Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,6,Mod(206,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("207.206");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(33.1994507013\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 206.10 | ||
Character | \(\chi\) | \(=\) | 207.206 |
Dual form | 207.6.c.a.206.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/207\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.32542i | 0.587856i | 0.955828 | + | 0.293928i | \(0.0949626\pi\) | ||||
−0.955828 | + | 0.293928i | \(0.905037\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 20.9416 | 0.654425 | ||||||||
\(5\) | −58.3890 | −1.04449 | −0.522247 | − | 0.852794i | \(-0.674906\pi\) | ||||
−0.522247 | + | 0.852794i | \(0.674906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 22.0963i | − | 0.170441i | −0.996362 | − | 0.0852205i | \(-0.972841\pi\) | ||
0.996362 | − | 0.0852205i | \(-0.0271595\pi\) | |||||||
\(8\) | 176.053i | 0.972564i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 194.168i | − | 0.614012i | ||||||
\(11\) | 772.113 | 1.92397 | 0.961987 | − | 0.273097i | \(-0.0880480\pi\) | ||||
0.961987 | + | 0.273097i | \(0.0880480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −840.212 | −1.37889 | −0.689447 | − | 0.724337i | \(-0.742146\pi\) | ||||
−0.689447 | + | 0.724337i | \(0.742146\pi\) | |||||||
\(14\) | 73.4793 | 0.100195 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 84.6829 | 0.0826981 | ||||||||
\(17\) | 1076.07 | 0.903067 | 0.451533 | − | 0.892254i | \(-0.350877\pi\) | ||||
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 726.287i | − | 0.461556i | −0.973006 | − | 0.230778i | \(-0.925873\pi\) | ||
0.973006 | − | 0.230778i | \(-0.0741271\pi\) | |||||||
\(20\) | −1222.76 | −0.683543 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2567.60i | 1.13102i | ||||||||
\(23\) | −958.808 | + | 2348.84i | −0.377931 | + | 0.925834i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 284.272 | 0.0909672 | ||||||||
\(26\) | − | 2794.05i | − | 0.810590i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 462.732i | − | 0.111541i | ||||||
\(29\) | 8098.76i | 1.78823i | 0.447836 | + | 0.894116i | \(0.352195\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 60.1277 | 0.0112375 | 0.00561876 | − | 0.999984i | \(-0.498211\pi\) | ||||
0.00561876 | + | 0.999984i | \(0.498211\pi\) | |||||||
\(32\) | 5915.30i | 1.02118i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3578.39i | 0.530873i | ||||||||
\(35\) | 1290.18i | 0.178025i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2590.57i | − | 0.311093i | −0.987829 | − | 0.155547i | \(-0.950286\pi\) | ||
0.987829 | − | 0.155547i | \(-0.0497139\pi\) | |||||||
\(38\) | 2415.21 | 0.271328 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 10279.5i | − | 1.01584i | ||||||
\(41\) | − | 3380.97i | − | 0.314110i | −0.987590 | − | 0.157055i | \(-0.949800\pi\) | ||
0.987590 | − | 0.157055i | \(-0.0501999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15940.7i | 1.31473i | 0.753572 | + | 0.657365i | \(0.228329\pi\) | ||||
−0.753572 | + | 0.657365i | \(0.771671\pi\) | |||||||
\(44\) | 16169.3 | 1.25910 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7810.85 | − | 3188.44i | −0.544257 | − | 0.222169i | ||||
\(47\) | 7434.87i | 0.490940i | 0.969404 | + | 0.245470i | \(0.0789423\pi\) | ||||
−0.969404 | + | 0.245470i | \(0.921058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16318.8 | 0.970950 | ||||||||
\(50\) | 945.324i | 0.0534756i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17595.4 | −0.902383 | ||||||||
\(53\) | −18754.5 | −0.917099 | −0.458550 | − | 0.888669i | \(-0.651631\pi\) | ||||
−0.458550 | + | 0.888669i | \(0.651631\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −45082.9 | −2.00958 | ||||||||
\(56\) | 3890.11 | 0.165765 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −26931.7 | −1.05122 | ||||||||
\(59\) | 31076.5i | 1.16226i | 0.813812 | + | 0.581128i | \(0.197388\pi\) | ||||
−0.813812 | + | 0.581128i | \(0.802612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40476.3i | 1.39276i | 0.717674 | + | 0.696379i | \(0.245207\pi\) | ||||
−0.717674 | + | 0.696379i | \(0.754793\pi\) | |||||||
\(62\) | 199.949i | 0.00660604i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −16961.0 | −0.517608 | ||||||||
\(65\) | 49059.1 | 1.44025 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 15803.0i | − | 0.430082i | −0.976605 | − | 0.215041i | \(-0.931011\pi\) | ||
0.976605 | − | 0.215041i | \(-0.0689886\pi\) | |||||||
\(68\) | 22534.7 | 0.590990 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4290.38 | −0.104653 | ||||||||
\(71\) | 37916.8i | 0.892660i | 0.894868 | + | 0.446330i | \(0.147269\pi\) | ||||
−0.894868 | + | 0.446330i | \(0.852731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51596.6 | −1.13322 | −0.566609 | − | 0.823987i | \(-0.691745\pi\) | ||||
−0.566609 | + | 0.823987i | \(0.691745\pi\) | |||||||
\(74\) | 8614.71 | 0.182878 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 15209.6i | − | 0.302054i | ||||||
\(77\) | − | 17060.8i | − | 0.327924i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 53278.7i | 0.960474i | 0.877139 | + | 0.480237i | \(0.159449\pi\) | ||||
−0.877139 | + | 0.480237i | \(0.840551\pi\) | |||||||
\(80\) | −4944.55 | −0.0863777 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11243.1 | 0.184651 | ||||||||
\(83\) | −114127. | −1.81842 | −0.909209 | − | 0.416341i | \(-0.863312\pi\) | ||||
−0.909209 | + | 0.416341i | \(0.863312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62830.9 | −0.943248 | ||||||||
\(86\) | −53009.5 | −0.772872 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 135933.i | 1.87119i | ||||||||
\(89\) | 36052.3 | 0.482457 | 0.241228 | − | 0.970468i | \(-0.422450\pi\) | ||||
0.241228 | + | 0.970468i | \(0.422450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18565.6i | 0.235020i | ||||||||
\(92\) | −20079.0 | + | 49188.4i | −0.247327 | + | 0.605889i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24724.0 | −0.288602 | ||||||||
\(95\) | 42407.1i | 0.482092i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 134874.i | − | 1.45546i | −0.685863 | − | 0.727730i | \(-0.740575\pi\) | ||
0.685863 | − | 0.727730i | \(-0.259425\pi\) | |||||||
\(98\) | 54266.6i | 0.570779i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5953.12 | 0.0595312 | ||||||||
\(101\) | − | 104342.i | − | 1.01778i | −0.860831 | − | 0.508890i | \(-0.830056\pi\) | ||
0.860831 | − | 0.508890i | \(-0.169944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 145443.i | 1.35082i | 0.737441 | + | 0.675412i | \(0.236034\pi\) | ||||
−0.737441 | + | 0.675412i | \(0.763966\pi\) | |||||||
\(104\) | − | 147922.i | − | 1.34106i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 62366.6i | − | 0.539122i | ||||||
\(107\) | 114667. | 0.968231 | 0.484115 | − | 0.875004i | \(-0.339141\pi\) | ||||
0.484115 | + | 0.875004i | \(0.339141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 213204.i | − | 1.71882i | −0.511291 | − | 0.859408i | \(-0.670833\pi\) | ||
