Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.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: | \(48.2695680219\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 7x^{7} + 20x^{6} + 20x^{5} - 38x^{4} - 27x^{3} + 13x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.139045\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.139045 | −0.0983200 | −0.0491600 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491600 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98067 | −0.990333 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.139045 | −0.0567651 | ||||||||
\(7\) | −0.572827 | −0.216508 | −0.108254 | − | 0.994123i | \(-0.534526\pi\) | ||||
−0.108254 | + | 0.994123i | \(0.534526\pi\) | |||||||
\(8\) | 0.553494 | 0.195690 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.139045 | −0.0439700 | ||||||||
\(11\) | −2.21820 | −0.668813 | −0.334406 | − | 0.942429i | \(-0.608536\pi\) | ||||
−0.334406 | + | 0.942429i | \(0.608536\pi\) | |||||||
\(12\) | −1.98067 | −0.571769 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.0796491 | 0.0212871 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.88437 | 0.971093 | ||||||||
\(17\) | 4.50920 | 1.09364 | 0.546820 | − | 0.837250i | \(-0.315838\pi\) | ||||
0.546820 | + | 0.837250i | \(0.315838\pi\) | |||||||
\(18\) | −0.139045 | −0.0327733 | ||||||||
\(19\) | −3.16026 | −0.725013 | −0.362507 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362507 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(20\) | −1.98067 | −0.442890 | ||||||||
\(21\) | −0.572827 | −0.125001 | ||||||||
\(22\) | 0.308431 | 0.0657577 | ||||||||
\(23\) | −5.35633 | −1.11687 | −0.558436 | − | 0.829547i | \(-0.688599\pi\) | ||||
−0.558436 | + | 0.829547i | \(0.688599\pi\) | |||||||
\(24\) | 0.553494 | 0.112981 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.139045 | 0.0272691 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.13458 | 0.214415 | ||||||||
\(29\) | −4.19191 | −0.778417 | −0.389209 | − | 0.921150i | \(-0.627252\pi\) | ||||
−0.389209 | + | 0.921150i | \(0.627252\pi\) | |||||||
\(30\) | −0.139045 | −0.0253861 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −1.64709 | −0.291167 | ||||||||
\(33\) | −2.21820 | −0.386139 | ||||||||
\(34\) | −0.626983 | −0.107527 | ||||||||
\(35\) | −0.572827 | −0.0968255 | ||||||||
\(36\) | −1.98067 | −0.330111 | ||||||||
\(37\) | 8.21655 | 1.35079 | 0.675396 | − | 0.737455i | \(-0.263973\pi\) | ||||
0.675396 | + | 0.737455i | \(0.263973\pi\) | |||||||
\(38\) | 0.439420 | 0.0712833 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.553494 | 0.0875150 | ||||||||
\(41\) | 4.93542 | 0.770783 | 0.385392 | − | 0.922753i | \(-0.374066\pi\) | ||||
0.385392 | + | 0.922753i | \(0.374066\pi\) | |||||||
\(42\) | 0.0796491 | 0.0122901 | ||||||||
\(43\) | 8.80730 | 1.34310 | 0.671551 | − | 0.740959i | \(-0.265629\pi\) | ||||
0.671551 | + | 0.740959i | \(0.265629\pi\) | |||||||
\(44\) | 4.39352 | 0.662347 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0.744774 | 0.109811 | ||||||||
\(47\) | 3.29882 | 0.481182 | 0.240591 | − | 0.970627i | \(-0.422659\pi\) | ||||
0.240591 | + | 0.970627i | \(0.422659\pi\) | |||||||
\(48\) | 3.88437 | 0.560661 | ||||||||
\(49\) | −6.67187 | −0.953124 | ||||||||
\(50\) | −0.139045 | −0.0196640 | ||||||||
\(51\) | 4.50920 | 0.631414 | ||||||||
\(52\) | 1.98067 | 0.274669 | ||||||||
\(53\) | 4.15951 | 0.571353 | 0.285676 | − | 0.958326i | \(-0.407782\pi\) | ||||
0.285676 | + | 0.958326i | \(0.407782\pi\) | |||||||
\(54\) | −0.139045 | −0.0189217 | ||||||||
\(55\) | −2.21820 | −0.299102 | ||||||||
\(56\) | −0.317056 | −0.0423684 | ||||||||
\(57\) | −3.16026 | −0.418587 | ||||||||
\(58\) | 0.582866 | 0.0765340 | ||||||||
\(59\) | −7.12913 | −0.928134 | −0.464067 | − | 0.885800i | \(-0.653610\pi\) | ||||
−0.464067 | + | 0.885800i | \(0.653610\pi\) | |||||||
\(60\) | −1.98067 | −0.255703 | ||||||||
\(61\) | −7.14025 | −0.914215 | −0.457108 | − | 0.889411i | \(-0.651115\pi\) | ||||
−0.457108 | + | 0.889411i | \(0.651115\pi\) | |||||||
\(62\) | 0.139045 | 0.0176588 | ||||||||
\(63\) | −0.572827 | −0.0721695 | ||||||||
\(64\) | −7.53972 | −0.942465 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0.308431 | 0.0379652 | ||||||||
\(67\) | −6.43070 | −0.785635 | −0.392817 | − | 0.919617i | \(-0.628500\pi\) | ||||
−0.392817 | + | 0.919617i | \(0.628500\pi\) | |||||||
\(68\) | −8.93121 | −1.08307 | ||||||||
\(69\) | −5.35633 | −0.644827 | ||||||||
\(70\) | 0.0796491 | 0.00951988 | ||||||||
\(71\) | −12.4404 | −1.47640 | −0.738200 | − | 0.674582i | \(-0.764324\pi\) | ||||
−0.738200 | + | 0.674582i | \(0.764324\pi\) | |||||||
\(72\) | 0.553494 | 0.0652299 | ||||||||
\(73\) | −16.2281 | −1.89936 | −0.949680 | − | 0.313220i | \(-0.898592\pi\) | ||||
−0.949680 | + | 0.313220i | \(0.898592\pi\) | |||||||
\(74\) | −1.14247 | −0.132810 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.25942 | 0.718005 | ||||||||
\(77\) | 1.27065 | 0.144804 | ||||||||
\(78\) | 0.139045 | 0.0157438 | ||||||||
\(79\) | 3.79218 | 0.426654 | 0.213327 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213327 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(80\) | 3.88437 | 0.434286 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.686248 | −0.0757834 | ||||||||
\(83\) | −8.15054 | −0.894638 | −0.447319 | − | 0.894375i | \(-0.647621\pi\) | ||||
−0.447319 | + | 0.894375i | \(0.647621\pi\) | |||||||
\(84\) | 1.13458 | 0.123793 | ||||||||
\(85\) | 4.50920 | 0.489091 | ||||||||
\(86\) | −1.22462 | −0.132054 | ||||||||
\(87\) | −4.19191 | −0.449420 | ||||||||
\(88\) | −1.22776 | −0.130880 | ||||||||
\(89\) | 17.6272 | 1.86848 | 0.934238 | − | 0.356649i | \(-0.116081\pi\) | ||||
0.934238 | + | 0.356649i | \(0.116081\pi\) | |||||||
\(90\) | −0.139045 | −0.0146567 | ||||||||
\(91\) | 0.572827 | 0.0600486 | ||||||||
\(92\) | 10.6091 | 1.10608 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −0.458686 | −0.0473099 | ||||||||
\(95\) | −3.16026 | −0.324236 | ||||||||
\(96\) | −1.64709 | −0.168106 | ||||||||
\(97\) | 1.30778 | 0.132785 | 0.0663924 | − | 0.997794i | \(-0.478851\pi\) | ||||
0.0663924 | + | 0.997794i | \(0.478851\pi\) | |||||||
\(98\) | 0.927693 | 0.0937112 | ||||||||
\(99\) | −2.21820 | −0.222938 | ||||||||
\(100\) | −1.98067 | −0.198067 | ||||||||
\(101\) | −15.0836 | −1.50088 | −0.750439 | − | 0.660939i | \(-0.770158\pi\) | ||||
−0.750439 | + | 0.660939i | \(0.770158\pi\) | |||||||
\(102\) | −0.626983 | −0.0620806 | ||||||||
\(103\) | −13.1610 | −1.29679 | −0.648397 | − | 0.761303i | \(-0.724560\pi\) | ||||
−0.648397 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(104\) | −0.553494 | −0.0542745 | ||||||||
\(105\) | −0.572827 | −0.0559022 | ||||||||
\(106\) | −0.578361 | −0.0561754 | ||||||||
\(107\) | −4.09875 | −0.396241 | −0.198120 | − | 0.980178i | \(-0.563484\pi\) | ||||
−0.198120 | + | 0.980178i | \(0.563484\pi\) | |||||||
\(108\) | −1.98067 | −0.190590 | ||||||||
\(109\) | 2.67095 | 0.255830 | 0.127915 | − | 0.991785i | \(-0.459171\pi\) | ||||
0.127915 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(110\) | 0.308431 | 0.0294077 | ||||||||
\(111\) | 8.21655 | 0.779880 | ||||||||
\(112\) | −2.22507 | −0.210250 | ||||||||
