | −24.4198 | −0.960041 | −0.480020 | − | 0.877257i | \(-0.659371\pi\) | ||||
−0.480020 | + | 0.877257i | \(0.659371\pi\) | |||||||
\(648\) | 6.72900 | 0.264340 | ||||||||
\(649\) | 3.73033 | 0.146428 | ||||||||
\(650\) | 3.71358 | 0.145658 | ||||||||
\(651\) | −1.68479 | −0.0660320 | ||||||||
\(652\) | 7.81901 | 0.306216 | ||||||||
\(653\) | −4.03721 | −0.157988 | −0.0789942 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789942 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(654\) | −28.2497 | −1.10465 | ||||||||
\(655\) | −0.531325 | −0.0207606 | ||||||||
\(656\) | −0.562653 | −0.0219679 | ||||||||
\(657\) | −20.4371 | −0.797328 | ||||||||
\(658\) | −0.617934 | −0.0240896 | ||||||||
\(659\) | −26.6748 | −1.03910 | −0.519551 | − | 0.854439i | \(-0.673901\pi\) | ||||
−0.519551 | + | 0.854439i | \(0.673901\pi\) | |||||||
\(660\) | 4.43850 | 0.172768 | ||||||||
\(661\) | −28.5012 | −1.10857 | −0.554285 | − | 0.832327i | \(-0.687008\pi\) | ||||
−0.554285 | + | 0.832327i | \(0.687008\pi\) | |||||||
\(662\) | 19.0048 | 0.738641 | ||||||||
\(663\) | 7.50512 | 0.291475 | ||||||||
\(664\) | 10.1482 | 0.393827 | ||||||||
\(665\) | −0.774686 | −0.0300411 | ||||||||
\(666\) | 12.7521 | 0.494133 | ||||||||
\(667\) | 67.9384 | 2.63059 | ||||||||
\(668\) | −1.89276 | −0.0732332 | ||||||||
\(669\) | 76.8657 | 2.97180 | ||||||||
\(670\) | 2.33961 | 0.0903869 | ||||||||
\(671\) | 21.0490 | 0.812587 | ||||||||
\(672\) | 0.843551 | 0.0325407 | ||||||||
\(673\) | 0.343447 | 0.0132389 | 0.00661945 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661945 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(674\) | −9.92416 | −0.382264 | ||||||||
\(675\) | 36.4882 | 1.40443 | ||||||||
\(676\) | −12.3202 | −0.473855 | ||||||||
\(677\) | 35.2177 | 1.35353 | 0.676764 | − | 0.736200i | \(-0.263382\pi\) | ||||
0.676764 | + | 0.736200i | \(0.263382\pi\) | |||||||
\(678\) | −7.02561 | −0.269817 | ||||||||
\(679\) | 1.68025 | 0.0644822 | ||||||||
\(680\) | −2.16813 | −0.0831438 | ||||||||
\(681\) | −58.2689 | −2.23287 | ||||||||
\(682\) | −4.25840 | −0.163063 | ||||||||
\(683\) | 9.12479 | 0.349150 | 0.174575 | − | 0.984644i | \(-0.444145\pi\) | ||||
0.174575 | + | 0.984644i | \(0.444145\pi\) | |||||||
\(684\) | −22.1328 | −0.846267 | ||||||||
\(685\) | −13.5485 | −0.517662 | ||||||||
\(686\) | 3.97143 | 0.151630 | ||||||||
\(687\) | −11.9673 | −0.456580 | ||||||||
\(688\) | −7.45494 | −0.284217 | ||||||||
\(689\) | 3.14643 | 0.119870 | ||||||||
\(690\) | 14.5464 | 0.553774 | ||||||||
\(691\) | −9.79494 | −0.372617 | −0.186309 | − | 0.982491i | \(-0.559652\pi\) | ||||
−0.186309 | + | 0.982491i | \(0.559652\pi\) | |||||||
\(692\) | −2.02229 | −0.0768760 | ||||||||
\(693\) | −3.49211 | −0.132654 | ||||||||
\(694\) | −12.7437 | −0.483743 | ||||||||
\(695\) | 11.2833 | 0.427998 | ||||||||