0.511291 | − | 0.859408i | \(-0.329167\pi\) | |||||||
\(110\) | − | 149919.i | − | 1.18134i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1871.18i | − | 0.0140952i | ||||||
\(113\) | 144078. | 1.06146 | 0.530728 | − | 0.847542i | \(-0.321919\pi\) | ||||
0.530728 | + | 0.847542i | \(0.321919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 55983.8 | − | 137146.i | 0.394746 | − | 0.967028i | ||||
\(116\) | 169601.i | 1.17026i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −103342. | −0.683239 | ||||||||
\(119\) | − | 23777.2i | − | 0.153920i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 435107. | 2.70167 | ||||||||
\(122\) | −134600. | −0.818741 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1259.17 | 0.00735411 | ||||||||
\(125\) | 165867. | 0.949479 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 149218. | 0.820943 | 0.410471 | − | 0.911873i | \(-0.365364\pi\) | ||||
0.410471 | + | 0.911873i | \(0.365364\pi\) | |||||||
\(128\) | 132887.i | 0.716900i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 163142.i | 0.846657i | ||||||||
\(131\) | 59735.2i | 0.304125i | 0.988371 | + | 0.152062i | \(0.0485915\pi\) | ||||
−0.988371 | + | 0.152062i | \(0.951409\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16048.2 | −0.0786680 | ||||||||
\(134\) | 52551.4 | 0.252826 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 189446.i | 0.878290i | ||||||||
\(137\) | −51774.6 | −0.235676 | −0.117838 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117838 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −83329.7 | −0.365816 | −0.182908 | − | 0.983130i | \(-0.558551\pi\) | ||||
−0.182908 | + | 0.983130i | \(0.558551\pi\) | |||||||
\(140\) | 27018.4i | 0.116504i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126089. | −0.524756 | ||||||||
\(143\) | −648739. | −2.65295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 472878.i | − | 1.86780i | ||||||
\(146\) | − | 171580.i | − | 0.666169i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 54250.6i | − | 0.203587i | ||||||
\(149\) | 149607. | 0.552062 | 0.276031 | − | 0.961149i | \(-0.410981\pi\) | ||||
0.276031 | + | 0.961149i | \(0.410981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 416254. | 1.48565 | 0.742824 | − | 0.669486i | \(-0.233486\pi\) | ||||
0.742824 | + | 0.669486i | \(0.233486\pi\) | |||||||
\(152\) | 127865. | 0.448892 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 56734.3 | 0.192772 | ||||||||
\(155\) | −3510.79 | −0.0117375 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 512939.i | 1.66080i | 0.557169 | + | 0.830399i | \(0.311888\pi\) | ||||
−0.557169 | + | 0.830399i | \(0.688112\pi\) | |||||||
\(158\) | −177174. | −0.564621 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 345388.i | − | 1.06661i | ||||||
\(161\) | 51900.5 | + | 21186.1i | 0.157800 | + | 0.0644149i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 345214. | 1.01770 | 0.508850 | − | 0.860855i | \(-0.330071\pi\) | ||||
0.508850 | + | 0.860855i | \(0.330071\pi\) | |||||||
\(164\) | − | 70802.9i | − | 0.205561i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 379520.i | − | 1.06897i | ||||||
\(167\) | − | 371376.i | − | 1.03044i | −0.857058 | − | 0.515220i | \(-0.827710\pi\) | ||
0.857058 | − | 0.515220i | \(-0.172290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 334664. | 0.901346 | ||||||||
\(170\) | − | 208939.i | − | 0.554494i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 333824.i | 0.860393i | ||||||||
\(173\) | − | 187699.i | − | 0.476811i | −0.971166 | − | 0.238405i | \(-0.923375\pi\) | ||
0.971166 | − | 0.238405i | \(-0.0766247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6281.36i | − | 0.0155045i | ||||||
\(176\) | 65384.7 | 0.159109 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 119889.i | 0.283615i | ||||||||
\(179\) | − | 199147.i | − | 0.464560i | −0.972649 | − | 0.232280i | \(-0.925381\pi\) | ||
0.972649 | − | 0.232280i | \(-0.0746185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 125464.i | − | 0.284657i | −0.989819 | − | 0.142329i | \(-0.954541\pi\) | ||
0.989819 | − | 0.142329i | \(-0.0454590\pi\) | |||||||
\(182\) | −61738.2 | −0.138158 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −413519. | − | 168801.i | −0.900432 | − | 0.367562i | ||||
\(185\) | 151260.i | 0.324935i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 830850. | 1.73748 | ||||||||
\(188\) | 155698.i | 0.321284i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −141021. | −0.283401 | ||||||||
\(191\) | −278416. | −0.552219 | −0.276109 | − | 0.961126i | \(-0.589045\pi\) | ||||
−0.276109 | + | 0.961126i | \(0.589045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −500877. | −0.967917 | −0.483958 | − | 0.875091i | \(-0.660801\pi\) | ||||
−0.483958 | + | 0.875091i | \(0.660801\pi\) | |||||||
\(194\) | 448514. | 0.855601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 341741. | 0.635414 | ||||||||
\(197\) | − | 102101.i | − | 0.187441i | −0.995599 | − | 0.0937205i | \(-0.970124\pi\) | ||
0.995599 | − | 0.0937205i | \(-0.0298760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 600453.i | − | 1.07485i | −0.843313 | − | 0.537423i | \(-0.819398\pi\) | ||
0.843313 | − | 0.537423i | \(-0.180602\pi\) | |||||||
\(200\) | 50047.0i | 0.0884714i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 346979. | 0.598308 | ||||||||
\(203\) | 178953. | 0.304788 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 197411.i | 0.328086i | ||||||||
\(206\) | −483657. | −0.794090 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −71151.6 | −0.114032 | ||||||||
\(209\) | − | 560775.i | − | 0.888021i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −444157. | −0.686800 | −0.343400 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343400 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(212\) | −392750. | −0.600173 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 381315.i | 0.569180i | ||||||||
\(215\) | − | 930762.i | − | 1.37323i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1328.60i | − | 0.00191533i | ||||||
\(218\) | 708992. | 1.01042 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −944108. | −1.31512 | ||||||||
\(221\) | −904131. | −1.24523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 144161. | 0.194127 | 0.0970633 | − | 0.995278i | \(-0.469055\pi\) | ||||
0.0970633 | + | 0.995278i | \(0.469055\pi\) | |||||||
\(224\) | 130706. | 0.174051 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 479120.i | 0.623983i | ||||||||
\(227\) | 642364. | 0.827402 | 0.413701 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413701 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.06969e6i | − | 1.34794i | −0.738758 | − | 0.673971i | \(-0.764587\pi\) | ||
0.738758 | − | 0.673971i | \(-0.235413\pi\) | |||||||
\(230\) | 456068. | + | 186169.i | 0.568473 | + | 0.232054i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.42581e6 | −1.73917 | ||||||||
\(233\) | − | 912914.i | − | 1.10164i | −0.834624 | − | 0.550820i | \(-0.814315\pi\) | ||
0.834624 | − | 0.550820i | \(-0.185685\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 434114.i | − | 0.512784i | ||||||
