Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,7,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not 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: | \(69.9364414204\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5090x^{6} + 8905881x^{4} + 5831691048x^{2} + 827887219200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.6 | ||
Root | \(38.1507i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.7.e.c.113.3 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 38.1507i | 1.41299i | 0.707719 | + | 0.706494i | \(0.249724\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 102.472 | 0.819777 | 0.409888 | − | 0.912136i | \(-0.365568\pi\) | ||||
0.409888 | + | 0.912136i | \(0.365568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −512.609 | −1.49449 | −0.747243 | − | 0.664551i | \(-0.768623\pi\) | ||||
−0.747243 | + | 0.664551i | \(0.768623\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −726.473 | −0.996533 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2416.13 | −1.81528 | −0.907638 | − | 0.419754i | \(-0.862116\pi\) | ||||
−0.907638 | + | 0.419754i | \(0.862116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3771.60i | 1.71671i | 0.513059 | + | 0.858353i | \(0.328512\pi\) | ||||
−0.513059 | + | 0.858353i | \(0.671488\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3909.38i | 1.15833i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1567.21 | 0.318993 | 0.159497 | − | 0.987198i | \(-0.449013\pi\) | ||||
0.159497 | + | 0.987198i | \(0.449013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2736.35 | + | 6289.54i | 0.398942 | + | 0.916976i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 19556.4i | − | 2.11169i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 626.209 | 0.0514678 | 0.0257339 | − | 0.999669i | \(-0.491808\pi\) | ||||
0.0257339 | + | 0.999669i | \(0.491808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5124.47 | −0.327966 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 96.4222i | 0.00489875i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 15705.3i | − | 0.643948i | −0.946748 | − | 0.321974i | \(-0.895654\pi\) | ||
0.946748 | − | 0.321974i | \(-0.104346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 26199.8i | − | 0.879454i | −0.898131 | − | 0.439727i | \(-0.855075\pi\) | ||
0.898131 | − | 0.439727i | \(-0.144925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 92177.0i | − | 2.56496i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −52528.1 | −1.22515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 49488.8i | − | 0.977015i | −0.872560 | − | 0.488508i | \(-0.837541\pi\) | ||
0.872560 | − | 0.488508i | \(-0.162459\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −143889. | −2.42568 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 119758.i | 1.73761i | 0.495155 | + | 0.868805i | \(0.335111\pi\) | ||||
−0.495155 | + | 0.868805i | \(0.664889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13335.4 | 0.167726 | 0.0838628 | − | 0.996477i | \(-0.473274\pi\) | ||||
0.0838628 | + | 0.996477i | \(0.473274\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −74443.2 | −0.816935 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 186343. | 1.79482 | 0.897408 | − | 0.441201i | \(-0.145447\pi\) | ||||
0.897408 | + | 0.441201i | \(0.145447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 145119. | 1.23349 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 59790.3i | 0.450734i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 204595.i | − | 1.37425i | −0.726537 | − | 0.687127i | \(-0.758872\pi\) | ||
0.726537 | − | 0.687127i | \(-0.241128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −247586. | −1.48812 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −239950. | + | 104393.i | −1.29568 | + | 0.563701i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 18264.5i | − | 0.0889306i | −0.999011 | − | 0.0444653i | \(-0.985842\pi\) | ||
0.999011 | − | 0.0444653i | \(-0.0141584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −353270. | −1.55639 | −0.778193 | − | 0.628025i | \(-0.783864\pi\) | ||||
−0.778193 | + | 0.628025i | \(0.783864\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 372396. | 1.48930 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 386484.i | 1.40732i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 519557.i | − | 1.72746i | −0.503952 | − | 0.863732i | \(-0.668121\pi\) | ||
0.503952 | − | 0.863732i | \(-0.331879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23890.3i | 0.0727234i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 268077.i | − | 0.749004i | −0.927226 | − | 0.374502i | \(-0.877814\pi\) | ||
0.927226 | − | 0.374502i | \(-0.122186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58589.5 | 0.150609 | 0.0753045 | − | 0.997161i | \(-0.476007\pi\) | ||||
0.0753045 | + | 0.997161i | \(0.476007\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 195502.i | − | 0.463412i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.23853e6 | 2.71290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 473406.i | 0.960179i | 0.877219 | + | 0.480090i | \(0.159396\pi\) | ||||
−0.877219 | + | 0.480090i | \(0.840604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −533277. | −1.00345 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −127056. | −0.222208 | −0.111104 | − | 0.993809i | \(-0.535439\pi\) | ||||
−0.111104 | + | 0.993809i | \(0.535439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 160596. | 0.261503 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 599166. | 0.909891 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 607216.i | − | 0.861337i | −0.902510 | − | 0.430669i | \(-0.858278\pi\) | ||
0.902510 | − | 0.430669i | \(-0.141722\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.93336e6i | − | 2.56559i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 999541. | 1.24266 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 280399. | + | 644502.i | 0.327044 | + | 0.751716i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 282195.i | 0.309196i | 0.987977 | + | 0.154598i | \(0.0494083\pi\) | ||||
−0.987977 | + | 0.154598i | \(0.950592\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.75525e6 | 1.80898 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 443149. | 0.430116 | 0.215058 | − | 0.976601i | \(-0.431006\pi\) | ||||
0.215058 | + | 0.976601i | \(0.431006\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 836042.i | 0.765097i | 0.923935 | + | 0.382549i | \(0.124954\pi\) | ||||
−0.923935 | + | 0.382549i | \(0.875046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.00398e6i | − | 1.73111i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 617387.i | − | 0.503972i | −0.967731 | − | 0.251986i | \(-0.918916\pi\) | ||
0.967731 | − | 0.251986i | \(-0.0810836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 955640.i | − | 0.737929i | −0.929443 | − | 0.368965i | \(-0.879712\pi\) | ||
0.929443 | − | 0.368965i | \(-0.120288\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.88803e6 | 1.38051 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 262850.i | − | 0.182168i | −0.995843 | − | 0.0910842i | \(-0.970967\pi\) | ||
0.995843 | − | 0.0910842i | \(-0.0290333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64169.0 | 0.0421921 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.73997e6i | − | 1.71075i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −803368. | −0.476731 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.06613e6 | 2.29523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.56884e6 | −2.45522 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.12624e6 | −1.08864 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 933464.i | 0.455708i | 0.973695 | + | 0.227854i | \(0.0731709\pi\) | ||||
−0.973695 | + | 0.227854i | \(0.926829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 508753.i | 0.236994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.46381e6 | 0.651135 | 0.325568 | − | 0.945519i | \(-0.394445\pi\) | ||||
0.325568 | + | 0.945519i | \(0.394445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.40267e6 | − | 3.22407e6i | −0.596214 | − | 1.37041i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9880.58i | 0.00401589i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.07931e6 | 0.419743 | 0.209871 | − | 0.977729i | \(-0.432695\pi\) | ||||
0.209871 | + | 0.977729i | \(0.432695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.79160e6 | −1.03946 | −0.519731 | − | 0.854330i | \(-0.673968\pi\) | ||||
−0.519731 | + | 0.854330i | \(0.673968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.10912e6i | 2.53605i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 9.11270e6i | − | 3.11630i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.60935e6i | − | 0.527894i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.53638e6i | 1.74290i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47423e6 | −0.445662 | −0.222831 | − | 0.974857i | \(-0.571530\pi\) | ||||
−0.222831 | + | 0.974857i | \(0.571530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.70643e6i | 1.07653i | 0.842776 | + | 0.538264i | \(0.180920\pi\) | ||||
−0.842776 | + | 0.538264i | \(0.819080\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.13854e6 | −0.317887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.68475e6i | − | 0.720956i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 517298. | 0.133673 | 0.0668363 | − | 0.997764i | \(-0.478709\pi\) | ||||
0.0668363 | + | 0.997764i | \(0.478709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.80543e6 | 1.94180 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −321000. | −0.0769180 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.07611e6 | −0.710296 | −0.355148 | − | 0.934810i | \(-0.615570\pi\) | ||||
−0.355148 | + | 0.934810i | \(0.615570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 9.44557e6i | − | 2.10270i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.20302e6i | − | 0.687717i | −0.939021 | − | 0.343859i | \(-0.888266\pi\) | ||
0.939021 | − | 0.343859i | \(-0.111734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.39819e6 | −1.94708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.98788e6 | − | 4.56918e6i | −0.397559 | − | 0.913797i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.52360e6i | 0.487395i | 0.969851 | + | 0.243698i | \(0.0783605\pi\) | ||||
−0.969851 | + | 0.243698i | \(0.921640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62685e6 | 0.490141 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 696802. | 0.125658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.68706e6i | − | 1.34030i | −0.742227 | − | 0.670149i | \(-0.766230\pi\) | ||
0.742227 | − | 0.670149i | \(-0.233770\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.05055e6i | 0.514449i | 0.966352 | + | 0.257225i | \(0.0828081\pi\) | ||||
−0.966352 | + | 0.257225i | \(0.917192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.34775e7i | − | 2.19915i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.07122e6i | − | 0.800934i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.78660e6 | −0.579061 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 49426.9i | − | 0.00732112i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.01067e7 | 1.45047 | 0.725234 | − | 0.688503i | \(-0.241732\pi\) | ||||
0.725234 | + | 0.688503i | \(0.241732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.57566e6i | 0.358275i | 0.983824 | + | 0.179138i | \(0.0573307\pi\) | ||||
−0.983824 | + | 0.179138i | \(0.942669\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.47446e7 | −1.98852 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −333309. | −0.0435962 | −0.0217981 | − | 0.999762i | \(-0.506939\pi\) | ||||
−0.0217981 | + | 0.999762i | \(0.506939\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.52584e6 | 1.20877 | 0.604385 | − | 0.796692i | \(-0.293419\pi\) | ||||
0.604385 | + | 0.796692i | \(0.293419\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.98214e7 | 2.44088 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.05065e6i | 0.962372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22718e7i | 1.42445i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −454924. | −0.0512894 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.61137e6 | − | 1.51964e7i | −0.724191 | − | 1.66456i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.87152e6i | 0.837937i | 0.908001 | + | 0.418969i | \(0.137608\pi\) | ||||
−0.908001 | + | 0.418969i | \(0.862392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.02273e7 | 1.05833 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.36650e6 | 0.137498 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.34303e7i | 1.31433i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.23523e6i | 0.212809i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.91091e6i | 0.547618i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.47262e7i | 1.32793i | 0.747762 | + | 0.663967i | \(0.231128\pi\) | ||||
−0.747762 | + | 0.663967i | \(0.768872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.72279e6 | 0.326829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.49958e6i | − | 0.641150i | −0.947223 | − | 0.320575i | \(-0.896124\pi\) | ||
0.947223 | − | 0.320575i | \(-0.103876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.68862e6 | 0.473697 | 0.236848 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236848 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.72508e7i | 3.83330i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.88368e7 | −1.48916 | −0.744578 | − | 0.667536i | \(-0.767349\pi\) | ||||
