Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} - 1853 x^{5} + 539 x^{4} + 891 x^{3} - 218 x^{2} - 133 x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.33696\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33696 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(3\) | −0.00757499 | −0.00437342 | −0.00218671 | − | 0.999998i | \(-0.500696\pi\) | ||||
−0.00218671 | + | 0.999998i | \(0.500696\pi\) | |||||||
\(4\) | 3.46136 | 1.73068 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0177024 | −0.00722699 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.41514 | 1.20744 | ||||||||
\(9\) | −2.99994 | −0.999981 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.99434 | −1.50585 | −0.752924 | − | 0.658107i | \(-0.771357\pi\) | ||||
−0.752924 | + | 0.658107i | \(0.771357\pi\) | |||||||
\(12\) | −0.0262198 | −0.00756901 | ||||||||
\(13\) | 3.87824 | 1.07563 | 0.537815 | − | 0.843063i | \(-0.319250\pi\) | ||||
0.537815 | + | 0.843063i | \(0.319250\pi\) | |||||||
\(14\) | −2.33696 | −0.624578 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.05832 | 0.264579 | ||||||||
\(17\) | 0.475637 | 0.115359 | 0.0576794 | − | 0.998335i | \(-0.481630\pi\) | ||||
0.0576794 | + | 0.998335i | \(0.481630\pi\) | |||||||
\(18\) | −7.01073 | −1.65245 | ||||||||
\(19\) | −1.54155 | −0.353655 | −0.176828 | − | 0.984242i | \(-0.556583\pi\) | ||||
−0.176828 | + | 0.984242i | \(0.556583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.00757499 | 0.00165300 | ||||||||
\(22\) | −11.6715 | −2.48838 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.0258697 | −0.00528063 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.06327 | 1.77745 | ||||||||
\(27\) | 0.0454495 | 0.00874677 | ||||||||
\(28\) | −3.46136 | −0.654136 | ||||||||
\(29\) | −9.38110 | −1.74203 | −0.871013 | − | 0.491259i | \(-0.836537\pi\) | ||||
−0.871013 | + | 0.491259i | \(0.836537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.0814 | −1.99028 | −0.995141 | − | 0.0984581i | \(-0.968609\pi\) | ||||
−0.995141 | + | 0.0984581i | \(0.968609\pi\) | |||||||
\(32\) | −4.35705 | −0.770226 | ||||||||
\(33\) | 0.0378321 | 0.00658572 | ||||||||
\(34\) | 1.11154 | 0.190628 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.3839 | −1.73065 | ||||||||
\(37\) | 4.42722 | 0.727830 | 0.363915 | − | 0.931432i | \(-0.381440\pi\) | ||||
0.363915 | + | 0.931432i | \(0.381440\pi\) | |||||||
\(38\) | −3.60253 | −0.584407 | ||||||||
\(39\) | −0.0293776 | −0.00470419 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.21792 | 0.502555 | 0.251278 | − | 0.967915i | \(-0.419149\pi\) | ||||
0.251278 | + | 0.967915i | \(0.419149\pi\) | |||||||
\(42\) | 0.0177024 | 0.00273154 | ||||||||
\(43\) | −3.40274 | −0.518912 | −0.259456 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259456 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(44\) | −17.2872 | −2.60615 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.33696 | −0.344565 | ||||||||
\(47\) | 8.07320 | 1.17760 | 0.588799 | − | 0.808280i | \(-0.299601\pi\) | ||||
0.588799 | + | 0.808280i | \(0.299601\pi\) | |||||||
\(48\) | −0.00801673 | −0.00115712 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.00360295 | −0.000504513 0 | ||||||||
\(52\) | 13.4240 | 1.86157 | ||||||||
\(53\) | 1.46842 | 0.201703 | 0.100852 | − | 0.994901i | \(-0.467843\pi\) | ||||
0.100852 | + | 0.994901i | \(0.467843\pi\) | |||||||
\(54\) | 0.106214 | 0.0144538 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.41514 | −0.456368 | ||||||||
\(57\) | 0.0116772 | 0.00154668 | ||||||||
\(58\) | −21.9232 | −2.87866 | ||||||||
\(59\) | −11.8954 | −1.54865 | −0.774326 | − | 0.632787i | \(-0.781911\pi\) | ||||
−0.774326 | + | 0.632787i | \(0.781911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24535 | 1.05571 | 0.527854 | − | 0.849335i | \(-0.322997\pi\) | ||||
0.527854 | + | 0.849335i | \(0.322997\pi\) | |||||||
\(62\) | −25.8968 | −3.28890 | ||||||||
\(63\) | 2.99994 | 0.377957 | ||||||||
\(64\) | −12.2989 | −1.53736 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0884119 | 0.0108827 | ||||||||
\(67\) | −4.54321 | −0.555041 | −0.277521 | − | 0.960720i | \(-0.589513\pi\) | ||||
−0.277521 | + | 0.960720i | \(0.589513\pi\) | |||||||
\(68\) | 1.64635 | 0.199650 | ||||||||
\(69\) | 0.00757499 | 0.000911922 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0031 | 1.30583 | 0.652916 | − | 0.757430i | \(-0.273545\pi\) | ||||
0.652916 | + | 0.757430i | \(0.273545\pi\) | |||||||
\(72\) | −10.2452 | −1.20741 | ||||||||
\(73\) | −13.6586 | −1.59862 | −0.799308 | − | 0.600921i | \(-0.794800\pi\) | ||||
−0.799308 | + | 0.600921i | \(0.794800\pi\) | |||||||
\(74\) | 10.3462 | 1.20272 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.33586 | −0.612065 | ||||||||
\(77\) | 4.99434 | 0.569157 | ||||||||
\(78\) | −0.0686542 | −0.00777356 | ||||||||
\(79\) | 13.1029 | 1.47419 | 0.737096 | − | 0.675788i | \(-0.236197\pi\) | ||||
0.737096 | + | 0.675788i | \(0.236197\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99948 | 0.999943 | ||||||||
\(82\) | 7.52014 | 0.830461 | ||||||||
\(83\) | −14.7630 | −1.62045 | −0.810225 | − | 0.586118i | \(-0.800655\pi\) | ||||
−0.810225 | + | 0.586118i | \(0.800655\pi\) | |||||||
\(84\) | 0.0262198 | 0.00286082 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.95205 | −0.857491 | ||||||||
\(87\) | 0.0710618 | 0.00761862 | ||||||||
\(88\) | −17.0564 | −1.81822 | ||||||||
\(89\) | −6.08219 | −0.644710 | −0.322355 | − | 0.946619i | \(-0.604475\pi\) | ||||
−0.322355 | + | 0.946619i | \(0.604475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.87824 | −0.406550 | ||||||||
\(92\) | −3.46136 | −0.360872 | ||||||||
\(93\) | 0.0839417 | 0.00870435 | ||||||||
\(94\) | 18.8667 | 1.94595 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0330047 | 0.00336852 | ||||||||
\(97\) | −3.91724 | −0.397735 | −0.198867 | − | 0.980026i | \(-0.563726\pi\) | ||||
−0.198867 | + | 0.980026i | \(0.563726\pi\) | |||||||
\(98\) | 2.33696 | 0.236068 | ||||||||
\(99\) | 14.9827 | 1.50582 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.79080 | 0.277695 | 0.138848 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138848 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(102\) | −0.00841993 | −0.000833697 0 | ||||||||
\(103\) | −13.1299 | −1.29373 | −0.646863 | − | 0.762606i | \(-0.723919\pi\) | ||||
−0.646863 | + | 0.762606i | \(0.723919\pi\) | |||||||
\(104\) | 13.2447 | 1.29875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.43164 | 0.333310 | ||||||||
\(107\) | 18.1208 | 1.75181 | 0.875903 | − | 0.482488i | \(-0.160267\pi\) | ||||
0.875903 | + | 0.482488i | \(0.160267\pi\) | |||||||
\(108\) | 0.157317 | 0.0151379 | ||||||||
\(109\) | −8.86577 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0335361 | −0.00318311 | ||||||||
\(112\) | −1.05832 | −0.100001 | ||||||||
\(113\) | 5.71585 | 0.537702 | 0.268851 | − | 0.963182i | \(-0.413356\pi\) | ||||