\(236\) | 650792.i | 0.760610i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 79069.2 | 0.0904826 | ||||||||
\(239\) | 1.29048e6i | 1.46136i | 0.682720 | + | 0.730680i | \(0.260797\pi\) | ||||
−0.682720 | + | 0.730680i | \(0.739203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 669866.i | 0.742925i | 0.928448 | + | 0.371463i | \(0.121144\pi\) | ||||
−0.928448 | + | 0.371463i | \(0.878856\pi\) | |||||||
\(242\) | 1.44691e6i | 1.58819i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 847638.i | 0.911457i | ||||||||
\(245\) | −952835. | −1.01415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 610235.i | 0.636436i | ||||||||
\(248\) | 10585.6i | 0.0109292i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 551577.i | 0.558157i | ||||||||
\(251\) | 677038. | 0.678310 | 0.339155 | − | 0.940730i | \(-0.389859\pi\) | ||||
0.339155 | + | 0.940730i | \(0.389859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −740308. | + | 1.81357e6i | −0.727129 | + | 1.78128i | ||||
\(254\) | 496213.i | 0.482596i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −984656. | −0.939041 | ||||||||
\(257\) | 890595.i | 0.841099i | 0.907270 | + | 0.420550i | \(0.138163\pi\) | ||||
−0.907270 | + | 0.420550i | \(0.861837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −57241.9 | −0.0530230 | ||||||||
\(260\) | 1.02738e6 | 0.942533 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −198644. | −0.178782 | ||||||||
\(263\) | −2.16840e6 | −1.93308 | −0.966538 | − | 0.256522i | \(-0.917423\pi\) | ||||
−0.966538 | + | 0.256522i | \(0.917423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.09506e6 | 0.957904 | ||||||||
\(266\) | − | 53367.1i | − | 0.0462455i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 330940.i | − | 0.281457i | ||||||
\(269\) | 2.10505e6i | 1.77371i | 0.462051 | + | 0.886853i | \(0.347114\pi\) | ||||
−0.462051 | + | 0.886853i | \(0.652886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −84020.0 | −0.0694959 | −0.0347480 | − | 0.999396i | \(-0.511063\pi\) | ||||
−0.0347480 | + | 0.999396i | \(0.511063\pi\) | |||||||
\(272\) | 91125.0 | 0.0746819 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 172172.i | − | 0.138543i | ||||||
\(275\) | 219490. | 0.175018 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 184609. | 0.144562 | 0.0722808 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722808 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(278\) | − | 277106.i | − | 0.215047i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −227140. | −0.173140 | ||||||||
\(281\) | 1.48283e6 | 1.12028 | 0.560140 | − | 0.828398i | \(-0.310747\pi\) | ||||
0.560140 | + | 0.828398i | \(0.310747\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 402405.i | − | 0.298674i | −0.988786 | − | 0.149337i | \(-0.952286\pi\) | ||
0.988786 | − | 0.149337i | \(-0.0477139\pi\) | |||||||
\(284\) | 794040.i | 0.584180i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.15733e6i | − | 1.55955i | ||||||
\(287\) | −74706.8 | −0.0535372 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −261922. | −0.184470 | ||||||||
\(290\) | 1.57252e6 | 1.09799 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.08052e6 | −0.741607 | ||||||||
\(293\) | 947678. | 0.644899 | 0.322450 | − | 0.946587i | \(-0.395494\pi\) | ||||
0.322450 | + | 0.946587i | \(0.395494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.81452e6i | − | 1.21397i | ||||||
\(296\) | 456076. | 0.302558 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 497507.i | 0.324533i | ||||||||
\(299\) | 805602. | − | 1.97352e6i | 0.521126 | − | 1.27663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 352230. | 0.224084 | ||||||||
\(302\) | 1.38422e6i | 0.873347i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 61504.1i | − | 0.0381698i | ||||||
\(305\) | − | 2.36337e6i | − | 1.45473i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.14928e6 | −1.30151 | −0.650754 | − | 0.759289i | \(-0.725547\pi\) | ||||
−0.650754 | + | 0.759289i | \(0.725547\pi\) | |||||||
\(308\) | − | 357281.i | − | 0.214602i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 11674.8i | − | 0.00689996i | ||||||
\(311\) | 825868.i | 0.484183i | 0.970253 | + | 0.242091i | \(0.0778334\pi\) | ||||
−0.970253 | + | 0.242091i | \(0.922167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.29977e6i | − | 1.32686i | −0.748240 | − | 0.663428i | \(-0.769101\pi\) | ||
0.748240 | − | 0.663428i | \(-0.230899\pi\) | |||||||
\(314\) | −1.70574e6 | −0.976310 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.11574e6i | 0.628559i | ||||||||
\(317\) | 1.51861e6i | 0.848788i | 0.905478 | + | 0.424394i | \(0.139513\pi\) | ||||
−0.905478 | + | 0.424394i | \(0.860487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.25316e6i | 3.44051i | ||||||||
\(320\) | 990333. | 0.540638 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −70452.6 | + | 172591.i | −0.0378667 | + | 0.0927637i | ||||
\(323\) | − | 781538.i | − | 0.416816i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −238849. | −0.125434 | ||||||||
\(326\) | 1.14798e6i | 0.598261i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 595229. | 0.305492 | ||||||||
\(329\) | 164283. | 0.0836764 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.61384e6 | 1.31132 | 0.655662 | − | 0.755055i | \(-0.272390\pi\) | ||||
0.655662 | + | 0.755055i | \(0.272390\pi\) | |||||||
\(332\) | −2.39001e6 | −1.19002 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.23498e6 | 0.605750 | ||||||||
\(335\) | 922719.i | 0.449218i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.30404e6i | − | 1.58479i | −0.610010 | − | 0.792394i | \(-0.708835\pi\) | ||
0.610010 | − | 0.792394i | \(-0.291165\pi\) | |||||||
\(338\) | 1.11290e6i | 0.529862i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.31578e6 | −0.617285 | ||||||||
\(341\) | 46425.3 | 0.0216207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 731956.i | − | 0.335931i | ||||||
\(344\) | −2.80641e6 | −1.27866 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 624176. | 0.280296 | ||||||||
\(347\) | − | 1.71268e6i | − | 0.763579i | −0.924249 | − | 0.381789i | \(-0.875308\pi\) | ||
0.924249 | − | 0.381789i | \(-0.124692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16530.5 | −0.00726477 | −0.00363238 | − | 0.999993i | \(-0.501156\pi\) | ||||
−0.00363238 | + | 0.999993i | \(0.501156\pi\) | |||||||
\(350\) | 20888.1 | 0.00911443 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.56728e6i | 1.96472i | ||||||||
\(353\) | − | 2.05582e6i | − | 0.878107i | −0.898461 | − | 0.439053i | \(-0.855314\pi\) | ||
0.898461 | − | 0.439053i | \(-0.144686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.21393e6i | − | 0.932378i | ||||||
\(356\) | 754994. | 0.315732 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 662247. | 0.273094 | ||||||||
\(359\) | −2.10257e6 | −0.861020 | −0.430510 | − | 0.902586i | \(-0.641666\pi\) | ||||
−0.430510 | + | 0.902586i | \(0.641666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.94861e6 | 0.786966 | ||||||||
\(362\) | 417219. | 0.167337 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 388793.i | 0.153803i | ||||||||
\(365\) | 3.01267e6 | 1.18364 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 907054.i | − | 0.351535i | −0.984432 | − | 0.175767i | \(-0.943759\pi\) | ||
0.984432 | − | 0.175767i | \(-0.0562406\pi\) | |||||||
\(368\) | −81194.6 | + | 198906.i | −0.0312542 | + | 0.0765647i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −503004. | −0.191015 | ||||||||
\(371\) | 414405.i | 0.156311i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16128.8i | − | 0.00600246i | −0.999995 | − | 0.00300123i | \(-0.999045\pi\) | ||
0.999995 | − | 0.00300123i | \(-0.000955323\pi\) | |||||||
\(374\) | 2.76292e6i | 1.02139i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.30893e6 | −0.477471 | ||||||||
\(377\) | − | 6.80468e6i | − | 2.46578i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.72620e6i | − | 0.617295i | −0.951176 | − | 0.308648i | \(-0.900124\pi\) | ||
0.951176 | − | 0.308648i | \(-0.0998764\pi\) | |||||||
\(380\) | 888074.i | 0.315493i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 925849.i | − | 0.324625i | ||||||
\(383\) | 795331. | 0.277046 | 0.138523 | − | 0.990359i | \(-0.455765\pi\) | ||||
0.138523 | + | 0.990359i | \(0.455765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 996164.i | 0.342514i | ||||||||
\(386\) | − | 1.66562e6i | − | 0.568995i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2.82449e6i | − | 0.952491i | ||||||
\(389\) | −4.97973e6 | −1.66852 | −0.834261 | − | 0.551369i | \(-0.814106\pi\) | ||||
−0.834261 | + | 0.551369i | \(0.814106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.03175e6 | + | 2.52752e6i | −0.341297 | + | 0.836090i | ||||
\(392\) | 2.87296e6i | 0.944311i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 339528. | 0.110188 | ||||||||
\(395\) | − | 3.11089e6i | − | 1.00321i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.14563e6 | −0.364811 | −0.182405 | − | 0.983223i | \(-0.558388\pi\) | ||||
−0.182405 | + | 0.983223i | \(0.558388\pi\) | |||||||
\(398\) | 1.99675e6 | 0.631854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24073.0 | 0.00752281 | ||||||||
\(401\) | −1.82077e6 | −0.565450 | −0.282725 | − | 0.959201i | \(-0.591238\pi\) | ||||
−0.282725 | + | 0.959201i | \(0.591238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50520.0 | −0.0154953 | ||||||||
\(404\) | − | 2.18508e6i | − | 0.666062i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 595091.i | 0.179171i | ||||||||
\(407\) | − | 2.00021e6i | − | 0.598535i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −876882. | −0.259199 | −0.129599 | − | 0.991566i | \(-0.541369\pi\) | ||||
−0.129599 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(410\) | −656474. | −0.192867 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.04580e6i | 0.884013i | ||||||||
\(413\) | 686675. | 0.198096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.66376e6 | 1.89933 | ||||||||
\(416\) | − | 4.97010e6i | − | 1.40810i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.86481e6 | 0.522028 | ||||||||
\(419\) | −719232. | −0.200140 | −0.100070 | − | 0.994980i | \(-0.531907\pi\) | ||||
−0.100070 | + | 0.994980i | \(0.531907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.40118e6i | − | 0.385292i | −0.981268 | − | 0.192646i | \(-0.938293\pi\) | ||
0.981268 | − | 0.192646i | \(-0.0617069\pi\) | |||||||
\(422\) | − | 1.47701e6i | − | 0.403739i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3.30179e6i | − | 0.891937i | ||||||
\(425\) | 305898. | 0.0821494 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 894375. | 0.237383 | ||||||||
\(428\) | 2.40131e6 | 0.633635 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.09517e6 | 0.807260 | ||||||||
\(431\) | −5.32487e6 | −1.38075 | −0.690377 | − | 0.723450i | \(-0.742555\pi\) | ||||
−0.690377 | + | 0.723450i | \(0.742555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 421470.i | 0.108031i | 0.998540 | + | 0.0540153i | \(0.0172020\pi\) | ||||
−0.998540 | + | 0.0540153i | \(0.982798\pi\) | |||||||
\(434\) | 4418.14 | 0.00112594 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.46484e6i | − | 1.12484i | ||||||
\(437\) | 1.70593e6 | + | 696370.i | 0.427324 | + | 0.174436i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.14641e6 | 1.52216 | 0.761080 | − | 0.648658i | \(-0.224670\pi\) | ||||
0.761080 | + | 0.648658i | \(0.224670\pi\) | |||||||
\(440\) | − | 7.93697e6i | − | 1.95444i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 3.00661e6i | − | 0.732017i | ||||||
\(443\) | 7.40665e6i | 1.79313i | 0.442908 | + | 0.896567i | \(0.353947\pi\) | ||||
−0.442908 | + | 0.896567i | \(0.646053\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.10506e6 | −0.503923 | ||||||||
\(446\) | 479394.i | 0.114118i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 374774.i | 0.0882216i | ||||||||
\(449\) | 690558.i | 0.161653i | 0.996728 | + | 0.0808266i | \(0.0257560\pi\) | ||||
−0.996728 | + | 0.0808266i | \(0.974244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.61049e6i | − | 0.604339i | ||||||
\(452\) | 3.01723e6 | 0.694644 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.13613e6i | 0.486393i | ||||||||
\(455\) | − | 1.08402e6i | − | 0.245477i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 755259.i | − | 0.169163i | −0.996417 | − | 0.0845815i | \(-0.973045\pi\) | ||
0.996417 | − | 0.0845815i | \(-0.0269553\pi\) | |||||||
\(458\) | 3.55718e6 | 0.792395 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.17239e6 | − | 2.87206e6i | 0.258332 | − | 0.632848i | ||||
\(461\) | − | 7.11457e6i | − | 1.55918i | −0.626290 | − | 0.779590i | \(-0.715427\pi\) | ||
0.626290 | − | 0.779590i | \(-0.284573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.59086e6 | 0.995272 | 0.497636 | − | 0.867386i | \(-0.334202\pi\) | ||||
0.497636 | + | 0.867386i | \(0.334202\pi\) | |||||||
\(464\) | 685826.i | 0.147883i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.03582e6 | 0.647606 | ||||||||
\(467\) | −2.05341e6 | −0.435696 | −0.217848 | − | 0.975983i | \(-0.569904\pi\) | ||||
−0.217848 | + | 0.975983i | \(0.569904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −349187. | −0.0733037 | ||||||||
\(470\) | 1.44361e6 | 0.301443 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.47110e6 | −1.13037 | ||||||||
\(473\) | 1.23080e7i | 2.52951i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 206463.i | − | 0.0419864i | ||||||
\(476\) | − | 497934.i | − | 0.100729i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.29139e6 | −0.859069 | ||||||||
\(479\) | 3.38495e6 | 0.674084 | 0.337042 | − | 0.941490i | \(-0.390574\pi\) | ||||
0.337042 | + | 0.941490i | \(0.390574\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.17662e6i | 0.428964i | ||||||||
\(482\) | −2.22758e6 | −0.436733 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.11184e6 | 1.76804 | ||||||||
\(485\) | 7.87518e6i | 1.52022i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.06385e6 | −0.394326 | −0.197163 | − | 0.980371i | \(-0.563173\pi\) | ||||
−0.197163 | + | 0.980371i | \(0.563173\pi\) | |||||||
\(488\) | −7.12596e6 | −1.35455 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 3.16857e6i | − | 0.596175i | ||||||
\(491\) | − | 971280.i | − | 0.181820i | −0.995859 | − | 0.0909098i | \(-0.971022\pi\) | ||
0.995859 | − | 0.0909098i | \(-0.0289775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.71487e6i | 1.61489i | ||||||||
\(494\) | −2.02929e6 | −0.374133 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5091.78 | 0.000929321 | ||||||||
\(497\) | 837821. | 0.152146 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.36873e6 | −0.785423 | −0.392712 | − | 0.919662i | \(-0.628463\pi\) | ||||
−0.392712 | + | 0.919662i | \(0.628463\pi\) | |||||||
\(500\) | 3.47353e6 | 0.621363 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.25143e6i | 0.398749i | ||||||||
\(503\) | 678984. | 0.119657 | 0.0598287 | − | 0.998209i | \(-0.480945\pi\) | ||||
0.0598287 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.09240e6i | 1.06307i | ||||||||
\(506\) | −6.03086e6 | − | 2.46183e6i | −1.04714 | − | 0.427447i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.12487e6 | 0.537246 | ||||||||
\(509\) | 6.95416e6i | 1.18974i | 0.803824 | + | 0.594868i | \(0.202796\pi\) | ||||
−0.803824 | + | 0.594868i | \(0.797204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.14009e6i | 0.193147i | ||||||||
\(512\) | 978002.i | 0.164879i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.96160e6 | −0.494445 | ||||||||
\(515\) | − | 8.49225e6i | − | 1.41093i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.74056e6i | 0.944556i | ||||||||
\(518\) | − | 190353.i | − | 0.0311699i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.63700e6i | 1.40073i | ||||||||
\(521\) | −5.69845e6 | −0.919735 | −0.459867 | − | 0.887988i | \(-0.652103\pi\) | ||||
−0.459867 | + | 0.887988i | \(0.652103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.59760e6i | − | 1.53429i | −0.641471 | − | 0.767147i | \(-0.721676\pi\) | ||
0.641471 | − | 0.767147i | \(-0.278324\pi\) | |||||||
\(524\) | 1.25095e6i | 0.199027i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 7.21081e6i | − | 1.13637i | ||||||
\(527\) | 64701.8 | 0.0101482 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.59772e6 | − | 4.50417e6i | −0.714337 | − | 0.699802i | ||||
\(530\) | 3.64152e6i | 0.563110i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −336076. | −0.0514824 | ||||||||
\(533\) | 2.84073e6i | 0.433124i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.69529e6 | −1.01131 | ||||||||
\(536\) | 2.78216e6 | 0.418282 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.00017e6 | −1.04268 | ||||||||
\(539\) | 1.25999e7 | 1.86808 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.57197e6 | 0.377810 | 0.188905 | − | 0.981995i | \(-0.439506\pi\) | ||||
0.188905 | + | 0.981995i | \(0.439506\pi\) | |||||||
\(542\) | − | 279401.i | − | 0.0408536i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.36530e6i | 0.922192i | ||||||||
\(545\) | 1.24488e7i | 1.79529i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.19546e6 | −0.313731 | −0.156866 | − | 0.987620i | \(-0.550139\pi\) | ||||
−0.156866 | + | 0.987620i | \(0.550139\pi\) | |||||||
\(548\) | −1.08424e6 | −0.154232 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 729896.i | 0.102886i | ||||||||
\(551\) | 5.88202e6 | 0.825368 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.17726e6 | 0.163704 | ||||||||
\(554\) | 613901.i | 0.0849814i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.74506e6 | −0.239399 | ||||||||
\(557\) | 2.05279e6 | 0.280353 | 0.140177 | − | 0.990127i | \(-0.455233\pi\) | ||||
0.140177 | + | 0.990127i | \(0.455233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.33936e7i | − | 1.81287i | ||||||
\(560\) | 109256.i | 0.0147223i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.93103e6i | 0.658563i | ||||||||
\(563\) | 8.39159e6 | 1.11577 | 0.557883 | − | 0.829920i | \(-0.311614\pi\) | ||||
0.557883 | + | 0.829920i | \(0.311614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.41257e6 | −1.10868 | ||||||||
\(566\) | 1.33816e6 | 0.175577 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.67537e6 | −0.868169 | ||||||||
\(569\) | 1.21065e7 | 1.56760 | 0.783802 | − | 0.621011i | \(-0.213278\pi\) | ||||
0.783802 | + | 0.621011i | \(0.213278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.53237e6i | 1.09517i | 0.836752 | + | 0.547583i | \(0.184452\pi\) | ||||
−0.836752 | + | 0.547583i | \(0.815548\pi\) | |||||||
\(572\) | −1.35856e7 | −1.73616 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 248431.i | − | 0.0314721i | ||||||
\(575\) | −272563. | + | 667709.i | −0.0343793 | + | 0.0842205i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03720e6 | −0.504825 | −0.252413 | − | 0.967620i | \(-0.581224\pi\) | ||||
−0.252413 | + | 0.967620i | \(0.581224\pi\) | |||||||
\(578\) | − | 870998.i | − | 0.108442i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 9.90284e6i | − | 1.22233i | ||||||
\(581\) | 2.52178e6i | 0.309933i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.44806e7 | −1.76447 | ||||||||
\(584\) | − | 9.08372e6i | − | 1.10213i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.15142e6i | 0.379108i | ||||||||
\(587\) | − | 1.87167e6i | − | 0.224200i | −0.993697 | − | 0.112100i | \(-0.964242\pi\) | ||
0.993697 | − | 0.112100i | \(-0.0357577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 43669.9i | − | 0.00518674i | ||||||
\(590\) | 6.03404e6 | 0.713639 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 219377.i | − | 0.0257268i | ||||||
\(593\) | 8.93054e6i | 1.04290i | 0.853283 | + | 0.521448i | \(0.174608\pi\) | ||||
−0.853283 | + | 0.521448i | \(0.825392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.38833e6i | 0.160768i | ||||||||
\(596\) | 3.13302e6 | 0.361283 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.56278e6 | + | 2.67896e6i | 0.750472 | + | 0.306347i | ||||
\(599\) | 4.76499e6i | 0.542619i | 0.962492 | + | 0.271309i | \(0.0874567\pi\) | ||||
−0.962492 | + | 0.271309i | \(0.912543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.06072e7 | −1.19789 | −0.598944 | − | 0.800791i | \(-0.704413\pi\) | ||||
−0.598944 | + | 0.800791i | \(0.704413\pi\) | |||||||
\(602\) | 1.17131e6i | 0.131729i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.71703e6 | 0.972246 | ||||||||
\(605\) | −2.54055e7 | −2.82188 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.37303e7 | 1.51255 | 0.756275 | − | 0.654254i | \(-0.227017\pi\) | ||||
0.756275 | + | 0.654254i | \(0.227017\pi\) | |||||||
\(608\) | 4.29620e6 | 0.471331 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.85918e6 | 0.855170 | ||||||||
\(611\) | − | 6.24687e6i | − | 0.676954i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.36411e7i | 1.46622i | 0.680110 | + | 0.733110i | \(0.261932\pi\) | ||||
−0.680110 | + | 0.733110i | \(0.738068\pi\) | |||||||
\(614\) | − | 7.14724e6i | − | 0.765099i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00361e6 | 0.318927 | ||||||||
\(617\) | 5.85548e6 | 0.619227 | 0.309613 | − | 0.950863i | \(-0.399800\pi\) | ||||
0.309613 | + | 0.950863i | \(0.399800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.00952e7i | − | 1.05899i | −0.848314 | − | 0.529493i | \(-0.822382\pi\) | ||
0.848314 | − | 0.529493i | \(-0.177618\pi\) | |||||||
\(620\) | −73521.7 | −0.00768132 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.74635e6 | −0.284630 | ||||||||
\(623\) | − | 796622.i | − | 0.0822304i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.05732e7 | −1.08269 | ||||||||
\(626\) | 7.64769e6 | 0.780000 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.07418e7i | 1.08687i | ||||||||
\(629\) | − | 2.78764e6i | − | 0.280938i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.41421e7i | 1.41397i | 0.707230 | + | 0.706984i | \(0.249945\pi\) | ||||
−0.707230 | + | 0.706984i | \(0.750055\pi\) | |||||||
\(632\) | −9.37986e6 | −0.934123 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.05002e6 | −0.498965 | ||||||||
\(635\) | −8.71271e6 | −0.857470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.37112e7 | −1.33884 | ||||||||
\(638\) | −2.07943e7 | −2.02252 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 7.75915e6i | − | 0.748797i | ||||||
\(641\) | −2.31120e6 | −0.222173 | −0.111087 | − | 0.993811i | \(-0.535433\pi\) | ||||
−0.111087 | + | 0.993811i | \(0.535433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.43098e6i | 0.231875i | 0.993257 | + | 0.115937i | \(0.0369872\pi\) | ||||
−0.993257 | + | 0.115937i | \(0.963013\pi\) | |||||||
\(644\) | 1.08688e6 | + | 443671.i | 0.103268 | + | 0.0421547i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.59894e6 | 0.245028 | ||||||||
\(647\) | − | 1.42011e7i | − | 1.33371i | −0.745189 | − | 0.666853i | \(-0.767641\pi\) | ||
0.745189 | − | 0.666853i | \(-0.232359\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.39945e7i | 2.23615i | ||||||||
\(650\) | − | 794272.i | − | 0.0737371i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.22934e6 | 0.666008 | ||||||||
\(653\) | 688639.i | 0.0631987i | 0.999501 | + | 0.0315994i | \(0.0100601\pi\) | ||||
−0.999501 | + | 0.0315994i | \(0.989940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.48788e6i | − | 0.317657i | ||||||
\(656\) | − | 286310.i | − | 0.0259763i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 546309.i | 0.0491896i | ||||||||
\(659\) | 7.43942e6 | 0.667307 | 0.333654 | − | 0.942696i | \(-0.391718\pi\) | ||||
0.333654 | + | 0.942696i | \(0.391718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.35233e7i | − | 1.20387i | −0.798546 | − | 0.601933i | \(-0.794397\pi\) | ||
0.798546 | − | 0.601933i | \(-0.205603\pi\) | |||||||
\(662\) | 8.69212e6i | 0.770869i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.00924e7i | − | 1.76853i | ||||||
\(665\) | 937040. | 0.0821683 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.90227e7 | − | 7.76516e6i | −1.65560 | − | 0.675827i | ||||
\(668\) | − | 7.77721e6i | − | 0.674346i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.06842e6 | −0.264076 | ||||||||
\(671\) | 3.12522e7i | 2.67963i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.98340e6 | 0.424119 | 0.212060 | − | 0.977257i | \(-0.431983\pi\) | ||||
0.212060 | + | 0.977257i | \(0.431983\pi\) | |||||||
\(674\) | 1.09873e7 | 0.931626 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00840e6 | 0.589864 | ||||||||
\(677\) | 4.62140e6 | 0.387527 | 0.193763 | − | 0.981048i | \(-0.437931\pi\) | ||||
0.193763 | + | 0.981048i | \(0.437931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.98023e6 | −0.248070 | ||||||||
\(680\) | − | 1.10616e7i | − | 0.917368i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 154384.i | 0.0127098i | ||||||||
\(683\) | 5.51387e6i | 0.452277i | 0.974095 | + | 0.226139i | \(0.0726102\pi\) | ||||
−0.974095 | + | 0.226139i | \(0.927390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.02306e6 | 0.246162 | ||||||||
\(686\) | 2.43406e6 | 0.197479 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.34991e6i | 0.108726i | ||||||||
\(689\) | 1.57578e7 | 1.26458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 861740. | 0.0686564 | 0.0343282 | − | 0.999411i | \(-0.489071\pi\) | ||||
0.0343282 | + | 0.999411i | \(0.489071\pi\) | |||||||
\(692\) | − | 3.93071e6i | − | 0.312037i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.69539e6 | 0.448874 | ||||||||
\(695\) | 4.86554e6 | 0.382093 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.63817e6i | − | 0.283662i | ||||||
\(698\) | − | 54970.7i | − | 0.00427064i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 131542.i | − | 0.0101466i | ||||||
\(701\) | −1.36300e7 | −1.04762 | −0.523808 | − | 0.851837i | \(-0.675489\pi\) | ||||
−0.523808 | + | 0.851837i | \(0.675489\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.88149e6 | −0.143587 | ||||||||
\(704\) | −1.30958e7 | −0.995863 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.83644e6 | 0.516200 | ||||||||
\(707\) | −2.30556e6 | −0.173472 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.42866e6i | − | 0.256158i | −0.991764 | − | 0.128079i | \(-0.959119\pi\) | ||
0.991764 | − | 0.128079i | \(-0.0408812\pi\) | |||||||
\(710\) | 7.36222e6 | 0.548104 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.34711e6i | 0.469220i | ||||||||
\(713\) | −57650.9 | + | 141230.i | −0.00424700 | + | 0.0104041i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.78792e7 | 2.77099 | ||||||||
\(716\) | − | 4.17046e6i | − | 0.304020i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 6.99190e6i | − | 0.506156i | ||||||
\(719\) | − | 1.80809e7i | − | 1.30436i | −0.758062 | − | 0.652182i | \(-0.773854\pi\) | ||
0.758062 | − | 0.652182i | \(-0.226146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.21374e6 | 0.230236 | ||||||||
\(722\) | 6.47992e6i | 0.462623i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2.62742e6i | − | 0.186287i | ||||||
\(725\) | 2.30225e6i | 0.162670i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.45058e6i | 0.242134i | 0.992644 | + | 0.121067i | \(0.0386316\pi\) | ||||
−0.992644 | + | 0.121067i | \(0.961368\pi\) | |||||||
\(728\) | −3.26852e6 | −0.228572 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.00184e7i | 0.695809i | ||||||||
\(731\) | 1.71534e7i | 1.18729i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.11140e7i | 0.764031i | 0.924156 | + | 0.382016i | \(0.124770\pi\) | ||||
−0.924156 | + | 0.382016i | \(0.875230\pi\) | |||||||
\(734\) | 3.01633e6 | 0.206652 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38941e7 | − | 5.67164e6i | −0.945441 | − | 0.385935i | ||||
\(737\) | − | 1.22017e7i | − | 0.827467i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00762e7 | 1.35229 | 0.676146 | − | 0.736768i | \(-0.263649\pi\) | ||||
0.676146 | + | 0.736768i | \(0.263649\pi\) | |||||||
\(740\) | 3.16764e6i | 0.212646i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.37807e6 | −0.0918885 | ||||||||
\(743\) | 9.79383e6 | 0.650849 | 0.325425 | − | 0.945568i | \(-0.394493\pi\) | ||||
0.325425 | + | 0.945568i | \(0.394493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.73543e6 | −0.576625 | ||||||||
\(746\) | 53634.9 | 0.00352858 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.73993e7 | 1.13705 | ||||||||
\(749\) | − | 2.53371e6i | − | 0.165026i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.58594e7i | − | 1.02609i | −0.858361 | − | 0.513046i | \(-0.828517\pi\) | ||
0.858361 | − | 0.513046i | \(-0.171483\pi\) | |||||||
\(752\) | 629606.i | 0.0405998i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.26284e7 | 1.44952 | ||||||||
\(755\) | −2.43046e7 | −1.55175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.68578e7i | − | 1.06921i | −0.845103 | − | 0.534604i | \(-0.820461\pi\) | ||
0.845103 | − | 0.534604i | \(-0.179539\pi\) | |||||||
\(758\) | 5.74033e6 | 0.362881 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.46590e6 | −0.468865 | ||||||||
\(761\) | 9.41728e6i | 0.589473i | 0.955579 | + | 0.294736i | \(0.0952318\pi\) | ||||
−0.955579 | + | 0.294736i | \(0.904768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.71102e6 | −0.292957 | ||||||||
\(764\) | −5.83048e6 | −0.361386 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.64481e6i | 0.162863i | ||||||||
\(767\) | − | 2.61108e7i | − | 1.60263i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.37459e7i | − | 1.44802i | −0.689791 | − | 0.724008i | \(-0.742298\pi\) | ||
0.689791 | − | 0.724008i | \(-0.257702\pi\) | |||||||
\(770\) | −3.31266e6 | −0.201349 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.04892e7 | −0.633429 | ||||||||
\(773\) | 2.90678e7 | 1.74970 | 0.874849 | − | 0.484397i | \(-0.160961\pi\) | ||||
0.874849 | + | 0.484397i | \(0.160961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17092.6 | 0.00102224 | ||||||||
\(776\) | 2.37450e7 | 1.41553 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1.65597e7i | − | 0.980851i | ||||||
\(779\) | −2.45555e6 | −0.144979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92761e7i | 1.71745i | ||||||||
\(782\) | −8.40506e6 | − | 3.43099e6i | −0.491500 | − | 0.200633i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.38192e6 | 0.0802957 | ||||||||
\(785\) | − | 2.99500e7i | − | 1.73469i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.29567e7i | 1.32122i | 0.750731 | + | 0.660608i | \(0.229701\pi\) | ||||
−0.750731 | + | 0.660608i | \(0.770299\pi\) | |||||||
\(788\) | − | 2.13816e6i | − | 0.122666i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.03450e7 | 0.589743 | ||||||||
\(791\) | − | 3.18359e6i | − | 0.180916i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.40087e7i | − | 1.92047i | ||||||
\(794\) | − | 3.80969e6i | − | 0.214456i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 1.25744e7i | − | 0.703406i | ||||||
\(797\) | 1.46871e7 | 0.819010 | 0.409505 | − | 0.912308i | \(-0.365701\pi\) | ||||
0.409505 | + | 0.912308i | \(0.365701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00047e6i | 0.443352i | ||||||||
\(800\) | 1.68156e6i | 0.0928937i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 6.05482e6i | − | 0.332403i | ||||||
\(803\) | −3.98384e7 | −2.18028 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.03042e6 | − | 1.23703e6i | −0.164821 | − | 0.0672810i | ||||
\(806\) | − | 168000.i | − | 0.00910902i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.83696e7 | 0.989857 | ||||||||
\(809\) | 1.93541e7i | 1.03968i | 0.854262 | + | 0.519842i | \(0.174009\pi\) | ||||
−0.854262 | + | 0.519842i | \(0.825991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.63564e7 | 0.873242 | 0.436621 | − | 0.899646i | \(-0.356175\pi\) | ||||
0.436621 | + | 0.899646i | \(0.356175\pi\) | |||||||
\(812\) | 3.74756e6 | 0.199461 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.65152e6 | 0.351852 | ||||||||
\(815\) | −2.01567e7 | −1.06298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.15775e7 | 0.606821 | ||||||||
\(818\) | − | 2.91599e6i | − | 0.152371i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.13411e6i | 0.214708i | ||||||||
\(821\) | − | 9.18663e6i | − | 0.475662i | −0.971307 | − | 0.237831i | \(-0.923564\pi\) | ||
0.971307 | − | 0.237831i | \(-0.0764364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.37028e7 | 1.21983 | 0.609915 | − | 0.792467i | \(-0.291204\pi\) | ||||
0.609915 | + | 0.792467i | \(0.291204\pi\) | |||||||
\(824\) | −2.56056e7 | −1.31376 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.28348e6i | 0.116452i | ||||||||
\(827\) | −2.32953e7 | −1.18441 | −0.592207 | − | 0.805786i | \(-0.701743\pi\) | ||||
−0.592207 | + | 0.805786i | \(0.701743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.92385e7 | 1.47764 | 0.738821 | − | 0.673902i | \(-0.235383\pi\) | ||||
0.738821 | + | 0.673902i | \(0.235383\pi\) | |||||||
\(830\) | 2.21598e7i | 1.11653i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.42508e7 | 0.713726 | ||||||||
\(833\) | 1.75602e7 | 0.876833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.16843e7i | 1.07629i | ||||||||
\(836\) | − | 1.17435e7i | − | 0.581144i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 2.39174e6i | − | 0.117653i | ||||||
\(839\) | −1.62630e7 | −0.797617 | −0.398809 | − | 0.917034i | \(-0.630576\pi\) | ||||
−0.398809 | + | 0.917034i | \(0.630576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50788e7 | −2.19777 | ||||||||
\(842\) | 4.65952e6 | 0.226496 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.30136e6 | −0.449459 | ||||||||
\(845\) | −1.95407e7 | −0.941451 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.61425e6i | − | 0.460476i | ||||||
\(848\) | −1.58819e6 | −0.0758424 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.01724e6i | 0.0482920i | ||||||||
\(851\) | 6.08481e6 | + | 2.48386e6i | 0.288020 | + | 0.117572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −898065. | −0.0422606 | −0.0211303 | − | 0.999777i | \(-0.506726\pi\) | ||||
−0.0211303 | + | 0.999777i | \(0.506726\pi\) | |||||||
\(854\) | 2.97417e6i | 0.139547i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.01874e7i | 0.941666i | ||||||||
\(857\) | 9.28556e6i | 0.431873i | 0.976407 | + | 0.215937i | \(0.0692804\pi\) | ||||
−0.976407 | + | 0.215937i | \(0.930720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.69543e7 | 0.783963 | 0.391982 | − | 0.919973i | \(-0.371790\pi\) | ||||
0.391982 | + | 0.919973i | \(0.371790\pi\) | |||||||
\(860\) | − | 1.94917e7i | − | 0.898675i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1.77074e7i | − | 0.811684i | ||||||
\(863\) | − | 3.28624e7i | − | 1.50201i | −0.660297 | − | 0.751005i | \(-0.729569\pi\) | ||
0.660297 | − | 0.751005i | \(-0.270431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.09595e7i | 0.498026i | ||||||||
\(866\) | −1.40156e6 | −0.0635064 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 27823.0i | − | 0.00125344i | ||||||
\(869\) | 4.11372e7i | 1.84793i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.32778e7i | 0.593038i | ||||||||
\(872\) | 3.75352e7 | 1.67166 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.31572e6 | + | 5.67292e6i | −0.102543 | + | 0.251205i | ||||
\(875\) | − | 3.66505e6i | − | 0.161830i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.51246e7 | −0.664024 | −0.332012 | − | 0.943275i | \(-0.607727\pi\) | ||||
−0.332012 | + | 0.943275i | \(0.607727\pi\) | |||||||
\(878\) | 2.04394e7i | 0.894810i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.81775e6 | −0.166188 | ||||||||
\(881\) | 4.00600e7 | 1.73889 | 0.869444 | − | 0.494032i | \(-0.164477\pi\) | ||||
0.869444 | + | 0.494032i | \(0.164477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.17336e7 | −0.938057 | −0.469028 | − | 0.883183i | \(-0.655396\pi\) | ||||
−0.469028 | + | 0.883183i | \(0.655396\pi\) | |||||||
\(884\) | −1.89340e7 | −0.814912 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.46302e7 | −1.05410 | ||||||||
\(887\) | − | 2.68081e7i | − | 1.14408i | −0.820225 | − | 0.572042i | \(-0.806152\pi\) | ||
0.820225 | − | 0.572042i | \(-0.193848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.29717e6i | − | 0.139922i | ||||||
\(890\) | − | 7.00019e6i | − | 0.296234i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.01896e6 | 0.127041 | ||||||||
\(893\) | 5.39985e6 | 0.226596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.16280e7i | 0.485230i | ||||||||
\(896\) | 2.93631e6 | 0.122189 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.29639e6 | −0.0950288 | ||||||||
\(899\) | 486960.i | 0.0200953i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.01813e7 | −0.828202 | ||||||||
\(902\) | 8.68096e6 | 0.355264 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.53654e7i | 1.03233i | ||||||||
\(905\) | 7.32571e6i | 0.297323i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.44022e6i | − | 0.0984942i | −0.998787 | − | 0.0492471i | \(-0.984318\pi\) | ||
0.998787 | − | 0.0492471i | \(-0.0156822\pi\) | |||||||
\(908\) | 1.34521e7 | 0.541473 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.60483e6 | 0.144305 | ||||||||
\(911\) | 1.03581e7 | 0.413506 | 0.206753 | − | 0.978393i | \(-0.433710\pi\) | ||||
0.206753 | + | 0.978393i | \(0.433710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.81190e7 | −3.49859 | ||||||||
\(914\) | 2.51155e6 | 0.0994434 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 2.24011e7i | − | 0.882127i | ||||||
\(917\) | 1.31993e6 | 0.0518354 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.51155e7i | − | 1.76213i | −0.472999 | − | 0.881063i | \(-0.656828\pi\) | ||
0.472999 | − | 0.881063i | \(-0.343172\pi\) | |||||||
\(920\) | 2.41450e7 | + | 9.85611e6i | 0.940496 | + | 0.383916i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.36589e7 | 0.916574 | ||||||||
\(923\) | − | 3.18582e7i | − | 1.23088i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 736426.i | − | 0.0282992i | ||||||
\(926\) | 1.52665e7i | 0.585077i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.79066e7 | −1.82610 | ||||||||
\(929\) | − | 2.31231e7i | − | 0.879038i | −0.898233 | − | 0.439519i | \(-0.855149\pi\) | ||
0.898233 | − | 0.439519i | \(-0.144851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.18521e7i | − | 0.448148i | ||||||
\(932\) | − | 1.91179e7i | − | 0.720942i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 6.82844e6i | − | 0.256126i | ||||||
\(935\) | −4.85125e7 | −1.81478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.04682e7i | 1.50579i | 0.658139 | + | 0.752896i | \(0.271344\pi\) | ||||
−0.658139 | + | 0.752896i | \(0.728656\pi\) | |||||||
\(938\) | − | 1.16119e6i | − | 0.0430920i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 9.09106e6i | − | 0.335579i | ||||||
\(941\) | −3.52131e7 | −1.29637 | −0.648186 | − | 0.761482i | \(-0.724472\pi\) | ||||
−0.648186 | + | 0.761482i | \(0.724472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.94134e6 | + | 3.24170e6i | 0.290813 | + | 0.118712i | ||||
\(944\) | 2.63165e6i | 0.0961164i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.09293e7 | −1.48698 | ||||||||
\(947\) | 2.02835e7i | 0.734966i | 0.930030 | + | 0.367483i | \(0.119780\pi\) | ||||
−0.930030 | + | 0.367483i | \(0.880220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.33521e7 | 1.56259 | ||||||||
\(950\) | 686576. | 0.0246820 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.18605e6 | 0.149697 | ||||||||
\(953\) | 2.40451e7 | 0.857618 | 0.428809 | − | 0.903395i | \(-0.358933\pi\) | ||||
0.428809 | + | 0.903395i | \(0.358933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.62564e7 | 0.576789 | ||||||||
\(956\) | 2.70248e7i | 0.956351i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.12564e7i | 0.396264i | ||||||||
\(959\) | 1.14403e6i | 0.0401688i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86255e7 | −0.999874 | ||||||||
\(962\) | −7.23818e6 | −0.252169 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.40281e7i | 0.486189i | ||||||||
\(965\) | 2.92457e7 | 1.01098 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.51724e6 | −0.292909 | −0.146454 | − | 0.989217i | \(-0.546786\pi\) | ||||
−0.146454 | + | 0.989217i | \(0.546786\pi\) | |||||||
\(968\) | 7.66018e7i | 2.62755i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.61883e7 | −0.893670 | ||||||||
\(971\) | 2.04367e7 | 0.695604 | 0.347802 | − | 0.937568i | \(-0.386928\pi\) | ||||
0.347802 | + | 0.937568i | \(0.386928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.84128e6i | 0.0623501i | ||||||||
\(974\) | − | 6.86316e6i | − | 0.231807i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.42765e6i | 0.115179i | ||||||||
\(977\) | 2.06610e7 | 0.692491 | 0.346245 | − | 0.938144i | \(-0.387456\pi\) | ||||
0.346245 | + | 0.938144i | \(0.387456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.78365e7 | 0.928233 | ||||||||
\(980\) | −1.99539e7 | −0.663686 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.22991e6 | 0.106884 | ||||||||
\(983\) | 2.99382e7 | 0.988192 | 0.494096 | − | 0.869407i | \(-0.335499\pi\) | ||||
0.494096 | + | 0.869407i | \(0.335499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.96158e6i | 0.195781i | ||||||||
\(986\) | −2.89806e7 | −0.949324 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.27793e7i | 0.416500i | ||||||||
\(989\) | −3.74421e7 | − | 1.52841e7i | −1.21722 | − | 0.496877i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.61416e7 | 1.81594 | 0.907968 | − | 0.419040i | \(-0.137633\pi\) | ||||
0.907968 | + | 0.419040i | \(0.137633\pi\) | |||||||
\(992\) | 355673.i | 0.0114755i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.78610e6i | 0.0894399i | ||||||||
\(995\) | 3.50598e7i | 1.12267i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14679e7 | −1.32122 | −0.660609 | − | 0.750730i | \(-0.729702\pi\) | ||||
−0.660609 | + | 0.750730i | \(0.729702\pi\) | |||||||
\(998\) | − | 1.45278e7i | − | 0.461716i | ||||||
\(999\) | 0 | 0 |
(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 | 207.6.c.a.206.10 | yes | 40 | |
3.2 | odd | 2 | inner | 207.6.c.a.206.31 | yes | 40 | |
23.22 | odd | 2 | inner | 207.6.c.a.206.32 | yes | 40 | |
69.68 | even | 2 | inner | 207.6.c.a.206.9 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
207.6.c.a.206.9 | ✓ | 40 | 69.68 | even | 2 | inner | |
207.6.c.a.206.10 | yes | 40 | 1.1 | even | 1 | trivial | |
207.6.c.a.206.31 | yes | 40 | 3.2 | odd | 2 | inner | |
207.6.c.a.206.32 | yes | 40 | 23.22 | odd | 2 | inner |