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: | \( x^{6} - x^{5} - 302081x^{4} - 2628147x^{3} + 19116974952x^{2} - 78725393748x - 5138711063280 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(472.635\) 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 | ||||||||
\(5\) | −479.635 | −1.71599 | −0.857997 | − | 0.513654i | \(-0.828291\pi\) | ||||
−0.857997 | + | 0.513654i | \(0.828291\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 3837.08 | 1.21339 | ||||||||
\(11\) | 6141.65 | 1.39127 | 0.695634 | − | 0.718397i | \(-0.255124\pi\) | ||||
0.695634 | + | 0.718397i | \(0.255124\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | −12950.1 | −0.990730 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −28277.0 | −1.39593 | −0.697963 | − | 0.716134i | \(-0.745910\pi\) | ||||
−0.697963 | + | 0.716134i | \(0.745910\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | −42997.9 | −1.43817 | −0.719084 | − | 0.694923i | \(-0.755438\pi\) | ||||
−0.719084 | + | 0.694923i | \(0.755438\pi\) | |||||||
\(20\) | −30696.6 | −0.857997 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −49133.2 | −0.983775 | ||||||||
\(23\) | 91517.2 | 1.56839 | 0.784197 | − | 0.620512i | \(-0.213075\pi\) | ||||
0.784197 | + | 0.620512i | \(0.213075\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 151925. | 1.94464 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | 38280.3 | 0.291462 | 0.145731 | − | 0.989324i | \(-0.453447\pi\) | ||||
0.145731 | + | 0.989324i | \(0.453447\pi\) | |||||||
\(30\) | 103601. | 0.700552 | ||||||||
\(31\) | 15397.8 | 0.0928312 | 0.0464156 | − | 0.998922i | \(-0.485220\pi\) | ||||
0.0464156 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 165825. | 0.803249 | ||||||||
\(34\) | 226216. | 0.987069 | ||||||||
\(35\) | −164515. | −0.648585 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −380722. | −1.23567 | −0.617834 | − | 0.786309i | \(-0.711989\pi\) | ||||
−0.617834 | + | 0.786309i | \(0.711989\pi\) | |||||||
\(38\) | 343983. | 1.01694 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | 245573. | 0.606696 | ||||||||
\(41\) | 82935.4 | 0.187930 | 0.0939650 | − | 0.995575i | \(-0.470046\pi\) | ||||
0.0939650 | + | 0.995575i | \(0.470046\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | 254960. | 0.489026 | 0.244513 | − | 0.969646i | \(-0.421372\pi\) | ||||
0.244513 | + | 0.969646i | \(0.421372\pi\) | |||||||
\(44\) | 393066. | 0.695634 | ||||||||
\(45\) | −349654. | −0.571998 | ||||||||
\(46\) | −732137. | −1.10902 | ||||||||
\(47\) | 800846. | 1.12514 | 0.562570 | − | 0.826750i | \(-0.309813\pi\) | ||||
0.562570 | + | 0.826750i | \(0.309813\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −1.21540e6 | −1.37507 | ||||||||
\(51\) | −763479. | −0.805938 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | −1.98040e6 | −1.82720 | −0.913601 | − | 0.406611i | \(-0.866711\pi\) | ||||
−0.913601 | + | 0.406611i | \(0.866711\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −2.94575e6 | −2.38741 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | −1.16094e6 | −0.830327 | ||||||||
\(58\) | −306242. | −0.206095 | ||||||||
\(59\) | −2.20647e6 | −1.39867 | −0.699336 | − | 0.714793i | \(-0.746521\pi\) | ||||
−0.699336 | + | 0.714793i | \(0.746521\pi\) | |||||||
\(60\) | −828809. | −0.495365 | ||||||||
\(61\) | −1.21835e6 | −0.687252 | −0.343626 | − | 0.939107i | \(-0.611655\pi\) | ||||
−0.343626 | + | 0.939107i | \(0.611655\pi\) | |||||||
\(62\) | −123183. | −0.0656416 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.05376e6 | 0.475931 | ||||||||
\(66\) | −1.32660e6 | −0.567983 | ||||||||
\(67\) | 1.98455e6 | 0.806122 | 0.403061 | − | 0.915173i | \(-0.367946\pi\) | ||||
0.403061 | + | 0.915173i | \(0.367946\pi\) | |||||||
\(68\) | −1.80973e6 | −0.697963 | ||||||||
\(69\) | 2.47096e6 | 0.905513 | ||||||||
\(70\) | 1.31612e6 | 0.458619 | ||||||||
\(71\) | 3.12075e6 | 1.03480 | 0.517398 | − | 0.855745i | \(-0.326901\pi\) | ||||
0.517398 | + | 0.855745i | \(0.326901\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | −883562. | −0.265832 | −0.132916 | − | 0.991127i | \(-0.542434\pi\) | ||||
−0.132916 | + | 0.991127i | \(0.542434\pi\) | |||||||
\(74\) | 3.04577e6 | 0.873749 | ||||||||
\(75\) | 4.10197e6 | 1.12274 | ||||||||
\(76\) | −2.75187e6 | −0.719084 | ||||||||
\(77\) | 2.10659e6 | 0.525850 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | −4.21311e6 | −0.961409 | −0.480705 | − | 0.876883i | \(-0.659619\pi\) | ||||
−0.480705 | + | 0.876883i | \(0.659619\pi\) | |||||||
\(80\) | −1.96459e6 | −0.428999 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −663483. | −0.132887 | ||||||||
\(83\) | 1.90022e6 | 0.364780 | 0.182390 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182390 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 1.35626e7 | 2.39540 | ||||||||
\(86\) | −2.03968e6 | −0.345794 | ||||||||
\(87\) | 1.03357e6 | 0.168276 | ||||||||
\(88\) | −3.14453e6 | −0.491887 | ||||||||
\(89\) | −1.19875e6 | −0.180244 | −0.0901222 | − | 0.995931i | \(-0.528726\pi\) | ||||
−0.0901222 | + | 0.995931i | \(0.528726\pi\) | |||||||
\(90\) | 2.79723e6 | 0.404464 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 5.85710e6 | 0.784197 | ||||||||
\(93\) | 415742. | 0.0535961 | ||||||||
\(94\) | −6.40677e6 | −0.795594 | ||||||||
\(95\) | 2.06233e7 | 2.46789 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −9.55500e6 | −1.06299 | −0.531496 | − | 0.847061i | \(-0.678370\pi\) | ||||
−0.531496 | + | 0.847061i | \(0.678370\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | 4.47726e6 | 0.463756 | ||||||||
\(100\) | 9.72318e6 | 0.972318 | ||||||||
\(101\) | −3.60039e6 | −0.347716 | −0.173858 | − | 0.984771i | \(-0.555623\pi\) | ||||
−0.173858 | + | 0.984771i | \(0.555623\pi\) | |||||||
\(102\) | 6.10784e6 | 0.569884 | ||||||||
\(103\) | −372595. | −0.0335974 | −0.0167987 | − | 0.999859i | \(-0.505347\pi\) | ||||
−0.0167987 | + | 0.999859i | \(0.505347\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | −4.44190e6 | −0.374461 | ||||||||
\(106\) | 1.58432e7 | 1.29203 | ||||||||
\(107\) | −3.08080e6 | −0.243119 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −2.69326e7 | −1.99198 | −0.995990 | − | 0.0894624i | \(-0.971485\pi\) | ||||
−0.995990 | + | 0.0894624i | \(0.971485\pi\) | |||||||
\(110\) | 2.35660e7 | 1.68815 | ||||||||
\(111\) | −1.02795e7 | −0.713413 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | 1.57681e7 | 1.02803 | 0.514013 | − | 0.857782i | \(-0.328158\pi\) | ||||
0.514013 | + | 0.857782i | \(0.328158\pi\) | |||||||
\(114\) | 9.28755e6 | 0.587130 | ||||||||
\(115\) | −4.38948e7 | −2.69136 | ||||||||
\(116\) | 2.44994e6 | 0.145731 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | 1.76518e7 | 0.989011 | ||||||||
\(119\) | −9.69902e6 | −0.527610 | ||||||||
\(120\) | 6.63047e6 | 0.350276 | ||||||||
\(121\) | 1.82327e7 | 0.935626 | ||||||||
\(122\) | 9.74677e6 | 0.485961 | ||||||||
\(123\) | 2.23926e6 | 0.108501 | ||||||||
\(124\) | 985462. | 0.0464156 | ||||||||
\(125\) | −3.53969e7 | −1.62099 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | 2.51985e7 | 1.09160 | 0.545799 | − | 0.837916i | \(-0.316226\pi\) | ||||