\(696\) | −28.7436 | −1.08952 | ||||||||
\(697\) | −1.73245 | −0.0656214 | ||||||||
\(698\) | −12.7200 | −0.481459 | ||||||||
\(699\) | −89.0284 | −3.36736 | ||||||||
\(700\) | 1.28519 | 0.0485756 | ||||||||
\(701\) | 19.3181 | 0.729635 | 0.364818 | − | 0.931079i | \(-0.381131\pi\) | ||||
0.364818 | + | 0.931079i | \(0.381131\pi\) | |||||||
\(702\) | 6.67903 | 0.252084 | ||||||||
\(703\) | −8.56580 | −0.323065 | ||||||||
\(704\) | 2.13212 | 0.0803575 | ||||||||
\(705\) | 4.50831 | 0.169793 | ||||||||
\(706\) | −15.5391 | −0.584823 | ||||||||
\(707\) | −0.913927 | −0.0343718 | ||||||||
\(708\) | −5.17242 | −0.194392 | ||||||||
\(709\) | 3.12558 | 0.117384 | 0.0586919 | − | 0.998276i | \(-0.481307\pi\) | ||||
0.0586919 | + | 0.998276i | \(0.481307\pi\) | |||||||
\(710\) | 6.41508 | 0.240754 | ||||||||
\(711\) | 30.0286 | 1.12616 | ||||||||
\(712\) | 1.32183 | 0.0495378 | ||||||||
\(713\) | −13.9562 | −0.522664 | ||||||||
\(714\) | 2.59736 | 0.0972038 | ||||||||
\(715\) | 1.23781 | 0.0462914 | ||||||||
\(716\) | −12.0044 | −0.448624 | ||||||||
\(717\) | −47.8328 | −1.78635 | ||||||||
\(718\) | 23.8705 | 0.890841 | ||||||||
\(719\) | −0.0899969 | −0.00335632 | −0.00167816 | − | 0.999999i | \(-0.500534\pi\) | ||||
−0.00167816 | + | 0.999999i | \(0.500534\pi\) | |||||||
\(720\) | −4.04192 | −0.150633 | ||||||||
\(721\) | 1.69509 | 0.0631285 | ||||||||
\(722\) | −4.13304 | −0.153816 | ||||||||
\(723\) | 82.8228 | 3.08021 | ||||||||
\(724\) | 4.31112 | 0.160221 | ||||||||
\(725\) | −43.7922 | −1.62640 | ||||||||
\(726\) | 19.0806 | 0.708147 | ||||||||
\(727\) | −21.2534 | −0.788246 | −0.394123 | − | 0.919058i | \(-0.628952\pi\) | ||||
−0.394123 | + | 0.919058i | \(0.628952\pi\) | |||||||
\(728\) | 0.235249 | 0.00871892 | ||||||||
\(729\) | −33.2229 | −1.23048 | ||||||||
\(730\) | 2.50702 | 0.0927891 | ||||||||
\(731\) | −22.9544 | −0.848998 | ||||||||
\(732\) | −29.1862 | −1.07875 | ||||||||
\(733\) | −5.35020 | −0.197614 | −0.0988071 | − | 0.995107i | \(-0.531503\pi\) | ||||
−0.0988071 | + | 0.995107i | \(0.531503\pi\) | |||||||
\(734\) | 28.9891 | 1.07001 | ||||||||
\(735\) | −14.4026 | −0.531247 | ||||||||
\(736\) | 6.98769 | 0.257570 | ||||||||
\(737\) | −7.08422 | −0.260951 | ||||||||
\(738\) | −3.22972 | −0.118888 | ||||||||
\(739\) | 47.1241 | 1.73349 | 0.866744 | − | 0.498754i | \(-0.166209\pi\) | ||||
0.866744 | + | 0.498754i | \(0.166209\pi\) | |||||||
\(740\) | −1.56430 | −0.0575048 | ||||||||
\(741\) | −9.39827 | −0.345254 | ||||||||
\(742\) | 1.08891 | 0.0399752 | ||||||||
\(743\) | 6.81194 | 0.249906 | 0.124953 | − | 0.992163i | \(-0.460122\pi\) | ||||
0.124953 | + | 0.992163i | \(0.460122\pi\) | |||||||
\(744\) | 5.90464 | 0.216475 | ||||||||
\(745\) | −5.03127 | −0.184331 | ||||||||
\(746\) | 10.7208 | 0.392516 | ||||||||
\(747\) | 58.2524 | 2.13134 | ||||||||
