Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.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: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59547 | −1.83528 | −0.917638 | − | 0.397417i | \(-0.869907\pi\) | ||||
−0.917638 | + | 0.397417i | \(0.869907\pi\) | |||||||
\(3\) | 1.19515 | 0.690021 | 0.345010 | − | 0.938599i | \(-0.387875\pi\) | ||||
0.345010 | + | 0.938599i | \(0.387875\pi\) | |||||||
\(4\) | 4.73648 | 2.36824 | ||||||||
\(5\) | −3.51521 | −1.57205 | −0.786025 | − | 0.618195i | \(-0.787864\pi\) | ||||
−0.786025 | + | 0.618195i | \(0.787864\pi\) | |||||||
\(6\) | −3.10198 | −1.26638 | ||||||||
\(7\) | 1.20876 | 0.456869 | 0.228435 | − | 0.973559i | \(-0.426639\pi\) | ||||
0.228435 | + | 0.973559i | \(0.426639\pi\) | |||||||
\(8\) | −7.10244 | −2.51109 | ||||||||
\(9\) | −1.57161 | −0.523871 | ||||||||
\(10\) | 9.12363 | 2.88515 | ||||||||
\(11\) | 4.18691 | 1.26240 | 0.631201 | − | 0.775620i | \(-0.282562\pi\) | ||||
0.631201 | + | 0.775620i | \(0.282562\pi\) | |||||||
\(12\) | 5.66080 | 1.63413 | ||||||||
\(13\) | −4.74438 | −1.31586 | −0.657928 | − | 0.753081i | \(-0.728567\pi\) | ||||
−0.657928 | + | 0.753081i | \(0.728567\pi\) | |||||||
\(14\) | −3.13731 | −0.838481 | ||||||||
\(15\) | −4.20121 | −1.08475 | ||||||||
\(16\) | 8.96125 | 2.24031 | ||||||||
\(17\) | 1.27570 | 0.309402 | 0.154701 | − | 0.987961i | \(-0.450559\pi\) | ||||
0.154701 | + | 0.987961i | \(0.450559\pi\) | |||||||
\(18\) | 4.07908 | 0.961449 | ||||||||
\(19\) | 3.12310 | 0.716489 | 0.358244 | − | 0.933628i | \(-0.383376\pi\) | ||||
0.358244 | + | 0.933628i | \(0.383376\pi\) | |||||||
\(20\) | −16.6497 | −3.72299 | ||||||||
\(21\) | 1.44465 | 0.315249 | ||||||||
\(22\) | −10.8670 | −2.31685 | ||||||||
\(23\) | 6.80267 | 1.41845 | 0.709227 | − | 0.704980i | \(-0.249044\pi\) | ||||
0.709227 | + | 0.704980i | \(0.249044\pi\) | |||||||
\(24\) | −8.48849 | −1.73271 | ||||||||
\(25\) | 7.35671 | 1.47134 | ||||||||
\(26\) | 12.3139 | 2.41496 | ||||||||
\(27\) | −5.46377 | −1.05150 | ||||||||
\(28\) | 5.72527 | 1.08198 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 10.9041 | 1.99081 | ||||||||
\(31\) | −3.50259 | −0.629083 | −0.314542 | − | 0.949244i | \(-0.601851\pi\) | ||||
−0.314542 | + | 0.949244i | \(0.601851\pi\) | |||||||
\(32\) | −9.05377 | −1.60050 | ||||||||
\(33\) | 5.00399 | 0.871083 | ||||||||
\(34\) | −3.31104 | −0.567839 | ||||||||
\(35\) | −4.24906 | −0.718221 | ||||||||
\(36\) | −7.44391 | −1.24065 | ||||||||
\(37\) | −8.65626 | −1.42308 | −0.711540 | − | 0.702645i | \(-0.752002\pi\) | ||||
−0.711540 | + | 0.702645i | \(0.752002\pi\) | |||||||
\(38\) | −8.10592 | −1.31495 | ||||||||
\(39\) | −5.67025 | −0.907967 | ||||||||
\(40\) | 24.9666 | 3.94756 | ||||||||
\(41\) | 10.0102 | 1.56334 | 0.781669 | − | 0.623694i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623694i | \(0.214369\pi\) | |||||||
\(42\) | −3.74956 | −0.578569 | ||||||||
\(43\) | −4.89375 | −0.746290 | −0.373145 | − | 0.927773i | \(-0.621721\pi\) | ||||
−0.373145 | + | 0.927773i | \(0.621721\pi\) | |||||||
\(44\) | 19.8312 | 2.98967 | ||||||||
\(45\) | 5.52456 | 0.823552 | ||||||||
\(46\) | −17.6561 | −2.60326 | ||||||||
\(47\) | −2.81653 | −0.410833 | −0.205417 | − | 0.978675i | \(-0.565855\pi\) | ||||
−0.205417 | + | 0.978675i | \(0.565855\pi\) | |||||||
\(48\) | 10.7100 | 1.54586 | ||||||||
\(49\) | −5.53889 | −0.791270 | ||||||||
\(50\) | −19.0941 | −2.70032 | ||||||||
\(51\) | 1.52465 | 0.213494 | ||||||||
\(52\) | −22.4717 | −3.11626 | ||||||||
\(53\) | 2.58742 | 0.355410 | 0.177705 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177705 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(54\) | 14.1811 | 1.92980 | ||||||||
\(55\) | −14.7179 | −1.98456 | ||||||||
\(56\) | −8.58517 | −1.14724 | ||||||||
\(57\) | 3.73258 | 0.494392 | ||||||||
\(58\) | 2.59547 | 0.340802 | ||||||||
\(59\) | −5.11804 | −0.666312 | −0.333156 | − | 0.942872i | \(-0.608114\pi\) | ||||
−0.333156 | + | 0.942872i | \(0.608114\pi\) | |||||||
\(60\) | −19.8989 | −2.56894 | ||||||||
\(61\) | 12.2315 | 1.56608 | 0.783040 | − | 0.621972i | \(-0.213668\pi\) | ||||
0.783040 | + | 0.621972i | \(0.213668\pi\) | |||||||
\(62\) | 9.09087 | 1.15454 | ||||||||
\(63\) | −1.89971 | −0.239341 | ||||||||
\(64\) | 5.57633 | 0.697041 | ||||||||
\(65\) | 16.6775 | 2.06859 | ||||||||
\(66\) | −12.9877 | −1.59868 | ||||||||
\(67\) | −6.35287 | −0.776127 | −0.388063 | − | 0.921633i | \(-0.626856\pi\) | ||||
−0.388063 | + | 0.921633i | \(0.626856\pi\) | |||||||
\(68\) | 6.04232 | 0.732738 | ||||||||
\(69\) | 8.13022 | 0.978763 | ||||||||
\(70\) | 11.0283 | 1.31813 | ||||||||
\(71\) | 1.20473 | 0.142976 | 0.0714878 | − | 0.997441i | \(-0.477225\pi\) | ||||
0.0714878 | + | 0.997441i | \(0.477225\pi\) | |||||||
\(72\) | 11.1623 | 1.31549 | ||||||||
\(73\) | −11.6941 | −1.36869 | −0.684346 | − | 0.729158i | \(-0.739912\pi\) | ||||
−0.684346 | + | 0.729158i | \(0.739912\pi\) | |||||||
\(74\) | 22.4671 | 2.61175 | ||||||||
\(75\) | 8.79238 | 1.01526 | ||||||||
\(76\) | 14.7925 | 1.69682 | ||||||||
\(77\) | 5.06098 | 0.576752 | ||||||||
\(78\) | 14.7170 | 1.66637 | ||||||||
\(79\) | 4.93390 | 0.555107 | 0.277554 | − | 0.960710i | \(-0.410476\pi\) | ||||
0.277554 | + | 0.960710i | \(0.410476\pi\) | |||||||
\(80\) | −31.5007 | −3.52188 | ||||||||
\(81\) | −1.81519 | −0.201687 | ||||||||
\(82\) | −25.9813 | −2.86916 | ||||||||
\(83\) | −2.91087 | −0.319509 | −0.159755 | − | 0.987157i | \(-0.551070\pi\) | ||||
−0.159755 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(84\) | 6.84257 | 0.746585 | ||||||||
\(85\) | −4.48435 | −0.486396 | ||||||||
\(86\) | 12.7016 | 1.36965 | ||||||||
\(87\) | −1.19515 | −0.128134 | ||||||||
\(88\) | −29.7373 | −3.17001 | ||||||||
\(89\) | 5.38970 | 0.571307 | 0.285654 | − | 0.958333i | \(-0.407789\pi\) | ||||
0.285654 | + | 0.958333i | \(0.407789\pi\) | |||||||
\(90\) | −14.3388 | −1.51145 | ||||||||
\(91\) | −5.73483 | −0.601174 | ||||||||
\(92\) | 32.2207 | 3.35924 | ||||||||
\(93\) | −4.18612 | −0.434080 | ||||||||
\(94\) | 7.31023 | 0.753992 | ||||||||
\(95\) | −10.9784 | −1.12636 | ||||||||
\(96\) | −10.8206 | −1.10438 | ||||||||
\(97\) | 19.1506 | 1.94445 | 0.972224 | − | 0.234051i | \(-0.0751981\pi\) | ||||
0.972224 | + | 0.234051i | \(0.0751981\pi\) | |||||||
\(98\) | 14.3760 | 1.45220 | ||||||||
\(99\) | −6.58021 | −0.661336 | ||||||||
\(100\) | 34.8449 | 3.48449 | ||||||||
\(101\) | −7.35382 | −0.731732 | −0.365866 | − | 0.930667i | \(-0.619227\pi\) | ||||
−0.365866 | + | 0.930667i | \(0.619227\pi\) | |||||||
\(102\) | −3.95719 | −0.391820 | ||||||||
\(103\) | −17.3093 | −1.70554 | −0.852770 | − | 0.522287i | \(-0.825079\pi\) | ||||
−0.852770 | + | 0.522287i | \(0.825079\pi\) | |||||||
\(104\) | 33.6967 | 3.30423 | ||||||||
\(105\) | −5.07826 | −0.495588 | ||||||||
\(106\) | −6.71558 | −0.652275 | ||||||||
\(107\) | −0.485892 | −0.0469730 | −0.0234865 | − | 0.999724i | \(-0.507477\pi\) | ||||
−0.0234865 | + | 0.999724i | \(0.507477\pi\) | |||||||
\(108\) | −25.8790 | −2.49021 | ||||||||
\(109\) | 16.1404 | 1.54597 | 0.772984 | − | 0.634426i | \(-0.218763\pi\) | ||||
0.772984 | + | 0.634426i | \(0.218763\pi\) | |||||||