\(113\) | 13.5481 | 1.27450 | 0.637248 | − | 0.770659i | \(-0.280073\pi\) | ||||
0.637248 | + | 0.770659i | \(0.280073\pi\) | |||||||
\(114\) | 0.439420 | 0.0411554 | ||||||||
\(115\) | −5.35633 | −0.499481 | ||||||||
\(116\) | 8.30277 | 0.770893 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0.991273 | 0.0912541 | ||||||||
\(119\) | −2.58299 | −0.236782 | ||||||||
\(120\) | 0.553494 | 0.0505268 | ||||||||
\(121\) | −6.07958 | −0.552689 | ||||||||
\(122\) | 0.992820 | 0.0898857 | ||||||||
\(123\) | 4.93542 | 0.445012 | ||||||||
\(124\) | 1.98067 | 0.177869 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.0796491 | 0.00709570 | ||||||||
\(127\) | 10.1759 | 0.902969 | 0.451484 | − | 0.892279i | \(-0.350895\pi\) | ||||
0.451484 | + | 0.892279i | \(0.350895\pi\) | |||||||
\(128\) | 4.34255 | 0.383831 | ||||||||
\(129\) | 8.80730 | 0.775440 | ||||||||
\(130\) | 0.139045 | 0.0121951 | ||||||||
\(131\) | 1.38145 | 0.120698 | 0.0603490 | − | 0.998177i | \(-0.480779\pi\) | ||||
0.0603490 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(132\) | 4.39352 | 0.382406 | ||||||||
\(133\) | 1.81028 | 0.156971 | ||||||||
\(134\) | 0.894159 | 0.0772436 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 2.49581 | 0.214014 | ||||||||
\(137\) | 0.0950928 | 0.00812433 | 0.00406216 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406216 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(138\) | 0.744774 | 0.0633994 | ||||||||
\(139\) | −13.9815 | −1.18589 | −0.592946 | − | 0.805242i | \(-0.702035\pi\) | ||||
−0.592946 | + | 0.805242i | \(0.702035\pi\) | |||||||
\(140\) | 1.13458 | 0.0958895 | ||||||||
\(141\) | 3.29882 | 0.277811 | ||||||||
\(142\) | 1.72978 | 0.145160 | ||||||||
\(143\) | 2.21820 | 0.185495 | ||||||||
\(144\) | 3.88437 | 0.323698 | ||||||||
\(145\) | −4.19191 | −0.348119 | ||||||||
\(146\) | 2.25645 | 0.186745 | ||||||||
\(147\) | −6.67187 | −0.550286 | ||||||||
\(148\) | −16.2742 | −1.33773 | ||||||||
\(149\) | −1.12543 | −0.0921987 | −0.0460994 | − | 0.998937i | \(-0.514679\pi\) | ||||
−0.0460994 | + | 0.998937i | \(0.514679\pi\) | |||||||
\(150\) | −0.139045 | −0.0113530 | ||||||||
\(151\) | 16.9006 | 1.37535 | 0.687674 | − | 0.726019i | \(-0.258632\pi\) | ||||
0.687674 | + | 0.726019i | \(0.258632\pi\) | |||||||
\(152\) | −1.74918 | −0.141878 | ||||||||
\(153\) | 4.50920 | 0.364547 | ||||||||
\(154\) | −0.176678 | −0.0142371 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 1.98067 | 0.158580 | ||||||||
\(157\) | −3.81444 | −0.304426 | −0.152213 | − | 0.988348i | \(-0.548640\pi\) | ||||
−0.152213 | + | 0.988348i | \(0.548640\pi\) | |||||||
\(158\) | −0.527286 | −0.0419486 | ||||||||
\(159\) | 4.15951 | 0.329871 | ||||||||
\(160\) | −1.64709 | −0.130214 | ||||||||
\(161\) | 3.06825 | 0.241812 | ||||||||
\(162\) | −0.139045 | −0.0109244 | ||||||||
\(163\) | 14.5778 | 1.14182 | 0.570912 | − | 0.821011i | \(-0.306590\pi\) | ||||
0.570912 | + | 0.821011i | \(0.306590\pi\) | |||||||
\(164\) | −9.77542 | −0.763332 | ||||||||
\(165\) | −2.21820 | −0.172687 | ||||||||
\(166\) | 1.13330 | 0.0879608 | ||||||||
\(167\) | −0.499655 | −0.0386645 | −0.0193322 | − | 0.999813i | \(-0.506154\pi\) | ||||
−0.0193322 | + | 0.999813i | \(0.506154\pi\) | |||||||
\(168\) | −0.317056 | −0.0244614 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.626983 | −0.0480874 | ||||||||
\(171\) | −3.16026 | −0.241671 | ||||||||
\(172\) | −17.4443 | −1.33012 | ||||||||
\(173\) | −3.60715 | −0.274246 | −0.137123 | − | 0.990554i | \(-0.543786\pi\) | ||||
−0.137123 | + | 0.990554i | \(0.543786\pi\) | |||||||
\(174\) | 0.582866 | 0.0441869 | ||||||||
\(175\) | −0.572827 | −0.0433017 | ||||||||
\(176\) | −8.61632 | −0.649479 | ||||||||
\(177\) | −7.12913 | −0.535858 | ||||||||
\(178\) | −2.45098 | −0.183709 | ||||||||
\(179\) | 2.39316 | 0.178873 | 0.0894364 | − | 0.995993i | \(-0.471493\pi\) | ||||
0.0894364 | + | 0.995993i | \(0.471493\pi\) | |||||||
\(180\) | −1.98067 | −0.147630 | ||||||||
\(181\) | −12.1618 | −0.903977 | −0.451989 | − | 0.892024i | \(-0.649285\pi\) | ||||
−0.451989 | + | 0.892024i | \(0.649285\pi\) | |||||||
\(182\) | −0.0796491 | −0.00590398 | ||||||||
\(183\) | −7.14025 | −0.527822 | ||||||||
\(184\) | −2.96470 | −0.218560 | ||||||||
\(185\) | 8.21655 | 0.604093 | ||||||||
\(186\) | 0.139045 | 0.0101953 | ||||||||
\(187\) | −10.0023 | −0.731441 | ||||||||
\(188\) | −6.53386 | −0.476531 | ||||||||
\(189\) | −0.572827 | −0.0416671 | ||||||||
\(190\) | 0.439420 | 0.0318789 | ||||||||
\(191\) | −26.6319 | −1.92702 | −0.963509 | − | 0.267676i | \(-0.913744\pi\) | ||||
−0.963509 | + | 0.267676i | \(0.913744\pi\) | |||||||
\(192\) | −7.53972 | −0.544133 | ||||||||
\(193\) | −19.3118 | −1.39010 | −0.695048 | − | 0.718963i | \(-0.744617\pi\) | ||||
−0.695048 | + | 0.718963i | \(0.744617\pi\) | |||||||
\(194\) | −0.181841 | −0.0130554 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 13.2147 | 0.943910 | ||||||||
\(197\) | 10.7291 | 0.764420 | 0.382210 | − | 0.924076i | \(-0.375163\pi\) | ||||
0.382210 | + | 0.924076i | \(0.375163\pi\) | |||||||
\(198\) | 0.308431 | 0.0219192 | ||||||||
\(199\) | −1.32078 | −0.0936278 | −0.0468139 | − | 0.998904i | \(-0.514907\pi\) | ||||
−0.0468139 | + | 0.998904i | \(0.514907\pi\) | |||||||
\(200\) | 0.553494 | 0.0391379 | ||||||||
\(201\) | −6.43070 | −0.453586 | ||||||||
\(202\) | 2.09731 | 0.147566 | ||||||||
\(203\) | 2.40124 | 0.168534 | ||||||||
\(204\) | −8.93121 | −0.625310 | ||||||||
\(205\) | 4.93542 | 0.344705 | ||||||||
\(206\) | 1.82998 | 0.127501 | ||||||||
\(207\) | −5.35633 | −0.372291 | ||||||||
\(208\) | −3.88437 | −0.269333 | ||||||||
\(209\) | 7.01009 | 0.484898 | ||||||||
\(210\) | 0.0796491 | 0.00549631 | ||||||||
\(211\) | −25.0872 | −1.72708 | −0.863538 | − | 0.504284i | \(-0.831757\pi\) | ||||
−0.863538 | + | 0.504284i | \(0.831757\pi\) | |||||||
\(212\) | −8.23860 | −0.565830 | ||||||||
\(213\) | −12.4404 | −0.852400 | ||||||||
\(214\) | 0.569912 | 0.0389584 | ||||||||
\(215\) | 8.80730 | 0.600653 | ||||||||
\(216\) | 0.553494 | 0.0376605 | ||||||||
\(217\) | 0.572827 | 0.0388861 | ||||||||
\(218\) | −0.371383 | −0.0251533 | ||||||||
\(219\) | −16.2281 | −1.09660 | ||||||||
\(220\) | 4.39352 | 0.296211 | ||||||||
\(221\) | −4.50920 | −0.303321 | ||||||||
\(222\) | −1.14247 | −0.0766778 | ||||||||
\(223\) | −13.4404 | −0.900039 | −0.450019 | − | 0.893019i | \(-0.648583\pi\) | ||||
−0.450019 | + | 0.893019i | \(0.648583\pi\) | |||||||
\(224\) | 0.943499 | 0.0630402 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −1.88380 | −0.125308 | ||||||||
\(227\) | −26.9758 | −1.79045 | −0.895223 | − | 0.445618i | \(-0.852984\pi\) | ||||
−0.895223 | + | 0.445618i | \(0.852984\pi\) | |||||||
\(228\) | 6.25942 | 0.414540 | ||||||||
\(229\) | −2.87887 | −0.190241 | −0.0951206 | − | 0.995466i | \(-0.530324\pi\) | ||||
−0.0951206 | + | 0.995466i | \(0.530324\pi\) | |||||||
\(230\) | 0.744774 | 0.0491090 | ||||||||
\(231\) | 1.27065 | 0.0836024 | ||||||||
\(232\) | −2.32019 | −0.152328 | ||||||||
\(233\) | −26.9954 | −1.76853 | −0.884264 | − | 0.466987i | \(-0.845339\pi\) | ||||
−0.884264 | + | 0.466987i | \(0.845339\pi\) | |||||||
\(234\) | 0.139045 | 0.00908969 | ||||||||
\(235\) | 3.29882 | 0.215191 | ||||||||
