Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (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: | \(10.1041806482\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(-0.874091 + 1.51397i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.37 |
Dual form | 63.6.e.e.46.3 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37409 | − | 2.37999i | 0.242907 | − | 0.420728i | −0.718634 | − | 0.695389i | \(-0.755232\pi\) |
0.961541 | + | 0.274661i | \(0.0885656\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.2237 | + | 21.1722i | 0.381992 | + | 0.661630i | ||||
\(5\) | 29.1836 | − | 50.5475i | 0.522053 | − | 0.904222i | −0.477618 | − | 0.878568i | \(-0.658500\pi\) |
0.999671 | − | 0.0256544i | \(-0.00816693\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.4366 | + | 127.857i | −0.165352 | + | 0.986235i | ||||
\(8\) | 155.128 | 0.856969 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −80.2019 | − | 138.914i | −0.253621 | − | 0.439284i | ||||
\(11\) | 8.71205 | + | 15.0897i | 0.0217089 | + | 0.0376010i | 0.876676 | − | 0.481082i | \(-0.159756\pi\) |
−0.854967 | + | 0.518683i | \(0.826423\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 889.933 | 1.46049 | 0.730246 | − | 0.683185i | \(-0.239406\pi\) | ||||
0.730246 | + | 0.683185i | \(0.239406\pi\) | |||||||
\(14\) | 274.844 | + | 226.706i | 0.374771 | + | 0.309132i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −178.000 | + | 308.305i | −0.173828 | + | 0.301079i | ||||
\(17\) | 513.318 | + | 889.092i | 0.430788 | + | 0.746147i | 0.996941 | − | 0.0781529i | \(-0.0249022\pi\) |
−0.566153 | + | 0.824300i | \(0.691569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 869.702 | − | 1506.37i | 0.552696 | − | 0.957297i | −0.445383 | − | 0.895340i | \(-0.646932\pi\) |
0.998079 | − | 0.0619572i | \(-0.0197342\pi\) | |||||||
\(20\) | 1426.93 | 0.797680 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 47.8846 | 0.0210930 | ||||||||
\(23\) | 1968.11 | − | 3408.87i | 0.775764 | − | 1.34366i | −0.158599 | − | 0.987343i | \(-0.550698\pi\) |
0.934364 | − | 0.356320i | \(-0.115969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −140.869 | − | 243.993i | −0.0450782 | − | 0.0780777i | ||||
\(26\) | 1222.85 | − | 2118.04i | 0.354764 | − | 0.614469i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2969.05 | + | 1109.04i | −0.715686 | + | 0.267332i | ||||
\(29\) | −5633.53 | −1.24390 | −0.621950 | − | 0.783057i | \(-0.713659\pi\) | ||||
−0.621950 | + | 0.783057i | \(0.713659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1548.27 | + | 2681.68i | 0.289362 | + | 0.501190i | 0.973658 | − | 0.228015i | \(-0.0732236\pi\) |
−0.684296 | + | 0.729205i | \(0.739890\pi\) | |||||||
\(32\) | 2971.22 | + | 5146.31i | 0.512933 | + | 0.888426i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2821.38 | 0.418566 | ||||||||
\(35\) | 5837.27 | + | 4814.91i | 0.805452 | + | 0.664382i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2513.43 | + | 4353.39i | −0.301830 | + | 0.522785i | −0.976551 | − | 0.215288i | \(-0.930931\pi\) |
0.674720 | + | 0.738073i | \(0.264264\pi\) | |||||||
\(38\) | −2390.10 | − | 4139.77i | −0.268508 | − | 0.465069i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4527.20 | − | 7841.34i | 0.447383 | − | 0.774890i | ||||
\(41\) | −18367.0 | −1.70639 | −0.853195 | − | 0.521592i | \(-0.825338\pi\) | ||||
−0.853195 | + | 0.521592i | \(0.825338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1630.91 | −0.134511 | −0.0672557 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672557 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(44\) | −212.988 | + | 368.906i | −0.0165853 | + | 0.0287266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5408.72 | − | 9368.19i | −0.376878 | − | 0.652771i | ||||
\(47\) | −4802.62 | + | 8318.38i | −0.317127 | + | 0.549280i | −0.979887 | − | 0.199551i | \(-0.936051\pi\) |
0.662760 | + | 0.748832i | \(0.269385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15887.9 | − | 5481.65i | −0.945317 | − | 0.326153i | ||||
\(50\) | −774.269 | −0.0437992 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10878.3 | + | 18841.8i | 0.557896 | + | 0.966305i | ||||
\(53\) | −11628.3 | − | 20140.7i | −0.568624 | − | 0.984886i | −0.996702 | − | 0.0811440i | \(-0.974143\pi\) |
0.428078 | − | 0.903742i | \(-0.359191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1017.00 | 0.0453328 | ||||||||
\(56\) | −3325.41 | + | 19834.2i | −0.141702 | + | 0.845172i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7740.98 | + | 13407.8i | −0.302152 | + | 0.523343i | ||||
\(59\) | −1801.62 | − | 3120.50i | −0.0673803 | − | 0.116706i | 0.830367 | − | 0.557217i | \(-0.188131\pi\) |
−0.897747 | + | 0.440511i | \(0.854797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11438.3 | + | 19811.7i | −0.393584 | + | 0.681707i | −0.992919 | − | 0.118791i | \(-0.962098\pi\) |
0.599336 | + | 0.800498i | \(0.295431\pi\) | |||||||
\(62\) | 8509.83 | 0.281152 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4938.92 | 0.150724 | ||||||||
\(65\) | 25971.5 | − | 44983.9i | 0.762454 | − | 1.32061i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23506.4 | − | 40714.2i | −0.639733 | − | 1.10805i | −0.985491 | − | 0.169726i | \(-0.945712\pi\) |
0.345758 | − | 0.938324i | \(-0.387622\pi\) | |||||||
\(68\) | −12549.3 | + | 21736.1i | −0.329116 | + | 0.570045i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 19480.4 | − | 7276.56i | 0.475174 | − | 0.177493i | ||||
\(71\) | 1599.63 | 0.0376595 | 0.0188298 | − | 0.999823i | \(-0.494006\pi\) | ||||
0.0188298 | + | 0.999823i | \(0.494006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2965.67 | − | 5136.70i | −0.0651353 | − | 0.112818i | 0.831619 | − | 0.555347i | \(-0.187415\pi\) |
−0.896754 | + | 0.442529i | \(0.854081\pi\) | |||||||
\(74\) | 6907.36 | + | 11963.9i | 0.146633 | + | 0.253976i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 42524.1 | 0.844502 | ||||||||
\(77\) | −2116.09 | + | 790.427i | −0.0406730 | + | 0.0151927i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44234.4 | − | 76616.3i | 0.797431 | − | 1.38119i | −0.123854 | − | 0.992300i | \(-0.539525\pi\) |
0.921284 | − | 0.388890i | \(-0.127141\pi\) | |||||||
\(80\) | 10389.4 | + | 17994.9i | 0.181495 | + | 0.314359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25237.9 | + | 43713.3i | −0.414495 | + | 0.717926i | ||||
\(83\) | 95823.9 | 1.52679 | 0.763394 | − | 0.645933i | \(-0.223531\pi\) | ||||
0.763394 | + | 0.645933i | \(0.223531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59921.9 | 0.899577 | ||||||||
\(86\) | −2241.02 | + | 3881.56i | −0.0326738 | + | 0.0565927i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1351.48 | + | 2340.84i | 0.0186039 | + | 0.0322229i | ||||
\(89\) | −23253.9 | + | 40277.0i | −0.311187 | + | 0.538992i | −0.978620 | − | 0.205679i | \(-0.934060\pi\) |
0.667433 | + | 0.744670i | \(0.267393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19077.1 | + | 113784.i | −0.241496 | + | 1.44039i | ||||
\(92\) | 96230.8 | 1.18534 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13198.5 | + | 22860.4i | 0.154065 | + | 0.266848i | ||||
\(95\) | −50762.1 | − | 87922.5i | −0.577073 | − | 0.999519i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −75981.8 | −0.819937 | −0.409968 | − | 0.912100i | \(-0.634460\pi\) | ||||
−0.409968 | + | 0.912100i | \(0.634460\pi\) | |||||||
\(98\) | −34877.8 | + | 30281.0i | −0.366846 | + | 0.318496i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3443.90 | − | 5965.01i | 0.0344390 | − | 0.0596501i | ||||
\(101\) | −23078.7 | − | 39973.5i | −0.225117 | − | 0.389914i | 0.731238 | − | 0.682123i | \(-0.238943\pi\) |
−0.956355 | + | 0.292209i | \(0.905610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 40986.8 | − | 70991.2i | 0.380672 | − | 0.659343i | −0.610487 | − | 0.792027i | \(-0.709026\pi\) |
0.991158 | + | 0.132683i | \(0.0423594\pi\) | |||||||
\(104\) | 138054. | 1.25160 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −63913.2 | −0.552491 | ||||||||
\(107\) | −1426.84 | + | 2471.35i | −0.0120480 | + | 0.0208677i | −0.871987 | − | 0.489530i | \(-0.837168\pi\) |
0.859939 | + | 0.510398i | \(0.170502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 83139.2 | + | 144001.i | 0.670254 | + | 1.16091i | 0.977832 | + | 0.209391i | \(0.0671483\pi\) |
−0.307578 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(110\) | 1397.45 | − | 2420.45i | 0.0110117 | − | 0.0190728i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −35603.3 | − | 29367.6i | −0.268192 | − | 0.221220i | ||||
\(113\) | −260304. | −1.91772 | −0.958858 | − | 0.283886i | \(-0.908376\pi\) | ||||
−0.958858 | + | 0.283886i | \(0.908376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −114873. | − | 198966.i | −0.809980 | − | 1.40293i | ||||
\(116\) | −68862.8 | − | 119274.i | −0.475160 | − | 0.823001i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9902.35 | −0.0654687 | ||||||||
\(119\) | −124681. | + | 46572.3i | −0.807108 | + | 0.301481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 80373.7 | − | 139211.i | 0.499057 | − | 0.864393i | ||||
\(122\) | 31434.5 | + | 54446.2i | 0.191209 | + | 0.331183i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −37851.2 | + | 65560.3i | −0.221068 | + | 0.382901i | ||||
\(125\) | 165953. | 0.949973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −233743. | −1.28596 | −0.642982 | − | 0.765882i | \(-0.722303\pi\) | ||||
−0.642982 | + | 0.765882i | \(0.722303\pi\) | |||||||
\(128\) | −88292.6 | + | 152927.i | −0.476321 | + | 0.825012i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −71374.4 | − | 123624.i | −0.370411 | − | 0.641571i | ||||
\(131\) | −78644.9 | + | 136217.i | −0.400398 | + | 0.693510i | −0.993774 | − | 0.111415i | \(-0.964462\pi\) |
0.593376 | + | 0.804926i | \(0.297795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 173957. | + | 143489.i | 0.852730 | + | 0.703379i | ||||
\(134\) | −129200. | −0.621583 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 79629.9 | + | 137923.i | 0.369172 | + | 0.639425i | ||||
\(137\) | −85773.8 | − | 148564.i | −0.390439 | − | 0.676260i | 0.602069 | − | 0.798444i | \(-0.294343\pi\) |
−0.992507 | + | 0.122185i | \(0.961010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 210625. | 0.924642 | 0.462321 | − | 0.886713i | \(-0.347017\pi\) | ||||
0.462321 | + | 0.886713i | \(0.347017\pi\) | |||||||
\(140\) | −30588.6 | + | 182444.i | −0.131898 | + | 0.786700i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2198.04 | − | 3807.12i | 0.00914777 | − | 0.0158444i | ||||
\(143\) | 7753.14 | + | 13428.8i | 0.0317057 | + | 0.0549159i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −164407. | + | 284761.i | −0.649381 | + | 1.12476i | ||||
\(146\) | −16300.4 | −0.0632873 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −122894. | −0.461187 | ||||||||
\(149\) | 119706. | − | 207338.i | 0.441725 | − | 0.765090i | −0.556093 | − | 0.831120i | \(-0.687700\pi\) |
0.997818 | + | 0.0660304i | \(0.0210334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −108520. | − | 187962.i | −0.387317 | − | 0.670852i | 0.604771 | − | 0.796400i | \(-0.293265\pi\) |
−0.992088 | + | 0.125547i | \(0.959931\pi\) | |||||||
\(152\) | 134915. | − | 233680.i | 0.473643 | − | 0.820374i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1026.48 | + | 6122.39i | −0.00348778 | + | 0.0208027i | ||||
\(155\) | 180736. | 0.604249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −83452.2 | − | 144543.i | −0.270202 | − | 0.468004i | 0.698711 | − | 0.715404i | \(-0.253757\pi\) |
−0.968913 | + | 0.247400i | \(0.920424\pi\) | |||||||
\(158\) | −121564. | − | 210556.i | −0.387403 | − | 0.671002i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 346844. | 1.07111 | ||||||||
\(161\) | 393659. | + | 324712.i | 1.19689 | + | 0.987264i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −253086. | + | 438358.i | −0.746104 | + | 1.29229i | 0.203574 | + | 0.979060i | \(0.434744\pi\) |
−0.949677 | + | 0.313230i | \(0.898589\pi\) | |||||||
\(164\) | −224514. | − | 388869.i | −0.651828 | − | 1.12900i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 131671. | − | 228061.i | 0.370868 | − | 0.642362i | ||||
\(167\) | 565560. | 1.56923 | 0.784616 | − | 0.619982i | \(-0.212860\pi\) | ||||
0.784616 | + | 0.619982i | \(0.212860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 420688. | 1.13304 | ||||||||
\(170\) | 82338.1 | − | 142614.i | 0.218514 | − | 0.378477i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19935.9 | − | 34529.9i | −0.0513823 | − | 0.0889968i | ||||
\(173\) | −329718. | + | 571088.i | −0.837581 | + | 1.45073i | 0.0543304 | + | 0.998523i | \(0.482698\pi\) |
−0.891911 | + | 0.452210i | \(0.850636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 34216.0 | − | 12780.8i | 0.0844567 | − | 0.0315473i | ||||
\(176\) | −6202.98 | −0.0150945 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 63906.0 | + | 110688.i | 0.151179 | + | 0.261850i | ||||
\(179\) | 82645.0 | + | 143145.i | 0.192790 | + | 0.333922i | 0.946174 | − | 0.323659i | \(-0.104913\pi\) |
−0.753384 | + | 0.657581i | \(0.771580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 148492. | 0.336904 | 0.168452 | − | 0.985710i | \(-0.446123\pi\) | ||||
0.168452 | + | 0.985710i | \(0.446123\pi\) | |||||||
\(182\) | 244593. | + | 201754.i | 0.547350 | + | 0.451484i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 305309. | − | 528811.i | 0.664806 | − | 1.15148i | ||||
\(185\) | 146702. | + | 254095.i | 0.315142 | + | 0.545843i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8944.10 | + | 15491.6i | −0.0187039 | + | 0.0323961i | ||||
\(188\) | −234824. | −0.484560 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −279007. | −0.560701 | ||||||||
\(191\) | 192955. | − | 334208.i | 0.382713 | − | 0.662879i | −0.608736 | − | 0.793373i | \(-0.708323\pi\) |
0.991449 | + | 0.130494i | \(0.0416564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −248148. | − | 429805.i | −0.479531 | − | 0.830573i | 0.520193 | − | 0.854049i | \(-0.325860\pi\) |
−0.999724 | + | 0.0234760i | \(0.992527\pi\) | |||||||
\(194\) | −104406. | + | 180836.i | −0.199169 | + | 0.344970i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −78152.0 | − | 403388.i | −0.145312 | − | 0.750038i | ||||
\(197\) | −441439. | −0.810411 | −0.405206 | − | 0.914226i | \(-0.632800\pi\) | ||||
−0.405206 | + | 0.914226i | \(0.632800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 37919.4 | + | 65678.3i | 0.0678779 | + | 0.117568i | 0.897967 | − | 0.440063i | \(-0.145044\pi\) |
−0.830089 | + | 0.557631i | \(0.811710\pi\) | |||||||
\(200\) | −21852.8 | − | 37850.1i | −0.0386306 | − | 0.0669102i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −126849. | −0.218730 | ||||||||
\(203\) | 120764. | − | 720287.i | 0.205682 | − | 1.22678i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −536016. | + | 928406.i | −0.890826 | + | 1.54296i | ||||
\(206\) | −112639. | − | 195097.i | −0.184936 | − | 0.320318i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −158408. | + | 274371.i | −0.253875 | + | 0.439724i | ||||
\(209\) | 30307.5 | 0.0479938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 778704. | 1.20411 | 0.602055 | − | 0.798454i | \(-0.294349\pi\) | ||||
0.602055 | + | 0.798454i | \(0.294349\pi\) | |||||||
\(212\) | 284282. | − | 492391.i | 0.434420 | − | 0.752437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3921.21 | + | 6791.73i | 0.00585309 | + | 0.0101379i | ||||
\(215\) | −47595.9 | + | 82438.6i | −0.0702221 | + | 0.121628i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −376061. | + | 140471.i | −0.542137 | + | 0.202506i | ||||
\(218\) | 456963. | 0.651238 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12431.5 | + | 21532.0i | 0.0173168 | + | 0.0299936i | ||||
\(221\) | 456818. | + | 791233.i | 0.629163 | + | 1.08974i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 738085. | 0.993903 | 0.496951 | − | 0.867778i | \(-0.334453\pi\) | ||||
0.496951 | + | 0.867778i | \(0.334453\pi\) | |||||||
\(224\) | −721686. | + | 269573.i | −0.961011 | + | 0.358969i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −357681. | + | 619522.i | −0.465827 | + | 0.806836i | ||||
\(227\) | −272058. | − | 471218.i | −0.350426 | − | 0.606956i | 0.635898 | − | 0.771773i | \(-0.280630\pi\) |
−0.986324 | + | 0.164817i | \(0.947297\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 116781. | − | 202271.i | 0.147158 | − | 0.254885i | −0.783018 | − | 0.621999i | \(-0.786321\pi\) |
0.930176 | + | 0.367114i | \(0.119654\pi\) | |||||||
\(230\) | −631385. | −0.787000 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −873917. | −1.06598 | ||||||||
\(233\) | −309050. | + | 535290.i | −0.372940 | + | 0.645951i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) |
0.617077 | + | 0.786903i | \(0.288317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 280316. | + | 485521.i | 0.331114 | + | 0.573506i | ||||
\(236\) | 44045.1 | − | 76288.3i | 0.0514775 | − | 0.0891617i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −60480.8 | + | 360734.i | −0.0692110 | + | 0.412805i | ||||
\(239\) | −937500. | −1.06164 | −0.530819 | − | 0.847485i | \(-0.678116\pi\) | ||||
−0.530819 | + | 0.847485i | \(0.678116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −466018. | − | 807167.i | −0.516845 | − | 0.895202i | −0.999809 | − | 0.0195613i | \(-0.993773\pi\) |
0.482964 | − | 0.875640i | \(-0.339560\pi\) | |||||||
\(242\) | −220882. | − | 382578.i | −0.242449 | − | 0.419935i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −559276. | −0.601383 | ||||||||
\(245\) | −740752. | + | 643122.i | −0.788420 | + | 0.684508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 773976. | − | 1.34057e6i | 0.807208 | − | 1.39812i | ||||
\(248\) | 240179. | + | 416003.i | 0.247974 | + | 0.429504i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 228035. | − | 394968.i | 0.230755 | − | 0.399680i | ||||
\(251\) | −214975. | −0.215379 | −0.107690 | − | 0.994185i | \(-0.534345\pi\) | ||||
−0.107690 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 68585.1 | 0.0673641 | ||||||||
\(254\) | −321184. | + | 556306.i | −0.312370 | + | 0.541040i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 321667. | + | 557143.i | 0.306765 | + | 0.531333i | ||||
\(257\) | 39593.5 | − | 68578.0i | 0.0373931 | − | 0.0647667i | −0.846723 | − | 0.532034i | \(-0.821428\pi\) |
0.884116 | + | 0.467267i | \(0.154761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −502733. | − | 414682.i | −0.465680 | − | 0.384119i | ||||
\(260\) | 1.26988e6 | 1.16501 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 216130. | + | 374349.i | 0.194519 | + | 0.336917i | ||||
\(263\) | −216414. | − | 374840.i | −0.192928 | − | 0.334162i | 0.753291 | − | 0.657687i | \(-0.228465\pi\) |
−0.946219 | + | 0.323526i | \(0.895132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.35742e6 | −1.18741 | ||||||||
\(266\) | 580535. | − | 216849.i | 0.503065 | − | 0.187911i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 574672. | − | 995361.i | 0.488746 | − | 0.846533i | ||||
\(269\) | −2345.93 | − | 4063.27i | −0.00197667 | − | 0.00342369i | 0.865035 | − | 0.501711i | \(-0.167296\pi\) |
−0.867012 | + | 0.498287i | \(0.833963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −52632.1 | + | 91161.5i | −0.0435339 | + | 0.0754029i | −0.886971 | − | 0.461825i | \(-0.847195\pi\) |
0.843437 | + | 0.537227i | \(0.180528\pi\) | |||||||
\(272\) | −365482. | −0.299533 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −471444. | −0.379362 | ||||||||
\(275\) | 2454.52 | − | 4251.35i | 0.00195720 | − | 0.00338997i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 381558. | + | 660879.i | 0.298787 | + | 0.517514i | 0.975859 | − | 0.218403i | \(-0.0700847\pi\) |
−0.677072 | + | 0.735917i | \(0.736751\pi\) | |||||||
\(278\) | 289418. | − | 501287.i | 0.224602 | − | 0.389023i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 905524. | + | 746927.i | 0.690248 | + | 0.569355i | ||||
\(281\) | 729540. | 0.551167 | 0.275584 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275584 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 595214. | + | 1.03094e6i | 0.441781 | + | 0.765188i | 0.997822 | − | 0.0659675i | \(-0.0210134\pi\) |
−0.556040 | + | 0.831155i | \(0.687680\pi\) | |||||||
\(284\) | 19553.5 | + | 33867.7i | 0.0143856 | + | 0.0249167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 42614.1 | 0.0308062 | ||||||||
\(287\) | 393726. | − | 2.34835e6i | 0.282156 | − | 1.68290i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 182938. | − | 316859.i | 0.128843 | − | 0.223162i | ||||
\(290\) | 451820. | + | 782575.i | 0.315479 | + | 0.546425i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 72503.3 | − | 125579.i | 0.0497623 | − | 0.0861909i | ||||
\(293\) | 1.02503e6 | 0.697537 | 0.348769 | − | 0.937209i | \(-0.386600\pi\) | ||||
0.348769 | + | 0.937209i | \(0.386600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −210311. | −0.140704 | ||||||||
\(296\) | −389903. | + | 675332.i | −0.258659 | + | 0.448011i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −328975. | − | 569801.i | −0.214596 | − | 0.371692i | ||||
\(299\) | 1.75149e6 | − | 3.03366e6i | 1.13300 | − | 1.96241i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34961.2 | − | 208524.i | 0.0222418 | − | 0.132660i | ||||
\(302\) | −596464. | −0.376328 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 309614. | + | 536267.i | 0.192148 | + | 0.332811i | ||||
\(305\) | 667623. | + | 1.15636e6i | 0.410943 | + | 0.711774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −709845. | −0.429850 | −0.214925 | − | 0.976631i | \(-0.568951\pi\) | ||||
−0.214925 | + | 0.976631i | \(0.568951\pi\) | |||||||
\(308\) | −42601.5 | − | 35140.1i | −0.0255887 | − | 0.0211070i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 248348. | − | 430151.i | 0.146776 | − | 0.254224i | ||||
\(311\) | 783816. | + | 1.35761e6i | 0.459529 | + | 0.795928i | 0.998936 | − | 0.0461175i | \(-0.0146849\pi\) |
−0.539407 | + | 0.842045i | \(0.681352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −186476. | + | 322986.i | −0.107588 | + | 0.186347i | −0.914792 | − | 0.403924i | \(-0.867646\pi\) |
0.807205 | + | 0.590271i | \(0.200979\pi\) | |||||||
\(314\) | −458684. | −0.262536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.16284e6 | 1.21845 | ||||||||
\(317\) | −1.51408e6 | + | 2.62246e6i | −0.846253 | + | 1.46575i | 0.0382747 | + | 0.999267i | \(0.487814\pi\) |
−0.884528 | + | 0.466487i | \(0.845520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −49079.6 | − | 85008.3i | −0.0270037 | − | 0.0467719i | ||||
\(320\) | 144136. | − | 249650.i | 0.0786858 | − | 0.136288i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.31373e6 | − | 490723.i | 0.706103 | − | 0.263752i | ||||
\(323\) | 1.78573e6 | 0.952380 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −125364. | − | 217137.i | −0.0658363 | − | 0.114032i | ||||
\(326\) | 695526. | + | 1.20469e6i | 0.362468 | + | 0.627813i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.84923e6 | −1.46232 | ||||||||
\(329\) | −960613. | − | 792367.i | −0.489281 | − | 0.403586i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −533448. | + | 923959.i | −0.267622 | + | 0.463535i | −0.968247 | − | 0.249995i | \(-0.919571\pi\) |
0.700625 | + | 0.713529i | \(0.252905\pi\) | |||||||
\(332\) | 1.17133e6 | + | 2.02880e6i | 0.583221 | + | 1.01017i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 777130. | − | 1.34603e6i | 0.381178 | − | 0.660219i | ||||
\(335\) | −2.74401e6 | −1.33590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55734e6 | 0.746981 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(338\) | 578064. | − | 1.00124e6i | 0.275222 | − | 0.476699i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 732470. | + | 1.26868e6i | 0.343631 | + | 0.595187i | ||||
\(341\) | −26977.1 | + | 46725.8i | −0.0125635 | + | 0.0217606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.04145e6 | − | 1.91388e6i | 0.477973 | − | 0.878374i | ||||
\(344\) | −253000. | −0.115272 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 906124. | + | 1.56945e6i | 0.406909 | + | 0.704787i | ||||
\(347\) | −1.11748e6 | − | 1.93553e6i | −0.498214 | − | 0.862932i | 0.501784 | − | 0.864993i | \(-0.332677\pi\) |
−0.999998 | + | 0.00206105i | \(0.999344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.72982e6 | −0.760218 | −0.380109 | − | 0.924942i | \(-0.624114\pi\) | ||||
−0.380109 | + | 0.924942i | \(0.624114\pi\) | |||||||
\(350\) | 16597.7 | − | 98995.8i | 0.00724231 | − | 0.0431963i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −51770.9 | + | 89669.8i | −0.0222705 | + | 0.0385736i | ||||
\(353\) | −1.18287e6 | − | 2.04879e6i | −0.505242 | − | 0.875105i | −0.999982 | − | 0.00606386i | \(-0.998070\pi\) |
0.494739 | − | 0.869041i | \(-0.335264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 46683.1 | − | 80857.6i | 0.0196603 | − | 0.0340526i | ||||
\(356\) | −1.13700e6 | −0.475484 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 454247. | 0.187320 | ||||||||
\(359\) | 25514.3 | − | 44192.1i | 0.0104484 | − | 0.0180971i | −0.860754 | − | 0.509021i | \(-0.830007\pi\) |
0.871202 | + | 0.490924i | \(0.163341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −274712. | − | 475815.i | −0.110945 | − | 0.192163i | ||||
\(362\) | 204041. | − | 353410.i | 0.0818364 | − | 0.141745i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.64226e6 | + | 986968.i | −1.04525 | + | 0.390436i | ||||
\(365\) | −346197. | −0.136016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.88411e6 | − | 3.26338e6i | −0.730200 | − | 1.26474i | −0.956797 | − | 0.290755i | \(-0.906093\pi\) |
0.226597 | − | 0.973989i | \(-0.427240\pi\) | |||||||
\(368\) | 700648. | + | 1.21356e6i | 0.269699 | + | 0.467133i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 806328. | 0.306201 | ||||||||
\(371\) | 2.82441e6 | − | 1.05501e6i | 1.06535 | − | 0.397943i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.31720e6 | + | 4.01351e6i | −0.862366 | + | 1.49366i | 0.00727258 | + | 0.999974i | \(0.497685\pi\) |
−0.869639 | + | 0.493689i | \(0.835648\pi\) | |||||||
\(374\) | 24580.0 | + | 42573.8i | 0.00908663 | + | 0.0157385i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −745020. | + | 1.29041e6i | −0.271768 | + | 0.470716i | ||||
\(377\) | −5.01346e6 | −1.81670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.17169e6 | −1.49181 | −0.745905 | − | 0.666052i | \(-0.767983\pi\) | ||||
−0.745905 | + | 0.666052i | \(0.767983\pi\) | |||||||
\(380\) | 1.24101e6 | − | 2.14949e6i | 0.440875 | − | 0.763617i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −530276. | − | 918465.i | −0.185928 | − | 0.322036i | ||||
\(383\) | −2.08586e6 | + | 3.61281e6i | −0.726588 | + | 1.25849i | 0.231730 | + | 0.972780i | \(0.425562\pi\) |
−0.958317 | + | 0.285706i | \(0.907772\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21800.9 | + | 130030.i | −0.00749590 | + | 0.0447088i | ||||
\(386\) | −1.36391e6 | −0.465927 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −928783. | − | 1.60870e6i | −0.313209 | − | 0.542495i | ||||
\(389\) | 1.37697e6 | + | 2.38498e6i | 0.461371 | + | 0.799119i | 0.999030 | − | 0.0440442i | \(-0.0140242\pi\) |
−0.537658 | + | 0.843163i | \(0.680691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04106e6 | 1.33676 | ||||||||
\(392\) | −2.46466e6 | − | 850357.i | −0.810108 | − | 0.279503i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −606578. | + | 1.05062e6i | −0.196855 | + | 0.340962i | ||||
\(395\) | −2.58184e6 | − | 4.47189e6i | −0.832602 | − | 1.44211i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.26602e6 | − | 2.19281e6i | 0.403148 | − | 0.698274i | −0.590956 | − | 0.806704i | \(-0.701249\pi\) |
0.994104 | + | 0.108430i | \(0.0345825\pi\) | |||||||
\(398\) | 208419. | 0.0659522 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 100299. | 0.0313434 | ||||||||
\(401\) | −1.07873e6 | + | 1.86842e6i | −0.335007 | + | 0.580249i | −0.983486 | − | 0.180983i | \(-0.942072\pi\) |
0.648479 | + | 0.761232i | \(0.275405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.37785e6 | + | 2.38651e6i | 0.422611 | + | 0.731983i | ||||
\(404\) | 564217. | − | 977252.i | 0.171986 | − | 0.297888i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.54834e6 | − | 1.27716e6i | −0.466177 | − | 0.384529i | ||||
\(407\) | −87588.5 | −0.0262096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.16402e6 | + | 3.74819e6i | 0.639665 | + | 1.10793i | 0.985506 | + | 0.169640i | \(0.0542604\pi\) |
−0.345841 | + | 0.938293i | \(0.612406\pi\) | |||||||
\(410\) | 1.47307e6 | + | 2.55143e6i | 0.432776 | + | 0.749590i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00405e6 | 0.581655 | ||||||||
\(413\) | 437599. | − | 163457.i | 0.126241 | − | 0.0471552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.79649e6 | − | 4.84366e6i | 0.797064 | − | 1.38056i | ||||
\(416\) | 2.64419e6 | + | 4.57987e6i | 0.749134 | + | 1.29754i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 41645.3 | − | 72131.8i | 0.0116580 | − | 0.0201923i | ||||
\(419\) | 1.51129e6 | 0.420544 | 0.210272 | − | 0.977643i | \(-0.432565\pi\) | ||||
0.210272 | + | 0.977643i | \(0.432565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.11586e6 | 0.306835 | 0.153418 | − | 0.988161i | \(-0.450972\pi\) | ||||
0.153418 | + | 0.988161i | \(0.450972\pi\) | |||||||
\(422\) | 1.07001e6 | − | 1.85331e6i | 0.292487 | − | 0.506603i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.80387e6 | − | 3.12439e6i | −0.487293 | − | 0.844016i | ||||
\(425\) | 144621. | − | 250492.i | 0.0388383 | − | 0.0672699i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.28787e6 | − | 1.88717e6i | −0.607243 | − | 0.500888i | ||||
\(428\) | −69765.2 | −0.0184090 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 130802. | + | 226556.i | 0.0341149 | + | 0.0590887i | ||||
\(431\) | 3.10672e6 | + | 5.38100e6i | 0.805581 | + | 1.39531i | 0.915898 | + | 0.401411i | \(0.131480\pi\) |
−0.110317 | + | 0.993896i | \(0.535187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.24118e6 | 0.830775 | 0.415388 | − | 0.909644i | \(-0.363646\pi\) | ||||
0.415388 | + | 0.909644i | \(0.363646\pi\) | |||||||
\(434\) | −182422. | + | 1.08804e6i | −0.0464892 | + | 0.277282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.03255e6 | + | 3.52047e6i | −0.512064 | + | 0.886920i | ||||
\(437\) | −3.42334e6 | − | 5.92939e6i | −0.857524 | − | 1.48527i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.15248e6 | + | 1.99616e6i | −0.285413 | + | 0.494349i | −0.972709 | − | 0.232028i | \(-0.925464\pi\) |
0.687297 | + | 0.726377i | \(0.258797\pi\) | |||||||
\(440\) | 157765. | 0.0388488 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.51084e6 | 0.611313 | ||||||||
\(443\) | 766328. | − | 1.32732e6i | 0.185526 | − | 0.321341i | −0.758228 | − | 0.651990i | \(-0.773934\pi\) |
0.943754 | + | 0.330649i | \(0.107268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.35727e6 | + | 2.35086e6i | 0.324912 | + | 0.562764i | ||||
\(446\) | 1.01420e6 | − | 1.75664e6i | 0.241426 | − | 0.418162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −105874. | + | 631476.i | −0.0249226 | + | 0.148649i | ||||
\(449\) | 3.55718e6 | 0.832702 | 0.416351 | − | 0.909204i | \(-0.363309\pi\) | ||||
0.416351 | + | 0.909204i | \(0.363309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −160014. | − | 277153.i | −0.0370439 | − | 0.0641620i | ||||
\(452\) | −3.18189e6 | − | 5.51119e6i | −0.732553 | − | 1.26882i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.49533e6 | −0.340484 | ||||||||
\(455\) | 5.19478e6 | + | 4.28494e6i | 1.17636 | + | 0.970324i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.25941e6 | + | 2.18137e6i | −0.282083 | + | 0.488583i | −0.971898 | − | 0.235403i | \(-0.924359\pi\) |
0.689814 | + | 0.723986i | \(0.257692\pi\) | |||||||
\(458\) | −320936. | − | 555877.i | −0.0714915 | − | 0.123827i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.80836e6 | − | 4.86423e6i | 0.618812 | − | 1.07181i | ||||
\(461\) | 6.63271e6 | 1.45358 | 0.726789 | − | 0.686861i | \(-0.241012\pi\) | ||||
0.726789 | + | 0.686861i | \(0.241012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.40432e6 | −0.954830 | −0.477415 | − | 0.878678i | \(-0.658426\pi\) | ||||
−0.477415 | + | 0.878678i | \(0.658426\pi\) | |||||||
\(464\) | 1.00277e6 | − | 1.73685e6i | 0.216225 | − | 0.374512i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 849325. | + | 1.47107e6i | 0.181180 | + | 0.313812i | ||||
\(467\) | 122922. | − | 212908.i | 0.0260819 | − | 0.0451751i | −0.852690 | − | 0.522417i | \(-0.825030\pi\) |
0.878772 | + | 0.477242i | \(0.158364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.70951e6 | − | 2.13269e6i | 1.19858 | − | 0.447708i | ||||
\(470\) | 1.54072e6 | 0.321720 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −279482. | − | 484076.i | −0.0577428 | − | 0.100014i | ||||
\(473\) | −14208.6 | − | 24610.0i | −0.00292010 | − | 0.00505776i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −490057. | −0.0996581 | ||||||||
\(476\) | −2.51010e6 | − | 2.07047e6i | −0.507778 | − | 0.418843i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.28821e6 | + | 2.23125e6i | −0.257880 | + | 0.446661i | ||||
\(479\) | −20175.6 | − | 34945.1i | −0.00401779 | − | 0.00695901i | 0.864010 | − | 0.503475i | \(-0.167946\pi\) |
−0.868027 | + | 0.496516i | \(0.834612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.23678e6 | + | 3.87422e6i | −0.440820 | + | 0.763523i | ||||
\(482\) | −2.56140e6 | −0.502181 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.92987e6 | 0.762544 | ||||||||
\(485\) | −2.21743e6 | + | 3.84069e6i | −0.428050 | + | 0.741405i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.65484e6 | + | 2.86627e6i | 0.316180 | + | 0.547639i | 0.979688 | − | 0.200530i | \(-0.0642664\pi\) |
−0.663508 | + | 0.748169i | \(0.730933\pi\) | |||||||
\(488\) | −1.77440e6 | + | 3.07335e6i | −0.337289 | + | 0.584202i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 512768. | + | 2.64669e6i | 0.0964785 | + | 0.497982i | ||||
\(491\) | 1.97959e6 | 0.370570 | 0.185285 | − | 0.982685i | \(-0.440679\pi\) | ||||
0.185285 | + | 0.982685i | \(0.440679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.89179e6 | − | 5.00872e6i | −0.535857 | − | 0.928132i | ||||
\(494\) | −2.12703e6 | − | 3.68412e6i | −0.392153 | − | 0.679229i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.10237e6 | −0.201197 | ||||||||
\(497\) | −34290.7 | + | 204525.i | −0.00622709 | + | 0.0371411i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.58498e6 | − | 2.74526e6i | 0.284952 | − | 0.493551i | −0.687646 | − | 0.726046i | \(-0.741356\pi\) |
0.972597 | + | 0.232495i | \(0.0746891\pi\) | |||||||
\(500\) | 2.02857e6 | + | 3.51359e6i | 0.362882 | + | 0.628530i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −295396. | + | 511640.i | −0.0523172 | + | 0.0906161i | ||||
\(503\) | 4.01273e6 | 0.707164 | 0.353582 | − | 0.935403i | \(-0.384963\pi\) | ||||
0.353582 | + | 0.935403i | \(0.384963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.69408e6 | −0.470092 | ||||||||
\(506\) | 94242.1 | − | 163232.i | 0.0163632 | − | 0.0283419i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.85721e6 | − | 4.94884e6i | −0.491228 | − | 0.850832i | ||||
\(509\) | 2.05629e6 | − | 3.56159e6i | 0.351795 | − | 0.609326i | −0.634769 | − | 0.772702i | \(-0.718905\pi\) |
0.986564 | + | 0.163375i | \(0.0522382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 720338. | − | 269070.i | 0.122035 | − | 0.0455840i | ||||
\(512\) | −3.88273e6 | −0.654580 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −108810. | − | 188465.i | −0.0181661 | − | 0.0314646i | ||||
\(515\) | −2.39229e6 | − | 4.14356e6i | −0.397462 | − | 0.688424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −167363. | −0.0275380 | ||||||||
\(518\) | −1.67774e6 | + | 626691.i | −0.274727 | + | 0.102619i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.02890e6 | − | 6.97827e6i | 0.653399 | − | 1.13172i | ||||
\(521\) | 4.27758e6 | + | 7.40898e6i | 0.690404 | + | 1.19582i | 0.971705 | + | 0.236196i | \(0.0759007\pi\) |
−0.281301 | + | 0.959620i | \(0.590766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 896820. | − | 1.55334e6i | 0.143368 | − | 0.248320i | −0.785395 | − | 0.618995i | \(-0.787540\pi\) |
0.928763 | + | 0.370675i | \(0.120874\pi\) | |||||||
\(524\) | −3.84534e6 | −0.611796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.18949e6 | −0.187455 | ||||||||
\(527\) | −1.58950e6 | + | 2.75310e6i | −0.249307 | + | 0.431813i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.52875e6 | − | 7.84402e6i | −0.703621 | − | 1.21871i | ||||
\(530\) | −1.86522e6 | + | 3.23065e6i | −0.288430 | + | 0.499575i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −911571. | + | 5.43701e6i | −0.139640 | + | 0.832877i | ||||
\(533\) | −1.63454e7 | −2.49217 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 83280.6 | + | 144246.i | 0.0125794 | + | 0.0217881i | ||||
\(536\) | −3.64650e6 | − | 6.31592e6i | −0.548231 | − | 0.949565i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12894.1 | −0.00192059 | ||||||||
\(539\) | −55700.1 | − | 287501.i | −0.00825818 | − | 0.0426253i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 178780. | − | 309657.i | 0.0262619 | − | 0.0454870i | −0.852596 | − | 0.522571i | \(-0.824973\pi\) |
0.878858 | + | 0.477084i | \(0.158306\pi\) | |||||||
\(542\) | 144643. | + | 250528.i | 0.0211494 | + | 0.0366318i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.05036e6 | + | 5.28338e6i | −0.441931 | + | 0.765447i | ||||
\(545\) | 9.70522e6 | 1.39963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.79404e6 | −0.542167 | −0.271084 | − | 0.962556i | \(-0.587382\pi\) | ||||
−0.271084 | + | 0.962556i | \(0.587382\pi\) | |||||||
\(548\) | 2.09695e6 | − | 3.63203e6i | 0.298289 | − | 0.516652i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6745.47 | − | 11683.5i | −0.000950835 | − | 0.00164689i | ||||
\(551\) | −4.89949e6 | + | 8.48616e6i | −0.687498 | + | 1.19078i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.84771e6 | + | 7.29809e6i | 1.23032 | + | 1.01484i | ||||
\(554\) | 2.09718e6 | 0.290310 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.57463e6 | + | 4.45939e6i | 0.353206 | + | 0.611771i | ||||
\(557\) | −2.44799e6 | − | 4.24005e6i | −0.334328 | − | 0.579072i | 0.649028 | − | 0.760765i | \(-0.275176\pi\) |
−0.983355 | + | 0.181692i | \(0.941843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.45140e6 | −0.196453 | ||||||||
\(560\) | −2.52350e6 | + | 942607.i | −0.340042 | + | 0.127017i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.00245e6 | − | 1.73630e6i | 0.133882 | − | 0.231891i | ||||
\(563\) | −2.16583e6 | − | 3.75133e6i | −0.287974 | − | 0.498786i | 0.685352 | − | 0.728212i | \(-0.259648\pi\) |
−0.973326 | + | 0.229426i | \(0.926315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.59661e6 | + | 1.31577e7i | −1.00115 | + | 1.73404i | ||||
\(566\) | 3.27151e6 | 0.429248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 248148. | 0.0322730 | ||||||||
\(569\) | −1.09848e6 | + | 1.90262e6i | −0.142236 | + | 0.246361i | −0.928338 | − | 0.371736i | \(-0.878763\pi\) |
0.786102 | + | 0.618097i | \(0.212096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.73846e6 | + | 6.47520e6i | 0.479846 | + | 0.831118i | 0.999733 | − | 0.0231172i | \(-0.00735908\pi\) |
−0.519886 | + | 0.854235i | \(0.674026\pi\) | |||||||
\(572\) | −189545. | + | 328301.i | −0.0242227 | + | 0.0419549i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.04805e6 | − | 4.16391e6i | −0.639505 | − | 0.527500i | ||||
\(575\) | −1.10899e6 | −0.139880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 683110. | + | 1.18318e6i | 0.0854183 | + | 0.147949i | 0.905569 | − | 0.424198i | \(-0.139444\pi\) |
−0.820151 | + | 0.572147i | \(0.806111\pi\) | |||||||
\(578\) | −502748. | − | 870785.i | −0.0625937 | − | 0.108415i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.03867e6 | −0.992234 | ||||||||
\(581\) | −2.05414e6 | + | 1.22518e7i | −0.252458 | + | 1.50577i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 202612. | − | 350934.i | 0.0246884 | − | 0.0427616i | ||||
\(584\) | −460059. | − | 796845.i | −0.0558189 | − | 0.0966812i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.40848e6 | − | 2.43956e6i | 0.169437 | − | 0.293473i | ||||
\(587\) | 9.27217e6 | 1.11067 | 0.555336 | − | 0.831626i | \(-0.312590\pi\) | ||||
0.555336 | + | 0.831626i | \(0.312590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.38612e6 | 0.639717 | ||||||||
\(590\) | −288987. | + | 500540.i | −0.0341781 | + | 0.0591982i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −894782. | − | 1.54981e6i | −0.104933 | − | 0.181750i | ||||
\(593\) | 4.60523e6 | − | 7.97649e6i | 0.537792 | − | 0.931483i | −0.461231 | − | 0.887280i | \(-0.652592\pi\) |
0.999023 | − | 0.0442028i | \(-0.0140748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.28452e6 | + | 7.66145e6i | −0.148747 | + | 0.887194i | ||||
\(596\) | 5.85305e6 | 0.674942 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.81340e6 | − | 8.33706e6i | −0.550426 | − | 0.953367i | ||||
\(599\) | −6.84581e6 | − | 1.18573e7i | −0.779575 | − | 1.35026i | −0.932187 | − | 0.361977i | \(-0.882102\pi\) |
0.152612 | − | 0.988286i | \(-0.451231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.61113e6 | 0.181946 | 0.0909732 | − | 0.995853i | \(-0.471002\pi\) | ||||
0.0909732 | + | 0.995853i | \(0.471002\pi\) | |||||||
\(602\) | −448246. | − | 369738.i | −0.0504110 | − | 0.0415818i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.65304e6 | − | 4.59519e6i | 0.295904 | − | 0.512521i | ||||
\(605\) | −4.69119e6 | − | 8.12539e6i | −0.521069 | − | 0.902517i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.03281e6 | − | 1.21812e7i | 0.774742 | − | 1.34189i | −0.160198 | − | 0.987085i | \(-0.551213\pi\) |
0.934940 | − | 0.354807i | \(-0.115453\pi\) | |||||||
\(608\) | 1.03363e7 | 1.13398 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.66950e6 | 0.399284 | ||||||||
\(611\) | −4.27401e6 | + | 7.40280e6i | −0.463161 | + | 0.802219i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.79842e6 | − | 1.17752e7i | −0.730729 | − | 1.26566i | −0.956572 | − | 0.291497i | \(-0.905847\pi\) |
0.225842 | − | 0.974164i | \(-0.427487\pi\) | |||||||
\(614\) | −975391. | + | 1.68943e6i | −0.104414 | + | 0.180850i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −328264. | + | 122617.i | −0.0348555 | + | 0.0130197i | ||||
\(617\) | 5.74287e6 | 0.607318 | 0.303659 | − | 0.952781i | \(-0.401792\pi\) | ||||
0.303659 | + | 0.952781i | \(0.401792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.01299e6 | + | 5.21865e6i | 0.316061 | + | 0.547434i | 0.979662 | − | 0.200653i | \(-0.0643063\pi\) |
−0.663602 | + | 0.748086i | \(0.730973\pi\) | |||||||
\(620\) | 2.20927e6 | + | 3.82657e6i | 0.230818 | + | 0.399789i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.30814e6 | 0.446492 | ||||||||
\(623\) | −4.65122e6 | − | 3.83658e6i | −0.480117 | − | 0.396027i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.28334e6 | − | 9.15101e6i | 0.541014 | − | 0.937064i | ||||
\(626\) | 512470. | + | 887625.i | 0.0522676 | + | 0.0905302i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.04020e6 | − | 3.53373e6i | 0.206430 | − | 0.357547i | ||||
\(629\) | −5.16075e6 | −0.520099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.90670e6 | −0.690554 | −0.345277 | − | 0.938501i | \(-0.612215\pi\) | ||||
−0.345277 | + | 0.938501i | \(0.612215\pi\) | |||||||
\(632\) | 6.86200e6 | − | 1.18853e7i | 0.683373 | − | 1.18364i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.16096e6 | + | 7.20700e6i | 0.411122 | + | 0.712084i | ||||
\(635\) | −6.82146e6 | + | 1.18151e7i | −0.671341 | + | 1.16280i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.41392e7 | − | 4.87830e6i | −1.38063 | − | 0.476343i | ||||
\(638\) | −269759. | −0.0262376 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.15340e6 | + | 8.92595e6i | 0.497329 | + | 0.861400i | ||||
\(641\) | 8.24828e6 | + | 1.42864e7i | 0.792900 | + | 1.37334i | 0.924164 | + | 0.381995i | \(0.124763\pi\) |
−0.131265 | + | 0.991347i | \(0.541904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.70171e7 | 1.62315 | 0.811576 | − | 0.584247i | \(-0.198610\pi\) | ||||
0.811576 | + | 0.584247i | \(0.198610\pi\) | |||||||
\(644\) | −2.06286e6 | + | 1.23038e7i | −0.195999 | + | 1.16903i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.45376e6 | − | 4.25003e6i | 0.231340 | − | 0.400692i | ||||
\(647\) | 1.74287e6 | + | 3.01873e6i | 0.163683 | + | 0.283507i | 0.936187 | − | 0.351503i | \(-0.114329\pi\) |
−0.772504 | + | 0.635010i | \(0.780996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31391.6 | − | 54371.8i | 0.00292551 | − | 0.00506713i | ||||
\(650\) | −689047. | −0.0639684 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.23746e7 | −1.14002 | ||||||||
\(653\) | 7.72245e6 | − | 1.33757e7i | 0.708716 | − | 1.22753i | −0.256618 | − | 0.966513i | \(-0.582608\pi\) |
0.965334 | − | 0.261019i | \(-0.0840586\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.59029e6 | + | 7.95061e6i | 0.418058 | + | 0.724098i | ||||
\(656\) | 3.26933e6 | − | 5.66264e6i | 0.296619 | − | 0.513759i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.20580e6 | + | 1.19747e6i | −0.288650 | + | 0.107820i | ||||
\(659\) | 3.11193e6 | 0.279136 | 0.139568 | − | 0.990212i | \(-0.455429\pi\) | ||||
0.139568 | + | 0.990212i | \(0.455429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.08610e6 | − | 7.07733e6i | −0.363752 | − | 0.630037i | 0.624823 | − | 0.780766i | \(-0.285171\pi\) |
−0.988575 | + | 0.150729i | \(0.951838\pi\) | |||||||
\(662\) | 1.46601e6 | + | 2.53921e6i | 0.130015 | + | 0.225192i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.48650e7 | 1.30841 | ||||||||
\(665\) | 1.23297e7 | − | 4.60554e6i | 1.08118 | − | 0.403856i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.10874e7 | + | 1.92039e7i | −0.964973 | + | 1.67138i | ||||
\(668\) | 6.91326e6 | + | 1.19741e7i | 0.599434 | + | 1.03825i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.77051e6 | + | 6.53072e6i | −0.324499 | + | 0.562049i | ||||
\(671\) | −398604. | −0.0341771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60182e7 | 1.36325 | 0.681627 | − | 0.731700i | \(-0.261273\pi\) | ||||
0.681627 | + | 0.731700i | \(0.261273\pi\) | |||||||
\(674\) | 2.13993e6 | − | 3.70647e6i | 0.181447 | − | 0.314276i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.14239e6 | + | 8.90687e6i | 0.432811 | + | 0.749650i | ||||
\(677\) | 512185. | − | 887131.i | 0.0429492 | − | 0.0743902i | −0.843752 | − | 0.536734i | \(-0.819658\pi\) |
0.886701 | + | 0.462344i | \(0.152991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.62879e6 | − | 9.71483e6i | 0.135579 | − | 0.808650i | ||||
\(680\) | 9.29556e6 | 0.770910 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 74138.1 | + | 128411.i | 0.00610352 | + | 0.0105716i | ||||
\(683\) | −2.69688e6 | − | 4.67114e6i | −0.221213 | − | 0.383152i | 0.733964 | − | 0.679189i | \(-0.237668\pi\) |
−0.955177 | + | 0.296037i | \(0.904335\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00128e7 | −0.815319 | ||||||||
\(686\) | −3.12398e6 | − | 5.10850e6i | −0.253453 | − | 0.414460i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 290302. | − | 502819.i | 0.0233819 | − | 0.0404986i | ||||
\(689\) | −1.03484e7 | − | 1.79239e7i | −0.830470 | − | 1.43842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 452826. | − | 784318.i | 0.0360775 | − | 0.0624881i | −0.847423 | − | 0.530919i | \(-0.821847\pi\) |
0.883500 | + | 0.468430i | \(0.155180\pi\) | |||||||
\(692\) | −1.61215e7 | −1.27980 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.14207e6 | −0.484079 | ||||||||
\(695\) | 6.14682e6 | − | 1.06466e7i | 0.482712 | − | 0.836082i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.42810e6 | − | 1.63300e7i | −0.735093 | − | 1.27322i | ||||
\(698\) | −2.37693e6 | + | 4.11697e6i | −0.184662 | + | 0.319845i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 688845. | + | 568197.i | 0.0531344 | + | 0.0438282i | ||||
\(701\) | −1.12573e7 | −0.865246 | −0.432623 | − | 0.901575i | \(-0.642412\pi\) | ||||
−0.432623 | + | 0.901575i | \(0.642412\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37187e6 | + | 7.57230e6i | 0.333640 | + | 0.577882i | ||||
\(704\) | 43028.1 | + | 74526.9i | 0.00327205 | + | 0.00566736i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.50147e6 | −0.490908 | ||||||||
\(707\) | 5.60563e6 | − | 2.09388e6i | 0.421770 | − | 0.157545i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.17755e6 | + | 3.77162e6i | −0.162687 | + | 0.281781i | −0.935831 | − | 0.352448i | \(-0.885349\pi\) |
0.773145 | + | 0.634230i | \(0.218683\pi\) | |||||||
\(710\) | −128294. | − | 222211.i | −0.00955123 | − | 0.0165432i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.60733e6 | + | 6.24809e6i | −0.266678 | + | 0.461899i | ||||
\(713\) | 1.21886e7 | 0.897907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 905060. | 0.0662082 | ||||||||
\(716\) | −2.02046e6 | + | 3.49955e6i | −0.147288 | + | 0.255111i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −70118.0 | − | 121448.i | −0.00507597 | − | 0.00879183i | ||||
\(719\) | −7.07221e6 | + | 1.22494e7i | −0.510191 | + | 0.883676i | 0.489739 | + | 0.871869i | \(0.337092\pi\) |
−0.999930 | + | 0.0118076i | \(0.996241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.19812e6 | + | 6.76227e6i | 0.587322 | + | 0.484456i | ||||
\(722\) | −1.50992e6 | −0.107798 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.81513e6 | + | 3.14389e6i | 0.128695 | + | 0.222906i | ||||
\(725\) | 793591. | + | 1.37454e6i | 0.0560727 | + | 0.0971208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.26406e6 | −0.439561 | −0.219781 | − | 0.975549i | \(-0.570534\pi\) | ||||
−0.219781 | + | 0.975549i | \(0.570534\pi\) | |||||||
\(728\) | −2.95940e6 | + | 1.76511e7i | −0.206954 | + | 1.23437i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −475705. | + | 823946.i | −0.0330393 | + | 0.0572258i | ||||
\(731\) | −837176. | − | 1.45003e6i | −0.0579460 | − | 0.100365i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.02089e7 | − | 1.76823e7i | 0.701806 | − | 1.21556i | −0.266025 | − | 0.963966i | \(-0.585710\pi\) |
0.967832 | − | 0.251598i | \(-0.0809562\pi\) | |||||||
\(734\) | −1.03558e7 | −0.709484 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.33908e7 | 1.59166 | ||||||||
\(737\) | 409577. | − | 709409.i | 0.0277758 | − | 0.0481092i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.42256e6 | − | 1.28563e7i | −0.499969 | − | 0.865971i | 0.500031 | − | 0.866007i | \(-0.333322\pi\) |
−1.00000 | 3.61537e-5i | \(0.999988\pi\) | ||||||||
\(740\) | −3.58650e6 | + | 6.21200e6i | −0.240764 | + | 0.417015i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.37008e6 | − | 8.17176e6i | 0.0913558 | − | 0.544886i | ||||
\(743\) | −2.36601e7 | −1.57234 | −0.786168 | − | 0.618013i | \(-0.787938\pi\) | ||||
−0.786168 | + | 0.618013i | \(0.787938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.98694e6 | − | 1.21017e7i | −0.461207 | − | 0.798834i | ||||
\(746\) | 6.36809e6 | + | 1.10299e7i | 0.418950 | + | 0.725643i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −437322. | −0.0285790 | ||||||||
\(749\) | −285394. | − | 235409.i | −0.0185883 | − | 0.0153327i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.03287e7 | + | 1.78898e7i | −0.668258 | + | 1.15746i | 0.310133 | + | 0.950693i | \(0.399627\pi\) |
−0.978391 | + | 0.206764i | \(0.933707\pi\) | |||||||
\(752\) | −1.70973e6 | − | 2.96134e6i | −0.110251 | − | 0.190961i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.88895e6 | + | 1.19320e7i | −0.441291 | + | 0.764338i | ||||
\(755\) | −1.26680e7 | −0.808799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.26697e7 | −0.803573 | −0.401787 | − | 0.915733i | \(-0.631611\pi\) | ||||
−0.401787 | + | 0.915733i | \(0.631611\pi\) | |||||||
\(758\) | −5.73228e6 | + | 9.92860e6i | −0.362372 | + | 0.627646i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.87462e6 | − | 1.36392e7i | −0.494534 | − | 0.856557i | ||||
\(761\) | 8.13761e6 | − | 1.40948e7i | 0.509372 | − | 0.882259i | −0.490569 | − | 0.871402i | \(-0.663211\pi\) |
0.999941 | − | 0.0108563i | \(-0.00345572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.01938e7 | + | 7.54305e6i | −1.25576 | + | 0.469068i | ||||
\(764\) | 9.43455e6 | 0.584774 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.73232e6 | + | 9.92867e6i | 0.352987 | + | 0.611391i | ||||
\(767\) | −1.60332e6 | − | 2.77703e6i | −0.0984084 | − | 0.170448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.60471e7 | 0.978547 | 0.489273 | − | 0.872130i | \(-0.337262\pi\) | ||||
0.489273 | + | 0.872130i | \(0.337262\pi\) | |||||||
\(770\) | 279515. | + | 230560.i | 0.0169894 | + | 0.0140138i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.06659e6 | − | 1.05076e7i | 0.366355 | − | 0.634545i | ||||
\(773\) | 1.07839e6 | + | 1.86782e6i | 0.0649121 | + | 0.112431i | 0.896655 | − | 0.442730i | \(-0.145990\pi\) |
−0.831743 | + | 0.555161i | \(0.812657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 436206. | − | 755531.i | 0.0260878 | − | 0.0451854i | ||||