Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8022,2,Mod(1,8022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.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: | \(64.0559925015\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 53 x^{13} - x^{12} + 1068 x^{11} + 45 x^{10} - 10139 x^{9} - 615 x^{8} + 45390 x^{7} + 2130 x^{6} - 84842 x^{5} + 7822 x^{4} + 62828 x^{3} - 16144 x^{2} + \cdots + 4704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.55328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.55328 | 0.694648 | 0.347324 | − | 0.937745i | \(-0.387090\pi\) | ||||
0.347324 | + | 0.937745i | \(0.387090\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.55328 | −0.491190 | ||||||||
\(11\) | 2.86410 | 0.863557 | 0.431779 | − | 0.901980i | \(-0.357886\pi\) | ||||
0.431779 | + | 0.901980i | \(0.357886\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.19533 | −0.331524 | −0.165762 | − | 0.986166i | \(-0.553008\pi\) | ||||
−0.165762 | + | 0.986166i | \(0.553008\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.55328 | 0.401055 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.13308 | 1.00242 | 0.501210 | − | 0.865326i | \(-0.332888\pi\) | ||||
0.501210 | + | 0.865326i | \(0.332888\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.34711 | −0.997295 | −0.498648 | − | 0.866805i | \(-0.666170\pi\) | ||||
−0.498648 | + | 0.866805i | \(0.666170\pi\) | |||||||
\(20\) | 1.55328 | 0.347324 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.86410 | −0.610627 | ||||||||
\(23\) | 5.31993 | 1.10928 | 0.554641 | − | 0.832090i | \(-0.312856\pi\) | ||||
0.554641 | + | 0.832090i | \(0.312856\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.58732 | −0.517464 | ||||||||
\(26\) | 1.19533 | 0.234423 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 6.80630 | 1.26390 | 0.631949 | − | 0.775010i | \(-0.282255\pi\) | ||||
0.631949 | + | 0.775010i | \(0.282255\pi\) | |||||||
\(30\) | −1.55328 | −0.283589 | ||||||||
\(31\) | 8.33433 | 1.49689 | 0.748445 | − | 0.663197i | \(-0.230801\pi\) | ||||
0.748445 | + | 0.663197i | \(0.230801\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.86410 | 0.498575 | ||||||||
\(34\) | −4.13308 | −0.708818 | ||||||||
\(35\) | 1.55328 | 0.262552 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.50201 | −1.23332 | −0.616661 | − | 0.787229i | \(-0.711515\pi\) | ||||
−0.616661 | + | 0.787229i | \(0.711515\pi\) | |||||||
\(38\) | 4.34711 | 0.705194 | ||||||||
\(39\) | −1.19533 | −0.191405 | ||||||||
\(40\) | −1.55328 | −0.245595 | ||||||||
\(41\) | 1.58747 | 0.247921 | 0.123960 | − | 0.992287i | \(-0.460440\pi\) | ||||
0.123960 | + | 0.992287i | \(0.460440\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 5.26207 | 0.802458 | 0.401229 | − | 0.915978i | \(-0.368583\pi\) | ||||
0.401229 | + | 0.915978i | \(0.368583\pi\) | |||||||
\(44\) | 2.86410 | 0.431779 | ||||||||
\(45\) | 1.55328 | 0.231549 | ||||||||
\(46\) | −5.31993 | −0.784381 | ||||||||
\(47\) | 4.76012 | 0.694336 | 0.347168 | − | 0.937803i | \(-0.387143\pi\) | ||||
0.347168 | + | 0.937803i | \(0.387143\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.58732 | 0.365902 | ||||||||
\(51\) | 4.13308 | 0.578748 | ||||||||
\(52\) | −1.19533 | −0.165762 | ||||||||
\(53\) | −9.50856 | −1.30610 | −0.653050 | − | 0.757314i | \(-0.726511\pi\) | ||||
−0.653050 | + | 0.757314i | \(0.726511\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.44874 | 0.599869 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −4.34711 | −0.575789 | ||||||||
\(58\) | −6.80630 | −0.893711 | ||||||||
\(59\) | 0.810529 | 0.105522 | 0.0527609 | − | 0.998607i | \(-0.483198\pi\) | ||||
0.0527609 | + | 0.998607i | \(0.483198\pi\) | |||||||
\(60\) | 1.55328 | 0.200528 | ||||||||
\(61\) | −0.00358361 | −0.000458834 0 | −0.000229417 | − | 1.00000i | \(-0.500073\pi\) | ||||
−0.000229417 | 1.00000i | \(0.500073\pi\) | ||||||||
\(62\) | −8.33433 | −1.05846 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.85668 | −0.230293 | ||||||||
\(66\) | −2.86410 | −0.352546 | ||||||||
\(67\) | 3.72543 | 0.455134 | 0.227567 | − | 0.973762i | \(-0.426923\pi\) | ||||
0.227567 | + | 0.973762i | \(0.426923\pi\) | |||||||
\(68\) | 4.13308 | 0.501210 | ||||||||
\(69\) | 5.31993 | 0.640444 | ||||||||
\(70\) | −1.55328 | −0.185653 | ||||||||
\(71\) | −14.4977 | −1.72056 | −0.860281 | − | 0.509820i | \(-0.829712\pi\) | ||||
−0.860281 | + | 0.509820i | \(0.829712\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −10.2295 | −1.19727 | −0.598635 | − | 0.801022i | \(-0.704290\pi\) | ||||
−0.598635 | + | 0.801022i | \(0.704290\pi\) | |||||||
\(74\) | 7.50201 | 0.872090 | ||||||||
\(75\) | −2.58732 | −0.298758 | ||||||||
\(76\) | −4.34711 | −0.498648 | ||||||||
\(77\) | 2.86410 | 0.326394 | ||||||||
\(78\) | 1.19533 | 0.135344 | ||||||||
\(79\) | 13.1530 | 1.47982 | 0.739912 | − | 0.672704i | \(-0.234867\pi\) | ||||
0.739912 | + | 0.672704i | \(0.234867\pi\) | |||||||
\(80\) | 1.55328 | 0.173662 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.58747 | −0.175307 | ||||||||
\(83\) | 3.27581 | 0.359567 | 0.179783 | − | 0.983706i | \(-0.442460\pi\) | ||||
0.179783 | + | 0.983706i | \(0.442460\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.41984 | 0.696329 | ||||||||
\(86\) | −5.26207 | −0.567423 | ||||||||
\(87\) | 6.80630 | 0.729712 | ||||||||
\(88\) | −2.86410 | −0.305314 | ||||||||
\(89\) | 4.89203 | 0.518554 | 0.259277 | − | 0.965803i | \(-0.416516\pi\) | ||||
0.259277 | + | 0.965803i | \(0.416516\pi\) | |||||||
\(90\) | −1.55328 | −0.163730 | ||||||||
\(91\) | −1.19533 | −0.125304 | ||||||||
\(92\) | 5.31993 | 0.554641 | ||||||||
\(93\) | 8.33433 | 0.864229 | ||||||||
\(94\) | −4.76012 | −0.490969 | ||||||||
\(95\) | −6.75228 | −0.692770 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.85955 | −0.493412 | −0.246706 | − | 0.969090i | \(-0.579348\pi\) | ||||
−0.246706 | + | 0.969090i | \(0.579348\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 2.86410 | 0.287852 | ||||||||
\(100\) | −2.58732 | −0.258732 | ||||||||
\(101\) | −2.55589 | −0.254321 | −0.127160 | − | 0.991882i | \(-0.540586\pi\) | ||||
−0.127160 | + | 0.991882i | \(0.540586\pi\) | |||||||
\(102\) | −4.13308 | −0.409236 | ||||||||
\(103\) | −4.03327 | −0.397410 | −0.198705 | − | 0.980059i | \(-0.563674\pi\) | ||||
−0.198705 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(104\) | 1.19533 | 0.117211 | ||||||||
\(105\) | 1.55328 | 0.151585 | ||||||||
\(106\) | 9.50856 | 0.923553 | ||||||||
\(107\) | 19.1063 | 1.84707 | 0.923536 | − | 0.383512i | \(-0.125286\pi\) | ||||
0.923536 | + | 0.383512i | \(0.125286\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.3693 | 1.18477 | 0.592383 | − | 0.805657i | \(-0.298187\pi\) | ||||
0.592383 | + | 0.805657i | \(0.298187\pi\) | |||||||
\(110\) | −4.44874 | −0.424171 | ||||||||
\(111\) | −7.50201 | −0.712059 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.7853 | 1.01460 | 0.507299 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507299 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(114\) | 4.34711 | 0.407144 | ||||||||