0.545799 | + | 0.837916i | \(0.316226\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 6.88391e6 | 0.282339 | ||||||||
\(130\) | −8.43007e6 | −0.336534 | ||||||||
\(131\) | 2.79431e7 | 1.08599 | 0.542994 | − | 0.839736i | \(-0.317290\pi\) | ||||
0.542994 | + | 0.839736i | \(0.317290\pi\) | |||||||
\(132\) | 1.06128e7 | 0.401624 | ||||||||
\(133\) | −1.47483e7 | −0.543577 | ||||||||
\(134\) | −1.58764e7 | −0.570014 | ||||||||
\(135\) | −9.44066e6 | −0.330243 | ||||||||
\(136\) | 1.44778e7 | 0.493534 | ||||||||
\(137\) | 48254.4 | 0.00160330 | 0.000801651 | − | 1.00000i | \(-0.499745\pi\) | ||||
0.000801651 | 1.00000i | \(0.499745\pi\) | ||||||||
\(138\) | −1.97677e7 | −0.640294 | ||||||||
\(139\) | 2.07595e7 | 0.655639 | 0.327819 | − | 0.944740i | \(-0.393686\pi\) | ||||
0.327819 | + | 0.944740i | \(0.393686\pi\) | |||||||
\(140\) | −1.05289e7 | −0.324292 | ||||||||
\(141\) | 2.16228e7 | 0.649600 | ||||||||
\(142\) | −2.49660e7 | −0.731711 | ||||||||
\(143\) | −1.34932e7 | −0.385868 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −1.83606e7 | −0.500147 | ||||||||
\(146\) | 7.06850e6 | 0.187971 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | −2.43662e7 | −0.617834 | ||||||||
\(149\) | 7.41183e7 | 1.83558 | 0.917791 | − | 0.397065i | \(-0.129971\pi\) | ||||
0.917791 | + | 0.397065i | \(0.129971\pi\) | |||||||
\(150\) | −3.28157e7 | −0.793895 | ||||||||
\(151\) | −6.13143e7 | −1.44925 | −0.724624 | − | 0.689144i | \(-0.757987\pi\) | ||||
−0.724624 | + | 0.689144i | \(0.757987\pi\) | |||||||
\(152\) | 2.20149e7 | 0.508469 | ||||||||
\(153\) | −2.06139e7 | −0.465309 | ||||||||
\(154\) | −1.68527e7 | −0.371832 | ||||||||
\(155\) | −7.38534e6 | −0.159298 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | 1.74448e7 | 0.359763 | 0.179882 | − | 0.983688i | \(-0.442429\pi\) | ||||
0.179882 | + | 0.983688i | \(0.442429\pi\) | |||||||
\(158\) | 3.37049e7 | 0.679819 | ||||||||
\(159\) | −5.34707e7 | −1.05494 | ||||||||
\(160\) | 1.57167e7 | 0.303348 | ||||||||
\(161\) | 3.13904e7 | 0.592797 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | −6.00021e7 | −1.08520 | −0.542600 | − | 0.839991i | \(-0.682560\pi\) | ||||
−0.542600 | + | 0.839991i | \(0.682560\pi\) | |||||||
\(164\) | 5.30786e6 | 0.0939650 | ||||||||
\(165\) | −7.95353e7 | −1.37837 | ||||||||
\(166\) | −1.52018e7 | −0.257938 | ||||||||
\(167\) | 5.97842e7 | 0.993297 | 0.496648 | − | 0.867952i | \(-0.334564\pi\) | ||||
0.496648 | + | 0.867952i | \(0.334564\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −1.08501e8 | −1.69380 | ||||||||
\(171\) | −3.13455e7 | −0.479389 | ||||||||
\(172\) | 1.63174e7 | 0.244513 | ||||||||
\(173\) | 4.45329e7 | 0.653913 | 0.326957 | − | 0.945039i | \(-0.393977\pi\) | ||||
0.326957 | + | 0.945039i | \(0.393977\pi\) | |||||||
\(174\) | −8.26854e6 | −0.118989 | ||||||||
\(175\) | 5.21102e7 | 0.735004 | ||||||||
\(176\) | 2.51562e7 | 0.347817 | ||||||||
\(177\) | −5.95747e7 | −0.807524 | ||||||||
\(178\) | 9.58996e6 | 0.127452 | ||||||||
\(179\) | 6.47574e6 | 0.0843925 | 0.0421962 | − | 0.999109i | \(-0.486565\pi\) | ||||
0.0421962 | + | 0.999109i | \(0.486565\pi\) | |||||||
\(180\) | −2.23779e7 | −0.285999 | ||||||||
\(181\) | 1.02887e8 | 1.28969 | 0.644846 | − | 0.764313i | \(-0.276922\pi\) | ||||
0.644846 | + | 0.764313i | \(0.276922\pi\) | |||||||
\(182\) | 6.02857e6 | 0.0741249 | ||||||||
\(183\) | −3.28953e7 | −0.396785 | ||||||||
\(184\) | −4.68568e7 | −0.554511 | ||||||||
\(185\) | 1.82607e8 | 2.12040 | ||||||||
\(186\) | −3.32593e6 | −0.0378982 | ||||||||
\(187\) | −1.73668e8 | −1.94211 | ||||||||
\(188\) | 5.12542e7 | 0.562570 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | −1.64986e8 | −1.74506 | ||||||||
\(191\) | 1.61049e8 | 1.67241 | 0.836204 | − | 0.548418i | \(-0.184770\pi\) | ||||
0.836204 | + | 0.548418i | \(0.184770\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | 7.30667e7 | 0.731592 | 0.365796 | − | 0.930695i | \(-0.380797\pi\) | ||||
0.365796 | + | 0.930695i | \(0.380797\pi\) | |||||||
\(194\) | 7.64400e7 | 0.751648 | ||||||||
\(195\) | 2.84515e7 | 0.274779 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 8.95011e7 | 0.834059 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(198\) | −3.58181e7 | −0.327925 | ||||||||
\(199\) | −9.67078e7 | −0.869913 | −0.434956 | − | 0.900452i | \(-0.643236\pi\) | ||||
−0.434956 | + | 0.900452i | \(0.643236\pi\) | |||||||
\(200\) | −7.77855e7 | −0.687533 | ||||||||
\(201\) | 5.35829e7 | 0.465415 | ||||||||
\(202\) | 2.88031e7 | 0.245872 | ||||||||
\(203\) | 1.31301e7 | 0.110162 | ||||||||
\(204\) | −4.88627e7 | −0.402969 | ||||||||
\(205\) | −3.97787e7 | −0.322487 | ||||||||
\(206\) | 2.98076e6 | 0.0237570 | ||||||||
\(207\) | 6.67160e7 | 0.522798 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | −2.64078e8 | −2.00088 | ||||||||
\(210\) | 3.55352e7 | 0.264784 | ||||||||
\(211\) | 1.09331e8 | 0.801225 | 0.400613 | − | 0.916248i | \(-0.368797\pi\) | ||||
0.400613 | + | 0.916248i | \(0.368797\pi\) | |||||||
\(212\) | −1.26745e8 | −0.913601 | ||||||||
\(213\) | 8.42603e7 | 0.597440 | ||||||||
\(214\) | 2.46464e7 | 0.171911 | ||||||||
\(215\) | −1.22288e8 | −0.839166 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | 5.28146e6 | 0.0350869 | ||||||||
\(218\) | 2.15461e8 | 1.40854 | ||||||||
\(219\) | −2.38562e7 | −0.153478 | ||||||||
\(220\) | −1.88528e8 | −1.19370 | ||||||||
\(221\) | 6.21246e7 | 0.387160 | ||||||||
\(222\) | 8.22359e7 | 0.504459 | ||||||||
\(223\) | 1.56478e8 | 0.944902 | 0.472451 | − | 0.881357i | \(-0.343369\pi\) | ||||
0.472451 | + | 0.881357i | \(0.343369\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.10753e8 | 0.648212 | ||||||||
\(226\) | −1.26145e8 | −0.726924 | ||||||||
\(227\) | −2.98940e8 | −1.69626 | −0.848131 | − | 0.529787i | \(-0.822272\pi\) | ||||
−0.848131 | + | 0.529787i | \(0.822272\pi\) | |||||||
\(228\) | −7.43004e7 | −0.415163 | ||||||||
\(229\) | −2.43669e8 | −1.34084 | −0.670418 | − | 0.741984i | \(-0.733885\pi\) | ||||
−0.670418 | + | 0.741984i | \(0.733885\pi\) | |||||||
\(230\) | 3.51159e8 | 1.90308 | ||||||||
\(231\) | 5.68778e7 | 0.303599 | ||||||||
\(232\) | −1.95995e7 | −0.103047 | ||||||||
\(233\) | 1.42543e8 | 0.738244 | 0.369122 | − | 0.929381i | \(-0.379658\pi\) | ||||
0.369122 | + | 0.929381i | \(0.379658\pi\) | |||||||
\(234\) | 1.28129e7 | 0.0653720 | ||||||||
\(235\) | −3.84114e8 | −1.93073 | ||||||||
\(236\) | −1.41214e8 | −0.699336 | ||||||||
\(237\) | −1.13754e8 | −0.555070 | ||||||||
\(238\) | 7.75921e7 | 0.373077 | ||||||||
\(239\) | 1.58648e8 | 0.751696 | 0.375848 | − | 0.926681i | \(-0.377351\pi\) | ||||
0.375848 | + | 0.926681i | \(0.377351\pi\) | |||||||
\(240\) | −5.30438e7 | −0.247682 | ||||||||
\(241\) | 2.93080e8 | 1.34873 | 0.674367 | − | 0.738396i | \(-0.264416\pi\) | ||||
0.674367 | + | 0.738396i | \(0.264416\pi\) | |||||||
\(242\) | −1.45862e8 | −0.661587 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −7.79741e7 | −0.343626 | ||||||||
\(245\) | −5.64286e7 | −0.245142 | ||||||||
\(246\) | −1.79140e7 | −0.0767221 | ||||||||
\(247\) | 9.44664e7 | 0.398876 | ||||||||
\(248\) | −7.88369e6 | −0.0328208 | ||||||||
\(249\) | 5.13060e7 | 0.210606 | ||||||||
\(250\) | 2.83176e8 | 1.14621 | ||||||||
