Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(29,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.c (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.7 | ||
Character | \(\chi\) | \(=\) | 210.29 |
Dual form | 210.3.c.a.29.8 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.07726 | − | 2.79991i | 0.359085 | − | 0.933305i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −2.52563 | + | 4.31523i | −0.505125 | + | 0.863046i | ||||
\(6\) | −1.52347 | + | 3.95968i | −0.253912 | + | 0.659946i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −6.67904 | − | 6.03245i | −0.742116 | − | 0.670272i | ||||
\(10\) | 3.57177 | − | 6.10266i | 0.357177 | − | 0.610266i | ||||
\(11\) | − | 5.98577i | − | 0.544161i | −0.962275 | − | 0.272080i | \(-0.912288\pi\) | ||
0.962275 | − | 0.272080i | \(-0.0877116\pi\) | |||||||
\(12\) | 2.15451 | − | 5.59983i | 0.179543 | − | 0.466652i | ||||
\(13\) | − | 19.0169i | − | 1.46284i | −0.681926 | − | 0.731421i | \(-0.738858\pi\) | ||
0.681926 | − | 0.731421i | \(-0.261142\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 9.36153 | + | 11.7201i | 0.624102 | + | 0.781343i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 2.02915 | 0.119362 | 0.0596809 | − | 0.998218i | \(-0.480992\pi\) | ||||
0.0596809 | + | 0.998218i | \(0.480992\pi\) | |||||||
\(18\) | 9.44559 | + | 8.53117i | 0.524755 | + | 0.473954i | ||||
\(19\) | −21.1068 | −1.11088 | −0.555442 | − | 0.831556i | \(-0.687451\pi\) | ||||
−0.555442 | + | 0.831556i | \(0.687451\pi\) | |||||||
\(20\) | −5.05125 | + | 8.63046i | −0.252563 | + | 0.431523i | ||||
\(21\) | −7.40788 | − | 2.85015i | −0.352756 | − | 0.135721i | ||||
\(22\) | 8.46515i | 0.384780i | ||||||||
\(23\) | −32.2716 | −1.40311 | −0.701555 | − | 0.712615i | \(-0.747511\pi\) | ||||
−0.701555 | + | 0.712615i | \(0.747511\pi\) | |||||||
\(24\) | −3.04694 | + | 7.91935i | −0.126956 | + | 0.329973i | ||||
\(25\) | −12.2424 | − | 21.7973i | −0.489697 | − | 0.871893i | ||||
\(26\) | 26.8940i | 1.03439i | ||||||||
\(27\) | −24.0854 | + | 12.2023i | −0.892051 | + | 0.451935i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | − | 12.2603i | − | 0.422768i | −0.977403 | − | 0.211384i | \(-0.932203\pi\) | ||
0.977403 | − | 0.211384i | \(-0.0677971\pi\) | |||||||
\(30\) | −13.2392 | − | 16.5748i | −0.441307 | − | 0.552493i | ||||
\(31\) | 39.3082 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −16.7596 | − | 6.44820i | −0.507868 | − | 0.195400i | ||||
\(34\) | −2.86965 | −0.0844015 | ||||||||
\(35\) | 11.4170 | + | 6.68218i | 0.326201 | + | 0.190919i | ||||
\(36\) | −13.3581 | − | 12.0649i | −0.371058 | − | 0.335136i | ||||
\(37\) | − | 20.3241i | − | 0.549301i | −0.961544 | − | 0.274650i | \(-0.911438\pi\) | ||
0.961544 | − | 0.274650i | \(-0.0885621\pi\) | |||||||
\(38\) | 29.8495 | 0.785513 | ||||||||
\(39\) | −53.2458 | − | 20.4861i | −1.36528 | − | 0.525285i | ||||
\(40\) | 7.14355 | − | 12.2053i | 0.178589 | − | 0.305133i | ||||
\(41\) | − | 34.7183i | − | 0.846788i | −0.905946 | − | 0.423394i | \(-0.860839\pi\) | ||
0.905946 | − | 0.423394i | \(-0.139161\pi\) | |||||||
\(42\) | 10.4763 | + | 4.03072i | 0.249436 | + | 0.0959696i | ||||
\(43\) | 40.3307i | 0.937924i | 0.883218 | + | 0.468962i | \(0.155372\pi\) | ||||
−0.883218 | + | 0.468962i | \(0.844628\pi\) | |||||||
\(44\) | − | 11.9715i | − | 0.272080i | ||||||
\(45\) | 42.9002 | − | 13.5859i | 0.953337 | − | 0.301909i | ||||
\(46\) | 45.6389 | 0.992149 | ||||||||
\(47\) | −72.4398 | −1.54127 | −0.770636 | − | 0.637275i | \(-0.780061\pi\) | ||||
−0.770636 | + | 0.637275i | \(0.780061\pi\) | |||||||
\(48\) | 4.30902 | − | 11.1997i | 0.0897713 | − | 0.233326i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 17.3134 | + | 30.8261i | 0.346268 | + | 0.616521i | ||||
\(51\) | 2.18591 | − | 5.68144i | 0.0428610 | − | 0.111401i | ||||
\(52\) | − | 38.0339i | − | 0.731421i | ||||||
\(53\) | 57.5848 | 1.08651 | 0.543253 | − | 0.839569i | \(-0.317193\pi\) | ||||
0.543253 | + | 0.839569i | \(0.317193\pi\) | |||||||
\(54\) | 34.0619 | − | 17.2566i | 0.630775 | − | 0.319566i | ||||
\(55\) | 25.8300 | + | 15.1178i | 0.469636 | + | 0.274869i | ||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | −22.7374 | + | 59.0972i | −0.398902 | + | 1.03679i | ||||
\(58\) | 17.3387i | 0.298942i | ||||||||
\(59\) | − | 71.7934i | − | 1.21684i | −0.793616 | − | 0.608419i | \(-0.791804\pi\) | ||
0.793616 | − | 0.608419i | \(-0.208196\pi\) | |||||||
\(60\) | 18.7231 | + | 23.4403i | 0.312051 | + | 0.390671i | ||||
\(61\) | 81.7294 | 1.33983 | 0.669913 | − | 0.742439i | \(-0.266331\pi\) | ||||
0.669913 | + | 0.742439i | \(0.266331\pi\) | |||||||
\(62\) | −55.5902 | −0.896617 | ||||||||
\(63\) | −15.9604 | + | 17.6711i | −0.253339 | + | 0.280493i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 82.0625 | + | 48.0297i | 1.26250 | + | 0.738918i | ||||
\(66\) | 23.7017 | + | 9.11913i | 0.359117 | + | 0.138169i | ||||
\(67\) | 81.7131i | 1.21960i | 0.792556 | + | 0.609799i | \(0.208750\pi\) | ||||
−0.792556 | + | 0.609799i | \(0.791250\pi\) | |||||||
\(68\) | 4.05830 | 0.0596809 | ||||||||
\(69\) | −34.7647 | + | 90.3576i | −0.503836 | + | 1.30953i | ||||
\(70\) | −16.1461 | − | 9.45003i | −0.230659 | − | 0.135000i | ||||
\(71\) | 7.70229i | 0.108483i | 0.998528 | + | 0.0542415i | \(0.0172741\pi\) | ||||
−0.998528 | + | 0.0542415i | \(0.982726\pi\) | |||||||
\(72\) | 18.8912 | + | 17.0623i | 0.262377 | + | 0.236977i | ||||
\(73\) | − | 12.0694i | − | 0.165334i | −0.996577 | − | 0.0826671i | \(-0.973656\pi\) | ||
0.996577 | − | 0.0826671i | \(-0.0263438\pi\) | |||||||
\(74\) | 28.7427i | 0.388414i | ||||||||
\(75\) | −74.2188 | + | 10.7965i | −0.989585 | + | 0.143953i | ||||
\(76\) | −42.2136 | −0.555442 | ||||||||
\(77\) | −15.8369 | −0.205673 | ||||||||
\(78\) | 75.3009 | + | 28.9717i | 0.965397 | + | 0.371433i | ||||
\(79\) | 131.622 | 1.66610 | 0.833049 | − | 0.553199i | \(-0.186593\pi\) | ||||
0.833049 | + | 0.553199i | \(0.186593\pi\) | |||||||
\(80\) | −10.1025 | + | 17.2609i | −0.126281 | + | 0.215762i | ||||
\(81\) | 8.21915 | + | 80.5819i | 0.101471 | + | 0.994838i | ||||
\(82\) | 49.0991i | 0.598769i | ||||||||
\(83\) | 115.864 | 1.39596 | 0.697978 | − | 0.716119i | \(-0.254083\pi\) | ||||
0.697978 | + | 0.716119i | \(0.254083\pi\) | |||||||
\(84\) | −14.8158 | − | 5.70030i | −0.176378 | − | 0.0678607i | ||||
\(85\) | −5.12487 | + | 8.75624i | −0.0602926 | + | 0.103015i | ||||
\(86\) | − | 57.0363i | − | 0.663212i | ||||||
\(87\) | −34.3277 | − | 13.2075i | −0.394572 | − | 0.151810i | ||||
\(88\) | 16.9303i | 0.192390i | ||||||||
\(89\) | 101.939i | 1.14538i | 0.819771 | + | 0.572692i | \(0.194101\pi\) | ||||
−0.819771 | + | 0.572692i | \(0.805899\pi\) | |||||||
\(90\) | −60.6700 | + | 19.2133i | −0.674111 | + | 0.213482i | ||||
\(91\) | −50.3141 | −0.552902 | ||||||||
\(92\) | −64.5431 | −0.701555 | ||||||||
\(93\) | 42.3450 | − | 110.060i | 0.455323 | − | 1.18344i | ||||
\(94\) | 102.445 | 1.08984 | ||||||||
\(95\) | 53.3078 | − | 91.0806i | 0.561135 | − | 0.958743i | ||||
\(96\) | −6.09388 | + | 15.8387i | −0.0634779 | + | 0.164987i | ||||
\(97\) | 8.19281i | 0.0844619i | 0.999108 | + | 0.0422310i | \(0.0134465\pi\) | ||||
−0.999108 | + | 0.0422310i | \(0.986553\pi\) | |||||||
\(98\) | 9.89949 | 0.101015 | ||||||||
\(99\) | −36.1088 | + | 39.9792i | −0.364736 | + | 0.403830i | ||||
\(100\) | −24.4848 | − | 43.5946i | −0.244848 | − | 0.435946i | ||||
\(101\) | − | 136.484i | − | 1.35133i | −0.737208 | − | 0.675665i | \(-0.763856\pi\) | ||
0.737208 | − | 0.675665i | \(-0.236144\pi\) | |||||||
\(102\) | −3.09135 | + | 8.03477i | −0.0303073 | + | 0.0787723i | ||||
\(103\) | − | 129.191i | − | 1.25428i | −0.778905 | − | 0.627142i | \(-0.784224\pi\) | ||
0.778905 | − | 0.627142i | \(-0.215776\pi\) | |||||||
\(104\) | 53.7880i | 0.517193i | ||||||||
\(105\) | 31.0086 | − | 24.7683i | 0.295320 | − | 0.235888i | ||||
\(106\) | −81.4372 | −0.768275 | ||||||||
\(107\) | −20.2629 | −0.189373 | −0.0946866 | − | 0.995507i | \(-0.530185\pi\) | ||||
−0.0946866 | + | 0.995507i | \(0.530185\pi\) | |||||||
\(108\) | −48.1707 | + | 24.4045i | −0.446025 | + | 0.225968i | ||||
\(109\) | −112.569 | −1.03275 | −0.516373 | − | 0.856364i | \(-0.672718\pi\) | ||||
−0.516373 | + | 0.856364i | \(0.672718\pi\) | |||||||
\(110\) | −36.5291 | − | 21.3798i | −0.332083 | − | 0.194362i | ||||
\(111\) | −56.9058 | − | 21.8943i | −0.512665 | − | 0.197246i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | −6.53779 | −0.0578565 | −0.0289283 | − | 0.999581i | \(-0.509209\pi\) | ||||
−0.0289283 | + | 0.999581i | \(0.509209\pi\) | |||||||
\(114\) | 32.1555 | − | 83.5760i | 0.282066 | − | 0.733123i | ||||
\(115\) | 81.5059 | − | 139.259i | 0.708747 | − | 1.21095i | ||||
\(116\) | − | 24.5206i | − | 0.211384i | ||||||
\(117\) | −114.719 | + | 127.015i | −0.980502 | + | 1.08560i | ||||
\(118\) | 101.531i | 0.860434i | ||||||||
\(119\) | − | 5.36862i | − | 0.0451145i | ||||||
\(120\) | −26.4784 | − | 33.1496i | −0.220653 | − | 0.276246i | ||||
\(121\) | 85.1706 | 0.703889 | ||||||||
\(122\) | −115.583 | −0.947400 | ||||||||
\(123\) | −97.2082 | − | 37.4005i | −0.790311 | − | 0.304069i | ||||
\(124\) | 78.6165 | 0.634004 | ||||||||
\(125\) | 124.980 | + | 2.22300i | 0.999842 | + | 0.0177840i | ||||
\(126\) | 22.5714 | − | 24.9907i | 0.179138 | − | 0.198339i | ||||
\(127\) | − | 15.0411i | − | 0.118434i | −0.998245 | − | 0.0592170i | \(-0.981140\pi\) | ||
0.998245 | − | 0.0592170i | \(-0.0188604\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 112.923 | + | 43.4465i | 0.875369 | + | 0.336795i | ||||
\(130\) | −116.054 | − | 67.9242i | −0.892722 | − | 0.522494i | ||||
\(131\) | − | 51.5923i | − | 0.393834i | −0.980420 | − | 0.196917i | \(-0.936907\pi\) | ||
0.980420 | − | 0.196917i | \(-0.0630930\pi\) | |||||||
\(132\) | −33.5193 | − | 12.8964i | −0.253934 | − | 0.0977000i | ||||
\(133\) | 55.8433i | 0.419874i | ||||||||
\(134\) | − | 115.560i | − | 0.862386i | ||||||
\(135\) | 8.17512 | − | 134.752i | 0.0605565 | − | 0.998165i | ||||
\(136\) | −5.73930 | −0.0422007 | ||||||||
\(137\) | 47.5888 | 0.347364 | 0.173682 | − | 0.984802i | \(-0.444434\pi\) | ||||
0.173682 | + | 0.984802i | \(0.444434\pi\) | |||||||
\(138\) | 49.1647 | − | 127.785i | 0.356266 | − | 0.925978i | ||||
\(139\) | −117.730 | −0.846975 | −0.423488 | − | 0.905902i | \(-0.639194\pi\) | ||||
−0.423488 | + | 0.905902i | \(0.639194\pi\) | |||||||
\(140\) | 22.8341 | + | 13.3644i | 0.163100 | + | 0.0954597i | ||||
\(141\) | −78.0362 | + | 202.825i | −0.553448 | + | 1.43848i | ||||
\(142\) | − | 10.8927i | − | 0.0767091i | ||||||
\(143\) | −113.831 | −0.796021 | ||||||||
\(144\) | −26.7162 | − | 24.1298i | −0.185529 | − | 0.167568i | ||||
\(145\) | 52.9059 | + | 30.9649i | 0.364869 | + | 0.213551i | ||||
\(146\) | 17.0687i | 0.116909i | ||||||||
\(147\) | −7.54079 | + | 19.5994i | −0.0512979 | + | 0.133329i | ||||
\(148\) | − | 40.6483i | − | 0.274650i | ||||||
\(149\) | 186.336i | 1.25057i | 0.780395 | + | 0.625287i | \(0.215018\pi\) | ||||
−0.780395 | + | 0.625287i | \(0.784982\pi\) | |||||||
\(150\) | 104.961 | − | 15.2685i | 0.699742 | − | 0.101790i | ||||
\(151\) | −183.560 | −1.21563 | −0.607816 | − | 0.794078i | \(-0.707954\pi\) | ||||
−0.607816 | + | 0.794078i | \(0.707954\pi\) | |||||||
\(152\) | 59.6990 | 0.392756 | ||||||||
\(153\) | −13.5528 | − | 12.2407i | −0.0885802 | − | 0.0800048i | ||||
\(154\) | 22.3967 | 0.145433 | ||||||||
\(155\) | −99.2779 | + | 169.624i | −0.640503 | + | 1.09435i | ||||
\(156\) | −106.492 | − | 40.9722i | −0.682639 | − | 0.262642i | ||||
\(157\) | − | 264.877i | − | 1.68712i | −0.537038 | − | 0.843558i | \(-0.680457\pi\) | ||
0.537038 | − | 0.843558i | \(-0.319543\pi\) | |||||||
\(158\) | −186.141 | −1.17811 | ||||||||
\(159\) | 62.0335 | − | 161.232i | 0.390148 | − | 1.01404i | ||||
\(160\) | 14.2871 | − | 24.4106i | 0.0892944 | − | 0.152566i | ||||
\(161\) | 85.3825i | 0.530326i | ||||||||
\(162\) | −11.6236 | − | 113.960i | −0.0717508 | − | 0.703457i | ||||
\(163\) | 214.877i | 1.31826i | 0.752027 | + | 0.659132i | \(0.229076\pi\) | ||||
−0.752027 | + | 0.659132i | \(0.770924\pi\) | |||||||
\(164\) | − | 69.4366i | − | 0.423394i | ||||||
\(165\) | 70.1540 | − | 56.0359i | 0.425176 | − | 0.339612i | ||||
\(166\) | −163.857 | −0.987090 | ||||||||
\(167\) | 54.5954 | 0.326919 | 0.163459 | − | 0.986550i | \(-0.447735\pi\) | ||||
0.163459 | + | 0.986550i | \(0.447735\pi\) | |||||||
\(168\) | 20.9526 | + | 8.06144i | 0.124718 | + | 0.0479848i | ||||
\(169\) | −192.644 | −1.13991 | ||||||||
\(170\) | 7.24766 | − | 12.3832i | 0.0426333 | − | 0.0728424i | ||||
\(171\) | 140.973 | + | 127.326i | 0.824404 | + | 0.744594i | ||||
\(172\) | 80.6615i | 0.468962i | ||||||||
\(173\) | 310.651 | 1.79567 | 0.897834 | − | 0.440334i | \(-0.145140\pi\) | ||||
0.897834 | + | 0.440334i | \(0.145140\pi\) | |||||||
\(174\) | 48.5468 | + | 18.6782i | 0.279004 | + | 0.107346i | ||||
\(175\) | −57.6703 | + | 32.3904i | −0.329544 | + | 0.185088i | ||||
\(176\) | − | 23.9431i | − | 0.136040i | ||||||
\(177\) | −201.015 | − | 77.3399i | −1.13568 | − | 0.436949i | ||||
\(178\) | − | 144.164i | − | 0.809909i | ||||||
\(179\) | 162.922i | 0.910181i | 0.890445 | + | 0.455090i | \(0.150393\pi\) | ||||
−0.890445 | + | 0.455090i | \(0.849607\pi\) | |||||||
\(180\) | 85.8003 | − | 27.1718i | 0.476668 | − | 0.150954i | ||||
\(181\) | −51.5088 | −0.284579 | −0.142289 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142289 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(182\) | 71.1549 | 0.390961 | ||||||||
\(183\) | 88.0435 | − | 228.835i | 0.481112 | − | 1.25047i | ||||
\(184\) | 91.2777 | 0.496075 | ||||||||
\(185\) | 87.7033 | + | 51.3311i | 0.474072 | + | 0.277466i | ||||
\(186\) | −59.8849 | + | 155.648i | −0.321962 | + | 0.836817i | ||||
\(187\) | − | 12.1460i | − | 0.0649519i | ||||||
\(188\) | −144.880 | −0.770636 | ||||||||
\(189\) | 32.2841 | + | 63.7239i | 0.170815 | + | 0.337163i | ||||
\(190\) | −75.3887 | + | 128.807i | −0.396782 | + | 0.677934i | ||||
\(191\) | − | 227.310i | − | 1.19011i | −0.803687 | − | 0.595053i | \(-0.797131\pi\) | ||
0.803687 | − | 0.595053i | \(-0.202869\pi\) | |||||||
\(192\) | 8.61805 | − | 22.3993i | 0.0448857 | − | 0.116663i | ||||
\(193\) | 239.861i | 1.24280i | 0.783493 | + | 0.621401i | \(0.213436\pi\) | ||||
−0.783493 | + | 0.621401i | \(0.786564\pi\) | |||||||
\(194\) | − | 11.5864i | − | 0.0597236i | ||||||
\(195\) | 222.881 | − | 178.028i | 1.14298 | − | 0.912962i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −184.116 | −0.934599 | −0.467300 | − | 0.884099i | \(-0.654773\pi\) | ||||
−0.467300 | + | 0.884099i | \(0.654773\pi\) | |||||||
\(198\) | 51.0656 | − | 56.5391i | 0.257907 | − | 0.285551i | ||||
\(199\) | −215.792 | −1.08438 | −0.542190 | − | 0.840256i | \(-0.682405\pi\) | ||||
−0.542190 | + | 0.840256i | \(0.682405\pi\) | |||||||
\(200\) | 34.6268 | + | 61.6521i | 0.173134 | + | 0.308261i | ||||
\(201\) | 228.790 | + | 88.0259i | 1.13826 | + | 0.437940i | ||||
\(202\) | 193.018i | 0.955535i | ||||||||
\(203\) | −32.4377 | −0.159791 | ||||||||
\(204\) | 4.37182 | − | 11.3629i | 0.0214305 | − | 0.0557004i | ||||
\(205\) | 149.817 | + | 87.6854i | 0.730817 | + | 0.427734i | ||||
\(206\) | 182.704i | 0.886913i | ||||||||
\(207\) | 215.543 | + | 194.676i | 1.04127 | + | 0.940466i | ||||
\(208\) | − | 76.0678i | − | 0.365710i | ||||||
\(209\) | 126.340i | 0.604499i | ||||||||
\(210\) | −43.8528 | + | 35.0276i | −0.208823 | + | 0.166798i | ||||
\(211\) | −122.387 | −0.580031 | −0.290015 | − | 0.957022i | \(-0.593660\pi\) | ||||
−0.290015 | + | 0.957022i | \(0.593660\pi\) | |||||||
\(212\) | 115.170 | 0.543253 | ||||||||
\(213\) | 21.5658 | + | 8.29734i | 0.101248 | + | 0.0389546i | ||||
\(214\) | 28.6561 | 0.133907 | ||||||||
\(215\) | −174.036 | − | 101.860i | −0.809472 | − | 0.473769i | ||||
\(216\) | 68.1237 | − | 34.5132i | 0.315388 | − | 0.159783i | ||||
\(217\) | − | 104.000i | − | 0.479262i | ||||||
\(218\) | 159.197 | 0.730262 | ||||||||
\(219\) | −33.7933 | − | 13.0018i | −0.154307 | − | 0.0593690i | ||||
\(220\) | 51.6599 | + | 30.2356i | 0.234818 | + | 0.137435i | ||||
\(221\) | − | 38.5882i | − | 0.174607i | ||||||
\(222\) | 80.4770 | + | 30.9632i | 0.362509 | + | 0.139474i | ||||
\(223\) | 70.1315i | 0.314491i | 0.987560 | + | 0.157245i | \(0.0502614\pi\) | ||||
−0.987560 | + | 0.157245i | \(0.949739\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | −49.7235 | + | 219.437i | −0.220993 | + | 0.975275i | ||||
\(226\) | 9.24583 | 0.0409108 | ||||||||
\(227\) | −31.4277 | −0.138448 | −0.0692240 | − | 0.997601i | \(-0.522052\pi\) | ||||
−0.0692240 | + | 0.997601i | \(0.522052\pi\) | |||||||
\(228\) | −45.4748 | + | 118.194i | −0.199451 | + | 0.518396i | ||||
\(229\) | 35.7207 | 0.155986 | 0.0779928 | − | 0.996954i | \(-0.475149\pi\) | ||||
0.0779928 | + | 0.996954i | \(0.475149\pi\) | |||||||
\(230\) | −115.267 | + | 196.942i | −0.501160 | + | 0.856271i | ||||
\(231\) | −17.0603 | + | 44.3418i | −0.0738543 | + | 0.191956i | ||||
\(232\) | 34.6773i | 0.149471i | ||||||||
\(233\) | −324.542 | −1.39288 | −0.696442 | − | 0.717613i | \(-0.745235\pi\) | ||||
−0.696442 | + | 0.717613i | \(0.745235\pi\) | |||||||
\(234\) | 162.237 | − | 179.626i | 0.693319 | − | 0.767633i | ||||
\(235\) | 182.956 | − | 312.594i | 0.778536 | − | 1.33019i | ||||
\(236\) | − | 143.587i | − | 0.608419i | ||||||
\(237\) | 141.790 | − | 368.530i | 0.598271 | − | 1.55498i | ||||
\(238\) | 7.59238i | 0.0319008i | ||||||||
\(239\) | − | 400.039i | − | 1.67380i | −0.547353 | − | 0.836902i | \(-0.684364\pi\) | ||
0.547353 | − | 0.836902i | \(-0.315636\pi\) | |||||||
\(240\) | 37.4461 | + | 46.8806i | 0.156025 | + | 0.195336i | ||||
\(241\) | 396.305 | 1.64442 | 0.822209 | − | 0.569185i | \(-0.192741\pi\) | ||||
0.822209 | + | 0.569185i | \(0.192741\pi\) | |||||||
\(242\) | −120.449 | −0.497725 | ||||||||
\(243\) | 234.477 | + | 63.7944i | 0.964924 | + | 0.262528i | ||||
\(244\) | 163.459 | 0.669913 | ||||||||
\(245\) | 17.6794 | − | 30.2066i | 0.0721607 | − | 0.123292i | ||||
\(246\) | 137.473 | + | 52.8923i | 0.558834 | + | 0.215009i | ||||
\(247\) | 401.386i | 1.62505i | ||||||||
\(248\) | −111.180 | −0.448308 | ||||||||
\(249\) | 124.816 | − | 324.410i | 0.501267 | − | 1.30285i | ||||
\(250\) | −176.749 | − | 3.14379i | −0.706995 | − | 0.0125752i | ||||
\(251\) | − | 221.226i | − | 0.881377i | −0.897660 | − | 0.440688i | \(-0.854734\pi\) | ||
0.897660 | − | 0.440688i | \(-0.145266\pi\) | |||||||
\(252\) | −31.9207 | + | 35.3422i | −0.126669 | + | 0.140247i | ||||
\(253\) | 193.170i | 0.763518i | ||||||||
\(254\) | 21.2714i | 0.0837455i | ||||||||
\(255\) | 18.9959 | + | 23.7819i | 0.0744939 | + | 0.0932624i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 203.815 | 0.793055 | 0.396528 | − | 0.918023i | \(-0.370215\pi\) | ||||
0.396528 | + | 0.918023i | \(0.370215\pi\) | |||||||
\(258\) | −159.697 | − | 61.4426i | −0.618979 | − | 0.238150i | ||||
\(259\) | −53.7726 | −0.207616 | ||||||||
\(260\) | 164.125 | + | 96.0594i | 0.631250 | + | 0.369459i | ||||
\(261\) | −73.9595 | + | 81.8869i | −0.283370 | + | 0.313743i | ||||
\(262\) | 72.9625i | 0.278483i | ||||||||
\(263\) | −98.2019 | −0.373391 | −0.186696 | − | 0.982418i | \(-0.559778\pi\) | ||||
−0.186696 | + | 0.982418i | \(0.559778\pi\) | |||||||
\(264\) | 47.4034 | + | 18.2383i | 0.179558 | + | 0.0690844i | ||||
\(265\) | −145.438 | + | 248.492i | −0.548821 | + | 0.937704i | ||||
\(266\) | − | 78.9743i | − | 0.296896i | ||||||
\(267\) | 285.421 | + | 109.815i | 1.06899 | + | 0.411290i | ||||
\(268\) | 163.426i | 0.609799i | ||||||||
\(269\) | − | 308.644i | − | 1.14738i | −0.819074 | − | 0.573688i | \(-0.805512\pi\) | ||
0.819074 | − | 0.573688i | \(-0.194488\pi\) | |||||||
\(270\) | −11.5614 | + | 190.568i | −0.0428199 | + | 0.705809i | ||||
\(271\) | −398.841 | −1.47174 | −0.735870 | − | 0.677123i | \(-0.763226\pi\) | ||||
−0.735870 | + | 0.677123i | \(0.763226\pi\) | |||||||
\(272\) | 8.11660 | 0.0298404 | ||||||||
\(273\) | −54.2012 | + | 140.875i | −0.198539 | + | 0.516026i | ||||
\(274\) | −67.3007 | −0.245623 | ||||||||
\(275\) | −130.474 | + | 73.2803i | −0.474450 | + | 0.266474i | ||||
\(276\) | −69.5294 | + | 180.715i | −0.251918 | + | 0.654765i | ||||
\(277\) | − | 79.7207i | − | 0.287800i | −0.989592 | − | 0.143900i | \(-0.954036\pi\) | ||
0.989592 | − | 0.143900i | \(-0.0459644\pi\) | |||||||
\(278\) | 166.495 | 0.598902 | ||||||||
\(279\) | −262.541 | − | 237.125i | −0.941008 | − | 0.849910i | ||||
\(280\) | −32.2922 | − | 18.9001i | −0.115329 | − | 0.0675002i | ||||
\(281\) | − | 210.169i | − | 0.747934i | −0.927442 | − | 0.373967i | \(-0.877997\pi\) | ||
0.927442 | − | 0.373967i | \(-0.122003\pi\) | |||||||
\(282\) | 110.360 | − | 286.838i | 0.391347 | − | 1.01716i | ||||
\(283\) | 262.941i | 0.929120i | 0.885542 | + | 0.464560i | \(0.153787\pi\) | ||||
−0.885542 | + | 0.464560i | \(0.846213\pi\) | |||||||
\(284\) | 15.4046i | 0.0542415i | ||||||||
\(285\) | −197.592 | − | 247.374i | −0.693304 | − | 0.867981i | ||||
\(286\) | 160.981 | 0.562872 | ||||||||
\(287\) | −91.8560 | −0.320056 | ||||||||
\(288\) | 37.7824 | + | 34.1247i | 0.131189 | + | 0.118488i | ||||
\(289\) | −284.883 | −0.985753 | ||||||||
\(290\) | −74.8203 | − | 43.7910i | −0.258001 | − | 0.151003i | ||||
\(291\) | 22.9392 | + | 8.82575i | 0.0788287 | + | 0.0303290i | ||||
\(292\) | − | 24.1388i | − | 0.0826671i | ||||||
\(293\) | 357.570 | 1.22037 | 0.610187 | − | 0.792257i | \(-0.291094\pi\) | ||||
0.610187 | + | 0.792257i | \(0.291094\pi\) | |||||||
\(294\) | 10.6643 | − | 27.7177i | 0.0362731 | − | 0.0942780i | ||||
\(295\) | 309.805 | + | 181.323i | 1.05019 | + | 0.614656i | ||||
\(296\) | 57.4853i | 0.194207i | ||||||||
\(297\) | 73.0398 | + | 144.169i | 0.245925 | + | 0.485419i | ||||
\(298\) | − | 263.518i | − | 0.884290i | ||||||
\(299\) | 613.706i | 2.05253i | ||||||||
\(300\) | −148.438 | + | 21.5929i | −0.494792 | + | 0.0719764i | ||||
\(301\) | 106.705 | 0.354502 | ||||||||
\(302\) | 259.593 | 0.859581 | ||||||||
\(303\) | −382.145 | − | 147.029i | −1.26120 | − | 0.485243i | ||||
\(304\) | −84.4271 | −0.277721 | ||||||||
\(305\) | −206.418 | + | 352.681i | −0.676780 | + | 1.15633i | ||||
\(306\) | 19.1665 | + | 17.3110i | 0.0626356 | + | 0.0565719i | ||||
\(307\) | − | 293.405i | − | 0.955717i | −0.878437 | − | 0.477858i | \(-0.841413\pi\) | ||
0.878437 | − | 0.477858i | \(-0.158587\pi\) | |||||||
\(308\) | −31.6737 | −0.102837 | ||||||||
\(309\) | −361.725 | − | 139.172i | −1.17063 | − | 0.450395i | ||||
\(310\) | 140.400 | − | 239.885i | 0.452904 | − | 0.773822i | ||||
\(311\) | − | 59.2465i | − | 0.190503i | −0.995453 | − | 0.0952517i | \(-0.969634\pi\) | ||
0.995453 | − | 0.0952517i | \(-0.0303656\pi\) | |||||||
\(312\) | 150.602 | + | 57.9435i | 0.482698 | + | 0.185716i | ||||
\(313\) | − | 450.587i | − | 1.43957i | −0.694195 | − | 0.719787i | \(-0.744239\pi\) | ||
0.694195 | − | 0.719787i | \(-0.255761\pi\) | |||||||
\(314\) | 374.593i | 1.19297i | ||||||||
\(315\) | −35.9449 | − | 113.503i | −0.114111 | − | 0.360327i | ||||
\(316\) | 263.243 | 0.833049 | ||||||||
\(317\) | 277.454 | 0.875249 | 0.437624 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437624 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(318\) | −87.7287 | + | 228.017i | −0.275876 | + | 0.717035i | ||||
\(319\) | −73.3872 | −0.230054 | ||||||||
\(320\) | −20.2050 | + | 34.5218i | −0.0631407 | + | 0.107881i | ||||
\(321\) | −21.8284 | + | 56.7345i | −0.0680011 | + | 0.176743i | ||||
\(322\) | − | 120.749i | − | 0.374997i | ||||||
\(323\) | −42.8288 | −0.132597 | ||||||||
\(324\) | 16.4383 | + | 161.164i | 0.0507355 | + | 0.497419i | ||||
\(325\) | −414.518 | + | 232.813i | −1.27544 | + | 0.716349i | ||||
\(326\) | − | 303.882i | − | 0.932153i | ||||||
\(327\) | −121.266 | + | 315.185i | −0.370844 | + | 0.963867i | ||||
\(328\) | 98.1982i | 0.299385i | ||||||||
\(329\) | 191.658i | 0.582546i | ||||||||
\(330\) | −99.2128 | + | 79.2468i | −0.300645 | + | 0.240142i | ||||
\(331\) | 275.898 | 0.833529 | 0.416764 | − | 0.909015i | \(-0.363164\pi\) | ||||
0.416764 | + | 0.909015i | \(0.363164\pi\) | |||||||
\(332\) | 231.729 | 0.697978 | ||||||||
\(333\) | −122.604 | + | 135.746i | −0.368181 | + | 0.407645i | ||||
\(334\) | −77.2096 | −0.231166 | ||||||||
\(335\) | −352.611 | − | 206.377i | −1.05257 | − | 0.616050i | ||||
\(336\) | −29.6315 | − | 11.4006i | −0.0881890 | − | 0.0339304i | ||||
\(337\) | − | 102.798i | − | 0.305038i | −0.988301 | − | 0.152519i | \(-0.951261\pi\) | ||
0.988301 | − | 0.152519i | \(-0.0487385\pi\) | |||||||
\(338\) | 272.440 | 0.806035 | ||||||||
\(339\) | −7.04287 | + | 18.3053i | −0.0207754 | + | 0.0539978i | ||||
\(340\) | −10.2497 | + | 17.5125i | −0.0301463 | + | 0.0515073i | ||||
\(341\) | − | 235.290i | − | 0.690000i | ||||||
\(342\) | −199.366 | − | 180.066i | −0.582941 | − | 0.526507i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 114.073i | − | 0.331606i | ||||||
\(345\) | −302.111 | − | 378.227i | −0.875684 | − | 1.09631i | ||||
\(346\) | −439.326 | −1.26973 | ||||||||
\(347\) | 456.590 | 1.31582 | 0.657910 | − | 0.753096i | \(-0.271441\pi\) | ||||
0.657910 | + | 0.753096i | \(0.271441\pi\) | |||||||
\(348\) | −68.6555 | − | 26.4149i | −0.197286 | − | 0.0759049i | ||||
\(349\) | 570.605 | 1.63497 | 0.817486 | − | 0.575948i | \(-0.195367\pi\) | ||||
0.817486 | + | 0.575948i | \(0.195367\pi\) | |||||||
\(350\) | 81.5581 | − | 45.8070i | 0.233023 | − | 0.130877i | ||||
\(351\) | 232.050 | + | 458.030i | 0.661110 | + | 1.30493i | ||||
\(352\) | 33.8606i | 0.0961949i | ||||||||
\(353\) | 4.74525 | 0.0134426 | 0.00672132 | − | 0.999977i | \(-0.497861\pi\) | ||||
0.00672132 | + | 0.999977i | \(0.497861\pi\) | |||||||
\(354\) | 284.279 | + | 109.375i | 0.803048 | + | 0.308969i | ||||
\(355\) | −33.2372 | − | 19.4531i | −0.0936258 | − | 0.0547975i | ||||
\(356\) | 203.878i | 0.572692i | ||||||||
\(357\) | −15.0317 | − | 5.78338i | −0.0421056 | − | 0.0161999i | ||||
\(358\) | − | 230.407i | − | 0.643595i | ||||||
\(359\) | 457.086i | 1.27322i | 0.771186 | + | 0.636610i | \(0.219664\pi\) | ||||
−0.771186 | + | 0.636610i | \(0.780336\pi\) | |||||||
\(360\) | −121.340 | + | 38.4267i | −0.337055 | + | 0.106741i | ||||
\(361\) | 84.4961 | 0.234061 | ||||||||
\(362\) | 72.8444 | 0.201228 | ||||||||
\(363\) | 91.7505 | − | 238.470i | 0.252756 | − | 0.656943i | ||||
\(364\) | −100.628 | −0.276451 | ||||||||
\(365\) | 52.0822 | + | 30.4828i | 0.142691 | + | 0.0835144i | ||||
\(366\) | −124.512 | + | 323.622i | −0.340198 | + | 0.884213i | ||||
\(367\) | − | 556.637i | − | 1.51672i | −0.651834 | − | 0.758361i | \(-0.726000\pi\) | ||
0.651834 | − | 0.758361i | \(-0.274000\pi\) | |||||||
\(368\) | −129.086 | −0.350778 | ||||||||
\(369\) | −209.436 | + | 231.885i | −0.567578 | + | 0.628414i | ||||
\(370\) | −124.031 | − | 72.5932i | −0.335219 | − | 0.196198i | ||||
\(371\) | − | 152.355i | − | 0.410660i | ||||||
\(372\) | 84.6900 | − | 220.119i | 0.227661 | − | 0.591719i | ||||
\(373\) | 77.2267i | 0.207042i | 0.994627 | + | 0.103521i | \(0.0330109\pi\) | ||||
−0.994627 | + | 0.103521i | \(0.966989\pi\) | |||||||
\(374\) | 17.1771i | 0.0459280i | ||||||||
\(375\) | 140.860 | − | 347.539i | 0.375626 | − | 0.926771i | ||||
\(376\) | 204.891 | 0.544922 | ||||||||
\(377\) | −233.153 | −0.618443 | ||||||||
\(378\) | −45.6566 | − | 90.1192i | −0.120785 | − | 0.238411i | ||||
\(379\) | 476.133 | 1.25629 | 0.628143 | − | 0.778098i | \(-0.283815\pi\) | ||||
0.628143 | + | 0.778098i | \(0.283815\pi\) | |||||||
\(380\) | 106.616 | − | 182.161i | 0.280568 | − | 0.479372i | ||||
\(381\) | −42.1138 | − | 16.2031i | −0.110535 | − | 0.0425279i | ||||
\(382\) | 321.465i | 0.841532i | ||||||||
\(383\) | −600.374 | −1.56756 | −0.783778 | − | 0.621041i | \(-0.786710\pi\) | ||||
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(384\) | −12.1878 | + | 31.6774i | −0.0317390 | + | 0.0824933i | ||||
\(385\) | 39.9980 | − | 68.3397i | 0.103891 | − | 0.177506i | ||||
\(386\) | − | 339.214i | − | 0.878794i | ||||||
\(387\) | 243.293 | − | 269.371i | 0.628664 | − | 0.696048i | ||||
\(388\) | 16.3856i | 0.0422310i | ||||||||
\(389\) | − | 315.387i | − | 0.810763i | −0.914148 | − | 0.405382i | \(-0.867139\pi\) | ||
0.914148 | − | 0.405382i | \(-0.132861\pi\) | |||||||
\(390\) | −315.202 | + | 251.769i | −0.808210 | + | 0.645562i | ||||
\(391\) | −65.4838 | −0.167478 | ||||||||
\(392\) | 19.7990 | 0.0505076 | ||||||||
\(393\) | −144.454 | − | 55.5781i | −0.367567 | − | 0.141420i | ||||
\(394\) | 260.379 | 0.660861 | ||||||||
\(395\) | −332.427 | + | 567.978i | −0.841588 | + | 1.43792i | ||||
\(396\) | −72.2176 | + | 79.9584i | −0.182368 | + | 0.201915i | ||||
\(397\) | − | 291.527i | − | 0.734325i | −0.930157 | − | 0.367163i | \(-0.880329\pi\) | ||
0.930157 | − | 0.367163i | \(-0.119671\pi\) | |||||||
\(398\) | 305.176 | 0.766773 | ||||||||
\(399\) | 156.356 | + | 60.1575i | 0.391871 | + | 0.150771i | ||||
\(400\) | −48.9697 | − | 87.1893i | −0.122424 | − | 0.217973i | ||||
\(401\) | − | 312.203i | − | 0.778560i | −0.921119 | − | 0.389280i | \(-0.872724\pi\) | ||
0.921119 | − | 0.389280i | \(-0.127276\pi\) | |||||||
\(402\) | −323.557 | − | 124.487i | −0.804869 | − | 0.309670i | ||||
\(403\) | − | 747.522i | − | 1.85489i | ||||||
\(404\) | − | 272.969i | − | 0.675665i | ||||||
\(405\) | −368.488 | − | 168.052i | −0.909847 | − | 0.414944i | ||||
\(406\) | 45.8738 | 0.112990 | ||||||||
\(407\) | −121.655 | −0.298908 | ||||||||
\(408\) | −6.18269 | + | 16.0695i | −0.0151537 | + | 0.0393861i | ||||
\(409\) | −602.689 | −1.47357 | −0.736784 | − | 0.676128i | \(-0.763657\pi\) | ||||
−0.736784 | + | 0.676128i | \(0.763657\pi\) | |||||||
\(410\) | −211.874 | − | 124.006i | −0.516765 | − | 0.302453i | ||||
\(411\) | 51.2653 | − | 133.245i | 0.124733 | − | 0.324196i | ||||
\(412\) | − | 258.383i | − | 0.627142i | ||||||
\(413\) | −189.948 | −0.459922 | ||||||||
\(414\) | −304.824 | − | 275.314i | −0.736289 | − | 0.665010i | ||||
\(415\) | −292.630 | + | 499.981i | −0.705133 | + | 1.20477i | ||||
\(416\) | 107.576i | 0.258596i | ||||||||
\(417\) | −126.825 | + | 329.633i | −0.304136 | + | 0.790486i | ||||
\(418\) | − | 178.672i | − | 0.427445i | ||||||
\(419\) | 179.970i | 0.429522i | 0.976667 | + | 0.214761i | \(0.0688972\pi\) | ||||
−0.976667 | + | 0.214761i | \(0.931103\pi\) | |||||||
\(420\) | 62.0172 | − | 49.5366i | 0.147660 | − | 0.117944i | ||||
\(421\) | 454.959 | 1.08066 | 0.540331 | − | 0.841453i | \(-0.318299\pi\) | ||||
0.540331 | + | 0.841453i | \(0.318299\pi\) | |||||||
\(422\) | 173.081 | 0.410144 | ||||||||
\(423\) | 483.828 | + | 436.989i | 1.14380 | + | 1.03307i | ||||
\(424\) | −162.874 | −0.384138 | ||||||||
\(425\) | −24.8417 | − | 44.2300i | −0.0584511 | − | 0.104071i | ||||
\(426\) | −30.4986 | − | 11.7342i | −0.0715929 | − | 0.0275451i | ||||
\(427\) | − | 216.236i | − | 0.506407i | ||||||
\(428\) | −40.5259 | −0.0946866 | ||||||||
\(429\) | −122.625 | + | 318.717i | −0.285839 | + | 0.742930i | ||||
\(430\) | 246.125 | + | 144.052i | 0.572383 | + | 0.335005i | ||||
\(431\) | 280.437i | 0.650665i | 0.945600 | + | 0.325333i | \(0.105476\pi\) | ||||
−0.945600 | + | 0.325333i | \(0.894524\pi\) | |||||||
\(432\) | −96.3415 | + | 48.8090i | −0.223013 | + | 0.112984i | ||||
\(433\) | − | 172.401i | − | 0.398155i | −0.979984 | − | 0.199077i | \(-0.936206\pi\) | ||
0.979984 | − | 0.199077i | \(-0.0637945\pi\) | |||||||
\(434\) | 147.078i | 0.338889i | ||||||||
\(435\) | 143.692 | − | 114.775i | 0.330327 | − | 0.263851i | ||||
\(436\) | −225.139 | −0.516373 | ||||||||
\(437\) | 681.149 | 1.55869 | ||||||||
\(438\) | 47.7909 | + | 18.3874i | 0.109112 | + | 0.0419803i | ||||
\(439\) | 299.659 | 0.682594 | 0.341297 | − | 0.939955i | \(-0.389134\pi\) | ||||
0.341297 | + | 0.939955i | \(0.389134\pi\) | |||||||
\(440\) | −73.0582 | − | 42.7596i | −0.166041 | − | 0.0971810i | ||||
\(441\) | 46.7533 | + | 42.2271i | 0.106017 | + | 0.0957531i | ||||
\(442\) | 54.5720i | 0.123466i | ||||||||
\(443\) | −389.448 | −0.879115 | −0.439558 | − | 0.898214i | \(-0.644865\pi\) | ||||
−0.439558 | + | 0.898214i | \(0.644865\pi\) | |||||||
\(444\) | −113.812 | − | 43.7886i | −0.256332 | − | 0.0986229i | ||||
\(445\) | −439.891 | − | 257.460i | −0.988519 | − | 0.578562i | ||||
\(446\) | − | 99.1809i | − | 0.222379i | ||||||
\(447\) | 521.724 | + | 200.731i | 1.16717 | + | 0.449063i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | − | 614.023i | − | 1.36753i | −0.729700 | − | 0.683767i | \(-0.760340\pi\) | ||
0.729700 | − | 0.683767i | \(-0.239660\pi\) | |||||||
\(450\) | 70.3197 | − | 310.331i | 0.156266 | − | 0.689624i | ||||
\(451\) | −207.816 | −0.460788 | ||||||||
\(452\) | −13.0756 | −0.0289283 | ||||||||
\(453\) | −197.741 | + | 513.953i | −0.436515 | + | 1.13455i | ||||
\(454\) | 44.4455 | 0.0978975 | ||||||||
\(455\) | 127.075 | − | 217.117i | 0.279285 | − | 0.477180i | ||||
\(456\) | 64.3111 | − | 167.152i | 0.141033 | − | 0.366562i | ||||
\(457\) | 215.558i | 0.471681i | 0.971792 | + | 0.235840i | \(0.0757843\pi\) | ||||
−0.971792 | + | 0.235840i | \(0.924216\pi\) | |||||||
\(458\) | −50.5167 | −0.110299 | ||||||||
\(459\) | −48.8728 | + | 24.7602i | −0.106477 | + | 0.0539438i | ||||
\(460\) | 163.012 | − | 278.518i | 0.354373 | − | 0.605475i | ||||
\(461\) | − | 369.603i | − | 0.801743i | −0.916134 | − | 0.400871i | \(-0.868707\pi\) | ||
0.916134 | − | 0.400871i | \(-0.131293\pi\) | |||||||
\(462\) | 24.1270 | − | 62.7088i | 0.0522229 | − | 0.135733i | ||||
\(463\) | 0.675303i | 0.00145854i | 1.00000 | 0.000729269i | \(0.000232133\pi\) | |||||
−1.00000 | 0.000729269i | \(0.999768\pi\) | ||||||||
\(464\) | − | 49.0411i | − | 0.105692i | ||||||
\(465\) | 367.985 | + | 460.698i | 0.791366 | + | 0.990749i | ||||
\(466\) | 458.972 | 0.984918 | ||||||||
\(467\) | 90.1341 | 0.193007 | 0.0965033 | − | 0.995333i | \(-0.469234\pi\) | ||||
0.0965033 | + | 0.995333i | \(0.469234\pi\) | |||||||
\(468\) | −229.437 | + | 254.030i | −0.490251 | + | 0.542799i | ||||
\(469\) | 216.193 | 0.460965 | ||||||||
\(470\) | −258.739 | + | 442.075i | −0.550508 | + | 0.940586i | ||||
\(471\) | −741.634 | − | 285.341i | −1.57459 | − | 0.605819i | ||||
\(472\) | 203.063i | 0.430217i | ||||||||
\(473\) | 241.410 | 0.510381 | ||||||||
\(474\) | −200.522 | + | 521.179i | −0.423042 | + | 1.09953i | ||||
\(475\) | 258.398 | + | 460.071i | 0.543996 | + | 0.968571i | ||||
\(476\) | − | 10.7372i | − | 0.0225572i | ||||||
\(477\) | −384.611 | − | 347.377i | −0.806313 | − | 0.728254i | ||||
\(478\) | 565.741i | 1.18356i | ||||||||
\(479\) | 422.277i | 0.881579i | 0.897610 | + | 0.440790i | \(0.145302\pi\) | ||||
−0.897610 | + | 0.440790i | \(0.854698\pi\) | |||||||
\(480\) | −52.9568 | − | 66.2991i | −0.110327 | − | 0.138123i | ||||
\(481\) | −386.503 | −0.803540 | ||||||||
\(482\) | −560.460 | −1.16278 | ||||||||
\(483\) | 239.064 | + | 91.9788i | 0.494956 | + | 0.190432i | ||||
\(484\) | 170.341 | 0.351945 | ||||||||
\(485\) | −35.3538 | − | 20.6920i | −0.0728945 | − | 0.0426638i | ||||
\(486\) | −331.600 | − | 90.2189i | −0.682304 | − | 0.185636i | ||||
\(487\) | − | 240.184i | − | 0.493191i | −0.969119 | − | 0.246595i | \(-0.920688\pi\) | ||
0.969119 | − | 0.246595i | \(-0.0793119\pi\) | |||||||
\(488\) | −231.166 | −0.473700 | ||||||||
\(489\) | 601.637 | + | 231.478i | 1.23034 | + | 0.473369i | ||||
\(490\) | −25.0024 | + | 42.7186i | −0.0510254 | + | 0.0871808i | ||||
\(491\) | 961.188i | 1.95761i | 0.204788 | + | 0.978806i | \(0.434349\pi\) | ||||
−0.204788 | + | 0.978806i | \(0.565651\pi\) | |||||||
\(492\) | −194.416 | − | 74.8010i | −0.395155 | − | 0.152034i | ||||
\(493\) | − | 24.8779i | − | 0.0504624i | ||||||
\(494\) | − | 567.646i | − | 1.14908i | ||||||
\(495\) | −81.3220 | − | 256.790i | −0.164287 | − | 0.518768i | ||||
\(496\) | 157.233 | 0.317002 | ||||||||
\(497\) | 20.3783 | 0.0410027 | ||||||||
\(498\) | −176.516 | + | 458.785i | −0.354450 | + | 0.921256i | ||||
\(499\) | 203.222 | 0.407259 | 0.203629 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203629 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(500\) | 249.960 | + | 4.44599i | 0.499921 | + | 0.00889199i | ||||
\(501\) | 58.8132 | − | 152.862i | 0.117392 | − | 0.305115i | ||||
\(502\) | 312.860i | 0.623228i | ||||||||
\(503\) | 112.900 | 0.224453 | 0.112226 | − | 0.993683i | \(-0.464202\pi\) | ||||
0.112226 | + | 0.993683i | \(0.464202\pi\) | |||||||
\(504\) | 45.1427 | − | 49.9814i | 0.0895689 | − | 0.0991694i | ||||
\(505\) | 588.962 | + | 344.709i | 1.16626 | + | 0.682591i | ||||
\(506\) | − | 273.184i | − | 0.539889i | ||||||
\(507\) | −207.527 | + | 539.387i | −0.409323 | + | 1.06388i | ||||
\(508\) | − | 30.0822i | − | 0.0592170i | ||||||
\(509\) | 876.657i | 1.72231i | 0.508341 | + | 0.861156i | \(0.330259\pi\) | ||||
−0.508341 | + | 0.861156i | \(0.669741\pi\) | |||||||
\(510\) | −26.8643 | − | 33.6327i | −0.0526751 | − | 0.0659465i | ||||
\(511\) | −31.9326 | −0.0624904 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 508.365 | − | 257.550i | 0.990964 | − | 0.502047i | ||||
\(514\) | −288.238 | −0.560775 | ||||||||
\(515\) | 557.490 | + | 326.289i | 1.08251 | + | 0.633571i | ||||
\(516\) | 225.845 | + | 86.8930i | 0.437684 | + | 0.168397i | ||||
\(517\) | 433.608i | 0.838700i | ||||||||
\(518\) | 76.0459 | 0.146807 | ||||||||
\(519\) | 334.650 | − | 869.795i | 0.644798 | − | 1.67591i | ||||
\(520\) | −232.108 | − | 135.848i | −0.446361 | − | 0.261247i | ||||
\(521\) | − | 497.586i | − | 0.955060i | −0.878616 | − | 0.477530i | \(-0.841532\pi\) | ||
0.878616 | − | 0.477530i | \(-0.158468\pi\) | |||||||
\(522\) | 104.595 | − | 115.806i | 0.200373 | − | 0.221850i | ||||
\(523\) | 519.528i | 0.993362i | 0.867933 | + | 0.496681i | \(0.165448\pi\) | ||||
−0.867933 | + | 0.496681i | \(0.834552\pi\) | |||||||
\(524\) | − | 103.185i | − | 0.196917i | ||||||
\(525\) | 28.5647 | + | 196.365i | 0.0544090 | + | 0.374028i | ||||
\(526\) | 138.878 | 0.264027 | ||||||||
\(527\) | 79.7623 | 0.151352 | ||||||||
\(528\) | −67.0385 | − | 25.7928i | −0.126967 | − | 0.0488500i | ||||
\(529\) | 512.453 | 0.968720 | ||||||||
\(530\) | 205.680 | − | 351.420i | 0.388075 | − | 0.663057i | ||||
\(531\) | −433.090 | + | 479.511i | −0.815612 | + | 0.903034i | ||||
\(532\) | 111.687i | 0.209937i | ||||||||
\(533\) | −660.236 | −1.23872 | ||||||||
\(534\) | −403.646 | − | 155.301i | −0.755892 | − | 0.290826i | ||||
\(535\) | 51.1766 | − | 87.4392i | 0.0956572 | − | 0.163438i | ||||
\(536\) | − | 231.120i | − | 0.431193i | ||||||
\(537\) | 456.169 | + | 175.509i | 0.849476 | + | 0.326832i | ||||
\(538\) | 436.488i | 0.811317i | ||||||||
\(539\) | 41.9004i | 0.0777372i | ||||||||
\(540\) | 16.3502 | − | 269.504i | 0.0302782 | − | 0.499082i | ||||
\(541\) | 853.843 | 1.57827 | 0.789134 | − | 0.614220i | \(-0.210529\pi\) | ||||
0.789134 | + | 0.614220i | \(0.210529\pi\) | |||||||
\(542\) | 564.047 | 1.04068 | ||||||||
\(543\) | −55.4881 | + | 144.220i | −0.102188 | + | 0.265599i | ||||
\(544\) | −11.4786 | −0.0211004 | ||||||||
\(545\) | 284.308 | − | 485.763i | 0.521666 | − | 0.891308i | ||||
\(546\) | 76.6520 | − | 199.228i | 0.140388 | − | 0.364886i | ||||
\(547\) | − | 468.232i | − | 0.855999i | −0.903779 | − | 0.428000i | \(-0.859218\pi\) | ||
0.903779 | − | 0.428000i | \(-0.140782\pi\) | |||||||
\(548\) | 95.1776 | 0.173682 | ||||||||
\(549\) | −545.874 | − | 493.028i | −0.994306 | − | 0.898048i | ||||
\(550\) | 184.518 | − | 103.634i | 0.335487 | − | 0.188425i | ||||
\(551\) | 258.775i | 0.469646i | ||||||||
\(552\) | 98.3295 | − | 255.570i | 0.178133 | − | 0.462989i | ||||
\(553\) | − | 348.238i | − | 0.629726i | ||||||
\(554\) | 112.742i | 0.203506i | ||||||||
\(555\) | 238.202 | − | 190.265i | 0.429192 | − | 0.342820i | ||||
\(556\) | −235.459 | −0.423488 | ||||||||
\(557\) | −260.390 | −0.467487 | −0.233744 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233744 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(558\) | 371.289 | + | 335.345i | 0.665393 | + | 0.600977i | ||||
\(559\) | 766.967 | 1.37203 | ||||||||
\(560\) | 45.6681 | + | 26.7287i | 0.0815502 | + | 0.0477298i | ||||
\(561\) | −34.0078 | − | 13.0844i | −0.0606200 | − | 0.0233233i | ||||
\(562\) | 297.224i | 0.528869i | ||||||||
\(563\) | 62.6717 | 0.111317 | 0.0556587 | − | 0.998450i | \(-0.482274\pi\) | ||||
0.0556587 | + | 0.998450i | \(0.482274\pi\) | |||||||
\(564\) | −156.072 | + | 405.650i | −0.276724 | + | 0.719238i | ||||
\(565\) | 16.5120 | − | 28.2121i | 0.0292248 | − | 0.0499329i | ||||
\(566\) | − | 371.855i | − | 0.656987i | ||||||
\(567\) | 213.200 | − | 21.7458i | 0.376014 | − | 0.0383524i | ||||
\(568\) | − | 21.7854i | − | 0.0383545i | ||||||
\(569\) | − | 221.137i | − | 0.388641i | −0.980938 | − | 0.194320i | \(-0.937750\pi\) | ||
0.980938 | − | 0.194320i | \(-0.0622501\pi\) | |||||||
\(570\) | 279.437 | + | 349.840i | 0.490240 | + | 0.613755i | ||||
\(571\) | 520.798 | 0.912080 | 0.456040 | − | 0.889959i | \(-0.349267\pi\) | ||||
0.456040 | + | 0.889959i | \(0.349267\pi\) | |||||||
\(572\) | −227.662 | −0.398010 | ||||||||
\(573\) | −636.449 | − | 244.871i | −1.11073 | − | 0.427349i | ||||
\(574\) | 129.904 | 0.226314 | ||||||||
\(575\) | 395.082 | + | 703.433i | 0.687099 | + | 1.22336i | ||||
\(576\) | −53.4323 | − | 48.2596i | −0.0927644 | − | 0.0837840i | ||||
\(577\) | − | 78.8359i | − | 0.136631i | −0.997664 | − | 0.0683154i | \(-0.978238\pi\) | ||
0.997664 | − | 0.0683154i | \(-0.0217624\pi\) | |||||||
\(578\) | 402.885 | 0.697032 | ||||||||
\(579\) | 671.590 | + | 258.391i | 1.15991 | + | 0.446272i | ||||
\(580\) | 105.812 | + | 61.9298i | 0.182434 | + | 0.106775i | ||||
\(581\) | − | 306.548i | − | 0.527622i | ||||||
\(582\) | −32.4409 | − | 12.4815i | −0.0557403 | − | 0.0214459i | ||||
\(583\) | − | 344.689i | − | 0.591234i | ||||||
\(584\) | 34.1374i | 0.0584544i | ||||||||
\(585\) | −258.362 | − | 815.830i | −0.441645 | − | 1.39458i | ||||
\(586\) | −505.680 | −0.862935 | ||||||||
\(587\) | −146.455 | −0.249498 | −0.124749 | − | 0.992188i | \(-0.539813\pi\) | ||||
−0.124749 | + | 0.992188i | \(0.539813\pi\) | |||||||
\(588\) | −15.0816 | + | 39.1988i | −0.0256489 | + | 0.0666646i | ||||
\(589\) | −829.670 | −1.40861 | ||||||||
\(590\) | −438.131 | − | 256.430i | −0.742595 | − | 0.434627i | ||||
\(591\) | −198.340 | + | 515.509i | −0.335601 | + | 0.872266i | ||||
\(592\) | − | 81.2965i | − | 0.137325i | ||||||
\(593\) | 240.021 | 0.404758 | 0.202379 | − | 0.979307i | \(-0.435133\pi\) | ||||
0.202379 | + | 0.979307i | \(0.435133\pi\) | |||||||
\(594\) | −103.294 | − | 203.886i | −0.173895 | − | 0.343243i | ||||
\(595\) | 23.1668 | + | 13.5591i | 0.0389359 | + | 0.0227885i | ||||
\(596\) | 372.671i | 0.625287i | ||||||||
\(597\) | −232.463 | + | 604.198i | −0.389385 | + | 1.01206i | ||||
\(598\) | − | 867.912i | − | 1.45136i | ||||||
\(599\) | − | 886.239i | − | 1.47953i | −0.672865 | − | 0.739766i | \(-0.734936\pi\) | ||
0.672865 | − | 0.739766i | \(-0.265064\pi\) | |||||||
\(600\) | 209.923 | − | 30.5370i | 0.349871 | − | 0.0508950i | ||||
\(601\) | −162.944 | −0.271121 | −0.135561 | − | 0.990769i | \(-0.543284\pi\) | ||||
−0.135561 | + | 0.990769i | \(0.543284\pi\) | |||||||
\(602\) | −150.904 | −0.250671 | ||||||||
\(603\) | 492.930 | − | 545.765i | 0.817463 | − | 0.905083i | ||||
\(604\) | −367.121 | −0.607816 | ||||||||
\(605\) | −215.109 | + | 367.531i | −0.355552 | + | 0.607489i | ||||
\(606\) | 540.434 | + | 207.930i | 0.891805 | + | 0.343119i | ||||
\(607\) | 649.221i | 1.06956i | 0.844992 | + | 0.534779i | \(0.179605\pi\) | ||||
−0.844992 | + | 0.534779i | \(0.820395\pi\) | |||||||
\(608\) | 119.398 | 0.196378 | ||||||||
\(609\) | −34.9437 | + | 90.8227i | −0.0573787 | + | 0.149134i | ||||
\(610\) | 291.919 | − | 498.767i | 0.478556 | − | 0.817650i | ||||
\(611\) | 1377.58i | 2.25464i | ||||||||
\(612\) | −27.1055 | − | 24.4815i | −0.0442901 | − | 0.0400024i | ||||
\(613\) | 109.849i | 0.179199i | 0.995978 | + | 0.0895994i | \(0.0285587\pi\) | ||||
−0.995978 | + | 0.0895994i | \(0.971441\pi\) | |||||||
\(614\) | 414.937i | 0.675794i | ||||||||
\(615\) | 406.903 | − | 325.016i | 0.661632 | − | 0.528482i | ||||
\(616\) | 44.7934 | 0.0727165 | ||||||||
\(617\) | −871.161 | −1.41193 | −0.705966 | − | 0.708246i | \(-0.749487\pi\) | ||||
−0.705966 | + | 0.708246i | \(0.749487\pi\) | |||||||
\(618\) | 511.556 | + | 196.819i | 0.827760 | + | 0.318477i | ||||
\(619\) | −153.281 | −0.247627 | −0.123814 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123814 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(620\) | −198.556 | + | 339.248i | −0.320251 | + | 0.547174i | ||||
\(621\) | 777.272 | − | 393.786i | 1.25165 | − | 0.634115i | ||||
\(622\) | 83.7873i | 0.134706i | ||||||||
\(623\) | 269.706 | 0.432914 | ||||||||
\(624\) | −212.983 | − | 81.9444i | −0.341319 | − | 0.131321i | ||||
\(625\) | −325.246 | + | 533.704i | −0.520394 | + | 0.853926i | ||||
\(626\) | 637.226i | 1.01793i | ||||||||
\(627\) | 353.742 | + | 136.101i | 0.564182 | + | 0.217067i | ||||
\(628\) | − | 529.755i | − | 0.843558i | ||||||
\(629\) | − | 41.2407i | − | 0.0655655i | ||||||
\(630\) | 50.8337 | + | 160.518i | 0.0806885 | + | 0.254790i | ||||
\(631\) | −959.345 | −1.52036 | −0.760178 | − | 0.649715i | \(-0.774888\pi\) | ||||
−0.760178 | + | 0.649715i | \(0.774888\pi\) | |||||||
\(632\) | −372.282 | −0.589055 | ||||||||
\(633\) | −131.842 | + | 342.672i | −0.208281 | + | 0.541346i | ||||
\(634\) | −392.379 | −0.618894 | ||||||||
\(635\) | 64.9059 | + | 37.9882i | 0.102214 | + | 0.0598240i | ||||
\(636\) | 124.067 | − | 322.465i | 0.195074 | − | 0.507020i | ||||
\(637\) | 133.119i | 0.208977i | ||||||||
\(638\) | 103.785 | 0.162673 | ||||||||
\(639\) | 46.4637 | − | 51.4439i | 0.0727131 | − | 0.0805069i | ||||
\(640\) | 28.5742 | − | 48.8213i | 0.0446472 | − | 0.0762832i | ||||
\(641\) | 733.758i | 1.14471i | 0.820007 | + | 0.572354i | \(0.193970\pi\) | ||||
−0.820007 | + | 0.572354i | \(0.806030\pi\) | |||||||
\(642\) | 30.8700 | − | 80.2346i | 0.0480840 | − | 0.124976i | ||||
\(643\) | − | 164.305i | − | 0.255529i | −0.991805 | − | 0.127765i | \(-0.959220\pi\) | ||
0.991805 | − | 0.127765i | \(-0.0407802\pi\) | |||||||
\(644\) | 170.765i | 0.265163i | ||||||||
\(645\) | −472.682 | + | 377.557i | −0.732840 | + | 0.585360i | ||||
\(646\) | 60.5691 | 0.0937602 | ||||||||
\(647\) | −1171.84 | −1.81119 | −0.905594 | − | 0.424146i | \(-0.860574\pi\) | ||||
−0.905594 | + | 0.424146i | \(0.860574\pi\) | |||||||
\(648\) | −23.2473 | − | 227.920i | −0.0358754 | − | 0.351729i | ||||
\(649\) | −429.739 | −0.662155 | ||||||||
\(650\) | 586.217 | − | 329.248i | 0.901873 | − | 0.506535i | ||||
\(651\) | −291.191 | − | 112.034i | −0.447297 | − | 0.172096i | ||||
\(652\) | 429.754i | 0.659132i | ||||||||
\(653\) | 804.521 | 1.23204 | 0.616019 | − | 0.787731i | \(-0.288744\pi\) | ||||
0.616019 | + | 0.787731i | \(0.288744\pi\) | |||||||
\(654\) | 171.496 | − | 445.738i | 0.262226 | − | 0.681557i | ||||
\(655\) | 222.632 | + | 130.303i | 0.339897 | + | 0.198936i | ||||
\(656\) | − | 138.873i | − | 0.211697i | ||||||
\(657\) | −72.8080 | + | 80.6119i | −0.110819 | + | 0.122697i | ||||
\(658\) | − | 271.045i | − | 0.411922i | ||||||
\(659\) | − | 864.248i | − | 1.31145i | −0.754999 | − | 0.655727i | \(-0.772362\pi\) | ||
0.754999 | − | 0.655727i | \(-0.227638\pi\) | |||||||
\(660\) | 140.308 | − | 112.072i | 0.212588 | − | 0.169806i | ||||
\(661\) | −963.638 | −1.45785 | −0.728924 | − | 0.684595i | \(-0.759979\pi\) | ||||
−0.728924 | + | 0.684595i | \(0.759979\pi\) | |||||||
\(662\) | −390.179 | −0.589394 | ||||||||
\(663\) | −108.044 | − | 41.5694i | −0.162962 | − | 0.0626989i | ||||
\(664\) | −327.714 | −0.493545 | ||||||||
\(665\) | −240.977 | − | 141.039i | −0.362371 | − | 0.212089i | ||||
\(666\) | 173.389 | − | 191.973i | 0.260343 | − | 0.288248i | ||||
\(667\) | 395.658i | 0.593191i | ||||||||
\(668\) | 109.191 | 0.163459 | ||||||||
\(669\) | 196.362 | + | 75.5496i | 0.293516 | + | 0.112929i | ||||
\(670\) | 498.667 | + | 291.861i | 0.744279 | + | 0.435613i | ||||
\(671\) | − | 489.213i | − | 0.729081i | ||||||
\(672\) | 41.9053 | + | 16.1229i | 0.0623590 | + | 0.0239924i | ||||
\(673\) | − | 149.734i | − | 0.222487i | −0.993793 | − | 0.111244i | \(-0.964517\pi\) | ||
0.993793 | − | 0.111244i | \(-0.0354834\pi\) | |||||||
\(674\) | 145.378i | 0.215694i | ||||||||
\(675\) | 560.840 | + | 375.611i | 0.830874 | + | 0.556461i | ||||
\(676\) | −385.288 | −0.569953 | ||||||||
\(677\) | −325.257 | −0.480439 | −0.240219 | − | 0.970719i | \(-0.577219\pi\) | ||||
−0.240219 | + | 0.970719i | \(0.577219\pi\) | |||||||
\(678\) | 9.96012 | − | 25.8875i | 0.0146904 | − | 0.0381822i | ||||
\(679\) | 21.6761 | 0.0319236 | ||||||||
\(680\) | 14.4953 | − | 24.7664i | 0.0213167 | − | 0.0364212i | ||||
\(681\) | −33.8557 | + | 87.9949i | −0.0497146 | + | 0.129214i | ||||
\(682\) | 332.750i | 0.487904i | ||||||||
\(683\) | 551.573 | 0.807575 | 0.403787 | − | 0.914853i | \(-0.367694\pi\) | ||||
0.403787 | + | 0.914853i | \(0.367694\pi\) | |||||||
\(684\) | 281.946 | + | 254.651i | 0.412202 | + | 0.372297i | ||||
\(685\) | −120.192 | + | 205.357i | −0.175462 | + | 0.299791i | ||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 38.4803 | − | 100.015i | 0.0560121 | − | 0.145582i | ||||
\(688\) | 161.323i | 0.234481i | ||||||||
\(689\) | − | 1095.09i | − | 1.58939i | ||||||
\(690\) | 427.250 | + | 534.894i | 0.619202 | + | 0.775209i | ||||
\(691\) | −495.558 | −0.717161 | −0.358580 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358580 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(692\) | 621.301 | 0.897834 | ||||||||
\(693\) | 105.775 | + | 95.5350i | 0.152633 | + | 0.137857i | ||||
\(694\) | −645.715 | −0.930426 | ||||||||
\(695\) | 297.341 | − | 508.030i | 0.427829 | − | 0.730979i | ||||
\(696\) | 97.0935 | + | 37.3563i | 0.139502 | + | 0.0536729i | ||||
\(697\) | − | 70.4486i | − | 0.101074i | ||||||
\(698\) | −806.958 | −1.15610 | ||||||||
\(699\) | −349.615 | + | 908.690i | −0.500164 | + | 1.29999i | ||||
\(700\) | −115.341 | + | 64.7808i | −0.164772 | + | 0.0925440i | ||||
\(701\) | 377.346i | 0.538297i | 0.963099 | + | 0.269149i | \(0.0867423\pi\) | ||||
−0.963099 | + | 0.269149i | \(0.913258\pi\) | |||||||
\(702\) | −328.168 | − | 647.752i | −0.467475 | − | 0.922724i | ||||
\(703\) | 428.977i | 0.610209i | ||||||||
\(704\) | − | 47.8861i | − | 0.0680201i | ||||||
\(705\) | −678.147 | − | 849.005i | −0.961911 | − | 1.20426i | ||||
\(706\) | −6.71080 | −0.00950539 | ||||||||
\(707\) | −361.104 | −0.510755 | ||||||||
\(708\) | −402.031 | − | 154.680i | −0.567840 | − | 0.218474i | ||||
\(709\) | 517.276 | 0.729585 | 0.364792 | − | 0.931089i | \(-0.381140\pi\) | ||||
0.364792 | + | 0.931089i | \(0.381140\pi\) | |||||||
\(710\) | 47.0044 | + | 27.5109i | 0.0662034 | + | 0.0387477i | ||||
\(711\) | −879.107 | − | 794.001i | −1.23644 | − | 1.11674i | ||||
\(712\) | − | 288.327i | − | 0.404954i | ||||||
\(713\) | −1268.54 | −1.77916 | ||||||||
\(714\) | 21.2580 | + | 8.17894i | 0.0297731 | + | 0.0114551i | ||||
\(715\) | 287.495 | − | 491.207i | 0.402090 | − | 0.687003i | ||||
\(716\) | 325.845i | 0.455090i | ||||||||
\(717\) | −1120.08 | − | 430.944i | −1.56217 | − | 0.601038i | ||||
\(718\) | − | 646.418i | − | 0.900303i | ||||||
\(719\) | − | 1187.74i | − | 1.65193i | −0.563720 | − | 0.825966i | \(-0.690630\pi\) | ||
0.563720 | − | 0.825966i | \(-0.309370\pi\) | |||||||
\(720\) | 171.601 | − | 54.3436i | 0.238334 | − | 0.0754772i | ||||
\(721\) | −341.808 | −0.474075 | ||||||||
\(722\) | −119.496 | −0.165506 | ||||||||
\(723\) | 426.922 | − | 1109.62i | 0.590487 | − | 1.53474i | ||||
\(724\) | −103.018 | −0.142289 | ||||||||
\(725\) | −267.241 | + | 150.096i | −0.368609 | + | 0.207028i | ||||
\(726\) | −129.755 | + | 337.248i | −0.178726 | + | 0.464529i | ||||
\(727\) | − | 892.878i | − | 1.22817i | −0.789241 | − | 0.614084i | \(-0.789526\pi\) | ||
0.789241 | − | 0.614084i | \(-0.210474\pi\) | |||||||
\(728\) | 142.310 | 0.195480 | ||||||||
\(729\) | 431.210 | − | 587.791i | 0.591509 | − | 0.806298i | ||||
\(730\) | −73.6553 | − | 43.1091i | −0.100898 | − | 0.0590536i | ||||
\(731\) | 81.8371i | 0.111952i | ||||||||
\(732\) | 176.087 | − | 457.671i | 0.240556 | − | 0.625233i | ||||
\(733\) | 868.737i | 1.18518i | 0.805504 | + | 0.592590i | \(0.201894\pi\) | ||||
−0.805504 | + | 0.592590i | \(0.798106\pi\) | |||||||
\(734\) | 787.204i | 1.07248i | ||||||||
\(735\) | −65.5307 | − | 82.0410i | −0.0891574 | − | 0.111620i | ||||
\(736\) | 182.555 | 0.248037 | ||||||||
\(737\) | 489.116 | 0.663657 | ||||||||
\(738\) | 296.188 | − | 327.935i | 0.401338 | − | 0.444356i | ||||
\(739\) | −356.963 | −0.483035 | −0.241517 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241517 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(740\) | 175.407 | + | 102.662i | 0.237036 | + | 0.138733i | ||||
\(741\) | 1123.85 | + | 432.396i | 1.51666 | + | 0.583530i | ||||
\(742\) | 215.463i | 0.290381i | ||||||||
\(743\) | 982.069 | 1.32176 | 0.660881 | − | 0.750491i | \(-0.270183\pi\) | ||||
0.660881 | + | 0.750491i | \(0.270183\pi\) | |||||||
\(744\) | −119.770 | + | 311.296i | −0.160981 | + | 0.418408i | ||||
\(745\) | −804.081 | − | 470.614i | −1.07930 | − | 0.631697i | ||||
\(746\) | − | 109.215i | − | 0.146401i | ||||||
\(747\) | −773.863 | − | 698.946i | −1.03596 | − | 0.935670i | ||||
\(748\) | − | 24.2920i | − | 0.0324760i | ||||||
\(749\) | 53.6107i | 0.0715763i | ||||||||
\(750\) | −199.206 | + | 491.495i | −0.265608 | + | 0.655326i | ||||
\(751\) | −710.167 | −0.945628 | −0.472814 | − | 0.881162i | \(-0.656762\pi\) | ||||
−0.472814 | + | 0.881162i | \(0.656762\pi\) | |||||||
\(752\) | −289.759 | −0.385318 | ||||||||
\(753\) | −619.413 | − | 238.317i | −0.822593 | − | 0.316489i | ||||
\(754\) | 329.728 | 0.437305 | ||||||||
\(755\) | 463.605 | − | 792.105i | 0.614046 | − | 1.04915i | ||||
\(756\) | 64.5682 | + | 127.448i | 0.0854077 | + | 0.168582i | ||||
\(757\) | 346.357i | 0.457540i | 0.973481 | + | 0.228770i | \(0.0734703\pi\) | ||||
−0.973481 | + | 0.228770i | \(0.926530\pi\) | |||||||
\(758\) | −673.353 | −0.888329 | ||||||||
\(759\) | 540.859 | + | 208.093i | 0.712595 | + | 0.274168i | ||||
\(760\) | −150.777 | + | 257.615i | −0.198391 | + | 0.338967i | ||||
\(761\) | − | 1138.06i | − | 1.49548i | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||
0.663994 | − | 0.747738i | \(-0.268860\pi\) | |||||||
\(762\) | 59.5580 | + | 22.9147i | 0.0781600 | + | 0.0300718i | ||||
\(763\) | 297.830i | 0.390341i | ||||||||
\(764\) | − | 454.620i | − | 0.595053i | ||||||
\(765\) | 87.0508 | − | 27.5678i | 0.113792 | − | 0.0360363i | ||||
\(766\) | 849.057 | 1.10843 | ||||||||
\(767\) | −1365.29 | −1.78004 | ||||||||
\(768\) | 17.2361 | − | 44.7986i | 0.0224428 | − | 0.0583315i | ||||
\(769\) | −395.138 | −0.513833 | −0.256917 | − | 0.966434i | \(-0.582707\pi\) | ||||
−0.256917 | + | 0.966434i | \(0.582707\pi\) | |||||||
\(770\) | −56.5657 | + | 96.6469i | −0.0734619 | + | 0.125515i | ||||
\(771\) | 219.561 | − | 570.665i | 0.284774 | − | 0.740162i | ||||
\(772\) | 479.722i | 0.621401i | ||||||||
\(773\) | 1244.98 | 1.61058 | 0.805290 | − | 0.592881i | \(-0.202010\pi\) | ||||
0.805290 | + | 0.592881i | \(0.202010\pi\) | |||||||
\(774\) | −344.068 | + | 380.947i | −0.444533 | + | 0.492180i | ||||
\(775\) | −481.228 | − | 856.814i | −0.620939 | − | 1.10557i | ||||
\(776\) | − | 23.1728i | − | 0.0298618i | ||||||
\(777\) | −57.9268 | + | 150.559i | −0.0745519 | + | 0.193769i | ||||
\(778\) | 446.024i | 0.573296i | ||||||||
\(779\) | 732.791i | 0.940682i | ||||||||
\(780\) | 445.763 | − | 356.055i | 0.571491 | − | 0.456481i | ||||
\(781\) | 46.1041 | 0.0590322 | ||||||||
\(782\) | 92.6081 | 0.118425 | ||||||||
\(783\) | 149.603 | + | 295.293i | 0.191064 | + | 0.377131i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 1143.01 | + | 668.981i | 1.45606 | + | 0.852205i | ||||
\(786\) | 204.289 | + | 78.5992i | 0.259909 | + | 0.0999990i | ||||
\(787\) | 333.519i | 0.423785i | 0.977293 | + | 0.211892i | \(0.0679627\pi\) | ||||
−0.977293 | + | 0.211892i | \(0.932037\pi\) | |||||||
\(788\) | −368.232 | −0.467300 | ||||||||
\(789\) | −105.789 | + | 274.957i | −0.134079 | + | 0.348488i | ||||
\(790\) | 470.123 | − | 803.242i | 0.595093 | − | 1.01676i | ||||
\(791\) | 17.2974i | 0.0218677i | ||||||||
\(792\) | 102.131 | − | 113.078i | 0.128954 | − | 0.142775i | ||||
\(793\) | − | 1554.24i | − | 1.95995i | ||||||
\(794\) | 412.281i | 0.519246i | ||||||||
\(795\) | 539.082 | + | 674.902i | 0.678090 | + | 0.848933i | ||||
\(796\) | −431.583 | −0.542190 | ||||||||
\(797\) | −541.407 | −0.679306 | −0.339653 | − | 0.940551i | \(-0.610310\pi\) | ||||
−0.339653 | + | 0.940551i | \(0.610310\pi\) | |||||||
\(798\) | −221.121 | − | 85.0756i | −0.277094 | − | 0.106611i | ||||
\(799\) | −146.991 | −0.183969 | ||||||||
\(800\) | 69.2536 | + | 123.304i | 0.0865670 | + | 0.154130i | ||||
\(801\) | 614.943 | − | 680.856i | 0.767719 | − | 0.850007i | ||||
\(802\) | 441.521i | 0.550525i | ||||||||
\(803\) | −72.2446 | −0.0899683 | ||||||||
\(804\) | 457.579 | + | 176.052i | 0.569128 | + | 0.218970i | ||||
\(805\) | −368.445 | − | 215.644i | −0.457696 | − | 0.267881i | ||||
\(806\) | 1057.16i | 1.31161i | ||||||||
\(807\) | −864.176 | − | 332.488i | −1.07085 | − | 0.412005i | ||||
\(808\) | 386.036i | 0.477768i | ||||||||
\(809\) | 812.942i | 1.00487i | 0.864614 | + | 0.502436i | \(0.167563\pi\) | ||||
−0.864614 | + | 0.502436i | \(0.832437\pi\) | |||||||
\(810\) | 521.121 | + | 237.662i | 0.643359 | + | 0.293410i | ||||
\(811\) | −750.662 | −0.925600 | −0.462800 | − | 0.886463i | \(-0.653155\pi\) | ||||
−0.462800 | + | 0.886463i | \(0.653155\pi\) | |||||||
\(812\) | −64.8753 | −0.0798957 | ||||||||
\(813\) | −429.654 | + | 1116.72i | −0.528480 | + | 1.37358i | ||||
\(814\) | 172.047 | 0.211360 | ||||||||
\(815\) | −927.244 | − | 542.699i | −1.13772 | − | 0.665888i | ||||
\(816\) | 8.74365 | − | 22.7258i | 0.0107153 | − | 0.0278502i | ||||
\(817\) | − | 851.252i | − | 1.04192i | ||||||
\(818\) | 852.331 | 1.04197 | ||||||||
\(819\) | 336.050 | + | 303.517i | 0.410317 | + | 0.370595i | ||||
\(820\) | 299.635 | + | 175.371i | 0.365408 | + | 0.213867i | ||||
\(821\) | − | 1216.71i | − | 1.48199i | −0.671513 | − | 0.740993i | \(-0.734355\pi\) | ||
0.671513 | − | 0.740993i | \(-0.265645\pi\) | |||||||
\(822\) | −72.5001 | + | 188.436i | −0.0881996 | + | 0.229241i | ||||
\(823\) | 918.365i | 1.11588i | 0.829883 | + | 0.557938i | \(0.188407\pi\) | ||||
−0.829883 | + | 0.557938i | \(0.811593\pi\) | |||||||
\(824\) | 365.408i | 0.443457i | ||||||||
\(825\) | 64.6251 | + | 444.257i | 0.0783334 | + | 0.538493i | ||||
\(826\) | 268.626 | 0.325214 | ||||||||
\(827\) | 973.601 | 1.17727 | 0.588634 | − | 0.808400i | \(-0.299666\pi\) | ||||
0.588634 | + | 0.808400i | \(0.299666\pi\) | |||||||
\(828\) | 431.086 | + | 389.353i | 0.520635 | + | 0.470233i | ||||
\(829\) | 759.447 | 0.916100 | 0.458050 | − | 0.888926i | \(-0.348548\pi\) | ||||
0.458050 | + | 0.888926i | \(0.348548\pi\) | |||||||
\(830\) | 413.841 | − | 707.081i | 0.498604 | − | 0.851904i | ||||
\(831\) | −223.211 | − | 85.8796i | −0.268606 | − | 0.103345i | ||||
\(832\) | − | 152.136i | − | 0.182855i | ||||||
\(833\) | −14.2040 | −0.0170517 | ||||||||
\(834\) | 179.357 | − | 466.171i | 0.215057 | − | 0.558958i | ||||
\(835\) | −137.888 | + | 235.592i | −0.165135 | + | 0.282146i | ||||
\(836\) | 252.681i | 0.302249i | ||||||||
\(837\) | −946.753 | + | 479.649i | −1.13113 | + | 0.573057i | ||||
\(838\) | − | 254.515i | − | 0.303718i | ||||||
\(839\) | 937.182i | 1.11702i | 0.829497 | + | 0.558512i | \(0.188627\pi\) | ||||
−0.829497 | + | 0.558512i | \(0.811373\pi\) | |||||||
\(840\) | −87.7055 | + | 70.0553i | −0.104411 | + | 0.0833991i | ||||
\(841\) | 690.685 | 0.821267 | ||||||||
\(842\) | −643.409 | −0.764144 | ||||||||
\(843\) | −588.456 | − | 226.406i | −0.698050 | − | 0.268572i | ||||
\(844\) | −244.773 | −0.290015 | ||||||||
\(845\) | 486.547 | − | 831.304i | 0.575795 | − | 0.983791i | ||||
\(846\) | −684.237 | − | 617.996i | −0.808790 | − | 0.730492i | ||||
\(847\) | − | 225.340i | − | 0.266045i | ||||||
\(848\) | 230.339 | 0.271626 | ||||||||
\(849\) | 736.212 | + | 283.255i | 0.867152 | + | 0.333633i | ||||
\(850\) | 35.1315 | + | 62.5507i | 0.0413311 | + | 0.0735890i | ||||
\(851\) | 655.891i | 0.770730i | ||||||||
\(852\) | 43.1315 | + | 16.5947i | 0.0506238 | + | 0.0194773i | ||||
\(853\) | 465.533i | 0.545760i | 0.962048 | + | 0.272880i | \(0.0879762\pi\) | ||||
−0.962048 | + | 0.272880i | \(0.912024\pi\) | |||||||
\(854\) | 305.803i | 0.358084i | ||||||||
\(855\) | −905.484 | + | 286.754i | −1.05905 | + | 0.335385i | ||||
\(856\) | 57.3122 | 0.0669535 | ||||||||
\(857\) | 1612.01 | 1.88099 | 0.940494 | − | 0.339811i | \(-0.110363\pi\) | ||||
0.940494 | + | 0.339811i | \(0.110363\pi\) | |||||||
\(858\) | 173.418 | − | 450.734i | 0.202119 | − | 0.525331i | ||||
\(859\) | 1111.27 | 1.29368 | 0.646842 | − | 0.762624i | \(-0.276089\pi\) | ||||
0.646842 | + | 0.762624i | \(0.276089\pi\) | |||||||
\(860\) | −348.073 | − | 203.721i | −0.404736 | − | 0.236885i | ||||
\(861\) | −98.9524 | + | 257.189i | −0.114927 | + | 0.298709i | ||||
\(862\) | − | 396.597i | − | 0.460090i | ||||||
\(863\) | −681.862 | −0.790106 | −0.395053 | − | 0.918658i | \(-0.629274\pi\) | ||||
−0.395053 | + | 0.918658i | \(0.629274\pi\) | |||||||
\(864\) | 136.247 | − | 69.0264i | 0.157694 | − | 0.0798916i | ||||
\(865\) | −784.587 | + | 1340.53i | −0.907037 | + | 1.54974i | ||||
\(866\) | 243.812i | 0.281538i | ||||||||
\(867\) | −306.891 | + | 797.647i | −0.353969 | + | 0.920008i | ||||
\(868\) | − | 208.000i | − | 0.239631i | ||||||
\(869\) | − | 787.857i | − | 0.906625i | ||||||
\(870\) | −203.212 | + | 162.316i | −0.233577 | + | 0.186571i | ||||
\(871\) | 1553.93 | 1.78408 | ||||||||
\(872\) | 318.394 | 0.365131 | ||||||||
\(873\) | 49.4227 | − | 54.7201i | 0.0566125 | − | 0.0626805i | ||||
\(874\) | −963.289 | −1.10216 | ||||||||
\(875\) | 5.88150 | − | 330.667i | 0.00672171 | − | 0.377905i | ||||
\(876\) | −67.5865 | − | 26.0036i | −0.0771536 | − | 0.0296845i | ||||
\(877\) | 206.003i | 0.234896i | 0.993079 | + | 0.117448i | \(0.0374713\pi\) | ||||
−0.993079 | + | 0.117448i | \(0.962529\pi\) | |||||||
\(878\) | −423.782 | −0.482667 | ||||||||
\(879\) | 385.194 | − | 1001.16i | 0.438219 | − | 1.13898i | ||||
\(880\) | 103.320 | + | 60.4712i | 0.117409 | + | 0.0687173i | ||||
\(881\) | 909.333i | 1.03216i | 0.856540 | + | 0.516080i | \(0.172609\pi\) | ||||
−0.856540 | + | 0.516080i | \(0.827391\pi\) | |||||||
\(882\) | −66.1191 | − | 59.7182i | −0.0749650 | − | 0.0677077i | ||||
\(883\) | 776.956i | 0.879905i | 0.898021 | + | 0.439952i | \(0.145005\pi\) | ||||
−0.898021 | + | 0.439952i | \(0.854995\pi\) | |||||||
\(884\) | − | 77.1764i | − | 0.0873036i | ||||||
\(885\) | 841.429 | − | 672.096i | 0.950768 | − | 0.759431i | ||||
\(886\) | 550.763 | 0.621628 | ||||||||
\(887\) | 1228.23 | 1.38470 | 0.692350 | − | 0.721562i | \(-0.256575\pi\) | ||||
0.692350 | + | 0.721562i | \(0.256575\pi\) | |||||||
\(888\) | 160.954 | + | 61.9264i | 0.181254 | + | 0.0697369i | ||||
\(889\) | −39.7951 | −0.0447638 | ||||||||
\(890\) | 622.100 | + | 364.104i | 0.698988 | + | 0.409105i | ||||
\(891\) | 482.345 | − | 49.1979i | 0.541352 | − | 0.0552165i | ||||
\(892\) | 140.263i | 0.157245i | ||||||||
\(893\) | 1528.97 | 1.71217 | ||||||||
\(894\) | −737.829 | − | 283.877i | −0.825312 | − | 0.317535i | ||||
\(895\) | −703.047 | − | 411.481i | −0.785528 | − | 0.459755i | ||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 1718.32 | + | 661.119i | 1.91564 | + | 0.737033i | ||||
\(898\) | 868.359i | 0.966993i | ||||||||
\(899\) | − | 481.930i | − | 0.536074i | ||||||
\(900\) | −99.4471 | + | 438.874i | −0.110497 | + | 0.487638i | ||||
\(901\) | 116.848 | 0.129687 | ||||||||
\(902\) | 293.896 | 0.325827 | ||||||||
\(903\) | 114.949 | − | 298.765i | 0.127296 | − | 0.330858i | ||||
\(904\) | 18.4917 | 0.0204554 | ||||||||
\(905\) | 130.092 | − | 222.272i | 0.143748 | − | 0.245605i | ||||
\(906\) | 279.649 | − | 726.840i | 0.308663 | − | 0.802251i | ||||
\(907\) | 254.429i | 0.280517i | 0.990115 | + | 0.140259i | \(0.0447934\pi\) | ||||
−0.990115 | + | 0.140259i | \(0.955207\pi\) | |||||||
\(908\) | −62.8554 | −0.0692240 | ||||||||
\(909\) | −823.335 | + | 911.585i | −0.905759 | + | 1.00284i | ||||
\(910\) | −179.711 | + | 307.050i | −0.197484 | + | 0.337417i | ||||
\(911\) | − | 231.235i | − | 0.253825i | −0.991914 | − | 0.126913i | \(-0.959493\pi\) | ||
0.991914 | − | 0.126913i | \(-0.0405068\pi\) | |||||||
\(912\) | −90.9496 | + | 236.389i | −0.0997254 | + | 0.259198i | ||||
\(913\) | − | 693.537i | − | 0.759624i | ||||||
\(914\) | − | 304.845i | − | 0.333529i | ||||||
\(915\) | 765.112 | + | 957.881i | 0.836188 | + | 1.04686i | ||||
\(916\) | 71.4414 | 0.0779928 | ||||||||
\(917\) | −136.500 | −0.148855 | ||||||||
\(918\) | 69.1166 | − | 35.0162i | 0.0752904 | − | 0.0381440i | ||||
\(919\) | 279.584 | 0.304226 | 0.152113 | − | 0.988363i | \(-0.451392\pi\) | ||||
0.152113 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(920\) | −230.533 | + | 393.884i | −0.250580 | + | 0.428135i | ||||
\(921\) | −821.509 | − | 316.072i | −0.891975 | − | 0.343184i | ||||
\(922\) | 522.698i | 0.566918i | ||||||||
\(923\) | 146.474 | 0.158693 | ||||||||
\(924\) | −34.1207 | + | 88.6836i | −0.0369271 | + | 0.0959780i | ||||
\(925\) | −443.011 | + | 248.817i | −0.478931 | + | 0.268991i | ||||
\(926\) | − | 0.955022i | − | 0.00103134i | ||||||
\(927\) | −779.340 | + | 862.874i | −0.840712 | + | 0.930824i | ||||
\(928\) | 69.3546i | 0.0747356i | ||||||||
\(929\) | 1522.35i | 1.63870i | 0.573294 | + | 0.819350i | \(0.305665\pi\) | ||||
−0.573294 | + | 0.819350i | \(0.694335\pi\) | |||||||
\(930\) | −520.410 | − | 651.526i | −0.559580 | − | 0.700565i | ||||
\(931\) | 147.747 | 0.158698 | ||||||||
\(932\) | −649.084 | −0.696442 | ||||||||
\(933\) | −165.885 | − | 63.8237i | −0.177798 | − | 0.0684069i | ||||
\(934\) | −127.469 | −0.136476 | ||||||||
\(935\) | 52.4128 | + | 30.6763i | 0.0560565 | + | 0.0328089i | ||||
\(936\) | 324.474 | − | 359.252i | 0.346660 | − | 0.383817i | ||||
\(937\) | 1402.37i | 1.49666i | 0.663328 | + | 0.748329i | \(0.269144\pi\) | ||||
−0.663328 | + | 0.748329i | \(0.730856\pi\) | |||||||
\(938\) | −305.742 | −0.325951 | ||||||||
\(939\) | −1261.60 | − | 485.397i | −1.34356 | − | 0.516930i | ||||
\(940\) | 365.912 | − | 625.189i | 0.389268 | − | 0.665095i | ||||
\(941\) | 569.377i | 0.605077i | 0.953137 | + | 0.302538i | \(0.0978340\pi\) | ||||
−0.953137 | + | 0.302538i | \(0.902166\pi\) | |||||||
\(942\) | 1048.83 | + | 403.533i | 1.11341 | + | 0.428379i | ||||
\(943\) | 1120.41i | 1.18814i | ||||||||
\(944\) | − | 287.174i | − | 0.304210i | ||||||
\(945\) | −356.521 | − | 21.6293i | −0.377271 | − | 0.0228882i | ||||
\(946\) | −341.406 | −0.360894 | ||||||||
\(947\) | −130.552 | −0.137858 | −0.0689290 | − | 0.997622i | \(-0.521958\pi\) | ||||
−0.0689290 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(948\) | 283.581 | − | 737.059i | 0.299136 | − | 0.777488i | ||||
\(949\) | −229.523 | −0.241858 | ||||||||
\(950\) | −365.430 | − | 650.639i | −0.384663 | − | 0.684883i | ||||
\(951\) | 298.889 | − | 776.847i | 0.314289 | − | 0.816874i | ||||
\(952\) | 15.1848i | 0.0159504i | ||||||||
\(953\) | −154.008 | −0.161603 | −0.0808016 | − | 0.996730i | \(-0.525748\pi\) | ||||
−0.0808016 | + | 0.996730i | \(0.525748\pi\) | |||||||
\(954\) | 543.922 | + | 491.266i | 0.570149 | + | 0.514953i | ||||
\(955\) | 980.896 | + | 574.100i | 1.02712 | + | 0.601152i | ||||
\(956\) | − | 800.078i | − | 0.836902i | ||||||
\(957\) | −79.0568 | + | 205.478i | −0.0826090 | + | 0.214710i | ||||
\(958\) | − | 597.189i | − | 0.623371i | ||||||
\(959\) | − | 125.908i | − | 0.131291i | ||||||
\(960\) | 74.8922 | + | 93.7611i | 0.0780127 | + | 0.0976679i | ||||
\(961\) | 584.137 | 0.607843 | ||||||||
\(962\) | 546.597 | 0.568189 | ||||||||
\(963\) | 135.337 | + | 122.235i | 0.140537 | + | 0.126932i | ||||
\(964\) | 792.610 | 0.822209 | ||||||||
\(965\) | −1035.05 | − | 605.799i | −1.07260 | − | 0.627771i | ||||
\(966\) | −338.087 | − | 130.078i | −0.349987 | − | 0.134656i | ||||
\(967\) | 614.131i | 0.635089i | 0.948243 | + | 0.317544i | \(0.102858\pi\) | ||||
−0.948243 | + | 0.317544i | \(0.897142\pi\) | |||||||
\(968\) | −240.899 | −0.248862 | ||||||||
\(969\) | −46.1376 | + | 119.917i | −0.0476136 | + | 0.123753i | ||||
\(970\) | 49.9979 | + | 29.2629i | 0.0515442 | + | 0.0301679i | ||||
\(971\) | 288.285i | 0.296895i | 0.988920 | + | 0.148448i | \(0.0474277\pi\) | ||||
−0.988920 | + | 0.148448i | \(0.952572\pi\) | |||||||
\(972\) | 468.953 | + | 127.589i | 0.482462 | + | 0.131264i | ||||
\(973\) | 311.483i | 0.320127i | ||||||||
\(974\) | 339.671i | 0.348739i | ||||||||
\(975\) | 205.316 | + | 1411.42i | 0.210580 | + | 1.44761i | ||||
\(976\) | 326.918 | 0.334957 | ||||||||
\(977\) | −480.732 | −0.492049 | −0.246025 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246025 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(978\) | −850.844 | − | 327.359i | −0.869983 | − | 0.334723i | ||||
\(979\) | 610.184 | 0.623273 | ||||||||
\(980\) | 35.3588 | − | 60.4132i | 0.0360804 | − | 0.0616461i | ||||
\(981\) | 751.855 | + | 679.069i | 0.766417 | + | 0.692221i | ||||
\(982\) | − | 1359.32i | − | 1.38424i | ||||||
\(983\) | −1414.59 | −1.43905 | −0.719526 | − | 0.694465i | \(-0.755641\pi\) | ||||
−0.719526 | + | 0.694465i | \(0.755641\pi\) | |||||||
\(984\) | 274.946 | + | 105.785i | 0.279417 | + | 0.107505i | ||||
\(985\) | 465.008 | − | 794.503i | 0.472090 | − | 0.806602i | ||||
\(986\) | 35.1827i | 0.0356823i | ||||||||
\(987\) | 536.625 | + | 206.464i | 0.543693 | + | 0.209184i | ||||
\(988\) | 802.773i | 0.812523i | ||||||||
\(989\) | − | 1301.54i | − | 1.31601i | ||||||
\(990\) | 115.007 | + | 363.156i | 0.116168 | + | 0.366825i | ||||
\(991\) | −549.944 | −0.554939 | −0.277469 | − | 0.960735i | \(-0.589496\pi\) | ||||
−0.277469 | + | 0.960735i | \(0.589496\pi\) | |||||||
\(992\) | −222.361 | −0.224154 | ||||||||
\(993\) | 297.213 | − | 772.491i | 0.299308 | − | 0.777937i | ||||
\(994\) | −28.8193 | −0.0289933 | ||||||||
\(995\) | 545.009 | − | 931.191i | 0.547748 | − | 0.935870i | ||||
\(996\) | 249.631 | − | 648.821i | 0.250634 | − | 0.651426i | ||||
\(997\) | − | 524.552i | − | 0.526130i | −0.964778 | − | 0.263065i | \(-0.915267\pi\) | ||
0.964778 | − | 0.263065i | \(-0.0847334\pi\) | |||||||
\(998\) | −287.399 | −0.287975 | ||||||||
\(999\) | 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 | 210.3.c.a.29.7 | ✓ | 24 | |
3.2 | odd | 2 | inner | 210.3.c.a.29.17 | yes | 24 | |
5.2 | odd | 4 | 1050.3.e.e.701.17 | 24 | |||
5.3 | odd | 4 | 1050.3.e.e.701.20 | 24 | |||
5.4 | even | 2 | inner | 210.3.c.a.29.18 | yes | 24 | |
15.2 | even | 4 | 1050.3.e.e.701.19 | 24 | |||
15.8 | even | 4 | 1050.3.e.e.701.18 | 24 | |||
15.14 | odd | 2 | inner | 210.3.c.a.29.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
210.3.c.a.29.8 | yes | 24 | 15.14 | odd | 2 | inner | |
210.3.c.a.29.17 | yes | 24 | 3.2 | odd | 2 | inner | |
210.3.c.a.29.18 | yes | 24 | 5.4 | even | 2 | inner | |
1050.3.e.e.701.17 | 24 | 5.2 | odd | 4 | |||
1050.3.e.e.701.18 | 24 | 15.8 | even | 4 | |||
1050.3.e.e.701.19 | 24 | 15.2 | even | 4 | |||
1050.3.e.e.701.20 | 24 | 5.3 | odd | 4 |