Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("294.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.e (of order \(3\), degree \(2\), not 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: | \(47.1528430250\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.67 |
Dual form | 294.6.e.x.79.2 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 3.46410i | 0.353553 | + | 0.612372i | ||||
\(3\) | −4.50000 | + | 7.79423i | −0.288675 | + | 0.500000i | ||||
\(4\) | −8.00000 | + | 13.8564i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.25126 | − | 3.89930i | −0.0402718 | − | 0.0697528i | 0.845187 | − | 0.534471i | \(-0.179489\pi\) |
−0.885459 | + | 0.464718i | \(0.846156\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 9.00505 | − | 15.5972i | 0.0284765 | − | 0.0493227i | ||||
\(11\) | 58.0955 | − | 100.624i | 0.144764 | − | 0.250739i | −0.784521 | − | 0.620102i | \(-0.787091\pi\) |
0.929285 | + | 0.369364i | \(0.120424\pi\) | |||||||
\(12\) | −72.0000 | − | 124.708i | −0.144338 | − | 0.250000i | ||||
\(13\) | −85.4773 | −0.140279 | −0.0701394 | − | 0.997537i | \(-0.522344\pi\) | ||||
−0.0701394 | + | 0.997537i | \(0.522344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.5227 | 0.0465019 | ||||||||
\(16\) | −128.000 | − | 221.703i | −0.125000 | − | 0.216506i | ||||
\(17\) | −16.6331 | + | 28.8093i | −0.0139589 | + | 0.0241775i | −0.872920 | − | 0.487863i | \(-0.837777\pi\) |
0.858962 | + | 0.512040i | \(0.171110\pi\) | |||||||
\(18\) | 162.000 | − | 280.592i | 0.117851 | − | 0.204124i | ||||
\(19\) | −317.688 | − | 550.252i | −0.201891 | − | 0.349686i | 0.747247 | − | 0.664547i | \(-0.231375\pi\) |
−0.949138 | + | 0.314861i | \(0.898042\pi\) | |||||||
\(20\) | 72.0404 | 0.0402718 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 464.764 | 0.204727 | ||||||||
\(23\) | −1363.71 | − | 2362.02i | −0.537531 | − | 0.931031i | −0.999036 | − | 0.0438936i | \(-0.986024\pi\) |
0.461505 | − | 0.887138i | \(-0.347310\pi\) | |||||||
\(24\) | 288.000 | − | 498.831i | 0.102062 | − | 0.176777i | ||||
\(25\) | 1552.36 | − | 2688.77i | 0.496756 | − | 0.860407i | ||||
\(26\) | −170.955 | − | 296.102i | −0.0495961 | − | 0.0859029i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5860.48 | 1.29401 | 0.647006 | − | 0.762485i | \(-0.276021\pi\) | ||||
0.647006 | + | 0.762485i | \(0.276021\pi\) | |||||||
\(30\) | 81.0455 | + | 140.375i | 0.0164409 | + | 0.0284765i | ||||
\(31\) | −139.568 | + | 241.739i | −0.0260845 | + | 0.0451796i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) |
0.852688 | + | 0.522420i | \(0.174971\pi\) | |||||||
\(32\) | 512.000 | − | 886.810i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 522.859 | + | 905.619i | 0.0835795 | + | 0.144764i | ||||
\(34\) | −133.065 | −0.0197408 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −1519.25 | − | 2631.41i | −0.182442 | − | 0.315998i | 0.760270 | − | 0.649607i | \(-0.225067\pi\) |
−0.942711 | + | 0.333609i | \(0.891733\pi\) | |||||||
\(38\) | 1270.75 | − | 2201.01i | 0.142759 | − | 0.247265i | ||||
\(39\) | 384.648 | − | 666.229i | 0.0404950 | − | 0.0701394i | ||||
\(40\) | 144.081 | + | 249.555i | 0.0142382 | + | 0.0246613i | ||||
\(41\) | 819.415 | 0.0761279 | 0.0380640 | − | 0.999275i | \(-0.487881\pi\) | ||||
0.0380640 | + | 0.999275i | \(0.487881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11100.2 | 0.915504 | 0.457752 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457752 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(44\) | 929.527 | + | 1609.99i | 0.0723820 | + | 0.125369i | ||||
\(45\) | −182.352 | + | 315.843i | −0.0134239 | + | 0.0232509i | ||||
\(46\) | 5454.85 | − | 9448.09i | 0.380092 | − | 0.658338i | ||||
\(47\) | 3703.70 | + | 6415.00i | 0.244563 | + | 0.423596i | 0.962009 | − | 0.273019i | \(-0.0880221\pi\) |
−0.717446 | + | 0.696615i | \(0.754689\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12418.9 | 0.702520 | ||||||||
\(51\) | −149.698 | − | 259.284i | −0.00805916 | − | 0.0139589i | ||||
\(52\) | 683.818 | − | 1184.41i | 0.0350697 | − | 0.0607425i | ||||
\(53\) | 6849.40 | − | 11863.5i | 0.334937 | − | 0.580128i | −0.648536 | − | 0.761184i | \(-0.724618\pi\) |
0.983473 | + | 0.181057i | \(0.0579517\pi\) | |||||||
\(54\) | 1458.00 | + | 2525.33i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −523.153 | −0.0233196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5718.39 | 0.233124 | ||||||||
\(58\) | 11721.0 | + | 20301.3i | 0.457502 | + | 0.792417i | ||||
\(59\) | −11187.8 | + | 19377.9i | −0.418424 | + | 0.724732i | −0.995781 | − | 0.0917601i | \(-0.970751\pi\) |
0.577357 | + | 0.816492i | \(0.304084\pi\) | |||||||
\(60\) | −324.182 | + | 561.499i | −0.0116255 | + | 0.0201359i | ||||
\(61\) | 6346.04 | + | 10991.7i | 0.218363 | + | 0.378215i | 0.954308 | − | 0.298826i | \(-0.0965951\pi\) |
−0.735945 | + | 0.677041i | \(0.763262\pi\) | |||||||
\(62\) | −1116.55 | −0.0368890 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 192.432 | + | 333.302i | 0.00564928 | + | 0.00978485i | ||||
\(66\) | −2091.44 | + | 3622.47i | −0.0590996 | + | 0.102364i | ||||
\(67\) | 26151.7 | − | 45296.0i | 0.711725 | − | 1.23274i | −0.252484 | − | 0.967601i | \(-0.581247\pi\) |
0.964209 | − | 0.265143i | \(-0.0854193\pi\) | |||||||
\(68\) | −266.129 | − | 460.949i | −0.00697944 | − | 0.0120887i | ||||
\(69\) | 24546.8 | 0.620687 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 60230.2 | 1.41798 | 0.708988 | − | 0.705221i | \(-0.249152\pi\) | ||||
0.708988 | + | 0.705221i | \(0.249152\pi\) | |||||||
\(72\) | 2592.00 | + | 4489.48i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −38479.2 | + | 66647.9i | −0.845121 | + | 1.46379i | 0.0403954 | + | 0.999184i | \(0.487138\pi\) |
−0.885516 | + | 0.464608i | \(0.846195\pi\) | |||||||
\(74\) | 6076.98 | − | 10525.6i | 0.129006 | − | 0.223444i | ||||
\(75\) | 13971.3 | + | 24199.0i | 0.286802 | + | 0.496756i | ||||
\(76\) | 10166.0 | 0.201891 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3077.18 | 0.0572686 | ||||||||
\(79\) | 16798.0 | + | 29095.0i | 0.302824 | + | 0.524506i | 0.976774 | − | 0.214270i | \(-0.0687374\pi\) |
−0.673951 | + | 0.738776i | \(0.735404\pi\) | |||||||
\(80\) | −576.323 | + | 998.221i | −0.0100680 | + | 0.0174382i | ||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1638.83 | + | 2838.54i | 0.0269153 | + | 0.0466187i | ||||
\(83\) | 60574.9 | 0.965157 | 0.482578 | − | 0.875853i | \(-0.339700\pi\) | ||||
0.482578 | + | 0.875853i | \(0.339700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 149.782 | 0.00224860 | ||||||||
\(86\) | 22200.4 | + | 38452.3i | 0.323680 | + | 0.560630i | ||||
\(87\) | −26372.2 | + | 45677.9i | −0.373549 | + | 0.647006i | ||||
\(88\) | −3718.11 | + | 6439.95i | −0.0511818 | + | 0.0886495i | ||||
\(89\) | −46095.1 | − | 79839.0i | −0.616850 | − | 1.06841i | −0.990057 | − | 0.140667i | \(-0.955075\pi\) |
0.373207 | − | 0.927748i | \(-0.378258\pi\) | |||||||
\(90\) | −1458.82 | −0.0189843 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 43638.8 | 0.537531 | ||||||||
\(93\) | −1256.11 | − | 2175.65i | −0.0150599 | − | 0.0260845i | ||||
\(94\) | −14814.8 | + | 25660.0i | −0.172932 | + | 0.299528i | ||||
\(95\) | −1430.40 | + | 2477.53i | −0.0162610 | + | 0.0281650i | ||||
\(96\) | 4608.00 | + | 7981.29i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 152287. | 1.64336 | 0.821680 | − | 0.569949i | \(-0.193037\pi\) | ||||
0.821680 | + | 0.569949i | \(0.193037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9411.46 | −0.0965093 | ||||||||
\(100\) | 24837.8 | + | 43020.4i | 0.248378 | + | 0.430204i | ||||
\(101\) | −53822.1 | + | 93222.6i | −0.524997 | + | 0.909322i | 0.474579 | + | 0.880213i | \(0.342600\pi\) |
−0.999576 | + | 0.0291091i | \(0.990733\pi\) | |||||||
\(102\) | 598.791 | − | 1037.14i | 0.00569869 | − | 0.00987041i | ||||
\(103\) | −60319.6 | − | 104477.i | −0.560229 | − | 0.970345i | −0.997476 | − | 0.0710033i | \(-0.977380\pi\) |
0.437247 | − | 0.899341i | \(-0.355953\pi\) | |||||||
\(104\) | 5470.55 | 0.0495961 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 54795.2 | 0.473672 | ||||||||
\(107\) | −43057.2 | − | 74577.2i | −0.363568 | − | 0.629719i | 0.624977 | − | 0.780643i | \(-0.285108\pi\) |
−0.988545 | + | 0.150924i | \(0.951775\pi\) | |||||||
\(108\) | −5832.00 | + | 10101.3i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 33069.6 | − | 57278.2i | 0.266602 | − | 0.461767i | −0.701380 | − | 0.712787i | \(-0.747433\pi\) |
0.967982 | + | 0.251020i | \(0.0807659\pi\) | |||||||
\(110\) | −1046.31 | − | 1812.25i | −0.00824473 | − | 0.0142803i | ||||
\(111\) | 27346.4 | 0.210665 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 131608. | 0.969588 | 0.484794 | − | 0.874628i | \(-0.338895\pi\) | ||||
0.484794 | + | 0.874628i | \(0.338895\pi\) | |||||||
\(114\) | 11436.8 | + | 19809.1i | 0.0824217 | + | 0.142759i | ||||
\(115\) | −6140.16 | + | 10635.1i | −0.0432947 | + | 0.0749886i | ||||
\(116\) | −46883.9 | + | 81205.2i | −0.323503 | + | 0.560324i | ||||
\(117\) | 3461.83 | + | 5996.06i | 0.0233798 | + | 0.0404950i | ||||
\(118\) | −89502.8 | −0.591741 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2593.45 | −0.0164409 | ||||||||
\(121\) | 73775.3 | + | 127783.i | 0.458087 | + | 0.793430i | ||||
\(122\) | −25384.2 | + | 43966.7i | −0.154406 | + | 0.267439i | ||||
\(123\) | −3687.37 | + | 6386.71i | −0.0219762 | + | 0.0380640i | ||||
\(124\) | −2233.09 | − | 3867.83i | −0.0130422 | − | 0.0225898i | ||||
\(125\) | −28049.5 | −0.160565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14437.3 | 0.0794284 | 0.0397142 | − | 0.999211i | \(-0.487355\pi\) | ||||
0.0397142 | + | 0.999211i | \(0.487355\pi\) | |||||||
\(128\) | 8192.00 | + | 14189.0i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −49951.0 | + | 86517.6i | −0.264283 | + | 0.457752i | ||||
\(130\) | −769.727 | + | 1333.21i | −0.00399465 | + | 0.00691893i | ||||
\(131\) | −159608. | − | 276450.i | −0.812600 | − | 1.40747i | −0.911038 | − | 0.412322i | \(-0.864718\pi\) |
0.0984380 | − | 0.995143i | \(-0.468615\pi\) | |||||||
\(132\) | −16731.5 | −0.0835795 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 209213. | 1.00653 | ||||||||
\(135\) | −1641.17 | − | 2842.59i | −0.00775031 | − | 0.0134239i | ||||
\(136\) | 1064.52 | − | 1843.80i | 0.00493521 | − | 0.00854803i | ||||
\(137\) | 25267.0 | − | 43763.7i | 0.115014 | − | 0.199211i | −0.802771 | − | 0.596287i | \(-0.796642\pi\) |
0.917785 | + | 0.397077i | \(0.129975\pi\) | |||||||
\(138\) | 49093.7 | + | 85032.8i | 0.219446 | + | 0.380092i | ||||
\(139\) | 223787. | 0.982422 | 0.491211 | − | 0.871041i | \(-0.336554\pi\) | ||||
0.491211 | + | 0.871041i | \(0.336554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −66666.6 | −0.282397 | ||||||||
\(142\) | 120460. | + | 208644.i | 0.501330 | + | 0.868329i | ||||
\(143\) | −4965.84 | + | 8601.09i | −0.0203073 | + | 0.0351733i | ||||
\(144\) | −10368.0 | + | 17957.9i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −13193.5 | − | 22851.8i | −0.0521122 | − | 0.0902610i | ||||
\(146\) | −307834. | −1.19518 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 48615.9 | 0.182442 | ||||||||
\(149\) | −129761. | − | 224752.i | −0.478825 | − | 0.829350i | 0.520880 | − | 0.853630i | \(-0.325604\pi\) |
−0.999705 | + | 0.0242802i | \(0.992271\pi\) | |||||||
\(150\) | −55885.1 | + | 96795.8i | −0.202800 | + | 0.351260i | ||||
\(151\) | 55446.4 | − | 96036.0i | 0.197893 | − | 0.342761i | −0.749952 | − | 0.661492i | \(-0.769923\pi\) |
0.947845 | + | 0.318731i | \(0.103257\pi\) | |||||||
\(152\) | 20332.1 | + | 35216.2i | 0.0713793 | + | 0.123633i | ||||
\(153\) | 2694.56 | 0.00930592 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1256.82 | 0.00420188 | ||||||||
\(156\) | 6154.36 | + | 10659.7i | 0.0202475 | + | 0.0350697i | ||||
\(157\) | 202693. | − | 351074.i | 0.656280 | − | 1.13671i | −0.325291 | − | 0.945614i | \(-0.605462\pi\) |
0.981571 | − | 0.191096i | \(-0.0612042\pi\) | |||||||
\(158\) | −67192.0 | + | 116380.i | −0.214129 | + | 0.370882i | ||||
\(159\) | 61644.6 | + | 106772.i | 0.193376 | + | 0.334937i | ||||
\(160\) | −4610.59 | −0.0142382 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −19309.3 | − | 33444.8i | −0.0569244 | − | 0.0985959i | 0.836159 | − | 0.548487i | \(-0.184796\pi\) |
−0.893083 | + | 0.449891i | \(0.851463\pi\) | |||||||
\(164\) | −6555.32 | + | 11354.1i | −0.0190320 | + | 0.0329644i | ||||
\(165\) | 2354.19 | − | 4077.57i | 0.00673180 | − | 0.0116598i | ||||
\(166\) | 121150. | + | 209838.i | 0.341234 | + | 0.591035i | ||||
\(167\) | −207255. | −0.575060 | −0.287530 | − | 0.957772i | \(-0.592834\pi\) | ||||
−0.287530 | + | 0.957772i | \(0.592834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −363987. | −0.980322 | ||||||||
\(170\) | 299.563 | + | 518.859i | 0.000794999 | + | 0.00137698i | ||||
\(171\) | −25732.8 | + | 44570.4i | −0.0672971 | + | 0.116562i | ||||
\(172\) | −88801.7 | + | 153809.i | −0.228876 | + | 0.396425i | ||||
\(173\) | 64128.7 | + | 111074.i | 0.162906 | + | 0.282161i | 0.935910 | − | 0.352240i | \(-0.114580\pi\) |
−0.773004 | + | 0.634401i | \(0.781247\pi\) | |||||||
\(174\) | −210977. | −0.528278 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −29744.9 | −0.0723820 | ||||||||
\(177\) | −100691. | − | 174401.i | −0.241577 | − | 0.418424i | ||||
\(178\) | 184380. | − | 319356.i | 0.436179 | − | 0.755483i | ||||
\(179\) | 49299.7 | − | 85389.6i | 0.115004 | − | 0.199192i | −0.802778 | − | 0.596279i | \(-0.796645\pi\) |
0.917781 | + | 0.397086i | \(0.129979\pi\) | |||||||
\(180\) | −2917.64 | − | 5053.49i | −0.00671197 | − | 0.0116255i | ||||
\(181\) | 599225. | 1.35954 | 0.679772 | − | 0.733423i | \(-0.262079\pi\) | ||||
0.679772 | + | 0.733423i | \(0.262079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −114229. | −0.252144 | ||||||||
\(184\) | 87277.7 | + | 151169.i | 0.190046 | + | 0.329169i | ||||
\(185\) | −6840.44 | + | 11848.0i | −0.0146945 | + | 0.0254516i | ||||
\(186\) | 5024.45 | − | 8702.61i | 0.0106489 | − | 0.0184445i | ||||
\(187\) | 1932.61 | + | 3347.38i | 0.00404148 | + | 0.00700005i | ||||
\(188\) | −118518. | −0.244563 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11443.2 | −0.0229966 | ||||||||
\(191\) | −414608. | − | 718122.i | −0.822346 | − | 1.42434i | −0.903931 | − | 0.427678i | \(-0.859332\pi\) |
0.0815852 | − | 0.996666i | \(-0.474002\pi\) | |||||||
\(192\) | −18432.0 | + | 31925.2i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 208193. | − | 360600.i | 0.402320 | − | 0.696839i | −0.591685 | − | 0.806169i | \(-0.701537\pi\) |
0.994006 | + | 0.109330i | \(0.0348705\pi\) | |||||||
\(194\) | 304574. | + | 527537.i | 0.581016 | + | 1.00635i | ||||
\(195\) | −3463.77 | −0.00652323 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −592061. | −1.08693 | −0.543464 | − | 0.839433i | \(-0.682887\pi\) | ||||
−0.543464 | + | 0.839433i | \(0.682887\pi\) | |||||||
\(198\) | −18822.9 | − | 32602.3i | −0.0341212 | − | 0.0590996i | ||||
\(199\) | 533040. | − | 923253.i | 0.954173 | − | 1.65268i | 0.217925 | − | 0.975966i | \(-0.430071\pi\) |
0.736249 | − | 0.676711i | \(-0.236595\pi\) | |||||||
\(200\) | −99351.3 | + | 172081.i | −0.175630 | + | 0.304200i | ||||
\(201\) | 235365. | + | 407664.i | 0.410915 | + | 0.711725i | ||||
\(202\) | −430577. | −0.742458 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4790.33 | 0.00805916 | ||||||||
\(205\) | −1844.72 | − | 3195.14i | −0.00306581 | − | 0.00531014i | ||||
\(206\) | 241278. | − | 417906.i | 0.396142 | − | 0.686137i | ||||
\(207\) | −110461. | + | 191324.i | −0.179177 | + | 0.310344i | ||||
\(208\) | 10941.1 | + | 18950.5i | 0.0175349 | + | 0.0303713i | ||||
\(209\) | −73825.0 | −0.116906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −846029. | −1.30822 | −0.654108 | − | 0.756401i | \(-0.726956\pi\) | ||||
−0.654108 | + | 0.756401i | \(0.726956\pi\) | |||||||
\(212\) | 109590. | + | 189816.i | 0.167468 | + | 0.290064i | ||||
\(213\) | −271036. | + | 469448.i | −0.409334 | + | 0.708988i | ||||
\(214\) | 172229. | − | 298309.i | 0.257082 | − | 0.445278i | ||||
\(215\) | −24989.5 | − | 43283.1i | −0.0368690 | − | 0.0638590i | ||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 264557. | 0.377032 | ||||||||
\(219\) | −346313. | − | 599831.i | −0.487931 | − | 0.845121i | ||||
\(220\) | 4185.22 | − | 7249.01i | 0.00582991 | − | 0.0100977i | ||||
\(221\) | 1421.75 | − | 2462.54i | 0.00195814 | − | 0.00339159i | ||||
\(222\) | 54692.8 | + | 94730.8i | 0.0744814 | + | 0.129006i | ||||
\(223\) | 112299. | 0.151222 | 0.0756109 | − | 0.997137i | \(-0.475909\pi\) | ||||
0.0756109 | + | 0.997137i | \(0.475909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −251483. | −0.331171 | ||||||||
\(226\) | 263217. | + | 455904.i | 0.342801 | + | 0.593749i | ||||
\(227\) | 89238.4 | − | 154565.i | 0.114944 | − | 0.199089i | −0.802813 | − | 0.596231i | \(-0.796664\pi\) |
0.917757 | + | 0.397141i | \(0.129998\pi\) | |||||||
\(228\) | −45747.1 | + | 79236.3i | −0.0582810 | + | 0.100946i | ||||
\(229\) | −229877. | − | 398158.i | −0.289672 | − | 0.501726i | 0.684060 | − | 0.729426i | \(-0.260213\pi\) |
−0.973731 | + | 0.227700i | \(0.926880\pi\) | |||||||
\(230\) | −49121.2 | −0.0612280 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −375071. | −0.457502 | ||||||||
\(233\) | −374334. | − | 648365.i | −0.451720 | − | 0.782402i | 0.546773 | − | 0.837281i | \(-0.315856\pi\) |
−0.998493 | + | 0.0548792i | \(0.982523\pi\) | |||||||
\(234\) | −13847.3 | + | 23984.3i | −0.0165320 | + | 0.0286343i | ||||
\(235\) | 16676.0 | − | 28883.7i | 0.0196980 | − | 0.0341179i | ||||
\(236\) | −179006. | − | 310047.i | −0.209212 | − | 0.362366i | ||||
\(237\) | −302364. | −0.349670 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −814752. | −0.922637 | −0.461319 | − | 0.887235i | \(-0.652623\pi\) | ||||
−0.461319 | + | 0.887235i | \(0.652623\pi\) | |||||||
\(240\) | −5186.91 | − | 8983.99i | −0.00581274 | − | 0.0100680i | ||||
\(241\) | 523816. | − | 907276.i | 0.580947 | − | 1.00623i | −0.414421 | − | 0.910085i | \(-0.636016\pi\) |
0.995367 | − | 0.0961439i | \(-0.0306509\pi\) | |||||||
\(242\) | −295101. | + | 511131.i | −0.323916 | + | 0.561039i | ||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −203073. | −0.218363 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −29498.9 | −0.0310791 | ||||||||
\(247\) | 27155.1 | + | 47034.1i | 0.0283211 | + | 0.0490535i | ||||
\(248\) | 8932.36 | − | 15471.3i | 0.00922226 | − | 0.0159734i | ||||
\(249\) | −272587. | + | 472135.i | −0.278617 | + | 0.482578i | ||||
\(250\) | −56099.0 | − | 97166.3i | −0.0567682 | − | 0.0983254i | ||||
\(251\) | −1.09401e6 | −1.09607 | −0.548034 | − | 0.836456i | \(-0.684623\pi\) | ||||
−0.548034 | + | 0.836456i | \(0.684623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −316902. | −0.311261 | ||||||||
\(254\) | 28874.5 | + | 50012.2i | 0.0280822 | + | 0.0486398i | ||||
\(255\) | −674.018 | + | 1167.43i | −0.000649114 | + | 0.00112430i | ||||
\(256\) | −32768.0 | + | 56755.8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 389195. | + | 674106.i | 0.367566 | + | 0.636642i | 0.989184 | − | 0.146678i | \(-0.0468580\pi\) |
−0.621619 | + | 0.783320i | \(0.713525\pi\) | |||||||
\(258\) | −399608. | −0.373753 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6157.82 | −0.00564928 | ||||||||
\(261\) | −237350. | − | 411101.i | −0.215669 | − | 0.373549i | ||||
\(262\) | 638433. | − | 1.10580e6i | 0.574595 | − | 0.995228i | ||||
\(263\) | −554881. | + | 961083.i | −0.494664 | + | 0.856784i | −0.999981 | − | 0.00615004i | \(-0.998042\pi\) |
0.505317 | + | 0.862934i | \(0.331376\pi\) | |||||||
\(264\) | −33463.0 | − | 57959.6i | −0.0295498 | − | 0.0511818i | ||||
\(265\) | −61679.2 | −0.0539540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 829711. | 0.712277 | ||||||||
\(268\) | 418427. | + | 724736.i | 0.355863 | + | 0.616372i | ||||
\(269\) | −668202. | + | 1.15736e6i | −0.563024 | + | 0.975187i | 0.434206 | + | 0.900813i | \(0.357029\pi\) |
−0.997230 | + | 0.0743731i | \(0.976304\pi\) | |||||||
\(270\) | 6564.68 | − | 11370.4i | 0.00548030 | − | 0.00949216i | ||||
\(271\) | −896005. | − | 1.55193e6i | −0.741118 | − | 1.28365i | −0.951987 | − | 0.306140i | \(-0.900963\pi\) |
0.210869 | − | 0.977514i | \(-0.432371\pi\) | |||||||
\(272\) | 8516.14 | 0.00697944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 202136. | 0.162655 | ||||||||
\(275\) | −180371. | − | 312411.i | −0.143825 | − | 0.249112i | ||||
\(276\) | −196375. | + | 340131.i | −0.155172 | + | 0.268766i | ||||
\(277\) | −28788.8 | + | 49863.6i | −0.0225436 | + | 0.0390467i | −0.877077 | − | 0.480350i | \(-0.840510\pi\) |
0.854533 | + | 0.519396i | \(0.173843\pi\) | |||||||
\(278\) | 447574. | + | 775221.i | 0.347339 | + | 0.601608i | ||||
\(279\) | 22610.0 | 0.0173897 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −550257. | −0.415719 | −0.207860 | − | 0.978159i | \(-0.566650\pi\) | ||||
−0.207860 | + | 0.978159i | \(0.566650\pi\) | |||||||
\(282\) | −133333. | − | 230940.i | −0.0998425 | − | 0.172932i | ||||
\(283\) | 588940. | − | 1.02007e6i | 0.437125 | − | 0.757122i | −0.560342 | − | 0.828261i | \(-0.689330\pi\) |
0.997466 | + | 0.0711395i | \(0.0226635\pi\) | |||||||
\(284\) | −481842. | + | 834575.i | −0.354494 | + | 0.614001i | ||||
\(285\) | −12873.6 | − | 22297.7i | −0.00938832 | − | 0.0162610i | ||||
\(286\) | −39726.7 | −0.0287189 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 709375. | + | 1.22867e6i | 0.499610 | + | 0.865350i | ||||
\(290\) | 52773.9 | − | 91407.1i | 0.0368489 | − | 0.0638242i | ||||
\(291\) | −685290. | + | 1.18696e6i | −0.474397 | + | 0.821680i | ||||
\(292\) | −615667. | − | 1.06637e6i | −0.422560 | − | 0.731896i | ||||
\(293\) | 300762. | 0.204670 | 0.102335 | − | 0.994750i | \(-0.467369\pi\) | ||||
0.102335 | + | 0.994750i | \(0.467369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 100747. | 0.0674028 | ||||||||
\(296\) | 97231.7 | + | 168410.i | 0.0645028 | + | 0.111722i | ||||
\(297\) | 42351.6 | − | 73355.1i | 0.0278598 | − | 0.0482547i | ||||
\(298\) | 519042. | − | 899008.i | 0.338581 | − | 0.586439i | ||||
\(299\) | 116567. | + | 201899.i | 0.0754043 | + | 0.130604i | ||||
\(300\) | −447081. | −0.286802 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 443571. | 0.279863 | ||||||||
\(303\) | −484399. | − | 839003.i | −0.303107 | − | 0.524997i | ||||
\(304\) | −81328.2 | + | 140865.i | −0.0504728 | + | 0.0874214i | ||||
\(305\) | 28573.2 | − | 49490.3i | 0.0175877 | − | 0.0304628i | ||||
\(306\) | 5389.12 | + | 9334.23i | 0.00329014 | + | 0.00569869i | ||||
\(307\) | 146787. | 0.0888874 | 0.0444437 | − | 0.999012i | \(-0.485848\pi\) | ||||
0.0444437 | + | 0.999012i | \(0.485848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.08575e6 | 0.646896 | ||||||||
\(310\) | 2513.64 | + | 4353.75i | 0.00148559 | + | 0.00257311i | ||||
\(311\) | −851554. | + | 1.47494e6i | −0.499242 | + | 0.864713i | −1.00000 | 0.000874814i | \(-0.999722\pi\) | |
0.500757 | + | 0.865588i | \(0.333055\pi\) | |||||||
\(312\) | −24617.5 | + | 42638.7i | −0.0143172 | + | 0.0247980i | ||||
\(313\) | −558474. | − | 967305.i | −0.322212 | − | 0.558088i | 0.658732 | − | 0.752378i | \(-0.271093\pi\) |
−0.980944 | + | 0.194290i | \(0.937760\pi\) | |||||||
\(314\) | 1.62154e6 | 0.928120 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −537536. | −0.302824 | ||||||||
\(317\) | 481447. | + | 833891.i | 0.269092 | + | 0.466081i | 0.968628 | − | 0.248517i | \(-0.0799432\pi\) |
−0.699536 | + | 0.714598i | \(0.746610\pi\) | |||||||
\(318\) | −246578. | + | 427086.i | −0.136737 | + | 0.236836i | ||||
\(319\) | 340467. | − | 589707.i | 0.187326 | − | 0.324459i | ||||
\(320\) | −9221.17 | − | 15971.5i | −0.00503398 | − | 0.00871910i | ||||
\(321\) | 775029. | 0.419812 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21136.5 | 0.0112727 | ||||||||
\(324\) | −52488.0 | − | 90911.9i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −132692. | + | 229829.i | −0.0696844 | + | 0.120697i | ||||
\(326\) | 77237.3 | − | 133779.i | 0.0402516 | − | 0.0697178i | ||||
\(327\) | 297626. | + | 515504.i | 0.153922 | + | 0.266602i | ||||
\(328\) | −52442.5 | −0.0269153 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18833.5 | 0.00952020 | ||||||||
\(331\) | 1.12998e6 | + | 1.95718e6i | 0.566891 | + | 0.981883i | 0.996871 | + | 0.0790451i | \(0.0251871\pi\) |
−0.429980 | + | 0.902838i | \(0.641480\pi\) | |||||||
\(332\) | −484600. | + | 839351.i | −0.241289 | + | 0.417925i | ||||
\(333\) | −123059. | + | 213144.i | −0.0608138 | + | 0.105333i | ||||
\(334\) | −414509. | − | 717951.i | −0.203314 | − | 0.352151i | ||||
\(335\) | −235497. | −0.114650 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.33338e6 | 0.639557 | 0.319778 | − | 0.947492i | \(-0.396392\pi\) | ||||
0.319778 | + | 0.947492i | \(0.396392\pi\) | |||||||
\(338\) | −727973. | − | 1.26089e6i | −0.346596 | − | 0.600322i | ||||
\(339\) | −592237. | + | 1.02578e6i | −0.279896 | + | 0.484794i | ||||
\(340\) | −1198.25 | + | 2075.44i | −0.000562149 | + | 0.000973671i | ||||
\(341\) | 16216.6 | + | 28087.9i | 0.00755219 | + | 0.0130808i | ||||
\(342\) | −205862. | −0.0951724 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −710414. | −0.323680 | ||||||||
\(345\) | −55261.4 | − | 95715.5i | −0.0249962 | − | 0.0432947i | ||||
\(346\) | −256515. | + | 444296.i | −0.115192 | + | 0.199518i | ||||
\(347\) | 717431. | − | 1.24263e6i | 0.319857 | − | 0.554009i | −0.660601 | − | 0.750737i | \(-0.729698\pi\) |
0.980458 | + | 0.196728i | \(0.0630317\pi\) | |||||||
\(348\) | −421955. | − | 730847.i | −0.186775 | − | 0.323503i | ||||
\(349\) | 3.34711e6 | 1.47098 | 0.735489 | − | 0.677536i | \(-0.236952\pi\) | ||||
0.735489 | + | 0.677536i | \(0.236952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −62312.9 | −0.0269967 | ||||||||
\(352\) | −59489.7 | − | 103039.i | −0.0255909 | − | 0.0443247i | ||||
\(353\) | −2.00209e6 | + | 3.46772e6i | −0.855160 | + | 1.48118i | 0.0213370 | + | 0.999772i | \(0.493208\pi\) |
−0.876497 | + | 0.481408i | \(0.840126\pi\) | |||||||
\(354\) | 402763. | − | 697605.i | 0.170821 | − | 0.295870i | ||||
\(355\) | −135594. | − | 234856.i | −0.0571044 | − | 0.0989078i | ||||
\(356\) | 1.47504e6 | 0.616850 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 394398. | 0.162640 | ||||||||
\(359\) | 297993. | + | 516139.i | 0.122031 | + | 0.211364i | 0.920568 | − | 0.390581i | \(-0.127726\pi\) |
−0.798538 | + | 0.601945i | \(0.794393\pi\) | |||||||
\(360\) | 11670.5 | − | 20214.0i | 0.00474608 | − | 0.00822045i | ||||
\(361\) | 1.03620e6 | − | 1.79475e6i | 0.418480 | − | 0.724828i | ||||
\(362\) | 1.19845e6 | + | 2.07578e6i | 0.480672 | + | 0.832548i | ||||
\(363\) | −1.32796e6 | −0.528953 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 346507. | 0.136138 | ||||||||
\(366\) | −228458. | − | 395700.i | −0.0891462 | − | 0.154406i | ||||
\(367\) | 1.65195e6 | − | 2.86126e6i | 0.640224 | − | 1.10890i | −0.345159 | − | 0.938544i | \(-0.612175\pi\) |
0.985383 | − | 0.170356i | \(-0.0544918\pi\) | |||||||
\(368\) | −349111. | + | 604677.i | −0.134383 | + | 0.232758i | ||||
\(369\) | −33186.3 | − | 57480.3i | −0.0126880 | − | 0.0219762i | ||||
\(370\) | −54723.5 | −0.0207812 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 40195.6 | 0.0150599 | ||||||||
\(373\) | 1.41532e6 | + | 2.45140e6i | 0.526722 | + | 0.912309i | 0.999515 | + | 0.0311353i | \(0.00991229\pi\) |
−0.472794 | + | 0.881173i | \(0.656754\pi\) | |||||||
\(374\) | −7730.45 | + | 13389.5i | −0.00285776 | + | 0.00494979i | ||||
\(375\) | 126223. | − | 218624.i | 0.0463510 | − | 0.0802824i | ||||
\(376\) | −237037. | − | 410560.i | −0.0864661 | − | 0.149764i | ||||
\(377\) | −500938. | −0.181523 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.45025e6 | 0.876218 | 0.438109 | − | 0.898922i | \(-0.355648\pi\) | ||||
0.438109 | + | 0.898922i | \(0.355648\pi\) | |||||||
\(380\) | −22886.4 | − | 39640.4i | −0.00813052 | − | 0.0140825i | ||||
\(381\) | −64967.7 | + | 112527.i | −0.0229290 | + | 0.0397142i | ||||
\(382\) | 1.65843e6 | − | 2.87249e6i | 0.581486 | − | 1.00716i | ||||
\(383\) | 1.69202e6 | + | 2.93067e6i | 0.589399 | + | 1.02087i | 0.994311 | + | 0.106514i | \(0.0339689\pi\) |
−0.404912 | + | 0.914356i | \(0.632698\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.66554e6 | 0.568967 | ||||||||
\(387\) | −449559. | − | 778659.i | −0.152584 | − | 0.264283i | ||||
\(388\) | −1.21829e6 | + | 2.11015e6i | −0.410840 | + | 0.711596i | ||||
\(389\) | 2.07480e6 | − | 3.59366e6i | 0.695189 | − | 1.20410i | −0.274928 | − | 0.961465i | \(-0.588654\pi\) |
0.970117 | − | 0.242638i | \(-0.0780127\pi\) | |||||||
\(390\) | −6927.54 | − | 11998.9i | −0.00230631 | − | 0.00399465i | ||||
\(391\) | 90731.0 | 0.0300133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.87295e6 | 0.938310 | ||||||||
\(394\) | −1.18412e6 | − | 2.05096e6i | −0.384287 | − | 0.665605i | ||||
\(395\) | 75633.4 | − | 131001.i | 0.0243905 | − | 0.0422456i | ||||
\(396\) | 75291.7 | − | 130409.i | 0.0241273 | − | 0.0417898i | ||||
\(397\) | 823330. | + | 1.42605e6i | 0.262179 | + | 0.454107i | 0.966821 | − | 0.255456i | \(-0.0822256\pi\) |
−0.704642 | + | 0.709563i | \(0.748892\pi\) | |||||||
\(398\) | 4.26432e6 | 1.34940 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −794810. | −0.248378 | ||||||||
\(401\) | 2.19332e6 | + | 3.79894e6i | 0.681147 | + | 1.17978i | 0.974631 | + | 0.223817i | \(0.0718520\pi\) |
−0.293484 | + | 0.955964i | \(0.594815\pi\) | |||||||
\(402\) | −941460. | + | 1.63066e6i | −0.290561 | + | 0.503266i | ||||
\(403\) | 11929.9 | − | 20663.2i | 0.00365910 | − | 0.00633775i | ||||
\(404\) | −861153. | − | 1.49156e6i | −0.262499 | − | 0.454661i | ||||
\(405\) | 29541.1 | 0.00894929 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −353045. | −0.105644 | ||||||||
\(408\) | 9580.65 | + | 16594.2i | 0.00284934 | + | 0.00493521i | ||||
\(409\) | −177296. | + | 307086.i | −0.0524072 | + | 0.0907719i | −0.891039 | − | 0.453927i | \(-0.850023\pi\) |
0.838632 | + | 0.544699i | \(0.183356\pi\) | |||||||
\(410\) | 7378.87 | − | 12780.6i | 0.00216786 | − | 0.00375484i | ||||
\(411\) | 227403. | + | 393873.i | 0.0664035 | + | 0.115014i | ||||
\(412\) | 1.93023e6 | 0.560229 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −883686. | −0.253395 | ||||||||
\(415\) | −136370. | − | 236200.i | −0.0388686 | − | 0.0673224i | ||||
\(416\) | −43764.4 | + | 75802.1i | −0.0123990 | + | 0.0214757i | ||||
\(417\) | −1.00704e6 | + | 1.74425e6i | −0.283601 | + | 0.491211i | ||||
\(418\) | −147650. | − | 255737.i | −0.0413326 | − | 0.0715902i | ||||
\(419\) | −1.79802e6 | −0.500335 | −0.250167 | − | 0.968203i | \(-0.580486\pi\) | ||||
−0.250167 | + | 0.968203i | \(0.580486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.10881e6 | 1.67978 | 0.839888 | − | 0.542760i | \(-0.182621\pi\) | ||||
0.839888 | + | 0.542760i | \(0.182621\pi\) | |||||||
\(422\) | −1.69206e6 | − | 2.93073e6i | −0.462524 | − | 0.801115i | ||||
\(423\) | 300000. | − | 519615.i | 0.0815211 | − | 0.141199i | ||||
\(424\) | −438362. | + | 759265.i | −0.118418 | + | 0.205106i | ||||
\(425\) | 51641.2 | + | 89445.1i | 0.0138683 | + | 0.0240206i | ||||
\(426\) | −2.16829e6 | −0.578886 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.37783e6 | 0.363568 | ||||||||
\(429\) | −44692.6 | − | 77409.8i | −0.0117244 | − | 0.0203073i | ||||
\(430\) | 99958.0 | − | 173132.i | 0.0260703 | − | 0.0451551i | ||||
\(431\) | 955880. | − | 1.65563e6i | 0.247862 | − | 0.429310i | −0.715070 | − | 0.699053i | \(-0.753605\pi\) |
0.962932 | + | 0.269743i | \(0.0869387\pi\) | |||||||
\(432\) | −93312.0 | − | 161621.i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 385530. | 0.0988186 | 0.0494093 | − | 0.998779i | \(-0.484266\pi\) | ||||
0.0494093 | + | 0.998779i | \(0.484266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 237483. | 0.0601740 | ||||||||
\(436\) | 529114. | + | 916452.i | 0.133301 | + | 0.230884i | ||||
\(437\) | −866472. | + | 1.50077e6i | −0.217046 | + | 0.375934i | ||||
\(438\) | 1.38525e6 | − | 2.39933e6i | 0.345019 | − | 0.597591i | ||||
\(439\) | 916909. | + | 1.58813e6i | 0.227073 | + | 0.393302i | 0.956939 | − | 0.290288i | \(-0.0937511\pi\) |
−0.729866 | + | 0.683590i | \(0.760418\pi\) | |||||||
\(440\) | 33481.8 | 0.00824473 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11374.0 | 0.00276922 | ||||||||
\(443\) | 966960. | + | 1.67482e6i | 0.234099 | + | 0.405471i | 0.959010 | − | 0.283371i | \(-0.0914527\pi\) |
−0.724912 | + | 0.688842i | \(0.758119\pi\) | |||||||
\(444\) | −218771. | + | 378923.i | −0.0526663 | + | 0.0912208i | ||||
\(445\) | −207544. | + | 359477.i | −0.0496833 | + | 0.0860540i | ||||
\(446\) | 224598. | + | 389016.i | 0.0534650 | + | 0.0926041i | ||||
\(447\) | 2.33569e6 | 0.552900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.76354e6 | 1.58328 | 0.791641 | − | 0.610987i | \(-0.209227\pi\) | ||||
0.791641 | + | 0.610987i | \(0.209227\pi\) | |||||||
\(450\) | −502966. | − | 871162.i | −0.117087 | − | 0.202800i | ||||
\(451\) | 47604.3 | − | 82453.0i | 0.0110206 | − | 0.0190882i | ||||
\(452\) | −1.05287e6 | + | 1.82362e6i | −0.242397 | + | 0.419844i | ||||
\(453\) | 499018. | + | 864324.i | 0.114254 | + | 0.197893i | ||||
\(454\) | 713907. | 0.162556 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −365977. | −0.0824217 | ||||||||
\(457\) | 1.19746e6 | + | 2.07406e6i | 0.268207 | + | 0.464548i | 0.968399 | − | 0.249407i | \(-0.0802356\pi\) |
−0.700192 | + | 0.713955i | \(0.746902\pi\) | |||||||
\(458\) | 919507. | − | 1.59263e6i | 0.204829 | − | 0.354774i | ||||
\(459\) | −12125.5 | + | 21002.0i | −0.00268639 | + | 0.00465296i | ||||
\(460\) | −98242.5 | − | 170161.i | −0.0216474 | − | 0.0374943i | ||||
\(461\) | −6.42949e6 | −1.40904 | −0.704522 | − | 0.709682i | \(-0.748838\pi\) | ||||
−0.704522 | + | 0.709682i | \(0.748838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.36524e6 | 0.295976 | 0.147988 | − | 0.988989i | \(-0.452720\pi\) | ||||
0.147988 | + | 0.988989i | \(0.452720\pi\) | |||||||
\(464\) | −750142. | − | 1.29928e6i | −0.161752 | − | 0.280162i | ||||
\(465\) | −5655.68 | + | 9795.93i | −0.00121298 | + | 0.00210094i | ||||
\(466\) | 1.49733e6 | − | 2.59346e6i | 0.319414 | − | 0.553241i | ||||
\(467\) | −2.18181e6 | − | 3.77900e6i | −0.462940 | − | 0.801835i | 0.536166 | − | 0.844113i | \(-0.319872\pi\) |
−0.999106 | + | 0.0422772i | \(0.986539\pi\) | |||||||
\(468\) | −110779. | −0.0233798 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 133408. | 0.0278572 | ||||||||
\(471\) | 1.82423e6 | + | 3.15967e6i | 0.378903 | + | 0.656280i | ||||
\(472\) | 716022. | − | 1.24019e6i | 0.147935 | − | 0.256231i | ||||
\(473\) | 644872. | − | 1.11695e6i | 0.132532 | − | 0.229552i | ||||
\(474\) | −604728. | − | 1.04742e6i | −0.123627 | − | 0.214129i | ||||
\(475\) | −1.97267e6 | −0.401163 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.10960e6 | −0.223291 | ||||||||
\(478\) | −1.62950e6 | − | 2.82239e6i | −0.326201 | − | 0.564998i | ||||
\(479\) | 696248. | − | 1.20594e6i | 0.138652 | − | 0.240152i | −0.788335 | − | 0.615247i | \(-0.789056\pi\) |
0.926986 | + | 0.375095i | \(0.122390\pi\) | |||||||
\(480\) | 20747.6 | − | 35936.0i | 0.00411022 | − | 0.00711912i | ||||
\(481\) | 129861. | + | 224926.i | 0.0255927 | + | 0.0443278i | ||||
\(482\) | 4.19053e6 | 0.821583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.36081e6 | −0.458087 | ||||||||
\(485\) | −342837. | − | 593812.i | −0.0661811 | − | 0.114629i | ||||
\(486\) | 118098. | − | 204552.i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −4.91460e6 | + | 8.51233e6i | −0.939000 | + | 1.62640i | −0.171659 | + | 0.985156i | \(0.554913\pi\) |
−0.767341 | + | 0.641239i | \(0.778421\pi\) | |||||||
\(488\) | −406147. | − | 703467.i | −0.0772029 | − | 0.133719i | ||||
\(489\) | 347568. | 0.0657306 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.67255e6 | −1.43627 | −0.718135 | − | 0.695904i | \(-0.755004\pi\) | ||||
−0.718135 | + | 0.695904i | \(0.755004\pi\) | |||||||
\(492\) | −58997.9 | − | 102187.i | −0.0109881 | − | 0.0190320i | ||||
\(493\) | −97477.9 | + | 168837.i | −0.0180630 | + | 0.0312859i | ||||
\(494\) | −108621. | + | 188136.i | −0.0200260 | + | 0.0346861i | ||||
\(495\) | 21187.7 | + | 36698.1i | 0.00388660 | + | 0.00673180i | ||||
\(496\) | 71458.9 | 0.0130422 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.18070e6 | −0.394024 | ||||||||
\(499\) | −1.69691e6 | − | 2.93914e6i | −0.305076 | − | 0.528408i | 0.672202 | − | 0.740368i | \(-0.265349\pi\) |
−0.977278 | + | 0.211960i | \(0.932015\pi\) | |||||||
\(500\) | 224396. | − | 388665.i | 0.0401412 | − | 0.0695266i | ||||
\(501\) | 932646. | − | 1.61539e6i | 0.166006 | − | 0.287530i | ||||
\(502\) | −2.18802e6 | − | 3.78976e6i | −0.387518 | − | 0.671201i | ||||
\(503\) | −8.36268e6 | −1.47376 | −0.736878 | − | 0.676026i | \(-0.763701\pi\) | ||||
−0.736878 | + | 0.676026i | \(0.763701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 484671. | 0.0845704 | ||||||||
\(506\) | −633805. | − | 1.09778e6i | −0.110047 | − | 0.190607i | ||||
\(507\) | 1.63794e6 | − | 2.83700e6i | 0.282995 | − | 0.490161i | ||||
\(508\) | −115498. | + | 200049.i | −0.0198571 | + | 0.0343935i | ||||
\(509\) | −1.93662e6 | − | 3.35432e6i | −0.331322 | − | 0.573866i | 0.651450 | − | 0.758692i | \(-0.274161\pi\) |
−0.982771 | + | 0.184826i | \(0.940828\pi\) | |||||||
\(510\) | −5392.14 | −0.000917986 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −231595. | − | 401134.i | −0.0388540 | − | 0.0672971i | ||||
\(514\) | −1.55678e6 | + | 2.69642e6i | −0.259908 | + | 0.450174i | ||||
\(515\) | −271590. | + | 470409.i | −0.0451228 | + | 0.0781551i | ||||
\(516\) | −799216. | − | 1.38428e6i | −0.132142 | − | 0.228876i | ||||
\(517\) | 860672. | 0.141616 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.15432e6 | −0.188108 | ||||||||
\(520\) | −12315.6 | − | 21331.3i | −0.00199732 | − | 0.00345947i | ||||
\(521\) | −365532. | + | 633120.i | −0.0589971 | + | 0.102186i | −0.894015 | − | 0.448036i | \(-0.852124\pi\) |
0.835018 | + | 0.550222i | \(0.185457\pi\) | |||||||
\(522\) | 949398. | − | 1.64441e6i | 0.152501 | − | 0.264139i | ||||
\(523\) | 3.55427e6 | + | 6.15618e6i | 0.568193 | + | 0.984140i | 0.996745 | + | 0.0806223i | \(0.0256908\pi\) |
−0.428551 | + | 0.903517i | \(0.640976\pi\) | |||||||
\(524\) | 5.10746e6 | 0.812600 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.43905e6 | −0.699561 | ||||||||
\(527\) | −4642.90 | − | 8041.73i | −0.000728220 | − | 0.00126131i | ||||
\(528\) | 133852. | − | 231838.i | 0.0208949 | − | 0.0361910i | ||||
\(529\) | −501258. | + | 868205.i | −0.0778794 | + | 0.134891i | ||||
\(530\) | −123358. | − | 213663.i | −0.0190756 | − | 0.0330400i | ||||
\(531\) | 1.81243e6 | 0.278949 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −70041.3 | −0.0106791 | ||||||||
\(534\) | 1.65942e6 | + | 2.87420e6i | 0.251828 | + | 0.436179i | ||||
\(535\) | −193866. | + | 335786.i | −0.0292831 | + | 0.0507198i | ||||
\(536\) | −1.67371e6 | + | 2.89895e6i | −0.251633 | + | 0.435841i | ||||
\(537\) | 443698. | + | 768507.i | 0.0663974 | + | 0.115004i | ||||
\(538\) | −5.34562e6 | −0.796237 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 52517.5 | 0.00775031 | ||||||||
\(541\) | −1.89757e6 | − | 3.28669e6i | −0.278743 | − | 0.482798i | 0.692329 | − | 0.721582i | \(-0.256585\pi\) |
−0.971073 | + | 0.238784i | \(0.923251\pi\) | |||||||
\(542\) | 3.58402e6 | − | 6.20771e6i | 0.524050 | − | 0.907680i | ||||
\(543\) | −2.69651e6 | + | 4.67050e6i | −0.392467 | + | 0.679772i | ||||
\(544\) | 17032.3 | + | 29500.8i | 0.00246760 | + | 0.00427401i | ||||
\(545\) | −297793. | −0.0429461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.34686e7 | −1.92466 | −0.962332 | − | 0.271879i | \(-0.912355\pi\) | ||||
−0.962332 | + | 0.271879i | \(0.912355\pi\) | |||||||
\(548\) | 404272. | + | 700219.i | 0.0575072 | + | 0.0996053i | ||||
\(549\) | 514030. | − | 890325.i | 0.0727876 | − | 0.126072i | ||||
\(550\) | 721482. | − | 1.24964e6i | 0.101700 | − | 0.176149i | ||||
\(551\) | −1.86181e6 | − | 3.22474e6i | −0.261250 | − | 0.452498i | ||||
\(552\) | −1.57100e6 | −0.219446 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −230310. | −0.0318815 | ||||||||
\(555\) | −61564.0 | − | 106632.i | −0.00848387 | − | 0.0146945i | ||||
\(556\) | −1.79030e6 | + | 3.10089e6i | −0.245606 | + | 0.425401i | ||||
\(557\) | −2.44744e6 | + | 4.23908e6i | −0.334251 | + | 0.578941i | −0.983341 | − | 0.181772i | \(-0.941817\pi\) |
0.649089 | + | 0.760712i | \(0.275150\pi\) | |||||||
\(558\) | 45220.1 | + | 78323.5i | 0.00614817 | + | 0.0106489i | ||||
\(559\) | −948816. | −0.128426 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34787.0 | −0.00466670 | ||||||||
\(562\) | −1.10051e6 | − | 1.90615e6i | −0.146979 | − | 0.254575i | ||||
\(563\) | 3.12803e6 | − | 5.41790e6i | 0.415910 | − | 0.720378i | −0.579613 | − | 0.814892i | \(-0.696796\pi\) |
0.995524 | + | 0.0945139i | \(0.0301297\pi\) | |||||||
\(564\) | 533333. | − | 923759.i | 0.0705993 | − | 0.122282i | ||||
\(565\) | −296285. | − | 513180.i | −0.0390470 | − | 0.0676315i | ||||
\(566\) | 4.71152e6 | 0.618188 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.85474e6 | −0.501330 | ||||||||
\(569\) | −714125. | − | 1.23690e6i | −0.0924685 | − | 0.160160i | 0.816081 | − | 0.577938i | \(-0.196142\pi\) |
−0.908549 | + | 0.417778i | \(0.862809\pi\) | |||||||
\(570\) | 51494.4 | − | 89190.9i | 0.00663854 | − | 0.0114983i | ||||
\(571\) | −4.52573e6 | + | 7.83880e6i | −0.580897 | + | 1.00614i | 0.414477 | + | 0.910060i | \(0.363965\pi\) |
−0.995373 | + | 0.0960825i | \(0.969369\pi\) | |||||||
\(572\) | −79453.5 | − | 137617.i | −0.0101537 | − | 0.0175867i | ||||
\(573\) | 7.46295e6 | 0.949563 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.46792e6 | −1.06809 | ||||||||
\(576\) | −165888. | − | 287326.i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −4.00960e6 | + | 6.94482e6i | −0.501373 | + | 0.868404i | 0.498626 | + | 0.866817i | \(0.333838\pi\) |
−0.999999 | + | 0.00158626i | \(0.999495\pi\) | |||||||
\(578\) | −2.83750e6 | + | 4.91470e6i | −0.353278 | + | 0.611895i | ||||
\(579\) | 1.87373e6 | + | 3.24540e6i | 0.232280 | + | 0.402320i | ||||
\(580\) | 422191. | 0.0521122 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.48232e6 | −0.670899 | ||||||||
\(583\) | −795838. | − | 1.37843e6i | −0.0969735 | − | 0.167963i | ||||
\(584\) | 2.46267e6 | − | 4.26547e6i | 0.298795 | − | 0.517529i | ||||
\(585\) | 15587.0 | − | 26997.4i | 0.00188309 | − | 0.00326162i | ||||
\(586\) | 601524. | + | 1.04187e6i | 0.0723617 | + | 0.125334i | ||||
\(587\) | −8.28470e6 | −0.992388 | −0.496194 | − | 0.868212i | \(-0.665270\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 177357. | 0.0210649 | ||||||||
\(590\) | 201494. | + | 348998.i | 0.0238305 | + | 0.0412756i | ||||
\(591\) | 2.66427e6 | − | 4.61466e6i | 0.313769 | − | 0.543464i | ||||
\(592\) | −388927. | + | 673641.i | −0.0456104 | + | 0.0789995i | ||||
\(593\) | −2.95722e6 | − | 5.12205e6i | −0.345340 | − | 0.598146i | 0.640076 | − | 0.768312i | \(-0.278903\pi\) |
−0.985415 | + | 0.170166i | \(0.945570\pi\) | |||||||
\(594\) | 338813. | 0.0393998 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.15234e6 | 0.478825 | ||||||||
\(597\) | 4.79736e6 | + | 8.30927e6i | 0.550892 | + | 0.954173i | ||||
\(598\) | −466266. | + | 807597.i | −0.0533189 | + | 0.0923510i | ||||
\(599\) | −1.66449e6 | + | 2.88298e6i | −0.189545 | + | 0.328302i | −0.945099 | − | 0.326785i | \(-0.894035\pi\) |
0.755553 | + | 0.655087i | \(0.227368\pi\) | |||||||
\(600\) | −894161. | − | 1.54873e6i | −0.101400 | − | 0.175630i | ||||
\(601\) | −4.87081e6 | −0.550066 | −0.275033 | − | 0.961435i | \(-0.588689\pi\) | ||||
−0.275033 | + | 0.961435i | \(0.588689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.23657e6 | −0.474484 | ||||||||
\(604\) | 887142. | + | 1.53658e6i | 0.0989466 | + | 0.171381i | ||||
\(605\) | 332175. | − | 575345.i | 0.0368960 | − | 0.0639057i | ||||
\(606\) | 1.93760e6 | − | 3.35601e6i | 0.214329 | − | 0.371229i | ||||
\(607\) | 7.58504e6 | + | 1.31377e7i | 0.835577 | + | 1.44726i | 0.893560 | + | 0.448944i | \(0.148200\pi\) |
−0.0579835 | + | 0.998318i | \(0.518467\pi\) | |||||||
\(608\) | −650626. | −0.0713793 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 228586. | 0.0248728 | ||||||||
\(611\) | −316582. | − | 548336.i | −0.0343070 | − | 0.0594216i | ||||
\(612\) | −21556.5 | + | 37336.9i | −0.00232648 | + | 0.00402958i | ||||
\(613\) | −2.59078e6 | + | 4.48736e6i | −0.278471 | + | 0.482325i | −0.971005 | − | 0.239060i | \(-0.923161\pi\) |
0.692534 | + | 0.721385i | \(0.256494\pi\) | |||||||
\(614\) | 293573. | + | 508483.i | 0.0314264 | + | 0.0544322i | ||||
\(615\) | 33204.9 | 0.00354009 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.55854e6 | 0.164818 | 0.0824092 | − | 0.996599i | \(-0.473739\pi\) | ||||
0.0824092 | + | 0.996599i | \(0.473739\pi\) | |||||||
\(618\) | 2.17151e6 | + | 3.76116e6i | 0.228712 | + | 0.396142i | ||||
\(619\) | 703756. | − | 1.21894e6i | 0.0738236 | − | 0.127866i | −0.826750 | − | 0.562569i | \(-0.809813\pi\) |
0.900574 | + | 0.434703i | \(0.143146\pi\) | |||||||
\(620\) | −10054.5 | + | 17415.0i | −0.00105047 | + | 0.00181947i | ||||
\(621\) | −994147. | − | 1.72191e6i | −0.103448 | − | 0.179177i | ||||
\(622\) | −6.81243e6 | −0.706035 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −196940. | −0.0202475 | ||||||||
\(625\) | −4.78799e6 | − | 8.29304e6i | −0.490290 | − | 0.849207i | ||||
\(626\) | 2.23389e6 | − | 3.86922e6i | 0.227838 | − | 0.394628i | ||||
\(627\) | 332213. | − | 575409.i | 0.0337479 | − | 0.0584531i | ||||
\(628\) | 3.24308e6 | + | 5.61719e6i | 0.328140 | + | 0.568355i | ||||
\(629\) | 101079. | 0.0101867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.09643e7 | −1.09624 | −0.548120 | − | 0.836399i | \(-0.684656\pi\) | ||||
−0.548120 | + | 0.836399i | \(0.684656\pi\) | |||||||
\(632\) | −1.07507e6 | − | 1.86208e6i | −0.107064 | − | 0.185441i | ||||
\(633\) | 3.80713e6 | − | 6.59415e6i | 0.377649 | − | 0.654108i | ||||
\(634\) | −1.92579e6 | + | 3.33556e6i | −0.190277 | + | 0.329569i | ||||
\(635\) | −32502.1 | − | 56295.3i | −0.00319873 | − | 0.00554036i | ||||
\(636\) | −1.97263e6 | −0.193376 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.72374e6 | 0.264919 | ||||||||
\(639\) | −2.43932e6 | − | 4.22503e6i | −0.236329 | − | 0.409334i | ||||
\(640\) | 36884.7 | − | 63886.2i | 0.00355956 | − | 0.00616534i | ||||
\(641\) | 7.10609e6 | − | 1.23081e7i | 0.683103 | − | 1.18317i | −0.290926 | − | 0.956745i | \(-0.593964\pi\) |
0.974029 | − | 0.226423i | \(-0.0727032\pi\) | |||||||
\(642\) | 1.55006e6 | + | 2.68478e6i | 0.148426 | + | 0.257082i | ||||
\(643\) | −9.13928e6 | −0.871735 | −0.435868 | − | 0.900011i | \(-0.643558\pi\) | ||||
−0.435868 | + | 0.900011i | \(0.643558\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 449811. | 0.0425727 | ||||||||
\(646\) | 42273.1 | + | 73219.1i | 0.00398550 | + | 0.00690309i | ||||
\(647\) | 9.46362e6 | − | 1.63915e7i | 0.888785 | − | 1.53942i | 0.0474724 | − | 0.998873i | \(-0.484883\pi\) |
0.841313 | − | 0.540549i | \(-0.181783\pi\) | |||||||
\(648\) | 209952. | − | 363648.i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.29993e6 | + | 2.25154e6i | 0.121145 | + | 0.209830i | ||||
\(650\) | −1.06153e6 | −0.0985487 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 617899. | 0.0569244 | ||||||||
\(653\) | 2.14991e6 | + | 3.72376e6i | 0.197305 | + | 0.341742i | 0.947654 | − | 0.319300i | \(-0.103448\pi\) |
−0.750349 | + | 0.661042i | \(0.770114\pi\) | |||||||
\(654\) | −1.19051e6 | + | 2.06202e6i | −0.108840 | + | 0.188516i | ||||
\(655\) | −718640. | + | 1.24472e6i | −0.0654498 | + | 0.113362i | ||||
\(656\) | −104885. | − | 181666.i | −0.00951599 | − | 0.0164822i | ||||
\(657\) | 6.23363e6 | 0.563414 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.15303e7 | −1.03425 | −0.517126 | − | 0.855909i | \(-0.672998\pi\) | ||||
−0.517126 | + | 0.855909i | \(0.672998\pi\) | |||||||
\(660\) | 37667.0 | + | 65241.1i | 0.00336590 | + | 0.00582991i | ||||
\(661\) | −7.35237e6 | + | 1.27347e7i | −0.654521 | + | 1.13366i | 0.327492 | + | 0.944854i | \(0.393796\pi\) |
−0.982014 | + | 0.188810i | \(0.939537\pi\) | |||||||
\(662\) | −4.51990e6 | + | 7.82870e6i | −0.400852 | + | 0.694296i | ||||
\(663\) | 12795.8 | + | 22162.9i | 0.00113053 | + | 0.00195814i | ||||
\(664\) | −3.87680e6 | −0.341234 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −984471. | −0.0860037 | ||||||||
\(667\) | −7.99202e6 | − | 1.38426e7i | −0.695572 | − | 1.20477i | ||||
\(668\) | 1.65804e6 | − | 2.87181e6i | 0.143765 | − | 0.249008i | ||||
\(669\) | −505346. | + | 875286.i | −0.0436540 | + | 0.0756109i | ||||
\(670\) | −470994. | − | 815786.i | −0.0405349 | − | 0.0702084i | ||||
\(671\) | 1.47471e6 | 0.126444 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42971e7 | 1.21678 | 0.608389 | − | 0.793639i | \(-0.291816\pi\) | ||||
0.608389 | + | 0.793639i | \(0.291816\pi\) | |||||||
\(674\) | 2.66676e6 | + | 4.61896e6i | 0.226117 | + | 0.391647i | ||||
\(675\) | 1.13167e6 | − | 1.96012e6i | 0.0956008 | − | 0.165585i | ||||
\(676\) | 2.91189e6 | − | 5.04355e6i | 0.245080 | − | 0.424492i | ||||
\(677\) | −4.56012e6 | − | 7.89836e6i | −0.382389 | − | 0.662316i | 0.609015 | − | 0.793159i | \(-0.291565\pi\) |
−0.991403 | + | 0.130843i | \(0.958232\pi\) | |||||||
\(678\) | −4.73790e6 | −0.395832 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9586.03 | −0.000794999 | ||||||||
\(681\) | 803146. | + | 1.39109e6i | 0.0663631 | + | 0.114944i | ||||
\(682\) | −64866.2 | + | 112352.i | −0.00534020 | + | 0.00924950i | ||||
\(683\) | 7.25762e6 | − | 1.25706e7i | 0.595309 | − | 1.03111i | −0.398194 | − | 0.917301i | \(-0.630363\pi\) |
0.993503 | − | 0.113804i | \(-0.0363037\pi\) | |||||||
\(684\) | −411724. | − | 713127.i | −0.0336485 | − | 0.0582810i | ||||
\(685\) | −227530. | −0.0185273 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.13778e6 | 0.334484 | ||||||||
\(688\) | −1.42083e6 | − | 2.46095e6i | −0.114438 | − | 0.198212i | ||||
\(689\) | −585468. | + | 1.01406e6i | −0.0469846 | + | 0.0813796i | ||||
\(690\) | 221046. | − | 382862.i | 0.0176750 | − | 0.0306140i | ||||
\(691\) | −1.04254e6 | − | 1.80573e6i | −0.0830608 | − | 0.143866i | 0.821502 | − | 0.570205i | \(-0.193136\pi\) |
−0.904563 | + | 0.426339i | \(0.859803\pi\) | |||||||
\(692\) | −2.05212e6 | −0.162906 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.73945e6 | 0.452347 | ||||||||
\(695\) | −503804. | − | 872613.i | −0.0395639 | − | 0.0685267i | ||||
\(696\) | 1.68782e6 | − | 2.92339e6i | 0.132070 | − | 0.228751i | ||||
\(697\) | −13629.4 | + | 23606.8i | −0.00106266 | + | 0.00184058i | ||||
\(698\) | 6.69422e6 | + | 1.15947e7i | 0.520069 | + | 0.900787i | ||||
\(699\) | 6.73801e6 | 0.521601 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.96513e6 | 0.765928 | 0.382964 | − | 0.923763i | \(-0.374903\pi\) | ||||
0.382964 | + | 0.923763i | \(0.374903\pi\) | |||||||
\(702\) | −124626. | − | 215858.i | −0.00954477 | − | 0.0165320i | ||||
\(703\) | −965293. | + | 1.67194e6i | −0.0736667 | + | 0.127594i | ||||
\(704\) | 237959. | − | 412157.i | 0.0180955 | − | 0.0313423i | ||||
\(705\) | 150084. | + | 259953.i | 0.0113726 | + | 0.0196980i | ||||
\(706\) | −1.60167e7 | −1.20938 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.22210e6 | 0.241577 | ||||||||
\(709\) | −3.54518e6 | − | 6.14043e6i | −0.264864 | − | 0.458757i | 0.702664 | − | 0.711522i | \(-0.251994\pi\) |
−0.967528 | + | 0.252764i | \(0.918660\pi\) | |||||||
\(710\) | 542376. | − | 939423.i | 0.0403789 | − | 0.0699384i | ||||
\(711\) | 1.36064e6 | − | 2.35669e6i | 0.100941 | − | 0.174835i | ||||
\(712\) | 2.95008e6 | + | 5.10969e6i | 0.218089 | + | 0.377742i | ||||
\(713\) | 761324. | 0.0560849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44717.6 | 0.00327125 | ||||||||
\(716\) | 788796. | + | 1.36623e6i | 0.0575019 | + | 0.0995962i | ||||
\(717\) | 3.66639e6 | − | 6.35037e6i | 0.266342 | − | 0.461319i | ||||
\(718\) | −1.19197e6 | + | 2.06456e6i | −0.0862889 | + | 0.149457i | ||||
\(719\) | −6.00833e6 | − | 1.04067e7i | −0.433443 | − | 0.750745i | 0.563724 | − | 0.825963i | \(-0.309368\pi\) |
−0.997167 | + | 0.0752181i | \(0.976035\pi\) | |||||||
\(720\) | 93364.4 | 0.00671197 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.28958e6 | 0.591820 | ||||||||
\(723\) | 4.71435e6 | + | 8.16549e6i | 0.335410 | + | 0.580947i | ||||
\(724\) | −4.79380e6 | + | 8.30310e6i | −0.339886 | + | 0.588700i | ||||
\(725\) | 9.09760e6 | − | 1.57575e7i | 0.642809 | − | 1.11338i | ||||
\(726\) | −2.65591e6 | − | 4.60017e6i | −0.187013 | − | 0.323916i | ||||
\(727\) | 1.32577e7 | 0.930318 | 0.465159 | − | 0.885227i | \(-0.345997\pi\) | ||||
0.465159 | + | 0.885227i | \(0.345997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 693014. | + | 1.20034e6i | 0.0481321 | + | 0.0833673i | ||||
\(731\) | −184631. | + | 319790.i | −0.0127794 | + | 0.0221346i | ||||
\(732\) | 913830. | − | 1.58280e6i | 0.0630359 | − | 0.109181i | ||||
\(733\) | 454651. | + | 787479.i | 0.0312549 | + | 0.0541351i | 0.881230 | − | 0.472688i | \(-0.156716\pi\) |
−0.849975 | + | 0.526823i | \(0.823383\pi\) | |||||||
\(734\) | 1.32156e7 | 0.905413 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.79289e6 | −0.190046 | ||||||||
\(737\) | −3.03859e6 | − | 5.26299e6i | −0.206064 | − | 0.356914i | ||||
\(738\) | 132745. | − | 229921.i | 0.00897176 | − | 0.0155396i | ||||
\(739\) | 143426. | − | 248421.i | 0.00966086 | − | 0.0167331i | −0.861155 | − | 0.508343i | \(-0.830258\pi\) |
0.870815 | + | 0.491610i | \(0.163591\pi\) | |||||||
\(740\) | −109447. | − | 189568.i | −0.00734725 | − | 0.0127258i | ||||
\(741\) | −488792. | −0.0327024 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.35906e6 | −0.0903163 | −0.0451582 | − | 0.998980i | \(-0.514379\pi\) | ||||
−0.0451582 | + | 0.998980i | \(0.514379\pi\) | |||||||
\(744\) | 80391.3 | + | 139242.i | 0.00532447 | + | 0.00922226i | ||||
\(745\) | −584250. | + | 1.01195e6i | −0.0385663 | + | 0.0667988i | ||||
\(746\) | −5.66126e6 | + | 9.80559e6i | −0.372448 | + | 0.645100i | ||||
\(747\) | −2.45329e6 | − | 4.24921e6i | −0.160859 | − | 0.278617i | ||||
\(748\) | −61843.6 | −0.00404148 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00978e6 | 0.0655503 | ||||||||
\(751\) | −7.72018e6 | − | 1.33718e7i | −0.499491 | − | 0.865144i | 0.500509 | − | 0.865732i | \(-0.333146\pi\) |
−1.00000 | 0.000587430i | \(0.999813\pi\) | ||||||||
\(752\) | 948147. | − | 1.64224e6i | 0.0611408 | − | 0.105899i | ||||
\(753\) | 4.92305e6 | − | 8.52697e6i | 0.316407 | − | 0.548034i | ||||
\(754\) | −1.00188e6 | − | 1.73530e6i | −0.0641779 | − | 0.111159i | ||||
\(755\) | −499298. | −0.0318781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.70683e7 | 1.08256 | 0.541279 | − | 0.840843i | \(-0.317940\pi\) | ||||
0.541279 | + | 0.840843i | \(0.317940\pi\) | |||||||
\(758\) | 4.90050e6 | + | 8.48792e6i | 0.309790 | + | 0.536572i | ||||
\(759\) | 1.42606e6 | − | 2.47001e6i | 0.0898532 | − | 0.155630i | ||||
\(760\) | 91545.6 | − | 158562.i | 0.00574915 | − | 0.00995782i | ||||
\(761\) | −1.54173e6 | − | 2.67035e6i | −0.0965041 | − | 0.167150i | 0.813731 | − | 0.581241i | \(-0.197433\pi\) |
−0.910235 | + | 0.414091i | \(0.864099\pi\) | |||||||
\(762\) | −519742. | −0.0324265 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.32675e7 | 0.822346 | ||||||||
\(765\) | −6066.16 | − | 10506.9i | −0.000374766 | − | 0.000649114i | ||||
\(766\) | −6.76810e6 | + | 1.17227e7i | −0.416768 | + | 0.721864i | ||||
\(767\) | 956307. | − | 1.65637e6i | 0.0586960 | − | 0.101665i | ||||
\(768\) | −294912. | − | 510803.i | −0.0180422 | − | 0.0312500i |