\(110\) | 38.1998 | 3.64221 | ||||||||
\(111\) | −10.3455 | −0.981955 | ||||||||
\(112\) | 10.8320 | 1.02353 | ||||||||
\(113\) | −3.56541 | −0.335405 | −0.167703 | − | 0.985838i | \(-0.553635\pi\) | ||||
−0.167703 | + | 0.985838i | \(0.553635\pi\) | |||||||
\(114\) | −9.68780 | −0.907346 | ||||||||
\(115\) | −23.9128 | −2.22988 | ||||||||
\(116\) | −4.73648 | −0.439771 | ||||||||
\(117\) | 7.45634 | 0.689339 | ||||||||
\(118\) | 13.2837 | 1.22287 | ||||||||
\(119\) | 1.54202 | 0.141356 | ||||||||
\(120\) | 29.8388 | 2.72390 | ||||||||
\(121\) | 6.53023 | 0.593657 | ||||||||
\(122\) | −31.7464 | −2.87419 | ||||||||
\(123\) | 11.9638 | 1.07874 | ||||||||
\(124\) | −16.5899 | −1.48982 | ||||||||
\(125\) | −8.28432 | −0.740972 | ||||||||
\(126\) | 4.93064 | 0.439256 | ||||||||
\(127\) | 0.342143 | 0.0303603 | 0.0151802 | − | 0.999885i | \(-0.495168\pi\) | ||||
0.0151802 | + | 0.999885i | \(0.495168\pi\) | |||||||
\(128\) | 3.63435 | 0.321234 | ||||||||
\(129\) | −5.84877 | −0.514956 | ||||||||
\(130\) | −43.2860 | −3.79643 | ||||||||
\(131\) | −4.78937 | −0.418450 | −0.209225 | − | 0.977868i | \(-0.567094\pi\) | ||||
−0.209225 | + | 0.977868i | \(0.567094\pi\) | |||||||
\(132\) | 23.7013 | 2.06293 | ||||||||
\(133\) | 3.77509 | 0.327342 | ||||||||
\(134\) | 16.4887 | 1.42441 | ||||||||
\(135\) | 19.2063 | 1.65302 | ||||||||
\(136\) | −9.06058 | −0.776938 | ||||||||
\(137\) | 4.11028 | 0.351165 | 0.175582 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175582 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(138\) | −21.1018 | −1.79630 | ||||||||
\(139\) | 18.7856 | 1.59337 | 0.796686 | − | 0.604393i | \(-0.206584\pi\) | ||||
0.796686 | + | 0.604393i | \(0.206584\pi\) | |||||||
\(140\) | −20.1255 | −1.70092 | ||||||||
\(141\) | −3.36618 | −0.283483 | ||||||||
\(142\) | −3.12685 | −0.262400 | ||||||||
\(143\) | −19.8643 | −1.66114 | ||||||||
\(144\) | −14.0836 | −1.17364 | ||||||||
\(145\) | 3.51521 | 0.291922 | ||||||||
\(146\) | 30.3517 | 2.51193 | ||||||||
\(147\) | −6.61981 | −0.545993 | ||||||||
\(148\) | −41.0002 | −3.37019 | ||||||||
\(149\) | −2.75537 | −0.225729 | −0.112864 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112864 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(150\) | −22.8204 | −1.86327 | ||||||||
\(151\) | 8.75549 | 0.712512 | 0.356256 | − | 0.934388i | \(-0.384053\pi\) | ||||
0.356256 | + | 0.934388i | \(0.384053\pi\) | |||||||
\(152\) | −22.1817 | −1.79917 | ||||||||
\(153\) | −2.00491 | −0.162087 | ||||||||
\(154\) | −13.1356 | −1.05850 | ||||||||
\(155\) | 12.3123 | 0.988950 | ||||||||
\(156\) | −26.8570 | −2.15028 | ||||||||
\(157\) | 6.31833 | 0.504258 | 0.252129 | − | 0.967694i | \(-0.418869\pi\) | ||||
0.252129 | + | 0.967694i | \(0.418869\pi\) | |||||||
\(158\) | −12.8058 | −1.01877 | ||||||||
\(159\) | 3.09236 | 0.245240 | ||||||||
\(160\) | 31.8259 | 2.51606 | ||||||||
\(161\) | 8.22281 | 0.648049 | ||||||||
\(162\) | 4.71126 | 0.370152 | ||||||||
\(163\) | −1.53713 | −0.120397 | −0.0601986 | − | 0.998186i | \(-0.519173\pi\) | ||||
−0.0601986 | + | 0.998186i | \(0.519173\pi\) | |||||||
\(164\) | 47.4133 | 3.70236 | ||||||||
\(165\) | −17.5901 | −1.36939 | ||||||||
\(166\) | 7.55508 | 0.586388 | ||||||||
\(167\) | 17.0137 | 1.31656 | 0.658279 | − | 0.752774i | \(-0.271285\pi\) | ||||
0.658279 | + | 0.752774i | \(0.271285\pi\) | |||||||
\(168\) | −10.2606 | −0.791620 | ||||||||
\(169\) | 9.50917 | 0.731475 | ||||||||
\(170\) | 11.6390 | 0.892671 | ||||||||
\(171\) | −4.90831 | −0.375348 | ||||||||
\(172\) | −23.1791 | −1.76739 | ||||||||
\(173\) | 12.8909 | 0.980078 | 0.490039 | − | 0.871700i | \(-0.336983\pi\) | ||||
0.490039 | + | 0.871700i | \(0.336983\pi\) | |||||||
\(174\) | 3.10198 | 0.235161 | ||||||||
\(175\) | 8.89251 | 0.672211 | ||||||||
\(176\) | 37.5199 | 2.82817 | ||||||||
\(177\) | −6.11683 | −0.459769 | ||||||||
\(178\) | −13.9888 | −1.04851 | ||||||||
\(179\) | 16.4353 | 1.22843 | 0.614215 | − | 0.789139i | \(-0.289473\pi\) | ||||
0.614215 | + | 0.789139i | \(0.289473\pi\) | |||||||
\(180\) | 26.1669 | 1.95037 | ||||||||
\(181\) | −7.62309 | −0.566620 | −0.283310 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283310 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(182\) | 14.8846 | 1.10332 | ||||||||
\(183\) | 14.6184 | 1.08063 | ||||||||
\(184\) | −48.3156 | −3.56187 | ||||||||
\(185\) | 30.4286 | 2.23715 | ||||||||
\(186\) | 10.8650 | 0.796657 | ||||||||
\(187\) | 5.34124 | 0.390590 | ||||||||
\(188\) | −13.3404 | −0.972951 | ||||||||
\(189\) | −6.60440 | −0.480399 | ||||||||
\(190\) | 28.4940 | 2.06717 | ||||||||
\(191\) | −7.83937 | −0.567237 | −0.283619 | − | 0.958937i | \(-0.591535\pi\) | ||||
−0.283619 | + | 0.958937i | \(0.591535\pi\) | |||||||
\(192\) | 6.66455 | 0.480973 | ||||||||
\(193\) | −8.10380 | −0.583324 | −0.291662 | − | 0.956521i | \(-0.594208\pi\) | ||||
−0.291662 | + | 0.956521i | \(0.594208\pi\) | |||||||
\(194\) | −49.7048 | −3.56860 | ||||||||
\(195\) | 19.9321 | 1.42737 | ||||||||
\(196\) | −26.2348 | −1.87392 | ||||||||
\(197\) | 22.1352 | 1.57706 | 0.788532 | − | 0.614994i | \(-0.210841\pi\) | ||||
0.788532 | + | 0.614994i | \(0.210841\pi\) | |||||||
\(198\) | 17.0788 | 1.21373 | ||||||||
\(199\) | −20.1335 | −1.42722 | −0.713612 | − | 0.700541i | \(-0.752942\pi\) | ||||
−0.713612 | + | 0.700541i | \(0.752942\pi\) | |||||||
\(200\) | −52.2506 | −3.69468 | ||||||||
\(201\) | −7.59264 | −0.535544 | ||||||||
\(202\) | 19.0866 | 1.34293 | ||||||||
\(203\) | −1.20876 | −0.0848385 | ||||||||
\(204\) | 7.22148 | 0.505605 | ||||||||
\(205\) | −35.1881 | −2.45765 | ||||||||
\(206\) | 44.9259 | 3.13014 | ||||||||
\(207\) | −10.6912 | −0.743088 | ||||||||
\(208\) | −42.5156 | −2.94793 | ||||||||
\(209\) | 13.0761 | 0.904496 | ||||||||
\(210\) | 13.1805 | 0.909540 | ||||||||
\(211\) | −21.8929 | −1.50717 | −0.753583 | − | 0.657352i | \(-0.771676\pi\) | ||||
−0.753583 | + | 0.657352i | \(0.771676\pi\) | |||||||
\(212\) | 12.2553 | 0.841695 | ||||||||
\(213\) | 1.43984 | 0.0986562 | ||||||||
\(214\) | 1.26112 | 0.0862084 | ||||||||
\(215\) | 17.2026 | 1.17321 | ||||||||
\(216\) | 38.8061 | 2.64042 | ||||||||
\(217\) | −4.23380 | −0.287409 | ||||||||
\(218\) | −41.8919 | −2.83728 | ||||||||
\(219\) | −13.9762 | −0.944425 | ||||||||
\(220\) | −69.7109 | −4.69990 | ||||||||
\(221\) | −6.05240 | −0.407129 | ||||||||
\(222\) | 26.8516 | 1.80216 | ||||||||
\(223\) | −2.58770 | −0.173285 | −0.0866426 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866426 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(224\) | −10.9439 | −0.731218 | ||||||||
\(225\) | −11.5619 | −0.770794 | ||||||||
\(226\) | 9.25391 | 0.615561 | ||||||||
\(227\) | −1.70962 | −0.113471 | −0.0567357 | − | 0.998389i | \(-0.518069\pi\) | ||||
−0.0567357 | + | 0.998389i | \(0.518069\pi\) | |||||||
\(228\) | 17.6793 | 1.17084 | ||||||||
\(229\) | 0.874116 | 0.0577632 | 0.0288816 | − | 0.999583i | \(-0.490805\pi\) | ||||
0.0288816 | + | 0.999583i | \(0.490805\pi\) | |||||||
\(230\) | 62.0651 | 4.09245 | ||||||||
\(231\) | 6.04864 | 0.397971 | ||||||||
\(232\) | 7.10244 | 0.466298 | ||||||||
