Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-9.60154\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.60154 | 1.69733 | 0.848664 | − | 0.528933i | \(-0.177408\pi\) | ||||
0.848664 | + | 0.528933i | \(0.177408\pi\) | |||||||
\(3\) | −25.9222 | −1.66291 | −0.831456 | − | 0.555590i | \(-0.812492\pi\) | ||||
−0.831456 | + | 0.555590i | \(0.812492\pi\) | |||||||
\(4\) | 60.1895 | 1.88092 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −248.893 | −2.82251 | ||||||||
\(7\) | −181.554 | −1.40042 | −0.700212 | − | 0.713935i | \(-0.746911\pi\) | ||||
−0.700212 | + | 0.713935i | \(0.746911\pi\) | |||||||
\(8\) | 270.662 | 1.49521 | ||||||||
\(9\) | 428.963 | 1.76528 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 512.944 | 1.27817 | 0.639084 | − | 0.769137i | \(-0.279313\pi\) | ||||
0.639084 | + | 0.769137i | \(0.279313\pi\) | |||||||
\(12\) | −1560.25 | −3.12781 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | −1743.19 | −2.37698 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 672.710 | 0.656943 | ||||||||
\(17\) | −1668.15 | −1.39995 | −0.699977 | − | 0.714165i | \(-0.746807\pi\) | ||||
−0.699977 | + | 0.714165i | \(0.746807\pi\) | |||||||
\(18\) | 4118.70 | 2.99626 | ||||||||
\(19\) | −464.071 | −0.294917 | −0.147459 | − | 0.989068i | \(-0.547109\pi\) | ||||
−0.147459 | + | 0.989068i | \(0.547109\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4706.28 | 2.32878 | ||||||||
\(22\) | 4925.05 | 2.16947 | ||||||||
\(23\) | 2095.04 | 0.825795 | 0.412897 | − | 0.910778i | \(-0.364517\pi\) | ||||
0.412897 | + | 0.910778i | \(0.364517\pi\) | |||||||
\(24\) | −7016.17 | −2.48641 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1622.66 | −0.470754 | ||||||||
\(27\) | −4820.57 | −1.27259 | ||||||||
\(28\) | −10927.6 | −2.63409 | ||||||||
\(29\) | 5935.75 | 1.31063 | 0.655316 | − | 0.755355i | \(-0.272535\pi\) | ||||
0.655316 | + | 0.755355i | \(0.272535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8397.76 | 1.56949 | 0.784746 | − | 0.619817i | \(-0.212793\pi\) | ||||
0.784746 | + | 0.619817i | \(0.212793\pi\) | |||||||
\(32\) | −2202.14 | −0.380164 | ||||||||
\(33\) | −13296.7 | −2.12548 | ||||||||
\(34\) | −16016.8 | −2.37618 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25819.0 | 3.32035 | ||||||||
\(37\) | 8909.35 | 1.06990 | 0.534948 | − | 0.844885i | \(-0.320331\pi\) | ||||
0.534948 | + | 0.844885i | \(0.320331\pi\) | |||||||
\(38\) | −4455.79 | −0.500571 | ||||||||
\(39\) | 4380.86 | 0.461209 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3256.85 | 0.302579 | 0.151289 | − | 0.988490i | \(-0.451657\pi\) | ||||
0.151289 | + | 0.988490i | \(0.451657\pi\) | |||||||
\(42\) | 45187.5 | 3.95271 | ||||||||
\(43\) | 5951.12 | 0.490826 | 0.245413 | − | 0.969419i | \(-0.421076\pi\) | ||||
0.245413 | + | 0.969419i | \(0.421076\pi\) | |||||||
\(44\) | 30873.8 | 2.40413 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20115.6 | 1.40164 | ||||||||
\(47\) | 10741.1 | 0.709255 | 0.354628 | − | 0.935008i | \(-0.384608\pi\) | ||||
0.354628 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(48\) | −17438.1 | −1.09244 | ||||||||
\(49\) | 16154.7 | 0.961190 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 43242.3 | 2.32800 | ||||||||
\(52\) | −10172.0 | −0.521674 | ||||||||
\(53\) | 39344.1 | 1.92393 | 0.961967 | − | 0.273167i | \(-0.0880710\pi\) | ||||
0.961967 | + | 0.273167i | \(0.0880710\pi\) | |||||||
\(54\) | −46284.9 | −2.16001 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −49139.7 | −2.09393 | ||||||||
\(57\) | 12029.8 | 0.490422 | ||||||||
\(58\) | 56992.4 | 2.22457 | ||||||||
\(59\) | −3940.20 | −0.147363 | −0.0736815 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736815 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41477.5 | −1.42721 | −0.713605 | − | 0.700548i | \(-0.752939\pi\) | ||||
−0.713605 | + | 0.700548i | \(0.752939\pi\) | |||||||
\(62\) | 80631.4 | 2.66394 | ||||||||
\(63\) | −77879.7 | −2.47214 | ||||||||
\(64\) | −42670.7 | −1.30221 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −127668. | −3.60764 | ||||||||
\(67\) | −18589.7 | −0.505923 | −0.252961 | − | 0.967476i | \(-0.581405\pi\) | ||||
−0.252961 | + | 0.967476i | \(0.581405\pi\) | |||||||
\(68\) | −100405. | −2.63320 | ||||||||
\(69\) | −54308.1 | −1.37322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70348.8 | 1.65619 | 0.828096 | − | 0.560586i | \(-0.189424\pi\) | ||||
0.828096 | + | 0.560586i | \(0.189424\pi\) | |||||||
\(72\) | 116104. | 2.63947 | ||||||||
\(73\) | 78602.6 | 1.72635 | 0.863176 | − | 0.504902i | \(-0.168471\pi\) | ||||
0.863176 | + | 0.504902i | \(0.168471\pi\) | |||||||
\(74\) | 85543.4 | 1.81596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27932.2 | −0.554716 | ||||||||
\(77\) | −93126.8 | −1.78998 | ||||||||
\(78\) | 42063.0 | 0.782823 | ||||||||
\(79\) | −71703.3 | −1.29262 | −0.646310 | − | 0.763075i | \(-0.723689\pi\) | ||||
−0.646310 | + | 0.763075i | \(0.723689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20722.1 | 0.350931 | ||||||||
\(82\) | 31270.8 | 0.513575 | ||||||||
\(83\) | −208.877 | −0.00332808 | −0.00166404 | − | 0.999999i | \(-0.500530\pi\) | ||||
−0.00166404 | + | 0.999999i | \(0.500530\pi\) | |||||||
\(84\) | 283268. | 4.38026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57139.9 | 0.833093 | ||||||||
\(87\) | −153868. | −2.17947 | ||||||||
\(88\) | 138835. | 1.91113 | ||||||||
\(89\) | −43537.5 | −0.582624 | −0.291312 | − | 0.956628i | \(-0.594092\pi\) | ||||
−0.291312 | + | 0.956628i | \(0.594092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30682.6 | 0.388408 | ||||||||
\(92\) | 126099. | 1.55325 | ||||||||
\(93\) | −217689. | −2.60993 | ||||||||
\(94\) | 103131. | 1.20384 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 57084.5 | 0.632179 | ||||||||
\(97\) | −15298.0 | −0.165084 | −0.0825419 | − | 0.996588i | \(-0.526304\pi\) | ||||
−0.0825419 | + | 0.996588i | \(0.526304\pi\) | |||||||
\(98\) | 155110. | 1.63145 | ||||||||
\(99\) | 220034. | 2.25632 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2600.25 | 0.0253636 | 0.0126818 | − | 0.999920i | \(-0.495963\pi\) | ||||
0.0126818 | + | 0.999920i | \(0.495963\pi\) | |||||||
\(102\) | 415193. | 3.95138 | ||||||||
\(103\) | 210878. | 1.95857 | 0.979283 | − | 0.202497i | \(-0.0649056\pi\) | ||||
0.979283 | + | 0.202497i | \(0.0649056\pi\) | |||||||
\(104\) | −45741.9 | −0.414697 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 377764. | 3.26555 | ||||||||
\(107\) | −107005. | −0.903531 | −0.451765 | − | 0.892137i | \(-0.649206\pi\) | ||||
−0.451765 | + | 0.892137i | \(0.649206\pi\) | |||||||
\(108\) | −290148. | −2.39365 | ||||||||
\(109\) | 151212. | 1.21904 | 0.609522 | − | 0.792769i | \(-0.291362\pi\) | ||||
0.609522 | + | 0.792769i | \(0.291362\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −230950. | −1.77914 | ||||||||
\(112\) | −122133. | −0.920000 | ||||||||
\(113\) | −176779. | −1.30237 | −0.651186 | − | 0.758918i | \(-0.725728\pi\) | ||||
−0.651186 | + | 0.758918i | \(0.725728\pi\) | |||||||
\(114\) | 115504. | 0.832407 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 357270. | 2.46520 | ||||||||
\(117\) | −72494.7 | −0.489600 | ||||||||
\(118\) | −37832.0 | −0.250123 | ||||||||
\(119\) | 302860. | 1.96053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 102060. | 0.633715 | ||||||||
\(122\) | −398248. | −2.42244 | ||||||||
\(123\) | −84424.9 | −0.503162 | ||||||||
\(124\) | 505457. | 2.95209 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −747765. | −4.19603 | ||||||||
\(127\) | 3379.52 | 0.0185929 | 0.00929643 | − | 0.999957i | \(-0.497041\pi\) | ||||
0.00929643 | + | 0.999957i | \(0.497041\pi\) | |||||||
\(128\) | −339235. | −1.83011 | ||||||||
\(129\) | −154266. | −0.816201 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −165563. | −0.842915 | −0.421458 | − | 0.906848i | \(-0.638481\pi\) | ||||
−0.421458 | + | 0.906848i | \(0.638481\pi\) | |||||||
\(132\) | −800319. | −3.99787 | ||||||||
\(133\) | 84253.8 | 0.413010 | ||||||||
\(134\) | −178489. | −0.858717 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −451507. | −2.09323 | ||||||||
\(137\) | −54105.0 | −0.246284 | −0.123142 | − | 0.992389i | \(-0.539297\pi\) | ||||
−0.123142 | + | 0.992389i | \(0.539297\pi\) | |||||||
\(138\) | −521441. | −2.33081 | ||||||||
\(139\) | −248178. | −1.08950 | −0.544749 | − | 0.838599i | \(-0.683375\pi\) | ||||
−0.544749 | + | 0.838599i | \(0.683375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −278432. | −1.17943 | ||||||||
\(142\) | 675457. | 2.81110 | ||||||||
\(143\) | −86687.5 | −0.354500 | ||||||||
\(144\) | 288567. | 1.15969 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 754705. | 2.93019 | ||||||||
\(147\) | −418767. | −1.59838 | ||||||||
\(148\) | 536249. | 2.01239 | ||||||||
\(149\) | 102637. | 0.378736 | 0.189368 | − | 0.981906i | \(-0.439356\pi\) | ||||
0.189368 | + | 0.981906i | \(0.439356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 513812. | 1.83384 | 0.916921 | − | 0.399068i | \(-0.130666\pi\) | ||||
0.916921 | + | 0.399068i | \(0.130666\pi\) | |||||||
\(152\) | −125606. | −0.440964 | ||||||||
\(153\) | −715576. | −2.47131 | ||||||||
\(154\) | −894161. | −3.03818 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 263682. | 0.867498 | ||||||||
\(157\) | 276514. | 0.895300 | 0.447650 | − | 0.894209i | \(-0.352261\pi\) | ||||
0.447650 | + | 0.894209i | \(0.352261\pi\) | |||||||
\(158\) | −688461. | −2.19400 | ||||||||
\(159\) | −1.01989e6 | −3.19933 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −380362. | −1.15646 | ||||||||
\(162\) | 198964. | 0.595644 | ||||||||
\(163\) | −278424. | −0.820801 | −0.410401 | − | 0.911905i | \(-0.634611\pi\) | ||||
−0.410401 | + | 0.911905i | \(0.634611\pi\) | |||||||
\(164\) | 196028. | 0.569127 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2005.54 | −0.00564885 | ||||||||
\(167\) | 407177. | 1.12978 | 0.564888 | − | 0.825167i | \(-0.308919\pi\) | ||||
0.564888 | + | 0.825167i | \(0.308919\pi\) | |||||||
\(168\) | 1.27381e6 | 3.48203 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −199069. | −0.520611 | ||||||||
\(172\) | 358195. | 0.923206 | ||||||||
\(173\) | −49123.8 | −0.124789 | −0.0623946 | − | 0.998052i | \(-0.519874\pi\) | ||||
−0.0623946 | + | 0.998052i | \(0.519874\pi\) | |||||||
\(174\) | −1.47737e6 | −3.69927 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 345062. | 0.839684 | ||||||||
\(177\) | 102139. | 0.245052 | ||||||||
\(178\) | −418026. | −0.988903 | ||||||||
\(179\) | 386317. | 0.901179 | 0.450590 | − | 0.892731i | \(-0.351214\pi\) | ||||
0.450590 | + | 0.892731i | \(0.351214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −218966. | −0.496799 | −0.248400 | − | 0.968658i | \(-0.579905\pi\) | ||||
−0.248400 | + | 0.968658i | \(0.579905\pi\) | |||||||
\(182\) | 294600. | 0.659256 | ||||||||
\(183\) | 1.07519e6 | 2.37333 | ||||||||
\(184\) | 567047. | 1.23474 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.09015e6 | −4.42991 | ||||||||
\(187\) | −855670. | −1.78938 | ||||||||
\(188\) | 646499. | 1.33405 | ||||||||
\(189\) | 875192. | 1.78217 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 277244. | 0.549894 | 0.274947 | − | 0.961459i | \(-0.411340\pi\) | ||||
0.274947 | + | 0.961459i | \(0.411340\pi\) | |||||||
\(192\) | 1.10612e6 | 2.16545 | ||||||||
\(193\) | −310407. | −0.599844 | −0.299922 | − | 0.953964i | \(-0.596961\pi\) | ||||
−0.299922 | + | 0.953964i | \(0.596961\pi\) | |||||||
\(194\) | −146884. | −0.280201 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 972344. | 1.80792 | ||||||||
\(197\) | −516120. | −0.947513 | −0.473757 | − | 0.880656i | \(-0.657102\pi\) | ||||
−0.473757 | + | 0.880656i | \(0.657102\pi\) | |||||||
\(198\) | 2.11266e6 | 3.82972 | ||||||||
\(199\) | 647020. | 1.15820 | 0.579102 | − | 0.815255i | \(-0.303403\pi\) | ||||
0.579102 | + | 0.815255i | \(0.303403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 481886. | 0.841306 | ||||||||
\(202\) | 24966.4 | 0.0430504 | ||||||||
\(203\) | −1.07766e6 | −1.83544 | ||||||||
\(204\) | 2.60273e6 | 4.37879 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.02475e6 | 3.32433 | ||||||||
\(207\) | 898693. | 1.45776 | ||||||||
\(208\) | −113688. | −0.182203 | ||||||||
\(209\) | −238042. | −0.376954 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 132130. | 0.204312 | 0.102156 | − | 0.994768i | \(-0.467426\pi\) | ||||
0.102156 | + | 0.994768i | \(0.467426\pi\) | |||||||
\(212\) | 2.36810e6 | 3.61877 | ||||||||
\(213\) | −1.82360e6 | −2.75410 | ||||||||
\(214\) | −1.02741e6 | −1.53359 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.30475e6 | −1.90279 | ||||||||
\(217\) | −1.52464e6 | −2.19796 | ||||||||
\(218\) | 1.45186e6 | 2.06912 | ||||||||
\(219\) | −2.03756e6 | −2.87077 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 281918. | 0.388278 | ||||||||
\(222\) | −2.21748e6 | −3.01979 | ||||||||
\(223\) | 919984. | 1.23885 | 0.619424 | − | 0.785057i | \(-0.287366\pi\) | ||||
0.619424 | + | 0.785057i | \(0.287366\pi\) | |||||||
\(224\) | 399807. | 0.532391 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.69735e6 | −2.21055 | ||||||||
\(227\) | 30962.8 | 0.0398819 | 0.0199409 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199409 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(228\) | 724065. | 0.922445 | ||||||||
\(229\) | 163086. | 0.205508 | 0.102754 | − | 0.994707i | \(-0.467235\pi\) | ||||
0.102754 | + | 0.994707i | \(0.467235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.41406e6 | 2.97658 | ||||||||
\(232\) | 1.60658e6 | 1.95967 | ||||||||
\(233\) | −1.19712e6 | −1.44460 | −0.722298 | − | 0.691582i | \(-0.756914\pi\) | ||||
−0.722298 | + | 0.691582i | \(0.756914\pi\) | |||||||
\(234\) | −696060. | −0.831012 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −237159. | −0.277178 | ||||||||
\(237\) | 1.85871e6 | 2.14952 | ||||||||
\(238\) | 2.90792e6 | 3.32766 | ||||||||
\(239\) | −769561. | −0.871462 | −0.435731 | − | 0.900077i | \(-0.643510\pi\) | ||||
−0.435731 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −850451. | −0.943206 | −0.471603 | − | 0.881811i | \(-0.656324\pi\) | ||||
−0.471603 | + | 0.881811i | \(0.656324\pi\) | |||||||
\(242\) | 979937. | 1.07562 | ||||||||
\(243\) | 634236. | 0.689025 | ||||||||
\(244\) | −2.49651e6 | −2.68447 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −810609. | −0.854031 | ||||||||
\(247\) | 78428.0 | 0.0817954 | ||||||||
\(248\) | 2.27296e6 | 2.34672 | ||||||||
\(249\) | 5414.55 | 0.00553431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 992979. | 0.994846 | 0.497423 | − | 0.867508i | \(-0.334280\pi\) | ||||
0.497423 | + | 0.867508i | \(0.334280\pi\) | |||||||
\(252\) | −4.68754e6 | −4.64990 | ||||||||
\(253\) | 1.07464e6 | 1.05550 | ||||||||
\(254\) | 32448.6 | 0.0315582 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.89172e6 | −1.80408 | ||||||||
\(257\) | −1.29318e6 | −1.22131 | −0.610655 | − | 0.791897i | \(-0.709094\pi\) | ||||
−0.610655 | + | 0.791897i | \(0.709094\pi\) | |||||||
\(258\) | −1.48120e6 | −1.38536 | ||||||||
\(259\) | −1.61752e6 | −1.49831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.54622e6 | 2.31363 | ||||||||
\(262\) | −1.58965e6 | −1.43070 | ||||||||
\(263\) | 1.69375e6 | 1.50994 | 0.754972 | − | 0.655757i | \(-0.227650\pi\) | ||||
0.754972 | + | 0.655757i | \(0.227650\pi\) | |||||||
\(264\) | −3.59890e6 | −3.17805 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 808966. | 0.701013 | ||||||||
\(267\) | 1.12859e6 | 0.968852 | ||||||||
\(268\) | −1.11890e6 | −0.951601 | ||||||||
\(269\) | −857080. | −0.722172 | −0.361086 | − | 0.932532i | \(-0.617594\pi\) | ||||
−0.361086 | + | 0.932532i | \(0.617594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.66147e6 | 1.37426 | 0.687130 | − | 0.726534i | \(-0.258870\pi\) | ||||
0.687130 | + | 0.726534i | \(0.258870\pi\) | |||||||
\(272\) | −1.12218e6 | −0.919691 | ||||||||
\(273\) | −795361. | −0.645889 | ||||||||
\(274\) | −519491. | −0.418024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.26877e6 | −2.58293 | ||||||||
\(277\) | −2.15375e6 | −1.68654 | −0.843269 | − | 0.537491i | \(-0.819372\pi\) | ||||
−0.843269 | + | 0.537491i | \(0.819372\pi\) | |||||||
\(278\) | −2.38289e6 | −1.84924 | ||||||||
\(279\) | 3.60233e6 | 2.77059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −547631. | −0.413735 | −0.206868 | − | 0.978369i | \(-0.566327\pi\) | ||||
−0.206868 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(282\) | −2.67338e6 | −2.00188 | ||||||||
\(283\) | 609080. | 0.452073 | 0.226036 | − | 0.974119i | \(-0.427423\pi\) | ||||
0.226036 | + | 0.974119i | \(0.427423\pi\) | |||||||
\(284\) | 4.23426e6 | 3.11517 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −832333. | −0.601703 | ||||||||
\(287\) | −591293. | −0.423739 | ||||||||
\(288\) | −944638. | −0.671095 | ||||||||
\(289\) | 1.36288e6 | 0.959874 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 396558. | 0.274520 | ||||||||
\(292\) | 4.73105e6 | 3.24713 | ||||||||
\(293\) | −927787. | −0.631363 | −0.315682 | − | 0.948865i | \(-0.602233\pi\) | ||||
−0.315682 | + | 0.948865i | \(0.602233\pi\) | |||||||
\(294\) | −4.02080e6 | −2.71297 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.41142e6 | 1.59972 | ||||||||
\(297\) | −2.47268e6 | −1.62659 | ||||||||
\(298\) | 985469. | 0.642839 | ||||||||
\(299\) | −354061. | −0.229034 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.08045e6 | −0.687365 | ||||||||
\(302\) | 4.93339e6 | 3.11263 | ||||||||
\(303\) | −67404.3 | −0.0421775 | ||||||||
\(304\) | −312185. | −0.193744 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.87063e6 | −4.19462 | ||||||||
\(307\) | 2.39073e6 | 1.44772 | 0.723859 | − | 0.689948i | \(-0.242367\pi\) | ||||
0.723859 | + | 0.689948i | \(0.242367\pi\) | |||||||
\(308\) | −5.60526e6 | −3.36681 | ||||||||
\(309\) | −5.46643e6 | −3.25692 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.27080e6 | −0.745032 | −0.372516 | − | 0.928026i | \(-0.621505\pi\) | ||||
−0.372516 | + | 0.928026i | \(0.621505\pi\) | |||||||
\(312\) | 1.18573e6 | 0.689605 | ||||||||
\(313\) | 1.69293e6 | 0.976738 | 0.488369 | − | 0.872637i | \(-0.337592\pi\) | ||||
0.488369 | + | 0.872637i | \(0.337592\pi\) | |||||||
\(314\) | 2.65496e6 | 1.51962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.31578e6 | −2.43132 | ||||||||
\(317\) | 958135. | 0.535523 | 0.267762 | − | 0.963485i | \(-0.413716\pi\) | ||||
0.267762 | + | 0.963485i | \(0.413716\pi\) | |||||||
\(318\) | −9.79249e6 | −5.43032 | ||||||||
\(319\) | 3.04471e6 | 1.67521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.77380e6 | 1.50249 | ||||||||
\(322\) | −3.65205e6 | −1.96290 | ||||||||
\(323\) | 774142. | 0.412871 | ||||||||
\(324\) | 1.24725e6 | 0.660073 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.67330e6 | −1.39317 | ||||||||
\(327\) | −3.91975e6 | −2.02716 | ||||||||
\(328\) | 881507. | 0.452419 | ||||||||
\(329\) | −1.95008e6 | −0.993259 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29139e6 | 1.14955 | 0.574777 | − | 0.818310i | \(-0.305089\pi\) | ||||
0.574777 | + | 0.818310i | \(0.305089\pi\) | |||||||
\(332\) | −12572.2 | −0.00625986 | ||||||||
\(333\) | 3.82178e6 | 1.88866 | ||||||||
\(334\) | 3.90953e6 | 1.91760 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.16596e6 | 1.52988 | ||||||||
\(337\) | 1.20806e6 | 0.579446 | 0.289723 | − | 0.957110i | \(-0.406437\pi\) | ||||
0.289723 | + | 0.957110i | \(0.406437\pi\) | |||||||
\(338\) | 274229. | 0.130564 | ||||||||
\(339\) | 4.58251e6 | 2.16573 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.30758e6 | 2.00608 | ||||||||
\(342\) | −1.91137e6 | −0.883648 | ||||||||
\(343\) | 118424. | 0.0543505 | ||||||||
\(344\) | 1.61074e6 | 0.733889 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −471664. | −0.211808 | ||||||||
\(347\) | 4.27369e6 | 1.90537 | 0.952684 | − | 0.303962i | \(-0.0983097\pi\) | ||||
0.952684 | + | 0.303962i | \(0.0983097\pi\) | |||||||
\(348\) | −9.26124e6 | −4.09941 | ||||||||
\(349\) | −1.49638e6 | −0.657625 | −0.328812 | − | 0.944395i | \(-0.606648\pi\) | ||||
−0.328812 | + | 0.944395i | \(0.606648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 814677. | 0.352954 | ||||||||
\(352\) | −1.12958e6 | −0.485914 | ||||||||
\(353\) | −730249. | −0.311914 | −0.155957 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155957 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(354\) | 980690. | 0.415933 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.62050e6 | −1.09587 | ||||||||
\(357\) | −7.85080e6 | −3.26019 | ||||||||
\(358\) | 3.70924e6 | 1.52960 | ||||||||
\(359\) | 1.04399e6 | 0.427522 | 0.213761 | − | 0.976886i | \(-0.431429\pi\) | ||||
0.213761 | + | 0.976886i | \(0.431429\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26074e6 | −0.913024 | ||||||||
\(362\) | −2.10241e6 | −0.843231 | ||||||||
\(363\) | −2.64564e6 | −1.05381 | ||||||||
\(364\) | 1.84677e6 | 0.730565 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.03235e7 | 4.02831 | ||||||||
\(367\) | 75157.4 | 0.0291277 | 0.0145639 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145639 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(368\) | 1.40935e6 | 0.542500 | ||||||||
\(369\) | 1.39707e6 | 0.534136 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.14307e6 | −2.69432 | ||||||||
\(372\) | −1.31026e7 | −4.90907 | ||||||||
\(373\) | 1.44619e6 | 0.538212 | 0.269106 | − | 0.963111i | \(-0.413272\pi\) | ||||
0.269106 | + | 0.963111i | \(0.413272\pi\) | |||||||
\(374\) | −8.21574e6 | −3.03716 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.90720e6 | 1.06049 | ||||||||
\(377\) | −1.00314e6 | −0.363504 | ||||||||
\(378\) | 8.40319e6 | 3.02493 | ||||||||
\(379\) | 291357. | 0.104190 | 0.0520951 | − | 0.998642i | \(-0.483410\pi\) | ||||
0.0520951 | + | 0.998642i | \(0.483410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −87604.8 | −0.0309183 | ||||||||
\(382\) | 2.66197e6 | 0.933350 | ||||||||
\(383\) | 3.40227e6 | 1.18515 | 0.592573 | − | 0.805517i | \(-0.298112\pi\) | ||||
0.592573 | + | 0.805517i | \(0.298112\pi\) | |||||||
\(384\) | 8.79374e6 | 3.04331 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.98038e6 | −1.01813 | ||||||||
\(387\) | 2.55281e6 | 0.866445 | ||||||||
\(388\) | −920777. | −0.310510 | ||||||||
\(389\) | 1.64309e6 | 0.550537 | 0.275268 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275268 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.49485e6 | −1.15608 | ||||||||
\(392\) | 4.37247e6 | 1.43718 | ||||||||
\(393\) | 4.29175e6 | 1.40169 | ||||||||
\(394\) | −4.95555e6 | −1.60824 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.32437e7 | 4.24397 | ||||||||
\(397\) | 2.47328e6 | 0.787585 | 0.393792 | − | 0.919199i | \(-0.371163\pi\) | ||||
0.393792 | + | 0.919199i | \(0.371163\pi\) | |||||||
\(398\) | 6.21239e6 | 1.96585 | ||||||||
\(399\) | −2.18405e6 | −0.686799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.41469e6 | 1.37100 | 0.685502 | − | 0.728071i | \(-0.259583\pi\) | ||||
0.685502 | + | 0.728071i | \(0.259583\pi\) | |||||||
\(402\) | 4.62684e6 | 1.42797 | ||||||||
\(403\) | −1.41922e6 | −0.435299 | ||||||||
\(404\) | 156508. | 0.0477070 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.03472e7 | −3.11535 | ||||||||
\(407\) | 4.56999e6 | 1.36751 | ||||||||
\(408\) | 1.17041e7 | 3.48086 | ||||||||
\(409\) | −2.67344e6 | −0.790244 | −0.395122 | − | 0.918629i | \(-0.629298\pi\) | ||||
−0.395122 | + | 0.918629i | \(0.629298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.40252e6 | 0.409549 | ||||||||
\(412\) | 1.26926e7 | 3.68391 | ||||||||
\(413\) | 715358. | 0.206371 | ||||||||
\(414\) | 8.62883e6 | 2.47429 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 372162. | 0.105439 | ||||||||
\(417\) | 6.43334e6 | 1.81174 | ||||||||
\(418\) | −2.28557e6 | −0.639815 | ||||||||
\(419\) | 2.27577e6 | 0.633277 | 0.316639 | − | 0.948546i | \(-0.397446\pi\) | ||||
0.316639 | + | 0.948546i | \(0.397446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.79147e6 | 1.31754 | 0.658770 | − | 0.752345i | \(-0.271077\pi\) | ||||
0.658770 | + | 0.752345i | \(0.271077\pi\) | |||||||
\(422\) | 1.26865e6 | 0.346785 | ||||||||
\(423\) | 4.60751e6 | 1.25203 | ||||||||
\(424\) | 1.06490e7 | 2.87669 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.75093e7 | −4.67462 | ||||||||
\(427\) | 7.53039e6 | 1.99870 | ||||||||
\(428\) | −6.44055e6 | −1.69947 | ||||||||
\(429\) | 2.24714e6 | 0.589503 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.09885e6 | −0.544238 | −0.272119 | − | 0.962264i | \(-0.587725\pi\) | ||||
−0.272119 | + | 0.962264i | \(0.587725\pi\) | |||||||
\(432\) | −3.24285e6 | −0.836021 | ||||||||
\(433\) | 2.53735e6 | 0.650370 | 0.325185 | − | 0.945650i | \(-0.394573\pi\) | ||||
0.325185 | + | 0.945650i | \(0.394573\pi\) | |||||||
\(434\) | −1.46389e7 | −3.73065 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.10135e6 | 2.29292 | ||||||||
\(437\) | −972246. | −0.243541 | ||||||||
\(438\) | −1.95637e7 | −4.87264 | ||||||||
\(439\) | 3.67042e6 | 0.908979 | 0.454490 | − | 0.890752i | \(-0.349822\pi\) | ||||
0.454490 | + | 0.890752i | \(0.349822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.92977e6 | 1.69677 | ||||||||
\(442\) | 2.70685e6 | 0.659034 | ||||||||
\(443\) | −2.32270e6 | −0.562321 | −0.281161 | − | 0.959661i | \(-0.590719\pi\) | ||||
−0.281161 | + | 0.959661i | \(0.590719\pi\) | |||||||
\(444\) | −1.39008e7 | −3.34643 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.83325e6 | 2.10273 | ||||||||
\(447\) | −2.66057e6 | −0.629805 | ||||||||
\(448\) | 7.74702e6 | 1.82364 | ||||||||
\(449\) | −4.30759e6 | −1.00837 | −0.504183 | − | 0.863597i | \(-0.668206\pi\) | ||||
−0.504183 | + | 0.863597i | \(0.668206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67058e6 | 0.386747 | ||||||||
\(452\) | −1.06403e7 | −2.44966 | ||||||||
\(453\) | −1.33192e7 | −3.04952 | ||||||||
\(454\) | 297290. | 0.0676926 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.25600e6 | 0.733285 | ||||||||
\(457\) | 1.14361e6 | 0.256145 | 0.128073 | − | 0.991765i | \(-0.459121\pi\) | ||||
0.128073 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(458\) | 1.56588e6 | 0.348814 | ||||||||
\(459\) | 8.04146e6 | 1.78157 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.73288e6 | −0.818071 | −0.409036 | − | 0.912518i | \(-0.634135\pi\) | ||||
−0.409036 | + | 0.912518i | \(0.634135\pi\) | |||||||
\(462\) | 2.31786e7 | 5.05223 | ||||||||
\(463\) | 4.46756e6 | 0.968540 | 0.484270 | − | 0.874919i | \(-0.339085\pi\) | ||||
0.484270 | + | 0.874919i | \(0.339085\pi\) | |||||||
\(464\) | 3.99304e6 | 0.861011 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.14942e7 | −2.45195 | ||||||||
\(467\) | −5.73689e6 | −1.21726 | −0.608632 | − | 0.793453i | \(-0.708281\pi\) | ||||
−0.608632 | + | 0.793453i | \(0.708281\pi\) | |||||||
\(468\) | −4.36342e6 | −0.920900 | ||||||||
\(469\) | 3.37502e6 | 0.708507 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.16787e6 | −1.48881 | ||||||||
\(472\) | −1.06646e6 | −0.220339 | ||||||||
\(473\) | 3.05259e6 | 0.627359 | ||||||||
\(474\) | 1.78465e7 | 3.64843 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.82290e7 | 3.68761 | ||||||||
\(477\) | 1.68772e7 | 3.39628 | ||||||||
\(478\) | −7.38897e6 | −1.47916 | ||||||||
\(479\) | −8.44282e6 | −1.68131 | −0.840657 | − | 0.541567i | \(-0.817831\pi\) | ||||
−0.840657 | + | 0.541567i | \(0.817831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50568e6 | −0.296736 | ||||||||
\(482\) | −8.16563e6 | −1.60093 | ||||||||
\(483\) | 9.85982e6 | 1.92310 | ||||||||
\(484\) | 6.14297e6 | 1.19197 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.08964e6 | 1.16950 | ||||||||
\(487\) | −2.30080e6 | −0.439599 | −0.219799 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219799 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(488\) | −1.12264e7 | −2.13398 | ||||||||
\(489\) | 7.21738e6 | 1.36492 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.83374e6 | −0.343269 | −0.171635 | − | 0.985161i | \(-0.554905\pi\) | ||||
−0.171635 | + | 0.985161i | \(0.554905\pi\) | |||||||
\(492\) | −5.08149e6 | −0.946408 | ||||||||
\(493\) | −9.90176e6 | −1.83483 | ||||||||
\(494\) | 753029. | 0.138834 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.64926e6 | 1.03107 | ||||||||
\(497\) | −1.27721e7 | −2.31937 | ||||||||
\(498\) | 51988.0 | 0.00939354 | ||||||||
\(499\) | −1.65708e6 | −0.297916 | −0.148958 | − | 0.988844i | \(-0.547592\pi\) | ||||
−0.148958 | + | 0.988844i | \(0.547592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.05550e7 | −1.87872 | ||||||||
\(502\) | 9.53412e6 | 1.68858 | ||||||||
\(503\) | 674839. | 0.118927 | 0.0594634 | − | 0.998230i | \(-0.481061\pi\) | ||||
0.0594634 | + | 0.998230i | \(0.481061\pi\) | |||||||
\(504\) | −2.10791e7 | −3.69637 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.03182e7 | 1.79154 | ||||||||
\(507\) | −740365. | −0.127916 | ||||||||
\(508\) | 203412. | 0.0349717 | ||||||||
\(509\) | 214603. | 0.0367148 | 0.0183574 | − | 0.999831i | \(-0.494156\pi\) | ||||
0.0183574 | + | 0.999831i | \(0.494156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.42706e7 | −2.41763 | ||||||||
\(512\) | −7.30787e6 | −1.23202 | ||||||||
\(513\) | 2.23709e6 | 0.375310 | ||||||||
\(514\) | −1.24165e7 | −2.07296 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.28522e6 | −1.53521 | ||||||||
\(517\) | 5.50956e6 | 0.906548 | ||||||||
\(518\) | −1.55307e7 | −2.54312 | ||||||||
\(519\) | 1.27340e6 | 0.207513 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.75675e6 | 1.57475 | 0.787373 | − | 0.616476i | \(-0.211440\pi\) | ||||
0.787373 | + | 0.616476i | \(0.211440\pi\) | |||||||
\(522\) | 2.44476e7 | 3.92699 | ||||||||
\(523\) | −1.41439e6 | −0.226107 | −0.113054 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113054 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(524\) | −9.96512e6 | −1.58546 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.62626e7 | 2.56287 | ||||||||
\(527\) | −1.40088e7 | −2.19722 | ||||||||
\(528\) | −8.94479e6 | −1.39632 | ||||||||
\(529\) | −2.04716e6 | −0.318063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.69020e6 | −0.260137 | ||||||||
\(532\) | 5.07119e6 | 0.776839 | ||||||||
\(533\) | −550408. | −0.0839203 | ||||||||
\(534\) | 1.08362e7 | 1.64446 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.03152e6 | −0.756462 | ||||||||
\(537\) | −1.00142e7 | −1.49858 | ||||||||
\(538\) | −8.22929e6 | −1.22576 | ||||||||
\(539\) | 8.28647e6 | 1.22856 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.38226e6 | 0.937522 | 0.468761 | − | 0.883325i | \(-0.344700\pi\) | ||||
0.468761 | + | 0.883325i | \(0.344700\pi\) | |||||||
\(542\) | 1.59527e7 | 2.33257 | ||||||||
\(543\) | 5.67610e6 | 0.826134 | ||||||||
\(544\) | 3.67352e6 | 0.532212 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.63669e6 | −1.09628 | ||||||||
\(547\) | −6.98550e6 | −0.998227 | −0.499113 | − | 0.866537i | \(-0.666341\pi\) | ||||
−0.499113 | + | 0.866537i | \(0.666341\pi\) | |||||||
\(548\) | −3.25655e6 | −0.463241 | ||||||||
\(549\) | −1.77923e7 | −2.51943 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.75461e6 | −0.386528 | ||||||||
\(552\) | −1.46991e7 | −2.05326 | ||||||||
\(553\) | 1.30180e7 | 1.81022 | ||||||||
\(554\) | −2.06793e7 | −2.86261 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.49377e7 | −2.04926 | ||||||||
\(557\) | −8.50622e6 | −1.16171 | −0.580856 | − | 0.814006i | \(-0.697282\pi\) | ||||
−0.580856 | + | 0.814006i | \(0.697282\pi\) | |||||||
\(558\) | 3.45879e7 | 4.70260 | ||||||||
\(559\) | −1.00574e6 | −0.136131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.21809e7 | 2.97558 | ||||||||
\(562\) | −5.25810e6 | −0.702244 | ||||||||
\(563\) | 5.22994e6 | 0.695386 | 0.347693 | − | 0.937608i | \(-0.386965\pi\) | ||||
0.347693 | + | 0.937608i | \(0.386965\pi\) | |||||||
\(564\) | −1.67587e7 | −2.21841 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.84810e6 | 0.767315 | ||||||||
\(567\) | −3.76217e6 | −0.491452 | ||||||||
\(568\) | 1.90408e7 | 2.47636 | ||||||||
\(569\) | 1.12412e7 | 1.45556 | 0.727781 | − | 0.685809i | \(-0.240552\pi\) | ||||
0.727781 | + | 0.685809i | \(0.240552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.42903e6 | −0.440130 | −0.220065 | − | 0.975485i | \(-0.570627\pi\) | ||||
−0.220065 | + | 0.975485i | \(0.570627\pi\) | |||||||
\(572\) | −5.21768e6 | −0.666787 | ||||||||
\(573\) | −7.18679e6 | −0.914426 | ||||||||
\(574\) | −5.67732e6 | −0.719224 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.83041e7 | −2.29876 | ||||||||
\(577\) | −1.39888e7 | −1.74920 | −0.874600 | − | 0.484845i | \(-0.838876\pi\) | ||||
−0.874600 | + | 0.484845i | \(0.838876\pi\) | |||||||
\(578\) | 1.30858e7 | 1.62922 | ||||||||
\(579\) | 8.04645e6 | 0.997488 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37922.3 | 0.00466073 | ||||||||
\(582\) | 3.80756e6 | 0.465950 | ||||||||
\(583\) | 2.01813e7 | 2.45911 | ||||||||
\(584\) | 2.12747e7 | 2.58126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.90818e6 | −1.07163 | ||||||||
\(587\) | 2.19504e6 | 0.262934 | 0.131467 | − | 0.991321i | \(-0.458031\pi\) | ||||
0.131467 | + | 0.991321i | \(0.458031\pi\) | |||||||
\(588\) | −2.52053e7 | −3.00642 | ||||||||
\(589\) | −3.89716e6 | −0.462871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.33790e7 | 1.57563 | ||||||||
\(592\) | 5.99340e6 | 0.702861 | ||||||||
\(593\) | 1.41425e6 | 0.165154 | 0.0825772 | − | 0.996585i | \(-0.473685\pi\) | ||||
0.0825772 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(594\) | −2.37416e7 | −2.76085 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.17765e6 | 0.712373 | ||||||||
\(597\) | −1.67722e7 | −1.92599 | ||||||||
\(598\) | −3.39953e6 | −0.388746 | ||||||||
\(599\) | −9.66661e6 | −1.10080 | −0.550398 | − | 0.834902i | \(-0.685524\pi\) | ||||
−0.550398 | + | 0.834902i | \(0.685524\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.23263e6 | −0.929721 | −0.464860 | − | 0.885384i | \(-0.653895\pi\) | ||||
−0.464860 | + | 0.885384i | \(0.653895\pi\) | |||||||
\(602\) | −1.03740e7 | −1.16668 | ||||||||
\(603\) | −7.97427e6 | −0.893095 | ||||||||
\(604\) | 3.09261e7 | 3.44931 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −647185. | −0.0715891 | ||||||||
\(607\) | 7.61203e6 | 0.838549 | 0.419275 | − | 0.907859i | \(-0.362284\pi\) | ||||
0.419275 | + | 0.907859i | \(0.362284\pi\) | |||||||
\(608\) | 1.02195e6 | 0.112117 | ||||||||
\(609\) | 2.79353e7 | 3.05218 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.81524e6 | −0.196712 | ||||||||
\(612\) | −4.30702e7 | −4.64834 | ||||||||
\(613\) | 1.04544e7 | 1.12369 | 0.561844 | − | 0.827243i | \(-0.310092\pi\) | ||||
0.561844 | + | 0.827243i | \(0.310092\pi\) | |||||||
\(614\) | 2.29546e7 | 2.45725 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.52059e7 | −2.67640 | ||||||||
\(617\) | −8.78600e6 | −0.929134 | −0.464567 | − | 0.885538i | \(-0.653790\pi\) | ||||
−0.464567 | + | 0.885538i | \(0.653790\pi\) | |||||||
\(618\) | −5.24861e7 | −5.52807 | ||||||||
\(619\) | 8.05994e6 | 0.845484 | 0.422742 | − | 0.906250i | \(-0.361068\pi\) | ||||
0.422742 | + | 0.906250i | \(0.361068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00993e7 | −1.05090 | ||||||||
\(622\) | −1.22016e7 | −1.26456 | ||||||||
\(623\) | 7.90438e6 | 0.815921 | ||||||||
\(624\) | 2.94705e6 | 0.302988 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.62547e7 | 1.65784 | ||||||||
\(627\) | 6.17059e6 | 0.626842 | ||||||||
\(628\) | 1.66433e7 | 1.68399 | ||||||||
\(629\) | −1.48622e7 | −1.49781 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.42505e6 | 0.142481 | 0.0712404 | − | 0.997459i | \(-0.477304\pi\) | ||||
0.0712404 | + | 0.997459i | \(0.477304\pi\) | |||||||
\(632\) | −1.94074e7 | −1.93274 | ||||||||
\(633\) | −3.42510e6 | −0.339754 | ||||||||
\(634\) | 9.19956e6 | 0.908959 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.13865e7 | −6.01769 | ||||||||
\(637\) | −2.73015e6 | −0.266586 | ||||||||
\(638\) | 2.92339e7 | 2.84338 | ||||||||
\(639\) | 3.01770e7 | 2.92364 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11250e6 | 0.106944 | 0.0534718 | − | 0.998569i | \(-0.482971\pi\) | ||||
0.0534718 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(642\) | 2.66327e7 | 2.55022 | ||||||||
\(643\) | −9.07113e6 | −0.865235 | −0.432617 | − | 0.901578i | \(-0.642410\pi\) | ||||
−0.432617 | + | 0.901578i | \(0.642410\pi\) | |||||||
\(644\) | −2.28938e7 | −2.17522 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.43295e6 | 0.700777 | ||||||||
\(647\) | 2.19842e6 | 0.206467 | 0.103234 | − | 0.994657i | \(-0.467081\pi\) | ||||
0.103234 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(648\) | 5.60869e6 | 0.524716 | ||||||||
\(649\) | −2.02110e6 | −0.188355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.95222e7 | 3.65501 | ||||||||
\(652\) | −1.67582e7 | −1.54386 | ||||||||
\(653\) | −1.42857e7 | −1.31105 | −0.655525 | − | 0.755173i | \(-0.727553\pi\) | ||||
−0.655525 | + | 0.755173i | \(0.727553\pi\) | |||||||
\(654\) | −3.76356e7 | −3.44076 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.19092e6 | 0.198777 | ||||||||
\(657\) | 3.37176e7 | 3.04749 | ||||||||
\(658\) | −1.87237e7 | −1.68589 | ||||||||
\(659\) | 1.54265e7 | 1.38374 | 0.691869 | − | 0.722023i | \(-0.256787\pi\) | ||||
0.691869 | + | 0.722023i | \(0.256787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.65514e7 | 1.47344 | 0.736719 | − | 0.676199i | \(-0.236374\pi\) | ||||
0.736719 | + | 0.676199i | \(0.236374\pi\) | |||||||
\(662\) | 2.20009e7 | 1.95117 | ||||||||
\(663\) | −7.30795e6 | −0.645672 | ||||||||
\(664\) | −56535.0 | −0.00497619 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.66949e7 | 3.20568 | ||||||||
\(667\) | 1.24356e7 | 1.08231 | ||||||||
\(668\) | 2.45078e7 | 2.12502 | ||||||||
\(669\) | −2.38480e7 | −2.06010 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.12756e7 | −1.82422 | ||||||||
\(672\) | −1.03639e7 | −0.885320 | ||||||||
\(673\) | 8.91603e6 | 0.758811 | 0.379406 | − | 0.925230i | \(-0.376129\pi\) | ||||
0.379406 | + | 0.925230i | \(0.376129\pi\) | |||||||
\(674\) | 1.15992e7 | 0.983510 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.71907e6 | 0.144686 | ||||||||
\(677\) | −8.15442e6 | −0.683788 | −0.341894 | − | 0.939739i | \(-0.611068\pi\) | ||||
−0.341894 | + | 0.939739i | \(0.611068\pi\) | |||||||
\(678\) | 4.39992e7 | 3.67596 | ||||||||
\(679\) | 2.77740e6 | 0.231187 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −802625. | −0.0663200 | ||||||||
\(682\) | 4.13594e7 | 3.40497 | ||||||||
\(683\) | 2.02314e6 | 0.165948 | 0.0829742 | − | 0.996552i | \(-0.473558\pi\) | ||||
0.0829742 | + | 0.996552i | \(0.473558\pi\) | |||||||
\(684\) | −1.19819e7 | −0.979229 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.13705e6 | 0.0922507 | ||||||||
\(687\) | −4.22756e6 | −0.341742 | ||||||||
\(688\) | 4.00338e6 | 0.322445 | ||||||||
\(689\) | −6.64915e6 | −0.533603 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.61163e6 | −0.447089 | −0.223545 | − | 0.974694i | \(-0.571763\pi\) | ||||
−0.223545 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(692\) | −2.95674e6 | −0.234719 | ||||||||
\(693\) | −3.99479e7 | −3.15981 | ||||||||
\(694\) | 4.10339e7 | 3.23403 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.16463e7 | −3.25877 | ||||||||
\(697\) | −5.43293e6 | −0.423597 | ||||||||
\(698\) | −1.43675e7 | −1.11620 | ||||||||
\(699\) | 3.10319e7 | 2.40224 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.09127e6 | −0.391319 | −0.195660 | − | 0.980672i | \(-0.562685\pi\) | ||||
−0.195660 | + | 0.980672i | \(0.562685\pi\) | |||||||
\(702\) | 7.82215e6 | 0.599078 | ||||||||
\(703\) | −4.13457e6 | −0.315531 | ||||||||
\(704\) | −2.18877e7 | −1.66444 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.01152e6 | −0.529420 | ||||||||
\(707\) | −472085. | −0.0355199 | ||||||||
\(708\) | 6.14769e6 | 0.460923 | ||||||||
\(709\) | 1.54906e7 | 1.15732 | 0.578658 | − | 0.815570i | \(-0.303577\pi\) | ||||
0.578658 | + | 0.815570i | \(0.303577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.07580e7 | −2.28184 | ||||||||
\(712\) | −1.17839e7 | −0.871146 | ||||||||
\(713\) | 1.75936e7 | 1.29608 | ||||||||
\(714\) | −7.53797e7 | −5.53362 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.32522e7 | 1.69505 | ||||||||
\(717\) | 1.99488e7 | 1.44916 | ||||||||
\(718\) | 1.00239e7 | 0.725645 | ||||||||
\(719\) | −1.12604e7 | −0.812328 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.82857e7 | −2.74282 | ||||||||
\(722\) | −2.17065e7 | −1.54970 | ||||||||
\(723\) | 2.20456e7 | 1.56847 | ||||||||
\(724\) | −1.31795e7 | −0.934440 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.54022e7 | −1.78867 | ||||||||
\(727\) | −8.14136e6 | −0.571296 | −0.285648 | − | 0.958335i | \(-0.592209\pi\) | ||||
−0.285648 | + | 0.958335i | \(0.592209\pi\) | |||||||
\(728\) | 8.30461e6 | 0.580752 | ||||||||
\(729\) | −2.14763e7 | −1.49672 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.92740e6 | −0.687135 | ||||||||
\(732\) | 6.47151e7 | 4.46404 | ||||||||
\(733\) | 1.30341e7 | 0.896025 | 0.448013 | − | 0.894027i | \(-0.352132\pi\) | ||||
0.448013 | + | 0.894027i | \(0.352132\pi\) | |||||||
\(734\) | 721626. | 0.0494393 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.61357e6 | −0.313937 | ||||||||
\(737\) | −9.53545e6 | −0.646655 | ||||||||
\(738\) | 1.34140e7 | 0.906604 | ||||||||
\(739\) | −1.95666e7 | −1.31796 | −0.658981 | − | 0.752159i | \(-0.729012\pi\) | ||||
−0.658981 | + | 0.752159i | \(0.729012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.03303e6 | −0.136019 | ||||||||
\(742\) | −6.85844e7 | −4.57315 | ||||||||
\(743\) | 1.78971e6 | 0.118935 | 0.0594675 | − | 0.998230i | \(-0.481060\pi\) | ||||
0.0594675 | + | 0.998230i | \(0.481060\pi\) | |||||||
\(744\) | −5.89201e7 | −3.90240 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.38857e7 | 0.913523 | ||||||||
\(747\) | −89600.2 | −0.00587500 | ||||||||
\(748\) | −5.15023e7 | −3.36568 | ||||||||
\(749\) | 1.94271e7 | 1.26533 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.13528e7 | −1.38151 | −0.690755 | − | 0.723089i | \(-0.742722\pi\) | ||||
−0.690755 | + | 0.723089i | \(0.742722\pi\) | |||||||
\(752\) | 7.22562e6 | 0.465940 | ||||||||
\(753\) | −2.57402e7 | −1.65434 | ||||||||
\(754\) | −9.63171e6 | −0.616985 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.26774e7 | 3.35212 | ||||||||
\(757\) | 7.21618e6 | 0.457686 | 0.228843 | − | 0.973463i | \(-0.426506\pi\) | ||||
0.228843 | + | 0.973463i | \(0.426506\pi\) | |||||||
\(758\) | 2.79747e6 | 0.176845 | ||||||||
\(759\) | −2.78570e7 | −1.75521 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.18696e7 | −0.742974 | −0.371487 | − | 0.928438i | \(-0.621152\pi\) | ||||
−0.371487 | + | 0.928438i | \(0.621152\pi\) | |||||||
\(762\) | −841141. | −0.0524785 | ||||||||
\(763\) | −2.74530e7 | −1.70718 | ||||||||
\(764\) | 1.66872e7 | 1.03431 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.26670e7 | 2.01158 | ||||||||
\(767\) | 665894. | 0.0408711 | ||||||||
\(768\) | 4.90376e7 | 3.00003 | ||||||||
\(769\) | −2.02111e7 | −1.23247 | −0.616233 | − | 0.787564i | \(-0.711342\pi\) | ||||
−0.616233 | + | 0.787564i | \(0.711342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.35221e7 | 2.03093 | ||||||||
\(772\) | −1.86832e7 | −1.12826 | ||||||||
\(773\) | 4.38847e6 | 0.264158 | 0.132079 | − | 0.991239i | \(-0.457835\pi\) | ||||
0.132079 | + | 0.991239i | \(0.457835\pi\) | |||||||
\(774\) | 2.45109e7 | 1.47064 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.14058e6 | −0.246835 | ||||||||
\(777\) | 4.19299e7 | 2.49156 | ||||||||
\(778\) | 1.57762e7 | 0.934442 | ||||||||
\(779\) | −1.51141e6 | −0.0892357 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.60850e7 | 2.11689 | ||||||||
\(782\) | −3.35559e7 | −1.96224 | ||||||||
\(783\) | −2.86137e7 | −1.66790 | ||||||||
\(784\) | 1.08674e7 | 0.631447 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.12074e7 | 2.37913 | ||||||||
\(787\) | −4.56154e6 | −0.262527 | −0.131264 | − | 0.991347i | \(-0.541903\pi\) | ||||
−0.131264 | + | 0.991347i | \(0.541903\pi\) | |||||||
\(788\) | −3.10650e7 | −1.78220 | ||||||||
\(789\) | −4.39059e7 | −2.51090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.20949e7 | 1.82387 | ||||||||
\(792\) | 5.95549e7 | 3.37368 | ||||||||
\(793\) | 7.00970e6 | 0.395837 | ||||||||
\(794\) | 2.37473e7 | 1.33679 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.89438e7 | 2.17849 | ||||||||
\(797\) | 1.86077e7 | 1.03764 | 0.518820 | − | 0.854883i | \(-0.326371\pi\) | ||||
0.518820 | + | 0.854883i | \(0.326371\pi\) | |||||||
\(798\) | −2.09702e7 | −1.16572 | ||||||||
\(799\) | −1.79177e7 | −0.992925 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.86759e7 | −1.02849 | ||||||||
\(802\) | 4.23878e7 | 2.32704 | ||||||||
\(803\) | 4.03187e7 | 2.20657 | ||||||||
\(804\) | 2.90044e7 | 1.58243 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.36267e7 | −0.738845 | ||||||||
\(807\) | 2.22175e7 | 1.20091 | ||||||||
\(808\) | 703789. | 0.0379240 | ||||||||
\(809\) | −1.95576e7 | −1.05062 | −0.525309 | − | 0.850911i | \(-0.676050\pi\) | ||||
−0.525309 | + | 0.850911i | \(0.676050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.88885e7 | −1.00843 | −0.504214 | − | 0.863579i | \(-0.668218\pi\) | ||||
−0.504214 | + | 0.863579i | \(0.668218\pi\) | |||||||
\(812\) | −6.48637e7 | −3.45232 | ||||||||
\(813\) | −4.30690e7 | −2.28528 | ||||||||
\(814\) | 4.38790e7 | 2.32111 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.90895e7 | 1.52937 | ||||||||
\(817\) | −2.76174e6 | −0.144753 | ||||||||
\(818\) | −2.56691e7 | −1.34130 | ||||||||
\(819\) | 1.31617e7 | 0.685648 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.00926e6 | 0.362923 | 0.181461 | − | 0.983398i | \(-0.441917\pi\) | ||||
0.181461 | + | 0.983398i | \(0.441917\pi\) | |||||||
\(822\) | 1.34664e7 | 0.695138 | ||||||||
\(823\) | −2.33685e7 | −1.20263 | −0.601313 | − | 0.799014i | \(-0.705355\pi\) | ||||
−0.601313 | + | 0.799014i | \(0.705355\pi\) | |||||||
\(824\) | 5.70767e7 | 2.92847 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.86853e6 | 0.350279 | ||||||||
\(827\) | 2.84662e7 | 1.44732 | 0.723662 | − | 0.690155i | \(-0.242458\pi\) | ||||
0.723662 | + | 0.690155i | \(0.242458\pi\) | |||||||
\(828\) | 5.40918e7 | 2.74193 | ||||||||
\(829\) | −1.37621e7 | −0.695503 | −0.347752 | − | 0.937587i | \(-0.613055\pi\) | ||||
−0.347752 | + | 0.937587i | \(0.613055\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.58301e7 | 2.80457 | ||||||||
\(832\) | 7.21135e6 | 0.361167 | ||||||||
\(833\) | −2.69486e7 | −1.34562 | ||||||||
\(834\) | 6.17699e7 | 3.07512 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.43276e7 | −0.709021 | ||||||||
\(837\) | −4.04820e7 | −1.99732 | ||||||||
\(838\) | 2.18509e7 | 1.07488 | ||||||||
\(839\) | −3.18392e7 | −1.56155 | −0.780776 | − | 0.624811i | \(-0.785176\pi\) | ||||
−0.780776 | + | 0.624811i | \(0.785176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.47220e7 | 0.717757 | ||||||||
\(842\) | 4.60055e7 | 2.23630 | ||||||||
\(843\) | 1.41958e7 | 0.688006 | ||||||||
\(844\) | 7.95282e6 | 0.384295 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.42392e7 | 2.12511 | ||||||||
\(847\) | −1.85294e7 | −0.887471 | ||||||||
\(848\) | 2.64672e7 | 1.26392 | ||||||||
\(849\) | −1.57887e7 | −0.751757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.86654e7 | 0.883514 | ||||||||
\(852\) | −1.09761e8 | −5.18025 | ||||||||
\(853\) | 2.97955e6 | 0.140210 | 0.0701049 | − | 0.997540i | \(-0.477667\pi\) | ||||
0.0701049 | + | 0.997540i | \(0.477667\pi\) | |||||||
\(854\) | 7.23033e7 | 3.39245 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.89621e7 | −1.35097 | ||||||||
\(857\) | −1.00599e7 | −0.467886 | −0.233943 | − | 0.972250i | \(-0.575163\pi\) | ||||
−0.233943 | + | 0.972250i | \(0.575163\pi\) | |||||||
\(858\) | 2.15759e7 | 1.00058 | ||||||||
\(859\) | 1.59873e7 | 0.739252 | 0.369626 | − | 0.929181i | \(-0.379486\pi\) | ||||
0.369626 | + | 0.929181i | \(0.379486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.53277e7 | 0.704641 | ||||||||
\(862\) | −2.01522e7 | −0.923751 | ||||||||
\(863\) | 9.59580e6 | 0.438586 | 0.219293 | − | 0.975659i | \(-0.429625\pi\) | ||||
0.219293 | + | 0.975659i | \(0.429625\pi\) | |||||||
\(864\) | 1.06156e7 | 0.483794 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.43624e7 | 1.10389 | ||||||||
\(867\) | −3.53290e7 | −1.59619 | ||||||||
\(868\) | −9.17675e7 | −4.13418 | ||||||||
\(869\) | −3.67797e7 | −1.65219 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14165e6 | 0.140318 | ||||||||
\(872\) | 4.09273e7 | 1.82273 | ||||||||
\(873\) | −6.56226e6 | −0.291419 | ||||||||
\(874\) | −9.33505e6 | −0.413369 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.22639e8 | −5.39970 | ||||||||
\(877\) | 1.09080e7 | 0.478902 | 0.239451 | − | 0.970908i | \(-0.423033\pi\) | ||||
0.239451 | + | 0.970908i | \(0.423033\pi\) | |||||||
\(878\) | 3.52416e7 | 1.54284 | ||||||||
\(879\) | 2.40503e7 | 1.04990 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −897407. | −0.0389538 | −0.0194769 | − | 0.999810i | \(-0.506200\pi\) | ||||
−0.0194769 | + | 0.999810i | \(0.506200\pi\) | |||||||
\(882\) | 6.65365e7 | 2.87997 | ||||||||
\(883\) | −3.37890e7 | −1.45839 | −0.729195 | − | 0.684306i | \(-0.760105\pi\) | ||||
−0.729195 | + | 0.684306i | \(0.760105\pi\) | |||||||
\(884\) | 1.69685e7 | 0.730320 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.23015e7 | −0.954443 | ||||||||
\(887\) | 2.26350e7 | 0.965989 | 0.482994 | − | 0.875623i | \(-0.339549\pi\) | ||||
0.482994 | + | 0.875623i | \(0.339549\pi\) | |||||||
\(888\) | −6.25095e7 | −2.66020 | ||||||||
\(889\) | −613565. | −0.0260379 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.06293e7 | 0.448549 | ||||||||
\(892\) | 5.53733e7 | 2.33017 | ||||||||
\(893\) | −4.98461e6 | −0.209172 | ||||||||
\(894\) | −2.55456e7 | −1.06899 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.15894e7 | 2.56293 | ||||||||
\(897\) | 9.17806e6 | 0.380864 | ||||||||
\(898\) | −4.13594e7 | −1.71153 | ||||||||
\(899\) | 4.98470e7 | 2.05703 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.56321e7 | −2.69342 | ||||||||
\(902\) | 1.60402e7 | 0.656436 | ||||||||
\(903\) | 2.80076e7 | 1.14303 | ||||||||
\(904\) | −4.78475e7 | −1.94732 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.27884e8 | −5.17604 | ||||||||
\(907\) | −3.13826e7 | −1.26669 | −0.633345 | − | 0.773870i | \(-0.718319\pi\) | ||||
−0.633345 | + | 0.773870i | \(0.718319\pi\) | |||||||
\(908\) | 1.86363e6 | 0.0750146 | ||||||||
\(909\) | 1.11541e6 | 0.0447739 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.54672e7 | −1.01668 | −0.508341 | − | 0.861156i | \(-0.669741\pi\) | ||||
−0.508341 | + | 0.861156i | \(0.669741\pi\) | |||||||
\(912\) | 8.09254e6 | 0.322179 | ||||||||
\(913\) | −107142. | −0.00425385 | ||||||||
\(914\) | 1.09804e7 | 0.434763 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.81608e6 | 0.386544 | ||||||||
\(917\) | 3.00585e7 | 1.18044 | ||||||||
\(918\) | 7.72104e7 | 3.02391 | ||||||||
\(919\) | −2.19820e7 | −0.858577 | −0.429288 | − | 0.903167i | \(-0.641236\pi\) | ||||
−0.429288 | + | 0.903167i | \(0.641236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.19730e7 | −2.40743 | ||||||||
\(922\) | −3.58413e7 | −1.38854 | ||||||||
\(923\) | −1.18889e7 | −0.459345 | ||||||||
\(924\) | 1.45301e8 | 5.59871 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.28954e7 | 1.64393 | ||||||||
\(927\) | 9.04588e7 | 3.45741 | ||||||||
\(928\) | −1.30714e7 | −0.498255 | ||||||||
\(929\) | 2.75340e7 | 1.04672 | 0.523359 | − | 0.852112i | \(-0.324679\pi\) | ||||
0.523359 | + | 0.852112i | \(0.324679\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.49694e6 | −0.283472 | ||||||||
\(932\) | −7.20538e7 | −2.71717 | ||||||||
\(933\) | 3.29419e7 | 1.23892 | ||||||||
\(934\) | −5.50830e7 | −2.06610 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.96216e7 | −0.732056 | ||||||||
\(937\) | −117742. | −0.00438111 | −0.00219055 | − | 0.999998i | \(-0.500697\pi\) | ||||
−0.00219055 | + | 0.999998i | \(0.500697\pi\) | |||||||
\(938\) | 3.24054e7 | 1.20257 | ||||||||
\(939\) | −4.38845e7 | −1.62423 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.19282e7 | 0.439136 | 0.219568 | − | 0.975597i | \(-0.429535\pi\) | ||||
0.219568 | + | 0.975597i | \(0.429535\pi\) | |||||||
\(942\) | −6.88226e7 | −2.52699 | ||||||||
\(943\) | 6.82323e6 | 0.249868 | ||||||||
\(944\) | −2.65061e6 | −0.0968091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.93096e7 | 1.06483 | ||||||||
\(947\) | 4.67856e7 | 1.69526 | 0.847632 | − | 0.530585i | \(-0.178028\pi\) | ||||
0.847632 | + | 0.530585i | \(0.178028\pi\) | |||||||
\(948\) | 1.11875e8 | 4.04307 | ||||||||
\(949\) | −1.32838e7 | −0.478804 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.48370e7 | −0.890529 | ||||||||
\(952\) | 8.19727e7 | 2.93141 | ||||||||
\(953\) | 1.84653e6 | 0.0658603 | 0.0329301 | − | 0.999458i | \(-0.489516\pi\) | ||||
0.0329301 | + | 0.999458i | \(0.489516\pi\) | |||||||
\(954\) | 1.62047e8 | 5.76460 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.63195e7 | −1.63915 | ||||||||
\(957\) | −7.89257e7 | −2.78573 | ||||||||
\(958\) | −8.10641e7 | −2.85374 | ||||||||
\(959\) | 9.82296e6 | 0.344902 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.18932e7 | 1.46331 | ||||||||
\(962\) | −1.44568e7 | −0.503658 | ||||||||
\(963\) | −4.59010e7 | −1.59498 | ||||||||
\(964\) | −5.11882e7 | −1.77410 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.46694e7 | 3.26413 | ||||||||
\(967\) | −3.47395e7 | −1.19470 | −0.597349 | − | 0.801982i | \(-0.703779\pi\) | ||||
−0.597349 | + | 0.801982i | \(0.703779\pi\) | |||||||
\(968\) | 2.76239e7 | 0.947538 | ||||||||
\(969\) | −2.00675e7 | −0.686569 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.02513e7 | 0.348923 | 0.174462 | − | 0.984664i | \(-0.444182\pi\) | ||||
0.174462 | + | 0.984664i | \(0.444182\pi\) | |||||||
\(972\) | 3.81743e7 | 1.29600 | ||||||||
\(973\) | 4.50577e7 | 1.52576 | ||||||||
\(974\) | −2.20912e7 | −0.746143 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.79023e7 | −0.937597 | ||||||||
\(977\) | 1.54408e6 | 0.0517528 | 0.0258764 | − | 0.999665i | \(-0.491762\pi\) | ||||
0.0258764 | + | 0.999665i | \(0.491762\pi\) | |||||||
\(978\) | 6.92980e7 | 2.31672 | ||||||||
\(979\) | −2.23323e7 | −0.744691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.48642e7 | 2.15195 | ||||||||
\(982\) | −1.76068e7 | −0.582640 | ||||||||
\(983\) | −3.24347e7 | −1.07060 | −0.535299 | − | 0.844663i | \(-0.679801\pi\) | ||||
−0.535299 | + | 0.844663i | \(0.679801\pi\) | |||||||
\(984\) | −2.28506e7 | −0.752334 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.50721e7 | −3.11430 | ||||||||
\(987\) | 5.05504e7 | 1.65170 | ||||||||
\(988\) | 4.72054e6 | 0.153851 | ||||||||
\(989\) | 1.24678e7 | 0.405322 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.76595e7 | −1.21812 | −0.609060 | − | 0.793124i | \(-0.708453\pi\) | ||||
−0.609060 | + | 0.793124i | \(0.708453\pi\) | |||||||
\(992\) | −1.84931e7 | −0.596664 | ||||||||
\(993\) | −5.93980e7 | −1.91161 | ||||||||
\(994\) | −1.22632e8 | −3.93674 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 325899. | 0.0104096 | ||||||||
\(997\) | −3.72285e7 | −1.18614 | −0.593072 | − | 0.805149i | \(-0.702085\pi\) | ||||
−0.593072 | + | 0.805149i | \(0.702085\pi\) | |||||||
\(998\) | −1.59106e7 | −0.505661 | ||||||||
\(999\) | −4.29481e7 | −1.36154 |
(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 | 325.6.a.j.1.10 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.20 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.3 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.2 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.2 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.3 | 22 | 5.3 | odd | 4 | |||
325.6.b.i.274.20 | 22 | 5.2 | odd | 4 |