Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(99,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.99");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.g (of order \(2\), degree \(1\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(-1.67467 + 1.09337i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.99 |
Dual form | 392.3.g.m.99.2 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67467 | − | 1.09337i | −0.837337 | − | 0.546687i | ||||
\(3\) | −4.56747 | −1.52249 | −0.761245 | − | 0.648464i | \(-0.775412\pi\) | ||||
−0.761245 | + | 0.648464i | \(0.775412\pi\) | |||||||
\(4\) | 1.60906 | + | 3.66209i | 0.402266 | + | 0.915523i | ||||
\(5\) | − | 5.73252i | − | 1.14650i | −0.819379 | − | 0.573252i | \(-0.805682\pi\) | ||
0.819379 | − | 0.573252i | \(-0.194318\pi\) | |||||||
\(6\) | 7.64902 | + | 4.99396i | 1.27484 | + | 0.832327i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.30939 | − | 7.89212i | 0.163673 | − | 0.986515i | ||||
\(9\) | 11.8618 | 1.31798 | ||||||||
\(10\) | −6.26779 | + | 9.60010i | −0.626779 | + | 0.960010i | ||||
\(11\) | −1.40065 | −0.127332 | −0.0636658 | − | 0.997971i | \(-0.520279\pi\) | ||||
−0.0636658 | + | 0.997971i | \(0.520279\pi\) | |||||||
\(12\) | −7.34935 | − | 16.7265i | −0.612446 | − | 1.39388i | ||||
\(13\) | 19.0821i | 1.46785i | 0.679228 | + | 0.733927i | \(0.262315\pi\) | ||||
−0.679228 | + | 0.733927i | \(0.737685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.1831i | 1.74554i | ||||||||
\(16\) | −10.8218 | + | 11.7851i | −0.676365 | + | 0.736567i | ||||
\(17\) | 32.2699 | 1.89823 | 0.949114 | − | 0.314932i | \(-0.101982\pi\) | ||||
0.949114 | + | 0.314932i | \(0.101982\pi\) | |||||||
\(18\) | −19.8646 | − | 12.9694i | −1.10359 | − | 0.720522i | ||||
\(19\) | −12.5675 | −0.661446 | −0.330723 | − | 0.943728i | \(-0.607293\pi\) | ||||
−0.330723 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(20\) | 20.9930 | − | 9.22398i | 1.04965 | − | 0.461199i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.34563 | + | 1.53143i | 0.106619 | + | 0.0696105i | ||||
\(23\) | 15.8893i | 0.690839i | 0.938448 | + | 0.345419i | \(0.112263\pi\) | ||||
−0.938448 | + | 0.345419i | \(0.887737\pi\) | |||||||
\(24\) | −5.98058 | + | 36.0470i | −0.249191 | + | 1.50196i | ||||
\(25\) | −7.86180 | −0.314472 | ||||||||
\(26\) | 20.8639 | − | 31.9563i | 0.802457 | − | 1.22909i | ||||
\(27\) | −13.0712 | −0.484118 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.29194i | − | 0.113515i | −0.998388 | − | 0.0567576i | \(-0.981924\pi\) | ||
0.998388 | − | 0.0567576i | \(-0.0180762\pi\) | |||||||
\(30\) | 28.6280 | − | 43.8482i | 0.954266 | − | 1.46161i | ||||
\(31\) | − | 22.6705i | − | 0.731306i | −0.930751 | − | 0.365653i | \(-0.880846\pi\) | ||
0.930751 | − | 0.365653i | \(-0.119154\pi\) | |||||||
\(32\) | 31.0085 | − | 7.90382i | 0.969017 | − | 0.246994i | ||||
\(33\) | 6.39741 | 0.193861 | ||||||||
\(34\) | −54.0415 | − | 35.2831i | −1.58946 | − | 1.03774i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.0864 | + | 43.4390i | 0.530177 | + | 1.20664i | ||||
\(37\) | − | 54.1537i | − | 1.46361i | −0.681512 | − | 0.731807i | \(-0.738677\pi\) | ||
0.681512 | − | 0.731807i | \(-0.261323\pi\) | |||||||
\(38\) | 21.0464 | + | 13.7410i | 0.553853 | + | 0.361604i | ||||
\(39\) | − | 87.1569i | − | 2.23479i | ||||||
\(40\) | −45.2417 | − | 7.50608i | −1.13104 | − | 0.187652i | ||||
\(41\) | 7.59607 | 0.185270 | 0.0926350 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926350 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.8478 | −0.484833 | −0.242417 | − | 0.970172i | \(-0.577940\pi\) | ||||
−0.242417 | + | 0.970172i | \(0.577940\pi\) | |||||||
\(44\) | −2.25373 | − | 5.12930i | −0.0512211 | − | 0.116575i | ||||
\(45\) | − | 67.9980i | − | 1.51107i | ||||||
\(46\) | 17.3729 | − | 26.6094i | 0.377673 | − | 0.578465i | ||||
\(47\) | − | 21.6384i | − | 0.460392i | −0.973144 | − | 0.230196i | \(-0.926063\pi\) | ||
0.973144 | − | 0.230196i | \(-0.0739367\pi\) | |||||||
\(48\) | 49.4284 | − | 53.8280i | 1.02976 | − | 1.12142i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1659 | + | 8.59589i | 0.263319 | + | 0.171918i | ||||
\(51\) | −147.392 | −2.89004 | ||||||||
\(52\) | −69.8804 | + | 30.7043i | −1.34385 | + | 0.590467i | ||||
\(53\) | 0.356667i | 0.00672957i | 0.999994 | + | 0.00336479i | \(0.00107105\pi\) | ||||
−0.999994 | + | 0.00336479i | \(0.998929\pi\) | |||||||
\(54\) | 21.8900 | + | 14.2917i | 0.405370 | + | 0.264661i | ||||
\(55\) | 8.02924i | 0.145986i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.4016 | 1.00705 | ||||||||
\(58\) | −3.59933 | + | 5.51293i | −0.0620574 | + | 0.0950505i | ||||
\(59\) | −26.8583 | −0.455226 | −0.227613 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227613 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(60\) | −95.8850 | + | 42.1303i | −1.59808 | + | 0.702171i | ||||
\(61\) | − | 86.2287i | − | 1.41359i | −0.707420 | − | 0.706793i | \(-0.750141\pi\) | ||
0.707420 | − | 0.706793i | \(-0.249859\pi\) | |||||||
\(62\) | −24.7873 | + | 37.9656i | −0.399796 | + | 0.612349i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −60.5710 | − | 20.6676i | −0.946422 | − | 0.322932i | ||||
\(65\) | 109.389 | 1.68290 | ||||||||
\(66\) | −10.7136 | − | 6.99477i | −0.162327 | − | 0.105981i | ||||
\(67\) | 114.523 | 1.70929 | 0.854646 | − | 0.519211i | \(-0.173774\pi\) | ||||
0.854646 | + | 0.519211i | \(0.173774\pi\) | |||||||
\(68\) | 51.9243 | + | 118.175i | 0.763592 | + | 1.73787i | ||||
\(69\) | − | 72.5739i | − | 1.05180i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 104.792i | − | 1.47594i | −0.674834 | − | 0.737969i | \(-0.735785\pi\) | ||
0.674834 | − | 0.737969i | \(-0.264215\pi\) | |||||||
\(72\) | 15.5317 | − | 93.6147i | 0.215718 | − | 1.30020i | ||||
\(73\) | 24.3974 | 0.334211 | 0.167106 | − | 0.985939i | \(-0.446558\pi\) | ||||
0.167106 | + | 0.985939i | \(0.446558\pi\) | |||||||
\(74\) | −59.2103 | + | 90.6898i | −0.800140 | + | 1.22554i | ||||
\(75\) | 35.9085 | 0.478781 | ||||||||
\(76\) | −20.2218 | − | 46.0232i | −0.266077 | − | 0.605569i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −95.2952 | + | 145.959i | −1.22173 | + | 1.87127i | ||||
\(79\) | 117.128i | 1.48263i | 0.671157 | + | 0.741315i | \(0.265798\pi\) | ||||
−0.671157 | + | 0.741315i | \(0.734202\pi\) | |||||||
\(80\) | 67.5582 | + | 62.0364i | 0.844477 | + | 0.775455i | ||||
\(81\) | −47.0539 | −0.580913 | ||||||||
\(82\) | −12.7209 | − | 8.30535i | −0.155133 | − | 0.101285i | ||||
\(83\) | −79.2706 | −0.955067 | −0.477534 | − | 0.878614i | \(-0.658469\pi\) | ||||
−0.477534 | + | 0.878614i | \(0.658469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 184.988i | − | 2.17633i | ||||||
\(86\) | 34.9133 | + | 22.7945i | 0.405969 | + | 0.265052i | ||||
\(87\) | 15.0359i | 0.172826i | ||||||||
\(88\) | −1.83399 | + | 11.0541i | −0.0208408 | + | 0.125614i | ||||
\(89\) | −2.66078 | −0.0298964 | −0.0149482 | − | 0.999888i | \(-0.504758\pi\) | ||||
−0.0149482 | + | 0.999888i | \(0.504758\pi\) | |||||||
\(90\) | −74.3473 | + | 113.874i | −0.826081 | + | 1.26527i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −58.1880 | + | 25.5669i | −0.632479 | + | 0.277901i | ||||
\(93\) | 103.547i | 1.11341i | ||||||||
\(94\) | −23.6589 | + | 36.2373i | −0.251691 | + | 0.385503i | ||||
\(95\) | 72.0433i | 0.758350i | ||||||||
\(96\) | −141.631 | + | 36.1005i | −1.47532 | + | 0.376046i | ||||
\(97\) | 52.0930 | 0.537042 | 0.268521 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268521 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.6142 | −0.167820 | ||||||||
\(100\) | −12.6501 | − | 28.7906i | −0.126501 | − | 0.287906i | ||||
\(101\) | − | 91.4742i | − | 0.905685i | −0.891591 | − | 0.452842i | \(-0.850410\pi\) | ||
0.891591 | − | 0.452842i | \(-0.149590\pi\) | |||||||
\(102\) | 246.833 | + | 161.154i | 2.41993 | + | 1.57995i | ||||
\(103\) | − | 39.7891i | − | 0.386302i | −0.981169 | − | 0.193151i | \(-0.938129\pi\) | ||
0.981169 | − | 0.193151i | \(-0.0618708\pi\) | |||||||
\(104\) | 150.598 | + | 24.9858i | 1.44806 | + | 0.240248i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.389971 | − | 0.597301i | 0.00367897 | − | 0.00563492i | ||||
\(107\) | 82.6631 | 0.772552 | 0.386276 | − | 0.922383i | \(-0.373761\pi\) | ||||
0.386276 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(108\) | −21.0323 | − | 47.8679i | −0.194744 | − | 0.443221i | ||||
\(109\) | − | 29.4719i | − | 0.270384i | −0.990819 | − | 0.135192i | \(-0.956835\pi\) | ||
0.990819 | − | 0.135192i | \(-0.0431652\pi\) | |||||||
\(110\) | 8.77897 | − | 13.4463i | 0.0798088 | − | 0.122240i | ||||
\(111\) | 247.346i | 2.22834i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 159.133 | 1.40826 | 0.704130 | − | 0.710071i | \(-0.251337\pi\) | ||||
0.704130 | + | 0.710071i | \(0.251337\pi\) | |||||||
\(114\) | −96.1289 | − | 62.7614i | −0.843236 | − | 0.550539i | ||||
\(115\) | 91.0857 | 0.792049 | ||||||||
\(116\) | 12.0554 | − | 5.29694i | 0.103926 | − | 0.0456633i | ||||
\(117\) | 226.348i | 1.93460i | ||||||||
\(118\) | 44.9789 | + | 29.3662i | 0.381177 | + | 0.248866i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 206.640 | + | 34.2838i | 1.72200 | + | 0.285698i | ||||
\(121\) | −119.038 | −0.983787 | ||||||||
\(122\) | −94.2803 | + | 144.405i | −0.772790 | + | 1.18365i | ||||
\(123\) | −34.6948 | −0.282072 | ||||||||
\(124\) | 83.0214 | − | 36.4782i | 0.669527 | − | 0.294179i | ||||
\(125\) | − | 98.2451i | − | 0.785961i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0834i | 0.126641i | 0.997993 | + | 0.0633205i | \(0.0201690\pi\) | ||||
−0.997993 | + | 0.0633205i | \(0.979831\pi\) | |||||||
\(128\) | 78.8392 | + | 100.838i | 0.615931 | + | 0.787800i | ||||
\(129\) | 95.2219 | 0.738154 | ||||||||
\(130\) | −183.190 | − | 119.603i | −1.40915 | − | 0.920021i | ||||
\(131\) | 118.136 | 0.901799 | 0.450899 | − | 0.892575i | \(-0.351103\pi\) | ||||
0.450899 | + | 0.892575i | \(0.351103\pi\) | |||||||
\(132\) | 10.2938 | + | 23.4279i | 0.0779836 | + | 0.177484i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −191.788 | − | 125.216i | −1.43125 | − | 0.934448i | ||||
\(135\) | 74.9308i | 0.555043i | ||||||||
\(136\) | 42.2537 | − | 254.678i | 0.310689 | − | 1.87263i | ||||
\(137\) | −19.1708 | −0.139933 | −0.0699664 | − | 0.997549i | \(-0.522289\pi\) | ||||
−0.0699664 | + | 0.997549i | \(0.522289\pi\) | |||||||
\(138\) | −79.3505 | + | 121.538i | −0.575003 | + | 0.880707i | ||||
\(139\) | −104.954 | −0.755062 | −0.377531 | − | 0.925997i | \(-0.623227\pi\) | ||||
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98.8329i | 0.700942i | ||||||||
\(142\) | −114.577 | + | 175.492i | −0.806877 | + | 1.23586i | ||||
\(143\) | − | 26.7273i | − | 0.186904i | ||||||
\(144\) | −128.366 | + | 139.792i | −0.891434 | + | 0.970779i | ||||
\(145\) | −18.8711 | −0.130146 | ||||||||
\(146\) | −40.8577 | − | 26.6755i | −0.279847 | − | 0.182709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 198.316 | − | 87.1367i | 1.33997 | − | 0.588762i | ||||
\(149\) | − | 82.3906i | − | 0.552957i | −0.961020 | − | 0.276478i | \(-0.910833\pi\) | ||
0.961020 | − | 0.276478i | \(-0.0891674\pi\) | |||||||
\(150\) | −60.1351 | − | 39.2615i | −0.400901 | − | 0.261743i | ||||
\(151\) | − | 57.7395i | − | 0.382381i | −0.981553 | − | 0.191190i | \(-0.938765\pi\) | ||
0.981553 | − | 0.191190i | \(-0.0612347\pi\) | |||||||
\(152\) | −16.4557 | + | 99.1840i | −0.108261 | + | 0.652526i | ||||
\(153\) | 382.779 | 2.50182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −129.959 | −0.838445 | ||||||||
\(156\) | 319.177 | − | 140.241i | 2.04600 | − | 0.898981i | ||||
\(157\) | − | 3.72975i | − | 0.0237564i | −0.999929 | − | 0.0118782i | \(-0.996219\pi\) | ||
0.999929 | − | 0.0118782i | \(-0.00378104\pi\) | |||||||
\(158\) | 128.065 | − | 196.151i | 0.810536 | − | 1.24146i | ||||
\(159\) | − | 1.62907i | − | 0.0102457i | ||||||
\(160\) | −45.3088 | − | 177.757i | −0.283180 | − | 1.11098i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 78.8000 | + | 51.4476i | 0.486420 | + | 0.317578i | ||||
\(163\) | 77.7069 | 0.476729 | 0.238365 | − | 0.971176i | \(-0.423389\pi\) | ||||
0.238365 | + | 0.971176i | \(0.423389\pi\) | |||||||
\(164\) | 12.2225 | + | 27.8175i | 0.0745277 | + | 0.169619i | ||||
\(165\) | − | 36.6733i | − | 0.222262i | ||||||
\(166\) | 132.752 | + | 86.6724i | 0.799713 | + | 0.522123i | ||||
\(167\) | − | 62.0837i | − | 0.371759i | −0.982573 | − | 0.185879i | \(-0.940487\pi\) | ||
0.982573 | − | 0.185879i | \(-0.0595133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −195.127 | −1.15459 | ||||||||
\(170\) | −202.261 | + | 309.794i | −1.18977 | + | 1.82232i | ||||
\(171\) | −149.073 | −0.871771 | ||||||||
\(172\) | −33.5455 | − | 76.3467i | −0.195032 | − | 0.443876i | ||||
\(173\) | 195.614i | 1.13072i | 0.824846 | + | 0.565358i | \(0.191262\pi\) | ||||
−0.824846 | + | 0.565358i | \(0.808738\pi\) | |||||||
\(174\) | 16.4398 | − | 25.1801i | 0.0944818 | − | 0.144713i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.1576 | − | 16.5067i | 0.0861225 | − | 0.0937882i | ||||
\(177\) | 122.675 | 0.693077 | ||||||||
\(178\) | 4.45594 | + | 2.90923i | 0.0250334 | + | 0.0163440i | ||||
\(179\) | 72.2099 | 0.403407 | 0.201704 | − | 0.979447i | \(-0.435352\pi\) | ||||
0.201704 | + | 0.979447i | \(0.435352\pi\) | |||||||
\(180\) | 249.015 | − | 109.413i | 1.38342 | − | 0.607850i | ||||
\(181\) | 140.980i | 0.778895i | 0.921049 | + | 0.389448i | \(0.127334\pi\) | ||||
−0.921049 | + | 0.389448i | \(0.872666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 393.847i | 2.15217i | ||||||||
\(184\) | 125.400 | + | 20.8052i | 0.681522 | + | 0.113072i | ||||
\(185\) | −310.437 | −1.67804 | ||||||||
\(186\) | 113.215 | − | 173.407i | 0.608685 | − | 0.932296i | ||||
\(187\) | −45.1987 | −0.241704 | ||||||||
\(188\) | 79.2419 | − | 34.8176i | 0.421499 | − | 0.185200i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 78.7703 | − | 120.649i | 0.414581 | − | 0.634995i | ||||
\(191\) | − | 284.473i | − | 1.48939i | −0.667407 | − | 0.744693i | \(-0.732596\pi\) | ||
0.667407 | − | 0.744693i | \(-0.267404\pi\) | |||||||
\(192\) | 276.656 | + | 94.3989i | 1.44092 | + | 0.491661i | ||||
\(193\) | −123.850 | −0.641710 | −0.320855 | − | 0.947128i | \(-0.603970\pi\) | ||||
−0.320855 | + | 0.947128i | \(0.603970\pi\) | |||||||
\(194\) | −87.2388 | − | 56.9572i | −0.449685 | − | 0.293594i | ||||
\(195\) | −499.629 | −2.56220 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 108.098i | 0.548721i | 0.961627 | + | 0.274361i | \(0.0884662\pi\) | ||||
−0.961627 | + | 0.274361i | \(0.911534\pi\) | |||||||
\(198\) | 27.8233 | + | 18.1655i | 0.140522 | + | 0.0917451i | ||||
\(199\) | − | 331.854i | − | 1.66761i | −0.552060 | − | 0.833804i | \(-0.686158\pi\) | ||
0.552060 | − | 0.833804i | \(-0.313842\pi\) | |||||||
\(200\) | −10.2941 | + | 62.0462i | −0.0514706 | + | 0.310231i | ||||
\(201\) | −523.079 | −2.60238 | ||||||||
\(202\) | −100.016 | + | 153.189i | −0.495127 | + | 0.758363i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −237.163 | − | 539.762i | −1.16256 | − | 2.64589i | ||||
\(205\) | − | 43.5446i | − | 0.212413i | ||||||
\(206\) | −43.5044 | + | 66.6338i | −0.211187 | + | 0.323465i | ||||
\(207\) | 188.476i | 0.910510i | ||||||||
\(208\) | −224.884 | − | 206.503i | −1.08117 | − | 0.992805i | ||||
\(209\) | 17.6026 | 0.0842229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3950 | 0.125095 | 0.0625475 | − | 0.998042i | \(-0.480078\pi\) | ||||
0.0625475 | + | 0.998042i | \(0.480078\pi\) | |||||||
\(212\) | −1.30615 | + | 0.573900i | −0.00616108 | + | 0.00270708i | ||||
\(213\) | 478.633i | 2.24710i | ||||||||
\(214\) | −138.434 | − | 90.3818i | −0.646887 | − | 0.422345i | ||||
\(215\) | 119.511i | 0.555864i | ||||||||
\(216\) | −17.1152 | + | 103.159i | −0.0792371 | + | 0.477589i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −32.2238 | + | 49.3558i | −0.147816 | + | 0.226403i | ||||
\(219\) | −111.434 | −0.508833 | ||||||||
\(220\) | −29.4038 | + | 12.9195i | −0.133654 | + | 0.0587252i | ||||
\(221\) | 615.777i | 2.78632i | ||||||||
\(222\) | 270.442 | − | 414.223i | 1.21821 | − | 1.86587i | ||||
\(223\) | 161.183i | 0.722796i | 0.932412 | + | 0.361398i | \(0.117700\pi\) | ||||
−0.932412 | + | 0.361398i | \(0.882300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.2551 | −0.414467 | ||||||||
\(226\) | −266.497 | − | 173.993i | −1.17919 | − | 0.769879i | ||||
\(227\) | 171.279 | 0.754533 | 0.377266 | − | 0.926105i | \(-0.376864\pi\) | ||||
0.377266 | + | 0.926105i | \(0.376864\pi\) | |||||||
\(228\) | 92.3627 | + | 210.210i | 0.405100 | + | 0.921973i | ||||
\(229\) | − | 229.251i | − | 1.00110i | −0.865709 | − | 0.500548i | \(-0.833132\pi\) | ||
0.865709 | − | 0.500548i | \(-0.166868\pi\) | |||||||
\(230\) | −152.539 | − | 99.5908i | −0.663212 | − | 0.433003i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.9804 | − | 4.31042i | −0.111984 | − | 0.0185794i | ||||
\(233\) | −270.154 | −1.15946 | −0.579730 | − | 0.814808i | \(-0.696842\pi\) | ||||
−0.579730 | + | 0.814808i | \(0.696842\pi\) | |||||||
\(234\) | 247.483 | − | 379.059i | 1.05762 | − | 1.61991i | ||||
\(235\) | −124.043 | −0.527841 | ||||||||
\(236\) | −43.2167 | − | 98.3576i | −0.183122 | − | 0.416770i | ||||
\(237\) | − | 534.978i | − | 2.25729i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 157.155i | − | 0.657551i | −0.944408 | − | 0.328776i | \(-0.893364\pi\) | ||
0.944408 | − | 0.328776i | \(-0.106636\pi\) | |||||||
\(240\) | −308.570 | − | 283.350i | −1.28571 | − | 1.18062i | ||||
\(241\) | 97.7124 | 0.405445 | 0.202723 | − | 0.979236i | \(-0.435021\pi\) | ||||
0.202723 | + | 0.979236i | \(0.435021\pi\) | |||||||
\(242\) | 199.350 | + | 130.153i | 0.823761 | + | 0.537824i | ||||
\(243\) | 332.558 | 1.36855 | ||||||||
\(244\) | 315.778 | − | 138.747i | 1.29417 | − | 0.568637i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 58.1025 | + | 37.9345i | 0.236189 | + | 0.154205i | ||||
\(247\) | − | 239.814i | − | 0.970906i | ||||||
\(248\) | −178.918 | − | 29.6844i | −0.721444 | − | 0.119695i | ||||
\(249\) | 362.066 | 1.45408 | ||||||||
\(250\) | −107.419 | + | 164.528i | −0.429675 | + | 0.658114i | ||||
\(251\) | 313.145 | 1.24759 | 0.623796 | − | 0.781587i | \(-0.285590\pi\) | ||||
0.623796 | + | 0.781587i | \(0.285590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.2553i | − | 0.0879655i | ||||||
\(254\) | 17.5852 | − | 26.9345i | 0.0692331 | − | 0.106041i | ||||
\(255\) | 844.927i | 3.31344i | ||||||||
\(256\) | −21.7757 | − | 255.072i | −0.0850614 | − | 0.996376i | ||||
\(257\) | 348.855 | 1.35741 | 0.678707 | − | 0.734409i | \(-0.262541\pi\) | ||||
0.678707 | + | 0.734409i | \(0.262541\pi\) | |||||||
\(258\) | −159.466 | − | 104.113i | −0.618084 | − | 0.403540i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 176.013 | + | 400.591i | 0.676973 | + | 1.54073i | ||||
\(261\) | − | 39.0484i | − | 0.149611i | ||||||
\(262\) | −197.839 | − | 129.167i | −0.755109 | − | 0.493002i | ||||
\(263\) | − | 384.364i | − | 1.46146i | −0.682667 | − | 0.730729i | \(-0.739180\pi\) | ||
0.682667 | − | 0.730729i | \(-0.260820\pi\) | |||||||
\(264\) | 8.37668 | − | 50.4891i | 0.0317299 | − | 0.191247i | ||||
\(265\) | 2.04460 | 0.00771548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1530 | 0.0455170 | ||||||||
\(268\) | 184.274 | + | 419.392i | 0.687589 | + | 1.56490i | ||||
\(269\) | 37.7613i | 0.140376i | 0.997534 | + | 0.0701882i | \(0.0223600\pi\) | ||||
−0.997534 | + | 0.0701882i | \(0.977640\pi\) | |||||||
\(270\) | 81.9275 | − | 125.485i | 0.303435 | − | 0.464758i | ||||
\(271\) | − | 308.730i | − | 1.13922i | −0.821914 | − | 0.569612i | \(-0.807093\pi\) | ||
0.821914 | − | 0.569612i | \(-0.192907\pi\) | |||||||
\(272\) | −349.219 | + | 380.303i | −1.28389 | + | 1.39817i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.1048 | + | 20.9609i | 0.117171 | + | 0.0764995i | ||||
\(275\) | 11.0116 | 0.0400422 | ||||||||
\(276\) | 265.772 | − | 116.776i | 0.962943 | − | 0.423101i | ||||
\(277\) | − | 244.210i | − | 0.881623i | −0.897600 | − | 0.440812i | \(-0.854691\pi\) | ||
0.897600 | − | 0.440812i | \(-0.145309\pi\) | |||||||
\(278\) | 175.763 | + | 114.754i | 0.632241 | + | 0.412783i | ||||
\(279\) | − | 268.913i | − | 0.963845i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 266.569 | 0.948646 | 0.474323 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474323 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(282\) | 108.061 | − | 165.513i | 0.383196 | − | 0.586925i | ||||
\(283\) | −165.605 | −0.585177 | −0.292589 | − | 0.956238i | \(-0.594517\pi\) | ||||
−0.292589 | + | 0.956238i | \(0.594517\pi\) | |||||||
\(284\) | 383.757 | − | 168.616i | 1.35126 | − | 0.593719i | ||||
\(285\) | − | 329.056i | − | 1.15458i | ||||||
\(286\) | −29.2229 | + | 44.7595i | −0.102178 | + | 0.156502i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 367.817 | − | 93.7535i | 1.27714 | − | 0.325533i | ||||
\(289\) | 752.346 | 2.60327 | ||||||||
\(290\) | 31.6030 | + | 20.6332i | 0.108976 | + | 0.0711490i | ||||
\(291\) | −237.933 | −0.817641 | ||||||||
\(292\) | 39.2570 | + | 89.3456i | 0.134442 | + | 0.305978i | ||||
\(293\) | 34.3652i | 0.117288i | 0.998279 | + | 0.0586438i | \(0.0186776\pi\) | ||||
−0.998279 | + | 0.0586438i | \(0.981322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 153.966i | 0.521918i | ||||||||
\(296\) | −427.388 | − | 70.9081i | −1.44388 | − | 0.239554i | ||||
\(297\) | 18.3081 | 0.0616434 | ||||||||
\(298\) | −90.0838 | + | 137.977i | −0.302295 | + | 0.463011i | ||||
\(299\) | −303.201 | −1.01405 | ||||||||
\(300\) | 57.7791 | + | 131.500i | 0.192597 | + | 0.438335i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −63.1309 | + | 96.6947i | −0.209043 | + | 0.320181i | ||||
\(303\) | 417.806i | 1.37890i | ||||||||
\(304\) | 136.003 | − | 148.109i | 0.447379 | − | 0.487199i | ||||
\(305\) | −494.308 | −1.62068 | ||||||||
\(306\) | −641.030 | − | 418.521i | −2.09487 | − | 1.36772i | ||||
\(307\) | 222.934 | 0.726170 | 0.363085 | − | 0.931756i | \(-0.381724\pi\) | ||||
0.363085 | + | 0.931756i | \(0.381724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 181.736i | 0.588141i | ||||||||
\(310\) | 217.639 | + | 142.094i | 0.702061 | + | 0.458367i | ||||
\(311\) | 419.934i | 1.35027i | 0.737694 | + | 0.675135i | \(0.235915\pi\) | ||||
−0.737694 | + | 0.675135i | \(0.764085\pi\) | |||||||
\(312\) | −687.853 | − | 114.122i | −2.20466 | − | 0.365776i | ||||
\(313\) | 293.869 | 0.938878 | 0.469439 | − | 0.882965i | \(-0.344456\pi\) | ||||
0.469439 | + | 0.882965i | \(0.344456\pi\) | |||||||
\(314\) | −4.07802 | + | 6.24612i | −0.0129873 | + | 0.0198921i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −428.933 | + | 188.466i | −1.35738 | + | 0.596411i | ||||
\(317\) | − | 423.461i | − | 1.33584i | −0.744234 | − | 0.667919i | \(-0.767185\pi\) | ||
0.744234 | − | 0.667919i | \(-0.232815\pi\) | |||||||
\(318\) | −1.78118 | + | 2.72816i | −0.00560120 | + | 0.00857911i | ||||
\(319\) | 4.61085i | 0.0144541i | ||||||||
\(320\) | −118.478 | + | 347.225i | −0.370243 | + | 1.08508i | ||||
\(321\) | −377.561 | −1.17620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −405.551 | −1.25558 | ||||||||
\(324\) | −75.7127 | − | 172.316i | −0.233681 | − | 0.531839i | ||||
\(325\) | − | 150.020i | − | 0.461599i | ||||||
\(326\) | −130.134 | − | 84.9627i | −0.399183 | − | 0.260622i | ||||
\(327\) | 134.612i | 0.411658i | ||||||||
\(328\) | 9.94618 | − | 59.9491i | 0.0303237 | − | 0.182772i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −40.0977 | + | 61.4158i | −0.121508 | + | 0.186109i | ||||
\(331\) | −126.666 | −0.382678 | −0.191339 | − | 0.981524i | \(-0.561283\pi\) | ||||
−0.191339 | + | 0.981524i | \(0.561283\pi\) | |||||||
\(332\) | −127.551 | − | 290.296i | −0.384191 | − | 0.874386i | ||||
\(333\) | − | 642.361i | − | 1.92901i | ||||||
\(334\) | −67.8807 | + | 103.970i | −0.203236 | + | 0.311287i | ||||
\(335\) | − | 656.503i | − | 1.95971i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 302.404 | 0.897341 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(338\) | 326.773 | + | 213.346i | 0.966785 | + | 0.631202i | ||||
\(339\) | −726.838 | −2.14406 | ||||||||
\(340\) | 677.442 | − | 297.657i | 1.99248 | − | 0.875462i | ||||
\(341\) | 31.7533i | 0.0931183i | ||||||||
\(342\) | 249.648 | + | 162.992i | 0.729966 | + | 0.476586i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.2979 | + | 164.534i | −0.0793542 | + | 0.478295i | ||||
\(345\) | −416.031 | −1.20589 | ||||||||
\(346\) | 213.879 | − | 327.589i | 0.618148 | − | 0.946790i | ||||
\(347\) | 320.532 | 0.923724 | 0.461862 | − | 0.886952i | \(-0.347182\pi\) | ||||
0.461862 | + | 0.886952i | \(0.347182\pi\) | |||||||
\(348\) | −55.0627 | + | 24.1936i | −0.158226 | + | 0.0695219i | ||||
\(349\) | 380.678i | 1.09077i | 0.838186 | + | 0.545385i | \(0.183616\pi\) | ||||
−0.838186 | + | 0.545385i | \(0.816384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 249.426i | − | 0.710614i | ||||||
\(352\) | −43.4320 | + | 11.0705i | −0.123386 | + | 0.0314502i | ||||
\(353\) | 364.369 | 1.03221 | 0.516104 | − | 0.856526i | \(-0.327382\pi\) | ||||
0.516104 | + | 0.856526i | \(0.327382\pi\) | |||||||
\(354\) | −205.440 | − | 134.129i | −0.580339 | − | 0.378896i | ||||
\(355\) | −600.720 | −1.69217 | ||||||||
\(356\) | −4.28137 | − | 9.74403i | −0.0120263 | − | 0.0273709i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −120.928 | − | 78.9525i | −0.337788 | − | 0.220538i | ||||
\(359\) | − | 111.995i | − | 0.311965i | −0.987760 | − | 0.155982i | \(-0.950146\pi\) | ||
0.987760 | − | 0.155982i | \(-0.0498543\pi\) | |||||||
\(360\) | −536.648 | − | 89.0356i | −1.49069 | − | 0.247321i | ||||
\(361\) | −203.059 | −0.562489 | ||||||||
\(362\) | 154.144 | − | 236.096i | 0.425812 | − | 0.652198i | ||||
\(363\) | 543.704 | 1.49781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 139.859i | − | 0.383174i | ||||||
\(366\) | 430.623 | − | 659.566i | 1.17657 | − | 1.80209i | ||||
\(367\) | − | 439.042i | − | 1.19630i | −0.801384 | − | 0.598150i | \(-0.795903\pi\) | ||
0.801384 | − | 0.598150i | \(-0.204097\pi\) | |||||||
\(368\) | −187.256 | − | 171.951i | −0.508849 | − | 0.467259i | ||||
\(369\) | 90.1030 | 0.244182 | ||||||||
\(370\) | 519.881 | + | 339.424i | 1.40508 | + | 0.917363i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −379.198 | + | 166.613i | −1.01935 | + | 0.447885i | ||||
\(373\) | 254.996i | 0.683637i | 0.939766 | + | 0.341818i | \(0.111043\pi\) | ||||
−0.939766 | + | 0.341818i | \(0.888957\pi\) | |||||||
\(374\) | 75.6931 | + | 49.4191i | 0.202388 | + | 0.132137i | ||||
\(375\) | 448.732i | 1.19662i | ||||||||
\(376\) | −170.773 | − | 28.3330i | −0.454183 | − | 0.0753538i | ||||
\(377\) | 62.8172 | 0.166624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 603.048 | 1.59116 | 0.795578 | − | 0.605852i | \(-0.207167\pi\) | ||||
0.795578 | + | 0.605852i | \(0.207167\pi\) | |||||||
\(380\) | −263.829 | + | 115.922i | −0.694287 | + | 0.305058i | ||||
\(381\) | − | 73.4605i | − | 0.192810i | ||||||
\(382\) | −311.035 | + | 476.399i | −0.814229 | + | 1.24712i | ||||
\(383\) | − | 73.3855i | − | 0.191607i | −0.995400 | − | 0.0958035i | \(-0.969458\pi\) | ||
0.995400 | − | 0.0958035i | \(-0.0305420\pi\) | |||||||
\(384\) | −360.096 | − | 460.577i | −0.937749 | − | 1.19942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 207.408 | + | 135.415i | 0.537328 | + | 0.350815i | ||||
\(387\) | −247.293 | −0.639000 | ||||||||
\(388\) | 83.8209 | + | 190.769i | 0.216033 | + | 0.491674i | ||||
\(389\) | 340.800i | 0.876092i | 0.898953 | + | 0.438046i | \(0.144329\pi\) | ||||
−0.898953 | + | 0.438046i | \(0.855671\pi\) | |||||||
\(390\) | 836.715 | + | 546.282i | 2.14542 | + | 1.40072i | ||||
\(391\) | 512.745i | 1.31137i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −539.581 | −1.37298 | ||||||||
\(394\) | 118.192 | − | 181.029i | 0.299979 | − | 0.459465i | ||||
\(395\) | 671.438 | 1.69984 | ||||||||
\(396\) | −26.7333 | − | 60.8427i | −0.0675082 | − | 0.153643i | ||||
\(397\) | 111.540i | 0.280957i | 0.990084 | + | 0.140478i | \(0.0448640\pi\) | ||||
−0.990084 | + | 0.140478i | \(0.955136\pi\) | |||||||
\(398\) | −362.841 | + | 555.747i | −0.911661 | + | 1.39635i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 85.0791 | − | 92.6518i | 0.212698 | − | 0.231630i | ||||
\(401\) | 340.535 | 0.849215 | 0.424607 | − | 0.905378i | \(-0.360412\pi\) | ||||
0.424607 | + | 0.905378i | \(0.360412\pi\) | |||||||
\(402\) | 875.986 | + | 571.921i | 2.17907 | + | 1.42269i | ||||
\(403\) | 432.600 | 1.07345 | ||||||||
\(404\) | 334.987 | − | 147.188i | 0.829175 | − | 0.364326i | ||||
\(405\) | 269.738i | 0.666019i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 75.8502i | 0.186364i | ||||||||
\(408\) | −192.993 | + | 1163.23i | −0.473021 | + | 2.85106i | ||||
\(409\) | −666.959 | −1.63071 | −0.815354 | − | 0.578963i | \(-0.803457\pi\) | ||||
−0.815354 | + | 0.578963i | \(0.803457\pi\) | |||||||
\(410\) | −47.6106 | + | 72.9230i | −0.116123 | + | 0.177861i | ||||
\(411\) | 87.5620 | 0.213046 | ||||||||
\(412\) | 145.711 | − | 64.0232i | 0.353669 | − | 0.155396i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 206.074 | − | 315.635i | 0.497764 | − | 0.762403i | ||||
\(415\) | 454.420i | 1.09499i | ||||||||
\(416\) | 150.821 | + | 591.708i | 0.362552 | + | 1.42238i | ||||
\(417\) | 479.373 | 1.14958 | ||||||||
\(418\) | −29.4786 | − | 19.2462i | −0.0705229 | − | 0.0460436i | ||||
\(419\) | 200.191 | 0.477783 | 0.238891 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238891 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.9136i | − | 0.0377996i | −0.999821 | − | 0.0188998i | \(-0.993984\pi\) | ||
0.999821 | − | 0.0188998i | \(-0.00601636\pi\) | |||||||
\(422\) | −44.2031 | − | 28.8597i | −0.104747 | − | 0.0683878i | ||||
\(423\) | − | 256.671i | − | 0.606786i | ||||||
\(424\) | 2.81486 | + | 0.467015i | 0.00663882 | + | 0.00110145i | ||||
\(425\) | −253.699 | −0.596940 | ||||||||
\(426\) | 523.325 | − | 801.554i | 1.22846 | − | 1.88158i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 133.010 | + | 302.720i | 0.310771 | + | 0.707290i | ||||
\(429\) | 122.076i | 0.284560i | ||||||||
\(430\) | 130.670 | − | 200.141i | 0.303884 | − | 0.465445i | ||||
\(431\) | 628.013i | 1.45711i | 0.684989 | + | 0.728553i | \(0.259807\pi\) | ||||
−0.684989 | + | 0.728553i | \(0.740193\pi\) | |||||||
\(432\) | 141.454 | − | 154.045i | 0.327440 | − | 0.356585i | ||||
\(433\) | −789.232 | −1.82271 | −0.911353 | − | 0.411625i | \(-0.864961\pi\) | ||||
−0.911353 | + | 0.411625i | \(0.864961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 86.1933 | 0.198146 | ||||||||
\(436\) | 107.929 | − | 47.4221i | 0.247543 | − | 0.108766i | ||||
\(437\) | − | 199.688i | − | 0.456952i | ||||||
\(438\) | 186.616 | + | 121.840i | 0.426065 | + | 0.278173i | ||||
\(439\) | 665.570i | 1.51610i | 0.652194 | + | 0.758052i | \(0.273849\pi\) | ||||
−0.652194 | + | 0.758052i | \(0.726151\pi\) | |||||||
\(440\) | 63.3677 | + | 10.5134i | 0.144017 | + | 0.0238940i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 673.275 | − | 1031.23i | 1.52325 | − | 2.33309i | ||||
\(443\) | 507.152 | 1.14481 | 0.572406 | − | 0.819970i | \(-0.306010\pi\) | ||||
0.572406 | + | 0.819970i | \(0.306010\pi\) | |||||||
\(444\) | −905.802 | + | 397.995i | −2.04010 | + | 0.896384i | ||||
\(445\) | 15.2530i | 0.0342764i | ||||||||
\(446\) | 176.234 | − | 269.930i | 0.395143 | − | 0.605224i | ||||
\(447\) | 376.317i | 0.841872i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −279.029 | −0.621446 | −0.310723 | − | 0.950501i | \(-0.600571\pi\) | ||||
−0.310723 | + | 0.950501i | \(0.600571\pi\) | |||||||
\(450\) | 156.172 | + | 101.963i | 0.347048 | + | 0.226584i | ||||
\(451\) | −10.6394 | −0.0235907 | ||||||||
\(452\) | 256.056 | + | 582.761i | 0.566495 | + | 1.28930i | ||||
\(453\) | 263.723i | 0.582171i | ||||||||
\(454\) | −286.836 | − | 187.272i | −0.631798 | − | 0.412494i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 75.1608 | − | 453.020i | 0.164826 | − | 0.993465i | ||||
\(457\) | −720.881 | −1.57742 | −0.788710 | − | 0.614765i | \(-0.789251\pi\) | ||||
−0.788710 | + | 0.614765i | \(0.789251\pi\) | |||||||
\(458\) | −250.657 | + | 383.921i | −0.547287 | + | 0.838255i | ||||
\(459\) | −421.805 | −0.918966 | ||||||||
\(460\) | 146.563 | + | 333.564i | 0.318614 | + | 0.725139i | ||||
\(461\) | 483.262i | 1.04829i | 0.851629 | + | 0.524145i | \(0.175615\pi\) | ||||
−0.851629 | + | 0.524145i | \(0.824385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6326i | 0.0855995i | 0.999084 | + | 0.0427997i | \(0.0136277\pi\) | ||||
−0.999084 | + | 0.0427997i | \(0.986372\pi\) | |||||||
\(464\) | 38.7958 | + | 35.6249i | 0.0836116 | + | 0.0767777i | ||||
\(465\) | 593.584 | 1.27652 | ||||||||
\(466\) | 452.420 | + | 295.380i | 0.970859 | + | 0.633863i | ||||
\(467\) | −17.7868 | −0.0380874 | −0.0190437 | − | 0.999819i | \(-0.506062\pi\) | ||||
−0.0190437 | + | 0.999819i | \(0.506062\pi\) | |||||||
\(468\) | −828.907 | + | 364.208i | −1.77117 | + | 0.778222i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 207.731 | + | 135.625i | 0.441981 | + | 0.288564i | ||||
\(471\) | 17.0355i | 0.0361689i | ||||||||
\(472\) | −35.1679 | + | 211.969i | −0.0745083 | + | 0.449087i | ||||
\(473\) | 29.2005 | 0.0617346 | ||||||||
\(474\) | −584.932 | + | 895.914i | −1.23403 | + | 1.89011i | ||||
\(475\) | 98.8029 | 0.208006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.23072i | 0.00886943i | ||||||||
\(478\) | −171.829 | + | 263.183i | −0.359475 | + | 0.550592i | ||||
\(479\) | − | 668.616i | − | 1.39586i | −0.716166 | − | 0.697930i | \(-0.754105\pi\) | ||
0.716166 | − | 0.697930i | \(-0.245895\pi\) | |||||||
\(480\) | 206.947 | + | 811.901i | 0.431139 | + | 1.69146i | ||||
\(481\) | 1033.37 | 2.14837 | ||||||||
\(482\) | −163.636 | − | 106.836i | −0.339494 | − | 0.221652i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −191.540 | − | 435.929i | −0.395744 | − | 0.900679i | ||||
\(485\) | − | 298.624i | − | 0.615720i | ||||||
\(486\) | −556.926 | − | 363.611i | −1.14594 | − | 0.748170i | ||||
\(487\) | − | 418.484i | − | 0.859311i | −0.902993 | − | 0.429656i | \(-0.858635\pi\) | ||
0.902993 | − | 0.429656i | \(-0.141365\pi\) | |||||||
\(488\) | −680.527 | − | 112.907i | −1.39452 | − | 0.231366i | ||||
\(489\) | −354.924 | −0.725816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 381.031 | 0.776030 | 0.388015 | − | 0.921653i | \(-0.373161\pi\) | ||||
0.388015 | + | 0.921653i | \(0.373161\pi\) | |||||||
\(492\) | −55.8261 | − | 127.056i | −0.113468 | − | 0.258243i | ||||
\(493\) | − | 106.231i | − | 0.215478i | ||||||
\(494\) | −262.206 | + | 401.610i | −0.530782 | + | 0.812975i | ||||
\(495\) | 95.2412i | 0.192406i | ||||||||
\(496\) | 267.173 | + | 245.336i | 0.538656 | + | 0.494629i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −606.342 | − | 395.874i | −1.21756 | − | 0.794928i | ||||
\(499\) | −438.392 | −0.878541 | −0.439271 | − | 0.898355i | \(-0.644763\pi\) | ||||
−0.439271 | + | 0.898355i | \(0.644763\pi\) | |||||||
\(500\) | 359.783 | − | 158.083i | 0.719565 | − | 0.316165i | ||||
\(501\) | 283.565i | 0.565999i | ||||||||
\(502\) | −524.416 | − | 342.385i | −1.04465 | − | 0.682043i | ||||
\(503\) | − | 754.754i | − | 1.50050i | −0.661151 | − | 0.750252i | \(-0.729932\pi\) | ||
0.661151 | − | 0.750252i | \(-0.270068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −524.378 | −1.03837 | ||||||||
\(506\) | −24.3334 | + | 37.2703i | −0.0480896 | + | 0.0736568i | ||||
\(507\) | 891.235 | 1.75786 | ||||||||
\(508\) | −58.8989 | + | 25.8792i | −0.115943 | + | 0.0509433i | ||||
\(509\) | 494.029i | 0.970588i | 0.874351 | + | 0.485294i | \(0.161287\pi\) | ||||
−0.874351 | + | 0.485294i | \(0.838713\pi\) | |||||||
\(510\) | 923.822 | − | 1414.98i | 1.81141 | − | 2.77446i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −242.422 | + | 450.972i | −0.473481 | + | 0.880804i | ||||
\(513\) | 164.272 | 0.320218 | ||||||||
\(514\) | −584.219 | − | 381.430i | −1.13661 | − | 0.742081i | ||||
\(515\) | −228.092 | −0.442897 | ||||||||
\(516\) | 153.218 | + | 348.711i | 0.296934 | + | 0.675797i | ||||
\(517\) | 30.3078i | 0.0586224i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 893.460i | − | 1.72150i | ||||||
\(520\) | 143.232 | − | 863.307i | 0.275446 | − | 1.66021i | ||||
\(521\) | 32.8747 | 0.0630993 | 0.0315496 | − | 0.999502i | \(-0.489956\pi\) | ||||
0.0315496 | + | 0.999502i | \(0.489956\pi\) | |||||||
\(522\) | −42.6945 | + | 65.3932i | −0.0817902 | + | 0.125274i | ||||
\(523\) | 28.2755 | 0.0540640 | 0.0270320 | − | 0.999635i | \(-0.491394\pi\) | ||||
0.0270320 | + | 0.999635i | \(0.491394\pi\) | |||||||
\(524\) | 190.088 | + | 432.624i | 0.362763 | + | 0.825617i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −420.254 | + | 643.684i | −0.798961 | + | 1.22373i | ||||
\(527\) | − | 731.574i | − | 1.38819i | ||||||
\(528\) | −69.2318 | + | 75.3940i | −0.131121 | + | 0.142792i | ||||
\(529\) | 276.531 | 0.522742 | ||||||||
\(530\) | −3.42404 | − | 2.23552i | −0.00646046 | − | 0.00421796i | ||||
\(531\) | −318.588 | −0.599977 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 144.949i | 0.271949i | ||||||||
\(534\) | −20.3524 | − | 13.2878i | −0.0381131 | − | 0.0248836i | ||||
\(535\) | − | 473.868i | − | 0.885735i | ||||||
\(536\) | 149.954 | − | 903.825i | 0.279765 | − | 1.68624i | ||||
\(537\) | −329.817 | −0.614183 | ||||||||
\(538\) | 41.2872 | − | 63.2378i | 0.0767420 | − | 0.117542i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −274.404 | + | 120.568i | −0.508155 | + | 0.223275i | ||||
\(541\) | 1071.59i | 1.98077i | 0.138352 | + | 0.990383i | \(0.455820\pi\) | ||||
−0.138352 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(542\) | −337.558 | + | 517.022i | −0.622800 | + | 0.953915i | ||||
\(543\) | − | 643.922i | − | 1.18586i | ||||||
\(544\) | 1000.64 | − | 255.055i | 1.83942 | − | 0.468852i | ||||
\(545\) | −168.948 | −0.309997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −986.888 | −1.80418 | −0.902091 | − | 0.431545i | \(-0.857968\pi\) | ||||
−0.902091 | + | 0.431545i | \(0.857968\pi\) | |||||||
\(548\) | −30.8470 | − | 70.2052i | −0.0562901 | − | 0.128112i | ||||
\(549\) | − | 1022.83i | − | 1.86307i | ||||||
\(550\) | −18.4408 | − | 12.0398i | −0.0335288 | − | 0.0218906i | ||||
\(551\) | 41.3714i | 0.0750842i | ||||||||
\(552\) | −572.761 | − | 95.0272i | −1.03761 | − | 0.172151i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −267.013 | + | 408.971i | −0.481972 | + | 0.738215i | ||||
\(555\) | 1417.91 | 2.55480 | ||||||||
\(556\) | −168.877 | − | 384.350i | −0.303736 | − | 0.691277i | ||||
\(557\) | − | 483.550i | − | 0.868133i | −0.900881 | − | 0.434067i | \(-0.857078\pi\) | ||
0.900881 | − | 0.434067i | \(-0.142922\pi\) | |||||||
\(558\) | −294.022 | + | 450.341i | −0.526922 | + | 0.807062i | ||||
\(559\) | − | 397.821i | − | 0.711665i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 206.444 | 0.367993 | ||||||||
\(562\) | −446.417 | − | 291.460i | −0.794336 | − | 0.518613i | ||||
\(563\) | −520.893 | −0.925210 | −0.462605 | − | 0.886564i | \(-0.653085\pi\) | ||||
−0.462605 | + | 0.886564i | \(0.653085\pi\) | |||||||
\(564\) | −361.935 | + | 159.028i | −0.641729 | + | 0.281965i | ||||
\(565\) | − | 912.236i | − | 1.61458i | ||||||
\(566\) | 277.334 | + | 181.068i | 0.489990 | + | 0.319909i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −827.028 | − | 137.213i | −1.45603 | − | 0.241572i | ||||
\(569\) | −732.959 | −1.28815 | −0.644077 | − | 0.764961i | \(-0.722758\pi\) | ||||
−0.644077 | + | 0.764961i | \(0.722758\pi\) | |||||||
\(570\) | −359.781 | + | 551.061i | −0.631195 | + | 0.966773i | ||||
\(571\) | −999.584 | −1.75058 | −0.875292 | − | 0.483595i | \(-0.839331\pi\) | ||||
−0.875292 | + | 0.483595i | \(0.839331\pi\) | |||||||
\(572\) | 97.8777 | − | 43.0059i | 0.171115 | − | 0.0751851i | ||||
\(573\) | 1299.32i | 2.26758i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 124.918i | − | 0.217249i | ||||||
\(576\) | −718.481 | − | 245.155i | −1.24736 | − | 0.425617i | ||||
\(577\) | −465.859 | −0.807381 | −0.403690 | − | 0.914896i | \(-0.632273\pi\) | ||||
−0.403690 | + | 0.914896i | \(0.632273\pi\) | |||||||
\(578\) | −1259.93 | − | 822.596i | −2.17982 | − | 1.42318i | ||||
\(579\) | 565.682 | 0.976998 | ||||||||
\(580\) | −30.3648 | − | 69.1078i | −0.0523531 | − | 0.119151i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 398.461 | + | 260.150i | 0.684641 | + | 0.446994i | ||||
\(583\) | − | 0.499565i | − | 0.000856887i | ||||||
\(584\) | 31.9456 | − | 192.547i | 0.0547014 | − | 0.329704i | ||||
\(585\) | 1297.54 | 2.21803 | ||||||||
\(586\) | 37.5741 | − | 57.5506i | 0.0641196 | − | 0.0982092i | ||||
\(587\) | 574.851 | 0.979303 | 0.489651 | − | 0.871918i | \(-0.337124\pi\) | ||||
0.489651 | + | 0.871918i | \(0.337124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 284.911i | 0.483719i | ||||||||
\(590\) | 168.342 | − | 257.843i | 0.285326 | − | 0.437021i | ||||
\(591\) | − | 493.735i | − | 0.835423i | ||||||
\(592\) | 638.205 | + | 586.043i | 1.07805 | + | 0.989937i | ||||
\(593\) | −943.055 | −1.59031 | −0.795156 | − | 0.606405i | \(-0.792611\pi\) | ||||
−0.795156 | + | 0.606405i | \(0.792611\pi\) | |||||||
\(594\) | −30.6601 | − | 20.0176i | −0.0516163 | − | 0.0336997i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 301.722 | − | 132.572i | 0.506245 | − | 0.222436i | ||||
\(597\) | 1515.73i | 2.53892i | ||||||||
\(598\) | 507.763 | + | 331.512i | 0.849101 | + | 0.554368i | ||||
\(599\) | 9.26699i | 0.0154708i | 0.999970 | + | 0.00773538i | \(0.00246227\pi\) | ||||
−0.999970 | + | 0.00773538i | \(0.997538\pi\) | |||||||
\(600\) | 47.0181 | − | 283.394i | 0.0783635 | − | 0.472324i | ||||
\(601\) | −57.7003 | −0.0960072 | −0.0480036 | − | 0.998847i | \(-0.515286\pi\) | ||||
−0.0480036 | + | 0.998847i | \(0.515286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1358.44 | 2.25281 | ||||||||
\(604\) | 211.447 | − | 92.9064i | 0.350078 | − | 0.153819i | ||||
\(605\) | 682.389i | 1.12792i | ||||||||
\(606\) | 456.818 | − | 699.688i | 0.753825 | − | 1.15460i | ||||
\(607\) | 1024.68i | 1.68810i | 0.536264 | + | 0.844050i | \(0.319835\pi\) | ||||
−0.536264 | + | 0.844050i | \(0.680165\pi\) | |||||||
\(608\) | −389.699 | + | 99.3310i | −0.640952 | + | 0.163373i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 827.805 | + | 540.464i | 1.35706 | + | 0.886007i | ||||
\(611\) | 412.906 | 0.675788 | ||||||||
\(612\) | 615.915 | + | 1401.77i | 1.00640 | + | 2.29048i | ||||
\(613\) | − | 404.818i | − | 0.660389i | −0.943913 | − | 0.330195i | \(-0.892886\pi\) | ||
0.943913 | − | 0.330195i | \(-0.107114\pi\) | |||||||
\(614\) | −373.342 | − | 243.750i | −0.608048 | − | 0.396988i | ||||
\(615\) | 198.889i | 0.323396i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 894.209 | 1.44928 | 0.724642 | − | 0.689125i | \(-0.242005\pi\) | ||||
0.724642 | + | 0.689125i | \(0.242005\pi\) | |||||||
\(618\) | 198.705 | − | 304.348i | 0.321530 | − | 0.492472i | ||||
\(619\) | 779.388 | 1.25911 | 0.629554 | − | 0.776957i | \(-0.283238\pi\) | ||||
0.629554 | + | 0.776957i | \(0.283238\pi\) | |||||||
\(620\) | −209.112 | − | 475.922i | −0.337278 | − | 0.767616i | ||||
\(621\) | − | 207.692i | − | 0.334447i | ||||||
\(622\) | 459.145 | − | 703.252i | 0.738176 | − | 1.13063i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1027.15 | + | 943.198i | 1.64607 | + | 1.51154i | ||||
\(625\) | −759.737 | −1.21558 | ||||||||
\(626\) | −492.134 | − | 321.309i | −0.786157 | − | 0.513273i | ||||
\(627\) | −80.3993 | −0.128229 | ||||||||
\(628\) | 13.6587 | − | 6.00140i | 0.0217495 | − | 0.00955638i | ||||
\(629\) | − | 1747.53i | − | 2.77827i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 780.191i | − | 1.23644i | −0.786007 | − | 0.618218i | \(-0.787855\pi\) | ||
0.786007 | − | 0.618218i | \(-0.212145\pi\) | |||||||
\(632\) | 924.387 | + | 153.366i | 1.46264 | + | 0.242667i | ||||
\(633\) | −120.559 | −0.190456 | ||||||||
\(634\) | −463.001 | + | 709.158i | −0.730286 | + | 1.11855i | ||||
\(635\) | 92.1985 | 0.145194 | ||||||||
\(636\) | 5.96580 | − | 2.62127i | 0.00938018 | − | 0.00412150i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.04139 | − | 7.72166i | 0.00790186 | − | 0.0121029i | ||||
\(639\) | − | 1243.02i | − | 1.94525i | ||||||
\(640\) | 578.058 | − | 451.947i | 0.903216 | − | 0.706168i | ||||
\(641\) | −23.3139 | −0.0363712 | −0.0181856 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181856 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(642\) | 632.292 | + | 412.816i | 0.984879 | + | 0.643016i | ||||
\(643\) | −530.706 | −0.825360 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 545.862i | − | 0.846297i | ||||||
\(646\) | 679.165 | + | 443.419i | 1.05134 | + | 0.686407i | ||||
\(647\) | 213.435i | 0.329883i | 0.986303 | + | 0.164942i | \(0.0527436\pi\) | ||||
−0.986303 | + | 0.164942i | \(0.947256\pi\) | |||||||
\(648\) | −61.6117 | + | 371.355i | −0.0950799 | + | 0.573079i | ||||
\(649\) | 37.6190 | 0.0579646 | ||||||||
\(650\) | −164.028 | + | 251.234i | −0.252350 | + | 0.386514i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 125.035 | + | 284.570i | 0.191772 | + | 0.436457i | ||||
\(653\) | 274.874i | 0.420941i | 0.977600 | + | 0.210470i | \(0.0674995\pi\) | ||||
−0.977600 | + | 0.210470i | \(0.932500\pi\) | |||||||
\(654\) | 147.181 | − | 225.431i | 0.225048 | − | 0.344696i | ||||
\(655\) | − | 677.215i | − | 1.03392i | ||||||
\(656\) | −82.2034 | + | 89.5202i | −0.125310 | + | 0.136464i | ||||
\(657\) | 289.397 | 0.440483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1234.48 | 1.87327 | 0.936633 | − | 0.350313i | \(-0.113925\pi\) | ||||
0.936633 | + | 0.350313i | \(0.113925\pi\) | |||||||
\(660\) | 134.301 | − | 59.0096i | 0.203486 | − | 0.0894085i | ||||
\(661\) | 582.733i | 0.881593i | 0.897607 | + | 0.440797i | \(0.145304\pi\) | ||||
−0.897607 | + | 0.440797i | \(0.854696\pi\) | |||||||
\(662\) | 212.125 | + | 138.494i | 0.320430 | + | 0.209205i | ||||
\(663\) | − | 2812.54i | − | 4.24215i | ||||||
\(664\) | −103.796 | + | 625.613i | −0.156319 | + | 0.942188i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −702.341 | + | 1075.74i | −1.05457 | + | 1.61523i | ||||
\(667\) | 52.3066 | 0.0784207 | ||||||||
\(668\) | 227.356 | − | 99.8965i | 0.340353 | − | 0.149546i | ||||
\(669\) | − | 736.201i | − | 1.10045i | ||||||
\(670\) | −717.804 | + | 1099.43i | −1.07135 | + | 1.64094i | ||||
\(671\) | 120.776i | 0.179994i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −399.145 | −0.593083 | −0.296542 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296542 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(674\) | −506.428 | − | 330.641i | −0.751377 | − | 0.490565i | ||||
\(675\) | 102.763 | 0.152241 | ||||||||
\(676\) | −313.971 | − | 714.571i | −0.464454 | − | 1.05706i | ||||
\(677\) | − | 754.467i | − | 1.11443i | −0.830369 | − | 0.557214i | \(-0.811870\pi\) | ||
0.830369 | − | 0.557214i | \(-0.188130\pi\) | |||||||
\(678\) | 1217.22 | + | 794.706i | 1.79530 | + | 1.17213i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1459.95 | − | 242.220i | −2.14698 | − | 0.356206i | ||||
\(681\) | −782.312 | −1.14877 | ||||||||
\(682\) | 34.7183 | − | 53.1765i | 0.0509066 | − | 0.0779713i | ||||
\(683\) | 288.264 | 0.422055 | 0.211028 | − | 0.977480i | \(-0.432319\pi\) | ||||
0.211028 | + | 0.977480i | \(0.432319\pi\) | |||||||
\(684\) | −239.867 | − | 545.918i | −0.350683 | − | 0.798126i | ||||
\(685\) | 109.897i | 0.160433i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1047.10i | 1.52416i | ||||||||
\(688\) | 225.612 | − | 245.693i | 0.327924 | − | 0.357112i | ||||
\(689\) | −6.80596 | −0.00987803 | ||||||||
\(690\) | 696.716 | + | 454.878i | 1.00973 | + | 0.659244i | ||||
\(691\) | 156.692 | 0.226761 | 0.113380 | − | 0.993552i | \(-0.463832\pi\) | ||||
0.113380 | + | 0.993552i | \(0.463832\pi\) | |||||||
\(692\) | −716.356 | + | 314.755i | −1.03520 | + | 0.454848i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −536.787 | − | 350.462i | −0.773468 | − | 0.504988i | ||||
\(695\) | 601.649i | 0.865682i | ||||||||
\(696\) | 118.665 | + | 19.6877i | 0.170495 | + | 0.0282870i | ||||
\(697\) | 245.124 | 0.351685 | ||||||||
\(698\) | 416.224 | − | 637.512i | 0.596310 | − | 0.913341i | ||||
\(699\) | 1233.92 | 1.76527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1126.50i | − | 1.60700i | −0.595307 | − | 0.803498i | \(-0.702970\pi\) | ||
0.595307 | − | 0.803498i | \(-0.297030\pi\) | |||||||
\(702\) | −272.716 | + | 417.706i | −0.388484 | + | 0.595023i | ||||
\(703\) | 680.575i | 0.968102i | ||||||||
\(704\) | 84.8386 | + | 28.9481i | 0.120509 | + | 0.0411194i | ||||
\(705\) | 566.562 | 0.803633 | ||||||||
\(706\) | −610.200 | − | 398.392i | −0.864306 | − | 0.564295i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 197.391 | + | 449.246i | 0.278801 | + | 0.634528i | ||||
\(709\) | − | 1096.17i | − | 1.54608i | −0.634356 | − | 0.773041i | \(-0.718734\pi\) | ||
0.634356 | − | 0.773041i | \(-0.281266\pi\) | |||||||
\(710\) | 1006.01 | + | 656.812i | 1.41692 | + | 0.925088i | ||||
\(711\) | 1389.35i | 1.95407i | ||||||||
\(712\) | −3.48399 | + | 20.9992i | −0.00489325 | + | 0.0294933i | ||||
\(713\) | 360.218 | 0.505214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −153.215 | −0.214286 | ||||||||
\(716\) | 116.190 | + | 264.439i | 0.162277 | + | 0.369328i | ||||
\(717\) | 717.800i | 1.00112i | ||||||||
\(718\) | −122.453 | + | 187.556i | −0.170547 | + | 0.261220i | ||||
\(719\) | − | 605.362i | − | 0.841949i | −0.907072 | − | 0.420975i | \(-0.861688\pi\) | ||
0.907072 | − | 0.420975i | \(-0.138312\pi\) | |||||||
\(720\) | 801.361 | + | 735.863i | 1.11300 | + | 1.02203i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 340.057 | + | 222.019i | 0.470993 | + | 0.307506i | ||||
\(723\) | −446.298 | −0.617287 | ||||||||
\(724\) | −516.282 | + | 226.846i | −0.713097 | + | 0.313323i | ||||
\(725\) | 25.8806i | 0.0356974i | ||||||||
\(726\) | −910.526 | − | 594.472i | −1.25417 | − | 0.818832i | ||||
\(727\) | 443.659i | 0.610260i | 0.952311 | + | 0.305130i | \(0.0986999\pi\) | ||||
−0.952311 | + | 0.305130i | \(0.901300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1095.46 | −1.50269 | ||||||||
\(730\) | −152.918 | + | 234.218i | −0.209477 | + | 0.320846i | ||||
\(731\) | −672.757 | −0.920325 | ||||||||
\(732\) | −1442.31 | + | 633.725i | −1.97036 | + | 0.865744i | ||||
\(733\) | − | 750.026i | − | 1.02323i | −0.859216 | − | 0.511614i | \(-0.829048\pi\) | ||
0.859216 | − | 0.511614i | \(-0.170952\pi\) | |||||||
\(734\) | −480.038 | + | 735.252i | −0.654002 | + | 1.00171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 125.586 | + | 492.704i | 0.170633 | + | 0.669434i | ||||
\(737\) | −160.406 | −0.217647 | ||||||||
\(738\) | −150.893 | − | 98.5164i | −0.204462 | − | 0.133491i | ||||
\(739\) | 619.293 | 0.838015 | 0.419007 | − | 0.907983i | \(-0.362378\pi\) | ||||
0.419007 | + | 0.907983i | \(0.362378\pi\) | |||||||
\(740\) | −499.513 | − | 1136.85i | −0.675018 | − | 1.53628i | ||||
\(741\) | 1095.34i | 1.47819i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.5255i | − | 0.0410842i | −0.999789 | − | 0.0205421i | \(-0.993461\pi\) | ||
0.999789 | − | 0.0205421i | \(-0.00653921\pi\) | |||||||
\(744\) | 817.203 | + | 135.583i | 1.09839 | + | 0.182235i | ||||
\(745\) | −472.306 | −0.633967 | ||||||||
\(746\) | 278.807 | − | 427.036i | 0.373736 | − | 0.572434i | ||||
\(747\) | −940.291 | −1.25876 | ||||||||
\(748\) | −72.7275 | − | 165.522i | −0.0972293 | − | 0.221286i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 490.632 | − | 751.479i | 0.654176 | − | 1.00197i | ||||
\(751\) | 968.214i | 1.28923i | 0.764506 | + | 0.644616i | \(0.222983\pi\) | ||||
−0.764506 | + | 0.644616i | \(0.777017\pi\) | |||||||
\(752\) | 255.010 | + | 234.167i | 0.339109 | + | 0.311393i | ||||
\(753\) | −1430.28 | −1.89945 | ||||||||
\(754\) | −105.198 | − | 68.6827i | −0.139520 | − | 0.0910911i | ||||
\(755\) | −330.993 | −0.438401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1171.15i | 1.54710i | 0.633736 | + | 0.773550i | \(0.281521\pi\) | ||||
−0.633736 | + | 0.773550i | \(0.718479\pi\) | |||||||
\(758\) | −1009.91 | − | 659.357i | −1.33233 | − | 0.869865i | ||||
\(759\) | 101.650i | 0.133927i | ||||||||
\(760\) | 568.574 | + | 94.3325i | 0.748124 | + | 0.124122i | ||||
\(761\) | −235.996 | −0.310113 | −0.155057 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155057 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(762\) | −80.3199 | + | 123.022i | −0.105407 | + | 0.161447i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1041.77 | − | 457.734i | 1.36357 | − | 0.599129i | ||||
\(765\) | − | 2194.29i | − | 2.86835i | ||||||
\(766\) | −80.2379 | + | 122.897i | −0.104749 | + | 0.160440i | ||||
\(767\) | − | 512.513i | − | 0.668205i | ||||||
\(768\) | 99.4599 | + | 1165.03i | 0.129505 | + | 1.51697i | ||||
\(769\) | 124.257 | 0.161582 | 0.0807912 | − | 0.996731i | \(-0.474255\pi\) | ||||
0.0807912 | + | 0.996731i | \(0.474255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1593.39 | −2.06665 | ||||||||
\(772\) | −199.283 | − | 453.550i | −0.258138 | − | 0.587501i | ||||
\(773\) | 178.223i | 0.230560i | 0.993333 | + | 0.115280i | \(0.0367765\pi\) | ||||
−0.993333 | + | 0.115280i | \(0.963224\pi\) | |||||||
\(774\) | 414.135 | + | 270.384i | 0.535058 | + | 0.349333i | ||||
\(775\) | 178.231i | 0.229975i | ||||||||
\(776\) | 68.2099 | − | 411.124i | 0.0878993 | − | 0.529799i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 372.622 | − | 570.728i | 0.478948 | − | 0.733584i | ||||
\(779\) | −95.4634 | −0.122546 | ||||||||
\(780\) | −803.934 | − | 1829.69i | −1.03068 | − | 2.34575i | ||||
\(781\) | 146.776i | 0.187933i | ||||||||
\(782\) | 560.623 | − | 858.681i | 0.716909 | − | 1.09806i | ||||
\(783\) | 43.0296i | 0.0549548i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3809 | −0.0272368 | ||||||||
\(786\) | 903.622 | + | 589.964i | 1.14965 | + | 0.750591i | ||||
\(787\) | 1107.90 | 1.40775 | 0.703873 | − | 0.710326i | \(-0.251453\pi\) | ||||
0.703873 | + | 0.710326i | \(0.251453\pi\) | |||||||
\(788\) | −395.865 | + | 173.937i | −0.502367 | + | 0.220732i | ||||
\(789\) | 1755.57i | 2.22506i | ||||||||
\(790\) | −1124.44 | − | 734.133i | −1.42334 | − | 0.929283i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −21.7544 | + | 131.121i | −0.0274676 | + | 0.165557i | ||||
\(793\) | 1645.43 | 2.07494 | ||||||||
\(794\) | 121.955 | − | 186.793i | 0.153595 | − | 0.235255i | ||||
\(795\) | −9.33867 | −0.0117468 | ||||||||
\(796\) | 1215.28 | − | 533.974i | 1.52673 | − | 0.670821i | ||||
\(797\) | − | 1094.69i | − | 1.37351i | −0.726889 | − | 0.686755i | \(-0.759034\pi\) | ||
0.726889 | − | 0.686755i | \(-0.240966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 698.269i | − | 0.873929i | ||||||
\(800\) | −243.783 | + | 62.1382i | −0.304729 | + | 0.0776728i | ||||
\(801\) | −31.5617 | −0.0394028 | ||||||||
\(802\) | −570.285 | − | 372.332i | −0.711079 | − | 0.464255i | ||||
\(803\) | −34.1722 | −0.0425556 | ||||||||
\(804\) | −841.666 | − | 1915.56i | −1.04685 | − | 2.38254i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −724.464 | − | 472.994i | −0.898839 | − | 0.586842i | ||||
\(807\) | − | 172.473i | − | 0.213722i | ||||||
\(808\) | −721.925 | − | 119.775i | −0.893471 | − | 0.148236i | ||||
\(809\) | −1386.75 | −1.71416 | −0.857079 | − | 0.515185i | \(-0.827723\pi\) | ||||
−0.857079 | + | 0.515185i | \(0.827723\pi\) | |||||||
\(810\) | 294.924 | − | 451.723i | 0.364104 | − | 0.557682i | ||||
\(811\) | 312.204 | 0.384962 | 0.192481 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192481 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1410.11i | 1.73446i | ||||||||
\(814\) | 82.9328 | − | 127.024i | 0.101883 | − | 0.156050i | ||||
\(815\) | − | 445.456i | − | 0.546572i | ||||||
\(816\) | 1595.05 | − | 1737.02i | 1.95472 | − | 2.12870i | ||||
\(817\) | 262.005 | 0.320691 | ||||||||
\(818\) | 1116.94 | + | 729.237i | 1.36545 | + | 0.891487i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 159.464 | − | 70.0660i | 0.194469 | − | 0.0854464i | ||||
\(821\) | 1092.89i | 1.33117i | 0.746324 | + | 0.665583i | \(0.231817\pi\) | ||||
−0.746324 | + | 0.665583i | \(0.768183\pi\) | |||||||
\(822\) | −146.638 | − | 95.7381i | −0.178391 | − | 0.116470i | ||||
\(823\) | 907.162i | 1.10226i | 0.834419 | + | 0.551131i | \(0.185804\pi\) | ||||
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(824\) | −314.020 | − | 52.0993i | −0.381093 | − | 0.0632273i | ||||
\(825\) | −50.2952 | −0.0609638 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −607.144 | −0.734152 | −0.367076 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367076 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(828\) | −690.215 | + | 303.269i | −0.833593 | + | 0.366267i | ||||
\(829\) | − | 427.969i | − | 0.516247i | −0.966112 | − | 0.258124i | \(-0.916896\pi\) | ||
0.966112 | − | 0.258124i | \(-0.0831042\pi\) | |||||||
\(830\) | 496.852 | − | 761.005i | 0.598616 | − | 0.916874i | ||||
\(831\) | 1115.42i | 1.34226i | ||||||||
\(832\) | 394.382 | − | 1155.82i | 0.474017 | − | 1.38921i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −802.793 | − | 524.134i | −0.962581 | − | 0.628458i | ||||
\(835\) | −355.896 | −0.426223 | ||||||||
\(836\) | 28.3237 | + | 64.4623i | 0.0338800 | + | 0.0771080i | ||||
\(837\) | 296.330i | 0.354038i | ||||||||
\(838\) | −335.255 | − | 218.884i | −0.400065 | − | 0.261198i | ||||
\(839\) | − | 1133.09i | − | 1.35053i | −0.737575 | − | 0.675265i | \(-0.764029\pi\) | ||
0.737575 | − | 0.675265i | \(-0.235971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.163 | 0.987114 | ||||||||
\(842\) | −17.3996 | + | 26.6502i | −0.0206646 | + | 0.0316510i | ||||
\(843\) | −1217.55 | −1.44430 | ||||||||
\(844\) | 42.4712 | + | 96.6610i | 0.0503214 | + | 0.114527i | ||||
\(845\) | 1118.57i | 1.32375i | ||||||||
\(846\) | −280.637 | + | 429.839i | −0.331722 | + | 0.508084i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.20335 | − | 3.85980i | −0.00495678 | − | 0.00455165i | ||||
\(849\) | 756.397 | 0.890927 | ||||||||
\(850\) | 424.864 | + | 277.388i | 0.499839 | + | 0.326339i | ||||
\(851\) | 860.464 | 1.01112 | ||||||||
\(852\) | −1752.80 | + | 770.150i | −2.05727 | + | 0.903932i | ||||
\(853\) | − | 169.502i | − | 0.198712i | −0.995052 | − | 0.0993562i | \(-0.968322\pi\) | ||
0.995052 | − | 0.0993562i | \(-0.0316783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 854.563i | 0.999489i | ||||||||
\(856\) | 108.238 | − | 652.387i | 0.126446 | − | 0.762134i | ||||
\(857\) | 234.079 | 0.273138 | 0.136569 | − | 0.990631i | \(-0.456393\pi\) | ||||
0.136569 | + | 0.990631i | \(0.456393\pi\) | |||||||
\(858\) | 133.475 | − | 204.438i | 0.155565 | − | 0.238272i | ||||
\(859\) | −894.342 | −1.04114 | −0.520571 | − | 0.853818i | \(-0.674281\pi\) | ||||
−0.520571 | + | 0.853818i | \(0.674281\pi\) | |||||||
\(860\) | −437.659 | + | 192.300i | −0.508906 | + | 0.223605i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 686.654 | − | 1051.72i | 0.796582 | − | 1.22009i | ||||
\(863\) | − | 778.580i | − | 0.902178i | −0.892479 | − | 0.451089i | \(-0.851036\pi\) | ||
0.892479 | − | 0.451089i | \(-0.148964\pi\) | |||||||
\(864\) | −405.318 | + | 103.312i | −0.469118 | + | 0.119574i | ||||
\(865\) | 1121.36 | 1.29637 | ||||||||
\(866\) | 1321.71 | + | 862.927i | 1.52622 | + | 0.996451i | ||||
\(867\) | −3436.32 | −3.96346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 164.055i | − | 0.188786i | ||||||
\(870\) | −144.346 | − | 94.2416i | −0.165915 | − | 0.108324i | ||||
\(871\) | 2185.33i | 2.50899i | ||||||||
\(872\) | −232.596 | − | 38.5901i | −0.266738 | − | 0.0442547i | ||||
\(873\) | 617.917 | 0.707809 | ||||||||
\(874\) | −218.334 | + | 334.412i | −0.249810 | + | 0.382623i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −179.305 | − | 408.083i | −0.204686 | − | 0.465849i | ||||
\(877\) | − | 17.2780i | − | 0.0197013i | −0.999951 | − | 0.00985064i | \(-0.996864\pi\) | ||
0.999951 | − | 0.00985064i | \(-0.00313561\pi\) | |||||||
\(878\) | 727.717 | − | 1114.61i | 0.828835 | − | 1.26949i | ||||
\(879\) | − | 156.962i | − | 0.178569i | ||||||
\(880\) | −94.6251 | − | 86.8911i | −0.107529 | − | 0.0987399i | ||||
\(881\) | −770.918 | −0.875049 | −0.437524 | − | 0.899207i | \(-0.644145\pi\) | ||||
−0.437524 | + | 0.899207i | \(0.644145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 776.362 | 0.879232 | 0.439616 | − | 0.898186i | \(-0.355114\pi\) | ||||
0.439616 | + | 0.898186i | \(0.355114\pi\) | |||||||
\(884\) | −2255.03 | + | 990.824i | −2.55094 | + | 1.12084i | ||||
\(885\) | − | 703.235i | − | 0.794616i | ||||||
\(886\) | −849.313 | − | 554.507i | −0.958593 | − | 0.625854i | ||||
\(887\) | 1630.80i | 1.83856i | 0.393603 | + | 0.919280i | \(0.371228\pi\) | ||||
−0.393603 | + | 0.919280i | \(0.628772\pi\) | |||||||
\(888\) | 1952.08 | + | 323.871i | 2.19829 | + | 0.364719i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.6772 | − | 25.5438i | 0.0187385 | − | 0.0287009i | ||||
\(891\) | 65.9059 | 0.0739685 | ||||||||
\(892\) | −590.269 | + | 259.354i | −0.661736 | + | 0.290756i | ||||
\(893\) | 271.940i | 0.304524i | ||||||||
\(894\) | 411.455 | − | 630.207i | 0.460241 | − | 0.704930i | ||||
\(895\) | − | 413.945i | − | 0.462508i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1384.86 | 1.54388 | ||||||||
\(898\) | 467.283 | + | 305.084i | 0.520360 | + | 0.339737i | ||||
\(899\) | −74.6299 | −0.0830144 | ||||||||
\(900\) | −150.053 | − | 341.509i | −0.166726 | − | 0.379454i | ||||
\(901\) | 11.5096i | 0.0127743i | ||||||||
\(902\) | 17.8175 | + | 11.6329i | 0.0197534 | + | 0.0128967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 208.367 | − | 1255.90i | 0.230495 | − | 1.38927i | ||||
\(905\) | 808.171 | 0.893007 | ||||||||
\(906\) | 288.349 | − | 441.650i | 0.318265 | − | 0.487473i | ||||
\(907\) | −953.863 | −1.05167 | −0.525834 | − | 0.850587i | \(-0.676247\pi\) | ||||
−0.525834 | + | 0.850587i | \(0.676247\pi\) | |||||||
\(908\) | 275.598 | + | 627.239i | 0.303523 | + | 0.690792i | ||||
\(909\) | − | 1085.05i | − | 1.19367i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1681.15i | 1.84539i | 0.385534 | + | 0.922694i | \(0.374017\pi\) | ||||
−0.385534 | + | 0.922694i | \(0.625983\pi\) | |||||||
\(912\) | −621.190 | + | 676.481i | −0.681130 | + | 0.741756i | ||||
\(913\) | 111.030 | 0.121610 | ||||||||
\(914\) | 1207.24 | + | 788.194i | 1.32083 | + | 0.862356i | ||||
\(915\) | 2257.74 | 2.46747 | ||||||||
\(916\) | 839.538 | − | 368.879i | 0.916527 | − | 0.402707i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 706.386 | + | 461.192i | 0.769484 | + | 0.502387i | ||||
\(919\) | 504.991i | 0.549500i | 0.961516 | + | 0.274750i | \(0.0885952\pi\) | ||||
−0.961516 | + | 0.274750i | \(0.911405\pi\) | |||||||
\(920\) | 119.266 | − | 718.859i | 0.129637 | − | 0.781368i | ||||
\(921\) | −1018.24 | −1.10559 | ||||||||
\(922\) | 528.387 | − | 809.306i | 0.573088 | − | 0.877773i | ||||
\(923\) | 1999.64 | 2.16646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 425.746i | 0.460266i | ||||||||
\(926\) | 43.3333 | − | 66.3716i | 0.0467962 | − | 0.0716756i | ||||
\(927\) | − | 471.971i | − | 0.509138i | ||||||
\(928\) | −26.0189 | − | 102.078i | −0.0280376 | − | 0.109998i | ||||
\(929\) | −983.851 | −1.05904 | −0.529521 | − | 0.848297i | \(-0.677628\pi\) | ||||
−0.529521 | + | 0.848297i | \(0.677628\pi\) | |||||||
\(930\) | −994.059 | − | 649.010i | −1.06888 | − | 0.697860i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −434.695 | − | 989.330i | −0.466411 | − | 1.06151i | ||||
\(933\) | − | 1918.04i | − | 2.05577i | ||||||
\(934\) | 29.7871 | + | 19.4476i | 0.0318919 | + | 0.0208219i | ||||
\(935\) | 259.103i | 0.277115i | ||||||||
\(936\) | 1786.36 | + | 296.377i | 1.90851 | + | 0.316642i | ||||
\(937\) | 389.648 | 0.415846 | 0.207923 | − | 0.978145i | \(-0.433330\pi\) | ||||
0.207923 | + | 0.978145i | \(0.433330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1342.24 | −1.42943 | ||||||||
\(940\) | −199.592 | − | 454.256i | −0.212332 | − | 0.483251i | ||||
\(941\) | − | 875.465i | − | 0.930356i | −0.885217 | − | 0.465178i | \(-0.845990\pi\) | ||
0.885217 | − | 0.465178i | \(-0.154010\pi\) | |||||||
\(942\) | 18.6262 | − | 28.5290i | 0.0197731 | − | 0.0302855i | ||||
\(943\) | 120.696i | 0.127992i | ||||||||
\(944\) | 290.656 | − | 316.527i | 0.307899 | − | 0.335304i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.9012 | − | 31.9270i | −0.0516926 | − | 0.0337495i | ||||
\(947\) | −1251.29 | −1.32132 | −0.660661 | − | 0.750685i | \(-0.729724\pi\) | ||||
−0.660661 | + | 0.750685i | \(0.729724\pi\) | |||||||
\(948\) | 1959.14 | − | 860.813i | 2.06660 | − | 0.908031i | ||||
\(949\) | 465.554i | 0.490573i | ||||||||
\(950\) | −165.463 | − | 108.029i | −0.174171 | − | 0.113714i | ||||
\(951\) | 1934.14i | 2.03380i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −882.129 | −0.925633 | −0.462817 | − | 0.886454i | \(-0.653161\pi\) | ||||
−0.462817 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(954\) | 4.62576 | − | 7.08507i | 0.00484880 | − | 0.00742670i | ||||
\(955\) | −1630.75 | −1.70759 | ||||||||
\(956\) | 575.515 | − | 252.872i | 0.602003 | − | 0.264510i | ||||
\(957\) | − | 21.0599i | − | 0.0220062i | ||||||
\(958\) | −731.049 | + | 1119.71i | −0.763099 | + | 1.16880i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 541.144 | − | 1585.94i | 0.563691 | − | 1.65202i | ||||
\(961\) | 447.049 | 0.465192 | ||||||||
\(962\) | −1730.55 | − | 1129.86i | −1.79891 | − | 1.17449i | ||||
\(963\) | 980.533 | 1.01821 | ||||||||
\(964\) | 157.225 | + | 357.832i | 0.163097 | + | 0.371195i | ||||
\(965\) | 709.973i | 0.735724i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1410.24i | 1.45836i | 0.684320 | + | 0.729182i | \(0.260099\pi\) | ||||
−0.684320 | + | 0.729182i | \(0.739901\pi\) | |||||||
\(968\) | −155.867 | + | 939.463i | −0.161020 | + | 0.970520i | ||||
\(969\) | 1852.34 | 1.91160 | ||||||||
\(970\) | −326.508 | + | 500.098i | −0.336607 | + | 0.515565i | ||||
\(971\) | −678.550 | −0.698815 | −0.349408 | − | 0.936971i | \(-0.613617\pi\) | ||||
−0.349408 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(972\) | 535.107 | + | 1217.86i | 0.550521 | + | 1.25294i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −457.560 | + | 700.825i | −0.469775 | + | 0.719533i | ||||
\(975\) | 685.210i | 0.702780i | ||||||||
\(976\) | 1016.21 | + | 933.153i | 1.04120 | + | 0.956100i | ||||
\(977\) | 111.815 | 0.114447 | 0.0572235 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572235 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(978\) | 594.382 | + | 388.065i | 0.607752 | + | 0.396794i | ||||
\(979\) | 3.72682 | 0.00380676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 349.590i | − | 0.356360i | ||||||
\(982\) | −638.102 | − | 416.609i | −0.649798 | − | 0.424246i | ||||
\(983\) | 202.226i | 0.205723i | 0.994696 | + | 0.102862i | \(0.0327999\pi\) | ||||
−0.994696 | + | 0.102862i | \(0.967200\pi\) | |||||||
\(984\) | −45.4289 | + | 273.816i | −0.0461676 | + | 0.278268i | ||||
\(985\) | 619.675 | 0.629111 | ||||||||
\(986\) | −116.150 | + | 177.902i | −0.117799 | + | 0.180428i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 878.220 | − | 385.875i | 0.888887 | − | 0.390562i | ||||
\(989\) | − | 331.257i | − | 0.334942i | ||||||
\(990\) | 104.134 | − | 159.498i | 0.105186 | − | 0.161109i | ||||
\(991\) | 189.064i | 0.190781i | 0.995440 | + | 0.0953907i | \(0.0304100\pi\) | ||||
−0.995440 | + | 0.0953907i | \(0.969590\pi\) | |||||||
\(992\) | −179.183 | − | 702.978i | −0.180628 | − | 0.708648i | ||||
\(993\) | 578.546 | 0.582624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1902.36 | −1.91192 | ||||||||
\(996\) | 582.587 | + | 1325.92i | 0.584927 | + | 1.33124i | ||||
\(997\) | 1632.91i | 1.63783i | 0.573917 | + | 0.818914i | \(0.305423\pi\) | ||||
−0.573917 | + | 0.818914i | \(0.694577\pi\) | |||||||
\(998\) | 734.164 | + | 479.327i | 0.735635 | + | 0.480288i | ||||
\(999\) | 707.853i | 0.708562i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 392.3.g.m.99.1 | 8 | ||
4.3 | odd | 2 | 1568.3.g.m.687.7 | 8 | |||
7.2 | even | 3 | 392.3.k.n.67.5 | 16 | |||
7.3 | odd | 6 | 392.3.k.o.275.7 | 16 | |||
7.4 | even | 3 | 392.3.k.n.275.7 | 16 | |||
7.5 | odd | 6 | 392.3.k.o.67.5 | 16 | |||
7.6 | odd | 2 | 56.3.g.b.43.1 | ✓ | 8 | ||
8.3 | odd | 2 | inner | 392.3.g.m.99.2 | 8 | ||
8.5 | even | 2 | 1568.3.g.m.687.8 | 8 | |||
21.20 | even | 2 | 504.3.g.b.379.8 | 8 | |||
28.27 | even | 2 | 224.3.g.b.15.2 | 8 | |||
56.3 | even | 6 | 392.3.k.o.275.5 | 16 | |||
56.11 | odd | 6 | 392.3.k.n.275.5 | 16 | |||
56.13 | odd | 2 | 224.3.g.b.15.1 | 8 | |||
56.19 | even | 6 | 392.3.k.o.67.7 | 16 | |||
56.27 | even | 2 | 56.3.g.b.43.2 | yes | 8 | ||
56.51 | odd | 6 | 392.3.k.n.67.7 | 16 | |||
84.83 | odd | 2 | 2016.3.g.b.1135.2 | 8 | |||
112.13 | odd | 4 | 1792.3.d.j.1023.14 | 16 | |||
112.27 | even | 4 | 1792.3.d.j.1023.13 | 16 | |||
112.69 | odd | 4 | 1792.3.d.j.1023.3 | 16 | |||
112.83 | even | 4 | 1792.3.d.j.1023.4 | 16 | |||
168.83 | odd | 2 | 504.3.g.b.379.7 | 8 | |||
168.125 | even | 2 | 2016.3.g.b.1135.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.1 | ✓ | 8 | 7.6 | odd | 2 | ||
56.3.g.b.43.2 | yes | 8 | 56.27 | even | 2 | ||
224.3.g.b.15.1 | 8 | 56.13 | odd | 2 | |||
224.3.g.b.15.2 | 8 | 28.27 | even | 2 | |||
392.3.g.m.99.1 | 8 | 1.1 | even | 1 | trivial | ||
392.3.g.m.99.2 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.n.67.5 | 16 | 7.2 | even | 3 | |||
392.3.k.n.67.7 | 16 | 56.51 | odd | 6 | |||
392.3.k.n.275.5 | 16 | 56.11 | odd | 6 | |||
392.3.k.n.275.7 | 16 | 7.4 | even | 3 | |||
392.3.k.o.67.5 | 16 | 7.5 | odd | 6 | |||
392.3.k.o.67.7 | 16 | 56.19 | even | 6 | |||
392.3.k.o.275.5 | 16 | 56.3 | even | 6 | |||
392.3.k.o.275.7 | 16 | 7.3 | odd | 6 | |||
504.3.g.b.379.7 | 8 | 168.83 | odd | 2 | |||
504.3.g.b.379.8 | 8 | 21.20 | even | 2 | |||
1568.3.g.m.687.7 | 8 | 4.3 | odd | 2 | |||
1568.3.g.m.687.8 | 8 | 8.5 | even | 2 | |||
1792.3.d.j.1023.3 | 16 | 112.69 | odd | 4 | |||
1792.3.d.j.1023.4 | 16 | 112.83 | even | 4 | |||
1792.3.d.j.1023.13 | 16 | 112.27 | even | 4 | |||
1792.3.d.j.1023.14 | 16 | 112.13 | odd | 4 | |||
2016.3.g.b.1135.2 | 8 | 84.83 | odd | 2 | |||
2016.3.g.b.1135.7 | 8 | 168.125 | even | 2 |