Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,6,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(35.9259756381\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 229x^{3} - 272x^{2} + 7973x - 13998 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.24605\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.49210 | −0.159868 | −0.0799340 | − | 0.996800i | \(-0.525471\pi\) | ||||
−0.0799340 | + | 0.996800i | \(0.525471\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −99.5911 | −1.78154 | −0.890769 | − | 0.454455i | \(-0.849834\pi\) | ||||
−0.890769 | + | 0.454455i | \(0.849834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −236.789 | −0.974442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −292.685 | −0.729321 | −0.364660 | − | 0.931141i | \(-0.618815\pi\) | ||||
−0.364660 | + | 0.931141i | \(0.618815\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −163.156 | −0.267759 | −0.133879 | − | 0.990998i | \(-0.542743\pi\) | ||||
−0.133879 | + | 0.990998i | \(0.542743\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 248.190 | 0.284811 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1509.24 | −1.26659 | −0.633293 | − | 0.773912i | \(-0.718297\pi\) | ||||
−0.633293 | + | 0.773912i | \(0.718297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2117.22 | 1.34550 | 0.672748 | − | 0.739871i | \(-0.265114\pi\) | ||||
0.672748 | + | 0.739871i | \(0.265114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 122.113 | 0.0604244 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4585.65 | −1.80751 | −0.903756 | − | 0.428048i | \(-0.859201\pi\) | ||||
−0.903756 | + | 0.428048i | \(0.859201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6793.38 | 2.17388 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1195.68 | 0.315650 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 800.137 | 0.176673 | 0.0883364 | − | 0.996091i | \(-0.471845\pi\) | ||||
0.0883364 | + | 0.996091i | \(0.471845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1276.43 | −0.238557 | −0.119278 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119278 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 729.399 | 0.116595 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4879.96 | 0.673358 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9375.25 | 1.12584 | 0.562922 | − | 0.826510i | \(-0.309677\pi\) | ||||
0.562922 | + | 0.826510i | \(0.309677\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 406.599 | 0.0428060 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6583.50 | 0.611642 | 0.305821 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305821 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4935.97 | 0.407100 | 0.203550 | − | 0.979065i | \(-0.434752\pi\) | ||||
0.203550 | + | 0.979065i | \(0.434752\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 23582.1 | 1.73601 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −25847.4 | −1.70676 | −0.853379 | − | 0.521291i | \(-0.825451\pi\) | ||||
−0.853379 | + | 0.521291i | \(0.825451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3761.16 | 0.202487 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6214.40 | −0.303885 | −0.151943 | − | 0.988389i | \(-0.548553\pi\) | ||||
−0.151943 | + | 0.988389i | \(0.548553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29148.8 | 1.29931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5276.32 | −0.215102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2803.61 | 0.104855 | 0.0524273 | − | 0.998625i | \(-0.483304\pi\) | ||||
0.0524273 | + | 0.998625i | \(0.483304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −828.062 | −0.0284930 | −0.0142465 | − | 0.999899i | \(-0.504535\pi\) | ||||
−0.0142465 | + | 0.999899i | \(0.504535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11602.7 | 0.368305 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16248.8 | 0.477022 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62870.3 | −1.71103 | −0.855517 | − | 0.517774i | \(-0.826761\pi\) | ||||
−0.855517 | + | 0.517774i | \(0.826761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11427.9 | 0.288963 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 60730.6 | 1.42976 | 0.714878 | − | 0.699249i | \(-0.246482\pi\) | ||||
0.714878 | + | 0.699249i | \(0.246482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26058.6 | 0.572327 | 0.286163 | − | 0.958181i | \(-0.407620\pi\) | ||||
0.286163 | + | 0.958181i | \(0.407620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16929.7 | −0.347534 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14341.6 | 0.275657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −55359.0 | −0.997976 | −0.498988 | − | 0.866609i | \(-0.666295\pi\) | ||||
−0.498988 | + | 0.866609i | \(0.666295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 54560.1 | 0.923980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118671. | 1.89081 | 0.945405 | − | 0.325898i | \(-0.105667\pi\) | ||||
0.945405 | + | 0.325898i | \(0.105667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 150306. | 2.25647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1994.02 | −0.0282443 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 98218.5 | 1.31437 | 0.657186 | − | 0.753728i | \(-0.271747\pi\) | ||||
0.657186 | + | 0.753728i | \(0.271747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7994.62 | 0.101203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3180.98 | 0.0381376 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −210856. | −2.39705 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 106682. | 1.15123 | 0.575615 | − | 0.817721i | \(-0.304763\pi\) | ||||
0.575615 | + | 0.817721i | \(0.304763\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 69304.7 | 0.710681 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −72914.8 | −0.711234 | −0.355617 | − | 0.934632i | \(-0.615729\pi\) | ||||
−0.355617 | + | 0.934632i | \(0.615729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −116173. | −1.07897 | −0.539487 | − | 0.841994i | \(-0.681382\pi\) | ||||
−0.539487 | + | 0.841994i | \(0.681382\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12161.3 | −0.107648 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27014.4 | −0.228106 | −0.114053 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114053 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 65745.1 | 0.530026 | 0.265013 | − | 0.964245i | \(-0.414624\pi\) | ||||