\(115\) | 8.26334 | 0.770561 | ||||||||
\(116\) | 6.80630 | 0.631949 | ||||||||
\(117\) | −1.19533 | −0.110508 | ||||||||
\(118\) | −0.810529 | −0.0746152 | ||||||||
\(119\) | 4.13308 | 0.378879 | ||||||||
\(120\) | −1.55328 | −0.141794 | ||||||||
\(121\) | −2.79696 | −0.254269 | ||||||||
\(122\) | 0.00358361 | 0.000324445 0 | ||||||||
\(123\) | 1.58747 | 0.143137 | ||||||||
\(124\) | 8.33433 | 0.748445 | ||||||||
\(125\) | −11.7852 | −1.05410 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 0.859505 | 0.0762688 | 0.0381344 | − | 0.999273i | \(-0.487859\pi\) | ||||
0.0381344 | + | 0.999273i | \(0.487859\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.26207 | 0.463299 | ||||||||
\(130\) | 1.85668 | 0.162841 | ||||||||
\(131\) | −21.3634 | −1.86652 | −0.933262 | − | 0.359195i | \(-0.883051\pi\) | ||||
−0.933262 | + | 0.359195i | \(0.883051\pi\) | |||||||
\(132\) | 2.86410 | 0.249288 | ||||||||
\(133\) | −4.34711 | −0.376942 | ||||||||
\(134\) | −3.72543 | −0.321828 | ||||||||
\(135\) | 1.55328 | 0.133685 | ||||||||
\(136\) | −4.13308 | −0.354409 | ||||||||
\(137\) | 1.68404 | 0.143878 | 0.0719388 | − | 0.997409i | \(-0.477081\pi\) | ||||
0.0719388 | + | 0.997409i | \(0.477081\pi\) | |||||||
\(138\) | −5.31993 | −0.452863 | ||||||||
\(139\) | 2.96087 | 0.251137 | 0.125569 | − | 0.992085i | \(-0.459924\pi\) | ||||
0.125569 | + | 0.992085i | \(0.459924\pi\) | |||||||
\(140\) | 1.55328 | 0.131276 | ||||||||
\(141\) | 4.76012 | 0.400875 | ||||||||
\(142\) | 14.4977 | 1.21662 | ||||||||
\(143\) | −3.42353 | −0.286290 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.5721 | 0.877964 | ||||||||
\(146\) | 10.2295 | 0.846598 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −7.50201 | −0.616661 | ||||||||
\(149\) | −10.7462 | −0.880360 | −0.440180 | − | 0.897910i | \(-0.645085\pi\) | ||||
−0.440180 | + | 0.897910i | \(0.645085\pi\) | |||||||
\(150\) | 2.58732 | 0.211254 | ||||||||
\(151\) | 8.98373 | 0.731085 | 0.365543 | − | 0.930795i | \(-0.380883\pi\) | ||||
0.365543 | + | 0.930795i | \(0.380883\pi\) | |||||||
\(152\) | 4.34711 | 0.352597 | ||||||||
\(153\) | 4.13308 | 0.334140 | ||||||||
\(154\) | −2.86410 | −0.230795 | ||||||||
\(155\) | 12.9455 | 1.03981 | ||||||||
\(156\) | −1.19533 | −0.0957027 | ||||||||
\(157\) | 9.02424 | 0.720213 | 0.360106 | − | 0.932911i | \(-0.382740\pi\) | ||||
0.360106 | + | 0.932911i | \(0.382740\pi\) | |||||||
\(158\) | −13.1530 | −1.04639 | ||||||||
\(159\) | −9.50856 | −0.754078 | ||||||||
\(160\) | −1.55328 | −0.122798 | ||||||||
\(161\) | 5.31993 | 0.419269 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 19.3344 | 1.51439 | 0.757193 | − | 0.653191i | \(-0.226570\pi\) | ||||
0.757193 | + | 0.653191i | \(0.226570\pi\) | |||||||
\(164\) | 1.58747 | 0.123960 | ||||||||
\(165\) | 4.44874 | 0.346334 | ||||||||
\(166\) | −3.27581 | −0.254252 | ||||||||
\(167\) | −4.60141 | −0.356068 | −0.178034 | − | 0.984024i | \(-0.556974\pi\) | ||||
−0.178034 | + | 0.984024i | \(0.556974\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −11.5712 | −0.890092 | ||||||||
\(170\) | −6.41984 | −0.492379 | ||||||||
\(171\) | −4.34711 | −0.332432 | ||||||||
\(172\) | 5.26207 | 0.401229 | ||||||||
\(173\) | 13.2466 | 1.00712 | 0.503559 | − | 0.863961i | \(-0.332024\pi\) | ||||
0.503559 | + | 0.863961i | \(0.332024\pi\) | |||||||
\(174\) | −6.80630 | −0.515984 | ||||||||
\(175\) | −2.58732 | −0.195583 | ||||||||
\(176\) | 2.86410 | 0.215889 | ||||||||
\(177\) | 0.810529 | 0.0609231 | ||||||||
\(178\) | −4.89203 | −0.366673 | ||||||||
\(179\) | −23.5313 | −1.75881 | −0.879405 | − | 0.476075i | \(-0.842059\pi\) | ||||
−0.879405 | + | 0.476075i | \(0.842059\pi\) | |||||||
\(180\) | 1.55328 | 0.115775 | ||||||||
\(181\) | 2.50296 | 0.186044 | 0.0930220 | − | 0.995664i | \(-0.470347\pi\) | ||||
0.0930220 | + | 0.995664i | \(0.470347\pi\) | |||||||
\(182\) | 1.19533 | 0.0886035 | ||||||||
\(183\) | −0.00358361 | −0.000264908 0 | ||||||||
\(184\) | −5.31993 | −0.392190 | ||||||||
\(185\) | −11.6527 | −0.856725 | ||||||||
\(186\) | −8.33433 | −0.611102 | ||||||||
\(187\) | 11.8375 | 0.865647 | ||||||||
\(188\) | 4.76012 | 0.347168 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 6.75228 | 0.489862 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 2.11787 | 0.152447 | 0.0762237 | − | 0.997091i | \(-0.475714\pi\) | ||||
0.0762237 | + | 0.997091i | \(0.475714\pi\) | |||||||
\(194\) | 4.85955 | 0.348895 | ||||||||
\(195\) | −1.85668 | −0.132959 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −18.5010 | −1.31814 | −0.659072 | − | 0.752080i | \(-0.729051\pi\) | ||||
−0.659072 | + | 0.752080i | \(0.729051\pi\) | |||||||
\(198\) | −2.86410 | −0.203542 | ||||||||
\(199\) | 16.1068 | 1.14178 | 0.570891 | − | 0.821026i | \(-0.306598\pi\) | ||||
0.570891 | + | 0.821026i | \(0.306598\pi\) | |||||||
\(200\) | 2.58732 | 0.182951 | ||||||||
\(201\) | 3.72543 | 0.262772 | ||||||||
\(202\) | 2.55589 | 0.179832 | ||||||||
\(203\) | 6.80630 | 0.477708 | ||||||||
\(204\) | 4.13308 | 0.289374 | ||||||||
\(205\) | 2.46578 | 0.172218 | ||||||||
\(206\) | 4.03327 | 0.281012 | ||||||||
\(207\) | 5.31993 | 0.369761 | ||||||||
\(208\) | −1.19533 | −0.0828810 | ||||||||
\(209\) | −12.4505 | −0.861222 | ||||||||
\(210\) | −1.55328 | −0.107187 | ||||||||
\(211\) | −12.7388 | −0.876978 | −0.438489 | − | 0.898736i | \(-0.644486\pi\) | ||||
−0.438489 | + | 0.898736i | \(0.644486\pi\) | |||||||
\(212\) | −9.50856 | −0.653050 | ||||||||
\(213\) | −14.4977 | −0.993367 | ||||||||
\(214\) | −19.1063 | −1.30608 | ||||||||
\(215\) | 8.17347 | 0.557426 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.33433 | 0.565771 | ||||||||
\(218\) | −12.3693 | −0.837755 | ||||||||
\(219\) | −10.2295 | −0.691245 | ||||||||
\(220\) | 4.44874 | 0.299934 | ||||||||
\(221\) | −4.94039 | −0.332326 | ||||||||
\(222\) | 7.50201 | 0.503502 | ||||||||
\(223\) | 24.3664 | 1.63169 | 0.815846 | − | 0.578269i | \(-0.196272\pi\) | ||||
0.815846 | + | 0.578269i | \(0.196272\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.58732 | −0.172488 | ||||||||
\(226\) | −10.7853 | −0.717429 | ||||||||
\(227\) | −12.6366 | −0.838719 | −0.419359 | − | 0.907820i | \(-0.637745\pi\) | ||||
−0.419359 | + | 0.907820i | \(0.637745\pi\) | |||||||
\(228\) | −4.34711 | −0.287894 | ||||||||
\(229\) | 13.9198 | 0.919845 | 0.459922 | − | 0.887959i | \(-0.347877\pi\) | ||||
0.459922 | + | 0.887959i | \(0.347877\pi\) | |||||||
\(230\) | −8.26334 | −0.544869 | ||||||||
\(231\) | 2.86410 | 0.188444 | ||||||||
\(232\) | −6.80630 | −0.446855 | ||||||||
\(233\) | 5.26643 | 0.345015 | 0.172508 | − | 0.985008i | \(-0.444813\pi\) | ||||
0.172508 | + | 0.985008i | \(0.444813\pi\) | |||||||
\(234\) | 1.19533 | 0.0781410 | ||||||||
\(235\) | 7.39381 | 0.482319 | ||||||||
\(236\) | 0.810529 | 0.0527609 | ||||||||
\(237\) | 13.1530 | 0.854376 | ||||||||
\(238\) | −4.13308 | −0.267908 | ||||||||
\(239\) | −18.1064 | −1.17120 | −0.585601 | − | 0.810599i | \(-0.699142\pi\) | ||||
−0.585601 | + | 0.810599i | \(0.699142\pi\) | |||||||
\(240\) | 1.55328 | 0.100264 | ||||||||