\(251\) | −2.85090e7 | −0.113795 | −0.0568976 | − | 0.998380i | \(-0.518121\pi\) | ||||
−0.0568976 | + | 0.998380i | \(0.518121\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 5.62067e8 | 2.18206 | ||||||||
\(254\) | −2.01588e8 | −0.771876 | ||||||||
\(255\) | 3.66191e8 | 1.38299 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −1.43945e8 | −0.528969 | −0.264484 | − | 0.964390i | \(-0.585202\pi\) | ||||
−0.264484 | + | 0.964390i | \(0.585202\pi\) | |||||||
\(258\) | −5.50713e7 | −0.199644 | ||||||||
\(259\) | −1.30588e8 | −0.467038 | ||||||||
\(260\) | 6.74405e7 | 0.237966 | ||||||||
\(261\) | 2.79063e7 | 0.0971540 | ||||||||
\(262\) | −2.23545e8 | −0.767910 | ||||||||
\(263\) | 5.25151e8 | 1.78008 | 0.890040 | − | 0.455883i | \(-0.150677\pi\) | ||||
0.890040 | + | 0.455883i | \(0.150677\pi\) | |||||||
\(264\) | −8.49022e7 | −0.283991 | ||||||||
\(265\) | 9.49868e8 | 3.13547 | ||||||||
\(266\) | 1.17986e8 | 0.384367 | ||||||||
\(267\) | −3.23661e7 | −0.104064 | ||||||||
\(268\) | 1.27011e8 | 0.403061 | ||||||||
\(269\) | 2.56559e8 | 0.803627 | 0.401814 | − | 0.915722i | \(-0.368380\pi\) | ||||
0.401814 | + | 0.915722i | \(0.368380\pi\) | |||||||
\(270\) | 7.55252e7 | 0.233517 | ||||||||
\(271\) | 2.69629e8 | 0.822950 | 0.411475 | − | 0.911421i | \(-0.365014\pi\) | ||||
0.411475 | + | 0.911421i | \(0.365014\pi\) | |||||||
\(272\) | −1.15823e8 | −0.348981 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | −386035. | −0.00113371 | ||||||||
\(275\) | 9.33069e8 | 2.70551 | ||||||||
\(276\) | 1.58142e8 | 0.452756 | ||||||||
\(277\) | 1.38687e8 | 0.392065 | 0.196032 | − | 0.980597i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980597i | \(0.437194\pi\) | |||||||
\(278\) | −1.66076e8 | −0.463607 | ||||||||
\(279\) | 1.12250e7 | 0.0309437 | ||||||||
\(280\) | 8.42316e7 | 0.229309 | ||||||||
\(281\) | 1.99903e8 | 0.537460 | 0.268730 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268730 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(282\) | −1.72983e8 | −0.459337 | ||||||||
\(283\) | −2.76398e8 | −0.724908 | −0.362454 | − | 0.932002i | \(-0.618061\pi\) | ||||
−0.362454 | + | 0.932002i | \(0.618061\pi\) | |||||||
\(284\) | 1.99728e8 | 0.517398 | ||||||||
\(285\) | 5.56829e8 | 1.42484 | ||||||||
\(286\) | 1.07946e8 | 0.272850 | ||||||||
\(287\) | 2.84468e7 | 0.0710309 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | 3.89251e8 | 0.948609 | ||||||||
\(290\) | 1.46884e8 | 0.353658 | ||||||||
\(291\) | −2.57985e8 | −0.613718 | ||||||||
\(292\) | −5.65480e7 | −0.132916 | ||||||||
\(293\) | −4.16733e8 | −0.967880 | −0.483940 | − | 0.875101i | \(-0.660795\pi\) | ||||
−0.483940 | + | 0.875101i | \(0.660795\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | 1.05830e9 | 2.40011 | ||||||||
\(296\) | 1.94929e8 | 0.436874 | ||||||||
\(297\) | 1.20886e8 | 0.267750 | ||||||||
\(298\) | −5.92947e8 | −1.29795 | ||||||||
\(299\) | −2.01063e8 | −0.434994 | ||||||||
\(300\) | 2.62526e8 | 0.561368 | ||||||||
\(301\) | 8.74512e7 | 0.184834 | ||||||||
\(302\) | 4.90515e8 | 1.02477 | ||||||||
\(303\) | −9.72105e7 | −0.200754 | ||||||||
\(304\) | −1.76119e8 | −0.359542 | ||||||||
\(305\) | 5.84361e8 | 1.17932 | ||||||||
\(306\) | 1.64912e8 | 0.329023 | ||||||||
\(307\) | 3.42872e6 | 0.00676313 | 0.00338157 | − | 0.999994i | \(-0.498924\pi\) | ||||
0.00338157 | + | 0.999994i | \(0.498924\pi\) | |||||||
\(308\) | 1.34822e8 | 0.262925 | ||||||||
\(309\) | −1.00601e7 | −0.0193975 | ||||||||
\(310\) | 5.90827e7 | 0.112641 | ||||||||
\(311\) | 5.83328e8 | 1.09964 | 0.549821 | − | 0.835282i | \(-0.314696\pi\) | ||||
0.549821 | + | 0.835282i | \(0.314696\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | 6.80001e8 | 1.25344 | 0.626721 | − | 0.779244i | \(-0.284396\pi\) | ||||
0.626721 | + | 0.779244i | \(0.284396\pi\) | |||||||
\(314\) | −1.39558e8 | −0.254391 | ||||||||
\(315\) | −1.19931e8 | −0.216195 | ||||||||
\(316\) | −2.69639e8 | −0.480705 | ||||||||
\(317\) | −2.78709e8 | −0.491409 | −0.245705 | − | 0.969345i | \(-0.579019\pi\) | ||||
−0.245705 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(318\) | 4.27766e8 | 0.745952 | ||||||||
\(319\) | 2.35104e8 | 0.405502 | ||||||||
\(320\) | −1.25733e8 | −0.214499 | ||||||||
\(321\) | −8.31815e7 | −0.140365 | ||||||||
\(322\) | −2.51123e8 | −0.419171 | ||||||||
\(323\) | 1.21585e9 | 2.00758 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −3.33779e8 | −0.539345 | ||||||||
\(326\) | 4.80017e8 | 0.767352 | ||||||||
\(327\) | −7.27179e8 | −1.15007 | ||||||||
\(328\) | −4.24629e7 | −0.0664433 | ||||||||
\(329\) | 2.74690e8 | 0.425263 | ||||||||
\(330\) | 6.36282e8 | 0.974655 | ||||||||
\(331\) | 8.50726e6 | 0.0128941 | 0.00644706 | − | 0.999979i | \(-0.497948\pi\) | ||||
0.00644706 | + | 0.999979i | \(0.497948\pi\) | |||||||
\(332\) | 1.21614e8 | 0.182390 | ||||||||
\(333\) | −2.77546e8 | −0.411889 | ||||||||
\(334\) | −4.78274e8 | −0.702367 | ||||||||
\(335\) | −9.51861e8 | −1.38330 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | 1.17226e9 | 1.66847 | 0.834236 | − | 0.551408i | \(-0.185909\pi\) | ||||
0.834236 | + | 0.551408i | \(0.185909\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | 4.25738e8 | 0.593531 | ||||||||
\(340\) | 8.68009e8 | 1.19770 | ||||||||
\(341\) | 9.45681e7 | 0.129153 | ||||||||
\(342\) | 2.50764e8 | 0.338980 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −1.30539e8 | −0.172897 | ||||||||
\(345\) | −1.18516e9 | −1.55385 | ||||||||
\(346\) | −3.56264e8 | −0.462386 | ||||||||
\(347\) | −3.54944e8 | −0.456044 | −0.228022 | − | 0.973656i | \(-0.573226\pi\) | ||||
−0.228022 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(348\) | 6.61483e7 | 0.0841379 | ||||||||
\(349\) | 4.68755e8 | 0.590278 | 0.295139 | − | 0.955454i | \(-0.404634\pi\) | ||||
0.295139 | + | 0.955454i | \(0.404634\pi\) | |||||||
\(350\) | −4.16882e8 | −0.519726 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | −2.01250e8 | −0.245944 | ||||||||
\(353\) | 4.99694e8 | 0.604634 | 0.302317 | − | 0.953207i | \(-0.402240\pi\) | ||||
0.302317 | + | 0.953207i | \(0.402240\pi\) | |||||||
\(354\) | 4.76598e8 | 0.571006 | ||||||||
\(355\) | −1.49682e9 | −1.77570 | ||||||||
\(356\) | −7.67197e7 | −0.0901222 | ||||||||
\(357\) | −2.61873e8 | −0.304616 | ||||||||
\(358\) | −5.18059e7 | −0.0596745 | ||||||||
\(359\) | 2.02205e8 | 0.230654 | 0.115327 | − | 0.993328i | \(-0.463208\pi\) | ||||
0.115327 | + | 0.993328i | \(0.463208\pi\) | |||||||
\(360\) | 1.79023e8 | 0.202232 | ||||||||
\(361\) | 9.54949e8 | 1.06833 | ||||||||
\(362\) | −8.23097e8 | −0.911950 | ||||||||
\(363\) | 4.92283e8 | 0.540184 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | 4.23787e8 | 0.456166 | ||||||||
\(366\) | 2.63163e8 | 0.280570 | ||||||||
\(367\) | −8.99197e8 | −0.949563 | −0.474782 | − | 0.880104i | \(-0.657473\pi\) | ||||
−0.474782 | + | 0.880104i | \(0.657473\pi\) | |||||||
\(368\) | 3.74854e8 | 0.392099 | ||||||||
\(369\) | 6.04599e7 | 0.0626434 | ||||||||
\(370\) | −1.46086e9 | −1.49935 | ||||||||
\(371\) | −6.79276e8 | −0.690618 | ||||||||
\(372\) | 2.66075e7 | 0.0267981 | ||||||||
\(373\) | −2.21113e8 | −0.220614 | −0.110307 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110307 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(374\) | 1.38934e9 | 1.37328 | ||||||||