0.268851 | + | 0.963182i | \(0.413356\pi\) | |||||||
\(114\) | 0.0272891 | 0.00255586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.4714 | −3.01489 | ||||||||
\(117\) | −11.6345 | −1.07561 | ||||||||
\(118\) | −27.7991 | −2.55911 | ||||||||
\(119\) | −0.475637 | −0.0436016 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.9434 | 1.26758 | ||||||||
\(122\) | 19.2690 | 1.74454 | ||||||||
\(123\) | −0.0243757 | −0.00219789 | ||||||||
\(124\) | −38.3568 | −3.44455 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.01073 | 0.624566 | ||||||||
\(127\) | −14.5563 | −1.29167 | −0.645833 | − | 0.763479i | \(-0.723490\pi\) | ||||
−0.645833 | + | 0.763479i | \(0.723490\pi\) | |||||||
\(128\) | −20.0278 | −1.77023 | ||||||||
\(129\) | 0.0257757 | 0.00226942 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.58099 | −0.574984 | −0.287492 | − | 0.957783i | \(-0.592821\pi\) | ||||
−0.287492 | + | 0.957783i | \(0.592821\pi\) | |||||||
\(132\) | 0.130951 | 0.0113978 | ||||||||
\(133\) | 1.54155 | 0.133669 | ||||||||
\(134\) | −10.6173 | −0.917193 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.62437 | 0.139288 | ||||||||
\(137\) | 7.37371 | 0.629978 | 0.314989 | − | 0.949095i | \(-0.397999\pi\) | ||||
0.314989 | + | 0.949095i | \(0.397999\pi\) | |||||||
\(138\) | 0.0177024 | 0.00150693 | ||||||||
\(139\) | −11.7472 | −0.996384 | −0.498192 | − | 0.867067i | \(-0.666003\pi\) | ||||
−0.498192 | + | 0.867067i | \(0.666003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0611545 | −0.00515014 | ||||||||
\(142\) | 25.7138 | 2.15786 | ||||||||
\(143\) | −19.3692 | −1.61974 | ||||||||
\(144\) | −3.17488 | −0.264574 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.9195 | −2.64168 | ||||||||
\(147\) | −0.00757499 | −0.000624775 0 | ||||||||
\(148\) | 15.3242 | 1.25964 | ||||||||
\(149\) | 0.282601 | 0.0231516 | 0.0115758 | − | 0.999933i | \(-0.496315\pi\) | ||||
0.0115758 | + | 0.999933i | \(0.496315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5423 | 1.59033 | 0.795166 | − | 0.606391i | \(-0.207384\pi\) | ||||
0.795166 | + | 0.606391i | \(0.207384\pi\) | |||||||
\(152\) | −5.26461 | −0.427016 | ||||||||
\(153\) | −1.42688 | −0.115357 | ||||||||
\(154\) | 11.6715 | 0.940520 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.101687 | −0.00814145 | ||||||||
\(157\) | 23.7122 | 1.89244 | 0.946220 | − | 0.323523i | \(-0.104867\pi\) | ||||
0.946220 | + | 0.323523i | \(0.104867\pi\) | |||||||
\(158\) | 30.6209 | 2.43607 | ||||||||
\(159\) | −0.0111233 | −0.000882134 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 21.0314 | 1.65238 | ||||||||
\(163\) | −0.0532661 | −0.00417212 | −0.00208606 | − | 0.999998i | \(-0.500664\pi\) | ||||
−0.00208606 | + | 0.999998i | \(0.500664\pi\) | |||||||
\(164\) | 11.1384 | 0.869763 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.5005 | −2.67776 | ||||||||
\(167\) | −6.63072 | −0.513101 | −0.256550 | − | 0.966531i | \(-0.582586\pi\) | ||||
−0.256550 | + | 0.966531i | \(0.582586\pi\) | |||||||
\(168\) | 0.0258697 | 0.00199589 | ||||||||
\(169\) | 2.04074 | 0.156980 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62455 | 0.353648 | ||||||||
\(172\) | −11.7781 | −0.898073 | ||||||||
\(173\) | 6.76778 | 0.514545 | 0.257273 | − | 0.966339i | \(-0.417176\pi\) | ||||
0.257273 | + | 0.966339i | \(0.417176\pi\) | |||||||
\(174\) | 0.166068 | 0.0125896 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.28558 | −0.398416 | ||||||||
\(177\) | 0.0901077 | 0.00677291 | ||||||||
\(178\) | −14.2138 | −1.06537 | ||||||||
\(179\) | 9.48534 | 0.708967 | 0.354484 | − | 0.935062i | \(-0.384657\pi\) | ||||
0.354484 | + | 0.935062i | \(0.384657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0503 | 1.34167 | 0.670834 | − | 0.741607i | \(-0.265936\pi\) | ||||
0.670834 | + | 0.741607i | \(0.265936\pi\) | |||||||
\(182\) | −9.06327 | −0.671815 | ||||||||
\(183\) | −0.0624585 | −0.00461706 | ||||||||
\(184\) | −3.41514 | −0.251768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.196168 | 0.0143837 | ||||||||
\(187\) | −2.37549 | −0.173713 | ||||||||
\(188\) | 27.9443 | 2.03805 | ||||||||
\(189\) | −0.0454495 | −0.00330597 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.6976 | −1.71470 | −0.857349 | − | 0.514735i | \(-0.827890\pi\) | ||||
−0.857349 | + | 0.514735i | \(0.827890\pi\) | |||||||
\(192\) | 0.0931639 | 0.00672352 | ||||||||
\(193\) | −14.5036 | −1.04399 | −0.521995 | − | 0.852948i | \(-0.674812\pi\) | ||||
−0.521995 | + | 0.852948i | \(0.674812\pi\) | |||||||
\(194\) | −9.15441 | −0.657248 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.46136 | 0.247240 | ||||||||
\(197\) | −2.63536 | −0.187762 | −0.0938809 | − | 0.995583i | \(-0.529927\pi\) | ||||
−0.0938809 | + | 0.995583i | \(0.529927\pi\) | |||||||
\(198\) | 35.0140 | 2.48833 | ||||||||
\(199\) | −19.5257 | −1.38414 | −0.692070 | − | 0.721830i | \(-0.743301\pi\) | ||||
−0.692070 | + | 0.721830i | \(0.743301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0344148 | 0.00242743 | ||||||||
\(202\) | 6.52198 | 0.458885 | ||||||||
\(203\) | 9.38110 | 0.658424 | ||||||||
\(204\) | −0.0124711 | −0.000873152 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −30.6840 | −2.13785 | ||||||||
\(207\) | 2.99994 | 0.208510 | ||||||||
\(208\) | 4.10440 | 0.284589 | ||||||||
\(209\) | 7.69900 | 0.532551 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5337 | −0.725168 | −0.362584 | − | 0.931951i | \(-0.618105\pi\) | ||||
−0.362584 | + | 0.931951i | \(0.618105\pi\) | |||||||
\(212\) | 5.08274 | 0.349084 | ||||||||
\(213\) | −0.0833487 | −0.00571096 | ||||||||
\(214\) | 42.3476 | 2.89482 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.155217 | 0.0105612 | ||||||||
\(217\) | 11.0814 | 0.752256 | ||||||||
\(218\) | −20.7189 | −1.40326 | ||||||||
\(219\) | 0.103464 | 0.00699143 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.84463 | 0.124083 | ||||||||
\(222\) | −0.0783725 | −0.00526002 | ||||||||
\(223\) | −15.2356 | −1.02025 | −0.510127 | − | 0.860099i | \(-0.670402\pi\) | ||||
−0.510127 | + | 0.860099i | \(0.670402\pi\) | |||||||
\(224\) | 4.35705 | 0.291118 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3577 | 0.888540 | ||||||||
\(227\) | 27.4434 | 1.82148 | 0.910740 | − | 0.412980i | \(-0.135512\pi\) | ||||
0.910740 | + | 0.412980i | \(0.135512\pi\) | |||||||
\(228\) | 0.0404191 | 0.00267682 | ||||||||
\(229\) | 29.8273 | 1.97105 | 0.985523 | − | 0.169540i | \(-0.0542283\pi\) | ||||
0.985523 | + | 0.169540i | \(0.0542283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0378321 | −0.00248917 | ||||||||
\(232\) | −32.0378 | −2.10339 | ||||||||
\(233\) | 22.9219 | 1.50166 | 0.750832 | − | 0.660494i | \(-0.229653\pi\) | ||||
0.750832 | + | 0.660494i | \(0.229653\pi\) | |||||||
\(234\) | −27.1893 | −1.77742 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −41.1744 | −2.68022 | ||||||||
\(237\) | −0.0992544 | −0.00644727 | ||||||||
\(238\) | −1.11154 | −0.0720506 | ||||||||
\(239\) | 15.2760 | 0.988122 | 0.494061 | − | 0.869427i | \(-0.335512\pi\) | ||||
0.494061 | + | 0.869427i | \(0.335512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.89087 | 0.379464 | 0.189732 | − | 0.981836i | \(-0.439238\pi\) | ||||
0.189732 | + | 0.981836i | \(0.439238\pi\) | |||||||
\(242\) | 32.5851 | 2.09465 | ||||||||
\(243\) | −0.204520 | −0.0131199 | ||||||||
\(244\) | 28.5402 | 1.82710 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0569650 | −0.00363196 | ||||||||
\(247\) | −5.97849 | −0.380402 | ||||||||
\(248\) | −37.8447 | −2.40314 | ||||||||
\(249\) | 0.111830 | 0.00708692 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.08671 | 0.257951 | 0.128975 | − | 0.991648i | \(-0.458831\pi\) | ||||
0.128975 | + | 0.991648i | \(0.458831\pi\) | |||||||
\(252\) | 10.3839 | 0.654124 | ||||||||
\(253\) | 4.99434 | 0.313991 | ||||||||
\(254\) | −34.0175 | −2.13445 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.2064 | −1.38790 | ||||||||
\(257\) | −19.2722 | −1.20216 | −0.601082 | − | 0.799187i | \(-0.705264\pi\) | ||||
−0.601082 | + | 0.799187i | \(0.705264\pi\) | |||||||
\(258\) | 0.0602367 | 0.00375017 | ||||||||
\(259\) | −4.42722 | −0.275094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.1428 | 1.74199 | ||||||||
\(262\) | −15.3795 | −0.950148 | ||||||||
\(263\) | 25.2660 | 1.55797 | 0.778984 | − | 0.627044i | \(-0.215736\pi\) | ||||
0.778984 | + | 0.627044i | \(0.215736\pi\) | |||||||
\(264\) | 0.129202 | 0.00795183 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.60253 | 0.220885 | ||||||||
\(267\) | 0.0460725 | 0.00281959 | ||||||||
\(268\) | −15.7257 | −0.960600 | ||||||||
\(269\) | 7.84347 | 0.478225 | 0.239112 | − | 0.970992i | \(-0.423144\pi\) | ||||
0.239112 | + | 0.970992i | \(0.423144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5068 | −1.18495 | −0.592477 | − | 0.805588i | \(-0.701850\pi\) | ||||
−0.592477 | + | 0.805588i | \(0.701850\pi\) | |||||||
\(272\) | 0.503374 | 0.0305215 | ||||||||
\(273\) | 0.0293776 | 0.00177802 | ||||||||
\(274\) | 17.2320 | 1.04103 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0262198 | 0.00157825 | ||||||||
\(277\) | −24.9162 | −1.49707 | −0.748534 | − | 0.663097i | \(-0.769242\pi\) | ||||
−0.748534 | + | 0.663097i | \(0.769242\pi\) | |||||||
\(278\) | −27.4527 | −1.64650 | ||||||||
\(279\) | 33.2436 | 1.99024 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.78384 | −0.166070 | −0.0830349 | − | 0.996547i | \(-0.526461\pi\) | ||||
−0.0830349 | + | 0.996547i | \(0.526461\pi\) | |||||||
\(282\) | −0.142915 | −0.00851048 | ||||||||
\(283\) | 12.1104 | 0.719891 | 0.359946 | − | 0.932973i | \(-0.382795\pi\) | ||||
0.359946 | + | 0.932973i | \(0.382795\pi\) | |||||||
\(284\) | 38.0859 | 2.25998 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −45.2650 | −2.67658 | ||||||||
\(287\) | −3.21792 | −0.189948 | ||||||||
\(288\) | 13.0709 | 0.770211 | ||||||||
\(289\) | −16.7738 | −0.986692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0296730 | 0.00173946 | ||||||||
\(292\) | −47.2773 | −2.76670 | ||||||||
\(293\) | 0.650821 | 0.0380214 | 0.0190107 | − | 0.999819i | \(-0.493948\pi\) | ||||
0.0190107 | + | 0.999819i | \(0.493948\pi\) | |||||||
\(294\) | −0.0177024 | −0.00103243 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.1196 | 0.878808 | ||||||||
\(297\) | −0.226990 | −0.0131713 | ||||||||
\(298\) | 0.660427 | 0.0382575 | ||||||||
\(299\) | −3.87824 | −0.224284 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.40274 | 0.196130 | ||||||||
\(302\) | 45.6696 | 2.62799 | ||||||||
\(303\) | −0.0211403 | −0.00121448 | ||||||||
\(304\) | −1.63144 | −0.0935697 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.33456 | −0.190624 | ||||||||
\(307\) | −22.5537 | −1.28721 | −0.643603 | − | 0.765359i | \(-0.722561\pi\) | ||||
−0.643603 | + | 0.765359i | \(0.722561\pi\) | |||||||
\(308\) | 17.2872 | 0.985031 | ||||||||
\(309\) | 0.0994587 | 0.00565801 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.7851 | 1.46214 | 0.731069 | − | 0.682303i | \(-0.239022\pi\) | ||||
0.731069 | + | 0.682303i | \(0.239022\pi\) | |||||||
\(312\) | −0.100329 | −0.00568000 | ||||||||
\(313\) | −5.58377 | −0.315613 | −0.157807 | − | 0.987470i | \(-0.550442\pi\) | ||||
−0.157807 | + | 0.987470i | \(0.550442\pi\) | |||||||
\(314\) | 55.4144 | 3.12722 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45.3539 | 2.55136 | ||||||||
\(317\) | 4.35295 | 0.244486 | 0.122243 | − | 0.992500i | \(-0.460991\pi\) | ||||
0.122243 | + | 0.992500i | \(0.460991\pi\) | |||||||
\(318\) | −0.0259946 | −0.00145771 | ||||||||
\(319\) | 46.8524 | 2.62323 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.137265 | −0.00766139 | ||||||||
\(322\) | 2.33696 | 0.130233 | ||||||||
\(323\) | −0.733217 | −0.0407973 | ||||||||
\(324\) | 31.1505 | 1.73058 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.124480 | −0.00689434 | ||||||||
\(327\) | 0.0671581 | 0.00371385 | ||||||||
\(328\) | 10.9897 | 0.606803 | ||||||||
\(329\) | −8.07320 | −0.445090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7648 | −0.591685 | −0.295842 | − | 0.955237i | \(-0.595600\pi\) | ||||
−0.295842 | + | 0.955237i | \(0.595600\pi\) | |||||||
\(332\) | −51.1002 | −2.80449 | ||||||||
\(333\) | −13.2814 | −0.727816 | ||||||||
\(334\) | −15.4957 | −0.847888 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.00801673 | 0.000437349 0 | ||||||||
\(337\) | 0.415084 | 0.0226111 | 0.0113055 | − | 0.999936i | \(-0.496401\pi\) | ||||
0.0113055 | + | 0.999936i | \(0.496401\pi\) | |||||||
\(338\) | 4.76911 | 0.259405 | ||||||||
\(339\) | −0.0432975 | −0.00235160 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.3443 | 2.99706 | ||||||||
\(342\) | 10.8074 | 0.584396 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.6208 | −0.626554 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.8160 | 0.850274 | ||||||||
\(347\) | 4.09489 | 0.219825 | 0.109913 | − | 0.993941i | \(-0.464943\pi\) | ||||
0.109913 | + | 0.993941i | \(0.464943\pi\) | |||||||
\(348\) | 0.245971 | 0.0131854 | ||||||||
\(349\) | −4.93152 | −0.263978 | −0.131989 | − | 0.991251i | \(-0.542136\pi\) | ||||
−0.131989 | + | 0.991251i | \(0.542136\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.176264 | 0.00940828 | ||||||||
\(352\) | 21.7606 | 1.15984 | ||||||||
\(353\) | −14.1977 | −0.755667 | −0.377833 | − | 0.925874i | \(-0.623331\pi\) | ||||
−0.377833 | + | 0.925874i | \(0.623331\pi\) | |||||||
\(354\) | 0.210578 | 0.0111921 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −21.0527 | −1.11579 | ||||||||
\(357\) | 0.00360295 | 0.000190688 0 | ||||||||
\(358\) | 22.1668 | 1.17155 | ||||||||
\(359\) | −24.5208 | −1.29416 | −0.647078 | − | 0.762424i | \(-0.724009\pi\) | ||||
−0.647078 | + | 0.762424i | \(0.724009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6236 | −0.874928 | ||||||||
\(362\) | 42.1828 | 2.21708 | ||||||||
