Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(701,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.e (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.19 | ||
Character | \(\chi\) | \(=\) | 1050.701 |
Dual form | 1050.3.e.e.701.17 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −2.79991 | + | 1.07726i | −0.933305 | + | 0.359085i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.52347 | − | 3.95968i | −0.253912 | − | 0.659946i | ||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 6.67904 | − | 6.03245i | 0.742116 | − | 0.670272i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.98577i | 0.544161i | 0.962275 | + | 0.272080i | \(0.0877116\pi\) | ||||
−0.962275 | + | 0.272080i | \(0.912288\pi\) | |||||||
\(12\) | 5.59983 | − | 2.15451i | 0.466652 | − | 0.179543i | ||||
\(13\) | −19.0169 | −1.46284 | −0.731421 | − | 0.681926i | \(-0.761142\pi\) | ||||
−0.731421 | + | 0.681926i | \(0.761142\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 2.02915i | − | 0.119362i | −0.998218 | − | 0.0596809i | \(-0.980992\pi\) | ||
0.998218 | − | 0.0596809i | \(-0.0190083\pi\) | |||||||
\(18\) | 8.53117 | + | 9.44559i | 0.473954 | + | 0.524755i | ||||
\(19\) | 21.1068 | 1.11088 | 0.555442 | − | 0.831556i | \(-0.312549\pi\) | ||||
0.555442 | + | 0.831556i | \(0.312549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.40788 | + | 2.85015i | −0.352756 | + | 0.135721i | ||||
\(22\) | −8.46515 | −0.384780 | ||||||||
\(23\) | − | 32.2716i | − | 1.40311i | −0.712615 | − | 0.701555i | \(-0.752489\pi\) | ||
0.712615 | − | 0.701555i | \(-0.247511\pi\) | |||||||
\(24\) | 3.04694 | + | 7.91935i | 0.126956 | + | 0.329973i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 26.8940i | − | 1.03439i | ||||||
\(27\) | −12.2023 | + | 24.0854i | −0.451935 | + | 0.892051i | ||||
\(28\) | −5.29150 | −0.188982 | ||||||||
\(29\) | − | 12.2603i | − | 0.422768i | −0.977403 | − | 0.211384i | \(-0.932203\pi\) | ||
0.977403 | − | 0.211384i | \(-0.0677971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.3082 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −6.44820 | − | 16.7596i | −0.195400 | − | 0.507868i | ||||
\(34\) | 2.86965 | 0.0844015 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.3581 | + | 12.0649i | −0.371058 | + | 0.335136i | ||||
\(37\) | 20.3241 | 0.549301 | 0.274650 | − | 0.961544i | \(-0.411438\pi\) | ||||
0.274650 | + | 0.961544i | \(0.411438\pi\) | |||||||
\(38\) | 29.8495i | 0.785513i | ||||||||
\(39\) | 53.2458 | − | 20.4861i | 1.36528 | − | 0.525285i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.7183i | 0.846788i | 0.905946 | + | 0.423394i | \(0.139161\pi\) | ||||
−0.905946 | + | 0.423394i | \(0.860839\pi\) | |||||||
\(42\) | −4.03072 | − | 10.4763i | −0.0959696 | − | 0.249436i | ||||
\(43\) | 40.3307 | 0.937924 | 0.468962 | − | 0.883218i | \(-0.344628\pi\) | ||||
0.468962 | + | 0.883218i | \(0.344628\pi\) | |||||||
\(44\) | − | 11.9715i | − | 0.272080i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 45.6389 | 0.992149 | ||||||||
\(47\) | 72.4398i | 1.54127i | 0.637275 | + | 0.770636i | \(0.280061\pi\) | ||||
−0.637275 | + | 0.770636i | \(0.719939\pi\) | |||||||
\(48\) | −11.1997 | + | 4.30902i | −0.233326 | + | 0.0897713i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.18591 | + | 5.68144i | 0.0428610 | + | 0.111401i | ||||
\(52\) | 38.0339 | 0.731421 | ||||||||
\(53\) | 57.5848i | 1.08651i | 0.839569 | + | 0.543253i | \(0.182807\pi\) | ||||
−0.839569 | + | 0.543253i | \(0.817193\pi\) | |||||||
\(54\) | −34.0619 | − | 17.2566i | −0.630775 | − | 0.319566i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | −59.0972 | + | 22.7374i | −1.03679 | + | 0.398902i | ||||
\(58\) | 17.3387 | 0.298942 | ||||||||
\(59\) | − | 71.7934i | − | 1.21684i | −0.793616 | − | 0.608419i | \(-0.791804\pi\) | ||
0.793616 | − | 0.608419i | \(-0.208196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 81.7294 | 1.33983 | 0.669913 | − | 0.742439i | \(-0.266331\pi\) | ||||
0.669913 | + | 0.742439i | \(0.266331\pi\) | |||||||
\(62\) | 55.5902i | 0.896617i | ||||||||
\(63\) | 17.6711 | − | 15.9604i | 0.280493 | − | 0.253339i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 23.7017 | − | 9.11913i | 0.359117 | − | 0.138169i | ||||
\(67\) | −81.7131 | −1.21960 | −0.609799 | − | 0.792556i | \(-0.708750\pi\) | ||||
−0.609799 | + | 0.792556i | \(0.708750\pi\) | |||||||
\(68\) | 4.05830i | 0.0596809i | ||||||||
\(69\) | 34.7647 | + | 90.3576i | 0.503836 | + | 1.30953i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.70229i | − | 0.108483i | −0.998528 | − | 0.0542415i | \(-0.982726\pi\) | ||
0.998528 | − | 0.0542415i | \(-0.0172741\pi\) | |||||||
\(72\) | −17.0623 | − | 18.8912i | −0.236977 | − | 0.262377i | ||||
\(73\) | −12.0694 | −0.165334 | −0.0826671 | − | 0.996577i | \(-0.526344\pi\) | ||||
−0.0826671 | + | 0.996577i | \(0.526344\pi\) | |||||||
\(74\) | 28.7427i | 0.388414i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −42.2136 | −0.555442 | ||||||||
\(77\) | 15.8369i | 0.205673i | ||||||||
\(78\) | 28.9717 | + | 75.3009i | 0.371433 | + | 0.965397i | ||||
\(79\) | −131.622 | −1.66610 | −0.833049 | − | 0.553199i | \(-0.813407\pi\) | ||||
−0.833049 | + | 0.553199i | \(0.813407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.21915 | − | 80.5819i | 0.101471 | − | 0.994838i | ||||
\(82\) | −49.0991 | −0.598769 | ||||||||
\(83\) | 115.864i | 1.39596i | 0.716119 | + | 0.697978i | \(0.245917\pi\) | ||||
−0.716119 | + | 0.697978i | \(0.754083\pi\) | |||||||
\(84\) | 14.8158 | − | 5.70030i | 0.176378 | − | 0.0678607i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57.0363i | 0.663212i | ||||||||
\(87\) | 13.2075 | + | 34.3277i | 0.151810 | + | 0.394572i | ||||
\(88\) | 16.9303 | 0.192390 | ||||||||
\(89\) | 101.939i | 1.14538i | 0.819771 | + | 0.572692i | \(0.194101\pi\) | ||||
−0.819771 | + | 0.572692i | \(0.805899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −50.3141 | −0.552902 | ||||||||
\(92\) | 64.5431i | 0.701555i | ||||||||
\(93\) | −110.060 | + | 42.3450i | −1.18344 | + | 0.455323i | ||||
\(94\) | −102.445 | −1.08984 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.09388 | − | 15.8387i | −0.0634779 | − | 0.164987i | ||||
\(97\) | −8.19281 | −0.0844619 | −0.0422310 | − | 0.999108i | \(-0.513447\pi\) | ||||
−0.0422310 | + | 0.999108i | \(0.513447\pi\) | |||||||
\(98\) | 9.89949i | 0.101015i | ||||||||
\(99\) | 36.1088 | + | 39.9792i | 0.364736 | + | 0.403830i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136.484i | 1.35133i | 0.737208 | + | 0.675665i | \(0.236144\pi\) | ||||
−0.737208 | + | 0.675665i | \(0.763856\pi\) | |||||||
\(102\) | −8.03477 | + | 3.09135i | −0.0787723 | + | 0.0303073i | ||||
\(103\) | −129.191 | −1.25428 | −0.627142 | − | 0.778905i | \(-0.715776\pi\) | ||||
−0.627142 | + | 0.778905i | \(0.715776\pi\) | |||||||
\(104\) | 53.7880i | 0.517193i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −81.4372 | −0.768275 | ||||||||
\(107\) | 20.2629i | 0.189373i | 0.995507 | + | 0.0946866i | \(0.0301849\pi\) | ||||
−0.995507 | + | 0.0946866i | \(0.969815\pi\) | |||||||
\(108\) | 24.4045 | − | 48.1707i | 0.225968 | − | 0.446025i | ||||
\(109\) | 112.569 | 1.03275 | 0.516373 | − | 0.856364i | \(-0.327282\pi\) | ||||
0.516373 | + | 0.856364i | \(0.327282\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −56.9058 | + | 21.8943i | −0.512665 | + | 0.197246i | ||||
\(112\) | 10.5830 | 0.0944911 | ||||||||
\(113\) | − | 6.53779i | − | 0.0578565i | −0.999581 | − | 0.0289283i | \(-0.990791\pi\) | ||
0.999581 | − | 0.0289283i | \(-0.00920944\pi\) | |||||||
\(114\) | −32.1555 | − | 83.5760i | −0.282066 | − | 0.733123i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 24.5206i | 0.211384i | ||||||||
\(117\) | −127.015 | + | 114.719i | −1.08560 | + | 0.980502i | ||||
\(118\) | 101.531 | 0.860434 | ||||||||
\(119\) | − | 5.36862i | − | 0.0451145i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 85.1706 | 0.703889 | ||||||||
\(122\) | 115.583i | 0.947400i | ||||||||
\(123\) | −37.4005 | − | 97.2082i | −0.304069 | − | 0.790311i | ||||
\(124\) | −78.6165 | −0.634004 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.5714 | + | 24.9907i | 0.179138 | + | 0.198339i | ||||
\(127\) | 15.0411 | 0.118434 | 0.0592170 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592170 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | −112.923 | + | 43.4465i | −0.875369 | + | 0.336795i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 51.5923i | 0.393834i | 0.980420 | + | 0.196917i | \(0.0630930\pi\) | ||||
−0.980420 | + | 0.196917i | \(0.936907\pi\) | |||||||
\(132\) | 12.8964 | + | 33.5193i | 0.0977000 | + | 0.253934i | ||||
\(133\) | 55.8433 | 0.419874 | ||||||||
\(134\) | − | 115.560i | − | 0.862386i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.73930 | −0.0422007 | ||||||||
\(137\) | − | 47.5888i | − | 0.347364i | −0.984802 | − | 0.173682i | \(-0.944434\pi\) | ||
0.984802 | − | 0.173682i | \(-0.0555664\pi\) | |||||||
\(138\) | −127.785 | + | 49.1647i | −0.925978 | + | 0.356266i | ||||
\(139\) | 117.730 | 0.846975 | 0.423488 | − | 0.905902i | \(-0.360806\pi\) | ||||
0.423488 | + | 0.905902i | \(0.360806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −78.0362 | − | 202.825i | −0.553448 | − | 1.43848i | ||||
\(142\) | 10.8927 | 0.0767091 | ||||||||
\(143\) | − | 113.831i | − | 0.796021i | ||||||
\(144\) | 26.7162 | − | 24.1298i | 0.185529 | − | 0.167568i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 17.0687i | − | 0.116909i | ||||||
\(147\) | −19.5994 | + | 7.54079i | −0.133329 | + | 0.0512979i | ||||
\(148\) | −40.6483 | −0.274650 | ||||||||
\(149\) | 186.336i | 1.25057i | 0.780395 | + | 0.625287i | \(0.215018\pi\) | ||||
−0.780395 | + | 0.625287i | \(0.784982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −183.560 | −1.21563 | −0.607816 | − | 0.794078i | \(-0.707954\pi\) | ||||
−0.607816 | + | 0.794078i | \(0.707954\pi\) | |||||||
\(152\) | − | 59.6990i | − | 0.392756i | ||||||
\(153\) | −12.2407 | − | 13.5528i | −0.0800048 | − | 0.0885802i | ||||
\(154\) | −22.3967 | −0.145433 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −106.492 | + | 40.9722i | −0.682639 | + | 0.262642i | ||||
\(157\) | 264.877 | 1.68712 | 0.843558 | − | 0.537038i | \(-0.180457\pi\) | ||||
0.843558 | + | 0.537038i | \(0.180457\pi\) | |||||||
\(158\) | − | 186.141i | − | 1.17811i | ||||||
\(159\) | −62.0335 | − | 161.232i | −0.390148 | − | 1.01404i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 85.3825i | − | 0.530326i | ||||||
\(162\) | 113.960 | + | 11.6236i | 0.703457 | + | 0.0717508i | ||||
\(163\) | 214.877 | 1.31826 | 0.659132 | − | 0.752027i | \(-0.270924\pi\) | ||||
0.659132 | + | 0.752027i | \(0.270924\pi\) | |||||||
\(164\) | − | 69.4366i | − | 0.423394i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −163.857 | −0.987090 | ||||||||
\(167\) | − | 54.5954i | − | 0.326919i | −0.986550 | − | 0.163459i | \(-0.947735\pi\) | ||
0.986550 | − | 0.163459i | \(-0.0522653\pi\) | |||||||
\(168\) | 8.06144 | + | 20.9526i | 0.0479848 | + | 0.124718i | ||||
\(169\) | 192.644 | 1.13991 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 140.973 | − | 127.326i | 0.824404 | − | 0.744594i | ||||
\(172\) | −80.6615 | −0.468962 | ||||||||
\(173\) | 310.651i | 1.79567i | 0.440334 | + | 0.897834i | \(0.354860\pi\) | ||||
−0.440334 | + | 0.897834i | \(0.645140\pi\) | |||||||
\(174\) | −48.5468 | + | 18.6782i | −0.279004 | + | 0.107346i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.9431i | 0.136040i | ||||||||
\(177\) | 77.3399 | + | 201.015i | 0.436949 | + | 1.13568i | ||||
\(178\) | −144.164 | −0.809909 | ||||||||
\(179\) | 162.922i | 0.910181i | 0.890445 | + | 0.455090i | \(0.150393\pi\) | ||||
−0.890445 | + | 0.455090i | \(0.849607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −51.5088 | −0.284579 | −0.142289 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142289 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(182\) | − | 71.1549i | − | 0.390961i | ||||||
\(183\) | −228.835 | + | 88.0435i | −1.25047 | + | 0.481112i | ||||
\(184\) | −91.2777 | −0.496075 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −59.8849 | − | 155.648i | −0.321962 | − | 0.836817i | ||||
\(187\) | 12.1460 | 0.0649519 | ||||||||
\(188\) | − | 144.880i | − | 0.770636i | ||||||
\(189\) | −32.2841 | + | 63.7239i | −0.170815 | + | 0.337163i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 227.310i | 1.19011i | 0.803687 | + | 0.595053i | \(0.202869\pi\) | ||||
−0.803687 | + | 0.595053i | \(0.797131\pi\) | |||||||
\(192\) | 22.3993 | − | 8.61805i | 0.116663 | − | 0.0448857i | ||||
\(193\) | 239.861 | 1.24280 | 0.621401 | − | 0.783493i | \(-0.286564\pi\) | ||||
0.621401 | + | 0.783493i | \(0.286564\pi\) | |||||||
\(194\) | − | 11.5864i | − | 0.0597236i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 184.116i | 0.934599i | 0.884099 | + | 0.467300i | \(0.154773\pi\) | ||||
−0.884099 | + | 0.467300i | \(0.845227\pi\) | |||||||
\(198\) | −56.5391 | + | 51.0656i | −0.285551 | + | 0.257907i | ||||
\(199\) | 215.792 | 1.08438 | 0.542190 | − | 0.840256i | \(-0.317595\pi\) | ||||
0.542190 | + | 0.840256i | \(0.317595\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 228.790 | − | 88.0259i | 1.13826 | − | 0.437940i | ||||
\(202\) | −193.018 | −0.955535 | ||||||||
\(203\) | − | 32.4377i | − | 0.159791i | ||||||
\(204\) | −4.37182 | − | 11.3629i | −0.0214305 | − | 0.0557004i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 182.704i | − | 0.886913i | ||||||
\(207\) | −194.676 | − | 215.543i | −0.940466 | − | 1.04127i | ||||
\(208\) | −76.0678 | −0.365710 | ||||||||
\(209\) | 126.340i | 0.604499i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −122.387 | −0.580031 | −0.290015 | − | 0.957022i | \(-0.593660\pi\) | ||||
−0.290015 | + | 0.957022i | \(0.593660\pi\) | |||||||
\(212\) | − | 115.170i | − | 0.543253i | ||||||
\(213\) | 8.29734 | + | 21.5658i | 0.0389546 | + | 0.101248i | ||||
\(214\) | −28.6561 | −0.133907 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 68.1237 | + | 34.5132i | 0.315388 | + | 0.159783i | ||||
\(217\) | 104.000 | 0.479262 | ||||||||
\(218\) | 159.197i | 0.730262i | ||||||||
\(219\) | 33.7933 | − | 13.0018i | 0.154307 | − | 0.0593690i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.5882i | 0.174607i | ||||||||
\(222\) | −30.9632 | − | 80.4770i | −0.139474 | − | 0.362509i | ||||
\(223\) | 70.1315 | 0.314491 | 0.157245 | − | 0.987560i | \(-0.449739\pi\) | ||||
0.157245 | + | 0.987560i | \(0.449739\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.24583 | 0.0409108 | ||||||||
\(227\) | 31.4277i | 0.138448i | 0.997601 | + | 0.0692240i | \(0.0220523\pi\) | ||||
−0.997601 | + | 0.0692240i | \(0.977948\pi\) | |||||||
\(228\) | 118.194 | − | 45.4748i | 0.518396 | − | 0.199451i | ||||
\(229\) | −35.7207 | −0.155986 | −0.0779928 | − | 0.996954i | \(-0.524851\pi\) | ||||
−0.0779928 | + | 0.996954i | \(0.524851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.0603 | − | 44.3418i | −0.0738543 | − | 0.191956i | ||||
\(232\) | −34.6773 | −0.149471 | ||||||||
\(233\) | − | 324.542i | − | 1.39288i | −0.717613 | − | 0.696442i | \(-0.754765\pi\) | ||
0.717613 | − | 0.696442i | \(-0.245235\pi\) | |||||||
\(234\) | −162.237 | − | 179.626i | −0.693319 | − | 0.767633i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 143.587i | 0.608419i | ||||||||
\(237\) | 368.530 | − | 141.790i | 1.55498 | − | 0.598271i | ||||
\(238\) | 7.59238 | 0.0319008 | ||||||||
\(239\) | − | 400.039i | − | 1.67380i | −0.547353 | − | 0.836902i | \(-0.684364\pi\) | ||
0.547353 | − | 0.836902i | \(-0.315636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 396.305 | 1.64442 | 0.822209 | − | 0.569185i | \(-0.192741\pi\) | ||||
0.822209 | + | 0.569185i | \(0.192741\pi\) | |||||||
\(242\) | 120.449i | 0.497725i | ||||||||
\(243\) | 63.7944 | + | 234.477i | 0.262528 | + | 0.964924i | ||||
\(244\) | −163.459 | −0.669913 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 137.473 | − | 52.8923i | 0.558834 | − | 0.215009i | ||||
\(247\) | −401.386 | −1.62505 | ||||||||
\(248\) | − | 111.180i | − | 0.448308i | ||||||
\(249\) | −124.816 | − | 324.410i | −0.501267 | − | 1.30285i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.226i | 0.881377i | 0.897660 | + | 0.440688i | \(0.145266\pi\) | ||||
−0.897660 | + | 0.440688i | \(0.854734\pi\) | |||||||
\(252\) | −35.3422 | + | 31.9207i | −0.140247 | + | 0.126669i | ||||
\(253\) | 193.170 | 0.763518 | ||||||||
\(254\) | 21.2714i | 0.0837455i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 203.815i | − | 0.793055i | −0.918023 | − | 0.396528i | \(-0.870215\pi\) | ||
0.918023 | − | 0.396528i | \(-0.129785\pi\) | |||||||
\(258\) | −61.4426 | − | 159.697i | −0.238150 | − | 0.618979i | ||||
\(259\) | 53.7726 | 0.207616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −73.9595 | − | 81.8869i | −0.283370 | − | 0.313743i | ||||
\(262\) | −72.9625 | −0.278483 | ||||||||
\(263\) | − | 98.2019i | − | 0.373391i | −0.982418 | − | 0.186696i | \(-0.940222\pi\) | ||
0.982418 | − | 0.186696i | \(-0.0597778\pi\) | |||||||
\(264\) | −47.4034 | + | 18.2383i | −0.179558 | + | 0.0690844i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 78.9743i | 0.296896i | ||||||||
\(267\) | −109.815 | − | 285.421i | −0.411290 | − | 1.06899i | ||||
\(268\) | 163.426 | 0.609799 | ||||||||
\(269\) | − | 308.644i | − | 1.14738i | −0.819074 | − | 0.573688i | \(-0.805512\pi\) | ||
0.819074 | − | 0.573688i | \(-0.194488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −398.841 | −1.47174 | −0.735870 | − | 0.677123i | \(-0.763226\pi\) | ||||
−0.735870 | + | 0.677123i | \(0.763226\pi\) | |||||||
\(272\) | − | 8.11660i | − | 0.0298404i | ||||||
\(273\) | 140.875 | − | 54.2012i | 0.516026 | − | 0.198539i | ||||
\(274\) | 67.3007 | 0.245623 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −69.5294 | − | 180.715i | −0.251918 | − | 0.654765i | ||||
\(277\) | 79.7207 | 0.287800 | 0.143900 | − | 0.989592i | \(-0.454036\pi\) | ||||
0.143900 | + | 0.989592i | \(0.454036\pi\) | |||||||
\(278\) | 166.495i | 0.598902i | ||||||||
\(279\) | 262.541 | − | 237.125i | 0.941008 | − | 0.849910i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 210.169i | 0.747934i | 0.927442 | + | 0.373967i | \(0.122003\pi\) | ||||
−0.927442 | + | 0.373967i | \(0.877997\pi\) | |||||||
\(282\) | 286.838 | − | 110.360i | 1.01716 | − | 0.391347i | ||||
\(283\) | 262.941 | 0.929120 | 0.464560 | − | 0.885542i | \(-0.346213\pi\) | ||||
0.464560 | + | 0.885542i | \(0.346213\pi\) | |||||||
\(284\) | 15.4046i | 0.0542415i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 160.981 | 0.562872 | ||||||||
\(287\) | 91.8560i | 0.320056i | ||||||||
\(288\) | 34.1247 | + | 37.7824i | 0.118488 | + | 0.131189i | ||||
\(289\) | 284.883 | 0.985753 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.9392 | − | 8.82575i | 0.0788287 | − | 0.0303290i | ||||
\(292\) | 24.1388 | 0.0826671 | ||||||||
\(293\) | 357.570i | 1.22037i | 0.792257 | + | 0.610187i | \(0.208906\pi\) | ||||
−0.792257 | + | 0.610187i | \(0.791094\pi\) | |||||||
\(294\) | −10.6643 | − | 27.7177i | −0.0362731 | − | 0.0942780i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 57.4853i | − | 0.194207i | ||||||
\(297\) | −144.169 | − | 73.0398i | −0.485419 | − | 0.245925i | ||||
\(298\) | −263.518 | −0.884290 | ||||||||
\(299\) | 613.706i | 2.05253i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 106.705 | 0.354502 | ||||||||
\(302\) | − | 259.593i | − | 0.859581i | ||||||
\(303\) | −147.029 | − | 382.145i | −0.485243 | − | 1.26120i | ||||
\(304\) | 84.4271 | 0.277721 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 19.1665 | − | 17.3110i | 0.0626356 | − | 0.0565719i | ||||
\(307\) | 293.405 | 0.955717 | 0.477858 | − | 0.878437i | \(-0.341413\pi\) | ||||
0.477858 | + | 0.878437i | \(0.341413\pi\) | |||||||
\(308\) | − | 31.6737i | − | 0.102837i | ||||||
\(309\) | 361.725 | − | 139.172i | 1.17063 | − | 0.450395i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 59.2465i | 0.190503i | 0.995453 | + | 0.0952517i | \(0.0303656\pi\) | ||||
−0.995453 | + | 0.0952517i | \(0.969634\pi\) | |||||||
\(312\) | −57.9435 | − | 150.602i | −0.185716 | − | 0.482698i | ||||
\(313\) | −450.587 | −1.43957 | −0.719787 | − | 0.694195i | \(-0.755761\pi\) | ||||
−0.719787 | + | 0.694195i | \(0.755761\pi\) | |||||||
\(314\) | 374.593i | 1.19297i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 263.243 | 0.833049 | ||||||||
\(317\) | − | 277.454i | − | 0.875249i | −0.899158 | − | 0.437624i | \(-0.855820\pi\) | ||
0.899158 | − | 0.437624i | \(-0.144180\pi\) | |||||||
\(318\) | 228.017 | − | 87.7287i | 0.717035 | − | 0.275876i | ||||
\(319\) | 73.3872 | 0.230054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.8284 | − | 56.7345i | −0.0680011 | − | 0.176743i | ||||
\(322\) | 120.749 | 0.374997 | ||||||||
\(323\) | − | 42.8288i | − | 0.132597i | ||||||
\(324\) | −16.4383 | + | 161.164i | −0.0507355 | + | 0.497419i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 303.882i | 0.932153i | ||||||||
\(327\) | −315.185 | + | 121.266i | −0.963867 | + | 0.370844i | ||||
\(328\) | 98.1982 | 0.299385 | ||||||||
\(329\) | 191.658i | 0.582546i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 275.898 | 0.833529 | 0.416764 | − | 0.909015i | \(-0.363164\pi\) | ||||
0.416764 | + | 0.909015i | \(0.363164\pi\) | |||||||
\(332\) | − | 231.729i | − | 0.697978i | ||||||
\(333\) | 135.746 | − | 122.604i | 0.407645 | − | 0.368181i | ||||
\(334\) | 77.2096 | 0.231166 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −29.6315 | + | 11.4006i | −0.0881890 | + | 0.0339304i | ||||
\(337\) | 102.798 | 0.305038 | 0.152519 | − | 0.988301i | \(-0.451261\pi\) | ||||
0.152519 | + | 0.988301i | \(0.451261\pi\) | |||||||
\(338\) | 272.440i | 0.806035i | ||||||||
\(339\) | 7.04287 | + | 18.3053i | 0.0207754 | + | 0.0539978i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 235.290i | 0.690000i | ||||||||
\(342\) | 180.066 | + | 199.366i | 0.526507 | + | 0.582941i | ||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | − | 114.073i | − | 0.331606i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −439.326 | −1.26973 | ||||||||
\(347\) | − | 456.590i | − | 1.31582i | −0.753096 | − | 0.657910i | \(-0.771441\pi\) | ||
0.753096 | − | 0.657910i | \(-0.228559\pi\) | |||||||
\(348\) | −26.4149 | − | 68.6555i | −0.0759049 | − | 0.197286i | ||||
\(349\) | −570.605 | −1.63497 | −0.817486 | − | 0.575948i | \(-0.804633\pi\) | ||||
−0.817486 | + | 0.575948i | \(0.804633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 232.050 | − | 458.030i | 0.661110 | − | 1.30493i | ||||
\(352\) | −33.8606 | −0.0961949 | ||||||||
\(353\) | 4.74525i | 0.0134426i | 0.999977 | + | 0.00672132i | \(0.00213948\pi\) | ||||
−0.999977 | + | 0.00672132i | \(0.997861\pi\) | |||||||
\(354\) | −284.279 | + | 109.375i | −0.803048 | + | 0.308969i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 203.878i | − | 0.572692i | ||||||
\(357\) | 5.78338 | + | 15.0317i | 0.0161999 | + | 0.0421056i | ||||
\(358\) | −230.407 | −0.643595 | ||||||||
\(359\) | 457.086i | 1.27322i | 0.771186 | + | 0.636610i | \(0.219664\pi\) | ||||
−0.771186 | + | 0.636610i | \(0.780336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 84.4961 | 0.234061 | ||||||||
\(362\) | − | 72.8444i | − | 0.201228i | ||||||
\(363\) | −238.470 | + | 91.7505i | −0.656943 | + | 0.252756i | ||||
\(364\) | 100.628 | 0.276451 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −124.512 | − | 323.622i | −0.340198 | − | 0.884213i | ||||
\(367\) | 556.637 | 1.51672 | 0.758361 | − | 0.651834i | \(-0.226000\pi\) | ||||
0.758361 | + | 0.651834i | \(0.226000\pi\) | |||||||
\(368\) | − | 129.086i | − | 0.350778i | ||||||
\(369\) | 209.436 | + | 231.885i | 0.567578 | + | 0.628414i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 152.355i | 0.410660i | ||||||||
\(372\) | 220.119 | − | 84.6900i | 0.591719 | − | 0.227661i | ||||
\(373\) | 77.2267 | 0.207042 | 0.103521 | − | 0.994627i | \(-0.466989\pi\) | ||||
0.103521 | + | 0.994627i | \(0.466989\pi\) | |||||||
\(374\) | 17.1771i | 0.0459280i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 204.891 | 0.544922 | ||||||||
\(377\) | 233.153i | 0.618443i | ||||||||
\(378\) | −90.1192 | − | 45.6566i | −0.238411 | − | 0.120785i | ||||
\(379\) | −476.133 | −1.25629 | −0.628143 | − | 0.778098i | \(-0.716185\pi\) | ||||
−0.628143 | + | 0.778098i | \(0.716185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42.1138 | + | 16.2031i | −0.110535 | + | 0.0425279i | ||||
\(382\) | −321.465 | −0.841532 | ||||||||
\(383\) | − | 600.374i | − | 1.56756i | −0.621041 | − | 0.783778i | \(-0.713290\pi\) | ||
0.621041 | − | 0.783778i | \(-0.286710\pi\) | |||||||
\(384\) | 12.1878 | + | 31.6774i | 0.0317390 | + | 0.0824933i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 339.214i | 0.878794i | ||||||||
\(387\) | 269.371 | − | 243.293i | 0.696048 | − | 0.628664i | ||||
\(388\) | 16.3856 | 0.0422310 | ||||||||
\(389\) | − | 315.387i | − | 0.810763i | −0.914148 | − | 0.405382i | \(-0.867139\pi\) | ||
0.914148 | − | 0.405382i | \(-0.132861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −65.4838 | −0.167478 | ||||||||
\(392\) | − | 19.7990i | − | 0.0505076i | ||||||
\(393\) | −55.5781 | − | 144.454i | −0.141420 | − | 0.367567i | ||||
\(394\) | −260.379 | −0.660861 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −72.2176 | − | 79.9584i | −0.182368 | − | 0.201915i | ||||
\(397\) | 291.527 | 0.734325 | 0.367163 | − | 0.930157i | \(-0.380329\pi\) | ||||
0.367163 | + | 0.930157i | \(0.380329\pi\) | |||||||
\(398\) | 305.176i | 0.766773i | ||||||||
\(399\) | −156.356 | + | 60.1575i | −0.391871 | + | 0.150771i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 312.203i | 0.778560i | 0.921119 | + | 0.389280i | \(0.127276\pi\) | ||||
−0.921119 | + | 0.389280i | \(0.872724\pi\) | |||||||
\(402\) | 124.487 | + | 323.557i | 0.309670 | + | 0.804869i | ||||
\(403\) | −747.522 | −1.85489 | ||||||||
\(404\) | − | 272.969i | − | 0.675665i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 45.8738 | 0.112990 | ||||||||
\(407\) | 121.655i | 0.298908i | ||||||||
\(408\) | 16.0695 | − | 6.18269i | 0.0393861 | − | 0.0151537i | ||||
\(409\) | 602.689 | 1.47357 | 0.736784 | − | 0.676128i | \(-0.236343\pi\) | ||||
0.736784 | + | 0.676128i | \(0.236343\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 51.2653 | + | 133.245i | 0.124733 | + | 0.324196i | ||||
\(412\) | 258.383 | 0.627142 | ||||||||
\(413\) | − | 189.948i | − | 0.459922i | ||||||
\(414\) | 304.824 | − | 275.314i | 0.736289 | − | 0.665010i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 107.576i | − | 0.258596i | ||||||
\(417\) | −329.633 | + | 126.825i | −0.790486 | + | 0.304136i | ||||
\(418\) | −178.672 | −0.427445 | ||||||||
\(419\) | 179.970i | 0.429522i | 0.976667 | + | 0.214761i | \(0.0688972\pi\) | ||||
−0.976667 | + | 0.214761i | \(0.931103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 454.959 | 1.08066 | 0.540331 | − | 0.841453i | \(-0.318299\pi\) | ||||
0.540331 | + | 0.841453i | \(0.318299\pi\) | |||||||
\(422\) | − | 173.081i | − | 0.410144i | ||||||
\(423\) | 436.989 | + | 483.828i | 1.03307 | + | 1.14380i | ||||
\(424\) | 162.874 | 0.384138 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −30.4986 | + | 11.7342i | −0.0715929 | + | 0.0275451i | ||||
\(427\) | 216.236 | 0.506407 | ||||||||
\(428\) | − | 40.5259i | − | 0.0946866i | ||||||
\(429\) | 122.625 | + | 318.717i | 0.285839 | + | 0.742930i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 280.437i | − | 0.650665i | −0.945600 | − | 0.325333i | \(-0.894524\pi\) | ||
0.945600 | − | 0.325333i | \(-0.105476\pi\) | |||||||
\(432\) | −48.8090 | + | 96.3415i | −0.112984 | + | 0.223013i | ||||
\(433\) | −172.401 | −0.398155 | −0.199077 | − | 0.979984i | \(-0.563794\pi\) | ||||
−0.199077 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(434\) | 147.078i | 0.338889i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −225.139 | −0.516373 | ||||||||
\(437\) | − | 681.149i | − | 1.55869i | ||||||
\(438\) | 18.3874 | + | 47.7909i | 0.0419803 | + | 0.109112i | ||||
\(439\) | −299.659 | −0.682594 | −0.341297 | − | 0.939955i | \(-0.610866\pi\) | ||||
−0.341297 | + | 0.939955i | \(0.610866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 46.7533 | − | 42.2271i | 0.106017 | − | 0.0957531i | ||||
\(442\) | −54.5720 | −0.123466 | ||||||||
\(443\) | − | 389.448i | − | 0.879115i | −0.898214 | − | 0.439558i | \(-0.855135\pi\) | ||
0.898214 | − | 0.439558i | \(-0.144865\pi\) | |||||||
\(444\) | 113.812 | − | 43.7886i | 0.256332 | − | 0.0986229i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 99.1809i | 0.222379i | ||||||||
\(447\) | −200.731 | − | 521.724i | −0.449063 | − | 1.16717i | ||||
\(448\) | −21.1660 | −0.0472456 | ||||||||
\(449\) | − | 614.023i | − | 1.36753i | −0.729700 | − | 0.683767i | \(-0.760340\pi\) | ||
0.729700 | − | 0.683767i | \(-0.239660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −207.816 | −0.460788 | ||||||||
\(452\) | 13.0756i | 0.0289283i | ||||||||
\(453\) | 513.953 | − | 197.741i | 1.13455 | − | 0.436515i | ||||
\(454\) | −44.4455 | −0.0978975 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 64.3111 | + | 167.152i | 0.141033 | + | 0.366562i | ||||
\(457\) | −215.558 | −0.471681 | −0.235840 | − | 0.971792i | \(-0.575784\pi\) | ||||
−0.235840 | + | 0.971792i | \(0.575784\pi\) | |||||||
\(458\) | − | 50.5167i | − | 0.110299i | ||||||
\(459\) | 48.8728 | + | 24.7602i | 0.106477 | + | 0.0539438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 369.603i | 0.801743i | 0.916134 | + | 0.400871i | \(0.131293\pi\) | ||||
−0.916134 | + | 0.400871i | \(0.868707\pi\) | |||||||
\(462\) | 62.7088 | − | 24.1270i | 0.135733 | − | 0.0522229i | ||||
\(463\) | 0.675303 | 0.00145854 | 0.000729269 | − | 1.00000i | \(-0.499768\pi\) | ||||
0.000729269 | 1.00000i | \(0.499768\pi\) | ||||||||
\(464\) | − | 49.0411i | − | 0.105692i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 458.972 | 0.984918 | ||||||||
\(467\) | − | 90.1341i | − | 0.193007i | −0.995333 | − | 0.0965033i | \(-0.969234\pi\) | ||
0.995333 | − | 0.0965033i | \(-0.0307658\pi\) | |||||||
\(468\) | 254.030 | − | 229.437i | 0.542799 | − | 0.490251i | ||||
\(469\) | −216.193 | −0.460965 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −741.634 | + | 285.341i | −1.57459 | + | 0.605819i | ||||
\(472\) | −203.063 | −0.430217 | ||||||||
\(473\) | 241.410i | 0.510381i | ||||||||
\(474\) | 200.522 | + | 521.179i | 0.423042 | + | 1.09953i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.7372i | 0.0225572i | ||||||||
\(477\) | 347.377 | + | 384.611i | 0.728254 | + | 0.806313i | ||||
\(478\) | 565.741 | 1.18356 | ||||||||
\(479\) | 422.277i | 0.881579i | 0.897610 | + | 0.440790i | \(0.145302\pi\) | ||||
−0.897610 | + | 0.440790i | \(0.854698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −386.503 | −0.803540 | ||||||||
\(482\) | 560.460i | 1.16278i | ||||||||
\(483\) | 91.9788 | + | 239.064i | 0.190432 | + | 0.494956i | ||||
\(484\) | −170.341 | −0.351945 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −331.600 | + | 90.2189i | −0.682304 | + | 0.185636i | ||||
\(487\) | 240.184 | 0.493191 | 0.246595 | − | 0.969119i | \(-0.420688\pi\) | ||||
0.246595 | + | 0.969119i | \(0.420688\pi\) | |||||||
\(488\) | − | 231.166i | − | 0.473700i | ||||||
\(489\) | −601.637 | + | 231.478i | −1.23034 | + | 0.473369i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 961.188i | − | 1.95761i | −0.204788 | − | 0.978806i | \(-0.565651\pi\) | ||
0.204788 | − | 0.978806i | \(-0.434349\pi\) | |||||||
\(492\) | 74.8010 | + | 194.416i | 0.152034 | + | 0.395155i | ||||
\(493\) | −24.8779 | −0.0504624 | ||||||||
\(494\) | − | 567.646i | − | 1.14908i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 157.233 | 0.317002 | ||||||||
\(497\) | − | 20.3783i | − | 0.0410027i | ||||||
\(498\) | 458.785 | − | 176.516i | 0.921256 | − | 0.354450i | ||||
\(499\) | −203.222 | −0.407259 | −0.203629 | − | 0.979048i | \(-0.565274\pi\) | ||||
−0.203629 | + | 0.979048i | \(0.565274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 58.8132 | + | 152.862i | 0.117392 | + | 0.305115i | ||||
\(502\) | −312.860 | −0.623228 | ||||||||
\(503\) | 112.900i | 0.224453i | 0.993683 | + | 0.112226i | \(0.0357982\pi\) | ||||
−0.993683 | + | 0.112226i | \(0.964202\pi\) | |||||||
\(504\) | −45.1427 | − | 49.9814i | −0.0895689 | − | 0.0991694i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 273.184i | 0.539889i | ||||||||
\(507\) | −539.387 | + | 207.527i | −1.06388 | + | 0.409323i | ||||
\(508\) | −30.0822 | −0.0592170 | ||||||||
\(509\) | 876.657i | 1.72231i | 0.508341 | + | 0.861156i | \(0.330259\pi\) | ||||
−0.508341 | + | 0.861156i | \(0.669741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.9326 | −0.0624904 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −257.550 | + | 508.365i | −0.502047 | + | 0.990964i | ||||
\(514\) | 288.238 | 0.560775 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 225.845 | − | 86.8930i | 0.437684 | − | 0.168397i | ||||
\(517\) | −433.608 | −0.838700 | ||||||||
\(518\) | 76.0459i | 0.146807i | ||||||||
\(519\) | −334.650 | − | 869.795i | −0.644798 | − | 1.67591i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 497.586i | 0.955060i | 0.878616 | + | 0.477530i | \(0.158468\pi\) | ||||
−0.878616 | + | 0.477530i | \(0.841532\pi\) | |||||||
\(522\) | 115.806 | − | 104.595i | 0.221850 | − | 0.200373i | ||||
\(523\) | 519.528 | 0.993362 | 0.496681 | − | 0.867933i | \(-0.334552\pi\) | ||||
0.496681 | + | 0.867933i | \(0.334552\pi\) | |||||||
\(524\) | − | 103.185i | − | 0.196917i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 138.878 | 0.264027 | ||||||||
\(527\) | − | 79.7623i | − | 0.151352i | ||||||
\(528\) | −25.7928 | − | 67.0385i | −0.0488500 | − | 0.126967i | ||||
\(529\) | −512.453 | −0.968720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −433.090 | − | 479.511i | −0.815612 | − | 0.903034i | ||||
\(532\) | −111.687 | −0.209937 | ||||||||
\(533\) | − | 660.236i | − | 1.23872i | ||||||
\(534\) | 403.646 | − | 155.301i | 0.755892 | − | 0.290826i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 231.120i | 0.431193i | ||||||||
\(537\) | −175.509 | − | 456.169i | −0.326832 | − | 0.849476i | ||||
\(538\) | 436.488 | 0.811317 | ||||||||
\(539\) | 41.9004i | 0.0777372i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 853.843 | 1.57827 | 0.789134 | − | 0.614220i | \(-0.210529\pi\) | ||||
0.789134 | + | 0.614220i | \(0.210529\pi\) | |||||||
\(542\) | − | 564.047i | − | 1.04068i | ||||||
\(543\) | 144.220 | − | 55.4881i | 0.265599 | − | 0.102188i | ||||
\(544\) | 11.4786 | 0.0211004 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 76.6520 | + | 199.228i | 0.140388 | + | 0.364886i | ||||
\(547\) | 468.232 | 0.855999 | 0.428000 | − | 0.903779i | \(-0.359218\pi\) | ||||
0.428000 | + | 0.903779i | \(0.359218\pi\) | |||||||
\(548\) | 95.1776i | 0.173682i | ||||||||
\(549\) | 545.874 | − | 493.028i | 0.994306 | − | 0.898048i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 258.775i | − | 0.469646i | ||||||
\(552\) | 255.570 | − | 98.3295i | 0.462989 | − | 0.178133i | ||||
\(553\) | −348.238 | −0.629726 | ||||||||
\(554\) | 112.742i | 0.203506i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −235.459 | −0.423488 | ||||||||
\(557\) | 260.390i | 0.467487i | 0.972298 | + | 0.233744i | \(0.0750976\pi\) | ||||
−0.972298 | + | 0.233744i | \(0.924902\pi\) | |||||||
\(558\) | 335.345 | + | 371.289i | 0.600977 | + | 0.665393i | ||||
\(559\) | −766.967 | −1.37203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.0078 | + | 13.0844i | −0.0606200 | + | 0.0233233i | ||||
\(562\) | −297.224 | −0.528869 | ||||||||
\(563\) | 62.6717i | 0.111317i | 0.998450 | + | 0.0556587i | \(0.0177259\pi\) | ||||
−0.998450 | + | 0.0556587i | \(0.982274\pi\) | |||||||
\(564\) | 156.072 | + | 405.650i | 0.276724 | + | 0.719238i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 371.855i | 0.656987i | ||||||||
\(567\) | 21.7458 | − | 213.200i | 0.0383524 | − | 0.376014i | ||||
\(568\) | −21.7854 | −0.0383545 | ||||||||
\(569\) | − | 221.137i | − | 0.388641i | −0.980938 | − | 0.194320i | \(-0.937750\pi\) | ||
0.980938 | − | 0.194320i | \(-0.0622501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 520.798 | 0.912080 | 0.456040 | − | 0.889959i | \(-0.349267\pi\) | ||||
0.456040 | + | 0.889959i | \(0.349267\pi\) | |||||||
\(572\) | 227.662i | 0.398010i | ||||||||
\(573\) | −244.871 | − | 636.449i | −0.427349 | − | 1.11073i | ||||
\(574\) | −129.904 | −0.226314 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −53.4323 | + | 48.2596i | −0.0927644 | + | 0.0837840i | ||||
\(577\) | 78.8359 | 0.136631 | 0.0683154 | − | 0.997664i | \(-0.478238\pi\) | ||||
0.0683154 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(578\) | 402.885i | 0.697032i | ||||||||
\(579\) | −671.590 | + | 258.391i | −1.15991 | + | 0.446272i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 306.548i | 0.527622i | ||||||||
\(582\) | 12.4815 | + | 32.4409i | 0.0214459 | + | 0.0557403i | ||||
\(583\) | −344.689 | −0.591234 | ||||||||
\(584\) | 34.1374i | 0.0584544i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −505.680 | −0.862935 | ||||||||
\(587\) | 146.455i | 0.249498i | 0.992188 | + | 0.124749i | \(0.0398125\pi\) | ||||
−0.992188 | + | 0.124749i | \(0.960187\pi\) | |||||||
\(588\) | 39.1988 | − | 15.0816i | 0.0666646 | − | 0.0256489i | ||||
\(589\) | 829.670 | 1.40861 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −198.340 | − | 515.509i | −0.335601 | − | 0.872266i | ||||
\(592\) | 81.2965 | 0.137325 | ||||||||
\(593\) | 240.021i | 0.404758i | 0.979307 | + | 0.202379i | \(0.0648672\pi\) | ||||
−0.979307 | + | 0.202379i | \(0.935133\pi\) | |||||||
\(594\) | 103.294 | − | 203.886i | 0.173895 | − | 0.343243i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 372.671i | − | 0.625287i | ||||||
\(597\) | −604.198 | + | 232.463i | −1.01206 | + | 0.389385i | ||||
\(598\) | −867.912 | −1.45136 | ||||||||
\(599\) | − | 886.239i | − | 1.47953i | −0.672865 | − | 0.739766i | \(-0.734936\pi\) | ||
0.672865 | − | 0.739766i | \(-0.265064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −162.944 | −0.271121 | −0.135561 | − | 0.990769i | \(-0.543284\pi\) | ||||
−0.135561 | + | 0.990769i | \(0.543284\pi\) | |||||||
\(602\) | 150.904i | 0.250671i | ||||||||
\(603\) | −545.765 | + | 492.930i | −0.905083 | + | 0.817463i | ||||
\(604\) | 367.121 | 0.607816 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 540.434 | − | 207.930i | 0.891805 | − | 0.343119i | ||||
\(607\) | −649.221 | −1.06956 | −0.534779 | − | 0.844992i | \(-0.679605\pi\) | ||||
−0.534779 | + | 0.844992i | \(0.679605\pi\) | |||||||
\(608\) | 119.398i | 0.196378i | ||||||||
\(609\) | 34.9437 | + | 90.8227i | 0.0573787 | + | 0.149134i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1377.58i | − | 2.25464i | ||||||
\(612\) | 24.4815 | + | 27.1055i | 0.0400024 | + | 0.0442901i | ||||
\(613\) | 109.849 | 0.179199 | 0.0895994 | − | 0.995978i | \(-0.471441\pi\) | ||||
0.0895994 | + | 0.995978i | \(0.471441\pi\) | |||||||
\(614\) | 414.937i | 0.675794i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 44.7934 | 0.0727165 | ||||||||
\(617\) | 871.161i | 1.41193i | 0.708246 | + | 0.705966i | \(0.249487\pi\) | ||||
−0.708246 | + | 0.705966i | \(0.750513\pi\) | |||||||
\(618\) | 196.819 | + | 511.556i | 0.318477 | + | 0.827760i | ||||
\(619\) | 153.281 | 0.247627 | 0.123814 | − | 0.992305i | \(-0.460487\pi\) | ||||
0.123814 | + | 0.992305i | \(0.460487\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 777.272 | + | 393.786i | 1.25165 | + | 0.634115i | ||||
\(622\) | −83.7873 | −0.134706 | ||||||||
\(623\) | 269.706i | 0.432914i | ||||||||
\(624\) | 212.983 | − | 81.9444i | 0.341319 | − | 0.131321i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 637.226i | − | 1.01793i | ||||||
\(627\) | −136.101 | − | 353.742i | −0.217067 | − | 0.564182i | ||||
\(628\) | −529.755 | −0.843558 | ||||||||
\(629\) | − | 41.2407i | − | 0.0655655i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −959.345 | −1.52036 | −0.760178 | − | 0.649715i | \(-0.774888\pi\) | ||||
−0.760178 | + | 0.649715i | \(0.774888\pi\) | |||||||
\(632\) | 372.282i | 0.589055i | ||||||||
\(633\) | 342.672 | − | 131.842i | 0.541346 | − | 0.208281i | ||||
\(634\) | 392.379 | 0.618894 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 124.067 | + | 322.465i | 0.195074 | + | 0.507020i | ||||
\(637\) | −133.119 | −0.208977 | ||||||||
\(638\) | 103.785i | 0.162673i | ||||||||
\(639\) | −46.4637 | − | 51.4439i | −0.0727131 | − | 0.0805069i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 733.758i | − | 1.14471i | −0.820007 | − | 0.572354i | \(-0.806030\pi\) | ||
0.820007 | − | 0.572354i | \(-0.193970\pi\) | |||||||
\(642\) | 80.2346 | − | 30.8700i | 0.124976 | − | 0.0480840i | ||||
\(643\) | −164.305 | −0.255529 | −0.127765 | − | 0.991805i | \(-0.540780\pi\) | ||||
−0.127765 | + | 0.991805i | \(0.540780\pi\) | |||||||
\(644\) | 170.765i | 0.265163i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 60.5691 | 0.0937602 | ||||||||
\(647\) | 1171.84i | 1.81119i | 0.424146 | + | 0.905594i | \(0.360574\pi\) | ||||
−0.424146 | + | 0.905594i | \(0.639426\pi\) | |||||||
\(648\) | −227.920 | − | 23.2473i | −0.351729 | − | 0.0358754i | ||||
\(649\) | 429.739 | 0.662155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −291.191 | + | 112.034i | −0.447297 | + | 0.172096i | ||||
\(652\) | −429.754 | −0.659132 | ||||||||
\(653\) | 804.521i | 1.23204i | 0.787731 | + | 0.616019i | \(0.211256\pi\) | ||||
−0.787731 | + | 0.616019i | \(0.788744\pi\) | |||||||
\(654\) | −171.496 | − | 445.738i | −0.262226 | − | 0.681557i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 138.873i | 0.211697i | ||||||||
\(657\) | −80.6119 | + | 72.8080i | −0.122697 | + | 0.110819i | ||||
\(658\) | −271.045 | −0.411922 | ||||||||
\(659\) | − | 864.248i | − | 1.31145i | −0.754999 | − | 0.655727i | \(-0.772362\pi\) | ||
0.754999 | − | 0.655727i | \(-0.227638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −963.638 | −1.45785 | −0.728924 | − | 0.684595i | \(-0.759979\pi\) | ||||
−0.728924 | + | 0.684595i | \(0.759979\pi\) | |||||||
\(662\) | 390.179i | 0.589394i | ||||||||
\(663\) | −41.5694 | − | 108.044i | −0.0626989 | − | 0.162962i | ||||
\(664\) | 327.714 | 0.493545 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 173.389 | + | 191.973i | 0.260343 | + | 0.288248i | ||||
\(667\) | −395.658 | −0.593191 | ||||||||
\(668\) | 109.191i | 0.163459i | ||||||||
\(669\) | −196.362 | + | 75.5496i | −0.293516 | + | 0.112929i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 489.213i | 0.729081i | ||||||||
\(672\) | −16.1229 | − | 41.9053i | −0.0239924 | − | 0.0623590i | ||||
\(673\) | −149.734 | −0.222487 | −0.111244 | − | 0.993793i | \(-0.535483\pi\) | ||||
−0.111244 | + | 0.993793i | \(0.535483\pi\) | |||||||
\(674\) | 145.378i | 0.215694i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −385.288 | −0.569953 | ||||||||
\(677\) | 325.257i | 0.480439i | 0.970719 | + | 0.240219i | \(0.0772194\pi\) | ||||
−0.970719 | + | 0.240219i | \(0.922781\pi\) | |||||||
\(678\) | −25.8875 | + | 9.96012i | −0.0381822 | + | 0.0146904i | ||||
\(679\) | −21.6761 | −0.0319236 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.8557 | − | 87.9949i | −0.0497146 | − | 0.129214i | ||||
\(682\) | −332.750 | −0.487904 | ||||||||
\(683\) | 551.573i | 0.807575i | 0.914853 | + | 0.403787i | \(0.132306\pi\) | ||||
−0.914853 | + | 0.403787i | \(0.867694\pi\) | |||||||
\(684\) | −281.946 | + | 254.651i | −0.412202 | + | 0.372297i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 100.015 | − | 38.4803i | 0.145582 | − | 0.0560121i | ||||
\(688\) | 161.323 | 0.234481 | ||||||||
\(689\) | − | 1095.09i | − | 1.58939i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −495.558 | −0.717161 | −0.358580 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358580 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(692\) | − | 621.301i | − | 0.897834i | ||||||
\(693\) | 95.5350 | + | 105.775i | 0.137857 | + | 0.152633i | ||||
\(694\) | 645.715 | 0.930426 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 97.0935 | − | 37.3563i | 0.139502 | − | 0.0536729i | ||||
\(697\) | 70.4486 | 0.101074 | ||||||||
\(698\) | − | 806.958i | − | 1.15610i | ||||||
\(699\) | 349.615 | + | 908.690i | 0.500164 | + | 1.29999i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 377.346i | − | 0.538297i | −0.963099 | − | 0.269149i | \(-0.913258\pi\) | ||
0.963099 | − | 0.269149i | \(-0.0867423\pi\) | |||||||
\(702\) | 647.752 | + | 328.168i | 0.922724 | + | 0.467475i | ||||
\(703\) | 428.977 | 0.610209 | ||||||||
\(704\) | − | 47.8861i | − | 0.0680201i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.71080 | −0.00950539 | ||||||||
\(707\) | 361.104i | 0.510755i | ||||||||
\(708\) | −154.680 | − | 402.031i | −0.218474 | − | 0.567840i | ||||
\(709\) | −517.276 | −0.729585 | −0.364792 | − | 0.931089i | \(-0.618860\pi\) | ||||
−0.364792 | + | 0.931089i | \(0.618860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −879.107 | + | 794.001i | −1.23644 | + | 1.11674i | ||||
\(712\) | 288.327 | 0.404954 | ||||||||
\(713\) | − | 1268.54i | − | 1.77916i | ||||||
\(714\) | −21.2580 | + | 8.17894i | −0.0297731 | + | 0.0114551i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 325.845i | − | 0.455090i | ||||||
\(717\) | 430.944 | + | 1120.08i | 0.601038 | + | 1.56217i | ||||
\(718\) | −646.418 | −0.900303 | ||||||||
\(719\) | − | 1187.74i | − | 1.65193i | −0.563720 | − | 0.825966i | \(-0.690630\pi\) | ||
0.563720 | − | 0.825966i | \(-0.309370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −341.808 | −0.474075 | ||||||||
\(722\) | 119.496i | 0.165506i | ||||||||
\(723\) | −1109.62 | + | 426.922i | −1.53474 | + | 0.590487i | ||||
\(724\) | 103.018 | 0.142289 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −129.755 | − | 337.248i | −0.178726 | − | 0.464529i | ||||
\(727\) | 892.878 | 1.22817 | 0.614084 | − | 0.789241i | \(-0.289526\pi\) | ||||
0.614084 | + | 0.789241i | \(0.289526\pi\) | |||||||
\(728\) | 142.310i | 0.195480i | ||||||||
\(729\) | −431.210 | − | 587.791i | −0.591509 | − | 0.806298i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 81.8371i | − | 0.111952i | ||||||
\(732\) | 457.671 | − | 176.087i | 0.625233 | − | 0.240556i | ||||
\(733\) | 868.737 | 1.18518 | 0.592590 | − | 0.805504i | \(-0.298106\pi\) | ||||
0.592590 | + | 0.805504i | \(0.298106\pi\) | |||||||
\(734\) | 787.204i | 1.07248i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 182.555 | 0.248037 | ||||||||
\(737\) | − | 489.116i | − | 0.663657i | ||||||
\(738\) | −327.935 | + | 296.188i | −0.444356 | + | 0.401338i | ||||
\(739\) | 356.963 | 0.483035 | 0.241517 | − | 0.970396i | \(-0.422355\pi\) | ||||
0.241517 | + | 0.970396i | \(0.422355\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1123.85 | − | 432.396i | 1.51666 | − | 0.583530i | ||||
\(742\) | −215.463 | −0.290381 | ||||||||
\(743\) | 982.069i | 1.32176i | 0.750491 | + | 0.660881i | \(0.229817\pi\) | ||||
−0.750491 | + | 0.660881i | \(0.770183\pi\) | |||||||
\(744\) | 119.770 | + | 311.296i | 0.160981 | + | 0.418408i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 109.215i | 0.146401i | ||||||||
\(747\) | 698.946 | + | 773.863i | 0.935670 | + | 1.03596i | ||||
\(748\) | −24.2920 | −0.0324760 | ||||||||
\(749\) | 53.6107i | 0.0715763i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −710.167 | −0.945628 | −0.472814 | − | 0.881162i | \(-0.656762\pi\) | ||||
−0.472814 | + | 0.881162i | \(0.656762\pi\) | |||||||
\(752\) | 289.759i | 0.385318i | ||||||||
\(753\) | −238.317 | − | 619.413i | −0.316489 | − | 0.822593i | ||||
\(754\) | −329.728 | −0.437305 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 64.5682 | − | 127.448i | 0.0854077 | − | 0.168582i | ||||
\(757\) | −346.357 | −0.457540 | −0.228770 | − | 0.973481i | \(-0.573470\pi\) | ||||
−0.228770 | + | 0.973481i | \(0.573470\pi\) | |||||||
\(758\) | − | 673.353i | − | 0.888329i | ||||||
\(759\) | −540.859 | + | 208.093i | −0.712595 | + | 0.274168i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1138.06i | 1.49548i | 0.663994 | + | 0.747738i | \(0.268860\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(762\) | −22.9147 | − | 59.5580i | −0.0300718 | − | 0.0781600i | ||||
\(763\) | 297.830 | 0.390341 | ||||||||
\(764\) | − | 454.620i | − | 0.595053i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 849.057 | 1.10843 | ||||||||
\(767\) | 1365.29i | 1.78004i | ||||||||
\(768\) | −44.7986 | + | 17.2361i | −0.0583315 | + | 0.0224428i | ||||
\(769\) | 395.138 | 0.513833 | 0.256917 | − | 0.966434i | \(-0.417293\pi\) | ||||
0.256917 | + | 0.966434i | \(0.417293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 219.561 | + | 570.665i | 0.284774 | + | 0.740162i | ||||
\(772\) | −479.722 | −0.621401 | ||||||||
\(773\) | 1244.98i | 1.61058i | 0.592881 | + | 0.805290i | \(0.297990\pi\) | ||||
−0.592881 | + | 0.805290i | \(0.702010\pi\) | |||||||
\(774\) | 344.068 | + | 380.947i | 0.444533 | + | 0.492180i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.1728i | 0.0298618i | ||||||||
\(777\) | −150.559 | + | 57.9268i | −0.193769 | + | 0.0745519i | ||||
\(778\) | 446.024 | 0.573296 | ||||||||
\(779\) | 732.791i | 0.940682i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.1041 | 0.0590322 | ||||||||
\(782\) | − | 92.6081i | − | 0.118425i | ||||||
\(783\) | 295.293 | + | 149.603i | 0.377131 | + | 0.191064i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 204.289 | − | 78.5992i | 0.259909 | − | 0.0999990i | ||||
\(787\) | −333.519 | −0.423785 | −0.211892 | − | 0.977293i | \(-0.567963\pi\) | ||||
−0.211892 | + | 0.977293i | \(0.567963\pi\) | |||||||
\(788\) | − | 368.232i | − | 0.467300i | ||||||
\(789\) | 105.789 | + | 274.957i | 0.134079 | + | 0.348488i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 17.2974i | − | 0.0218677i | ||||||
\(792\) | 113.078 | − | 102.131i | 0.142775 | − | 0.128954i | ||||
\(793\) | −1554.24 | −1.95995 | ||||||||
\(794\) | 412.281i | 0.519246i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −431.583 | −0.542190 | ||||||||
\(797\) | 541.407i | 0.679306i | 0.940551 | + | 0.339653i | \(0.110310\pi\) | ||||
−0.940551 | + | 0.339653i | \(0.889690\pi\) | |||||||
\(798\) | −85.0756 | − | 221.121i | −0.106611 | − | 0.277094i | ||||
\(799\) | 146.991 | 0.183969 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 614.943 | + | 680.856i | 0.767719 | + | 0.850007i | ||||
\(802\) | −441.521 | −0.550525 | ||||||||
\(803\) | − | 72.2446i | − | 0.0899683i | ||||||
\(804\) | −457.579 | + | 176.052i | −0.569128 | + | 0.218970i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1057.16i | − | 1.31161i | ||||||
\(807\) | 332.488 | + | 864.176i | 0.412005 | + | 1.07085i | ||||
\(808\) | 386.036 | 0.477768 | ||||||||
\(809\) | 812.942i | 1.00487i | 0.864614 | + | 0.502436i | \(0.167563\pi\) | ||||
−0.864614 | + | 0.502436i | \(0.832437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −750.662 | −0.925600 | −0.462800 | − | 0.886463i | \(-0.653155\pi\) | ||||
−0.462800 | + | 0.886463i | \(0.653155\pi\) | |||||||
\(812\) | 64.8753i | 0.0798957i | ||||||||
\(813\) | 1116.72 | − | 429.654i | 1.37358 | − | 0.528480i | ||||
\(814\) | −172.047 | −0.211360 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.74365 | + | 22.7258i | 0.0107153 | + | 0.0278502i | ||||
\(817\) | 851.252 | 1.04192 | ||||||||
\(818\) | 852.331i | 1.04197i | ||||||||
\(819\) | −336.050 | + | 303.517i | −0.410317 | + | 0.370595i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1216.71i | 1.48199i | 0.671513 | + | 0.740993i | \(0.265645\pi\) | ||||
−0.671513 | + | 0.740993i | \(0.734355\pi\) | |||||||
\(822\) | −188.436 | + | 72.5001i | −0.229241 | + | 0.0881996i | ||||
\(823\) | 918.365 | 1.11588 | 0.557938 | − | 0.829883i | \(-0.311593\pi\) | ||||
0.557938 | + | 0.829883i | \(0.311593\pi\) | |||||||
\(824\) | 365.408i | 0.443457i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 268.626 | 0.325214 | ||||||||
\(827\) | − | 973.601i | − | 1.17727i | −0.808400 | − | 0.588634i | \(-0.799666\pi\) | ||
0.808400 | − | 0.588634i | \(-0.200334\pi\) | |||||||
\(828\) | 389.353 | + | 431.086i | 0.470233 | + | 0.520635i | ||||
\(829\) | −759.447 | −0.916100 | −0.458050 | − | 0.888926i | \(-0.651452\pi\) | ||||
−0.458050 | + | 0.888926i | \(0.651452\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −223.211 | + | 85.8796i | −0.268606 | + | 0.103345i | ||||
\(832\) | 152.136 | 0.182855 | ||||||||
\(833\) | − | 14.2040i | − | 0.0170517i | ||||||
\(834\) | −179.357 | − | 466.171i | −0.215057 | − | 0.558958i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 252.681i | − | 0.302249i | ||||||
\(837\) | −479.649 | + | 946.753i | −0.573057 | + | 1.13113i | ||||
\(838\) | −254.515 | −0.303718 | ||||||||
\(839\) | 937.182i | 1.11702i | 0.829497 | + | 0.558512i | \(0.188627\pi\) | ||||
−0.829497 | + | 0.558512i | \(0.811373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 690.685 | 0.821267 | ||||||||
\(842\) | 643.409i | 0.764144i | ||||||||
\(843\) | −226.406 | − | 588.456i | −0.268572 | − | 0.698050i | ||||
\(844\) | 244.773 | 0.290015 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −684.237 | + | 617.996i | −0.808790 | + | 0.730492i | ||||
\(847\) | 225.340 | 0.266045 | ||||||||
\(848\) | 230.339i | 0.271626i | ||||||||
\(849\) | −736.212 | + | 283.255i | −0.867152 | + | 0.333633i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 655.891i | − | 0.770730i | ||||||
\(852\) | −16.5947 | − | 43.1315i | −0.0194773 | − | 0.0506238i | ||||
\(853\) | 465.533 | 0.545760 | 0.272880 | − | 0.962048i | \(-0.412024\pi\) | ||||
0.272880 | + | 0.962048i | \(0.412024\pi\) | |||||||
\(854\) | 305.803i | 0.358084i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 57.3122 | 0.0669535 | ||||||||
\(857\) | − | 1612.01i | − | 1.88099i | −0.339811 | − | 0.940494i | \(-0.610363\pi\) | ||
0.339811 | − | 0.940494i | \(-0.389637\pi\) | |||||||
\(858\) | −450.734 | + | 173.418i | −0.525331 | + | 0.202119i | ||||
\(859\) | −1111.27 | −1.29368 | −0.646842 | − | 0.762624i | \(-0.723911\pi\) | ||||
−0.646842 | + | 0.762624i | \(0.723911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −98.9524 | − | 257.189i | −0.114927 | − | 0.298709i | ||||
\(862\) | 396.597 | 0.460090 | ||||||||
\(863\) | − | 681.862i | − | 0.790106i | −0.918658 | − | 0.395053i | \(-0.870726\pi\) | ||
0.918658 | − | 0.395053i | \(-0.129274\pi\) | |||||||
\(864\) | −136.247 | − | 69.0264i | −0.157694 | − | 0.0798916i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 243.812i | − | 0.281538i | ||||||
\(867\) | −797.647 | + | 306.891i | −0.920008 | + | 0.353969i | ||||
\(868\) | −208.000 | −0.239631 | ||||||||
\(869\) | − | 787.857i | − | 0.906625i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1553.93 | 1.78408 | ||||||||
\(872\) | − | 318.394i | − | 0.365131i | ||||||
\(873\) | −54.7201 | + | 49.4227i | −0.0626805 | + | 0.0566125i | ||||
\(874\) | 963.289 | 1.10216 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −67.5865 | + | 26.0036i | −0.0771536 | + | 0.0296845i | ||||
\(877\) | −206.003 | −0.234896 | −0.117448 | − | 0.993079i | \(-0.537471\pi\) | ||||
−0.117448 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(878\) | − | 423.782i | − | 0.482667i | ||||||
\(879\) | −385.194 | − | 1001.16i | −0.438219 | − | 1.13898i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 909.333i | − | 1.03216i | −0.856540 | − | 0.516080i | \(-0.827391\pi\) | ||
0.856540 | − | 0.516080i | \(-0.172609\pi\) | |||||||
\(882\) | 59.7182 | + | 66.1191i | 0.0677077 | + | 0.0749650i | ||||
\(883\) | 776.956 | 0.879905 | 0.439952 | − | 0.898021i | \(-0.354995\pi\) | ||||
0.439952 | + | 0.898021i | \(0.354995\pi\) | |||||||
\(884\) | − | 77.1764i | − | 0.0873036i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 550.763 | 0.621628 | ||||||||
\(887\) | − | 1228.23i | − | 1.38470i | −0.721562 | − | 0.692350i | \(-0.756575\pi\) | ||
0.721562 | − | 0.692350i | \(-0.243425\pi\) | |||||||
\(888\) | 61.9264 | + | 160.954i | 0.0697369 | + | 0.181254i | ||||
\(889\) | 39.7951 | 0.0447638 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 482.345 | + | 49.1979i | 0.541352 | + | 0.0552165i | ||||
\(892\) | −140.263 | −0.157245 | ||||||||
\(893\) | 1528.97i | 1.71217i | ||||||||
\(894\) | 737.829 | − | 283.877i | 0.825312 | − | 0.317535i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −661.119 | − | 1718.32i | −0.737033 | − | 1.91564i | ||||
\(898\) | 868.359 | 0.966993 | ||||||||
\(899\) | − | 481.930i | − | 0.536074i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 116.848 | 0.129687 | ||||||||
\(902\) | − | 293.896i | − | 0.325827i | ||||||
\(903\) | −298.765 | + | 114.949i | −0.330858 | + | 0.127296i | ||||
\(904\) | −18.4917 | −0.0204554 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 279.649 | + | 726.840i | 0.308663 | + | 0.802251i | ||||
\(907\) | −254.429 | −0.280517 | −0.140259 | − | 0.990115i | \(-0.544793\pi\) | ||||
−0.140259 | + | 0.990115i | \(0.544793\pi\) | |||||||
\(908\) | − | 62.8554i | − | 0.0692240i | ||||||
\(909\) | 823.335 | + | 911.585i | 0.905759 | + | 1.00284i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 231.235i | 0.253825i | 0.991914 | + | 0.126913i | \(0.0405068\pi\) | ||||
−0.991914 | + | 0.126913i | \(0.959493\pi\) | |||||||
\(912\) | −236.389 | + | 90.9496i | −0.259198 | + | 0.0997254i | ||||
\(913\) | −693.537 | −0.759624 | ||||||||
\(914\) | − | 304.845i | − | 0.333529i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 71.4414 | 0.0779928 | ||||||||
\(917\) | 136.500i | 0.148855i | ||||||||
\(918\) | −35.0162 | + | 69.1166i | −0.0381440 | + | 0.0752904i | ||||
\(919\) | −279.584 | −0.304226 | −0.152113 | − | 0.988363i | \(-0.548608\pi\) | ||||
−0.152113 | + | 0.988363i | \(0.548608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −821.509 | + | 316.072i | −0.891975 | + | 0.343184i | ||||
\(922\) | −522.698 | −0.566918 | ||||||||
\(923\) | 146.474i | 0.158693i | ||||||||
\(924\) | 34.1207 | + | 88.6836i | 0.0369271 | + | 0.0959780i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.955022i | 0.00103134i | ||||||||
\(927\) | −862.874 | + | 779.340i | −0.930824 | + | 0.840712i | ||||
\(928\) | 69.3546 | 0.0747356 | ||||||||
\(929\) | 1522.35i | 1.63870i | 0.573294 | + | 0.819350i | \(0.305665\pi\) | ||||
−0.573294 | + | 0.819350i | \(0.694335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 147.747 | 0.158698 | ||||||||
\(932\) | 649.084i | 0.696442i | ||||||||
\(933\) | −63.8237 | − | 165.885i | −0.0684069 | − | 0.177798i | ||||
\(934\) | 127.469 | 0.136476 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 324.474 | + | 359.252i | 0.346660 | + | 0.383817i | ||||
\(937\) | −1402.37 | −1.49666 | −0.748329 | − | 0.663328i | \(-0.769144\pi\) | ||||
−0.748329 | + | 0.663328i | \(0.769144\pi\) | |||||||
\(938\) | − | 305.742i | − | 0.325951i | ||||||
\(939\) | 1261.60 | − | 485.397i | 1.34356 | − | 0.516930i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 569.377i | − | 0.605077i | −0.953137 | − | 0.302538i | \(-0.902166\pi\) | ||
0.953137 | − | 0.302538i | \(-0.0978340\pi\) | |||||||
\(942\) | −403.533 | − | 1048.83i | −0.428379 | − | 1.11341i | ||||
\(943\) | 1120.41 | 1.18814 | ||||||||
\(944\) | − | 287.174i | − | 0.304210i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −341.406 | −0.360894 | ||||||||
\(947\) | 130.552i | 0.137858i | 0.997622 | + | 0.0689290i | \(0.0219582\pi\) | ||||
−0.997622 | + | 0.0689290i | \(0.978042\pi\) | |||||||
\(948\) | −737.059 | + | 283.581i | −0.777488 | + | 0.299136i | ||||
\(949\) | 229.523 | 0.241858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 298.889 | + | 776.847i | 0.314289 | + | 0.816874i | ||||
\(952\) | −15.1848 | −0.0159504 | ||||||||
\(953\) | − | 154.008i | − | 0.161603i | −0.996730 | − | 0.0808016i | \(-0.974252\pi\) | ||
0.996730 | − | 0.0808016i | \(-0.0257480\pi\) | |||||||
\(954\) | −543.922 | + | 491.266i | −0.570149 | + | 0.514953i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 800.078i | 0.836902i | ||||||||
\(957\) | −205.478 | + | 79.0568i | −0.214710 | + | 0.0826090i | ||||
\(958\) | −597.189 | −0.623371 | ||||||||
\(959\) | − | 125.908i | − | 0.131291i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 584.137 | 0.607843 | ||||||||
\(962\) | − | 546.597i | − | 0.568189i | ||||||
\(963\) | 122.235 | + | 135.337i | 0.126932 | + | 0.140537i | ||||
\(964\) | −792.610 | −0.822209 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −338.087 | + | 130.078i | −0.349987 | + | 0.134656i | ||||
\(967\) | −614.131 | −0.635089 | −0.317544 | − | 0.948243i | \(-0.602858\pi\) | ||||
−0.317544 | + | 0.948243i | \(0.602858\pi\) | |||||||
\(968\) | − | 240.899i | − | 0.248862i | ||||||
\(969\) | 46.1376 | + | 119.917i | 0.0476136 | + | 0.123753i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 288.285i | − | 0.296895i | −0.988920 | − | 0.148448i | \(-0.952572\pi\) | ||
0.988920 | − | 0.148448i | \(-0.0474277\pi\) | |||||||
\(972\) | −127.589 | − | 468.953i | −0.131264 | − | 0.482462i | ||||
\(973\) | 311.483 | 0.320127 | ||||||||
\(974\) | 339.671i | 0.348739i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 326.918 | 0.334957 | ||||||||
\(977\) | 480.732i | 0.492049i | 0.969264 | + | 0.246025i | \(0.0791244\pi\) | ||||
−0.969264 | + | 0.246025i | \(0.920876\pi\) | |||||||
\(978\) | −327.359 | − | 850.844i | −0.334723 | − | 0.869983i | ||||
\(979\) | −610.184 | −0.623273 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 751.855 | − | 679.069i | 0.766417 | − | 0.692221i | ||||
\(982\) | 1359.32 | 1.38424 | ||||||||
\(983\) | − | 1414.59i | − | 1.43905i | −0.694465 | − | 0.719526i | \(-0.744359\pi\) | ||
0.694465 | − | 0.719526i | \(-0.255641\pi\) | |||||||
\(984\) | −274.946 | + | 105.785i | −0.279417 | + | 0.107505i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 35.1827i | − | 0.0356823i | ||||||
\(987\) | −206.464 | − | 536.625i | −0.209184 | − | 0.543693i | ||||
\(988\) | 802.773 | 0.812523 | ||||||||
\(989\) | − | 1301.54i | − | 1.31601i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −549.944 | −0.554939 | −0.277469 | − | 0.960735i | \(-0.589496\pi\) | ||||
−0.277469 | + | 0.960735i | \(0.589496\pi\) | |||||||
\(992\) | 222.361i | 0.224154i | ||||||||
\(993\) | −772.491 | + | 297.213i | −0.777937 | + | 0.299308i | ||||
\(994\) | 28.8193 | 0.0289933 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 249.631 | + | 648.821i | 0.250634 | + | 0.651426i | ||||
\(997\) | 524.552 | 0.526130 | 0.263065 | − | 0.964778i | \(-0.415267\pi\) | ||||
0.263065 | + | 0.964778i | \(0.415267\pi\) | |||||||
\(998\) | − | 287.399i | − | 0.287975i | ||||||
\(999\) | −248.000 | + | 489.514i | −0.248248 | + | 0.490004i |
(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 | 1050.3.e.e.701.19 | 24 | ||
3.2 | odd | 2 | inner | 1050.3.e.e.701.17 | 24 | ||
5.2 | odd | 4 | 210.3.c.a.29.8 | yes | 24 | ||
5.3 | odd | 4 | 210.3.c.a.29.17 | yes | 24 | ||
5.4 | even | 2 | inner | 1050.3.e.e.701.18 | 24 | ||
15.2 | even | 4 | 210.3.c.a.29.18 | yes | 24 | ||
15.8 | even | 4 | 210.3.c.a.29.7 | ✓ | 24 | ||
15.14 | odd | 2 | inner | 1050.3.e.e.701.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.7 | ✓ | 24 | 15.8 | even | 4 | ||
210.3.c.a.29.8 | yes | 24 | 5.2 | odd | 4 | ||
210.3.c.a.29.17 | yes | 24 | 5.3 | odd | 4 | ||
210.3.c.a.29.18 | yes | 24 | 15.2 | even | 4 | ||
1050.3.e.e.701.17 | 24 | 3.2 | odd | 2 | inner | ||
1050.3.e.e.701.18 | 24 | 5.4 | even | 2 | inner | ||
1050.3.e.e.701.19 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.e.e.701.20 | 24 | 15.14 | odd | 2 | inner |