\(236\) | 14.1204 | 0.919162 | ||||||||
\(237\) | 3.79218 | 0.246329 | ||||||||
\(238\) | 0.359153 | 0.0232804 | ||||||||
\(239\) | 9.53702 | 0.616898 | 0.308449 | − | 0.951241i | \(-0.400190\pi\) | ||||
0.308449 | + | 0.951241i | \(0.400190\pi\) | |||||||
\(240\) | 3.88437 | 0.250735 | ||||||||
\(241\) | −21.8420 | −1.40697 | −0.703485 | − | 0.710711i | \(-0.748374\pi\) | ||||
−0.703485 | + | 0.710711i | \(0.748374\pi\) | |||||||
\(242\) | 0.845339 | 0.0543404 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.1425 | 0.905378 | ||||||||
\(245\) | −6.67187 | −0.426250 | ||||||||
\(246\) | −0.686248 | −0.0437536 | ||||||||
\(247\) | 3.16026 | 0.201082 | ||||||||
\(248\) | −0.553494 | −0.0351469 | ||||||||
\(249\) | −8.15054 | −0.516519 | ||||||||
\(250\) | −0.139045 | −0.00879401 | ||||||||
\(251\) | −28.5385 | −1.80133 | −0.900666 | − | 0.434512i | \(-0.856921\pi\) | ||||
−0.900666 | + | 0.434512i | \(0.856921\pi\) | |||||||
\(252\) | 1.13458 | 0.0714718 | ||||||||
\(253\) | 11.8814 | 0.746979 | ||||||||
\(254\) | −1.41492 | −0.0887799 | ||||||||
\(255\) | 4.50920 | 0.282377 | ||||||||
\(256\) | 14.4756 | 0.904727 | ||||||||
\(257\) | 15.6846 | 0.978380 | 0.489190 | − | 0.872177i | \(-0.337292\pi\) | ||||
0.489190 | + | 0.872177i | \(0.337292\pi\) | |||||||
\(258\) | −1.22462 | −0.0762412 | ||||||||
\(259\) | −4.70666 | −0.292458 | ||||||||
\(260\) | 1.98067 | 0.122836 | ||||||||
\(261\) | −4.19191 | −0.259472 | ||||||||
\(262\) | −0.192085 | −0.0118670 | ||||||||
\(263\) | 7.54877 | 0.465477 | 0.232739 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232739 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(264\) | −1.22776 | −0.0755634 | ||||||||
\(265\) | 4.15951 | 0.255517 | ||||||||
\(266\) | −0.251712 | −0.0154334 | ||||||||
\(267\) | 17.6272 | 1.07877 | ||||||||
\(268\) | 12.7371 | 0.778040 | ||||||||
\(269\) | 1.58459 | 0.0966139 | 0.0483069 | − | 0.998833i | \(-0.484617\pi\) | ||||
0.0483069 | + | 0.998833i | \(0.484617\pi\) | |||||||
\(270\) | −0.139045 | −0.00846204 | ||||||||
\(271\) | 12.5812 | 0.764256 | 0.382128 | − | 0.924109i | \(-0.375191\pi\) | ||||
0.382128 | + | 0.924109i | \(0.375191\pi\) | |||||||
\(272\) | 17.5154 | 1.06203 | ||||||||
\(273\) | 0.572827 | 0.0346691 | ||||||||
\(274\) | −0.0132222 | −0.000798784 0 | ||||||||
\(275\) | −2.21820 | −0.133763 | ||||||||
\(276\) | 10.6091 | 0.638593 | ||||||||
\(277\) | 20.5670 | 1.23575 | 0.617875 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617875 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(278\) | 1.94406 | 0.116597 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | −0.317056 | −0.0189477 | ||||||||
\(281\) | 22.9342 | 1.36814 | 0.684068 | − | 0.729418i | \(-0.260209\pi\) | ||||
0.684068 | + | 0.729418i | \(0.260209\pi\) | |||||||
\(282\) | −0.458686 | −0.0273144 | ||||||||
\(283\) | −9.06800 | −0.539037 | −0.269518 | − | 0.962995i | \(-0.586865\pi\) | ||||
−0.269518 | + | 0.962995i | \(0.586865\pi\) | |||||||
\(284\) | 24.6402 | 1.46213 | ||||||||
\(285\) | −3.16026 | −0.187198 | ||||||||
\(286\) | −0.308431 | −0.0182379 | ||||||||
\(287\) | −2.82714 | −0.166881 | ||||||||
\(288\) | −1.64709 | −0.0970558 | ||||||||
\(289\) | 3.33284 | 0.196050 | ||||||||
\(290\) | 0.582866 | 0.0342270 | ||||||||
\(291\) | 1.30778 | 0.0766633 | ||||||||
\(292\) | 32.1425 | 1.88100 | ||||||||
\(293\) | −4.86408 | −0.284163 | −0.142081 | − | 0.989855i | \(-0.545379\pi\) | ||||
−0.142081 | + | 0.989855i | \(0.545379\pi\) | |||||||
\(294\) | 0.927693 | 0.0541042 | ||||||||
\(295\) | −7.12913 | −0.415074 | ||||||||
\(296\) | 4.54781 | 0.264336 | ||||||||
\(297\) | −2.21820 | −0.128713 | ||||||||
\(298\) | 0.156486 | 0.00906498 | ||||||||
\(299\) | 5.35633 | 0.309765 | ||||||||
\(300\) | −1.98067 | −0.114354 | ||||||||
\(301\) | −5.04506 | −0.290793 | ||||||||
\(302\) | −2.34995 | −0.135224 | ||||||||
\(303\) | −15.0836 | −0.866533 | ||||||||
\(304\) | −12.2756 | −0.704055 | ||||||||
\(305\) | −7.14025 | −0.408850 | ||||||||
\(306\) | −0.626983 | −0.0358422 | ||||||||
\(307\) | 10.5924 | 0.604542 | 0.302271 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302271 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(308\) | −2.51673 | −0.143404 | ||||||||
\(309\) | −13.1610 | −0.748704 | ||||||||
\(310\) | 0.139045 | 0.00789725 | ||||||||
\(311\) | −30.8772 | −1.75089 | −0.875443 | − | 0.483321i | \(-0.839430\pi\) | ||||
−0.875443 | + | 0.483321i | \(0.839430\pi\) | |||||||
\(312\) | −0.553494 | −0.0313354 | ||||||||
\(313\) | −4.59814 | −0.259902 | −0.129951 | − | 0.991520i | \(-0.541482\pi\) | ||||
−0.129951 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(314\) | 0.530381 | 0.0299311 | ||||||||
\(315\) | −0.572827 | −0.0322752 | ||||||||
\(316\) | −7.51105 | −0.422530 | ||||||||
\(317\) | 7.73196 | 0.434270 | 0.217135 | − | 0.976142i | \(-0.430329\pi\) | ||||
0.217135 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(318\) | −0.578361 | −0.0324329 | ||||||||
\(319\) | 9.29849 | 0.520616 | ||||||||
\(320\) | −7.53972 | −0.421483 | ||||||||
\(321\) | −4.09875 | −0.228770 | ||||||||
\(322\) | −0.426627 | −0.0237750 | ||||||||
\(323\) | −14.2502 | −0.792904 | ||||||||
\(324\) | −1.98067 | −0.110037 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −2.02698 | −0.112264 | ||||||||
\(327\) | 2.67095 | 0.147704 | ||||||||
\(328\) | 2.73172 | 0.150834 | ||||||||
\(329\) | −1.88965 | −0.104180 | ||||||||
\(330\) | 0.308431 | 0.0169786 | ||||||||
\(331\) | 1.86476 | 0.102496 | 0.0512482 | − | 0.998686i | \(-0.483680\pi\) | ||||
0.0512482 | + | 0.998686i | \(0.483680\pi\) | |||||||
\(332\) | 16.1435 | 0.885989 | ||||||||
\(333\) | 8.21655 | 0.450264 | ||||||||
\(334\) | 0.0694748 | 0.00380149 | ||||||||
\(335\) | −6.43070 | −0.351347 | ||||||||
\(336\) | −2.22507 | −0.121388 | ||||||||
\(337\) | 21.4216 | 1.16691 | 0.583454 | − | 0.812146i | \(-0.301701\pi\) | ||||
0.583454 | + | 0.812146i | \(0.301701\pi\) | |||||||
\(338\) | −0.139045 | −0.00756308 | ||||||||
\(339\) | 13.5481 | 0.735831 | ||||||||
\(340\) | −8.93121 | −0.484363 | ||||||||
\(341\) | 2.21820 | 0.120122 | ||||||||
\(342\) | 0.439420 | 0.0237611 | ||||||||
\(343\) | 7.83162 | 0.422868 | ||||||||
\(344\) | 4.87479 | 0.262831 | ||||||||
\(345\) | −5.35633 | −0.288375 | ||||||||
\(346\) | 0.501558 | 0.0269639 | ||||||||
\(347\) | 15.0132 | 0.805951 | 0.402975 | − | 0.915211i | \(-0.367976\pi\) | ||||
0.402975 | + | 0.915211i | \(0.367976\pi\) | |||||||
\(348\) | 8.30277 | 0.445075 | ||||||||
\(349\) | 13.2725 | 0.710461 | 0.355231 | − | 0.934779i | \(-0.384402\pi\) | ||||
0.355231 | + | 0.934779i | \(0.384402\pi\) | |||||||
\(350\) | 0.0796491 | 0.00425742 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.65358 | 0.194737 | ||||||||
\(353\) | −27.0581 | −1.44016 | −0.720079 | − | 0.693892i | \(-0.755894\pi\) | ||||
−0.720079 | + | 0.693892i | \(0.755894\pi\) | |||||||
\(354\) | 0.991273 | 0.0526856 | ||||||||
\(355\) | −12.4404 | −0.660266 | ||||||||
\(356\) | −34.9136 | −1.85041 | ||||||||
\(357\) | −2.58299 | −0.136706 | ||||||||
\(358\) | −0.332757 | −0.0175868 | ||||||||
\(359\) | −21.5595 | −1.13787 | −0.568934 | − | 0.822383i | \(-0.692644\pi\) | ||||
−0.568934 | + | 0.822383i | \(0.692644\pi\) | |||||||