\(748\) | 6.56498 | 0.240040 | ||||||||
\(749\) | −0.0806103 | −0.00294544 | ||||||||
\(750\) | −19.7851 | −0.722449 | ||||||||
\(751\) | −24.4179 | −0.891023 | −0.445512 | − | 0.895276i | \(-0.646978\pi\) | ||||
−0.445512 | + | 0.895276i | \(0.646978\pi\) | |||||||
\(752\) | 2.16566 | 0.0789735 | ||||||||
\(753\) | 46.0389 | 1.67775 | ||||||||
\(754\) | −8.01602 | −0.291926 | ||||||||
\(755\) | 14.0891 | 0.512755 | ||||||||
\(756\) | 2.31147 | 0.0840673 | ||||||||
\(757\) | 9.76422 | 0.354887 | 0.177443 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177443 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(758\) | 26.4805 | 0.961815 | ||||||||
\(759\) | −44.0460 | −1.59877 | ||||||||
\(760\) | 2.71503 | 0.0984845 | ||||||||
\(761\) | −3.43046 | −0.124354 | −0.0621770 | − | 0.998065i | \(-0.519804\pi\) | ||||
−0.0621770 | + | 0.998065i | \(0.519804\pi\) | |||||||
\(762\) | −36.2219 | −1.31218 | ||||||||
\(763\) | −2.72650 | −0.0987058 | ||||||||
\(764\) | 24.4644 | 0.885092 | ||||||||
\(765\) | −12.4454 | −0.449964 | ||||||||
\(766\) | 12.9398 | 0.467535 | ||||||||
\(767\) | −1.44248 | −0.0520851 | ||||||||
\(768\) | −2.95638 | −0.106679 | ||||||||
\(769\) | 37.3099 | 1.34543 | 0.672715 | − | 0.739902i | \(-0.265128\pi\) | ||||
0.672715 | + | 0.739902i | \(0.265128\pi\) | |||||||
\(770\) | 0.428378 | 0.0154377 | ||||||||
\(771\) | −86.7385 | −3.12381 | ||||||||
\(772\) | 16.1289 | 0.580491 | ||||||||
\(773\) | −18.3212 | −0.658967 | −0.329484 | − | 0.944161i | \(-0.606875\pi\) | ||||
−0.329484 | + | 0.944161i | \(0.606875\pi\) | |||||||
\(774\) | −42.7926 | −1.53815 | ||||||||
\(775\) | 8.99599 | 0.323146 | ||||||||
\(776\) | −5.88876 | −0.211394 | ||||||||
\(777\) | 1.87399 | 0.0672292 | ||||||||
\(778\) | 5.05213 | 0.181128 | ||||||||
\(779\) | 2.16946 | 0.0777290 | ||||||||
\(780\) | −1.71633 | −0.0614544 | ||||||||
\(781\) | −19.4246 | −0.695066 | ||||||||
\(782\) | 21.5157 | 0.769398 | ||||||||
\(783\) | −78.7623 | −2.81473 | ||||||||
\(784\) | −6.91859 | −0.247092 | ||||||||
\(785\) | −9.25760 | −0.330418 | ||||||||
\(786\) | −2.23078 | −0.0795692 | ||||||||
\(787\) | −6.71808 | −0.239474 | −0.119737 | − | 0.992806i | \(-0.538205\pi\) | ||||
−0.119737 | + | 0.992806i | \(0.538205\pi\) | |||||||
\(788\) | 26.6450 | 0.949191 | ||||||||
\(789\) | 21.2104 | 0.755110 | ||||||||
\(790\) | −3.68362 | −0.131057 | ||||||||
\(791\) | −0.678072 | −0.0241095 | ||||||||
\(792\) | 12.2387 | 0.434885 | ||||||||
\(793\) | −8.13946 | −0.289041 | ||||||||
\(794\) | 29.8019 | 1.05763 | ||||||||
\(795\) | −7.94446 | −0.281761 | ||||||||
\(796\) | −8.63087 | −0.305913 | ||||||||
\(797\) | 39.4318 | 1.39675 | 0.698374 | − | 0.715733i | \(-0.253907\pi\) | ||||
0.698374 | + | 0.715733i | \(0.253907\pi\) | |||||||
\(798\) | −3.25254 | −0.115139 | ||||||||