\(241\) | 29.4501 | 1.89705 | 0.948525 | − | 0.316702i | \(-0.102576\pi\) | ||||
0.948525 | + | 0.316702i | \(0.102576\pi\) | |||||||
\(242\) | 2.79696 | 0.179795 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.00358361 | −0.000229417 0 | ||||||||
\(245\) | 1.55328 | 0.0992355 | ||||||||
\(246\) | −1.58747 | −0.101213 | ||||||||
\(247\) | 5.19622 | 0.330627 | ||||||||
\(248\) | −8.33433 | −0.529230 | ||||||||
\(249\) | 3.27581 | 0.207596 | ||||||||
\(250\) | 11.7852 | 0.745364 | ||||||||
\(251\) | 16.6181 | 1.04893 | 0.524463 | − | 0.851433i | \(-0.324266\pi\) | ||||
0.524463 | + | 0.851433i | \(0.324266\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 15.2368 | 0.957929 | ||||||||
\(254\) | −0.859505 | −0.0539302 | ||||||||
\(255\) | 6.41984 | 0.402026 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.3033 | 1.57838 | 0.789189 | − | 0.614150i | \(-0.210501\pi\) | ||||
0.789189 | + | 0.614150i | \(0.210501\pi\) | |||||||
\(258\) | −5.26207 | −0.327602 | ||||||||
\(259\) | −7.50201 | −0.466152 | ||||||||
\(260\) | −1.85668 | −0.115146 | ||||||||
\(261\) | 6.80630 | 0.421299 | ||||||||
\(262\) | 21.3634 | 1.31983 | ||||||||
\(263\) | −15.0413 | −0.927485 | −0.463743 | − | 0.885970i | \(-0.653494\pi\) | ||||
−0.463743 | + | 0.885970i | \(0.653494\pi\) | |||||||
\(264\) | −2.86410 | −0.176273 | ||||||||
\(265\) | −14.7695 | −0.907281 | ||||||||
\(266\) | 4.34711 | 0.266538 | ||||||||
\(267\) | 4.89203 | 0.299387 | ||||||||
\(268\) | 3.72543 | 0.227567 | ||||||||
\(269\) | 0.347738 | 0.0212020 | 0.0106010 | − | 0.999944i | \(-0.496626\pi\) | ||||
0.0106010 | + | 0.999944i | \(0.496626\pi\) | |||||||
\(270\) | −1.55328 | −0.0945297 | ||||||||
\(271\) | −21.8338 | −1.32631 | −0.663155 | − | 0.748482i | \(-0.730783\pi\) | ||||
−0.663155 | + | 0.748482i | \(0.730783\pi\) | |||||||
\(272\) | 4.13308 | 0.250605 | ||||||||
\(273\) | −1.19533 | −0.0723445 | ||||||||
\(274\) | −1.68404 | −0.101737 | ||||||||
\(275\) | −7.41033 | −0.446860 | ||||||||
\(276\) | 5.31993 | 0.320222 | ||||||||
\(277\) | 2.45754 | 0.147659 | 0.0738297 | − | 0.997271i | \(-0.476478\pi\) | ||||
0.0738297 | + | 0.997271i | \(0.476478\pi\) | |||||||
\(278\) | −2.96087 | −0.177581 | ||||||||
\(279\) | 8.33433 | 0.498963 | ||||||||
\(280\) | −1.55328 | −0.0928263 | ||||||||
\(281\) | −4.17887 | −0.249291 | −0.124645 | − | 0.992201i | \(-0.539779\pi\) | ||||
−0.124645 | + | 0.992201i | \(0.539779\pi\) | |||||||
\(282\) | −4.76012 | −0.283461 | ||||||||
\(283\) | −11.7209 | −0.696737 | −0.348369 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348369 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(284\) | −14.4977 | −0.860281 | ||||||||
\(285\) | −6.75228 | −0.399971 | ||||||||
\(286\) | 3.42353 | 0.202438 | ||||||||
\(287\) | 1.58747 | 0.0937053 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0.0823856 | 0.00484621 | ||||||||
\(290\) | −10.5721 | −0.620814 | ||||||||
\(291\) | −4.85955 | −0.284872 | ||||||||
\(292\) | −10.2295 | −0.598635 | ||||||||
\(293\) | −5.34331 | −0.312160 | −0.156080 | − | 0.987744i | \(-0.549886\pi\) | ||||
−0.156080 | + | 0.987744i | \(0.549886\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 1.25898 | 0.0733006 | ||||||||
\(296\) | 7.50201 | 0.436045 | ||||||||
\(297\) | 2.86410 | 0.166192 | ||||||||
\(298\) | 10.7462 | 0.622508 | ||||||||
\(299\) | −6.35906 | −0.367754 | ||||||||
\(300\) | −2.58732 | −0.149379 | ||||||||
\(301\) | 5.26207 | 0.303300 | ||||||||
\(302\) | −8.98373 | −0.516955 | ||||||||
\(303\) | −2.55589 | −0.146832 | ||||||||
\(304\) | −4.34711 | −0.249324 | ||||||||
\(305\) | −0.00556635 | −0.000318728 0 | ||||||||
\(306\) | −4.13308 | −0.236273 | ||||||||
\(307\) | 12.1496 | 0.693413 | 0.346707 | − | 0.937974i | \(-0.387300\pi\) | ||||
0.346707 | + | 0.937974i | \(0.387300\pi\) | |||||||
\(308\) | 2.86410 | 0.163197 | ||||||||
\(309\) | −4.03327 | −0.229445 | ||||||||
\(310\) | −12.9455 | −0.735258 | ||||||||
\(311\) | −16.5576 | −0.938896 | −0.469448 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469448 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(312\) | 1.19533 | 0.0676721 | ||||||||
\(313\) | 19.8617 | 1.12265 | 0.561324 | − | 0.827596i | \(-0.310292\pi\) | ||||
0.561324 | + | 0.827596i | \(0.310292\pi\) | |||||||
\(314\) | −9.02424 | −0.509267 | ||||||||
\(315\) | 1.55328 | 0.0875175 | ||||||||
\(316\) | 13.1530 | 0.739912 | ||||||||
\(317\) | 17.5364 | 0.984942 | 0.492471 | − | 0.870329i | \(-0.336094\pi\) | ||||
0.492471 | + | 0.870329i | \(0.336094\pi\) | |||||||
\(318\) | 9.50856 | 0.533213 | ||||||||
\(319\) | 19.4939 | 1.09145 | ||||||||
\(320\) | 1.55328 | 0.0868310 | ||||||||
\(321\) | 19.1063 | 1.06641 | ||||||||
\(322\) | −5.31993 | −0.296468 | ||||||||
\(323\) | −17.9670 | −0.999709 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.09269 | 0.171552 | ||||||||
\(326\) | −19.3344 | −1.07083 | ||||||||
\(327\) | 12.3693 | 0.684024 | ||||||||
\(328\) | −1.58747 | −0.0876533 | ||||||||
\(329\) | 4.76012 | 0.262434 | ||||||||
\(330\) | −4.44874 | −0.244895 | ||||||||
\(331\) | 6.91301 | 0.379973 | 0.189987 | − | 0.981787i | \(-0.439156\pi\) | ||||
0.189987 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(332\) | 3.27581 | 0.179783 | ||||||||
\(333\) | −7.50201 | −0.411107 | ||||||||
\(334\) | 4.60141 | 0.251778 | ||||||||
\(335\) | 5.78664 | 0.316158 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −23.7749 | −1.29510 | −0.647550 | − | 0.762023i | \(-0.724206\pi\) | ||||
−0.647550 | + | 0.762023i | \(0.724206\pi\) | |||||||
\(338\) | 11.5712 | 0.629390 | ||||||||
\(339\) | 10.7853 | 0.585778 | ||||||||
\(340\) | 6.41984 | 0.348165 | ||||||||
\(341\) | 23.8703 | 1.29265 | ||||||||
\(342\) | 4.34711 | 0.235065 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.26207 | −0.283712 | ||||||||
\(345\) | 8.26334 | 0.444884 | ||||||||
\(346\) | −13.2466 | −0.712140 | ||||||||
\(347\) | 20.6915 | 1.11078 | 0.555390 | − | 0.831590i | \(-0.312569\pi\) | ||||
0.555390 | + | 0.831590i | \(0.312569\pi\) | |||||||
\(348\) | 6.80630 | 0.364856 | ||||||||
\(349\) | −13.6257 | −0.729366 | −0.364683 | − | 0.931132i | \(-0.618823\pi\) | ||||
−0.364683 | + | 0.931132i | \(0.618823\pi\) | |||||||
\(350\) | 2.58732 | 0.138298 | ||||||||
\(351\) | −1.19533 | −0.0638018 | ||||||||
\(352\) | −2.86410 | −0.152657 | ||||||||
\(353\) | 19.9014 | 1.05924 | 0.529621 | − | 0.848234i | \(-0.322334\pi\) | ||||
0.529621 | + | 0.848234i | \(0.322334\pi\) | |||||||
\(354\) | −0.810529 | −0.0430791 | ||||||||
\(355\) | −22.5190 | −1.19519 | ||||||||
\(356\) | 4.89203 | 0.259277 | ||||||||
\(357\) | 4.13308 | 0.218746 | ||||||||
\(358\) | 23.5313 | 1.24367 | ||||||||
\(359\) | −29.8262 | −1.57416 | −0.787082 | − | 0.616848i | \(-0.788409\pi\) | ||||
−0.787082 | + | 0.616848i | \(0.788409\pi\) | |||||||
\(360\) | −1.55328 | −0.0818651 | ||||||||
\(361\) | −0.102635 | −0.00540184 | ||||||||
\(362\) | −2.50296 | −0.131553 | ||||||||
\(363\) | −2.79696 | −0.146802 | ||||||||
\(364\) | −1.19533 | −0.0626521 | ||||||||
\(365\) | −15.8893 | −0.831682 | ||||||||
\(366\) | 0.00358361 | 0.000187318 0 | ||||||||
