Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,6,Mod(25,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.25");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.i (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(13.4722408643\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7081})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(-20.7872 - 36.0044i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.25 |
Dual form | 84.6.i.b.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.50000 | + | 7.79423i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −32.7872 | − | 56.7890i | −0.586515 | − | 1.01587i | −0.994685 | − | 0.102967i | \(-0.967166\pi\) |
0.408170 | − | 0.912906i | \(-0.366167\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 40.6487 | + | 123.104i | 0.313546 | + | 0.949573i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 122.787 | − | 212.674i | 0.305965 | − | 0.529946i | −0.671511 | − | 0.740995i | \(-0.734354\pi\) |
0.977476 | + | 0.211048i | \(0.0676877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 434.872 | 0.713679 | 0.356839 | − | 0.934166i | \(-0.383854\pi\) | ||||
0.356839 | + | 0.934166i | \(0.383854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 590.169 | 0.677249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 551.149 | − | 954.618i | 0.462537 | − | 0.801138i | −0.536550 | − | 0.843869i | \(-0.680273\pi\) |
0.999087 | + | 0.0427312i | \(0.0136059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1438.65 | + | 2491.81i | 0.914260 | + | 1.58355i | 0.807981 | + | 0.589209i | \(0.200560\pi\) |
0.106279 | + | 0.994336i | \(0.466106\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1142.42 | − | 237.145i | −0.565299 | − | 0.117345i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2114.72 | + | 3662.80i | 0.833552 | + | 1.44375i | 0.895204 | + | 0.445657i | \(0.147030\pi\) |
−0.0616521 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −587.497 | + | 1017.57i | −0.187999 | + | 0.325624i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4969.60 | 1.09730 | 0.548652 | − | 0.836051i | \(-0.315141\pi\) | ||||
0.548652 | + | 0.836051i | \(0.315141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4391.32 | − | 7606.00i | 0.820713 | − | 1.42152i | −0.0844390 | − | 0.996429i | \(-0.526910\pi\) |
0.905152 | − | 0.425088i | \(-0.139757\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1105.08 | + | 1914.06i | 0.176649 | + | 0.305965i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5658.22 | − | 6344.64i | 0.780746 | − | 0.875462i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1220.03 | + | 2113.15i | 0.146510 | + | 0.253762i | 0.929935 | − | 0.367723i | \(-0.119863\pi\) |
−0.783425 | + | 0.621486i | \(0.786529\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1956.92 | + | 3389.49i | −0.206021 | + | 0.356839i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3668.55 | −0.340828 | −0.170414 | − | 0.985373i | \(-0.554511\pi\) | ||||
−0.170414 | + | 0.985373i | \(0.554511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7198.06 | −0.593669 | −0.296835 | − | 0.954929i | \(-0.595931\pi\) | ||||
−0.296835 | + | 0.954929i | \(0.595931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2655.76 | + | 4599.91i | −0.195505 | + | 0.338624i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1636.66 | − | 2834.78i | −0.108072 | − | 0.187187i | 0.806917 | − | 0.590665i | \(-0.201134\pi\) |
−0.914989 | + | 0.403478i | \(0.867801\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13502.4 | + | 10008.1i | −0.803378 | + | 0.595470i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4960.34 | + | 8591.56i | 0.267046 | + | 0.462537i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1510.84 | − | 2616.84i | 0.0738801 | − | 0.127964i | −0.826719 | − | 0.562616i | \(-0.809795\pi\) |
0.900599 | + | 0.434651i | \(0.143128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16103.4 | −0.717811 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −25895.6 | −1.05570 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 25743.7 | − | 44589.5i | 0.962812 | − | 1.66764i | 0.247432 | − | 0.968905i | \(-0.420413\pi\) |
0.715381 | − | 0.698735i | \(-0.246253\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6656.65 | + | 11529.6i | 0.229050 | + | 0.396727i | 0.957527 | − | 0.288344i | \(-0.0931046\pi\) |
−0.728477 | + | 0.685071i | \(0.759771\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6989.26 | − | 7837.15i | 0.221860 | − | 0.248775i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14258.2 | − | 24695.9i | −0.418583 | − | 0.725007i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15447.9 | + | 26756.5i | −0.420418 | + | 0.728186i | −0.995980 | − | 0.0895723i | \(-0.971450\pi\) |
0.575562 | + | 0.817758i | \(0.304783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −38064.9 | −0.962503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −41882.8 | −0.986030 | −0.493015 | − | 0.870021i | \(-0.664105\pi\) | ||||
−0.493015 | + | 0.870021i | \(0.664105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17308.7 | + | 29979.5i | −0.380151 | + | 0.658441i | −0.991084 | − | 0.133242i | \(-0.957461\pi\) |
0.610932 | + | 0.791683i | \(0.290795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5287.47 | − | 9158.17i | −0.108541 | − | 0.187999i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31172.2 | + | 6470.74i | 0.599157 | + | 0.124373i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38771.7 | − | 67154.6i | −0.698952 | − | 1.21062i | −0.968830 | − | 0.247726i | \(-0.920317\pi\) |
0.269878 | − | 0.962895i | \(-0.413017\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 100908. | 1.60779 | 0.803897 | − | 0.594768i | \(-0.202756\pi\) | ||||
0.803897 | + | 0.594768i | \(0.202756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72282.4 | −1.08514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22363.2 | + | 38734.2i | −0.316764 | + | 0.548652i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −20391.8 | − | 35319.7i | −0.272886 | − | 0.472652i | 0.696714 | − | 0.717349i | \(-0.254645\pi\) |
−0.969600 | + | 0.244697i | \(0.921312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17677.0 | + | 53534.6i | 0.223771 | + | 0.677690i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 39521.9 | + | 68454.0i | 0.473839 | + | 0.820713i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 94338.2 | − | 163399.i | 1.07245 | − | 1.85755i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140147. | 1.51236 | 0.756178 | − | 0.654366i | \(-0.227064\pi\) | ||||
0.756178 | + | 0.654366i | \(0.227064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19891.5 | −0.203976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4288.23 | + | 7427.43i | −0.0418287 | + | 0.0724494i | −0.886182 | − | 0.463338i | \(-0.846652\pi\) |
0.844353 | + | 0.535787i | \(0.179985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17630.1 | + | 30536.2i | 0.163742 | + | 0.283610i | 0.936208 | − | 0.351447i | \(-0.114310\pi\) |
−0.772466 | + | 0.635057i | \(0.780977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23989.6 | + | 72652.4i | 0.212349 | + | 0.643097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 96314.3 | + | 166821.i | 0.813264 | + | 1.40861i | 0.910568 | + | 0.413360i | \(0.135645\pi\) |
−0.0973041 | + | 0.995255i | \(0.531022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61646.1 | + | 106774.i | −0.496980 | + | 0.860795i | −0.999994 | − | 0.00348322i | \(-0.998891\pi\) |
0.503014 | + | 0.864279i | \(0.332225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21960.6 | −0.169175 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28400.9 | 0.209236 | 0.104618 | − | 0.994512i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994512i | \(0.466638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 138671. | − | 240186.i | 0.977781 | − | 1.69357i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17612.3 | − | 30505.4i | −0.118946 | − | 0.206021i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 139921. | + | 29044.9i | 0.905765 | + | 0.188019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 50372.1 | + | 87247.1i | 0.312771 | + | 0.541736i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16508.5 | − | 28593.5i | 0.0983886 | − | 0.170414i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −127870. | −0.731973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −47198.8 | −0.259670 | −0.129835 | − | 0.991536i | \(-0.541445\pi\) | ||||
−0.129835 | + | 0.991536i | \(0.541445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32391.3 | − | 56103.3i | 0.171377 | − | 0.296835i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −39904.7 | − | 69116.9i | −0.203163 | − | 0.351889i | 0.746383 | − | 0.665517i | \(-0.231789\pi\) |
−0.949546 | + | 0.313628i | \(0.898456\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −248273. | + | 278392.i | −1.21703 | + | 1.36467i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23901.8 | − | 41399.2i | −0.112875 | − | 0.195505i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 43032.1 | − | 74533.9i | 0.195881 | − | 0.339275i | −0.751308 | − | 0.659952i | \(-0.770577\pi\) |
0.947189 | + | 0.320676i | \(0.103910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 270587. | 1.18787 | 0.593935 | − | 0.804513i | \(-0.297573\pi\) | ||||
0.593935 | + | 0.804513i | \(0.297573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29459.9 | 0.124791 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 53396.7 | − | 92485.7i | 0.218360 | − | 0.378211i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −162939. | − | 282219.i | −0.643585 | − | 1.11472i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17244.4 | − | 150277.i | −0.0658197 | − | 0.573586i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 86273.9 | + | 149431.i | 0.318356 | + | 0.551410i | 0.980145 | − | 0.198281i | \(-0.0635358\pi\) |
−0.661789 | + | 0.749690i | \(0.730202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8949.75 | − | 15501.4i | 0.0319425 | − | 0.0553260i | −0.849612 | − | 0.527408i | \(-0.823164\pi\) |
0.881555 | + | 0.472082i | \(0.156497\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −89286.1 | −0.308358 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −575916. | −1.92544 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 89509.3 | − | 155035.i | 0.289814 | − | 0.501972i | −0.683951 | − | 0.729528i | \(-0.739740\pi\) |
0.973765 | + | 0.227555i | \(0.0730733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13597.5 | + | 23551.6i | 0.0426547 | + | 0.0738801i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −364946. | + | 409219.i | −1.10959 | + | 1.24420i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 118645. | + | 205498.i | 0.349767 | + | 0.605814i | 0.986208 | − | 0.165511i | \(-0.0529275\pi\) |
−0.636441 | + | 0.771325i | \(0.719594\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 72465.2 | − | 125513.i | 0.207214 | − | 0.358906i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −94040.0 | −0.260928 | −0.130464 | − | 0.991453i | \(-0.541647\pi\) | ||||
−0.130464 | + | 0.991453i | \(0.541647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182180. | −0.490663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 116530. | − | 201836.i | 0.304753 | − | 0.527848i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −244357. | − | 423238.i | −0.620739 | − | 1.07515i | −0.989348 | − | 0.145567i | \(-0.953499\pi\) |
0.368609 | − | 0.929584i | \(-0.379834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −149149. | − | 30960.4i | −0.368150 | − | 0.0764207i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 231694. | + | 401305.i | 0.555880 | + | 0.962812i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −406498. | + | 704075.i | −0.948257 | + | 1.64243i | −0.199161 | + | 0.979967i | \(0.563822\pi\) |
−0.749095 | + | 0.662462i | \(0.769512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −332961. | −0.755434 | −0.377717 | − | 0.925921i | \(-0.623291\pi\) | ||||
−0.377717 | + | 0.925921i | \(0.623291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −119820. | −0.264484 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 80002.7 | − | 138569.i | 0.171860 | − | 0.297671i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −135348. | − | 234430.i | −0.283040 | − | 0.490240i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 29632.9 | + | 89743.1i | 0.0603420 | + | 0.182745i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 72143.9 | + | 124957.i | 0.143092 | + | 0.247843i | 0.928660 | − | 0.370933i | \(-0.120962\pi\) |
−0.785567 | + | 0.618776i | \(0.787629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 447310. | − | 774763.i | 0.864400 | − | 1.49719i | −0.00324119 | − | 0.999995i | \(-0.501032\pi\) |
0.867641 | − | 0.497190i | \(-0.165635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 256648. | 0.483338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −599462. | −1.10052 | −0.550258 | − | 0.834995i | \(-0.685470\pi\) | ||||
−0.550258 | + | 0.834995i | \(0.685470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 389129. | − | 673992.i | 0.696564 | − | 1.20648i | −0.273086 | − | 0.961990i | \(-0.588044\pi\) |
0.969651 | − | 0.244495i | \(-0.0786222\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −139031. | − | 240808.i | −0.242729 | − | 0.420418i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 202008. | + | 611780.i | 0.344055 | + | 1.04197i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 120282. | + | 208334.i | 0.199901 | + | 0.346238i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 171292. | − | 296687.i | 0.277851 | − | 0.481251i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 706589. | 1.11893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −810532. | −1.25333 | −0.626663 | − | 0.779291i | \(-0.715580\pi\) | ||||
−0.626663 | + | 0.779291i | \(0.715580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 188473. | − | 326444.i | 0.284642 | − | 0.493015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 236004. | + | 408771.i | 0.348196 | + | 0.603093i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.11483e6 | + | 231418.i | 1.60717 | + | 0.333616i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −155778. | − | 269815.i | −0.219480 | − | 0.380151i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 239679. | − | 415136.i | 0.330103 | − | 0.571755i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 220486. | 0.296905 | 0.148453 | − | 0.988920i | \(-0.452571\pi\) | ||||
0.148453 | + | 0.988920i | \(0.452571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 95174.5 | 0.125333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −671890. | + | 1.16375e6i | −0.865433 | + | 1.49897i | 0.00118391 | + | 0.999999i | \(0.499623\pi\) |
−0.866617 | + | 0.498974i | \(0.833710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 521292. | + | 902904.i | 0.656889 | + | 1.13777i | 0.981417 | + | 0.191889i | \(0.0614614\pi\) |
−0.324528 | + | 0.945876i | \(0.605205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −190709. | + | 213845.i | −0.235148 | + | 0.263675i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −316256. | − | 547771.i | −0.381635 | − | 0.661011i | 0.609661 | − | 0.792662i | \(-0.291306\pi\) |
−0.991296 | + | 0.131651i | \(0.957972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107323. | + | 185889.i | −0.126772 | + | 0.219575i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 697891. | 0.807081 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −684919. | −0.775612 | −0.387806 | − | 0.921741i | \(-0.626767\pi\) | ||||
−0.387806 | + | 0.921741i | \(0.626767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3866.44 | − | 6696.87i | 0.00428814 | − | 0.00742728i | −0.863873 | − | 0.503709i | \(-0.831968\pi\) |
0.868162 | + | 0.496282i | \(0.165302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.01105e6 | + | 438651.i | 1.07611 | + | 0.466878i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 625626. | + | 1.08362e6i | 0.652488 | + | 1.13014i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −454086. | + | 786500.i | −0.464130 | + | 0.803897i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.09614e6 | 1.09820 | 0.549098 | − | 0.835758i | \(-0.314971\pi\) | ||||
0.549098 | + | 0.835758i | \(0.314971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03864e6 | 1.02015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 325271. | − | 563386.i | 0.313253 | − | 0.542570i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −357460. | − | 619139.i | −0.337594 | − | 0.584730i | 0.646386 | − | 0.763011i | \(-0.276280\pi\) |
−0.983980 | + | 0.178281i | \(0.942946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −210546. | + | 236088.i | −0.195028 | + | 0.218688i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −201269. | − | 348608.i | −0.182884 | − | 0.316764i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 298256. | − | 516595.i | 0.265889 | − | 0.460533i | −0.701907 | − | 0.712268i | \(-0.747668\pi\) |
0.967796 | + | 0.251735i | \(0.0810012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −198144. | −0.173327 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 367053. | 0.315102 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.01654e6 | − | 1.76070e6i | 0.856531 | − | 1.48356i | −0.0186864 | − | 0.999825i | \(-0.505948\pi\) |
0.875217 | − | 0.483730i | \(-0.160718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −897277. | − | 1.55413e6i | −0.742170 | − | 1.28548i | −0.951505 | − | 0.307632i | \(-0.900463\pi\) |
0.209336 | − | 0.977844i | \(-0.432870\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −496807. | − | 103127.i | −0.403442 | − | 0.0837467i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 144274. | + | 249890.i | 0.115042 | + | 0.199259i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −211790. | + | 366831.i | −0.165846 | + | 0.287254i | −0.936956 | − | 0.349449i | \(-0.886369\pi\) |
0.771109 | + | 0.636703i | \(0.219702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −711395. | −0.547142 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.63799e6 | −1.23750 | −0.618749 | − | 0.785589i | \(-0.712360\pi\) | ||||
−0.618749 | + | 0.785589i | \(0.712360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 147018. | − | 254642.i | 0.109120 | − | 0.189001i | −0.806294 | − | 0.591515i | \(-0.798530\pi\) |
0.915414 | + | 0.402514i | \(0.131863\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 849044. | + | 1.47059e6i | 0.619182 | + | 1.07245i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −149122. | − | 451615.i | −0.106865 | − | 0.323641i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 102399. | + | 177360.i | 0.0721191 | + | 0.124914i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −630661. | + | 1.09234e6i | −0.436580 | + | 0.756178i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −356961. | −0.242913 | −0.121457 | − | 0.992597i | \(-0.538757\pi\) | ||||
−0.121457 | + | 0.992597i | \(0.538757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.37626e6 | −2.25881 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 89511.8 | − | 155039.i | 0.0588829 | − | 0.101988i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 919631. | + | 1.59285e6i | 0.594888 | + | 1.03038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −292592. | − | 886113.i | −0.186143 | − | 0.563732i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −38594.0 | − | 66846.8i | −0.0241498 | − | 0.0418287i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 436505. | − | 756049.i | 0.268683 | − | 0.465372i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.04097e6 | −1.23592 | −0.617960 | − | 0.786210i | \(-0.712041\pi\) | ||||
−0.617960 | + | 0.786210i | \(0.712041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −317341. | −0.189073 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.02337e6 | + | 1.77253e6i | −0.599972 | + | 1.03918i | 0.392852 | + | 0.919602i | \(0.371488\pi\) |
−0.992824 | + | 0.119581i | \(0.961845\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −319272. | − | 552996.i | −0.184205 | − | 0.319052i | 0.759104 | − | 0.650970i | \(-0.225638\pi\) |
−0.943308 | + | 0.331918i | \(0.892304\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −674222. | − | 139955.i | −0.382848 | − | 0.0794718i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.74954e6 | − | 3.03030e6i | −0.977860 | − | 1.69370i | −0.670155 | − | 0.742221i | \(-0.733772\pi\) |
−0.307705 | − | 0.951482i | \(-0.599561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 610203. | − | 1.05690e6i | 0.335736 | − | 0.581512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.73366e6 | −0.939076 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.17163e6 | 1.69152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −255486. | + | 442514.i | −0.134171 | + | 0.232391i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −554815. | − | 960967.i | −0.286932 | − | 0.496980i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 282446. | − | 316710.i | 0.143862 | − | 0.161314i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.47089e6 | + | 2.54766e6i | 0.737923 | + | 1.27812i | 0.953429 | + | 0.301618i | \(0.0975266\pi\) |
−0.215506 | + | 0.976503i | \(0.569140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 98822.5 | − | 171166.i | 0.0488366 | − | 0.0845874i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.02597e6 | 0.986326 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.77854e6 | 1.33273 | 0.666364 | − | 0.745627i | \(-0.267850\pi\) | ||||
0.666364 | + | 0.745627i | \(0.267850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −127804. | + | 221363.i | −0.0604012 | + | 0.104618i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.07840e6 | − | 1.86784e6i | −0.502218 | − | 0.869868i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.78089e6 | − | 1.25539e6i | −0.817338 | − | 0.576159i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.24804e6 | + | 2.16167e6i | 0.564522 | + | 0.977781i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 86001.9 | − | 148960.i | 0.0383429 | − | 0.0664118i | −0.846217 | − | 0.532838i | \(-0.821125\pi\) |
0.884560 | + | 0.466426i | \(0.154459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.88321e6 | −1.70658 | −0.853290 | − | 0.521436i | \(-0.825397\pi\) | ||||
−0.853290 | + | 0.521436i | \(0.825397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 317021. | 0.137348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 385467. | − | 667649.i | 0.164646 | − | 0.285175i | −0.771884 | − | 0.635764i | \(-0.780685\pi\) |
0.936529 | + | 0.350589i | \(0.114019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37322e6 | + | 2.37849e6i | 0.578321 | + | 1.00168i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −856027. | + | 959875.i | −0.355481 | + | 0.398606i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.57017e6 | − | 2.71961e6i | −0.642998 | − | 1.11370i | −0.984760 | − | 0.173918i | \(-0.944357\pi\) |
0.341763 | − | 0.939786i | \(-0.388976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.90135e6 | + | 5.02529e6i | −1.17174 | + | 2.02952i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −906698. | −0.361157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.27001e6 | 0.891857 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 182842. | − | 316691.i | 0.0708615 | − | 0.122736i | −0.828418 | − | 0.560111i | \(-0.810758\pi\) |
0.899279 | + | 0.437375i | \(0.144092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 148576. | + | 257342.i | 0.0568047 | + | 0.0983886i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 383559. | + | 79619.2i | 0.144676 | + | 0.0300319i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 77129.9 | + | 133593.i | 0.0287045 | + | 0.0497177i | 0.880021 | − | 0.474935i | \(-0.157528\pi\) |
−0.851316 | + | 0.524653i | \(0.824195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 575417. | − | 996651.i | 0.211302 | − | 0.365986i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.16114e6 | 0.783122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06013e6 | 1.45192 | 0.725959 | − | 0.687738i | \(-0.241396\pi\) | ||||
0.725959 | + | 0.687738i | \(0.241396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 212395. | − | 367878.i | 0.0749602 | − | 0.129835i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.02152e6 | − | 1.76932e6i | −0.355834 | − | 0.616323i | 0.631426 | − | 0.775436i | \(-0.282470\pi\) |
−0.987260 | + | 0.159113i | \(0.949137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −654581. | − | 1.98240e6i | −0.225067 | − | 0.681614i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 291521. | + | 504930.i | 0.0989448 | + | 0.171377i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.06183e6 | − | 1.83915e6i | 0.355780 | − | 0.616229i | −0.631471 | − | 0.775399i | \(-0.717549\pi\) |
0.987251 | + | 0.159170i | \(0.0508819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66209e6 | 1.54219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 718284. | 0.234593 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.54243e6 | + | 4.40362e6i | −0.819892 | + | 1.42009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.83182e6 | + | 3.17280e6i | 0.583319 | + | 1.01034i | 0.995083 | + | 0.0990473i | \(0.0315795\pi\) |
−0.411764 | + | 0.911291i | \(0.635087\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.05262e6 | − | 3.18786e6i | −0.331010 | − | 1.00246i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32044.9 | + | 55503.3i | 0.00995170 | + | 0.0172369i | 0.870958 | − | 0.491357i | \(-0.163499\pi\) |
−0.861007 | + | 0.508594i | \(0.830166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90966e6 | − | 3.30763e6i | 0.585725 | − | 1.01451i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 430233. | 0.130337 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 599216. | 0.179307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.01287e6 | + | 1.75434e6i | −0.299395 | + | 0.518568i | −0.975998 | − | 0.217781i | \(-0.930118\pi\) |
0.676603 | + | 0.736348i | \(0.263452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 387289. | + | 670805.i | 0.113092 | + | 0.195881i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.53561e6 | + | 1.35666e6i | 1.88543 | + | 0.391379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.30849e6 | − | 5.73047e6i | −0.942995 | − | 1.63332i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.21764e6 | + | 2.10901e6i | −0.342909 | + | 0.593935i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.38986e6 | 0.665025 | 0.332513 | − | 0.943099i | \(-0.392104\pi\) | ||||
0.332513 | + | 0.943099i | \(0.392104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46875e6 | 0.953822 | 0.476911 | − | 0.878952i | \(-0.341756\pi\) | ||||
0.476911 | + | 0.878952i | \(0.341756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −132570. | + | 229617.i | −0.0360241 | + | 0.0623956i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 647596. | + | 1.12167e6i | 0.173913 | + | 0.301226i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.14877e6 | + | 1.28813e6i | −0.304903 | + | 0.341892i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 480570. | + | 832372.i | 0.126070 | + | 0.218360i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 802201. | − | 1.38945e6i | 0.208013 | − | 0.360289i | −0.743076 | − | 0.669207i | \(-0.766634\pi\) |
0.951088 | + | 0.308919i | \(0.0999671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 741661. | 0.190102 | 0.0950508 | − | 0.995472i | \(-0.469699\pi\) | ||||
0.0950508 | + | 0.995472i | \(0.469699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.93291e6 | 0.743147 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.08466e6 | + | 1.05389e7i | −1.52417 | + | 2.63993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.43394e6 | − | 2.48365e6i | −0.355115 | − | 0.615077i | 0.632023 | − | 0.774950i | \(-0.282225\pi\) |
−0.987138 | + | 0.159873i | \(0.948892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.24889e6 | + | 541839.i | 0.305794 | + | 0.132670i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 89148.9 | + | 154410.i | 0.0215827 | + | 0.0373824i | 0.876615 | − | 0.481192i | \(-0.159796\pi\) |
−0.855032 | + | 0.518575i | \(0.826463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33718e6 | + | 2.31607e6i | −0.320103 | + | 0.554435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.55293e6 | −0.367606 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.77890e6 | −0.650515 | −0.325258 | − | 0.945625i | \(-0.605451\pi\) | ||||
−0.325258 | + | 0.945625i | \(0.605451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −450451. | + | 780205.i | −0.104281 | + | 0.180621i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 80547.7 | + | 139513.i | 0.0184420 | + | 0.0319425i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.46060e6 | − | 2.75911e6i | 0.557202 | − | 0.624798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.20669e6 | − | 5.55416e6i | −0.718236 | − | 1.24402i | −0.961698 | − | 0.274111i | \(-0.911617\pi\) |
0.243462 | − | 0.969910i | \(-0.421717\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 401787. | − | 695916.i | 0.0890153 | − | 0.154179i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.88393e6 | −1.50864 | −0.754318 | − | 0.656510i | \(-0.772032\pi\) | ||||
−0.754318 | + | 0.656510i | \(0.772032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.70530e6 | 1.45367 | 0.726835 | − | 0.686812i | \(-0.240991\pi\) | ||||
0.726835 | + | 0.686812i | \(0.240991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.59162e6 | − | 4.48882e6i | 0.555827 | − | 0.962721i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.62836e6 | + | 2.82041e6i | 0.345509 | + | 0.598439i | 0.985446 | − | 0.169988i | \(-0.0543730\pi\) |
−0.639937 | + | 0.768427i | \(0.721040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.92178e6 | − | 814084.i | −0.823286 | − | 0.170898i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 805584. | + | 1.39531e6i | 0.167324 | + | 0.289814i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −883830. | + | 1.53084e6i | −0.181642 | + | 0.314613i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.38080e6 | −0.687520 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −244755. | −0.0492534 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.67916e6 | + | 8.10454e6i | −0.931814 | + | 1.61395i | −0.151595 | + | 0.988443i | \(0.548441\pi\) |
−0.780219 | + | 0.625506i | \(0.784892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 530557. | + | 918951.i | 0.104561 | + | 0.181105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.54729e6 | − | 4.68596e6i | −0.301789 | − | 0.913967i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.59502e6 | − | 7.95881e6i | −0.887019 | − | 1.53636i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.31470e6 | − | 2.27712e6i | 0.251191 | − | 0.435075i | −0.712663 | − | 0.701506i | \(-0.752511\pi\) |
0.963854 | + | 0.266431i | \(0.0858445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.13560e6 | −0.403876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.81856e6 | −0.902015 | −0.451008 | − | 0.892520i | \(-0.648935\pi\) | ||||
−0.451008 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.73899e6 | − | 4.74407e6i | 0.507543 | − | 0.879091i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 652187. | + | 1.12962e6i | 0.119635 | + | 0.207214i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.70248e6 | − | 5.15596e6i | −0.309166 | − | 0.936308i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.09549e6 | + | 3.62949e6i | 0.376733 | + | 0.652521i | 0.990585 | − | 0.136900i | \(-0.0437139\pi\) |
−0.613851 | + | 0.789422i | \(0.710381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 423180. | − | 732969.i | 0.0753236 | − | 0.130464i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.75338e6 | −0.308999 | −0.154500 | − | 0.987993i | \(-0.549377\pi\) | ||||
−0.154500 | + | 0.987993i | \(0.549377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 562395. | 0.0981326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 819808. | − | 1.41995e6i | 0.141642 | − | 0.245331i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.80923e6 | − | 4.86573e6i | −0.480610 | − | 0.832441i | 0.519142 | − | 0.854688i | \(-0.326251\pi\) |
−0.999753 | + | 0.0222464i | \(0.992918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.39418e6 | − | 912146.i | −0.744433 | − | 0.154530i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.04877e6 | + | 1.81653e6i | 0.175949 | + | 0.304753i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.15608e6 | − | 2.00239e6i | 0.192075 | − | 0.332683i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −803844. | −0.132265 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.39842e6 | 0.716768 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.53589e6 | + | 9.58845e6i | −0.893498 | + | 1.54758i | −0.0578446 | + | 0.998326i | \(0.518423\pi\) |
−0.835653 | + | 0.549258i | \(0.814911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.79894e6 | + | 6.57996e6i | 0.607307 | + | 1.05189i | 0.991682 | + | 0.128710i | \(0.0410836\pi\) |
−0.384375 | + | 0.923177i | \(0.625583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 912482. | − | 1.02318e6i | 0.144486 | − | 0.162014i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.84055e6 | − | 8.38407e6i | −0.759220 | − | 1.31501i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.72588e6 | + | 9.91752e6i | −0.889618 | + | 1.54086i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.17049e6 | −0.641875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.59535e6 | −0.243242 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.31575e6 | − | 1.09392e7i | 0.953982 | − | 1.65235i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.65848e6 | − | 6.33668e6i | −0.547476 | − | 0.948257i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 470532. | + | 4.10046e6i | 0.0697618 | + | 0.607940i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.67539e6 | + | 2.90187e6i | 0.246107 | + | 0.426270i | 0.962442 | − | 0.271486i | \(-0.0875152\pi\) |
−0.716335 | + | 0.697756i | \(0.754182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.49832e6 | − | 2.59517e6i | 0.218075 | − | 0.377717i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.08480e6 | 1.16595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00856e7 | −1.44123 | −0.720615 | − | 0.693335i | \(-0.756140\pi\) | ||||
−0.720615 | + | 0.693335i | \(0.756140\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 539188. | − | 933901.i | 0.0763501 | − | 0.132242i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.14950e6 | + | 1.23833e7i | 1.00322 | + | 1.73763i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.69101e6 | − | 7.50272e6i | 0.930419 | − | 1.04329i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 720024. | + | 1.24712e6i | 0.0992235 | + | 0.171860i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.78337e6 | + | 1.17491e7i | −0.926419 | + | 1.60460i | −0.137155 | + | 0.990550i | \(0.543796\pi\) |
−0.789263 | + | 0.614055i | \(0.789537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.13023e6 | −0.423689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.43626e6 | 0.326826 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.98494e6 | − | 3.43802e6i | 0.263922 | − | 0.457127i | −0.703358 | − | 0.710835i | \(-0.748317\pi\) |
0.967281 | + | 0.253708i | \(0.0816504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −931185. | − | 1.61286e6i | −0.122720 | − | 0.212557i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −832826. | − | 172878.i | −0.108792 | − | 0.0225831i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.08724e6 | + | 3.61521e6i | 0.270267 | + | 0.468116i | 0.968930 | − | 0.247335i | \(-0.0795548\pi\) |
−0.698663 | + | 0.715451i | \(0.746221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.92833e6 | + | 3.33996e6i | −0.247509 | + | 0.428698i | −0.962834 | − | 0.270094i | \(-0.912945\pi\) |
0.715325 | + | 0.698792i | \(0.246279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.29859e6 | −0.165229 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.96956e6 | −0.626828 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.12288e6 | − | 1.94488e6i | 0.140408 | − | 0.243194i | −0.787242 | − | 0.616644i | \(-0.788492\pi\) |
0.927650 | + | 0.373450i | \(0.121825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.02579e6 | + | 6.97287e6i | 0.499062 | + | 0.864400i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.10178e6 | + | 1.24222e7i | 0.504118 | + | 1.52672i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −371023. | − | 642630.i | −0.0452094 | − | 0.0783050i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.15492e6 | + | 2.00037e6i | −0.139528 | + | 0.241669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.40082e6 | 0.766726 | 0.383363 | − | 0.923598i | \(-0.374766\pi\) | ||||
0.383363 | + | 0.923598i | \(0.374766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.52702e7 | 3.00138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.69758e6 | − | 4.67234e6i | 0.317691 | − | 0.550258i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.56031e6 | − | 9.63074e6i | −0.649325 | − | 1.12466i | −0.983284 | − | 0.182077i | \(-0.941718\pi\) |
0.333959 | − | 0.942588i | \(-0.391615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.93818e6 | − | 8.89828e6i | −0.340241 | − | 1.03042i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.50216e6 | + | 6.06592e6i | 0.402162 | + | 0.696564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.56707e6 | − | 1.13745e7i | 0.747833 | − | 1.29528i | −0.201027 | − | 0.979586i | \(-0.564428\pi\) |
0.948860 | − | 0.315698i | \(-0.102239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.88546e6 | −0.890514 | −0.445257 | − | 0.895403i | \(-0.646888\pi\) | ||||
−0.445257 | + | 0.895403i | \(0.646888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.50255e6 | 0.280279 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.30312e6 | − | 5.72117e6i | 0.366890 | − | 0.635472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.82967e6 | + | 6.63319e6i | 0.421881 | + | 0.730719i | 0.996123 | − | 0.0879660i | \(-0.0280367\pi\) |
−0.574243 | + | 0.818685i | \(0.694703\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.67739e6 | − | 1.17851e6i | −0.620305 | − | 0.128763i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −711738. | − | 1.23277e6i | −0.0771289 | − | 0.133591i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.62066e6 | − | 1.31994e7i | 0.819108 | − | 1.41874i | −0.0872322 | − | 0.996188i | \(-0.527802\pi\) |
0.906340 | − | 0.422549i | \(-0.138864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.16507e6 | −0.230825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.35844e7 | 1.43657 | 0.718285 | − | 0.695749i | \(-0.244927\pi\) | ||||
0.718285 | + | 0.695749i | \(0.244927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.18709e6 | + | 5.52019e6i | −0.334324 | + | 0.579066i | −0.983355 | − | 0.181696i | \(-0.941841\pi\) |
0.649031 | + | 0.760762i | \(0.275175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.54163e6 | + | 2.67018e6i | 0.160417 | + | 0.277851i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.51911e6 | − | 3.94602e6i | 0.363256 | − | 0.407323i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.02844e6 | + | 1.04416e7i | 0.617312 | + | 1.06922i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.17965e6 | + | 5.50732e6i | −0.323006 | + | 0.559463i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.68967e6 | 0.271065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.42736e7 | −1.42712 | −0.713561 | − | 0.700593i | \(-0.752919\pi\) | ||||
−0.713561 | + | 0.700593i | \(0.752919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.64739e6 | − | 6.31747e6i | 0.361804 | − | 0.626663i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.54751e6 | + | 2.68037e6i | 0.152300 | + | 0.263792i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.87180e6 | + | 4.35222e6i | −0.573354 | + | 0.424974i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.69625e6 | + | 2.93800e6i | 0.164338 | + | 0.284642i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.63480e6 | − | 8.02771e6i | 0.445539 | − | 0.771697i | −0.552550 | − | 0.833480i | \(-0.686345\pi\) |
0.998090 | + | 0.0617828i | \(0.0196786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17375e7 | 1.11956 | 0.559780 | − | 0.828641i | \(-0.310885\pi\) | ||||
0.559780 | + | 0.828641i | \(0.310885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.24807e6 | −0.402062 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.12724e6 | + | 8.88063e6i | −0.481529 | + | 0.834033i | −0.999775 | − | 0.0211984i | \(-0.993252\pi\) |
0.518246 | + | 0.855232i | \(0.326585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32200e6 | − | 1.09500e7i | −0.589173 | − | 1.02048i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.82047e6 | + | 7.64789e6i | −0.630757 | + | 0.707276i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.14489e6 | − | 7.17915e6i | −0.380391 | − | 0.658856i | 0.610727 | − | 0.791841i | \(-0.290877\pi\) |
−0.991118 | + | 0.132985i | \(0.957544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.61672e6 | + | 4.53230e6i | −0.238317 | + | 0.412776i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.80400e6 | 0.253434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.06731e7 | −1.85435 | −0.927174 | − | 0.374631i | \(-0.877770\pi\) | ||||
−0.927174 | + | 0.374631i | \(0.877770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −97171.2 | + | 168305.i | −0.00865035 | + | 0.0149829i | −0.870318 | − | 0.492490i | \(-0.836087\pi\) |
0.861668 | + | 0.507473i | \(0.169420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.15711e6 | + | 3.73623e6i | 0.190585 | + | 0.330103i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.39498e7 | + | 4.97151e6i | 2.10014 | + | 0.435948i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.05093e7 | + | 1.82026e7i | 0.914659 | + | 1.58424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −992186. | + | 1.71852e6i | −0.0857092 | + | 0.148453i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.26940e6 | 0.280325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.14437e7 | −0.973929 | −0.486965 | − | 0.873422i | \(-0.661896\pi\) | ||||
−0.486965 | + | 0.873422i | \(0.661896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −428285. | + | 741812.i | −0.0361804 | + | 0.0626663i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.51869e6 | − | 7.82660e6i | −0.378914 | − | 0.656299i | 0.611990 | − | 0.790865i | \(-0.290369\pi\) |
−0.990905 | + | 0.134567i | \(0.957036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.69679e6 | + | 1.72527e7i | 0.474193 | + | 1.43609i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.04701e6 | − | 1.04737e7i | −0.499658 | − | 0.865433i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.59212e6 | − | 9.68584e6i | 0.458696 | − | 0.794485i | −0.540196 | − | 0.841539i | \(-0.681650\pi\) |
0.998892 | + | 0.0470541i | \(0.0149833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.64361e6 | −0.459548 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.38325e6 | −0.758510 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 657020. | − | 1.13799e6i | 0.0527267 | − | 0.0913253i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.83465e6 | − | 4.90976e6i | −0.225842 | − | 0.391170i | 0.730730 | − | 0.682667i | \(-0.239180\pi\) |
−0.956572 | + | 0.291497i | \(0.905847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −808564. | − | 2.44873e6i | −0.0639560 | − | 0.193691i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.87177e6 | − | 1.53664e7i | −0.696704 | − | 1.20673i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.02192e6 | + | 3.50207e6i | −0.157646 | + | 0.273050i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.69260e6 | 0.440674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.31822e6 | −0.101320 | −0.0506599 | − | 0.998716i | \(-0.516132\pi\) | ||||
−0.0506599 | + | 0.998716i | \(0.516132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.51038e6 | + | 6.08016e6i | −0.267896 | + | 0.464009i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −965907. | − | 1.67300e6i | −0.0731918 | − | 0.126772i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.08866e6 | − | 225984.i | −0.0819112 | − | 0.0170032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.13018e6 | − | 7.15368e6i | −0.308570 | − | 0.534458i | 0.669480 | − | 0.742830i | \(-0.266517\pi\) |
−0.978050 | + | 0.208372i | \(0.933184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.14051e6 | + | 5.43952e6i | −0.232984 | + | 0.403540i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.71456e7 | 2.73643 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.00290e6 | −0.512287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.08214e6 | − | 5.33842e6i | 0.223900 | − | 0.387806i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.13372e7 | − | 1.96365e7i | −0.817865 | − | 1.41658i | −0.907252 | − | 0.420587i | \(-0.861824\pi\) |
0.0893870 | − | 0.995997i | \(-0.471509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.04250e6 | + | 3.41159e6i | −0.217968 | + | 0.244410i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34798.0 | + | 60271.9i | 0.00247576 | + | 0.00428814i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.91963e6 | + | 5.05694e6i | −0.206292 | + | 0.357308i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.93477e7 | −1.35767 | −0.678833 | − | 0.734293i | \(-0.737514\pi\) | ||||
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.96720e6 | + | 6.87140e6i | −0.274594 | + | 0.475611i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.42922e6 | − | 1.28678e7i | −0.510720 | − | 0.884593i | −0.999923 | − | 0.0124232i | \(-0.996045\pi\) |
0.489203 | − | 0.872170i | \(-0.337288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.96868e6 | + | 5.90645e6i | −0.544087 | + | 0.403281i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.79360e6 | + | 6.57071e6i | 0.257266 | + | 0.445598i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.84089e6 | − | 1.53129e7i | 0.595504 | − | 1.03144i | −0.397971 | − | 0.917398i | \(-0.630286\pi\) |
0.993476 | − | 0.114045i | \(-0.0363810\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12613e7 | −0.753428 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.28756e6 | −0.550750 | −0.275375 | − | 0.961337i | \(-0.588802\pi\) | ||||
−0.275375 | + | 0.961337i | \(0.588802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.65735e6 | − | 9.79882e6i | 0.373442 | − | 0.646820i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.08678e6 | − | 7.07850e6i | −0.267966 | − | 0.464130i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.66214e7 | + | 1.86378e7i | −1.08259 | + | 1.21392i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15682e7 | + | 2.00368e7i | 0.748457 | + | 1.29637i | 0.948562 | + | 0.316592i | \(0.102539\pi\) |
−0.200104 | + | 0.979775i | \(0.564128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.93261e6 | + | 8.54354e6i | −0.317022 | + | 0.549098i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.17375e6 | −0.0749389 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.95475e7 | −1.23980 | −0.619900 | − | 0.784681i | \(-0.712827\pi\) | ||||
−0.619900 | + | 0.784681i | \(0.712827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.67388e6 | + | 8.09540e6i | −0.294492 | + | 0.510075i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.91233e6 | − | 6.77635e6i | −0.244891 | − | 0.424164i | 0.717210 | − | 0.696857i | \(-0.245419\pi\) |
−0.962101 | + | 0.272693i | \(0.912086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.56502e7 | − | 3.24867e6i | −0.973214 | − | 0.202020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.92744e6 | + | 5.07047e6i | 0.180857 | + | 0.313253i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.11952e7 | − | 1.93907e7i | 0.687139 | − | 1.19016i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.27325e6 | −0.504499 | −0.252250 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252250 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.43428e6 | 0.389820 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.41844e6 | − | 1.63132e7i | 0.566931 | − | 0.981953i | −0.429936 | − | 0.902859i | \(-0.641464\pi\) |
0.996867 | − | 0.0790941i | \(-0.0252028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.15978e6 | + | 8.93700e6i | 0.308587 | + | 0.534488i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −892667. | − | 2.70344e6i | −0.0530441 | − | 0.160644i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.27775e6 | − | 9.14133e6i | −0.311605 | − | 0.539717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.14267e6 | + | 8.90737e6i | −0.301690 | + | 0.522543i | ||||
\(782\) | 0 | 0 |