Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{385})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 97x^{2} + 96x + 9216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-4.65535 - 8.06331i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.109 |
Dual form | 252.4.k.e.37.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.81071 | + | 16.9926i | 0.877496 | + | 1.51987i | 0.854079 | + | 0.520143i | \(0.174121\pi\) |
0.0234170 | + | 0.999726i | \(0.492545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50000 | + | 18.1865i | 0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.81071 | + | 16.9926i | −0.268913 | + | 0.465770i | −0.968581 | − | 0.248697i | \(-0.919998\pi\) |
0.699669 | + | 0.714468i | \(0.253331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.0000 | −1.15207 | −0.576035 | − | 0.817425i | \(-0.695401\pi\) | ||||
−0.576035 | + | 0.817425i | \(0.695401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.6214 | − | 33.9853i | 0.279935 | − | 0.484861i | −0.691433 | − | 0.722440i | \(-0.743020\pi\) |
0.971368 | + | 0.237579i | \(0.0763538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.0120745 | − | 0.0209137i | 0.859925 | − | 0.510420i | \(-0.170510\pi\) |
−0.872000 | + | 0.489507i | \(0.837177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −98.1071 | − | 169.926i | −0.889424 | − | 1.54053i | −0.840558 | − | 0.541721i | \(-0.817773\pi\) |
−0.0488654 | − | 0.998805i | \(-0.515561\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −130.000 | + | 225.167i | −1.04000 | + | 1.80133i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 98.1071 | 0.628208 | 0.314104 | − | 0.949389i | \(-0.398296\pi\) | ||||
0.314104 | + | 0.949389i | \(0.398296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −100.500 | + | 174.071i | −0.582269 | + | 1.00852i | 0.412941 | + | 0.910758i | \(0.364502\pi\) |
−0.995210 | + | 0.0977614i | \(0.968832\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −274.700 | + | 237.897i | −1.32665 | + | 1.14891i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 101.000 | + | 174.937i | 0.448765 | + | 0.777283i | 0.998306 | − | 0.0581832i | \(-0.0185308\pi\) |
−0.549541 | + | 0.835467i | \(0.685197\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 470.914 | 1.79377 | 0.896883 | − | 0.442268i | \(-0.145826\pi\) | ||||
0.896883 | + | 0.442268i | \(0.145826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −244.000 | −0.865341 | −0.432670 | − | 0.901552i | \(-0.642429\pi\) | ||||
−0.432670 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 117.729 | + | 203.912i | 0.365372 | + | 0.632842i | 0.988836 | − | 0.149010i | \(-0.0476086\pi\) |
−0.623464 | + | 0.781852i | \(0.714275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −318.500 | + | 127.306i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −323.753 | + | 560.757i | −0.839074 | + | 1.45332i | 0.0515949 | + | 0.998668i | \(0.483570\pi\) |
−0.890669 | + | 0.454652i | \(0.849764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −385.000 | −0.943880 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 304.132 | − | 526.772i | 0.671095 | − | 1.16237i | −0.306499 | − | 0.951871i | \(-0.599158\pi\) |
0.977594 | − | 0.210500i | \(-0.0675091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 294.000 | + | 509.223i | 0.617096 | + | 1.06884i | 0.990013 | + | 0.140977i | \(0.0450242\pi\) |
−0.372917 | + | 0.927865i | \(0.621642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −529.778 | − | 917.603i | −1.01094 | − | 1.75099i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 151.000 | − | 261.540i | 0.275337 | − | 0.476898i | −0.694883 | − | 0.719123i | \(-0.744544\pi\) |
0.970220 | + | 0.242225i | \(0.0778772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −156.971 | −0.262381 | −0.131191 | − | 0.991357i | \(-0.541880\pi\) | ||||
−0.131191 | + | 0.991357i | \(0.541880\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 223.000 | − | 386.247i | 0.357537 | − | 0.619272i | −0.630012 | − | 0.776585i | \(-0.716950\pi\) |
0.987549 | + | 0.157314i | \(0.0502834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −343.375 | − | 118.949i | −0.508197 | − | 0.176045i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 133.500 | + | 231.229i | 0.190126 | + | 0.329307i | 0.945292 | − | 0.326226i | \(-0.105777\pi\) |
−0.755166 | + | 0.655533i | \(0.772444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 725.992 | 0.960097 | 0.480048 | − | 0.877242i | \(-0.340619\pi\) | ||||
0.480048 | + | 0.877242i | \(0.340619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 770.000 | 0.982567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 58.8643 | + | 101.956i | 0.0701078 | + | 0.121430i | 0.898948 | − | 0.438055i | \(-0.144332\pi\) |
−0.828841 | + | 0.559485i | \(0.810999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −189.000 | − | 982.073i | −0.217721 | − | 1.13131i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.6214 | − | 33.9853i | 0.0211907 | − | 0.0367033i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 595.000 | 0.622815 | 0.311408 | − | 0.950276i | \(-0.399200\pi\) | ||||
0.311408 | + | 0.950276i | \(0.399200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −608.264 | + | 1053.54i | −0.599253 | + | 1.03794i | 0.393679 | + | 0.919248i | \(0.371202\pi\) |
−0.992932 | + | 0.118688i | \(0.962131\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −832.000 | − | 1441.07i | −0.795916 | − | 1.37857i | −0.922256 | − | 0.386581i | \(-0.873656\pi\) |
0.126339 | − | 0.991987i | \(-0.459677\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 794.667 | + | 1376.40i | 0.717976 | + | 1.24357i | 0.961801 | + | 0.273751i | \(0.0882644\pi\) |
−0.243825 | + | 0.969819i | \(0.578402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −179.000 | + | 310.037i | −0.157294 | + | 0.272442i | −0.933892 | − | 0.357555i | \(-0.883610\pi\) |
0.776598 | + | 0.629997i | \(0.216944\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1098.80 | 0.914746 | 0.457373 | − | 0.889275i | \(-0.348790\pi\) | ||||
0.457373 | + | 0.889275i | \(0.348790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1925.00 | − | 3334.20i | 1.56093 | − | 2.70361i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 686.750 | + | 237.897i | 0.529027 | + | 0.183260i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 473.000 | + | 819.260i | 0.355372 | + | 0.615522i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2648.89 | −1.89539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2127.00 | 1.48615 | 0.743074 | − | 0.669210i | \(-0.233367\pi\) | ||||
0.743074 | + | 0.669210i | \(0.233367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −755.425 | − | 1308.43i | −0.503830 | − | 0.872659i | −0.999990 | − | 0.00442833i | \(-0.998590\pi\) |
0.496160 | − | 0.868231i | \(-0.334743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.0000 | − | 24.2487i | 0.0182549 | − | 0.0158092i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1275.39 | − | 2209.04i | 0.795358 | − | 1.37760i | −0.127253 | − | 0.991870i | \(-0.540616\pi\) |
0.922611 | − | 0.385731i | \(-0.126051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2438.00 | −1.48769 | −0.743843 | − | 0.668354i | \(-0.766999\pi\) | ||||
−0.743843 | + | 0.668354i | \(0.766999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 529.778 | − | 917.603i | 0.309806 | − | 0.536600i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 962.500 | + | 1667.10i | 0.551250 | + | 0.954793i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 765.235 | + | 1325.43i | 0.420742 | + | 0.728746i | 0.996012 | − | 0.0892172i | \(-0.0284365\pi\) |
−0.575270 | + | 0.817963i | \(0.695103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 473.500 | − | 820.126i | 0.255185 | − | 0.441993i | −0.709761 | − | 0.704443i | \(-0.751197\pi\) |
0.964946 | + | 0.262450i | \(0.0845304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3943.90 | −2.04376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 770.000 | − | 1333.68i | 0.391418 | − | 0.677957i | −0.601218 | − | 0.799085i | \(-0.705318\pi\) |
0.992637 | + | 0.121128i | \(0.0386512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2747.00 | − | 2378.97i | 1.34468 | − | 1.16453i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 545.000 | + | 943.968i | 0.261888 | + | 0.453603i | 0.966744 | − | 0.255748i | \(-0.0823217\pi\) |
−0.704856 | + | 0.709351i | \(0.748988\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2079.87 | −0.963744 | −0.481872 | − | 0.876242i | \(-0.660043\pi\) | ||||
−0.481872 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 922.207 | + | 1597.31i | 0.405284 | + | 0.701972i | 0.994354 | − | 0.106110i | \(-0.0338394\pi\) |
−0.589071 | + | 0.808081i | \(0.700506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4550.00 | − | 1576.17i | −1.96542 | − | 0.680840i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 588.643 | − | 1019.56i | 0.245794 | − | 0.425728i | −0.716560 | − | 0.697525i | \(-0.754285\pi\) |
0.962355 | + | 0.271797i | \(0.0876178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2004.00 | −0.822962 | −0.411481 | − | 0.911418i | \(-0.634988\pi\) | ||||
−0.411481 | + | 0.911418i | \(0.634988\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1981.76 | + | 3432.51i | −0.787579 | + | 1.36413i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 385.000 | + | 666.840i | 0.150556 | + | 0.260771i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2236.84 | + | 3874.32i | 0.847394 | + | 1.46773i | 0.883526 | + | 0.468382i | \(0.155163\pi\) |
−0.0361326 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2324.50 | + | 4026.15i | −0.866949 | + | 1.50160i | −0.00185031 | + | 0.999998i | \(0.500589\pi\) |
−0.865099 | + | 0.501602i | \(0.832744\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4198.98 | 1.51860 | 0.759302 | − | 0.650738i | \(-0.225540\pi\) | ||||
0.759302 | + | 0.650738i | \(0.225540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 308.000 | − | 533.472i | 0.109716 | − | 0.190034i | −0.805939 | − | 0.591999i | \(-0.798339\pi\) |
0.915655 | + | 0.401964i | \(0.131672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 343.375 | + | 1784.23i | 0.118720 | + | 0.616888i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4620.00 | + | 8002.07i | 1.57402 | + | 2.72629i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.2428 | 0.0129880 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3208.00 | −1.04667 | −0.523336 | − | 0.852126i | \(-0.675313\pi\) | ||||
−0.523336 | + | 0.852126i | \(0.675313\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2393.81 | − | 4146.21i | −0.759333 | − | 1.31520i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3517.50 | − | 1218.50i | −1.10038 | − | 0.381184i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1059.56 | + | 1835.21i | −0.322504 | + | 0.558594i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2065.00 | −0.620101 | −0.310051 | − | 0.950720i | \(-0.600346\pi\) | ||||
−0.310051 | + | 0.950720i | \(0.600346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 912.396 | − | 1580.32i | 0.266775 | − | 0.462067i | −0.701252 | − | 0.712913i | \(-0.747375\pi\) |
0.968027 | + | 0.250846i | \(0.0807087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1954.00 | + | 3384.43i | 0.563860 | + | 0.976634i | 0.997155 | + | 0.0753820i | \(0.0240176\pi\) |
−0.433295 | + | 0.901252i | \(0.642649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2217.22 | − | 3840.34i | −0.623412 | − | 1.07978i | −0.988846 | − | 0.148943i | \(-0.952413\pi\) |
0.365434 | − | 0.930837i | \(-0.380921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2310.00 | + | 4001.04i | −0.641225 | + | 1.11063i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1530.47 | −0.414217 | −0.207109 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207109 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1956.50 | − | 3388.76i | 0.522943 | − | 0.905764i | −0.476701 | − | 0.879066i | \(-0.658167\pi\) |
0.999644 | − | 0.0266980i | \(-0.00849925\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5287.97 | − | 4163.20i | −1.37892 | − | 1.08562i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.0000 | + | 93.5307i | 0.0139107 | + | 0.0240940i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4650.28 | 1.16941 | 0.584707 | − | 0.811245i | \(-0.301210\pi\) | ||||
0.584707 | + | 0.811245i | \(0.301210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3850.00 | 0.956709 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1000.69 | + | 1733.25i | 0.242885 | + | 0.420689i | 0.961535 | − | 0.274683i | \(-0.0885729\pi\) |
−0.718650 | + | 0.695372i | \(0.755240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2828.00 | + | 2449.12i | −0.678469 | + | 0.587571i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 235.457 | − | 407.823i | 0.0552049 | − | 0.0956178i | −0.837102 | − | 0.547046i | \(-0.815752\pi\) |
0.892307 | + | 0.451429i | \(0.149085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12705.0 | −2.94514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1010.50 | − | 1750.24i | 0.229039 | − | 0.396707i | −0.728485 | − | 0.685062i | \(-0.759775\pi\) |
0.957524 | + | 0.288355i | \(0.0931084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −598.500 | − | 1036.63i | −0.134156 | − | 0.232365i | 0.791119 | − | 0.611663i | \(-0.209499\pi\) |
−0.925275 | + | 0.379298i | \(0.876166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2550.78 | − | 4418.09i | −0.559338 | − | 0.968803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −766.000 | + | 1326.75i | −0.166153 | + | 0.287786i | −0.937064 | − | 0.349157i | \(-0.886468\pi\) |
0.770911 | + | 0.636943i | \(0.219801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −510.157 | −0.108304 | −0.0541520 | − | 0.998533i | \(-0.517246\pi\) | ||||
−0.0541520 | + | 0.998533i | \(0.517246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3142.00 | − | 5442.10i | 0.659974 | − | 1.14311i | −0.320648 | − | 0.947198i | \(-0.603901\pi\) |
0.980622 | − | 0.195909i | \(-0.0627659\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1648.20 | + | 8564.29i | 0.338990 | + | 1.76144i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1686.50 | + | 2921.10i | 0.343273 | + | 0.594566i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3708.45 | 0.739419 | 0.369710 | − | 0.929147i | \(-0.379457\pi\) | ||||
0.369710 | + | 0.929147i | \(0.379457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11935.0 | 2.35553 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5297.78 | + | 9176.03i | 1.02468 | + | 1.77479i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −854.000 | − | 4437.51i | −0.163534 | − | 0.849748i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5768.70 | + | 9991.68i | −1.08300 | + | 1.87581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1762.00 | 0.327566 | 0.163783 | − | 0.986496i | \(-0.447630\pi\) | ||||
0.163783 | + | 0.986496i | \(0.447630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3335.64 | − | 5777.50i | 0.608189 | − | 1.05341i | −0.383350 | − | 0.923603i | \(-0.625230\pi\) |
0.991539 | − | 0.129811i | \(-0.0414371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −660.500 | − | 1144.02i | −0.119277 | − | 0.206594i | 0.800204 | − | 0.599727i | \(-0.204724\pi\) |
−0.919481 | + | 0.393134i | \(0.871391\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3149.24 | − | 5454.64i | −0.557977 | − | 0.966445i | −0.997665 | − | 0.0682944i | \(-0.978244\pi\) |
0.439688 | − | 0.898151i | \(-0.355089\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −962.500 | + | 1667.10i | −0.168933 | + | 0.292601i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −78.4857 | −0.0135203 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7020.00 | − | 12159.0i | 1.19815 | − | 2.07526i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3296.40 | + | 2854.76i | −0.552390 | + | 0.478384i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4868.00 | + | 8431.62i | 0.808367 | + | 1.40013i | 0.913994 | + | 0.405727i | \(0.132982\pi\) |
−0.105627 | + | 0.994406i | \(0.533685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5925.67 | 0.966429 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6747.00 | −1.09060 | −0.545300 | − | 0.838241i | \(-0.683584\pi\) | ||||
−0.545300 | + | 0.838241i | \(0.683584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1971.95 | − | 3415.52i | −0.313159 | − | 0.542407i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3430.00 | − | 5346.84i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1059.56 | − | 1835.21i | 0.163919 | − | 0.283916i | −0.772352 | − | 0.635195i | \(-0.780920\pi\) |
0.936271 | + | 0.351279i | \(0.114253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9646.00 | 1.47948 | 0.739740 | − | 0.672893i | \(-0.234948\pi\) | ||||
0.739740 | + | 0.672893i | \(0.234948\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −235.457 | + | 407.823i | −0.0355017 | + | 0.0614908i | −0.883230 | − | 0.468939i | \(-0.844636\pi\) |
0.847729 | + | 0.530430i | \(0.177970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1540.00 | − | 2667.36i | −0.230239 | − | 0.398785i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3198.29 | − | 5539.60i | −0.470193 | − | 0.814398i | 0.529226 | − | 0.848481i | \(-0.322482\pi\) |
−0.999419 | + | 0.0340826i | \(0.989149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3427.50 | − | 5936.60i | 0.499708 | − | 0.865520i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8751.15 | 1.25495 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3378.50 | − | 5851.73i | 0.480535 | − | 0.832311i | −0.519216 | − | 0.854643i | \(-0.673776\pi\) |
0.999751 | + | 0.0223325i | \(0.00710925\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11331.4 | − | 3925.30i | −1.58570 | − | 0.549303i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4322.00 | − | 7485.92i | −0.599959 | − | 1.03916i | −0.992826 | − | 0.119564i | \(-0.961850\pi\) |
0.392868 | − | 0.919595i | \(-0.371483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5297.78 | −0.723739 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7372.00 | 0.999140 | 0.499570 | − | 0.866273i | \(-0.333491\pi\) | ||||
0.499570 | + | 0.866273i | \(0.333491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3747.69 | − | 6491.19i | −0.499995 | − | 0.866017i | 0.500005 | − | 0.866022i | \(-0.333331\pi\) |
−1.00000 | 5.89356e-6i | \(0.999998\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1347.50 | − | 7001.82i | −0.178377 | − | 0.926872i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6808.63 | − | 11792.9i | 0.887433 | − | 1.53708i | 0.0445330 | − | 0.999008i | \(-0.485820\pi\) |
0.842900 | − | 0.538071i | \(-0.180847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7700.00 | −0.995923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2619.46 | + | 4537.04i | −0.333669 | + | 0.577932i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2316.00 | + | 4011.43i | 0.292788 | + | 0.507123i | 0.974468 | − | 0.224527i | \(-0.0720838\pi\) |
−0.681680 | + | 0.731650i | \(0.738750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2590.03 | + | 4486.06i | 0.322543 | + | 0.558661i | 0.981012 | − | 0.193947i | \(-0.0621289\pi\) |
−0.658469 | + | 0.752608i | \(0.728796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5427.00 | − | 9399.84i | 0.670814 | − | 1.16188i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3963.53 | −0.482714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2286.50 | − | 3960.33i | 0.276431 | − | 0.478792i | −0.694064 | − | 0.719913i | \(-0.744182\pi\) |
0.970495 | + | 0.241121i | \(0.0775150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10644.6 | + | 3687.40i | 1.26825 | + | 0.439335i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7122.50 | + | 12336.5i | 0.842481 | + | 1.45922i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2590.03 | −0.301984 | −0.150992 | − | 0.988535i | \(-0.548247\pi\) | ||||
−0.150992 | + | 0.988535i | \(0.548247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6096.00 | 0.705703 | 0.352851 | − | 0.935679i | \(-0.385212\pi\) | ||||
0.352851 | + | 0.935679i | \(0.385212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5101.57 | + | 8836.18i | 0.582265 | + | 1.00851i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8232.00 | + | 7129.12i | −0.932961 | + | 0.807968i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8476.45 | + | 14681.6i | −0.947323 | + | 1.64081i | −0.196292 | + | 0.980546i | \(0.562890\pi\) |
−0.751031 | + | 0.660267i | \(0.770443\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5206.00 | −0.577793 | −0.288897 | − | 0.957360i | \(-0.593288\pi\) | ||||
−0.288897 | + | 0.957360i | \(0.593288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −196.214 | + | 339.853i | −0.0214787 | + | 0.0372022i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6205.50 | + | 10748.2i | 0.674652 | + | 1.16853i | 0.976570 | + | 0.215198i | \(0.0690397\pi\) |
−0.301918 | + | 0.953334i | \(0.597627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6700.71 | + | 11606.0i | 0.718647 | + | 1.24473i | 0.961536 | + | 0.274679i | \(0.0885715\pi\) |
−0.242889 | + | 0.970054i | \(0.578095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1155.00 | + | 2000.52i | −0.123039 | + | 0.213109i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4669.90 | −0.490838 | −0.245419 | − | 0.969417i | \(-0.578925\pi\) | ||||
−0.245419 | + | 0.969417i | \(0.578925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4620.00 | + | 8002.07i | −0.482367 | + | 0.835483i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14833.8 | − | 12846.4i | 1.52839 | − | 1.32363i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7413.50 | − | 12840.6i | −0.758838 | − | 1.31435i | −0.943444 | − | 0.331533i | \(-0.892434\pi\) |
0.184606 | − | 0.982813i | \(-0.440899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1451.98 | 0.146693 | 0.0733467 | − | 0.997307i | \(-0.476632\pi\) | ||||
0.0733467 | + | 0.997307i | \(0.476632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2276.00 | −0.228455 | −0.114228 | − | 0.993455i | \(-0.536439\pi\) | ||||
−0.114228 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2786.24 | − | 4825.91i | −0.276085 | − | 0.478194i | 0.694323 | − | 0.719664i | \(-0.255704\pi\) |
−0.970408 | + | 0.241470i | \(0.922371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5285.00 | + | 1830.78i | 0.520338 | + | 0.180250i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2393.81 | − | 4146.21i | 0.232701 | − | 0.403050i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 520.000 | 0.0502300 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5572.48 | + | 9651.82i | −0.531552 | + | 0.920674i | 0.467770 | + | 0.883850i | \(0.345058\pi\) |
−0.999322 | + | 0.0368242i | \(0.988276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5454.00 | − | 9446.61i | −0.517008 | − | 0.895485i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5837.37 | + | 10110.6i | 0.546518 | + | 0.946598i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9233.50 | + | 15992.9i | −0.859158 | + | 1.48810i | 0.0135757 | + | 0.999908i | \(0.495679\pi\) |
−0.872733 | + | 0.488197i | \(0.837655\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3826.18 | −0.351676 | −0.175838 | − | 0.984419i | \(-0.556263\pi\) | ||||
−0.175838 | + | 0.984419i | \(0.556263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1925.00 | − | 3334.20i | 0.175857 | − | 0.304594i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −549.400 | − | 2854.76i | −0.0495854 | − | 0.257653i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6961.00 | + | 12056.8i | 0.624483 | + | 1.08164i | 0.988641 | + | 0.150299i | \(0.0480237\pi\) |
−0.364157 | + | 0.931337i | \(0.618643\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20837.9 | −1.84715 | −0.923577 | − | 0.383414i | \(-0.874748\pi\) | ||||
−0.923577 | + | 0.383414i | \(0.874748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23870.0 | −2.10337 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7034.28 | − | 12183.7i | −0.612552 | − | 1.06097i | −0.990809 | − | 0.135270i | \(-0.956810\pi\) |
0.378257 | − | 0.925701i | \(-0.376524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7805.00 | + | 2703.73i | 0.675681 | + | 0.234063i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16325.0 | − | 28275.8i | 1.39683 | − | 2.41938i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4620.00 | −0.393012 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6357.34 | − | 11011.2i | 0.534587 | − | 0.925933i | −0.464596 | − | 0.885523i | \(-0.653800\pi\) |
0.999183 | − | 0.0404098i | \(-0.0128663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8233.00 | − | 14260.0i | −0.688344 | − | 1.19225i | −0.972373 | − | 0.233431i | \(-0.925005\pi\) |
0.284029 | − | 0.958816i | \(-0.408329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3943.90 | + | 6831.04i | 0.325995 | + | 0.564639i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13166.5 | + | 22805.0i | −1.08215 | + | 1.87434i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25429.4 | −2.06654 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15592.5 | + | 27007.0i | −1.26004 | + | 2.18246i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 961.449 | − | 6661.12i | 0.0768322 | − | 0.532309i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −192.000 | − | 332.554i | −0.0152583 | − | 0.0264281i | 0.858295 | − | 0.513156i | \(-0.171524\pi\) |
−0.873554 | + | 0.486728i | \(0.838190\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7024.47 | −0.552101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10110.0 | 0.790260 | 0.395130 | − | 0.918625i | \(-0.370699\pi\) | ||||
0.395130 | + | 0.918625i | \(0.370699\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −98.1071 | − | 169.926i | −0.00758530 | − | 0.0131381i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3738.00 | + | 3237.20i | −0.287443 | + | 0.248933i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −814.289 | + | 1410.39i | −0.0619435 | + | 0.107289i | −0.895334 | − | 0.445395i | \(-0.853063\pi\) |
0.833391 | + | 0.552684i | \(0.186397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13176.0 | 0.996933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6838.06 | + | 11843.9i | −0.511883 | + | 0.886607i | 0.488022 | + | 0.872831i | \(0.337718\pi\) |
−0.999905 | + | 0.0137759i | \(0.995615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10780.0 | + | 18671.5i | 0.802687 | + | 1.39029i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7475.76 | + | 12948.4i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596776i | \(0.0190073\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5268.00 | − | 9124.44i | 0.386093 | − | 0.668732i | −0.605827 | − | 0.795596i | \(-0.707158\pi\) |
0.991920 | + | 0.126864i | \(0.0404911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 51015.7 | 3.70000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1143.50 | + | 1980.60i | −0.0825035 | + | 0.142900i | −0.904325 | − | 0.426845i | \(-0.859625\pi\) |
0.821821 | + | 0.569746i | \(0.192958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2540.97 | + | 13203.3i | 0.181441 | + | 0.942796i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6352.50 | − | 11002.9i | −0.451276 | − | 0.781632i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3904.66 | 0.274553 | 0.137277 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137277 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 402.000 | 0.0281224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7828.95 | − | 13560.1i | −0.542152 | − | 0.939035i | −0.998780 | − | 0.0493774i | \(-0.984276\pi\) |
0.456628 | − | 0.889658i | \(-0.349057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2695.00 | + | 14003.6i | 0.185688 | + | 0.964862i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10772.2 | + | 18657.9i | −0.734789 | + | 1.27269i | 0.220027 | + | 0.975494i | \(0.429385\pi\) |
−0.954816 | + | 0.297198i | \(0.903948\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17089.0 | −1.15986 | −0.579929 | − | 0.814667i | \(-0.696920\pi\) | ||||
−0.579929 | + | 0.814667i | \(0.696920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9280.93 | + | 16075.0i | −0.623675 | + | 1.08024i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2473.50 | − | 4284.23i | −0.165397 | − | 0.286477i | 0.771399 | − | 0.636352i | \(-0.219557\pi\) |
−0.936796 | + | 0.349875i | \(0.886224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6357.34 | − | 11011.2i | −0.420934 | − | 0.729078i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9015.00 | − | 15614.4i | 0.593984 | − | 1.02881i | −0.399705 | − | 0.916644i | \(-0.630887\pi\) |
0.993689 | − | 0.112167i | \(-0.0357792\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16403.5 | −1.07031 | −0.535154 | − | 0.844754i | \(-0.679746\pi\) | ||||
−0.535154 | + | 0.844754i | \(0.679746\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13154.0 | + | 22783.4i | −0.854126 | + | 1.47939i | 0.0233278 | + | 0.999728i | \(0.492574\pi\) |
−0.877454 | + | 0.479661i | \(0.840759\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1648.20 | + | 1427.38i | −0.105993 | + | 0.0917927i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9737.50 | − | 16865.8i | −0.623200 | − | 1.07941i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7927.05 | 0.502500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10813.0 | −0.682185 | −0.341092 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341092 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20867.4 | + | 36143.4i | 1.30409 | + | 2.25875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17199.0 | − | 6874.51i | 1.06978 | − | 0.427595i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6318.10 | − | 10943.3i | 0.389313 | − | 0.674310i | −0.603044 | − | 0.797708i | \(-0.706046\pi\) |
0.992357 | + | 0.123398i | \(0.0393790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11174.0 | 0.685318 | 0.342659 | − | 0.939460i | \(-0.388672\pi\) | ||||
0.342659 | + | 0.939460i | \(0.388672\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9771.47 | − | 16924.7i | 0.593750 | − | 1.02840i | −0.399972 | − | 0.916527i | \(-0.630980\pi\) |
0.993722 | − | 0.111877i | \(-0.0356863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5967.50 | + | 10336.0i | 0.360932 | + | 0.625153i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7328.60 | − | 12693.5i | −0.439189 | − | 0.760697i | 0.558438 | − | 0.829546i | \(-0.311401\pi\) |
−0.997627 | + | 0.0688488i | \(0.978067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14822.5 | − | 25673.3i | 0.884218 | − | 1.53151i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9810.71 | −0.579926 | −0.289963 | − | 0.957038i | \(-0.593643\pi\) | ||||
−0.289963 | + | 0.957038i | \(0.593643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4012.00 | − | 6948.99i | 0.236080 | − | 0.408902i | −0.723506 | − | 0.690318i | \(-0.757471\pi\) |
0.959586 | + | 0.281416i | \(0.0908040\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 686.750 | + | 237.897i | 0.0400466 | + | 0.0138726i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9625.00 | − | 16671.0i | −0.558743 | − | 0.967771i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11537.4 | −0.663780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29791.0 | −1.70633 | −0.853164 | − | 0.521643i | \(-0.825319\pi\) | ||||
−0.853164 | + | 0.521643i | \(0.825319\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4444.25 | + | 7697.67i | 0.252299 | + | 0.436995i | 0.964158 | − | 0.265327i | \(-0.0854800\pi\) |
−0.711859 | + | 0.702322i | \(0.752147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2082.50 | + | 10821.0i | 0.117701 | + | 0.611593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2501.73 | + | 4333.12i | −0.140155 | + | 0.242756i | −0.927555 | − | 0.373687i | \(-0.878094\pi\) |
0.787400 | + | 0.616443i | \(0.211427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50050.0 | 2.79170 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17482.7 | − | 30280.9i | 0.966672 | − | 1.67433i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13588.0 | − | 23535.1i | −0.748064 | − | 1.29568i | −0.948750 | − | 0.316028i | \(-0.897651\pi\) |
0.200686 | − | 0.979656i | \(-0.435683\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23918.5 | − | 41428.1i | −1.30544 | − | 2.26109i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9240.00 | − | 16004.1i | 0.502138 | − | 0.869728i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9320.17 | −0.502166 | −0.251083 | − | 0.967966i | \(-0.580787\pi\) | ||||
−0.251083 | + | 0.967966i | \(0.580787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 202.000 | − | 349.874i | 0.0108372 | − | 0.0187706i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21289.2 | − | 7374.81i | −1.13248 | − | 0.392303i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2717.00 | + | 4705.98i | 0.143920 | + | 0.249276i | 0.928969 | − | 0.370157i | \(-0.120696\pi\) |
−0.785050 | + | 0.619433i | \(0.787363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39439.0 | 2.07153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20790.0 | 1.08742 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9006.23 | − | 15599.2i | −0.467143 | − | 0.809115i | 0.532153 | − | 0.846649i | \(-0.321383\pi\) |
−0.999295 | + | 0.0375333i | \(0.988050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23296.0 | − | 20174.9i | 1.20331 | − | 1.04210i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12753.9 | + | 22090.4i | −0.653336 | + | 1.13161i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29353.0 | 1.49744 | 0.748722 | − | 0.662884i | \(-0.230668\pi\) | ||||
0.748722 | + | 0.662884i | \(0.230668\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4787.63 | + | 8292.41i | −0.242239 | + | 0.419570i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5718.00 | + | 9903.87i | 0.288130 | + | 0.499055i | 0.973363 | − | 0.229268i | \(-0.0736332\pi\) |
−0.685234 | + | 0.728323i | \(0.740300\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2962.83 | + | 5131.78i | 0.148083 | + | 0.256488i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.0000 | − | 67.5500i | 0.00194132 | − | 0.00336247i | −0.865053 | − | 0.501680i | \(-0.832715\pi\) |
0.866994 | + | 0.498318i | \(0.166049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17306.1 | 0.854507 | 0.427254 | − | 0.904132i | \(-0.359481\pi\) | ||||
0.427254 | + | 0.904132i | \(0.359481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15015.0 | + | 26006.7i | −0.738399 | + | 1.27894i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22250.7 | + | 19269.7i | −1.08548 | + | 0.940051i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13195.5 | − | 22855.3i | −0.641159 | − | 1.11052i | −0.985174 | − | 0.171556i | \(-0.945120\pi\) |
0.344015 | − | 0.938964i | \(-0.388213\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18581.5 | 0.895695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −660.000 | −0.0316884 | −0.0158442 | − | 0.999874i | \(-0.505044\pi\) | ||||
−0.0158442 | + | 0.999874i | \(0.505044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2570.41 | − | 4452.07i | −0.122440 | − | 0.212073i | 0.798289 | − | 0.602274i | \(-0.205739\pi\) |
−0.920730 | + | 0.390201i | \(0.872405\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6265.00 | − | 2170.26i | −0.297258 | − | 0.102973i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16423.1 | + | 28445.7i | −0.773148 | + | 1.33913i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8773.00 | 0.411395 | 0.205697 | − | 0.978616i | \(-0.434054\pi\) | ||||
0.205697 | + | 0.978616i | \(0.434054\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5513.62 | − | 9549.87i | 0.256547 | − | 0.444353i | −0.708767 | − | 0.705442i | \(-0.750748\pi\) |
0.965315 | + | 0.261089i | \(0.0840817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26130.0 | − | 45258.5i | −1.21112 | − | 2.09772i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −470.914 | − | 815.647i | −0.0216589 | − | 0.0375142i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1540.00 | − | 2667.36i | 0.0705577 | − | 0.122209i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30217.0 | 1.37387 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2940.00 | − | 5092.23i | 0.133164 | − | 0.230646i | −0.791731 | − | 0.610870i | \(-0.790820\pi\) |
0.924894 | + | 0.380224i | \(0.124153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3845.80 | + | 19983.4i | 0.172871 | + | 0.898263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15876.0 | − | 27498.0i | −0.710937 | − | 1.23138i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22898.2 | 1.01769 | 0.508843 | − | 0.860859i | \(-0.330073\pi\) | ||||
0.508843 | + | 0.860859i | \(0.330073\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9240.00 | 0.409121 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4375.58 | + | 7578.72i | 0.192292 | + | 0.333060i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67375.0 | + | 23339.4i | 2.94988 | + | 1.02187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1608.96 | + | 2786.79i | −0.0699232 | + | 0.121111i | −0.898867 | − | 0.438221i | \(-0.855609\pi\) |
0.828944 | + | 0.559331i | \(0.188942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6062.00 | −0.262473 | −0.131237 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131237 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10693.7 | + | 18522.0i | −0.459611 | + | 0.796070i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 244.000 | + | 422.620i | 0.0104486 | + | 0.0180974i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3404.32 | + | 5896.45i | 0.144716 | + | 0.250655i | 0.929267 | − | 0.369409i | \(-0.120440\pi\) |
−0.784551 | + | 0.620064i | \(0.787107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16120.0 | − | 27920.7i | 0.682756 | − | 1.18257i | −0.291381 | − | 0.956607i | \(-0.594115\pi\) |
0.974137 | − | 0.225960i | \(-0.0725520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28313.7 | −1.19052 | −0.595262 | − | 0.803531i | \(-0.702952\pi\) | ||||
−0.595262 | + | 0.803531i | \(0.702952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16001.0 | + | 27714.5i | −0.670371 | + | 1.16112i | 0.307428 | + | 0.951571i | \(0.400532\pi\) |
−0.977799 | + | 0.209545i | \(0.932802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1922.90 | + | 13322.2i | −0.0799814 | + | 0.554127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20405.0 | − | 35342.5i | −0.845682 | − | 1.46476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5376.27 | 0.221227 | 0.110613 | − | 0.993864i | \(-0.464718\pi\) | ||||
0.110613 | + | 0.993864i | \(0.464718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14764.0 | −0.605355 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7053.90 | + | 12217.7i | 0.287173 | + | 0.497399i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13244.0 | + | 11469.6i | −0.537272 | + | 0.465291i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19817.6 | − | 34325.1i | 0.798284 | − | 1.38267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19966.0 | −0.801434 | −0.400717 | − | 0.916202i | \(-0.631239\pi\) | ||||
−0.400717 | + | 0.916202i | \(0.631239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6945.98 | − | 12030.8i | 0.276861 | − | 0.479538i | −0.693742 | − | 0.720224i | \(-0.744039\pi\) |
0.970603 | + | 0.240686i | \(0.0773724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16688.0 | + | 28904.5i | 0.662849 | + | 1.14809i | 0.979864 | + | 0.199667i | \(0.0639862\pi\) |
−0.317015 | + | 0.948421i | \(0.602680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4493.30 | − | 7782.63i | −0.177235 | − | 0.306980i | 0.763697 | − | 0.645574i | \(-0.223382\pi\) |
−0.940932 | + | 0.338594i | \(0.890049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18095.0 | + | 31341.5i | −0.711270 | + | 1.23196i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5238.92 | −0.204509 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8154.00 | + | 14123.1i | −0.317208 | + | 0.549420i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9271.12 | − | 48174.1i | −0.358195 | − | 1.86124i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2260.00 | + | 3914.43i | 0.0870180 | + | 0.150720i | 0.906249 | − | 0.422744i | \(-0.138933\pi\) |
−0.819231 | + | 0.573463i | \(0.805600\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37555.4 | −1.43618 | −0.718089 | − | 0.695951i | \(-0.754983\pi\) | ||||
−0.718089 | + | 0.695951i | \(0.754983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7636.00 | −0.291021 | −0.145511 | − | 0.989357i | \(-0.546483\pi\) | ||||
−0.145511 | + | 0.989357i | \(0.546483\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12184.9 | − | 21104.9i | −0.461250 | − | 0.798909i | 0.537773 | − | 0.843089i | \(-0.319266\pi\) |
−0.999024 | + | 0.0441807i | \(0.985932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7444.50 | + | 38682.8i | 0.280855 | + | 1.45937i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 235.457 | − | 407.823i | 0.00882337 | − | 0.0152825i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23100.0 | 0.862735 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9859.76 | + | 17077.6i | −0.365786 | + | 0.633560i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12705.0 | + | 22005.7i | 0.469772 | + | 0.813670i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19660.7 | − | 34053.3i | −0.722146 | − | 1.25079i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6051.00 | − | 10480.6i | 0.221522 | − | 0.383687i | −0.733749 | − | 0.679421i | \(-0.762231\pi\) |
0.955270 | + | 0.295734i | \(0.0955643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5180.05 | 0.188390 | 0.0941948 | − | 0.995554i | \(-0.469972\pi\) | ||||
0.0941948 | + | 0.995554i | \(0.469972\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7122.50 | + | 12336.5i | −0.258182 | + | 0.447185i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21151.9 | − | 18318.1i | 0.761720 | − | 0.659669i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16894.0 | + | 29261.3i | 0.606400 | + | 1.05032i | 0.991829 | + | 0.127578i | \(0.0407203\pi\) |
−0.385429 | + | 0.922738i | \(0.625946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8476.45 | 0.302281 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52520.0 | −1.86686 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 706.371 | + | 1223.47i | 0.0249465 | + | 0.0432086i | 0.878229 | − | 0.478240i | \(-0.158725\pi\) |
−0.853283 | + | 0.521449i | \(0.825392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 539.000 | + | 424.352i | 0.0189742 | + | 0.0149383i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7554.25 | + | 13084.3i | −0.264225 | + | 0.457651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17603.0 | 0.613730 | 0.306865 | − | 0.951753i | \(-0.400720\pi\) | ||||
0.306865 | + | 0.951753i | \(0.400720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9545.82 | − | 16533.8i | 0.330696 | − | 0.572782i | −0.651953 | − | 0.758260i | \(-0.726050\pi\) |
0.982648 | + | 0.185478i | \(0.0593832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46200.0 | − | 80020.7i | −1.59542 | − | 2.76334i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27823.2 | + | 48191.1i | 0.954732 | + | 1.65364i | 0.734980 | + | 0.678089i | \(0.237192\pi\) |
0.219753 | + | 0.975556i | \(0.429475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12042.0 | + | 20857.4i | −0.411907 | + | 0.713444i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17345.3 | −0.589581 | −0.294790 | − | 0.955562i | \(-0.595250\pi\) | ||||
−0.294790 | + | 0.955562i | \(0.595250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43890.0 | + | 76019.7i | −1.48717 | + | 2.57585i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44638.7 | + | 15463.3i | 1.50309 | + | 0.520684i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5305.00 | − | 9188.53i | −0.178074 | − | 0.308433i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −91220.0 | −3.04298 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4747.00 | −0.157863 | −0.0789313 | − | 0.996880i | \(-0.525151\pi\) | ||||
−0.0789313 | + | 0.996880i | \(0.525151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16452.6 | + | 28496.7i | 0.543757 | + | 0.941814i | 0.998684 | + | 0.0512856i | \(0.0163319\pi\) |
−0.454927 | + | 0.890529i | \(0.650335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8533.00 | − | 44338.8i | −0.281146 | − | 1.46088i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10477.8 | − | 18148.1i | 0.343107 | − | 0.594279i | −0.641901 | − | 0.766788i | \(-0.721854\pi\) |
0.985008 | + | 0.172509i | \(0.0551873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2310.00 | −0.0754116 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16952.9 | − | 29363.3i | 0.550065 | − | 0.952740i | −0.448204 | − | 0.893931i | \(-0.647936\pi\) |
0.998269 | − | 0.0588091i | \(-0.0187303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41195.0 | + | 71351.8i | 1.33257 | + | 2.30808i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23938.1 | + | 41462.1i | 0.769654 | + | 1.33308i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6734.50 | + | 11664.5i | −0.215871 | + | 0.373900i | −0.953542 | − | 0.301261i | \(-0.902592\pi\) |
0.737670 | + | 0.675161i | \(0.235926\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12086.8 | 0.385103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7141.00 | + | 12368.6i | −0.226838 | + | 0.392895i | −0.956869 | − | 0.290519i | \(-0.906172\pi\) |
0.730031 | + | 0.683414i | \(0.239506\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.4.k.e.109.2 | yes | 4 | |
3.2 | odd | 2 | inner | 252.4.k.e.109.1 | yes | 4 | |
7.2 | even | 3 | inner | 252.4.k.e.37.2 | yes | 4 | |
7.3 | odd | 6 | 1764.4.a.u.1.2 | 2 | |||
7.4 | even | 3 | 1764.4.a.r.1.1 | 2 | |||
7.5 | odd | 6 | 1764.4.k.x.1549.1 | 4 | |||
7.6 | odd | 2 | 1764.4.k.x.361.1 | 4 | |||
21.2 | odd | 6 | inner | 252.4.k.e.37.1 | ✓ | 4 | |
21.5 | even | 6 | 1764.4.k.x.1549.2 | 4 | |||
21.11 | odd | 6 | 1764.4.a.r.1.2 | 2 | |||
21.17 | even | 6 | 1764.4.a.u.1.1 | 2 | |||
21.20 | even | 2 | 1764.4.k.x.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.k.e.37.1 | ✓ | 4 | 21.2 | odd | 6 | inner | |
252.4.k.e.37.2 | yes | 4 | 7.2 | even | 3 | inner | |
252.4.k.e.109.1 | yes | 4 | 3.2 | odd | 2 | inner | |
252.4.k.e.109.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1764.4.a.r.1.1 | 2 | 7.4 | even | 3 | |||
1764.4.a.r.1.2 | 2 | 21.11 | odd | 6 | |||
1764.4.a.u.1.1 | 2 | 21.17 | even | 6 | |||
1764.4.a.u.1.2 | 2 | 7.3 | odd | 6 | |||
1764.4.k.x.361.1 | 4 | 7.6 | odd | 2 | |||
1764.4.k.x.361.2 | 4 | 21.20 | even | 2 | |||
1764.4.k.x.1549.1 | 4 | 7.5 | odd | 6 | |||
1764.4.k.x.1549.2 | 4 | 21.5 | even | 6 |