\(367\) | −15.6431 | −0.816561 | −0.408280 | − | 0.912857i | \(-0.633871\pi\) | ||||
−0.408280 | + | 0.912857i | \(0.633871\pi\) | |||||||
\(368\) | 5.31993 | 0.277321 | ||||||||
\(369\) | 1.58747 | 0.0826403 | ||||||||
\(370\) | 11.6527 | 0.605796 | ||||||||
\(371\) | −9.50856 | −0.493660 | ||||||||
\(372\) | 8.33433 | 0.432115 | ||||||||
\(373\) | 10.4280 | 0.539940 | 0.269970 | − | 0.962869i | \(-0.412986\pi\) | ||||
0.269970 | + | 0.962869i | \(0.412986\pi\) | |||||||
\(374\) | −11.8375 | −0.612105 | ||||||||
\(375\) | −11.7852 | −0.608587 | ||||||||
\(376\) | −4.76012 | −0.245485 | ||||||||
\(377\) | −8.13575 | −0.419012 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −15.5075 | −0.796567 | −0.398284 | − | 0.917262i | \(-0.630394\pi\) | ||||
−0.398284 | + | 0.917262i | \(0.630394\pi\) | |||||||
\(380\) | −6.75228 | −0.346385 | ||||||||
\(381\) | 0.859505 | 0.0440338 | ||||||||
\(382\) | −1.00000 | −0.0511645 | ||||||||
\(383\) | −17.7275 | −0.905835 | −0.452918 | − | 0.891552i | \(-0.649617\pi\) | ||||
−0.452918 | + | 0.891552i | \(0.649617\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.44874 | 0.226729 | ||||||||
\(386\) | −2.11787 | −0.107797 | ||||||||
\(387\) | 5.26207 | 0.267486 | ||||||||
\(388\) | −4.85955 | −0.246706 | ||||||||
\(389\) | 26.9359 | 1.36570 | 0.682851 | − | 0.730558i | \(-0.260740\pi\) | ||||
0.682851 | + | 0.730558i | \(0.260740\pi\) | |||||||
\(390\) | 1.85668 | 0.0940166 | ||||||||
\(391\) | 21.9877 | 1.11197 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −21.3634 | −1.07764 | ||||||||
\(394\) | 18.5010 | 0.932068 | ||||||||
\(395\) | 20.4302 | 1.02796 | ||||||||
\(396\) | 2.86410 | 0.143926 | ||||||||
\(397\) | −24.9829 | −1.25386 | −0.626928 | − | 0.779077i | \(-0.715688\pi\) | ||||
−0.626928 | + | 0.779077i | \(0.715688\pi\) | |||||||
\(398\) | −16.1068 | −0.807361 | ||||||||
\(399\) | −4.34711 | −0.217628 | ||||||||
\(400\) | −2.58732 | −0.129366 | ||||||||
\(401\) | 5.32228 | 0.265782 | 0.132891 | − | 0.991131i | \(-0.457574\pi\) | ||||
0.132891 | + | 0.991131i | \(0.457574\pi\) | |||||||
\(402\) | −3.72543 | −0.185808 | ||||||||
\(403\) | −9.96224 | −0.496255 | ||||||||
\(404\) | −2.55589 | −0.127160 | ||||||||
\(405\) | 1.55328 | 0.0771831 | ||||||||
\(406\) | −6.80630 | −0.337791 | ||||||||
\(407\) | −21.4865 | −1.06504 | ||||||||
\(408\) | −4.13308 | −0.204618 | ||||||||
\(409\) | 14.7703 | 0.730345 | 0.365172 | − | 0.930940i | \(-0.381010\pi\) | ||||
0.365172 | + | 0.930940i | \(0.381010\pi\) | |||||||
\(410\) | −2.46578 | −0.121776 | ||||||||
\(411\) | 1.68404 | 0.0830677 | ||||||||
\(412\) | −4.03327 | −0.198705 | ||||||||
\(413\) | 0.810529 | 0.0398835 | ||||||||
\(414\) | −5.31993 | −0.261460 | ||||||||
\(415\) | 5.08825 | 0.249772 | ||||||||
\(416\) | 1.19533 | 0.0586057 | ||||||||
\(417\) | 2.96087 | 0.144994 | ||||||||
\(418\) | 12.4505 | 0.608976 | ||||||||
\(419\) | 18.8559 | 0.921171 | 0.460586 | − | 0.887615i | \(-0.347639\pi\) | ||||
0.460586 | + | 0.887615i | \(0.347639\pi\) | |||||||
\(420\) | 1.55328 | 0.0757923 | ||||||||
\(421\) | 11.9762 | 0.583686 | 0.291843 | − | 0.956466i | \(-0.405732\pi\) | ||||
0.291843 | + | 0.956466i | \(0.405732\pi\) | |||||||
\(422\) | 12.7388 | 0.620117 | ||||||||
\(423\) | 4.76012 | 0.231445 | ||||||||
\(424\) | 9.50856 | 0.461776 | ||||||||
\(425\) | −10.6936 | −0.518716 | ||||||||
\(426\) | 14.4977 | 0.702416 | ||||||||
\(427\) | −0.00358361 | −0.000173423 0 | ||||||||
\(428\) | 19.1063 | 0.923536 | ||||||||
\(429\) | −3.42353 | −0.165290 | ||||||||
\(430\) | −8.17347 | −0.394160 | ||||||||
\(431\) | 33.6954 | 1.62305 | 0.811524 | − | 0.584319i | \(-0.198638\pi\) | ||||
0.811524 | + | 0.584319i | \(0.198638\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −25.9712 | −1.24810 | −0.624048 | − | 0.781386i | \(-0.714513\pi\) | ||||
−0.624048 | + | 0.781386i | \(0.714513\pi\) | |||||||
\(434\) | −8.33433 | −0.400060 | ||||||||
\(435\) | 10.5721 | 0.506893 | ||||||||
\(436\) | 12.3693 | 0.592383 | ||||||||
\(437\) | −23.1263 | −1.10628 | ||||||||
\(438\) | 10.2295 | 0.488784 | ||||||||
\(439\) | −10.6796 | −0.509711 | −0.254856 | − | 0.966979i | \(-0.582028\pi\) | ||||
−0.254856 | + | 0.966979i | \(0.582028\pi\) | |||||||
\(440\) | −4.44874 | −0.212086 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 4.94039 | 0.234990 | ||||||||
\(443\) | 28.3258 | 1.34580 | 0.672899 | − | 0.739735i | \(-0.265049\pi\) | ||||
0.672899 | + | 0.739735i | \(0.265049\pi\) | |||||||
\(444\) | −7.50201 | −0.356029 | ||||||||
\(445\) | 7.59869 | 0.360213 | ||||||||
\(446\) | −24.3664 | −1.15378 | ||||||||
\(447\) | −10.7462 | −0.508276 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −37.2750 | −1.75912 | −0.879558 | − | 0.475792i | \(-0.842162\pi\) | ||||
−0.879558 | + | 0.475792i | \(0.842162\pi\) | |||||||
\(450\) | 2.58732 | 0.121967 | ||||||||
\(451\) | 4.54666 | 0.214094 | ||||||||
\(452\) | 10.7853 | 0.507299 | ||||||||
\(453\) | 8.98373 | 0.422092 | ||||||||
\(454\) | 12.6366 | 0.593064 | ||||||||
\(455\) | −1.85668 | −0.0870424 | ||||||||
\(456\) | 4.34711 | 0.203572 | ||||||||
\(457\) | −23.9922 | −1.12231 | −0.561154 | − | 0.827711i | \(-0.689643\pi\) | ||||
−0.561154 | + | 0.827711i | \(0.689643\pi\) | |||||||
\(458\) | −13.9198 | −0.650429 | ||||||||
\(459\) | 4.13308 | 0.192916 | ||||||||
\(460\) | 8.26334 | 0.385280 | ||||||||
\(461\) | 32.3022 | 1.50447 | 0.752233 | − | 0.658898i | \(-0.228977\pi\) | ||||
0.752233 | + | 0.658898i | \(0.228977\pi\) | |||||||
\(462\) | −2.86410 | −0.133250 | ||||||||
\(463\) | −18.2217 | −0.846836 | −0.423418 | − | 0.905934i | \(-0.639170\pi\) | ||||
−0.423418 | + | 0.905934i | \(0.639170\pi\) | |||||||
\(464\) | 6.80630 | 0.315974 | ||||||||
\(465\) | 12.9455 | 0.600335 | ||||||||
\(466\) | −5.26643 | −0.243963 | ||||||||
\(467\) | −19.4182 | −0.898565 | −0.449283 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449283 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(468\) | −1.19533 | −0.0552540 | ||||||||
\(469\) | 3.72543 | 0.172024 | ||||||||
\(470\) | −7.39381 | −0.341051 | ||||||||
\(471\) | 9.02424 | 0.415815 | ||||||||
\(472\) | −0.810529 | −0.0373076 | ||||||||
\(473\) | 15.0711 | 0.692968 | ||||||||
\(474\) | −13.1530 | −0.604135 | ||||||||
\(475\) | 11.2474 | 0.516064 | ||||||||
\(476\) | 4.13308 | 0.189440 | ||||||||
\(477\) | −9.50856 | −0.435367 | ||||||||
\(478\) | 18.1064 | 0.828165 | ||||||||
\(479\) | −16.8579 | −0.770257 | −0.385129 | − | 0.922863i | \(-0.625843\pi\) | ||||
−0.385129 | + | 0.922863i | \(0.625843\pi\) | |||||||
\(480\) | −1.55328 | −0.0708972 | ||||||||
\(481\) | 8.96735 | 0.408876 | ||||||||
\(482\) | −29.4501 | −1.34142 | ||||||||
\(483\) | 5.31993 | 0.242065 | ||||||||
\(484\) | −2.79696 | −0.127134 | ||||||||
\(485\) | −7.54824 | −0.342748 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −27.2722 | −1.23582 | −0.617910 | − | 0.786248i | \(-0.712021\pi\) | ||||
−0.617910 | + | 0.786248i | \(0.712021\pi\) | |||||||
\(488\) | 0.00358361 | 0.000162222 0 | ||||||||
\(489\) | 19.3344 | 0.874331 | ||||||||
\(490\) | −1.55328 | −0.0701701 | ||||||||