\(363\) | −0.105621 | −0.00554367 | ||||||||
\(364\) | −13.4240 | −0.703609 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.145963 | −0.00762959 | ||||||||
\(367\) | 16.4023 | 0.856191 | 0.428096 | − | 0.903733i | \(-0.359185\pi\) | ||||
0.428096 | + | 0.903733i | \(0.359185\pi\) | |||||||
\(368\) | −1.05832 | −0.0551685 | ||||||||
\(369\) | −9.65358 | −0.502546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.46842 | −0.0762367 | ||||||||
\(372\) | 0.290553 | 0.0150645 | ||||||||
\(373\) | 3.44368 | 0.178307 | 0.0891535 | − | 0.996018i | \(-0.471584\pi\) | ||||
0.0891535 | + | 0.996018i | \(0.471584\pi\) | |||||||
\(374\) | −5.55142 | −0.287057 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.5712 | 1.42187 | ||||||||
\(377\) | −36.3822 | −1.87378 | ||||||||
\(378\) | −0.106214 | −0.00546304 | ||||||||
\(379\) | −3.28827 | −0.168907 | −0.0844536 | − | 0.996427i | \(-0.526914\pi\) | ||||
−0.0844536 | + | 0.996427i | \(0.526914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.110264 | 0.00564900 | ||||||||
\(382\) | −55.3803 | −2.83350 | ||||||||
\(383\) | 18.1838 | 0.929151 | 0.464576 | − | 0.885533i | \(-0.346207\pi\) | ||||
0.464576 | + | 0.885533i | \(0.346207\pi\) | |||||||
\(384\) | 0.151711 | 0.00774195 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −33.8942 | −1.72517 | ||||||||
\(387\) | 10.2080 | 0.518903 | ||||||||
\(388\) | −13.5590 | −0.688353 | ||||||||
\(389\) | −27.9376 | −1.41649 | −0.708246 | − | 0.705966i | \(-0.750513\pi\) | ||||
−0.708246 | + | 0.705966i | \(0.750513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.475637 | −0.0240540 | ||||||||
\(392\) | 3.41514 | 0.172491 | ||||||||
\(393\) | 0.0498510 | 0.00251465 | ||||||||
\(394\) | −6.15872 | −0.310272 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 51.8607 | 2.60610 | ||||||||
\(397\) | 20.5903 | 1.03340 | 0.516699 | − | 0.856167i | \(-0.327161\pi\) | ||||
0.516699 | + | 0.856167i | \(0.327161\pi\) | |||||||
\(398\) | −45.6307 | −2.28726 | ||||||||
\(399\) | −0.0116772 | −0.000584592 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.448572 | 0.0224006 | 0.0112003 | − | 0.999937i | \(-0.496435\pi\) | ||||
0.0112003 | + | 0.999937i | \(0.496435\pi\) | |||||||
\(402\) | 0.0804258 | 0.00401127 | ||||||||
\(403\) | −42.9764 | −2.14081 | ||||||||
\(404\) | 9.65998 | 0.480602 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.9232 | 1.08803 | ||||||||
\(407\) | −22.1110 | −1.09600 | ||||||||
\(408\) | −0.0123046 | −0.000609168 0 | ||||||||
\(409\) | −6.40103 | −0.316511 | −0.158255 | − | 0.987398i | \(-0.550587\pi\) | ||||
−0.158255 | + | 0.987398i | \(0.550587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0558558 | −0.00275516 | ||||||||
\(412\) | −45.4473 | −2.23903 | ||||||||
\(413\) | 11.8954 | 0.585335 | ||||||||
\(414\) | 7.01073 | 0.344559 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.8977 | −0.828478 | ||||||||
\(417\) | 0.0889850 | 0.00435761 | ||||||||
\(418\) | 17.9922 | 0.880029 | ||||||||
\(419\) | −8.49010 | −0.414768 | −0.207384 | − | 0.978260i | \(-0.566495\pi\) | ||||
−0.207384 | + | 0.978260i | \(0.566495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3915 | −1.23751 | −0.618753 | − | 0.785585i | \(-0.712362\pi\) | ||||
−0.618753 | + | 0.785585i | \(0.712362\pi\) | |||||||
\(422\) | −24.6167 | −1.19832 | ||||||||
\(423\) | −24.2192 | −1.17758 | ||||||||
\(424\) | 5.01487 | 0.243544 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.194782 | −0.00943723 | ||||||||
\(427\) | −8.24535 | −0.399020 | ||||||||
\(428\) | 62.7227 | 3.03182 | ||||||||
\(429\) | 0.146722 | 0.00708379 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3251 | 0.930857 | 0.465428 | − | 0.885086i | \(-0.345900\pi\) | ||||
0.465428 | + | 0.885086i | \(0.345900\pi\) | |||||||
\(432\) | 0.0480999 | 0.00231421 | ||||||||
\(433\) | −35.6715 | −1.71426 | −0.857132 | − | 0.515097i | \(-0.827756\pi\) | ||||
−0.857132 | + | 0.515097i | \(0.827756\pi\) | |||||||
\(434\) | 25.8968 | 1.24309 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.6876 | −1.46967 | ||||||||
\(437\) | 1.54155 | 0.0737422 | ||||||||
\(438\) | 0.241790 | 0.0115532 | ||||||||
\(439\) | −18.2969 | −0.873261 | −0.436631 | − | 0.899641i | \(-0.643828\pi\) | ||||
−0.436631 | + | 0.899641i | \(0.643828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.99994 | −0.142854 | ||||||||
\(442\) | 4.31083 | 0.205045 | ||||||||
\(443\) | 4.02535 | 0.191250 | 0.0956251 | − | 0.995417i | \(-0.469515\pi\) | ||||
0.0956251 | + | 0.995417i | \(0.469515\pi\) | |||||||
\(444\) | −0.116081 | −0.00550895 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −35.6050 | −1.68595 | ||||||||
\(447\) | −0.00214070 | −0.000101252 0 | ||||||||
\(448\) | 12.2989 | 0.581067 | ||||||||
\(449\) | 29.7863 | 1.40570 | 0.702851 | − | 0.711337i | \(-0.251910\pi\) | ||||
0.702851 | + | 0.711337i | \(0.251910\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0714 | −0.756772 | ||||||||
\(452\) | 19.7846 | 0.930591 | ||||||||
\(453\) | −0.148033 | −0.00695520 | ||||||||
\(454\) | 64.1339 | 3.00996 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0398794 | 0.00186752 | ||||||||
\(457\) | 19.5513 | 0.914572 | 0.457286 | − | 0.889320i | \(-0.348822\pi\) | ||||
0.457286 | + | 0.889320i | \(0.348822\pi\) | |||||||
\(458\) | 69.7052 | 3.25711 | ||||||||
\(459\) | 0.0216175 | 0.00100902 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.191900 | 0.00893768 | 0.00446884 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446884 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(462\) | −0.0884119 | −0.00411329 | ||||||||
\(463\) | −26.2178 | −1.21845 | −0.609223 | − | 0.792999i | \(-0.708519\pi\) | ||||
−0.609223 | + | 0.792999i | \(0.708519\pi\) | |||||||
\(464\) | −9.92816 | −0.460903 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 53.5675 | 2.48147 | ||||||||
\(467\) | −41.2187 | −1.90737 | −0.953687 | − | 0.300799i | \(-0.902747\pi\) | ||||
−0.953687 | + | 0.300799i | \(0.902747\pi\) | |||||||
\(468\) | −40.2712 | −1.86154 | ||||||||
\(469\) | 4.54321 | 0.209786 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.179620 | −0.00827645 | ||||||||
\(472\) | −40.6246 | −1.86990 | ||||||||
\(473\) | 16.9944 | 0.781404 | ||||||||
\(474\) | −0.231953 | −0.0106540 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.64635 | −0.0754604 | ||||||||
\(477\) | −4.40518 | −0.201699 | ||||||||
\(478\) | 35.6993 | 1.63285 | ||||||||
\(479\) | −4.54688 | −0.207752 | −0.103876 | − | 0.994590i | \(-0.533125\pi\) | ||||
−0.103876 | + | 0.994590i | \(0.533125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1698 | 0.782876 | ||||||||
\(482\) | 13.7667 | 0.627056 | ||||||||
\(483\) | −0.00757499 | −0.000344674 0 | ||||||||
\(484\) | 48.2632 | 2.19378 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.477953 | −0.0216804 | ||||||||
\(487\) | −9.38327 | −0.425197 | −0.212598 | − | 0.977140i | \(-0.568193\pi\) | ||||
