Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.58461.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 65x - 126 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.16736\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1566 | −0.908437 | −0.454218 | − | 0.890890i | \(-0.650081\pi\) | ||||
−0.454218 | + | 0.890890i | \(0.650081\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 37.8005 | 1.03612 | 0.518058 | − | 0.855346i | \(-0.326655\pi\) | ||||
0.518058 | + | 0.855346i | \(0.326655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 74.0881 | 1.58064 | 0.790321 | − | 0.612693i | \(-0.209914\pi\) | ||||
0.790321 | + | 0.612693i | \(0.209914\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.4699 | −0.524486 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.6694 | 0.637290 | 0.318645 | − | 0.947874i | \(-0.396772\pi\) | ||||
0.318645 | + | 0.947874i | \(0.396772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 139.367 | 1.68279 | 0.841397 | − | 0.540418i | \(-0.181734\pi\) | ||||
0.841397 | + | 0.540418i | \(0.181734\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −57.8200 | −0.524187 | −0.262094 | − | 0.965042i | \(-0.584413\pi\) | ||||
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.8428 | −0.174742 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.5039 | 0.252955 | 0.126477 | − | 0.991969i | \(-0.459633\pi\) | ||||
0.126477 | + | 0.991969i | \(0.459633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −254.837 | −1.47645 | −0.738226 | − | 0.674553i | \(-0.764336\pi\) | ||||
−0.738226 | + | 0.674553i | \(0.764336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 113.401 | 0.598201 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.1048 | 0.0804435 | 0.0402217 | − | 0.999191i | \(-0.487194\pi\) | ||||
0.0402217 | + | 0.999191i | \(0.487194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 222.264 | 0.912584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 420.819 | 1.60295 | 0.801475 | − | 0.598028i | \(-0.204049\pi\) | ||||
0.801475 | + | 0.598028i | \(0.204049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 382.346 | 1.35598 | 0.677991 | − | 0.735070i | \(-0.262851\pi\) | ||||
0.677991 | + | 0.735070i | \(0.262851\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −91.4097 | −0.302812 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −484.901 | −1.50490 | −0.752448 | − | 0.658651i | \(-0.771127\pi\) | ||||
−0.752448 | + | 0.658651i | \(0.771127\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 134.008 | 0.367940 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.0875 | 0.0935283 | 0.0467642 | − | 0.998906i | \(-0.485109\pi\) | ||||
0.0467642 | + | 0.998906i | \(0.485109\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −383.925 | −0.941245 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 418.102 | 0.971561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −145.831 | −0.321790 | −0.160895 | − | 0.986972i | \(-0.551438\pi\) | ||||
−0.160895 | + | 0.986972i | \(0.551438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.1359 | −0.164005 | −0.0820023 | − | 0.996632i | \(-0.526131\pi\) | ||||
−0.0820023 | + | 0.996632i | \(0.526131\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −752.486 | −1.43591 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 273.053 | 0.497891 | 0.248946 | − | 0.968517i | \(-0.419916\pi\) | ||||
0.248946 | + | 0.968517i | \(0.419916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −173.460 | −0.302640 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −717.642 | −1.19956 | −0.599778 | − | 0.800167i | \(-0.704744\pi\) | ||||
−0.599778 | + | 0.800167i | \(0.704744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1108.28 | −1.77691 | −0.888453 | − | 0.458968i | \(-0.848219\pi\) | ||||
−0.888453 | + | 0.458968i | \(0.848219\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −65.5283 | −0.100887 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1085.66 | 1.54615 | 0.773076 | − | 0.634314i | \(-0.218717\pi\) | ||||
0.773076 | + | 0.634314i | \(0.218717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 404.777 | 0.535301 | 0.267651 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267651 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −453.691 | −0.578938 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 118.512 | 0.146043 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1354.42 | −1.61312 | −0.806561 | − | 0.591151i | \(-0.798674\pi\) | ||||
−0.806561 | + | 0.591151i | \(0.798674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −764.510 | −0.852430 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1415.50 | −1.52871 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 681.847 | 0.713723 | 0.356861 | − | 0.934157i | \(-0.383847\pi\) | ||||
0.356861 | + | 0.934157i | \(0.383847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 340.204 | 0.345372 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 798.533 | 0.786703 | 0.393352 | − | 0.919388i | \(-0.371316\pi\) | ||||
0.393352 | + | 0.919388i | \(0.371316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 453.726 | 0.434048 | 0.217024 | − | 0.976166i | \(-0.430365\pi\) | ||||
0.217024 | + | 0.976166i | \(0.430365\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 911.741 | 0.823751 | 0.411875 | − | 0.911240i | \(-0.364874\pi\) | ||||
0.411875 | + | 0.911240i | \(0.364874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22.8441 | 0.0200740 | 0.0100370 | − | 0.999950i | \(-0.496805\pi\) | ||||
0.0100370 | + | 0.999950i | \(0.496805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 54.3144 | 0.0464441 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 462.542 | 0.385065 | 0.192532 | − | 0.981291i | \(-0.438330\pi\) | ||||