\(233\) | −21.8141 | −1.42909 | −0.714543 | − | 0.699591i | \(-0.753366\pi\) | ||||
−0.714543 | + | 0.699591i | \(0.753366\pi\) | |||||||
\(234\) | −19.3527 | −1.26513 | ||||||||
\(235\) | 9.90070 | 0.645850 | ||||||||
\(236\) | −24.2415 | −1.57798 | ||||||||
\(237\) | 5.89676 | 0.383035 | ||||||||
\(238\) | −4.00226 | −0.259428 | ||||||||
\(239\) | 9.85174 | 0.637256 | 0.318628 | − | 0.947880i | \(-0.396778\pi\) | ||||
0.318628 | + | 0.947880i | \(0.396778\pi\) | |||||||
\(240\) | −37.6481 | −2.43017 | ||||||||
\(241\) | −4.52319 | −0.291364 | −0.145682 | − | 0.989331i | \(-0.546538\pi\) | ||||
−0.145682 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(242\) | −16.9490 | −1.08952 | ||||||||
\(243\) | 14.2219 | 0.912334 | ||||||||
\(244\) | 57.9340 | 3.70885 | ||||||||
\(245\) | 19.4704 | 1.24392 | ||||||||
\(246\) | −31.0516 | −1.97978 | ||||||||
\(247\) | −14.8172 | −0.942795 | ||||||||
\(248\) | 24.8769 | 1.57969 | ||||||||
\(249\) | −3.47893 | −0.220468 | ||||||||
\(250\) | 21.5017 | 1.35989 | ||||||||
\(251\) | 19.4279 | 1.22628 | 0.613139 | − | 0.789975i | \(-0.289906\pi\) | ||||
0.613139 | + | 0.789975i | \(0.289906\pi\) | |||||||
\(252\) | −8.99792 | −0.566816 | ||||||||
\(253\) | 28.4822 | 1.79066 | ||||||||
\(254\) | −0.888023 | −0.0557195 | ||||||||
\(255\) | −5.35947 | −0.335623 | ||||||||
\(256\) | −20.5855 | −1.28659 | ||||||||
\(257\) | −6.31920 | −0.394181 | −0.197090 | − | 0.980385i | \(-0.563149\pi\) | ||||
−0.197090 | + | 0.980385i | \(0.563149\pi\) | |||||||
\(258\) | 15.1803 | 0.945086 | ||||||||
\(259\) | −10.4634 | −0.650162 | ||||||||
\(260\) | 78.9926 | 4.89891 | ||||||||
\(261\) | 1.57161 | 0.0972805 | ||||||||
\(262\) | 12.4307 | 0.767970 | ||||||||
\(263\) | −11.4910 | −0.708568 | −0.354284 | − | 0.935138i | \(-0.615275\pi\) | ||||
−0.354284 | + | 0.935138i | \(0.615275\pi\) | |||||||
\(264\) | −35.5406 | −2.18737 | ||||||||
\(265\) | −9.09533 | −0.558722 | ||||||||
\(266\) | −9.79814 | −0.600762 | ||||||||
\(267\) | 6.44151 | 0.394214 | ||||||||
\(268\) | −30.0902 | −1.83805 | ||||||||
\(269\) | −25.2203 | −1.53771 | −0.768854 | − | 0.639424i | \(-0.779173\pi\) | ||||
−0.768854 | + | 0.639424i | \(0.779173\pi\) | |||||||
\(270\) | −49.8494 | −3.03374 | ||||||||
\(271\) | −21.2041 | −1.28806 | −0.644029 | − | 0.765001i | \(-0.722739\pi\) | ||||
−0.644029 | + | 0.765001i | \(0.722739\pi\) | |||||||
\(272\) | 11.4318 | 0.693158 | ||||||||
\(273\) | −6.85399 | −0.414822 | ||||||||
\(274\) | −10.6681 | −0.644484 | ||||||||
\(275\) | 30.8019 | 1.85742 | ||||||||
\(276\) | 38.5086 | 2.31794 | ||||||||
\(277\) | −1.00000 | −0.0600842 | ||||||||
\(278\) | −48.7575 | −2.92428 | ||||||||
\(279\) | 5.50472 | 0.329559 | ||||||||
\(280\) | 30.1787 | 1.80352 | ||||||||
\(281\) | 18.9231 | 1.12885 | 0.564427 | − | 0.825483i | \(-0.309097\pi\) | ||||
0.564427 | + | 0.825483i | \(0.309097\pi\) | |||||||
\(282\) | 8.73682 | 0.520270 | ||||||||
\(283\) | 22.6363 | 1.34559 | 0.672793 | − | 0.739830i | \(-0.265094\pi\) | ||||
0.672793 | + | 0.739830i | \(0.265094\pi\) | |||||||
\(284\) | 5.70619 | 0.338600 | ||||||||
\(285\) | −13.1208 | −0.777209 | ||||||||
\(286\) | 51.5573 | 3.04864 | ||||||||
\(287\) | 12.1000 | 0.714241 | ||||||||
\(288\) | 14.2290 | 0.838454 | ||||||||
\(289\) | −15.3726 | −0.904270 | ||||||||
\(290\) | −9.12363 | −0.535758 | ||||||||
\(291\) | 22.8879 | 1.34171 | ||||||||
\(292\) | −55.3888 | −3.24139 | ||||||||
\(293\) | −31.4878 | −1.83954 | −0.919769 | − | 0.392460i | \(-0.871624\pi\) | ||||
−0.919769 | + | 0.392460i | \(0.871624\pi\) | |||||||
\(294\) | 17.1815 | 1.00205 | ||||||||
\(295\) | 17.9910 | 1.04748 | ||||||||
\(296\) | 61.4806 | 3.57349 | ||||||||
\(297\) | −22.8763 | −1.32742 | ||||||||
\(298\) | 7.15149 | 0.414275 | ||||||||
\(299\) | −32.2745 | −1.86648 | ||||||||
\(300\) | 41.6449 | 2.40437 | ||||||||
\(301\) | −5.91539 | −0.340957 | ||||||||
\(302\) | −22.7246 | −1.30766 | ||||||||
\(303\) | −8.78892 | −0.504910 | ||||||||
\(304\) | 27.9869 | 1.60516 | ||||||||
\(305\) | −42.9962 | −2.46195 | ||||||||
\(306\) | 5.20368 | 0.297475 | ||||||||
\(307\) | −4.93345 | −0.281567 | −0.140784 | − | 0.990040i | \(-0.544962\pi\) | ||||
−0.140784 | + | 0.990040i | \(0.544962\pi\) | |||||||
\(308\) | 23.9712 | 1.36589 | ||||||||
\(309\) | −20.6873 | −1.17686 | ||||||||
\(310\) | −31.9563 | −1.81500 | ||||||||
\(311\) | −26.0780 | −1.47875 | −0.739374 | − | 0.673295i | \(-0.764878\pi\) | ||||
−0.739374 | + | 0.673295i | \(0.764878\pi\) | |||||||
\(312\) | 40.2727 | 2.27999 | ||||||||
\(313\) | −31.3904 | −1.77429 | −0.887144 | − | 0.461492i | \(-0.847314\pi\) | ||||
−0.887144 | + | 0.461492i | \(0.847314\pi\) | |||||||
\(314\) | −16.3991 | −0.925452 | ||||||||
\(315\) | 6.67788 | 0.376256 | ||||||||
\(316\) | 23.3693 | 1.31463 | ||||||||
\(317\) | 11.3222 | 0.635921 | 0.317960 | − | 0.948104i | \(-0.397002\pi\) | ||||
0.317960 | + | 0.948104i | \(0.397002\pi\) | |||||||
\(318\) | −8.02613 | −0.450083 | ||||||||
\(319\) | −4.18691 | −0.234422 | ||||||||
\(320\) | −19.6020 | −1.09578 | ||||||||
\(321\) | −0.580715 | −0.0324123 | ||||||||
\(322\) | −21.3421 | −1.18935 | ||||||||
\(323\) | 3.98414 | 0.221683 | ||||||||
\(324\) | −8.59758 | −0.477643 | ||||||||
\(325\) | −34.9030 | −1.93607 | ||||||||
\(326\) | 3.98958 | 0.220962 | ||||||||
\(327\) | 19.2902 | 1.06675 | ||||||||
\(328\) | −71.0972 | −3.92569 | ||||||||
\(329\) | −3.40452 | −0.187697 | ||||||||
\(330\) | 45.6546 | 2.51320 | ||||||||
\(331\) | −21.2962 | −1.17055 | −0.585273 | − | 0.810836i | \(-0.699013\pi\) | ||||
−0.585273 | + | 0.810836i | \(0.699013\pi\) | |||||||
\(332\) | −13.7873 | −0.756674 | ||||||||
\(333\) | 13.6043 | 0.745511 | ||||||||
\(334\) | −44.1585 | −2.41625 | ||||||||
\(335\) | 22.3317 | 1.22011 | ||||||||
\(336\) | 12.9459 | 0.706257 | ||||||||
\(337\) | −13.9059 | −0.757500 | −0.378750 | − | 0.925499i | \(-0.623646\pi\) | ||||
−0.378750 | + | 0.925499i | \(0.623646\pi\) | |||||||
\(338\) | −24.6808 | −1.34246 | ||||||||
\(339\) | −4.26120 | −0.231437 | ||||||||
\(340\) | −21.2400 | −1.15190 | ||||||||
\(341\) | −14.6650 | −0.794155 | ||||||||
\(342\) | 12.7394 | 0.688867 | ||||||||
\(343\) | −15.1565 | −0.818377 | ||||||||
\(344\) | 34.7576 | 1.87400 | ||||||||
\(345\) | −28.5794 | −1.53866 | ||||||||
\(346\) | −33.4580 | −1.79871 | ||||||||
\(347\) | −17.1101 | −0.918518 | −0.459259 | − | 0.888302i | \(-0.651885\pi\) | ||||
−0.459259 | + | 0.888302i | \(0.651885\pi\) | |||||||
\(348\) | −5.66080 | −0.303451 | ||||||||
\(349\) | −18.3144 | −0.980350 | −0.490175 | − | 0.871624i | \(-0.663067\pi\) | ||||
−0.490175 | + | 0.871624i | \(0.663067\pi\) | |||||||
\(350\) | −23.0803 | −1.23369 | ||||||||
\(351\) | 25.9222 | 1.38363 | ||||||||
\(352\) | −37.9074 | −2.02047 | ||||||||
\(353\) | −0.813463 | −0.0432963 | −0.0216481 | − | 0.999766i | \(-0.506891\pi\) | ||||
−0.0216481 | + | 0.999766i | \(0.506891\pi\) | |||||||
\(354\) | 15.8761 | 0.843803 | ||||||||
\(355\) | −4.23490 | −0.224765 | ||||||||
\(356\) | 25.5282 | 1.35299 | ||||||||
\(357\) | 1.84294 | 0.0975389 | ||||||||
\(358\) | −42.6573 | −2.25451 | ||||||||
\(359\) | −25.0221 | −1.32062 | −0.660308 | − | 0.750995i | \(-0.729574\pi\) | ||||
−0.660308 | + | 0.750995i | \(0.729574\pi\) | |||||||
\(360\) | −39.2379 | −2.06802 | ||||||||
\(361\) | −9.24624 | −0.486644 | ||||||||
\(362\) | 19.7855 | 1.03990 | ||||||||
\(363\) | 7.80461 | 0.409636 | ||||||||
\(364\) | −27.1629 | −1.42372 | ||||||||
\(365\) | 41.1072 | 2.15165 | ||||||||
\(366\) | −37.9418 | −1.98325 | ||||||||
\(367\) | 14.0266 | 0.732185 | 0.366093 | − | 0.930578i | \(-0.380695\pi\) | ||||
0.366093 | + | 0.930578i | \(0.380695\pi\) | |||||||
\(368\) | 60.9604 | 3.17778 | ||||||||
\(369\) | −15.7322 | −0.818988 | ||||||||
\(370\) | −78.9765 | −4.10579 | ||||||||
\(371\) | 3.12758 | 0.162376 | ||||||||
\(372\) | −19.8274 | −1.02801 | ||||||||
\(373\) | 14.9927 | 0.776291 | 0.388146 | − | 0.921598i | \(-0.373116\pi\) | ||||
0.388146 | + | 0.921598i | \(0.373116\pi\) | |||||||
\(374\) | −13.8630 | −0.716840 | ||||||||
\(375\) | −9.90102 | −0.511286 | ||||||||
\(376\) | 20.0042 | 1.03164 | ||||||||
\(377\) | 4.74438 | 0.244348 | ||||||||
\(378\) | 17.1415 | 0.881665 | ||||||||
\(379\) | 19.7808 | 1.01607 | 0.508035 | − | 0.861336i | \(-0.330372\pi\) | ||||
0.508035 | + | 0.861336i | \(0.330372\pi\) | |||||||
\(380\) | −51.9987 | −2.66748 | ||||||||
\(381\) | 0.408913 | 0.0209492 | ||||||||
\(382\) | 20.3469 | 1.04104 | ||||||||
\(383\) | −4.66112 | −0.238172 | −0.119086 | − | 0.992884i | \(-0.537996\pi\) | ||||
−0.119086 | + | 0.992884i | \(0.537996\pi\) | |||||||
\(384\) | 4.34360 | 0.221658 | ||||||||
\(385\) | −17.7904 | −0.906684 | ||||||||
\(386\) | 21.0332 | 1.07056 | ||||||||
\(387\) | 7.69109 | 0.390960 | ||||||||
\(388\) | 90.7063 | 4.60492 | ||||||||
\(389\) | 17.2193 | 0.873051 | 0.436526 | − | 0.899692i | \(-0.356209\pi\) | ||||
0.436526 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(390\) | −51.7333 | −2.61962 | ||||||||
\(391\) | 8.67816 | 0.438873 | ||||||||
\(392\) | 39.3397 | 1.98695 | ||||||||
\(393\) | −5.72403 | −0.288739 | ||||||||
\(394\) | −57.4512 | −2.89435 | ||||||||
\(395\) | −17.3437 | −0.872656 | ||||||||
\(396\) | −31.1670 | −1.56620 | ||||||||
\(397\) | −7.96676 | −0.399840 | −0.199920 | − | 0.979812i | \(-0.564068\pi\) | ||||
−0.199920 | + | 0.979812i | \(0.564068\pi\) | |||||||
\(398\) | 52.2559 | 2.61935 | ||||||||
\(399\) | 4.51180 | 0.225873 | ||||||||
\(400\) | 65.9253 | 3.29626 | ||||||||
\(401\) | 17.4253 | 0.870178 | 0.435089 | − | 0.900387i | \(-0.356717\pi\) | ||||
0.435089 | + | 0.900387i | \(0.356717\pi\) | |||||||
\(402\) | 19.7065 | 0.982870 | ||||||||
\(403\) | 16.6176 | 0.827782 | ||||||||
\(404\) | −34.8312 | −1.73292 | ||||||||
\(405\) | 6.38076 | 0.317062 | ||||||||
\(406\) | 3.13731 | 0.155702 | ||||||||
\(407\) | −36.2430 | −1.79650 | ||||||||
\(408\) | −10.8288 | −0.536103 | ||||||||
\(409\) | 8.19295 | 0.405115 | 0.202558 | − | 0.979270i | \(-0.435075\pi\) | ||||
0.202558 | + | 0.979270i | \(0.435075\pi\) | |||||||
\(410\) | 91.3298 | 4.51046 | ||||||||
\(411\) | 4.91240 | 0.242311 | ||||||||
\(412\) | −81.9852 | −4.03912 | ||||||||
\(413\) | −6.18649 | −0.304417 | ||||||||
\(414\) | 27.7486 | 1.36377 | ||||||||
\(415\) | 10.2323 | 0.502285 | ||||||||
\(416\) | 42.9546 | 2.10602 | ||||||||
\(417\) | 22.4516 | 1.09946 | ||||||||
\(418\) | −33.9388 | −1.66000 | ||||||||
\(419\) | 8.05920 | 0.393718 | 0.196859 | − | 0.980432i | \(-0.436926\pi\) | ||||
0.196859 | + | 0.980432i | \(0.436926\pi\) | |||||||
\(420\) | −24.0531 | −1.17367 | ||||||||
\(421\) | −26.1683 | −1.27537 | −0.637683 | − | 0.770299i | \(-0.720107\pi\) | ||||
−0.637683 | + | 0.770299i | \(0.720107\pi\) | |||||||
\(422\) | 56.8223 | 2.76607 | ||||||||
\(423\) | 4.42650 | 0.215224 | ||||||||
\(424\) | −18.3770 | −0.892467 | ||||||||
\(425\) | 9.38494 | 0.455237 | ||||||||
\(426\) | −3.73706 | −0.181061 | ||||||||
\(427\) | 14.7849 | 0.715493 | ||||||||
\(428\) | −2.30142 | −0.111243 | ||||||||
\(429\) | −23.7408 | −1.14622 | ||||||||
\(430\) | −44.6488 | −2.15316 | ||||||||
\(431\) | 8.51845 | 0.410319 | 0.205160 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205160 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(432\) | −48.9622 | −2.35569 | ||||||||
\(433\) | −17.1435 | −0.823864 | −0.411932 | − | 0.911215i | \(-0.635146\pi\) | ||||
−0.411932 | + | 0.911215i | \(0.635146\pi\) | |||||||
\(434\) | 10.9887 | 0.527474 | ||||||||
\(435\) | 4.20121 | 0.201432 | ||||||||
\(436\) | 76.4485 | 3.66122 | ||||||||
\(437\) | 21.2454 | 1.01631 | ||||||||
\(438\) | 36.2749 | 1.73328 | ||||||||
\(439\) | 10.3646 | 0.494673 | 0.247337 | − | 0.968930i | \(-0.420445\pi\) | ||||
0.247337 | + | 0.968930i | \(0.420445\pi\) | |||||||
\(440\) | 104.533 | 4.98341 | ||||||||
\(441\) | 8.70500 | 0.414524 | ||||||||
\(442\) | 15.7088 | 0.747193 | ||||||||
\(443\) | 3.36989 | 0.160108 | 0.0800541 | − | 0.996791i | \(-0.474491\pi\) | ||||
0.0800541 | + | 0.996791i | \(0.474491\pi\) | |||||||
\(444\) | −49.0014 | −2.32550 | ||||||||
\(445\) | −18.9459 | −0.898123 | ||||||||
\(446\) | 6.71630 | 0.318026 | ||||||||
\(447\) | −3.29309 | −0.155758 | ||||||||
\(448\) | 6.74045 | 0.318457 | ||||||||
\(449\) | 9.22512 | 0.435360 | 0.217680 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217680 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(450\) | 30.0086 | 1.41462 | ||||||||
\(451\) | 41.9120 | 1.97356 | ||||||||
\(452\) | −16.8875 | −0.794319 | ||||||||
\(453\) | 10.4641 | 0.491648 | ||||||||
\(454\) | 4.43727 | 0.208251 | ||||||||
\(455\) | 20.1591 | 0.945075 | ||||||||
\(456\) | −26.5104 | −1.24146 | ||||||||
\(457\) | 34.3169 | 1.60528 | 0.802639 | − | 0.596466i | \(-0.203429\pi\) | ||||
0.802639 | + | 0.596466i | \(0.203429\pi\) | |||||||
\(458\) | −2.26874 | −0.106011 | ||||||||
\(459\) | −6.97012 | −0.325337 | ||||||||
\(460\) | −113.262 | −5.28089 | ||||||||
\(461\) | −34.2515 | −1.59525 | −0.797625 | − | 0.603154i | \(-0.793911\pi\) | ||||
−0.797625 | + | 0.603154i | \(0.793911\pi\) | |||||||
\(462\) | −15.6991 | −0.730387 | ||||||||
\(463\) | −18.0716 | −0.839858 | −0.419929 | − | 0.907557i | \(-0.637945\pi\) | ||||
−0.419929 | + | 0.907557i | \(0.637945\pi\) | |||||||
\(464\) | −8.96125 | −0.416015 | ||||||||
\(465\) | 14.7151 | 0.682396 | ||||||||
\(466\) | 56.6178 | 2.62277 | ||||||||
\(467\) | −1.88839 | −0.0873843 | −0.0436921 | − | 0.999045i | \(-0.513912\pi\) | ||||
−0.0436921 | + | 0.999045i | \(0.513912\pi\) | |||||||
\(468\) | 35.3168 | 1.63252 | ||||||||
\(469\) | −7.67911 | −0.354589 | ||||||||
\(470\) | −25.6970 | −1.18531 | ||||||||
\(471\) | 7.55136 | 0.347948 | ||||||||
\(472\) | 36.3506 | 1.67317 | ||||||||
\(473\) | −20.4897 | −0.942118 | ||||||||
\(474\) | −15.3049 | −0.702976 | ||||||||
\(475\) | 22.9757 | 1.05420 | ||||||||
\(476\) | 7.30372 | 0.334766 | ||||||||
\(477\) | −4.06643 | −0.186189 | ||||||||
\(478\) | −25.5699 | −1.16954 | ||||||||
\(479\) | −21.2788 | −0.972252 | −0.486126 | − | 0.873889i | \(-0.661590\pi\) | ||||
−0.486126 | + | 0.873889i | \(0.661590\pi\) | |||||||
\(480\) | 38.0368 | 1.73613 | ||||||||
\(481\) | 41.0686 | 1.87257 | ||||||||
\(482\) | 11.7398 | 0.534734 | ||||||||
\(483\) | 9.82750 | 0.447167 | ||||||||
\(484\) | 30.9303 | 1.40592 | ||||||||
\(485\) | −67.3184 | −3.05677 | ||||||||
