Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,6,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(79.3899908074\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 149x^{4} + 297x^{3} + 4052x^{2} - 6522x - 20692 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-10.2169\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.2169 | −1.98288 | −0.991441 | − | 0.130556i | \(-0.958324\pi\) | ||||
−0.991441 | + | 0.130556i | \(0.958324\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 93.8183 | 2.93182 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −132.518 | −1.02218 | −0.511091 | − | 0.859527i | \(-0.670759\pi\) | ||||
−0.511091 | + | 0.859527i | \(0.670759\pi\) | |||||||
\(8\) | −693.408 | −3.83057 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −280.422 | −0.886772 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −916.014 | −1.50329 | −0.751646 | − | 0.659566i | \(-0.770740\pi\) | ||||
−0.751646 | + | 0.659566i | \(0.770740\pi\) | |||||||
\(14\) | 1486.43 | 2.02687 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4775.68 | 4.66375 | ||||||||
\(17\) | 607.561 | 0.509879 | 0.254940 | − | 0.966957i | \(-0.417944\pi\) | ||||
0.254940 | + | 0.966957i | \(0.417944\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2342.75 | 1.48882 | 0.744411 | − | 0.667722i | \(-0.232731\pi\) | ||||
0.744411 | + | 0.667722i | \(0.232731\pi\) | |||||||
\(20\) | 2345.46 | 1.31115 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1357.24 | 0.597861 | ||||||||
\(23\) | −15.5282 | −0.00612072 | −0.00306036 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00306036 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 10274.8 | 2.98085 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12432.6 | −2.99686 | ||||||||
\(29\) | −837.103 | −0.184835 | −0.0924174 | − | 0.995720i | \(-0.529459\pi\) | ||||
−0.0924174 | + | 0.995720i | \(0.529459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2763.55 | 0.516492 | 0.258246 | − | 0.966079i | \(-0.416856\pi\) | ||||
0.258246 | + | 0.966079i | \(0.416856\pi\) | |||||||
\(32\) | −31379.2 | −5.41710 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6814.93 | −1.01103 | ||||||||
\(35\) | −3312.94 | −0.457134 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5914.18 | 0.710216 | 0.355108 | − | 0.934825i | \(-0.384444\pi\) | ||||
0.355108 | + | 0.934825i | \(0.384444\pi\) | |||||||
\(38\) | −26278.4 | −2.95216 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17335.2 | −1.71308 | ||||||||
\(41\) | 9477.40 | 0.880500 | 0.440250 | − | 0.897875i | \(-0.354890\pi\) | ||||
0.440250 | + | 0.897875i | \(0.354890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3470.90 | −0.286267 | −0.143133 | − | 0.989703i | \(-0.545718\pi\) | ||||
−0.143133 | + | 0.989703i | \(0.545718\pi\) | |||||||
\(44\) | −11352.0 | −0.883977 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 174.178 | 0.0121367 | ||||||||
\(47\) | 5638.78 | 0.372341 | 0.186170 | − | 0.982517i | \(-0.440392\pi\) | ||||
0.186170 | + | 0.982517i | \(0.440392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 753.904 | 0.0448566 | ||||||||
\(50\) | −7010.55 | −0.396576 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −85938.8 | −4.40739 | ||||||||
\(53\) | 10588.9 | 0.517797 | 0.258898 | − | 0.965905i | \(-0.416641\pi\) | ||||
0.258898 | + | 0.965905i | \(0.416641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 91888.7 | 3.91554 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9389.68 | 0.366506 | ||||||||
\(59\) | −29479.8 | −1.10254 | −0.551270 | − | 0.834327i | \(-0.685856\pi\) | ||||
−0.551270 | + | 0.834327i | \(0.685856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32344.0 | −1.11294 | −0.556468 | − | 0.830869i | \(-0.687844\pi\) | ||||
−0.556468 | + | 0.830869i | \(0.687844\pi\) | |||||||
\(62\) | −30998.4 | −1.02414 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 199154. | 6.07771 | ||||||||
\(65\) | −22900.3 | −0.672293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 58356.9 | 1.58820 | 0.794100 | − | 0.607787i | \(-0.207942\pi\) | ||||
0.794100 | + | 0.607787i | \(0.207942\pi\) | |||||||
\(68\) | 57000.3 | 1.49487 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 37160.8 | 0.906442 | ||||||||
\(71\) | 1075.01 | 0.0253086 | 0.0126543 | − | 0.999920i | \(-0.495972\pi\) | ||||
0.0126543 | + | 0.999920i | \(0.495972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28035.0 | 0.615734 | 0.307867 | − | 0.951429i | \(-0.400385\pi\) | ||||
0.307867 | + | 0.951429i | \(0.400385\pi\) | |||||||
\(74\) | −66338.6 | −1.40827 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 219793. | 4.36496 | ||||||||
\(77\) | 16034.6 | 0.308200 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23231.7 | 0.418806 | 0.209403 | − | 0.977829i | \(-0.432848\pi\) | ||||
0.209403 | + | 0.977829i | \(0.432848\pi\) | |||||||
\(80\) | 119392. | 2.08569 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −106307. | −1.74593 | ||||||||
\(83\) | −23943.0 | −0.381491 | −0.190745 | − | 0.981640i | \(-0.561090\pi\) | ||||
−0.190745 | + | 0.981640i | \(0.561090\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15189.0 | 0.228025 | ||||||||
\(86\) | 38932.6 | 0.567633 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 83902.3 | 1.15496 | ||||||||
\(89\) | −95010.4 | −1.27144 | −0.635721 | − | 0.771919i | \(-0.719297\pi\) | ||||
−0.635721 | + | 0.771919i | \(0.719297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 121388. | 1.53664 | ||||||||
\(92\) | −1456.83 | −0.0179449 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −63249.5 | −0.738307 | ||||||||
\(95\) | 58568.8 | 0.665821 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −33677.1 | −0.363418 | −0.181709 | − | 0.983352i | \(-0.558163\pi\) | ||||
−0.181709 | + | 0.983352i | \(0.558163\pi\) | |||||||
\(98\) | −8456.45 | −0.0889453 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 58636.4 | 0.586364 | ||||||||
\(101\) | 78905.4 | 0.769668 | 0.384834 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384834 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −56918.2 | −0.528638 | −0.264319 | − | 0.964435i | \(-0.585147\pi\) | ||||
−0.264319 | + | 0.964435i | \(0.585147\pi\) | |||||||
\(104\) | 635171. | 5.75847 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −118774. | −1.02673 | ||||||||
\(107\) | −190035. | −1.60463 | −0.802313 | − | 0.596904i | \(-0.796397\pi\) | ||||
−0.802313 | + | 0.596904i | \(0.796397\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 108794. | 0.877078 | 0.438539 | − | 0.898712i | \(-0.355496\pi\) | ||||
0.438539 | + | 0.898712i | \(0.355496\pi\) | |||||||
\(110\) | 33931.0 | 0.267372 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −632862. | −4.76720 | ||||||||
\(113\) | 208092. | 1.53306 | 0.766532 | − | 0.642207i | \(-0.221981\pi\) | ||||
0.766532 | + | 0.642207i | \(0.221981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −388.206 | −0.00273727 | ||||||||
\(116\) | −78535.5 | −0.541903 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 330671. | 2.18621 | ||||||||
\(119\) | −80512.5 | −0.521189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 362799. | 2.20682 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 259272. | 1.51426 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −308832. | −1.69908 | −0.849538 | − | 0.527527i | \(-0.823119\pi\) | ||||
−0.849538 | + | 0.527527i | \(0.823119\pi\) | |||||||
\(128\) | −1.22976e6 | −6.63429 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 256870. | 1.33308 | ||||||||
\(131\) | 63060.0 | 0.321052 | 0.160526 | − | 0.987032i | \(-0.448681\pi\) | ||||
0.160526 | + | 0.987032i | \(0.448681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −310456. | −1.52185 | ||||||||
\(134\) | −654582. | −3.14921 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −421287. | −1.95313 | ||||||||
\(137\) | 41313.4 | 0.188057 | 0.0940284 | − | 0.995570i | \(-0.470026\pi\) | ||||
0.0940284 | + | 0.995570i | \(0.470026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −257986. | −1.13256 | −0.566278 | − | 0.824214i | \(-0.691617\pi\) | ||||
−0.566278 | + | 0.824214i | \(0.691617\pi\) | |||||||
\(140\) | −310814. | −1.34023 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12058.3 | −0.0501839 | ||||||||
\(143\) | 110838. | 0.453260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20927.6 | −0.0826607 | ||||||||
\(146\) | −314465. | −1.22093 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 554858. | 2.08222 | ||||||||
\(149\) | −233787. | −0.862689 | −0.431344 | − | 0.902187i | \(-0.641961\pi\) | ||||
−0.431344 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −398038. | −1.42063 | −0.710317 | − | 0.703882i | \(-0.751448\pi\) | ||||
−0.710317 | + | 0.703882i | \(0.751448\pi\) | |||||||
\(152\) | −1.62448e6 | −5.70304 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −179858. | −0.611123 | ||||||||
\(155\) | 69088.8 | 0.230982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 283315. | 0.917318 | 0.458659 | − | 0.888612i | \(-0.348330\pi\) | ||||
0.458659 | + | 0.888612i | \(0.348330\pi\) | |||||||
\(158\) | −260587. | −0.830444 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −784479. | −2.42260 | ||||||||
\(161\) | 2057.76 | 0.00625649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −491644. | −1.44938 | −0.724688 | − | 0.689077i | \(-0.758016\pi\) | ||||
−0.724688 | + | 0.689077i | \(0.758016\pi\) | |||||||
\(164\) | 889153. | 2.58147 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 268566. | 0.756451 | ||||||||
\(167\) | 454917. | 1.26224 | 0.631118 | − | 0.775687i | \(-0.282596\pi\) | ||||
0.631118 | + | 0.775687i | \(0.282596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 467788. | 1.25989 | ||||||||
\(170\) | −170373. | −0.452146 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −325634. | −0.839282 | ||||||||
\(173\) | 275876. | 0.700807 | 0.350404 | − | 0.936599i | \(-0.386044\pi\) | ||||
0.350404 | + | 0.936599i | \(0.386044\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −82823.5 | −0.204436 | ||||||||
\(176\) | −577858. | −1.40617 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.06572e6 | 2.52112 | ||||||||
\(179\) | 19479.7 | 0.0454411 | 0.0227206 | − | 0.999742i | \(-0.492767\pi\) | ||||
0.0227206 | + | 0.999742i | \(0.492767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −542896. | −1.23174 | −0.615871 | − | 0.787847i | \(-0.711196\pi\) | ||||
−0.615871 | + | 0.787847i | \(0.711196\pi\) | |||||||
\(182\) | −1.36159e6 | −3.04697 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10767.4 | 0.0234459 | ||||||||
\(185\) | 147855. | 0.317618 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −73514.8 | −0.153734 | ||||||||
\(188\) | 529020. | 1.09164 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −656959. | −1.32024 | ||||||||
\(191\) | −242935. | −0.481845 | −0.240922 | − | 0.970544i | \(-0.577450\pi\) | ||||
−0.240922 | + | 0.970544i | \(0.577450\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −207159. | −0.400322 | −0.200161 | − | 0.979763i | \(-0.564147\pi\) | ||||
−0.200161 | + | 0.979763i | \(0.564147\pi\) | |||||||
\(194\) | 377752. | 0.720614 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 70730.0 | 0.131511 | ||||||||
\(197\) | −253518. | −0.465417 | −0.232709 | − | 0.972547i | \(-0.574759\pi\) | ||||
−0.232709 | + | 0.972547i | \(0.574759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 756118. | 1.35350 | 0.676748 | − | 0.736215i | \(-0.263389\pi\) | ||||
0.676748 | + | 0.736215i | \(0.263389\pi\) | |||||||
\(200\) | −433380. | −0.766114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −885072. | −1.52616 | ||||||||
\(203\) | 110931. | 0.188935 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 236935. | 0.393772 | ||||||||
\(206\) | 638444. | 1.04823 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.37459e6 | −7.01098 | ||||||||
\(209\) | −283473. | −0.448896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01855e6 | 1.57499 | 0.787494 | − | 0.616322i | \(-0.211378\pi\) | ||||
0.787494 | + | 0.616322i | \(0.211378\pi\) | |||||||
\(212\) | 993428. | 1.51809 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.13160e6 | 3.18178 | ||||||||
\(215\) | −86772.4 | −0.128022 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −366219. | −0.527949 | ||||||||
\(218\) | −1.22033e6 | −1.73914 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −283800. | −0.395327 | ||||||||
\(221\) | −556534. | −0.766498 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −612261. | −0.824469 | −0.412235 | − | 0.911078i | \(-0.635252\pi\) | ||||
−0.412235 | + | 0.911078i | \(0.635252\pi\) | |||||||
\(224\) | 4.15829e6 | 5.53726 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.33415e6 | −3.03988 | ||||||||
\(227\) | 625281. | 0.805398 | 0.402699 | − | 0.915332i | \(-0.368072\pi\) | ||||
0.402699 | + | 0.915332i | \(0.368072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11167e6 | 1.40083 | 0.700415 | − | 0.713736i | \(-0.252998\pi\) | ||||
0.700415 | + | 0.713736i | \(0.252998\pi\) | |||||||
\(230\) | 4354.46 | 0.00542768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 580454. | 0.708023 | ||||||||
\(233\) | −927589. | −1.11935 | −0.559675 | − | 0.828712i | \(-0.689074\pi\) | ||||
−0.559675 | + | 0.828712i | \(0.689074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 140969. | 0.166516 | ||||||||
\(236\) | −2.76574e6 | −3.23245 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 903098. | 1.03346 | ||||||||
\(239\) | 225927. | 0.255843 | 0.127921 | − | 0.991784i | \(-0.459169\pi\) | ||||
0.127921 | + | 0.991784i | \(0.459169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.32668e6 | −1.47138 | −0.735688 | − | 0.677320i | \(-0.763141\pi\) | ||||
−0.735688 | + | 0.677320i | \(0.763141\pi\) | |||||||
\(242\) | −164226. | −0.180262 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.03446e6 | −3.26293 | ||||||||
\(245\) | 18847.6 | 0.0200605 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.14599e6 | −2.23813 | ||||||||
\(248\) | −1.91627e6 | −1.97846 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −175264. | −0.177354 | ||||||||
\(251\) | −717486. | −0.718834 | −0.359417 | − | 0.933177i | \(-0.617025\pi\) | ||||
−0.359417 | + | 0.933177i | \(0.617025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1878.92 | 0.00184547 | ||||||||
\(254\) | 3.46413e6 | 3.36907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.42108e6 | 7.07730 | ||||||||
\(257\) | −716981. | −0.677135 | −0.338567 | − | 0.940942i | \(-0.609942\pi\) | ||||
−0.338567 | + | 0.940942i | \(0.609942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −783733. | −0.725970 | ||||||||
\(260\) | −2.14847e6 | −1.97104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −707336. | −0.636608 | ||||||||
\(263\) | 1.58342e6 | 1.41158 | 0.705791 | − | 0.708420i | \(-0.250592\pi\) | ||||
0.705791 | + | 0.708420i | \(0.250592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 264721. | 0.231566 | ||||||||
\(266\) | 3.48235e6 | 3.01764 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.47494e6 | 4.65632 | ||||||||
\(269\) | −148436. | −0.125072 | −0.0625359 | − | 0.998043i | \(-0.519919\pi\) | ||||
−0.0625359 | + | 0.998043i | \(0.519919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −703775. | −0.582117 | −0.291059 | − | 0.956705i | \(-0.594007\pi\) | ||||
−0.291059 | + | 0.956705i | \(0.594007\pi\) | |||||||
\(272\) | 2.90152e6 | 2.37795 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −463407. | −0.372894 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −917597. | −0.718542 | −0.359271 | − | 0.933233i | \(-0.616975\pi\) | ||||
−0.359271 | + | 0.933233i | \(0.616975\pi\) | |||||||
\(278\) | 2.89380e6 | 2.24572 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.29722e6 | 1.75108 | ||||||||
\(281\) | −2.27113e6 | −1.71584 | −0.857921 | − | 0.513782i | \(-0.828244\pi\) | ||||
−0.857921 | + | 0.513782i | \(0.828244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −576587. | −0.427956 | −0.213978 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213978 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(284\) | 100856. | 0.0742001 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.24325e6 | −0.898761 | ||||||||
\(287\) | −1.25592e6 | −0.900032 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.05073e6 | −0.740023 | ||||||||
\(290\) | 234742. | 0.163906 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.63019e6 | 1.80522 | ||||||||
\(293\) | 954488. | 0.649533 | 0.324767 | − | 0.945794i | \(-0.394714\pi\) | ||||
0.324767 | + | 0.945794i | \(0.394714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −736994. | −0.493071 | ||||||||
\(296\) | −4.10094e6 | −2.72053 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.62236e6 | 1.71061 | ||||||||
\(299\) | 14224.1 | 0.00920123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 459955. | 0.292617 | ||||||||
\(302\) | 4.46474e6 | 2.81695 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.11882e7 | 6.94349 | ||||||||
\(305\) | −808601. | −0.497720 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 252381. | 0.152831 | 0.0764153 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764153 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(308\) | 1.50434e6 | 0.903586 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −774961. | −0.458010 | ||||||||
\(311\) | −784287. | −0.459805 | −0.229903 | − | 0.973214i | \(-0.573841\pi\) | ||||
−0.229903 | + | 0.973214i | \(0.573841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.16086e6 | −1.24671 | −0.623356 | − | 0.781938i | \(-0.714231\pi\) | ||||
−0.623356 | + | 0.781938i | \(0.714231\pi\) | |||||||
\(314\) | −3.17790e6 | −1.81893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.17956e6 | 1.22787 | ||||||||
\(317\) | −3.39464e6 | −1.89734 | −0.948670 | − | 0.316269i | \(-0.897570\pi\) | ||||
−0.948670 | + | 0.316269i | \(0.897570\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 101289. | 0.0557298 | ||||||||
\(320\) | 4.97886e6 | 2.71804 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −23081.7 | −0.0124059 | ||||||||
\(323\) | 1.42336e6 | 0.759119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −572509. | −0.300659 | ||||||||
\(326\) | 5.51470e6 | 2.87394 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.57170e6 | −3.37282 | ||||||||
\(329\) | −747237. | −0.380600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50736e6 | −0.756216 | −0.378108 | − | 0.925762i | \(-0.623425\pi\) | ||||
−0.378108 | + | 0.925762i | \(0.623425\pi\) | |||||||
\(332\) | −2.24629e6 | −1.11846 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.10274e6 | −2.50287 | ||||||||
\(335\) | 1.45892e6 | 0.710265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −301876. | −0.144795 | −0.0723976 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723976 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(338\) | −5.24712e6 | −2.49821 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.42501e6 | 0.668528 | ||||||||
\(341\) | −334390. | −0.155728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.12732e6 | 0.976331 | ||||||||
\(344\) | 2.40675e6 | 1.09656 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.09447e6 | −1.38962 | ||||||||
\(347\) | −325201. | −0.144987 | −0.0724934 | − | 0.997369i | \(-0.523096\pi\) | ||||
−0.0724934 | + | 0.997369i | \(0.523096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.73891e6 | −1.20369 | −0.601845 | − | 0.798613i | \(-0.705568\pi\) | ||||
−0.601845 | + | 0.798613i | \(0.705568\pi\) | |||||||
\(350\) | 929020. | 0.405373 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.79688e6 | 1.63332 | ||||||||
\(353\) | −2.86184e6 | −1.22238 | −0.611192 | − | 0.791482i | \(-0.709310\pi\) | ||||
−0.611192 | + | 0.791482i | \(0.709310\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26875.3 | 0.0113183 | ||||||||
\(356\) | −8.91371e6 | −3.72764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −218501. | −0.0901043 | ||||||||
\(359\) | 3.49224e6 | 1.43011 | 0.715053 | − | 0.699071i | \(-0.246403\pi\) | ||||
0.715053 | + | 0.699071i | \(0.246403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.01239e6 | 1.21659 | ||||||||
\(362\) | 6.08959e6 | 2.44240 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.13884e7 | 4.50515 | ||||||||
\(365\) | 700875. | 0.275365 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −420097. | −0.162811 | −0.0814056 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814056 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(368\) | −74157.9 | −0.0285455 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.65847e6 | −0.629799 | ||||||||
\(371\) | −1.40321e6 | −0.529283 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −281554. | −0.104783 | −0.0523914 | − | 0.998627i | \(-0.516684\pi\) | ||||
−0.0523914 | + | 0.998627i | \(0.516684\pi\) | |||||||
\(374\) | 824607. | 0.304837 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.90997e6 | −1.42628 | ||||||||
\(377\) | 766798. | 0.277861 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.41256e6 | −0.505138 | −0.252569 | − | 0.967579i | \(-0.581275\pi\) | ||||
−0.252569 | + | 0.967579i | \(0.581275\pi\) | |||||||
\(380\) | 5.49483e6 | 1.95207 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.72497e6 | 0.955441 | ||||||||
\(383\) | −2.23548e6 | −0.778708 | −0.389354 | − | 0.921088i | \(-0.627302\pi\) | ||||
−0.389354 | + | 0.921088i | \(0.627302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 400866. | 0.137831 | ||||||||
\(386\) | 2.32367e6 | 0.793792 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.15953e6 | −1.06548 | ||||||||
\(389\) | −5.10434e6 | −1.71027 | −0.855136 | − | 0.518403i | \(-0.826527\pi\) | ||||
−0.855136 | + | 0.518403i | \(0.826527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9434.34 | −0.00312083 | ||||||||
\(392\) | −522763. | −0.171826 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.84367e6 | 0.922867 | ||||||||
\(395\) | 580793. | 0.187296 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −252110. | −0.0802813 | −0.0401406 | − | 0.999194i | \(-0.512781\pi\) | ||||
−0.0401406 | + | 0.999194i | \(0.512781\pi\) | |||||||
\(398\) | −8.48128e6 | −2.68382 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.98480e6 | 0.932750 | ||||||||
\(401\) | −1.61321e6 | −0.500991 | −0.250496 | − | 0.968118i | \(-0.580594\pi\) | ||||
−0.250496 | + | 0.968118i | \(0.580594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.53145e6 | −0.776439 | ||||||||
\(404\) | 7.40277e6 | 2.25653 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.24430e6 | −0.374636 | ||||||||
\(407\) | −715616. | −0.214138 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.08687e6 | 0.321270 | 0.160635 | − | 0.987014i | \(-0.448646\pi\) | ||||
0.160635 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(410\) | −2.65767e6 | −0.780803 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.33997e6 | −1.54987 | ||||||||
\(413\) | 3.90659e6 | 1.12700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −598576. | −0.170608 | ||||||||
\(416\) | 2.87438e7 | 8.14348 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.17968e6 | 0.890109 | ||||||||
\(419\) | 740488. | 0.206055 | 0.103027 | − | 0.994679i | \(-0.467147\pi\) | ||||
0.103027 | + | 0.994679i | \(0.467147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.54748e6 | 1.80040 | 0.900199 | − | 0.435478i | \(-0.143421\pi\) | ||||
0.900199 | + | 0.435478i | \(0.143421\pi\) | |||||||
\(422\) | −1.14250e7 | −3.12302 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.34239e6 | −1.98346 | ||||||||
\(425\) | 379725. | 0.101976 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.28615e6 | 1.13762 | ||||||||
\(428\) | −1.78287e7 | −4.70447 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 973315. | 0.253853 | ||||||||
\(431\) | 2.75325e6 | 0.713925 | 0.356963 | − | 0.934119i | \(-0.383812\pi\) | ||||
0.356963 | + | 0.934119i | \(0.383812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.26541e6 | −0.324349 | −0.162175 | − | 0.986762i | \(-0.551851\pi\) | ||||
−0.162175 | + | 0.986762i | \(0.551851\pi\) | |||||||
\(434\) | 4.10784e6 | 1.04686 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.02069e7 | 2.57144 | ||||||||
\(437\) | −36378.8 | −0.00911266 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.77205e6 | −0.438850 | −0.219425 | − | 0.975629i | \(-0.570418\pi\) | ||||
−0.219425 | + | 0.975629i | \(0.570418\pi\) | |||||||
\(440\) | 2.09756e6 | 0.516514 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.24257e6 | 1.51987 | ||||||||
\(443\) | −3.87503e6 | −0.938135 | −0.469068 | − | 0.883162i | \(-0.655410\pi\) | ||||
−0.469068 | + | 0.883162i | \(0.655410\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.37526e6 | −0.568606 | ||||||||
\(446\) | 6.86766e6 | 1.63483 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.63915e7 | −6.21253 | ||||||||
\(449\) | −5.14887e6 | −1.20530 | −0.602651 | − | 0.798005i | \(-0.705889\pi\) | ||||
−0.602651 | + | 0.798005i | \(0.705889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.14677e6 | −0.265481 | ||||||||
\(452\) | 1.95229e7 | 4.49467 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.01370e6 | −1.59701 | ||||||||
\(455\) | 3.03470e6 | 0.687206 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.37155e6 | −0.531179 | −0.265590 | − | 0.964086i | \(-0.585567\pi\) | ||||
−0.265590 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(458\) | −1.24694e7 | −2.77768 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −36420.8 | −0.00802518 | ||||||||
\(461\) | 2.82106e6 | 0.618244 | 0.309122 | − | 0.951022i | \(-0.399965\pi\) | ||||
0.309122 | + | 0.951022i | \(0.399965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.26742e6 | 1.14194 | 0.570972 | − | 0.820969i | \(-0.306566\pi\) | ||||
0.570972 | + | 0.820969i | \(0.306566\pi\) | |||||||
\(464\) | −3.99774e6 | −0.862024 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.04047e7 | 2.21954 | ||||||||
\(467\) | −1.18996e6 | −0.252487 | −0.126243 | − | 0.991999i | \(-0.540292\pi\) | ||||
−0.126243 | + | 0.991999i | \(0.540292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.73332e6 | −1.62343 | ||||||||
\(470\) | −1.58124e6 | −0.330181 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.04415e7 | 4.22336 | ||||||||
\(473\) | 419979. | 0.0863126 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.46422e6 | 0.297764 | ||||||||
\(476\) | −7.55354e6 | −1.52803 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.53419e6 | −0.507306 | ||||||||
\(479\) | 5.62901e6 | 1.12097 | 0.560484 | − | 0.828165i | \(-0.310615\pi\) | ||||
0.560484 | + | 0.828165i | \(0.310615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.41747e6 | −1.06766 | ||||||||
\(482\) | 1.48812e7 | 2.91757 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.37359e6 | 0.266529 | ||||||||
\(485\) | −841929. | −0.162525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.09746e6 | −0.209684 | −0.104842 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104842 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(488\) | 2.24276e7 | 4.26318 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −211411. | −0.0397775 | ||||||||
\(491\) | −1.33860e6 | −0.250580 | −0.125290 | − | 0.992120i | \(-0.539986\pi\) | ||||
−0.125290 | + | 0.992120i | \(0.539986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −508591. | −0.0942435 | ||||||||
\(494\) | 2.40713e7 | 4.43796 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.31978e7 | 2.40879 | ||||||||
\(497\) | −142458. | −0.0258700 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.29736e6 | 0.233243 | 0.116622 | − | 0.993176i | \(-0.462794\pi\) | ||||
0.116622 | + | 0.993176i | \(0.462794\pi\) | |||||||
\(500\) | 1.46591e6 | 0.262230 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.04795e6 | 1.42536 | ||||||||
\(503\) | −5.44945e6 | −0.960357 | −0.480179 | − | 0.877171i | \(-0.659428\pi\) | ||||
−0.480179 | + | 0.877171i | \(0.659428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.97264e6 | 0.344206 | ||||||||
\(506\) | −21075.6 | −0.00365934 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.89741e7 | −4.98139 | ||||||||
\(509\) | −9.81233e6 | −1.67872 | −0.839359 | − | 0.543578i | \(-0.817069\pi\) | ||||
−0.839359 | + | 0.543578i | \(0.817069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.71513e6 | −0.629393 | ||||||||
\(512\) | −4.38892e7 | −7.39916 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.04229e6 | 1.34268 | ||||||||
\(515\) | −1.42295e6 | −0.236414 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −682292. | −0.112265 | ||||||||
\(518\) | 8.79103e6 | 1.43951 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.58793e7 | 2.57527 | ||||||||
\(521\) | −8.84276e6 | −1.42723 | −0.713614 | − | 0.700539i | \(-0.752943\pi\) | ||||
−0.713614 | + | 0.700539i | \(0.752943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.57320e6 | 0.890944 | 0.445472 | − | 0.895296i | \(-0.353036\pi\) | ||||
0.445472 | + | 0.895296i | \(0.353036\pi\) | |||||||
\(524\) | 5.91618e6 | 0.941267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.77610e7 | −2.79900 | ||||||||
\(527\) | 1.67903e6 | 0.263348 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.43610e6 | −0.999963 | ||||||||
\(530\) | −2.96935e6 | −0.459168 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.91264e7 | −4.46178 | ||||||||
\(533\) | −8.68143e6 | −1.32365 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.75087e6 | −0.717610 | ||||||||
\(536\) | −4.04651e7 | −6.08372 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.66499e6 | 0.248003 | ||||||||
\(539\) | −91222.4 | −0.0135248 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.05506e6 | −1.03635 | −0.518176 | − | 0.855274i | \(-0.673389\pi\) | ||||
−0.518176 | + | 0.855274i | \(0.673389\pi\) | |||||||
\(542\) | 7.89415e6 | 1.15427 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.90648e7 | −2.76207 | ||||||||
\(545\) | 2.71985e6 | 0.392241 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.22859e7 | −1.75565 | −0.877823 | − | 0.478985i | \(-0.841005\pi\) | ||||
−0.877823 | + | 0.478985i | \(0.841005\pi\) | |||||||
\(548\) | 3.87595e6 | 0.551349 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 848276. | 0.119572 | ||||||||
\(551\) | −1.96113e6 | −0.275186 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.07861e6 | −0.428097 | ||||||||
\(554\) | 1.02926e7 | 1.42478 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.42038e7 | −3.32045 | ||||||||
\(557\) | 8.42444e6 | 1.15054 | 0.575272 | − | 0.817962i | \(-0.304896\pi\) | ||||
0.575272 | + | 0.817962i | \(0.304896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.17939e6 | 0.430342 | ||||||||
\(560\) | −1.58215e7 | −2.13196 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.54750e7 | 3.40231 | ||||||||
\(563\) | −7.88182e6 | −1.04799 | −0.523993 | − | 0.851723i | \(-0.675558\pi\) | ||||
−0.523993 | + | 0.851723i | \(0.675558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.20231e6 | 0.685607 | ||||||||
\(566\) | 6.46751e6 | 0.848586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −745421. | −0.0969462 | ||||||||
\(569\) | −7.11408e6 | −0.921167 | −0.460583 | − | 0.887616i | \(-0.652360\pi\) | ||||
−0.460583 | + | 0.887616i | \(0.652360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −71565.4 | −0.00918572 | −0.00459286 | − | 0.999989i | \(-0.501462\pi\) | ||||
−0.00459286 | + | 0.999989i | \(0.501462\pi\) | |||||||
\(572\) | 1.03986e7 | 1.32888 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.40875e7 | 1.78466 | ||||||||
\(575\) | −9705.15 | −0.00122414 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.17667e6 | −0.272179 | −0.136089 | − | 0.990697i | \(-0.543453\pi\) | ||||
−0.136089 | + | 0.990697i | \(0.543453\pi\) | |||||||
\(578\) | 1.17859e7 | 1.46738 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.96339e6 | −0.242346 | ||||||||
\(581\) | 3.17287e6 | 0.389953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.28125e6 | −0.156122 | ||||||||
\(584\) | −1.94397e7 | −2.35861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.07064e7 | −1.28795 | ||||||||
\(587\) | 852228. | 0.102085 | 0.0510423 | − | 0.998696i | \(-0.483746\pi\) | ||||
0.0510423 | + | 0.998696i | \(0.483746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.47432e6 | 0.768964 | ||||||||
\(590\) | 8.26677e6 | 0.977701 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.82442e7 | 3.31227 | ||||||||
\(593\) | −9.10178e6 | −1.06289 | −0.531446 | − | 0.847092i | \(-0.678351\pi\) | ||||
−0.531446 | + | 0.847092i | \(0.678351\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.01281e6 | −0.233083 | ||||||||
\(596\) | −2.19335e7 | −2.52925 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −159550. | −0.0182450 | ||||||||
\(599\) | 3.68657e6 | 0.419813 | 0.209906 | − | 0.977721i | \(-0.432684\pi\) | ||||
0.209906 | + | 0.977721i | \(0.432684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18735e7 | 1.34088 | 0.670442 | − | 0.741962i | \(-0.266104\pi\) | ||||
0.670442 | + | 0.741962i | \(0.266104\pi\) | |||||||
\(602\) | −5.15926e6 | −0.580224 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.73432e7 | −4.16504 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.77821e6 | 0.967017 | 0.483509 | − | 0.875340i | \(-0.339362\pi\) | ||||
0.483509 | + | 0.875340i | \(0.339362\pi\) | |||||||
\(608\) | −7.35137e7 | −8.06509 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.06998e6 | 0.986919 | ||||||||
\(611\) | −5.16520e6 | −0.559737 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.52076e7 | 1.63459 | 0.817294 | − | 0.576220i | \(-0.195473\pi\) | ||||
0.817294 | + | 0.576220i | \(0.195473\pi\) | |||||||
\(614\) | −2.83092e6 | −0.303045 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.11185e7 | −1.18058 | ||||||||
\(617\) | 1.13759e7 | 1.20302 | 0.601511 | − | 0.798865i | \(-0.294566\pi\) | ||||
0.601511 | + | 0.798865i | \(0.294566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.14541e6 | 0.749550 | 0.374775 | − | 0.927116i | \(-0.377720\pi\) | ||||
0.374775 | + | 0.927116i | \(0.377720\pi\) | |||||||
\(620\) | 6.48179e6 | 0.677198 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.79725e6 | 0.911739 | ||||||||
\(623\) | 1.25905e7 | 1.29964 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.42381e7 | 2.47208 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.65801e7 | 2.68941 | ||||||||
\(629\) | 3.59322e6 | 0.362124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.11229e6 | 0.411159 | 0.205580 | − | 0.978640i | \(-0.434092\pi\) | ||||
0.205580 | + | 0.978640i | \(0.434092\pi\) | |||||||
\(632\) | −1.61090e7 | −1.60427 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.80772e7 | 3.76220 | ||||||||
\(635\) | −7.72080e6 | −0.759850 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −690587. | −0.0674326 | ||||||||
\(638\) | −1.13615e6 | −0.110506 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.07439e7 | −2.96694 | ||||||||
\(641\) | −2.34166e6 | −0.225102 | −0.112551 | − | 0.993646i | \(-0.535902\pi\) | ||||
−0.112551 | + | 0.993646i | \(0.535902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.71655e6 | −0.354497 | −0.177248 | − | 0.984166i | \(-0.556720\pi\) | ||||
−0.177248 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(644\) | 193056. | 0.0183429 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.59657e7 | −1.50524 | ||||||||
\(647\) | −8.96177e6 | −0.841653 | −0.420826 | − | 0.907141i | \(-0.638260\pi\) | ||||
−0.420826 | + | 0.907141i | \(0.638260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.56705e6 | 0.332428 | ||||||||
\(650\) | 6.42176e6 | 0.596170 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.61251e7 | −4.24931 | ||||||||
\(653\) | 1.79019e7 | 1.64292 | 0.821460 | − | 0.570267i | \(-0.193160\pi\) | ||||
0.821460 | + | 0.570267i | \(0.193160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.57650e6 | 0.143579 | ||||||||
\(656\) | 4.52610e7 | 4.10643 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.38166e6 | 0.754685 | ||||||||
\(659\) | −1.90122e7 | −1.70537 | −0.852686 | − | 0.522423i | \(-0.825028\pi\) | ||||
−0.852686 | + | 0.522423i | \(0.825028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.58472e6 | −0.408140 | −0.204070 | − | 0.978956i | \(-0.565417\pi\) | ||||
−0.204070 | + | 0.978956i | \(0.565417\pi\) | |||||||
\(662\) | 1.69078e7 | 1.49949 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.66023e7 | 1.46133 | ||||||||
\(665\) | −7.76140e6 | −0.680590 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12998.7 | 0.00113132 | ||||||||
\(668\) | 4.26795e7 | 3.70065 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.63646e7 | −1.40837 | ||||||||
\(671\) | 3.91363e6 | 0.335563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.51723e7 | −1.29126 | −0.645630 | − | 0.763651i | \(-0.723405\pi\) | ||||
−0.645630 | + | 0.763651i | \(0.723405\pi\) | |||||||
\(674\) | 3.38611e6 | 0.287112 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.38871e7 | 3.69377 | ||||||||
\(677\) | 1.08298e7 | 0.908129 | 0.454064 | − | 0.890969i | \(-0.349974\pi\) | ||||
0.454064 | + | 0.890969i | \(0.349974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.46281e6 | 0.371479 | ||||||||
\(680\) | −1.05322e7 | −0.873466 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.75081e6 | 0.308791 | ||||||||
\(683\) | 1.41968e7 | 1.16450 | 0.582248 | − | 0.813012i | \(-0.302173\pi\) | ||||
0.582248 | + | 0.813012i | \(0.302173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03283e6 | 0.0841016 | ||||||||
\(686\) | −2.38618e7 | −1.93595 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.65759e7 | −1.33508 | ||||||||
\(689\) | −9.69954e6 | −0.778400 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.99651e6 | 0.796440 | 0.398220 | − | 0.917290i | \(-0.369628\pi\) | ||||
0.398220 | + | 0.917290i | \(0.369628\pi\) | |||||||
\(692\) | 2.58822e7 | 2.05464 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.64774e6 | 0.287492 | ||||||||
\(695\) | −6.44966e6 | −0.506494 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.75809e6 | 0.448949 | ||||||||
\(698\) | 3.07221e7 | 2.38678 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.77035e6 | −0.599371 | ||||||||
\(701\) | 3.82320e6 | 0.293854 | 0.146927 | − | 0.989147i | \(-0.453062\pi\) | ||||
0.146927 | + | 0.989147i | \(0.453062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.38555e7 | 1.05738 | ||||||||
\(704\) | −2.40977e7 | −1.83250 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.21009e7 | 2.42385 | ||||||||
\(707\) | −1.04564e7 | −0.786741 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.38358e6 | 0.402213 | 0.201106 | − | 0.979569i | \(-0.435546\pi\) | ||||
0.201106 | + | 0.979569i | \(0.435546\pi\) | |||||||
\(710\) | −301457. | −0.0224429 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.58810e7 | 4.87035 | ||||||||
\(713\) | −42913.1 | −0.00316130 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.77094e6 | 0.202704 | ||||||||
\(716\) | 1.82755e6 | 0.133225 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.91720e7 | −2.83573 | ||||||||
\(719\) | 1.66113e7 | 1.19834 | 0.599171 | − | 0.800621i | \(-0.295497\pi\) | ||||
0.599171 | + | 0.800621i | \(0.295497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.54266e6 | 0.540364 | ||||||||
\(722\) | −3.37896e7 | −2.41235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.09335e7 | −3.61125 | ||||||||
\(725\) | −523189. | −0.0369670 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.47622e7 | 1.03589 | 0.517947 | − | 0.855413i | \(-0.326697\pi\) | ||||
0.517947 | + | 0.855413i | \(0.326697\pi\) | |||||||
\(728\) | −8.41713e7 | −5.88621 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.86163e6 | −0.546016 | ||||||||
\(731\) | −2.10878e6 | −0.145961 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.48819e6 | −0.583519 | −0.291760 | − | 0.956492i | \(-0.594241\pi\) | ||||
−0.291760 | + | 0.956492i | \(0.594241\pi\) | |||||||
\(734\) | 4.71217e6 | 0.322835 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 487263. | 0.0331565 | ||||||||
\(737\) | −7.06119e6 | −0.478861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.60406e7 | 1.75404 | 0.877022 | − | 0.480450i | \(-0.159527\pi\) | ||||
0.877022 | + | 0.480450i | \(0.159527\pi\) | |||||||
\(740\) | 1.38715e7 | 0.931199 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.57396e7 | 1.04951 | ||||||||
\(743\) | 791476. | 0.0525975 | 0.0262988 | − | 0.999654i | \(-0.491628\pi\) | ||||
0.0262988 | + | 0.999654i | \(0.491628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.84467e6 | −0.385806 | ||||||||
\(746\) | 3.15816e6 | 0.207772 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.89703e6 | −0.450722 | ||||||||
\(749\) | 2.51829e7 | 1.64022 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.80752e6 | −0.246344 | −0.123172 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123172 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(752\) | 2.69290e7 | 1.73650 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.60107e6 | −0.550965 | ||||||||
\(755\) | −9.95095e6 | −0.635327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.46270e7 | −1.56197 | −0.780983 | − | 0.624552i | \(-0.785281\pi\) | ||||
−0.780983 | + | 0.624552i | \(0.785281\pi\) | |||||||
\(758\) | 1.58445e7 | 1.00163 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.06121e7 | −2.55048 | ||||||||
\(761\) | 1.49393e7 | 0.935123 | 0.467561 | − | 0.883961i | \(-0.345133\pi\) | ||||
0.467561 | + | 0.883961i | \(0.345133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.44171e7 | −0.896534 | ||||||||
\(764\) | −2.27918e7 | −1.41268 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.50752e7 | 1.54409 | ||||||||
\(767\) | 2.70039e7 | 1.65744 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.19320e6 | 0.560597 | 0.280299 | − | 0.959913i | \(-0.409566\pi\) | ||||
0.280299 | + | 0.959913i | \(0.409566\pi\) | |||||||
\(770\) | −4.49646e6 | −0.273303 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.94353e7 | −1.17367 | ||||||||
\(773\) | 2.65966e7 | 1.60095 | 0.800474 | − | 0.599367i | \(-0.204581\pi\) | ||||
0.800474 | + | 0.599367i | \(0.204581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.72722e6 | 0.103298 | ||||||||
\(776\) | 2.33520e7 | 1.39210 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.72547e7 | 3.39127 | ||||||||
\(779\) | 2.22032e7 | 1.31091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −130076. | −0.00763082 | ||||||||
\(782\) | 105824. | 0.00618823 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.60041e6 | 0.209200 | ||||||||
\(785\) | 7.08286e6 | 0.410237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.01592e7 | −0.584684 | −0.292342 | − | 0.956314i | \(-0.594435\pi\) | ||||
−0.292342 | + | 0.956314i | \(0.594435\pi\) | |||||||
\(788\) | −2.37846e7 | −1.36452 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.51468e6 | −0.371386 | ||||||||
\(791\) | −2.75759e7 | −1.56707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.96276e7 | 1.67307 | ||||||||
\(794\) | 2.82789e6 | 0.159188 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.09377e7 | 3.96821 | ||||||||
\(797\) | 1.13291e7 | 0.631756 | 0.315878 | − | 0.948800i | \(-0.397701\pi\) | ||||
0.315878 | + | 0.948800i | \(0.397701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.42590e6 | 0.189849 | ||||||||
\(800\) | −1.96120e7 | −1.08342 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.80952e7 | 0.993406 | ||||||||
\(803\) | −3.39223e6 | −0.185651 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51444.1 | 0.00279799 | ||||||||
\(806\) | 2.83950e7 | 1.53959 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.47136e7 | −2.94827 | ||||||||
\(809\) | −2.78519e7 | −1.49618 | −0.748091 | − | 0.663597i | \(-0.769029\pi\) | ||||
−0.748091 | + | 0.663597i | \(0.769029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.02449e7 | −1.61473 | −0.807365 | − | 0.590052i | \(-0.799107\pi\) | ||||
−0.807365 | + | 0.590052i | \(0.799107\pi\) | |||||||
\(812\) | 1.04073e7 | 0.553923 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.02697e6 | 0.424611 | ||||||||
\(815\) | −1.22911e7 | −0.648181 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.13146e6 | −0.426200 | ||||||||
\(818\) | −1.21913e7 | −0.637040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.22288e7 | 1.15447 | ||||||||
\(821\) | 1.98523e7 | 1.02790 | 0.513952 | − | 0.857819i | \(-0.328181\pi\) | ||||
0.513952 | + | 0.857819i | \(0.328181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.25066e7 | 0.643636 | 0.321818 | − | 0.946802i | \(-0.395706\pi\) | ||||
0.321818 | + | 0.946802i | \(0.395706\pi\) | |||||||
\(824\) | 3.94675e7 | 2.02498 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.38197e7 | −2.23470 | ||||||||
\(827\) | 8.51692e6 | 0.433031 | 0.216515 | − | 0.976279i | \(-0.430531\pi\) | ||||
0.216515 | + | 0.976279i | \(0.430531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.94676e6 | 0.148922 | 0.0744609 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744609 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(830\) | 6.71415e6 | 0.338295 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.82428e8 | −9.13658 | ||||||||
\(833\) | 458043. | 0.0228714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.13729e7 | 0.564489 | ||||||||
\(836\) | −2.65950e7 | −1.31608 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.30596e6 | −0.408583 | ||||||||
\(839\) | 5.40609e6 | 0.265142 | 0.132571 | − | 0.991174i | \(-0.457677\pi\) | ||||
0.132571 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.98104e7 | −0.965836 | ||||||||
\(842\) | −7.34422e7 | −3.56998 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.55589e7 | 4.61758 | ||||||||
\(845\) | 1.16947e7 | 0.563440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.94019e6 | −0.0929257 | ||||||||
\(848\) | 5.05690e7 | 2.41488 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.25933e6 | −0.202206 | ||||||||
\(851\) | −91836.8 | −0.00434703 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −473034. | −0.0222597 | −0.0111299 | − | 0.999938i | \(-0.503543\pi\) | ||||
−0.0111299 | + | 0.999938i | \(0.503543\pi\) | |||||||
\(854\) | −4.80773e7 | −2.25577 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.31772e8 | 6.14663 | ||||||||
\(857\) | −6.34036e6 | −0.294891 | −0.147446 | − | 0.989070i | \(-0.547105\pi\) | ||||
−0.147446 | + | 0.989070i | \(0.547105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.40671e7 | −1.11286 | −0.556430 | − | 0.830895i | \(-0.687829\pi\) | ||||
−0.556430 | + | 0.830895i | \(0.687829\pi\) | |||||||
\(860\) | −8.14084e6 | −0.375338 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.08829e7 | −1.41563 | ||||||||
\(863\) | 1.06639e6 | 0.0487402 | 0.0243701 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243701 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.89690e6 | 0.313411 | ||||||||
\(866\) | 1.41940e7 | 0.643146 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.43581e7 | −1.54785 | ||||||||
\(869\) | −2.81104e6 | −0.126275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.34557e7 | −2.38753 | ||||||||
\(872\) | −7.54385e7 | −3.35971 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 408057. | 0.0180693 | ||||||||
\(875\) | −2.07059e6 | −0.0914268 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.28432e7 | −0.563864 | −0.281932 | − | 0.959434i | \(-0.590975\pi\) | ||||
−0.281932 | + | 0.959434i | \(0.590975\pi\) | |||||||
\(878\) | 1.98769e7 | 0.870187 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.44464e7 | −0.628860 | ||||||||
\(881\) | −2.79947e6 | −0.121517 | −0.0607583 | − | 0.998153i | \(-0.519352\pi\) | ||||
−0.0607583 | + | 0.998153i | \(0.519352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.81700e7 | 1.21587 | 0.607933 | − | 0.793988i | \(-0.291999\pi\) | ||||
0.607933 | + | 0.793988i | \(0.291999\pi\) | |||||||
\(884\) | −5.22130e7 | −2.24723 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.34657e7 | 1.86021 | ||||||||
\(887\) | −4.42238e7 | −1.88733 | −0.943664 | − | 0.330905i | \(-0.892646\pi\) | ||||
−0.943664 | + | 0.330905i | \(0.892646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.09257e7 | 1.73677 | ||||||||
\(890\) | 2.66430e7 | 1.12748 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.74413e7 | −2.41720 | ||||||||
\(893\) | 1.32103e7 | 0.554348 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 486992. | 0.0203219 | ||||||||
\(896\) | 1.62964e8 | 6.78145 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.77542e7 | 2.38997 | ||||||||
\(899\) | −2.31338e6 | −0.0954657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.43337e6 | 0.264014 | ||||||||
\(902\) | 1.28631e7 | 0.526417 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.44293e8 | −5.87251 | ||||||||
\(905\) | −1.35724e7 | −0.550852 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.22787e6 | 0.251375 | 0.125687 | − | 0.992070i | \(-0.459886\pi\) | ||||
0.125687 | + | 0.992070i | \(0.459886\pi\) | |||||||
\(908\) | 5.86628e7 | 2.36128 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.40398e7 | −1.36265 | ||||||||
\(911\) | −1.08864e7 | −0.434599 | −0.217300 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217300 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.89711e6 | 0.115024 | ||||||||
\(914\) | 2.66013e7 | 1.05327 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.04295e8 | 4.10698 | ||||||||
\(917\) | −8.35655e6 | −0.328174 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.61046e7 | −0.629014 | −0.314507 | − | 0.949255i | \(-0.601839\pi\) | ||||
−0.314507 | + | 0.949255i | \(0.601839\pi\) | |||||||
\(920\) | 269185. | 0.0104853 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.16435e7 | −1.22590 | ||||||||
\(923\) | −984726. | −0.0380462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.69636e6 | 0.142043 | ||||||||
\(926\) | −5.90839e7 | −2.26434 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.62676e7 | 1.00127 | ||||||||
\(929\) | −1.97673e6 | −0.0751465 | −0.0375732 | − | 0.999294i | \(-0.511963\pi\) | ||||
−0.0375732 | + | 0.999294i | \(0.511963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76621e6 | 0.0667834 | ||||||||
\(932\) | −8.70248e7 | −3.28173 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.33476e7 | 0.500652 | ||||||||
\(935\) | −1.83787e6 | −0.0687521 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.38945e7 | 0.517003 | 0.258502 | − | 0.966011i | \(-0.416771\pi\) | ||||
0.258502 | + | 0.966011i | \(0.416771\pi\) | |||||||
\(938\) | 8.67436e7 | 3.21907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.32255e7 | 0.488194 | ||||||||
\(941\) | −4.33771e7 | −1.59693 | −0.798466 | − | 0.602040i | \(-0.794355\pi\) | ||||
−0.798466 | + | 0.602040i | \(0.794355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −147167. | −0.00538930 | ||||||||
\(944\) | −1.40786e8 | −5.14197 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.71085e6 | −0.171148 | ||||||||
\(947\) | 1.79958e7 | 0.652075 | 0.326037 | − | 0.945357i | \(-0.394286\pi\) | ||||
0.326037 | + | 0.945357i | \(0.394286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.56804e7 | −0.925629 | ||||||||
\(950\) | −1.64240e7 | −0.590431 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.58280e7 | 1.99645 | ||||||||
\(953\) | −2.95957e7 | −1.05559 | −0.527796 | − | 0.849371i | \(-0.676982\pi\) | ||||
−0.527796 | + | 0.849371i | \(0.676982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.07338e6 | −0.215487 | ||||||||
\(956\) | 2.11961e7 | 0.750085 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.31399e7 | −2.22275 | ||||||||
\(959\) | −5.47475e6 | −0.192228 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09919e7 | −0.733236 | ||||||||
\(962\) | 6.07671e7 | 2.11705 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.24467e8 | −4.31381 | ||||||||
\(965\) | −5.17897e6 | −0.179030 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.50973e7 | 1.89480 | 0.947402 | − | 0.320046i | \(-0.103699\pi\) | ||||
0.947402 | + | 0.320046i | \(0.103699\pi\) | |||||||
\(968\) | −1.01522e7 | −0.348234 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.44381e6 | 0.322268 | ||||||||
\(971\) | −1.86888e7 | −0.636112 | −0.318056 | − | 0.948072i | \(-0.603030\pi\) | ||||
−0.318056 | + | 0.948072i | \(0.603030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.41877e7 | 1.15768 | ||||||||
\(974\) | 1.23100e7 | 0.415778 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.54465e8 | −5.19045 | ||||||||
\(977\) | 7.09223e6 | 0.237710 | 0.118855 | − | 0.992912i | \(-0.462078\pi\) | ||||
0.118855 | + | 0.992912i | \(0.462078\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14963e7 | 0.383354 | ||||||||
\(980\) | 1.76825e6 | 0.0588137 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.50149e7 | 0.496870 | ||||||||
\(983\) | −2.97902e7 | −0.983307 | −0.491653 | − | 0.870791i | \(-0.663607\pi\) | ||||
−0.491653 | + | 0.870791i | \(0.663607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.33794e6 | −0.208141 | ||||||||
\(986\) | 5.70480e6 | 0.186874 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.01333e8 | −6.56181 | ||||||||
\(989\) | 53896.9 | 0.00175216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.60948e7 | −0.844054 | −0.422027 | − | 0.906583i | \(-0.638681\pi\) | ||||
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(992\) | −8.67180e7 | −2.79789 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.59793e6 | 0.0512971 | ||||||||
\(995\) | 1.89030e7 | 0.605302 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.68998e7 | −0.857061 | −0.428531 | − | 0.903527i | \(-0.640969\pi\) | ||||
−0.428531 | + | 0.903527i | \(0.640969\pi\) | |||||||
\(998\) | −1.45523e7 | −0.462494 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.6.a.l.1.1 | 6 | ||
3.2 | odd | 2 | 55.6.a.d.1.6 | ✓ | 6 | ||
12.11 | even | 2 | 880.6.a.u.1.3 | 6 | |||
15.2 | even | 4 | 275.6.b.f.199.12 | 12 | |||
15.8 | even | 4 | 275.6.b.f.199.1 | 12 | |||
15.14 | odd | 2 | 275.6.a.f.1.1 | 6 | |||
33.32 | even | 2 | 605.6.a.e.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.a.d.1.6 | ✓ | 6 | 3.2 | odd | 2 | ||
275.6.a.f.1.1 | 6 | 15.14 | odd | 2 | |||
275.6.b.f.199.1 | 12 | 15.8 | even | 4 | |||
275.6.b.f.199.12 | 12 | 15.2 | even | 4 | |||
495.6.a.l.1.1 | 6 | 1.1 | even | 1 | trivial | ||
605.6.a.e.1.1 | 6 | 33.32 | even | 2 | |||
880.6.a.u.1.3 | 6 | 12.11 | even | 2 |