0.192532 | + | 0.981291i | \(0.438330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 587.257 | 0.476191 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 666.793 | 0.526880 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 97.8742 | 0.0735344 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1262.46 | 0.925464 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1491.43 | 1.06718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1792.58 | 1.25249 | 0.626244 | − | 0.779627i | \(-0.284592\pi\) | ||||
0.626244 | + | 0.779627i | \(0.284592\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1147.04 | 0.782877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 580.446 | 0.387128 | 0.193564 | − | 0.981088i | \(-0.437995\pi\) | ||||
0.193564 | + | 0.981088i | \(0.437995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −274.229 | −0.174829 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2850.82 | −1.77783 | −0.888913 | − | 0.458077i | \(-0.848538\pi\) | ||||
−0.888913 | + | 0.458077i | \(0.848538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −187.777 | −0.114583 | −0.0572915 | − | 0.998357i | \(-0.518246\pi\) | ||||
−0.0572915 | + | 0.998357i | \(0.518246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1454.70 | −0.868852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2800.56 | 1.63773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −401.226 | −0.229793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 497.684 | 0.273637 | 0.136818 | − | 0.990596i | \(-0.456312\pi\) | ||||
0.136818 | + | 0.990596i | \(0.456312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 968.646 | 0.522035 | 0.261018 | − | 0.965334i | \(-0.415942\pi\) | ||||
0.261018 | + | 0.965334i | \(0.415942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 402.025 | 0.212430 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2588.28 | 1.34126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −176.120 | −0.0895281 | −0.0447640 | − | 0.998998i | \(-0.514254\pi\) | ||||
−0.0447640 | + | 0.998998i | \(0.514254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 108.263 | 0.0539986 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7766 | 0.00902267 | 0.00451133 | − | 0.999990i | \(-0.498564\pi\) | ||||
0.00451133 | + | 0.999990i | \(0.498564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1151.78 | −0.543428 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1325.80 | −0.614334 | −0.307167 | − | 0.951656i | \(-0.599381\pi\) | ||||
−0.307167 | + | 0.951656i | \(0.599381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3292.05 | 1.49843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1254.31 | 0.560931 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3701.94 | −1.62690 | −0.813449 | − | 0.581636i | \(-0.802413\pi\) | ||||
−0.813449 | + | 0.581636i | \(0.802413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −437.494 | −0.185785 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4363.41 | 1.82199 | 0.910996 | − | 0.412416i | \(-0.135315\pi\) | ||||
0.910996 | + | 0.412416i | \(0.135315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −130.885 | −0.0537494 | −0.0268747 | − | 0.999639i | \(-0.508556\pi\) | ||||
−0.0268747 | + | 0.999639i | \(0.508556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −234.408 | −0.0946881 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −183.884 | −0.0730778 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1688.53 | 0.660306 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4592.05 | 1.73963 | 0.869814 | − | 0.493379i | \(-0.164239\pi\) | ||||
0.869814 | + | 0.493379i | \(0.164239\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 843.489 | 0.314589 | 0.157294 | − | 0.987552i | \(-0.449723\pi\) | ||||
0.157294 | + | 0.987552i | \(0.449723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2257.46 | −0.829025 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1881.79 | 0.680570 | 0.340285 | − | 0.940322i | \(-0.389476\pi\) | ||||
0.340285 | + | 0.940322i | \(0.389476\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1546.11 | 0.550759 | 0.275380 | − | 0.961336i | \(-0.411196\pi\) | ||||
0.275380 | + | 0.961336i | \(0.411196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 819.159 | 0.287458 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4274.11 | −1.45618 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −520.380 | −0.174729 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5268.15 | 1.74357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1520.42 | 0.496068 | 0.248034 | − | 0.968751i | \(-0.420216\pi\) | ||||
0.248034 | + | 0.968751i | \(0.420216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2152.93 | −0.692564 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3883.35 | −1.23182 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3324.83 | −1.02590 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3309.47 | 1.00733 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4735.42 | 1.42201 | 0.711003 | − | 0.703189i | \(-0.248241\pi\) | ||||
0.711003 | + | 0.703189i | \(0.248241\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −196.585 | −0.0582474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2285.64 | 0.668296 | 0.334148 | − | 0.942521i | \(-0.391551\pi\) | ||||
0.334148 | + | 0.942521i | \(0.391551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 479.209 | 0.138284 | 0.0691420 | − | 0.997607i | \(-0.477974\pi\) | ||||
0.0691420 | + | 0.997607i | \(0.477974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5152.71 | 1.44878 | 0.724389 | − | 0.689392i | \(-0.242122\pi\) | ||||
0.724389 | + | 0.689392i | \(0.242122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4924.97 | 1.36710 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3256.97 | 0.892671 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2378.94 | −0.643852 | −0.321926 | − | 0.946765i | \(-0.604330\pi\) | ||||
−0.321926 | + | 0.946765i | \(0.604330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.2202 | −0.00593914 | −0.00296957 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296957 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10325.5 | 2.65989 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1214.33 | 0.309056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4845.08 | −1.21840 | −0.609201 | − | 0.793016i | \(-0.708510\pi\) | ||||
−0.609201 | + | 0.793016i | \(0.708510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2185.62 | −0.543118 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1361.07 | −0.334250 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4714.05 | 1.14418 | 0.572090 | − | 0.820191i | \(-0.306133\pi\) | ||||
0.572090 | + | 0.820191i | \(0.306133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 355.535 | 0.0843182 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3481.06 | 0.816165 | 0.408082 | − | 0.912945i | \(-0.366198\pi\) | ||||
0.408082 | + | 0.912945i | \(0.366198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −366.528 | −0.0849646 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4063.25 | −0.931336 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 297.092 | 0.0673384 | 0.0336692 | − | 0.999433i | \(-0.489281\pi\) | ||||
0.0336692 | + | 0.999433i | \(0.489281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −812.504 | −0.182126 | −0.0910629 | − | 0.995845i | \(-0.529026\pi\) | ||||
−0.0910629 | + | 0.995845i | \(0.529026\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −825.667 | −0.181053 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7209.01 | 1.56371 | 0.781855 | − | 0.623460i | \(-0.214274\pi\) | ||||
0.781855 | + | 0.623460i | \(0.214274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2293.53 | −0.492151 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7861.53 | −1.66897 | −0.834483 | − | 0.551034i | \(-0.814233\pi\) | ||||
−0.834483 | + | 0.551034i | \(0.814233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2051.70 | −0.430957 | −0.215479 | − | 0.976509i | \(-0.569131\pi\) | ||||
−0.215479 | + | 0.976509i | \(0.569131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4246.51 | −0.882602 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2917.64 | −0.593861 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2045.54 | 0.412068 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6247.59 | −1.24569 | −0.622847 | − | 0.782344i | \(-0.714024\pi\) | ||||
−0.622847 | + | 0.782344i | \(0.714024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1481.15 | 0.292326 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1020.61 | 0.199400 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4283.77 | −0.828552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2395.60 | 0.454203 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 793.598 | 0.148988 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9872.98 | 1.83544 | 0.917721 | − | 0.397225i | \(-0.130027\pi\) | ||||
0.917721 | + | 0.397225i | \(0.130027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1361.18 | 0.250598 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1584.47 | −0.288898 | −0.144449 | − | 0.989512i | \(-0.546141\pi\) | ||||
−0.144449 | + | 0.989512i | \(0.546141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7403.93 | −1.33704 | −0.668522 | − | 0.743693i | \(-0.733073\pi\) | ||||
−0.668522 | + | 0.743693i | \(0.733073\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10223.8 | −1.81143 | −0.905716 | − | 0.423884i | \(-0.860666\pi\) | ||||
−0.905716 | + | 0.423884i | \(0.860666\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1493.26 | 0.262090 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2735.22 | 0.475593 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6225.46 | 1.07243 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1618.29 | −0.276205 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 68.5322 | 0.0115897 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6847.01 | −1.13700 | −0.568498 | − | 0.822684i | \(-0.692475\pi\) | ||||
−0.568498 | + | 0.822684i | \(0.692475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 162.943 | 0.0268145 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2773.30 | −0.452303 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6735.78 | 1.08879 | 0.544394 | − | 0.838830i | \(-0.316760\pi\) | ||||
0.544394 | + | 0.838830i | \(0.316760\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1387.63 | 0.222317 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9632.94 | −1.52977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1761.77 | 0.274929 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7776.58 | 1.20308 | 0.601540 | − | 0.798843i | \(-0.294554\pi\) | ||||
0.601540 | + | 0.798843i | \(0.294554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3043.15 | 0.466750 | 0.233375 | − | 0.972387i | \(-0.425023\pi\) | ||||
0.233375 | + | 0.972387i | \(0.425023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2000.38 | 0.304195 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2410.49 | 0.363449 | 0.181724 | − | 0.983350i | \(-0.441832\pi\) | ||||
0.181724 | + | 0.983350i | \(0.441832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7288.83 | 1.08972 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11356.6 | −1.66957 | −0.834786 | − | 0.550574i | \(-0.814409\pi\) | ||||
−0.834786 | + | 0.550574i | \(0.814409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12564.3 | 1.83179 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 293.623 | 0.0424551 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11256.4 | 1.61421 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1860.34 | 0.264602 | 0.132301 | − | 0.991210i | \(-0.457763\pi\) | ||||
0.132301 | + | 0.991210i | \(0.457763\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3787.37 | 0.534317 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3507.96 | 0.486957 | 0.243479 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243479 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4474.29 | 0.616136 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2926.77 | 0.399831 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 766.351 | 0.103865 | 0.0519324 | − | 0.998651i | \(-0.483462\pi\) | ||||
0.0519324 | + | 0.998651i | \(0.483462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5377.74 | 0.723124 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13914.7 | −1.85642 | −0.928212 | − | 0.372053i | \(-0.878654\pi\) | ||||
−0.928212 | + | 0.372053i | \(0.878654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3441.12 | 0.451994 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4598.31 | −0.599340 | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299670 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2582.79 | −0.334059 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1741.34 | 0.223509 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11026.6 | −1.40458 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12735.2 | −1.60998 | −0.804991 | − | 0.593287i | \(-0.797830\pi\) | ||||
−0.804991 | + | 0.593287i | \(0.797830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1802.56 | 0.224477 | 0.112239 | − | 0.993681i | \(-0.464198\pi\) | ||||
0.112239 | + | 0.993681i | \(0.464198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18880.4 | −2.33374 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −822.687 | −0.100937 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 684.369 | 0.0833487 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8336.30 | 1.00783 | 0.503916 | − | 0.863753i | \(-0.331892\pi\) | ||||
0.503916 | + | 0.863753i | \(0.331892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8552.46 | −1.02643 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4111.17 | −0.486288 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −563.331 | −0.0661546 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11940.4 | 1.39219 | 0.696093 | − | 0.717952i | \(-0.254920\pi\) | ||||
0.696093 | + | 0.717952i | \(0.254920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3876.28 | −0.448737 | −0.224368 | − | 0.974504i | \(-0.572032\pi\) | ||||
−0.224368 | + | 0.974504i | \(0.572032\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4364.11 | −0.501632 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −975.705 | −0.111362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8401.69 | 0.945542 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6252.60 | 0.698786 | 0.349393 | − | 0.936976i | \(-0.386388\pi\) | ||||
0.349393 | + | 0.936976i | \(0.386388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12189.7 | −1.35289 | −0.676446 | − | 0.736493i | \(-0.736481\pi\) | ||||
−0.676446 | + | 0.736493i | \(0.736481\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1203.68 | −0.132671 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8058.22 | −0.882098 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8281.78 | −0.900382 | −0.450191 | − | 0.892932i | \(-0.648644\pi\) | ||||
−0.450191 | + | 0.892932i | \(0.648644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −626.486 | −0.0671902 | −0.0335951 | − | 0.999436i | \(-0.510696\pi\) | ||||
−0.0335951 | + | 0.999436i | \(0.510696\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13756.3 | 1.46542 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1493.05 | 0.157984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12789.8 | 1.34430 | 0.672148 | − | 0.740416i | \(-0.265372\pi\) | ||||
0.672148 | + | 0.740416i | \(0.265372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15907.2 | 1.66084 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2905.94 | 0.301397 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10708.8 | 1.09614 | 0.548069 | − | 0.836433i | \(-0.315363\pi\) | ||||
0.548069 | + | 0.836433i | \(0.315363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1206.08 | 0.122647 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2549.45 | 0.257570 | 0.128785 | − | 0.991673i | \(-0.458892\pi\) | ||||
0.128785 | + | 0.991673i | \(0.458892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13906.1 | 1.39584 | 0.697919 | − | 0.716177i | \(-0.254110\pi\) | ||||
0.697919 | + | 0.716177i | \(0.254110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7764.85 | 0.774379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5827.33 | −0.577423 | −0.288712 | − | 0.957416i | \(-0.593227\pi\) | ||||
−0.288712 | + | 0.957416i | \(0.593227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −528.360 | −0.0516891 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14452.9 | 1.40495 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3044.17 | −0.294055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 324.788 | 0.0311761 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3813.03 | −0.363720 | −0.181860 | − | 0.983324i | \(-0.558212\pi\) | ||||
−0.181860 | + | 0.983324i | \(0.558212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1341.35 | 0.127152 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6925.27 | −0.648372 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5783.76 | 0.538167 | 0.269083 | − | 0.963117i | \(-0.413279\pi\) | ||||
0.269083 | + | 0.963117i | \(0.413279\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 56.3297 | 0.00520924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10840.9 | 0.996419 | 0.498209 | − | 0.867057i | \(-0.333991\pi\) | ||||
0.498209 | + | 0.867057i | \(0.333991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1764.62 | 0.161206 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3455.33 | −0.313748 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12738.1 | 1.14276 | 0.571379 | − | 0.820686i | \(-0.306409\pi\) | ||||
0.571379 | + | 0.820686i | \(0.306409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3977.41 | −0.354686 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5014.31 | −0.444487 | −0.222243 | − | 0.974991i | \(-0.571338\pi\) | ||||
−0.222243 | + | 0.974991i | \(0.571338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8110.41 | −0.714670 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9876.14 | 0.865117 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14977.5 | 1.30425 | 0.652126 | − | 0.758111i | \(-0.273877\pi\) | ||||
0.652126 | + | 0.758111i | \(0.273877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3762.92 | 0.323854 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4608.33 | −0.394306 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18329.5 | −1.55925 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11105.8 | −0.939290 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3122.30 | −0.262553 | −0.131277 | − | 0.991346i | \(-0.541908\pi\) | ||||
−0.131277 | + | 0.991346i | \(0.541908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9649.39 | −0.806765 | −0.403383 | − | 0.915031i | \(-0.632166\pi\) | ||||
−0.403383 | + | 0.915031i | \(0.632166\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11383.4 | −0.940929 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8823.85 | −0.725228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1312.48 | −0.107263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31177.7 | 2.53369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9260.22 | −0.748326 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13090.2 | 1.05193 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15861.6 | 1.26052 | 0.630262 | − | 0.776382i | \(-0.282947\pi\) | ||||
0.630262 | + | 0.776382i | \(0.282947\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −392.656 | −0.0310322 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −232.019 | −0.0182360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7477.29 | −0.584471 | −0.292236 | − | 0.956346i | \(-0.594399\pi\) | ||||
−0.292236 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −703.223 | −0.0546682 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5505.55 | 0.425670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −551.651 | −0.0421915 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18170.4 | −1.38224 | −0.691119 | − | 0.722741i | \(-0.742882\pi\) | ||||
−0.691119 | + | 0.722741i | \(0.742882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28327.3 | 2.14332 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5065.58 | 0.381228 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 467.613 | 0.0350045 | 0.0175023 | − | 0.999847i | \(-0.494429\pi\) | ||||
0.0175023 | + | 0.999847i | \(0.494429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4697.87 | −0.349807 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26449.8 | 1.94874 | 0.974368 | − | 0.224958i | \(-0.0722245\pi\) | ||||
0.974368 | + | 0.224958i | \(0.0722245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8770.96 | −0.642826 | −0.321413 | − | 0.946939i | \(-0.604158\pi\) | ||||
−0.321413 | + | 0.946939i | \(0.604158\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13776.1 | 1.00438 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1262.95 | 0.0915976 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3036.56 | 0.219088 | 0.109544 | − | 0.993982i | \(-0.465061\pi\) | ||||
0.109544 | + | 0.993982i | \(0.465061\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2530.47 | 0.181628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1364.12 | 0.0969061 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6772.37 | −0.478638 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1620.33 | 0.113932 | 0.0569661 | − | 0.998376i | \(-0.481857\pi\) | ||||
0.0569661 | + | 0.998376i | \(0.481857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35515.9 | −2.48456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5645.38 | 0.392927 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27146.4 | −1.87988 | −0.939940 | − | 0.341340i | \(-0.889119\pi\) | ||||
−0.939940 | + | 0.341340i | \(0.889119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4638.34 | 0.317981 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19211.0 | −1.31042 | −0.655209 | − | 0.755448i | \(-0.727420\pi\) | ||||
−0.655209 | + | 0.755448i | \(0.727420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24463.9 | −1.66041 | −0.830204 | − | 0.557460i | \(-0.811776\pi\) | ||||
−0.830204 | + | 0.557460i | \(0.811776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2457.48 | 0.165964 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −994.073 | −0.0668013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20270.4 | 1.35544 | 0.677718 | − | 0.735322i | \(-0.262969\pi\) | ||||
0.677718 | + | 0.735322i | \(0.262969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35925.4 | −2.37870 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15584.8 | 1.02686 | 0.513429 | − | 0.858132i | \(-0.328375\pi\) | ||||
0.513429 | + | 0.858132i | \(0.328375\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12822.3 | −0.840725 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2276.13 | 0.148515 | 0.0742573 | − | 0.997239i | \(-0.476341\pi\) | ||||
0.0742573 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14493.2 | 0.941081 | 0.470540 | − | 0.882378i | \(-0.344059\pi\) | ||||
0.470540 | + | 0.882378i | \(0.344059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1561.14 | −0.100880 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12417.5 | −0.794723 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15804.4 | 1.00665 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 808.731 | 0.0512658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8517.07 | −0.537336 | −0.268668 | − | 0.963233i | \(-0.586583\pi\) | ||||
−0.268668 | + | 0.963233i | \(0.586583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4561.27 | 0.286405 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18206.6 | −1.13781 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6458.78 | −0.399852 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21914.3 | 1.35033 | 0.675167 | − | 0.737665i | \(-0.264072\pi\) | ||||
0.675167 | + | 0.737665i | \(0.264072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26799.5 | 1.64365 | 0.821826 | − | 0.569739i | \(-0.192956\pi\) | ||||
0.821826 | + | 0.569739i | \(0.192956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11650.1 | −0.711194 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32176.4 | −1.95515 | −0.977577 | − | 0.210578i | \(-0.932465\pi\) | ||||
−0.977577 | + | 0.210578i | \(0.932465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5512.49 | −0.333411 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −270.878 | −0.0162332 | −0.00811660 | − | 0.999967i | \(-0.502584\pi\) | ||||
−0.00811660 | + | 0.999967i | \(0.502584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5895.38 | −0.351682 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9974.50 | −0.592302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 913.255 | 0.0539838 | 0.0269919 | − | 0.999636i | \(-0.491407\pi\) | ||||
0.0269919 | + | 0.999636i | \(0.491407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17642.8 | 1.03816 | 0.519080 | − | 0.854726i | \(-0.326275\pi\) | ||||
0.519080 | + | 0.854726i | \(0.326275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9928.42 | 0.581581 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2284.11 | −0.132596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14206.3 | 0.820995 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2953.57 | −0.169928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9839.88 | 0.563595 | 0.281798 | − | 0.959474i | \(-0.409069\pi\) | ||||
0.281798 | + | 0.959474i | \(0.409069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −589.755 | −0.0336292 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27471.3 | 1.55954 | 0.779769 | − | 0.626067i | \(-0.215336\pi\) | ||||
0.779769 | + | 0.626067i | \(0.215336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6856.92 | 0.385841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6363.61 | 0.356511 | 0.178255 | − | 0.983984i | \(-0.442955\pi\) | ||||
0.178255 | + | 0.983984i | \(0.442955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28954.7 | 1.61504 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1437.63 | 0.0798383 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2673.65 | 0.147835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16512.5 | 0.909068 | 0.454534 | − | 0.890729i | \(-0.349806\pi\) | ||||
0.454534 | + | 0.890729i | \(0.349806\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1907.18 | 0.104091 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18797.8 | 1.02154 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15458.1 | 0.836452 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32633.2 | −1.75826 | −0.879128 | − | 0.476585i | \(-0.841874\pi\) | ||||
−0.879128 | + | 0.476585i | \(0.841874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2523.22 | 0.135370 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14774.9 | 0.789298 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22641.5 | −1.19932 | −0.599660 | − | 0.800255i | \(-0.704698\pi\) | ||||
−0.599660 | + | 0.800255i | \(0.704698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9770.92 | 0.515384 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14734.7 | 0.773937 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28444.3 | −1.48777 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7136.81 | −0.371728 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28786.0 | 1.49310 | 0.746549 | − | 0.665330i | \(-0.231709\pi\) | ||||
0.746549 | + | 0.665330i | \(0.231709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −66.6607 | −0.00342896 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −862.875 | −0.0442019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15302.1 | 0.780639 | 0.390319 | − | 0.920679i | \(-0.372365\pi\) | ||||
0.390319 | + | 0.920679i | \(0.372365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17079.2 | 0.864155 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16451.3 | 0.828983 | 0.414491 | − | 0.910053i | \(-0.363960\pi\) | ||||
0.414491 | + | 0.910053i | \(0.363960\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10321.5 | 0.515873 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3878.19 | 0.193047 | 0.0965233 | − | 0.995331i | \(-0.469228\pi\) | ||||
0.0965233 | + | 0.995331i | \(0.469228\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30976.4 | 1.53569 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7702.39 | 0.380314 | 0.190157 | − | 0.981754i | \(-0.439100\pi\) | ||||
0.190157 | + | 0.981754i | \(0.439100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5054.79 | −0.248582 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3642.99 | 0.178434 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7068.66 | −0.343461 | −0.171730 | − | 0.985144i | \(-0.554936\pi\) | ||||
−0.171730 | + | 0.985144i | \(0.554936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14535.2 | −0.703445 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9838.19 | −0.474236 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21371.0 | 1.02608 | 0.513039 | − | 0.858365i | \(-0.328520\pi\) | ||||
0.513039 | + | 0.858365i | \(0.328520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6556.87 | −0.313569 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16307.2 | −0.776786 | −0.388393 | − | 0.921494i | \(-0.626970\pi\) | ||||
−0.388393 | + | 0.921494i | \(0.626970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4083.22 | −0.192979 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10804.4 | −0.508634 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40553.7 | −1.90169 | −0.950847 | − | 0.309660i | \(-0.899785\pi\) | ||||
−0.950847 | + | 0.309660i | \(0.899785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14142.2 | 0.660593 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11220.5 | 0.522089 | 0.261045 | − | 0.965327i | \(-0.415933\pi\) | ||||
0.261045 | + | 0.965327i | \(0.415933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5566.34 | 0.257999 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58648.5 | 2.69743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27127.2 | −1.24288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1066.60 | 0.0486812 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1788.79 | 0.0813306 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7836.87 | −0.354961 | −0.177480 | − | 0.984124i | \(-0.556795\pi\) | ||||
−0.177480 | + | 0.984124i | \(0.556795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10443.2 | 0.471213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5788.94 | −0.259232 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1099.58 | −0.0490543 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6521.90 | 0.289859 | 0.144929 | − | 0.989442i | \(-0.453704\pi\) | ||||
0.144929 | + | 0.989442i | \(0.453704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21660.3 | −0.959056 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12189.7 | −0.537707 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41893.4 | −1.84108 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 891.277 | 0.0388779 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22997.8 | −0.999457 | −0.499728 | − | 0.866182i | \(-0.666567\pi\) | ||||
−0.499728 | + | 0.866182i | \(0.666567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5253.94 | 0.227485 | 0.113743 | − | 0.993510i | \(-0.463716\pi\) | ||||
0.113743 | + | 0.993510i | \(0.463716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2437.51 | −0.105150 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −190.707 | −0.00819653 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53286.6 | 2.28184 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14044.6 | −0.597029 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13677.4 | −0.579300 | −0.289650 | − | 0.957133i | \(-0.593539\pi\) | ||||
−0.289650 | + | 0.957133i | \(0.593539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2477.00 | −0.104531 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3206.14 | −0.134811 | −0.0674054 | − | 0.997726i | \(-0.521472\pi\) | ||||
−0.0674054 | + | 0.997726i | \(0.521472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30876.6 | −1.29359 | −0.646796 | − | 0.762663i | \(-0.723892\pi\) | ||||
−0.646796 | + | 0.762663i | \(0.723892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21627.0 | 0.902808 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13465.7 | 0.558083 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6880.59 | −0.284143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11040.6 | −0.454306 | −0.227153 | − | 0.973859i | \(-0.572942\pi\) | ||||
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22828.4 | −0.936014 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23584.6 | −0.963578 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33436.1 | −1.36123 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6155.10 | −0.248813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1046.82 | −0.0421674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12245.3 | 0.491524 | 0.245762 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245762 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12739.5 | −0.509570 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18764.2 | −0.747925 | −0.373962 | − | 0.927444i | \(-0.622001\pi\) | ||||
−0.373962 | + | 0.927444i | \(0.622001\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30566.2 | 1.21409 | 0.607046 | − | 0.794667i | \(-0.292354\pi\) | ||||
0.607046 | + | 0.794667i | \(0.292354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14027.6 | 0.553307 | 0.276654 | − | 0.960970i | \(-0.410775\pi\) | ||||
0.276654 | + | 0.960970i | \(0.410775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37599.3 | 1.47793 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8752.92 | −0.342866 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41038.3 | 1.60199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20230.0 | 0.786988 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6136.62 | 0.237908 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33737.9 | −1.29903 | −0.649514 | − | 0.760349i | \(-0.725028\pi\) | ||||
−0.649514 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18742.8 | −0.719201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8512.70 | −0.325539 | −0.162770 | − | 0.986664i | \(-0.552043\pi\) | ||||
−0.162770 | + | 0.986664i | \(0.552043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27302.9 | 1.04056 | 0.520281 | − | 0.853995i | \(-0.325827\pi\) | ||||
0.520281 | + | 0.853995i | \(0.325827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4443.46 | 0.168774 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25804.0 | −0.976789 | −0.488395 | − | 0.872623i | \(-0.662417\pi\) | ||||
−0.488395 | + | 0.872623i | \(0.662417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3061.84 | 0.115124 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67579.4 | −2.53243 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44317.5 | −1.65516 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12851.3 | −0.478365 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10067.0 | −0.373476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1612.01 | 0.0596047 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1329.36 | 0.0488279 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29536.1 | −1.08129 | −0.540645 | − | 0.841251i | \(-0.681820\pi\) | ||||
−0.540645 | + | 0.841251i | \(0.681820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7186.80 | 0.262234 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19543.9 | 0.710777 | 0.355389 | − | 0.934719i | \(-0.384349\pi\) | ||||
0.355389 | + | 0.934719i | \(0.384349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15300.7 | 0.554634 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2380.79 | 0.0860182 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8300.26 | 0.297933 | 0.148967 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148967 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29618.9 | 1.05969 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53168.7 | −1.89607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −395.459 | −0.0140569 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4083.54 | 0.144683 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11835.8 | −0.417999 | −0.208999 | − | 0.977916i | \(-0.567021\pi\) | ||||
−0.208999 | + | 0.977916i | \(0.567021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4753.42 | −0.166795 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17149.7 | −0.599846 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19702.4 | 0.686926 | 0.343463 | − | 0.939166i | \(-0.388400\pi\) | ||||
0.343463 | + | 0.939166i | \(0.388400\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22211.8 | −0.771942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32940.6 | −1.14116 | −0.570581 | − | 0.821241i | \(-0.693282\pi\) | ||||
−0.570581 | + | 0.821241i | \(0.693282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24331.8 | −0.840246 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37692.0 | −1.29337 | −0.646687 | − | 0.762755i | \(-0.723846\pi\) | ||||
−0.646687 | + | 0.762755i | \(0.723846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −82110.2 | −2.80865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30671.3 | −1.04583 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2904.61 | 0.0987298 | 0.0493649 | − | 0.998781i | \(-0.484280\pi\) | ||||
0.0493649 | + | 0.998781i | \(0.484280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46639.8 | −1.58034 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4479.79 | 0.151318 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35150.7 | 1.17991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8205.67 | 0.274584 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8567.01 | −0.285784 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7954.56 | 0.264531 | 0.132266 | − | 0.991214i | \(-0.457775\pi\) | ||||
0.132266 | + | 0.991214i | \(0.457775\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18676.4 | 0.619166 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15318.3 | −0.506268 | −0.253134 | − | 0.967431i | \(-0.581461\pi\) | ||||
−0.253134 | + | 0.967431i | \(0.581461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4854.87 | −0.159467 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34372.3 | −1.12555 | −0.562777 | − | 0.826609i | \(-0.690267\pi\) | ||||
−0.562777 | + | 0.826609i | \(0.690267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51197.5 | −1.67138 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 205.597 | 0.00669133 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15356.6 | −0.498271 | −0.249136 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249136 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19112.7 | −0.618255 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22107.3 | −0.710789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50048.5 | 1.60428 | 0.802141 | − | 0.597134i | \(-0.203694\pi\) | ||||
0.802141 | + | 0.597134i | \(0.203694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20541.0 | −0.656445 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15703.3 | −0.500330 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7695.26 | 0.244445 | 0.122222 | − | 0.992503i | \(-0.460998\pi\) | ||||
0.122222 | + | 0.992503i | \(0.460998\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 488.829 | 0.0154814 |
(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 | 2352.4.a.cj.1.1 | 3 | ||
4.3 | odd | 2 | 1176.4.a.x.1.1 | 3 | |||
7.3 | odd | 6 | 336.4.q.l.289.1 | 6 | |||
7.5 | odd | 6 | 336.4.q.l.193.1 | 6 | |||
7.6 | odd | 2 | 2352.4.a.ch.1.3 | 3 | |||
28.3 | even | 6 | 168.4.q.e.121.1 | yes | 6 | ||
28.19 | even | 6 | 168.4.q.e.25.1 | ✓ | 6 | ||
28.27 | even | 2 | 1176.4.a.y.1.3 | 3 | |||
84.47 | odd | 6 | 504.4.s.g.361.3 | 6 | |||
84.59 | odd | 6 | 504.4.s.g.289.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.e.25.1 | ✓ | 6 | 28.19 | even | 6 | ||
168.4.q.e.121.1 | yes | 6 | 28.3 | even | 6 | ||
336.4.q.l.193.1 | 6 | 7.5 | odd | 6 | |||
336.4.q.l.289.1 | 6 | 7.3 | odd | 6 | |||
504.4.s.g.289.3 | 6 | 84.59 | odd | 6 | |||
504.4.s.g.361.3 | 6 | 84.47 | odd | 6 | |||
1176.4.a.x.1.1 | 3 | 4.3 | odd | 2 | |||
1176.4.a.y.1.3 | 3 | 28.27 | even | 2 | |||
2352.4.a.ch.1.3 | 3 | 7.6 | odd | 2 | |||
2352.4.a.cj.1.1 | 3 | 1.1 | even | 1 | trivial |