Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(83,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("287.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.b (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: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 83.15 | ||
Character | \(\chi\) | \(=\) | 287.83 |
Dual form | 287.3.b.a.83.16 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45610 | −0.728049 | −0.364025 | − | 0.931389i | \(-0.618598\pi\) | ||||
−0.364025 | + | 0.931389i | \(0.618598\pi\) | |||||||
\(3\) | − | 1.32130i | − | 0.440433i | −0.975451 | − | 0.220217i | \(-0.929324\pi\) | ||
0.975451 | − | 0.220217i | \(-0.0706764\pi\) | |||||||
\(4\) | −1.87978 | −0.469944 | ||||||||
\(5\) | 7.87741i | 1.57548i | 0.616006 | + | 0.787741i | \(0.288750\pi\) | ||||
−0.616006 | + | 0.787741i | \(0.711250\pi\) | |||||||
\(6\) | 1.92394i | 0.320657i | ||||||||
\(7\) | −0.510666 | − | 6.98135i | −0.0729523 | − | 0.997335i | ||||
\(8\) | 8.56153 | 1.07019 | ||||||||
\(9\) | 7.25417 | 0.806019 | ||||||||
\(10\) | − | 11.4703i | − | 1.14703i | ||||||
\(11\) | −14.9743 | −1.36130 | −0.680649 | − | 0.732610i | \(-0.738302\pi\) | ||||
−0.680649 | + | 0.732610i | \(0.738302\pi\) | |||||||
\(12\) | 2.48375i | 0.206979i | ||||||||
\(13\) | 17.8748i | 1.37498i | 0.726193 | + | 0.687490i | \(0.241288\pi\) | ||||
−0.726193 | + | 0.687490i | \(0.758712\pi\) | |||||||
\(14\) | 0.743580 | + | 10.1655i | 0.0531129 | + | 0.726109i | ||||
\(15\) | 10.4084 | 0.693895 | ||||||||
\(16\) | −4.94732 | −0.309208 | ||||||||
\(17\) | − | 31.3052i | − | 1.84148i | −0.390172 | − | 0.920742i | \(-0.627585\pi\) | ||
0.390172 | − | 0.920742i | \(-0.372415\pi\) | |||||||
\(18\) | −10.5628 | −0.586821 | ||||||||
\(19\) | 3.88622i | 0.204538i | 0.994757 | + | 0.102269i | \(0.0326102\pi\) | ||||
−0.994757 | + | 0.102269i | \(0.967390\pi\) | |||||||
\(20\) | − | 14.8078i | − | 0.740390i | ||||||
\(21\) | −9.22445 | + | 0.674743i | −0.439259 | + | 0.0321306i | ||||
\(22\) | 21.8040 | 0.991091 | ||||||||
\(23\) | −31.4353 | −1.36675 | −0.683377 | − | 0.730066i | \(-0.739489\pi\) | ||||
−0.683377 | + | 0.730066i | \(0.739489\pi\) | |||||||
\(24\) | − | 11.3123i | − | 0.471348i | ||||||
\(25\) | −37.0537 | −1.48215 | ||||||||
\(26\) | − | 26.0274i | − | 1.00105i | ||||||
\(27\) | − | 21.4766i | − | 0.795430i | ||||||
\(28\) | 0.959939 | + | 13.1234i | 0.0342835 | + | 0.468692i | ||||
\(29\) | −25.4865 | −0.878846 | −0.439423 | − | 0.898280i | \(-0.644817\pi\) | ||||
−0.439423 | + | 0.898280i | \(0.644817\pi\) | |||||||
\(30\) | −15.1557 | −0.505189 | ||||||||
\(31\) | 28.3835i | 0.915598i | 0.889056 | + | 0.457799i | \(0.151362\pi\) | ||||
−0.889056 | + | 0.457799i | \(0.848638\pi\) | |||||||
\(32\) | −27.0423 | −0.845073 | ||||||||
\(33\) | 19.7855i | 0.599560i | ||||||||
\(34\) | 45.5835i | 1.34069i | ||||||||
\(35\) | 54.9950 | − | 4.02273i | 1.57129 | − | 0.114935i | ||||
\(36\) | −13.6362 | −0.378784 | ||||||||
\(37\) | −55.2687 | −1.49375 | −0.746875 | − | 0.664965i | \(-0.768447\pi\) | ||||
−0.746875 | + | 0.664965i | \(0.768447\pi\) | |||||||
\(38\) | − | 5.65872i | − | 0.148914i | ||||||
\(39\) | 23.6179 | 0.605587 | ||||||||
\(40\) | 67.4428i | 1.68607i | ||||||||
\(41\) | 6.40312i | 0.156174i | ||||||||
\(42\) | 13.4317 | − | 0.982492i | 0.319802 | − | 0.0233927i | ||||
\(43\) | −35.3624 | −0.822382 | −0.411191 | − | 0.911549i | \(-0.634887\pi\) | ||||
−0.411191 | + | 0.911549i | \(0.634887\pi\) | |||||||
\(44\) | 28.1483 | 0.639734 | ||||||||
\(45\) | 57.1441i | 1.26987i | ||||||||
\(46\) | 45.7729 | 0.995064 | ||||||||
\(47\) | − | 32.0142i | − | 0.681154i | −0.940217 | − | 0.340577i | \(-0.889378\pi\) | ||
0.940217 | − | 0.340577i | \(-0.110622\pi\) | |||||||
\(48\) | 6.53689i | 0.136185i | ||||||||
\(49\) | −48.4784 | + | 7.13028i | −0.989356 | + | 0.145516i | ||||
\(50\) | 53.9538 | 1.07908 | ||||||||
\(51\) | −41.3636 | −0.811050 | ||||||||
\(52\) | − | 33.6006i | − | 0.646165i | ||||||
\(53\) | −29.9533 | −0.565157 | −0.282578 | − | 0.959244i | \(-0.591190\pi\) | ||||
−0.282578 | + | 0.959244i | \(0.591190\pi\) | |||||||
\(54\) | 31.2721i | 0.579112i | ||||||||
\(55\) | − | 117.959i | − | 2.14470i | ||||||
\(56\) | −4.37209 | − | 59.7710i | −0.0780730 | − | 1.06734i | ||||
\(57\) | 5.13486 | 0.0900853 | ||||||||
\(58\) | 37.1109 | 0.639843 | ||||||||
\(59\) | − | 71.2624i | − | 1.20784i | −0.797046 | − | 0.603918i | \(-0.793605\pi\) | ||
0.797046 | − | 0.603918i | \(-0.206395\pi\) | |||||||
\(60\) | −19.5655 | −0.326092 | ||||||||
\(61\) | 35.0491i | 0.574576i | 0.957844 | + | 0.287288i | \(0.0927536\pi\) | ||||
−0.957844 | + | 0.287288i | \(0.907246\pi\) | |||||||
\(62\) | − | 41.3292i | − | 0.666600i | ||||||
\(63\) | −3.70446 | − | 50.6439i | −0.0588009 | − | 0.803871i | ||||
\(64\) | 59.1656 | 0.924463 | ||||||||
\(65\) | −140.807 | −2.16626 | ||||||||
\(66\) | − | 28.8096i | − | 0.436509i | ||||||
\(67\) | 69.4294 | 1.03626 | 0.518130 | − | 0.855302i | \(-0.326628\pi\) | ||||
0.518130 | + | 0.855302i | \(0.326628\pi\) | |||||||
\(68\) | 58.8469i | 0.865395i | ||||||||
\(69\) | 41.5355i | 0.601963i | ||||||||
\(70\) | −80.0781 | + | 5.85749i | −1.14397 | + | 0.0836784i | ||||
\(71\) | −65.7118 | −0.925519 | −0.462759 | − | 0.886484i | \(-0.653141\pi\) | ||||
−0.462759 | + | 0.886484i | \(0.653141\pi\) | |||||||
\(72\) | 62.1068 | 0.862595 | ||||||||
\(73\) | − | 3.48586i | − | 0.0477516i | −0.999715 | − | 0.0238758i | \(-0.992399\pi\) | ||
0.999715 | − | 0.0238758i | \(-0.00760062\pi\) | |||||||
\(74\) | 80.4767 | 1.08752 | ||||||||
\(75\) | 48.9590i | 0.652786i | ||||||||
\(76\) | − | 7.30523i | − | 0.0961215i | ||||||
\(77\) | 7.64685 | + | 104.541i | 0.0993098 | + | 1.35767i | ||||
\(78\) | −34.3900 | −0.440897 | ||||||||
\(79\) | 127.692 | 1.61635 | 0.808176 | − | 0.588941i | \(-0.200455\pi\) | ||||
0.808176 | + | 0.588941i | \(0.200455\pi\) | |||||||
\(80\) | − | 38.9721i | − | 0.487151i | ||||||
\(81\) | 36.9105 | 0.455685 | ||||||||
\(82\) | − | 9.32358i | − | 0.113702i | ||||||
\(83\) | − | 78.7499i | − | 0.948794i | −0.880311 | − | 0.474397i | \(-0.842666\pi\) | ||
0.880311 | − | 0.474397i | \(-0.157334\pi\) | |||||||
\(84\) | 17.3399 | − | 1.26837i | 0.206428 | − | 0.0150996i | ||||
\(85\) | 246.604 | 2.90123 | ||||||||
\(86\) | 51.4911 | 0.598734 | ||||||||
\(87\) | 33.6754i | 0.387073i | ||||||||
\(88\) | −128.203 | −1.45685 | ||||||||
\(89\) | − | 12.3819i | − | 0.139123i | −0.997578 | − | 0.0695614i | \(-0.977840\pi\) | ||
0.997578 | − | 0.0695614i | \(-0.0221600\pi\) | |||||||
\(90\) | − | 83.2074i | − | 0.924527i | ||||||
\(91\) | 124.790 | − | 9.12803i | 1.37132 | − | 0.100308i | ||||
\(92\) | 59.0914 | 0.642298 | ||||||||
\(93\) | 37.5031 | 0.403259 | ||||||||
\(94\) | 46.6159i | 0.495914i | ||||||||
\(95\) | −30.6134 | −0.322246 | ||||||||
\(96\) | 35.7310i | 0.372198i | ||||||||
\(97\) | − | 64.6638i | − | 0.666637i | −0.942814 | − | 0.333319i | \(-0.891832\pi\) | ||
0.942814 | − | 0.333319i | \(-0.108168\pi\) | |||||||
\(98\) | 70.5894 | − | 10.3824i | 0.720300 | − | 0.105943i | ||||
\(99\) | −108.626 | −1.09723 | ||||||||
\(100\) | 69.6527 | 0.696527 | ||||||||
\(101\) | 136.285i | 1.34936i | 0.738111 | + | 0.674680i | \(0.235718\pi\) | ||||
−0.738111 | + | 0.674680i | \(0.764282\pi\) | |||||||
\(102\) | 60.2294 | 0.590484 | ||||||||
\(103\) | 42.1111i | 0.408846i | 0.978883 | + | 0.204423i | \(0.0655318\pi\) | ||||
−0.978883 | + | 0.204423i | \(0.934468\pi\) | |||||||
\(104\) | 153.035i | 1.47149i | ||||||||
\(105\) | −5.31523 | − | 72.6648i | −0.0506212 | − | 0.692046i | ||||
\(106\) | 43.6150 | 0.411462 | ||||||||
\(107\) | 40.9960 | 0.383140 | 0.191570 | − | 0.981479i | \(-0.438642\pi\) | ||||
0.191570 | + | 0.981479i | \(0.438642\pi\) | |||||||
\(108\) | 40.3713i | 0.373808i | ||||||||
\(109\) | −141.122 | −1.29470 | −0.647350 | − | 0.762193i | \(-0.724123\pi\) | ||||
−0.647350 | + | 0.762193i | \(0.724123\pi\) | |||||||
\(110\) | 171.759i | 1.56145i | ||||||||
\(111\) | 73.0265i | 0.657897i | ||||||||
\(112\) | 2.52643 | + | 34.5390i | 0.0225574 | + | 0.308384i | ||||
\(113\) | −140.335 | −1.24190 | −0.620950 | − | 0.783851i | \(-0.713253\pi\) | ||||
−0.620950 | + | 0.783851i | \(0.713253\pi\) | |||||||
\(114\) | −7.47686 | −0.0655865 | ||||||||
\(115\) | − | 247.629i | − | 2.15330i | ||||||
\(116\) | 47.9090 | 0.413009 | ||||||||
\(117\) | 129.666i | 1.10826i | ||||||||
\(118\) | 103.765i | 0.879365i | ||||||||
\(119\) | −218.553 | + | 15.9865i | −1.83658 | + | 0.134340i | ||||
\(120\) | 89.1121 | 0.742600 | ||||||||
\(121\) | 103.229 | 0.853131 | ||||||||
\(122\) | − | 51.0349i | − | 0.418319i | ||||||
\(123\) | 8.46044 | 0.0687841 | ||||||||
\(124\) | − | 53.3547i | − | 0.430280i | ||||||
\(125\) | − | 94.9517i | − | 0.759614i | ||||||
\(126\) | 5.39405 | + | 73.7425i | 0.0428100 | + | 0.585258i | ||||
\(127\) | −65.5068 | −0.515801 | −0.257901 | − | 0.966171i | \(-0.583031\pi\) | ||||
−0.257901 | + | 0.966171i | \(0.583031\pi\) | |||||||
\(128\) | 22.0185 | 0.172019 | ||||||||
\(129\) | 46.7243i | 0.362204i | ||||||||
\(130\) | 205.029 | 1.57714 | ||||||||
\(131\) | 56.0225i | 0.427653i | 0.976872 | + | 0.213826i | \(0.0685927\pi\) | ||||
−0.976872 | + | 0.213826i | \(0.931407\pi\) | |||||||
\(132\) | − | 37.1923i | − | 0.281760i | ||||||
\(133\) | 27.1311 | − | 1.98456i | 0.203993 | − | 0.0149215i | ||||
\(134\) | −101.096 | −0.754448 | ||||||||
\(135\) | 169.180 | 1.25319 | ||||||||
\(136\) | − | 268.021i | − | 1.97074i | ||||||
\(137\) | 207.977 | 1.51808 | 0.759042 | − | 0.651042i | \(-0.225668\pi\) | ||||
0.759042 | + | 0.651042i | \(0.225668\pi\) | |||||||
\(138\) | − | 60.4797i | − | 0.438259i | ||||||
\(139\) | 88.9230i | 0.639734i | 0.947463 | + | 0.319867i | \(0.103638\pi\) | ||||
−0.947463 | + | 0.319867i | \(0.896362\pi\) | |||||||
\(140\) | −103.378 | + | 7.56184i | −0.738417 | + | 0.0540131i | ||||
\(141\) | −42.3004 | −0.300003 | ||||||||
\(142\) | 95.6829 | 0.673823 | ||||||||
\(143\) | − | 267.661i | − | 1.87176i | ||||||
\(144\) | −35.8887 | −0.249227 | ||||||||
\(145\) | − | 200.768i | − | 1.38461i | ||||||
\(146\) | 5.07576i | 0.0347655i | ||||||||
\(147\) | 9.42123 | + | 64.0545i | 0.0640900 | + | 0.435745i | ||||
\(148\) | 103.893 | 0.701979 | ||||||||
\(149\) | −121.086 | −0.812659 | −0.406329 | − | 0.913727i | \(-0.633191\pi\) | ||||
−0.406329 | + | 0.913727i | \(0.633191\pi\) | |||||||
\(150\) | − | 71.2891i | − | 0.475261i | ||||||
\(151\) | −27.5981 | −0.182769 | −0.0913843 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913843 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(152\) | 33.2720i | 0.218895i | ||||||||
\(153\) | − | 227.093i | − | 1.48427i | ||||||
\(154\) | −11.1346 | − | 152.221i | −0.0723024 | − | 0.988451i | ||||
\(155\) | −223.589 | −1.44251 | ||||||||
\(156\) | −44.3964 | −0.284592 | ||||||||
\(157\) | 223.047i | 1.42068i | 0.703857 | + | 0.710342i | \(0.251460\pi\) | ||||
−0.703857 | + | 0.710342i | \(0.748540\pi\) | |||||||
\(158\) | −185.932 | −1.17678 | ||||||||
\(159\) | 39.5773i | 0.248914i | ||||||||
\(160\) | − | 213.024i | − | 1.33140i | ||||||
\(161\) | 16.0530 | + | 219.461i | 0.0997078 | + | 1.36311i | ||||
\(162\) | −53.7453 | −0.331761 | ||||||||
\(163\) | 199.426 | 1.22347 | 0.611735 | − | 0.791063i | \(-0.290472\pi\) | ||||
0.611735 | + | 0.791063i | \(0.290472\pi\) | |||||||
\(164\) | − | 12.0365i | − | 0.0733930i | ||||||
\(165\) | −155.859 | −0.944597 | ||||||||
\(166\) | 114.668i | 0.690769i | ||||||||
\(167\) | − | 50.1567i | − | 0.300340i | −0.988660 | − | 0.150170i | \(-0.952018\pi\) | ||
0.988660 | − | 0.150170i | \(-0.0479820\pi\) | |||||||
\(168\) | −78.9754 | + | 5.77683i | −0.470092 | + | 0.0343859i | ||||
\(169\) | −150.507 | −0.890573 | ||||||||
\(170\) | −359.080 | −2.11224 | ||||||||
\(171\) | 28.1913i | 0.164861i | ||||||||
\(172\) | 66.4735 | 0.386474 | ||||||||
\(173\) | 206.813i | 1.19545i | 0.801701 | + | 0.597726i | \(0.203929\pi\) | ||||
−0.801701 | + | 0.597726i | \(0.796071\pi\) | |||||||
\(174\) | − | 49.0346i | − | 0.281808i | ||||||
\(175\) | 18.9221 | + | 258.685i | 0.108126 | + | 1.47820i | ||||
\(176\) | 74.0826 | 0.420924 | ||||||||
\(177\) | −94.1589 | −0.531971 | ||||||||
\(178\) | 18.0293i | 0.101288i | ||||||||
\(179\) | 177.062 | 0.989176 | 0.494588 | − | 0.869128i | \(-0.335319\pi\) | ||||
0.494588 | + | 0.869128i | \(0.335319\pi\) | |||||||
\(180\) | − | 107.418i | − | 0.596768i | ||||||
\(181\) | 96.2124i | 0.531560i | 0.964034 | + | 0.265780i | \(0.0856295\pi\) | ||||
−0.964034 | + | 0.265780i | \(0.914370\pi\) | |||||||
\(182\) | −181.706 | + | 13.2913i | −0.998386 | + | 0.0730292i | ||||
\(183\) | 46.3104 | 0.253062 | ||||||||
\(184\) | −269.135 | −1.46269 | ||||||||
\(185\) | − | 435.375i | − | 2.35338i | ||||||
\(186\) | −54.6082 | −0.293593 | ||||||||
\(187\) | 468.773i | 2.50681i | ||||||||
\(188\) | 60.1797i | 0.320105i | ||||||||
\(189\) | −149.936 | + | 10.9674i | −0.793311 | + | 0.0580285i | ||||
\(190\) | 44.5761 | 0.234611 | ||||||||
\(191\) | −261.211 | −1.36760 | −0.683799 | − | 0.729671i | \(-0.739673\pi\) | ||||
−0.683799 | + | 0.729671i | \(0.739673\pi\) | |||||||
\(192\) | − | 78.1755i | − | 0.407164i | ||||||
\(193\) | −58.6810 | −0.304047 | −0.152023 | − | 0.988377i | \(-0.548579\pi\) | ||||
−0.152023 | + | 0.988377i | \(0.548579\pi\) | |||||||
\(194\) | 94.1569i | 0.485345i | ||||||||
\(195\) | 186.048i | 0.954092i | ||||||||
\(196\) | 91.1287 | − | 13.4033i | 0.464942 | − | 0.0683844i | ||||
\(197\) | −123.905 | −0.628962 | −0.314481 | − | 0.949264i | \(-0.601830\pi\) | ||||
−0.314481 | + | 0.949264i | \(0.601830\pi\) | |||||||
\(198\) | 158.170 | 0.798838 | ||||||||
\(199\) | 10.3149i | 0.0518335i | 0.999664 | + | 0.0259167i | \(0.00825048\pi\) | ||||
−0.999664 | + | 0.0259167i | \(0.991750\pi\) | |||||||
\(200\) | −317.236 | −1.58618 | ||||||||
\(201\) | − | 91.7370i | − | 0.456403i | ||||||
\(202\) | − | 198.445i | − | 0.982400i | ||||||
\(203\) | 13.0151 | + | 177.930i | 0.0641139 | + | 0.876505i | ||||
\(204\) | 77.7543 | 0.381149 | ||||||||
\(205\) | −50.4401 | −0.246049 | ||||||||
\(206\) | − | 61.3180i | − | 0.297660i | ||||||
\(207\) | −228.037 | −1.10163 | ||||||||
\(208\) | − | 88.4322i | − | 0.425155i | ||||||
\(209\) | − | 58.1933i | − | 0.278437i | ||||||
\(210\) | 7.73949 | + | 105.807i | 0.0368547 | + | 0.503843i | ||||
\(211\) | 13.9761 | 0.0662372 | 0.0331186 | − | 0.999451i | \(-0.489456\pi\) | ||||
0.0331186 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(212\) | 56.3056 | 0.265592 | ||||||||
\(213\) | 86.8250i | 0.407629i | ||||||||
\(214\) | −59.6942 | −0.278945 | ||||||||
\(215\) | − | 278.564i | − | 1.29565i | ||||||
\(216\) | − | 183.873i | − | 0.851263i | ||||||
\(217\) | 198.155 | − | 14.4945i | 0.913158 | − | 0.0667950i | ||||
\(218\) | 205.488 | 0.942605 | ||||||||
\(219\) | −4.60587 | −0.0210314 | ||||||||
\(220\) | 221.736i | 1.00789i | ||||||||
\(221\) | 559.573 | 2.53201 | ||||||||
\(222\) | − | 106.334i | − | 0.478981i | ||||||
\(223\) | − | 221.071i | − | 0.991351i | −0.868508 | − | 0.495675i | \(-0.834921\pi\) | ||
0.868508 | − | 0.495675i | \(-0.165079\pi\) | |||||||
\(224\) | 13.8096 | + | 188.792i | 0.0616501 | + | 0.842822i | ||||
\(225\) | −268.794 | −1.19464 | ||||||||
\(226\) | 204.341 | 0.904164 | ||||||||
\(227\) | − | 50.4017i | − | 0.222034i | −0.993819 | − | 0.111017i | \(-0.964589\pi\) | ||
0.993819 | − | 0.111017i | \(-0.0354108\pi\) | |||||||
\(228\) | −9.65240 | −0.0423351 | ||||||||
\(229\) | − | 1.09640i | − | 0.00478777i | −0.999997 | − | 0.00239389i | \(-0.999238\pi\) | ||
0.999997 | − | 0.00239389i | \(-0.000761998\pi\) | |||||||
\(230\) | 360.572i | 1.56771i | ||||||||
\(231\) | 138.129 | − | 10.1038i | 0.597963 | − | 0.0437393i | ||||
\(232\) | −218.204 | −0.940534 | ||||||||
\(233\) | −62.0131 | −0.266151 | −0.133075 | − | 0.991106i | \(-0.542485\pi\) | ||||
−0.133075 | + | 0.991106i | \(0.542485\pi\) | |||||||
\(234\) | − | 188.807i | − | 0.806868i | ||||||
\(235\) | 252.189 | 1.07315 | ||||||||
\(236\) | 133.957i | 0.567616i | ||||||||
\(237\) | − | 168.719i | − | 0.711895i | ||||||
\(238\) | 318.234 | − | 23.2779i | 1.33712 | − | 0.0978065i | ||||
\(239\) | −406.937 | −1.70266 | −0.851332 | − | 0.524628i | \(-0.824204\pi\) | ||||
−0.851332 | + | 0.524628i | \(0.824204\pi\) | |||||||
\(240\) | −51.4938 | −0.214558 | ||||||||
\(241\) | 13.6742i | 0.0567396i | 0.999597 | + | 0.0283698i | \(0.00903159\pi\) | ||||
−0.999597 | + | 0.0283698i | \(0.990968\pi\) | |||||||
\(242\) | −150.311 | −0.621121 | ||||||||
\(243\) | − | 242.059i | − | 0.996129i | ||||||
\(244\) | − | 65.8845i | − | 0.270019i | ||||||
\(245\) | −56.1681 | − | 381.885i | −0.229258 | − | 1.55871i | ||||
\(246\) | −12.3192 | −0.0500782 | ||||||||
\(247\) | −69.4652 | −0.281236 | ||||||||
\(248\) | 243.007i | 0.979865i | ||||||||
\(249\) | −104.052 | −0.417880 | ||||||||
\(250\) | 138.259i | 0.553036i | ||||||||
\(251\) | 92.7847i | 0.369660i | 0.982770 | + | 0.184830i | \(0.0591735\pi\) | ||||
−0.982770 | + | 0.184830i | \(0.940827\pi\) | |||||||
\(252\) | 6.96356 | + | 95.1992i | 0.0276332 | + | 0.377775i | ||||
\(253\) | 470.721 | 1.86056 | ||||||||
\(254\) | 95.3843 | 0.375529 | ||||||||
\(255\) | − | 325.838i | − | 1.27780i | ||||||
\(256\) | −268.723 | −1.04970 | ||||||||
\(257\) | 79.9349i | 0.311031i | 0.987833 | + | 0.155515i | \(0.0497038\pi\) | ||||
−0.987833 | + | 0.155515i | \(0.950296\pi\) | |||||||
\(258\) | − | 68.0352i | − | 0.263702i | ||||||
\(259\) | 28.2239 | + | 385.850i | 0.108972 | + | 1.48977i | ||||
\(260\) | 264.686 | 1.01802 | ||||||||
\(261\) | −184.884 | −0.708367 | ||||||||
\(262\) | − | 81.5743i | − | 0.311352i | ||||||
\(263\) | 441.120 | 1.67726 | 0.838631 | − | 0.544700i | \(-0.183356\pi\) | ||||
0.838631 | + | 0.544700i | \(0.183356\pi\) | |||||||
\(264\) | 169.394i | 0.641645i | ||||||||
\(265\) | − | 235.955i | − | 0.890395i | ||||||
\(266\) | −39.5055 | + | 2.88972i | −0.148517 | + | 0.0108636i | ||||
\(267\) | −16.3602 | −0.0612743 | ||||||||
\(268\) | −130.512 | −0.486985 | ||||||||
\(269\) | − | 248.875i | − | 0.925185i | −0.886571 | − | 0.462592i | \(-0.846919\pi\) | ||
0.886571 | − | 0.462592i | \(-0.153081\pi\) | |||||||
\(270\) | −246.343 | −0.912382 | ||||||||
\(271\) | 163.181i | 0.602144i | 0.953601 | + | 0.301072i | \(0.0973444\pi\) | ||||
−0.953601 | + | 0.301072i | \(0.902656\pi\) | |||||||
\(272\) | 154.877i | 0.569401i | ||||||||
\(273\) | −12.0609 | − | 164.885i | −0.0441790 | − | 0.603973i | ||||
\(274\) | −302.835 | −1.10524 | ||||||||
\(275\) | 554.852 | 2.01764 | ||||||||
\(276\) | − | 78.0775i | − | 0.282889i | ||||||
\(277\) | −67.3157 | −0.243017 | −0.121508 | − | 0.992590i | \(-0.538773\pi\) | ||||
−0.121508 | + | 0.992590i | \(0.538773\pi\) | |||||||
\(278\) | − | 129.481i | − | 0.465758i | ||||||
\(279\) | 205.899i | 0.737989i | ||||||||
\(280\) | 470.841 | − | 34.4407i | 1.68158 | − | 0.123003i | ||||
\(281\) | 264.913 | 0.942750 | 0.471375 | − | 0.881933i | \(-0.343758\pi\) | ||||
0.471375 | + | 0.881933i | \(0.343758\pi\) | |||||||
\(282\) | 61.5935 | 0.218417 | ||||||||
\(283\) | 181.793i | 0.642380i | 0.947015 | + | 0.321190i | \(0.104083\pi\) | ||||
−0.947015 | + | 0.321190i | \(0.895917\pi\) | |||||||
\(284\) | 123.524 | 0.434942 | ||||||||
\(285\) | 40.4494i | 0.141928i | ||||||||
\(286\) | 389.741i | 1.36273i | ||||||||
\(287\) | 44.7024 | − | 3.26986i | 0.155758 | − | 0.0113932i | ||||
\(288\) | −196.170 | −0.681145 | ||||||||
\(289\) | −691.017 | −2.39106 | ||||||||
\(290\) | 292.338i | 1.00806i | ||||||||
\(291\) | −85.4402 | −0.293609 | ||||||||
\(292\) | 6.55265i | 0.0224406i | ||||||||
\(293\) | 501.075i | 1.71015i | 0.518502 | + | 0.855077i | \(0.326490\pi\) | ||||
−0.518502 | + | 0.855077i | \(0.673510\pi\) | |||||||
\(294\) | −13.7182 | − | 93.2697i | −0.0466607 | − | 0.317244i | ||||
\(295\) | 561.363 | 1.90293 | ||||||||
\(296\) | −473.185 | −1.59860 | ||||||||
\(297\) | 321.597i | 1.08282i | ||||||||
\(298\) | 176.313 | 0.591656 | ||||||||
\(299\) | − | 561.899i | − | 1.87926i | ||||||
\(300\) | − | 92.0320i | − | 0.306773i | ||||||
\(301\) | 18.0584 | + | 246.877i | 0.0599946 | + | 0.820190i | ||||
\(302\) | 40.1855 | 0.133064 | ||||||||
\(303\) | 180.074 | 0.594303 | ||||||||
\(304\) | − | 19.2264i | − | 0.0632447i | ||||||
\(305\) | −276.096 | −0.905234 | ||||||||
\(306\) | 330.670i | 1.08062i | ||||||||
\(307\) | − | 214.578i | − | 0.698951i | −0.936946 | − | 0.349475i | \(-0.886360\pi\) | ||
0.936946 | − | 0.349475i | \(-0.113640\pi\) | |||||||
\(308\) | −14.3744 | − | 196.513i | −0.0466701 | − | 0.638030i | ||||
\(309\) | 55.6414 | 0.180069 | ||||||||
\(310\) | 325.567 | 1.05022 | ||||||||
\(311\) | − | 454.796i | − | 1.46237i | −0.682181 | − | 0.731183i | \(-0.738968\pi\) | ||
0.682181 | − | 0.731183i | \(-0.261032\pi\) | |||||||
\(312\) | 202.205 | 0.648094 | ||||||||
\(313\) | − | 116.264i | − | 0.371450i | −0.982602 | − | 0.185725i | \(-0.940537\pi\) | ||
0.982602 | − | 0.185725i | \(-0.0594634\pi\) | |||||||
\(314\) | − | 324.779i | − | 1.03433i | ||||||
\(315\) | 398.943 | − | 29.1816i | 1.26649 | − | 0.0926399i | ||||
\(316\) | −240.032 | −0.759596 | ||||||||
\(317\) | 242.467 | 0.764881 | 0.382441 | − | 0.923980i | \(-0.375084\pi\) | ||||
0.382441 | + | 0.923980i | \(0.375084\pi\) | |||||||
\(318\) | − | 57.6284i | − | 0.181221i | ||||||
\(319\) | 381.642 | 1.19637 | ||||||||
\(320\) | 466.072i | 1.45648i | ||||||||
\(321\) | − | 54.1680i | − | 0.168748i | ||||||
\(322\) | −23.3747 | − | 319.557i | −0.0725922 | − | 0.992412i | ||||
\(323\) | 121.659 | 0.376653 | ||||||||
\(324\) | −69.3835 | −0.214147 | ||||||||
\(325\) | − | 662.325i | − | 2.03792i | ||||||
\(326\) | −290.383 | −0.890747 | ||||||||
\(327\) | 186.465i | 0.570229i | ||||||||
\(328\) | 54.8206i | 0.167136i | ||||||||
\(329\) | −223.503 | + | 16.3486i | −0.679339 | + | 0.0496918i | ||||
\(330\) | 226.945 | 0.687713 | ||||||||
\(331\) | −76.9100 | −0.232357 | −0.116178 | − | 0.993228i | \(-0.537064\pi\) | ||||
−0.116178 | + | 0.993228i | \(0.537064\pi\) | |||||||
\(332\) | 148.032i | 0.445881i | ||||||||
\(333\) | −400.929 | −1.20399 | ||||||||
\(334\) | 73.0331i | 0.218662i | ||||||||
\(335\) | 546.924i | 1.63261i | ||||||||
\(336\) | 45.6363 | − | 3.33817i | 0.135822 | − | 0.00993503i | ||||
\(337\) | 179.426 | 0.532422 | 0.266211 | − | 0.963915i | \(-0.414228\pi\) | ||||
0.266211 | + | 0.963915i | \(0.414228\pi\) | |||||||
\(338\) | 219.153 | 0.648381 | ||||||||
\(339\) | 185.424i | 0.546973i | ||||||||
\(340\) | −463.561 | −1.36342 | ||||||||
\(341\) | − | 425.023i | − | 1.24640i | ||||||
\(342\) | − | 41.0493i | − | 0.120027i | ||||||
\(343\) | 74.5352 | + | 334.804i | 0.217304 | + | 0.976104i | ||||
\(344\) | −302.756 | −0.880106 | ||||||||
\(345\) | −327.192 | −0.948383 | ||||||||
\(346\) | − | 301.140i | − | 0.870348i | ||||||
\(347\) | 452.745 | 1.30474 | 0.652370 | − | 0.757901i | \(-0.273775\pi\) | ||||
0.652370 | + | 0.757901i | \(0.273775\pi\) | |||||||
\(348\) | − | 63.3022i | − | 0.181903i | ||||||
\(349\) | 369.379i | 1.05839i | 0.848499 | + | 0.529197i | \(0.177507\pi\) | ||||
−0.848499 | + | 0.529197i | \(0.822493\pi\) | |||||||
\(350\) | −27.5524 | − | 376.670i | −0.0787210 | − | 1.07620i | ||||
\(351\) | 383.889 | 1.09370 | ||||||||
\(352\) | 404.940 | 1.15040 | ||||||||
\(353\) | − | 114.503i | − | 0.324370i | −0.986760 | − | 0.162185i | \(-0.948146\pi\) | ||
0.986760 | − | 0.162185i | \(-0.0518541\pi\) | |||||||
\(354\) | 137.105 | 0.387301 | ||||||||
\(355\) | − | 517.639i | − | 1.45814i | ||||||
\(356\) | 23.2753i | 0.0653800i | ||||||||
\(357\) | 21.1230 | + | 288.773i | 0.0591680 | + | 0.808889i | ||||
\(358\) | −257.820 | −0.720169 | ||||||||
\(359\) | −402.956 | −1.12244 | −0.561220 | − | 0.827667i | \(-0.689668\pi\) | ||||
−0.561220 | + | 0.827667i | \(0.689668\pi\) | |||||||
\(360\) | 489.241i | 1.35900i | ||||||||
\(361\) | 345.897 | 0.958164 | ||||||||
\(362\) | − | 140.095i | − | 0.387002i | ||||||
\(363\) | − | 136.396i | − | 0.375747i | ||||||
\(364\) | −234.577 | + | 17.1587i | −0.644443 | + | 0.0471392i | ||||
\(365\) | 27.4596 | 0.0752318 | ||||||||
\(366\) | −67.4324 | −0.184242 | ||||||||
\(367\) | 103.133i | 0.281016i | 0.990080 | + | 0.140508i | \(0.0448736\pi\) | ||||
−0.990080 | + | 0.140508i | \(0.955126\pi\) | |||||||
\(368\) | 155.521 | 0.422611 | ||||||||
\(369\) | 46.4493i | 0.125879i | ||||||||
\(370\) | 633.948i | 1.71337i | ||||||||
\(371\) | 15.2961 | + | 209.115i | 0.0412295 | + | 0.563651i | ||||
\(372\) | −70.4976 | −0.189510 | ||||||||
\(373\) | 17.4499 | 0.0467825 | 0.0233912 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233912 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(374\) | − | 682.579i | − | 1.82508i | ||||||
\(375\) | −125.460 | −0.334559 | ||||||||
\(376\) | − | 274.091i | − | 0.728965i | ||||||
\(377\) | − | 455.566i | − | 1.20840i | ||||||
\(378\) | 218.321 | − | 15.9696i | 0.577569 | − | 0.0422476i | ||||
\(379\) | 225.752 | 0.595653 | 0.297827 | − | 0.954620i | \(-0.403738\pi\) | ||||
0.297827 | + | 0.954620i | \(0.403738\pi\) | |||||||
\(380\) | 57.5463 | 0.151438 | ||||||||
\(381\) | 86.5540i | 0.227176i | ||||||||
\(382\) | 380.349 | 0.995678 | ||||||||
\(383\) | − | 372.599i | − | 0.972843i | −0.873724 | − | 0.486421i | \(-0.838302\pi\) | ||
0.873724 | − | 0.486421i | \(-0.161698\pi\) | |||||||
\(384\) | − | 29.0930i | − | 0.0757630i | ||||||
\(385\) | −823.510 | + | 60.2374i | −2.13899 | + | 0.156461i | ||||
\(386\) | 85.4453 | 0.221361 | ||||||||
\(387\) | −256.525 | −0.662855 | ||||||||
\(388\) | 121.554i | 0.313283i | ||||||||
\(389\) | 209.375 | 0.538239 | 0.269119 | − | 0.963107i | \(-0.413267\pi\) | ||||
0.269119 | + | 0.963107i | \(0.413267\pi\) | |||||||
\(390\) | − | 270.904i | − | 0.694626i | ||||||
\(391\) | 984.090i | 2.51685i | ||||||||
\(392\) | −415.050 | + | 61.0461i | −1.05880 | + | 0.155730i | ||||
\(393\) | 74.0225 | 0.188352 | ||||||||
\(394\) | 180.419 | 0.457915 | ||||||||
\(395\) | 1005.88i | 2.54654i | ||||||||
\(396\) | 204.193 | 0.515638 | ||||||||
\(397\) | − | 582.691i | − | 1.46773i | −0.679293 | − | 0.733867i | \(-0.737713\pi\) | ||
0.679293 | − | 0.733867i | \(-0.262287\pi\) | |||||||
\(398\) | − | 15.0194i | − | 0.0377373i | ||||||
\(399\) | −2.62220 | − | 35.8482i | −0.00657193 | − | 0.0898452i | ||||
\(400\) | 183.316 | 0.458291 | ||||||||
\(401\) | 317.065 | 0.790686 | 0.395343 | − | 0.918533i | \(-0.370626\pi\) | ||||
0.395343 | + | 0.918533i | \(0.370626\pi\) | |||||||
\(402\) | 133.578i | 0.332284i | ||||||||
\(403\) | −507.348 | −1.25893 | ||||||||
\(404\) | − | 256.186i | − | 0.634124i | ||||||
\(405\) | 290.759i | 0.717924i | ||||||||
\(406\) | −18.9513 | − | 259.084i | −0.0466780 | − | 0.638138i | ||||
\(407\) | 827.609 | 2.03344 | ||||||||
\(408\) | −354.136 | −0.867979 | ||||||||
\(409\) | − | 309.038i | − | 0.755595i | −0.925888 | − | 0.377798i | \(-0.876681\pi\) | ||
0.925888 | − | 0.377798i | \(-0.123319\pi\) | |||||||
\(410\) | 73.4457 | 0.179136 | ||||||||
\(411\) | − | 274.800i | − | 0.668614i | ||||||
\(412\) | − | 79.1596i | − | 0.192135i | ||||||
\(413\) | −497.507 | + | 36.3913i | −1.20462 | + | 0.0881145i | ||||
\(414\) | 332.045 | 0.802040 | ||||||||
\(415\) | 620.346 | 1.49481 | ||||||||
\(416\) | − | 483.375i | − | 1.16196i | ||||||
\(417\) | 117.494 | 0.281760 | ||||||||
\(418\) | 84.7352i | 0.202716i | ||||||||
\(419\) | − | 433.901i | − | 1.03556i | −0.855513 | − | 0.517782i | \(-0.826758\pi\) | ||
0.855513 | − | 0.517782i | \(-0.173242\pi\) | |||||||
\(420\) | 9.99145 | + | 136.594i | 0.0237892 | + | 0.325223i | ||||
\(421\) | 244.765 | 0.581389 | 0.290695 | − | 0.956816i | \(-0.406114\pi\) | ||||
0.290695 | + | 0.956816i | \(0.406114\pi\) | |||||||
\(422\) | −20.3505 | −0.0482240 | ||||||||
\(423\) | − | 232.237i | − | 0.549023i | ||||||
\(424\) | −256.446 | −0.604826 | ||||||||
\(425\) | 1159.97i | 2.72935i | ||||||||
\(426\) | − | 126.426i | − | 0.296774i | ||||||
\(427\) | 244.690 | − | 17.8984i | 0.573045 | − | 0.0419166i | ||||
\(428\) | −77.0634 | −0.180055 | ||||||||
\(429\) | −353.661 | −0.824384 | ||||||||
\(430\) | 405.617i | 0.943295i | ||||||||
\(431\) | −364.787 | −0.846374 | −0.423187 | − | 0.906042i | \(-0.639089\pi\) | ||||
−0.423187 | + | 0.906042i | \(0.639089\pi\) | |||||||
\(432\) | 106.252i | 0.245953i | ||||||||
\(433\) | 530.061i | 1.22416i | 0.790796 | + | 0.612080i | \(0.209667\pi\) | ||||
−0.790796 | + | 0.612080i | \(0.790333\pi\) | |||||||
\(434\) | −288.534 | + | 21.1054i | −0.664824 | + | 0.0486300i | ||||
\(435\) | −265.275 | −0.609827 | ||||||||
\(436\) | 265.279 | 0.608437 | ||||||||
\(437\) | − | 122.165i | − | 0.279553i | ||||||
\(438\) | 6.70660 | 0.0153119 | ||||||||
\(439\) | 187.033i | 0.426044i | 0.977047 | + | 0.213022i | \(0.0683306\pi\) | ||||
−0.977047 | + | 0.213022i | \(0.931669\pi\) | |||||||
\(440\) | − | 1009.91i | − | 2.29524i | ||||||
\(441\) | −351.671 | + | 51.7242i | −0.797439 | + | 0.117288i | ||||
\(442\) | −814.793 | −1.84342 | ||||||||
\(443\) | −313.872 | −0.708515 | −0.354258 | − | 0.935148i | \(-0.615266\pi\) | ||||
−0.354258 | + | 0.935148i | \(0.615266\pi\) | |||||||
\(444\) | − | 137.274i | − | 0.309175i | ||||||
\(445\) | 97.5376 | 0.219186 | ||||||||
\(446\) | 321.901i | 0.721752i | ||||||||
\(447\) | 159.991i | 0.357922i | ||||||||
\(448\) | −30.2139 | − | 413.056i | −0.0674417 | − | 0.921999i | ||||
\(449\) | −737.074 | −1.64159 | −0.820795 | − | 0.571223i | \(-0.806469\pi\) | ||||
−0.820795 | + | 0.571223i | \(0.806469\pi\) | |||||||
\(450\) | 391.390 | 0.869755 | ||||||||
\(451\) | − | 95.8821i | − | 0.212599i | ||||||
\(452\) | 263.798 | 0.583624 | ||||||||
\(453\) | 36.4653i | 0.0804973i | ||||||||
\(454\) | 73.3899i | 0.161652i | ||||||||
\(455\) | 71.9053 | + | 983.022i | 0.158034 | + | 2.16049i | ||||
\(456\) | 43.9623 | 0.0964085 | ||||||||
\(457\) | 766.856 | 1.67802 | 0.839011 | − | 0.544115i | \(-0.183135\pi\) | ||||
0.839011 | + | 0.544115i | \(0.183135\pi\) | |||||||
\(458\) | 1.59647i | 0.00348573i | ||||||||
\(459\) | −672.330 | −1.46477 | ||||||||
\(460\) | 465.488i | 1.01193i | ||||||||
\(461\) | − | 689.894i | − | 1.49652i | −0.663408 | − | 0.748258i | \(-0.730891\pi\) | ||
0.663408 | − | 0.748258i | \(-0.269109\pi\) | |||||||
\(462\) | −201.130 | + | 14.7121i | −0.435346 | + | 0.0318444i | ||||
\(463\) | 196.171 | 0.423696 | 0.211848 | − | 0.977303i | \(-0.432052\pi\) | ||||
0.211848 | + | 0.977303i | \(0.432052\pi\) | |||||||
\(464\) | 126.090 | 0.271746 | ||||||||
\(465\) | 295.428i | 0.635328i | ||||||||
\(466\) | 90.2972 | 0.193771 | ||||||||
\(467\) | 739.115i | 1.58269i | 0.611371 | + | 0.791344i | \(0.290618\pi\) | ||||
−0.611371 | + | 0.791344i | \(0.709382\pi\) | |||||||
\(468\) | − | 243.744i | − | 0.520821i | ||||||
\(469\) | −35.4553 | − | 484.711i | −0.0755976 | − | 1.03350i | ||||
\(470\) | −367.213 | −0.781303 | ||||||||
\(471\) | 294.712 | 0.625716 | ||||||||
\(472\) | − | 610.115i | − | 1.29262i | ||||||
\(473\) | 529.526 | 1.11951 | ||||||||
\(474\) | 245.672i | 0.518295i | ||||||||
\(475\) | − | 143.999i | − | 0.303155i | ||||||
\(476\) | 410.831 | − | 30.0511i | 0.863089 | − | 0.0631326i | ||||
\(477\) | −217.286 | −0.455527 | ||||||||
\(478\) | 592.540 | 1.23962 | ||||||||
\(479\) | − | 97.3743i | − | 0.203287i | −0.994821 | − | 0.101643i | \(-0.967590\pi\) | ||
0.994821 | − | 0.101643i | \(-0.0324100\pi\) | |||||||
\(480\) | −281.468 | −0.586392 | ||||||||
\(481\) | − | 987.915i | − | 2.05388i | ||||||
\(482\) | − | 19.9110i | − | 0.0413092i | ||||||
\(483\) | 289.974 | − | 21.2108i | 0.600359 | − | 0.0439146i | ||||
\(484\) | −194.047 | −0.400924 | ||||||||
\(485\) | 509.384 | 1.05028 | ||||||||
\(486\) | 352.462i | 0.725231i | ||||||||
\(487\) | −624.316 | −1.28196 | −0.640982 | − | 0.767556i | \(-0.721473\pi\) | ||||
−0.640982 | + | 0.767556i | \(0.721473\pi\) | |||||||
\(488\) | 300.074i | 0.614906i | ||||||||
\(489\) | − | 263.501i | − | 0.538857i | ||||||
\(490\) | 81.7863 | + | 556.062i | 0.166911 | + | 1.13482i | ||||
\(491\) | −436.382 | −0.888761 | −0.444380 | − | 0.895838i | \(-0.646576\pi\) | ||||
−0.444380 | + | 0.895838i | \(0.646576\pi\) | |||||||
\(492\) | −15.9038 | −0.0323247 | ||||||||
\(493\) | 797.862i | 1.61838i | ||||||||
\(494\) | 101.148 | 0.204753 | ||||||||
\(495\) | − | 855.691i | − | 1.72867i | ||||||
\(496\) | − | 140.422i | − | 0.283110i | ||||||
\(497\) | 33.5568 | + | 458.757i | 0.0675187 | + | 0.923053i | ||||
\(498\) | 151.510 | 0.304237 | ||||||||
\(499\) | −201.548 | −0.403904 | −0.201952 | − | 0.979395i | \(-0.564728\pi\) | ||||
−0.201952 | + | 0.979395i | \(0.564728\pi\) | |||||||
\(500\) | 178.488i | 0.356976i | ||||||||
\(501\) | −66.2720 | −0.132279 | ||||||||
\(502\) | − | 135.104i | − | 0.269131i | ||||||
\(503\) | 389.359i | 0.774074i | 0.922064 | + | 0.387037i | \(0.126501\pi\) | ||||
−0.922064 | + | 0.387037i | \(0.873499\pi\) | |||||||
\(504\) | −31.7158 | − | 433.589i | −0.0629283 | − | 0.860296i | ||||
\(505\) | −1073.58 | −2.12589 | ||||||||
\(506\) | −685.416 | −1.35458 | ||||||||
\(507\) | 198.864i | 0.392238i | ||||||||
\(508\) | 123.138 | 0.242398 | ||||||||
\(509\) | − | 298.276i | − | 0.586004i | −0.956112 | − | 0.293002i | \(-0.905346\pi\) | ||
0.956112 | − | 0.293002i | \(-0.0946542\pi\) | |||||||
\(510\) | 474.452i | 0.930298i | ||||||||
\(511\) | −24.3360 | + | 1.78011i | −0.0476243 | + | 0.00348359i | ||||
\(512\) | 303.214 | 0.592215 | ||||||||
\(513\) | 83.4629 | 0.162696 | ||||||||
\(514\) | − | 116.393i | − | 0.226446i | ||||||
\(515\) | −331.727 | −0.644130 | ||||||||
\(516\) | − | 87.8313i | − | 0.170216i | ||||||
\(517\) | 479.390i | 0.927253i | ||||||||
\(518\) | −41.0967 | − | 561.836i | −0.0793373 | − | 1.08463i | ||||
\(519\) | 273.262 | 0.526516 | ||||||||
\(520\) | −1205.52 | −2.31831 | ||||||||
\(521\) | 749.351i | 1.43829i | 0.694858 | + | 0.719147i | \(0.255467\pi\) | ||||
−0.694858 | + | 0.719147i | \(0.744533\pi\) | |||||||
\(522\) | 269.209 | 0.515726 | ||||||||
\(523\) | − | 730.100i | − | 1.39599i | −0.716105 | − | 0.697993i | \(-0.754077\pi\) | ||
0.716105 | − | 0.697993i | \(-0.245923\pi\) | |||||||
\(524\) | − | 105.310i | − | 0.200973i | ||||||
\(525\) | 341.800 | − | 25.0017i | 0.651047 | − | 0.0476223i | ||||
\(526\) | −642.314 | −1.22113 | ||||||||
\(527\) | 888.553 | 1.68606 | ||||||||
\(528\) | − | 97.8852i | − | 0.185389i | ||||||
\(529\) | 459.180 | 0.868016 | ||||||||
\(530\) | 343.573i | 0.648251i | ||||||||
\(531\) | − | 516.949i | − | 0.973539i | ||||||
\(532\) | −51.0004 | + | 3.73053i | −0.0958653 | + | 0.00701228i | ||||
\(533\) | −114.454 | −0.214736 | ||||||||
\(534\) | 23.8221 | 0.0446107 | ||||||||
\(535\) | 322.942i | 0.603631i | ||||||||
\(536\) | 594.422 | 1.10900 | ||||||||
\(537\) | − | 233.952i | − | 0.435666i | ||||||
\(538\) | 362.386i | 0.673580i | ||||||||
\(539\) | 725.929 | − | 106.771i | 1.34681 | − | 0.198090i | ||||
\(540\) | −318.021 | −0.588928 | ||||||||
\(541\) | −328.785 | −0.607736 | −0.303868 | − | 0.952714i | \(-0.598278\pi\) | ||||
−0.303868 | + | 0.952714i | \(0.598278\pi\) | |||||||
\(542\) | − | 237.608i | − | 0.438390i | ||||||
\(543\) | 127.125 | 0.234117 | ||||||||
\(544\) | 846.567i | 1.55619i | ||||||||
\(545\) | − | 1111.68i | − | 2.03978i | ||||||
\(546\) | 17.5618 | + | 240.088i | 0.0321645 | + | 0.439722i | ||||
\(547\) | −936.113 | −1.71136 | −0.855679 | − | 0.517507i | \(-0.826860\pi\) | ||||
−0.855679 | + | 0.517507i | \(0.826860\pi\) | |||||||
\(548\) | −390.951 | −0.713415 | ||||||||
\(549\) | 254.252i | 0.463119i | ||||||||
\(550\) | −807.919 | −1.46894 | ||||||||
\(551\) | − | 99.0463i | − | 0.179757i | ||||||
\(552\) | 355.607i | 0.644216i | ||||||||
\(553\) | −65.2079 | − | 891.461i | −0.117917 | − | 1.61205i | ||||
\(554\) | 98.0182 | 0.176928 | ||||||||
\(555\) | −575.260 | −1.03650 | ||||||||
\(556\) | − | 167.155i | − | 0.300639i | ||||||
\(557\) | −155.016 | −0.278305 | −0.139152 | − | 0.990271i | \(-0.544438\pi\) | ||||
−0.139152 | + | 0.990271i | \(0.544438\pi\) | |||||||
\(558\) | − | 299.809i | − | 0.537292i | ||||||
\(559\) | − | 632.094i | − | 1.13076i | ||||||
\(560\) | −272.078 | + | 19.9017i | −0.485853 | + | 0.0355388i | ||||
\(561\) | 619.389 | 1.10408 | ||||||||
\(562\) | −385.739 | −0.686368 | ||||||||
\(563\) | 85.7911i | 0.152382i | 0.997093 | + | 0.0761910i | \(0.0242759\pi\) | ||||
−0.997093 | + | 0.0761910i | \(0.975724\pi\) | |||||||
\(564\) | 79.5153 | 0.140985 | ||||||||
\(565\) | − | 1105.47i | − | 1.95659i | ||||||
\(566\) | − | 264.709i | − | 0.467684i | ||||||
\(567\) | −18.8489 | − | 257.685i | −0.0332433 | − | 0.454471i | ||||
\(568\) | −562.594 | −0.990483 | ||||||||
\(569\) | 298.630 | 0.524833 | 0.262416 | − | 0.964955i | \(-0.415481\pi\) | ||||
0.262416 | + | 0.964955i | \(0.415481\pi\) | |||||||
\(570\) | − | 58.8983i | − | 0.103330i | ||||||
\(571\) | −329.213 | −0.576554 | −0.288277 | − | 0.957547i | \(-0.593082\pi\) | ||||
−0.288277 | + | 0.957547i | \(0.593082\pi\) | |||||||
\(572\) | 503.144i | 0.879622i | ||||||||
\(573\) | 345.138i | 0.602335i | ||||||||
\(574\) | −65.0911 | + | 4.76124i | −0.113399 | + | 0.00829483i | ||||
\(575\) | 1164.79 | 2.02573 | ||||||||
\(576\) | 429.197 | 0.745134 | ||||||||
\(577\) | 324.811i | 0.562931i | 0.959571 | + | 0.281465i | \(0.0908204\pi\) | ||||
−0.959571 | + | 0.281465i | \(0.909180\pi\) | |||||||
\(578\) | 1006.19 | 1.74081 | ||||||||
\(579\) | 77.5351i | 0.133912i | ||||||||
\(580\) | 377.399i | 0.650689i | ||||||||
\(581\) | −549.781 | + | 40.2149i | −0.946266 | + | 0.0692167i | ||||
\(582\) | 124.409 | 0.213762 | ||||||||
\(583\) | 448.529 | 0.769347 | ||||||||
\(584\) | − | 29.8443i | − | 0.0511033i | ||||||
\(585\) | −1021.44 | −1.74605 | ||||||||
\(586\) | − | 729.614i | − | 1.24508i | ||||||
\(587\) | − | 901.749i | − | 1.53620i | −0.640331 | − | 0.768099i | \(-0.721203\pi\) | ||
0.640331 | − | 0.768099i | \(-0.278797\pi\) | |||||||
\(588\) | −17.7098 | − | 120.408i | −0.0301187 | − | 0.204776i | ||||
\(589\) | −110.305 | −0.187274 | ||||||||
\(590\) | −817.400 | −1.38542 | ||||||||
\(591\) | 163.716i | 0.277016i | ||||||||
\(592\) | 273.432 | 0.461879 | ||||||||
\(593\) | 444.484i | 0.749552i | 0.927115 | + | 0.374776i | \(0.122280\pi\) | ||||
−0.927115 | + | 0.374776i | \(0.877720\pi\) | |||||||
\(594\) | − | 468.276i | − | 0.788344i | ||||||
\(595\) | −125.932 | − | 1721.63i | −0.211651 | − | 2.89350i | ||||
\(596\) | 227.615 | 0.381905 | ||||||||
\(597\) | 13.6290 | 0.0228292 | ||||||||
\(598\) | 818.180i | 1.36819i | ||||||||
\(599\) | −1001.31 | −1.67164 | −0.835818 | − | 0.549006i | \(-0.815006\pi\) | ||||
−0.835818 | + | 0.549006i | \(0.815006\pi\) | |||||||
\(600\) | 419.164i | 0.698607i | ||||||||
\(601\) | 499.342i | 0.830852i | 0.909627 | + | 0.415426i | \(0.136367\pi\) | ||||
−0.909627 | + | 0.415426i | \(0.863633\pi\) | |||||||
\(602\) | −26.2948 | − | 359.478i | −0.0436790 | − | 0.597139i | ||||
\(603\) | 503.653 | 0.835245 | ||||||||
\(604\) | 51.8782 | 0.0858911 | ||||||||
\(605\) | 813.176i | 1.34409i | ||||||||
\(606\) | −262.205 | −0.432681 | ||||||||
\(607\) | − | 390.190i | − | 0.642817i | −0.946941 | − | 0.321409i | \(-0.895844\pi\) | ||
0.946941 | − | 0.321409i | \(-0.104156\pi\) | |||||||
\(608\) | − | 105.093i | − | 0.172850i | ||||||
\(609\) | 235.099 | − | 17.1969i | 0.386042 | − | 0.0282379i | ||||
\(610\) | 402.023 | 0.659055 | ||||||||
\(611\) | 572.247 | 0.936574 | ||||||||
\(612\) | 426.885i | 0.697525i | ||||||||
\(613\) | 1110.61 | 1.81177 | 0.905883 | − | 0.423528i | \(-0.139208\pi\) | ||||
0.905883 | + | 0.423528i | \(0.139208\pi\) | |||||||
\(614\) | 312.446i | 0.508870i | ||||||||
\(615\) | 66.6464i | 0.108368i | ||||||||
\(616\) | 65.4688 | + | 895.028i | 0.106281 | + | 1.45297i | ||||
\(617\) | 909.843 | 1.47462 | 0.737312 | − | 0.675552i | \(-0.236095\pi\) | ||||
0.737312 | + | 0.675552i | \(0.236095\pi\) | |||||||
\(618\) | −81.0194 | −0.131099 | ||||||||
\(619\) | 789.543i | 1.27551i | 0.770237 | + | 0.637757i | \(0.220138\pi\) | ||||
−0.770237 | + | 0.637757i | \(0.779862\pi\) | |||||||
\(620\) | 420.297 | 0.677899 | ||||||||
\(621\) | 675.125i | 1.08716i | ||||||||
\(622\) | 662.228i | 1.06467i | ||||||||
\(623\) | −86.4425 | + | 6.32303i | −0.138752 | + | 0.0101493i | ||||
\(624\) | −116.845 | −0.187252 | ||||||||
\(625\) | −178.367 | −0.285388 | ||||||||
\(626\) | 169.292i | 0.270434i | ||||||||
\(627\) | −76.8908 | −0.122633 | ||||||||
\(628\) | − | 419.279i | − | 0.667642i | ||||||
\(629\) | 1730.20i | 2.75072i | ||||||||
\(630\) | −580.900 | + | 42.4912i | −0.922063 | + | 0.0674464i | ||||
\(631\) | −129.683 | −0.205520 | −0.102760 | − | 0.994706i | \(-0.532767\pi\) | ||||
−0.102760 | + | 0.994706i | \(0.532767\pi\) | |||||||
\(632\) | 1093.24 | 1.72981 | ||||||||
\(633\) | − | 18.4666i | − | 0.0291731i | ||||||
\(634\) | −353.056 | −0.556871 | ||||||||
\(635\) | − | 516.024i | − | 0.812636i | ||||||
\(636\) | − | 74.3965i | − | 0.116976i | ||||||
\(637\) | −127.452 | − | 866.540i | −0.200081 | − | 1.36035i | ||||
\(638\) | −555.709 | −0.871017 | ||||||||
\(639\) | −476.685 | −0.745986 | ||||||||
\(640\) | 173.449i | 0.271013i | ||||||||
\(641\) | −1056.43 | −1.64810 | −0.824051 | − | 0.566515i | \(-0.808291\pi\) | ||||
−0.824051 | + | 0.566515i | \(0.808291\pi\) | |||||||
\(642\) | 78.8739i | 0.122857i | ||||||||
\(643\) | 161.719i | 0.251506i | 0.992062 | + | 0.125753i | \(0.0401347\pi\) | ||||
−0.992062 | + | 0.125753i | \(0.959865\pi\) | |||||||
\(644\) | −30.1760 | − | 412.538i | −0.0468571 | − | 0.640587i | ||||
\(645\) | −368.067 | −0.570646 | ||||||||
\(646\) | −177.147 | −0.274222 | ||||||||
\(647\) | 338.032i | 0.522460i | 0.965277 | + | 0.261230i | \(0.0841282\pi\) | ||||
−0.965277 | + | 0.261230i | \(0.915872\pi\) | |||||||
\(648\) | 316.010 | 0.487670 | ||||||||
\(649\) | 1067.10i | 1.64423i | ||||||||
\(650\) | 964.410i | 1.48371i | ||||||||
\(651\) | −19.1516 | − | 261.822i | −0.0294187 | − | 0.402185i | ||||
\(652\) | −374.876 | −0.574963 | ||||||||
\(653\) | −809.820 | −1.24015 | −0.620076 | − | 0.784542i | \(-0.712898\pi\) | ||||
−0.620076 | + | 0.784542i | \(0.712898\pi\) | |||||||
\(654\) | − | 271.511i | − | 0.415155i | ||||||
\(655\) | −441.312 | −0.673759 | ||||||||
\(656\) | − | 31.6783i | − | 0.0482901i | ||||||
\(657\) | − | 25.2870i | − | 0.0384886i | ||||||
\(658\) | 325.442 | − | 23.8051i | 0.494592 | − | 0.0361780i | ||||
\(659\) | 89.0519 | 0.135132 | 0.0675660 | − | 0.997715i | \(-0.478477\pi\) | ||||
0.0675660 | + | 0.997715i | \(0.478477\pi\) | |||||||
\(660\) | 292.979 | 0.443908 | ||||||||
\(661\) | − | 1248.26i | − | 1.88844i | −0.329320 | − | 0.944218i | \(-0.606820\pi\) | ||
0.329320 | − | 0.944218i | \(-0.393180\pi\) | |||||||
\(662\) | 111.989 | 0.169167 | ||||||||
\(663\) | − | 739.363i | − | 1.11518i | ||||||
\(664\) | − | 674.220i | − | 1.01539i | ||||||
\(665\) | 15.6332 | + | 213.723i | 0.0235086 | + | 0.321387i | ||||
\(666\) | 583.792 | 0.876564 | ||||||||
\(667\) | 801.178 | 1.20117 | ||||||||
\(668\) | 94.2835i | 0.141143i | ||||||||
\(669\) | −292.101 | −0.436624 | ||||||||
\(670\) | − | 796.376i | − | 1.18862i | ||||||
\(671\) | − | 524.835i | − | 0.782168i | ||||||
\(672\) | 249.451 | − | 18.2466i | 0.371207 | − | 0.0271527i | ||||
\(673\) | 117.757 | 0.174973 | 0.0874865 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874865 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(674\) | −261.262 | −0.387629 | ||||||||
\(675\) | 795.787i | 1.17894i | ||||||||
\(676\) | 282.919 | 0.418520 | ||||||||
\(677\) | − | 238.601i | − | 0.352439i | −0.984351 | − | 0.176219i | \(-0.943613\pi\) | ||
0.984351 | − | 0.176219i | \(-0.0563868\pi\) | |||||||
\(678\) | − | 269.996i | − | 0.398224i | ||||||
\(679\) | −451.441 | + | 33.0216i | −0.664861 | + | 0.0486327i | ||||
\(680\) | 2111.31 | 3.10487 | ||||||||
\(681\) | −66.5958 | −0.0977912 | ||||||||
\(682\) | 618.875i | 0.907441i | ||||||||
\(683\) | −977.551 | −1.43126 | −0.715630 | − | 0.698479i | \(-0.753860\pi\) | ||||
−0.715630 | + | 0.698479i | \(0.753860\pi\) | |||||||
\(684\) | − | 52.9934i | − | 0.0774757i | ||||||
\(685\) | 1638.32i | 2.39171i | ||||||||
\(686\) | −108.531 | − | 487.507i | −0.158208 | − | 0.710652i | ||||
\(687\) | −1.44867 | −0.00210869 | ||||||||
\(688\) | 174.949 | 0.254287 | ||||||||
\(689\) | − | 535.408i | − | 0.777080i | ||||||
\(690\) | 476.424 | 0.690470 | ||||||||
\(691\) | 618.478i | 0.895048i | 0.894272 | + | 0.447524i | \(0.147694\pi\) | ||||
−0.894272 | + | 0.447524i | \(0.852306\pi\) | |||||||
\(692\) | − | 388.763i | − | 0.561796i | ||||||
\(693\) | 55.4716 | + | 758.355i | 0.0800455 | + | 1.09431i | ||||
\(694\) | −659.241 | −0.949915 | ||||||||
\(695\) | −700.483 | −1.00789 | ||||||||
\(696\) | 288.313i | 0.414242i | ||||||||
\(697\) | 200.451 | 0.287591 | ||||||||
\(698\) | − | 537.853i | − | 0.770562i | ||||||
\(699\) | 81.9379i | 0.117222i | ||||||||
\(700\) | −35.5693 | − | 486.270i | −0.0508132 | − | 0.694671i | ||||
\(701\) | −838.901 | −1.19672 | −0.598360 | − | 0.801227i | \(-0.704181\pi\) | ||||
−0.598360 | + | 0.801227i | \(0.704181\pi\) | |||||||
\(702\) | −558.980 | −0.796268 | ||||||||
\(703\) | − | 214.786i | − | 0.305528i | ||||||
\(704\) | −885.962 | −1.25847 | ||||||||
\(705\) | − | 333.218i | − | 0.472649i | ||||||
\(706\) | 166.727i | 0.236157i | ||||||||
\(707\) | 951.455 | − | 69.5963i | 1.34576 | − | 0.0984389i | ||||
\(708\) | 176.998 | 0.249997 | ||||||||
\(709\) | −604.689 | −0.852876 | −0.426438 | − | 0.904517i | \(-0.640232\pi\) | ||||
−0.426438 | + | 0.904517i | \(0.640232\pi\) | |||||||
\(710\) | 753.734i | 1.06160i | ||||||||
\(711\) | 926.298 | 1.30281 | ||||||||
\(712\) | − | 106.008i | − | 0.148888i | ||||||
\(713\) | − | 892.246i | − | 1.25140i | ||||||
\(714\) | −30.7571 | − | 420.483i | −0.0430772 | − | 0.588911i | ||||
\(715\) | 2108.48 | 2.94892 | ||||||||
\(716\) | −332.838 | −0.464858 | ||||||||
\(717\) | 537.685i | 0.749909i | ||||||||
\(718\) | 586.743 | 0.817191 | ||||||||
\(719\) | 1058.54i | 1.47223i | 0.676854 | + | 0.736117i | \(0.263343\pi\) | ||||
−0.676854 | + | 0.736117i | \(0.736657\pi\) | |||||||
\(720\) | − | 282.710i | − | 0.392653i | ||||||
\(721\) | 293.993 | − | 21.5047i | 0.407757 | − | 0.0298263i | ||||
\(722\) | −503.660 | −0.697591 | ||||||||
\(723\) | 18.0678 | 0.0249900 | ||||||||
\(724\) | − | 180.858i | − | 0.249804i | ||||||
\(725\) | 944.370 | 1.30258 | ||||||||
\(726\) | 198.606i | 0.273562i | ||||||||
\(727\) | − | 1107.76i | − | 1.52375i | −0.647726 | − | 0.761873i | \(-0.724280\pi\) | ||
0.647726 | − | 0.761873i | \(-0.275720\pi\) | |||||||
\(728\) | 1068.39 | − | 78.1499i | 1.46757 | − | 0.107349i | ||||
\(729\) | 12.3615 | 0.0169568 | ||||||||
\(730\) | −39.9839 | −0.0547724 | ||||||||
\(731\) | 1107.03i | 1.51440i | ||||||||
\(732\) | −87.0532 | −0.118925 | ||||||||
\(733\) | 949.586i | 1.29548i | 0.761862 | + | 0.647739i | \(0.224285\pi\) | ||||
−0.761862 | + | 0.647739i | \(0.775715\pi\) | |||||||
\(734\) | − | 150.172i | − | 0.204594i | ||||||
\(735\) | −504.584 | + | 74.2149i | −0.686509 | + | 0.100973i | ||||
\(736\) | 850.085 | 1.15501 | ||||||||
\(737\) | −1039.66 | −1.41066 | ||||||||
\(738\) | − | 67.6348i | − | 0.0916461i | ||||||
\(739\) | −139.798 | −0.189171 | −0.0945857 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945857 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(740\) | 818.408i | 1.10596i | ||||||||
\(741\) | 91.7843i | 0.123866i | ||||||||
\(742\) | −22.2727 | − | 304.491i | −0.0300171 | − | 0.410366i | ||||
\(743\) | 64.2328 | 0.0864507 | 0.0432253 | − | 0.999065i | \(-0.486237\pi\) | ||||
0.0432253 | + | 0.999065i | \(0.486237\pi\) | |||||||
\(744\) | 321.084 | 0.431565 | ||||||||
\(745\) | − | 953.846i | − | 1.28033i | ||||||
\(746\) | −25.4087 | −0.0340599 | ||||||||
\(747\) | − | 571.265i | − | 0.764746i | ||||||
\(748\) | − | 881.189i | − | 1.17806i | ||||||
\(749\) | −20.9353 | − | 286.207i | −0.0279510 | − | 0.382119i | ||||
\(750\) | 182.682 | 0.243575 | ||||||||
\(751\) | 339.344 | 0.451857 | 0.225928 | − | 0.974144i | \(-0.427458\pi\) | ||||
0.225928 | + | 0.974144i | \(0.427458\pi\) | |||||||
\(752\) | 158.385i | 0.210618i | ||||||||
\(753\) | 122.596 | 0.162811 | ||||||||
\(754\) | 663.348i | 0.879772i | ||||||||
\(755\) | − | 217.401i | − | 0.287949i | ||||||
\(756\) | 281.846 | − | 20.6162i | 0.372812 | − | 0.0272702i | ||||
\(757\) | 1069.94 | 1.41339 | 0.706697 | − | 0.707517i | \(-0.250184\pi\) | ||||
0.706697 | + | 0.707517i | \(0.250184\pi\) | |||||||
\(758\) | −328.718 | −0.433665 | ||||||||
\(759\) | − | 621.964i | − | 0.819451i | ||||||
\(760\) | −262.097 | −0.344865 | ||||||||
\(761\) | − | 380.247i | − | 0.499667i | −0.968289 | − | 0.249834i | \(-0.919624\pi\) | ||
0.968289 | − | 0.249834i | \(-0.0803759\pi\) | |||||||
\(762\) | − | 126.031i | − | 0.165395i | ||||||
\(763\) | 72.0664 | + | 985.224i | 0.0944514 | + | 1.29125i | ||||
\(764\) | 491.019 | 0.642695 | ||||||||
\(765\) | 1788.91 | 2.33844 | ||||||||
\(766\) | 542.540i | 0.708277i | ||||||||
\(767\) | 1273.80 | 1.66075 | ||||||||
\(768\) | 355.064i | 0.462323i | ||||||||
\(769\) | 810.738i | 1.05428i | 0.849780 | + | 0.527138i | \(0.176735\pi\) | ||||
−0.849780 | + | 0.527138i | \(0.823265\pi\) | |||||||
\(770\) | 1199.11 | − | 87.7116i | 1.55729 | − | 0.113911i | ||||
\(771\) | 105.618 | 0.136988 | ||||||||
\(772\) | 110.307 | 0.142885 | ||||||||
\(773\) | − | 1031.23i | − | 1.33406i | −0.745030 | − | 0.667031i | \(-0.767565\pi\) | ||
0.745030 | − | 0.667031i | \(-0.232435\pi\) | |||||||
\(774\) | 373.525 | 0.482591 | ||||||||
\(775\) | − | 1051.71i | − | 1.35705i | ||||||
\(776\) | − | 553.622i | − | 0.713430i | ||||||
\(777\) | 509.824 | − | 37.2922i | 0.656144 | − | 0.0479951i | ||||
\(778\) | −304.870 | −0.391864 | ||||||||
\(779\) | −24.8840 | −0.0319435 | ||||||||
\(780\) | − | 349.729i | − | 0.448370i | ||||||
\(781\) | 983.987 | 1.25991 | ||||||||
\(782\) | − | 1432.93i | − | 1.83239i | ||||||
\(783\) | 547.365i | 0.699061i | ||||||||
\(784\) | 239.838 | − | 35.2758i | 0.305916 | − | 0.0449946i | ||||
\(785\) | −1757.04 | −2.23826 | ||||||||
\(786\) | −107.784 | −0.137130 | ||||||||
\(787\) | − | 1215.13i | − | 1.54400i | −0.635623 | − | 0.772000i | \(-0.719257\pi\) | ||
0.635623 | − | 0.772000i | \(-0.280743\pi\) | |||||||
\(788\) | 232.915 | 0.295577 | ||||||||
\(789\) | − | 582.851i | − | 0.738722i | ||||||
\(790\) | − | 1464.66i | − | 1.85400i | ||||||
\(791\) | 71.6641 | + | 979.725i | 0.0905994 | + | 1.23859i | ||||
\(792\) | −930.004 | −1.17425 | ||||||||
\(793\) | −626.494 | −0.790030 | ||||||||
\(794\) | 848.455i | 1.06858i | ||||||||
\(795\) | −311.767 | −0.392159 | ||||||||
\(796\) | − | 19.3896i | − | 0.0243589i | ||||||
\(797\) | − | 1408.15i | − | 1.76681i | −0.468606 | − | 0.883407i | \(-0.655244\pi\) | ||
0.468606 | − | 0.883407i | \(-0.344756\pi\) | |||||||
\(798\) | 3.81818 | + | 52.1986i | 0.00478469 | + | 0.0654117i | ||||
\(799\) | −1002.21 | −1.25433 | ||||||||
\(800\) | 1002.02 | 1.25252 | ||||||||
\(801\) | − | 89.8206i | − | 0.112136i | ||||||
\(802\) | −461.678 | −0.575659 | ||||||||
\(803\) | 52.1983i | 0.0650041i | ||||||||
\(804\) | 172.445i | 0.214484i | ||||||||
\(805\) | −1728.79 | + | 126.456i | −2.14756 | + | 0.157088i | ||||
\(806\) | 738.749 | 0.916562 | ||||||||
\(807\) | −328.838 | −0.407482 | ||||||||
\(808\) | 1166.81i | 1.44407i | ||||||||
\(809\) | 688.348 | 0.850863 | 0.425432 | − | 0.904991i | \(-0.360122\pi\) | ||||
0.425432 | + | 0.904991i | \(0.360122\pi\) | |||||||
\(810\) | − | 423.374i | − | 0.522684i | ||||||
\(811\) | − | 583.581i | − | 0.719582i | −0.933033 | − | 0.359791i | \(-0.882848\pi\) | ||
0.933033 | − | 0.359791i | \(-0.117152\pi\) | |||||||
\(812\) | −24.4655 | − | 334.470i | −0.0301300 | − | 0.411909i | ||||
\(813\) | 215.611 | 0.265204 | ||||||||
\(814\) | −1205.08 | −1.48044 | ||||||||
\(815\) | 1570.96i | 1.92756i | ||||||||
\(816\) | 204.639 | 0.250783 | ||||||||
\(817\) | − | 137.426i | − | 0.168208i | ||||||
\(818\) | 449.990i | 0.550110i | ||||||||
\(819\) | 905.247 | − | 66.2163i | 1.10531 | − | 0.0808501i | ||||
\(820\) | 94.8161 | 0.115629 | ||||||||
\(821\) | −113.713 | −0.138506 | −0.0692529 | − | 0.997599i | \(-0.522062\pi\) | ||||
−0.0692529 | + | 0.997599i | \(0.522062\pi\) | |||||||
\(822\) | 400.136i | 0.486784i | ||||||||
\(823\) | 271.726 | 0.330166 | 0.165083 | − | 0.986280i | \(-0.447211\pi\) | ||||
0.165083 | + | 0.986280i | \(0.447211\pi\) | |||||||
\(824\) | 360.536i | 0.437544i | ||||||||
\(825\) | − | 733.125i | − | 0.888636i | ||||||
\(826\) | 724.420 | − | 52.9893i | 0.877021 | − | 0.0641517i | ||||
\(827\) | −589.805 | −0.713186 | −0.356593 | − | 0.934260i | \(-0.616062\pi\) | ||||
−0.356593 | + | 0.934260i | \(0.616062\pi\) | |||||||
\(828\) | 428.659 | 0.517705 | ||||||||
\(829\) | 1071.46i | 1.29247i | 0.763137 | + | 0.646236i | \(0.223658\pi\) | ||||
−0.763137 | + | 0.646236i | \(0.776342\pi\) | |||||||
\(830\) | −903.285 | −1.08829 | ||||||||
\(831\) | 88.9442i | 0.107033i | ||||||||
\(832\) | 1057.57i | 1.27112i | ||||||||
\(833\) | 223.215 | + | 1517.63i | 0.267965 | + | 1.82188i | ||||
\(834\) | −171.083 | −0.205135 | ||||||||
\(835\) | 395.105 | 0.473180 | ||||||||
\(836\) | 109.391i | 0.130850i | ||||||||
\(837\) | 609.582 | 0.728294 | ||||||||
\(838\) | 631.803i | 0.753941i | ||||||||
\(839\) | 1116.06i | 1.33023i | 0.746740 | + | 0.665116i | \(0.231618\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(840\) | −45.5065 | − | 622.122i | −0.0541744 | − | 0.740622i | ||||
\(841\) | −191.436 | −0.227629 | ||||||||
\(842\) | −356.402 | −0.423280 | ||||||||
\(843\) | − | 350.029i | − | 0.415218i | ||||||
\(844\) | −26.2719 | −0.0311278 | ||||||||
\(845\) | − | 1185.60i | − | 1.40308i | ||||||
\(846\) | 338.159i | 0.399716i | ||||||||
\(847\) | −52.7155 | − | 720.676i | −0.0622379 | − | 0.850858i | ||||
\(848\) | 148.189 | 0.174751 | ||||||||
\(849\) | 240.203 | 0.282925 | ||||||||
\(850\) | − | 1689.04i | − | 1.98710i | ||||||
\(851\) | 1737.39 | 2.04159 | ||||||||
\(852\) | − | 163.212i | − | 0.191563i | ||||||
\(853\) | 1193.28i | 1.39892i | 0.714669 | + | 0.699462i | \(0.246577\pi\) | ||||
−0.714669 | + | 0.699462i | \(0.753423\pi\) | |||||||
\(854\) | −356.293 | + | 26.0618i | −0.417205 | + | 0.0305173i | ||||
\(855\) | −222.075 | −0.259736 | ||||||||
\(856\) | 350.989 | 0.410033 | ||||||||
\(857\) | − | 215.366i | − | 0.251303i | −0.992074 | − | 0.125651i | \(-0.959898\pi\) | ||
0.992074 | − | 0.125651i | \(-0.0401021\pi\) | |||||||
\(858\) | 514.965 | 0.600192 | ||||||||
\(859\) | 822.323i | 0.957302i | 0.878005 | + | 0.478651i | \(0.158874\pi\) | ||||
−0.878005 | + | 0.478651i | \(0.841126\pi\) | |||||||
\(860\) | 523.639i | 0.608883i | ||||||||
\(861\) | −4.32046 | − | 59.0653i | −0.00501796 | − | 0.0686008i | ||||
\(862\) | 531.166 | 0.616202 | ||||||||
\(863\) | 761.095 | 0.881918 | 0.440959 | − | 0.897527i | \(-0.354638\pi\) | ||||
0.440959 | + | 0.897527i | \(0.354638\pi\) | |||||||
\(864\) | 580.778i | 0.672197i | ||||||||
\(865\) | −1629.15 | −1.88341 | ||||||||
\(866\) | − | 771.821i | − | 0.891248i | ||||||
\(867\) | 913.040i | 1.05310i | ||||||||
\(868\) | −372.488 | + | 27.2465i | −0.429134 | + | 0.0313899i | ||||
\(869\) | −1912.09 | −2.20034 | ||||||||
\(870\) | 386.266 | 0.443984 | ||||||||
\(871\) | 1241.03i | 1.42484i | ||||||||
\(872\) | −1208.22 | −1.38558 | ||||||||
\(873\) | − | 469.082i | − | 0.537322i | ||||||
\(874\) | 177.884i | 0.203528i | ||||||||
\(875\) | −662.891 | + | 48.4886i | −0.757590 | + | 0.0554156i | ||||
\(876\) | 8.65801 | 0.00988357 | ||||||||
\(877\) | −349.758 | −0.398812 | −0.199406 | − | 0.979917i | \(-0.563901\pi\) | ||||
−0.199406 | + | 0.979917i | \(0.563901\pi\) | |||||||
\(878\) | − | 272.339i | − | 0.310181i | ||||||
\(879\) | 662.070 | 0.753208 | ||||||||
\(880\) | 583.579i | 0.663158i | ||||||||
\(881\) | − | 772.690i | − | 0.877061i | −0.898716 | − | 0.438530i | \(-0.855499\pi\) | ||
0.898716 | − | 0.438530i | \(-0.144501\pi\) | |||||||
\(882\) | 512.067 | − | 75.3155i | 0.580575 | − | 0.0853918i | ||||
\(883\) | −297.771 | −0.337227 | −0.168613 | − | 0.985682i | \(-0.553929\pi\) | ||||
−0.168613 | + | 0.985682i | \(0.553929\pi\) | |||||||
\(884\) | −1051.87 | −1.18990 | ||||||||
\(885\) | − | 741.729i | − | 0.838112i | ||||||
\(886\) | 457.029 | 0.515834 | ||||||||
\(887\) | 1392.32i | 1.56970i | 0.619688 | + | 0.784848i | \(0.287259\pi\) | ||||
−0.619688 | + | 0.784848i | \(0.712741\pi\) | |||||||
\(888\) | 625.219i | 0.704076i | ||||||||
\(889\) | 33.4521 | + | 457.326i | 0.0376289 | + | 0.514427i | ||||
\(890\) | −142.024 | −0.159578 | ||||||||
\(891\) | −552.708 | −0.620323 | ||||||||
\(892\) | 415.565i | 0.465880i | ||||||||
\(893\) | 124.414 | 0.139322 | ||||||||
\(894\) | − | 232.963i | − | 0.260585i | ||||||
\(895\) | 1394.79i | 1.55843i | ||||||||
\(896\) | −11.2441 | − | 153.719i | −0.0125492 | − | 0.171561i | ||||
\(897\) | −742.436 | −0.827688 | ||||||||
\(898\) | 1073.25 | 1.19516 | ||||||||
\(899\) | − | 723.398i | − | 0.804670i | ||||||
\(900\) | 505.272 | 0.561414 | ||||||||
\(901\) | 937.695i | 1.04073i | ||||||||
\(902\) | 139.614i | 0.154782i | ||||||||
\(903\) | 326.199 | − | 23.8605i | 0.361239 | − | 0.0264236i | ||||
\(904\) | −1201.48 | −1.32907 | ||||||||
\(905\) | −757.905 | −0.837464 | ||||||||
\(906\) | − | 53.0970i | − | 0.0586060i | ||||||
\(907\) | −1450.35 | −1.59907 | −0.799534 | − | 0.600621i | \(-0.794920\pi\) | ||||
−0.799534 | + | 0.600621i | \(0.794920\pi\) | |||||||
\(908\) | 94.7441i | 0.104344i | ||||||||
\(909\) | 988.637i | 1.08761i | ||||||||
\(910\) | −104.701 | − | 1431.38i | −0.115056 | − | 1.57294i | ||||
\(911\) | −756.503 | −0.830409 | −0.415205 | − | 0.909728i | \(-0.636290\pi\) | ||||
−0.415205 | + | 0.909728i | \(0.636290\pi\) | |||||||
\(912\) | −25.4038 | −0.0278551 | ||||||||
\(913\) | 1179.22i | 1.29159i | ||||||||
\(914\) | −1116.62 | −1.22168 | ||||||||
\(915\) | 364.806i | 0.398695i | ||||||||
\(916\) | 2.06099i | 0.00224999i | ||||||||
\(917\) | 391.113 | − | 28.6088i | 0.426513 | − | 0.0311982i | ||||
\(918\) | 978.979 | 1.06643 | ||||||||
\(919\) | 582.345 | 0.633673 | 0.316836 | − | 0.948480i | \(-0.397379\pi\) | ||||
0.316836 | + | 0.948480i | \(0.397379\pi\) | |||||||
\(920\) | − | 2120.09i | − | 2.30444i | ||||||
\(921\) | −283.522 | −0.307841 | ||||||||
\(922\) | 1004.55i | 1.08954i | ||||||||
\(923\) | − | 1174.58i | − | 1.27257i | ||||||
\(924\) | −259.653 | + | 18.9929i | −0.281009 | + | 0.0205550i | ||||
\(925\) | 2047.91 | 2.21396 | ||||||||
\(926\) | −285.645 | −0.308472 | ||||||||
\(927\) | 305.481i | 0.329538i | ||||||||
\(928\) | 689.216 | 0.742690 | ||||||||
\(929\) | − | 1752.86i | − | 1.88683i | −0.331615 | − | 0.943415i | \(-0.607594\pi\) | ||
0.331615 | − | 0.943415i | \(-0.392406\pi\) | |||||||
\(930\) | − | 430.172i | − | 0.462550i | ||||||
\(931\) | −27.7098 | − | 188.398i | −0.0297635 | − | 0.202361i | ||||
\(932\) | 116.571 | 0.125076 | ||||||||
\(933\) | −600.921 | −0.644074 | ||||||||
\(934\) | − | 1076.22i | − | 1.15227i | ||||||
\(935\) | −3692.72 | −3.94943 | ||||||||
\(936\) | 1110.14i | 1.18605i | ||||||||
\(937\) | − | 122.902i | − | 0.131165i | −0.997847 | − | 0.0655825i | \(-0.979109\pi\) | ||
0.997847 | − | 0.0655825i | \(-0.0208905\pi\) | |||||||
\(938\) | 51.6263 | + | 705.787i | 0.0550387 | + | 0.752438i | ||||
\(939\) | −153.619 | −0.163599 | ||||||||
\(940\) | −474.060 | −0.504319 | ||||||||
\(941\) | − | 1602.28i | − | 1.70274i | −0.524568 | − | 0.851369i | \(-0.675773\pi\) | ||
0.524568 | − | 0.851369i | \(-0.324227\pi\) | |||||||
\(942\) | −429.130 | −0.455552 | ||||||||
\(943\) | − | 201.284i | − | 0.213451i | ||||||
\(944\) | 352.558i | 0.373472i | ||||||||
\(945\) | −86.3946 | − | 1181.11i | −0.0914229 | − | 1.24985i | ||||
\(946\) | −771.042 | −0.815055 | ||||||||
\(947\) | −173.249 | −0.182946 | −0.0914728 | − | 0.995808i | \(-0.529157\pi\) | ||||
−0.0914728 | + | 0.995808i | \(0.529157\pi\) | |||||||
\(948\) | 317.154i | 0.334551i | ||||||||
\(949\) | 62.3089 | 0.0656575 | ||||||||
\(950\) | 209.676i | 0.220712i | ||||||||
\(951\) | − | 320.372i | − | 0.336879i | ||||||
\(952\) | −1871.15 | + | 136.869i | −1.96549 | + | 0.143770i | ||||
\(953\) | −177.101 | −0.185835 | −0.0929174 | − | 0.995674i | \(-0.529619\pi\) | ||||
−0.0929174 | + | 0.995674i | \(0.529619\pi\) | |||||||
\(954\) | 316.390 | 0.331646 | ||||||||
\(955\) | − | 2057.67i | − | 2.15463i | ||||||
\(956\) | 764.950 | 0.800157 | ||||||||
\(957\) | − | 504.264i | − | 0.526922i | ||||||
\(958\) | 141.787i | 0.148003i | ||||||||
\(959\) | −106.207 | − | 1451.96i | −0.110748 | − | 1.51404i | ||||
\(960\) | 615.821 | 0.641480 | ||||||||
\(961\) | 155.375 | 0.161681 | ||||||||
\(962\) | 1438.50i | 1.49532i | ||||||||
\(963\) | 297.392 | 0.308818 | ||||||||
\(964\) | − | 25.7045i | − | 0.0266644i | ||||||
\(965\) | − | 462.254i | − | 0.479020i | ||||||
\(966\) | −422.230 | + | 30.8850i | −0.437091 | + | 0.0319720i | ||||
\(967\) | −1152.74 | −1.19208 | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(968\) | 883.797 | 0.913014 | ||||||||
\(969\) | − | 160.748i | − | 0.165891i | ||||||
\(970\) | −741.713 | −0.764652 | ||||||||
\(971\) | 350.030i | 0.360484i | 0.983622 | + | 0.180242i | \(0.0576882\pi\) | ||||
−0.983622 | + | 0.180242i | \(0.942312\pi\) | |||||||
\(972\) | 455.018i | 0.468125i | ||||||||
\(973\) | 620.802 | − | 45.4100i | 0.638029 | − | 0.0466700i | ||||
\(974\) | 909.066 | 0.933332 | ||||||||
\(975\) | −875.130 | −0.897569 | ||||||||
\(976\) | − | 173.399i | − | 0.177663i | ||||||
\(977\) | 765.337 | 0.783354 | 0.391677 | − | 0.920103i | \(-0.371895\pi\) | ||||
0.391677 | + | 0.920103i | \(0.371895\pi\) | |||||||
\(978\) | 383.683i | 0.392314i | ||||||||
\(979\) | 185.410i | 0.189387i | ||||||||
\(980\) | 105.584 | + | 717.859i | 0.107738 | + | 0.732509i | ||||
\(981\) | −1023.73 | −1.04355 | ||||||||
\(982\) | 635.414 | 0.647062 | ||||||||
\(983\) | 98.2372i | 0.0999362i | 0.998751 | + | 0.0499681i | \(0.0159120\pi\) | ||||
−0.998751 | + | 0.0499681i | \(0.984088\pi\) | |||||||
\(984\) | 72.4344 | 0.0736122 | ||||||||
\(985\) | − | 976.055i | − | 0.990919i | ||||||
\(986\) | − | 1161.77i | − | 1.17826i | ||||||
\(987\) | 21.6014 | + | 295.314i | 0.0218859 | + | 0.299203i | ||||
\(988\) | 130.579 | 0.132165 | ||||||||
\(989\) | 1111.63 | 1.12399 | ||||||||
\(990\) | 1245.97i | 1.25856i | ||||||||
\(991\) | 546.637 | 0.551602 | 0.275801 | − | 0.961215i | \(-0.411057\pi\) | ||||
0.275801 | + | 0.961215i | \(0.411057\pi\) | |||||||
\(992\) | − | 767.557i | − | 0.773747i | ||||||
\(993\) | 101.621i | 0.102337i | ||||||||
\(994\) | −48.8620 | − | 667.996i | −0.0491570 | − | 0.672028i | ||||
\(995\) | −81.2544 | −0.0816627 | ||||||||
\(996\) | 195.595 | 0.196381 | ||||||||
\(997\) | − | 976.998i | − | 0.979938i | −0.871740 | − | 0.489969i | \(-0.837008\pi\) | ||
0.871740 | − | 0.489969i | \(-0.162992\pi\) | |||||||
\(998\) | 293.474 | 0.294062 | ||||||||
\(999\) | 1186.99i | 1.18817i |
(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 | 287.3.b.a.83.15 | ✓ | 52 | |
7.6 | odd | 2 | inner | 287.3.b.a.83.16 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.b.a.83.15 | ✓ | 52 | 1.1 | even | 1 | trivial | |
287.3.b.a.83.16 | yes | 52 | 7.6 | odd | 2 | inner |