\(486\) | −36.9125 | −1.67439 | ||||||||
\(487\) | −36.9935 | −1.67633 | −0.838167 | − | 0.545414i | \(-0.816372\pi\) | ||||
−0.838167 | + | 0.545414i | \(0.816372\pi\) | |||||||
\(488\) | −86.8733 | −3.93257 | ||||||||
\(489\) | −1.83710 | −0.0830766 | ||||||||
\(490\) | −50.5348 | −2.28293 | ||||||||
\(491\) | 10.9179 | 0.492720 | 0.246360 | − | 0.969178i | \(-0.420765\pi\) | ||||
0.246360 | + | 0.969178i | \(0.420765\pi\) | |||||||
\(492\) | 56.6660 | 2.55470 | ||||||||
\(493\) | −1.27570 | −0.0574546 | ||||||||
\(494\) | 38.4576 | 1.73029 | ||||||||
\(495\) | 23.1308 | 1.03965 | ||||||||
\(496\) | −31.3875 | −1.40934 | ||||||||
\(497\) | 1.45624 | 0.0653212 | ||||||||
\(498\) | 9.02946 | 0.404620 | ||||||||
\(499\) | 31.4617 | 1.40842 | 0.704210 | − | 0.709992i | \(-0.251302\pi\) | ||||
0.704210 | + | 0.709992i | \(0.251302\pi\) | |||||||
\(500\) | −39.2385 | −1.75480 | ||||||||
\(501\) | 20.3339 | 0.908452 | ||||||||
\(502\) | −50.4246 | −2.25056 | ||||||||
\(503\) | −20.9221 | −0.932872 | −0.466436 | − | 0.884555i | \(-0.654462\pi\) | ||||
−0.466436 | + | 0.884555i | \(0.654462\pi\) | |||||||
\(504\) | 13.4926 | 0.601007 | ||||||||
\(505\) | 25.8502 | 1.15032 | ||||||||
\(506\) | −73.9247 | −3.28635 | ||||||||
\(507\) | 11.3649 | 0.504733 | ||||||||
\(508\) | 1.62055 | 0.0719004 | ||||||||
\(509\) | 18.6651 | 0.827318 | 0.413659 | − | 0.910432i | \(-0.364251\pi\) | ||||
0.413659 | + | 0.910432i | \(0.364251\pi\) | |||||||
\(510\) | 13.9104 | 0.615961 | ||||||||
\(511\) | −14.1354 | −0.625313 | ||||||||
\(512\) | 46.1604 | 2.04002 | ||||||||
\(513\) | −17.0639 | −0.753390 | ||||||||
\(514\) | 16.4013 | 0.723430 | ||||||||
\(515\) | 60.8460 | 2.68119 | ||||||||
\(516\) | −27.7026 | −1.21954 | ||||||||
\(517\) | −11.7926 | −0.518636 | ||||||||
\(518\) | 27.1574 | 1.19323 | ||||||||
\(519\) | 15.4066 | 0.676274 | ||||||||
\(520\) | −118.451 | −5.19442 | ||||||||
\(521\) | 23.3120 | 1.02132 | 0.510659 | − | 0.859783i | \(-0.329401\pi\) | ||||
0.510659 | + | 0.859783i | \(0.329401\pi\) | |||||||
\(522\) | −4.07908 | −0.178537 | ||||||||
\(523\) | −22.0354 | −0.963540 | −0.481770 | − | 0.876298i | \(-0.660006\pi\) | ||||
−0.481770 | + | 0.876298i | \(0.660006\pi\) | |||||||
\(524\) | −22.6848 | −0.990988 | ||||||||
\(525\) | 10.6279 | 0.463839 | ||||||||
\(526\) | 29.8247 | 1.30042 | ||||||||
\(527\) | −4.46824 | −0.194640 | ||||||||
\(528\) | 44.8420 | 1.95150 | ||||||||
\(529\) | 23.2763 | 1.01201 | ||||||||
\(530\) | 23.6067 | 1.02541 | ||||||||
\(531\) | 8.04358 | 0.349062 | ||||||||
\(532\) | 17.8806 | 0.775223 | ||||||||
\(533\) | −47.4924 | −2.05713 | ||||||||
\(534\) | −16.7187 | −0.723491 | ||||||||
\(535\) | 1.70801 | 0.0738439 | ||||||||
\(536\) | 45.1209 | 1.94893 | ||||||||
\(537\) | 19.6426 | 0.847641 | ||||||||
\(538\) | 65.4586 | 2.82212 | ||||||||
\(539\) | −23.1909 | −0.998901 | ||||||||
\(540\) | 90.9702 | 3.91473 | ||||||||
\(541\) | 19.0266 | 0.818016 | 0.409008 | − | 0.912531i | \(-0.365875\pi\) | ||||
0.409008 | + | 0.912531i | \(0.365875\pi\) | |||||||
\(542\) | 55.0347 | 2.36394 | ||||||||
\(543\) | −9.11075 | −0.390980 | ||||||||
\(544\) | −11.5499 | −0.495197 | ||||||||
\(545\) | −56.7368 | −2.43034 | ||||||||
\(546\) | 17.7893 | 0.761314 | ||||||||
\(547\) | 25.7110 | 1.09932 | 0.549662 | − | 0.835387i | \(-0.314757\pi\) | ||||
0.549662 | + | 0.835387i | \(0.314757\pi\) | |||||||
\(548\) | 19.4682 | 0.831642 | ||||||||
\(549\) | −19.2232 | −0.820424 | ||||||||
\(550\) | −79.9454 | −3.40888 | ||||||||
\(551\) | −3.12310 | −0.133049 | ||||||||
\(552\) | −57.7444 | −2.45777 | ||||||||
\(553\) | 5.96391 | 0.253611 | ||||||||
\(554\) | 2.59547 | 0.110271 | ||||||||
\(555\) | 36.3667 | 1.54368 | ||||||||
\(556\) | 88.9775 | 3.77348 | ||||||||
\(557\) | −23.2382 | −0.984632 | −0.492316 | − | 0.870416i | \(-0.663850\pi\) | ||||
−0.492316 | + | 0.870416i | \(0.663850\pi\) | |||||||
\(558\) | −14.2873 | −0.604831 | ||||||||
\(559\) | 23.2178 | 0.982010 | ||||||||
\(560\) | −38.0768 | −1.60904 | ||||||||
\(561\) | 6.38358 | 0.269515 | ||||||||
\(562\) | −49.1143 | −2.07176 | ||||||||
\(563\) | 26.2317 | 1.10554 | 0.552768 | − | 0.833335i | \(-0.313571\pi\) | ||||
0.552768 | + | 0.833335i | \(0.313571\pi\) | |||||||
\(564\) | −15.9438 | −0.671356 | ||||||||
\(565\) | 12.5332 | 0.527274 | ||||||||
\(566\) | −58.7518 | −2.46952 | ||||||||
\(567\) | −2.19413 | −0.0921447 | ||||||||
\(568\) | −8.55656 | −0.359025 | ||||||||
\(569\) | −8.10312 | −0.339700 | −0.169850 | − | 0.985470i | \(-0.554328\pi\) | ||||
−0.169850 | + | 0.985470i | \(0.554328\pi\) | |||||||
\(570\) | 34.0547 | 1.42639 | ||||||||
\(571\) | −26.7954 | −1.12135 | −0.560676 | − | 0.828035i | \(-0.689459\pi\) | ||||
−0.560676 | + | 0.828035i | \(0.689459\pi\) | |||||||
\(572\) | −94.0868 | −3.93397 | ||||||||
\(573\) | −9.36923 | −0.391405 | ||||||||
\(574\) | −31.4052 | −1.31083 | ||||||||
\(575\) | 50.0453 | 2.08703 | ||||||||
\(576\) | −8.76383 | −0.365160 | ||||||||
\(577\) | −4.05206 | −0.168690 | −0.0843448 | − | 0.996437i | \(-0.526880\pi\) | ||||
−0.0843448 | + | 0.996437i | \(0.526880\pi\) | |||||||
\(578\) | 39.8991 | 1.65959 | ||||||||
\(579\) | −9.68526 | −0.402506 | ||||||||
\(580\) | 16.6497 | 0.691342 | ||||||||
\(581\) | −3.51855 | −0.145974 | ||||||||
\(582\) | −59.4048 | −2.46241 | ||||||||
\(583\) | 10.8333 | 0.448670 | ||||||||
\(584\) | 83.0567 | 3.43691 | ||||||||
\(585\) | −26.2106 | −1.08368 | ||||||||
\(586\) | 81.7257 | 3.37606 | ||||||||
\(587\) | −6.15403 | −0.254004 | −0.127002 | − | 0.991902i | \(-0.540535\pi\) | ||||
−0.127002 | + | 0.991902i | \(0.540535\pi\) | |||||||
\(588\) | −31.3546 | −1.29304 | ||||||||
\(589\) | −10.9389 | −0.450731 | ||||||||
\(590\) | −46.6951 | −1.92241 | ||||||||
\(591\) | 26.4548 | 1.08821 | ||||||||
\(592\) | −77.5709 | −3.18814 | ||||||||
\(593\) | −38.8296 | −1.59454 | −0.797270 | − | 0.603623i | \(-0.793723\pi\) | ||||
−0.797270 | + | 0.603623i | \(0.793723\pi\) | |||||||
\(594\) | 59.3748 | 2.43618 | ||||||||
\(595\) | −5.42051 | −0.222219 | ||||||||
\(596\) | −13.0508 | −0.534580 | ||||||||
\(597\) | −24.0625 | −0.984814 | ||||||||
\(598\) | 83.7675 | 3.42551 | ||||||||
\(599\) | −31.1787 | −1.27393 | −0.636964 | − | 0.770894i | \(-0.719810\pi\) | ||||
−0.636964 | + | 0.770894i | \(0.719810\pi\) | |||||||
\(600\) | −62.4474 | −2.54940 | ||||||||
\(601\) | 18.7786 | 0.765994 | 0.382997 | − | 0.923749i | \(-0.374892\pi\) | ||||
0.382997 | + | 0.923749i | \(0.374892\pi\) | |||||||
\(602\) | 15.3532 | 0.625750 | ||||||||
\(603\) | 9.98427 | 0.406591 | ||||||||
\(604\) | 41.4702 | 1.68740 | ||||||||
\(605\) | −22.9551 | −0.933258 | ||||||||
\(606\) | 22.8114 | 0.926650 | ||||||||
\(607\) | −34.2672 | −1.39086 | −0.695431 | − | 0.718593i | \(-0.744787\pi\) | ||||
−0.695431 | + | 0.718593i | \(0.744787\pi\) | |||||||
\(608\) | −28.2759 | −1.14674 | ||||||||
\(609\) | −1.44465 | −0.0585403 | ||||||||
\(610\) | 111.595 | 4.51837 | ||||||||
\(611\) | 13.3627 | 0.540597 | ||||||||
\(612\) | −9.49619 | −0.383861 | ||||||||
\(613\) | −28.1065 | −1.13521 | −0.567606 | − | 0.823300i | \(-0.692130\pi\) | ||||
−0.567606 | + | 0.823300i | \(0.692130\pi\) | |||||||