\(375\) | −9.55718e8 | −0.935880 | ||||||||
\(376\) | −4.10033e8 | −0.397797 | ||||||||
\(377\) | −8.41018e7 | −0.0808370 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | −3.08848e8 | −0.291412 | −0.145706 | − | 0.989328i | \(-0.546545\pi\) | ||||
−0.145706 | + | 0.989328i | \(0.546545\pi\) | |||||||
\(380\) | 1.31989e9 | 1.23394 | ||||||||
\(381\) | 6.80361e8 | 0.630234 | ||||||||
\(382\) | −1.28840e9 | −1.18257 | ||||||||
\(383\) | −7.66524e8 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −1.01039e9 | −0.902355 | ||||||||
\(386\) | −5.84534e8 | −0.517314 | ||||||||
\(387\) | 1.85866e8 | 0.163009 | ||||||||
\(388\) | −6.11520e8 | −0.531496 | ||||||||
\(389\) | −6.89048e7 | −0.0593507 | −0.0296754 | − | 0.999560i | \(-0.509447\pi\) | ||||
−0.0296754 | + | 0.999560i | \(0.509447\pi\) | |||||||
\(390\) | −2.27612e8 | −0.194298 | ||||||||
\(391\) | −2.58783e9 | −2.18936 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | 7.54464e8 | 0.626996 | ||||||||
\(394\) | −7.16009e8 | −0.589769 | ||||||||
\(395\) | 2.02076e9 | 1.64977 | ||||||||
\(396\) | 2.86545e8 | 0.231878 | ||||||||
\(397\) | 2.18830e9 | 1.75525 | 0.877627 | − | 0.479343i | \(-0.159125\pi\) | ||||
0.877627 | + | 0.479343i | \(0.159125\pi\) | |||||||
\(398\) | 7.73662e8 | 0.615121 | ||||||||
\(399\) | −3.98204e8 | −0.313834 | ||||||||
\(400\) | 6.22284e8 | 0.486159 | ||||||||
\(401\) | 6.73081e8 | 0.521269 | 0.260635 | − | 0.965438i | \(-0.416068\pi\) | ||||
0.260635 | + | 0.965438i | \(0.416068\pi\) | |||||||
\(402\) | −4.28663e8 | −0.329098 | ||||||||
\(403\) | −3.38291e7 | −0.0257467 | ||||||||
\(404\) | −2.30425e8 | −0.173858 | ||||||||
\(405\) | −2.54898e8 | −0.190666 | ||||||||
\(406\) | −1.05041e8 | −0.0778965 | ||||||||
\(407\) | −2.33826e9 | −1.71914 | ||||||||
\(408\) | 3.90901e8 | 0.284942 | ||||||||
\(409\) | 2.44101e9 | 1.76416 | 0.882078 | − | 0.471103i | \(-0.156144\pi\) | ||||
0.882078 | + | 0.471103i | \(0.156144\pi\) | |||||||
\(410\) | 3.18230e8 | 0.228033 | ||||||||
\(411\) | 1.30287e6 | 0.000925667 0 | ||||||||
\(412\) | −2.38461e7 | −0.0167987 | ||||||||
\(413\) | −7.56819e8 | −0.528649 | ||||||||
\(414\) | −5.33728e8 | −0.369674 | ||||||||
\(415\) | −9.11412e8 | −0.625960 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | 5.60506e8 | 0.378533 | ||||||||
\(418\) | 2.11263e9 | 1.41483 | ||||||||
\(419\) | 1.37884e9 | 0.915725 | 0.457863 | − | 0.889023i | \(-0.348615\pi\) | ||||
0.457863 | + | 0.889023i | \(0.348615\pi\) | |||||||
\(420\) | −2.84282e8 | −0.187230 | ||||||||
\(421\) | 1.78764e9 | 1.16760 | 0.583800 | − | 0.811898i | \(-0.301565\pi\) | ||||
0.583800 | + | 0.811898i | \(0.301565\pi\) | |||||||
\(422\) | −8.74648e8 | −0.566552 | ||||||||
\(423\) | 5.83817e8 | 0.375047 | ||||||||
\(424\) | 1.01396e9 | 0.646014 | ||||||||
\(425\) | −4.29598e9 | −2.71457 | ||||||||
\(426\) | −6.74082e8 | −0.422454 | ||||||||
\(427\) | −4.17893e8 | −0.259757 | ||||||||
\(428\) | −1.97171e8 | −0.121560 | ||||||||
\(429\) | −3.64317e8 | −0.222781 | ||||||||
\(430\) | 9.78301e8 | 0.593380 | ||||||||
\(431\) | −2.91772e8 | −0.175539 | −0.0877695 | − | 0.996141i | \(-0.527974\pi\) | ||||
−0.0877695 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | −1.15485e9 | −0.683623 | −0.341811 | − | 0.939769i | \(-0.611040\pi\) | ||||
−0.341811 | + | 0.939769i | \(0.611040\pi\) | |||||||
\(434\) | −4.22517e7 | −0.0248102 | ||||||||
\(435\) | −4.95735e8 | −0.288760 | ||||||||
\(436\) | −1.72368e9 | −0.995990 | ||||||||
\(437\) | −3.93505e9 | −2.25562 | ||||||||
\(438\) | 1.90849e8 | 0.108525 | ||||||||
\(439\) | 2.62647e9 | 1.48166 | 0.740828 | − | 0.671695i | \(-0.234433\pi\) | ||||
0.740828 | + | 0.671695i | \(0.234433\pi\) | |||||||
\(440\) | 1.50822e9 | 0.844076 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −4.96997e8 | −0.273764 | ||||||||
\(443\) | 2.50764e9 | 1.37042 | 0.685209 | − | 0.728347i | \(-0.259711\pi\) | ||||
0.685209 | + | 0.728347i | \(0.259711\pi\) | |||||||
\(444\) | −6.57887e8 | −0.356706 | ||||||||
\(445\) | 5.74960e8 | 0.309299 | ||||||||
\(446\) | −1.25183e9 | −0.668146 | ||||||||
\(447\) | 2.00119e9 | 1.05977 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −2.66780e9 | −1.39088 | −0.695442 | − | 0.718583i | \(-0.744791\pi\) | ||||
−0.695442 | + | 0.718583i | \(0.744791\pi\) | |||||||
\(450\) | −8.86025e8 | −0.458355 | ||||||||
\(451\) | 5.09360e8 | 0.261461 | ||||||||
\(452\) | 1.00916e9 | 0.514013 | ||||||||
\(453\) | −1.65549e9 | −0.836724 | ||||||||
\(454\) | 2.39152e9 | 1.19944 | ||||||||
\(455\) | 3.61439e8 | 0.179885 | ||||||||
\(456\) | 5.94403e8 | 0.293565 | ||||||||
\(457\) | −9.89279e8 | −0.484855 | −0.242428 | − | 0.970169i | \(-0.577944\pi\) | ||||
−0.242428 | + | 0.970169i | \(0.577944\pi\) | |||||||
\(458\) | 1.94935e9 | 0.948114 | ||||||||
\(459\) | −5.56576e8 | −0.268646 | ||||||||
\(460\) | −2.80927e9 | −1.34568 | ||||||||
\(461\) | 1.54225e9 | 0.733165 | 0.366583 | − | 0.930386i | \(-0.380528\pi\) | ||||
0.366583 | + | 0.930386i | \(0.380528\pi\) | |||||||
\(462\) | −4.55023e8 | −0.214677 | ||||||||
\(463\) | 2.35562e9 | 1.10299 | 0.551496 | − | 0.834178i | \(-0.314057\pi\) | ||||
0.551496 | + | 0.834178i | \(0.314057\pi\) | |||||||
\(464\) | 1.56796e8 | 0.0728655 | ||||||||
\(465\) | −1.99404e8 | −0.0919706 | ||||||||
\(466\) | −1.14034e9 | −0.522017 | ||||||||
\(467\) | 2.80161e9 | 1.27291 | 0.636455 | − | 0.771314i | \(-0.280400\pi\) | ||||
0.636455 | + | 0.771314i | \(0.280400\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | 6.80701e8 | 0.304685 | ||||||||
\(470\) | 3.07291e9 | 1.36524 | ||||||||
\(471\) | 4.71009e8 | 0.207709 | ||||||||
\(472\) | 1.12971e9 | 0.494505 | ||||||||
\(473\) | 1.56587e9 | 0.680366 | ||||||||
\(474\) | 9.10032e8 | 0.392494 | ||||||||
\(475\) | −6.53245e9 | −2.79672 | ||||||||
\(476\) | −6.20737e8 | −0.263805 | ||||||||
\(477\) | −1.44371e9 | −0.609068 | ||||||||
\(478\) | −1.26919e9 | −0.531530 | ||||||||
\(479\) | −3.51487e9 | −1.46129 | −0.730643 | − | 0.682760i | \(-0.760780\pi\) | ||||
−0.730643 | + | 0.682760i | \(0.760780\pi\) | |||||||
\(480\) | 4.24350e8 | 0.175138 | ||||||||
\(481\) | 8.36445e8 | 0.342712 | ||||||||
\(482\) | −2.34464e9 | −0.953699 | ||||||||
\(483\) | 8.47541e8 | 0.342252 | ||||||||
\(484\) | 1.16689e9 | 0.467813 | ||||||||
\(485\) | 4.58291e9 | 1.82409 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 1.17215e9 | 0.459866 | 0.229933 | − | 0.973206i | \(-0.426149\pi\) | ||||
0.229933 | + | 0.973206i | \(0.426149\pi\) | |||||||
\(488\) | 6.23793e8 | 0.242980 | ||||||||
\(489\) | −1.62006e9 | −0.626540 | ||||||||
\(490\) | 4.51429e8 | 0.173342 | ||||||||
\(491\) | 3.21207e9 | 1.22461 | 0.612307 | − | 0.790620i | \(-0.290242\pi\) | ||||
0.612307 | + | 0.790620i | \(0.290242\pi\) | |||||||
\(492\) | 1.43312e8 | 0.0542507 | ||||||||
\(493\) | −1.08245e9 | −0.406859 | ||||||||
\(494\) | −7.55731e8 | −0.282048 | ||||||||
\(495\) | −2.14745e9 | −0.795803 | ||||||||
\(496\) | 6.30695e7 | 0.0232078 | ||||||||
\(497\) | 1.07042e9 | 0.391116 | ||||||||
\(498\) | −4.10448e8 | −0.148921 | ||||||||
\(499\) | −5.25523e9 | −1.89339 | −0.946695 | − | 0.322132i | \(-0.895601\pi\) | ||||