\(360\) | 0.553494 | 0.0291717 | ||||||||
\(361\) | −9.01276 | −0.474356 | ||||||||
\(362\) | 1.69104 | 0.0888791 | ||||||||
\(363\) | −6.07958 | −0.319095 | ||||||||
\(364\) | −1.13458 | −0.0594681 | ||||||||
\(365\) | −16.2281 | −0.849420 | ||||||||
\(366\) | 0.992820 | 0.0518955 | ||||||||
\(367\) | 7.09284 | 0.370243 | 0.185121 | − | 0.982716i | \(-0.440732\pi\) | ||||
0.185121 | + | 0.982716i | \(0.440732\pi\) | |||||||
\(368\) | −20.8060 | −1.08459 | ||||||||
\(369\) | 4.93542 | 0.256928 | ||||||||
\(370\) | −1.14247 | −0.0593944 | ||||||||
\(371\) | −2.38268 | −0.123703 | ||||||||
\(372\) | 1.98067 | 0.102693 | ||||||||
\(373\) | 12.3960 | 0.641839 | 0.320920 | − | 0.947106i | \(-0.396008\pi\) | ||||
0.320920 | + | 0.947106i | \(0.396008\pi\) | |||||||
\(374\) | 1.39077 | 0.0719153 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 1.82588 | 0.0941624 | ||||||||
\(377\) | 4.19191 | 0.215894 | ||||||||
\(378\) | 0.0796491 | 0.00409671 | ||||||||
\(379\) | −29.2985 | −1.50496 | −0.752481 | − | 0.658614i | \(-0.771143\pi\) | ||||
−0.752481 | + | 0.658614i | \(0.771143\pi\) | |||||||
\(380\) | 6.25942 | 0.321101 | ||||||||
\(381\) | 10.1759 | 0.521329 | ||||||||
\(382\) | 3.70305 | 0.189464 | ||||||||
\(383\) | −22.5140 | −1.15041 | −0.575205 | − | 0.818009i | \(-0.695078\pi\) | ||||
−0.575205 | + | 0.818009i | \(0.695078\pi\) | |||||||
\(384\) | 4.34255 | 0.221605 | ||||||||
\(385\) | 1.27065 | 0.0647581 | ||||||||
\(386\) | 2.68522 | 0.136674 | ||||||||
\(387\) | 8.80730 | 0.447700 | ||||||||
\(388\) | −2.59027 | −0.131501 | ||||||||
\(389\) | −19.1098 | −0.968904 | −0.484452 | − | 0.874818i | \(-0.660981\pi\) | ||||
−0.484452 | + | 0.874818i | \(0.660981\pi\) | |||||||
\(390\) | 0.139045 | 0.00704084 | ||||||||
\(391\) | −24.1528 | −1.22146 | ||||||||
\(392\) | −3.69284 | −0.186516 | ||||||||
\(393\) | 1.38145 | 0.0696851 | ||||||||
\(394\) | −1.49184 | −0.0751578 | ||||||||
\(395\) | 3.79218 | 0.190806 | ||||||||
\(396\) | 4.39352 | 0.220782 | ||||||||
\(397\) | −32.3728 | −1.62474 | −0.812372 | − | 0.583140i | \(-0.801824\pi\) | ||||
−0.812372 | + | 0.583140i | \(0.801824\pi\) | |||||||
\(398\) | 0.183649 | 0.00920548 | ||||||||
\(399\) | 1.81028 | 0.0906275 | ||||||||
\(400\) | 3.88437 | 0.194219 | ||||||||
\(401\) | −37.5706 | −1.87619 | −0.938093 | − | 0.346383i | \(-0.887410\pi\) | ||||
−0.938093 | + | 0.346383i | \(0.887410\pi\) | |||||||
\(402\) | 0.894159 | 0.0445966 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | 29.8757 | 1.48637 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −0.333881 | −0.0165703 | ||||||||
\(407\) | −18.2260 | −0.903427 | ||||||||
\(408\) | 2.49581 | 0.123561 | ||||||||
\(409\) | −14.2358 | −0.703913 | −0.351956 | − | 0.936016i | \(-0.614483\pi\) | ||||
−0.351956 | + | 0.936016i | \(0.614483\pi\) | |||||||
\(410\) | −0.686248 | −0.0338914 | ||||||||
\(411\) | 0.0950928 | 0.00469058 | ||||||||
\(412\) | 26.0676 | 1.28426 | ||||||||
\(413\) | 4.08376 | 0.200949 | ||||||||
\(414\) | 0.744774 | 0.0366037 | ||||||||
\(415\) | −8.15054 | −0.400094 | ||||||||
\(416\) | 1.64709 | 0.0807553 | ||||||||
\(417\) | −13.9815 | −0.684675 | ||||||||
\(418\) | −0.974721 | −0.0476752 | ||||||||
\(419\) | 4.18121 | 0.204266 | 0.102133 | − | 0.994771i | \(-0.467433\pi\) | ||||
0.102133 | + | 0.994771i | \(0.467433\pi\) | |||||||
\(420\) | 1.13458 | 0.0553618 | ||||||||
\(421\) | 36.2826 | 1.76830 | 0.884152 | − | 0.467199i | \(-0.154737\pi\) | ||||
0.884152 | + | 0.467199i | \(0.154737\pi\) | |||||||
\(422\) | 3.48827 | 0.169806 | ||||||||
\(423\) | 3.29882 | 0.160394 | ||||||||
\(424\) | 2.30226 | 0.111808 | ||||||||
\(425\) | 4.50920 | 0.218728 | ||||||||
\(426\) | 1.72978 | 0.0838080 | ||||||||
\(427\) | 4.09013 | 0.197935 | ||||||||
\(428\) | 8.11825 | 0.392410 | ||||||||
\(429\) | 2.21820 | 0.107096 | ||||||||
\(430\) | −1.22462 | −0.0590562 | ||||||||
\(431\) | 26.4188 | 1.27255 | 0.636275 | − | 0.771462i | \(-0.280474\pi\) | ||||
0.636275 | + | 0.771462i | \(0.280474\pi\) | |||||||
\(432\) | 3.88437 | 0.186887 | ||||||||
\(433\) | −0.442744 | −0.0212769 | −0.0106385 | − | 0.999943i | \(-0.503386\pi\) | ||||
−0.0106385 | + | 0.999943i | \(0.503386\pi\) | |||||||
\(434\) | −0.0796491 | −0.00382328 | ||||||||
\(435\) | −4.19191 | −0.200987 | ||||||||
\(436\) | −5.29026 | −0.253357 | ||||||||
\(437\) | 16.9274 | 0.809748 | ||||||||
\(438\) | 2.25645 | 0.107817 | ||||||||
\(439\) | −17.0399 | −0.813270 | −0.406635 | − | 0.913591i | \(-0.633298\pi\) | ||||
−0.406635 | + | 0.913591i | \(0.633298\pi\) | |||||||
\(440\) | −1.22776 | −0.0585312 | ||||||||
\(441\) | −6.67187 | −0.317708 | ||||||||
\(442\) | 0.626983 | 0.0298226 | ||||||||
\(443\) | 5.82115 | 0.276571 | 0.138285 | − | 0.990392i | \(-0.455841\pi\) | ||||
0.138285 | + | 0.990392i | \(0.455841\pi\) | |||||||
\(444\) | −16.2742 | −0.772341 | ||||||||
\(445\) | 17.6272 | 0.835608 | ||||||||
\(446\) | 1.86883 | 0.0884918 | ||||||||
\(447\) | −1.12543 | −0.0532310 | ||||||||
\(448\) | 4.31896 | 0.204052 | ||||||||
\(449\) | 25.9864 | 1.22637 | 0.613187 | − | 0.789938i | \(-0.289887\pi\) | ||||
0.613187 | + | 0.789938i | \(0.289887\pi\) | |||||||
\(450\) | −0.139045 | −0.00655467 | ||||||||
\(451\) | −10.9478 | −0.515510 | ||||||||
\(452\) | −26.8342 | −1.26218 | ||||||||
\(453\) | 16.9006 | 0.794058 | ||||||||
\(454\) | 3.75086 | 0.176037 | ||||||||
\(455\) | 0.572827 | 0.0268546 | ||||||||
\(456\) | −1.74918 | −0.0819130 | ||||||||
\(457\) | −1.19736 | −0.0560100 | −0.0280050 | − | 0.999608i | \(-0.508915\pi\) | ||||
−0.0280050 | + | 0.999608i | \(0.508915\pi\) | |||||||
\(458\) | 0.400294 | 0.0187045 | ||||||||
\(459\) | 4.50920 | 0.210471 | ||||||||
\(460\) | 10.6091 | 0.494652 | ||||||||
\(461\) | 13.2899 | 0.618974 | 0.309487 | − | 0.950904i | \(-0.399843\pi\) | ||||
0.309487 | + | 0.950904i | \(0.399843\pi\) | |||||||
\(462\) | −0.176678 | −0.00821979 | ||||||||
\(463\) | 31.1387 | 1.44714 | 0.723569 | − | 0.690252i | \(-0.242500\pi\) | ||||
0.723569 | + | 0.690252i | \(0.242500\pi\) | |||||||
\(464\) | −16.2829 | −0.755916 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 3.75359 | 0.173882 | ||||||||
\(467\) | 1.62106 | 0.0750136 | 0.0375068 | − | 0.999296i | \(-0.488058\pi\) | ||||
0.0375068 | + | 0.999296i | \(0.488058\pi\) | |||||||
\(468\) | 1.98067 | 0.0915563 | ||||||||
\(469\) | 3.68368 | 0.170097 | ||||||||
\(470\) | −0.458686 | −0.0211576 | ||||||||
\(471\) | −3.81444 | −0.175760 | ||||||||
\(472\) | −3.94593 | −0.181626 | ||||||||
\(473\) | −19.5364 | −0.898283 | ||||||||
\(474\) | −0.527286 | −0.0242191 | ||||||||
\(475\) | −3.16026 | −0.145003 | ||||||||
\(476\) | 5.11604 | 0.234493 | ||||||||
\(477\) | 4.15951 | 0.190451 | ||||||||
\(478\) | −1.32608 | −0.0606534 | ||||||||
\(479\) | 17.2796 | 0.789526 | 0.394763 | − | 0.918783i | \(-0.370827\pi\) | ||||
0.394763 | + | 0.918783i | \(0.370827\pi\) | |||||||
\(480\) | −1.64709 | −0.0751791 | ||||||||
\(481\) | −8.21655 | −0.374642 | ||||||||
\(482\) | 3.03704 | 0.138333 | ||||||||
\(483\) | 3.06825 | 0.139610 | ||||||||
\(484\) | 12.0416 | 0.547347 | ||||||||
\(485\) | 1.30778 | 0.0593832 | ||||||||
\(486\) | −0.139045 | −0.00630723 | ||||||||
\(487\) | −36.9963 | −1.67646 | −0.838230 | − | 0.545316i | \(-0.816410\pi\) | ||||
−0.838230 | + | 0.545316i | \(0.816410\pi\) | |||||||
\(488\) | −3.95208 | −0.178902 | ||||||||
\(489\) | 14.5778 | 0.659232 | ||||||||
\(490\) | 0.927693 | 0.0419089 | ||||||||
\(491\) | −21.1470 | −0.954351 | −0.477176 | − | 0.878808i | \(-0.658339\pi\) | ||||
−0.477176 | + | 0.878808i | \(0.658339\pi\) | |||||||
\(492\) | −9.77542 | −0.440710 | ||||||||
\(493\) | −18.9021 | −0.851309 | ||||||||
\(494\) | −0.439420 | −0.0197704 | ||||||||
\(495\) | −2.21820 | −0.0997007 | ||||||||
\(496\) | −3.88437 | −0.174413 | ||||||||
\(497\) | 7.12618 | 0.319653 | ||||||||
\(498\) | 1.13330 | 0.0507842 | ||||||||
\(499\) | −36.5425 | −1.63587 | −0.817935 | − | 0.575311i | \(-0.804881\pi\) | ||||
−0.817935 | + | 0.575311i | \(0.804881\pi\) | |||||||
\(500\) | −1.98067 | −0.0885781 | ||||||||
\(501\) | −0.499655 | −0.0223229 | ||||||||
\(502\) | 3.96814 | 0.177107 | ||||||||
\(503\) | −32.1191 | −1.43212 | −0.716059 | − | 0.698039i | \(-0.754056\pi\) | ||||
−0.716059 | + | 0.698039i | \(0.754056\pi\) | |||||||
\(504\) | −0.317056 | −0.0141228 | ||||||||
\(505\) | −15.0836 | −0.671213 | ||||||||
\(506\) | −1.65206 | −0.0734430 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −20.1551 | −0.894240 | ||||||||
\(509\) | −9.09674 | −0.403206 | −0.201603 | − | 0.979467i | \(-0.564615\pi\) | ||||
−0.201603 | + | 0.979467i | \(0.564615\pi\) | |||||||
\(510\) | −0.626983 | −0.0277633 | ||||||||
\(511\) | 9.29593 | 0.411228 | ||||||||
\(512\) | −10.6979 | −0.472783 | ||||||||
\(513\) | −3.16026 | −0.139529 | ||||||||
\(514\) | −2.18088 | −0.0961943 | ||||||||
\(515\) | −13.1610 | −0.579943 | ||||||||
\(516\) | −17.4443 | −0.767944 | ||||||||
\(517\) | −7.31745 | −0.321821 | ||||||||
\(518\) | 0.654440 | 0.0287545 | ||||||||
\(519\) | −3.60715 | −0.158336 | ||||||||
\(520\) | −0.553494 | −0.0242723 | ||||||||
\(521\) | 28.2263 | 1.23662 | 0.618309 | − | 0.785935i | \(-0.287818\pi\) | ||||
0.618309 | + | 0.785935i | \(0.287818\pi\) | |||||||
\(522\) | 0.582866 | 0.0255113 | ||||||||
\(523\) | 30.9402 | 1.35292 | 0.676461 | − | 0.736479i | \(-0.263513\pi\) | ||||
0.676461 | + | 0.736479i | \(0.263513\pi\) | |||||||
\(524\) | −2.73620 | −0.119531 | ||||||||
\(525\) | −0.572827 | −0.0250002 | ||||||||
\(526\) | −1.04962 | −0.0457657 | ||||||||
\(527\) | −4.50920 | −0.196424 | ||||||||
\(528\) | −8.61632 | −0.374977 | ||||||||
\(529\) | 5.69032 | 0.247405 | ||||||||
\(530\) | −0.578361 | −0.0251224 | ||||||||
\(531\) | −7.12913 | −0.309378 | ||||||||
\(532\) | −3.58557 | −0.155454 | ||||||||
\(533\) | −4.93542 | −0.213777 | ||||||||
\(534\) | −2.45098 | −0.106064 | ||||||||
\(535\) | −4.09875 | −0.177204 | ||||||||
\(536\) | −3.55935 | −0.153741 | ||||||||
\(537\) | 2.39316 | 0.103272 | ||||||||
\(538\) | −0.220329 | −0.00949908 | ||||||||
\(539\) | 14.7995 | 0.637462 | ||||||||
\(540\) | −1.98067 | −0.0852343 | ||||||||
\(541\) | 30.2412 | 1.30017 | 0.650085 | − | 0.759862i | \(-0.274733\pi\) | ||||
0.650085 | + | 0.759862i | \(0.274733\pi\) | |||||||
\(542\) | −1.74936 | −0.0751416 | ||||||||
\(543\) | −12.1618 | −0.521912 | ||||||||
\(544\) | −7.42706 | −0.318433 | ||||||||
\(545\) | 2.67095 | 0.114411 | ||||||||
\(546\) | −0.0796491 | −0.00340867 | ||||||||
\(547\) | 12.4204 | 0.531056 | 0.265528 | − | 0.964103i | \(-0.414454\pi\) | ||||
0.265528 | + | 0.964103i | \(0.414454\pi\) | |||||||
\(548\) | −0.188347 | −0.00804579 | ||||||||
\(549\) | −7.14025 | −0.304738 | ||||||||
\(550\) | 0.308431 | 0.0131515 | ||||||||
\(551\) | 13.2475 | 0.564363 | ||||||||
\(552\) | −2.96470 | −0.126186 | ||||||||
\(553\) | −2.17227 | −0.0923742 | ||||||||
\(554\) | −2.85974 | −0.121499 | ||||||||
\(555\) | 8.21655 | 0.348773 | ||||||||
\(556\) | 27.6926 | 1.17443 | ||||||||
\(557\) | 10.6141 | 0.449735 | 0.224867 | − | 0.974389i | \(-0.427805\pi\) | ||||
0.224867 | + | 0.974389i | \(0.427805\pi\) | |||||||
\(558\) | 0.139045 | 0.00588626 | ||||||||
\(559\) | −8.80730 | −0.372509 | ||||||||
\(560\) | −2.22507 | −0.0940266 | ||||||||
\(561\) | −10.0023 | −0.422298 | ||||||||
\(562\) | −3.18889 | −0.134515 | ||||||||
\(563\) | −42.6666 | −1.79818 | −0.899091 | − | 0.437762i | \(-0.855771\pi\) | ||||
−0.899091 | + | 0.437762i | \(0.855771\pi\) | |||||||
\(564\) | −6.53386 | −0.275125 | ||||||||
\(565\) | 13.5481 | 0.569972 | ||||||||
\(566\) | 1.26086 | 0.0529981 | ||||||||
\(567\) | −0.572827 | −0.0240565 | ||||||||
\(568\) | −6.88567 | −0.288916 | ||||||||
\(569\) | −21.1736 | −0.887644 | −0.443822 | − | 0.896115i | \(-0.646378\pi\) | ||||
−0.443822 | + | 0.896115i | \(0.646378\pi\) | |||||||
\(570\) | 0.439420 | 0.0184053 | ||||||||
\(571\) | 28.9731 | 1.21249 | 0.606244 | − | 0.795279i | \(-0.292676\pi\) | ||||
0.606244 | + | 0.795279i | \(0.292676\pi\) | |||||||
\(572\) | −4.39352 | −0.183702 | ||||||||
\(573\) | −26.6319 | −1.11256 | ||||||||
\(574\) | 0.393102 | 0.0164077 | ||||||||
\(575\) | −5.35633 | −0.223375 | ||||||||
\(576\) | −7.53972 | −0.314155 | ||||||||
\(577\) | 7.75154 | 0.322701 | 0.161350 | − | 0.986897i | \(-0.448415\pi\) | ||||
0.161350 | + | 0.986897i | \(0.448415\pi\) | |||||||
\(578\) | −0.463417 | −0.0192756 | ||||||||
\(579\) | −19.3118 | −0.802573 | ||||||||
\(580\) | 8.30277 | 0.344754 | ||||||||
\(581\) | 4.66885 | 0.193697 | ||||||||
\(582\) | −0.181841 | −0.00753754 | ||||||||
\(583\) | −9.22663 | −0.382128 | ||||||||
\(584\) | −8.98218 | −0.371685 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0.676328 | 0.0279389 | ||||||||
\(587\) | −8.81242 | −0.363727 | −0.181864 | − | 0.983324i | \(-0.558213\pi\) | ||||
−0.181864 | + | 0.983324i | \(0.558213\pi\) | |||||||
\(588\) | 13.2147 | 0.544967 | ||||||||
\(589\) | 3.16026 | 0.130216 | ||||||||
\(590\) | 0.991273 | 0.0408101 | ||||||||
\(591\) | 10.7291 | 0.441338 | ||||||||
\(592\) | 31.9161 | 1.31174 | ||||||||
\(593\) | 22.1476 | 0.909493 | 0.454746 | − | 0.890621i | \(-0.349730\pi\) | ||||
0.454746 | + | 0.890621i | \(0.349730\pi\) | |||||||
\(594\) | 0.308431 | 0.0126551 | ||||||||
\(595\) | −2.58299 | −0.105892 | ||||||||
\(596\) | 2.22910 | 0.0913075 | ||||||||
\(597\) | −1.32078 | −0.0540560 | ||||||||
\(598\) | −0.744774 | −0.0304561 | ||||||||
\(599\) | 26.7739 | 1.09395 | 0.546977 | − | 0.837148i | \(-0.315779\pi\) | ||||
0.546977 | + | 0.837148i | \(0.315779\pi\) | |||||||
\(600\) | 0.553494 | 0.0225963 | ||||||||
\(601\) | 1.67854 | 0.0684689 | 0.0342344 | − | 0.999414i | \(-0.489101\pi\) | ||||
0.0342344 | + | 0.999414i | \(0.489101\pi\) | |||||||
\(602\) | 0.701493 | 0.0285907 | ||||||||
\(603\) | −6.43070 | −0.261878 | ||||||||
\(604\) | −33.4744 | −1.36205 | ||||||||
\(605\) | −6.07958 | −0.247170 | ||||||||
\(606\) | 2.09731 | 0.0851975 | ||||||||
\(607\) | −15.2329 | −0.618285 | −0.309142 | − | 0.951016i | \(-0.600042\pi\) | ||||
−0.309142 | + | 0.951016i | \(0.600042\pi\) | |||||||
\(608\) | 5.20524 | 0.211100 | ||||||||
\(609\) | 2.40124 | 0.0973031 | ||||||||
\(610\) | 0.992820 | 0.0401981 | ||||||||
\(611\) | −3.29882 | −0.133456 | ||||||||
\(612\) | −8.93121 | −0.361023 | ||||||||
\(613\) | 35.5594 | 1.43623 | 0.718115 | − | 0.695925i | \(-0.245005\pi\) | ||||
0.718115 | + | 0.695925i | \(0.245005\pi\) | |||||||
\(614\) | −1.47283 | −0.0594386 | ||||||||
\(615\) | 4.93542 | 0.199015 | ||||||||
\(616\) | 0.703295 | 0.0283366 | ||||||||
\(617\) | 19.1432 | 0.770675 | 0.385338 | − | 0.922776i | \(-0.374085\pi\) | ||||
0.385338 | + | 0.922776i | \(0.374085\pi\) | |||||||
\(618\) | 1.82998 | 0.0736126 | ||||||||
\(619\) | 11.7348 | 0.471660 | 0.235830 | − | 0.971794i | \(-0.424219\pi\) | ||||
0.235830 | + | 0.971794i | \(0.424219\pi\) | |||||||
\(620\) | 1.98067 | 0.0795455 | ||||||||
\(621\) | −5.35633 | −0.214942 | ||||||||
\(622\) | 4.29334 | 0.172147 | ||||||||
\(623\) | −10.0973 | −0.404541 | ||||||||
\(624\) | −3.88437 | −0.155499 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.639351 | 0.0255536 | ||||||||
\(627\) | 7.01009 | 0.279956 | ||||||||
\(628\) | 7.55514 | 0.301483 | ||||||||
\(629\) | 37.0500 | 1.47728 | ||||||||
\(630\) | 0.0796491 | 0.00317329 | ||||||||
\(631\) | 31.2055 | 1.24227 | 0.621135 | − | 0.783703i | \(-0.286672\pi\) | ||||
0.621135 | + | 0.783703i | \(0.286672\pi\) | |||||||
\(632\) | 2.09895 | 0.0834918 | ||||||||
\(633\) | −25.0872 | −0.997128 | ||||||||
\(634\) | −1.07509 | −0.0426974 | ||||||||
\(635\) | 10.1759 | 0.403820 | ||||||||
\(636\) | −8.23860 | −0.326682 | ||||||||
\(637\) | 6.67187 | 0.264349 | ||||||||
\(638\) | −1.29291 | −0.0511869 | ||||||||
\(639\) | −12.4404 | −0.492133 | ||||||||
\(640\) | 4.34255 | 0.171654 | ||||||||
\(641\) | 7.15917 | 0.282770 | 0.141385 | − | 0.989955i | \(-0.454844\pi\) | ||||
0.141385 | + | 0.989955i | \(0.454844\pi\) | |||||||
\(642\) | 0.569912 | 0.0224926 | ||||||||
\(643\) | −30.5949 | −1.20655 | −0.603273 | − | 0.797535i | \(-0.706137\pi\) | ||||
−0.603273 | + | 0.797535i | \(0.706137\pi\) | |||||||
\(644\) | −6.07719 | −0.239475 | ||||||||
\(645\) | 8.80730 | 0.346787 | ||||||||
\(646\) | 1.98143 | 0.0779583 | ||||||||
\(647\) | 20.6823 | 0.813107 | 0.406554 | − | 0.913627i | \(-0.366730\pi\) | ||||
0.406554 | + | 0.913627i | \(0.366730\pi\) | |||||||
\(648\) | 0.553494 | 0.0217433 | ||||||||
\(649\) | 15.8138 | 0.620748 | ||||||||
\(650\) | 0.139045 | 0.00545381 | ||||||||
\(651\) | 0.572827 | 0.0224509 | ||||||||
\(652\) | −28.8738 | −1.13079 | ||||||||
\(653\) | 10.5815 | 0.414085 | 0.207043 | − | 0.978332i | \(-0.433616\pi\) | ||||
0.207043 | + | 0.978332i | \(0.433616\pi\) | |||||||
\(654\) | −0.371383 | −0.0145222 | ||||||||
\(655\) | 1.38145 | 0.0539778 | ||||||||
\(656\) | 19.1710 | 0.748502 | ||||||||
\(657\) | −16.2281 | −0.633120 | ||||||||
\(658\) | 0.262748 | 0.0102430 | ||||||||
\(659\) | 1.43861 | 0.0560403 | 0.0280202 | − | 0.999607i | \(-0.491080\pi\) | ||||
0.0280202 | + | 0.999607i | \(0.491080\pi\) | |||||||
\(660\) | 4.39352 | 0.171017 | ||||||||
\(661\) | 8.89638 | 0.346029 | 0.173015 | − | 0.984919i | \(-0.444649\pi\) | ||||
0.173015 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(662\) | −0.259286 | −0.0100775 | ||||||||
\(663\) | −4.50920 | −0.175123 | ||||||||
\(664\) | −4.51127 | −0.175071 | ||||||||
\(665\) | 1.81028 | 0.0701998 | ||||||||
\(666\) | −1.14247 | −0.0442700 | ||||||||
\(667\) | 22.4533 | 0.869393 | ||||||||
\(668\) | 0.989650 | 0.0382907 | ||||||||
\(669\) | −13.4404 | −0.519638 | ||||||||
\(670\) | 0.894159 | 0.0345444 | ||||||||
\(671\) | 15.8385 | 0.611439 | ||||||||
\(672\) | 0.943499 | 0.0363963 | ||||||||
\(673\) | −16.7089 | −0.644080 | −0.322040 | − | 0.946726i | \(-0.604369\pi\) | ||||
−0.322040 | + | 0.946726i | \(0.604369\pi\) | |||||||
\(674\) | −2.97857 | −0.114730 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −1.98067 | −0.0761795 | ||||||||
\(677\) | −50.1028 | −1.92561 | −0.962803 | − | 0.270205i | \(-0.912909\pi\) | ||||
−0.962803 | + | 0.270205i | \(0.912909\pi\) | |||||||
\(678\) | −1.88380 | −0.0723469 | ||||||||
\(679\) | −0.749131 | −0.0287490 | ||||||||
\(680\) | 2.49581 | 0.0957100 | ||||||||
\(681\) | −26.9758 | −1.03371 | ||||||||
\(682\) | −0.308431 | −0.0118104 | ||||||||
\(683\) | −43.3776 | −1.65980 | −0.829899 | − | 0.557914i | \(-0.811602\pi\) | ||||
−0.829899 | + | 0.557914i | \(0.811602\pi\) | |||||||
\(684\) | 6.25942 | 0.239335 | ||||||||
\(685\) | 0.0950928 | 0.00363331 | ||||||||
\(686\) | −1.08895 | −0.0415764 | ||||||||
\(687\) | −2.87887 | −0.109836 | ||||||||
\(688\) | 34.2108 | 1.30428 | ||||||||
\(689\) | −4.15951 | −0.158465 | ||||||||
\(690\) | 0.744774 | 0.0283531 | ||||||||
\(691\) | 26.5170 | 1.00875 | 0.504376 | − | 0.863484i | \(-0.331722\pi\) | ||||
0.504376 | + | 0.863484i | \(0.331722\pi\) | |||||||
\(692\) | 7.14455 | 0.271595 | ||||||||
\(693\) | 1.27065 | 0.0482679 | ||||||||
\(694\) | −2.08752 | −0.0792411 | ||||||||
\(695\) | −13.9815 | −0.530347 | ||||||||
\(696\) | −2.32019 | −0.0879467 | ||||||||
\(697\) | 22.2548 | 0.842960 | ||||||||
\(698\) | −1.84548 | −0.0698526 | ||||||||
\(699\) | −26.9954 | −1.02106 | ||||||||
\(700\) | 1.13458 | 0.0428831 | ||||||||
\(701\) | −50.0706 | −1.89114 | −0.945570 | − | 0.325419i | \(-0.894495\pi\) | ||||
−0.945570 | + | 0.325419i | \(0.894495\pi\) | |||||||
\(702\) | 0.139045 | 0.00524793 | ||||||||
\(703\) | −25.9664 | −0.979342 | ||||||||
\(704\) | 16.7246 | 0.630333 | ||||||||
\(705\) | 3.29882 | 0.124241 | ||||||||
\(706\) | 3.76231 | 0.141596 | ||||||||
\(707\) | 8.64032 | 0.324953 | ||||||||
\(708\) | 14.1204 | 0.530678 | ||||||||
\(709\) | −16.5320 | −0.620874 | −0.310437 | − | 0.950594i | \(-0.600475\pi\) | ||||
−0.310437 | + | 0.950594i | \(0.600475\pi\) | |||||||
\(710\) | 1.72978 | 0.0649174 | ||||||||
\(711\) | 3.79218 | 0.142218 | ||||||||
\(712\) | 9.75653 | 0.365641 | ||||||||
\(713\) | 5.35633 | 0.200596 | ||||||||
\(714\) | 0.359153 | 0.0134410 | ||||||||
\(715\) | 2.21820 | 0.0829560 | ||||||||
\(716\) | −4.74004 | −0.177144 | ||||||||
\(717\) | 9.53702 | 0.356166 | ||||||||
\(718\) | 2.99775 | 0.111875 | ||||||||
\(719\) | −38.8188 | −1.44770 | −0.723849 | − | 0.689959i | \(-0.757629\pi\) | ||||
−0.723849 | + | 0.689959i | \(0.757629\pi\) | |||||||
\(720\) | 3.88437 | 0.144762 | ||||||||
\(721\) | 7.53899 | 0.280767 | ||||||||
\(722\) | 1.25318 | 0.0466387 | ||||||||
\(723\) | −21.8420 | −0.812314 | ||||||||
\(724\) | 24.0884 | 0.895239 | ||||||||
\(725\) | −4.19191 | −0.155683 | ||||||||
\(726\) | 0.845339 | 0.0313735 | ||||||||
\(727\) | 35.8064 | 1.32798 | 0.663992 | − | 0.747739i | \(-0.268861\pi\) | ||||
0.663992 | + | 0.747739i | \(0.268861\pi\) | |||||||
\(728\) | 0.317056 | 0.0117509 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.25645 | 0.0835150 | ||||||||
\(731\) | 39.7138 | 1.46887 | ||||||||
\(732\) | 14.1425 | 0.522720 | ||||||||
\(733\) | 42.8390 | 1.58229 | 0.791147 | − | 0.611626i | \(-0.209484\pi\) | ||||
0.791147 | + | 0.611626i | \(0.209484\pi\) | |||||||
\(734\) | −0.986227 | −0.0364023 | ||||||||
\(735\) | −6.67187 | −0.246096 | ||||||||
\(736\) | 8.82237 | 0.325197 | ||||||||
\(737\) | 14.2646 | 0.525443 | ||||||||
\(738\) | −0.686248 | −0.0252611 | ||||||||
\(739\) | −35.1972 | −1.29475 | −0.647374 | − | 0.762172i | \(-0.724133\pi\) | ||||
−0.647374 | + | 0.762172i | \(0.724133\pi\) | |||||||
\(740\) | −16.2742 | −0.598253 | ||||||||
\(741\) | 3.16026 | 0.116095 | ||||||||
\(742\) | 0.331301 | 0.0121624 | ||||||||
\(743\) | −23.1843 | −0.850551 | −0.425275 | − | 0.905064i | \(-0.639823\pi\) | ||||
−0.425275 | + | 0.905064i | \(0.639823\pi\) | |||||||
\(744\) | −0.553494 | −0.0202921 | ||||||||
\(745\) | −1.12543 | −0.0412325 | ||||||||
\(746\) | −1.72360 | −0.0631056 | ||||||||
\(747\) | −8.15054 | −0.298213 | ||||||||
\(748\) | 19.8112 | 0.724370 | ||||||||
\(749\) | 2.34787 | 0.0857894 | ||||||||
\(750\) | −0.139045 | −0.00507722 | ||||||||
\(751\) | 12.5973 | 0.459682 | 0.229841 | − | 0.973228i | \(-0.426179\pi\) | ||||
0.229841 | + | 0.973228i | \(0.426179\pi\) | |||||||
\(752\) | 12.8138 | 0.467273 | ||||||||
\(753\) | −28.5385 | −1.04000 | ||||||||
\(754\) | −0.582866 | −0.0212267 | ||||||||
\(755\) | 16.9006 | 0.615075 | ||||||||
\(756\) | 1.13458 | 0.0412643 | ||||||||
\(757\) | 5.43341 | 0.197481 | 0.0987403 | − | 0.995113i | \(-0.468519\pi\) | ||||
0.0987403 | + | 0.995113i | \(0.468519\pi\) | |||||||
\(758\) | 4.07382 | 0.147968 | ||||||||
\(759\) | 11.8814 | 0.431268 | ||||||||
\(760\) | −1.74918 | −0.0634496 | ||||||||
\(761\) | −7.85036 | −0.284575 | −0.142288 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142288 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(762\) | −1.41492 | −0.0512571 | ||||||||
\(763\) | −1.52999 | −0.0553894 | ||||||||
\(764\) | 52.7489 | 1.90839 | ||||||||
\(765\) | 4.50920 | 0.163030 | ||||||||
\(766\) | 3.13046 | 0.113108 | ||||||||
\(767\) | 7.12913 | 0.257418 | ||||||||
\(768\) | 14.4756 | 0.522344 | ||||||||
\(769\) | −7.20271 | −0.259736 | −0.129868 | − | 0.991531i | \(-0.541455\pi\) | ||||
−0.129868 | + | 0.991531i | \(0.541455\pi\) | |||||||
\(770\) | −0.176678 | −0.00636702 | ||||||||
\(771\) | 15.6846 | 0.564868 | ||||||||
\(772\) | 38.2503 | 1.37666 | ||||||||
\(773\) | −30.2615 | −1.08843 | −0.544215 | − | 0.838946i | \(-0.683172\pi\) | ||||
−0.544215 | + | 0.838946i | \(0.683172\pi\) | |||||||
\(774\) | −1.22462 | −0.0440179 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0.723847 | 0.0259846 | ||||||||
\(777\) | −4.70666 | −0.168851 | ||||||||
\(778\) | 2.65713 | 0.0952626 | ||||||||
\(779\) | −15.5972 | −0.558828 | ||||||||
\(780\) | 1.98067 | 0.0709192 | ||||||||
\(781\) | 27.5952 | 0.987435 | ||||||||
\(782\) | 3.35833 | 0.120094 | ||||||||
\(783\) | −4.19191 | −0.149807 | ||||||||
\(784\) | −25.9160 | −0.925572 | ||||||||
\(785\) | −3.81444 | −0.136143 | ||||||||
\(786\) | −0.192085 | −0.00685144 | ||||||||
\(787\) | 47.1870 | 1.68203 | 0.841017 | − | 0.541009i | \(-0.181958\pi\) | ||||
0.841017 | + | 0.541009i | \(0.181958\pi\) | |||||||
\(788\) | −21.2509 | −0.757030 | ||||||||
\(789\) | 7.54877 | 0.268743 | ||||||||
\(790\) | −0.527286 | −0.0187600 | ||||||||
\(791\) | −7.76071 | −0.275939 | ||||||||
\(792\) | −1.22776 | −0.0436266 | ||||||||
\(793\) | 7.14025 | 0.253558 | ||||||||
\(794\) | 4.50129 | 0.159745 | ||||||||
\(795\) | 4.15951 | 0.147523 | ||||||||
\(796\) | 2.61603 | 0.0927227 | ||||||||
\(797\) | −5.83478 | −0.206679 | −0.103339 | − | 0.994646i | \(-0.532953\pi\) | ||||
−0.103339 | + | 0.994646i | \(0.532953\pi\) | |||||||
\(798\) | −0.251712 | −0.00891050 | ||||||||
\(799\) | 14.8750 | 0.526241 | ||||||||
\(800\) | −1.64709 | −0.0582335 | ||||||||
\(801\) | 17.6272 | 0.622826 | ||||||||
\(802\) | 5.22402 | 0.184467 | ||||||||
\(803\) | 35.9973 | 1.27032 | ||||||||
\(804\) | 12.7371 | 0.449202 | ||||||||
\(805\) | 3.06825 | 0.108142 | ||||||||
\(806\) | −0.139045 | −0.00489767 | ||||||||
\(807\) | 1.58459 | 0.0557801 | ||||||||
\(808\) | −8.34870 | −0.293706 | ||||||||
\(809\) | 0.484590 | 0.0170373 | 0.00851864 | − | 0.999964i | \(-0.497288\pi\) | ||||
0.00851864 | + | 0.999964i | \(0.497288\pi\) | |||||||
\(810\) | −0.139045 | −0.00488556 | ||||||||
\(811\) | −3.02746 | −0.106309 | −0.0531543 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531543 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(812\) | −4.75605 | −0.166905 | ||||||||
\(813\) | 12.5812 | 0.441243 | ||||||||
\(814\) | 2.53424 | 0.0888249 | ||||||||
\(815\) | 14.5778 | 0.510639 | ||||||||
\(816\) | 17.5154 | 0.613161 | ||||||||
\(817\) | −27.8334 | −0.973766 | ||||||||
\(818\) | 1.97942 | 0.0692087 | ||||||||
\(819\) | 0.572827 | 0.0200162 | ||||||||
\(820\) | −9.77542 | −0.341373 | ||||||||
\(821\) | −5.54554 | −0.193541 | −0.0967704 | − | 0.995307i | \(-0.530851\pi\) | ||||
−0.0967704 | + | 0.995307i | \(0.530851\pi\) | |||||||
\(822\) | −0.0132222 | −0.000461178 0 | ||||||||
\(823\) | −10.9108 | −0.380326 | −0.190163 | − | 0.981753i | \(-0.560902\pi\) | ||||
−0.190163 | + | 0.981753i | \(0.560902\pi\) | |||||||
\(824\) | −7.28454 | −0.253769 | ||||||||
\(825\) | −2.21820 | −0.0772278 | ||||||||
\(826\) | −0.567829 | −0.0197573 | ||||||||
\(827\) | −18.0861 | −0.628917 | −0.314458 | − | 0.949271i | \(-0.601823\pi\) | ||||
−0.314458 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(828\) | 10.6091 | 0.368692 | ||||||||
\(829\) | 7.49750 | 0.260399 | 0.130199 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130199 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(830\) | 1.13330 | 0.0393373 | ||||||||
\(831\) | 20.5670 | 0.713460 | ||||||||
\(832\) | 7.53972 | 0.261393 | ||||||||
\(833\) | −30.0848 | −1.04238 | ||||||||
\(834\) | 1.94406 | 0.0673172 | ||||||||
\(835\) | −0.499655 | −0.0172913 | ||||||||
\(836\) | −13.8846 | −0.480211 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | −0.581379 | −0.0200834 | ||||||||
\(839\) | −13.1527 | −0.454082 | −0.227041 | − | 0.973885i | \(-0.572905\pi\) | ||||
−0.227041 | + | 0.973885i | \(0.572905\pi\) | |||||||
\(840\) | −0.317056 | −0.0109395 | ||||||||
\(841\) | −11.4279 | −0.394066 | ||||||||
\(842\) | −5.04493 | −0.173860 | ||||||||
\(843\) | 22.9342 | 0.789894 | ||||||||
\(844\) | 49.6894 | 1.71038 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −0.458686 | −0.0157700 | ||||||||
\(847\) | 3.48255 | 0.119662 | ||||||||
\(848\) | 16.1571 | 0.554837 | ||||||||
\(849\) | −9.06800 | −0.311213 | ||||||||
\(850\) | −0.626983 | −0.0215053 | ||||||||
\(851\) | −44.0106 | −1.50866 | ||||||||
\(852\) | 24.6402 | 0.844160 | ||||||||
\(853\) | −2.94671 | −0.100893 | −0.0504466 | − | 0.998727i | \(-0.516064\pi\) | ||||
−0.0504466 | + | 0.998727i | \(0.516064\pi\) | |||||||
\(854\) | −0.568714 | −0.0194610 | ||||||||
\(855\) | −3.16026 | −0.108079 | ||||||||
\(856\) | −2.26863 | −0.0775402 | ||||||||
\(857\) | 48.8117 | 1.66738 | 0.833688 | − | 0.552235i | \(-0.186225\pi\) | ||||
0.833688 | + | 0.552235i | \(0.186225\pi\) | |||||||
\(858\) | −0.308431 | −0.0105297 | ||||||||
\(859\) | 56.6764 | 1.93377 | 0.966887 | − | 0.255205i | \(-0.0821429\pi\) | ||||
0.966887 | + | 0.255205i | \(0.0821429\pi\) | |||||||
\(860\) | −17.4443 | −0.594847 | ||||||||
\(861\) | −2.82714 | −0.0963488 | ||||||||
\(862\) | −3.67342 | −0.125117 | ||||||||
\(863\) | −14.2424 | −0.484817 | −0.242408 | − | 0.970174i | \(-0.577937\pi\) | ||||
−0.242408 | + | 0.970174i | \(0.577937\pi\) | |||||||
\(864\) | −1.64709 | −0.0560352 | ||||||||
\(865\) | −3.60715 | −0.122647 | ||||||||
\(866\) | 0.0615616 | 0.00209195 | ||||||||
\(867\) | 3.33284 | 0.113189 | ||||||||
\(868\) | −1.13458 | −0.0385101 | ||||||||
\(869\) | −8.41183 | −0.285352 | ||||||||
\(870\) | 0.582866 | 0.0197610 | ||||||||
\(871\) | 6.43070 | 0.217896 | ||||||||
\(872\) | 1.47835 | 0.0500633 | ||||||||