\(491\) | 39.7906 | 1.79572 | 0.897862 | − | 0.440278i | \(-0.145120\pi\) | ||||
0.897862 | + | 0.440278i | \(0.145120\pi\) | |||||||
\(492\) | 1.58747 | 0.0715686 | ||||||||
\(493\) | 28.1310 | 1.26696 | ||||||||
\(494\) | −5.19622 | −0.233789 | ||||||||
\(495\) | 4.44874 | 0.199956 | ||||||||
\(496\) | 8.33433 | 0.374222 | ||||||||
\(497\) | −14.4977 | −0.650311 | ||||||||
\(498\) | −3.27581 | −0.146793 | ||||||||
\(499\) | 14.3592 | 0.642806 | 0.321403 | − | 0.946943i | \(-0.395846\pi\) | ||||
0.321403 | + | 0.946943i | \(0.395846\pi\) | |||||||
\(500\) | −11.7852 | −0.527052 | ||||||||
\(501\) | −4.60141 | −0.205576 | ||||||||
\(502\) | −16.6181 | −0.741703 | ||||||||
\(503\) | −8.85752 | −0.394937 | −0.197469 | − | 0.980309i | \(-0.563272\pi\) | ||||
−0.197469 | + | 0.980309i | \(0.563272\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −3.97002 | −0.176663 | ||||||||
\(506\) | −15.2368 | −0.677358 | ||||||||
\(507\) | −11.5712 | −0.513895 | ||||||||
\(508\) | 0.859505 | 0.0381344 | ||||||||
\(509\) | −14.9787 | −0.663919 | −0.331959 | − | 0.943294i | \(-0.607710\pi\) | ||||
−0.331959 | + | 0.943294i | \(0.607710\pi\) | |||||||
\(510\) | −6.41984 | −0.284275 | ||||||||
\(511\) | −10.2295 | −0.452526 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.34711 | −0.191930 | ||||||||
\(514\) | −25.3033 | −1.11608 | ||||||||
\(515\) | −6.26481 | −0.276060 | ||||||||
\(516\) | 5.26207 | 0.231650 | ||||||||
\(517\) | 13.6335 | 0.599599 | ||||||||
\(518\) | 7.50201 | 0.329619 | ||||||||
\(519\) | 13.2466 | 0.581460 | ||||||||
\(520\) | 1.85668 | 0.0814207 | ||||||||
\(521\) | 0.958358 | 0.0419864 | 0.0209932 | − | 0.999780i | \(-0.493317\pi\) | ||||
0.0209932 | + | 0.999780i | \(0.493317\pi\) | |||||||
\(522\) | −6.80630 | −0.297904 | ||||||||
\(523\) | 40.3532 | 1.76452 | 0.882260 | − | 0.470762i | \(-0.156021\pi\) | ||||
0.882260 | + | 0.470762i | \(0.156021\pi\) | |||||||
\(524\) | −21.3634 | −0.933262 | ||||||||
\(525\) | −2.58732 | −0.112920 | ||||||||
\(526\) | 15.0413 | 0.655831 | ||||||||
\(527\) | 34.4465 | 1.50051 | ||||||||
\(528\) | 2.86410 | 0.124644 | ||||||||
\(529\) | 5.30166 | 0.230507 | ||||||||
\(530\) | 14.7695 | 0.641544 | ||||||||
\(531\) | 0.810529 | 0.0351739 | ||||||||
\(532\) | −4.34711 | −0.188471 | ||||||||
\(533\) | −1.89754 | −0.0821918 | ||||||||
\(534\) | −4.89203 | −0.211699 | ||||||||
\(535\) | 29.6774 | 1.28307 | ||||||||
\(536\) | −3.72543 | −0.160914 | ||||||||
\(537\) | −23.5313 | −1.01545 | ||||||||
\(538\) | −0.347738 | −0.0149920 | ||||||||
\(539\) | 2.86410 | 0.123365 | ||||||||
\(540\) | 1.55328 | 0.0668426 | ||||||||
\(541\) | 31.8764 | 1.37047 | 0.685236 | − | 0.728321i | \(-0.259699\pi\) | ||||
0.685236 | + | 0.728321i | \(0.259699\pi\) | |||||||
\(542\) | 21.8338 | 0.937843 | ||||||||
\(543\) | 2.50296 | 0.107413 | ||||||||
\(544\) | −4.13308 | −0.177205 | ||||||||
\(545\) | 19.2130 | 0.822995 | ||||||||
\(546\) | 1.19533 | 0.0511553 | ||||||||
\(547\) | −0.0898509 | −0.00384175 | −0.00192087 | − | 0.999998i | \(-0.500611\pi\) | ||||
−0.00192087 | + | 0.999998i | \(0.500611\pi\) | |||||||
\(548\) | 1.68404 | 0.0719388 | ||||||||
\(549\) | −0.00358361 | −0.000152945 0 | ||||||||
\(550\) | 7.41033 | 0.315978 | ||||||||
\(551\) | −29.5877 | −1.26048 | ||||||||
\(552\) | −5.31993 | −0.226431 | ||||||||
\(553\) | 13.1530 | 0.559321 | ||||||||
\(554\) | −2.45754 | −0.104411 | ||||||||
\(555\) | −11.6527 | −0.494630 | ||||||||
\(556\) | 2.96087 | 0.125569 | ||||||||
\(557\) | −1.06503 | −0.0451266 | −0.0225633 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225633 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(558\) | −8.33433 | −0.352820 | ||||||||
\(559\) | −6.28989 | −0.266034 | ||||||||
\(560\) | 1.55328 | 0.0656381 | ||||||||
\(561\) | 11.8375 | 0.499782 | ||||||||
\(562\) | 4.17887 | 0.176275 | ||||||||
\(563\) | 1.32372 | 0.0557882 | 0.0278941 | − | 0.999611i | \(-0.491120\pi\) | ||||
0.0278941 | + | 0.999611i | \(0.491120\pi\) | |||||||
\(564\) | 4.76012 | 0.200437 | ||||||||
\(565\) | 16.7526 | 0.704788 | ||||||||
\(566\) | 11.7209 | 0.492667 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 14.4977 | 0.608310 | ||||||||
\(569\) | −17.2551 | −0.723370 | −0.361685 | − | 0.932300i | \(-0.617798\pi\) | ||||
−0.361685 | + | 0.932300i | \(0.617798\pi\) | |||||||
\(570\) | 6.75228 | 0.282822 | ||||||||
\(571\) | 21.5220 | 0.900670 | 0.450335 | − | 0.892860i | \(-0.351305\pi\) | ||||
0.450335 | + | 0.892860i | \(0.351305\pi\) | |||||||
\(572\) | −3.42353 | −0.143145 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −1.58747 | −0.0662597 | ||||||||
\(575\) | −13.7644 | −0.574013 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −24.6862 | −1.02770 | −0.513850 | − | 0.857880i | \(-0.671781\pi\) | ||||
−0.513850 | + | 0.857880i | \(0.671781\pi\) | |||||||
\(578\) | −0.0823856 | −0.00342679 | ||||||||
\(579\) | 2.11787 | 0.0880155 | ||||||||
\(580\) | 10.5721 | 0.438982 | ||||||||
\(581\) | 3.27581 | 0.135903 | ||||||||
\(582\) | 4.85955 | 0.201435 | ||||||||
\(583\) | −27.2334 | −1.12789 | ||||||||
\(584\) | 10.2295 | 0.423299 | ||||||||
\(585\) | −1.85668 | −0.0767642 | ||||||||
\(586\) | 5.34331 | 0.220730 | ||||||||
\(587\) | 29.8961 | 1.23394 | 0.616972 | − | 0.786985i | \(-0.288359\pi\) | ||||
0.616972 | + | 0.786985i | \(0.288359\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −36.2302 | −1.49284 | ||||||||
\(590\) | −1.25898 | −0.0518313 | ||||||||
\(591\) | −18.5010 | −0.761031 | ||||||||
\(592\) | −7.50201 | −0.308331 | ||||||||
\(593\) | −36.7644 | −1.50973 | −0.754867 | − | 0.655878i | \(-0.772298\pi\) | ||||
−0.754867 | + | 0.655878i | \(0.772298\pi\) | |||||||
\(594\) | −2.86410 | −0.117515 | ||||||||
\(595\) | 6.41984 | 0.263188 | ||||||||
\(596\) | −10.7462 | −0.440180 | ||||||||
\(597\) | 16.1068 | 0.659208 | ||||||||
\(598\) | 6.35906 | 0.260041 | ||||||||
\(599\) | −33.8172 | −1.38173 | −0.690866 | − | 0.722983i | \(-0.742771\pi\) | ||||
−0.690866 | + | 0.722983i | \(0.742771\pi\) | |||||||
\(600\) | 2.58732 | 0.105627 | ||||||||
\(601\) | 16.9016 | 0.689429 | 0.344715 | − | 0.938708i | \(-0.387976\pi\) | ||||
0.344715 | + | 0.938708i | \(0.387976\pi\) | |||||||
\(602\) | −5.26207 | −0.214466 | ||||||||
\(603\) | 3.72543 | 0.151711 | ||||||||
\(604\) | 8.98373 | 0.365543 | ||||||||
\(605\) | −4.34446 | −0.176627 | ||||||||
\(606\) | 2.55589 | 0.103826 | ||||||||
\(607\) | −26.5600 | −1.07804 | −0.539019 | − | 0.842293i | \(-0.681205\pi\) | ||||
−0.539019 | + | 0.842293i | \(0.681205\pi\) | |||||||
\(608\) | 4.34711 | 0.176299 | ||||||||
\(609\) | 6.80630 | 0.275805 | ||||||||
\(610\) | 0.00556635 | 0.000225375 0 | ||||||||
\(611\) | −5.68990 | −0.230189 | ||||||||
\(612\) | 4.13308 | 0.167070 | ||||||||
\(613\) | −43.8711 | −1.77194 | −0.885969 | − | 0.463745i | \(-0.846505\pi\) | ||||
−0.885969 | + | 0.463745i | \(0.846505\pi\) | |||||||
\(614\) | −12.1496 | −0.490317 | ||||||||
\(615\) | 2.46578 | 0.0994300 | ||||||||
\(616\) | −2.86410 | −0.115398 | ||||||||
\(617\) | 7.23786 | 0.291385 | 0.145693 | − | 0.989330i | \(-0.453459\pi\) | ||||
0.145693 | + | 0.989330i | \(0.453459\pi\) | |||||||
\(618\) | 4.03327 | 0.162242 | ||||||||
\(619\) | −8.61387 | −0.346221 | −0.173110 | − | 0.984902i | \(-0.555382\pi\) | ||||
−0.173110 | + | 0.984902i | \(0.555382\pi\) | |||||||
\(620\) | 12.9455 | 0.519906 | ||||||||
\(621\) | 5.31993 | 0.213481 | ||||||||
\(622\) | 16.5576 | 0.663900 | ||||||||
\(623\) | 4.89203 | 0.195995 | ||||||||
\(624\) | −1.19533 | −0.0478514 | ||||||||
\(625\) | −5.36918 | −0.214767 | ||||||||
\(626\) | −19.8617 | −0.793832 | ||||||||
\(627\) | −12.4505 | −0.497227 | ||||||||
\(628\) | 9.02424 | 0.360106 | ||||||||
\(629\) | −31.0064 | −1.23631 | ||||||||
\(630\) | −1.55328 | −0.0618842 | ||||||||
\(631\) | 29.7736 | 1.18527 | 0.592633 | − | 0.805472i | \(-0.298088\pi\) | ||||
0.592633 | + | 0.805472i | \(0.298088\pi\) | |||||||
\(632\) | −13.1530 | −0.523196 | ||||||||
\(633\) | −12.7388 | −0.506324 | ||||||||
\(634\) | −17.5364 | −0.696459 | ||||||||
\(635\) | 1.33505 | 0.0529800 | ||||||||
\(636\) | −9.50856 | −0.377039 | ||||||||
\(637\) | −1.19533 | −0.0473606 | ||||||||
\(638\) | −19.4939 | −0.771770 | ||||||||
\(639\) | −14.4977 | −0.573521 | ||||||||
\(640\) | −1.55328 | −0.0613988 | ||||||||
\(641\) | −38.6310 | −1.52583 | −0.762916 | − | 0.646498i | \(-0.776233\pi\) | ||||
−0.762916 | + | 0.646498i | \(0.776233\pi\) | |||||||
\(642\) | −19.1063 | −0.754064 | ||||||||
\(643\) | −50.6263 | −1.99651 | −0.998253 | − | 0.0590920i | \(-0.981179\pi\) | ||||
−0.998253 | + | 0.0590920i | \(0.981179\pi\) | |||||||
\(644\) | 5.31993 | 0.209635 | ||||||||
\(645\) | 8.17347 | 0.321830 | ||||||||
\(646\) | 17.9670 | 0.706901 | ||||||||
\(647\) | 43.4769 | 1.70925 | 0.854626 | − | 0.519244i | \(-0.173786\pi\) | ||||
0.854626 | + | 0.519244i | \(0.173786\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 2.32143 | 0.0911242 | ||||||||
\(650\) | −3.09269 | −0.121305 | ||||||||
\(651\) | 8.33433 | 0.326648 | ||||||||
\(652\) | 19.3344 | 0.757193 | ||||||||
\(653\) | −7.90470 | −0.309335 | −0.154667 | − | 0.987967i | \(-0.549431\pi\) | ||||
−0.154667 | + | 0.987967i | \(0.549431\pi\) | |||||||
\(654\) | −12.3693 | −0.483678 | ||||||||
\(655\) | −33.1833 | −1.29658 | ||||||||
\(656\) | 1.58747 | 0.0619802 | ||||||||
\(657\) | −10.2295 | −0.399090 | ||||||||
\(658\) | −4.76012 | −0.185569 | ||||||||
\(659\) | −17.9527 | −0.699340 | −0.349670 | − | 0.936873i | \(-0.613706\pi\) | ||||
−0.349670 | + | 0.936873i | \(0.613706\pi\) | |||||||
\(660\) | 4.44874 | 0.173167 | ||||||||
\(661\) | −7.50028 | −0.291727 | −0.145863 | − | 0.989305i | \(-0.546596\pi\) | ||||
−0.145863 | + | 0.989305i | \(0.546596\pi\) | |||||||
\(662\) | −6.91301 | −0.268682 | ||||||||
\(663\) | −4.94039 | −0.191869 | ||||||||
\(664\) | −3.27581 | −0.127126 | ||||||||
\(665\) | −6.75228 | −0.261842 | ||||||||
\(666\) | 7.50201 | 0.290697 | ||||||||
\(667\) | 36.2090 | 1.40202 | ||||||||
\(668\) | −4.60141 | −0.178034 | ||||||||
\(669\) | 24.3664 | 0.942058 | ||||||||
\(670\) | −5.78664 | −0.223557 | ||||||||
\(671\) | −0.0102638 | −0.000396230 0 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 9.35453 | 0.360591 | 0.180295 | − | 0.983613i | \(-0.442295\pi\) | ||||
0.180295 | + | 0.983613i | \(0.442295\pi\) | |||||||
\(674\) | 23.7749 | 0.915774 | ||||||||
\(675\) | −2.58732 | −0.0995860 | ||||||||
\(676\) | −11.5712 | −0.445046 | ||||||||
\(677\) | 41.8837 | 1.60972 | 0.804861 | − | 0.593464i | \(-0.202240\pi\) | ||||
0.804861 | + | 0.593464i | \(0.202240\pi\) | |||||||
\(678\) | −10.7853 | −0.414208 | ||||||||
\(679\) | −4.85955 | −0.186492 | ||||||||
\(680\) | −6.41984 | −0.246190 | ||||||||
\(681\) | −12.6366 | −0.484235 | ||||||||
\(682\) | −23.8703 | −0.914041 | ||||||||
\(683\) | −15.4568 | −0.591438 | −0.295719 | − | 0.955275i | \(-0.595559\pi\) | ||||
−0.295719 | + | 0.955275i | \(0.595559\pi\) | |||||||
\(684\) | −4.34711 | −0.166216 | ||||||||
\(685\) | 2.61579 | 0.0999443 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 13.9198 | 0.531073 | ||||||||
\(688\) | 5.26207 | 0.200614 | ||||||||
\(689\) | 11.3658 | 0.433004 | ||||||||
\(690\) | −8.26334 | −0.314580 | ||||||||
\(691\) | 27.0170 | 1.02777 | 0.513887 | − | 0.857858i | \(-0.328205\pi\) | ||||
0.513887 | + | 0.857858i | \(0.328205\pi\) | |||||||
\(692\) | 13.2466 | 0.503559 | ||||||||
\(693\) | 2.86410 | 0.108798 | ||||||||
\(694\) | −20.6915 | −0.785440 | ||||||||
\(695\) | 4.59905 | 0.174452 | ||||||||
\(696\) | −6.80630 | −0.257992 | ||||||||
\(697\) | 6.56114 | 0.248521 | ||||||||
\(698\) | 13.6257 | 0.515740 | ||||||||
\(699\) | 5.26643 | 0.199195 | ||||||||
\(700\) | −2.58732 | −0.0977915 | ||||||||
\(701\) | 28.6484 | 1.08204 | 0.541018 | − | 0.841011i | \(-0.318039\pi\) | ||||
0.541018 | + | 0.841011i | \(0.318039\pi\) | |||||||
\(702\) | 1.19533 | 0.0451147 | ||||||||
\(703\) | 32.6120 | 1.22999 | ||||||||
\(704\) | 2.86410 | 0.107945 | ||||||||
\(705\) | 7.39381 | 0.278467 | ||||||||
\(706\) | −19.9014 | −0.748997 | ||||||||
\(707\) | −2.55589 | −0.0961242 | ||||||||
\(708\) | 0.810529 | 0.0304615 | ||||||||
\(709\) | 47.8566 | 1.79729 | 0.898647 | − | 0.438672i | \(-0.144551\pi\) | ||||
0.898647 | + | 0.438672i | \(0.144551\pi\) | |||||||
\(710\) | 22.5190 | 0.845124 | ||||||||
\(711\) | 13.1530 | 0.493274 | ||||||||
\(712\) | −4.89203 | −0.183337 | ||||||||
\(713\) | 44.3380 | 1.66047 | ||||||||
\(714\) | −4.13308 | −0.154677 | ||||||||
\(715\) | −5.31770 | −0.198871 | ||||||||
\(716\) | −23.5313 | −0.879405 | ||||||||
\(717\) | −18.1064 | −0.676194 | ||||||||
\(718\) | 29.8262 | 1.11310 | ||||||||
\(719\) | −31.0095 | −1.15646 | −0.578229 | − | 0.815874i | \(-0.696256\pi\) | ||||
−0.578229 | + | 0.815874i | \(0.696256\pi\) | |||||||
\(720\) | 1.55328 | 0.0578874 | ||||||||
\(721\) | −4.03327 | −0.150207 | ||||||||
\(722\) | 0.102635 | 0.00381968 | ||||||||
\(723\) | 29.4501 | 1.09526 | ||||||||
\(724\) | 2.50296 | 0.0930220 | ||||||||
\(725\) | −17.6101 | −0.654021 | ||||||||
\(726\) | 2.79696 | 0.103805 | ||||||||
\(727\) | −16.8622 | −0.625383 | −0.312691 | − | 0.949855i | \(-0.601231\pi\) | ||||
−0.312691 | + | 0.949855i | \(0.601231\pi\) | |||||||
\(728\) | 1.19533 | 0.0443018 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.8893 | 0.588088 | ||||||||
\(731\) | 21.7486 | 0.804400 | ||||||||
\(732\) | −0.00358361 | −0.000132454 0 | ||||||||
\(733\) | −22.0591 | −0.814770 | −0.407385 | − | 0.913256i | \(-0.633559\pi\) | ||||
−0.407385 | + | 0.913256i | \(0.633559\pi\) | |||||||
\(734\) | 15.6431 | 0.577396 | ||||||||
\(735\) | 1.55328 | 0.0572936 | ||||||||
\(736\) | −5.31993 | −0.196095 | ||||||||
\(737\) | 10.6700 | 0.393034 | ||||||||
\(738\) | −1.58747 | −0.0584355 | ||||||||
\(739\) | −6.75125 | −0.248349 | −0.124174 | − | 0.992260i | \(-0.539628\pi\) | ||||
−0.124174 | + | 0.992260i | \(0.539628\pi\) | |||||||
\(740\) | −11.6527 | −0.428363 | ||||||||
\(741\) | 5.19622 | 0.190888 | ||||||||
\(742\) | 9.50856 | 0.349070 | ||||||||
\(743\) | 46.9249 | 1.72151 | 0.860754 | − | 0.509022i | \(-0.169993\pi\) | ||||
0.860754 | + | 0.509022i | \(0.169993\pi\) | |||||||
\(744\) | −8.33433 | −0.305551 | ||||||||
\(745\) | −16.6918 | −0.611540 | ||||||||
\(746\) | −10.4280 | −0.381795 | ||||||||
\(747\) | 3.27581 | 0.119856 | ||||||||
\(748\) | 11.8375 | 0.432824 | ||||||||
\(749\) | 19.1063 | 0.698127 | ||||||||
\(750\) | 11.7852 | 0.430336 | ||||||||
\(751\) | 11.2306 | 0.409809 | 0.204905 | − | 0.978782i | \(-0.434312\pi\) | ||||
0.204905 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(752\) | 4.76012 | 0.173584 | ||||||||
\(753\) | 16.6181 | 0.605598 | ||||||||
\(754\) | 8.13575 | 0.296287 | ||||||||
\(755\) | 13.9542 | 0.507847 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 49.8845 | 1.81308 | 0.906541 | − | 0.422117i | \(-0.138713\pi\) | ||||
0.906541 | + | 0.422117i | \(0.138713\pi\) | |||||||
\(758\) | 15.5075 | 0.563258 | ||||||||
\(759\) | 15.2368 | 0.553060 | ||||||||
\(760\) | 6.75228 | 0.244931 | ||||||||
\(761\) | 15.7307 | 0.570236 | 0.285118 | − | 0.958492i | \(-0.407967\pi\) | ||||
0.285118 | + | 0.958492i | \(0.407967\pi\) | |||||||
\(762\) | −0.859505 | −0.0311366 | ||||||||
\(763\) | 12.3693 | 0.447799 | ||||||||
\(764\) | 1.00000 | 0.0361787 | ||||||||
\(765\) | 6.41984 | 0.232110 | ||||||||
\(766\) | 17.7275 | 0.640522 | ||||||||
\(767\) | −0.968847 | −0.0349830 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 28.3474 | 1.02223 | 0.511117 | − | 0.859511i | \(-0.329232\pi\) | ||||
0.511117 | + | 0.859511i | \(0.329232\pi\) | |||||||
\(770\) | −4.44874 | −0.160322 | ||||||||
\(771\) | 25.3033 | 0.911277 | ||||||||
\(772\) | 2.11787 | 0.0762237 | ||||||||
\(773\) | −38.8034 | −1.39566 | −0.697830 | − | 0.716263i | \(-0.745851\pi\) | ||||
−0.697830 | + | 0.716263i | \(0.745851\pi\) | |||||||
\(774\) | −5.26207 | −0.189141 | ||||||||
\(775\) | −21.5636 | −0.774586 | ||||||||
\(776\) | 4.85955 | 0.174448 | ||||||||
\(777\) | −7.50201 | −0.269133 | ||||||||
\(778\) | −26.9359 | −0.965697 | ||||||||
\(779\) | −6.90090 | −0.247250 | ||||||||
\(780\) | −1.85668 | −0.0664797 | ||||||||
\(781\) | −41.5228 | −1.48580 | ||||||||
\(782\) | −21.9877 | −0.786279 | ||||||||
\(783\) | 6.80630 | 0.243237 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 14.0172 | 0.500295 | ||||||||
\(786\) | 21.3634 | 0.762006 | ||||||||
\(787\) | 2.67641 | 0.0954039 | 0.0477019 | − | 0.998862i | \(-0.484810\pi\) | ||||
0.0477019 | + | 0.998862i | \(0.484810\pi\) | |||||||
\(788\) | −18.5010 | −0.659072 | ||||||||
\(789\) | −15.0413 | −0.535484 | ||||||||
\(790\) | −20.4302 | −0.726875 | ||||||||
\(791\) | 10.7853 | 0.383482 | ||||||||
\(792\) | −2.86410 | −0.101771 | ||||||||
\(793\) | 0.00428358 | 0.000152115 0 | ||||||||
\(794\) | 24.9829 | 0.886610 | ||||||||
\(795\) | −14.7695 | −0.523819 | ||||||||
\(796\) | 16.1068 | 0.570891 | ||||||||
\(797\) | −4.33781 | −0.153653 | −0.0768266 | − | 0.997044i | \(-0.524479\pi\) | ||||
−0.0768266 | + | 0.997044i | \(0.524479\pi\) | |||||||
\(798\) | 4.34711 | 0.153886 | ||||||||
\(799\) | 19.6740 | 0.696016 | ||||||||
\(800\) | 2.58732 | 0.0914755 | ||||||||
\(801\) | 4.89203 | 0.172851 | ||||||||
\(802\) | −5.32228 | −0.187936 | ||||||||
\(803\) | −29.2982 | −1.03391 | ||||||||
\(804\) | 3.72543 | 0.131386 | ||||||||
\(805\) | 8.26334 | 0.291245 | ||||||||
\(806\) | 9.96224 | 0.350905 | ||||||||
\(807\) | 0.347738 | 0.0122410 | ||||||||
\(808\) | 2.55589 | 0.0899160 | ||||||||
\(809\) | −21.4548 | −0.754310 | −0.377155 | − | 0.926150i | \(-0.623098\pi\) | ||||
−0.377155 | + | 0.926150i | \(0.623098\pi\) | |||||||
\(810\) | −1.55328 | −0.0545767 | ||||||||
\(811\) | −20.5867 | −0.722898 | −0.361449 | − | 0.932392i | \(-0.617718\pi\) | ||||
−0.361449 | + | 0.932392i | \(0.617718\pi\) | |||||||
\(812\) | 6.80630 | 0.238854 | ||||||||
\(813\) | −21.8338 | −0.765746 | ||||||||
\(814\) | 21.4865 | 0.753100 | ||||||||
\(815\) | 30.0317 | 1.05197 | ||||||||
\(816\) | 4.13308 | 0.144687 | ||||||||
\(817\) | −22.8748 | −0.800287 | ||||||||
\(818\) | −14.7703 | −0.516432 | ||||||||
\(819\) | −1.19533 | −0.0417681 | ||||||||
\(820\) | 2.46578 | 0.0861089 | ||||||||
\(821\) | 10.6861 | 0.372946 | 0.186473 | − | 0.982460i | \(-0.440294\pi\) | ||||
0.186473 | + | 0.982460i | \(0.440294\pi\) | |||||||
\(822\) | −1.68404 | −0.0587377 | ||||||||
\(823\) | 55.2231 | 1.92496 | 0.962478 | − | 0.271361i | \(-0.0874738\pi\) | ||||
0.962478 | + | 0.271361i | \(0.0874738\pi\) | |||||||
\(824\) | 4.03327 | 0.140506 | ||||||||
\(825\) | −7.41033 | −0.257995 | ||||||||
\(826\) | −0.810529 | −0.0282019 | ||||||||
\(827\) | −18.1488 | −0.631094 | −0.315547 | − | 0.948910i | \(-0.602188\pi\) | ||||
−0.315547 | + | 0.948910i | \(0.602188\pi\) | |||||||
\(828\) | 5.31993 | 0.184880 | ||||||||
\(829\) | 27.9310 | 0.970083 | 0.485042 | − | 0.874491i | \(-0.338804\pi\) | ||||
0.485042 | + | 0.874491i | \(0.338804\pi\) | |||||||
\(830\) | −5.08825 | −0.176616 | ||||||||
\(831\) | 2.45754 | 0.0852512 | ||||||||
\(832\) | −1.19533 | −0.0414405 | ||||||||
\(833\) | 4.13308 | 0.143203 | ||||||||
\(834\) | −2.96087 | −0.102526 | ||||||||
\(835\) | −7.14729 | −0.247342 | ||||||||
\(836\) | −12.4505 | −0.430611 | ||||||||
\(837\) | 8.33433 | 0.288076 | ||||||||
\(838\) | −18.8559 | −0.651366 | ||||||||
\(839\) | −26.9531 | −0.930524 | −0.465262 | − | 0.885173i | \(-0.654040\pi\) | ||||
−0.465262 | + | 0.885173i | \(0.654040\pi\) | |||||||
\(840\) | −1.55328 | −0.0535933 | ||||||||
\(841\) | 17.3257 | 0.597437 | ||||||||
\(842\) | −11.9762 | −0.412728 | ||||||||
\(843\) | −4.17887 | −0.143928 | ||||||||
\(844\) | −12.7388 | −0.438489 | ||||||||
\(845\) | −17.9733 | −0.618301 | ||||||||
\(846\) | −4.76012 | −0.163656 | ||||||||
\(847\) | −2.79696 | −0.0961045 | ||||||||
\(848\) | −9.50856 | −0.326525 | ||||||||
\(849\) | −11.7209 | −0.402261 | ||||||||
\(850\) | 10.6936 | 0.366788 | ||||||||
\(851\) | −39.9101 | −1.36810 | ||||||||
\(852\) | −14.4977 | −0.496683 | ||||||||
\(853\) | 35.8583 | 1.22776 | 0.613882 | − | 0.789398i | \(-0.289607\pi\) | ||||
0.613882 | + | 0.789398i | \(0.289607\pi\) | |||||||
\(854\) | 0.00358361 | 0.000122629 0 | ||||||||
\(855\) | −6.75228 | −0.230923 | ||||||||
\(856\) | −19.1063 | −0.653038 | ||||||||
\(857\) | 15.0412 | 0.513799 | 0.256899 | − | 0.966438i | \(-0.417299\pi\) | ||||
0.256899 | + | 0.966438i | \(0.417299\pi\) | |||||||
\(858\) | 3.42353 | 0.116877 | ||||||||
\(859\) | −5.55659 | −0.189589 | −0.0947943 | − | 0.995497i | \(-0.530219\pi\) | ||||
−0.0947943 | + | 0.995497i | \(0.530219\pi\) | |||||||
\(860\) | 8.17347 | 0.278713 | ||||||||
\(861\) | 1.58747 | 0.0541008 | ||||||||
\(862\) | −33.6954 | −1.14767 | ||||||||
\(863\) | 8.47162 | 0.288377 | 0.144189 | − | 0.989550i | \(-0.453943\pi\) | ||||
0.144189 | + | 0.989550i | \(0.453943\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 20.5756 | 0.699592 | ||||||||
\(866\) | 25.9712 | 0.882537 | ||||||||
\(867\) | 0.0823856 | 0.00279796 | ||||||||
\(868\) | 8.33433 | 0.282885 | ||||||||
\(869\) | 37.6713 | 1.27791 | ||||||||
\(870\) | −10.5721 | −0.358427 | ||||||||
\(871\) | −4.45311 | −0.150888 | ||||||||
\(872\) | −12.3693 | −0.418878 | ||||||||
\(873\) | −4.85955 | −0.164471 | ||||||||
\(874\) | 23.1263 | 0.782259 | ||||||||
\(875\) | −11.7852 | −0.398414 | ||||||||
\(876\) | −10.2295 | −0.345622 | ||||||||
\(877\) | 49.4745 | 1.67063 | 0.835317 | − | 0.549769i | \(-0.185284\pi\) | ||||
0.835317 | + | 0.549769i | \(0.185284\pi\) | |||||||
\(878\) | 10.6796 | 0.360420 | ||||||||
\(879\) | −5.34331 | −0.180225 | ||||||||
\(880\) | 4.44874 | 0.149967 | ||||||||
\(881\) | 26.0956 | 0.879184 | 0.439592 | − | 0.898198i | \(-0.355123\pi\) | ||||
0.439592 | + | 0.898198i | \(0.355123\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 52.2438 | 1.75814 | 0.879072 | − | 0.476689i | \(-0.158163\pi\) | ||||
0.879072 | + | 0.476689i | \(0.158163\pi\) | |||||||
\(884\) | −4.94039 | −0.166163 | ||||||||
\(885\) | 1.25898 | 0.0423201 | ||||||||
\(886\) | −28.3258 | −0.951622 | ||||||||
\(887\) | 37.2719 | 1.25147 | 0.625733 | − | 0.780037i | \(-0.284800\pi\) | ||||
0.625733 | + | 0.780037i | \(0.284800\pi\) | |||||||
\(888\) | 7.50201 | 0.251751 | ||||||||
\(889\) | 0.859505 | 0.0288269 | ||||||||
\(890\) | −7.59869 | −0.254709 | ||||||||
\(891\) | 2.86410 | 0.0959508 | ||||||||
\(892\) | 24.3664 | 0.815846 | ||||||||
\(893\) | −20.6928 | −0.692458 | ||||||||
\(894\) | 10.7462 | 0.359405 | ||||||||
\(895\) | −36.5507 | −1.22175 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −6.35906 | −0.212323 | ||||||||
\(898\) | 37.2750 | 1.24388 | ||||||||
\(899\) | 56.7259 | 1.89191 | ||||||||
\(900\) | −2.58732 | −0.0862440 | ||||||||
\(901\) | −39.2997 | −1.30926 | ||||||||
\(902\) | −4.54666 | −0.151387 | ||||||||
\(903\) | 5.26207 | 0.175111 | ||||||||
\(904\) | −10.7853 | −0.358714 | ||||||||
\(905\) | 3.88781 | 0.129235 | ||||||||
\(906\) | −8.98373 | −0.298464 | ||||||||
\(907\) | 18.7648 | 0.623075 | 0.311538 | − | 0.950234i | \(-0.399156\pi\) | ||||
0.311538 | + | 0.950234i | \(0.399156\pi\) | |||||||
\(908\) | −12.6366 | −0.419359 | ||||||||
\(909\) | −2.55589 | −0.0847736 | ||||||||
\(910\) | 1.85668 | 0.0615483 | ||||||||
\(911\) | −7.10704 | −0.235467 | −0.117733 | − | 0.993045i | \(-0.537563\pi\) | ||||
−0.117733 | + | 0.993045i | \(0.537563\pi\) | |||||||
\(912\) | −4.34711 | −0.143947 | ||||||||
\(913\) | 9.38223 | 0.310506 | ||||||||
\(914\) | 23.9922 | 0.793592 | ||||||||
\(915\) | −0.00556635 | −0.000184018 0 | ||||||||
\(916\) | 13.9198 | 0.459922 | ||||||||
\(917\) | −21.3634 | −0.705480 | ||||||||
\(918\) | −4.13308 | −0.136412 | ||||||||
\(919\) | −37.6799 | −1.24295 | −0.621473 | − | 0.783436i | \(-0.713465\pi\) | ||||
−0.621473 | + | 0.783436i | \(0.713465\pi\) | |||||||
\(920\) | −8.26334 | −0.272434 | ||||||||
\(921\) | 12.1496 | 0.400342 | ||||||||
\(922\) | −32.3022 | −1.06382 | ||||||||
\(923\) | 17.3295 | 0.570408 | ||||||||
\(924\) | 2.86410 | 0.0942218 | ||||||||
\(925\) | 19.4101 | 0.638200 | ||||||||
\(926\) | 18.2217 | 0.598804 | ||||||||
\(927\) | −4.03327 | −0.132470 | ||||||||
\(928\) | −6.80630 | −0.223428 | ||||||||
\(929\) | 40.7813 | 1.33799 | 0.668995 | − | 0.743267i | \(-0.266725\pi\) | ||||
0.668995 | + | 0.743267i | \(0.266725\pi\) | |||||||
\(930\) | −12.9455 | −0.424501 | ||||||||
\(931\) | −4.34711 | −0.142471 | ||||||||
\(932\) | 5.26643 | 0.172508 | ||||||||
\(933\) | −16.5576 | −0.542072 | ||||||||
\(934\) | 19.4182 | 0.635382 | ||||||||
\(935\) | 18.3870 | 0.601320 | ||||||||
\(936\) | 1.19533 | 0.0390705 | ||||||||
\(937\) | −53.1076 | −1.73495 | −0.867475 | − | 0.497480i | \(-0.834259\pi\) | ||||
−0.867475 | + | 0.497480i | \(0.834259\pi\) | |||||||
\(938\) | −3.72543 | −0.121640 | ||||||||
\(939\) | 19.8617 | 0.648162 | ||||||||
\(940\) | 7.39381 | 0.241159 | ||||||||
\(941\) | −9.22469 | −0.300716 | −0.150358 | − | 0.988632i | \(-0.548043\pi\) | ||||
−0.150358 | + | 0.988632i | \(0.548043\pi\) | |||||||
\(942\) | −9.02424 | −0.294026 | ||||||||
\(943\) | 8.44522 | 0.275014 | ||||||||
\(944\) | 0.810529 | 0.0263805 | ||||||||
\(945\) | 1.55328 | 0.0505282 | ||||||||
\(946\) | −15.0711 | −0.490002 | ||||||||
\(947\) | −21.1285 | −0.686583 | −0.343292 | − | 0.939229i | \(-0.611542\pi\) | ||||
−0.343292 | + | 0.939229i | \(0.611542\pi\) | |||||||
\(948\) | 13.1530 | 0.427188 | ||||||||
\(949\) | 12.2276 | 0.396924 | ||||||||
\(950\) | −11.2474 | −0.364913 | ||||||||
\(951\) | 17.5364 | 0.568656 | ||||||||
\(952\) | −4.13308 | −0.133954 | ||||||||
\(953\) | −0.300712 | −0.00974102 | −0.00487051 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00487051 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(954\) | 9.50856 | 0.307851 | ||||||||
\(955\) | 1.55328 | 0.0502630 | ||||||||
\(956\) | −18.1064 | −0.585601 | ||||||||
\(957\) | 19.4939 | 0.630148 | ||||||||
\(958\) | 16.8579 | 0.544654 | ||||||||
\(959\) | 1.68404 | 0.0543806 | ||||||||
\(960\) | 1.55328 | 0.0501319 | ||||||||
\(961\) | 38.4610 | 1.24068 | ||||||||
\(962\) | −8.96735 | −0.289119 | ||||||||
\(963\) | 19.1063 | 0.615691 | ||||||||
\(964\) | 29.4501 | 0.948525 | ||||||||
\(965\) | 3.28964 | 0.105897 | ||||||||
\(966\) | −5.31993 | −0.171166 | ||||||||
\(967\) | 46.8460 | 1.50647 | 0.753233 | − | 0.657754i | \(-0.228493\pi\) | ||||
0.753233 | + | 0.657754i | \(0.228493\pi\) | |||||||
\(968\) | 2.79696 | 0.0898976 | ||||||||
\(969\) | −17.9670 | −0.577182 | ||||||||
\(970\) | 7.54824 | 0.242359 | ||||||||
\(971\) | −31.3331 | −1.00553 | −0.502764 | − | 0.864424i | \(-0.667683\pi\) | ||||
−0.502764 | + | 0.864424i | \(0.667683\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.96087 | 0.0949210 | ||||||||
\(974\) | 27.2722 | 0.873857 | ||||||||
\(975\) | 3.09269 | 0.0990454 | ||||||||
\(976\) | −0.00358361 | −0.000114709 0 | ||||||||
\(977\) | −37.1856 | −1.18967 | −0.594836 | − | 0.803847i | \(-0.702783\pi\) | ||||
−0.594836 | + | 0.803847i | \(0.702783\pi\) | |||||||
\(978\) | −19.3344 | −0.618246 | ||||||||
\(979\) | 14.0112 | 0.447801 | ||||||||
\(980\) | 1.55328 | 0.0496177 | ||||||||
\(981\) | 12.3693 | 0.394922 | ||||||||
\(982\) | −39.7906 | −1.26977 | ||||||||
\(983\) | −19.8750 | −0.633915 | −0.316958 | − | 0.948440i | \(-0.602661\pi\) | ||||
−0.316958 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(984\) | −1.58747 | −0.0506067 | ||||||||
\(985\) | −28.7373 | −0.915646 | ||||||||
\(986\) | −28.1310 | −0.895873 | ||||||||
\(987\) | 4.76012 | 0.151516 | ||||||||
\(988\) | 5.19622 | 0.165314 | ||||||||
\(989\) | 27.9938 | 0.890152 | ||||||||
\(990\) | −4.44874 | −0.141390 | ||||||||
\(991\) | −32.2524 | −1.02453 | −0.512266 | − | 0.858827i | \(-0.671194\pi\) | ||||
−0.512266 | + | 0.858827i | \(0.671194\pi\) | |||||||
\(992\) | −8.33433 | −0.264615 | ||||||||
\(993\) | 6.91301 | 0.219378 | ||||||||
\(994\) | 14.4977 | 0.459839 | ||||||||
\(995\) | 25.0184 | 0.793136 | ||||||||
\(996\) | 3.27581 | 0.103798 | ||||||||
\(997\) | −7.87706 | −0.249469 | −0.124734 | − | 0.992190i | \(-0.539808\pi\) | ||||
−0.124734 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(998\) | −14.3592 | −0.454532 | ||||||||
\(999\) | −7.50201 | −0.237353 |
(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 | 8022.2.a.z.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8022.2.a.z.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial |