Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{86}, \sqrt{134})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 110x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 392) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.15111\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −2.30222 | −0.147687 | −0.0738437 | − | 0.997270i | \(-0.523527\pi\) | ||||
−0.0738437 | + | 0.997270i | \(0.523527\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −81.0956 | −1.45068 | −0.725341 | − | 0.688390i | \(-0.758318\pi\) | ||||
−0.725341 | + | 0.688390i | \(0.758318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −237.700 | −0.978188 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 732.099 | 1.82427 | 0.912133 | − | 0.409894i | \(-0.134434\pi\) | ||||
0.912133 | + | 0.409894i | \(0.134434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −919.678 | −1.50931 | −0.754653 | − | 0.656124i | \(-0.772195\pi\) | ||||
−0.754653 | + | 0.656124i | \(0.772195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 186.700 | 0.214247 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1728.85 | −1.45089 | −0.725446 | − | 0.688279i | \(-0.758366\pi\) | ||||
−0.725446 | + | 0.688279i | \(0.758366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2443.34 | −1.55275 | −0.776373 | − | 0.630274i | \(-0.782943\pi\) | ||||
−0.776373 | + | 0.630274i | \(0.782943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2424.30 | −0.955579 | −0.477789 | − | 0.878474i | \(-0.658562\pi\) | ||||
−0.477789 | + | 0.878474i | \(0.658562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3451.50 | 1.10448 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1106.68 | 0.292153 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1010.00 | 0.223011 | 0.111506 | − | 0.993764i | \(-0.464433\pi\) | ||||
0.111506 | + | 0.993764i | \(0.464433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6128.04 | 1.14530 | 0.572648 | − | 0.819802i | \(-0.305916\pi\) | ||||
0.572648 | + | 0.819802i | \(0.305916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1685.45 | −0.269421 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1238.60 | −0.148739 | −0.0743696 | − | 0.997231i | \(-0.523694\pi\) | ||||
−0.0743696 | + | 0.997231i | \(0.523694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2117.30 | 0.222906 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15388.6 | −1.42968 | −0.714841 | − | 0.699287i | \(-0.753501\pi\) | ||||
−0.714841 | + | 0.699287i | \(0.753501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12980.9 | −1.07062 | −0.535308 | − | 0.844657i | \(-0.679804\pi\) | ||||
−0.535308 | + | 0.844657i | \(0.679804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19276.4 | 1.41904 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6557.64 | −0.433015 | −0.216507 | − | 0.976281i | \(-0.569467\pi\) | ||||
−0.216507 | + | 0.976281i | \(0.569467\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3980.19 | 0.214278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31549.8 | −1.54279 | −0.771395 | − | 0.636357i | \(-0.780441\pi\) | ||||
−0.771395 | + | 0.636357i | \(0.780441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −59370.0 | −2.64643 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5625.11 | 0.229321 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −21881.4 | −0.818362 | −0.409181 | − | 0.912453i | \(-0.634186\pi\) | ||||
−0.409181 | + | 0.912453i | \(0.634186\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27003.0 | −0.929153 | −0.464577 | − | 0.885533i | \(-0.653793\pi\) | ||||
−0.464577 | + | 0.885533i | \(0.653793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 74581.9 | 2.18952 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8264.07 | −0.224909 | −0.112455 | − | 0.993657i | \(-0.535871\pi\) | ||||
−0.112455 | + | 0.993657i | \(0.535871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5581.26 | 0.141127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −17131.8 | −0.403327 | −0.201664 | − | 0.979455i | \(-0.564635\pi\) | ||||
−0.201664 | + | 0.979455i | \(0.564635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9282.54 | −0.203873 | −0.101937 | − | 0.994791i | \(-0.532504\pi\) | ||||
−0.101937 | + | 0.994791i | \(0.532504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7946.10 | −0.163118 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39144.8 | −0.705678 | −0.352839 | − | 0.935684i | \(-0.614784\pi\) | ||||
−0.352839 | + | 0.935684i | \(0.614784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 55213.2 | 0.935041 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 108829. | 1.73399 | 0.866997 | − | 0.498313i | \(-0.166047\pi\) | ||||
0.866997 | + | 0.498313i | \(0.166047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 140202. | 2.10478 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2325.24 | −0.0329359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17842.6 | 0.238772 | 0.119386 | − | 0.992848i | \(-0.461907\pi\) | ||||
0.119386 | + | 0.992848i | \(0.461907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14108.1 | −0.169146 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 198144. | 2.25254 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 26643.9 | 0.287520 | 0.143760 | − | 0.989613i | \(-0.454081\pi\) | ||||
0.143760 | + | 0.989613i | \(0.454081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −174020. | −1.78448 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −125773. | −1.22683 | −0.613416 | − | 0.789760i | \(-0.710205\pi\) | ||||
−0.613416 | + | 0.789760i | \(0.710205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42069.8 | 0.390731 | 0.195365 | − | 0.980731i | \(-0.437411\pi\) | ||||
0.195365 | + | 0.980731i | \(0.437411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −88464.9 | −0.746984 | −0.373492 | − | 0.927633i | \(-0.621840\pi\) | ||||
−0.373492 | + | 0.927633i | \(0.621840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56483.8 | −0.455363 | −0.227681 | − | 0.973736i | \(-0.573114\pi\) | ||||
−0.227681 | + | 0.973736i | \(0.573114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2851.52 | 0.0219669 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7649.01 | 0.0563520 | 0.0281760 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281760 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 196600. | 1.38624 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 218607. | 1.47639 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 374918. | 2.32795 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35427.9 | 0.211146 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −26477.5 | −0.151566 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −239070. | −1.31527 | −0.657636 | − | 0.753336i | \(-0.728444\pi\) | ||||
−0.657636 | + | 0.753336i | \(0.728444\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 29884.9 | 0.158116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 195792. | 0.996818 | 0.498409 | − | 0.866942i | \(-0.333918\pi\) | ||||
0.498409 | + | 0.866942i | \(0.333918\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −89746.6 | −0.423822 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −35505.9 | −0.161622 | −0.0808109 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808109 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 116321. | 0.510646 | 0.255323 | − | 0.966856i | \(-0.417818\pi\) | ||||
0.255323 | + | 0.966856i | \(0.417818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15097.1 | 0.0639508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −673296. | −2.75338 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −81906.6 | −0.323518 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 441169. | 1.62794 | 0.813971 | − | 0.580905i | \(-0.197301\pi\) | ||||
0.813971 | + | 0.580905i | \(0.197301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 139896. | 0.499302 | 0.249651 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249651 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 410947. | 1.41925 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −496957. | −1.66146 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 224372. | 0.726474 | 0.363237 | − | 0.931697i | \(-0.381671\pi\) | ||||
0.363237 | + | 0.931697i | \(0.381671\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 72634.5 | 0.227851 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 506920. | 1.49441 | 0.747206 | − | 0.664592i | \(-0.231395\pi\) | ||||
0.747206 | + | 0.664592i | \(0.231395\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 136683. | 0.390844 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −200404. | −0.556053 | −0.278026 | − | 0.960573i | \(-0.589680\pi\) | ||||
−0.278026 | + | 0.960573i | \(0.589680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 474515. | 1.27801 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 580782. | 1.51888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −447074. | −1.13570 | −0.567851 | − | 0.823131i | \(-0.692225\pi\) | ||||
−0.567851 | + | 0.823131i | \(0.692225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 50375.8 | 0.120862 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 503571. | 1.17470 | 0.587352 | − | 0.809332i | \(-0.300170\pi\) | ||||
0.587352 | + | 0.809332i | \(0.300170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −33323.4 | −0.0756054 | −0.0378027 | − | 0.999285i | \(-0.512036\pi\) | ||||
−0.0378027 | + | 0.999285i | \(0.512036\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 62166.8 | 0.137224 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 100445. | 0.215773 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26569e6 | −2.64681 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 241698. | 0.479390 | 0.239695 | − | 0.970848i | \(-0.422953\pi\) | ||||
0.239695 | + | 0.970848i | \(0.422953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 306901. | 0.593068 | 0.296534 | − | 0.955022i | \(-0.404169\pi\) | ||||
0.296534 | + | 0.955022i | \(0.404169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −171704. | −0.323365 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −335701. | −0.616293 | −0.308147 | − | 0.951339i | \(-0.599709\pi\) | ||||
−0.308147 | + | 0.951339i | \(0.599709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −89682.8 | −0.160538 | −0.0802688 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802688 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19025.7 | 0.0332162 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.24795e6 | 2.07401 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 576255. | 0.934736 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.78877e6 | −2.83262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 883193. | 1.36568 | 0.682841 | − | 0.730567i | \(-0.260744\pi\) | ||||
0.682841 | + | 0.730567i | \(0.260744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 39441.2 | 0.0595664 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.05269e6 | 1.55312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21370.4 | 0.0301095 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.58999e6 | 2.18984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −550430. | −0.741208 | −0.370604 | − | 0.928791i | \(-0.620849\pi\) | ||||
−0.370604 | + | 0.928791i | \(0.620849\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −820420. | −1.08039 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.25332e6 | 1.61435 | 0.807173 | − | 0.590315i | \(-0.200997\pi\) | ||||
0.807173 | + | 0.590315i | \(0.200997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 357868. | 0.450956 | 0.225478 | − | 0.974248i | \(-0.427606\pi\) | ||||
0.225478 | + | 0.974248i | \(0.427606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −771152. | −0.930572 | −0.465286 | − | 0.885160i | \(-0.654049\pi\) | ||||
−0.465286 | + | 0.885160i | \(0.654049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 531795. | 0.628167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 90119.9 | 0.104220 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.49577e6 | −1.69384 | −0.846918 | − | 0.531723i | \(-0.821545\pi\) | ||||
−0.846918 | + | 0.531723i | \(0.821545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −891400. | −0.988622 | −0.494311 | − | 0.869285i | \(-0.664580\pi\) | ||||
−0.494311 | + | 0.869285i | \(0.664580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −396035. | −0.430247 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24709e6 | 2.34357 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −250547. | −0.256089 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.36229e6 | 1.36485 | 0.682425 | − | 0.730956i | \(-0.260926\pi\) | ||||
0.682425 | + | 0.730956i | \(0.260926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.77483e6 | −1.74323 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −322776. | −0.310850 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −144356. | −0.136333 | −0.0681667 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681667 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −240077. | −0.218147 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −827054. | −0.737300 | −0.368650 | − | 0.929568i | \(-0.620180\pi\) | ||||
−0.368650 | + | 0.929568i | \(0.620180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.55855e6 | 2.23810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −41077.7 | −0.0352637 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.13644e6 | 0.957558 | 0.478779 | − | 0.877935i | \(-0.341079\pi\) | ||||
0.478779 | + | 0.877935i | \(0.341079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −580417. | −0.480084 | −0.240042 | − | 0.970763i | \(-0.577161\pi\) | ||||
−0.240042 | + | 0.970763i | \(0.577161\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.52684e6 | 2.01486 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 789917. | 0.618560 | 0.309280 | − | 0.950971i | \(-0.399912\pi\) | ||||
0.309280 | + | 0.950971i | \(0.399912\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.45663e6 | −1.12031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.93626e6 | −1.46284 | −0.731421 | − | 0.681927i | \(-0.761142\pi\) | ||||
−0.731421 | + | 0.681927i | \(0.761142\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.05996e6 | −1.52895 | −0.764474 | − | 0.644654i | \(-0.777001\pi\) | ||||
−0.764474 | + | 0.644654i | \(0.777001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −456172. | −0.332672 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.56907e6 | 1.10509 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −61340.1 | −0.0424631 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5616.09 | 0.00382177 | 0.00191089 | − | 0.999998i | \(-0.499392\pi\) | ||||
0.00191089 | + | 0.999998i | \(0.499392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.77449e6 | 1.18718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 810197. | 0.532966 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.22957e6 | 1.44226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 289558. | 0.181188 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18982e6 | 1.34791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.53244e6 | 0.927978 | 0.463989 | − | 0.885841i | \(-0.346418\pi\) | ||||
0.463989 | + | 0.885841i | \(0.346418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −96853.9 | −0.0577060 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −755438. | −0.442892 | −0.221446 | − | 0.975173i | \(-0.571078\pi\) | ||||
−0.221446 | + | 0.975173i | \(0.571078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.11217e6 | −0.641670 | −0.320835 | − | 0.947135i | \(-0.603964\pi\) | ||||
−0.320835 | + | 0.947135i | \(0.603964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −221462. | −0.123780 | −0.0618901 | − | 0.998083i | \(-0.519713\pi\) | ||||
−0.0618901 | + | 0.998083i | \(0.519713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 739420. | 0.406832 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 203665. | 0.110320 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.22417e6 | 2.25287 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.17427e6 | −1.66700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 130038. | 0.0672513 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.22590e6 | 0.615013 | 0.307507 | − | 0.951546i | \(-0.400505\pi\) | ||||
0.307507 | + | 0.951546i | \(0.400505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 294414. | 0.145495 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 670180. | 0.326272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −914368. | −0.438578 | −0.219289 | − | 0.975660i | \(-0.570374\pi\) | ||||
−0.219289 | + | 0.975660i | \(0.570374\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17609.7 | −0.00832247 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.48634e6 | 2.08932 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −452616. | −0.204730 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.18915e6 | 0.976005 | 0.488003 | − | 0.872842i | \(-0.337726\pi\) | ||||
0.488003 | + | 0.872842i | \(0.337726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 165745. | 0.0728411 | 0.0364205 | − | 0.999337i | \(-0.488404\pi\) | ||||
0.0364205 | + | 0.999337i | \(0.488404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.01779e6 | −0.440949 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 582347. | 0.248740 | 0.124370 | − | 0.992236i | \(-0.460309\pi\) | ||||
0.124370 | + | 0.992236i | \(0.460309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.38932e6 | 0.585100 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.92164e6 | 0.786928 | 0.393464 | − | 0.919340i | \(-0.371277\pi\) | ||||
0.393464 | + | 0.919340i | \(0.371277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.49383e6 | 1.41102 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −863144. | −0.343809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 752774. | 0.295755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.89745e6 | 0.735370 | 0.367685 | − | 0.929950i | \(-0.380150\pi\) | ||||
0.367685 | + | 0.929950i | \(0.380150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.65787e6 | 1.39850 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.67351e6 | −1.36713 | −0.683564 | − | 0.729890i | \(-0.739571\pi\) | ||||
−0.683564 | + | 0.729890i | \(0.739571\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 60956.9 | 0.0223844 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −928875. | −0.336592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.94056e6 | −1.05156 | −0.525778 | − | 0.850622i | \(-0.676226\pi\) | ||||
−0.525778 | + | 0.850622i | \(0.676226\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 550391. | 0.194249 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.24999e6 | −1.13210 | −0.566050 | − | 0.824371i | \(-0.691529\pi\) | ||||
−0.566050 | + | 0.824371i | \(0.691529\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.08556e6 | 1.04726 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.86718e6 | −1.29575 | −0.647873 | − | 0.761748i | \(-0.724341\pi\) | ||||
−0.647873 | + | 0.761748i | \(0.724341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.19125e6 | 1.38644 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −450755. | −0.147217 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.17447e6 | 1.02371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.85455e6 | −1.86431 | −0.932153 | − | 0.362064i | \(-0.882072\pi\) | ||||
−0.932153 | + | 0.362064i | \(0.882072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.54533e6 | 1.41158 | 0.705789 | − | 0.708422i | \(-0.250593\pi\) | ||||
0.705789 | + | 0.708422i | \(0.250593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.63583e6 | −1.72860 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.47755e6 | −1.35645 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −906776. | −0.271340 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31306e6 | −0.683721 | −0.341861 | − | 0.939751i | \(-0.611057\pi\) | ||||
−0.341861 | + | 0.939751i | \(0.611057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 81742.5 | 0.0238695 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.82552e6 | −2.51547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −267796. | −0.0754160 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.55278e6 | −1.82344 | −0.911718 | − | 0.410816i | \(-0.865244\pi\) | ||||
−0.911718 | + | 0.410816i | \(0.865244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.62048e6 | −0.720570 | −0.360285 | − | 0.932842i | \(-0.617321\pi\) | ||||
−0.360285 | + | 0.932842i | \(0.617321\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.55875e6 | 0.423570 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.96712e6 | −1.60248 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.55007e6 | 0.406639 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.73182e6 | 0.967671 | 0.483836 | − | 0.875159i | \(-0.339243\pi\) | ||||
0.483836 | + | 0.875159i | \(0.339243\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.49129e6 | −0.638564 | −0.319282 | − | 0.947660i | \(-0.603442\pi\) | ||||
−0.319282 | + | 0.947660i | \(0.603442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 188567. | 0.0477796 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.92339e6 | 1.48377 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.13887e6 | −1.27264 | −0.636322 | − | 0.771424i | \(-0.719545\pi\) | ||||
−0.636322 | + | 0.771424i | \(0.719545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.04437e6 | −0.737034 | −0.368517 | − | 0.929621i | \(-0.620134\pi\) | ||||
−0.368517 | + | 0.929621i | \(0.620134\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.44696e6 | −0.346383 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.01567e6 | −0.240427 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.03852e6 | 0.477199 | 0.238599 | − | 0.971118i | \(-0.423312\pi\) | ||||
0.238599 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12660e7 | −2.60812 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −322071. | −0.0737405 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.39673e6 | −0.312841 | −0.156420 | − | 0.987691i | \(-0.549995\pi\) | ||||
−0.156420 | + | 0.987691i | \(0.549995\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.91328e6 | −0.423883 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.37595e6 | 1.83562 | 0.917808 | − | 0.397024i | \(-0.129957\pi\) | ||||
0.917808 | + | 0.397024i | \(0.129957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.39026e6 | −1.38537 | −0.692685 | − | 0.721240i | \(-0.743572\pi\) | ||||
−0.692685 | + | 0.721240i | \(0.743572\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.14410e6 | 0.245377 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.86526e6 | −0.607955 | −0.303978 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303978 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −516554. | −0.107291 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.50330e6 | −1.95309 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.43319e6 | −1.71498 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.49938e6 | 1.50914 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.39613e6 | 1.07459 | 0.537296 | − | 0.843394i | \(-0.319446\pi\) | ||||
0.537296 | + | 0.843394i | \(0.319446\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13911e6 | 0.224493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.16070e6 | −0.417101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.10377e6 | 0.784081 | 0.392040 | − | 0.919948i | \(-0.371769\pi\) | ||||
0.392040 | + | 0.919948i | \(0.371769\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.16704e6 | −0.220706 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 320967. | 0.0600837 | 0.0300418 | − | 0.999549i | \(-0.490436\pi\) | ||||
0.0300418 | + | 0.999549i | \(0.490436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.74614e6 | −0.323565 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41122e7 | 2.58871 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.87878e6 | −0.877123 | −0.438561 | − | 0.898701i | \(-0.644512\pi\) | ||||
−0.438561 | + | 0.898701i | \(0.644512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 461374. | 0.0821219 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.03631e6 | 0.887548 | 0.443774 | − | 0.896139i | \(-0.353639\pi\) | ||||
0.443774 | + | 0.896139i | \(0.353639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.01997e7 | 1.77974 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.09244e6 | −0.188746 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.54564e6 | 0.777680 | 0.388840 | − | 0.921305i | \(-0.372876\pi\) | ||||
0.388840 | + | 0.921305i | \(0.372876\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.70399e6 | −0.453640 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.41168e6 | −0.566826 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.80084e6 | −0.789934 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.02926e6 | 0.167729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.89492e6 | −0.467242 | −0.233621 | − | 0.972328i | \(-0.575057\pi\) | ||||
−0.233621 | + | 0.972328i | \(0.575057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.14411e6 | −0.342762 | −0.171381 | − | 0.985205i | \(-0.554823\pi\) | ||||
−0.171381 | + | 0.985205i | \(0.554823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.05945e7 | −1.66170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −559122. | −0.0868695 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.20121e6 | 0.800512 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.41526e7 | 2.15783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.17411e6 | 1.08364 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.15933e6 | −0.173489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.14490e7 | 1.68180 | 0.840901 | − | 0.541189i | \(-0.182026\pi\) | ||||
0.840901 | + | 0.541189i | \(0.182026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 76717.7 | 0.0111660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.58058e6 | 0.660586 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.26051e6 | 0.894626 | 0.447313 | − | 0.894377i | \(-0.352381\pi\) | ||||
0.447313 | + | 0.894377i | \(0.352381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.41861e6 | 0.908887 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46778e6 | −0.346280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −231246. | −0.0318670 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.29773e6 | 0.450378 | 0.225189 | − | 0.974315i | \(-0.427700\pi\) | ||||
0.225189 | + | 0.974315i | \(0.427700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.19382e7 | 1.61589 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.91389e6 | 0.390901 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.69396e6 | 0.491158 | 0.245579 | − | 0.969377i | \(-0.421022\pi\) | ||||
0.245579 | + | 0.969377i | \(0.421022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −620301. | −0.0817488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.08934e7 | −1.41053 | −0.705267 | − | 0.708942i | \(-0.749173\pi\) | ||||
−0.705267 | + | 0.708942i | \(0.749173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.07769e6 | −0.780096 | −0.390048 | − | 0.920795i | \(-0.627542\pi\) | ||||
−0.390048 | + | 0.920795i | \(0.627542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −556441. | −0.0707998 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.36746e6 | −1.05542 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.98523e6 | 0.373283 | 0.186641 | − | 0.982428i | \(-0.440240\pi\) | ||||
0.186641 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −706553. | −0.0875887 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.30976e7 | −2.81446 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.77281e7 | −2.14177 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 201262. | 0.0241083 | 0.0120541 | − | 0.999927i | \(-0.496163\pi\) | ||||
0.0120541 | + | 0.999927i | \(0.496163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.49729e7 | −1.77835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 772858. | 0.0910188 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.62091e7 | 1.89288 | 0.946441 | − | 0.322877i | \(-0.104650\pi\) | ||||
0.946441 | + | 0.322877i | \(0.104650\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 206469. | 0.0237094 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.05095e6 | −0.575183 | −0.287591 | − | 0.957753i | \(-0.592855\pi\) | ||||
−0.287591 | + | 0.957753i | \(0.592855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.01246e6 | 0.678994 | 0.339497 | − | 0.940607i | \(-0.389743\pi\) | ||||
0.339497 | + | 0.940607i | \(0.389743\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.96437e6 | 0.220004 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.04042e7 | −3.37711 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.55760e6 | −1.05288 | −0.526438 | − | 0.850214i | \(-0.676473\pi\) | ||||
−0.526438 | + | 0.850214i | \(0.676473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.03092e6 | 0.653552 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.30424e7 | −1.40187 | −0.700934 | − | 0.713226i | \(-0.747233\pi\) | ||||
−0.700934 | + | 0.713226i | \(0.747233\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.87305e6 | −0.306306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.67329e6 | 0.388456 | 0.194228 | − | 0.980956i | \(-0.437780\pi\) | ||||
0.194228 | + | 0.980956i | \(0.437780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.11671e7 | −1.17142 | −0.585712 | − | 0.810519i | \(-0.699185\pi\) | ||||
−0.585712 | + | 0.810519i | \(0.699185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.68291e6 | −0.279176 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.63872e6 | −0.884605 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.11814e6 | 0.418343 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.14135e6 | 0.215804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.52709e7 | −1.52684 | −0.763418 | − | 0.645904i | \(-0.776480\pi\) | ||||
−0.763418 | + | 0.645904i | \(0.776480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.03330e6 | −0.201694 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.93875e7 | 1.90804 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.07223e6 | 0.394530 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.78973e6 | −0.364303 | −0.182152 | − | 0.983270i | \(-0.558306\pi\) | ||||
−0.182152 | + | 0.983270i | \(0.558306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.15155e7 | 1.09838 | 0.549192 | − | 0.835697i | \(-0.314936\pi\) | ||||
0.549192 | + | 0.835697i | \(0.314936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.42353e6 | −0.229377 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.75894e7 | −1.65193 | −0.825963 | − | 0.563724i | \(-0.809368\pi\) | ||||
−0.825963 | + | 0.563724i | \(0.809368\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.60194e7 | −1.49291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.79853e7 | −1.65057 | −0.825286 | − | 0.564715i | \(-0.808986\pi\) | ||||
−0.825286 | + | 0.564715i | \(0.808986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.58778e7 | −1.44607 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.20646e6 | 0.199426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.27198e7 | 1.14095 | 0.570476 | − | 0.821314i | \(-0.306759\pi\) | ||||
0.570476 | + | 0.821314i | \(0.306759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00171e7 | 1.78196 | 0.890979 | − | 0.454045i | \(-0.150020\pi\) | ||||
0.890979 | + | 0.454045i | \(0.150020\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.66049e6 | −0.323412 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.44854e6 | −0.213105 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.26721e6 | 0.109467 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.97689e7 | −1.69502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 869505. | 0.0740005 | 0.0370002 | − | 0.999315i | \(-0.488220\pi\) | ||||
0.0370002 | + | 0.999315i | \(0.488220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.81969e6 | 0.322677 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.00374e7 | 0.841689 | 0.420845 | − | 0.907133i | \(-0.361734\pi\) | ||||
0.420845 | + | 0.907133i | \(0.361734\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.88541e6 | −0.238418 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.04666e7 | −0.858525 | −0.429263 | − | 0.903180i | \(-0.641227\pi\) | ||||
−0.429263 | + | 0.903180i | \(0.641227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.87938e6 | 0.234462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −823890. | −0.0666005 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.90156e7 | 2.32854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.68589e6 | 0.612349 | 0.306175 | − | 0.951975i | \(-0.400951\pi\) | ||||
0.306175 | + | 0.951975i | \(0.400951\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.43310e6 | −0.740785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.66046e7 | 2.07431 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.77536e6 | 0.137434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.25870e6 | 0.557910 | 0.278955 | − | 0.960304i | \(-0.410012\pi\) | ||||
0.278955 | + | 0.960304i | \(0.410012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.02632e6 | 0.230954 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.22431e6 | −0.0927723 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.86619e6 | 0.214136 | 0.107068 | − | 0.994252i | \(-0.465854\pi\) | ||||
0.107068 | + | 0.994252i | \(0.465854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.30471e6 | 0.690286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.48562e7 | −1.09442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.46013e7 | 3.99428 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.44360e6 | 0.250158 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.16044e7 | −0.837147 | −0.418574 | − | 0.908183i | \(-0.637470\pi\) | ||||
−0.418574 | + | 0.908183i | \(0.637470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.05220e6 | 0.146007 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.48601e6 | 0.246311 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.19891e7 | −1.54302 | −0.771509 | − | 0.636218i | \(-0.780498\pi\) | ||||
−0.771509 | + | 0.636218i | \(0.780498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.25051e7 | −0.871499 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.24420e7 | 1.55335 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.49448e7 | −1.02738 | −0.513689 | − | 0.857976i | \(-0.671722\pi\) | ||||
−0.513689 | + | 0.857976i | \(0.671722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.05012e6 | −0.410294 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.33592e7 | −0.899850 | −0.449925 | − | 0.893066i | \(-0.648549\pi\) | ||||
−0.449925 | + | 0.893066i | \(0.648549\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.17329e6 | −0.346116 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.12788e6 | −0.473683 | −0.236842 | − | 0.971548i | \(-0.576112\pi\) | ||||
−0.236842 | + | 0.971548i | \(0.576112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.57768e7 | −2.36163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.58685e7 | −1.69617 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.67411e6 | 0.496510 | 0.248255 | − | 0.968695i | \(-0.420143\pi\) | ||||
0.248255 | + | 0.968695i | \(0.420143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.13629e6 | −0.201571 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.13450e7 | −0.724328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.39278e6 | −0.278612 | −0.139306 | − | 0.990249i | \(-0.544487\pi\) | ||||
−0.139306 | + | 0.990249i | \(0.544487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.08604e6 | 0.257453 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.78783e6 | −0.424883 | −0.212441 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212441 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.33260e7 | −2.05887 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.01239e7 | 1.23516 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.12821e6 | −0.495655 | −0.247827 | − | 0.968804i | \(-0.579717\pi\) | ||||
−0.247827 | + | 0.968804i | \(0.579717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 332339. | 0.0201347 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.55236e7 | 0.934422 | 0.467211 | − | 0.884146i | \(-0.345259\pi\) | ||||
0.467211 | + | 0.884146i | \(0.345259\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.11509e7 | 1.26495 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.75996e7 | 2.21993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.25422e7 | −0.735777 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.11774e6 | 0.0651535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.81956e7 | −1.05388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87463e7 | 1.07889 | 0.539446 | − | 0.842020i | \(-0.318634\pi\) | ||||
0.539446 | + | 0.842020i | \(0.318634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.90406e6 | 0.108890 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.48341e7 | 1.40238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.89034e6 | −0.330539 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.85929e7 | −1.03682 | −0.518408 | − | 0.855133i | \(-0.673475\pi\) | ||||
−0.518408 | + | 0.855133i | \(0.673475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.13372e7 | 0.628258 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.24119e6 | −0.233564 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.79575e6 | −0.371919 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.61633e6 | −0.141419 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.49558e6 | −0.241498 | −0.120749 | − | 0.992683i | \(-0.538530\pi\) | ||||
−0.120749 | + | 0.992683i | \(0.538530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.75509e7 | 1.47090 | 0.735452 | − | 0.677577i | \(-0.236970\pi\) | ||||
0.735452 | + | 0.677577i | \(0.236970\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.33625e6 | 0.0709023 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.11090e7 | −2.16792 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.17168e7 | 1.66239 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.25426e7 | −1.16720 | −0.583602 | − | 0.812040i | \(-0.698357\pi\) | ||||
−0.583602 | + | 0.812040i | \(0.698357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.70610e7 | −1.39266 | −0.696329 | − | 0.717723i | \(-0.745184\pi\) | ||||
−0.696329 | + | 0.717723i | \(0.745184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.81733e6 | −0.297570 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.90437e7 | 1.47668 | 0.738342 | − | 0.674426i | \(-0.235609\pi\) | ||||
0.738342 | + | 0.674426i | \(0.235609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.64956e7 | −1.33902 | −0.669511 | − | 0.742802i | \(-0.733497\pi\) | ||||
−0.669511 | + | 0.742802i | \(0.733497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.81856e6 | −0.0913535 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.62519e7 | 0.806656 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.78176e6 | 0.334602 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.65076e7 | 1.30007 | 0.650034 | − | 0.759905i | \(-0.274755\pi\) | ||||
0.650034 | + | 0.759905i | \(0.274755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.94910e7 | −0.950266 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.45769e6 | 0.216043 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.84811e7 | −1.85398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.74248e6 | 0.225806 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00273e6 | 0.142132 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78106e7 | 1.30869 | 0.654347 | − | 0.756194i | \(-0.272943\pi\) | ||||
0.654347 | + | 0.756194i | \(0.272943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.70989e7 | −2.20341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.92803e7 | −0.896732 | −0.448366 | − | 0.893850i | \(-0.647994\pi\) | ||||
−0.448366 | + | 0.893850i | \(0.647994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.43578e7 | −1.12630 | −0.563150 | − | 0.826354i | \(-0.690411\pi\) | ||||
−0.563150 | + | 0.826354i | \(0.690411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.03724e6 | −0.275938 | −0.137969 | − | 0.990437i | \(-0.544057\pi\) | ||||
−0.137969 | + | 0.990437i | \(0.544057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.62557e7 | 1.64754 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.61233e6 | −0.163207 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.86579e7 | −1.28734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.60029e6 | 0.339457 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.33325e6 | −0.281249 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.04735e7 | 1.33790 | 0.668949 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668949 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12929.5 | −0.000564428 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 398779. | 0.0173098 | 0.00865491 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865491 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.86675e6 | −0.0805721 | −0.0402860 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402860 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.08526e6 | −0.175332 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.00861e7 | 1.71074 | 0.855371 | − | 0.518015i | \(-0.173329\pi\) | ||||
0.855371 | + | 0.518015i | \(0.173329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.04216e7 | 1.70576 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.60226e7 | 0.672362 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.08374e7 | −1.70412 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.13297e6 | −0.213004 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.18932e6 | 0.255413 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.45448e7 | 2.23842 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.70238e6 | 0.109679 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.24212e7 | −1.30861 | −0.654307 | − | 0.756229i | \(-0.727040\pi\) | ||||
−0.654307 | + | 0.756229i | \(0.727040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.98963e7 | 1.20007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.27656e7 | −0.509620 | −0.254810 | − | 0.966991i | \(-0.582013\pi\) | ||||
−0.254810 | + | 0.966991i | \(0.582013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.96733e7 | 3.16327 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.04145e6 | −0.199069 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.41131e7 | −1.72297 | −0.861487 | − | 0.507780i | \(-0.830466\pi\) | ||||
−0.861487 | + | 0.507780i | \(0.830466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.52801e6 | −0.137051 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.57558e7 | 0.608745 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.27501e6 | −0.164279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.99998e6 | −0.382208 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.66127e7 | −0.631541 | −0.315770 | − | 0.948836i | \(-0.602263\pi\) | ||||
−0.315770 | + | 0.948836i | \(0.602263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.73918e6 | 0.0654096 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.02642e8 | 3.83969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.38174e7 | 1.63041 | 0.815207 | − | 0.579170i | \(-0.196623\pi\) | ||||
0.815207 | + | 0.579170i | \(0.196623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.56047e6 | 0.0947666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.59498e7 | 0.587195 | 0.293597 | − | 0.955929i | \(-0.405147\pi\) | ||||
0.293597 | + | 0.955929i | \(0.405147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.73065e7 | 1.36617 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.61841e7 | 0.948774 | 0.474387 | − | 0.880316i | \(-0.342670\pi\) | ||||
0.474387 | + | 0.880316i | \(0.342670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.53695e6 | 0.307707 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 509854. | 0.0182808 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.43052e6 | 0.336359 | 0.168180 | − | 0.985756i | \(-0.446211\pi\) | ||||
0.168180 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.96006e7 | −0.695442 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.70231e6 | −0.0600839 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.92374e6 | 0.311701 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.10281e7 | 0.730691 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.48883e7 | −0.860354 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.95159e7 | −0.671155 | −0.335578 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335578 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.72497e6 | −0.332720 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.11647e6 | −0.106075 | −0.0530377 | − | 0.998593i | \(-0.516890\pi\) | ||||
−0.0530377 | + | 0.998593i | \(0.516890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.30786e6 | 0.246195 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.42502e6 | −0.315897 | −0.157949 | − | 0.987447i | \(-0.550488\pi\) | ||||
−0.157949 | + | 0.987447i | \(0.550488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.30626e7 | 0.435585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.34262e7 | 0.445430 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.87703e7 | −0.619566 | −0.309783 | − | 0.950807i | \(-0.600256\pi\) | ||||
−0.309783 | + | 0.950807i | \(0.600256\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.72239e7 | 0.894046 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.14696e7 | 1.02306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.53382e7 | 0.819581 | 0.409791 | − | 0.912180i | \(-0.365602\pi\) | ||||
0.409791 | + | 0.912180i | \(0.365602\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.82229e6 | −0.0908297 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.27288e6 | 0.232889 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.56262e6 | −0.177232 | −0.0886158 | − | 0.996066i | \(-0.528244\pi\) | ||||
−0.0886158 | + | 0.996066i | \(0.528244\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.37072e6 | −0.0434547 |
(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 | 784.6.a.be.1.2 | 4 | ||
4.3 | odd | 2 | 392.6.a.g.1.3 | yes | 4 | ||
7.6 | odd | 2 | inner | 784.6.a.be.1.3 | 4 | ||
28.3 | even | 6 | 392.6.i.n.177.3 | 8 | |||
28.11 | odd | 6 | 392.6.i.n.177.2 | 8 | |||
28.19 | even | 6 | 392.6.i.n.361.3 | 8 | |||
28.23 | odd | 6 | 392.6.i.n.361.2 | 8 | |||
28.27 | even | 2 | 392.6.a.g.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.6.a.g.1.2 | ✓ | 4 | 28.27 | even | 2 | ||
392.6.a.g.1.3 | yes | 4 | 4.3 | odd | 2 | ||
392.6.i.n.177.2 | 8 | 28.11 | odd | 6 | |||
392.6.i.n.177.3 | 8 | 28.3 | even | 6 | |||
392.6.i.n.361.2 | 8 | 28.23 | odd | 6 | |||
392.6.i.n.361.3 | 8 | 28.19 | even | 6 | |||
784.6.a.be.1.2 | 4 | 1.1 | even | 1 | trivial | ||
784.6.a.be.1.3 | 4 | 7.6 | odd | 2 | inner |