\(614\) | 12.8046 | 0.516753 | ||||||||
\(615\) | −42.0551 | −1.69583 | ||||||||
\(616\) | −35.9453 | −1.44828 | ||||||||
\(617\) | −6.40885 | −0.258011 | −0.129005 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129005 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(618\) | 53.6932 | 2.15986 | ||||||||
\(619\) | −39.1342 | −1.57294 | −0.786469 | − | 0.617630i | \(-0.788093\pi\) | ||||
−0.786469 | + | 0.617630i | \(0.788093\pi\) | |||||||
\(620\) | 58.3170 | 2.34207 | ||||||||
\(621\) | −37.1682 | −1.49151 | ||||||||
\(622\) | 67.6847 | 2.71391 | ||||||||
\(623\) | 6.51487 | 0.261013 | ||||||||
\(624\) | −50.8125 | −2.03413 | ||||||||
\(625\) | −7.66239 | −0.306496 | ||||||||
\(626\) | 81.4728 | 3.25631 | ||||||||
\(627\) | 15.6280 | 0.624121 | ||||||||
\(628\) | 29.9266 | 1.19420 | ||||||||
\(629\) | −11.0428 | −0.440305 | ||||||||
\(630\) | −17.3322 | −0.690533 | ||||||||
\(631\) | −28.0061 | −1.11491 | −0.557453 | − | 0.830208i | \(-0.688221\pi\) | ||||
−0.557453 | + | 0.830208i | \(0.688221\pi\) | |||||||
\(632\) | −35.0428 | −1.39393 | ||||||||
\(633\) | −26.1653 | −1.03998 | ||||||||
\(634\) | −29.3866 | −1.16709 | ||||||||
\(635\) | −1.20271 | −0.0477279 | ||||||||
\(636\) | 14.6469 | 0.580787 | ||||||||
\(637\) | 26.2786 | 1.04120 | ||||||||
\(638\) | 10.8670 | 0.430229 | ||||||||
\(639\) | −1.89338 | −0.0749009 | ||||||||
\(640\) | −12.7755 | −0.504996 | ||||||||
\(641\) | −41.6314 | −1.64434 | −0.822172 | − | 0.569240i | \(-0.807238\pi\) | ||||
−0.822172 | + | 0.569240i | \(0.807238\pi\) | |||||||
\(642\) | 1.50723 | 0.0594856 | ||||||||
\(643\) | 34.6942 | 1.36820 | 0.684102 | − | 0.729386i | \(-0.260194\pi\) | ||||
0.684102 | + | 0.729386i | \(0.260194\pi\) | |||||||
\(644\) | 38.9472 | 1.53473 | ||||||||
\(645\) | 20.5597 | 0.809536 | ||||||||
\(646\) | −10.3407 | −0.406850 | ||||||||
\(647\) | −36.2524 | −1.42523 | −0.712614 | − | 0.701556i | \(-0.752489\pi\) | ||||
−0.712614 | + | 0.701556i | \(0.752489\pi\) | |||||||
\(648\) | 12.8923 | 0.506455 | ||||||||
\(649\) | −21.4288 | −0.841153 | ||||||||
\(650\) | 90.5899 | 3.55323 | ||||||||
\(651\) | −5.06002 | −0.198318 | ||||||||
\(652\) | −7.28057 | −0.285129 | ||||||||
\(653\) | 42.5915 | 1.66673 | 0.833367 | − | 0.552719i | \(-0.186410\pi\) | ||||
0.833367 | + | 0.552719i | \(0.186410\pi\) | |||||||
\(654\) | −50.0671 | −1.95778 | ||||||||
\(655\) | 16.8357 | 0.657824 | ||||||||
\(656\) | 89.7043 | 3.50236 | ||||||||
\(657\) | 18.3786 | 0.717018 | ||||||||
\(658\) | 8.83633 | 0.344476 | ||||||||
\(659\) | 33.1995 | 1.29327 | 0.646634 | − | 0.762801i | \(-0.276176\pi\) | ||||
0.646634 | + | 0.762801i | \(0.276176\pi\) | |||||||
\(660\) | −83.3150 | −3.24303 | ||||||||
\(661\) | −28.1030 | −1.09308 | −0.546539 | − | 0.837433i | \(-0.684055\pi\) | ||||
−0.546539 | + | 0.837433i | \(0.684055\pi\) | |||||||
\(662\) | 55.2738 | 2.14828 | ||||||||
\(663\) | −7.23354 | −0.280927 | ||||||||
\(664\) | 20.6743 | 0.802318 | ||||||||
\(665\) | −13.2702 | −0.514597 | ||||||||
\(666\) | −35.3096 | −1.36822 | ||||||||
\(667\) | −6.80267 | −0.263400 | ||||||||
\(668\) | 80.5848 | 3.11792 | ||||||||
\(669\) | −3.09269 | −0.119570 | ||||||||
\(670\) | −57.9613 | −2.23924 | ||||||||
\(671\) | 51.2121 | 1.97702 | ||||||||
\(672\) | −13.0796 | −0.504555 | ||||||||
\(673\) | 3.46345 | 0.133506 | 0.0667531 | − | 0.997770i | \(-0.478736\pi\) | ||||
0.0667531 | + | 0.997770i | \(0.478736\pi\) | |||||||
\(674\) | 36.0923 | 1.39022 | ||||||||
\(675\) | −40.1953 | −1.54712 | ||||||||
\(676\) | 45.0399 | 1.73231 | ||||||||
\(677\) | −24.9028 | −0.957093 | −0.478546 | − | 0.878062i | \(-0.658836\pi\) | ||||
−0.478546 | + | 0.878062i | \(0.658836\pi\) | |||||||
\(678\) | 11.0598 | 0.424750 | ||||||||
\(679\) | 23.1485 | 0.888359 | ||||||||
\(680\) | 31.8498 | 1.22139 | ||||||||
\(681\) | −2.04325 | −0.0782977 | ||||||||
\(682\) | 38.0626 | 1.45749 | ||||||||
\(683\) | 34.8449 | 1.33330 | 0.666651 | − | 0.745370i | \(-0.267727\pi\) | ||||
0.666651 | + | 0.745370i | \(0.267727\pi\) | |||||||
\(684\) | −23.2481 | −0.888913 | ||||||||
\(685\) | −14.4485 | −0.552049 | ||||||||
\(686\) | 39.3384 | 1.50195 | ||||||||
\(687\) | 1.04470 | 0.0398578 | ||||||||
\(688\) | −43.8541 | −1.67192 | ||||||||
\(689\) | −12.2757 | −0.467668 | ||||||||
\(690\) | 74.1771 | 2.82387 | ||||||||
\(691\) | −0.341332 | −0.0129849 | −0.00649243 | − | 0.999979i | \(-0.502067\pi\) | ||||
−0.00649243 | + | 0.999979i | \(0.502067\pi\) | |||||||
\(692\) | 61.0575 | 2.32106 | ||||||||
\(693\) | −7.95391 | −0.302144 | ||||||||
\(694\) | 44.4088 | 1.68573 | ||||||||
\(695\) | −66.0353 | −2.50486 | ||||||||
\(696\) | 8.48849 | 0.321755 | ||||||||
\(697\) | 12.7701 | 0.483700 | ||||||||
\(698\) | 47.5346 | 1.79921 | ||||||||
\(699\) | −26.0711 | −0.986100 | ||||||||
\(700\) | 42.1192 | 1.59195 | ||||||||
\(701\) | 6.85905 | 0.259063 | 0.129531 | − | 0.991575i | \(-0.458653\pi\) | ||||
0.129531 | + | 0.991575i | \(0.458653\pi\) | |||||||
\(702\) | −67.2804 | −2.53933 | ||||||||
\(703\) | −27.0344 | −1.01962 | ||||||||
\(704\) | 23.3476 | 0.879945 | ||||||||
\(705\) | 11.8328 | 0.445650 | ||||||||
\(706\) | 2.11132 | 0.0794606 | ||||||||
\(707\) | −8.88902 | −0.334306 | ||||||||
\(708\) | −28.9722 | −1.08884 | ||||||||
\(709\) | 25.1923 | 0.946115 | 0.473057 | − | 0.881032i | \(-0.343150\pi\) | ||||
0.473057 | + | 0.881032i | \(0.343150\pi\) | |||||||
\(710\) | 10.9916 | 0.412506 | ||||||||
\(711\) | −7.75419 | −0.290805 | ||||||||
\(712\) | −38.2801 | −1.43461 | ||||||||
\(713\) | −23.8269 | −0.892326 | ||||||||
\(714\) | −4.78331 | −0.179011 | ||||||||
\(715\) | 69.8272 | 2.61139 | ||||||||
\(716\) | 77.8452 | 2.90921 | ||||||||
\(717\) | 11.7743 | 0.439720 | ||||||||
\(718\) | 64.9442 | 2.42370 | ||||||||
\(719\) | 19.8187 | 0.739113 | 0.369557 | − | 0.929208i | \(-0.379510\pi\) | ||||
0.369557 | + | 0.929208i | \(0.379510\pi\) | |||||||
\(720\) | 49.5069 | 1.84501 | ||||||||
\(721\) | −20.9229 | −0.779209 | ||||||||
\(722\) | 23.9984 | 0.893126 | ||||||||
\(723\) | −5.40589 | −0.201047 | ||||||||
\(724\) | −36.1066 | −1.34189 | ||||||||
\(725\) | −7.35671 | −0.273221 | ||||||||
\(726\) | −20.2566 | −0.751794 | ||||||||
\(727\) | 46.8615 | 1.73800 | 0.868998 | − | 0.494815i | \(-0.164764\pi\) | ||||
0.868998 | + | 0.494815i | \(0.164764\pi\) | |||||||
\(728\) | 40.7313 | 1.50960 | ||||||||
\(729\) | 22.4429 | 0.831217 | ||||||||
\(730\) | −106.693 | −3.94887 | ||||||||
\(731\) | −6.24295 | −0.230904 | ||||||||
\(732\) | 69.2399 | 2.55918 | ||||||||
\(733\) | −8.94812 | −0.330506 | −0.165253 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165253 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(734\) | −36.4058 | −1.34376 | ||||||||
\(735\) | 23.2700 | 0.858328 | ||||||||
\(736\) | −61.5898 | −2.27023 | ||||||||
\(737\) | −26.5989 | −0.979784 | ||||||||
\(738\) | 40.8326 | 1.50307 | ||||||||
\(739\) | 27.5019 | 1.01167 | 0.505837 | − | 0.862629i | \(-0.331184\pi\) | ||||
0.505837 | + | 0.862629i | \(0.331184\pi\) | |||||||
\(740\) | 144.124 | 5.29811 | ||||||||
\(741\) | −17.7088 | −0.650548 | ||||||||
\(742\) | −8.11754 | −0.298004 | ||||||||