0.265013 | + | 0.964245i | \(0.414624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23364.0 | −0.179987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −237242. | −1.74782 | −0.873908 | − | 0.486091i | \(-0.838422\pi\) | ||||
−0.873908 | + | 0.486091i | \(0.838422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 456690. | 3.22015 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38633.5 | 0.260915 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 73952.5 | 0.478725 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −75386.5 | −0.468091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16406.7 | −0.0977820 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −365338. | −2.09131 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −277543. | −1.52694 | −0.763469 | − | 0.645845i | \(-0.776505\pi\) | ||||
−0.763469 | + | 0.645845i | \(0.776505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12300.9 | −0.0650823 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −46802.2 | −0.238280 | −0.119140 | − | 0.992877i | \(-0.538014\pi\) | ||||
−0.119140 | + | 0.992877i | \(0.538014\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −103744. | −0.508550 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −119079. | −0.562343 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −303785. | −1.38282 | −0.691410 | − | 0.722463i | \(-0.743010\pi\) | ||||
−0.691410 | + | 0.722463i | \(0.743010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 118250. | 0.519116 | 0.259558 | − | 0.965727i | \(-0.416423\pi\) | ||||
0.259558 | + | 0.965727i | \(0.416423\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 64414.1 | 0.272856 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 47753.2 | 0.195282 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −79686.5 | −0.314749 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5983.52 | −0.0228383 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −192791. | −0.711413 | −0.355707 | − | 0.934598i | \(-0.615760\pi\) | ||||
−0.355707 | + | 0.934598i | \(0.615760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −197879. | −0.706248 | −0.353124 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353124 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 357371. | 1.23422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 127121. | 0.424999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 431399. | 1.39679 | 0.698394 | − | 0.715714i | \(-0.253899\pi\) | ||||
0.698394 | + | 0.715714i | \(0.253899\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15486.9 | 0.0485815 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 224697. | 0.683175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 220103. | 0.648868 | 0.324434 | − | 0.945908i | \(-0.394826\pi\) | ||||
0.324434 | + | 0.945908i | \(0.394826\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −72641.6 | −0.207719 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 350625. | 0.972862 | 0.486431 | − | 0.873719i | \(-0.338298\pi\) | ||||
0.486431 | + | 0.873719i | \(0.338298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −344673. | −0.928305 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −501336. | −1.31111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −618823. | −1.57200 | −0.785998 | − | 0.618229i | \(-0.787850\pi\) | ||||
−0.785998 | + | 0.618229i | \(0.787850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −332876. | −0.821650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6986.85 | −0.0167629 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 233031. | 0.543602 | 0.271801 | − | 0.962353i | \(-0.412381\pi\) | ||||
0.271801 | + | 0.962353i | \(0.412381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −336718. | −0.763960 | −0.381980 | − | 0.924171i | \(-0.624758\pi\) | ||||
−0.381980 | + | 0.924171i | \(0.624758\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2063.61 | 0.00455512 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −933691. | −2.00574 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 441731. | 0.923748 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −58588.4 | −0.119305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −186039. | −0.368996 | −0.184498 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184498 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 210636. | 0.407043 | 0.203521 | − | 0.979071i | \(-0.434761\pi\) | ||||
0.203521 | + | 0.979071i | \(0.434761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40493.6 | −0.0762606 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 579772. | 1.06437 | 0.532184 | − | 0.846629i | \(-0.321371\pi\) | ||||
0.532184 | + | 0.846629i | \(0.321371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −162586. | −0.291038 | −0.145519 | − | 0.989355i | \(-0.546485\pi\) | ||||
−0.145519 | + | 0.989355i | \(0.546485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 156679. | 0.273540 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −39206.7 | −0.0667760 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −655658. | −1.08966 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.08583e6 | 1.76132 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −619679. | −0.981299 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −663978. | −1.02671 | −0.513355 | − | 0.858176i | \(-0.671598\pi\) | ||||
−0.513355 | + | 0.858176i | \(0.671598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −151346. | −0.228572 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −491579. | −0.725265 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 62545.0 | 0.0901661 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −64940.5 | −0.0914967 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 246240. | 0.339139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −635216. | −0.855380 | −0.427690 | − | 0.903926i | \(-0.640672\pi\) | ||||
−0.427690 | + | 0.903926i | \(0.640672\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.60860e6 | −2.11832 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −833129. | −1.07312 | −0.536559 | − | 0.843863i | \(-0.680276\pi\) | ||||
−0.536559 | + | 0.843863i | \(0.680276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259565. | −0.327082 | −0.163541 | − | 0.986537i | \(-0.552292\pi\) | ||||
−0.163541 | + | 0.986537i | \(0.552292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35740.5 | −0.0440688 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.11572e6 | 1.34638 | 0.673189 | − | 0.739471i | \(-0.264924\pi\) | ||||
0.673189 | + | 0.739471i | \(0.264924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.57417e6 | 3.04066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 137960. | 0.159544 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −662116. | −0.749789 | −0.374895 | − | 0.927067i | \(-0.622321\pi\) | ||||
−0.374895 | + | 0.927067i | \(0.622321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 918955. | 1.01918 | 0.509591 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509591 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −426519. | −0.463365 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −239118. | −0.254506 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −345437. | −0.360268 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −295738. | −0.302280 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 861484. | 0.863104 | 0.431552 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431552 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34215e6 | 1.31826 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −374578. | −0.360738 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.01631e6 | 1.90425 | 0.952124 | − | 0.305713i | \(-0.0988947\pi\) | ||||
0.952124 | + | 0.305713i | \(0.0988947\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −459387. | −0.425529 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −189464. | −0.172157 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.34088e6 | 1.19536 | 0.597682 | − | 0.801733i | \(-0.296089\pi\) | ||||
0.597682 | + | 0.801733i | \(0.296089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 618899. | 0.541384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −244770. | −0.210126 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.24957e6 | 1.05288 | 0.526440 | − | 0.850212i | \(-0.323526\pi\) | ||||
0.526440 | + | 0.850212i | \(0.323526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.18725e6 | 0.982016 | 0.491008 | − | 0.871155i | \(-0.336629\pi\) | ||||
0.491008 | + | 0.871155i | \(0.336629\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19923.4 | −0.0161792 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.98832e6 | −1.58546 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 805766. | 0.630971 | 0.315486 | − | 0.948930i | \(-0.397833\pi\) | ||||
0.315486 | + | 0.948930i | \(0.397833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 302245. | 0.232460 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21309e6 | 0.916490 | 0.458245 | − | 0.888826i | \(-0.348478\pi\) | ||||
0.458245 | + | 0.888826i | \(0.348478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 196007. | 0.145481 | 0.0727403 | − | 0.997351i | \(-0.476826\pi\) | ||||
0.0727403 | + | 0.997351i | \(0.476826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 525474. | 0.383212 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −322592. | −0.231179 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 857935. | 0.604241 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −265862. | −0.184045 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.96904e6 | 1.33994 | 0.669969 | − | 0.742389i | \(-0.266307\pi\) | ||||
0.669969 | + | 0.742389i | \(0.266307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −279214. | −0.186802 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −349958. | −0.230210 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 748174. | 0.483977 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −241863. | −0.153869 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 181711. | 0.113703 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 82467.5 | 0.0507614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 445961. | 0.270054 | 0.135027 | − | 0.990842i | \(-0.456888\pi\) | ||||
0.135027 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 289513. | 0.172493 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.76254e6 | 1.03333 | 0.516664 | − | 0.856188i | \(-0.327174\pi\) | ||||
0.516664 | + | 0.856188i | \(0.327174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.43435e6 | −0.827549 | −0.413774 | − | 0.910379i | \(-0.635790\pi\) | ||||
−0.413774 | + | 0.910379i | \(0.635790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.15552e6 | −0.656149 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −983837. | −0.549889 | −0.274944 | − | 0.961460i | \(-0.588659\pi\) | ||||
−0.274944 | + | 0.961460i | \(0.588659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −234188. | −0.128851 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 67322.6 | 0.0364668 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.19539e6 | −1.70419 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.10838e6 | −0.582075 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −163843. | −0.0847341 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.26652e6 | 0.645094 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −606501. | −0.304272 | −0.152136 | − | 0.988360i | \(-0.548615\pi\) | ||||
−0.152136 | + | 0.988360i | \(0.548615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.21996e6 | −1.09707 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.26132e6 | 3.04827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50022e6 | 0.719580 | 0.359790 | − | 0.933033i | \(-0.382848\pi\) | ||||
0.359790 | + | 0.933033i | \(0.382848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 591230. | 0.279420 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 373591. | 0.173985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.13811e6 | −0.514799 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.03086e6 | −1.35127 | −0.675635 | − | 0.737236i | \(-0.736130\pi\) | ||||
−0.675635 | + | 0.737236i | \(0.736130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 294660. | 0.129496 | 0.0647482 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647482 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −195082. | −0.0845180 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −834926. | −0.356625 | −0.178312 | − | 0.983974i | \(-0.557064\pi\) | ||||
−0.178312 | + | 0.983974i | \(0.557064\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.04823e6 | −2.54717 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −184297. | −0.0765327 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.59728e6 | 0.654099 | 0.327050 | − | 0.945007i | \(-0.393946\pi\) | ||||
0.327050 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.00653e6 | 0.810361 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 187870. | 0.0748328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.59521e6 | −1.01962 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37342e6 | 0.532277 | 0.266139 | − | 0.963935i | \(-0.414252\pi\) | ||||
0.266139 | + | 0.963935i | \(0.414252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.55890e6 | −0.596010 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 304506. | 0.114858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.62695e6 | 1.72196 | 0.860980 | − | 0.508640i | \(-0.169851\pi\) | ||||
0.860980 | + | 0.508640i | \(0.169851\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 910456. | 0.334334 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −130547. | −0.0473056 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −216405. | −0.0773874 | −0.0386937 | − | 0.999251i | \(-0.512320\pi\) | ||||
−0.0386937 | + | 0.999251i | \(0.512320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 691664. | 0.244108 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.14346e6 | −1.44333 | −0.721665 | − | 0.692242i | \(-0.756623\pi\) | ||||
−0.721665 | + | 0.692242i | \(0.756623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.42829e6 | −0.491094 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.16879e6 | −0.396696 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.41596e6 | 1.14456 | 0.572280 | − | 0.820059i | \(-0.306059\pi\) | ||||
0.572280 | + | 0.820059i | \(0.306059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.92082e6 | 2.28937 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 116636. | 0.0380934 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.51326e6 | 1.77793 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.12761e6 | 1.63282 | 0.816411 | − | 0.577471i | \(-0.195960\pi\) | ||||
0.816411 | + | 0.577471i | \(0.195960\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 258540. | 0.0813008 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 65538.5 | 0.0203533 | 0.0101767 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101767 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 208256. | 0.0638757 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.43370e6 | −1.64611 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74399e6 | −0.821102 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.28095e6 | 1.56100 | 0.780501 | − | 0.625154i | \(-0.214964\pi\) | ||||
0.780501 | + | 0.625154i | \(0.214964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 757062. | 0.221069 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −137377. | −0.0396313 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18185e7 | −3.36855 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −294691. | −0.0829901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.18612e6 | 1.72141 | 0.860703 | − | 0.509107i | \(-0.170024\pi\) | ||||
0.860703 | + | 0.509107i | \(0.170024\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.52682e6 | −0.969792 | −0.484896 | − | 0.874572i | \(-0.661143\pi\) | ||||
−0.484896 | + | 0.874572i | \(0.661143\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.12039e6 | 1.66314 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.02528e7 | −2.75341 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40575.0 | 0.0107693 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −119005. | −0.0312193 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.38322e6 | −1.13658 | −0.568290 | − | 0.822828i | \(-0.692395\pi\) | ||||
−0.568290 | + | 0.822828i | \(0.692395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.55834e6 | −0.912070 | −0.456035 | − | 0.889962i | \(-0.650731\pi\) | ||||
−0.456035 | + | 0.889962i | \(0.650731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 198586. | 0.0503183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.70884e6 | −2.43200 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −512004. | −0.126798 | −0.0633990 | − | 0.997988i | \(-0.520194\pi\) | ||||
−0.0633990 | + | 0.997988i | \(0.520194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −568531. | −0.139206 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.17109e6 | −1.00981 | −0.504906 | − | 0.863174i | \(-0.668473\pi\) | ||||
−0.504906 | + | 0.863174i | \(0.668473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.78169e6 | −2.34161 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 480454. | 0.113732 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.70167e6 | −0.632435 | −0.316217 | − | 0.948687i | \(-0.602413\pi\) | ||||
−0.316217 | + | 0.948687i | \(0.602413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.92689e6 | −0.446083 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 493133. | 0.112907 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −796193. | −0.180298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.36210e6 | −0.529063 | −0.264531 | − | 0.964377i | \(-0.585217\pi\) | ||||
−0.264531 | + | 0.964377i | \(0.585217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.80456e6 | −0.399798 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.98494e6 | 1.31162 | 0.655809 | − | 0.754927i | \(-0.272328\pi\) | ||||
0.655809 | + | 0.754927i | \(0.272328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00684e6 | 1.08545 | 0.542727 | − | 0.839909i | \(-0.317392\pi\) | ||||
0.542727 | + | 0.839909i | \(0.317392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −316797. | −0.0679437 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.65286e6 | 0.350706 | 0.175353 | − | 0.984506i | \(-0.443893\pi\) | ||||
0.175353 | + | 0.984506i | \(0.443893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.08065e6 | 0.646710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.07509e6 | −0.223302 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.44468e6 | −0.296907 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.43831e7 | 2.92495 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.47151e6 | 0.296119 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.95428e6 | −1.18574 | −0.592871 | − | 0.805297i | \(-0.702006\pi\) | ||||
−0.592871 | + | 0.805297i | \(0.702006\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.52962e6 | −0.301455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −559966. | −0.109218 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.06246e7 | −2.05096 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.14901e6 | 1.17485 | 0.587426 | − | 0.809278i | \(-0.300142\pi\) | ||||
0.587426 | + | 0.809278i | \(0.300142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −548517. | −0.103733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.26140e6 | −1.17211 | −0.586054 | − | 0.810272i | \(-0.699319\pi\) | ||||
−0.586054 | + | 0.810272i | \(0.699319\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.20760e6 | −0.223771 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.90213e6 | −1.26611 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.97580e6 | −0.540397 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.10012e6 | −1.27648 | −0.638240 | − | 0.769837i | \(-0.720337\pi\) | ||||
−0.638240 | + | 0.769837i | \(0.720337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −873790. | −0.155530 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65833e6 | 0.997168 | 0.498584 | − | 0.866841i | \(-0.333854\pi\) | ||||
0.498584 | + | 0.866841i | \(0.333854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.26166e6 | 1.26709 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 858959. | 0.148406 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 607346. | 0.103906 | 0.0519532 | − | 0.998650i | \(-0.483455\pi\) | ||||
0.0519532 | + | 0.998650i | \(0.483455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.27687e6 | −0.216319 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.53152e6 | 0.424706 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.15698e7 | 1.92223 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.56514e6 | 1.24477 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.54217e6 | 0.251312 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 502953. | 0.0811770 | 0.0405885 | − | 0.999176i | \(-0.487077\pi\) | ||||
0.0405885 | + | 0.999176i | \(0.487077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.59744e6 | −1.53427 | −0.767134 | − | 0.641487i | \(-0.778318\pi\) | ||||
−0.767134 | + | 0.641487i | \(0.778318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 829557. | 0.131355 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.92643e6 | 0.302153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.45918e7 | 2.26710 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −663865. | −0.102175 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.07414e6 | −0.163772 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.69040e6 | 0.406380 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −580735. | −0.0869046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −702737. | −0.104189 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.46010e6 | 1.38964 | 0.694821 | − | 0.719183i | \(-0.255484\pi\) | ||||
0.694821 | + | 0.719183i | \(0.255484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 839134. | 0.122133 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.54762e6 | −0.944261 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.26708e6 | −0.609765 | −0.304882 | − | 0.952390i | \(-0.598617\pi\) | ||||
−0.304882 | + | 0.952390i | \(0.598617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 196076. | 0.0277648 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.69407e6 | 0.237713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.71259e6 | 0.377200 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.32685e6 | 0.320653 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.19790e7 | −1.63600 | −0.818001 | − | 0.575216i | \(-0.804918\pi\) | ||||
−0.818001 | + | 0.575216i | \(0.804918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −805331. | −0.109005 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10083e6 | −0.147678 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.63496e6 | −0.749238 | −0.374619 | − | 0.927179i | \(-0.622226\pi\) | ||||
−0.374619 | + | 0.927179i | \(0.622226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.36272e7 | 3.11380 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.67344e6 | −0.349232 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.23993e6 | −0.549008 | −0.274504 | − | 0.961586i | \(-0.588514\pi\) | ||||
−0.274504 | + | 0.961586i | \(0.588514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26701e7 | 1.62626 | 0.813129 | − | 0.582084i | \(-0.197762\pi\) | ||||
0.813129 | + | 0.582084i | \(0.197762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 463628. | 0.0589906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11520e7 | −3.92932 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.16763e6 | 0.771221 | 0.385610 | − | 0.922662i | \(-0.373991\pi\) | ||||
0.385610 | + | 0.922662i | \(0.373991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −524926. | −0.0650731 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.81486e6 | −0.714659 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.81886e6 | 0.221630 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.84755e6 | −0.464831 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.30640e6 | 1.11477 | 0.557387 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557387 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.70248e6 | −0.320978 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44485e6 | −0.170158 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.23152e6 | −1.07804 | −0.539022 | − | 0.842292i | \(-0.681206\pi\) | ||||
−0.539022 | + | 0.842292i | \(0.681206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.36501e6 | −0.852867 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 405180. | 0.0465277 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.33587e6 | 0.949257 | 0.474629 | − | 0.880186i | \(-0.342582\pi\) | ||||
0.474629 | + | 0.880186i | \(0.342582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.13490e6 | 0.692821 | 0.346411 | − | 0.938083i | \(-0.387400\pi\) | ||||
0.346411 | + | 0.938083i | \(0.387400\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.48870e7 | 1.66730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.50782e6 | 0.833922 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.03253e6 | 0.223905 | 0.111953 | − | 0.993714i | \(-0.464290\pi\) | ||||
0.111953 | + | 0.993714i | \(0.464290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 97706.9 | 0.0106753 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.21714e6 | 0.456999 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.12990e7 | 1.21448 | 0.607238 | − | 0.794520i | \(-0.292277\pi\) | ||||
0.607238 | + | 0.794520i | \(0.292277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63396e6 | 0.174202 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.42817e6 | 0.468286 | 0.234143 | − | 0.972202i | \(-0.424772\pi\) | ||||
0.234143 | + | 0.972202i | \(0.424772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.33489e6 | 0.874325 | 0.437163 | − | 0.899382i | \(-0.355983\pi\) | ||||
0.437163 | + | 0.899382i | \(0.355983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.48297e6 | −0.570541 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.81271e6 | −0.496786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.51551e7 | 1.55188 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54430e6 | 0.156878 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.41495e7 | −1.42598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.07865e6 | −0.607762 | −0.303881 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303881 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.65470e6 | 0.164138 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.76408e7 | 2.72030 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −391737. | −0.0382512 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.43804e7 | −1.39321 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.56516e7 | 1.50457 | 0.752287 | − | 0.658836i | \(-0.228951\pi\) | ||||
0.752287 | + | 0.658836i | \(0.228951\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.01616e7 | −0.969245 | −0.484623 | − | 0.874723i | \(-0.661043\pi\) | ||||
−0.484623 | + | 0.874723i | \(0.661043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.22506e6 | 0.115947 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.29888e7 | −1.21986 | −0.609930 | − | 0.792455i | \(-0.708802\pi\) | ||||
−0.609930 | + | 0.792455i | \(0.708802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −820573. | −0.0764726 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −155868. | −0.0144147 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.43248e6 | −0.590331 | −0.295166 | − | 0.955446i | \(-0.595375\pi\) | ||||
−0.295166 | + | 0.955446i | \(0.595375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.66108e6 | 0.424506 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.17041e6 | −0.557700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.44738e7 | −1.29828 | −0.649140 | − | 0.760669i | \(-0.724871\pi\) | ||||
−0.649140 | + | 0.760669i | \(0.724871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.72612e6 | −0.509750 | −0.254875 | − | 0.966974i | \(-0.582034\pi\) | ||||
−0.254875 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −613654. | −0.0542175 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.03320e7 | 0.906002 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.66915e6 | −0.319338 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.58302e6 | 0.136748 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 242361. | 0.0207805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.63951e6 | −0.565065 | −0.282533 | − | 0.959258i | \(-0.591175\pi\) | ||||
−0.282533 | + | 0.959258i | \(0.591175\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.12271e6 | 0.686186 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.60011e7 | 1.34177 | 0.670885 | − | 0.741562i | \(-0.265915\pi\) | ||||
0.670885 | + | 0.741562i | \(0.265915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.22742e6 | −0.435124 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.07624e6 | 0.171557 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.15548e7 | 1.76804 | 0.884020 | − | 0.467450i | \(-0.154827\pi\) | ||||
0.884020 | + | 0.467450i | \(0.154827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.02543e7 | 2.46355 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 646859. | 0.0522899 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.01391e6 | 0.0813679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.75267e6 | −0.458325 | −0.229163 | − | 0.973388i | \(-0.573599\pi\) | ||||
−0.229163 | + | 0.973388i | \(0.573599\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.39593e6 | −0.268612 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.17767e7 | −0.924826 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.93606e6 | −0.774697 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.78049e6 | −0.215243 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.26190e7 | 1.73851 | 0.869257 | − | 0.494360i | \(-0.164598\pi\) | ||||
0.869257 | + | 0.494360i | \(0.164598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.98495e7 | 1.51482 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.41507e6 | −0.486103 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.57283e6 | 0.268821 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.02453e7 | −0.765434 | −0.382717 | − | 0.923866i | \(-0.625012\pi\) | ||||
−0.382717 | + | 0.923866i | \(0.625012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.31084e7 | 0.972470 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.85325e6 | 0.431195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.75579e6 | −0.347902 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.65006e6 | 0.119867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 953623. | 0.0687946 | 0.0343973 | − | 0.999408i | \(-0.489049\pi\) | ||||
0.0343973 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.69246e6 | 0.407814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.29012e6 | −0.162935 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.43563e6 | 0.384065 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.15807e6 | −0.151436 | −0.0757182 | − | 0.997129i | \(-0.524125\pi\) | ||||
−0.0757182 | + | 0.997129i | \(0.524125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.21952e7 | −0.849903 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.44954e6 | −0.515628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.47257e7 | −1.01232 | −0.506158 | − | 0.862441i | \(-0.668935\pi\) | ||||
−0.506158 | + | 0.862441i | \(0.668935\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 595905. | 0.0406873 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.84012e7 | 1.24789 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.65235e7 | −1.78657 | −0.893286 | − | 0.449489i | \(-0.851606\pi\) | ||||
−0.893286 | + | 0.449489i | \(0.851606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 860861. | 0.0575954 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.35953e6 | −0.223258 | −0.111629 | − | 0.993750i | \(-0.535607\pi\) | ||||
−0.111629 | + | 0.993750i | \(0.535607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.92003e7 | 1.26741 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.80999e7 | −1.84248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.32371e6 | 0.0862160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.35689e7 | 1.52489 | 0.762446 | − | 0.647051i | \(-0.223998\pi\) | ||||
0.762446 | + | 0.647051i | \(0.223998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.14690e6 | −0.137983 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.97070e7 | 1.25821 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.80124e7 | 1.14244 | 0.571219 | − | 0.820798i | \(-0.306471\pi\) | ||||
0.571219 | + | 0.820798i | \(0.306471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.34477e6 | −0.210747 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.04944e7 | −0.656898 | −0.328449 | − | 0.944522i | \(-0.606526\pi\) | ||||
−0.328449 | + | 0.944522i | \(0.606526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.22151e6 | −0.200331 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.55910e7 | −2.19880 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −457424. | −0.0280757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.03672e7 | −1.24198 | −0.620991 | − | 0.783818i | \(-0.713270\pi\) | ||||
−0.620991 | + | 0.783818i | \(0.713270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.02482e6 | −0.304428 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.41705e7 | −0.852978 | −0.426489 | − | 0.904493i | \(-0.640250\pi\) | ||||
−0.426489 | + | 0.904493i | \(0.640250\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.67126e6 | −0.518594 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.14484e6 | 0.0680285 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.39387e7 | 0.822962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.77749e7 | −1.04275 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 956709. | 0.0557668 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.29635e7 | −2.48843 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.94138e6 | 0.111731 | 0.0558655 | − | 0.998438i | \(-0.482208\pi\) | ||||
0.0558655 | + | 0.998438i | \(0.482208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.34160e6 | −0.191100 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.16249e7 | 0.660612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135103. | 0.00762925 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.54236e6 | −0.0865499 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.44578e7 | −1.36387 | −0.681933 | − | 0.731415i | \(-0.738860\pi\) | ||||
−0.681933 | + | 0.731415i | \(0.738860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.90098e7 | 2.16176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.32571e7 | −1.28078 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.62696e6 | −0.417410 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.23778e7 | −1.21710 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.11404e6 | −0.168322 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.18414e7 | −1.17330 | −0.586651 | − | 0.809840i | \(-0.699554\pi\) | ||||
−0.586651 | + | 0.809840i | \(0.699554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.22026e6 | 0.438867 | 0.219434 | − | 0.975627i | \(-0.429579\pi\) | ||||
0.219434 | + | 0.975627i | \(0.429579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.95874e6 | −0.156993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.19203e7 | −1.15598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.04506e7 | 0.547752 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.89304e6 | −0.0986167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.77947e6 | 0.299247 | 0.149624 | − | 0.988743i | \(-0.452194\pi\) | ||||
0.149624 | + | 0.988743i | \(0.452194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.01035e7 | −1.03460 | −0.517300 | − | 0.855804i | \(-0.673063\pi\) | ||||
−0.517300 | + | 0.855804i | \(0.673063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.95508e6 | 0.253464 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.33274e7 | −0.677615 | −0.338808 | − | 0.940856i | \(-0.610024\pi\) | ||||
−0.338808 | + | 0.940856i | \(0.610024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.21926e6 | 0.364843 | 0.182422 | − | 0.983220i | \(-0.441606\pi\) | ||||
0.182422 | + | 0.983220i | \(0.441606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00805e6 | −0.100872 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.62367e6 | −0.180941 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49191e7 | −1.73319 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.52620e6 | −0.0753005 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.63257e7 | 1.78159 | 0.890797 | − | 0.454401i | \(-0.150147\pi\) | ||||
0.890797 | + | 0.454401i | \(0.150147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.98709e7 | −0.968787 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.02314e6 | −0.146517 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43264e7 | 1.65381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.69394e6 | 0.176922 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −488468. | −0.0232577 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.29916e7 | −2.03498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.39547e7 | −1.12725 | −0.563623 | − | 0.826032i | \(-0.690593\pi\) | ||||
−0.563623 | + | 0.826032i | \(0.690593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.99286e7 | 2.33579 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.22646e6 | −0.150063 | −0.0750316 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750316 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.71503e6 | 0.402983 | 0.201491 | − | 0.979490i | \(-0.435421\pi\) | ||||
0.201491 | + | 0.979490i | \(0.435421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 803929. | 0.0369581 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.23457e6 | −0.330663 | −0.165332 | − | 0.986238i | \(-0.552869\pi\) | ||||
−0.165332 | + | 0.986238i | \(0.552869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.16293e7 | 2.80057 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.13806e6 | −0.0965987 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.62027e7 | 0.727845 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.02576e7 | 0.458144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.52612e7 | −1.12181 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.79015e7 | 0.790443 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.33000e7 | −1.02295 | −0.511477 | − | 0.859297i | \(-0.670902\pi\) | ||||
−0.511477 | + | 0.859297i | \(0.670902\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.90702e6 | −0.214213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.69404e7 | 0.735333 | 0.367666 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367666 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.40145e7 | 1.46812 | 0.734060 | − | 0.679084i | \(-0.237623\pi\) | ||||
0.734060 | + | 0.679084i | \(0.237623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 695828. | 0.0298637 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.67616e7 | 1.14210 | 0.571049 | − | 0.820916i | \(-0.306537\pi\) | ||||
0.571049 | + | 0.820916i | \(0.306537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.35996e7 | 0.577128 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.59689e7 | −0.673878 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.47247e7 | −2.29644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.32078e7 | −0.968448 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.86452e6 | −0.0773724 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.02132e6 | −0.0421465 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.37900e6 | 0.384897 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 602745. | 0.0245988 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.35341e7 | 1.36102 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.76702e7 | −0.713221 | −0.356610 | − | 0.934253i | \(-0.616068\pi\) | ||||
−0.356610 | + | 0.934253i | \(0.616068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.72655e7 | 0.693056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.31389e7 | −1.72216 | −0.861079 | − | 0.508471i | \(-0.830211\pi\) | ||||
−0.861079 | + | 0.508471i | \(0.830211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.47331e7 | −1.37901 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −205517. | −0.00811512 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.29331e6 | 0.0900615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.25403e7 | 0.489800 | 0.244900 | − | 0.969548i | \(-0.421245\pi\) | ||||
0.244900 | + | 0.969548i | \(0.421245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.11138e6 | −0.0431731 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.90854e6 | −0.382829 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.36896e7 | 2.44745 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.75084e7 | 1.05140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.84854e6 | −0.298366 | −0.149183 | − | 0.988810i | \(-0.547664\pi\) | ||||
−0.149183 | + | 0.988810i | \(0.547664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.08345e6 | 0.192214 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.39242e6 | −0.165196 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.39924e7 | −1.64569 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.03129e7 | 0.383736 | 0.191868 | − | 0.981421i | \(-0.438545\pi\) | ||||
0.191868 | + | 0.981421i | \(0.438545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.57453e6 | 0.132299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.04037e6 | 0.332822 | 0.166411 | − | 0.986056i | \(-0.446782\pi\) | ||||
0.166411 | + | 0.986056i | \(0.446782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.01896e7 | −1.10555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.83488e6 | 0.212546 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.69853e7 | 1.70250 | 0.851251 | − | 0.524759i | \(-0.175845\pi\) | ||||
0.851251 | + | 0.524759i | \(0.175845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.25161e6 | −0.153245 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.45181e6 | 0.0879096 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.63875e7 | −0.941165 | −0.470582 | − | 0.882356i | \(-0.655956\pi\) | ||||
−0.470582 | + | 0.882356i | \(0.655956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.85278e7 | 0.657380 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 583619. | 0.0205992 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.48855e7 | 0.522657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.69999e7 | −0.943091 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.39674e6 | 0.222276 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.09775e7 | −0.725162 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.08697e6 | −0.140551 | −0.0702757 | − | 0.997528i | \(-0.522388\pi\) | ||||
−0.0702757 | + | 0.997528i | \(0.522388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.96321e6 | 0.272445 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.58015e7 | −0.537837 | −0.268919 | − | 0.963163i | \(-0.586666\pi\) | ||||
−0.268919 | + | 0.963163i | \(0.586666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.79426e6 | −0.196208 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.76218e6 | 0.0930552 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.78593e7 | 0.933757 | 0.466879 | − | 0.884321i | \(-0.345378\pi\) | ||||
0.466879 | + | 0.884321i | \(0.345378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.87471e7 | −0.958599 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.55677e7 | −0.516479 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.89667e7 | 0.956128 | 0.478064 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478064 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.77401e7 | −1.89621 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.15629e6 | −0.103130 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.26346e7 | −0.735839 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.98714e7 | 1.28967 | 0.644833 | − | 0.764324i | \(-0.276927\pi\) | ||||
0.644833 | + | 0.764324i | \(0.276927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.51146e6 | 0.0486433 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.61921e7 | 0.518496 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42645e7 | −0.454484 | −0.227242 | − | 0.973838i | \(-0.572971\pi\) | ||||
−0.227242 | + | 0.973838i | \(0.572971\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.12098e7 | 0.355373 |
(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 | 224.6.a.j.1.3 | yes | 5 | |
4.3 | odd | 2 | 224.6.a.i.1.3 | ✓ | 5 | ||
8.3 | odd | 2 | 448.6.a.bf.1.3 | 5 | |||
8.5 | even | 2 | 448.6.a.be.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.i.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
224.6.a.j.1.3 | yes | 5 | 1.1 | even | 1 | trivial | |
448.6.a.be.1.3 | 5 | 8.5 | even | 2 | |||
448.6.a.bf.1.3 | 5 | 8.3 | odd | 2 |