\(873\) | 1.30778 | 0.0442616 | ||||||||
\(874\) | −2.35368 | −0.0796144 | ||||||||
\(875\) | −0.572827 | −0.0193651 | ||||||||
\(876\) | 32.1425 | 1.08600 | ||||||||
\(877\) | 20.6287 | 0.696582 | 0.348291 | − | 0.937386i | \(-0.386762\pi\) | ||||
0.348291 | + | 0.937386i | \(0.386762\pi\) | |||||||
\(878\) | 2.36932 | 0.0799607 | ||||||||
\(879\) | −4.86408 | −0.164061 | ||||||||
\(880\) | −8.61632 | −0.290456 | ||||||||
\(881\) | 18.0664 | 0.608671 | 0.304336 | − | 0.952565i | \(-0.401566\pi\) | ||||
0.304336 | + | 0.952565i | \(0.401566\pi\) | |||||||
\(882\) | 0.927693 | 0.0312371 | ||||||||
\(883\) | 22.8825 | 0.770057 | 0.385029 | − | 0.922905i | \(-0.374192\pi\) | ||||
0.385029 | + | 0.922905i | \(0.374192\pi\) | |||||||
\(884\) | 8.93121 | 0.300389 | ||||||||
\(885\) | −7.12913 | −0.239643 | ||||||||
\(886\) | −0.809404 | −0.0271925 | ||||||||
\(887\) | 10.8095 | 0.362947 | 0.181474 | − | 0.983396i | \(-0.441913\pi\) | ||||
0.181474 | + | 0.983396i | \(0.441913\pi\) | |||||||
\(888\) | 4.54781 | 0.152614 | ||||||||
\(889\) | −5.82906 | −0.195500 | ||||||||
\(890\) | −2.45098 | −0.0821570 | ||||||||
\(891\) | −2.21820 | −0.0743125 | ||||||||
\(892\) | 26.6210 | 0.891338 | ||||||||
\(893\) | −10.4251 | −0.348864 | ||||||||
\(894\) | 0.156486 | 0.00523367 | ||||||||
\(895\) | 2.39316 | 0.0799944 | ||||||||
\(896\) | −2.48753 | −0.0831026 | ||||||||
\(897\) | 5.35633 | 0.178843 | ||||||||
\(898\) | −3.61329 | −0.120577 | ||||||||
\(899\) | 4.19191 | 0.139808 | ||||||||
\(900\) | −1.98067 | −0.0660222 | ||||||||
\(901\) | 18.7560 | 0.624854 | ||||||||
\(902\) | 1.52224 | 0.0506849 | ||||||||
\(903\) | −5.04506 | −0.167889 | ||||||||
\(904\) | 7.49878 | 0.249406 | ||||||||
\(905\) | −12.1618 | −0.404271 | ||||||||
\(906\) | −2.34995 | −0.0780718 | ||||||||
\(907\) | 31.4214 | 1.04333 | 0.521664 | − | 0.853151i | \(-0.325311\pi\) | ||||
0.521664 | + | 0.853151i | \(0.325311\pi\) | |||||||
\(908\) | 53.4301 | 1.77314 | ||||||||
\(909\) | −15.0836 | −0.500293 | ||||||||
\(910\) | −0.0796491 | −0.00264034 | ||||||||
\(911\) | 44.8119 | 1.48468 | 0.742342 | − | 0.670021i | \(-0.233715\pi\) | ||||
0.742342 | + | 0.670021i | \(0.233715\pi\) | |||||||
\(912\) | −12.2756 | −0.406486 | ||||||||
\(913\) | 18.0795 | 0.598345 | ||||||||
\(914\) | 0.166487 | 0.00550691 | ||||||||
\(915\) | −7.14025 | −0.236049 | ||||||||
\(916\) | 5.70208 | 0.188402 | ||||||||
\(917\) | −0.791334 | −0.0261321 | ||||||||
\(918\) | −0.626983 | −0.0206935 | ||||||||
\(919\) | 25.4826 | 0.840594 | 0.420297 | − | 0.907387i | \(-0.361926\pi\) | ||||
0.420297 | + | 0.907387i | \(0.361926\pi\) | |||||||
\(920\) | −2.96470 | −0.0977432 | ||||||||
\(921\) | 10.5924 | 0.349033 | ||||||||
\(922\) | −1.84790 | −0.0608575 | ||||||||
\(923\) | 12.4404 | 0.409480 | ||||||||
\(924\) | −2.51673 | −0.0827942 | ||||||||
\(925\) | 8.21655 | 0.270158 | ||||||||
\(926\) | −4.32970 | −0.142283 | ||||||||
\(927\) | −13.1610 | −0.432264 | ||||||||
\(928\) | 6.90445 | 0.226650 | ||||||||
\(929\) | 42.5100 | 1.39471 | 0.697354 | − | 0.716727i | \(-0.254361\pi\) | ||||
0.697354 | + | 0.716727i | \(0.254361\pi\) | |||||||
\(930\) | 0.139045 | 0.00455948 | ||||||||
\(931\) | 21.0848 | 0.691028 | ||||||||
\(932\) | 53.4689 | 1.75143 | ||||||||
\(933\) | −30.8772 | −1.01087 | ||||||||
\(934\) | −0.225401 | −0.00737534 | ||||||||
\(935\) | −10.0023 | −0.327110 | ||||||||
\(936\) | −0.553494 | −0.0180915 | ||||||||
\(937\) | −46.2539 | −1.51105 | −0.755524 | − | 0.655121i | \(-0.772618\pi\) | ||||
−0.755524 | + | 0.655121i | \(0.772618\pi\) | |||||||
\(938\) | −0.512199 | −0.0167239 | ||||||||
\(939\) | −4.59814 | −0.150055 | ||||||||
\(940\) | −6.53386 | −0.213111 | ||||||||
\(941\) | −43.3103 | −1.41187 | −0.705937 | − | 0.708274i | \(-0.749474\pi\) | ||||
−0.705937 | + | 0.708274i | \(0.749474\pi\) | |||||||
\(942\) | 0.530381 | 0.0172807 | ||||||||
\(943\) | −26.4358 | −0.860867 | ||||||||
\(944\) | −27.6922 | −0.901304 | ||||||||
\(945\) | −0.572827 | −0.0186341 | ||||||||
\(946\) | 2.71644 | 0.0883192 | ||||||||
\(947\) | 8.06709 | 0.262145 | 0.131073 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131073 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(948\) | −7.51105 | −0.243948 | ||||||||
\(949\) | 16.2281 | 0.526788 | ||||||||
\(950\) | 0.439420 | 0.0142567 | ||||||||
\(951\) | 7.73196 | 0.250726 | ||||||||
\(952\) | −1.42967 | −0.0463358 | ||||||||
\(953\) | −49.9390 | −1.61768 | −0.808842 | − | 0.588027i | \(-0.799905\pi\) | ||||
−0.808842 | + | 0.588027i | \(0.799905\pi\) | |||||||
\(954\) | −0.578361 | −0.0187251 | ||||||||
\(955\) | −26.6319 | −0.861789 | ||||||||
\(956\) | −18.8896 | −0.610935 | ||||||||
\(957\) | 9.29849 | 0.300578 | ||||||||
\(958\) | −2.40265 | −0.0776262 | ||||||||
\(959\) | −0.0544718 | −0.00175899 | ||||||||
\(960\) | −7.53972 | −0.243344 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 1.14247 | 0.0368348 | ||||||||
\(963\) | −4.09875 | −0.132080 | ||||||||
\(964\) | 43.2618 | 1.39337 | ||||||||
\(965\) | −19.3118 | −0.621670 | ||||||||
\(966\) | −0.426627 | −0.0137265 | ||||||||
\(967\) | −12.6369 | −0.406377 | −0.203188 | − | 0.979140i | \(-0.565130\pi\) | ||||
−0.203188 | + | 0.979140i | \(0.565130\pi\) | |||||||
\(968\) | −3.36501 | −0.108156 | ||||||||
\(969\) | −14.2502 | −0.457783 | ||||||||
\(970\) | −0.181841 | −0.00583855 | ||||||||
\(971\) | −14.5601 | −0.467255 | −0.233628 | − | 0.972326i | \(-0.575060\pi\) | ||||
−0.233628 | + | 0.972326i | \(0.575060\pi\) | |||||||
\(972\) | −1.98067 | −0.0635299 | ||||||||
\(973\) | 8.00896 | 0.256756 | ||||||||
\(974\) | 5.14416 | 0.164830 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −27.7354 | −0.887788 | ||||||||
\(977\) | 14.8551 | 0.475257 | 0.237628 | − | 0.971356i | \(-0.423630\pi\) | ||||
0.237628 | + | 0.971356i | \(0.423630\pi\) | |||||||
\(978\) | −2.02698 | −0.0648157 | ||||||||
\(979\) | −39.1006 | −1.24966 | ||||||||
\(980\) | 13.2147 | 0.422130 | ||||||||
\(981\) | 2.67095 | 0.0852768 | ||||||||
\(982\) | 2.94040 | 0.0938318 | ||||||||
\(983\) | −0.0118985 | −0.000379504 0 | −0.000189752 | − | 1.00000i | \(-0.500060\pi\) | ||||
−0.000189752 | 1.00000i | \(0.500060\pi\) | ||||||||
\(984\) | 2.73172 | 0.0870842 | ||||||||
\(985\) | 10.7291 | 0.341859 | ||||||||
\(986\) | 2.62826 | 0.0837007 | ||||||||
\(987\) | −1.88965 | −0.0601484 | ||||||||
\(988\) | −6.25942 | −0.199139 | ||||||||
\(989\) | −47.1749 | −1.50007 | ||||||||
\(990\) | 0.308431 | 0.00980258 | ||||||||
\(991\) | 43.1316 | 1.37012 | 0.685060 | − | 0.728486i | \(-0.259776\pi\) | ||||
0.685060 | + | 0.728486i | \(0.259776\pi\) | |||||||
\(992\) | 1.64709 | 0.0522952 | ||||||||
\(993\) | 1.86476 | 0.0591764 | ||||||||
\(994\) | −0.990864 | −0.0314283 | ||||||||
\(995\) | −1.32078 | −0.0418716 | ||||||||
\(996\) | 16.1435 | 0.511526 | ||||||||
\(997\) | −34.5009 | −1.09265 | −0.546327 | − | 0.837572i | \(-0.683974\pi\) | ||||
−0.546327 | + | 0.837572i | \(0.683974\pi\) | |||||||
\(998\) | 5.08108 | 0.160839 | ||||||||
\(999\) | 8.21655 | 0.259960 |
(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 | 6045.2.a.u.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.u.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |