Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [841,6,Mod(1,841)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(841, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("841.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 841 = 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 841.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: | \(134.882792463\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(9.56883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 841.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.56883 | 1.51477 | 0.757385 | − | 0.652968i | \(-0.226477\pi\) | ||||
0.757385 | + | 0.652968i | \(0.226477\pi\) | |||||||
\(3\) | −18.3274 | −1.17571 | −0.587853 | − | 0.808968i | \(-0.700027\pi\) | ||||
−0.587853 | + | 0.808968i | \(0.700027\pi\) | |||||||
\(4\) | 41.4249 | 1.29453 | ||||||||
\(5\) | −84.3249 | −1.50845 | −0.754225 | − | 0.656616i | \(-0.771987\pi\) | ||||
−0.754225 | + | 0.656616i | \(0.771987\pi\) | |||||||
\(6\) | −157.045 | −1.78092 | ||||||||
\(7\) | 216.816 | 1.67242 | 0.836212 | − | 0.548406i | \(-0.184765\pi\) | ||||
0.836212 | + | 0.548406i | \(0.184765\pi\) | |||||||
\(8\) | 80.7606 | 0.446143 | ||||||||
\(9\) | 92.8952 | 0.382285 | ||||||||
\(10\) | −722.566 | −2.28496 | ||||||||
\(11\) | −380.662 | −0.948546 | −0.474273 | − | 0.880378i | \(-0.657289\pi\) | ||||
−0.474273 | + | 0.880378i | \(0.657289\pi\) | |||||||
\(12\) | −759.213 | −1.52199 | ||||||||
\(13\) | 1058.05 | 1.73638 | 0.868192 | − | 0.496228i | \(-0.165282\pi\) | ||||
0.868192 | + | 0.496228i | \(0.165282\pi\) | |||||||
\(14\) | 1857.86 | 2.53334 | ||||||||
\(15\) | 1545.46 | 1.77349 | ||||||||
\(16\) | −633.574 | −0.618724 | ||||||||
\(17\) | −801.385 | −0.672541 | −0.336271 | − | 0.941765i | \(-0.609166\pi\) | ||||
−0.336271 | + | 0.941765i | \(0.609166\pi\) | |||||||
\(18\) | 796.004 | 0.579074 | ||||||||
\(19\) | 288.487 | 0.183334 | 0.0916669 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916669 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(20\) | −3493.15 | −1.95273 | ||||||||
\(21\) | −3973.69 | −1.96628 | ||||||||
\(22\) | −3261.83 | −1.43683 | ||||||||
\(23\) | 334.571 | 0.131877 | 0.0659385 | − | 0.997824i | \(-0.478996\pi\) | ||||
0.0659385 | + | 0.997824i | \(0.478996\pi\) | |||||||
\(24\) | −1480.13 | −0.524533 | ||||||||
\(25\) | 3985.69 | 1.27542 | ||||||||
\(26\) | 9066.22 | 2.63022 | ||||||||
\(27\) | 2751.04 | 0.726252 | ||||||||
\(28\) | 8981.59 | 2.16500 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 13242.8 | 2.68644 | ||||||||
\(31\) | 3280.54 | 0.613115 | 0.306557 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306557 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(32\) | −8013.32 | −1.38337 | ||||||||
\(33\) | 6976.57 | 1.11521 | ||||||||
\(34\) | −6866.93 | −1.01875 | ||||||||
\(35\) | −18283.0 | −2.52277 | ||||||||
\(36\) | 3848.18 | 0.494879 | ||||||||
\(37\) | 11158.5 | 1.33999 | 0.669994 | − | 0.742366i | \(-0.266297\pi\) | ||||
0.669994 | + | 0.742366i | \(0.266297\pi\) | |||||||
\(38\) | 2472.00 | 0.277709 | ||||||||
\(39\) | −19391.3 | −2.04148 | ||||||||
\(40\) | −6810.13 | −0.672985 | ||||||||
\(41\) | 887.943 | 0.0824946 | 0.0412473 | − | 0.999149i | \(-0.486867\pi\) | ||||
0.0412473 | + | 0.999149i | \(0.486867\pi\) | |||||||
\(42\) | −34049.9 | −2.97846 | ||||||||
\(43\) | −13247.9 | −1.09264 | −0.546318 | − | 0.837578i | \(-0.683971\pi\) | ||||
−0.546318 | + | 0.837578i | \(0.683971\pi\) | |||||||
\(44\) | −15768.9 | −1.22792 | ||||||||
\(45\) | −7833.38 | −0.576657 | ||||||||
\(46\) | 2866.89 | 0.199763 | ||||||||
\(47\) | 2338.13 | 0.154392 | 0.0771959 | − | 0.997016i | \(-0.475403\pi\) | ||||
0.0771959 | + | 0.997016i | \(0.475403\pi\) | |||||||
\(48\) | 11611.8 | 0.727438 | ||||||||
\(49\) | 30202.3 | 1.79700 | ||||||||
\(50\) | 34152.7 | 1.93197 | ||||||||
\(51\) | 14687.3 | 0.790711 | ||||||||
\(52\) | 43829.4 | 2.24780 | ||||||||
\(53\) | 1850.38 | 0.0904840 | 0.0452420 | − | 0.998976i | \(-0.485594\pi\) | ||||
0.0452420 | + | 0.998976i | \(0.485594\pi\) | |||||||
\(54\) | 23573.2 | 1.10010 | ||||||||
\(55\) | 32099.3 | 1.43083 | ||||||||
\(56\) | 17510.2 | 0.746141 | ||||||||
\(57\) | −5287.23 | −0.215547 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7102.05 | 0.265616 | 0.132808 | − | 0.991142i | \(-0.457601\pi\) | ||||
0.132808 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(60\) | 64020.6 | 2.29584 | ||||||||
\(61\) | −9622.02 | −0.331087 | −0.165543 | − | 0.986203i | \(-0.552938\pi\) | ||||
−0.165543 | + | 0.986203i | \(0.552938\pi\) | |||||||
\(62\) | 28110.4 | 0.928728 | ||||||||
\(63\) | 20141.2 | 0.639343 | ||||||||
\(64\) | −48390.5 | −1.47676 | ||||||||
\(65\) | −89219.6 | −2.61925 | ||||||||
\(66\) | 59781.1 | 1.68929 | ||||||||
\(67\) | 11714.6 | 0.318816 | 0.159408 | − | 0.987213i | \(-0.449042\pi\) | ||||
0.159408 | + | 0.987213i | \(0.449042\pi\) | |||||||
\(68\) | −33197.3 | −0.870624 | ||||||||
\(69\) | −6131.84 | −0.155049 | ||||||||
\(70\) | −156664. | −3.82142 | ||||||||
\(71\) | −67084.1 | −1.57933 | −0.789667 | − | 0.613536i | \(-0.789747\pi\) | ||||
−0.789667 | + | 0.613536i | \(0.789747\pi\) | |||||||
\(72\) | 7502.27 | 0.170554 | ||||||||
\(73\) | 2340.00 | 0.0513935 | 0.0256967 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256967 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(74\) | 95615.2 | 2.02977 | ||||||||
\(75\) | −73047.5 | −1.49952 | ||||||||
\(76\) | 11950.6 | 0.237331 | ||||||||
\(77\) | −82533.8 | −1.58637 | ||||||||
\(78\) | −166161. | −3.09237 | ||||||||
\(79\) | −33928.9 | −0.611649 | −0.305825 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305825 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(80\) | 53426.0 | 0.933314 | ||||||||
\(81\) | −72993.0 | −1.23614 | ||||||||
\(82\) | 7608.63 | 0.124960 | ||||||||
\(83\) | −97350.5 | −1.55111 | −0.775555 | − | 0.631279i | \(-0.782530\pi\) | ||||
−0.775555 | + | 0.631279i | \(0.782530\pi\) | |||||||
\(84\) | −164610. | −2.54541 | ||||||||
\(85\) | 67576.7 | 1.01449 | ||||||||
\(86\) | −113519. | −1.65509 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30742.5 | −0.423187 | ||||||||
\(89\) | −101586. | −1.35943 | −0.679716 | − | 0.733475i | \(-0.737897\pi\) | ||||
−0.679716 | + | 0.733475i | \(0.737897\pi\) | |||||||
\(90\) | −67122.9 | −0.873504 | ||||||||
\(91\) | 229401. | 2.90397 | ||||||||
\(92\) | 13859.6 | 0.170719 | ||||||||
\(93\) | −60124.0 | −0.720843 | ||||||||
\(94\) | 20035.1 | 0.233868 | ||||||||
\(95\) | −24326.7 | −0.276550 | ||||||||
\(96\) | 146864. | 1.62643 | ||||||||
\(97\) | 84674.6 | 0.913743 | 0.456871 | − | 0.889533i | \(-0.348970\pi\) | ||||
0.456871 | + | 0.889533i | \(0.348970\pi\) | |||||||
\(98\) | 258798. | 2.72205 | ||||||||
\(99\) | −35361.7 | −0.362615 | ||||||||
\(100\) | 165107. | 1.65107 | ||||||||
\(101\) | −59936.3 | −0.584637 | −0.292318 | − | 0.956321i | \(-0.594427\pi\) | ||||
−0.292318 | + | 0.956321i | \(0.594427\pi\) | |||||||
\(102\) | 125853. | 1.19774 | ||||||||
\(103\) | −196075. | −1.82108 | −0.910542 | − | 0.413417i | \(-0.864335\pi\) | ||||
−0.910542 | + | 0.413417i | \(0.864335\pi\) | |||||||
\(104\) | 85448.3 | 0.774676 | ||||||||
\(105\) | 335081. | 2.96604 | ||||||||
\(106\) | 15855.6 | 0.137063 | ||||||||
\(107\) | 82447.0 | 0.696170 | 0.348085 | − | 0.937463i | \(-0.386832\pi\) | ||||
0.348085 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(108\) | 113961. | 0.940153 | ||||||||
\(109\) | −152195. | −1.22697 | −0.613484 | − | 0.789707i | \(-0.710233\pi\) | ||||
−0.613484 | + | 0.789707i | \(0.710233\pi\) | |||||||
\(110\) | 275054. | 2.16738 | ||||||||
\(111\) | −204507. | −1.57543 | ||||||||
\(112\) | −137369. | −1.03477 | ||||||||
\(113\) | −168561. | −1.24182 | −0.620912 | − | 0.783880i | \(-0.713238\pi\) | ||||
−0.620912 | + | 0.783880i | \(0.713238\pi\) | |||||||
\(114\) | −45305.4 | −0.326504 | ||||||||
\(115\) | −28212.7 | −0.198930 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 98287.3 | 0.663793 | ||||||||
\(118\) | 60856.3 | 0.402347 | ||||||||
\(119\) | −173753. | −1.12477 | ||||||||
\(120\) | 124812. | 0.791232 | ||||||||
\(121\) | −16147.1 | −0.100261 | ||||||||
\(122\) | −82449.5 | −0.501520 | ||||||||
\(123\) | −16273.7 | −0.0969893 | ||||||||
\(124\) | 135896. | 0.793695 | ||||||||
\(125\) | −72577.8 | −0.415460 | ||||||||
\(126\) | 172586. | 0.968457 | ||||||||
\(127\) | 21587.4 | 0.118766 | 0.0593829 | − | 0.998235i | \(-0.481087\pi\) | ||||
0.0593829 | + | 0.998235i | \(0.481087\pi\) | |||||||
\(128\) | −158224. | −0.853585 | ||||||||
\(129\) | 242800. | 1.28462 | ||||||||
\(130\) | −764508. | −3.96756 | ||||||||
\(131\) | −137802. | −0.701581 | −0.350790 | − | 0.936454i | \(-0.614087\pi\) | ||||
−0.350790 | + | 0.936454i | \(0.614087\pi\) | |||||||
\(132\) | 289004. | 1.44367 | ||||||||
\(133\) | 62548.7 | 0.306612 | ||||||||
\(134\) | 100380. | 0.482933 | ||||||||
\(135\) | −231981. | −1.09551 | ||||||||
\(136\) | −64720.3 | −0.300050 | ||||||||
\(137\) | 422084. | 1.92131 | 0.960654 | − | 0.277747i | \(-0.0895877\pi\) | ||||
0.960654 | + | 0.277747i | \(0.0895877\pi\) | |||||||
\(138\) | −52542.7 | −0.234863 | ||||||||
\(139\) | 79419.8 | 0.348652 | 0.174326 | − | 0.984688i | \(-0.444225\pi\) | ||||
0.174326 | + | 0.984688i | \(0.444225\pi\) | |||||||
\(140\) | −757372. | −3.26580 | ||||||||
\(141\) | −42852.0 | −0.181519 | ||||||||
\(142\) | −574833. | −2.39233 | ||||||||
\(143\) | −402758. | −1.64704 | ||||||||
\(144\) | −58855.9 | −0.236529 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20051.0 | 0.0778493 | ||||||||
\(147\) | −553530. | −2.11275 | ||||||||
\(148\) | 462239. | 1.73465 | ||||||||
\(149\) | −144641. | −0.533736 | −0.266868 | − | 0.963733i | \(-0.585989\pi\) | ||||
−0.266868 | + | 0.963733i | \(0.585989\pi\) | |||||||
\(150\) | −625932. | −2.27143 | ||||||||
\(151\) | −446697. | −1.59430 | −0.797152 | − | 0.603779i | \(-0.793661\pi\) | ||||
−0.797152 | + | 0.603779i | \(0.793661\pi\) | |||||||
\(152\) | 23298.4 | 0.0817931 | ||||||||
\(153\) | −74444.8 | −0.257102 | ||||||||
\(154\) | −707218. | −2.40299 | ||||||||
\(155\) | −276632. | −0.924853 | ||||||||
\(156\) | −803282. | −2.64275 | ||||||||
\(157\) | 136908. | 0.443282 | 0.221641 | − | 0.975128i | \(-0.428859\pi\) | ||||
0.221641 | + | 0.975128i | \(0.428859\pi\) | |||||||
\(158\) | −290731. | −0.926508 | ||||||||
\(159\) | −33912.8 | −0.106383 | ||||||||
\(160\) | 675723. | 2.08674 | ||||||||
\(161\) | 72540.5 | 0.220554 | ||||||||
\(162\) | −625465. | −1.87247 | ||||||||
\(163\) | −5407.16 | −0.0159404 | −0.00797022 | − | 0.999968i | \(-0.502537\pi\) | ||||
−0.00797022 | + | 0.999968i | \(0.502537\pi\) | |||||||
\(164\) | 36783.0 | 0.106792 | ||||||||
\(165\) | −588299. | −1.68224 | ||||||||
\(166\) | −834180. | −2.34958 | ||||||||
\(167\) | −303826. | −0.843013 | −0.421506 | − | 0.906825i | \(-0.638498\pi\) | ||||
−0.421506 | + | 0.906825i | \(0.638498\pi\) | |||||||
\(168\) | −320917. | −0.877243 | ||||||||
\(169\) | 748167. | 2.01503 | ||||||||
\(170\) | 579054. | 1.53673 | ||||||||
\(171\) | 26799.1 | 0.0700857 | ||||||||
\(172\) | −548792. | −1.41445 | ||||||||
\(173\) | −45069.8 | −0.114491 | −0.0572454 | − | 0.998360i | \(-0.518232\pi\) | ||||
−0.0572454 | + | 0.998360i | \(0.518232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 864163. | 2.13305 | ||||||||
\(176\) | 241178. | 0.586888 | ||||||||
\(177\) | −130162. | −0.312286 | ||||||||
\(178\) | −870471. | −2.05923 | ||||||||
\(179\) | 348392. | 0.812710 | 0.406355 | − | 0.913715i | \(-0.366800\pi\) | ||||
0.406355 | + | 0.913715i | \(0.366800\pi\) | |||||||
\(180\) | −324497. | −0.746500 | ||||||||
\(181\) | −754876. | −1.71269 | −0.856346 | − | 0.516403i | \(-0.827271\pi\) | ||||
−0.856346 | + | 0.516403i | \(0.827271\pi\) | |||||||
\(182\) | 1.96570e6 | 4.39885 | ||||||||
\(183\) | 176347. | 0.389261 | ||||||||
\(184\) | 27020.2 | 0.0588361 | ||||||||
\(185\) | −940939. | −2.02131 | ||||||||
\(186\) | −515193. | −1.09191 | ||||||||
\(187\) | 305057. | 0.637936 | ||||||||
\(188\) | 96856.9 | 0.199865 | ||||||||
\(189\) | 596469. | 1.21460 | ||||||||
\(190\) | −208451. | −0.418909 | ||||||||
\(191\) | 559504. | 1.10974 | 0.554868 | − | 0.831938i | \(-0.312769\pi\) | ||||
0.554868 | + | 0.831938i | \(0.312769\pi\) | |||||||
\(192\) | 886874. | 1.73624 | ||||||||
\(193\) | −915469. | −1.76909 | −0.884546 | − | 0.466453i | \(-0.845532\pi\) | ||||
−0.884546 | + | 0.466453i | \(0.845532\pi\) | |||||||
\(194\) | 725563. | 1.38411 | ||||||||
\(195\) | 1.63517e6 | 3.07947 | ||||||||
\(196\) | 1.25113e6 | 2.32627 | ||||||||
\(197\) | 149660. | 0.274751 | 0.137375 | − | 0.990519i | \(-0.456133\pi\) | ||||
0.137375 | + | 0.990519i | \(0.456133\pi\) | |||||||
\(198\) | −303009. | −0.549278 | ||||||||
\(199\) | 2043.12 | 0.00365731 | 0.00182865 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182865 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(200\) | 321887. | 0.569021 | ||||||||
\(201\) | −214698. | −0.374834 | ||||||||
\(202\) | −513584. | −0.885591 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 608422. | 1.02360 | ||||||||
\(205\) | −74875.7 | −0.124439 | ||||||||
\(206\) | −1.68014e6 | −2.75852 | ||||||||
\(207\) | 31080.1 | 0.0504146 | ||||||||
\(208\) | −670350. | −1.07434 | ||||||||
\(209\) | −109816. | −0.173900 | ||||||||
\(210\) | 2.87125e6 | 4.49286 | ||||||||
\(211\) | 94629.7 | 0.146326 | 0.0731630 | − | 0.997320i | \(-0.476691\pi\) | ||||
0.0731630 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(212\) | 76652.0 | 0.117134 | ||||||||
\(213\) | 1.22948e6 | 1.85683 | ||||||||
\(214\) | 706474. | 1.05454 | ||||||||
\(215\) | 1.11713e6 | 1.64819 | ||||||||
\(216\) | 222175. | 0.324012 | ||||||||
\(217\) | 711275. | 1.02539 | ||||||||
\(218\) | −1.30413e6 | −1.85857 | ||||||||
\(219\) | −42886.1 | −0.0604236 | ||||||||
\(220\) | 1.32971e6 | 1.85226 | ||||||||
\(221\) | −847902. | −1.16779 | ||||||||
\(222\) | −1.75238e6 | −2.38642 | ||||||||
\(223\) | 33151.7 | 0.0446420 | 0.0223210 | − | 0.999751i | \(-0.492894\pi\) | ||||
0.0223210 | + | 0.999751i | \(0.492894\pi\) | |||||||
\(224\) | −1.73742e6 | −2.31358 | ||||||||
\(225\) | 370252. | 0.487574 | ||||||||
\(226\) | −1.44437e6 | −1.88108 | ||||||||
\(227\) | −886146. | −1.14141 | −0.570704 | − | 0.821156i | \(-0.693329\pi\) | ||||
−0.570704 | + | 0.821156i | \(0.693329\pi\) | |||||||
\(228\) | −219023. | −0.279031 | ||||||||
\(229\) | 51324.5 | 0.0646749 | 0.0323375 | − | 0.999477i | \(-0.489705\pi\) | ||||
0.0323375 | + | 0.999477i | \(0.489705\pi\) | |||||||
\(230\) | −241750. | −0.301333 | ||||||||
\(231\) | 1.51263e6 | 1.86511 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −854399. | −1.03103 | −0.515515 | − | 0.856881i | \(-0.672399\pi\) | ||||
−0.515515 | + | 0.856881i | \(0.672399\pi\) | |||||||
\(234\) | 842208. | 1.00549 | ||||||||
\(235\) | −197163. | −0.232892 | ||||||||
\(236\) | 294202. | 0.343847 | ||||||||
\(237\) | 621831. | 0.719120 | ||||||||
\(238\) | −1.48886e6 | −1.70377 | ||||||||
\(239\) | 750885. | 0.850313 | 0.425156 | − | 0.905120i | \(-0.360219\pi\) | ||||
0.425156 | + | 0.905120i | \(0.360219\pi\) | |||||||
\(240\) | −979163. | −1.09730 | ||||||||
\(241\) | −71808.1 | −0.0796400 | −0.0398200 | − | 0.999207i | \(-0.512678\pi\) | ||||
−0.0398200 | + | 0.999207i | \(0.512678\pi\) | |||||||
\(242\) | −138362. | −0.151872 | ||||||||
\(243\) | 669273. | 0.727089 | ||||||||
\(244\) | −398591. | −0.428601 | ||||||||
\(245\) | −2.54680e6 | −2.71069 | ||||||||
\(246\) | −139447. | −0.146917 | ||||||||
\(247\) | 305233. | 0.318338 | ||||||||
\(248\) | 264939. | 0.273537 | ||||||||
\(249\) | 1.78419e6 | 1.82365 | ||||||||
\(250\) | −621907. | −0.629326 | ||||||||
\(251\) | −897843. | −0.899531 | −0.449765 | − | 0.893147i | \(-0.648492\pi\) | ||||
−0.449765 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(252\) | 834347. | 0.827647 | ||||||||
\(253\) | −127359. | −0.125091 | ||||||||
\(254\) | 184979. | 0.179903 | ||||||||
\(255\) | −1.23851e6 | −1.19275 | ||||||||
\(256\) | 192703. | 0.183776 | ||||||||
\(257\) | 848562. | 0.801402 | 0.400701 | − | 0.916209i | \(-0.368767\pi\) | ||||
0.400701 | + | 0.916209i | \(0.368767\pi\) | |||||||
\(258\) | 2.08051e6 | 1.94590 | ||||||||
\(259\) | 2.41934e6 | 2.24103 | ||||||||
\(260\) | −3.69591e6 | −3.39069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.18080e6 | −1.06273 | ||||||||
\(263\) | 592909. | 0.528565 | 0.264283 | − | 0.964445i | \(-0.414865\pi\) | ||||
0.264283 | + | 0.964445i | \(0.414865\pi\) | |||||||
\(264\) | 563432. | 0.497544 | ||||||||
\(265\) | −156033. | −0.136491 | ||||||||
\(266\) | 535969. | 0.464447 | ||||||||
\(267\) | 1.86181e6 | 1.59829 | ||||||||
\(268\) | 485276. | 0.412716 | ||||||||
\(269\) | −833107. | −0.701973 | −0.350986 | − | 0.936381i | \(-0.614154\pi\) | ||||
−0.350986 | + | 0.936381i | \(0.614154\pi\) | |||||||
\(270\) | −1.98781e6 | −1.65945 | ||||||||
\(271\) | −728989. | −0.602973 | −0.301487 | − | 0.953470i | \(-0.597483\pi\) | ||||
−0.301487 | + | 0.953470i | \(0.597483\pi\) | |||||||
\(272\) | 507736. | 0.416117 | ||||||||
\(273\) | −4.20434e6 | −3.41422 | ||||||||
\(274\) | 3.61676e6 | 2.91034 | ||||||||
\(275\) | −1.51720e6 | −1.20980 | ||||||||
\(276\) | −254011. | −0.200715 | ||||||||
\(277\) | 1.44549e6 | 1.13192 | 0.565961 | − | 0.824432i | \(-0.308505\pi\) | ||||
0.565961 | + | 0.824432i | \(0.308505\pi\) | |||||||
\(278\) | 680535. | 0.528127 | ||||||||
\(279\) | 304747. | 0.234384 | ||||||||
\(280\) | −1.47655e6 | −1.12552 | ||||||||
\(281\) | 1.71312e6 | 1.29426 | 0.647131 | − | 0.762379i | \(-0.275969\pi\) | ||||
0.647131 | + | 0.762379i | \(0.275969\pi\) | |||||||
\(282\) | −367191. | −0.274960 | ||||||||
\(283\) | 2.14168e6 | 1.58960 | 0.794799 | − | 0.606872i | \(-0.207576\pi\) | ||||
0.794799 | + | 0.606872i | \(0.207576\pi\) | |||||||
\(284\) | −2.77896e6 | −2.04449 | ||||||||
\(285\) | 445845. | 0.325141 | ||||||||
\(286\) | −3.45117e6 | −2.49489 | ||||||||
\(287\) | 192520. | 0.137966 | ||||||||
\(288\) | −744399. | −0.528841 | ||||||||
\(289\) | −777639. | −0.547688 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.55187e6 | −1.07429 | ||||||||
\(292\) | 96934.1 | 0.0665303 | ||||||||
\(293\) | −663344. | −0.451408 | −0.225704 | − | 0.974196i | \(-0.572468\pi\) | ||||
−0.225704 | + | 0.974196i | \(0.572468\pi\) | |||||||
\(294\) | −4.74311e6 | −3.20033 | ||||||||
\(295\) | −598880. | −0.400668 | ||||||||
\(296\) | 901166. | 0.597827 | ||||||||
\(297\) | −1.04722e6 | −0.688883 | ||||||||
\(298\) | −1.23941e6 | −0.808488 | ||||||||
\(299\) | 353992. | 0.228989 | ||||||||
\(300\) | −3.02599e6 | −1.94117 | ||||||||
\(301\) | −2.87236e6 | −1.82735 | ||||||||
\(302\) | −3.82768e6 | −2.41500 | ||||||||
\(303\) | 1.09848e6 | 0.687361 | ||||||||
\(304\) | −182778. | −0.113433 | ||||||||
\(305\) | 811376. | 0.499428 | ||||||||
\(306\) | −637905. | −0.389451 | ||||||||
\(307\) | −615215. | −0.372547 | −0.186274 | − | 0.982498i | \(-0.559641\pi\) | ||||
−0.186274 | + | 0.982498i | \(0.559641\pi\) | |||||||
\(308\) | −3.41896e6 | −2.05360 | ||||||||
\(309\) | 3.59356e6 | 2.14106 | ||||||||
\(310\) | −2.37041e6 | −1.40094 | ||||||||
\(311\) | 1.17303e6 | 0.687712 | 0.343856 | − | 0.939022i | \(-0.388267\pi\) | ||||
0.343856 | + | 0.939022i | \(0.388267\pi\) | |||||||
\(312\) | −1.56605e6 | −0.910792 | ||||||||
\(313\) | −2.58664e6 | −1.49237 | −0.746184 | − | 0.665740i | \(-0.768116\pi\) | ||||
−0.746184 | + | 0.665740i | \(0.768116\pi\) | |||||||
\(314\) | 1.17314e6 | 0.671470 | ||||||||
\(315\) | −1.69840e6 | −0.964416 | ||||||||
\(316\) | −1.40550e6 | −0.791798 | ||||||||
\(317\) | 934239. | 0.522167 | 0.261084 | − | 0.965316i | \(-0.415920\pi\) | ||||
0.261084 | + | 0.965316i | \(0.415920\pi\) | |||||||
\(318\) | −290593. | −0.161145 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.08052e6 | 2.22762 | ||||||||
\(321\) | −1.51104e6 | −0.818491 | ||||||||
\(322\) | 621587. | 0.334089 | ||||||||
\(323\) | −231189. | −0.123299 | ||||||||
\(324\) | −3.02373e6 | −1.60022 | ||||||||
\(325\) | 4.21704e6 | 2.21462 | ||||||||
\(326\) | −46333.1 | −0.0241461 | ||||||||
\(327\) | 2.78934e6 | 1.44255 | ||||||||
\(328\) | 71710.7 | 0.0368044 | ||||||||
\(329\) | 506945. | 0.258209 | ||||||||
\(330\) | −5.04103e6 | −2.54821 | ||||||||
\(331\) | 3.77955e6 | 1.89614 | 0.948070 | − | 0.318061i | \(-0.103032\pi\) | ||||
0.948070 | + | 0.318061i | \(0.103032\pi\) | |||||||
\(332\) | −4.03274e6 | −2.00796 | ||||||||
\(333\) | 1.03657e6 | 0.512257 | ||||||||
\(334\) | −2.60344e6 | −1.27697 | ||||||||
\(335\) | −987831. | −0.480918 | ||||||||
\(336\) | 2.51762e6 | 1.21658 | ||||||||
\(337\) | −2.10980e6 | −1.01197 | −0.505983 | − | 0.862544i | \(-0.668870\pi\) | ||||
−0.505983 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(338\) | 6.41092e6 | 3.05231 | ||||||||
\(339\) | 3.08929e6 | 1.46002 | ||||||||
\(340\) | 2.79936e6 | 1.31329 | ||||||||
\(341\) | −1.24878e6 | −0.581567 | ||||||||
\(342\) | 229637. | 0.106164 | ||||||||
\(343\) | 2.90431e6 | 1.33293 | ||||||||
\(344\) | −1.06991e6 | −0.487472 | ||||||||
\(345\) | 517067. | 0.233883 | ||||||||
\(346\) | −386196. | −0.173427 | ||||||||
\(347\) | 37808.7 | 0.0168565 | 0.00842827 | − | 0.999964i | \(-0.497317\pi\) | ||||
0.00842827 | + | 0.999964i | \(0.497317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 632608. | 0.278017 | 0.139008 | − | 0.990291i | \(-0.455608\pi\) | ||||
0.139008 | + | 0.990291i | \(0.455608\pi\) | |||||||
\(350\) | 7.40487e6 | 3.23108 | ||||||||
\(351\) | 2.91072e6 | 1.26105 | ||||||||
\(352\) | 3.05037e6 | 1.31219 | ||||||||
\(353\) | −2.76871e6 | −1.18261 | −0.591304 | − | 0.806449i | \(-0.701387\pi\) | ||||
−0.591304 | + | 0.806449i | \(0.701387\pi\) | |||||||
\(354\) | −1.11534e6 | −0.473041 | ||||||||
\(355\) | 5.65687e6 | 2.38235 | ||||||||
\(356\) | −4.20818e6 | −1.75982 | ||||||||
\(357\) | 3.18445e6 | 1.32240 | ||||||||
\(358\) | 2.98531e6 | 1.23107 | ||||||||
\(359\) | 2.50490e6 | 1.02578 | 0.512889 | − | 0.858455i | \(-0.328575\pi\) | ||||
0.512889 | + | 0.858455i | \(0.328575\pi\) | |||||||
\(360\) | −632628. | −0.257272 | ||||||||
\(361\) | −2.39287e6 | −0.966389 | ||||||||
\(362\) | −6.46841e6 | −2.59433 | ||||||||
\(363\) | 295935. | 0.117877 | ||||||||
\(364\) | 9.50293e6 | 3.75928 | ||||||||
\(365\) | −197320. | −0.0775245 | ||||||||
\(366\) | 1.51109e6 | 0.589640 | ||||||||
\(367\) | −3.09219e6 | −1.19840 | −0.599199 | − | 0.800600i | \(-0.704514\pi\) | ||||
−0.599199 | + | 0.800600i | \(0.704514\pi\) | |||||||
\(368\) | −211976. | −0.0815955 | ||||||||
\(369\) | 82485.6 | 0.0315364 | ||||||||
\(370\) | −8.06275e6 | −3.06181 | ||||||||
\(371\) | 401193. | 0.151328 | ||||||||
\(372\) | −2.49063e6 | −0.933151 | ||||||||
\(373\) | 2.44054e6 | 0.908266 | 0.454133 | − | 0.890934i | \(-0.349949\pi\) | ||||
0.454133 | + | 0.890934i | \(0.349949\pi\) | |||||||
\(374\) | 2.61398e6 | 0.966327 | ||||||||
\(375\) | 1.33017e6 | 0.488458 | ||||||||
\(376\) | 188829. | 0.0688809 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.11105e6 | 1.83984 | ||||||||
\(379\) | −2.64306e6 | −0.945168 | −0.472584 | − | 0.881286i | \(-0.656679\pi\) | ||||
−0.472584 | + | 0.881286i | \(0.656679\pi\) | |||||||
\(380\) | −1.00773e6 | −0.358002 | ||||||||
\(381\) | −395642. | −0.139634 | ||||||||
\(382\) | 4.79430e6 | 1.68099 | ||||||||
\(383\) | −460287. | −0.160336 | −0.0801682 | − | 0.996781i | \(-0.525546\pi\) | ||||
−0.0801682 | + | 0.996781i | \(0.525546\pi\) | |||||||
\(384\) | 2.89984e6 | 1.00356 | ||||||||
\(385\) | 6.95965e6 | 2.39296 | ||||||||
\(386\) | −7.84450e6 | −2.67977 | ||||||||
\(387\) | −1.23066e6 | −0.417698 | ||||||||
\(388\) | 3.50764e6 | 1.18287 | ||||||||
\(389\) | 2.72948e6 | 0.914547 | 0.457273 | − | 0.889326i | \(-0.348826\pi\) | ||||
0.457273 | + | 0.889326i | \(0.348826\pi\) | |||||||
\(390\) | 1.40115e7 | 4.66469 | ||||||||
\(391\) | −268120. | −0.0886927 | ||||||||
\(392\) | 2.43915e6 | 0.801722 | ||||||||
\(393\) | 2.52556e6 | 0.824853 | ||||||||
\(394\) | 1.28241e6 | 0.416184 | ||||||||
\(395\) | 2.86106e6 | 0.922643 | ||||||||
\(396\) | −1.46486e6 | −0.469415 | ||||||||
\(397\) | 530743. | 0.169008 | 0.0845041 | − | 0.996423i | \(-0.473069\pi\) | ||||
0.0845041 | + | 0.996423i | \(0.473069\pi\) | |||||||
\(398\) | 17507.2 | 0.00553998 | ||||||||
\(399\) | −1.14636e6 | −0.360486 | ||||||||
\(400\) | −2.52523e6 | −0.789134 | ||||||||
\(401\) | 1.65453e6 | 0.513822 | 0.256911 | − | 0.966435i | \(-0.417295\pi\) | ||||
0.256911 | + | 0.966435i | \(0.417295\pi\) | |||||||
\(402\) | −1.83971e6 | −0.567787 | ||||||||
\(403\) | 3.47097e6 | 1.06460 | ||||||||
\(404\) | −2.48286e6 | −0.756829 | ||||||||
\(405\) | 6.15513e6 | 1.86466 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24762e6 | −1.27104 | ||||||||
\(408\) | 1.18616e6 | 0.352770 | ||||||||
\(409\) | 5.20484e6 | 1.53851 | 0.769253 | − | 0.638944i | \(-0.220628\pi\) | ||||
0.769253 | + | 0.638944i | \(0.220628\pi\) | |||||||
\(410\) | −641597. | −0.188496 | ||||||||
\(411\) | −7.73571e6 | −2.25889 | ||||||||
\(412\) | −8.12240e6 | −2.35744 | ||||||||
\(413\) | 1.53984e6 | 0.444222 | ||||||||
\(414\) | 266320. | 0.0763665 | ||||||||
\(415\) | 8.20907e6 | 2.33977 | ||||||||
\(416\) | −8.47846e6 | −2.40206 | ||||||||
\(417\) | −1.45556e6 | −0.409912 | ||||||||
\(418\) | −940997. | −0.263419 | ||||||||
\(419\) | 191911. | 0.0534030 | 0.0267015 | − | 0.999643i | \(-0.491500\pi\) | ||||
0.0267015 | + | 0.999643i | \(0.491500\pi\) | |||||||
\(420\) | 1.38807e7 | 3.83962 | ||||||||
\(421\) | −5.00002e6 | −1.37488 | −0.687442 | − | 0.726239i | \(-0.741266\pi\) | ||||
−0.687442 | + | 0.726239i | \(0.741266\pi\) | |||||||
\(422\) | 810866. | 0.221650 | ||||||||
\(423\) | 217201. | 0.0590216 | ||||||||
\(424\) | 149438. | 0.0403688 | ||||||||
\(425\) | −3.19407e6 | −0.857773 | ||||||||
\(426\) | 1.05352e7 | 2.81267 | ||||||||
\(427\) | −2.08621e6 | −0.553718 | ||||||||
\(428\) | 3.41536e6 | 0.901212 | ||||||||
\(429\) | 7.38153e6 | 1.93644 | ||||||||
\(430\) | 9.57247e6 | 2.49662 | ||||||||
\(431\) | −3.04923e6 | −0.790672 | −0.395336 | − | 0.918537i | \(-0.629372\pi\) | ||||
−0.395336 | + | 0.918537i | \(0.629372\pi\) | |||||||
\(432\) | −1.74298e6 | −0.449349 | ||||||||
\(433\) | −3.79886e6 | −0.973719 | −0.486860 | − | 0.873480i | \(-0.661858\pi\) | ||||
−0.486860 | + | 0.873480i | \(0.661858\pi\) | |||||||
\(434\) | 6.09480e6 | 1.55323 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.30465e6 | −1.58835 | ||||||||
\(437\) | 96519.5 | 0.0241775 | ||||||||
\(438\) | −367484. | −0.0915279 | ||||||||
\(439\) | 3.28829e6 | 0.814345 | 0.407173 | − | 0.913351i | \(-0.366515\pi\) | ||||
0.407173 | + | 0.913351i | \(0.366515\pi\) | |||||||
\(440\) | 2.59236e6 | 0.638357 | ||||||||
\(441\) | 2.80565e6 | 0.686968 | ||||||||
\(442\) | −7.26553e6 | −1.76893 | ||||||||
\(443\) | −97599.9 | −0.0236287 | −0.0118144 | − | 0.999930i | \(-0.503761\pi\) | ||||
−0.0118144 | + | 0.999930i | \(0.503761\pi\) | |||||||
\(444\) | −8.47167e6 | −2.03944 | ||||||||
\(445\) | 8.56621e6 | 2.05064 | ||||||||
\(446\) | 284072. | 0.0676224 | ||||||||
\(447\) | 2.65091e6 | 0.627517 | ||||||||
\(448\) | −1.04918e7 | −2.46977 | ||||||||
\(449\) | −4.55742e6 | −1.06685 | −0.533424 | − | 0.845848i | \(-0.679095\pi\) | ||||
−0.533424 | + | 0.845848i | \(0.679095\pi\) | |||||||
\(450\) | 3.17263e6 | 0.738563 | ||||||||
\(451\) | −338006. | −0.0782499 | ||||||||
\(452\) | −6.98261e6 | −1.60758 | ||||||||
\(453\) | 8.18682e6 | 1.87443 | ||||||||
\(454\) | −7.59324e6 | −1.72897 | ||||||||
\(455\) | −1.93443e7 | −4.38050 | ||||||||
\(456\) | −427000. | −0.0961647 | ||||||||
\(457\) | 491699. | 0.110131 | 0.0550654 | − | 0.998483i | \(-0.482463\pi\) | ||||
0.0550654 | + | 0.998483i | \(0.482463\pi\) | |||||||
\(458\) | 439791. | 0.0979677 | ||||||||
\(459\) | −2.20464e6 | −0.488434 | ||||||||
\(460\) | −1.16871e6 | −0.257520 | ||||||||
\(461\) | −2.55180e6 | −0.559234 | −0.279617 | − | 0.960112i | \(-0.590208\pi\) | ||||
−0.279617 | + | 0.960112i | \(0.590208\pi\) | |||||||
\(462\) | 1.29615e7 | 2.82521 | ||||||||
\(463\) | −6.25797e6 | −1.35669 | −0.678345 | − | 0.734743i | \(-0.737303\pi\) | ||||
−0.678345 | + | 0.734743i | \(0.737303\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.06995e6 | 1.08736 | ||||||||
\(466\) | −7.32120e6 | −1.56177 | ||||||||
\(467\) | −2.34350e6 | −0.497247 | −0.248624 | − | 0.968600i | \(-0.579978\pi\) | ||||
−0.248624 | + | 0.968600i | \(0.579978\pi\) | |||||||
\(468\) | 4.07155e6 | 0.859300 | ||||||||
\(469\) | 2.53991e6 | 0.533195 | ||||||||
\(470\) | −1.68945e6 | −0.352778 | ||||||||
\(471\) | −2.50918e6 | −0.521169 | ||||||||
\(472\) | 573565. | 0.118503 | ||||||||
\(473\) | 5.04297e6 | 1.03641 | ||||||||
\(474\) | 5.32837e6 | 1.08930 | ||||||||
\(475\) | 1.14982e6 | 0.233828 | ||||||||
\(476\) | −7.19771e6 | −1.45605 | ||||||||
\(477\) | 171892. | 0.0345907 | ||||||||
\(478\) | 6.43421e6 | 1.28803 | ||||||||
\(479\) | −4.98927e6 | −0.993570 | −0.496785 | − | 0.867874i | \(-0.665486\pi\) | ||||
−0.496785 | + | 0.867874i | \(0.665486\pi\) | |||||||
\(480\) | −1.23843e7 | −2.45339 | ||||||||
\(481\) | 1.18062e7 | 2.32674 | ||||||||
\(482\) | −615312. | −0.120636 | ||||||||
\(483\) | −1.32948e6 | −0.259307 | ||||||||
\(484\) | −668892. | −0.129790 | ||||||||
\(485\) | −7.14018e6 | −1.37834 | ||||||||
\(486\) | 5.73489e6 | 1.10137 | ||||||||
\(487\) | −1.75440e6 | −0.335202 | −0.167601 | − | 0.985855i | \(-0.553602\pi\) | ||||
−0.167601 | + | 0.985855i | \(0.553602\pi\) | |||||||
\(488\) | −777080. | −0.147712 | ||||||||
\(489\) | 99099.5 | 0.0187413 | ||||||||
\(490\) | −2.18231e7 | −4.10608 | ||||||||
\(491\) | −2.28688e6 | −0.428094 | −0.214047 | − | 0.976823i | \(-0.568665\pi\) | ||||
−0.214047 | + | 0.976823i | \(0.568665\pi\) | |||||||
\(492\) | −674137. | −0.125555 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.61549e6 | 0.482209 | ||||||||
\(495\) | 2.98187e6 | 0.546986 | ||||||||
\(496\) | −2.07847e6 | −0.379349 | ||||||||
\(497\) | −1.45449e7 | −2.64132 | ||||||||
\(498\) | 1.52884e7 | 2.76241 | ||||||||
\(499\) | 6.03762e6 | 1.08546 | 0.542730 | − | 0.839907i | \(-0.317391\pi\) | ||||
0.542730 | + | 0.839907i | \(0.317391\pi\) | |||||||
\(500\) | −3.00653e6 | −0.537824 | ||||||||
\(501\) | 5.56836e6 | 0.991135 | ||||||||
\(502\) | −7.69347e6 | −1.36258 | ||||||||
\(503\) | 1.11239e6 | 0.196036 | 0.0980182 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980182 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(504\) | 1.62661e6 | 0.285238 | ||||||||
\(505\) | 5.05412e6 | 0.881896 | ||||||||
\(506\) | −1.09132e6 | −0.189485 | ||||||||
\(507\) | −1.37120e7 | −2.36909 | ||||||||
\(508\) | 894257. | 0.153746 | ||||||||
\(509\) | −3.45813e6 | −0.591625 | −0.295813 | − | 0.955246i | \(-0.595590\pi\) | ||||
−0.295813 | + | 0.955246i | \(0.595590\pi\) | |||||||
\(510\) | −1.06126e7 | −1.80674 | ||||||||
\(511\) | 507349. | 0.0859517 | ||||||||
\(512\) | 6.71440e6 | 1.13196 | ||||||||
\(513\) | 793639. | 0.133146 | ||||||||
\(514\) | 7.27118e6 | 1.21394 | ||||||||
\(515\) | 1.65340e7 | 2.74701 | ||||||||
\(516\) | 1.00580e7 | 1.66298 | ||||||||
\(517\) | −890039. | −0.146448 | ||||||||
\(518\) | 2.07309e7 | 3.39465 | ||||||||
\(519\) | 826015. | 0.134608 | ||||||||
\(520\) | −7.20542e6 | −1.16856 | ||||||||
\(521\) | −9.29125e6 | −1.49961 | −0.749807 | − | 0.661656i | \(-0.769854\pi\) | ||||
−0.749807 | + | 0.661656i | \(0.769854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.62992e6 | 0.260563 | 0.130282 | − | 0.991477i | \(-0.458412\pi\) | ||||
0.130282 | + | 0.991477i | \(0.458412\pi\) | |||||||
\(524\) | −5.70844e6 | −0.908216 | ||||||||
\(525\) | −1.58379e7 | −2.50784 | ||||||||
\(526\) | 5.08054e6 | 0.800655 | ||||||||
\(527\) | −2.62898e6 | −0.412345 | ||||||||
\(528\) | −4.42017e6 | −0.690008 | ||||||||
\(529\) | −6.32441e6 | −0.982608 | ||||||||
\(530\) | −1.33702e6 | −0.206752 | ||||||||
\(531\) | 659746. | 0.101541 | ||||||||
\(532\) | 2.59107e6 | 0.396918 | ||||||||
\(533\) | 939484. | 0.143242 | ||||||||
\(534\) | 1.59535e7 | 2.42105 | ||||||||
\(535\) | −6.95233e6 | −1.05014 | ||||||||
\(536\) | 946076. | 0.142238 | ||||||||
\(537\) | −6.38514e6 | −0.955509 | ||||||||
\(538\) | −7.13876e6 | −1.06333 | ||||||||
\(539\) | −1.14969e7 | −1.70454 | ||||||||
\(540\) | −9.60979e6 | −1.41817 | ||||||||
\(541\) | 1.04884e7 | 1.54070 | 0.770348 | − | 0.637624i | \(-0.220083\pi\) | ||||
0.770348 | + | 0.637624i | \(0.220083\pi\) | |||||||
\(542\) | −6.24659e6 | −0.913366 | ||||||||
\(543\) | 1.38349e7 | 2.01362 | ||||||||
\(544\) | 6.42176e6 | 0.930372 | ||||||||
\(545\) | 1.28338e7 | 1.85082 | ||||||||
\(546\) | −3.60263e7 | −5.17176 | ||||||||
\(547\) | 4.48107e6 | 0.640345 | 0.320172 | − | 0.947359i | \(-0.396259\pi\) | ||||
0.320172 | + | 0.947359i | \(0.396259\pi\) | |||||||
\(548\) | 1.74848e7 | 2.48719 | ||||||||
\(549\) | −893839. | −0.126569 | ||||||||
\(550\) | −1.30007e7 | −1.83256 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −495211. | −0.0691739 | ||||||||
\(553\) | −7.35634e6 | −1.02294 | ||||||||
\(554\) | 1.23862e7 | 1.71460 | ||||||||
\(555\) | 1.72450e7 | 2.37646 | ||||||||
\(556\) | 3.28996e6 | 0.451339 | ||||||||
\(557\) | −720322. | −0.0983759 | −0.0491879 | − | 0.998790i | \(-0.515663\pi\) | ||||
−0.0491879 | + | 0.998790i | \(0.515663\pi\) | |||||||
\(558\) | 2.61132e6 | 0.355038 | ||||||||
\(559\) | −1.40169e7 | −1.89724 | ||||||||
\(560\) | 1.15836e7 | 1.56090 | ||||||||
\(561\) | −5.59092e6 | −0.750025 | ||||||||
\(562\) | 1.46795e7 | 1.96051 | ||||||||
\(563\) | −1.26872e7 | −1.68692 | −0.843458 | − | 0.537196i | \(-0.819484\pi\) | ||||
−0.843458 | + | 0.537196i | \(0.819484\pi\) | |||||||
\(564\) | −1.77514e6 | −0.234982 | ||||||||
\(565\) | 1.42139e7 | 1.87323 | ||||||||
\(566\) | 1.83517e7 | 2.40788 | ||||||||
\(567\) | −1.58261e7 | −2.06736 | ||||||||
\(568\) | −5.41775e6 | −0.704609 | ||||||||
\(569\) | 7.93605e6 | 1.02760 | 0.513799 | − | 0.857910i | \(-0.328238\pi\) | ||||
0.513799 | + | 0.857910i | \(0.328238\pi\) | |||||||
\(570\) | 3.82038e6 | 0.492514 | ||||||||
\(571\) | 9.14124e6 | 1.17332 | 0.586658 | − | 0.809835i | \(-0.300443\pi\) | ||||
0.586658 | + | 0.809835i | \(0.300443\pi\) | |||||||
\(572\) | −1.66842e7 | −2.13214 | ||||||||
\(573\) | −1.02543e7 | −1.30472 | ||||||||
\(574\) | 1.64967e6 | 0.208987 | ||||||||
\(575\) | 1.33350e6 | 0.168199 | ||||||||
\(576\) | −4.49524e6 | −0.564543 | ||||||||
\(577\) | −2.52312e6 | −0.315499 | −0.157750 | − | 0.987479i | \(-0.550424\pi\) | ||||
−0.157750 | + | 0.987479i | \(0.550424\pi\) | |||||||
\(578\) | −6.66346e6 | −0.829622 | ||||||||
\(579\) | 1.67782e7 | 2.07993 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.11072e7 | −2.59412 | ||||||||
\(582\) | −1.32977e7 | −1.62731 | ||||||||
\(583\) | −704371. | −0.0858283 | ||||||||
\(584\) | 188979. | 0.0229288 | ||||||||
\(585\) | −8.28807e6 | −1.00130 | ||||||||
\(586\) | −5.68408e6 | −0.683780 | ||||||||
\(587\) | −1.02895e7 | −1.23254 | −0.616268 | − | 0.787536i | \(-0.711356\pi\) | ||||
−0.616268 | + | 0.787536i | \(0.711356\pi\) | |||||||
\(588\) | −2.29299e7 | −2.73502 | ||||||||
\(589\) | 946395. | 0.112405 | ||||||||
\(590\) | −5.13170e6 | −0.606920 | ||||||||
\(591\) | −2.74288e6 | −0.323026 | ||||||||
\(592\) | −7.06972e6 | −0.829083 | ||||||||
\(593\) | −573757. | −0.0670025 | −0.0335013 | − | 0.999439i | \(-0.510666\pi\) | ||||
−0.0335013 | + | 0.999439i | \(0.510666\pi\) | |||||||
\(594\) | −8.97343e6 | −1.04350 | ||||||||
\(595\) | 1.46517e7 | 1.69667 | ||||||||
\(596\) | −5.99176e6 | −0.690937 | ||||||||
\(597\) | −37445.2 | −0.00429992 | ||||||||
\(598\) | 3.03330e6 | 0.346866 | ||||||||
\(599\) | −1.61434e7 | −1.83835 | −0.919173 | − | 0.393853i | \(-0.871142\pi\) | ||||
−0.919173 | + | 0.393853i | \(0.871142\pi\) | |||||||
\(600\) | −5.89936e6 | −0.669001 | ||||||||
\(601\) | −3.97295e6 | −0.448670 | −0.224335 | − | 0.974512i | \(-0.572021\pi\) | ||||
−0.224335 | + | 0.974512i | \(0.572021\pi\) | |||||||
\(602\) | −2.46127e7 | −2.76802 | ||||||||
\(603\) | 1.08823e6 | 0.121878 | ||||||||
\(604\) | −1.85044e7 | −2.06387 | ||||||||
\(605\) | 1.36160e6 | 0.151238 | ||||||||
\(606\) | 9.41268e6 | 1.04119 | ||||||||
\(607\) | −5.65644e6 | −0.623119 | −0.311560 | − | 0.950227i | \(-0.600851\pi\) | ||||
−0.311560 | + | 0.950227i | \(0.600851\pi\) | |||||||
\(608\) | −2.31174e6 | −0.253618 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.95255e6 | 0.756518 | ||||||||
\(611\) | 2.47385e6 | 0.268084 | ||||||||
\(612\) | −3.08387e6 | −0.332826 | ||||||||
\(613\) | 7.65406e6 | 0.822699 | 0.411349 | − | 0.911478i | \(-0.365058\pi\) | ||||
0.411349 | + | 0.911478i | \(0.365058\pi\) | |||||||
\(614\) | −5.27168e6 | −0.564323 | ||||||||
\(615\) | 1.37228e6 | 0.146304 | ||||||||
\(616\) | −6.66548e6 | −0.707749 | ||||||||
\(617\) | 1.06193e7 | 1.12301 | 0.561505 | − | 0.827473i | \(-0.310222\pi\) | ||||
0.561505 | + | 0.827473i | \(0.310222\pi\) | |||||||
\(618\) | 3.07926e7 | 3.24321 | ||||||||
\(619\) | 4.45953e6 | 0.467802 | 0.233901 | − | 0.972260i | \(-0.424851\pi\) | ||||
0.233901 | + | 0.972260i | \(0.424851\pi\) | |||||||
\(620\) | −1.14594e7 | −1.19725 | ||||||||
\(621\) | 920418. | 0.0957759 | ||||||||
\(622\) | 1.00515e7 | 1.04173 | ||||||||
\(623\) | −2.20254e7 | −2.27355 | ||||||||
\(624\) | 1.22858e7 | 1.26311 | ||||||||
\(625\) | −6.33517e6 | −0.648722 | ||||||||
\(626\) | −2.21645e7 | −2.26059 | ||||||||
\(627\) | 2.01265e6 | 0.204456 | ||||||||
\(628\) | 5.67141e6 | 0.573841 | ||||||||
\(629\) | −8.94224e6 | −0.901197 | ||||||||
\(630\) | −1.45533e7 | −1.46087 | ||||||||
\(631\) | 1.51771e7 | 1.51745 | 0.758725 | − | 0.651411i | \(-0.225823\pi\) | ||||
0.758725 | + | 0.651411i | \(0.225823\pi\) | |||||||
\(632\) | −2.74012e6 | −0.272883 | ||||||||
\(633\) | −1.73432e6 | −0.172036 | ||||||||
\(634\) | 8.00534e6 | 0.790964 | ||||||||
\(635\) | −1.82036e6 | −0.179152 | ||||||||
\(636\) | −1.40483e6 | −0.137715 | ||||||||
\(637\) | 3.19554e7 | 3.12029 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.23180e6 | −0.603755 | ||||||||
\(640\) | 1.33422e7 | 1.28759 | ||||||||
\(641\) | −1.33769e7 | −1.28591 | −0.642957 | − | 0.765903i | \(-0.722292\pi\) | ||||
−0.642957 | + | 0.765903i | \(0.722292\pi\) | |||||||
\(642\) | −1.29479e7 | −1.23983 | ||||||||
\(643\) | −5.68424e6 | −0.542182 | −0.271091 | − | 0.962554i | \(-0.587384\pi\) | ||||
−0.271091 | + | 0.962554i | \(0.587384\pi\) | |||||||
\(644\) | 3.00498e6 | 0.285514 | ||||||||
\(645\) | −2.04741e7 | −1.93778 | ||||||||
\(646\) | −1.98102e6 | −0.186770 | ||||||||
\(647\) | −1.93095e7 | −1.81347 | −0.906735 | − | 0.421702i | \(-0.861433\pi\) | ||||
−0.906735 | + | 0.421702i | \(0.861433\pi\) | |||||||
\(648\) | −5.89496e6 | −0.551497 | ||||||||
\(649\) | −2.70348e6 | −0.251949 | ||||||||
\(650\) | 3.61351e7 | 3.35464 | ||||||||
\(651\) | −1.30359e7 | −1.20556 | ||||||||
\(652\) | −223991. | −0.0206354 | ||||||||
\(653\) | −151435. | −0.0138977 | −0.00694884 | − | 0.999976i | \(-0.502212\pi\) | ||||
−0.00694884 | + | 0.999976i | \(0.502212\pi\) | |||||||
\(654\) | 2.39014e7 | 2.18514 | ||||||||
\(655\) | 1.16201e7 | 1.05830 | ||||||||
\(656\) | −562577. | −0.0510414 | ||||||||
\(657\) | 217374. | 0.0196469 | ||||||||
\(658\) | 4.34392e6 | 0.391127 | ||||||||
\(659\) | 9.74503e6 | 0.874117 | 0.437058 | − | 0.899433i | \(-0.356020\pi\) | ||||
0.437058 | + | 0.899433i | \(0.356020\pi\) | |||||||
\(660\) | −2.43702e7 | −2.17771 | ||||||||
\(661\) | −8.52857e6 | −0.759229 | −0.379614 | − | 0.925145i | \(-0.623943\pi\) | ||||
−0.379614 | + | 0.925145i | \(0.623943\pi\) | |||||||
\(662\) | 3.23864e7 | 2.87222 | ||||||||
\(663\) | 1.55399e7 | 1.37298 | ||||||||
\(664\) | −7.86208e6 | −0.692018 | ||||||||
\(665\) | −5.27441e6 | −0.462509 | ||||||||
\(666\) | 8.88220e6 | 0.775952 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.25860e7 | −1.09130 | ||||||||
\(669\) | −607586. | −0.0524859 | ||||||||
\(670\) | −8.46456e6 | −0.728480 | ||||||||
\(671\) | 3.66274e6 | 0.314051 | ||||||||
\(672\) | 3.18424e7 | 2.72009 | ||||||||
\(673\) | −1.53606e7 | −1.30729 | −0.653643 | − | 0.756803i | \(-0.726760\pi\) | ||||
−0.653643 | + | 0.756803i | \(0.726760\pi\) | |||||||
\(674\) | −1.80785e7 | −1.53290 | ||||||||
\(675\) | 1.09648e7 | 0.926277 | ||||||||
\(676\) | 3.09928e7 | 2.60852 | ||||||||
\(677\) | 2.37603e6 | 0.199241 | 0.0996207 | − | 0.995025i | \(-0.468237\pi\) | ||||
0.0996207 | + | 0.995025i | \(0.468237\pi\) | |||||||
\(678\) | 2.64716e7 | 2.21159 | ||||||||
\(679\) | 1.83588e7 | 1.52817 | ||||||||
\(680\) | 5.45753e6 | 0.452610 | ||||||||
\(681\) | 1.62408e7 | 1.34196 | ||||||||
\(682\) | −1.07006e7 | −0.880941 | ||||||||
\(683\) | −6.86181e6 | −0.562842 | −0.281421 | − | 0.959584i | \(-0.590806\pi\) | ||||
−0.281421 | + | 0.959584i | \(0.590806\pi\) | |||||||
\(684\) | 1.11015e6 | 0.0907280 | ||||||||
\(685\) | −3.55922e7 | −2.89820 | ||||||||
\(686\) | 2.48865e7 | 2.01908 | ||||||||
\(687\) | −940647. | −0.0760387 | ||||||||
\(688\) | 8.39351e6 | 0.676040 | ||||||||
\(689\) | 1.95779e6 | 0.157115 | ||||||||
\(690\) | 4.43066e6 | 0.354279 | ||||||||
\(691\) | 1.86887e7 | 1.48896 | 0.744480 | − | 0.667645i | \(-0.232698\pi\) | ||||
0.744480 | + | 0.667645i | \(0.232698\pi\) | |||||||
\(692\) | −1.86701e6 | −0.148212 | ||||||||
\(693\) | −7.66699e6 | −0.606446 | ||||||||
\(694\) | 323977. | 0.0255338 | ||||||||
\(695\) | −6.69706e6 | −0.525923 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −711584. | −0.0554810 | ||||||||
\(698\) | 5.42071e6 | 0.421132 | ||||||||
\(699\) | 1.56589e7 | 1.21219 | ||||||||
\(700\) | 3.57979e7 | 2.76129 | ||||||||
\(701\) | −5.85780e6 | −0.450235 | −0.225118 | − | 0.974332i | \(-0.572277\pi\) | ||||
−0.225118 | + | 0.974332i | \(0.572277\pi\) | |||||||
\(702\) | 2.49415e7 | 1.91020 | ||||||||
\(703\) | 3.21908e6 | 0.245665 | ||||||||
\(704\) | 1.84204e7 | 1.40078 | ||||||||
\(705\) | 3.61349e6 | 0.273813 | ||||||||
\(706\) | −2.37246e7 | −1.79138 | ||||||||
\(707\) | −1.29952e7 | −0.977761 | ||||||||
\(708\) | −5.39197e6 | −0.404263 | ||||||||
\(709\) | −3.17834e6 | −0.237457 | −0.118728 | − | 0.992927i | \(-0.537882\pi\) | ||||
−0.118728 | + | 0.992927i | \(0.537882\pi\) | |||||||
\(710\) | 4.84727e7 | 3.60871 | ||||||||
\(711\) | −3.15184e6 | −0.233824 | ||||||||
\(712\) | −8.20412e6 | −0.606502 | ||||||||
\(713\) | 1.09758e6 | 0.0808557 | ||||||||
\(714\) | 2.72870e7 | 2.00314 | ||||||||
\(715\) | 3.39626e7 | 2.48448 | ||||||||
\(716\) | 1.44321e7 | 1.05208 | ||||||||
\(717\) | −1.37618e7 | −0.999718 | ||||||||
\(718\) | 2.14640e7 | 1.55382 | ||||||||
\(719\) | 2.62515e7 | 1.89379 | 0.946894 | − | 0.321546i | \(-0.104202\pi\) | ||||
0.946894 | + | 0.321546i | \(0.104202\pi\) | |||||||
\(720\) | 4.96302e6 | 0.356792 | ||||||||
\(721\) | −4.25123e7 | −3.04563 | ||||||||
\(722\) | −2.05041e7 | −1.46386 | ||||||||
\(723\) | 1.31606e6 | 0.0936332 | ||||||||
\(724\) | −3.12707e7 | −2.21713 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.53582e6 | 0.178557 | ||||||||
\(727\) | 1.53808e7 | 1.07930 | 0.539651 | − | 0.841889i | \(-0.318556\pi\) | ||||
0.539651 | + | 0.841889i | \(0.318556\pi\) | |||||||
\(728\) | 1.85266e7 | 1.29559 | ||||||||
\(729\) | 5.47123e6 | 0.381300 | ||||||||
\(730\) | −1.69080e6 | −0.117432 | ||||||||
\(731\) | 1.06167e7 | 0.734842 | ||||||||
\(732\) | 7.30516e6 | 0.503909 | ||||||||
\(733\) | −1.07403e7 | −0.738338 | −0.369169 | − | 0.929362i | \(-0.620358\pi\) | ||||
−0.369169 | + | 0.929362i | \(0.620358\pi\) | |||||||
\(734\) | −2.64965e7 | −1.81530 | ||||||||
\(735\) | 4.66764e7 | 3.18698 | ||||||||
\(736\) | −2.68103e6 | −0.182434 | ||||||||
\(737\) | −4.45930e6 | −0.302411 | ||||||||
\(738\) | 706805. | 0.0477704 | ||||||||
\(739\) | −1.50225e7 | −1.01189 | −0.505943 | − | 0.862567i | \(-0.668855\pi\) | ||||
−0.505943 | + | 0.862567i | \(0.668855\pi\) | |||||||
\(740\) | −3.89783e7 | −2.61664 | ||||||||
\(741\) | −5.59413e6 | −0.374272 | ||||||||
\(742\) | 3.43776e6 | 0.229227 | ||||||||
\(743\) | 1.20298e7 | 0.799440 | 0.399720 | − | 0.916637i | \(-0.369107\pi\) | ||||
0.399720 | + | 0.916637i | \(0.369107\pi\) | |||||||
\(744\) | −4.85565e6 | −0.321599 | ||||||||
\(745\) | 1.21969e7 | 0.805115 | ||||||||
\(746\) | 2.09126e7 | 1.37581 | ||||||||
\(747\) | −9.04339e6 | −0.592966 | ||||||||
\(748\) | 1.26370e7 | 0.825827 | ||||||||
\(749\) | 1.78758e7 | 1.16429 | ||||||||
\(750\) | 1.13980e7 | 0.739902 | ||||||||
\(751\) | −1.27308e7 | −0.823674 | −0.411837 | − | 0.911258i | \(-0.635113\pi\) | ||||
−0.411837 | + | 0.911258i | \(0.635113\pi\) | |||||||
\(752\) | −1.48138e6 | −0.0955259 | ||||||||
\(753\) | 1.64552e7 | 1.05758 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.76677e7 | 2.40493 | ||||||||
\(756\) | 2.47087e7 | 1.57234 | ||||||||
\(757\) | 2.61540e7 | 1.65882 | 0.829408 | − | 0.558643i | \(-0.188678\pi\) | ||||
0.829408 | + | 0.558643i | \(0.188678\pi\) | |||||||
\(758\) | −2.26479e7 | −1.43171 | ||||||||
\(759\) | 2.33416e6 | 0.147071 | ||||||||
\(760\) | −1.96463e6 | −0.123381 | ||||||||
\(761\) | 1.26786e7 | 0.793612 | 0.396806 | − | 0.917903i | \(-0.370119\pi\) | ||||
0.396806 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(762\) | −3.39019e6 | −0.211513 | ||||||||
\(763\) | −3.29983e7 | −2.05201 | ||||||||
\(764\) | 2.31774e7 | 1.43658 | ||||||||
\(765\) | 6.27755e6 | 0.387826 | ||||||||
\(766\) | −3.94412e6 | −0.242873 | ||||||||
\(767\) | 7.51429e6 | 0.461211 | ||||||||
\(768\) | −3.53175e6 | −0.216066 | ||||||||
\(769\) | −2.28743e7 | −1.39486 | −0.697431 | − | 0.716652i | \(-0.745674\pi\) | ||||
−0.697431 | + | 0.716652i | \(0.745674\pi\) | |||||||
\(770\) | 5.96361e7 | 3.62479 | ||||||||
\(771\) | −1.55520e7 | −0.942213 | ||||||||
\(772\) | −3.79232e7 | −2.29014 | ||||||||
\(773\) | −2.65876e7 | −1.60041 | −0.800204 | − | 0.599728i | \(-0.795275\pi\) | ||||
−0.800204 | + | 0.599728i | \(0.795275\pi\) | |||||||
\(774\) | −1.05454e7 | −0.632716 | ||||||||
\(775\) | 1.30752e7 | 0.781980 | ||||||||
\(776\) | 6.83837e6 | 0.407660 | ||||||||
\(777\) | −4.43403e7 | −2.63479 | ||||||||
\(778\) | 2.33885e7 | 1.38533 | ||||||||
\(779\) | 256160. | 0.0151240 | ||||||||
\(780\) | 6.77367e7 | 3.98646 | ||||||||
\(781\) | 2.55364e7 | 1.49807 | ||||||||
\(782\) | −2.29748e6 | −0.134349 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.91354e7 | −1.11185 | ||||||||
\(785\) | −1.15448e7 | −0.668669 | ||||||||
\(786\) | 2.16411e7 | 1.24946 | ||||||||
\(787\) | −9.06273e6 | −0.521582 | −0.260791 | − | 0.965395i | \(-0.583983\pi\) | ||||
−0.260791 | + | 0.965395i | \(0.583983\pi\) | |||||||
\(788\) | 6.19963e6 | 0.355673 | ||||||||
\(789\) | −1.08665e7 | −0.621437 | ||||||||
\(790\) | 2.45159e7 | 1.39759 | ||||||||
\(791\) | −3.65467e7 | −2.07686 | ||||||||
\(792\) | −2.85583e6 | −0.161778 | ||||||||
\(793\) | −1.01805e7 | −0.574894 | ||||||||
\(794\) | 4.54785e6 | 0.256009 | ||||||||
\(795\) | 2.85969e6 | 0.160473 | ||||||||
\(796\) | 84636.1 | 0.00473449 | ||||||||
\(797\) | 2.52271e7 | 1.40676 | 0.703382 | − | 0.710812i | \(-0.251672\pi\) | ||||
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(798\) | −9.82295e6 | −0.546053 | ||||||||
\(799\) | −1.87374e6 | −0.103835 | ||||||||
\(800\) | −3.19386e7 | −1.76438 | ||||||||
\(801\) | −9.43683e6 | −0.519690 | ||||||||
\(802\) | 1.41774e7 | 0.778322 | ||||||||
\(803\) | −890748. | −0.0487491 | ||||||||
\(804\) | −8.89386e6 | −0.485233 | ||||||||
\(805\) | −6.11697e6 | −0.332695 | ||||||||
\(806\) | 2.97421e7 | 1.61263 | ||||||||
\(807\) | 1.52687e7 | 0.825314 | ||||||||
\(808\) | −4.84049e6 | −0.260832 | ||||||||
\(809\) | 8.69627e6 | 0.467156 | 0.233578 | − | 0.972338i | \(-0.424957\pi\) | ||||
0.233578 | + | 0.972338i | \(0.424957\pi\) | |||||||
\(810\) | 5.27423e7 | 2.82453 | ||||||||
\(811\) | 1.94112e7 | 1.03633 | 0.518166 | − | 0.855280i | \(-0.326615\pi\) | ||||
0.518166 | + | 0.855280i | \(0.326615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.33605e7 | 0.708919 | ||||||||
\(814\) | −3.63971e7 | −1.92533 | ||||||||
\(815\) | 455959. | 0.0240454 | ||||||||
\(816\) | −9.30551e6 | −0.489232 | ||||||||
\(817\) | −3.82184e6 | −0.200317 | ||||||||
\(818\) | 4.45994e7 | 2.33048 | ||||||||
\(819\) | 2.13103e7 | 1.11014 | ||||||||
\(820\) | −3.10172e6 | −0.161090 | ||||||||
\(821\) | 1.78189e7 | 0.922620 | 0.461310 | − | 0.887239i | \(-0.347380\pi\) | ||||
0.461310 | + | 0.887239i | \(0.347380\pi\) | |||||||
\(822\) | −6.62861e7 | −3.42171 | ||||||||
\(823\) | 1.73515e7 | 0.892969 | 0.446485 | − | 0.894791i | \(-0.352676\pi\) | ||||
0.446485 | + | 0.894791i | \(0.352676\pi\) | |||||||
\(824\) | −1.58352e7 | −0.812464 | ||||||||
\(825\) | 2.78065e7 | 1.42236 | ||||||||
\(826\) | 1.31946e7 | 0.672894 | ||||||||
\(827\) | −8.83226e6 | −0.449064 | −0.224532 | − | 0.974467i | \(-0.572085\pi\) | ||||
−0.224532 | + | 0.974467i | \(0.572085\pi\) | |||||||
\(828\) | 1.28749e6 | 0.0652631 | ||||||||
\(829\) | 1.69640e7 | 0.857316 | 0.428658 | − | 0.903467i | \(-0.358986\pi\) | ||||
0.428658 | + | 0.903467i | \(0.358986\pi\) | |||||||
\(830\) | 7.03422e7 | 3.54422 | ||||||||
\(831\) | −2.64922e7 | −1.33081 | ||||||||
\(832\) | −5.11993e7 | −2.56422 | ||||||||
\(833\) | −2.42036e7 | −1.20856 | ||||||||
\(834\) | −1.24725e7 | −0.620922 | ||||||||
\(835\) | 2.56201e7 | 1.27164 | ||||||||
\(836\) | −4.54913e6 | −0.225119 | ||||||||
\(837\) | 9.02490e6 | 0.445275 | ||||||||
\(838\) | 1.64446e6 | 0.0808933 | ||||||||
\(839\) | 2.68046e7 | 1.31463 | 0.657316 | − | 0.753615i | \(-0.271692\pi\) | ||||
0.657316 | + | 0.753615i | \(0.271692\pi\) | |||||||
\(840\) | 2.70613e7 | 1.32328 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −4.28443e7 | −2.08263 | ||||||||
\(843\) | −3.13971e7 | −1.52167 | ||||||||
\(844\) | 3.92003e6 | 0.189423 | ||||||||
\(845\) | −6.30891e7 | −3.03957 | ||||||||
\(846\) | 1.86116e6 | 0.0894042 | ||||||||
\(847\) | −3.50095e6 | −0.167678 | ||||||||
\(848\) | −1.17235e6 | −0.0559847 | ||||||||
\(849\) | −3.92514e7 | −1.86890 | ||||||||
\(850\) | −2.73695e7 | −1.29933 | ||||||||
\(851\) | 3.73331e6 | 0.176714 | ||||||||
\(852\) | 5.09311e7 | 2.40372 | ||||||||
\(853\) | −2.65626e7 | −1.24997 | −0.624983 | − | 0.780638i | \(-0.714894\pi\) | ||||
−0.624983 | + | 0.780638i | \(0.714894\pi\) | |||||||
\(854\) | −1.78764e7 | −0.838755 | ||||||||
\(855\) | −2.25983e6 | −0.105721 | ||||||||
\(856\) | 6.65846e6 | 0.310591 | ||||||||
\(857\) | −1.81681e7 | −0.845003 | −0.422501 | − | 0.906362i | \(-0.638848\pi\) | ||||
−0.422501 | + | 0.906362i | \(0.638848\pi\) | |||||||
\(858\) | 6.32511e7 | 2.93325 | ||||||||
\(859\) | −2.68029e7 | −1.23936 | −0.619681 | − | 0.784854i | \(-0.712738\pi\) | ||||
−0.619681 | + | 0.784854i | \(0.712738\pi\) | |||||||
\(860\) | 4.62769e7 | 2.13362 | ||||||||
\(861\) | −3.52841e6 | −0.162207 | ||||||||
\(862\) | −2.61283e7 | −1.19769 | ||||||||
\(863\) | −2.87179e7 | −1.31258 | −0.656291 | − | 0.754508i | \(-0.727876\pi\) | ||||
−0.656291 | + | 0.754508i | \(0.727876\pi\) | |||||||
\(864\) | −2.20450e7 | −1.00467 | ||||||||
\(865\) | 3.80051e6 | 0.172704 | ||||||||
\(866\) | −3.25518e7 | −1.47496 | ||||||||
\(867\) | 1.42521e7 | 0.643921 | ||||||||
\(868\) | 2.94645e7 | 1.32739 | ||||||||
\(869\) | 1.29155e7 | 0.580178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.23946e7 | 0.553587 | ||||||||
\(872\) | −1.22913e7 | −0.547404 | ||||||||
\(873\) | 7.86586e6 | 0.349310 | ||||||||
\(874\) | 827060. | 0.0366234 | ||||||||
\(875\) | −1.57360e7 | −0.694825 | ||||||||
\(876\) | −1.77655e6 | −0.0782201 | ||||||||
\(877\) | 139217. | 0.00611213 | 0.00305606 | − | 0.999995i | \(-0.499027\pi\) | ||||
0.00305606 | + | 0.999995i | \(0.499027\pi\) | |||||||
\(878\) | 2.81768e7 | 1.23355 | ||||||||
\(879\) | 1.21574e7 | 0.530723 | ||||||||
\(880\) | −2.03373e7 | −0.885292 | ||||||||
\(881\) | 8.68118e6 | 0.376824 | 0.188412 | − | 0.982090i | \(-0.439666\pi\) | ||||
0.188412 | + | 0.982090i | \(0.439666\pi\) | |||||||
\(882\) | 2.40411e7 | 1.04060 | ||||||||
\(883\) | −2.65874e7 | −1.14756 | −0.573778 | − | 0.819011i | \(-0.694523\pi\) | ||||
−0.573778 | + | 0.819011i | \(0.694523\pi\) | |||||||
\(884\) | −3.51243e7 | −1.51174 | ||||||||
\(885\) | 1.09759e7 | 0.471068 | ||||||||
\(886\) | −836317. | −0.0357921 | ||||||||
\(887\) | 4.43687e7 | 1.89351 | 0.946754 | − | 0.321956i | \(-0.104340\pi\) | ||||
0.946754 | + | 0.321956i | \(0.104340\pi\) | |||||||
\(888\) | −1.65161e7 | −0.702869 | ||||||||
\(889\) | 4.68050e6 | 0.198627 | ||||||||
\(890\) | 7.34024e7 | 3.10624 | ||||||||
\(891\) | 2.77857e7 | 1.17254 | ||||||||
\(892\) | 1.37331e6 | 0.0577904 | ||||||||
\(893\) | 674521. | 0.0283052 | ||||||||
\(894\) | 2.27152e7 | 0.950544 | ||||||||
\(895\) | −2.93781e7 | −1.22593 | ||||||||
\(896\) | −3.43055e7 | −1.42756 | ||||||||
\(897\) | −6.48776e6 | −0.269224 | ||||||||
\(898\) | −3.90517e7 | −1.61603 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.53376e7 | 0.631179 | ||||||||
\(901\) | −1.48287e6 | −0.0608542 | ||||||||
\(902\) | −2.89632e6 | −0.118531 | ||||||||
\(903\) | 5.26429e7 | 2.14843 | ||||||||
\(904\) | −1.36131e7 | −0.554031 | ||||||||
\(905\) | 6.36548e7 | 2.58351 | ||||||||
\(906\) | 7.01515e7 | 2.83934 | ||||||||
\(907\) | 1.96923e7 | 0.794839 | 0.397420 | − | 0.917637i | \(-0.369906\pi\) | ||||
0.397420 | + | 0.917637i | \(0.369906\pi\) | |||||||
\(908\) | −3.67085e7 | −1.47758 | ||||||||
\(909\) | −5.56779e6 | −0.223498 | ||||||||
\(910\) | −1.65758e8 | −6.63545 | ||||||||
\(911\) | −4.33698e6 | −0.173138 | −0.0865688 | − | 0.996246i | \(-0.527590\pi\) | ||||
−0.0865688 | + | 0.996246i | \(0.527590\pi\) | |||||||
\(912\) | 3.34985e6 | 0.133364 | ||||||||
\(913\) | 3.70577e7 | 1.47130 | ||||||||
\(914\) | 4.21329e6 | 0.166823 | ||||||||
\(915\) | −1.48704e7 | −0.587180 | ||||||||
\(916\) | 2.12611e6 | 0.0837236 | ||||||||
\(917\) | −2.98777e7 | −1.17334 | ||||||||
\(918\) | −1.88912e7 | −0.739865 | ||||||||
\(919\) | 2.13300e7 | 0.833110 | 0.416555 | − | 0.909110i | \(-0.363237\pi\) | ||||
0.416555 | + | 0.909110i | \(0.363237\pi\) | |||||||
\(920\) | −2.27847e6 | −0.0887512 | ||||||||
\(921\) | 1.12753e7 | 0.438006 | ||||||||
\(922\) | −2.18659e7 | −0.847112 | ||||||||
\(923\) | −7.09781e7 | −2.74233 | ||||||||
\(924\) | 6.26607e7 | 2.41443 | ||||||||
\(925\) | 4.44743e7 | 1.70905 | ||||||||
\(926\) | −5.36235e7 | −2.05507 | ||||||||
\(927\) | −1.82145e7 | −0.696172 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.41448e7 | 1.67819 | 0.839093 | − | 0.543988i | \(-0.183086\pi\) | ||||
0.839093 | + | 0.543988i | \(0.183086\pi\) | |||||||
\(930\) | 4.34436e7 | 1.64709 | ||||||||
\(931\) | 8.71296e6 | 0.329452 | ||||||||
\(932\) | −3.53934e7 | −1.33470 | ||||||||
\(933\) | −2.14986e7 | −0.808547 | ||||||||
\(934\) | −2.00810e7 | −0.753215 | ||||||||
\(935\) | −2.57239e7 | −0.962295 | ||||||||
\(936\) | 7.93774e6 | 0.296147 | ||||||||
\(937\) | 5.10338e7 | 1.89893 | 0.949466 | − | 0.313871i | \(-0.101626\pi\) | ||||
0.949466 | + | 0.313871i | \(0.101626\pi\) | |||||||
\(938\) | 2.17641e7 | 0.807669 | ||||||||
\(939\) | 4.74066e7 | 1.75459 | ||||||||
\(940\) | −8.16745e6 | −0.301486 | ||||||||
\(941\) | 4.69231e7 | 1.72748 | 0.863739 | − | 0.503939i | \(-0.168116\pi\) | ||||
0.863739 | + | 0.503939i | \(0.168116\pi\) | |||||||
\(942\) | −2.15007e7 | −0.789452 | ||||||||
\(943\) | 297080. | 0.0108791 | ||||||||
\(944\) | −4.49967e6 | −0.164343 | ||||||||
\(945\) | −5.02972e7 | −1.83217 | ||||||||
\(946\) | 4.32124e7 | 1.56993 | ||||||||
\(947\) | −1.22405e7 | −0.443533 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(948\) | 2.57593e7 | 0.930922 | ||||||||
\(949\) | 2.47582e6 | 0.0892388 | ||||||||
\(950\) | 9.85263e6 | 0.354195 | ||||||||
\(951\) | −1.71222e7 | −0.613915 | ||||||||
\(952\) | −1.40324e7 | −0.501811 | ||||||||
\(953\) | −4.02315e7 | −1.43494 | −0.717470 | − | 0.696590i | \(-0.754700\pi\) | ||||
−0.717470 | + | 0.696590i | \(0.754700\pi\) | |||||||
\(954\) | 1.47291e6 | 0.0523969 | ||||||||
\(955\) | −4.71801e7 | −1.67398 | ||||||||
\(956\) | 3.11053e7 | 1.10075 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.27523e7 | −1.50503 | ||||||||
\(959\) | 9.15146e7 | 3.21324 | ||||||||
\(960\) | −7.47856e7 | −2.61903 | ||||||||
\(961\) | −1.78672e7 | −0.624090 | ||||||||
\(962\) | 1.01165e8 | 3.52447 | ||||||||
\(963\) | 7.65893e6 | 0.266135 | ||||||||
\(964\) | −2.97465e6 | −0.103096 | ||||||||
\(965\) | 7.71969e7 | 2.66859 | ||||||||
\(966\) | −1.13921e7 | −0.392791 | ||||||||
\(967\) | −1.72628e7 | −0.593668 | −0.296834 | − | 0.954929i | \(-0.595931\pi\) | ||||
−0.296834 | + | 0.954929i | \(0.595931\pi\) | |||||||
\(968\) | −1.30405e6 | −0.0447306 | ||||||||
\(969\) | 4.23711e6 | 0.144964 | ||||||||
\(970\) | −6.11830e7 | −2.08786 | ||||||||
\(971\) | −1.32907e7 | −0.452378 | −0.226189 | − | 0.974083i | \(-0.572627\pi\) | ||||
−0.226189 | + | 0.974083i | \(0.572627\pi\) | |||||||
\(972\) | 2.77246e7 | 0.941238 | ||||||||
\(973\) | 1.72195e7 | 0.583093 | ||||||||
\(974\) | −1.50332e7 | −0.507754 | ||||||||
\(975\) | −7.72876e7 | −2.60374 | ||||||||
\(976\) | 6.09626e6 | 0.204851 | ||||||||
\(977\) | −4.16592e7 | −1.39629 | −0.698144 | − | 0.715957i | \(-0.745990\pi\) | ||||
−0.698144 | + | 0.715957i | \(0.745990\pi\) | |||||||
\(978\) | 849167. | 0.0283887 | ||||||||
\(979\) | 3.86699e7 | 1.28948 | ||||||||
\(980\) | −1.05501e8 | −3.50907 | ||||||||
\(981\) | −1.41382e7 | −0.469051 | ||||||||
\(982\) | −1.95959e7 | −0.648464 | ||||||||
\(983\) | −2.91834e6 | −0.0963278 | −0.0481639 | − | 0.998839i | \(-0.515337\pi\) | ||||
−0.0481639 | + | 0.998839i | \(0.515337\pi\) | |||||||
\(984\) | −1.31427e6 | −0.0432711 | ||||||||
\(985\) | −1.26200e7 | −0.414448 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.29100e6 | −0.303577 | ||||||||
\(988\) | 1.26442e7 | 0.412098 | ||||||||
\(989\) | −4.43236e6 | −0.144094 | ||||||||
\(990\) | 2.55512e7 | 0.828558 | ||||||||
\(991\) | −5.12994e7 | −1.65931 | −0.829657 | − | 0.558274i | \(-0.811464\pi\) | ||||
−0.829657 | + | 0.558274i | \(0.811464\pi\) | |||||||
\(992\) | −2.62881e7 | −0.848163 | ||||||||
\(993\) | −6.92696e7 | −2.22930 | ||||||||
\(994\) | −1.24633e8 | −4.00099 | ||||||||
\(995\) | −172286. | −0.00551686 | ||||||||
\(996\) | 7.39097e7 | 2.36077 | ||||||||
\(997\) | −3.15013e7 | −1.00367 | −0.501834 | − | 0.864964i | \(-0.667341\pi\) | ||||
−0.501834 | + | 0.864964i | \(0.667341\pi\) | |||||||
\(998\) | 5.17353e7 | 1.64422 | ||||||||
\(999\) | 3.06974e7 | 0.973169 |
(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 | 841.6.a.b.1.7 | 7 | ||
29.28 | even | 2 | 29.6.a.b.1.1 | ✓ | 7 | ||
87.86 | odd | 2 | 261.6.a.e.1.7 | 7 | |||
116.115 | odd | 2 | 464.6.a.k.1.2 | 7 | |||
145.144 | even | 2 | 725.6.a.b.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.b.1.1 | ✓ | 7 | 29.28 | even | 2 | ||
261.6.a.e.1.7 | 7 | 87.86 | odd | 2 | |||
464.6.a.k.1.2 | 7 | 116.115 | odd | 2 | |||
725.6.a.b.1.7 | 7 | 145.144 | even | 2 | |||
841.6.a.b.1.7 | 7 | 1.1 | even | 1 | trivial |