−0.946695 | + | 0.322132i | \(0.895601\pi\) | |||||||
\(500\) | −2.26540e9 | −0.810496 | ||||||||
\(501\) | 1.61417e9 | 0.573480 | ||||||||
\(502\) | 2.28072e8 | 0.0804653 | ||||||||
\(503\) | −4.58055e9 | −1.60483 | −0.802416 | − | 0.596765i | \(-0.796453\pi\) | ||||
−0.802416 | + | 0.596765i | \(0.796453\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 1.72687e9 | 0.596679 | ||||||||
\(506\) | −4.49653e9 | −1.54295 | ||||||||
\(507\) | 1.30324e8 | 0.0444116 | ||||||||
\(508\) | 1.61271e9 | 0.545799 | ||||||||
\(509\) | 2.78712e9 | 0.936793 | 0.468397 | − | 0.883518i | \(-0.344832\pi\) | ||||
0.468397 | + | 0.883518i | \(0.344832\pi\) | |||||||
\(510\) | −2.92953e9 | −0.977918 | ||||||||
\(511\) | −3.03062e8 | −0.100475 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −8.46328e8 | −0.276776 | ||||||||
\(514\) | 1.15156e9 | 0.374037 | ||||||||
\(515\) | 1.78709e8 | 0.0576530 | ||||||||
\(516\) | 4.40570e8 | 0.141170 | ||||||||
\(517\) | 4.91852e9 | 1.56537 | ||||||||
\(518\) | 1.04470e9 | 0.330246 | ||||||||
\(519\) | 1.20239e9 | 0.377537 | ||||||||
\(520\) | −5.39524e8 | −0.168267 | ||||||||
\(521\) | −3.50734e8 | −0.108654 | −0.0543270 | − | 0.998523i | \(-0.517301\pi\) | ||||
−0.0543270 | + | 0.998523i | \(0.517301\pi\) | |||||||
\(522\) | −2.23251e8 | −0.0686983 | ||||||||
\(523\) | −5.56937e9 | −1.70235 | −0.851177 | − | 0.524879i | \(-0.824111\pi\) | ||||
−0.851177 | + | 0.524879i | \(0.824111\pi\) | |||||||
\(524\) | 1.78836e9 | 0.542994 | ||||||||
\(525\) | 1.40698e9 | 0.424355 | ||||||||
\(526\) | −4.20121e9 | −1.25871 | ||||||||
\(527\) | −4.35405e8 | −0.129585 | ||||||||
\(528\) | 6.79217e8 | 0.200812 | ||||||||
\(529\) | 4.97057e9 | 1.45986 | ||||||||
\(530\) | −7.59894e9 | −2.21711 | ||||||||
\(531\) | −1.60852e9 | −0.466224 | ||||||||
\(532\) | −9.43890e8 | −0.271788 | ||||||||
\(533\) | −1.82209e8 | −0.0521224 | ||||||||
\(534\) | 2.58929e8 | 0.0735845 | ||||||||
\(535\) | 1.47766e9 | 0.417192 | ||||||||
\(536\) | −1.01609e9 | −0.285007 | ||||||||
\(537\) | 1.74845e8 | 0.0487240 | ||||||||
\(538\) | −2.05247e9 | −0.568250 | ||||||||
\(539\) | 7.22559e8 | 0.198753 | ||||||||
\(540\) | −6.04202e8 | −0.165122 | ||||||||
\(541\) | −2.30163e9 | −0.624950 | −0.312475 | − | 0.949926i | \(-0.601158\pi\) | ||||
−0.312475 | + | 0.949926i | \(0.601158\pi\) | |||||||
\(542\) | −2.15703e9 | −0.581914 | ||||||||
\(543\) | 2.77795e9 | 0.744604 | ||||||||
\(544\) | 9.26581e8 | 0.246767 | ||||||||
\(545\) | 1.29178e10 | 3.41823 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −3.53474e9 | −0.923425 | −0.461712 | − | 0.887030i | \(-0.652765\pi\) | ||||
−0.461712 | + | 0.887030i | \(0.652765\pi\) | |||||||
\(548\) | 3.08828e6 | 0.000801651 0 | ||||||||
\(549\) | −8.88174e8 | −0.229084 | ||||||||
\(550\) | −7.46455e9 | −1.91308 | ||||||||
\(551\) | −1.64597e9 | −0.419172 | ||||||||
\(552\) | −1.26513e9 | −0.320147 | ||||||||
\(553\) | −1.44510e9 | −0.363378 | ||||||||
\(554\) | −1.10950e9 | −0.277232 | ||||||||
\(555\) | 4.93040e9 | 1.22421 | ||||||||
\(556\) | 1.32861e9 | 0.327819 | ||||||||
\(557\) | −1.42066e9 | −0.348335 | −0.174167 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174167 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(558\) | −8.98002e7 | −0.0218805 | ||||||||
\(559\) | −5.60147e8 | −0.135631 | ||||||||
\(560\) | −6.73853e8 | −0.162146 | ||||||||
\(561\) | −4.68902e9 | −1.12128 | ||||||||
\(562\) | −1.59922e9 | −0.380042 | ||||||||
\(563\) | −7.14098e8 | −0.168647 | −0.0843235 | − | 0.996438i | \(-0.526873\pi\) | ||||
−0.0843235 | + | 0.996438i | \(0.526873\pi\) | |||||||
\(564\) | 1.38386e9 | 0.324800 | ||||||||
\(565\) | −7.56292e9 | −1.76409 | ||||||||
\(566\) | 2.21119e9 | 0.512587 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | −1.59782e9 | −0.365856 | ||||||||
\(569\) | 6.03946e9 | 1.37437 | 0.687187 | − | 0.726481i | \(-0.258845\pi\) | ||||
0.687187 | + | 0.726481i | \(0.258845\pi\) | |||||||
\(570\) | −4.45463e9 | −1.00751 | ||||||||
\(571\) | −8.20167e9 | −1.84364 | −0.921820 | − | 0.387619i | \(-0.873298\pi\) | ||||
−0.921820 | + | 0.387619i | \(0.873298\pi\) | |||||||
\(572\) | −8.63565e8 | −0.192934 | ||||||||
\(573\) | 4.34833e9 | 0.965565 | ||||||||
\(574\) | −2.27575e8 | −0.0502264 | ||||||||
\(575\) | 1.39037e10 | 3.04996 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −6.95530e9 | −1.50730 | −0.753651 | − | 0.657275i | \(-0.771709\pi\) | ||||
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(578\) | −3.11401e9 | −0.670768 | ||||||||
\(579\) | 1.97280e9 | 0.422385 | ||||||||
\(580\) | −1.17508e9 | −0.250074 | ||||||||
\(581\) | 6.51776e8 | 0.137874 | ||||||||
\(582\) | 2.06388e9 | 0.433964 | ||||||||
\(583\) | −1.21629e10 | −2.54213 | ||||||||
\(584\) | 4.52384e8 | 0.0939857 | ||||||||
\(585\) | 7.68190e8 | 0.158644 | ||||||||
\(586\) | 3.33387e9 | 0.684394 | ||||||||
\(587\) | 7.08547e9 | 1.44589 | 0.722945 | − | 0.690905i | \(-0.242788\pi\) | ||||
0.722945 | + | 0.690905i | \(0.242788\pi\) | |||||||
\(588\) | 2.03297e8 | 0.0412393 | ||||||||
\(589\) | −6.62075e8 | −0.133507 | ||||||||
\(590\) | −8.46640e9 | −1.69714 | ||||||||
\(591\) | 2.41653e9 | 0.481544 | ||||||||
\(592\) | −1.55944e9 | −0.308917 | ||||||||
\(593\) | −6.49353e9 | −1.27876 | −0.639381 | − | 0.768890i | \(-0.720809\pi\) | ||||
−0.639381 | + | 0.768890i | \(0.720809\pi\) | |||||||
\(594\) | −9.67089e8 | −0.189328 | ||||||||
\(595\) | 4.65199e9 | 0.905376 | ||||||||
\(596\) | 4.74357e9 | 0.917791 | ||||||||
\(597\) | −2.61111e9 | −0.502244 | ||||||||
\(598\) | 1.60851e9 | 0.307587 | ||||||||
\(599\) | −4.35434e9 | −0.827806 | −0.413903 | − | 0.910321i | \(-0.635835\pi\) | ||||
−0.413903 | + | 0.910321i | \(0.635835\pi\) | |||||||
\(600\) | −2.10021e9 | −0.396947 | ||||||||
\(601\) | 3.14701e9 | 0.591341 | 0.295670 | − | 0.955290i | \(-0.404457\pi\) | ||||
0.295670 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(602\) | −6.99610e8 | −0.130698 | ||||||||
\(603\) | 1.44674e9 | 0.268707 | ||||||||
\(604\) | −3.92412e9 | −0.724624 | ||||||||
\(605\) | −8.74504e9 | −1.60553 | ||||||||
\(606\) | 7.77684e8 | 0.141954 | ||||||||
\(607\) | −1.93569e9 | −0.351298 | −0.175649 | − | 0.984453i | \(-0.556202\pi\) | ||||
−0.175649 | + | 0.984453i | \(0.556202\pi\) | |||||||
\(608\) | 1.40896e9 | 0.254235 | ||||||||
\(609\) | 3.54514e8 | 0.0636022 | ||||||||
\(610\) | −4.67489e9 | −0.833906 | ||||||||
\(611\) | −1.75946e9 | −0.312058 | ||||||||
\(612\) | −1.31929e9 | −0.232654 | ||||||||
\(613\) | −3.11478e9 | −0.546154 | −0.273077 | − | 0.961992i | \(-0.588041\pi\) | ||||
−0.273077 | + | 0.961992i | \(0.588041\pi\) | |||||||
\(614\) | −2.74298e7 | −0.00478226 | ||||||||
\(615\) | −1.07403e9 | −0.186188 | ||||||||
\(616\) | −1.07857e9 | −0.185916 | ||||||||
\(617\) | 2.70867e9 | 0.464257 | 0.232128 | − | 0.972685i | \(-0.425431\pi\) | ||||
0.232128 | + | 0.972685i | \(0.425431\pi\) | |||||||
\(618\) | 8.04804e7 | 0.0137161 | ||||||||
\(619\) | −4.55504e9 | −0.771925 | −0.385963 | − | 0.922514i | \(-0.626131\pi\) | ||||
−0.385963 | + | 0.922514i | \(0.626131\pi\) | |||||||
\(620\) | −4.72662e8 | −0.0796489 | ||||||||
\(621\) | 1.80133e9 | 0.301838 | ||||||||