−0.212598 | + | 0.977140i | \(0.568193\pi\) | |||||||
\(488\) | 28.1591 | 1.27470 | ||||||||
\(489\) | 0.000403490 0 | 1.82465e−5 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4624 | 1.10397 | 0.551987 | − | 0.833853i | \(-0.313870\pi\) | ||||
0.551987 | + | 0.833853i | \(0.313870\pi\) | |||||||
\(492\) | −0.0843733 | −0.00380384 | ||||||||
\(493\) | −4.46200 | −0.200958 | ||||||||
\(494\) | −13.9715 | −0.628606 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7276 | −0.526587 | ||||||||
\(497\) | −11.0031 | −0.493558 | ||||||||
\(498\) | 0.261341 | 0.0117110 | ||||||||
\(499\) | 9.26057 | 0.414560 | 0.207280 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207280 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0502277 | 0.00224401 | ||||||||
\(502\) | 9.55045 | 0.426258 | ||||||||
\(503\) | −5.76022 | −0.256836 | −0.128418 | − | 0.991720i | \(-0.540990\pi\) | ||||
−0.128418 | + | 0.991720i | \(0.540990\pi\) | |||||||
\(504\) | 10.2452 | 0.456359 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.6715 | 0.518863 | ||||||||
\(507\) | −0.0154586 | −0.000686539 0 | ||||||||
\(508\) | −50.3848 | −2.23546 | ||||||||
\(509\) | 10.7526 | 0.476600 | 0.238300 | − | 0.971192i | \(-0.423410\pi\) | ||||
0.238300 | + | 0.971192i | \(0.423410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6586 | 0.604220 | ||||||||
\(512\) | −11.8397 | −0.523247 | ||||||||
\(513\) | −0.0700626 | −0.00309334 | ||||||||
\(514\) | −45.0382 | −1.98655 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0892191 | 0.00392765 | ||||||||
\(517\) | −40.3203 | −1.77328 | ||||||||
\(518\) | −10.3462 | −0.454586 | ||||||||
\(519\) | −0.0512659 | −0.00225032 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.29984 | 0.0569470 | 0.0284735 | − | 0.999595i | \(-0.490935\pi\) | ||||
0.0284735 | + | 0.999595i | \(0.490935\pi\) | |||||||
\(522\) | 65.7684 | 2.87861 | ||||||||
\(523\) | 4.59165 | 0.200779 | 0.100390 | − | 0.994948i | \(-0.467991\pi\) | ||||
0.100390 | + | 0.994948i | \(0.467991\pi\) | |||||||
\(524\) | −22.7792 | −0.995114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 59.0455 | 2.57451 | ||||||||
\(527\) | −5.27073 | −0.229597 | ||||||||
\(528\) | 0.0400382 | 0.00174244 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.6856 | 1.54862 | ||||||||
\(532\) | 5.33586 | 0.231339 | ||||||||
\(533\) | 12.4799 | 0.540563 | ||||||||
\(534\) | 0.107669 | 0.00465931 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.5157 | −0.670177 | ||||||||
\(537\) | −0.0718514 | −0.00310062 | ||||||||
\(538\) | 18.3298 | 0.790256 | ||||||||
\(539\) | −4.99434 | −0.215121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9259 | 1.50158 | 0.750791 | − | 0.660540i | \(-0.229673\pi\) | ||||
0.750791 | + | 0.660540i | \(0.229673\pi\) | |||||||
\(542\) | −45.5865 | −1.95811 | ||||||||
\(543\) | −0.136731 | −0.00586769 | ||||||||
\(544\) | −2.07238 | −0.0888524 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0686542 | 0.00293813 | ||||||||
\(547\) | −27.0941 | −1.15846 | −0.579229 | − | 0.815165i | \(-0.696646\pi\) | ||||
−0.579229 | + | 0.815165i | \(0.696646\pi\) | |||||||
\(548\) | 25.5231 | 1.09029 | ||||||||
\(549\) | −24.7356 | −1.05569 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4614 | 0.616077 | ||||||||
\(552\) | 0.0258697 | 0.00110109 | ||||||||
\(553\) | −13.1029 | −0.557192 | ||||||||
\(554\) | −58.2280 | −2.47387 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.6613 | −1.72442 | ||||||||
\(557\) | −23.9676 | −1.01554 | −0.507770 | − | 0.861492i | \(-0.669530\pi\) | ||||
−0.507770 | + | 0.861492i | \(0.669530\pi\) | |||||||
\(558\) | 77.6889 | 3.28883 | ||||||||
\(559\) | −13.1966 | −0.558158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0179943 | 0.000759721 0 | ||||||||
\(562\) | −6.50571 | −0.274427 | ||||||||
\(563\) | −33.5325 | −1.41323 | −0.706613 | − | 0.707601i | \(-0.749778\pi\) | ||||
−0.706613 | + | 0.707601i | \(0.749778\pi\) | |||||||
\(564\) | −0.211678 | −0.00891325 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.3016 | 1.18960 | ||||||||
\(567\) | −8.99948 | −0.377943 | ||||||||
\(568\) | 37.5773 | 1.57671 | ||||||||
\(569\) | −8.02616 | −0.336474 | −0.168237 | − | 0.985747i | \(-0.553807\pi\) | ||||
−0.168237 | + | 0.985747i | \(0.553807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.76773 | 0.408767 | 0.204383 | − | 0.978891i | \(-0.434481\pi\) | ||||
0.204383 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(572\) | −67.0440 | −2.80325 | ||||||||
\(573\) | 0.179509 | 0.00749911 | ||||||||
\(574\) | −7.52014 | −0.313885 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 36.8959 | 1.53733 | ||||||||
\(577\) | −4.38607 | −0.182595 | −0.0912973 | − | 0.995824i | \(-0.529101\pi\) | ||||
−0.0912973 | + | 0.995824i | \(0.529101\pi\) | |||||||
\(578\) | −39.1996 | −1.63049 | ||||||||
\(579\) | 0.109865 | 0.00456581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7630 | 0.612473 | ||||||||
\(582\) | 0.0693446 | 0.00287442 | ||||||||
\(583\) | −7.33379 | −0.303735 | ||||||||
\(584\) | −46.6460 | −1.93023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.52094 | 0.0628295 | ||||||||
\(587\) | 18.7391 | 0.773445 | 0.386723 | − | 0.922196i | \(-0.373607\pi\) | ||||
0.386723 | + | 0.922196i | \(0.373607\pi\) | |||||||
\(588\) | −0.0262198 | −0.00108129 | ||||||||
\(589\) | 17.0825 | 0.703874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0199628 | 0.000821162 0 | ||||||||
\(592\) | 4.68539 | 0.192568 | ||||||||
\(593\) | 22.0316 | 0.904731 | 0.452366 | − | 0.891833i | \(-0.350580\pi\) | ||||
0.452366 | + | 0.891833i | \(0.350580\pi\) | |||||||
\(594\) | −0.530466 | −0.0217653 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.978186 | 0.0400681 | ||||||||
\(597\) | 0.147907 | 0.00605343 | ||||||||
\(598\) | −9.06327 | −0.370625 | ||||||||
\(599\) | 0.514129 | 0.0210067 | 0.0105034 | − | 0.999945i | \(-0.496657\pi\) | ||||
0.0105034 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.8191 | −1.54267 | −0.771337 | − | 0.636427i | \(-0.780412\pi\) | ||||
−0.771337 | + | 0.636427i | \(0.780412\pi\) | |||||||
\(602\) | 7.95205 | 0.324101 | ||||||||
\(603\) | 13.6294 | 0.555030 | ||||||||
\(604\) | 67.6431 | 2.75236 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.0494040 | −0.00200690 | ||||||||
\(607\) | 41.2268 | 1.67334 | 0.836672 | − | 0.547704i | \(-0.184498\pi\) | ||||
0.836672 | + | 0.547704i | \(0.184498\pi\) | |||||||
\(608\) | 6.71660 | 0.272394 | ||||||||
\(609\) | −0.0710618 | −0.00287957 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.3098 | 1.26666 | ||||||||
\(612\) | −4.93896 | −0.199646 | ||||||||
\(613\) | −0.810033 | −0.0327169 | −0.0163585 | − | 0.999866i | \(-0.505207\pi\) | ||||
−0.0163585 | + | 0.999866i | \(0.505207\pi\) | |||||||
\(614\) | −52.7069 | −2.12708 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.0564 | 0.687221 | ||||||||
\(617\) | −21.8594 | −0.880025 | −0.440012 | − | 0.897992i | \(-0.645026\pi\) | ||||
−0.440012 | + | 0.897992i | \(0.645026\pi\) | |||||||
\(618\) | 0.232431 | 0.00934974 | ||||||||
\(619\) | −1.80602 | −0.0725901 | −0.0362950 | − | 0.999341i | \(-0.511556\pi\) | ||||
−0.0362950 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0454495 | −0.00182383 | ||||||||
\(622\) | 60.2586 | 2.41615 | ||||||||
\(623\) | 6.08219 | 0.243678 | ||||||||
\(624\) | −0.0310908 | −0.00124463 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.0490 | −0.521544 | ||||||||
\(627\) | −0.0583199 | −0.00232907 | ||||||||
\(628\) | 82.0766 | 3.27521 | ||||||||
\(629\) | 2.10575 | 0.0839616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9474 | 1.70971 | 0.854854 | − | 0.518869i | \(-0.173647\pi\) | ||||
0.854854 | + | 0.518869i | \(0.173647\pi\) | |||||||
\(632\) | 44.7483 | 1.77999 | ||||||||
\(633\) | 0.0797925 | 0.00317147 | ||||||||
\(634\) | 10.1726 | 0.404007 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0385018 | −0.00152669 | ||||||||
\(637\) | 3.87824 | 0.153661 | ||||||||
\(638\) | 109.492 | 4.33483 | ||||||||
\(639\) | −33.0088 | −1.30581 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.7586 | 1.60987 | 0.804933 | − | 0.593365i | \(-0.202201\pi\) | ||||
0.804933 | + | 0.593365i | \(0.202201\pi\) | |||||||
\(642\) | −0.320782 | −0.0126603 | ||||||||
\(643\) | −40.0053 | −1.57765 | −0.788827 | − | 0.614615i | \(-0.789311\pi\) | ||||
−0.788827 | + | 0.614615i | \(0.789311\pi\) | |||||||
\(644\) | 3.46136 | 0.136397 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.71350 | −0.0674166 | ||||||||
\(647\) | −12.2909 | −0.483207 | −0.241604 | − | 0.970375i | \(-0.577673\pi\) | ||||
−0.241604 | + | 0.970375i | \(0.577673\pi\) | |||||||
\(648\) | 30.7345 | 1.20737 | ||||||||
\(649\) | 59.4097 | 2.33203 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0839417 | −0.00328993 | ||||||||
\(652\) | −0.184373 | −0.00722061 | ||||||||
\(653\) | −18.1745 | −0.711221 | −0.355611 | − | 0.934634i | \(-0.615727\pi\) | ||||
−0.355611 | + | 0.934634i | \(0.615727\pi\) | |||||||
\(654\) | 0.156946 | 0.00613706 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.40558 | 0.132965 | ||||||||
\(657\) | 40.9750 | 1.59859 | ||||||||
\(658\) | −18.8667 | −0.735502 | ||||||||
\(659\) | 4.72077 | 0.183895 | 0.0919476 | − | 0.995764i | \(-0.470691\pi\) | ||||
0.0919476 | + | 0.995764i | \(0.470691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.3257 | −1.25732 | −0.628662 | − | 0.777679i | \(-0.716397\pi\) | ||||
−0.628662 | + | 0.777679i | \(0.716397\pi\) | |||||||
\(662\) | −25.1568 | −0.977746 | ||||||||
\(663\) | −0.0139731 | −0.000542670 0 | ||||||||
\(664\) | −50.4178 | −1.95659 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −31.0380 | −1.20270 | ||||||||
\(667\) | 9.38110 | 0.363238 | ||||||||
\(668\) | −22.9514 | −0.888014 | ||||||||
\(669\) | 0.115410 | 0.00446200 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.1800 | −1.58974 | ||||||||
\(672\) | −0.0330047 | −0.00127318 | ||||||||
\(673\) | 24.3701 | 0.939398 | 0.469699 | − | 0.882827i | \(-0.344363\pi\) | ||||
0.469699 | + | 0.882827i | \(0.344363\pi\) | |||||||
\(674\) | 0.970033 | 0.0373643 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.06373 | 0.271682 | ||||||||
\(677\) | −4.98060 | −0.191420 | −0.0957101 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957101 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(678\) | −0.101184 | −0.00388596 | ||||||||
\(679\) | 3.91724 | 0.150330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.207883 | −0.00796611 | ||||||||
\(682\) | 129.337 | 4.95258 | ||||||||
\(683\) | −46.8124 | −1.79122 | −0.895612 | − | 0.444835i | \(-0.853262\pi\) | ||||
−0.895612 | + | 0.444835i | \(0.853262\pi\) | |||||||
\(684\) | 16.0073 | 0.612053 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.33696 | −0.0892254 | ||||||||
\(687\) | −0.225942 | −0.00862022 | ||||||||
\(688\) | −3.60117 | −0.137293 | ||||||||
\(689\) | 5.69489 | 0.216958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7972 | −1.28571 | −0.642853 | − | 0.765990i | \(-0.722249\pi\) | ||||
−0.642853 | + | 0.765990i | \(0.722249\pi\) | |||||||
\(692\) | 23.4258 | 0.890514 | ||||||||
\(693\) | −14.9827 | −0.569147 | ||||||||
\(694\) | 9.56957 | 0.363256 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.242686 | 0.00919900 | ||||||||
\(697\) | 1.53056 | 0.0579742 | ||||||||
\(698\) | −11.5248 | −0.436218 | ||||||||
\(699\) | −0.173633 | −0.00656741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.84137 | 0.145087 | 0.0725433 | − | 0.997365i | \(-0.476888\pi\) | ||||
0.0725433 | + | 0.997365i | \(0.476888\pi\) | |||||||
\(702\) | 0.411922 | 0.0155470 | ||||||||
\(703\) | −6.82476 | −0.257401 | ||||||||
\(704\) | 61.4247 | 2.31503 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1794 | −1.24872 | ||||||||
\(707\) | −2.79080 | −0.104959 | ||||||||
\(708\) | 0.311896 | 0.0117218 | ||||||||
\(709\) | −16.3215 | −0.612966 | −0.306483 | − | 0.951876i | \(-0.599152\pi\) | ||||
−0.306483 | + | 0.951876i | \(0.599152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.3080 | −1.47416 | ||||||||
\(712\) | −20.7715 | −0.778447 | ||||||||
\(713\) | 11.0814 | 0.415003 | ||||||||
\(714\) | 0.00841993 | 0.000315108 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.8322 | 1.22700 | ||||||||
\(717\) | −0.115716 | −0.00432148 | ||||||||
\(718\) | −57.3039 | −2.13856 | ||||||||
\(719\) | 22.4621 | 0.837694 | 0.418847 | − | 0.908057i | \(-0.362434\pi\) | ||||
0.418847 | + | 0.908057i | \(0.362434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1299 | 0.488982 | ||||||||
\(722\) | −38.8487 | −1.44580 | ||||||||
\(723\) | −0.0446233 | −0.00165956 | ||||||||
\(724\) | 62.4787 | 2.32200 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.246832 | −0.00916079 | ||||||||
\(727\) | −22.6321 | −0.839378 | −0.419689 | − | 0.907668i | \(-0.637861\pi\) | ||||
−0.419689 | + | 0.907668i | \(0.637861\pi\) | |||||||
\(728\) | −13.2447 | −0.490883 | ||||||||
\(729\) | −26.9969 | −0.999885 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.61847 | −0.0598612 | ||||||||
\(732\) | −0.216192 | −0.00799067 | ||||||||
\(733\) | −39.9481 | −1.47552 | −0.737758 | − | 0.675065i | \(-0.764116\pi\) | ||||
−0.737758 | + | 0.675065i | \(0.764116\pi\) | |||||||
\(734\) | 38.3314 | 1.41484 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.35705 | 0.160603 | ||||||||
\(737\) | 22.6903 | 0.835808 | ||||||||
\(738\) | −22.5600 | −0.830445 | ||||||||
\(739\) | −30.1882 | −1.11049 | −0.555246 | − | 0.831686i | \(-0.687376\pi\) | ||||
−0.555246 | + | 0.831686i | \(0.687376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0452870 | 0.00166366 | ||||||||
\(742\) | −3.43164 | −0.125979 | ||||||||
\(743\) | 31.0282 | 1.13831 | 0.569156 | − | 0.822229i | \(-0.307270\pi\) | ||||
0.569156 | + | 0.822229i | \(0.307270\pi\) | |||||||
\(744\) | 0.286673 | 0.0105099 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.04773 | 0.294648 | ||||||||
\(747\) | 44.2882 | 1.62042 | ||||||||
\(748\) | −8.22244 | −0.300642 | ||||||||
\(749\) | −18.1208 | −0.662120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.9950 | 1.45944 | 0.729720 | − | 0.683746i | \(-0.239651\pi\) | ||||
0.729720 | + | 0.683746i | \(0.239651\pi\) | |||||||
\(752\) | 8.54400 | 0.311567 | ||||||||
\(753\) | −0.0309568 | −0.00112813 | ||||||||
\(754\) | −85.0235 | −3.09637 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.157317 | −0.00572158 | ||||||||
\(757\) | 35.1223 | 1.27654 | 0.638270 | − | 0.769812i | \(-0.279650\pi\) | ||||
0.638270 | + | 0.769812i | \(0.279650\pi\) | |||||||
\(758\) | −7.68455 | −0.279115 | ||||||||
\(759\) | −0.0378321 | −0.00137322 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.62354 | 0.203853 | 0.101927 | − | 0.994792i | \(-0.467499\pi\) | ||||
0.101927 | + | 0.994792i | \(0.467499\pi\) | |||||||
\(762\) | 0.257682 | 0.00933485 | ||||||||
\(763\) | 8.86577 | 0.320962 | ||||||||
\(764\) | −82.0261 | −2.96760 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.4949 | 1.53540 | ||||||||
\(767\) | −46.1333 | −1.66578 | ||||||||
\(768\) | 0.168213 | 0.00606988 | ||||||||
\(769\) | −29.0696 | −1.04828 | −0.524138 | − | 0.851634i | \(-0.675612\pi\) | ||||
−0.524138 | + | 0.851634i | \(0.675612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.145986 | 0.00525758 | ||||||||
\(772\) | −50.2022 | −1.80682 | ||||||||
\(773\) | 32.3579 | 1.16383 | 0.581917 | − | 0.813248i | \(-0.302303\pi\) | ||||
0.581917 | + | 0.813248i | \(0.302303\pi\) | |||||||
\(774\) | 23.8557 | 0.857475 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.3779 | −0.480240 | ||||||||
\(777\) | 0.0335361 | 0.00120310 | ||||||||
\(778\) | −65.2889 | −2.34072 | ||||||||
\(779\) | −4.96058 | −0.177731 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.9533 | −1.96639 | ||||||||
\(782\) | −1.11154 | −0.0397487 | ||||||||
\(783\) | −0.426367 | −0.0152371 | ||||||||
\(784\) | 1.05832 | 0.0377970 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.116500 | 0.00415540 | ||||||||
\(787\) | −12.6066 | −0.449378 | −0.224689 | − | 0.974431i | \(-0.572137\pi\) | ||||
−0.224689 | + | 0.974431i | \(0.572137\pi\) | |||||||
\(788\) | −9.12195 | −0.324956 | ||||||||
\(789\) | −0.191390 | −0.00681365 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.71585 | −0.203232 | ||||||||
\(792\) | 51.1682 | 1.81818 | ||||||||
\(793\) | 31.9774 | 1.13555 | ||||||||
\(794\) | 48.1187 | 1.70767 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67.5856 | −2.39551 | ||||||||
\(797\) | 31.7455 | 1.12448 | 0.562242 | − | 0.826973i | \(-0.309939\pi\) | ||||
0.562242 | + | 0.826973i | \(0.309939\pi\) | |||||||
\(798\) | −0.0272891 | −0.000966025 0 | ||||||||
\(799\) | 3.83991 | 0.135846 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.2462 | 0.644698 | ||||||||
\(802\) | 1.04829 | 0.0370165 | ||||||||
\(803\) | 68.2155 | 2.40727 | ||||||||
\(804\) | 0.119122 | 0.00420111 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −100.434 | −3.53764 | ||||||||
\(807\) | −0.0594142 | −0.00209148 | ||||||||
\(808\) | 9.53099 | 0.335299 | ||||||||
\(809\) | −21.5831 | −0.758821 | −0.379411 | − | 0.925228i | \(-0.623873\pi\) | ||||
−0.379411 | + | 0.925228i | \(0.623873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.27428 | −0.220320 | −0.110160 | − | 0.993914i | \(-0.535136\pi\) | ||||
−0.110160 | + | 0.993914i | \(0.535136\pi\) | |||||||
\(812\) | 32.4714 | 1.13952 | ||||||||
\(813\) | 0.147764 | 0.00518230 | ||||||||
\(814\) | −51.6724 | −1.81112 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.00381305 | −0.000133484 0 | ||||||||
\(817\) | 5.24548 | 0.183516 | ||||||||
\(818\) | −14.9589 | −0.523027 | ||||||||
\(819\) | 11.6345 | 0.406542 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.7376 | −1.77075 | −0.885377 | − | 0.464874i | \(-0.846100\pi\) | ||||
−0.885377 | + | 0.464874i | \(0.846100\pi\) | |||||||
\(822\) | −0.130533 | −0.00455285 | ||||||||
\(823\) | 20.6689 | 0.720473 | 0.360236 | − | 0.932861i | \(-0.382696\pi\) | ||||
0.360236 | + | 0.932861i | \(0.382696\pi\) | |||||||
\(824\) | −44.8404 | −1.56209 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.7991 | 0.967253 | ||||||||
\(827\) | −9.51670 | −0.330928 | −0.165464 | − | 0.986216i | \(-0.552912\pi\) | ||||
−0.165464 | + | 0.986216i | \(0.552912\pi\) | |||||||
\(828\) | 10.3839 | 0.360865 | ||||||||
\(829\) | 43.2509 | 1.50217 | 0.751083 | − | 0.660208i | \(-0.229532\pi\) | ||||
0.751083 | + | 0.660208i | \(0.229532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.188740 | 0.00654731 | ||||||||
\(832\) | −47.6980 | −1.65363 | ||||||||
\(833\) | 0.475637 | 0.0164798 | ||||||||
\(834\) | 0.207954 | 0.00720086 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.6491 | 0.921677 | ||||||||
\(837\) | −0.503645 | −0.0174085 | ||||||||
\(838\) | −19.8410 | −0.685396 | ||||||||
\(839\) | 12.6656 | 0.437264 | 0.218632 | − | 0.975807i | \(-0.429841\pi\) | ||||
0.218632 | + | 0.975807i | \(0.429841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0051 | 2.03466 | ||||||||
\(842\) | −59.3389 | −2.04495 | ||||||||
\(843\) | 0.0210876 | 0.000726294 0 | ||||||||
\(844\) | −36.4609 | −1.25504 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −56.5991 | −1.94592 | ||||||||
\(847\) | −13.9434 | −0.479101 | ||||||||
\(848\) | 1.55405 | 0.0533664 | ||||||||
\(849\) | −0.0917365 | −0.00314839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.42722 | −0.151763 | ||||||||
\(852\) | −0.288500 | −0.00988385 | ||||||||
\(853\) | −5.14537 | −0.176174 | −0.0880871 | − | 0.996113i | \(-0.528075\pi\) | ||||
−0.0880871 | + | 0.996113i | \(0.528075\pi\) | |||||||
\(854\) | −19.2690 | −0.659372 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 61.8852 | 2.11519 | ||||||||
\(857\) | 13.1648 | 0.449702 | 0.224851 | − | 0.974393i | \(-0.427810\pi\) | ||||
0.224851 | + | 0.974393i | \(0.427810\pi\) | |||||||
\(858\) | 0.342882 | 0.0117058 | ||||||||
\(859\) | −27.8506 | −0.950249 | −0.475124 | − | 0.879919i | \(-0.657597\pi\) | ||||
−0.475124 | + | 0.879919i | \(0.657597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0243757 | 0.000830723 0 | ||||||||
\(862\) | 45.1619 | 1.53822 | ||||||||
\(863\) | −36.4254 | −1.23994 | −0.619968 | − | 0.784627i | \(-0.712854\pi\) | ||||
−0.619968 | + | 0.784627i | \(0.712854\pi\) | |||||||
\(864\) | −0.198026 | −0.00673698 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −83.3628 | −2.83278 | ||||||||
\(867\) | 0.127061 | 0.00431522 | ||||||||
\(868\) | 38.3568 | 1.30192 | ||||||||
\(869\) | −65.4403 | −2.21991 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.6196 | −0.597019 | ||||||||
\(872\) | −30.2779 | −1.02534 | ||||||||
\(873\) | 11.7515 | 0.397727 | ||||||||
\(874\) | 3.60253 | 0.121857 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.358125 | 0.0120999 | ||||||||
\(877\) | 32.5408 | 1.09882 | 0.549412 | − | 0.835551i | \(-0.314852\pi\) | ||||
0.549412 | + | 0.835551i | \(0.314852\pi\) | |||||||
\(878\) | −42.7589 | −1.44304 | ||||||||
\(879\) | −0.00492997 | −0.000166284 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.7388 | −0.766088 | −0.383044 | − | 0.923730i | \(-0.625124\pi\) | ||||
−0.383044 | + | 0.923730i | \(0.625124\pi\) | |||||||
\(882\) | −7.01073 | −0.236064 | ||||||||
\(883\) | 13.1029 | 0.440946 | 0.220473 | − | 0.975393i | \(-0.429240\pi\) | ||||
0.220473 | + | 0.975393i | \(0.429240\pi\) | |||||||
\(884\) | 6.38495 | 0.214749 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.40707 | 0.316037 | ||||||||
\(887\) | 16.4374 | 0.551914 | 0.275957 | − | 0.961170i | \(-0.411005\pi\) | ||||
0.275957 | + | 0.961170i | \(0.411005\pi\) | |||||||
\(888\) | −0.114531 | −0.00384340 | ||||||||
\(889\) | 14.5563 | 0.488204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.9464 | −1.50576 | ||||||||
\(892\) | −52.7361 | −1.76574 | ||||||||
\(893\) | −12.4452 | −0.416464 | ||||||||
\(894\) | −0.00500273 | −0.000167316 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.0278 | 0.669083 | ||||||||
\(897\) | 0.0293776 | 0.000980891 0 | ||||||||
\(898\) | 69.6093 | 2.32289 | ||||||||
\(899\) | 103.956 | 3.46713 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.698436 | 0.0232683 | ||||||||
\(902\) | −37.5581 | −1.25055 | ||||||||
\(903\) | −0.0257757 | −0.000857762 0 | ||||||||
\(904\) | 19.5205 | 0.649241 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.345947 | −0.0114933 | ||||||||
\(907\) | 49.2654 | 1.63583 | 0.817916 | − | 0.575338i | \(-0.195129\pi\) | ||||
0.817916 | + | 0.575338i | \(0.195129\pi\) | |||||||
\(908\) | 94.9915 | 3.15240 | ||||||||
\(909\) | −8.37225 | −0.277690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.82158 | 0.259140 | 0.129570 | − | 0.991570i | \(-0.458640\pi\) | ||||
0.129570 | + | 0.991570i | \(0.458640\pi\) | |||||||
\(912\) | 0.0123582 | 0.000409220 0 | ||||||||
\(913\) | 73.7314 | 2.44015 | ||||||||
\(914\) | 45.6906 | 1.51131 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 103.243 | 3.41126 | ||||||||
\(917\) | 6.58099 | 0.217323 | ||||||||
\(918\) | 0.0505191 | 0.00166738 | ||||||||
\(919\) | 47.8000 | 1.57678 | 0.788388 | − | 0.615178i | \(-0.210916\pi\) | ||||
0.788388 | + | 0.615178i | \(0.210916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.170844 | 0.00562950 | ||||||||
\(922\) | 0.448462 | 0.0147693 | ||||||||
\(923\) | 42.6728 | 1.40459 | ||||||||
\(924\) | −0.130951 | −0.00430796 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −61.2699 | −2.01345 | ||||||||
\(927\) | 39.3889 | 1.29370 | ||||||||
\(928\) | 40.8740 | 1.34175 | ||||||||
\(929\) | −22.2564 | −0.730210 | −0.365105 | − | 0.930966i | \(-0.618967\pi\) | ||||
−0.365105 | + | 0.930966i | \(0.618967\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.54155 | −0.0505222 | ||||||||
\(932\) | 79.3410 | 2.59890 | ||||||||
\(933\) | −0.195322 | −0.00639455 | ||||||||
\(934\) | −96.3263 | −3.15189 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.7335 | −1.29873 | ||||||||
\(937\) | 3.52344 | 0.115106 | 0.0575529 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575529 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(938\) | 10.6173 | 0.346666 | ||||||||
\(939\) | 0.0422970 | 0.00138031 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.9747 | −0.716355 | −0.358178 | − | 0.933653i | \(-0.616602\pi\) | ||||
−0.358178 | + | 0.933653i | \(0.616602\pi\) | |||||||
\(942\) | −0.419764 | −0.0136766 | ||||||||
\(943\) | −3.21792 | −0.104790 | ||||||||
\(944\) | −12.5891 | −0.409740 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.7152 | 1.29125 | ||||||||
\(947\) | −8.71337 | −0.283146 | −0.141573 | − | 0.989928i | \(-0.545216\pi\) | ||||
−0.141573 | + | 0.989928i | \(0.545216\pi\) | |||||||
\(948\) | −0.343556 | −0.0111582 | ||||||||
\(949\) | −52.9712 | −1.71952 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0329736 | −0.00106924 | ||||||||
\(952\) | −1.62437 | −0.0526461 | ||||||||
\(953\) | −22.0600 | −0.714594 | −0.357297 | − | 0.933991i | \(-0.616302\pi\) | ||||
−0.357297 | + | 0.933991i | \(0.616302\pi\) | |||||||
\(954\) | −10.2947 | −0.333304 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 52.8758 | 1.71013 | ||||||||
\(957\) | −0.354906 | −0.0114725 | ||||||||
\(958\) | −10.6259 | −0.343306 | ||||||||
\(959\) | −7.37371 | −0.238109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 91.7979 | 2.96122 | ||||||||
\(962\) | 40.1251 | 1.29368 | ||||||||
\(963\) | −54.3614 | −1.75177 | ||||||||
\(964\) | 20.3904 | 0.656732 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.0177024 | −0.000569566 0 | ||||||||
\(967\) | −14.8633 | −0.477973 | −0.238986 | − | 0.971023i | \(-0.576815\pi\) | ||||
−0.238986 | + | 0.971023i | \(0.576815\pi\) | |||||||
\(968\) | 47.6187 | 1.53052 | ||||||||
\(969\) | 0.00555411 | 0.000178424 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4718 | −1.04207 | −0.521036 | − | 0.853535i | \(-0.674454\pi\) | ||||
−0.521036 | + | 0.853535i | \(0.674454\pi\) | |||||||
\(972\) | −0.707917 | −0.0227064 | ||||||||
\(973\) | 11.7472 | 0.376598 | ||||||||
\(974\) | −21.9283 | −0.702628 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.72618 | 0.279318 | ||||||||
\(977\) | −17.9922 | −0.575622 | −0.287811 | − | 0.957687i | \(-0.592928\pi\) | ||||
−0.287811 | + | 0.957687i | \(0.592928\pi\) | |||||||
\(978\) | 0.000942939 0 | 3.01519e−5 0 | ||||||||
\(979\) | 30.3765 | 0.970836 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.5968 | 0.849170 | ||||||||
\(982\) | 57.1677 | 1.82429 | ||||||||
\(983\) | −7.91109 | −0.252325 | −0.126162 | − | 0.992010i | \(-0.540266\pi\) | ||||
−0.126162 | + | 0.992010i | \(0.540266\pi\) | |||||||
\(984\) | −0.0832467 | −0.00265381 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.4275 | −0.332079 | ||||||||
\(987\) | 0.0611545 | 0.00194657 | ||||||||
\(988\) | −20.6937 | −0.658355 | ||||||||
\(989\) | 3.40274 | 0.108201 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.8214 | 0.756712 | 0.378356 | − | 0.925660i | \(-0.376490\pi\) | ||||
0.378356 | + | 0.925660i | \(0.376490\pi\) | |||||||
\(992\) | 48.2824 | 1.53297 | ||||||||
\(993\) | 0.0815430 | 0.00258769 | ||||||||
\(994\) | −25.7138 | −0.815594 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.387083 | 0.0122652 | ||||||||
\(997\) | −3.86775 | −0.122493 | −0.0612464 | − | 0.998123i | \(-0.519508\pi\) | ||||
−0.0612464 | + | 0.998123i | \(0.519508\pi\) | |||||||
\(998\) | 21.6415 | 0.685051 | ||||||||
\(999\) | 0.201215 | 0.00636616 |
(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 | 4025.2.a.z.1.13 | ✓ | 14 | |
5.4 | even | 2 | 4025.2.a.bc.1.2 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.z.1.13 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4025.2.a.bc.1.2 | yes | 14 | 5.4 | even | 2 |