Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 309949x^{4} - 14548431x^{3} + 25221499020x^{2} + 1862570808000x - 308009568384000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(457.447\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −487.447 | −1.74394 | −0.871972 | − | 0.489555i | \(-0.837159\pi\) | ||||
−0.871972 | + | 0.489555i | \(0.837159\pi\) | |||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 3899.58 | 1.23316 | ||||||||
\(11\) | −6609.14 | −1.49717 | −0.748585 | − | 0.663039i | \(-0.769266\pi\) | ||||
−0.748585 | + | 0.663039i | \(0.769266\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 13161.1 | 1.00687 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 8891.52 | 0.438940 | 0.219470 | − | 0.975619i | \(-0.429567\pi\) | ||||
0.219470 | + | 0.975619i | \(0.429567\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | 7882.69 | 0.263656 | 0.131828 | − | 0.991273i | \(-0.457915\pi\) | ||||
0.131828 | + | 0.991273i | \(0.457915\pi\) | |||||||
\(20\) | −31196.6 | −0.871972 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | 52873.2 | 1.05866 | ||||||||
\(23\) | −107716. | −1.84601 | −0.923005 | − | 0.384788i | \(-0.874274\pi\) | ||||
−0.923005 | + | 0.384788i | \(0.874274\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 159480. | 2.04134 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −127254. | −0.968901 | −0.484450 | − | 0.874819i | \(-0.660980\pi\) | ||||
−0.484450 | + | 0.874819i | \(0.660980\pi\) | |||||||
\(30\) | −105289. | −0.711963 | ||||||||
\(31\) | 86977.9 | 0.524376 | 0.262188 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262188 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 178447. | 0.864391 | ||||||||
\(34\) | −71132.2 | −0.310377 | ||||||||
\(35\) | −167194. | −0.659149 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −233049. | −0.756383 | −0.378192 | − | 0.925727i | \(-0.623454\pi\) | ||||
−0.378192 | + | 0.925727i | \(0.623454\pi\) | |||||||
\(38\) | −63061.6 | −0.186433 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | 249573. | 0.616578 | ||||||||
\(41\) | 293448. | 0.664947 | 0.332473 | − | 0.943113i | \(-0.392117\pi\) | ||||
0.332473 | + | 0.943113i | \(0.392117\pi\) | |||||||
\(42\) | 74088.0 | 0.154303 | ||||||||
\(43\) | −259605. | −0.497936 | −0.248968 | − | 0.968512i | \(-0.580091\pi\) | ||||
−0.248968 | + | 0.968512i | \(0.580091\pi\) | |||||||
\(44\) | −422985. | −0.748585 | ||||||||
\(45\) | −355349. | −0.581315 | ||||||||
\(46\) | 861730. | 1.30533 | ||||||||
\(47\) | −244441. | −0.343425 | −0.171713 | − | 0.985147i | \(-0.554930\pi\) | ||||
−0.171713 | + | 0.985147i | \(0.554930\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −1.27584e6 | −1.44345 | ||||||||
\(51\) | −240071. | −0.253422 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | −1.77201e6 | −1.63494 | −0.817468 | − | 0.575975i | \(-0.804623\pi\) | ||||
−0.817468 | + | 0.575975i | \(0.804623\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | 3.22161e6 | 2.61098 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | −212833. | −0.152222 | ||||||||
\(58\) | 1.01803e6 | 0.685116 | ||||||||
\(59\) | −1.29914e6 | −0.823519 | −0.411759 | − | 0.911293i | \(-0.635086\pi\) | ||||
−0.411759 | + | 0.911293i | \(0.635086\pi\) | |||||||
\(60\) | 842309. | 0.503434 | ||||||||
\(61\) | −2.80338e6 | −1.58135 | −0.790674 | − | 0.612238i | \(-0.790269\pi\) | ||||
−0.790674 | + | 0.612238i | \(0.790269\pi\) | |||||||
\(62\) | −695823. | −0.370790 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −1.07092e6 | −0.483683 | ||||||||
\(66\) | −1.42758e6 | −0.611217 | ||||||||
\(67\) | −3.33358e6 | −1.35410 | −0.677048 | − | 0.735939i | \(-0.736741\pi\) | ||||
−0.677048 | + | 0.735939i | \(0.736741\pi\) | |||||||
\(68\) | 569057. | 0.219470 | ||||||||
\(69\) | 2.90834e6 | 1.06579 | ||||||||
\(70\) | 1.33756e6 | 0.466089 | ||||||||
\(71\) | 1.67692e6 | 0.556041 | 0.278021 | − | 0.960575i | \(-0.410322\pi\) | ||||
0.278021 | + | 0.960575i | \(0.410322\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | −932381. | −0.280520 | −0.140260 | − | 0.990115i | \(-0.544794\pi\) | ||||
−0.140260 | + | 0.990115i | \(0.544794\pi\) | |||||||
\(74\) | 1.86439e6 | 0.534844 | ||||||||
\(75\) | −4.30596e6 | −1.17857 | ||||||||
\(76\) | 504492. | 0.131828 | ||||||||
\(77\) | −2.26694e6 | −0.565877 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | −3.16827e6 | −0.722982 | −0.361491 | − | 0.932376i | \(-0.617732\pi\) | ||||
−0.361491 | + | 0.932376i | \(0.617732\pi\) | |||||||
\(80\) | −1.99658e6 | −0.435986 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −2.34758e6 | −0.470188 | ||||||||
\(83\) | 4.51858e6 | 0.867418 | 0.433709 | − | 0.901053i | \(-0.357205\pi\) | ||||
0.433709 | + | 0.901053i | \(0.357205\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | −4.33415e6 | −0.765487 | ||||||||
\(86\) | 2.07684e6 | 0.352094 | ||||||||
\(87\) | 3.43587e6 | 0.559395 | ||||||||
\(88\) | 3.38388e6 | 0.529329 | ||||||||
\(89\) | −1.31198e7 | −1.97271 | −0.986355 | − | 0.164633i | \(-0.947356\pi\) | ||||
−0.986355 | + | 0.164633i | \(0.947356\pi\) | |||||||
\(90\) | 2.84279e6 | 0.411052 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −6.89384e6 | −0.923005 | ||||||||
\(93\) | −2.34840e6 | −0.302749 | ||||||||
\(94\) | 1.95553e6 | 0.242838 | ||||||||
\(95\) | −3.84240e6 | −0.459801 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | −1.12922e7 | −1.25626 | −0.628130 | − | 0.778109i | \(-0.716179\pi\) | ||||
−0.628130 | + | 0.778109i | \(0.716179\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | −4.81807e6 | −0.499056 | ||||||||
\(100\) | 1.02067e7 | 1.02067 | ||||||||
\(101\) | −1.18245e7 | −1.14198 | −0.570989 | − | 0.820958i | \(-0.693440\pi\) | ||||
−0.570989 | + | 0.820958i | \(0.693440\pi\) | |||||||
\(102\) | 1.92057e6 | 0.179196 | ||||||||
\(103\) | 4.09889e6 | 0.369603 | 0.184802 | − | 0.982776i | \(-0.440836\pi\) | ||||
0.184802 | + | 0.982776i | \(0.440836\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | 4.51425e6 | 0.380560 | ||||||||
\(106\) | 1.41761e7 | 1.15607 | ||||||||
\(107\) | −6.61765e6 | −0.522228 | −0.261114 | − | 0.965308i | \(-0.584090\pi\) | ||||
−0.261114 | + | 0.965308i | \(0.584090\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 1.16847e6 | 0.0864222 | 0.0432111 | − | 0.999066i | \(-0.486241\pi\) | ||||
0.0432111 | + | 0.999066i | \(0.486241\pi\) | |||||||
\(110\) | −2.57729e7 | −1.84624 | ||||||||
\(111\) | 6.29233e6 | 0.436698 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | 5.46121e6 | 0.356053 | 0.178026 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178026 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(114\) | 1.70266e6 | 0.107637 | ||||||||
\(115\) | 5.25060e7 | 3.21934 | ||||||||
\(116\) | −8.14427e6 | −0.484450 | ||||||||
\(117\) | 1.60161e6 | 0.0924500 | ||||||||
\(118\) | 1.03931e7 | 0.582316 | ||||||||
\(119\) | 3.04979e6 | 0.165904 | ||||||||
\(120\) | −6.73847e6 | −0.355981 | ||||||||
\(121\) | 2.41936e7 | 1.24152 | ||||||||
\(122\) | 2.24270e7 | 1.11818 | ||||||||
\(123\) | −7.92308e6 | −0.383907 | ||||||||
\(124\) | 5.56659e6 | 0.262188 | ||||||||
\(125\) | −3.96563e7 | −1.81605 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | −1.67741e6 | −0.0726653 | −0.0363327 | − | 0.999340i | \(-0.511568\pi\) | ||||
−0.0363327 | + | 0.999340i | \(0.511568\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 7.00933e6 | 0.287483 | ||||||||
\(130\) | 8.56738e6 | 0.342016 | ||||||||
\(131\) | 2.17219e6 | 0.0844207 | 0.0422104 | − | 0.999109i | \(-0.486560\pi\) | ||||
0.0422104 | + | 0.999109i | \(0.486560\pi\) | |||||||
\(132\) | 1.14206e7 | 0.432196 | ||||||||
\(133\) | 2.70376e6 | 0.0996525 | ||||||||
\(134\) | 2.66687e7 | 0.957490 | ||||||||
\(135\) | 9.59443e6 | 0.335622 | ||||||||
\(136\) | −4.55246e6 | −0.155189 | ||||||||
\(137\) | −1.05432e7 | −0.350308 | −0.175154 | − | 0.984541i | \(-0.556042\pi\) | ||||
−0.175154 | + | 0.984541i | \(0.556042\pi\) | |||||||
\(138\) | −2.32667e7 | −0.753630 | ||||||||
\(139\) | −4.52825e7 | −1.43014 | −0.715071 | − | 0.699052i | \(-0.753606\pi\) | ||||
−0.715071 | + | 0.699052i | \(0.753606\pi\) | |||||||
\(140\) | −1.07004e7 | −0.329575 | ||||||||
\(141\) | 6.59992e6 | 0.198277 | ||||||||
\(142\) | −1.34153e7 | −0.393181 | ||||||||
\(143\) | −1.45203e7 | −0.415240 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 6.20298e7 | 1.68971 | ||||||||
\(146\) | 7.45905e6 | 0.198357 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | −1.49152e7 | −0.378192 | ||||||||
\(149\) | 1.45929e7 | 0.361400 | 0.180700 | − | 0.983538i | \(-0.442164\pi\) | ||||
0.180700 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(150\) | 3.44477e7 | 0.833375 | ||||||||
\(151\) | −4.39361e7 | −1.03849 | −0.519245 | − | 0.854626i | \(-0.673787\pi\) | ||||
−0.519245 | + | 0.854626i | \(0.673787\pi\) | |||||||
\(152\) | −4.03594e6 | −0.0932163 | ||||||||
\(153\) | 6.48192e6 | 0.146313 | ||||||||
\(154\) | 1.81355e7 | 0.400135 | ||||||||
\(155\) | −4.23972e7 | −0.914483 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | −2.12373e7 | −0.437977 | −0.218989 | − | 0.975727i | \(-0.570276\pi\) | ||||
−0.218989 | + | 0.975727i | \(0.570276\pi\) | |||||||
\(158\) | 2.53462e7 | 0.511226 | ||||||||
\(159\) | 4.78443e7 | 0.943930 | ||||||||
\(160\) | 1.59727e7 | 0.308289 | ||||||||
\(161\) | −3.69467e7 | −0.697726 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | −1.03718e8 | −1.87584 | −0.937920 | − | 0.346852i | \(-0.887251\pi\) | ||||
−0.937920 | + | 0.346852i | \(0.887251\pi\) | |||||||
\(164\) | 1.87806e7 | 0.332473 | ||||||||
\(165\) | −8.69835e7 | −1.50745 | ||||||||
\(166\) | −3.61486e7 | −0.613357 | ||||||||
\(167\) | −4.39460e7 | −0.730150 | −0.365075 | − | 0.930978i | \(-0.618957\pi\) | ||||
−0.365075 | + | 0.930978i | \(0.618957\pi\) | |||||||
\(168\) | 4.74163e6 | 0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 3.46732e7 | 0.541281 | ||||||||
\(171\) | 5.74648e6 | 0.0878852 | ||||||||
\(172\) | −1.66147e7 | −0.248968 | ||||||||
\(173\) | −8.09232e7 | −1.18826 | −0.594130 | − | 0.804369i | \(-0.702504\pi\) | ||||
−0.594130 | + | 0.804369i | \(0.702504\pi\) | |||||||
\(174\) | −2.74869e7 | −0.395552 | ||||||||
\(175\) | 5.47016e7 | 0.771555 | ||||||||
\(176\) | −2.70711e7 | −0.374292 | ||||||||
\(177\) | 3.50767e7 | 0.475459 | ||||||||
\(178\) | 1.04959e8 | 1.39492 | ||||||||
\(179\) | −7.35345e7 | −0.958309 | −0.479154 | − | 0.877731i | \(-0.659057\pi\) | ||||
−0.479154 | + | 0.877731i | \(0.659057\pi\) | |||||||
\(180\) | −2.27423e7 | −0.290657 | ||||||||
\(181\) | −8.97687e7 | −1.12525 | −0.562626 | − | 0.826711i | \(-0.690209\pi\) | ||||
−0.562626 | + | 0.826711i | \(0.690209\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | 7.56912e7 | 0.912991 | ||||||||
\(184\) | 5.51507e7 | 0.652663 | ||||||||
\(185\) | 1.13599e8 | 1.31909 | ||||||||
\(186\) | 1.87872e7 | 0.214076 | ||||||||
\(187\) | −5.87654e7 | −0.657167 | ||||||||
\(188\) | −1.56443e7 | −0.171713 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | 3.07392e7 | 0.325128 | ||||||||
\(191\) | 1.23836e8 | 1.28597 | 0.642985 | − | 0.765879i | \(-0.277696\pi\) | ||||
0.642985 | + | 0.765879i | \(0.277696\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 3.79864e7 | 0.380345 | 0.190172 | − | 0.981751i | \(-0.439095\pi\) | ||||
0.190172 | + | 0.981751i | \(0.439095\pi\) | |||||||
\(194\) | 9.03380e7 | 0.888309 | ||||||||
\(195\) | 2.89149e7 | 0.279255 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 8.33840e7 | 0.777053 | 0.388527 | − | 0.921437i | \(-0.372984\pi\) | ||||
0.388527 | + | 0.921437i | \(0.372984\pi\) | |||||||
\(198\) | 3.85445e7 | 0.352886 | ||||||||
\(199\) | 1.59684e8 | 1.43640 | 0.718199 | − | 0.695838i | \(-0.244967\pi\) | ||||
0.718199 | + | 0.695838i | \(0.244967\pi\) | |||||||
\(200\) | −8.16538e7 | −0.721724 | ||||||||
\(201\) | 9.00067e7 | 0.781788 | ||||||||
\(202\) | 9.45959e7 | 0.807500 | ||||||||
\(203\) | −4.36482e7 | −0.366210 | ||||||||
\(204\) | −1.53645e7 | −0.126711 | ||||||||
\(205\) | −1.43040e8 | −1.15963 | ||||||||
\(206\) | −3.27911e7 | −0.261349 | ||||||||
\(207\) | −7.85252e7 | −0.615337 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | −5.20979e7 | −0.394737 | ||||||||
\(210\) | −3.61140e7 | −0.269097 | ||||||||
\(211\) | −2.41498e8 | −1.76980 | −0.884901 | − | 0.465779i | \(-0.845774\pi\) | ||||
−0.884901 | + | 0.465779i | \(0.845774\pi\) | |||||||
\(212\) | −1.13409e8 | −0.817468 | ||||||||
\(213\) | −4.52767e7 | −0.321031 | ||||||||
\(214\) | 5.29412e7 | 0.369271 | ||||||||
\(215\) | 1.26544e8 | 0.868373 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 2.98334e7 | 0.198196 | ||||||||
\(218\) | −9.34777e6 | −0.0611097 | ||||||||
\(219\) | 2.51743e7 | 0.161958 | ||||||||
\(220\) | 2.06183e8 | 1.30549 | ||||||||
\(221\) | 1.95347e7 | 0.121740 | ||||||||
\(222\) | −5.03387e7 | −0.308792 | ||||||||
\(223\) | 1.35473e8 | 0.818063 | 0.409031 | − | 0.912520i | \(-0.365867\pi\) | ||||
0.409031 | + | 0.912520i | \(0.365867\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.16261e8 | 0.680448 | ||||||||
\(226\) | −4.36897e7 | −0.251767 | ||||||||
\(227\) | 1.35605e8 | 0.769460 | 0.384730 | − | 0.923029i | \(-0.374295\pi\) | ||||
0.384730 | + | 0.923029i | \(0.374295\pi\) | |||||||
\(228\) | −1.36213e7 | −0.0761108 | ||||||||
\(229\) | 2.56868e8 | 1.41347 | 0.706733 | − | 0.707481i | \(-0.250168\pi\) | ||||
0.706733 | + | 0.707481i | \(0.250168\pi\) | |||||||
\(230\) | −4.20048e8 | −2.27642 | ||||||||
\(231\) | 6.12073e7 | 0.326709 | ||||||||
\(232\) | 6.51542e7 | 0.342558 | ||||||||
\(233\) | 1.02475e8 | 0.530729 | 0.265364 | − | 0.964148i | \(-0.414508\pi\) | ||||
0.265364 | + | 0.964148i | \(0.414508\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | 1.19152e8 | 0.598915 | ||||||||
\(236\) | −8.31449e7 | −0.411759 | ||||||||
\(237\) | 8.55434e7 | 0.417414 | ||||||||
\(238\) | −2.43983e7 | −0.117312 | ||||||||
\(239\) | 4.12642e8 | 1.95515 | 0.977577 | − | 0.210577i | \(-0.0675343\pi\) | ||||
0.977577 | + | 0.210577i | \(0.0675343\pi\) | |||||||
\(240\) | 5.39078e7 | 0.251717 | ||||||||
\(241\) | −1.55197e8 | −0.714208 | −0.357104 | − | 0.934065i | \(-0.616236\pi\) | ||||
−0.357104 | + | 0.934065i | \(0.616236\pi\) | |||||||
\(242\) | −1.93549e8 | −0.877884 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −1.79416e8 | −0.790674 | ||||||||
\(245\) | −5.73477e7 | −0.249135 | ||||||||
\(246\) | 6.33847e7 | 0.271463 | ||||||||
\(247\) | 1.73183e7 | 0.0731249 | ||||||||
\(248\) | −4.45327e7 | −0.185395 | ||||||||
\(249\) | −1.22002e8 | −0.500804 | ||||||||
\(250\) | 3.17250e8 | 1.28414 | ||||||||
\(251\) | 8.61766e7 | 0.343979 | 0.171989 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171989 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 7.11913e8 | 2.76379 | ||||||||
\(254\) | 1.34193e7 | 0.0513821 | ||||||||
\(255\) | 1.17022e8 | 0.441954 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −3.02243e8 | −1.11068 | −0.555342 | − | 0.831622i | \(-0.687413\pi\) | ||||
−0.555342 | + | 0.831622i | \(0.687413\pi\) | |||||||
\(258\) | −5.60747e7 | −0.203281 | ||||||||
\(259\) | −7.99359e7 | −0.285886 | ||||||||
\(260\) | −6.85390e7 | −0.241842 | ||||||||
\(261\) | −9.27684e7 | −0.322967 | ||||||||
\(262\) | −1.73776e7 | −0.0596945 | ||||||||
\(263\) | 1.59520e8 | 0.540719 | 0.270359 | − | 0.962760i | \(-0.412858\pi\) | ||||
0.270359 | + | 0.962760i | \(0.412858\pi\) | |||||||
\(264\) | −9.13648e7 | −0.305608 | ||||||||
\(265\) | 8.63761e8 | 2.85124 | ||||||||
\(266\) | −2.16301e7 | −0.0704649 | ||||||||
\(267\) | 3.54235e8 | 1.13894 | ||||||||
\(268\) | −2.13349e8 | −0.677048 | ||||||||
\(269\) | 4.07599e8 | 1.27673 | 0.638366 | − | 0.769733i | \(-0.279611\pi\) | ||||
0.638366 | + | 0.769733i | \(0.279611\pi\) | |||||||
\(270\) | −7.67554e7 | −0.237321 | ||||||||
\(271\) | 2.12138e8 | 0.647479 | 0.323740 | − | 0.946146i | \(-0.395060\pi\) | ||||
0.323740 | + | 0.946146i | \(0.395060\pi\) | |||||||
\(272\) | 3.64197e7 | 0.109735 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | 8.43455e7 | 0.247705 | ||||||||
\(275\) | −1.05403e9 | −3.05624 | ||||||||
\(276\) | 1.86134e8 | 0.532897 | ||||||||
\(277\) | 2.37111e8 | 0.670305 | 0.335152 | − | 0.942164i | \(-0.391212\pi\) | ||||
0.335152 | + | 0.942164i | \(0.391212\pi\) | |||||||
\(278\) | 3.62260e8 | 1.01126 | ||||||||
\(279\) | 6.34069e7 | 0.174792 | ||||||||
\(280\) | 8.56036e7 | 0.233044 | ||||||||
\(281\) | 4.12563e6 | 0.0110922 | 0.00554610 | − | 0.999985i | \(-0.498235\pi\) | ||||
0.00554610 | + | 0.999985i | \(0.498235\pi\) | |||||||
\(282\) | −5.27994e7 | −0.140203 | ||||||||
\(283\) | 2.41524e8 | 0.633442 | 0.316721 | − | 0.948519i | \(-0.397418\pi\) | ||||
0.316721 | + | 0.948519i | \(0.397418\pi\) | |||||||
\(284\) | 1.07323e8 | 0.278021 | ||||||||
\(285\) | 1.03745e8 | 0.265466 | ||||||||
\(286\) | 1.16162e8 | 0.293619 | ||||||||
\(287\) | 1.00652e8 | 0.251326 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | −3.31280e8 | −0.807332 | ||||||||
\(290\) | −4.96238e8 | −1.19481 | ||||||||
\(291\) | 3.04891e8 | 0.725302 | ||||||||
\(292\) | −5.96724e7 | −0.140260 | ||||||||
\(293\) | 6.11484e8 | 1.42020 | 0.710099 | − | 0.704102i | \(-0.248650\pi\) | ||||
0.710099 | + | 0.704102i | \(0.248650\pi\) | |||||||
\(294\) | 2.54122e7 | 0.0583212 | ||||||||
\(295\) | 6.33262e8 | 1.43617 | ||||||||
\(296\) | 1.19321e8 | 0.267422 | ||||||||
\(297\) | 1.30088e8 | 0.288130 | ||||||||
\(298\) | −1.16743e8 | −0.255548 | ||||||||
\(299\) | −2.36653e8 | −0.511991 | ||||||||
\(300\) | −2.75581e8 | −0.589285 | ||||||||
\(301\) | −8.90445e7 | −0.188202 | ||||||||
\(302\) | 3.51489e8 | 0.734323 | ||||||||
\(303\) | 3.19261e8 | 0.659321 | ||||||||
\(304\) | 3.22875e7 | 0.0659139 | ||||||||
\(305\) | 1.36650e9 | 2.75778 | ||||||||
\(306\) | −5.18554e7 | −0.103459 | ||||||||
\(307\) | −4.86960e8 | −0.960525 | −0.480263 | − | 0.877125i | \(-0.659459\pi\) | ||||
−0.480263 | + | 0.877125i | \(0.659459\pi\) | |||||||
\(308\) | −1.45084e8 | −0.282938 | ||||||||
\(309\) | −1.10670e8 | −0.213391 | ||||||||
\(310\) | 3.39177e8 | 0.646637 | ||||||||
\(311\) | −6.84194e8 | −1.28979 | −0.644893 | − | 0.764273i | \(-0.723098\pi\) | ||||
−0.644893 | + | 0.764273i | \(0.723098\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | −5.66327e8 | −1.04391 | −0.521954 | − | 0.852974i | \(-0.674797\pi\) | ||||
−0.521954 | + | 0.852974i | \(0.674797\pi\) | |||||||
\(314\) | 1.69899e8 | 0.309697 | ||||||||
\(315\) | −1.21885e8 | −0.219716 | ||||||||
\(316\) | −2.02769e8 | −0.361491 | ||||||||
\(317\) | 8.09106e8 | 1.42659 | 0.713293 | − | 0.700866i | \(-0.247203\pi\) | ||||
0.713293 | + | 0.700866i | \(0.247203\pi\) | |||||||
\(318\) | −3.82754e8 | −0.667459 | ||||||||
\(319\) | 8.41042e8 | 1.45061 | ||||||||
\(320\) | −1.27781e8 | −0.217993 | ||||||||
\(321\) | 1.78676e8 | 0.301509 | ||||||||
\(322\) | 2.95573e8 | 0.493367 | ||||||||
\(323\) | 7.00891e7 | 0.115729 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 3.50378e8 | 0.566167 | ||||||||
\(326\) | 8.29741e8 | 1.32642 | ||||||||
\(327\) | −3.15487e7 | −0.0498959 | ||||||||
\(328\) | −1.50245e8 | −0.235094 | ||||||||
\(329\) | −8.38434e7 | −0.129803 | ||||||||
\(330\) | 6.95868e8 | 1.06593 | ||||||||
\(331\) | 1.12449e9 | 1.70435 | 0.852176 | − | 0.523255i | \(-0.175283\pi\) | ||||
0.852176 | + | 0.523255i | \(0.175283\pi\) | |||||||
\(332\) | 2.89189e8 | 0.433709 | ||||||||
\(333\) | −1.69893e8 | −0.252128 | ||||||||
\(334\) | 3.51568e8 | 0.516294 | ||||||||
\(335\) | 1.62495e9 | 2.36147 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | 3.87721e8 | 0.551841 | 0.275921 | − | 0.961180i | \(-0.411017\pi\) | ||||
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | −1.47453e8 | −0.205567 | ||||||||
\(340\) | −2.77386e8 | −0.382743 | ||||||||
\(341\) | −5.74850e8 | −0.785080 | ||||||||
\(342\) | −4.59719e7 | −0.0621442 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 1.32918e8 | 0.176047 | ||||||||
\(345\) | −1.41766e9 | −1.85869 | ||||||||
\(346\) | 6.47386e8 | 0.840227 | ||||||||
\(347\) | 1.45355e9 | 1.86757 | 0.933786 | − | 0.357832i | \(-0.116484\pi\) | ||||
0.933786 | + | 0.357832i | \(0.116484\pi\) | |||||||
\(348\) | 2.19895e8 | 0.279698 | ||||||||
\(349\) | −3.34462e8 | −0.421170 | −0.210585 | − | 0.977576i | \(-0.567537\pi\) | ||||
−0.210585 | + | 0.977576i | \(0.567537\pi\) | |||||||
\(350\) | −4.37613e8 | −0.545572 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | 2.16568e8 | 0.264665 | ||||||||
\(353\) | −1.12211e9 | −1.35776 | −0.678880 | − | 0.734249i | \(-0.737534\pi\) | ||||
−0.678880 | + | 0.734249i | \(0.737534\pi\) | |||||||
\(354\) | −2.80614e8 | −0.336200 | ||||||||
\(355\) | −8.17408e8 | −0.969705 | ||||||||
\(356\) | −8.39669e8 | −0.986355 | ||||||||
\(357\) | −8.23444e7 | −0.0957845 | ||||||||
\(358\) | 5.88276e8 | 0.677627 | ||||||||
\(359\) | 1.20452e8 | 0.137399 | 0.0686996 | − | 0.997637i | \(-0.478115\pi\) | ||||
0.0686996 | + | 0.997637i | \(0.478115\pi\) | |||||||
\(360\) | 1.81939e8 | 0.205526 | ||||||||
\(361\) | −8.31735e8 | −0.930486 | ||||||||
\(362\) | 7.18150e8 | 0.795674 | ||||||||
\(363\) | −6.53228e8 | −0.716789 | ||||||||
\(364\) | 4.82285e7 | 0.0524142 | ||||||||
\(365\) | 4.54487e8 | 0.489211 | ||||||||
\(366\) | −6.05530e8 | −0.645582 | ||||||||
\(367\) | −3.56903e8 | −0.376894 | −0.188447 | − | 0.982083i | \(-0.560345\pi\) | ||||
−0.188447 | + | 0.982083i | \(0.560345\pi\) | |||||||
\(368\) | −4.41206e8 | −0.461502 | ||||||||
\(369\) | 2.13923e8 | 0.221649 | ||||||||
\(370\) | −9.08794e8 | −0.932738 | ||||||||
\(371\) | −6.07799e8 | −0.617947 | ||||||||
\(372\) | −1.50298e8 | −0.151374 | ||||||||
\(373\) | −3.38889e8 | −0.338125 | −0.169062 | − | 0.985605i | \(-0.554074\pi\) | ||||
−0.169062 | + | 0.985605i | \(0.554074\pi\) | |||||||
\(374\) | 4.70123e8 | 0.464687 | ||||||||
\(375\) | 1.07072e9 | 1.04849 | ||||||||
\(376\) | 1.25154e8 | 0.121419 | ||||||||
\(377\) | −2.79578e8 | −0.268725 | ||||||||
\(378\) | 5.40102e7 | 0.0514344 | ||||||||
\(379\) | −1.76775e9 | −1.66796 | −0.833978 | − | 0.551797i | \(-0.813942\pi\) | ||||
−0.833978 | + | 0.551797i | \(0.813942\pi\) | |||||||
\(380\) | −2.45914e8 | −0.229900 | ||||||||
\(381\) | 4.52902e7 | 0.0419533 | ||||||||
\(382\) | −9.90690e8 | −0.909318 | ||||||||
\(383\) | −1.99915e9 | −1.81824 | −0.909118 | − | 0.416538i | \(-0.863243\pi\) | ||||
−0.909118 | + | 0.416538i | \(0.863243\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 1.10501e9 | 0.986858 | ||||||||
\(386\) | −3.03891e8 | −0.268944 | ||||||||
\(387\) | −1.89252e8 | −0.165979 | ||||||||
\(388\) | −7.22704e8 | −0.628130 | ||||||||
\(389\) | −2.84545e8 | −0.245091 | −0.122546 | − | 0.992463i | \(-0.539106\pi\) | ||||
−0.122546 | + | 0.992463i | \(0.539106\pi\) | |||||||
\(390\) | −2.31319e8 | −0.197463 | ||||||||
\(391\) | −9.57762e8 | −0.810287 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | −5.86492e7 | −0.0487403 | ||||||||
\(394\) | −6.67072e8 | −0.549460 | ||||||||
\(395\) | 1.54437e9 | 1.26084 | ||||||||
\(396\) | −3.08356e8 | −0.249528 | ||||||||
\(397\) | 4.52749e8 | 0.363154 | 0.181577 | − | 0.983377i | \(-0.441880\pi\) | ||||
0.181577 | + | 0.983377i | \(0.441880\pi\) | |||||||
\(398\) | −1.27747e9 | −1.01569 | ||||||||
\(399\) | −7.30016e7 | −0.0575344 | ||||||||
\(400\) | 6.53230e8 | 0.510336 | ||||||||
\(401\) | −2.30471e7 | −0.0178489 | −0.00892446 | − | 0.999960i | \(-0.502841\pi\) | ||||
−0.00892446 | + | 0.999960i | \(0.502841\pi\) | |||||||
\(402\) | −7.20054e8 | −0.552807 | ||||||||
\(403\) | 1.91090e8 | 0.145436 | ||||||||
\(404\) | −7.56767e8 | −0.570989 | ||||||||
\(405\) | −2.59050e8 | −0.193772 | ||||||||
\(406\) | 3.49186e8 | 0.258950 | ||||||||
\(407\) | 1.54026e9 | 1.13243 | ||||||||
\(408\) | 1.22916e8 | 0.0895982 | ||||||||
\(409\) | 1.37257e9 | 0.991983 | 0.495992 | − | 0.868327i | \(-0.334805\pi\) | ||||
0.495992 | + | 0.868327i | \(0.334805\pi\) | |||||||
\(410\) | 1.14432e9 | 0.819983 | ||||||||
\(411\) | 2.84666e8 | 0.202250 | ||||||||
\(412\) | 2.62329e8 | 0.184802 | ||||||||
\(413\) | −4.45605e8 | −0.311261 | ||||||||
\(414\) | 6.28201e8 | 0.435109 | ||||||||
\(415\) | −2.20257e9 | −1.51273 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | 1.22263e9 | 0.825693 | ||||||||
\(418\) | 4.16783e8 | 0.279121 | ||||||||
\(419\) | −6.69063e7 | −0.0444343 | −0.0222171 | − | 0.999753i | \(-0.507073\pi\) | ||||
−0.0222171 | + | 0.999753i | \(0.507073\pi\) | |||||||
\(420\) | 2.88912e8 | 0.190280 | ||||||||
\(421\) | 1.13412e9 | 0.740752 | 0.370376 | − | 0.928882i | \(-0.379229\pi\) | ||||
0.370376 | + | 0.928882i | \(0.379229\pi\) | |||||||
\(422\) | 1.93198e9 | 1.25144 | ||||||||
\(423\) | −1.78198e8 | −0.114475 | ||||||||
\(424\) | 9.07269e8 | 0.578037 | ||||||||
\(425\) | 1.41802e9 | 0.896027 | ||||||||
\(426\) | 3.62214e8 | 0.227003 | ||||||||
\(427\) | −9.61559e8 | −0.597693 | ||||||||
\(428\) | −4.23529e8 | −0.261114 | ||||||||
\(429\) | 3.92048e8 | 0.239739 | ||||||||
\(430\) | −1.01235e9 | −0.614032 | ||||||||
\(431\) | −3.16683e9 | −1.90526 | −0.952629 | − | 0.304135i | \(-0.901633\pi\) | ||||
−0.952629 | + | 0.304135i | \(0.901633\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −1.36383e9 | −0.807331 | −0.403666 | − | 0.914907i | \(-0.632264\pi\) | ||||
−0.403666 | + | 0.914907i | \(0.632264\pi\) | |||||||
\(434\) | −2.38667e8 | −0.140145 | ||||||||
\(435\) | −1.67480e9 | −0.975554 | ||||||||
\(436\) | 7.47822e7 | 0.0432111 | ||||||||
\(437\) | −8.49095e8 | −0.486711 | ||||||||
\(438\) | −2.01394e8 | −0.114522 | ||||||||
\(439\) | −3.17867e9 | −1.79316 | −0.896580 | − | 0.442881i | \(-0.853956\pi\) | ||||
−0.896580 | + | 0.442881i | \(0.853956\pi\) | |||||||
\(440\) | −1.64946e9 | −0.923121 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −1.56277e8 | −0.0860832 | ||||||||
\(443\) | −1.37499e9 | −0.751428 | −0.375714 | − | 0.926736i | \(-0.622602\pi\) | ||||
−0.375714 | + | 0.926736i | \(0.622602\pi\) | |||||||
\(444\) | 4.02709e8 | 0.218349 | ||||||||
\(445\) | 6.39523e9 | 3.44030 | ||||||||
\(446\) | −1.08379e9 | −0.578458 | ||||||||
\(447\) | −3.94007e8 | −0.208654 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 5.84627e8 | 0.304801 | 0.152401 | − | 0.988319i | \(-0.451300\pi\) | ||||
0.152401 | + | 0.988319i | \(0.451300\pi\) | |||||||
\(450\) | −9.30087e8 | −0.481149 | ||||||||
\(451\) | −1.93944e9 | −0.995538 | ||||||||
\(452\) | 3.49517e8 | 0.178026 | ||||||||
\(453\) | 1.18627e9 | 0.599572 | ||||||||
\(454\) | −1.08484e9 | −0.544091 | ||||||||
\(455\) | −3.67326e8 | −0.182815 | ||||||||
\(456\) | 1.08970e8 | 0.0538185 | ||||||||
\(457\) | 2.47958e9 | 1.21527 | 0.607634 | − | 0.794217i | \(-0.292119\pi\) | ||||
0.607634 | + | 0.794217i | \(0.292119\pi\) | |||||||
\(458\) | −2.05494e9 | −0.999471 | ||||||||
\(459\) | −1.75012e8 | −0.0844740 | ||||||||
\(460\) | 3.36039e9 | 1.60967 | ||||||||
\(461\) | 1.16093e9 | 0.551890 | 0.275945 | − | 0.961173i | \(-0.411009\pi\) | ||||
0.275945 | + | 0.961173i | \(0.411009\pi\) | |||||||
\(462\) | −4.89658e8 | −0.231018 | ||||||||
\(463\) | 2.66646e9 | 1.24854 | 0.624268 | − | 0.781210i | \(-0.285397\pi\) | ||||
0.624268 | + | 0.781210i | \(0.285397\pi\) | |||||||
\(464\) | −5.21234e8 | −0.242225 | ||||||||
\(465\) | 1.14472e9 | 0.527977 | ||||||||
\(466\) | −8.19801e8 | −0.375282 | ||||||||
\(467\) | −4.30406e8 | −0.195555 | −0.0977776 | − | 0.995208i | \(-0.531173\pi\) | ||||
−0.0977776 | + | 0.995208i | \(0.531173\pi\) | |||||||
\(468\) | 1.02503e8 | 0.0462250 | ||||||||
\(469\) | −1.14342e9 | −0.511800 | ||||||||
\(470\) | −9.53219e8 | −0.423497 | ||||||||
\(471\) | 5.73408e8 | 0.252866 | ||||||||
\(472\) | 6.65159e8 | 0.291158 | ||||||||
\(473\) | 1.71577e9 | 0.745494 | ||||||||
\(474\) | −6.84347e8 | −0.295156 | ||||||||
\(475\) | 1.25713e9 | 0.538212 | ||||||||
\(476\) | 1.95187e8 | 0.0829518 | ||||||||
\(477\) | −1.29179e9 | −0.544978 | ||||||||
\(478\) | −3.30114e9 | −1.38250 | ||||||||
\(479\) | 1.60185e9 | 0.665960 | 0.332980 | − | 0.942934i | \(-0.391946\pi\) | ||||
0.332980 | + | 0.942934i | \(0.391946\pi\) | |||||||
\(480\) | −4.31262e8 | −0.177991 | ||||||||
\(481\) | −5.12009e8 | −0.209783 | ||||||||
\(482\) | 1.24158e9 | 0.505022 | ||||||||
\(483\) | 9.97561e8 | 0.402832 | ||||||||
\(484\) | 1.54839e9 | 0.620758 | ||||||||
\(485\) | 5.50438e9 | 2.19085 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | 2.62672e9 | 1.03054 | 0.515268 | − | 0.857029i | \(-0.327692\pi\) | ||||
0.515268 | + | 0.857029i | \(0.327692\pi\) | |||||||
\(488\) | 1.43533e9 | 0.559091 | ||||||||
\(489\) | 2.80037e9 | 1.08302 | ||||||||
\(490\) | 4.58782e8 | 0.176165 | ||||||||
\(491\) | 4.97690e9 | 1.89746 | 0.948732 | − | 0.316083i | \(-0.102368\pi\) | ||||
0.948732 | + | 0.316083i | \(0.102368\pi\) | |||||||
\(492\) | −5.07077e8 | −0.191954 | ||||||||
\(493\) | −1.13148e9 | −0.425289 | ||||||||
\(494\) | −1.38546e8 | −0.0517071 | ||||||||
\(495\) | 2.34855e9 | 0.870327 | ||||||||
\(496\) | 3.56261e8 | 0.131094 | ||||||||
\(497\) | 5.75182e8 | 0.210164 | ||||||||
\(498\) | 9.76012e8 | 0.354122 | ||||||||
\(499\) | −2.98769e9 | −1.07642 | −0.538212 | − | 0.842809i | \(-0.680900\pi\) | ||||
−0.538212 | + | 0.842809i | \(0.680900\pi\) | |||||||
\(500\) | −2.53800e9 | −0.908023 | ||||||||
\(501\) | 1.18654e9 | 0.421552 | ||||||||
\(502\) | −6.89413e8 | −0.243230 | ||||||||
\(503\) | −3.10846e9 | −1.08907 | −0.544537 | − | 0.838737i | \(-0.683295\pi\) | ||||
−0.544537 | + | 0.838737i | \(0.683295\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 5.76382e9 | 1.99155 | ||||||||
\(506\) | −5.69530e9 | −1.95429 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | −1.07354e8 | −0.0363327 | ||||||||
\(509\) | −1.21043e9 | −0.406845 | −0.203422 | − | 0.979091i | \(-0.565206\pi\) | ||||
−0.203422 | + | 0.979091i | \(0.565206\pi\) | |||||||
\(510\) | −9.36176e8 | −0.312509 | ||||||||
\(511\) | −3.19807e8 | −0.106026 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −1.55155e8 | −0.0507406 | ||||||||
\(514\) | 2.41795e9 | 0.785372 | ||||||||
\(515\) | −1.99799e9 | −0.644568 | ||||||||
\(516\) | 4.48597e8 | 0.143742 | ||||||||
\(517\) | 1.61555e9 | 0.514166 | ||||||||
\(518\) | 6.39487e8 | 0.202152 | ||||||||
\(519\) | 2.18493e9 | 0.686043 | ||||||||
\(520\) | 5.48312e8 | 0.171008 | ||||||||
\(521\) | −7.31274e8 | −0.226542 | −0.113271 | − | 0.993564i | \(-0.536133\pi\) | ||||
−0.113271 | + | 0.993564i | \(0.536133\pi\) | |||||||
\(522\) | 7.42147e8 | 0.228372 | ||||||||
\(523\) | −6.22512e9 | −1.90280 | −0.951398 | − | 0.307965i | \(-0.900352\pi\) | ||||
−0.951398 | + | 0.307965i | \(0.900352\pi\) | |||||||
\(524\) | 1.39020e8 | 0.0422104 | ||||||||
\(525\) | −1.47694e9 | −0.445458 | ||||||||
\(526\) | −1.27616e9 | −0.382346 | ||||||||
\(527\) | 7.73366e8 | 0.230170 | ||||||||
\(528\) | 7.30919e8 | 0.216098 | ||||||||
\(529\) | 8.19797e9 | 2.40775 | ||||||||
\(530\) | −6.91009e9 | −2.01613 | ||||||||
\(531\) | −9.47072e8 | −0.274506 | ||||||||
\(532\) | 1.73041e8 | 0.0498262 | ||||||||
\(533\) | 6.44704e8 | 0.184423 | ||||||||
\(534\) | −2.83388e9 | −0.805355 | ||||||||
\(535\) | 3.22575e9 | 0.910737 | ||||||||
\(536\) | 1.70679e9 | 0.478745 | ||||||||
\(537\) | 1.98543e9 | 0.553280 | ||||||||
\(538\) | −3.26079e9 | −0.902786 | ||||||||
\(539\) | −7.77559e8 | −0.213881 | ||||||||
\(540\) | 6.14043e8 | 0.167811 | ||||||||
\(541\) | −2.23903e9 | −0.607953 | −0.303976 | − | 0.952680i | \(-0.598314\pi\) | ||||
−0.303976 | + | 0.952680i | \(0.598314\pi\) | |||||||
\(542\) | −1.69710e9 | −0.457837 | ||||||||
\(543\) | 2.42376e9 | 0.649665 | ||||||||
\(544\) | −2.91357e8 | −0.0775943 | ||||||||
\(545\) | −5.69568e8 | −0.150716 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −2.84122e9 | −0.742248 | −0.371124 | − | 0.928583i | \(-0.621027\pi\) | ||||
−0.371124 | + | 0.928583i | \(0.621027\pi\) | |||||||
\(548\) | −6.74764e8 | −0.175154 | ||||||||
\(549\) | −2.04366e9 | −0.527116 | ||||||||
\(550\) | 8.43221e9 | 2.16109 | ||||||||
\(551\) | −1.00311e9 | −0.255456 | ||||||||
\(552\) | −1.48907e9 | −0.376815 | ||||||||
\(553\) | −1.08672e9 | −0.273262 | ||||||||
\(554\) | −1.89689e9 | −0.473977 | ||||||||
\(555\) | −3.06718e9 | −0.761577 | ||||||||
\(556\) | −2.89808e9 | −0.715071 | ||||||||
\(557\) | −3.15591e9 | −0.773804 | −0.386902 | − | 0.922121i | \(-0.626455\pi\) | ||||
−0.386902 | + | 0.922121i | \(0.626455\pi\) | |||||||
\(558\) | −5.07255e8 | −0.123597 | ||||||||
\(559\) | −5.70352e8 | −0.138103 | ||||||||
\(560\) | −6.84829e8 | −0.164787 | ||||||||
\(561\) | 1.58666e9 | 0.379416 | ||||||||
\(562\) | −3.30050e7 | −0.00784337 | ||||||||
\(563\) | 4.29568e9 | 1.01450 | 0.507250 | − | 0.861799i | \(-0.330662\pi\) | ||||
0.507250 | + | 0.861799i | \(0.330662\pi\) | |||||||
\(564\) | 4.22395e8 | 0.0991384 | ||||||||
\(565\) | −2.66205e9 | −0.620936 | ||||||||
\(566\) | −1.93219e9 | −0.447911 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | −8.58581e8 | −0.196590 | ||||||||
\(569\) | −6.87856e9 | −1.56532 | −0.782662 | − | 0.622447i | \(-0.786139\pi\) | ||||
−0.782662 | + | 0.622447i | \(0.786139\pi\) | |||||||
\(570\) | −8.29958e8 | −0.187713 | ||||||||
\(571\) | 3.19999e9 | 0.719319 | 0.359660 | − | 0.933084i | \(-0.382893\pi\) | ||||
0.359660 | + | 0.933084i | \(0.382893\pi\) | |||||||
\(572\) | −9.29299e8 | −0.207620 | ||||||||
\(573\) | −3.34358e9 | −0.742455 | ||||||||
\(574\) | −8.05220e8 | −0.177715 | ||||||||
\(575\) | −1.71786e10 | −3.76834 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −6.66011e9 | −1.44333 | −0.721666 | − | 0.692242i | \(-0.756623\pi\) | ||||
−0.721666 | + | 0.692242i | \(0.756623\pi\) | |||||||
\(578\) | 2.65024e9 | 0.570870 | ||||||||
\(579\) | −1.02563e9 | −0.219592 | ||||||||
\(580\) | 3.96991e9 | 0.844855 | ||||||||
\(581\) | 1.54987e9 | 0.327853 | ||||||||
\(582\) | −2.43912e9 | −0.512866 | ||||||||
\(583\) | 1.17115e10 | 2.44777 | ||||||||
\(584\) | 4.77379e8 | 0.0991787 | ||||||||
\(585\) | −7.80702e8 | −0.161228 | ||||||||
\(586\) | −4.89188e9 | −1.00423 | ||||||||
\(587\) | −2.95382e9 | −0.602769 | −0.301384 | − | 0.953503i | \(-0.597449\pi\) | ||||
−0.301384 | + | 0.953503i | \(0.597449\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | 6.85620e8 | 0.138255 | ||||||||
\(590\) | −5.06610e9 | −1.01553 | ||||||||
\(591\) | −2.25137e9 | −0.448632 | ||||||||
\(592\) | −9.54570e8 | −0.189096 | ||||||||
\(593\) | −4.54892e9 | −0.895813 | −0.447906 | − | 0.894080i | \(-0.647830\pi\) | ||||
−0.447906 | + | 0.894080i | \(0.647830\pi\) | |||||||
\(594\) | −1.04070e9 | −0.203739 | ||||||||
\(595\) | −1.48661e9 | −0.289327 | ||||||||
\(596\) | 9.33942e8 | 0.180700 | ||||||||
\(597\) | −4.31146e9 | −0.829305 | ||||||||
\(598\) | 1.89322e9 | 0.362032 | ||||||||
\(599\) | −8.80898e9 | −1.67468 | −0.837340 | − | 0.546683i | \(-0.815890\pi\) | ||||
−0.837340 | + | 0.546683i | \(0.815890\pi\) | |||||||
\(600\) | 2.20465e9 | 0.416688 | ||||||||
\(601\) | −4.78732e9 | −0.899563 | −0.449781 | − | 0.893139i | \(-0.648498\pi\) | ||||
−0.449781 | + | 0.893139i | \(0.648498\pi\) | |||||||
\(602\) | 7.12356e8 | 0.133079 | ||||||||
\(603\) | −2.43018e9 | −0.451365 | ||||||||
\(604\) | −2.81191e9 | −0.519245 | ||||||||
\(605\) | −1.17931e10 | −2.16513 | ||||||||
\(606\) | −2.55409e9 | −0.466210 | ||||||||
\(607\) | −5.37360e9 | −0.975226 | −0.487613 | − | 0.873060i | \(-0.662132\pi\) | ||||
−0.487613 | + | 0.873060i | \(0.662132\pi\) | |||||||
\(608\) | −2.58300e8 | −0.0466082 | ||||||||
\(609\) | 1.17850e9 | 0.211432 | ||||||||
\(610\) | −1.09320e10 | −1.95005 | ||||||||
\(611\) | −5.37038e8 | −0.0952491 | ||||||||
\(612\) | 4.14843e8 | 0.0731566 | ||||||||
\(613\) | 1.02097e9 | 0.179020 | 0.0895100 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895100 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(614\) | 3.89568e9 | 0.679194 | ||||||||
\(615\) | 3.86209e9 | 0.669513 | ||||||||
\(616\) | 1.16067e9 | 0.200068 | ||||||||
\(617\) | 4.36863e9 | 0.748768 | 0.374384 | − | 0.927274i | \(-0.377854\pi\) | ||||
0.374384 | + | 0.927274i | \(0.377854\pi\) | |||||||
\(618\) | 8.85360e8 | 0.150890 | ||||||||
\(619\) | 9.55909e9 | 1.61994 | 0.809970 | − | 0.586471i | \(-0.199483\pi\) | ||||
0.809970 | + | 0.586471i | \(0.199483\pi\) | |||||||
\(620\) | −2.71342e9 | −0.457242 | ||||||||
\(621\) | 2.12018e9 | 0.355265 | ||||||||
\(622\) | 5.47355e9 | 0.912017 | ||||||||
\(623\) | −4.50010e9 | −0.745614 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | 6.87098e9 | 1.12574 | ||||||||
\(626\) | 4.53062e9 | 0.738154 | ||||||||
\(627\) | 1.40664e9 | 0.227902 | ||||||||
\(628\) | −1.35919e9 | −0.218989 | ||||||||
\(629\) | −2.07216e9 | −0.332007 | ||||||||
\(630\) | 9.75078e8 | 0.155363 | ||||||||
\(631\) | 3.76791e9 | 0.597032 | 0.298516 | − | 0.954405i | \(-0.403508\pi\) | ||||
0.298516 | + | 0.954405i | \(0.403508\pi\) | |||||||
\(632\) | 1.62216e9 | 0.255613 | ||||||||
\(633\) | 6.52044e9 | 1.02180 | ||||||||
\(634\) | −6.47284e9 | −1.00875 | ||||||||
\(635\) | 8.17651e8 | 0.126724 | ||||||||
\(636\) | 3.06203e9 | 0.471965 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | −6.72834e9 | −1.02574 | ||||||||
\(639\) | 1.22247e9 | 0.185347 | ||||||||
\(640\) | 1.02225e9 | 0.154144 | ||||||||
\(641\) | −1.10760e10 | −1.66104 | −0.830519 | − | 0.556991i | \(-0.811956\pi\) | ||||
−0.830519 | + | 0.556991i | \(0.811956\pi\) | |||||||
\(642\) | −1.42941e9 | −0.213199 | ||||||||
\(643\) | 1.71600e9 | 0.254553 | 0.127276 | − | 0.991867i | \(-0.459376\pi\) | ||||
0.127276 | + | 0.991867i | \(0.459376\pi\) | |||||||
\(644\) | −2.36459e9 | −0.348863 | ||||||||
\(645\) | −3.41668e9 | −0.501355 | ||||||||
\(646\) | −5.60713e8 | −0.0818327 | ||||||||
\(647\) | 3.74804e9 | 0.544050 | 0.272025 | − | 0.962290i | \(-0.412307\pi\) | ||||
0.272025 | + | 0.962290i | \(0.412307\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | 8.58620e9 | 1.23295 | ||||||||
\(650\) | −2.80302e9 | −0.400340 | ||||||||
\(651\) | −8.05502e8 | −0.114428 | ||||||||
\(652\) | −6.63793e9 | −0.937920 | ||||||||
\(653\) | −2.89195e9 | −0.406438 | −0.203219 | − | 0.979133i | \(-0.565140\pi\) | ||||
−0.203219 | + | 0.979133i | \(0.565140\pi\) | |||||||
\(654\) | 2.52390e8 | 0.0352817 | ||||||||
\(655\) | −1.05883e9 | −0.147225 | ||||||||
\(656\) | 1.20196e9 | 0.166237 | ||||||||
\(657\) | −6.79706e8 | −0.0935066 | ||||||||
\(658\) | 6.70747e8 | 0.0917843 | ||||||||
\(659\) | 5.98887e7 | 0.00815166 | 0.00407583 | − | 0.999992i | \(-0.498703\pi\) | ||||
0.00407583 | + | 0.999992i | \(0.498703\pi\) | |||||||
\(660\) | −5.56694e9 | −0.753725 | ||||||||
\(661\) | 2.69737e9 | 0.363275 | 0.181637 | − | 0.983366i | \(-0.441860\pi\) | ||||
0.181637 | + | 0.983366i | \(0.441860\pi\) | |||||||
\(662\) | −8.99596e9 | −1.20516 | ||||||||
\(663\) | −5.27436e8 | −0.0702866 | ||||||||
\(664\) | −2.31351e9 | −0.306678 | ||||||||
\(665\) | −1.31794e9 | −0.173788 | ||||||||
\(666\) | 1.35914e9 | 0.178281 | ||||||||
\(667\) | 1.37074e10 | 1.78860 | ||||||||
\(668\) | −2.81255e9 | −0.365075 | ||||||||
\(669\) | −3.65778e9 | −0.472309 | ||||||||
\(670\) | −1.29996e10 | −1.66981 | ||||||||
\(671\) | 1.85279e10 | 2.36754 | ||||||||
\(672\) | 3.03464e8 | 0.0385758 | ||||||||
\(673\) | −1.57258e9 | −0.198866 | −0.0994329 | − | 0.995044i | \(-0.531703\pi\) | ||||
−0.0994329 | + | 0.995044i | \(0.531703\pi\) | |||||||
\(674\) | −3.10177e9 | −0.390211 | ||||||||
\(675\) | −3.13904e9 | −0.392857 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | −6.48212e9 | −0.802891 | −0.401446 | − | 0.915883i | \(-0.631492\pi\) | ||||
−0.401446 | + | 0.915883i | \(0.631492\pi\) | |||||||
\(678\) | 1.17962e9 | 0.145358 | ||||||||
\(679\) | −3.87324e9 | −0.474821 | ||||||||
\(680\) | 2.21908e9 | 0.270640 | ||||||||
\(681\) | −3.66134e9 | −0.444248 | ||||||||
\(682\) | 4.59880e9 | 0.555135 | ||||||||
\(683\) | 7.54875e9 | 0.906573 | 0.453286 | − | 0.891365i | \(-0.350252\pi\) | ||||
0.453286 | + | 0.891365i | \(0.350252\pi\) | |||||||
\(684\) | 3.67775e8 | 0.0439426 | ||||||||
\(685\) | 5.13925e9 | 0.610918 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −6.93543e9 | −0.816065 | ||||||||
\(688\) | −1.06334e9 | −0.124484 | ||||||||
\(689\) | −3.89310e9 | −0.453449 | ||||||||
\(690\) | 1.13413e10 | 1.31429 | ||||||||
\(691\) | −1.97717e9 | −0.227966 | −0.113983 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113983 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(692\) | −5.17908e9 | −0.594130 | ||||||||
\(693\) | −1.65260e9 | −0.188626 | ||||||||
\(694\) | −1.16284e10 | −1.32057 | ||||||||
\(695\) | 2.20729e10 | 2.49409 | ||||||||
\(696\) | −1.75916e9 | −0.197776 | ||||||||
\(697\) | 2.60919e9 | 0.291872 | ||||||||
\(698\) | 2.67569e9 | 0.297812 | ||||||||
\(699\) | −2.76683e9 | −0.306416 | ||||||||
\(700\) | 3.50090e9 | 0.385778 | ||||||||
\(701\) | 9.57044e9 | 1.04935 | 0.524673 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524673 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | −1.83706e9 | −0.199425 | ||||||||
\(704\) | −1.73255e9 | −0.187146 | ||||||||
\(705\) | −3.21711e9 | −0.345784 | ||||||||
\(706\) | 8.97686e9 | 0.960082 | ||||||||
\(707\) | −4.05580e9 | −0.431627 | ||||||||
\(708\) | 2.24491e9 | 0.237729 | ||||||||
\(709\) | −1.34890e10 | −1.42141 | −0.710704 | − | 0.703492i | \(-0.751623\pi\) | ||||
−0.710704 | + | 0.703492i | \(0.751623\pi\) | |||||||
\(710\) | 6.53927e9 | 0.685685 | ||||||||
\(711\) | −2.30967e9 | −0.240994 | ||||||||
\(712\) | 6.71735e9 | 0.697458 | ||||||||
\(713\) | −9.36894e9 | −0.968004 | ||||||||
\(714\) | 6.58755e8 | 0.0677299 | ||||||||
\(715\) | 7.07788e9 | 0.724156 | ||||||||
\(716\) | −4.70621e9 | −0.479154 | ||||||||
\(717\) | −1.11413e10 | −1.12881 | ||||||||
\(718\) | −9.63618e8 | −0.0971560 | ||||||||
\(719\) | −7.99651e9 | −0.802323 | −0.401161 | − | 0.916007i | \(-0.631393\pi\) | ||||
−0.401161 | + | 0.916007i | \(0.631393\pi\) | |||||||
\(720\) | −1.45551e9 | −0.145329 | ||||||||
\(721\) | 1.40592e9 | 0.139697 | ||||||||
\(722\) | 6.65388e9 | 0.657953 | ||||||||
\(723\) | 4.19033e9 | 0.412348 | ||||||||
\(724\) | −5.74520e9 | −0.562626 | ||||||||
\(725\) | −2.02945e10 | −1.97786 | ||||||||
\(726\) | 5.22582e9 | 0.506847 | ||||||||
\(727\) | 4.80961e9 | 0.464237 | 0.232118 | − | 0.972688i | \(-0.425434\pi\) | ||||
0.232118 | + | 0.972688i | \(0.425434\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.63589e9 | −0.345924 | ||||||||
\(731\) | −2.30828e9 | −0.218564 | ||||||||
\(732\) | 4.84424e9 | 0.456496 | ||||||||
\(733\) | 1.74677e10 | 1.63822 | 0.819109 | − | 0.573638i | \(-0.194468\pi\) | ||||
0.819109 | + | 0.573638i | \(0.194468\pi\) | |||||||
\(734\) | 2.85522e9 | 0.266504 | ||||||||
\(735\) | 1.54839e9 | 0.143838 | ||||||||
\(736\) | 3.52965e9 | 0.326331 | ||||||||
\(737\) | 2.20321e10 | 2.02731 | ||||||||
\(738\) | −1.71139e9 | −0.156729 | ||||||||
\(739\) | 8.05884e9 | 0.734543 | 0.367271 | − | 0.930114i | \(-0.380292\pi\) | ||||
0.367271 | + | 0.930114i | \(0.380292\pi\) | |||||||
\(740\) | 7.27035e9 | 0.659545 | ||||||||
\(741\) | −4.67594e8 | −0.0422187 | ||||||||
\(742\) | 4.86239e9 | 0.436955 | ||||||||
\(743\) | −1.74429e10 | −1.56012 | −0.780058 | − | 0.625707i | \(-0.784810\pi\) | ||||
−0.780058 | + | 0.625707i | \(0.784810\pi\) | |||||||
\(744\) | 1.20238e9 | 0.107038 | ||||||||
\(745\) | −7.11325e9 | −0.630262 | ||||||||
\(746\) | 2.71111e9 | 0.239090 | ||||||||
\(747\) | 3.29404e9 | 0.289139 | ||||||||
\(748\) | −3.76098e9 | −0.328583 | ||||||||
\(749\) | −2.26985e9 | −0.197384 | ||||||||
\(750\) | −8.56576e9 | −0.741398 | ||||||||
\(751\) | 9.80161e9 | 0.844418 | 0.422209 | − | 0.906498i | \(-0.361255\pi\) | ||||
0.422209 | + | 0.906498i | \(0.361255\pi\) | |||||||
\(752\) | −1.00123e9 | −0.0858563 | ||||||||
\(753\) | −2.32677e9 | −0.198596 | ||||||||
\(754\) | 2.23662e9 | 0.190017 | ||||||||
\(755\) | 2.14165e10 | 1.81107 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | −9.93192e9 | −0.832142 | −0.416071 | − | 0.909332i | \(-0.636593\pi\) | ||||
−0.416071 | + | 0.909332i | \(0.636593\pi\) | |||||||
\(758\) | 1.41420e10 | 1.17942 | ||||||||
\(759\) | −1.92216e10 | −1.59567 | ||||||||
\(760\) | 1.96731e9 | 0.162564 | ||||||||
\(761\) | 1.50372e9 | 0.123686 | 0.0618432 | − | 0.998086i | \(-0.480302\pi\) | ||||
0.0618432 | + | 0.998086i | \(0.480302\pi\) | |||||||
\(762\) | −3.62321e8 | −0.0296655 | ||||||||
\(763\) | 4.00786e8 | 0.0326645 | ||||||||
\(764\) | 7.92552e9 | 0.642985 | ||||||||
\(765\) | −3.15959e9 | −0.255162 | ||||||||
\(766\) | 1.59932e10 | 1.28569 | ||||||||
\(767\) | −2.85421e9 | −0.228403 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | 2.10157e9 | 0.166649 | 0.0833244 | − | 0.996522i | \(-0.473446\pi\) | ||||
0.0833244 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(770\) | −8.84010e9 | −0.697814 | ||||||||
\(771\) | 8.16057e9 | 0.641254 | ||||||||
\(772\) | 2.43113e9 | 0.190172 | ||||||||
\(773\) | −1.88721e10 | −1.46958 | −0.734788 | − | 0.678297i | \(-0.762718\pi\) | ||||
−0.734788 | + | 0.678297i | \(0.762718\pi\) | |||||||
\(774\) | 1.51402e9 | 0.117365 | ||||||||
\(775\) | 1.38712e10 | 1.07043 | ||||||||
\(776\) | 5.78163e9 | 0.444155 | ||||||||
\(777\) | 2.15827e9 | 0.165056 | ||||||||
\(778\) | 2.27636e9 | 0.173306 | ||||||||
\(779\) | 2.31316e9 | 0.175317 | ||||||||
\(780\) | 1.85055e9 | 0.139627 | ||||||||
\(781\) | −1.10830e10 | −0.832488 | ||||||||
\(782\) | 7.66209e9 | 0.572959 | ||||||||
\(783\) | 2.50475e9 | 0.186465 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 1.03521e10 | 0.763808 | ||||||||
\(786\) | 4.69194e8 | 0.0344646 | ||||||||
\(787\) | 1.27674e10 | 0.933668 | 0.466834 | − | 0.884345i | \(-0.345395\pi\) | ||||
0.466834 | + | 0.884345i | \(0.345395\pi\) | |||||||
\(788\) | 5.33657e9 | 0.388527 | ||||||||
\(789\) | −4.30705e9 | −0.312184 | ||||||||
\(790\) | −1.23549e10 | −0.891550 | ||||||||
\(791\) | 1.87320e9 | 0.134575 | ||||||||
\(792\) | 2.46685e9 | 0.176443 | ||||||||
\(793\) | −6.15902e9 | −0.438587 | ||||||||
\(794\) | −3.62199e9 | −0.256788 | ||||||||
\(795\) | −2.33216e10 | −1.64616 | ||||||||
\(796\) | 1.02198e10 | 0.718199 | ||||||||
\(797\) | 1.13285e10 | 0.792629 | 0.396315 | − | 0.918115i | \(-0.370289\pi\) | ||||
0.396315 | + | 0.918115i | \(0.370289\pi\) | |||||||
\(798\) | 5.84013e8 | 0.0406830 | ||||||||
\(799\) | −2.17346e9 | −0.150743 | ||||||||
\(800\) | −5.22584e9 | −0.360862 | ||||||||
\(801\) | −9.56436e9 | −0.657570 | ||||||||
\(802\) | 1.84377e8 | 0.0126211 | ||||||||
\(803\) | 6.16224e9 | 0.419986 | ||||||||
\(804\) | 5.76043e9 | 0.390894 | ||||||||
\(805\) | 1.80096e10 | 1.21680 | ||||||||
\(806\) | −1.52872e9 | −0.102839 | ||||||||
\(807\) | −1.10052e10 | −0.737122 | ||||||||
\(808\) | 6.05414e9 | 0.403750 | ||||||||
\(809\) | −1.20927e9 | −0.0802975 | −0.0401487 | − | 0.999194i | \(-0.512783\pi\) | ||||
−0.0401487 | + | 0.999194i | \(0.512783\pi\) | |||||||
\(810\) | 2.07240e9 | 0.137017 | ||||||||
\(811\) | −1.99159e10 | −1.31107 | −0.655535 | − | 0.755164i | \(-0.727557\pi\) | ||||
−0.655535 | + | 0.755164i | \(0.727557\pi\) | |||||||
\(812\) | −2.79349e9 | −0.183105 | ||||||||
\(813\) | −5.72772e9 | −0.373822 | ||||||||
\(814\) | −1.23221e10 | −0.800751 | ||||||||
\(815\) | 5.05569e10 | 3.27136 | ||||||||
\(816\) | −9.83331e8 | −0.0633555 | ||||||||
\(817\) | −2.04639e9 | −0.131284 | ||||||||
\(818\) | −1.09806e10 | −0.701438 | ||||||||
\(819\) | 5.49353e8 | 0.0349428 | ||||||||
\(820\) | −9.15457e9 | −0.579815 | ||||||||
\(821\) | 1.79789e9 | 0.113387 | 0.0566934 | − | 0.998392i | \(-0.481944\pi\) | ||||
0.0566934 | + | 0.998392i | \(0.481944\pi\) | |||||||
\(822\) | −2.27733e9 | −0.143013 | ||||||||
\(823\) | 2.96870e10 | 1.85638 | 0.928191 | − | 0.372103i | \(-0.121363\pi\) | ||||
0.928191 | + | 0.372103i | \(0.121363\pi\) | |||||||
\(824\) | −2.09863e9 | −0.130675 | ||||||||
\(825\) | 2.84587e10 | 1.76452 | ||||||||
\(826\) | 3.56484e9 | 0.220095 | ||||||||
\(827\) | −1.82607e10 | −1.12266 | −0.561329 | − | 0.827593i | \(-0.689710\pi\) | ||||
−0.561329 | + | 0.827593i | \(0.689710\pi\) | |||||||
\(828\) | −5.02561e9 | −0.307668 | ||||||||
\(829\) | −1.11037e9 | −0.0676904 | −0.0338452 | − | 0.999427i | \(-0.510775\pi\) | ||||
−0.0338452 | + | 0.999427i | \(0.510775\pi\) | |||||||
\(830\) | 1.76205e10 | 1.06966 | ||||||||
\(831\) | −6.40199e9 | −0.387001 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | 1.04608e9 | 0.0627057 | ||||||||
\(834\) | −9.78103e9 | −0.583853 | ||||||||
\(835\) | 2.14214e10 | 1.27334 | ||||||||
\(836\) | −3.33426e9 | −0.197369 | ||||||||
\(837\) | −1.71199e9 | −0.100916 | ||||||||
\(838\) | 5.35251e8 | 0.0314198 | ||||||||
\(839\) | −9.11686e9 | −0.532940 | −0.266470 | − | 0.963843i | \(-0.585857\pi\) | ||||
−0.266470 | + | 0.963843i | \(0.585857\pi\) | |||||||
\(840\) | −2.31130e9 | −0.134548 | ||||||||
\(841\) | −1.05623e9 | −0.0612309 | ||||||||
\(842\) | −9.07299e9 | −0.523791 | ||||||||
\(843\) | −1.11392e8 | −0.00640409 | ||||||||
\(844\) | −1.54559e10 | −0.884901 | ||||||||
\(845\) | −2.35282e9 | −0.134150 | ||||||||
\(846\) | 1.42558e9 | 0.0809461 | ||||||||
\(847\) | 8.29841e9 | 0.469249 | ||||||||
\(848\) | −7.25815e9 | −0.408734 | ||||||||
\(849\) | −6.52114e9 | −0.365718 | ||||||||
\(850\) | −1.13442e10 | −0.633587 | ||||||||
\(851\) | 2.51032e10 | 1.39629 | ||||||||
\(852\) | −2.89771e9 | −0.160515 | ||||||||
\(853\) | 2.39883e10 | 1.32336 | 0.661680 | − | 0.749787i | \(-0.269844\pi\) | ||||
0.661680 | + | 0.749787i | \(0.269844\pi\) | |||||||
\(854\) | 7.69247e9 | 0.422633 | ||||||||
\(855\) | −2.80111e9 | −0.153267 | ||||||||
\(856\) | 3.38823e9 | 0.184636 | ||||||||
\(857\) | −4.74952e9 | −0.257761 | −0.128880 | − | 0.991660i | \(-0.541138\pi\) | ||||
−0.128880 | + | 0.991660i | \(0.541138\pi\) | |||||||
\(858\) | −3.13638e9 | −0.169521 | ||||||||
\(859\) | 2.55278e10 | 1.37416 | 0.687079 | − | 0.726583i | \(-0.258893\pi\) | ||||
0.687079 | + | 0.726583i | \(0.258893\pi\) | |||||||
\(860\) | 8.09880e9 | 0.434186 | ||||||||
\(861\) | −2.71762e9 | −0.145103 | ||||||||
\(862\) | 2.53346e10 | 1.34722 | ||||||||
\(863\) | 8.21920e9 | 0.435303 | 0.217651 | − | 0.976027i | \(-0.430160\pi\) | ||||
0.217651 | + | 0.976027i | \(0.430160\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | 3.94458e10 | 2.07226 | ||||||||
\(866\) | 1.09106e10 | 0.570869 | ||||||||
\(867\) | 8.94455e9 | 0.466113 | ||||||||
\(868\) | 1.90934e9 | 0.0990978 | ||||||||
\(869\) | 2.09396e10 | 1.08243 | ||||||||
\(870\) | 1.33984e10 | 0.689821 | ||||||||
\(871\) | −7.32388e9 | −0.375559 | ||||||||
\(872\) | −5.98257e8 | −0.0305549 | ||||||||
\(873\) | −8.23205e9 | −0.418753 | ||||||||
\(874\) | 6.79276e9 | 0.344157 | ||||||||
\(875\) | −1.36021e10 | −0.686401 | ||||||||
\(876\) | 1.61115e9 | 0.0809791 | ||||||||
\(877\) | −3.69625e10 | −1.85039 | −0.925194 | − | 0.379493i | \(-0.876098\pi\) | ||||
−0.925194 | + | 0.379493i | \(0.876098\pi\) | |||||||
\(878\) | 2.54293e10 | 1.26796 | ||||||||
\(879\) | −1.65101e10 | −0.819951 | ||||||||
\(880\) | 1.31957e10 | 0.652745 | ||||||||
\(881\) | −2.66580e10 | −1.31345 | −0.656723 | − | 0.754132i | \(-0.728058\pi\) | ||||
−0.656723 | + | 0.754132i | \(0.728058\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | −2.02249e10 | −0.988607 | −0.494304 | − | 0.869289i | \(-0.664577\pi\) | ||||
−0.494304 | + | 0.869289i | \(0.664577\pi\) | |||||||
\(884\) | 1.25022e9 | 0.0608700 | ||||||||
\(885\) | −1.70981e10 | −0.829174 | ||||||||
\(886\) | 1.09999e10 | 0.531340 | ||||||||
\(887\) | 3.02784e9 | 0.145680 | 0.0728400 | − | 0.997344i | \(-0.476794\pi\) | ||||
0.0728400 | + | 0.997344i | \(0.476794\pi\) | |||||||
\(888\) | −3.22167e9 | −0.154396 | ||||||||
\(889\) | −5.75353e8 | −0.0274649 | ||||||||
\(890\) | −5.11618e10 | −2.43266 | ||||||||
\(891\) | −3.51237e9 | −0.166352 | ||||||||
\(892\) | 8.67029e9 | 0.409031 | ||||||||
\(893\) | −1.92686e9 | −0.0905460 | ||||||||
\(894\) | 3.15206e9 | 0.147541 | ||||||||
\(895\) | 3.58442e10 | 1.67124 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | 6.38962e9 | 0.295598 | ||||||||
\(898\) | −4.67702e9 | −0.215527 | ||||||||
\(899\) | −1.10683e10 | −0.508069 | ||||||||
\(900\) | 7.44070e9 | 0.340224 | ||||||||
\(901\) | −1.57559e10 | −0.717638 | ||||||||
\(902\) | 1.55155e10 | 0.703952 | ||||||||
\(903\) | 2.40420e9 | 0.108659 | ||||||||
\(904\) | −2.79614e9 | −0.125884 | ||||||||
\(905\) | 4.37575e10 | 1.96238 | ||||||||
\(906\) | −9.49019e9 | −0.423961 | ||||||||
\(907\) | 3.44478e10 | 1.53298 | 0.766490 | − | 0.642257i | \(-0.222002\pi\) | ||||
0.766490 | + | 0.642257i | \(0.222002\pi\) | |||||||
\(908\) | 8.67874e9 | 0.384730 | ||||||||
\(909\) | −8.62005e9 | −0.380659 | ||||||||
\(910\) | 2.93861e9 | 0.129270 | ||||||||
\(911\) | −2.62762e10 | −1.15146 | −0.575729 | − | 0.817641i | \(-0.695282\pi\) | ||||
−0.575729 | + | 0.817641i | \(0.695282\pi\) | |||||||
\(912\) | −8.71763e8 | −0.0380554 | ||||||||
\(913\) | −2.98639e10 | −1.29867 | ||||||||
\(914\) | −1.98367e10 | −0.859324 | ||||||||
\(915\) | −3.68955e10 | −1.59221 | ||||||||
\(916\) | 1.64395e10 | 0.706733 | ||||||||
\(917\) | 7.45062e8 | 0.0319080 | ||||||||
\(918\) | 1.40009e9 | 0.0597321 | ||||||||
\(919\) | 1.02393e10 | 0.435178 | 0.217589 | − | 0.976041i | \(-0.430181\pi\) | ||||
0.217589 | + | 0.976041i | \(0.430181\pi\) | |||||||
\(920\) | −2.68831e10 | −1.13821 | ||||||||
\(921\) | 1.31479e10 | 0.554560 | ||||||||
\(922\) | −9.28744e9 | −0.390245 | ||||||||
\(923\) | 3.68418e9 | 0.154218 | ||||||||
\(924\) | 3.91727e9 | 0.163355 | ||||||||
\(925\) | −3.71667e10 | −1.54404 | ||||||||
\(926\) | −2.13317e10 | −0.882848 | ||||||||
\(927\) | 2.98809e9 | 0.123201 | ||||||||
\(928\) | 4.16987e9 | 0.171279 | ||||||||
\(929\) | 2.65627e10 | 1.08697 | 0.543485 | − | 0.839419i | \(-0.317105\pi\) | ||||
0.543485 | + | 0.839419i | \(0.317105\pi\) | |||||||
\(930\) | −9.15779e9 | −0.373336 | ||||||||
\(931\) | 9.27391e8 | 0.0376651 | ||||||||
\(932\) | 6.55841e9 | 0.265364 | ||||||||
\(933\) | 1.84732e10 | 0.744659 | ||||||||
\(934\) | 3.44325e9 | 0.138278 | ||||||||
\(935\) | 2.86450e10 | 1.14606 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | 3.40056e10 | 1.35040 | 0.675199 | − | 0.737636i | \(-0.264058\pi\) | ||||
0.675199 | + | 0.737636i | \(0.264058\pi\) | |||||||
\(938\) | 9.14735e9 | 0.361897 | ||||||||
\(939\) | 1.52908e10 | 0.602700 | ||||||||
\(940\) | 7.62575e9 | 0.299457 | ||||||||
\(941\) | −2.47895e10 | −0.969848 | −0.484924 | − | 0.874556i | \(-0.661153\pi\) | ||||
−0.484924 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(942\) | −4.58727e9 | −0.178803 | ||||||||
\(943\) | −3.16091e10 | −1.22750 | ||||||||
\(944\) | −5.32127e9 | −0.205880 | ||||||||
\(945\) | 3.29089e9 | 0.126853 | ||||||||
\(946\) | −1.37261e10 | −0.527144 | ||||||||
\(947\) | 2.16151e10 | 0.827052 | 0.413526 | − | 0.910492i | \(-0.364297\pi\) | ||||
0.413526 | + | 0.910492i | \(0.364297\pi\) | |||||||
\(948\) | 5.47478e9 | 0.208707 | ||||||||
\(949\) | −2.04844e9 | −0.0778022 | ||||||||
\(950\) | −1.00571e10 | −0.380573 | ||||||||
\(951\) | −2.18459e10 | −0.823639 | ||||||||
\(952\) | −1.56149e9 | −0.0586558 | ||||||||
\(953\) | 1.62128e10 | 0.606782 | 0.303391 | − | 0.952866i | \(-0.401881\pi\) | ||||
0.303391 | + | 0.952866i | \(0.401881\pi\) | |||||||
\(954\) | 1.03344e10 | 0.385358 | ||||||||
\(955\) | −6.03637e10 | −2.24266 | ||||||||
\(956\) | 2.64091e10 | 0.977577 | ||||||||
\(957\) | −2.27081e10 | −0.837509 | ||||||||
\(958\) | −1.28148e10 | −0.470905 | ||||||||
\(959\) | −3.61632e9 | −0.132404 | ||||||||
\(960\) | 3.45010e9 | 0.125858 | ||||||||
\(961\) | −1.99475e10 | −0.725030 | ||||||||
\(962\) | 4.09607e9 | 0.148339 | ||||||||
\(963\) | −4.82426e9 | −0.174076 | ||||||||
\(964\) | −9.93264e9 | −0.357104 | ||||||||
\(965\) | −1.85164e10 | −0.663300 | ||||||||
\(966\) | −7.98048e9 | −0.284845 | ||||||||
\(967\) | −3.00338e10 | −1.06811 | −0.534057 | − | 0.845449i | \(-0.679333\pi\) | ||||
−0.534057 | + | 0.845449i | \(0.679333\pi\) | |||||||
\(968\) | −1.23871e10 | −0.438942 | ||||||||
\(969\) | −1.89241e9 | −0.0668161 | ||||||||
\(970\) | −4.40350e10 | −1.54916 | ||||||||
\(971\) | −1.32906e10 | −0.465884 | −0.232942 | − | 0.972491i | \(-0.574835\pi\) | ||||
−0.232942 | + | 0.972491i | \(0.574835\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | −1.55319e10 | −0.540543 | ||||||||
\(974\) | −2.10138e10 | −0.728699 | ||||||||
\(975\) | −9.46019e9 | −0.326877 | ||||||||
\(976\) | −1.14826e10 | −0.395337 | ||||||||
\(977\) | 1.99798e10 | 0.685424 | 0.342712 | − | 0.939440i | \(-0.388654\pi\) | ||||
0.342712 | + | 0.939440i | \(0.388654\pi\) | |||||||
\(978\) | −2.24030e10 | −0.765808 | ||||||||
\(979\) | 8.67109e10 | 2.95348 | ||||||||
\(980\) | −3.67025e9 | −0.124567 | ||||||||
\(981\) | 8.51816e8 | 0.0288074 | ||||||||
\(982\) | −3.98152e10 | −1.34171 | ||||||||
\(983\) | 5.18069e9 | 0.173960 | 0.0869802 | − | 0.996210i | \(-0.472278\pi\) | ||||
0.0869802 | + | 0.996210i | \(0.472278\pi\) | |||||||
\(984\) | 4.05662e9 | 0.135732 | ||||||||
\(985\) | −4.06453e10 | −1.35514 | ||||||||
\(986\) | 9.05187e9 | 0.300725 | ||||||||
\(987\) | 2.26377e9 | 0.0749416 | ||||||||
\(988\) | 1.10837e9 | 0.0365625 | ||||||||
\(989\) | 2.79637e10 | 0.919194 | ||||||||
\(990\) | −1.87884e10 | −0.615414 | ||||||||
\(991\) | 5.16222e10 | 1.68492 | 0.842459 | − | 0.538761i | \(-0.181107\pi\) | ||||
0.842459 | + | 0.538761i | \(0.181107\pi\) | |||||||
\(992\) | −2.85009e9 | −0.0926975 | ||||||||
\(993\) | −3.03613e10 | −0.984008 | ||||||||
\(994\) | −4.60146e9 | −0.148608 | ||||||||
\(995\) | −7.78374e10 | −2.50500 | ||||||||
\(996\) | −7.80810e9 | −0.250402 | ||||||||
\(997\) | −1.99089e10 | −0.636229 | −0.318115 | − | 0.948052i | \(-0.603050\pi\) | ||||
−0.318115 | + | 0.948052i | \(0.603050\pi\) | |||||||
\(998\) | 2.39015e10 | 0.761147 | ||||||||
\(999\) | 4.58711e9 | 0.145566 |
(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 | 546.8.a.n.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.n.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial |