Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
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: | yes |
Analytic conductor: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.149116 | −0.105441 | −0.0527205 | − | 0.998609i | \(-0.516789\pi\) | ||||
−0.0527205 | + | 0.998609i | \(0.516789\pi\) | |||||||
\(3\) | −3.21882 | −1.85838 | −0.929192 | − | 0.369598i | \(-0.879495\pi\) | ||||
−0.929192 | + | 0.369598i | \(0.879495\pi\) | |||||||
\(4\) | −1.97776 | −0.988882 | ||||||||
\(5\) | −1.07607 | −0.481231 | −0.240616 | − | 0.970621i | \(-0.577349\pi\) | ||||
−0.240616 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(6\) | 0.479977 | 0.195950 | ||||||||
\(7\) | 3.58386 | 1.35457 | 0.677286 | − | 0.735720i | \(-0.263156\pi\) | ||||
0.677286 | + | 0.735720i | \(0.263156\pi\) | |||||||
\(8\) | 0.593149 | 0.209710 | ||||||||
\(9\) | 7.36077 | 2.45359 | ||||||||
\(10\) | 0.160459 | 0.0507415 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 6.36606 | 1.83772 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.534411 | −0.142827 | ||||||||
\(15\) | 3.46366 | 0.894312 | ||||||||
\(16\) | 3.86708 | 0.966770 | ||||||||
\(17\) | −5.78160 | −1.40224 | −0.701121 | − | 0.713042i | \(-0.747317\pi\) | ||||
−0.701121 | + | 0.713042i | \(0.747317\pi\) | |||||||
\(18\) | −1.09761 | −0.258709 | ||||||||
\(19\) | 7.32598 | 1.68070 | 0.840348 | − | 0.542048i | \(-0.182351\pi\) | ||||
0.840348 | + | 0.542048i | \(0.182351\pi\) | |||||||
\(20\) | 2.12820 | 0.475881 | ||||||||
\(21\) | −11.5358 | −2.51731 | ||||||||
\(22\) | 0.149116 | 0.0317916 | ||||||||
\(23\) | −5.23635 | −1.09186 | −0.545928 | − | 0.837832i | \(-0.683823\pi\) | ||||
−0.545928 | + | 0.837832i | \(0.683823\pi\) | |||||||
\(24\) | −1.90924 | −0.389721 | ||||||||
\(25\) | −3.84208 | −0.768417 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.0365 | −2.70133 | ||||||||
\(28\) | −7.08803 | −1.33951 | ||||||||
\(29\) | −3.62640 | −0.673406 | −0.336703 | − | 0.941611i | \(-0.609312\pi\) | ||||
−0.336703 | + | 0.941611i | \(0.609312\pi\) | |||||||
\(30\) | −0.516487 | −0.0942971 | ||||||||
\(31\) | 2.65097 | 0.476129 | 0.238064 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238064 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(32\) | −1.76294 | −0.311647 | ||||||||
\(33\) | 3.21882 | 0.560324 | ||||||||
\(34\) | 0.862129 | 0.147854 | ||||||||
\(35\) | −3.85647 | −0.651862 | ||||||||
\(36\) | −14.5579 | −2.42631 | ||||||||
\(37\) | 3.91220 | 0.643161 | 0.321581 | − | 0.946882i | \(-0.395786\pi\) | ||||
0.321581 | + | 0.946882i | \(0.395786\pi\) | |||||||
\(38\) | −1.09242 | −0.177214 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.638267 | −0.100919 | ||||||||
\(41\) | 1.04212 | 0.162752 | 0.0813762 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813762 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(42\) | 1.72017 | 0.265428 | ||||||||
\(43\) | −1.21675 | −0.185553 | −0.0927766 | − | 0.995687i | \(-0.529574\pi\) | ||||
−0.0927766 | + | 0.995687i | \(0.529574\pi\) | |||||||
\(44\) | 1.97776 | 0.298159 | ||||||||
\(45\) | −7.92067 | −1.18074 | ||||||||
\(46\) | 0.780824 | 0.115126 | ||||||||
\(47\) | −11.9180 | −1.73843 | −0.869213 | − | 0.494438i | \(-0.835374\pi\) | ||||
−0.869213 | + | 0.494438i | \(0.835374\pi\) | |||||||
\(48\) | −12.4474 | −1.79663 | ||||||||
\(49\) | 5.84406 | 0.834866 | ||||||||
\(50\) | 0.572916 | 0.0810226 | ||||||||
\(51\) | 18.6099 | 2.60591 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.145014 | 0.0199192 | 0.00995961 | − | 0.999950i | \(-0.496830\pi\) | ||||
0.00995961 | + | 0.999950i | \(0.496830\pi\) | |||||||
\(54\) | 2.09307 | 0.284831 | ||||||||
\(55\) | 1.07607 | 0.145097 | ||||||||
\(56\) | 2.12576 | 0.284067 | ||||||||
\(57\) | −23.5810 | −3.12338 | ||||||||
\(58\) | 0.540755 | 0.0710046 | ||||||||
\(59\) | 2.35799 | 0.306984 | 0.153492 | − | 0.988150i | \(-0.450948\pi\) | ||||
0.153492 | + | 0.988150i | \(0.450948\pi\) | |||||||
\(60\) | −6.85029 | −0.884369 | ||||||||
\(61\) | 9.46701 | 1.21213 | 0.606063 | − | 0.795416i | \(-0.292748\pi\) | ||||
0.606063 | + | 0.795416i | \(0.292748\pi\) | |||||||
\(62\) | −0.395303 | −0.0502035 | ||||||||
\(63\) | 26.3800 | 3.32356 | ||||||||
\(64\) | −7.47128 | −0.933910 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.479977 | −0.0590811 | ||||||||
\(67\) | 5.14020 | 0.627976 | 0.313988 | − | 0.949427i | \(-0.398335\pi\) | ||||
0.313988 | + | 0.949427i | \(0.398335\pi\) | |||||||
\(68\) | 11.4346 | 1.38665 | ||||||||
\(69\) | 16.8549 | 2.02909 | ||||||||
\(70\) | 0.575061 | 0.0687330 | ||||||||
\(71\) | 0.0702735 | 0.00833993 | 0.00416996 | − | 0.999991i | \(-0.498673\pi\) | ||||
0.00416996 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(72\) | 4.36603 | 0.514542 | ||||||||
\(73\) | 10.7002 | 1.25237 | 0.626183 | − | 0.779676i | \(-0.284616\pi\) | ||||
0.626183 | + | 0.779676i | \(0.284616\pi\) | |||||||
\(74\) | −0.583372 | −0.0678156 | ||||||||
\(75\) | 12.3670 | 1.42801 | ||||||||
\(76\) | −14.4891 | −1.66201 | ||||||||
\(77\) | −3.58386 | −0.408419 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.20655 | 0.248257 | 0.124128 | − | 0.992266i | \(-0.460387\pi\) | ||||
0.124128 | + | 0.992266i | \(0.460387\pi\) | |||||||
\(80\) | −4.16123 | −0.465240 | ||||||||
\(81\) | 23.0986 | 2.56651 | ||||||||
\(82\) | −0.155397 | −0.0171608 | ||||||||
\(83\) | 3.82400 | 0.419738 | 0.209869 | − | 0.977730i | \(-0.432696\pi\) | ||||
0.209869 | + | 0.977730i | \(0.432696\pi\) | |||||||
\(84\) | 22.8151 | 2.48933 | ||||||||
\(85\) | 6.22138 | 0.674803 | ||||||||
\(86\) | 0.181438 | 0.0195649 | ||||||||
\(87\) | 11.6727 | 1.25145 | ||||||||
\(88\) | −0.593149 | −0.0632298 | ||||||||
\(89\) | −10.4246 | −1.10501 | −0.552504 | − | 0.833510i | \(-0.686328\pi\) | ||||
−0.552504 | + | 0.833510i | \(0.686328\pi\) | |||||||
\(90\) | 1.18110 | 0.124499 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.3563 | 1.07972 | ||||||||
\(93\) | −8.53299 | −0.884830 | ||||||||
\(94\) | 1.77717 | 0.183301 | ||||||||
\(95\) | −7.88323 | −0.808803 | ||||||||
\(96\) | 5.67458 | 0.579159 | ||||||||
\(97\) | −11.8987 | −1.20813 | −0.604065 | − | 0.796935i | \(-0.706453\pi\) | ||||
−0.604065 | + | 0.796935i | \(0.706453\pi\) | |||||||
\(98\) | −0.871443 | −0.0880291 | ||||||||
\(99\) | −7.36077 | −0.739785 | ||||||||
\(100\) | 7.59874 | 0.759874 | ||||||||
\(101\) | 8.30901 | 0.826778 | 0.413389 | − | 0.910555i | \(-0.364345\pi\) | ||||
0.413389 | + | 0.910555i | \(0.364345\pi\) | |||||||
\(102\) | −2.77503 | −0.274769 | ||||||||
\(103\) | 0.278096 | 0.0274016 | 0.0137008 | − | 0.999906i | \(-0.495639\pi\) | ||||
0.0137008 | + | 0.999906i | \(0.495639\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.4133 | 1.21141 | ||||||||
\(106\) | −0.0216239 | −0.00210030 | ||||||||
\(107\) | −9.10157 | −0.879882 | −0.439941 | − | 0.898027i | \(-0.645001\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(108\) | 27.7609 | 2.67130 | ||||||||
\(109\) | −0.848663 | −0.0812872 | −0.0406436 | − | 0.999174i | \(-0.512941\pi\) | ||||
−0.0406436 | + | 0.999174i | \(0.512941\pi\) | |||||||
\(110\) | −0.160459 | −0.0152991 | ||||||||
\(111\) | −12.5926 | −1.19524 | ||||||||
\(112\) | 13.8591 | 1.30956 | ||||||||
\(113\) | 15.6738 | 1.47446 | 0.737231 | − | 0.675640i | \(-0.236133\pi\) | ||||
0.737231 | + | 0.675640i | \(0.236133\pi\) | |||||||
\(114\) | 3.51630 | 0.329332 | ||||||||
\(115\) | 5.63466 | 0.525435 | ||||||||
\(116\) | 7.17217 | 0.665919 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.351614 | −0.0323687 | ||||||||
\(119\) | −20.7204 | −1.89944 | ||||||||
\(120\) | 2.05446 | 0.187546 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.41168 | −0.127808 | ||||||||
\(123\) | −3.35440 | −0.302456 | ||||||||
\(124\) | −5.24300 | −0.470835 | ||||||||
\(125\) | 9.51466 | 0.851017 | ||||||||
\(126\) | −3.93368 | −0.350440 | ||||||||
\(127\) | −21.4994 | −1.90776 | −0.953882 | − | 0.300183i | \(-0.902952\pi\) | ||||
−0.953882 | + | 0.300183i | \(0.902952\pi\) | |||||||
\(128\) | 4.63997 | 0.410119 | ||||||||
\(129\) | 3.91651 | 0.344829 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2612 | 0.896524 | 0.448262 | − | 0.893902i | \(-0.352043\pi\) | ||||
0.448262 | + | 0.893902i | \(0.352043\pi\) | |||||||
\(132\) | −6.36606 | −0.554094 | ||||||||
\(133\) | 26.2553 | 2.27662 | ||||||||
\(134\) | −0.766487 | −0.0662144 | ||||||||
\(135\) | 15.1042 | 1.29996 | ||||||||
\(136\) | −3.42935 | −0.294064 | ||||||||
\(137\) | 13.7245 | 1.17256 | 0.586282 | − | 0.810107i | \(-0.300591\pi\) | ||||
0.586282 | + | 0.810107i | \(0.300591\pi\) | |||||||
\(138\) | −2.51333 | −0.213949 | ||||||||
\(139\) | −6.42879 | −0.545283 | −0.272642 | − | 0.962116i | \(-0.587897\pi\) | ||||
−0.272642 | + | 0.962116i | \(0.587897\pi\) | |||||||
\(140\) | 7.62719 | 0.644615 | ||||||||
\(141\) | 38.3620 | 3.23066 | ||||||||
\(142\) | −0.0104789 | −0.000879370 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 28.4647 | 2.37206 | ||||||||
\(145\) | 3.90225 | 0.324064 | ||||||||
\(146\) | −1.59557 | −0.132051 | ||||||||
\(147\) | −18.8109 | −1.55150 | ||||||||
\(148\) | −7.73741 | −0.636011 | ||||||||
\(149\) | −3.00186 | −0.245922 | −0.122961 | − | 0.992411i | \(-0.539239\pi\) | ||||
−0.122961 | + | 0.992411i | \(0.539239\pi\) | |||||||
\(150\) | −1.84411 | −0.150571 | ||||||||
\(151\) | 23.4105 | 1.90512 | 0.952560 | − | 0.304352i | \(-0.0984400\pi\) | ||||
0.952560 | + | 0.304352i | \(0.0984400\pi\) | |||||||
\(152\) | 4.34539 | 0.352458 | ||||||||
\(153\) | −42.5570 | −3.44053 | ||||||||
\(154\) | 0.534411 | 0.0430641 | ||||||||
\(155\) | −2.85262 | −0.229128 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1431 | 0.809508 | 0.404754 | − | 0.914426i | \(-0.367357\pi\) | ||||
0.404754 | + | 0.914426i | \(0.367357\pi\) | |||||||
\(158\) | −0.329032 | −0.0261764 | ||||||||
\(159\) | −0.466773 | −0.0370175 | ||||||||
\(160\) | 1.89704 | 0.149974 | ||||||||
\(161\) | −18.7664 | −1.47900 | ||||||||
\(162\) | −3.44438 | −0.270616 | ||||||||
\(163\) | 0.616582 | 0.0482944 | 0.0241472 | − | 0.999708i | \(-0.492313\pi\) | ||||
0.0241472 | + | 0.999708i | \(0.492313\pi\) | |||||||
\(164\) | −2.06108 | −0.160943 | ||||||||
\(165\) | −3.46366 | −0.269645 | ||||||||
\(166\) | −0.570219 | −0.0442576 | ||||||||
\(167\) | −7.60997 | −0.588877 | −0.294439 | − | 0.955670i | \(-0.595133\pi\) | ||||
−0.294439 | + | 0.955670i | \(0.595133\pi\) | |||||||
\(168\) | −6.84243 | −0.527905 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.927707 | −0.0711519 | ||||||||
\(171\) | 53.9249 | 4.12374 | ||||||||
\(172\) | 2.40645 | 0.183490 | ||||||||
\(173\) | 20.9159 | 1.59020 | 0.795102 | − | 0.606475i | \(-0.207417\pi\) | ||||
0.795102 | + | 0.606475i | \(0.207417\pi\) | |||||||
\(174\) | −1.74059 | −0.131954 | ||||||||
\(175\) | −13.7695 | −1.04088 | ||||||||
\(176\) | −3.86708 | −0.291492 | ||||||||
\(177\) | −7.58992 | −0.570494 | ||||||||
\(178\) | 1.55448 | 0.116513 | ||||||||
\(179\) | 12.3488 | 0.922995 | 0.461498 | − | 0.887141i | \(-0.347312\pi\) | ||||
0.461498 | + | 0.887141i | \(0.347312\pi\) | |||||||
\(180\) | 15.6652 | 1.16762 | ||||||||
\(181\) | 4.12806 | 0.306836 | 0.153418 | − | 0.988161i | \(-0.450972\pi\) | ||||
0.153418 | + | 0.988161i | \(0.450972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.4726 | −2.25260 | ||||||||
\(184\) | −3.10594 | −0.228973 | ||||||||
\(185\) | −4.20978 | −0.309509 | ||||||||
\(186\) | 1.27241 | 0.0932973 | ||||||||
\(187\) | 5.78160 | 0.422792 | ||||||||
\(188\) | 23.5711 | 1.71910 | ||||||||
\(189\) | −50.3049 | −3.65914 | ||||||||
\(190\) | 1.17552 | 0.0852809 | ||||||||
\(191\) | 3.93901 | 0.285017 | 0.142508 | − | 0.989794i | \(-0.454483\pi\) | ||||
0.142508 | + | 0.989794i | \(0.454483\pi\) | |||||||
\(192\) | 24.0487 | 1.73556 | ||||||||
\(193\) | 5.12303 | 0.368763 | 0.184382 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184382 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(194\) | 1.77429 | 0.127386 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.5582 | −0.825584 | ||||||||
\(197\) | 5.39700 | 0.384520 | 0.192260 | − | 0.981344i | \(-0.438418\pi\) | ||||
0.192260 | + | 0.981344i | \(0.438418\pi\) | |||||||
\(198\) | 1.09761 | 0.0780037 | ||||||||
\(199\) | −5.09868 | −0.361436 | −0.180718 | − | 0.983535i | \(-0.557842\pi\) | ||||
−0.180718 | + | 0.983535i | \(0.557842\pi\) | |||||||
\(200\) | −2.27893 | −0.161144 | ||||||||
\(201\) | −16.5454 | −1.16702 | ||||||||
\(202\) | −1.23901 | −0.0871762 | ||||||||
\(203\) | −12.9965 | −0.912177 | ||||||||
\(204\) | −36.8060 | −2.57693 | ||||||||
\(205\) | −1.12139 | −0.0783215 | ||||||||
\(206\) | −0.0414686 | −0.00288925 | ||||||||
\(207\) | −38.5436 | −2.67897 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.32598 | −0.506749 | ||||||||
\(210\) | −1.85102 | −0.127732 | ||||||||
\(211\) | −4.67412 | −0.321780 | −0.160890 | − | 0.986972i | \(-0.551436\pi\) | ||||
−0.160890 | + | 0.986972i | \(0.551436\pi\) | |||||||
\(212\) | −0.286804 | −0.0196978 | ||||||||
\(213\) | −0.226197 | −0.0154988 | ||||||||
\(214\) | 1.35719 | 0.0927757 | ||||||||
\(215\) | 1.30931 | 0.0892940 | ||||||||
\(216\) | −8.32574 | −0.566495 | ||||||||
\(217\) | 9.50072 | 0.644951 | ||||||||
\(218\) | 0.126549 | 0.00857100 | ||||||||
\(219\) | −34.4420 | −2.32738 | ||||||||
\(220\) | −2.12820 | −0.143483 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.87777 | 0.126027 | ||||||||
\(223\) | 1.69577 | 0.113557 | 0.0567786 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567786 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(224\) | −6.31814 | −0.422148 | ||||||||
\(225\) | −28.2807 | −1.88538 | ||||||||
\(226\) | −2.33721 | −0.155469 | ||||||||
\(227\) | −14.5217 | −0.963836 | −0.481918 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481918 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(228\) | 46.6376 | 3.08865 | ||||||||
\(229\) | 9.18634 | 0.607050 | 0.303525 | − | 0.952823i | \(-0.401836\pi\) | ||||
0.303525 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(230\) | −0.840218 | −0.0554023 | ||||||||
\(231\) | 11.5358 | 0.758999 | ||||||||
\(232\) | −2.15099 | −0.141220 | ||||||||
\(233\) | 24.6516 | 1.61498 | 0.807491 | − | 0.589880i | \(-0.200825\pi\) | ||||
0.807491 | + | 0.589880i | \(0.200825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8246 | 0.836585 | ||||||||
\(236\) | −4.66354 | −0.303571 | ||||||||
\(237\) | −7.10249 | −0.461356 | ||||||||
\(238\) | 3.08975 | 0.200279 | ||||||||
\(239\) | 7.91543 | 0.512006 | 0.256003 | − | 0.966676i | \(-0.417594\pi\) | ||||
0.256003 | + | 0.966676i | \(0.417594\pi\) | |||||||
\(240\) | 13.3942 | 0.864594 | ||||||||
\(241\) | −24.3689 | −1.56974 | −0.784871 | − | 0.619660i | \(-0.787271\pi\) | ||||
−0.784871 | + | 0.619660i | \(0.787271\pi\) | |||||||
\(242\) | −0.149116 | −0.00958554 | ||||||||
\(243\) | −32.2407 | −2.06824 | ||||||||
\(244\) | −18.7235 | −1.19865 | ||||||||
\(245\) | −6.28859 | −0.401763 | ||||||||
\(246\) | 0.500195 | 0.0318913 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.57242 | 0.0998488 | ||||||||
\(249\) | −12.3087 | −0.780034 | ||||||||
\(250\) | −1.41879 | −0.0897321 | ||||||||
\(251\) | 9.17729 | 0.579265 | 0.289633 | − | 0.957138i | \(-0.406467\pi\) | ||||
0.289633 | + | 0.957138i | \(0.406467\pi\) | |||||||
\(252\) | −52.1734 | −3.28661 | ||||||||
\(253\) | 5.23635 | 0.329207 | ||||||||
\(254\) | 3.20591 | 0.201156 | ||||||||
\(255\) | −20.0255 | −1.25404 | ||||||||
\(256\) | 14.2507 | 0.890666 | ||||||||
\(257\) | 13.4037 | 0.836100 | 0.418050 | − | 0.908424i | \(-0.362714\pi\) | ||||
0.418050 | + | 0.908424i | \(0.362714\pi\) | |||||||
\(258\) | −0.584014 | −0.0363591 | ||||||||
\(259\) | 14.0208 | 0.871209 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.6931 | −1.65226 | ||||||||
\(262\) | −1.53011 | −0.0945303 | ||||||||
\(263\) | −21.9734 | −1.35494 | −0.677468 | − | 0.735552i | \(-0.736923\pi\) | ||||
−0.677468 | + | 0.735552i | \(0.736923\pi\) | |||||||
\(264\) | 1.90924 | 0.117505 | ||||||||
\(265\) | −0.156045 | −0.00958575 | ||||||||
\(266\) | −3.91509 | −0.240049 | ||||||||
\(267\) | 33.5550 | 2.05353 | ||||||||
\(268\) | −10.1661 | −0.620994 | ||||||||
\(269\) | 20.4798 | 1.24868 | 0.624339 | − | 0.781154i | \(-0.285369\pi\) | ||||
0.624339 | + | 0.781154i | \(0.285369\pi\) | |||||||
\(270\) | −2.25228 | −0.137069 | ||||||||
\(271\) | −15.0426 | −0.913775 | −0.456888 | − | 0.889524i | \(-0.651036\pi\) | ||||
−0.456888 | + | 0.889524i | \(0.651036\pi\) | |||||||
\(272\) | −22.3579 | −1.35565 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.04654 | −0.123636 | ||||||||
\(275\) | 3.84208 | 0.231686 | ||||||||
\(276\) | −33.3349 | −2.00653 | ||||||||
\(277\) | −16.4731 | −0.989771 | −0.494886 | − | 0.868958i | \(-0.664790\pi\) | ||||
−0.494886 | + | 0.868958i | \(0.664790\pi\) | |||||||
\(278\) | 0.958636 | 0.0574952 | ||||||||
\(279\) | 19.5132 | 1.16822 | ||||||||
\(280\) | −2.28746 | −0.136702 | ||||||||
\(281\) | −19.0800 | −1.13822 | −0.569109 | − | 0.822262i | \(-0.692712\pi\) | ||||
−0.569109 | + | 0.822262i | \(0.692712\pi\) | |||||||
\(282\) | −5.72039 | −0.340644 | ||||||||
\(283\) | 22.0454 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(284\) | −0.138984 | −0.00824721 | ||||||||
\(285\) | 25.3747 | 1.50307 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.73483 | 0.220460 | ||||||||
\(288\) | −12.9766 | −0.764654 | ||||||||
\(289\) | 16.4268 | 0.966285 | ||||||||
\(290\) | −0.581887 | −0.0341696 | ||||||||
\(291\) | 38.2997 | 2.24517 | ||||||||
\(292\) | −21.1625 | −1.23844 | ||||||||
\(293\) | 22.6759 | 1.32474 | 0.662369 | − | 0.749177i | \(-0.269551\pi\) | ||||
0.662369 | + | 0.749177i | \(0.269551\pi\) | |||||||
\(294\) | 2.80501 | 0.163592 | ||||||||
\(295\) | −2.53735 | −0.147730 | ||||||||
\(296\) | 2.32051 | 0.134877 | ||||||||
\(297\) | 14.0365 | 0.814481 | ||||||||
\(298\) | 0.447626 | 0.0259303 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −24.4589 | −1.41214 | ||||||||
\(301\) | −4.36068 | −0.251345 | ||||||||
\(302\) | −3.49088 | −0.200878 | ||||||||
\(303\) | −26.7452 | −1.53647 | ||||||||
\(304\) | 28.3302 | 1.62485 | ||||||||
\(305\) | −10.1871 | −0.583313 | ||||||||
\(306\) | 6.34593 | 0.362773 | ||||||||
\(307\) | 21.0536 | 1.20159 | 0.600796 | − | 0.799402i | \(-0.294850\pi\) | ||||
0.600796 | + | 0.799402i | \(0.294850\pi\) | |||||||
\(308\) | 7.08803 | 0.403878 | ||||||||
\(309\) | −0.895139 | −0.0509227 | ||||||||
\(310\) | 0.425371 | 0.0241595 | ||||||||
\(311\) | 27.9213 | 1.58327 | 0.791636 | − | 0.610993i | \(-0.209229\pi\) | ||||
0.791636 | + | 0.610993i | \(0.209229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.67710 | 0.264365 | 0.132183 | − | 0.991225i | \(-0.457801\pi\) | ||||
0.132183 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(314\) | −1.51250 | −0.0853554 | ||||||||
\(315\) | −28.3866 | −1.59940 | ||||||||
\(316\) | −4.36404 | −0.245497 | ||||||||
\(317\) | 25.4219 | 1.42784 | 0.713919 | − | 0.700228i | \(-0.246919\pi\) | ||||
0.713919 | + | 0.700228i | \(0.246919\pi\) | |||||||
\(318\) | 0.0696034 | 0.00390317 | ||||||||
\(319\) | 3.62640 | 0.203040 | ||||||||
\(320\) | 8.03959 | 0.449426 | ||||||||
\(321\) | 29.2963 | 1.63516 | ||||||||
\(322\) | 2.79837 | 0.155947 | ||||||||
\(323\) | −42.3559 | −2.35674 | ||||||||
\(324\) | −45.6836 | −2.53798 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0919422 | −0.00509221 | ||||||||
\(327\) | 2.73169 | 0.151063 | ||||||||
\(328\) | 0.618134 | 0.0341307 | ||||||||
\(329\) | −42.7126 | −2.35482 | ||||||||
\(330\) | 0.516487 | 0.0284317 | ||||||||
\(331\) | −31.0792 | −1.70827 | −0.854133 | − | 0.520054i | \(-0.825912\pi\) | ||||
−0.854133 | + | 0.520054i | \(0.825912\pi\) | |||||||
\(332\) | −7.56296 | −0.415072 | ||||||||
\(333\) | 28.7968 | 1.57805 | ||||||||
\(334\) | 1.13477 | 0.0620918 | ||||||||
\(335\) | −5.53119 | −0.302201 | ||||||||
\(336\) | −44.6098 | −2.43367 | ||||||||
\(337\) | −11.1008 | −0.604698 | −0.302349 | − | 0.953197i | \(-0.597771\pi\) | ||||
−0.302349 | + | 0.953197i | \(0.597771\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50.4509 | −2.74012 | ||||||||
\(340\) | −12.3044 | −0.667301 | ||||||||
\(341\) | −2.65097 | −0.143558 | ||||||||
\(342\) | −8.04106 | −0.434811 | ||||||||
\(343\) | −4.14273 | −0.223686 | ||||||||
\(344\) | −0.721716 | −0.0389123 | ||||||||
\(345\) | −18.1369 | −0.976459 | ||||||||
\(346\) | −3.11889 | −0.167673 | ||||||||
\(347\) | 4.83227 | 0.259410 | 0.129705 | − | 0.991553i | \(-0.458597\pi\) | ||||
0.129705 | + | 0.991553i | \(0.458597\pi\) | |||||||
\(348\) | −23.0859 | −1.23753 | ||||||||
\(349\) | 6.80301 | 0.364157 | 0.182078 | − | 0.983284i | \(-0.441718\pi\) | ||||
0.182078 | + | 0.983284i | \(0.441718\pi\) | |||||||
\(350\) | 2.05325 | 0.109751 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.76294 | 0.0939651 | ||||||||
\(353\) | 26.6753 | 1.41978 | 0.709892 | − | 0.704310i | \(-0.248744\pi\) | ||||
0.709892 | + | 0.704310i | \(0.248744\pi\) | |||||||
\(354\) | 1.13178 | 0.0601534 | ||||||||
\(355\) | −0.0756189 | −0.00401343 | ||||||||
\(356\) | 20.6175 | 1.09272 | ||||||||
\(357\) | 66.6953 | 3.52989 | ||||||||
\(358\) | −1.84141 | −0.0973215 | ||||||||
\(359\) | 16.3829 | 0.864657 | 0.432329 | − | 0.901716i | \(-0.357692\pi\) | ||||
0.432329 | + | 0.901716i | \(0.357692\pi\) | |||||||
\(360\) | −4.69813 | −0.247613 | ||||||||
\(361\) | 34.6700 | 1.82474 | ||||||||
\(362\) | −0.615560 | −0.0323531 | ||||||||
\(363\) | −3.21882 | −0.168944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.5141 | −0.602678 | ||||||||
\(366\) | 4.54395 | 0.237516 | ||||||||
\(367\) | −11.0696 | −0.577830 | −0.288915 | − | 0.957355i | \(-0.593294\pi\) | ||||
−0.288915 | + | 0.957355i | \(0.593294\pi\) | |||||||
\(368\) | −20.2494 | −1.05557 | ||||||||
\(369\) | 7.67083 | 0.399328 | ||||||||
\(370\) | 0.627746 | 0.0326350 | ||||||||
\(371\) | 0.519710 | 0.0269820 | ||||||||
\(372\) | 16.8762 | 0.874993 | ||||||||
\(373\) | −20.2838 | −1.05026 | −0.525128 | − | 0.851023i | \(-0.675982\pi\) | ||||
−0.525128 | + | 0.851023i | \(0.675982\pi\) | |||||||
\(374\) | −0.862129 | −0.0445796 | ||||||||
\(375\) | −30.6259 | −1.58152 | ||||||||
\(376\) | −7.06917 | −0.364565 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7.50127 | 0.385824 | ||||||||
\(379\) | −21.9402 | −1.12699 | −0.563496 | − | 0.826119i | \(-0.690544\pi\) | ||||
−0.563496 | + | 0.826119i | \(0.690544\pi\) | |||||||
\(380\) | 15.5912 | 0.799811 | ||||||||
\(381\) | 69.2026 | 3.54536 | ||||||||
\(382\) | −0.587369 | −0.0300524 | ||||||||
\(383\) | 25.2157 | 1.28846 | 0.644230 | − | 0.764832i | \(-0.277178\pi\) | ||||
0.644230 | + | 0.764832i | \(0.277178\pi\) | |||||||
\(384\) | −14.9352 | −0.762159 | ||||||||
\(385\) | 3.85647 | 0.196544 | ||||||||
\(386\) | −0.763925 | −0.0388828 | ||||||||
\(387\) | −8.95625 | −0.455272 | ||||||||
\(388\) | 23.5328 | 1.19470 | ||||||||
\(389\) | −10.8999 | −0.552649 | −0.276324 | − | 0.961064i | \(-0.589116\pi\) | ||||
−0.276324 | + | 0.961064i | \(0.589116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.2745 | 1.53105 | ||||||||
\(392\) | 3.46640 | 0.175079 | ||||||||
\(393\) | −33.0289 | −1.66609 | ||||||||
\(394\) | −0.804779 | −0.0405442 | ||||||||
\(395\) | −2.37440 | −0.119469 | ||||||||
\(396\) | 14.5579 | 0.731560 | ||||||||
\(397\) | 31.5621 | 1.58405 | 0.792027 | − | 0.610486i | \(-0.209026\pi\) | ||||
0.792027 | + | 0.610486i | \(0.209026\pi\) | |||||||
\(398\) | 0.760295 | 0.0381102 | ||||||||
\(399\) | −84.5109 | −4.23084 | ||||||||
\(400\) | −14.8576 | −0.742882 | ||||||||
\(401\) | 33.6361 | 1.67971 | 0.839854 | − | 0.542812i | \(-0.182640\pi\) | ||||
0.839854 | + | 0.542812i | \(0.182640\pi\) | |||||||
\(402\) | 2.46718 | 0.123052 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −16.4333 | −0.817586 | ||||||||
\(405\) | −24.8556 | −1.23509 | ||||||||
\(406\) | 1.93799 | 0.0961808 | ||||||||
\(407\) | −3.91220 | −0.193920 | ||||||||
\(408\) | 11.0384 | 0.546484 | ||||||||
\(409\) | 29.0107 | 1.43449 | 0.717244 | − | 0.696822i | \(-0.245403\pi\) | ||||
0.717244 | + | 0.696822i | \(0.245403\pi\) | |||||||
\(410\) | 0.167218 | 0.00825830 | ||||||||
\(411\) | −44.1767 | −2.17907 | ||||||||
\(412\) | −0.550008 | −0.0270970 | ||||||||
\(413\) | 8.45070 | 0.415832 | ||||||||
\(414\) | 5.74747 | 0.282473 | ||||||||
\(415\) | −4.11487 | −0.201991 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.6931 | 1.01335 | ||||||||
\(418\) | 1.09242 | 0.0534321 | ||||||||
\(419\) | 16.9025 | 0.825743 | 0.412871 | − | 0.910789i | \(-0.364526\pi\) | ||||
0.412871 | + | 0.910789i | \(0.364526\pi\) | |||||||
\(420\) | −24.5505 | −1.19794 | ||||||||
\(421\) | 9.39424 | 0.457847 | 0.228924 | − | 0.973444i | \(-0.426479\pi\) | ||||
0.228924 | + | 0.973444i | \(0.426479\pi\) | |||||||
\(422\) | 0.696987 | 0.0339288 | ||||||||
\(423\) | −87.7260 | −4.26538 | ||||||||
\(424\) | 0.0860149 | 0.00417725 | ||||||||
\(425\) | 22.2134 | 1.07751 | ||||||||
\(426\) | 0.0337297 | 0.00163421 | ||||||||
\(427\) | 33.9285 | 1.64191 | ||||||||
\(428\) | 18.0008 | 0.870100 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.195239 | −0.00941524 | ||||||||
\(431\) | −5.72759 | −0.275888 | −0.137944 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137944 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(432\) | −54.2803 | −2.61156 | ||||||||
\(433\) | 19.2956 | 0.927289 | 0.463644 | − | 0.886021i | \(-0.346542\pi\) | ||||
0.463644 | + | 0.886021i | \(0.346542\pi\) | |||||||
\(434\) | −1.41671 | −0.0680042 | ||||||||
\(435\) | −12.5606 | −0.602235 | ||||||||
\(436\) | 1.67846 | 0.0803834 | ||||||||
\(437\) | −38.3614 | −1.83508 | ||||||||
\(438\) | 5.13586 | 0.245401 | ||||||||
\(439\) | 24.0666 | 1.14864 | 0.574318 | − | 0.818632i | \(-0.305267\pi\) | ||||
0.574318 | + | 0.818632i | \(0.305267\pi\) | |||||||
\(440\) | 0.638267 | 0.0304282 | ||||||||
\(441\) | 43.0168 | 2.04842 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.19960 | −0.199529 | −0.0997646 | − | 0.995011i | \(-0.531809\pi\) | ||||
−0.0997646 | + | 0.995011i | \(0.531809\pi\) | |||||||
\(444\) | 24.9053 | 1.18195 | ||||||||
\(445\) | 11.2176 | 0.531764 | ||||||||
\(446\) | −0.252866 | −0.0119736 | ||||||||
\(447\) | 9.66244 | 0.457018 | ||||||||
\(448\) | −26.7760 | −1.26505 | ||||||||
\(449\) | 8.18012 | 0.386044 | 0.193022 | − | 0.981194i | \(-0.438171\pi\) | ||||
0.193022 | + | 0.981194i | \(0.438171\pi\) | |||||||
\(450\) | 4.21711 | 0.198796 | ||||||||
\(451\) | −1.04212 | −0.0490717 | ||||||||
\(452\) | −30.9990 | −1.45807 | ||||||||
\(453\) | −75.3541 | −3.54044 | ||||||||
\(454\) | 2.16541 | 0.101628 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.9870 | −0.655002 | ||||||||
\(457\) | −17.6613 | −0.826160 | −0.413080 | − | 0.910695i | \(-0.635547\pi\) | ||||
−0.413080 | + | 0.910695i | \(0.635547\pi\) | |||||||
\(458\) | −1.36983 | −0.0640080 | ||||||||
\(459\) | 81.1534 | 3.78792 | ||||||||
\(460\) | −11.1440 | −0.519593 | ||||||||
\(461\) | 34.4679 | 1.60533 | 0.802666 | − | 0.596429i | \(-0.203414\pi\) | ||||
0.802666 | + | 0.596429i | \(0.203414\pi\) | |||||||
\(462\) | −1.72017 | −0.0800296 | ||||||||
\(463\) | 0.882146 | 0.0409968 | 0.0204984 | − | 0.999790i | \(-0.493475\pi\) | ||||
0.0204984 | + | 0.999790i | \(0.493475\pi\) | |||||||
\(464\) | −14.0236 | −0.651029 | ||||||||
\(465\) | 9.18206 | 0.425808 | ||||||||
\(466\) | −3.67595 | −0.170285 | ||||||||
\(467\) | −21.6018 | −0.999612 | −0.499806 | − | 0.866137i | \(-0.666595\pi\) | ||||
−0.499806 | + | 0.866137i | \(0.666595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.4218 | 0.850638 | ||||||||
\(470\) | −1.91235 | −0.0882103 | ||||||||
\(471\) | −32.6488 | −1.50438 | ||||||||
\(472\) | 1.39864 | 0.0643775 | ||||||||
\(473\) | 1.21675 | 0.0559464 | ||||||||
\(474\) | 1.05909 | 0.0486458 | ||||||||
\(475\) | −28.1470 | −1.29147 | ||||||||
\(476\) | 40.9801 | 1.87832 | ||||||||
\(477\) | 1.06742 | 0.0488736 | ||||||||
\(478\) | −1.18032 | −0.0539865 | ||||||||
\(479\) | −6.49086 | −0.296575 | −0.148287 | − | 0.988944i | \(-0.547376\pi\) | ||||
−0.148287 | + | 0.988944i | \(0.547376\pi\) | |||||||
\(480\) | −6.10622 | −0.278710 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.63380 | 0.165515 | ||||||||
\(483\) | 60.4055 | 2.74854 | ||||||||
\(484\) | −1.97776 | −0.0898984 | ||||||||
\(485\) | 12.8038 | 0.581390 | ||||||||
\(486\) | 4.80760 | 0.218077 | ||||||||
\(487\) | 10.8211 | 0.490353 | 0.245176 | − | 0.969479i | \(-0.421154\pi\) | ||||
0.245176 | + | 0.969479i | \(0.421154\pi\) | |||||||
\(488\) | 5.61534 | 0.254195 | ||||||||
\(489\) | −1.98466 | −0.0897496 | ||||||||
\(490\) | 0.937730 | 0.0423623 | ||||||||
\(491\) | 11.3336 | 0.511480 | 0.255740 | − | 0.966746i | \(-0.417681\pi\) | ||||
0.255740 | + | 0.966746i | \(0.417681\pi\) | |||||||
\(492\) | 6.63422 | 0.299094 | ||||||||
\(493\) | 20.9664 | 0.944279 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.92067 | 0.356008 | ||||||||
\(496\) | 10.2515 | 0.460307 | ||||||||
\(497\) | 0.251850 | 0.0112970 | ||||||||
\(498\) | 1.83543 | 0.0822476 | ||||||||
\(499\) | 16.4178 | 0.734961 | 0.367481 | − | 0.930031i | \(-0.380220\pi\) | ||||
0.367481 | + | 0.930031i | \(0.380220\pi\) | |||||||
\(500\) | −18.8178 | −0.841556 | ||||||||
\(501\) | 24.4951 | 1.09436 | ||||||||
\(502\) | −1.36848 | −0.0610783 | ||||||||
\(503\) | −30.5761 | −1.36332 | −0.681661 | − | 0.731668i | \(-0.738742\pi\) | ||||
−0.681661 | + | 0.731668i | \(0.738742\pi\) | |||||||
\(504\) | 15.6472 | 0.696984 | ||||||||
\(505\) | −8.94104 | −0.397871 | ||||||||
\(506\) | −0.780824 | −0.0347119 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 42.5207 | 1.88655 | ||||||||
\(509\) | 21.3391 | 0.945840 | 0.472920 | − | 0.881105i | \(-0.343200\pi\) | ||||
0.472920 | + | 0.881105i | \(0.343200\pi\) | |||||||
\(510\) | 2.98612 | 0.132227 | ||||||||
\(511\) | 38.3481 | 1.69642 | ||||||||
\(512\) | −11.4049 | −0.504032 | ||||||||
\(513\) | −102.831 | −4.54011 | ||||||||
\(514\) | −1.99871 | −0.0881592 | ||||||||
\(515\) | −0.299249 | −0.0131865 | ||||||||
\(516\) | −7.74593 | −0.340995 | ||||||||
\(517\) | 11.9180 | 0.524155 | ||||||||
\(518\) | −2.09072 | −0.0918611 | ||||||||
\(519\) | −67.3243 | −2.95521 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.2230 | −0.842175 | −0.421087 | − | 0.907020i | \(-0.638351\pi\) | ||||
−0.421087 | + | 0.907020i | \(0.638351\pi\) | |||||||
\(522\) | 3.98037 | 0.174216 | ||||||||
\(523\) | −17.2005 | −0.752127 | −0.376063 | − | 0.926594i | \(-0.622723\pi\) | ||||
−0.376063 | + | 0.926594i | \(0.622723\pi\) | |||||||
\(524\) | −20.2942 | −0.886556 | ||||||||
\(525\) | 44.3214 | 1.93435 | ||||||||
\(526\) | 3.27658 | 0.142866 | ||||||||
\(527\) | −15.3269 | −0.667648 | ||||||||
\(528\) | 12.4474 | 0.541704 | ||||||||
\(529\) | 4.41940 | 0.192148 | ||||||||
\(530\) | 0.0232688 | 0.00101073 | ||||||||
\(531\) | 17.3566 | 0.753212 | ||||||||
\(532\) | −51.9268 | −2.25131 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.00358 | −0.216526 | ||||||||
\(535\) | 9.79389 | 0.423427 | ||||||||
\(536\) | 3.04890 | 0.131693 | ||||||||
\(537\) | −39.7486 | −1.71528 | ||||||||
\(538\) | −3.05387 | −0.131662 | ||||||||
\(539\) | −5.84406 | −0.251722 | ||||||||
\(540\) | −29.8726 | −1.28551 | ||||||||
\(541\) | 7.08996 | 0.304821 | 0.152411 | − | 0.988317i | \(-0.451296\pi\) | ||||
0.152411 | + | 0.988317i | \(0.451296\pi\) | |||||||
\(542\) | 2.24310 | 0.0963493 | ||||||||
\(543\) | −13.2875 | −0.570220 | ||||||||
\(544\) | 10.1926 | 0.437005 | ||||||||
\(545\) | 0.913217 | 0.0391179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7944 | 1.61597 | 0.807986 | − | 0.589202i | \(-0.200558\pi\) | ||||
0.807986 | + | 0.589202i | \(0.200558\pi\) | |||||||
\(548\) | −27.1438 | −1.15953 | ||||||||
\(549\) | 69.6845 | 2.97406 | ||||||||
\(550\) | −0.572916 | −0.0244292 | ||||||||
\(551\) | −26.5669 | −1.13179 | ||||||||
\(552\) | 9.99743 | 0.425519 | ||||||||
\(553\) | 7.90798 | 0.336282 | ||||||||
\(554\) | 2.45640 | 0.104362 | ||||||||
\(555\) | 13.5505 | 0.575187 | ||||||||
\(556\) | 12.7146 | 0.539221 | ||||||||
\(557\) | −37.9585 | −1.60835 | −0.804176 | − | 0.594391i | \(-0.797393\pi\) | ||||
−0.804176 | + | 0.594391i | \(0.797393\pi\) | |||||||
\(558\) | −2.90973 | −0.123179 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −14.9133 | −0.630201 | ||||||||
\(561\) | −18.6099 | −0.785710 | ||||||||
\(562\) | 2.84514 | 0.120015 | ||||||||
\(563\) | 4.28580 | 0.180625 | 0.0903125 | − | 0.995913i | \(-0.471213\pi\) | ||||
0.0903125 | + | 0.995913i | \(0.471213\pi\) | |||||||
\(564\) | −75.8710 | −3.19474 | ||||||||
\(565\) | −16.8660 | −0.709557 | ||||||||
\(566\) | −3.28732 | −0.138177 | ||||||||
\(567\) | 82.7823 | 3.47653 | ||||||||
\(568\) | 0.0416826 | 0.00174896 | ||||||||
\(569\) | −28.5526 | −1.19699 | −0.598493 | − | 0.801128i | \(-0.704234\pi\) | ||||
−0.598493 | + | 0.801128i | \(0.704234\pi\) | |||||||
\(570\) | −3.78377 | −0.158485 | ||||||||
\(571\) | 12.3136 | 0.515310 | 0.257655 | − | 0.966237i | \(-0.417050\pi\) | ||||
0.257655 | + | 0.966237i | \(0.417050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6789 | −0.529670 | ||||||||
\(574\) | −0.556923 | −0.0232455 | ||||||||
\(575\) | 20.1185 | 0.839000 | ||||||||
\(576\) | −54.9944 | −2.29143 | ||||||||
\(577\) | −16.5468 | −0.688854 | −0.344427 | − | 0.938813i | \(-0.611927\pi\) | ||||
−0.344427 | + | 0.938813i | \(0.611927\pi\) | |||||||
\(578\) | −2.44951 | −0.101886 | ||||||||
\(579\) | −16.4901 | −0.685304 | ||||||||
\(580\) | −7.71772 | −0.320461 | ||||||||
\(581\) | 13.7047 | 0.568566 | ||||||||
\(582\) | −5.71110 | −0.236733 | ||||||||
\(583\) | −0.145014 | −0.00600587 | ||||||||
\(584\) | 6.34682 | 0.262633 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.38134 | −0.139682 | ||||||||
\(587\) | −28.2129 | −1.16447 | −0.582235 | − | 0.813021i | \(-0.697822\pi\) | ||||
−0.582235 | + | 0.813021i | \(0.697822\pi\) | |||||||
\(588\) | 37.2036 | 1.53425 | ||||||||
\(589\) | 19.4210 | 0.800227 | ||||||||
\(590\) | 0.378359 | 0.0155768 | ||||||||
\(591\) | −17.3719 | −0.714586 | ||||||||
\(592\) | 15.1288 | 0.621789 | ||||||||
\(593\) | 32.5980 | 1.33864 | 0.669320 | − | 0.742974i | \(-0.266586\pi\) | ||||
0.669320 | + | 0.742974i | \(0.266586\pi\) | |||||||
\(594\) | −2.09307 | −0.0858797 | ||||||||
\(595\) | 22.2965 | 0.914069 | ||||||||
\(596\) | 5.93698 | 0.243188 | ||||||||
\(597\) | 16.4117 | 0.671687 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.75703 | 0.398661 | 0.199331 | − | 0.979932i | \(-0.436123\pi\) | ||||
0.199331 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(600\) | 7.33544 | 0.299468 | ||||||||
\(601\) | 21.9155 | 0.893950 | 0.446975 | − | 0.894546i | \(-0.352501\pi\) | ||||
0.446975 | + | 0.894546i | \(0.352501\pi\) | |||||||
\(602\) | 0.650247 | 0.0265021 | ||||||||
\(603\) | 37.8358 | 1.54079 | ||||||||
\(604\) | −46.3004 | −1.88394 | ||||||||
\(605\) | −1.07607 | −0.0437483 | ||||||||
\(606\) | 3.98814 | 0.162007 | ||||||||
\(607\) | 35.3675 | 1.43552 | 0.717762 | − | 0.696289i | \(-0.245167\pi\) | ||||
0.717762 | + | 0.696289i | \(0.245167\pi\) | |||||||
\(608\) | −12.9153 | −0.523783 | ||||||||
\(609\) | 41.8334 | 1.69517 | ||||||||
\(610\) | 1.51906 | 0.0615051 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 84.1677 | 3.40228 | ||||||||
\(613\) | −29.9389 | −1.20922 | −0.604611 | − | 0.796521i | \(-0.706672\pi\) | ||||
−0.604611 | + | 0.796521i | \(0.706672\pi\) | |||||||
\(614\) | −3.13943 | −0.126697 | ||||||||
\(615\) | 3.60956 | 0.145551 | ||||||||
\(616\) | −2.12576 | −0.0856494 | ||||||||
\(617\) | 12.1838 | 0.490499 | 0.245250 | − | 0.969460i | \(-0.421130\pi\) | ||||
0.245250 | + | 0.969460i | \(0.421130\pi\) | |||||||
\(618\) | 0.133480 | 0.00536934 | ||||||||
\(619\) | 15.3580 | 0.617288 | 0.308644 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308644 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(620\) | 5.64181 | 0.226581 | ||||||||
\(621\) | 73.5001 | 2.94946 | ||||||||
\(622\) | −4.16352 | −0.166942 | ||||||||
\(623\) | −37.3604 | −1.49681 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.97202 | 0.358881 | ||||||||
\(626\) | −0.697430 | −0.0278749 | ||||||||
\(627\) | 23.5810 | 0.941733 | ||||||||
\(628\) | −20.0607 | −0.800508 | ||||||||
\(629\) | −22.6187 | −0.901869 | ||||||||
\(630\) | 4.23290 | 0.168643 | ||||||||
\(631\) | −40.1765 | −1.59940 | −0.799701 | − | 0.600398i | \(-0.795009\pi\) | ||||
−0.799701 | + | 0.600398i | \(0.795009\pi\) | |||||||
\(632\) | 1.30881 | 0.0520618 | ||||||||
\(633\) | 15.0451 | 0.597990 | ||||||||
\(634\) | −3.79082 | −0.150553 | ||||||||
\(635\) | 23.1348 | 0.918075 | ||||||||
\(636\) | 0.923168 | 0.0366060 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.540755 | −0.0214087 | ||||||||
\(639\) | 0.517267 | 0.0204628 | ||||||||
\(640\) | −4.99291 | −0.197362 | ||||||||
\(641\) | −12.9238 | −0.510458 | −0.255229 | − | 0.966881i | \(-0.582151\pi\) | ||||
−0.255229 | + | 0.966881i | \(0.582151\pi\) | |||||||
\(642\) | −4.36855 | −0.172413 | ||||||||
\(643\) | −30.9303 | −1.21977 | −0.609885 | − | 0.792490i | \(-0.708784\pi\) | ||||
−0.609885 | + | 0.792490i | \(0.708784\pi\) | |||||||
\(644\) | 37.1154 | 1.46255 | ||||||||
\(645\) | −4.21442 | −0.165942 | ||||||||
\(646\) | 6.31594 | 0.248497 | ||||||||
\(647\) | 20.0880 | 0.789740 | 0.394870 | − | 0.918737i | \(-0.370790\pi\) | ||||
0.394870 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(648\) | 13.7009 | 0.538223 | ||||||||
\(649\) | −2.35799 | −0.0925591 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.5811 | −1.19857 | ||||||||
\(652\) | −1.21945 | −0.0477575 | ||||||||
\(653\) | 28.1012 | 1.09968 | 0.549842 | − | 0.835269i | \(-0.314688\pi\) | ||||
0.549842 | + | 0.835269i | \(0.314688\pi\) | |||||||
\(654\) | −0.407339 | −0.0159282 | ||||||||
\(655\) | −11.0417 | −0.431435 | ||||||||
\(656\) | 4.02998 | 0.157344 | ||||||||
\(657\) | 78.7619 | 3.07279 | ||||||||
\(658\) | 6.36914 | 0.248295 | ||||||||
\(659\) | −26.3236 | −1.02542 | −0.512711 | − | 0.858561i | \(-0.671359\pi\) | ||||
−0.512711 | + | 0.858561i | \(0.671359\pi\) | |||||||
\(660\) | 6.85029 | 0.266647 | ||||||||
\(661\) | −9.22306 | −0.358735 | −0.179368 | − | 0.983782i | \(-0.557405\pi\) | ||||
−0.179368 | + | 0.983782i | \(0.557405\pi\) | |||||||
\(662\) | 4.63441 | 0.180121 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.26820 | 0.0880231 | ||||||||
\(665\) | −28.2524 | −1.09558 | ||||||||
\(666\) | −4.29406 | −0.166392 | ||||||||
\(667\) | 18.9891 | 0.735262 | ||||||||
\(668\) | 15.0507 | 0.582330 | ||||||||
\(669\) | −5.45837 | −0.211033 | ||||||||
\(670\) | 0.824790 | 0.0318644 | ||||||||
\(671\) | −9.46701 | −0.365470 | ||||||||
\(672\) | 20.3369 | 0.784513 | ||||||||
\(673\) | 2.33710 | 0.0900884 | 0.0450442 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450442 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(674\) | 1.65530 | 0.0637600 | ||||||||
\(675\) | 53.9294 | 2.07575 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.49884 | 0.0960382 | 0.0480191 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480191 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(678\) | 7.52304 | 0.288921 | ||||||||
\(679\) | −42.6433 | −1.63650 | ||||||||
\(680\) | 3.69020 | 0.141513 | ||||||||
\(681\) | 46.7425 | 1.79118 | ||||||||
\(682\) | 0.395303 | 0.0151369 | ||||||||
\(683\) | −47.0092 | −1.79876 | −0.899379 | − | 0.437170i | \(-0.855981\pi\) | ||||
−0.899379 | + | 0.437170i | \(0.855981\pi\) | |||||||
\(684\) | −106.651 | −4.07789 | ||||||||
\(685\) | −14.7685 | −0.564274 | ||||||||
\(686\) | 0.617747 | 0.0235857 | ||||||||
\(687\) | −29.5691 | −1.12813 | ||||||||
\(688\) | −4.70529 | −0.179387 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.70451 | 0.102959 | ||||||||
\(691\) | 43.9719 | 1.67277 | 0.836385 | − | 0.548143i | \(-0.184665\pi\) | ||||
0.836385 | + | 0.548143i | \(0.184665\pi\) | |||||||
\(692\) | −41.3667 | −1.57253 | ||||||||
\(693\) | −26.3800 | −1.00209 | ||||||||
\(694\) | −0.720569 | −0.0273524 | ||||||||
\(695\) | 6.91780 | 0.262407 | ||||||||
\(696\) | 6.92365 | 0.262440 | ||||||||
\(697\) | −6.02514 | −0.228218 | ||||||||
\(698\) | −1.01444 | −0.0383970 | ||||||||
\(699\) | −79.3490 | −3.00125 | ||||||||
\(700\) | 27.2328 | 1.02930 | ||||||||
\(701\) | 8.08400 | 0.305328 | 0.152664 | − | 0.988278i | \(-0.451215\pi\) | ||||
0.152664 | + | 0.988278i | \(0.451215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.6607 | 1.08096 | ||||||||
\(704\) | 7.47128 | 0.281584 | ||||||||
\(705\) | −41.2800 | −1.55470 | ||||||||
\(706\) | −3.97772 | −0.149703 | ||||||||
\(707\) | 29.7783 | 1.11993 | ||||||||
\(708\) | 15.0111 | 0.564151 | ||||||||
\(709\) | −23.1084 | −0.867855 | −0.433927 | − | 0.900948i | \(-0.642873\pi\) | ||||
−0.433927 | + | 0.900948i | \(0.642873\pi\) | |||||||
\(710\) | 0.0112760 | 0.000423180 0 | ||||||||
\(711\) | 16.2419 | 0.609120 | ||||||||
\(712\) | −6.18335 | −0.231731 | ||||||||
\(713\) | −13.8814 | −0.519864 | ||||||||
\(714\) | −9.94533 | −0.372195 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.4231 | −0.912734 | ||||||||
\(717\) | −25.4783 | −0.951504 | ||||||||
\(718\) | −2.44296 | −0.0911703 | ||||||||
\(719\) | −0.262823 | −0.00980164 | −0.00490082 | − | 0.999988i | \(-0.501560\pi\) | ||||
−0.00490082 | + | 0.999988i | \(0.501560\pi\) | |||||||
\(720\) | −30.6299 | −1.14151 | ||||||||
\(721\) | 0.996657 | 0.0371174 | ||||||||
\(722\) | −5.16985 | −0.192402 | ||||||||
\(723\) | 78.4391 | 2.91718 | ||||||||
\(724\) | −8.16433 | −0.303425 | ||||||||
\(725\) | 13.9329 | 0.517456 | ||||||||
\(726\) | 0.479977 | 0.0178136 | ||||||||
\(727\) | −33.8486 | −1.25537 | −0.627687 | − | 0.778466i | \(-0.715998\pi\) | ||||
−0.627687 | + | 0.778466i | \(0.715998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.4809 | 1.27707 | ||||||||
\(730\) | 1.71694 | 0.0635469 | ||||||||
\(731\) | 7.03478 | 0.260191 | ||||||||
\(732\) | 60.2675 | 2.22755 | ||||||||
\(733\) | −34.3896 | −1.27021 | −0.635105 | − | 0.772426i | \(-0.719043\pi\) | ||||
−0.635105 | + | 0.772426i | \(0.719043\pi\) | |||||||
\(734\) | 1.65066 | 0.0609269 | ||||||||
\(735\) | 20.2418 | 0.746631 | ||||||||
\(736\) | 9.23138 | 0.340273 | ||||||||
\(737\) | −5.14020 | −0.189342 | ||||||||
\(738\) | −1.14384 | −0.0421055 | ||||||||
\(739\) | 39.6452 | 1.45837 | 0.729186 | − | 0.684315i | \(-0.239899\pi\) | ||||
0.729186 | + | 0.684315i | \(0.239899\pi\) | |||||||
\(740\) | 8.32596 | 0.306068 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.0774972 | −0.00284501 | ||||||||
\(743\) | −0.204133 | −0.00748891 | −0.00374445 | − | 0.999993i | \(-0.501192\pi\) | ||||
−0.00374445 | + | 0.999993i | \(0.501192\pi\) | |||||||
\(744\) | −5.06133 | −0.185557 | ||||||||
\(745\) | 3.23020 | 0.118345 | ||||||||
\(746\) | 3.02464 | 0.110740 | ||||||||
\(747\) | 28.1476 | 1.02987 | ||||||||
\(748\) | −11.4346 | −0.418092 | ||||||||
\(749\) | −32.6188 | −1.19186 | ||||||||
\(750\) | 4.56682 | 0.166757 | ||||||||
\(751\) | −19.3915 | −0.707605 | −0.353802 | − | 0.935320i | \(-0.615111\pi\) | ||||
−0.353802 | + | 0.935320i | \(0.615111\pi\) | |||||||
\(752\) | −46.0881 | −1.68066 | ||||||||
\(753\) | −29.5400 | −1.07650 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.1912 | −0.916803 | ||||||||
\(756\) | 99.4913 | 3.61846 | ||||||||
\(757\) | 17.5291 | 0.637107 | 0.318553 | − | 0.947905i | \(-0.396803\pi\) | ||||
0.318553 | + | 0.947905i | \(0.396803\pi\) | |||||||
\(758\) | 3.27163 | 0.118831 | ||||||||
\(759\) | −16.8549 | −0.611792 | ||||||||
\(760\) | −4.67593 | −0.169614 | ||||||||
\(761\) | 10.7721 | 0.390487 | 0.195244 | − | 0.980755i | \(-0.437450\pi\) | ||||
0.195244 | + | 0.980755i | \(0.437450\pi\) | |||||||
\(762\) | −10.3192 | −0.373826 | ||||||||
\(763\) | −3.04149 | −0.110109 | ||||||||
\(764\) | −7.79043 | −0.281848 | ||||||||
\(765\) | 45.7941 | 1.65569 | ||||||||
\(766\) | −3.76006 | −0.135857 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −45.8703 | −1.65520 | ||||||||
\(769\) | 12.9519 | 0.467059 | 0.233530 | − | 0.972350i | \(-0.424972\pi\) | ||||
0.233530 | + | 0.972350i | \(0.424972\pi\) | |||||||
\(770\) | −0.575061 | −0.0207238 | ||||||||
\(771\) | −43.1440 | −1.55379 | ||||||||
\(772\) | −10.1321 | −0.364664 | ||||||||
\(773\) | 19.3529 | 0.696077 | 0.348038 | − | 0.937480i | \(-0.386848\pi\) | ||||
0.348038 | + | 0.937480i | \(0.386848\pi\) | |||||||
\(774\) | 1.33552 | 0.0480043 | ||||||||
\(775\) | −10.1853 | −0.365865 | ||||||||
\(776\) | −7.05770 | −0.253357 | ||||||||
\(777\) | −45.1303 | −1.61904 | ||||||||
\(778\) | 1.62536 | 0.0582718 | ||||||||
\(779\) | 7.63458 | 0.273537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0702735 | −0.00251458 | ||||||||
\(782\) | −4.51441 | −0.161435 | ||||||||
\(783\) | 50.9020 | 1.81909 | ||||||||
\(784\) | 22.5995 | 0.807123 | ||||||||
\(785\) | −10.9147 | −0.389561 | ||||||||
\(786\) | 4.92513 | 0.175674 | ||||||||
\(787\) | −21.6840 | −0.772952 | −0.386476 | − | 0.922300i | \(-0.626308\pi\) | ||||
−0.386476 | + | 0.922300i | \(0.626308\pi\) | |||||||
\(788\) | −10.6740 | −0.380245 | ||||||||
\(789\) | 70.7282 | 2.51799 | ||||||||
\(790\) | 0.354060 | 0.0125969 | ||||||||
\(791\) | 56.1726 | 1.99727 | ||||||||
\(792\) | −4.36603 | −0.155140 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.70641 | −0.167024 | ||||||||
\(795\) | 0.502279 | 0.0178140 | ||||||||
\(796\) | 10.0840 | 0.357418 | ||||||||
\(797\) | −2.75951 | −0.0977470 | −0.0488735 | − | 0.998805i | \(-0.515563\pi\) | ||||
−0.0488735 | + | 0.998805i | \(0.515563\pi\) | |||||||
\(798\) | 12.6019 | 0.446104 | ||||||||
\(799\) | 68.9053 | 2.43770 | ||||||||
\(800\) | 6.77337 | 0.239475 | ||||||||
\(801\) | −76.7333 | −2.71124 | ||||||||
\(802\) | −5.01569 | −0.177110 | ||||||||
\(803\) | −10.7002 | −0.377603 | ||||||||
\(804\) | 32.7228 | 1.15404 | ||||||||
\(805\) | 20.1938 | 0.711739 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −65.9208 | −2.32052 | ||||||||
\(808\) | 4.92848 | 0.173383 | ||||||||
\(809\) | −45.8834 | −1.61317 | −0.806587 | − | 0.591115i | \(-0.798688\pi\) | ||||
−0.806587 | + | 0.591115i | \(0.798688\pi\) | |||||||
\(810\) | 3.70637 | 0.130229 | ||||||||
\(811\) | −12.3618 | −0.434083 | −0.217042 | − | 0.976162i | \(-0.569641\pi\) | ||||
−0.217042 | + | 0.976162i | \(0.569641\pi\) | |||||||
\(812\) | 25.7041 | 0.902035 | ||||||||
\(813\) | 48.4195 | 1.69814 | ||||||||
\(814\) | 0.583372 | 0.0204472 | ||||||||
\(815\) | −0.663482 | −0.0232408 | ||||||||
\(816\) | 71.9659 | 2.51931 | ||||||||
\(817\) | −8.91391 | −0.311858 | ||||||||
\(818\) | −4.32597 | −0.151254 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.21785 | 0.0774507 | ||||||||
\(821\) | 32.6089 | 1.13806 | 0.569029 | − | 0.822317i | \(-0.307319\pi\) | ||||
0.569029 | + | 0.822317i | \(0.307319\pi\) | |||||||
\(822\) | 6.58745 | 0.229764 | ||||||||
\(823\) | 22.7067 | 0.791504 | 0.395752 | − | 0.918357i | \(-0.370484\pi\) | ||||
0.395752 | + | 0.918357i | \(0.370484\pi\) | |||||||
\(824\) | 0.164952 | 0.00574638 | ||||||||
\(825\) | −12.3670 | −0.430562 | ||||||||
\(826\) | −1.26013 | −0.0438457 | ||||||||
\(827\) | 7.61671 | 0.264859 | 0.132429 | − | 0.991192i | \(-0.457722\pi\) | ||||
0.132429 | + | 0.991192i | \(0.457722\pi\) | |||||||
\(828\) | 76.2302 | 2.64918 | ||||||||
\(829\) | −7.63802 | −0.265279 | −0.132640 | − | 0.991164i | \(-0.542345\pi\) | ||||
−0.132640 | + | 0.991164i | \(0.542345\pi\) | |||||||
\(830\) | 0.613593 | 0.0212981 | ||||||||
\(831\) | 53.0238 | 1.83938 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.7880 | −1.17068 | ||||||||
\(834\) | −3.08567 | −0.106848 | ||||||||
\(835\) | 8.18882 | 0.283386 | ||||||||
\(836\) | 14.4891 | 0.501115 | ||||||||
\(837\) | −37.2104 | −1.28618 | ||||||||
\(838\) | −2.52044 | −0.0870671 | ||||||||
\(839\) | 29.8606 | 1.03090 | 0.515451 | − | 0.856919i | \(-0.327624\pi\) | ||||
0.515451 | + | 0.856919i | \(0.327624\pi\) | |||||||
\(840\) | 7.36291 | 0.254044 | ||||||||
\(841\) | −15.8492 | −0.546525 | ||||||||
\(842\) | −1.40083 | −0.0482758 | ||||||||
\(843\) | 61.4150 | 2.11525 | ||||||||
\(844\) | 9.24431 | 0.318202 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.0814 | 0.449746 | ||||||||
\(847\) | 3.58386 | 0.123143 | ||||||||
\(848\) | 0.560781 | 0.0192573 | ||||||||
\(849\) | −70.9601 | −2.43534 | ||||||||
\(850\) | −3.31237 | −0.113613 | ||||||||
\(851\) | −20.4857 | −0.702239 | ||||||||
\(852\) | 0.447365 | 0.0153265 | ||||||||
\(853\) | −32.2985 | −1.10588 | −0.552941 | − | 0.833221i | \(-0.686494\pi\) | ||||
−0.552941 | + | 0.833221i | \(0.686494\pi\) | |||||||
\(854\) | −5.05928 | −0.173125 | ||||||||
\(855\) | −58.0267 | −1.98447 | ||||||||
\(856\) | −5.39859 | −0.184520 | ||||||||
\(857\) | 7.77734 | 0.265669 | 0.132834 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132834 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.28099 | 0.248424 | 0.124212 | − | 0.992256i | \(-0.460360\pi\) | ||||
0.124212 | + | 0.992256i | \(0.460360\pi\) | |||||||
\(860\) | −2.58950 | −0.0883012 | ||||||||
\(861\) | −12.0217 | −0.409699 | ||||||||
\(862\) | 0.854076 | 0.0290899 | ||||||||
\(863\) | −26.3739 | −0.897778 | −0.448889 | − | 0.893588i | \(-0.648180\pi\) | ||||
−0.448889 | + | 0.893588i | \(0.648180\pi\) | |||||||
\(864\) | 24.7455 | 0.841860 | ||||||||
\(865\) | −22.5069 | −0.765256 | ||||||||
\(866\) | −2.87729 | −0.0977742 | ||||||||
\(867\) | −52.8750 | −1.79573 | ||||||||
\(868\) | −18.7902 | −0.637780 | ||||||||
\(869\) | −2.20655 | −0.0748522 | ||||||||
\(870\) | 1.87299 | 0.0635002 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.503383 | −0.0170467 | ||||||||
\(873\) | −87.5836 | −2.96426 | ||||||||
\(874\) | 5.72030 | 0.193492 | ||||||||
\(875\) | 34.0992 | 1.15276 | ||||||||
\(876\) | 68.1182 | 2.30150 | ||||||||
\(877\) | 29.9767 | 1.01224 | 0.506121 | − | 0.862462i | \(-0.331079\pi\) | ||||
0.506121 | + | 0.862462i | \(0.331079\pi\) | |||||||
\(878\) | −3.58872 | −0.121113 | ||||||||
\(879\) | −72.9895 | −2.46187 | ||||||||
\(880\) | 4.16123 | 0.140275 | ||||||||
\(881\) | −19.1781 | −0.646128 | −0.323064 | − | 0.946377i | \(-0.604713\pi\) | ||||
−0.323064 | + | 0.946377i | \(0.604713\pi\) | |||||||
\(882\) | −6.41449 | −0.215987 | ||||||||
\(883\) | −4.66507 | −0.156992 | −0.0784960 | − | 0.996914i | \(-0.525012\pi\) | ||||
−0.0784960 | + | 0.996914i | \(0.525012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.16725 | 0.274539 | ||||||||
\(886\) | 0.626228 | 0.0210385 | ||||||||
\(887\) | 6.43856 | 0.216186 | 0.108093 | − | 0.994141i | \(-0.465526\pi\) | ||||
0.108093 | + | 0.994141i | \(0.465526\pi\) | |||||||
\(888\) | −7.46931 | −0.250654 | ||||||||
\(889\) | −77.0509 | −2.58420 | ||||||||
\(890\) | −1.67272 | −0.0560698 | ||||||||
\(891\) | −23.0986 | −0.773833 | ||||||||
\(892\) | −3.35383 | −0.112295 | ||||||||
\(893\) | −87.3114 | −2.92176 | ||||||||
\(894\) | −1.44083 | −0.0481884 | ||||||||
\(895\) | −13.2882 | −0.444174 | ||||||||
\(896\) | 16.6290 | 0.555536 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.21979 | −0.0407048 | ||||||||
\(899\) | −9.61349 | −0.320628 | ||||||||
\(900\) | 55.9325 | 1.86442 | ||||||||
\(901\) | −0.838413 | −0.0279316 | ||||||||
\(902\) | 0.155397 | 0.00517417 | ||||||||
\(903\) | 14.0362 | 0.467096 | ||||||||
\(904\) | 9.29687 | 0.309209 | ||||||||
\(905\) | −4.44206 | −0.147659 | ||||||||
\(906\) | 11.2365 | 0.373308 | ||||||||
\(907\) | 17.1170 | 0.568359 | 0.284180 | − | 0.958771i | \(-0.408279\pi\) | ||||
0.284180 | + | 0.958771i | \(0.408279\pi\) | |||||||
\(908\) | 28.7204 | 0.953120 | ||||||||
\(909\) | 61.1607 | 2.02857 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.3331 | 0.441746 | 0.220873 | − | 0.975303i | \(-0.429109\pi\) | ||||
0.220873 | + | 0.975303i | \(0.429109\pi\) | |||||||
\(912\) | −91.1895 | −3.01959 | ||||||||
\(913\) | −3.82400 | −0.126556 | ||||||||
\(914\) | 2.63358 | 0.0871111 | ||||||||
\(915\) | 32.7905 | 1.08402 | ||||||||
\(916\) | −18.1684 | −0.600301 | ||||||||
\(917\) | 36.7747 | 1.21441 | ||||||||
\(918\) | −12.1013 | −0.399402 | ||||||||
\(919\) | −3.68329 | −0.121501 | −0.0607503 | − | 0.998153i | \(-0.519349\pi\) | ||||
−0.0607503 | + | 0.998153i | \(0.519349\pi\) | |||||||
\(920\) | 3.34219 | 0.110189 | ||||||||
\(921\) | −67.7676 | −2.23302 | ||||||||
\(922\) | −5.13972 | −0.169268 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −22.8151 | −0.750561 | ||||||||
\(925\) | −15.0310 | −0.494216 | ||||||||
\(926\) | −0.131542 | −0.00432274 | ||||||||
\(927\) | 2.04700 | 0.0672323 | ||||||||
\(928\) | 6.39313 | 0.209865 | ||||||||
\(929\) | 13.0683 | 0.428757 | 0.214379 | − | 0.976751i | \(-0.431227\pi\) | ||||
0.214379 | + | 0.976751i | \(0.431227\pi\) | |||||||
\(930\) | −1.36919 | −0.0448976 | ||||||||
\(931\) | 42.8135 | 1.40315 | ||||||||
\(932\) | −48.7551 | −1.59703 | ||||||||
\(933\) | −89.8736 | −2.94233 | ||||||||
\(934\) | 3.22117 | 0.105400 | ||||||||
\(935\) | −6.22138 | −0.203461 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.8440 | −0.844287 | −0.422144 | − | 0.906529i | \(-0.638722\pi\) | ||||
−0.422144 | + | 0.906529i | \(0.638722\pi\) | |||||||
\(938\) | −2.74698 | −0.0896921 | ||||||||
\(939\) | −15.0547 | −0.491292 | ||||||||
\(940\) | −25.3640 | −0.827284 | ||||||||
\(941\) | 24.4292 | 0.796370 | 0.398185 | − | 0.917305i | \(-0.369640\pi\) | ||||
0.398185 | + | 0.917305i | \(0.369640\pi\) | |||||||
\(942\) | 4.86846 | 0.158623 | ||||||||
\(943\) | −5.45693 | −0.177702 | ||||||||
\(944\) | 9.11853 | 0.296783 | ||||||||
\(945\) | 54.1314 | 1.76089 | ||||||||
\(946\) | −0.181438 | −0.00589904 | ||||||||
\(947\) | 4.16646 | 0.135392 | 0.0676959 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676959 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(948\) | 14.0470 | 0.456227 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.19717 | 0.136174 | ||||||||
\(951\) | −81.8285 | −2.65347 | ||||||||
\(952\) | −12.2903 | −0.398331 | ||||||||
\(953\) | −39.4339 | −1.27739 | −0.638695 | − | 0.769460i | \(-0.720526\pi\) | ||||
−0.638695 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(954\) | −0.159169 | −0.00515328 | ||||||||
\(955\) | −4.23863 | −0.137159 | ||||||||
\(956\) | −15.6549 | −0.506314 | ||||||||
\(957\) | −11.6727 | −0.377325 | ||||||||
\(958\) | 0.967892 | 0.0312712 | ||||||||
\(959\) | 49.1867 | 1.58832 | ||||||||
\(960\) | −25.8779 | −0.835207 | ||||||||
\(961\) | −23.9723 | −0.773301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −66.9946 | −2.15887 | ||||||||
\(964\) | 48.1960 | 1.55229 | ||||||||
\(965\) | −5.51271 | −0.177460 | ||||||||
\(966\) | −9.00742 | −0.289809 | ||||||||
\(967\) | 5.25113 | 0.168865 | 0.0844325 | − | 0.996429i | \(-0.473092\pi\) | ||||
0.0844325 | + | 0.996429i | \(0.473092\pi\) | |||||||
\(968\) | 0.593149 | 0.0190645 | ||||||||
\(969\) | 136.336 | 4.37973 | ||||||||
\(970\) | −1.90925 | −0.0613023 | ||||||||
\(971\) | 56.9977 | 1.82914 | 0.914572 | − | 0.404422i | \(-0.132527\pi\) | ||||
0.914572 | + | 0.404422i | \(0.132527\pi\) | |||||||
\(972\) | 63.7644 | 2.04525 | ||||||||
\(973\) | −23.0399 | −0.738625 | ||||||||
\(974\) | −1.61361 | −0.0517032 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.6097 | 1.17185 | ||||||||
\(977\) | 42.9772 | 1.37496 | 0.687481 | − | 0.726202i | \(-0.258716\pi\) | ||||
0.687481 | + | 0.726202i | \(0.258716\pi\) | |||||||
\(978\) | 0.295945 | 0.00946328 | ||||||||
\(979\) | 10.4246 | 0.333173 | ||||||||
\(980\) | 12.4374 | 0.397297 | ||||||||
\(981\) | −6.24681 | −0.199445 | ||||||||
\(982\) | −1.69003 | −0.0539310 | ||||||||
\(983\) | −15.5764 | −0.496809 | −0.248404 | − | 0.968656i | \(-0.579906\pi\) | ||||
−0.248404 | + | 0.968656i | \(0.579906\pi\) | |||||||
\(984\) | −1.98966 | −0.0634280 | ||||||||
\(985\) | −5.80753 | −0.185043 | ||||||||
\(986\) | −3.12643 | −0.0995657 | ||||||||
\(987\) | 137.484 | 4.37617 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.37135 | 0.202597 | ||||||||
\(990\) | −1.18110 | −0.0375378 | ||||||||
\(991\) | 12.2598 | 0.389446 | 0.194723 | − | 0.980858i | \(-0.437619\pi\) | ||||
0.194723 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(992\) | −4.67351 | −0.148384 | ||||||||
\(993\) | 100.038 | 3.17462 | ||||||||
\(994\) | −0.0375549 | −0.00119117 | ||||||||
\(995\) | 5.48651 | 0.173934 | ||||||||
\(996\) | 24.3438 | 0.771362 | ||||||||
\(997\) | −10.7308 | −0.339848 | −0.169924 | − | 0.985457i | \(-0.554352\pi\) | ||||
−0.169924 | + | 0.985457i | \(0.554352\pi\) | |||||||
\(998\) | −2.44816 | −0.0774950 | ||||||||
\(999\) | −54.9136 | −1.73739 |
(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 | 1859.2.a.s.1.10 | ✓ | 21 | |
13.12 | even | 2 | 1859.2.a.t.1.12 | yes | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.10 | ✓ | 21 | 1.1 | even | 1 | trivial | |
1859.2.a.t.1.12 | yes | 21 | 13.12 | even | 2 |