\(799\) | 6.66824 | 0.235906 | ||||||||
\(800\) | −4.50418 | −0.159247 | ||||||||
\(801\) | 7.58754 | 0.268092 | ||||||||
\(802\) | −13.1336 | −0.463765 | ||||||||
\(803\) | −7.59115 | −0.267886 | ||||||||
\(804\) | 9.82289 | 0.346427 | ||||||||
\(805\) | 1.40394 | 0.0494824 | ||||||||
\(806\) | 1.64669 | 0.0580020 | ||||||||
\(807\) | −33.4672 | −1.17810 | ||||||||
\(808\) | 3.20302 | 0.112682 | ||||||||
\(809\) | −39.5274 | −1.38971 | −0.694854 | − | 0.719151i | \(-0.744531\pi\) | ||||
−0.694854 | + | 0.719151i | \(0.744531\pi\) | |||||||
\(810\) | −4.73820 | −0.166484 | ||||||||
\(811\) | −5.83106 | −0.204756 | −0.102378 | − | 0.994746i | \(-0.532645\pi\) | ||||
−0.102378 | + | 0.994746i | \(0.532645\pi\) | |||||||
\(812\) | −2.77417 | −0.0973543 | ||||||||
\(813\) | 58.3946 | 2.04799 | ||||||||
\(814\) | 4.73663 | 0.166019 | ||||||||
\(815\) | −5.50574 | −0.192858 | ||||||||
\(816\) | −9.10292 | −0.318666 | ||||||||
\(817\) | 28.7445 | 1.00564 | ||||||||
\(818\) | −2.53363 | −0.0885862 | ||||||||
\(819\) | 1.35037 | 0.0471858 | ||||||||
\(820\) | 0.396190 | 0.0138356 | ||||||||
\(821\) | −5.56543 | −0.194235 | −0.0971173 | − | 0.995273i | \(-0.530962\pi\) | ||||
−0.0971173 | + | 0.995273i | \(0.530962\pi\) | |||||||
\(822\) | −56.8837 | −1.98405 | ||||||||
\(823\) | 22.4957 | 0.784149 | 0.392075 | − | 0.919933i | \(-0.371758\pi\) | ||||
0.392075 | + | 0.919933i | \(0.371758\pi\) | |||||||
\(824\) | −5.94076 | −0.206956 | ||||||||
\(825\) | 28.3915 | 0.988464 | ||||||||
\(826\) | −0.499213 | −0.0173698 | ||||||||
\(827\) | 2.38134 | 0.0828073 | 0.0414037 | − | 0.999143i | \(-0.486817\pi\) | ||||
0.0414037 | + | 0.999143i | \(0.486817\pi\) | |||||||
\(828\) | 40.1105 | 1.39394 | ||||||||
\(829\) | 0.101100 | 0.00351135 | 0.00175568 | − | 0.999998i | \(-0.499441\pi\) | ||||
0.00175568 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(830\) | −7.14583 | −0.248035 | ||||||||
\(831\) | −58.3213 | −2.02314 | ||||||||
\(832\) | −0.824474 | −0.0285835 | ||||||||
\(833\) | −21.3029 | −0.738101 | ||||||||
\(834\) | 47.3730 | 1.64039 | ||||||||
\(835\) | 1.33278 | 0.0461229 | ||||||||
\(836\) | −8.22098 | −0.284329 | ||||||||
\(837\) | 16.1797 | 0.559252 | ||||||||
\(838\) | −38.1765 | −1.31878 | ||||||||
\(839\) | −37.3398 | −1.28911 | −0.644557 | − | 0.764556i | \(-0.722958\pi\) | ||||
−0.644557 | + | 0.764556i | \(0.722958\pi\) | |||||||
\(840\) | −0.593984 | −0.0204944 | ||||||||
\(841\) | 65.5286 | 2.25961 | ||||||||
\(842\) | 33.4945 | 1.15430 | ||||||||
\(843\) | −31.6622 | −1.09050 | ||||||||
\(844\) | 28.0721 | 0.966282 | ||||||||
\(845\) | 8.67526 | 0.298438 | ||||||||
\(846\) | 12.4313 | 0.427395 | ||||||||
\(847\) | 1.84155 | 0.0632764 | ||||||||
\(848\) | −3.81629 | −0.131052 | ||||||||
\(849\) | 15.6226 | 0.536167 | ||||||||
\(850\) | −13.8687 | −0.475693 | ||||||||
\(851\) | 15.5235 | 0.532140 | ||||||||
\(852\) | 26.9339 | 0.922739 | ||||||||
\(853\) | 30.5829 | 1.04714 | 0.523569 | − | 0.851983i | \(-0.324600\pi\) | ||||
0.523569 | + | 0.851983i | \(0.324600\pi\) | |||||||
\(854\) | −2.81689 | −0.0963920 | ||||||||
\(855\) | 15.5847 | 0.532986 | ||||||||
\(856\) | 0.282513 | 0.00965611 | ||||||||
\(857\) | 48.0912 | 1.64276 | 0.821382 | − | 0.570378i | \(-0.193203\pi\) | ||||
0.821382 | + | 0.570378i | \(0.193203\pi\) | |||||||
\(858\) | 5.19696 | 0.177421 | ||||||||
\(859\) | 25.9453 | 0.885243 | 0.442622 | − | 0.896708i | \(-0.354048\pi\) | ||||
0.442622 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(860\) | 5.24938 | 0.179002 | ||||||||
\(861\) | −0.474626 | −0.0161752 | ||||||||
\(862\) | 30.0466 | 1.02339 | ||||||||
\(863\) | −18.5722 | −0.632205 | −0.316103 | − | 0.948725i | \(-0.602374\pi\) | ||||
−0.316103 | + | 0.948725i | \(0.602374\pi\) | |||||||
\(864\) | −8.10096 | −0.275600 | ||||||||
\(865\) | 1.42399 | 0.0484171 | ||||||||
\(866\) | 34.8119 | 1.18296 | ||||||||
\(867\) | 22.2298 | 0.754963 | ||||||||
\(868\) | 0.569882 | 0.0193431 | ||||||||
\(869\) | 11.1538 | 0.378368 | ||||||||
\(870\) | 20.2397 | 0.686191 | ||||||||
\(871\) | 2.73941 | 0.0928212 | ||||||||
\(872\) | 9.55550 | 0.323590 | ||||||||
\(873\) | −33.8024 | −1.14404 | ||||||||
\(874\) | −26.9429 | −0.911358 | ||||||||
\(875\) | −1.90954 | −0.0645543 | ||||||||
\(876\) | 10.5258 | 0.355634 | ||||||||
\(877\) | −24.0744 | −0.812935 | −0.406468 | − | 0.913665i | \(-0.633240\pi\) | ||||
−0.406468 | + | 0.913665i | \(0.633240\pi\) | |||||||
\(878\) | −1.05540 | −0.0356181 | ||||||||
\(879\) | −93.1501 | −3.14187 | ||||||||
\(880\) | −1.50133 | −0.0506098 | ||||||||
\(881\) | −52.1740 | −1.75779 | −0.878893 | − | 0.477019i | \(-0.841717\pi\) | ||||
−0.878893 | + | 0.477019i | \(0.841717\pi\) | |||||||
\(882\) | −39.7138 | −1.33723 | ||||||||
\(883\) | −34.5789 | −1.16367 | −0.581836 | − | 0.813306i | \(-0.697666\pi\) | ||||
−0.581836 | + | 0.813306i | \(0.697666\pi\) | |||||||
\(884\) | −2.53862 | −0.0853831 | ||||||||
\(885\) | 3.64215 | 0.122429 | ||||||||
\(886\) | −30.0688 | −1.01018 | ||||||||
\(887\) | 27.1937 | 0.913076 | 0.456538 | − | 0.889704i | \(-0.349089\pi\) | ||||
0.456538 | + | 0.889704i | \(0.349089\pi\) | |||||||
\(888\) | −6.56775 | −0.220399 | ||||||||
\(889\) | −3.49593 | −0.117250 | ||||||||
\(890\) | −0.930765 | −0.0311993 | ||||||||
\(891\) | 14.3471 | 0.480645 | ||||||||
\(892\) | −26.0000 | −0.870543 | ||||||||
\(893\) | −8.35029 | −0.279432 | ||||||||
\(894\) | −21.1239 | −0.706488 | ||||||||
\(895\) | 8.45284 | 0.282547 | ||||||||
\(896\) | −0.285333 | −0.00953230 | ||||||||
\(897\) | 17.0322 | 0.568688 | ||||||||
\(898\) | 20.0551 | 0.669246 | ||||||||
\(899\) | −19.4185 | −0.647643 | ||||||||
\(900\) | −25.8547 | −0.861824 | ||||||||
\(901\) | −11.7507 | −0.391471 | ||||||||
\(902\) | −1.19965 | −0.0399438 | ||||||||
\(903\) | −6.28862 | −0.209272 | ||||||||
\(904\) | 2.37643 | 0.0790387 | ||||||||
\(905\) | −3.03566 | −0.100909 | ||||||||
\(906\) | 59.1534 | 1.96524 | ||||||||
\(907\) | −28.3537 | −0.941469 | −0.470734 | − | 0.882275i | \(-0.656011\pi\) | ||||
−0.470734 | + | 0.882275i | \(0.656011\pi\) | |||||||
\(908\) | 19.7096 | 0.654084 | ||||||||
\(909\) | 18.3859 | 0.609821 | ||||||||
\(910\) | −0.165650 | −0.00549125 | ||||||||
\(911\) | −13.5599 | −0.449259 | −0.224629 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224629 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(912\) | 11.3991 | 0.377462 | ||||||||
\(913\) | 21.6372 | 0.716088 | ||||||||
\(914\) | −19.1140 | −0.632236 | ||||||||
\(915\) | 20.5514 | 0.679409 | ||||||||
\(916\) | 4.04796 | 0.133748 | ||||||||
\(917\) | −0.215302 | −0.00710990 | ||||||||
\(918\) | −24.9435 | −0.823258 | ||||||||
\(919\) | 12.2663 | 0.404629 | 0.202314 | − | 0.979321i | \(-0.435154\pi\) | ||||
0.202314 | + | 0.979321i | \(0.435154\pi\) | |||||||
\(920\) | −4.92036 | −0.162220 | ||||||||
\(921\) | −37.4456 | −1.23387 | ||||||||
\(922\) | 11.4975 | 0.378650 | ||||||||
\(923\) | 7.51131 | 0.247238 | ||||||||
\(924\) | 1.79856 | 0.0591681 | ||||||||
\(925\) | −10.0063 | −0.329004 | ||||||||
\(926\) | −12.4145 | −0.407965 | ||||||||
\(927\) | −34.1009 | −1.12002 | ||||||||
\(928\) | 9.72258 | 0.319159 | ||||||||
\(929\) | 16.6035 | 0.544743 | 0.272372 | − | 0.962192i | \(-0.412192\pi\) | ||||
0.272372 | + | 0.962192i | \(0.412192\pi\) | |||||||
\(930\) | −4.15774 | −0.136338 | ||||||||
\(931\) | 26.6765 | 0.874286 | ||||||||
\(932\) | 30.1140 | 0.986417 | ||||||||
\(933\) | −74.7695 | −2.44784 | ||||||||
\(934\) | −9.23241 | −0.302094 | ||||||||
\(935\) | −4.62271 | −0.151179 | ||||||||
\(936\) | −4.73262 | −0.154690 | ||||||||
\(937\) | 44.4184 | 1.45109 | 0.725543 | − | 0.688177i | \(-0.241589\pi\) | ||||
0.725543 | + | 0.688177i | \(0.241589\pi\) | |||||||
\(938\) | 0.948049 | 0.0309549 | ||||||||
\(939\) | 8.33283 | 0.271932 | ||||||||
\(940\) | −1.52494 | −0.0497382 | ||||||||
\(941\) | −23.1607 | −0.755016 | −0.377508 | − | 0.926006i | \(-0.623219\pi\) | ||||
−0.377508 | + | 0.926006i | \(0.623219\pi\) | |||||||
\(942\) | −38.8682 | −1.26640 | ||||||||
\(943\) | −3.93164 | −0.128032 | ||||||||
\(944\) | 1.74958 | 0.0569440 | ||||||||
\(945\) | −1.62761 | −0.0529463 | ||||||||
\(946\) | −15.8949 | −0.516787 | ||||||||
\(947\) | −53.7244 | −1.74581 | −0.872904 | − | 0.487892i | \(-0.837766\pi\) | ||||
−0.872904 | + | 0.487892i | \(0.837766\pi\) | |||||||
\(948\) | −15.4658 | −0.502304 | ||||||||
\(949\) | 2.93543 | 0.0952882 | ||||||||
\(950\) | 17.3671 | 0.563462 | ||||||||
\(951\) | 28.0976 | 0.911128 | ||||||||
\(952\) | −0.878562 | −0.0284744 | ||||||||
\(953\) | −36.8374 | −1.19328 | −0.596640 | − | 0.802509i | \(-0.703498\pi\) | ||||
−0.596640 | + | 0.802509i | \(0.703498\pi\) | |||||||
\(954\) | −21.9061 | −0.709237 | ||||||||
\(955\) | −17.2266 | −0.557438 | ||||||||
\(956\) | 16.1795 | 0.523284 | ||||||||
\(957\) | −61.2850 | −1.98106 | ||||||||
\(958\) | −22.6355 | −0.731320 | ||||||||
\(959\) | −5.49009 | −0.177284 | ||||||||
\(960\) | 2.08172 | 0.0671874 | ||||||||
\(961\) | −27.0110 | −0.871322 | ||||||||
\(962\) | −1.83161 | −0.0590536 | ||||||||
\(963\) | 1.62167 | 0.0522577 | ||||||||
\(964\) | −28.0150 | −0.902301 | ||||||||
\(965\) | −11.3571 | −0.365598 | ||||||||
\(966\) | 5.89447 | 0.189652 | ||||||||
\(967\) | 58.3548 | 1.87656 | 0.938282 | − | 0.345872i | \(-0.112417\pi\) | ||||
0.938282 | + | 0.345872i | \(0.112417\pi\) | |||||||
\(968\) | −6.45404 | −0.207441 | ||||||||
\(969\) | 35.0988 | 1.12753 | ||||||||
\(970\) | 4.14655 | 0.133138 | ||||||||
\(971\) | 25.0537 | 0.804012 | 0.402006 | − | 0.915637i | \(-0.368313\pi\) | ||||
0.402006 | + | 0.915637i | \(0.368313\pi\) | |||||||
\(972\) | 4.40943 | 0.141432 | ||||||||
\(973\) | 4.57217 | 0.146577 | ||||||||
\(974\) | 12.0008 | 0.384530 | ||||||||
\(975\) | −10.9787 | −0.351601 | ||||||||
\(976\) | 9.87230 | 0.316005 | ||||||||
\(977\) | 39.9809 | 1.27910 | 0.639551 | − | 0.768749i | \(-0.279120\pi\) | ||||
0.639551 | + | 0.768749i | \(0.279120\pi\) | |||||||
\(978\) | −23.1160 | −0.739167 | ||||||||
\(979\) | 2.81831 | 0.0900737 | ||||||||
\(980\) | 4.87170 | 0.155621 | ||||||||
\(981\) | 54.8502 | 1.75123 | ||||||||
\(982\) | 37.5969 | 1.19976 | ||||||||
\(983\) | −5.20270 | −0.165941 | −0.0829703 | − | 0.996552i | \(-0.526441\pi\) | ||||
−0.0829703 | + | 0.996552i | \(0.526441\pi\) | |||||||
\(984\) | 1.66341 | 0.0530277 | ||||||||
\(985\) | −18.7620 | −0.597808 | ||||||||
\(986\) | 29.9366 | 0.953376 | ||||||||
\(987\) | 1.82685 | 0.0581491 | ||||||||
\(988\) | 3.17898 | 0.101137 | ||||||||
\(989\) | −52.0928 | −1.65646 | ||||||||
\(990\) | −8.61788 | −0.273894 | ||||||||
\(991\) | 51.6907 | 1.64201 | 0.821004 | − | 0.570922i | \(-0.193414\pi\) | ||||
0.821004 | + | 0.570922i | \(0.193414\pi\) | |||||||
\(992\) | −1.99726 | −0.0634129 | ||||||||
\(993\) | −56.1852 | −1.78298 | ||||||||
\(994\) | 2.59950 | 0.0824512 | ||||||||
\(995\) | 6.07740 | 0.192667 | ||||||||
\(996\) | −30.0019 | −0.950647 | ||||||||
\(997\) | −45.8094 | −1.45080 | −0.725400 | − | 0.688328i | \(-0.758345\pi\) | ||||
−0.725400 | + | 0.688328i | \(0.758345\pi\) | |||||||
\(998\) | −5.33365 | −0.168834 | ||||||||
\(999\) | −17.9967 | −0.569391 |
(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 | 6002.2.a.d.1.6 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.d.1.6 | ✓ | 79 | 1.1 | even | 1 | trivial |