\(743\) | −32.7046 | −1.19982 | −0.599908 | − | 0.800069i | \(-0.704796\pi\) | ||||
−0.599908 | + | 0.800069i | \(0.704796\pi\) | |||||||
\(744\) | 29.7317 | 1.09002 | ||||||||
\(745\) | 9.68572 | 0.354857 | ||||||||
\(746\) | −38.9131 | −1.42471 | ||||||||
\(747\) | 4.57476 | 0.167382 | ||||||||
\(748\) | 25.2986 | 0.925010 | ||||||||
\(749\) | −0.587328 | −0.0214605 | ||||||||
\(750\) | 25.6978 | 0.938351 | ||||||||
\(751\) | −6.75891 | −0.246636 | −0.123318 | − | 0.992367i | \(-0.539354\pi\) | ||||
−0.123318 | + | 0.992367i | \(0.539354\pi\) | |||||||
\(752\) | −25.2396 | −0.920394 | ||||||||
\(753\) | 23.2193 | 0.846158 | ||||||||
\(754\) | −12.3139 | −0.448446 | ||||||||
\(755\) | −30.7774 | −1.12010 | ||||||||
\(756\) | −31.2816 | −1.13770 | ||||||||
\(757\) | 16.3912 | 0.595748 | 0.297874 | − | 0.954605i | \(-0.403722\pi\) | ||||
0.297874 | + | 0.954605i | \(0.403722\pi\) | |||||||
\(758\) | −51.3405 | −1.86477 | ||||||||
\(759\) | 34.0405 | 1.23559 | ||||||||
\(760\) | 77.9732 | 2.82838 | ||||||||
\(761\) | 21.4598 | 0.777916 | 0.388958 | − | 0.921255i | \(-0.372835\pi\) | ||||
0.388958 | + | 0.921255i | \(0.372835\pi\) | |||||||
\(762\) | −1.06132 | −0.0384476 | ||||||||
\(763\) | 19.5099 | 0.706305 | ||||||||
\(764\) | −37.1310 | −1.34335 | ||||||||
\(765\) | 7.04767 | 0.254809 | ||||||||
\(766\) | 12.0978 | 0.437112 | ||||||||
\(767\) | 24.2819 | 0.876770 | ||||||||
\(768\) | −24.6028 | −0.887777 | ||||||||
\(769\) | 37.2079 | 1.34175 | 0.670876 | − | 0.741570i | \(-0.265918\pi\) | ||||
0.670876 | + | 0.741570i | \(0.265918\pi\) | |||||||
\(770\) | 46.1745 | 1.66401 | ||||||||
\(771\) | −7.55239 | −0.271993 | ||||||||
\(772\) | −38.3834 | −1.38145 | ||||||||
\(773\) | 4.40043 | 0.158272 | 0.0791362 | − | 0.996864i | \(-0.474784\pi\) | ||||
0.0791362 | + | 0.996864i | \(0.474784\pi\) | |||||||
\(774\) | −19.9620 | −0.717520 | ||||||||
\(775\) | −25.7675 | −0.925596 | ||||||||
\(776\) | −136.016 | −4.88269 | ||||||||
\(777\) | −12.5053 | −0.448625 | ||||||||
\(778\) | −44.6921 | −1.60229 | ||||||||
\(779\) | 31.2630 | 1.12011 | ||||||||
\(780\) | 94.4081 | 3.38035 | ||||||||
\(781\) | 5.04412 | 0.180493 | ||||||||
\(782\) | −22.5239 | −0.805454 | ||||||||
\(783\) | 5.46377 | 0.195259 | ||||||||
\(784\) | −49.6354 | −1.77269 | ||||||||
\(785\) | −22.2103 | −0.792718 | ||||||||
\(786\) | 14.8565 | 0.529915 | ||||||||
\(787\) | −1.75508 | −0.0625620 | −0.0312810 | − | 0.999511i | \(-0.509959\pi\) | ||||
−0.0312810 | + | 0.999511i | \(0.509959\pi\) | |||||||
\(788\) | 104.843 | 3.73486 | ||||||||
\(789\) | −13.7335 | −0.488927 | ||||||||
\(790\) | 45.0151 | 1.60156 | ||||||||
\(791\) | −4.30973 | −0.153236 | ||||||||
\(792\) | 46.7356 | 1.66068 | ||||||||
\(793\) | −58.0308 | −2.06073 | ||||||||
\(794\) | 20.6775 | 0.733817 | ||||||||
\(795\) | −10.8703 | −0.385530 | ||||||||
\(796\) | −95.3617 | −3.38000 | ||||||||
\(797\) | −27.4055 | −0.970753 | −0.485377 | − | 0.874305i | \(-0.661317\pi\) | ||||
−0.485377 | + | 0.874305i | \(0.661317\pi\) | |||||||
\(798\) | −11.7103 | −0.414538 | ||||||||
\(799\) | −3.59304 | −0.127113 | ||||||||
\(800\) | −66.6060 | −2.35488 | ||||||||
\(801\) | −8.47053 | −0.299292 | ||||||||
\(802\) | −45.2269 | −1.59702 | ||||||||
\(803\) | −48.9622 | −1.72784 | ||||||||
\(804\) | −35.9624 | −1.26829 | ||||||||
\(805\) | −28.9049 | −1.01876 | ||||||||
\(806\) | −43.1305 | −1.51921 | ||||||||
\(807\) | −30.1421 | −1.06105 | ||||||||
\(808\) | 52.2301 | 1.83745 | ||||||||
\(809\) | −43.0475 | −1.51347 | −0.756736 | − | 0.653721i | \(-0.773207\pi\) | ||||
−0.756736 | + | 0.653721i | \(0.773207\pi\) | |||||||
\(810\) | −16.5611 | −0.581897 | ||||||||
\(811\) | −31.4746 | −1.10522 | −0.552612 | − | 0.833439i | \(-0.686369\pi\) | ||||
−0.552612 | + | 0.833439i | \(0.686369\pi\) | |||||||
\(812\) | −5.72527 | −0.200918 | ||||||||
\(813\) | −25.3421 | −0.888787 | ||||||||
\(814\) | 94.0677 | 3.29707 | ||||||||
\(815\) | 5.40333 | 0.189271 | ||||||||
\(816\) | 13.6628 | 0.478293 | ||||||||
\(817\) | −15.2837 | −0.534708 | ||||||||
\(818\) | −21.2646 | −0.743498 | ||||||||
\(819\) | 9.01295 | 0.314938 | ||||||||
\(820\) | −166.668 | −5.82029 | ||||||||
\(821\) | −3.32560 | −0.116064 | −0.0580320 | − | 0.998315i | \(-0.518483\pi\) | ||||
−0.0580320 | + | 0.998315i | \(0.518483\pi\) | |||||||
\(822\) | −12.7500 | −0.444708 | ||||||||
\(823\) | −48.8380 | −1.70239 | −0.851193 | − | 0.524853i | \(-0.824120\pi\) | ||||
−0.851193 | + | 0.524853i | \(0.824120\pi\) | |||||||
\(824\) | 122.939 | 4.28277 | ||||||||
\(825\) | 36.8129 | 1.28166 | ||||||||
\(826\) | 16.0569 | 0.558690 | ||||||||
\(827\) | −15.1141 | −0.525568 | −0.262784 | − | 0.964855i | \(-0.584641\pi\) | ||||
−0.262784 | + | 0.964855i | \(0.584641\pi\) | |||||||
\(828\) | −50.6385 | −1.75981 | ||||||||
\(829\) | −9.62165 | −0.334174 | −0.167087 | − | 0.985942i | \(-0.553436\pi\) | ||||
−0.167087 | + | 0.985942i | \(0.553436\pi\) | |||||||
\(830\) | −26.5577 | −0.921831 | ||||||||
\(831\) | −1.19515 | −0.0414593 | ||||||||
\(832\) | −26.4562 | −0.917205 | ||||||||
\(833\) | −7.06596 | −0.244821 | ||||||||
\(834\) | −58.2725 | −2.01781 | ||||||||
\(835\) | −59.8067 | −2.06969 | ||||||||
\(836\) | 61.9348 | 2.14206 | ||||||||
\(837\) | 19.1373 | 0.661483 | ||||||||
\(838\) | −20.9174 | −0.722581 | ||||||||
\(839\) | 30.2720 | 1.04510 | 0.522552 | − | 0.852607i | \(-0.324980\pi\) | ||||
0.522552 | + | 0.852607i | \(0.324980\pi\) | |||||||
\(840\) | 36.0681 | 1.24447 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 67.9191 | 2.34065 | ||||||||
\(843\) | 22.6159 | 0.778933 | ||||||||
\(844\) | −103.695 | −3.56933 | ||||||||
\(845\) | −33.4267 | −1.14991 | ||||||||
\(846\) | −11.4889 | −0.394995 | ||||||||
\(847\) | 7.89349 | 0.271224 | ||||||||
\(848\) | 23.1865 | 0.796228 | ||||||||
\(849\) | 27.0538 | 0.928483 | ||||||||
\(850\) | −24.3584 | −0.835485 | ||||||||
\(851\) | −58.8857 | −2.01858 | ||||||||
\(852\) | 6.81976 | 0.233641 | ||||||||
\(853\) | −11.3716 | −0.389356 | −0.194678 | − | 0.980867i | \(-0.562366\pi\) | ||||
−0.194678 | + | 0.980867i | \(0.562366\pi\) | |||||||
\(854\) | −38.3739 | −1.31313 | ||||||||
\(855\) | 17.2537 | 0.590066 | ||||||||
\(856\) | 3.45102 | 0.117954 | ||||||||
\(857\) | −43.9805 | −1.50235 | −0.751173 | − | 0.660105i | \(-0.770512\pi\) | ||||
−0.751173 | + | 0.660105i | \(0.770512\pi\) | |||||||
\(858\) | 61.6187 | 2.10363 | ||||||||
\(859\) | 1.11221 | 0.0379481 | 0.0189741 | − | 0.999820i | \(-0.493960\pi\) | ||||
0.0189741 | + | 0.999820i | \(0.493960\pi\) | |||||||
\(860\) | 81.4796 | 2.77843 | ||||||||
\(861\) | 14.4613 | 0.492841 | ||||||||
\(862\) | −22.1094 | −0.753049 | ||||||||
\(863\) | −11.2556 | −0.383144 | −0.191572 | − | 0.981479i | \(-0.561359\pi\) | ||||
−0.191572 | + | 0.981479i | \(0.561359\pi\) | |||||||
\(864\) | 49.4677 | 1.68293 | ||||||||
\(865\) | −45.3143 | −1.54073 | ||||||||
\(866\) | 44.4955 | 1.51202 | ||||||||
\(867\) | −18.3726 | −0.623965 | ||||||||
\(868\) | −20.0533 | −0.680652 | ||||||||
\(869\) | 20.6578 | 0.700768 | ||||||||
\(870\) | −10.9041 | −0.369684 | ||||||||
\(871\) | 30.1405 | 1.02127 | ||||||||
\(872\) | −114.636 | −3.88207 | ||||||||
\(873\) | −30.0974 | −1.01864 | ||||||||
\(874\) | −55.1419 | −1.86520 | ||||||||
\(875\) | −10.0138 | −0.338528 | ||||||||
\(876\) | −66.1980 | −2.23662 | ||||||||
\(877\) | 19.5806 | 0.661189 | 0.330595 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330595 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(878\) | −26.9009 | −0.907862 | ||||||||
\(879\) | −37.6327 | −1.26932 | ||||||||
\(880\) | −131.891 | −4.44603 | ||||||||
\(881\) | −2.61183 | −0.0879947 | −0.0439973 | − | 0.999032i | \(-0.514009\pi\) | ||||
−0.0439973 | + | 0.999032i | \(0.514009\pi\) | |||||||
\(882\) | −22.5936 | −0.760766 | ||||||||
\(883\) | −40.0782 | −1.34874 | −0.674369 | − | 0.738395i | \(-0.735584\pi\) | ||||
−0.674369 | + | 0.738395i | \(0.735584\pi\) | |||||||
\(884\) | −28.6671 | −0.964177 | ||||||||
\(885\) | 21.5019 | 0.722780 | ||||||||
\(886\) | −8.74645 | −0.293843 | ||||||||
\(887\) | −33.6910 | −1.13123 | −0.565616 | − | 0.824668i | \(-0.691362\pi\) | ||||
−0.565616 | + | 0.824668i | \(0.691362\pi\) | |||||||
\(888\) | 73.4786 | 2.46578 | ||||||||
\(889\) | 0.413570 | 0.0138707 | ||||||||
\(890\) | 49.1736 | 1.64830 | ||||||||
\(891\) | −7.60002 | −0.254610 | ||||||||
\(892\) | −12.2566 | −0.410380 | ||||||||
\(893\) | −8.79631 | −0.294357 | ||||||||
\(894\) | 8.54711 | 0.285858 | ||||||||
\(895\) | −57.7734 | −1.93115 | ||||||||
\(896\) | 4.39307 | 0.146762 | ||||||||
\(897\) | −38.5729 | −1.28791 | ||||||||
\(898\) | −23.9435 | −0.799006 | ||||||||
\(899\) | 3.50259 | 0.116818 | ||||||||
\(900\) | −54.7627 | −1.82542 | ||||||||
\(901\) | 3.30077 | 0.109965 | ||||||||
\(902\) | −108.781 | −3.62203 | ||||||||
\(903\) | −7.06978 | −0.235268 | ||||||||
\(904\) | 25.3231 | 0.842234 | ||||||||
\(905\) | 26.7968 | 0.890755 | ||||||||
\(906\) | −27.1594 | −0.902309 | ||||||||
\(907\) | 3.23262 | 0.107338 | 0.0536688 | − | 0.998559i | \(-0.482908\pi\) | ||||
0.0536688 | + | 0.998559i | \(0.482908\pi\) | |||||||
\(908\) | −8.09757 | −0.268727 | ||||||||
\(909\) | 11.5574 | 0.383334 | ||||||||
\(910\) | −52.3225 | −1.73447 | ||||||||
\(911\) | −10.8448 | −0.359304 | −0.179652 | − | 0.983730i | \(-0.557497\pi\) | ||||
−0.179652 | + | 0.983730i | \(0.557497\pi\) | |||||||
\(912\) | 33.4485 | 1.10759 | ||||||||
\(913\) | −12.1875 | −0.403349 | ||||||||
\(914\) | −89.0686 | −2.94613 | ||||||||
\(915\) | −51.3869 | −1.69880 | ||||||||
\(916\) | 4.14023 | 0.136797 | ||||||||
\(917\) | −5.78922 | −0.191177 | ||||||||
\(918\) | 18.0908 | 0.597084 | ||||||||
\(919\) | 20.7175 | 0.683409 | 0.341704 | − | 0.939808i | \(-0.388996\pi\) | ||||
0.341704 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(920\) | 169.839 | 5.59944 | ||||||||
\(921\) | −5.89622 | −0.194287 | ||||||||
\(922\) | 88.8987 | 2.92772 | ||||||||
\(923\) | −5.71572 | −0.188135 | ||||||||
\(924\) | 28.6492 | 0.942490 | ||||||||
\(925\) | −63.6816 | −2.09384 | ||||||||
\(926\) | 46.9043 | 1.54137 | ||||||||
\(927\) | 27.2036 | 0.893483 | ||||||||
\(928\) | 9.05377 | 0.297205 | ||||||||
\(929\) | −14.7468 | −0.483826 | −0.241913 | − | 0.970298i | \(-0.577775\pi\) | ||||
−0.241913 | + | 0.970298i | \(0.577775\pi\) | |||||||
\(930\) | −38.1926 | −1.25238 | ||||||||
\(931\) | −17.2985 | −0.566936 | ||||||||
\(932\) | −103.322 | −3.38442 | ||||||||
\(933\) | −31.1672 | −1.02037 | ||||||||
\(934\) | 4.90126 | 0.160374 | ||||||||
\(935\) | −18.7756 | −0.614027 | ||||||||
\(936\) | −52.9582 | −1.73099 | ||||||||
\(937\) | −14.3318 | −0.468201 | −0.234100 | − | 0.972212i | \(-0.575214\pi\) | ||||
−0.234100 | + | 0.972212i | \(0.575214\pi\) | |||||||
\(938\) | 19.9309 | 0.650768 | ||||||||
\(939\) | −37.5162 | −1.22430 | ||||||||
\(940\) | 46.8944 | 1.52953 | ||||||||
\(941\) | −52.9303 | −1.72548 | −0.862739 | − | 0.505650i | \(-0.831253\pi\) | ||||
−0.862739 | + | 0.505650i | \(0.831253\pi\) | |||||||
\(942\) | −19.5993 | −0.638581 | ||||||||
\(943\) | 68.0964 | 2.21752 | ||||||||
\(944\) | −45.8640 | −1.49275 | ||||||||
\(945\) | 23.2159 | 0.755212 | ||||||||
\(946\) | 53.1805 | 1.72905 | ||||||||
\(947\) | 2.38532 | 0.0775124 | 0.0387562 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387562 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(948\) | 27.9298 | 0.907119 | ||||||||
\(949\) | 55.4813 | 1.80100 | ||||||||
\(950\) | −59.6329 | −1.93475 | ||||||||
\(951\) | 13.5318 | 0.438798 | ||||||||
\(952\) | −10.9521 | −0.354959 | ||||||||
\(953\) | 16.5195 | 0.535120 | 0.267560 | − | 0.963541i | \(-0.413783\pi\) | ||||
0.267560 | + | 0.963541i | \(0.413783\pi\) | |||||||
\(954\) | 10.5543 | 0.341708 | ||||||||
\(955\) | 27.5571 | 0.891725 | ||||||||
\(956\) | 46.6625 | 1.50917 | ||||||||
\(957\) | −5.00399 | −0.161756 | ||||||||
\(958\) | 55.2285 | 1.78435 | ||||||||
\(959\) | 4.96835 | 0.160436 | ||||||||
\(960\) | −23.4273 | −0.756113 | ||||||||
\(961\) | −18.7319 | −0.604254 | ||||||||
\(962\) | −106.592 | −3.43668 | ||||||||
\(963\) | 0.763635 | 0.0246078 | ||||||||
\(964\) | −21.4240 | −0.690020 | ||||||||
\(965\) | 28.4866 | 0.917015 | ||||||||
\(966\) | −25.5070 | −0.820675 | ||||||||
\(967\) | −53.7935 | −1.72988 | −0.864942 | − | 0.501873i | \(-0.832645\pi\) | ||||
−0.864942 | + | 0.501873i | \(0.832645\pi\) | |||||||
\(968\) | −46.3806 | −1.49073 | ||||||||
\(969\) | 4.76164 | 0.152966 | ||||||||
\(970\) | 174.723 | 5.61002 | ||||||||
\(971\) | 27.2423 | 0.874248 | 0.437124 | − | 0.899401i | \(-0.355997\pi\) | ||||
0.437124 | + | 0.899401i | \(0.355997\pi\) | |||||||
\(972\) | 67.3616 | 2.16062 | ||||||||
\(973\) | 22.7073 | 0.727963 | ||||||||
\(974\) | 96.0155 | 3.07653 | ||||||||
\(975\) | −41.7144 | −1.33593 | ||||||||
\(976\) | 109.609 | 3.50850 | ||||||||
\(977\) | −41.3841 | −1.32400 | −0.661998 | − | 0.749506i | \(-0.730291\pi\) | ||||
−0.661998 | + | 0.749506i | \(0.730291\pi\) | |||||||
\(978\) | 4.76815 | 0.152468 | ||||||||
\(979\) | 22.5662 | 0.721219 | ||||||||
\(980\) | 92.2210 | 2.94589 | ||||||||
\(981\) | −25.3664 | −0.809888 | ||||||||
\(982\) | −28.3372 | −0.904277 | ||||||||
\(983\) | −53.6967 | −1.71266 | −0.856330 | − | 0.516429i | \(-0.827261\pi\) | ||||
−0.856330 | + | 0.516429i | \(0.827261\pi\) | |||||||
\(984\) | −84.9719 | −2.70881 | ||||||||
\(985\) | −77.8097 | −2.47922 | ||||||||
\(986\) | 3.31104 | 0.105445 | ||||||||
\(987\) | −4.06891 | −0.129515 | ||||||||
\(988\) | −70.1812 | −2.23276 | ||||||||
\(989\) | −33.2906 | −1.05858 | ||||||||
\(990\) | −60.0354 | −1.90805 | ||||||||
\(991\) | −39.1892 | −1.24489 | −0.622443 | − | 0.782665i | \(-0.713860\pi\) | ||||
−0.622443 | + | 0.782665i | \(0.713860\pi\) | |||||||
\(992\) | 31.7116 | 1.00685 | ||||||||
\(993\) | −25.4522 | −0.807702 | ||||||||
\(994\) | −3.77962 | −0.119882 | ||||||||
\(995\) | 70.7734 | 2.24367 | ||||||||
\(996\) | −16.4779 | −0.522121 | ||||||||
\(997\) | −12.6043 | −0.399182 | −0.199591 | − | 0.979879i | \(-0.563961\pi\) | ||||
−0.199591 | + | 0.979879i | \(0.563961\pi\) | |||||||
\(998\) | −81.6580 | −2.58484 | ||||||||
\(999\) | 47.2958 | 1.49637 |
(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 | 8033.2.a.b.1.9 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8033.2.a.b.1.9 | ✓ | 153 | 1.1 | even | 1 | trivial |