−0.744578 | + | 0.667536i | \(0.767349\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.90950e7 | 1.47135 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.80607e7 | −1.35672 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.34352e6 | −0.611161 | −0.305581 | − | 0.952166i | \(-0.598851\pi\) | ||||
−0.305581 | + | 0.952166i | \(0.598851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.05537e7i | − | 0.753970i | −0.926219 | − | 0.376985i | \(-0.876961\pi\) | ||
0.926219 | − | 0.376985i | \(-0.123039\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 2.02746e7i | − | 1.41297i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.48706e7 | 1.01119 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.37217e7 | + | 1.03204e7i | −1.57418 | + | 0.684867i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.84726e6i | − | 0.313977i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.91869e6 | 0.121335 | 0.0606673 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606673 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.51300e6 | −0.0934283 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.12683e6i | 0.369501i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62596e7i | 0.957877i | 0.877848 | + | 0.478938i | \(0.158978\pi\) | ||||
−0.877848 | + | 0.478938i | \(0.841022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.53684e7i | 1.46014i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14094e7i | 0.641716i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.66631e6 | 0.366453 | 0.183226 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183226 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.09653e7i | − | 1.12658i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.31657e7 | 1.21706 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.25023e7i | 1.15603i | 0.816025 | + | 0.578016i | \(0.196173\pi\) | ||||
−0.816025 | + | 0.578016i | \(0.803827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.63688e7 | −1.32490 | −0.662448 | − | 0.749108i | \(-0.730483\pi\) | ||||
−0.662448 | + | 0.749108i | \(0.730483\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.37589e7 | 3.62515 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.23814e7 | 0.595349 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.95860e7 | −1.39203 | −0.696013 | − | 0.718030i | \(-0.745044\pi\) | ||||
−0.696013 | + | 0.718030i | \(0.745044\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.90335e7i | 0.876405i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.14941e7i | 0.518029i | 0.965873 | + | 0.259015i | \(0.0833978\pi\) | ||||
−0.965873 | + | 0.259015i | \(0.916602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.92088e7 | −1.72991 | −0.864957 | − | 0.501846i | \(-0.832655\pi\) | ||||
−0.864957 | + | 0.501846i | \(0.832655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.45882e7 | + | 1.06974e7i | −1.06216 | + | 0.462109i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.13889e7i | − | 2.59683i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.16814e7 | −0.898243 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07659e7 | −0.436891 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.81821e6i | 0.231306i | 0.993290 | + | 0.115653i | \(0.0368960\pi\) | ||||
−0.993290 | + | 0.115653i | \(0.963104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.87160e6i | − | 0.0729033i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 232969.i | − | 0.00889259i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.36181e6i | 0.0883552i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.83583e6 | −0.250664 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.69064e7i | 0.607748i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.62003e7 | −1.27589 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.09554e7i | − | 0.724236i | −0.932132 | − | 0.362118i | \(-0.882054\pi\) | ||
0.932132 | − | 0.362118i | \(-0.117946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.18956e7 | −1.08107 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.79502e7 | −0.929189 | −0.464594 | − | 0.885524i | \(-0.653800\pi\) | ||||
−0.464594 | + | 0.885524i | \(0.653800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.47351e7 | 0.480528 | 0.240264 | − | 0.970708i | \(-0.422766\pi\) | ||||
0.240264 | + | 0.970708i | \(0.422766\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.81602e7 | 1.22090 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.55764e7i | 1.11682i | 0.829564 | + | 0.558411i | \(0.188589\pi\) | ||||
−0.829564 | + | 0.558411i | \(0.811411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.79460e7i | 1.16894i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.35537e7 | 0.712106 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.28844e6 | + | 9.85706e6i | 0.127260 | + | 0.292509i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.93275e7i | − | 0.563021i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.64583e7 | 1.04268 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.55212e7 | −2.68233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.77022e7i | − | 1.31539i | −0.753285 | − | 0.657694i | \(-0.771532\pi\) | ||
0.753285 | − | 0.657694i | \(-0.228468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.59522e7i | 0.973628i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.32401e7i | − | 1.41613i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.64803e7i | − | 1.21445i | −0.794530 | − | 0.607225i | \(-0.792283\pi\) | ||
0.794530 | − | 0.607225i | \(-0.207717\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00279e7 | 0.257402 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.33022e7i | 1.59645i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.40812e7 | −0.348946 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.44809e6i | 0.0596170i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.43540e7 | −1.30090 | −0.650448 | − | 0.759550i | \(-0.725419\pi\) | ||||
−0.650448 | + | 0.759550i | \(0.725419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.19672e7 | 0.752018 | 0.376009 | − | 0.926616i | \(-0.377296\pi\) | ||||
0.376009 | + | 0.926616i | \(0.377296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −363666. | −0.00840972 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.94618e7 | 0.442444 | 0.221222 | − | 0.975224i | \(-0.428995\pi\) | ||||
0.221222 | + | 0.975224i | \(0.428995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.74704e7i | − | 0.614016i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.06490e7i | − | 0.673615i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.12905e6 | −0.175694 | −0.0878469 | − | 0.996134i | \(-0.527999\pi\) | ||||
−0.0878469 | + | 0.996134i | \(0.527999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.20707e7 | + | 3.44207e7i | −0.681690 | + | 0.731641i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.55126e8i | 3.24313i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00379e6 | 0.123466 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.45918e7 | −1.91362 | −0.956809 | − | 0.290716i | \(-0.906107\pi\) | ||||
−0.956809 | + | 0.290716i | \(0.906107\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.70008e7i | − | 1.73159i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.04877e8i | 2.05380i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.41683e7i | − | 0.273018i | −0.990639 | − | 0.136509i | \(-0.956412\pi\) | ||
0.990639 | − | 0.136509i | \(-0.0435882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 8.11175e7i | − | 1.53823i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.92340e7 | 1.10547 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.66625e6i | − | 0.104083i | −0.998645 | − | 0.0520413i | \(-0.983427\pi\) | ||
0.998645 | − | 0.0520413i | \(-0.0165727\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.56123e7 | −0.643909 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.42138e7i | − | 1.49895i | −0.662034 | − | 0.749474i | \(-0.730306\pi\) | ||
0.662034 | − | 0.749474i | \(-0.269694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.26915e8 | 2.22398 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.68778e6 | −0.167144 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.89837e7 | 0.322501 | 0.161251 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161251 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 981404. | 0.0164179 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.58454e7i | 0.920046i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.85109e7i | 0.787133i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.79727e7 | −0.447057 | −0.223528 | − | 0.974697i | \(-0.571758\pi\) | ||||
−0.223528 | + | 0.974697i | \(0.571758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.23000e8 | − | 5.35130e7i | 1.93637 | − | 0.842443i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.08568e7i | 1.40904i | 0.709682 | + | 0.704522i | \(0.248839\pi\) | ||||
−0.709682 | + | 0.704522i | \(0.751161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.88154e7 | 1.50977 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.46460e7 | −0.822609 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.19571e8i | 1.77355i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.73970e7i | − | 1.42356i | −0.702403 | − | 0.711780i | \(-0.747889\pi\) | ||
0.702403 | − | 0.711780i | \(-0.252111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.11763e7i | 0.593091i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.36253e6i | 0.132906i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.30197e7 | −0.182161 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.06501e8i | − | 1.46875i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.44767e7 | 0.604631 | 0.302316 | − | 0.953208i | \(-0.402240\pi\) | ||||
0.302316 | + | 0.953208i | \(0.402240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.49965e7i | − | 1.13908i | −0.821963 | − | 0.569541i | \(-0.807121\pi\) | ||
0.821963 | − | 0.569541i | \(-0.192879\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.35373e8 | −1.78859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.03114e6 | −0.104619 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.81089e8 | 2.32600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.47655e8 | 4.40329 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.20089e8i | 1.49993i | 0.661476 | + | 0.749966i | \(0.269930\pi\) | ||||
−0.661476 | + | 0.749966i | \(0.730070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.72220e7i | − | 0.704854i | −0.935839 | − | 0.352427i | \(-0.885356\pi\) | ||
0.935839 | − | 0.352427i | \(-0.114644\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.13978e7 | 0.745907 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.71352e6 | + | 3.93857e6i | 0.0205327 | + | 0.0471948i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.39003e7i | − | 0.518889i | −0.965758 | − | 0.259444i | \(-0.916461\pi\) | ||
0.965758 | − | 0.259444i | \(-0.0835394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05425e8 | −1.22921 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.04729e7 | −0.810608 | −0.405304 | − | 0.914182i | \(-0.632834\pi\) | ||||
−0.405304 | + | 0.914182i | \(0.632834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.22227e7i | − | 0.706105i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.62428e7i | − | 0.629715i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.26837e8i | − | 1.40122i | −0.713543 | − | 0.700611i | \(-0.752911\pi\) | ||
0.713543 | − | 0.700611i | \(-0.247089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.89351e8i | − | 3.15424i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.41403e8 | −1.52112 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.98115e8i | − | 2.10321i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.93303e7 | −0.202530 | −0.101265 | − | 0.994859i | \(-0.532289\pi\) | ||||
−0.101265 | + | 0.994859i | \(0.532289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 151114.i | 0.00156267i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.62945e7 | −0.676667 | −0.338333 | − | 0.941026i | \(-0.609863\pi\) | ||||
−0.338333 | + | 0.941026i | \(0.609863\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.57206e7 | 0.259142 | 0.129571 | − | 0.991570i | \(-0.458640\pi\) | ||||
0.129571 | + | 0.991570i | \(0.458640\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.02425e8 | 1.01870 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.14641e7 | −0.603491 | −0.301745 | − | 0.953389i | \(-0.597569\pi\) | ||||
−0.301745 | + | 0.953389i | \(0.597569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.66330e8i | 2.58167i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.97353e7i | 0.188878i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.22200e7 | −0.304468 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.40223e7 | − | 3.22305e7i | −0.130840 | − | 0.300737i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.48633e8i | 1.36949i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.28933e8 | −1.17316 | −0.586581 | − | 0.809890i | \(-0.699527\pi\) | ||||
−0.586581 | + | 0.809890i | \(0.699527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.86652e8 | 1.67725 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.22464e7i | − | 0.108684i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.89171e7i | 0.253472i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.30778e8i | 1.13227i | 0.824314 | + | 0.566133i | \(0.191561\pi\) | ||||
−0.824314 | + | 0.566133i | \(0.808439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.17356e8i | − | 1.00364i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.59776e8 | 1.34980 | 0.674898 | − | 0.737911i | \(-0.264188\pi\) | ||||
0.674898 | + | 0.737911i | \(0.264188\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.46135e7i | − | 0.205415i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.79865e8 | 1.48296 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37419e8i | 1.11938i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.75200e7 | −0.784860 | −0.392430 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392430 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.22197e8 | 0.971736 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.63836e8 | 1.28738 | 0.643690 | − | 0.765286i | \(-0.277403\pi\) | ||||
0.643690 | + | 0.765286i | \(0.277403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.54104e7 | 0.352599 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.58547e8i | − | 2.75120i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.33348e8i | − | 1.01119i | −0.862771 | − | 0.505594i | \(-0.831273\pi\) | ||
0.862771 | − | 0.505594i | \(-0.168727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00335e7 | −0.225083 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −606451. | + | 263844.i | −0.00449204 | + | 0.00195432i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.56710e7i | 0.627209i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50230e8 | −3.25809 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.62768e7 | −0.688684 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.78512e8i | − | 1.26228i | −0.775669 | − | 0.631139i | \(-0.782588\pi\) | ||
0.775669 | − | 0.631139i | \(-0.217412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.67427e8i | 1.17036i | 0.810902 | + | 0.585181i | \(0.198977\pi\) | ||||
−0.810902 | + | 0.585181i | \(0.801023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00216e8i | 0.692562i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.10607e7i | − | 0.280540i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.47644e8 | −0.997351 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.32686e7i | 0.0886223i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.51679e8 | −2.98297 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.32649e7i | − | 0.413144i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.93266e8 | 1.89382 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.50626e8 | −2.23912 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.01782e8 | −0.642808 | −0.321404 | − | 0.946942i | \(-0.604155\pi\) | ||||
−0.321404 | + | 0.946942i | \(0.604155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16381e8 | −0.726911 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.79264e7i | − | 0.604937i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.32682e8i | − | 1.42168i | −0.703354 | − | 0.710840i | \(-0.748315\pi\) | ||
0.703354 | − | 0.710840i | \(-0.251685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.56641e8 | 1.55099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.87788e7 | − | 4.29750e7i | 0.590485 | − | 0.256898i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.42672e8i | − | 1.43497i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.93470e8 | 1.13171 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.88543e7 | −0.572045 | −0.286022 | − | 0.958223i | \(-0.592333\pi\) | ||||
−0.286022 | + | 0.958223i | \(0.592333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.02957e7i | 0.287936i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.44461e8i | − | 0.818206i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.96849e8i | − | 1.66345i | −0.555187 | − | 0.831726i | \(-0.687353\pi\) | ||
0.555187 | − | 0.831726i | \(-0.312647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.69348e7i | − | 0.149338i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.73363e8 | 1.49965 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.25877e8i | − | 1.22613i | −0.790034 | − | 0.613063i | \(-0.789937\pi\) | ||
0.790034 | − | 0.613063i | \(-0.210063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.34657e8 | −0.723303 | −0.361652 | − | 0.932313i | \(-0.617787\pi\) | ||||
−0.361652 | + | 0.932313i | \(0.617787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.85576e8i | 2.04949i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.20899e6 | −0.0168797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.22386e8 | 0.637097 | 0.318549 | − | 0.947907i | \(-0.396805\pi\) | ||||
0.318549 | + | 0.947907i | \(0.396805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.82631e7 | −0.506238 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.51298e7 | 0.332087 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.94328e8i | 2.49465i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.80770e8i | − | 1.40244i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.54883e8 | −1.75457 | −0.877285 | − | 0.479970i | \(-0.840647\pi\) | ||||
−0.877285 | + | 0.479970i | \(0.840647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.64785e8 | − | 7.16918e7i | 0.806439 | − | 0.350852i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.27160e7i | − | 0.0616009i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.36642e8 | 1.61437 | 0.807186 | − | 0.590297i | \(-0.200989\pi\) | ||||
0.807186 | + | 0.590297i | \(0.200989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.23228e7 | −0.390813 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.63417e8i | 1.70798i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.74144e7i | − | 0.267141i | −0.991039 | − | 0.133571i | \(-0.957356\pi\) | ||
0.991039 | − | 0.133571i | \(-0.0426443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.19611e7i | − | 0.0550994i | −0.999620 | − | 0.0275497i | \(-0.991230\pi\) | ||
0.999620 | − | 0.0275497i | \(-0.00877045\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.77444e8i | 1.72147i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.16665e8 | 1.88157 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.53084e8i | − | 1.13161i | −0.824538 | − | 0.565807i | \(-0.808565\pi\) | ||
0.824538 | − | 0.565807i | \(-0.191435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.07138e8 | −1.35982 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.02813e8i | 3.08117i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.80487e7 | 0.208593 | 0.104297 | − | 0.994546i | \(-0.466741\pi\) | ||||
0.104297 | + | 0.994546i | \(0.466741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.68179e8 | −2.01273 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50367e8 | −0.640174 | −0.320087 | − | 0.947388i | \(-0.603712\pi\) | ||||
−0.320087 | + | 0.947388i | \(0.603712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.30454e8 | 0.971657 | 0.485828 | − | 0.874054i | \(-0.338518\pi\) | ||||
0.485828 | + | 0.874054i | \(0.338518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 60380.5i | 0.000252128i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.11264e8i | 1.28726i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.37811e8 | −0.564472 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.79751e8 | − | 2.52228e8i | 2.35201 | − | 1.02327i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.75595e7i | − | 0.311661i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.64740e8 | 1.05374 | 0.526868 | − | 0.849947i | \(-0.323366\pi\) | ||||
0.526868 | + | 0.849947i | \(0.323366\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.00304e8 | −1.18399 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.56540e7i | 0.373579i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.47331e8i | 2.11754i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.94751e8i | 0.746408i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.39436e8i | 0.909108i | 0.890719 | + | 0.454554i | \(0.150201\pi\) | ||||
−0.890719 | + | 0.454554i | \(0.849799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.28913e8 | −1.23722 | −0.618611 | − | 0.785697i | \(-0.712304\pi\) | ||||
−0.618611 | + | 0.785697i | \(0.712304\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.21330e7i | 0.194282i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.24926e8 | 0.830476 | 0.415238 | − | 0.909713i | \(-0.363698\pi\) | ||||
0.415238 | + | 0.909713i | \(0.363698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.41294e7i | 0.161434i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.12373e8 | −1.85714 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.25975e8 | 0.811560 | 0.405780 | − | 0.913971i | \(-0.367000\pi\) | ||||
0.405780 | + | 0.913971i | \(0.367000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.50000e8 | 0.533786 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.25637e7 | −0.150087 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.30068e8i | 1.15331i | 0.816987 | + | 0.576656i | \(0.195643\pi\) | ||||
−0.816987 | + | 0.576656i | \(0.804357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.67503e8i | 1.27250i | 0.771484 | + | 0.636248i | \(0.219515\pi\) | ||||
−0.771484 | + | 0.636248i | \(0.780485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.25505e8 | −0.773777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.43735e8 | − | 3.30378e8i | −0.488762 | − | 1.12343i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.83477e6i | − | 0.0331426i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.61815e8 | −1.87635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.53547e8 | 2.82527 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.21489e8i | 1.05468i | 0.849654 | + | 0.527340i | \(0.176811\pi\) | ||||
−0.849654 | + | 0.527340i | \(0.823189\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 494112.i | − | 0.00160662i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.83480e8i | − | 1.23588i | −0.786225 | − | 0.617941i | \(-0.787967\pi\) | ||
0.786225 | − | 0.617941i | \(-0.212033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.44656e8i | − | 0.462090i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.86114e8 | 0.905936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.83834e7i | 0.277401i | 0.990334 | + | 0.138701i | \(0.0442926\pi\) | ||||
−0.990334 | + | 0.138701i | \(0.955707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10599e8 | 0.344095 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.17025e8i | 0.669328i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.71651e8 | 2.35919 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24144e8 | 0.376262 | 0.188131 | − | 0.982144i | \(-0.439757\pi\) | ||||
0.188131 | + | 0.982144i | \(0.439757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.99759e8 | −2.70350 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.86061e8 | −0.852127 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.87686e8i | 0.554286i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 7.18637e8i | − | 2.10416i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.26176e8 | 0.656588 | 0.328294 | − | 0.944576i | \(-0.393526\pi\) | ||||
0.328294 | + | 0.944576i | \(0.393526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.11261e8 | − | 1.35418e8i | 0.895900 | − | 0.389773i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.28486e8i | 2.07900i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.27162e8 | −0.642802 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.83198e8 | 1.35577 | 0.677886 | − | 0.735167i | \(-0.262896\pi\) | ||||
0.677886 | + | 0.735167i | \(0.262896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.43916e8i | − | 0.956851i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.64066e7i | − | 0.0452636i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 9.33797e8i | − | 2.55467i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.18311e8i | − | 0.863563i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.11946e8 | −0.839253 | −0.419627 | − | 0.907697i | \(-0.637839\pi\) | ||||
−0.419627 | + | 0.907697i | \(0.637839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.28563e8i | − | 1.14343i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.02631e8 | 1.06535 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.04811e7i | 0.211193i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.30234e8 | 0.338938 | 0.169469 | − | 0.985535i | \(-0.445795\pi\) | ||||
0.169469 | + | 0.985535i | \(0.445795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.84730e8 | 0.993054 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08994e7 | 0.0535034 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.90792e8 | 0.484448 | 0.242224 | − | 0.970220i | \(-0.422123\pi\) | ||||
0.242224 | + | 0.970220i | \(0.422123\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.67324e8i | 1.42879i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.25532e9i | 3.13582i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.48582e8 | −1.11150 | −0.555749 | − | 0.831350i | \(-0.687568\pi\) | ||||
−0.555749 | + | 0.831350i | \(0.687568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.93731e8 | − | 9.04997e8i | −0.967708 | − | 2.22429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.16076e8i | 0.526794i | 0.964687 | + | 0.263397i | \(0.0848430\pi\) | ||||
−0.964687 | + | 0.263397i | \(0.915157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.51067e8 | −0.365344 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.23024e7 | 0.221438 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.16478e8i | 0.753179i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.56034e8i | − | 0.368383i | −0.982890 | − | 0.184191i | \(-0.941033\pi\) | ||
0.982890 | − | 0.184191i | \(-0.0589667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.31994e7i | 0.171444i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.79806e8i | 0.882512i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.85982e8 | −1.12030 | −0.560148 | − | 0.828393i | \(-0.689256\pi\) | ||||
−0.560148 | + | 0.828393i | \(0.689256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.77221e7i | − | 0.132013i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.11783e8 | −0.934360 | −0.467180 | − | 0.884162i | \(-0.654730\pi\) | ||||
−0.467180 | + | 0.884162i | \(0.654730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89869e8i | 1.10282i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.16668e8 | −0.260597 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.88864e7 | 0.152668 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.85308e7 | 0.0627386 | 0.0313693 | − | 0.999508i | \(-0.490013\pi\) | ||||
0.0313693 | + | 0.999508i | \(0.490013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.20313e8 | −1.35347 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.67394e8i | 1.44492i | 0.691413 | + | 0.722460i | \(0.256989\pi\) | ||||
−0.691413 | + | 0.722460i | \(0.743011\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.34260e8i | 0.288431i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.67820e8 | −2.06315 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.53221e8 | + | 3.27699e8i | −1.59335 | + | 0.693206i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.47709e8i | 1.35965i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.51433e6 | 0.00315454 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.30087e7 | 0.109582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.31663e8i | 0.680413i | 0.940351 | + | 0.340206i | \(0.110497\pi\) | ||||
−0.940351 | + | 0.340206i | \(0.889503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.54324e8i | 0.517793i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.34739e8i | 0.272248i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.33240e9i | − | 2.67186i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.99839e8 | 1.59185 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.09251e7i | − | 0.0215799i | −0.999942 | − | 0.0107900i | \(-0.996565\pi\) | ||
0.999942 | − | 0.0107900i | \(-0.00343462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.92040e8 | 0.572535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.41126e8i | 0.858351i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.41560e8 | −0.273397 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.28936e7 | −0.0630556 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.58478e8 | −1.63346 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.74089e8 | −1.46199 | −0.730997 | − | 0.682381i | \(-0.760945\pi\) | ||||
−0.730997 | + | 0.682381i | \(0.760945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.16901e8i | 0.594102i | 0.954862 | + | 0.297051i | \(0.0960031\pi\) | ||||
−0.954862 | + | 0.297051i | \(0.903997\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.00599e9i | − | 1.87206i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.15216e8 | −0.582285 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.64902e7 | + | 8.38733e7i | 0.0669129 | + | 0.153800i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.40453e9i | 2.55670i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.01886e8 | −0.184113 | −0.0920567 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920567 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.89000e8 | −0.339050 | −0.169525 | − | 0.985526i | \(-0.554223\pi\) | ||||
−0.169525 | + | 0.985526i | \(0.554223\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.72358e8i | 0.841220i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.96997e8i | − | 0.348291i | −0.984720 | − | 0.174146i | \(-0.944284\pi\) | ||
0.984720 | − | 0.174146i | \(-0.0557163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.54314e8i | − | 1.14848i | −0.818688 | − | 0.574239i | \(-0.805298\pi\) | ||
0.818688 | − | 0.574239i | \(-0.194702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.12873e9i | − | 1.96691i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.27432e8 | 0.393475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.28220e8i | − | 0.563775i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.52624e6 | 0.00430823 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.25960e8i | 1.56786i | 0.620852 | + | 0.783928i | \(0.286787\pi\) | ||||
−0.620852 | + | 0.783928i | \(0.713213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.48168e8 | 0.585331 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.38506e8 | −0.731969 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.63052e8 | −1.59617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.08434e9 | −3.43018 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.49584e9i | − | 2.44435i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.09903e7i | − | 0.0502849i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.08485e9 | 1.74793 | 0.873963 | − | 0.485993i | \(-0.161542\pi\) | ||||
0.873963 | + | 0.485993i | \(0.161542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.03702e8 | − | 4.68213e8i | −0.325910 | − | 0.749110i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 5.87373e7i | − | 0.0933192i | −0.998911 | − | 0.0466596i | \(-0.985142\pi\) | ||
0.998911 | − | 0.0466596i | \(-0.0148576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.00505e9 | 1.58566 | 0.792828 | − | 0.609446i | \(-0.208608\pi\) | ||||
0.792828 | + | 0.609446i | \(0.208608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.34203e9 | 3.66929 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.11029e9i | − | 1.72745i | −0.503963 | − | 0.863725i | \(-0.668125\pi\) | ||
0.503963 | − | 0.863725i | \(-0.331875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.58598e8i | 0.399556i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.27160e8i | − | 1.26921i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.14381e9i | − | 1.74299i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.95956e9 | 2.96555 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.05007e8i | − | 0.308124i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.08993e9 | 1.62695 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.01362e7i | − | 0.0891532i | −0.999006 | − | 0.0445766i | \(-0.985806\pi\) | ||
0.999006 | − | 0.0445766i | \(-0.0141939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.21969e8 | −0.326832 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.07347e8 | 1.03444 | 0.517220 | − | 0.855853i | \(-0.326967\pi\) | ||||
0.517220 | + | 0.855853i | \(0.326967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66827e8 | −0.242317 | −0.121159 | − | 0.992633i | \(-0.538661\pi\) | ||||
−0.121159 | + | 0.992633i | \(0.538661\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.14028e7 | 0.103011 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.94226e8i | 0.708198i | 0.935208 | + | 0.354099i | \(0.115212\pi\) | ||||
−0.935208 | + | 0.354099i | \(0.884788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.78502e8i | − | 0.681049i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.28847e9 | 1.82155 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.09900e8 | + | 1.17201e9i | 0.716028 | + | 1.64580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.87709e8i | − | 1.09874i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.01047e7 | −0.124845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.11475e8 | −0.566323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.20644e8i | − | 0.438378i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.60791e8i | − | 0.354185i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12596e8i | 0.421734i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.07109e9i | − | 1.43551i | −0.696297 | − | 0.717754i | \(-0.745170\pi\) | ||
0.696297 | − | 0.717754i | \(-0.254830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.21935e8 | −0.428625 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.35204e9i | 1.78828i | 0.447788 | + | 0.894140i | \(0.352212\pi\) | ||||
−0.447788 | + | 0.894140i | \(0.647788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.06983e8 | 0.403369 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.38107e9i | − | 1.80282i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.50362e8 | −0.973113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.68790e8 | 0.603994 | 0.301997 | − | 0.953309i | \(-0.402347\pi\) | ||||
0.301997 | + | 0.953309i | \(0.402347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.99461e8 | 1.02334 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.01108e9 | 1.28582 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53604e8i | 0.320428i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 6.07362e8i | − | 0.762445i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.00888e8 | −0.998906 | −0.499453 | − | 0.866341i | \(-0.666466\pi\) | ||||
−0.499453 | + | 0.866341i | \(0.666466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.97095e8 | + | 9.12730e8i | 0.492091 | + | 1.13108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.06632e9i | − | 1.31293i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.88021e8 | −0.474701 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10661e9 | −1.34516 | −0.672582 | − | 0.740023i | \(-0.734815\pi\) | ||||
−0.672582 | + | 0.740023i | \(0.734815\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.62152e8i | 0.678980i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.80204e8i | − | 0.336284i | −0.985763 | − | 0.168142i | \(-0.946223\pi\) | ||
0.985763 | − | 0.168142i | \(-0.0537766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.49934e7i | 0.0894310i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.06487e6i | − | 0.00600169i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.65023e8 | −0.783045 | −0.391522 | − | 0.920169i | \(-0.628051\pi\) | ||||
−0.391522 | + | 0.920169i | \(0.628051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.20976e8i | 0.258552i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.35726e9 | −1.57806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.34859e8i | 0.502423i | 0.967932 | + | 0.251212i | \(0.0808290\pi\) | ||||
−0.967932 | + | 0.251212i | \(0.919171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.03565e9 | 1.18906 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.44766e9 | −1.65170 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.53262e8 | −0.627300 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.01073e8 | 0.226560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.48515e8i | 0.502224i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.63933e8i | 0.293706i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.10495e9 | 1.22198 | 0.610991 | − | 0.791637i | \(-0.290771\pi\) | ||||
0.610991 | + | 0.791637i | \(0.290771\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.76053e8 | + | 1.63607e8i | −0.413312 | + | 0.179817i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.04768e8i | − | 0.660588i | −0.943878 | − | 0.330294i | \(-0.892852\pi\) | ||
0.943878 | − | 0.330294i | \(-0.107148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.43100e9 | 1.55346 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.37355e8 | 0.795542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 7.39173e8i | − | 0.792616i | −0.918118 | − | 0.396308i | \(-0.870291\pi\) | ||
0.918118 | − | 0.396308i | \(-0.129709\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.46711e9i | 1.56357i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.94246e8i | 0.735371i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.51347e9i | − | 1.59336i | −0.604403 | − | 0.796679i | \(-0.706588\pi\) | ||
0.604403 | − | 0.796679i | \(-0.293412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.41549e7 | −0.0357392 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.64420e9i | − | 3.79010i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.35073e6 | 0.00863248 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.25442e8i | 0.642638i | 0.946971 | + | 0.321319i | \(0.104126\pi\) | ||||
−0.946971 | + | 0.321319i | \(0.895874\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.81987e9 | 1.85863 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.76133e8 | 0.990922 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.76728e8 | −0.380139 | −0.190070 | − | 0.981771i | \(-0.560871\pi\) | ||||
−0.190070 | + | 0.981771i | \(0.560871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.77181e6 | 0.00478616 |
(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 | 304.7.e.c.113.6 | 8 | ||
4.3 | odd | 2 | 76.7.c.b.37.3 | ✓ | 8 | ||
12.11 | even | 2 | 684.7.h.c.37.4 | 8 | |||
19.18 | odd | 2 | inner | 304.7.e.c.113.3 | 8 | ||
76.75 | even | 2 | 76.7.c.b.37.6 | yes | 8 | ||
228.227 | odd | 2 | 684.7.h.c.37.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.c.b.37.3 | ✓ | 8 | 4.3 | odd | 2 | ||
76.7.c.b.37.6 | yes | 8 | 76.75 | even | 2 | ||
304.7.e.c.113.3 | 8 | 19.18 | odd | 2 | inner | ||
304.7.e.c.113.6 | 8 | 1.1 | even | 1 | trivial | ||
684.7.h.c.37.3 | 8 | 228.227 | odd | 2 | |||
684.7.h.c.37.4 | 8 | 12.11 | even | 2 |