\(622\) | −4.66663e9 | −0.777565 | ||||||||
\(623\) | −4.11170e8 | −0.0681260 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | 5.10849e9 | 0.836976 | ||||||||
\(626\) | −5.44001e9 | −0.886318 | ||||||||
\(627\) | −7.13011e9 | −1.15521 | ||||||||
\(628\) | 1.11647e9 | 0.179882 | ||||||||
\(629\) | 1.07657e10 | 1.72490 | ||||||||
\(630\) | 9.59450e8 | 0.152873 | ||||||||
\(631\) | 6.79597e9 | 1.07683 | 0.538417 | − | 0.842679i | \(-0.319023\pi\) | ||||
0.538417 | + | 0.842679i | \(0.319023\pi\) | |||||||
\(632\) | 2.15711e9 | 0.339909 | ||||||||
\(633\) | 2.95194e9 | 0.462588 | ||||||||
\(634\) | 2.22967e9 | 0.347479 | ||||||||
\(635\) | −1.20861e10 | −1.87317 | ||||||||
\(636\) | −3.42213e9 | −0.527468 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −1.88083e9 | −0.286733 | ||||||||
\(639\) | 2.27503e9 | 0.344932 | ||||||||
\(640\) | 1.00587e9 | 0.151674 | ||||||||
\(641\) | 1.28737e10 | 1.93063 | 0.965316 | − | 0.261083i | \(-0.0840796\pi\) | ||||
0.965316 | + | 0.261083i | \(0.0840796\pi\) | |||||||
\(642\) | 6.65452e8 | 0.0992531 | ||||||||
\(643\) | 9.44890e9 | 1.40166 | 0.700830 | − | 0.713328i | \(-0.252813\pi\) | ||||
0.700830 | + | 0.713328i | \(0.252813\pi\) | |||||||
\(644\) | 2.00899e9 | 0.296399 | ||||||||
\(645\) | −3.30177e9 | −0.484493 | ||||||||
\(646\) | −9.72682e9 | −1.41957 | ||||||||
\(647\) | 3.05647e9 | 0.443666 | 0.221833 | − | 0.975085i | \(-0.428796\pi\) | ||||
0.221833 | + | 0.975085i | \(0.428796\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | −1.35514e10 | −1.94593 | ||||||||
\(650\) | 2.67023e9 | 0.381375 | ||||||||
\(651\) | 1.42599e8 | 0.0202574 | ||||||||
\(652\) | −3.84013e9 | −0.542600 | ||||||||
\(653\) | 7.10654e9 | 0.998762 | 0.499381 | − | 0.866382i | \(-0.333561\pi\) | ||||
0.499381 | + | 0.866382i | \(0.333561\pi\) | |||||||
\(654\) | 5.81744e9 | 0.813223 | ||||||||
\(655\) | −1.34025e10 | −1.86355 | ||||||||
\(656\) | 3.39703e8 | 0.0469825 | ||||||||
\(657\) | −6.44117e8 | −0.0886106 | ||||||||
\(658\) | −2.19752e9 | −0.300706 | ||||||||
\(659\) | 3.63623e9 | 0.494940 | 0.247470 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247470 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(660\) | −5.09026e9 | −0.689185 | ||||||||
\(661\) | 6.86469e9 | 0.924519 | 0.462259 | − | 0.886745i | \(-0.347039\pi\) | ||||
0.462259 | + | 0.886745i | \(0.347039\pi\) | |||||||
\(662\) | −6.80581e7 | −0.00911752 | ||||||||
\(663\) | 1.67736e9 | 0.223527 | ||||||||
\(664\) | −9.72913e8 | −0.128969 | ||||||||
\(665\) | 7.07379e9 | 0.932774 | ||||||||
\(666\) | 2.22037e9 | 0.291250 | ||||||||
\(667\) | 3.50330e9 | 0.457127 | ||||||||
\(668\) | 3.82619e9 | 0.496648 | ||||||||
\(669\) | 4.22491e9 | 0.545539 | ||||||||
\(670\) | 7.61489e9 | 0.978141 | ||||||||
\(671\) | −7.48266e9 | −0.956152 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −1.37598e10 | −1.74004 | −0.870020 | − | 0.493016i | \(-0.835895\pi\) | ||||
−0.870020 | + | 0.493016i | \(0.835895\pi\) | |||||||
\(674\) | −9.37807e9 | −1.17979 | ||||||||
\(675\) | 2.99033e9 | 0.374246 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 1.29093e10 | 1.59897 | 0.799487 | − | 0.600683i | \(-0.205105\pi\) | ||||
0.799487 | + | 0.600683i | \(0.205105\pi\) | |||||||
\(678\) | −3.40590e9 | −0.419690 | ||||||||
\(679\) | −3.27737e9 | −0.401773 | ||||||||
\(680\) | −6.94408e9 | −0.846902 | ||||||||
\(681\) | −8.07137e9 | −0.979337 | ||||||||
\(682\) | −7.56545e8 | −0.0913250 | ||||||||
\(683\) | −4.67362e9 | −0.561282 | −0.280641 | − | 0.959813i | \(-0.590547\pi\) | ||||
−0.280641 | + | 0.959813i | \(0.590547\pi\) | |||||||
\(684\) | −2.00611e9 | −0.239695 | ||||||||
\(685\) | −2.31445e7 | −0.00275126 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −6.57906e9 | −0.774132 | ||||||||
\(688\) | 1.04432e9 | 0.122257 | ||||||||
\(689\) | 4.35093e9 | 0.506775 | ||||||||
\(690\) | 9.48129e9 | 1.09874 | ||||||||
\(691\) | 1.39132e10 | 1.60418 | 0.802092 | − | 0.597200i | \(-0.203720\pi\) | ||||
0.802092 | + | 0.597200i | \(0.203720\pi\) | |||||||
\(692\) | 2.85011e9 | 0.326957 | ||||||||
\(693\) | 1.53570e9 | 0.175283 | ||||||||
\(694\) | 2.83955e9 | 0.322472 | ||||||||
\(695\) | −9.95697e9 | −1.12507 | ||||||||
\(696\) | −5.29187e8 | −0.0594944 | ||||||||
\(697\) | −2.34516e9 | −0.262336 | ||||||||
\(698\) | −3.75004e9 | −0.417390 | ||||||||
\(699\) | 3.84866e9 | 0.426225 | ||||||||
\(700\) | 3.33505e9 | 0.367502 | ||||||||
\(701\) | 3.95020e9 | 0.433117 | 0.216559 | − | 0.976270i | \(-0.430517\pi\) | ||||
0.216559 | + | 0.976270i | \(0.430517\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | 1.63702e10 | 1.77710 | ||||||||
\(704\) | 1.61000e9 | 0.173908 | ||||||||
\(705\) | −1.03711e10 | −1.11471 | ||||||||
\(706\) | −3.99755e9 | −0.427541 | ||||||||
\(707\) | −1.23493e9 | −0.131424 | ||||||||
\(708\) | −3.81278e9 | −0.403762 | ||||||||
\(709\) | 9.43852e9 | 0.994585 | 0.497293 | − | 0.867583i | \(-0.334328\pi\) | ||||
0.497293 | + | 0.867583i | \(0.334328\pi\) | |||||||
\(710\) | 1.19746e10 | 1.25561 | ||||||||
\(711\) | −3.07136e9 | −0.320470 | ||||||||
\(712\) | 6.13758e8 | 0.0637260 | ||||||||
\(713\) | 1.40917e9 | 0.145596 | ||||||||
\(714\) | 2.09499e9 | 0.215396 | ||||||||
\(715\) | 6.47181e9 | 0.662148 | ||||||||
\(716\) | 4.14447e8 | 0.0421962 | ||||||||
\(717\) | 4.28350e9 | 0.433992 | ||||||||
\(718\) | −1.61764e9 | −0.163097 | ||||||||
\(719\) | −1.77940e10 | −1.78535 | −0.892673 | − | 0.450704i | \(-0.851173\pi\) | ||||
−0.892673 | + | 0.450704i | \(0.851173\pi\) | |||||||
\(720\) | −1.43218e9 | −0.143000 | ||||||||
\(721\) | −1.27800e8 | −0.0126986 | ||||||||
\(722\) | −7.63959e9 | −0.755422 | ||||||||
\(723\) | 7.91316e9 | 0.778692 | ||||||||
\(724\) | 6.58477e9 | 0.644846 | ||||||||
\(725\) | 5.81572e9 | 0.566788 | ||||||||
\(726\) | −3.93826e9 | −0.381968 | ||||||||
\(727\) | −1.27477e10 | −1.23045 | −0.615224 | − | 0.788353i | \(-0.710934\pi\) | ||||
−0.615224 | + | 0.788353i | \(0.710934\pi\) | |||||||
\(728\) | 3.85828e8 | 0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.39030e9 | −0.322558 | ||||||||
\(731\) | −7.20950e9 | −0.682644 | ||||||||
\(732\) | −2.10530e9 | −0.198393 | ||||||||
\(733\) | −1.26461e10 | −1.18602 | −0.593012 | − | 0.805194i | \(-0.702061\pi\) | ||||
−0.593012 | + | 0.805194i | \(0.702061\pi\) | |||||||
\(734\) | 7.19358e9 | 0.671442 | ||||||||
\(735\) | −1.52357e9 | −0.141533 | ||||||||
\(736\) | −2.99884e9 | −0.277256 | ||||||||
\(737\) | 1.21884e10 | 1.12153 | ||||||||
\(738\) | −4.83679e8 | −0.0442955 | ||||||||
\(739\) | −1.25576e10 | −1.14459 | −0.572297 | − | 0.820046i | \(-0.693948\pi\) | ||||
−0.572297 | + | 0.820046i | \(0.693948\pi\) | |||||||
\(740\) | 1.16869e10 | 1.06020 | ||||||||
\(741\) | 2.55059e9 | 0.230291 | ||||||||
\(742\) | 5.43421e9 | 0.488341 | ||||||||
\(743\) | −1.09171e10 | −0.976445 | −0.488222 | − | 0.872719i | \(-0.662354\pi\) | ||||
−0.488222 | + | 0.872719i | \(0.662354\pi\) | |||||||
\(744\) | −2.12860e8 | −0.0189491 | ||||||||
\(745\) | −3.55497e10 | −3.14985 | ||||||||
\(746\) | 1.76890e9 | 0.155997 | ||||||||
\(747\) | 1.38526e9 | 0.121593 | ||||||||
\(748\) | −1.11147e10 | −0.971053 | ||||||||
\(749\) | −1.05671e9 | −0.0918905 | ||||||||
\(750\) | 7.64574e9 | 0.661767 | ||||||||
\(751\) | 1.05692e10 | 0.910548 | 0.455274 | − | 0.890351i | \(-0.349541\pi\) | ||||
0.455274 | + | 0.890351i | \(0.349541\pi\) | |||||||
\(752\) | 3.28027e9 | 0.281285 | ||||||||
\(753\) | −7.69742e8 | −0.0656996 | ||||||||
\(754\) | 6.72814e8 | 0.0571604 | ||||||||
\(755\) | 2.94085e10 | 2.48690 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | 1.52485e10 | 1.27759 | 0.638794 | − | 0.769378i | \(-0.279434\pi\) | ||||
0.638794 | + | 0.769378i | \(0.279434\pi\) | |||||||
\(758\) | 2.47079e9 | 0.206060 | ||||||||
\(759\) | 1.51758e10 | 1.25981 | ||||||||
\(760\) | −1.05591e10 | −0.872531 | ||||||||
\(761\) | −3.85782e9 | −0.317319 | −0.158659 | − | 0.987333i | \(-0.550717\pi\) | ||||
−0.158659 | + | 0.987333i | \(0.550717\pi\) | |||||||
\(762\) | −5.44288e9 | −0.445643 | ||||||||
\(763\) | −9.23787e9 | −0.752898 | ||||||||
\(764\) | 1.03072e10 | 0.836204 | ||||||||
\(765\) | 9.88717e9 | 0.798467 | ||||||||
\(766\) | 6.13219e9 | 0.492964 | ||||||||
\(767\) | 4.84762e9 | 0.387922 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 2.02192e10 | 1.60333 | 0.801663 | − | 0.597777i | \(-0.203949\pi\) | ||||
0.801663 | + | 0.597777i | \(0.203949\pi\) | |||||||
\(770\) | 8.08314e9 | 0.638062 | ||||||||
\(771\) | −3.88651e9 | −0.305400 | ||||||||
\(772\) | 4.67627e9 | 0.365796 | ||||||||
\(773\) | −8.17755e9 | −0.636788 | −0.318394 | − | 0.947958i | \(-0.603144\pi\) | ||||
−0.318394 | + | 0.947958i | \(0.603144\pi\) | |||||||
\(774\) | −1.48693e9 | −0.115265 | ||||||||
\(775\) | 2.33931e9 | 0.180523 | ||||||||
\(776\) | 4.89216e9 | 0.375824 | ||||||||
\(777\) | −3.52586e9 | −0.269645 | ||||||||
\(778\) | 5.51238e8 | 0.0419673 | ||||||||
\(779\) | −3.56605e9 | −0.270275 | ||||||||
\(780\) | 1.82089e9 | 0.137390 | ||||||||
\(781\) | 1.91666e10 | 1.43968 | ||||||||
\(782\) | 2.07027e10 | 1.54811 | ||||||||
\(783\) | 7.53471e8 | 0.0560919 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −8.36713e9 | −0.617352 | ||||||||
\(786\) | −6.03571e9 | −0.443353 | ||||||||
\(787\) | −8.75406e9 | −0.640174 | −0.320087 | − | 0.947388i | \(-0.603712\pi\) | ||||
−0.320087 | + | 0.947388i | \(0.603712\pi\) | |||||||
\(788\) | 5.72807e9 | 0.417029 | ||||||||
\(789\) | 1.41791e10 | 1.02773 | ||||||||
\(790\) | −1.61660e10 | −1.16657 | ||||||||
\(791\) | 5.40845e9 | 0.388557 | ||||||||
\(792\) | −2.29236e9 | −0.163962 | ||||||||
\(793\) | 2.67671e9 | 0.190610 | ||||||||
\(794\) | −1.75064e10 | −1.24115 | ||||||||
\(795\) | 2.56464e10 | 1.81026 | ||||||||
\(796\) | −6.18930e9 | −0.434956 | ||||||||
\(797\) | −7.25916e9 | −0.507905 | −0.253952 | − | 0.967217i | \(-0.581731\pi\) | ||||
−0.253952 | + | 0.967217i | \(0.581731\pi\) | |||||||
\(798\) | 3.18563e9 | 0.221914 | ||||||||
\(799\) | −2.26455e10 | −1.57061 | ||||||||
\(800\) | −4.97827e9 | −0.343766 | ||||||||
\(801\) | −8.73885e8 | −0.0600815 | ||||||||
\(802\) | −5.38465e9 | −0.368593 | ||||||||
\(803\) | −5.42653e9 | −0.369843 | ||||||||
\(804\) | 3.42931e9 | 0.232707 | ||||||||
\(805\) | −1.50559e10 | −1.01724 | ||||||||
\(806\) | 2.70632e8 | 0.0182057 | ||||||||
\(807\) | 6.92710e9 | 0.463974 | ||||||||
\(808\) | 1.84340e9 | 0.122936 | ||||||||
\(809\) | 1.05605e9 | 0.0701235 | 0.0350618 | − | 0.999385i | \(-0.488837\pi\) | ||||
0.0350618 | + | 0.999385i | \(0.488837\pi\) | |||||||
\(810\) | 2.03918e9 | 0.134821 | ||||||||
\(811\) | 2.15233e10 | 1.41689 | 0.708446 | − | 0.705765i | \(-0.249397\pi\) | ||||
0.708446 | + | 0.705765i | \(0.249397\pi\) | |||||||
\(812\) | 8.40329e8 | 0.0550812 | ||||||||
\(813\) | 7.27998e9 | 0.475131 | ||||||||
\(814\) | 1.87061e10 | 1.21562 | ||||||||
\(815\) | 2.87791e10 | 1.86220 | ||||||||
\(816\) | −3.12721e9 | −0.201485 | ||||||||
\(817\) | −1.09627e10 | −0.703302 | ||||||||
\(818\) | −1.95280e10 | −1.24745 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | −2.54584e9 | −0.161243 | ||||||||
\(821\) | −2.08774e10 | −1.31666 | −0.658331 | − | 0.752728i | \(-0.728737\pi\) | ||||
−0.658331 | + | 0.752728i | \(0.728737\pi\) | |||||||
\(822\) | −1.04230e7 | −0.000654545 0 | ||||||||
\(823\) | 7.12682e9 | 0.445653 | 0.222826 | − | 0.974858i | \(-0.428472\pi\) | ||||
0.222826 | + | 0.974858i | \(0.428472\pi\) | |||||||
\(824\) | 1.90768e8 | 0.0118785 | ||||||||
\(825\) | 2.51929e10 | 1.56203 | ||||||||
\(826\) | 6.05455e9 | 0.373811 | ||||||||
\(827\) | −2.41290e10 | −1.48344 | −0.741720 | − | 0.670709i | \(-0.765990\pi\) | ||||
−0.741720 | + | 0.670709i | \(0.765990\pi\) | |||||||
\(828\) | 4.26983e9 | 0.261399 | ||||||||
\(829\) | 1.23027e10 | 0.749996 | 0.374998 | − | 0.927026i | \(-0.377643\pi\) | ||||
0.374998 | + | 0.927026i | \(0.377643\pi\) | |||||||
\(830\) | 7.29130e9 | 0.442621 | ||||||||
\(831\) | 3.74456e9 | 0.226359 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | −3.32676e9 | −0.199418 | ||||||||
\(834\) | −4.48405e9 | −0.267663 | ||||||||
\(835\) | −2.86746e10 | −1.70449 | ||||||||
\(836\) | −1.69010e10 | −1.00044 | ||||||||
\(837\) | 3.03076e8 | 0.0178654 | ||||||||
\(838\) | −1.10307e10 | −0.647516 | ||||||||
\(839\) | 1.47506e10 | 0.862269 | 0.431134 | − | 0.902288i | \(-0.358113\pi\) | ||||
0.431134 | + | 0.902288i | \(0.358113\pi\) | |||||||
\(840\) | 2.27425e9 | 0.132392 | ||||||||
\(841\) | −1.57845e10 | −0.915050 | ||||||||
\(842\) | −1.43012e10 | −0.825617 | ||||||||
\(843\) | 5.39737e9 | 0.310303 | ||||||||
\(844\) | 6.99718e9 | 0.400613 | ||||||||
\(845\) | −2.31511e9 | −0.132000 | ||||||||
\(846\) | −4.67054e9 | −0.265198 | ||||||||
\(847\) | 6.25382e9 | 0.353633 | ||||||||
\(848\) | −8.11171e9 | −0.456801 | ||||||||
\(849\) | −7.46275e9 | −0.418526 | ||||||||
\(850\) | 3.43678e10 | 1.91949 | ||||||||
\(851\) | −3.48426e10 | −1.93801 | ||||||||
\(852\) | 5.39266e9 | 0.298720 | ||||||||
\(853\) | 1.07693e10 | 0.594109 | 0.297055 | − | 0.954860i | \(-0.403996\pi\) | ||||
0.297055 | + | 0.954860i | \(0.403996\pi\) | |||||||
\(854\) | 3.34314e9 | 0.183676 | ||||||||
\(855\) | 1.50344e10 | 0.822630 | ||||||||
\(856\) | 1.57737e9 | 0.0859557 | ||||||||
\(857\) | −1.90321e10 | −1.03289 | −0.516444 | − | 0.856321i | \(-0.672744\pi\) | ||||
−0.516444 | + | 0.856321i | \(0.672744\pi\) | |||||||
\(858\) | 2.91453e9 | 0.157530 | ||||||||
\(859\) | 2.90696e9 | 0.156482 | 0.0782408 | − | 0.996934i | \(-0.475070\pi\) | ||||
0.0782408 | + | 0.996934i | \(0.475070\pi\) | |||||||
\(860\) | −7.82641e9 | −0.419583 | ||||||||
\(861\) | 7.68064e8 | 0.0410097 | ||||||||
\(862\) | 2.33418e9 | 0.124125 | ||||||||
\(863\) | 6.55988e9 | 0.347423 | 0.173711 | − | 0.984797i | \(-0.444424\pi\) | ||||
0.173711 | + | 0.984797i | \(0.444424\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −2.13596e10 | −1.12211 | ||||||||
\(866\) | 9.23877e9 | 0.483394 | ||||||||
\(867\) | 1.05098e10 | 0.547680 | ||||||||
\(868\) | 3.38013e8 | 0.0175434 | ||||||||
\(869\) | −2.58755e10 | −1.33758 | ||||||||
\(870\) | 3.96588e9 | 0.204184 | ||||||||
\(871\) | −4.36006e9 | −0.223578 | ||||||||
\(872\) | 1.37895e10 | 0.704271 | ||||||||
\(873\) | −6.96560e9 | −0.354330 | ||||||||
\(874\) | 3.14804e10 | 1.59496 | ||||||||
\(875\) | −1.21412e10 | −0.612677 | ||||||||
\(876\) | −1.52680e9 | −0.0767390 | ||||||||
\(877\) | 1.55910e10 | 0.780502 | 0.390251 | − | 0.920709i | \(-0.372388\pi\) | ||||
0.390251 | + | 0.920709i | \(0.372388\pi\) | |||||||
\(878\) | −2.10118e10 | −1.04769 | ||||||||
\(879\) | −1.12518e10 | −0.558806 | ||||||||
\(880\) | −1.20658e10 | −0.596852 | ||||||||
\(881\) | 2.06150e10 | 1.01571 | 0.507854 | − | 0.861443i | \(-0.330439\pi\) | ||||
0.507854 | + | 0.861443i | \(0.330439\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | −2.09284e10 | −1.02299 | −0.511497 | − | 0.859285i | \(-0.670909\pi\) | ||||
−0.511497 | + | 0.859285i | \(0.670909\pi\) | |||||||
\(884\) | 3.97597e9 | 0.193580 | ||||||||
\(885\) | 2.85741e10 | 1.38571 | ||||||||
\(886\) | −2.00612e10 | −0.969031 | ||||||||
\(887\) | 1.89135e10 | 0.909995 | 0.454998 | − | 0.890493i | \(-0.349640\pi\) | ||||
0.454998 | + | 0.890493i | \(0.349640\pi\) | |||||||
\(888\) | 5.26310e9 | 0.252229 | ||||||||
\(889\) | 8.64310e9 | 0.412585 | ||||||||
\(890\) | −4.59968e9 | −0.218707 | ||||||||
\(891\) | 3.26392e9 | 0.154585 | ||||||||
\(892\) | 1.00146e10 | 0.472451 | ||||||||
\(893\) | −3.44347e10 | −1.61814 | ||||||||
\(894\) | −1.60096e10 | −0.749373 | ||||||||
\(895\) | −3.10599e9 | −0.144817 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −5.42871e9 | −0.251144 | ||||||||
\(898\) | 2.13424e10 | 0.983503 | ||||||||
\(899\) | 5.89433e8 | 0.0270568 | ||||||||
\(900\) | 7.08820e9 | 0.324106 | ||||||||
\(901\) | 5.59997e10 | 2.55064 | ||||||||
\(902\) | −4.07488e9 | −0.184881 | ||||||||
\(903\) | 2.36118e9 | 0.106714 | ||||||||
\(904\) | −8.07325e9 | −0.363462 | ||||||||
\(905\) | −4.93483e10 | −2.21310 | ||||||||
\(906\) | 1.32439e10 | 0.591653 | ||||||||
\(907\) | 5.08875e9 | 0.226457 | 0.113228 | − | 0.993569i | \(-0.463881\pi\) | ||||
0.113228 | + | 0.993569i | \(0.463881\pi\) | |||||||
\(908\) | −1.91321e10 | −0.848131 | ||||||||
\(909\) | −2.62468e9 | −0.115905 | ||||||||
\(910\) | −2.89151e9 | −0.127198 | ||||||||
\(911\) | 8.88416e9 | 0.389316 | 0.194658 | − | 0.980871i | \(-0.437640\pi\) | ||||
0.194658 | + | 0.980871i | \(0.437640\pi\) | |||||||
\(912\) | −4.75523e9 | −0.207582 | ||||||||
\(913\) | 1.16705e10 | 0.507506 | ||||||||
\(914\) | 7.91424e9 | 0.342845 | ||||||||
\(915\) | 1.57778e10 | 0.680881 | ||||||||
\(916\) | −1.55948e10 | −0.670418 | ||||||||
\(917\) | 9.58449e9 | 0.410465 | ||||||||
\(918\) | 4.45261e9 | 0.189961 | ||||||||
\(919\) | −1.06207e10 | −0.451386 | −0.225693 | − | 0.974198i | \(-0.572465\pi\) | ||||
−0.225693 | + | 0.974198i | \(0.572465\pi\) | |||||||
\(920\) | 2.24742e10 | 0.951538 | ||||||||
\(921\) | 9.25755e7 | 0.00390470 | ||||||||
\(922\) | −1.23380e10 | −0.518426 | ||||||||
\(923\) | −6.85629e9 | −0.287001 | ||||||||
\(924\) | 3.64018e9 | 0.151800 | ||||||||
\(925\) | −5.78410e10 | −2.40292 | ||||||||
\(926\) | −1.88450e10 | −0.779933 | ||||||||
\(927\) | −2.71621e8 | −0.0111991 | ||||||||
\(928\) | −1.25437e9 | −0.0515237 | ||||||||
\(929\) | 2.32764e10 | 0.952492 | 0.476246 | − | 0.879312i | \(-0.341997\pi\) | ||||
0.476246 | + | 0.879312i | \(0.341997\pi\) | |||||||
\(930\) | 1.59523e9 | 0.0650330 | ||||||||
\(931\) | −5.05866e9 | −0.205453 | ||||||||
\(932\) | 9.12275e9 | 0.369122 | ||||||||
\(933\) | 1.57499e10 | 0.634879 | ||||||||
\(934\) | −2.24128e10 | −0.900084 | ||||||||
\(935\) | 8.32970e10 | 3.33264 | ||||||||
\(936\) | 8.20026e8 | 0.0326860 | ||||||||
\(937\) | 3.85180e9 | 0.152959 | 0.0764796 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764796 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(938\) | −5.44561e9 | −0.215445 | ||||||||
\(939\) | 1.83600e10 | 0.723675 | ||||||||
\(940\) | −2.45833e10 | −0.965367 | ||||||||
\(941\) | −3.57401e10 | −1.39827 | −0.699137 | − | 0.714988i | \(-0.746432\pi\) | ||||
−0.699137 | + | 0.714988i | \(0.746432\pi\) | |||||||
\(942\) | −3.76807e9 | −0.146873 | ||||||||
\(943\) | 7.59001e9 | 0.294748 | ||||||||
\(944\) | −9.03770e9 | −0.349668 | ||||||||
\(945\) | −3.23815e9 | −0.124820 | ||||||||
\(946\) | −1.25270e10 | −0.481092 | ||||||||
\(947\) | 4.60758e10 | 1.76298 | 0.881491 | − | 0.472201i | \(-0.156540\pi\) | ||||
0.881491 | + | 0.472201i | \(0.156540\pi\) | |||||||
\(948\) | −7.28026e9 | −0.277535 | ||||||||
\(949\) | 1.94119e9 | 0.0737285 | ||||||||
\(950\) | 5.22596e10 | 1.97758 | ||||||||
\(951\) | −7.52514e9 | −0.283715 | ||||||||
\(952\) | 4.96590e9 | 0.186538 | ||||||||
\(953\) | −3.69639e10 | −1.38342 | −0.691709 | − | 0.722177i | \(-0.743142\pi\) | ||||
−0.691709 | + | 0.722177i | \(0.743142\pi\) | |||||||
\(954\) | 1.15497e10 | 0.430676 | ||||||||
\(955\) | −7.72449e10 | −2.86984 | ||||||||
\(956\) | 1.01535e10 | 0.375848 | ||||||||
\(957\) | 6.34781e9 | 0.234117 | ||||||||
\(958\) | 2.81190e10 | 1.03329 | ||||||||
\(959\) | 1.65513e7 | 0.000605991 0 | ||||||||
\(960\) | −3.39480e9 | −0.123841 | ||||||||
\(961\) | −2.72755e10 | −0.991382 | ||||||||
\(962\) | −6.69156e9 | −0.242334 | ||||||||
\(963\) | −2.24590e9 | −0.0810398 | ||||||||
\(964\) | 1.87571e10 | 0.674367 | ||||||||
\(965\) | −3.50453e10 | −1.25541 | ||||||||
\(966\) | −6.78033e9 | −0.242008 | ||||||||
\(967\) | 1.06965e10 | 0.380408 | 0.190204 | − | 0.981745i | \(-0.439085\pi\) | ||||
0.190204 | + | 0.981745i | \(0.439085\pi\) | |||||||
\(968\) | −9.33514e9 | −0.330794 | ||||||||
\(969\) | 3.28280e10 | 1.15907 | ||||||||
\(970\) | −3.66633e10 | −1.28982 | ||||||||
\(971\) | −9.50978e9 | −0.333352 | −0.166676 | − | 0.986012i | \(-0.553303\pi\) | ||||
−0.166676 | + | 0.986012i | \(0.553303\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | 7.12050e9 | 0.247808 | ||||||||
\(974\) | −9.37720e9 | −0.325175 | ||||||||
\(975\) | −9.01202e9 | −0.311391 | ||||||||
\(976\) | −4.99035e9 | −0.171813 | ||||||||
\(977\) | −1.79177e10 | −0.614682 | −0.307341 | − | 0.951599i | \(-0.599439\pi\) | ||||
−0.307341 | + | 0.951599i | \(0.599439\pi\) | |||||||
\(978\) | 1.29604e10 | 0.443031 | ||||||||
\(979\) | −7.36228e9 | −0.250768 | ||||||||
\(980\) | −3.61143e9 | −0.122571 | ||||||||
\(981\) | −1.96338e10 | −0.663993 | ||||||||
\(982\) | −2.56965e10 | −0.865933 | ||||||||
\(983\) | −4.35337e10 | −1.46180 | −0.730901 | − | 0.682483i | \(-0.760900\pi\) | ||||
−0.730901 | + | 0.682483i | \(0.760900\pi\) | |||||||
\(984\) | −1.14650e9 | −0.0383611 | ||||||||
\(985\) | −4.29279e10 | −1.43124 | ||||||||
\(986\) | 8.65962e9 | 0.287693 | ||||||||
\(987\) | 7.41664e9 | 0.245526 | ||||||||
\(988\) | 6.04585e9 | 0.199438 | ||||||||
\(989\) | 2.33332e10 | 0.766986 | ||||||||
\(990\) | 1.71796e10 | 0.562717 | ||||||||
\(991\) | −4.10553e10 | −1.34002 | −0.670010 | − | 0.742352i | \(-0.733710\pi\) | ||||
−0.670010 | + | 0.742352i | \(0.733710\pi\) | |||||||
\(992\) | −5.04556e8 | −0.0164104 | ||||||||
\(993\) | 2.29696e8 | 0.00744443 | ||||||||
\(994\) | −8.56334e9 | −0.276561 | ||||||||
\(995\) | 4.63844e10 | 1.49277 | ||||||||
\(996\) | 3.28358e9 | 0.105303 | ||||||||
\(997\) | 3.76132e10 | 1.20201 | 0.601004 | − | 0.799246i | \(-0.294768\pi\) | ||||
0.601004 | + | 0.799246i | \(0.294768\pi\) | |||||||
\(998\) | 4.20419e10 | 1.33883 | ||||||||
\(999\) | −7.49374e9 | −0.237804 |
(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.p.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.p.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial |