Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8012,2,Mod(1,8012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8012, 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("8012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8012 = 2^{2} \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8012.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: | \(63.9761420994\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8012.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.68647 | −1.55104 | −0.775518 | − | 0.631325i | \(-0.782511\pi\) | ||||
−0.775518 | + | 0.631325i | \(0.782511\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.588575 | −0.263219 | −0.131609 | − | 0.991302i | \(-0.542014\pi\) | ||||
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.13984 | −0.430820 | −0.215410 | − | 0.976524i | \(-0.569109\pi\) | ||||
−0.215410 | + | 0.976524i | \(0.569109\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.21715 | 1.40572 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.44297 | 1.33961 | 0.669804 | − | 0.742538i | \(-0.266378\pi\) | ||||
0.669804 | + | 0.742538i | \(0.266378\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.61182 | 1.27909 | 0.639544 | − | 0.768754i | \(-0.279123\pi\) | ||||
0.639544 | + | 0.768754i | \(0.279123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.58119 | 0.408262 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.78229 | 1.40241 | 0.701205 | − | 0.712959i | \(-0.252646\pi\) | ||||
0.701205 | + | 0.712959i | \(0.252646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.59831 | −1.51376 | −0.756878 | − | 0.653556i | \(-0.773277\pi\) | ||||
−0.756878 | + | 0.653556i | \(0.773277\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.06216 | 0.668218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.93873 | −0.821282 | −0.410641 | − | 0.911797i | \(-0.634695\pi\) | ||||
−0.410641 | + | 0.911797i | \(0.634695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65358 | −0.930716 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.26983 | −0.629279 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.50173 | −1.20734 | −0.603670 | − | 0.797234i | \(-0.706296\pi\) | ||||
−0.603670 | + | 0.797234i | \(0.706296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.98799 | −0.357054 | −0.178527 | − | 0.983935i | \(-0.557133\pi\) | ||||
−0.178527 | + | 0.983935i | \(0.557133\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.9359 | −2.07778 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.670883 | 0.113400 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93340 | 0.811047 | 0.405523 | − | 0.914085i | \(-0.367089\pi\) | ||||
0.405523 | + | 0.914085i | \(0.367089\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.3895 | −1.98391 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.81524 | 0.908189 | 0.454094 | − | 0.890954i | \(-0.349963\pi\) | ||||
0.454094 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.68453 | −0.714384 | −0.357192 | − | 0.934031i | \(-0.616266\pi\) | ||||
−0.357192 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.48210 | −0.370010 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.11178 | −0.162170 | −0.0810851 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810851 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.70076 | −0.814394 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.5340 | −2.17519 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.55100 | −0.625128 | −0.312564 | − | 0.949897i | \(-0.601188\pi\) | ||||
−0.312564 | + | 0.949897i | \(0.601188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.61502 | −0.352609 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.7262 | 2.34789 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.13024 | −0.537711 | −0.268855 | − | 0.963181i | \(-0.586645\pi\) | ||||
−0.268855 | + | 0.963181i | \(0.586645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0444 | 1.54213 | 0.771064 | − | 0.636758i | \(-0.219725\pi\) | ||||
0.771064 | + | 0.636758i | \(0.219725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.80688 | −0.605611 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.71440 | −0.336680 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.65722 | −0.935478 | −0.467739 | − | 0.883867i | \(-0.654931\pi\) | ||||
−0.467739 | + | 0.883867i | \(0.654931\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5813 | 1.27384 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.21273 | 0.381281 | 0.190640 | − | 0.981660i | \(-0.438944\pi\) | ||||
0.190640 | + | 0.981660i | \(0.438944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.14241 | 0.835956 | 0.417978 | − | 0.908457i | \(-0.362739\pi\) | ||||
0.417978 | + | 0.908457i | \(0.362739\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5017 | 1.44357 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.06429 | −0.577130 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.89847 | −0.888647 | −0.444324 | − | 0.895866i | \(-0.646556\pi\) | ||||
−0.444324 | + | 0.895866i | \(0.646556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.86712 | −0.429680 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.40674 | −0.154409 | −0.0772047 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772047 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40331 | −0.369141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.4667 | 1.87263 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.25688 | −0.769228 | −0.384614 | − | 0.923077i | \(-0.625665\pi\) | ||||
−0.384614 | + | 0.923077i | \(0.625665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.25675 | −0.551057 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.34069 | 0.553804 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.88360 | 0.398449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.0412 | 1.73027 | 0.865135 | − | 0.501538i | \(-0.167232\pi\) | ||||
0.865135 | + | 0.501538i | \(0.167232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.7367 | 1.88311 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6291 | −1.35614 | −0.678071 | − | 0.734996i | \(-0.737184\pi\) | ||||
−0.678071 | + | 0.734996i | \(0.737184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.44163 | 0.536180 | 0.268090 | − | 0.963394i | \(-0.413608\pi\) | ||||
0.268090 | + | 0.963394i | \(0.413608\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.80231 | −0.175887 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.9896 | 1.73912 | 0.869562 | − | 0.493824i | \(-0.164401\pi\) | ||||
0.869562 | + | 0.493824i | \(0.164401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.7027 | 1.59983 | 0.799913 | − | 0.600116i | \(-0.204879\pi\) | ||||
0.799913 | + | 0.600116i | \(0.204879\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.2535 | −1.25796 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.85049 | −0.738512 | −0.369256 | − | 0.929328i | \(-0.620387\pi\) | ||||
−0.369256 | + | 0.929328i | \(0.620387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.31824 | 0.216177 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.4487 | 1.79803 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.59090 | −0.604187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.74002 | 0.794548 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.6225 | −1.40863 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.68185 | 0.508200 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6340 | 1.56477 | 0.782384 | − | 0.622797i | \(-0.214004\pi\) | ||||
0.782384 | + | 0.622797i | \(0.214004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5849 | 1.10804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0381 | 1.22652 | 0.613258 | − | 0.789882i | \(-0.289858\pi\) | ||||
0.613258 | + | 0.789882i | \(0.289858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.52104 | 0.652157 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.92454 | 0.165638 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.98726 | −0.767833 | −0.383917 | − | 0.923368i | \(-0.625425\pi\) | ||||
−0.383917 | + | 0.923368i | \(0.625425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.64546 | −0.224385 | −0.112192 | − | 0.993686i | \(-0.535787\pi\) | ||||
−0.112192 | + | 0.993686i | \(0.535787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.98678 | 0.251532 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.4902 | 1.71348 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.82675 | 0.317795 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.3149 | 1.26315 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.9135 | −0.894067 | −0.447034 | − | 0.894517i | \(-0.647520\pi\) | ||||
−0.447034 | + | 0.894517i | \(0.647520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7257 | −1.11698 | −0.558491 | − | 0.829511i | \(-0.688619\pi\) | ||||
−0.558491 | + | 0.829511i | \(0.688619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.3847 | 1.97139 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17008 | 0.0939832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.69697 | −0.374859 | −0.187430 | − | 0.982278i | \(-0.560016\pi\) | ||||
−0.187430 | + | 0.982278i | \(0.560016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2261 | 0.969597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.48954 | 0.353825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.310071 | 0.0242866 | 0.0121433 | − | 0.999926i | \(-0.496135\pi\) | ||||
0.0121433 | + | 0.999926i | \(0.496135\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.02519 | 0.546910 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.1527 | −1.71423 | −0.857113 | − | 0.515129i | \(-0.827744\pi\) | ||||
−0.857113 | + | 0.515129i | \(0.827744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.26887 | 0.636067 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.8260 | −2.12791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.4511 | −1.85899 | −0.929493 | − | 0.368839i | \(-0.879755\pi\) | ||||
−0.929493 | + | 0.368839i | \(0.879755\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.30435 | 0.400971 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0958 | 0.834010 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.99995 | 0.224227 | 0.112113 | − | 0.993695i | \(-0.464238\pi\) | ||||
0.112113 | + | 0.993695i | \(0.464238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.62272 | 0.492263 | 0.246131 | − | 0.969236i | \(-0.420841\pi\) | ||||
0.246131 | + | 0.969236i | \(0.420841\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −32.3570 | −2.39190 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.90368 | −0.213483 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.6906 | 1.87868 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.72709 | 0.271106 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.3074 | 1.46939 | 0.734695 | − | 0.678398i | \(-0.237325\pi\) | ||||
0.734695 | + | 0.678398i | \(0.237325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.69413 | −0.193928 | −0.0969640 | − | 0.995288i | \(-0.530913\pi\) | ||||
−0.0969640 | + | 0.995288i | \(0.530913\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.29216 | 0.522203 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.27799 | −0.233547 | −0.116774 | − | 0.993159i | \(-0.537255\pi\) | ||||
−0.116774 | + | 0.993159i | \(0.537255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4085 | 1.30495 | 0.652474 | − | 0.757812i | \(-0.273731\pi\) | ||||
0.652474 | + | 0.757812i | \(0.273731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.5709 | 1.45096 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.41095 | 0.520147 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.42270 | −0.239052 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.6102 | −1.15449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.3161 | −2.02784 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4501 | −1.40784 | −0.703921 | − | 0.710278i | \(-0.748569\pi\) | ||||
−0.703921 | + | 0.710278i | \(0.748569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.63092 | −0.591381 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.75719 | 0.188039 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.26600 | 0.153826 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.1879 | −1.29660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.6669 | 1.79381 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2014 | −1.08493 | −0.542465 | − | 0.840079i | \(-0.682509\pi\) | ||||
−0.542465 | + | 0.840079i | \(0.682509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.6248 | −1.30832 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.8118 | −1.24858 | −0.624291 | − | 0.781192i | \(-0.714612\pi\) | ||||
−0.624291 | + | 0.781192i | \(0.714612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.07186 | 0.136912 | 0.0684562 | − | 0.997654i | \(-0.478193\pi\) | ||||
0.0684562 | + | 0.997654i | \(0.478193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6051 | 0.895150 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.3012 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.654367 | 0.0426862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.2190 | 1.37832 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.88060 | −0.186331 | −0.0931654 | − | 0.995651i | \(-0.529699\pi\) | ||||
−0.0931654 | + | 0.995651i | \(0.529699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.9437 | −1.28469 | −0.642343 | − | 0.766417i | \(-0.722038\pi\) | ||||
−0.642343 | + | 0.766417i | \(0.722038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.1984 | 1.29573 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.35532 | 0.214364 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.4302 | −1.93623 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.77916 | 0.239495 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9629 | 1.13381 | 0.566904 | − | 0.823784i | \(-0.308141\pi\) | ||||
0.566904 | + | 0.823784i | \(0.308141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.4997 | −1.10020 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.14290 | 0.572551 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.5817 | 1.65812 | 0.829062 | − | 0.559157i | \(-0.188875\pi\) | ||||
0.829062 | + | 0.559157i | \(0.188875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.62331 | −0.349415 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.4187 | −1.69718 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.8898 | −1.59643 | −0.798217 | − | 0.602370i | \(-0.794223\pi\) | ||||
−0.798217 | + | 0.602370i | \(0.794223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67860 | 0.164545 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4954 | 1.19310 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8940 | 0.786162 | 0.393081 | − | 0.919504i | \(-0.371409\pi\) | ||||
0.393081 | + | 0.919504i | \(0.371409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7829 | −0.715763 | −0.357881 | − | 0.933767i | \(-0.616501\pi\) | ||||
−0.357881 | + | 0.933767i | \(0.616501\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1221 | 0.854710 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.6757 | −1.24679 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6877 | 0.882498 | 0.441249 | − | 0.897385i | \(-0.354536\pi\) | ||||
0.441249 | + | 0.897385i | \(0.354536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.38365 | −0.501916 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6726 | 0.875292 | 0.437646 | − | 0.899147i | \(-0.355812\pi\) | ||||
0.437646 | + | 0.899147i | \(0.355812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.9171 | −1.77839 | −0.889194 | − | 0.457531i | \(-0.848734\pi\) | ||||
−0.889194 | + | 0.457531i | \(0.848734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.4332 | −0.618009 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.62847 | −0.391266 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4348 | 0.966756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45.7807 | −2.68371 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.00633 | −0.526155 | −0.263078 | − | 0.964775i | \(-0.584738\pi\) | ||||
−0.263078 | + | 0.964775i | \(0.584738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.43095 | 0.141536 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.5278 | −0.842987 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1647 | −1.05049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.33963 | 0.307771 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.6141 | 2.10343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.08903 | −0.405917 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.8875 | −1.42040 | −0.710202 | − | 0.703998i | \(-0.751396\pi\) | ||||
−0.710202 | + | 0.703998i | \(0.751396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.6188 | −0.831634 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4826 | −1.21817 | −0.609084 | − | 0.793106i | \(-0.708463\pi\) | ||||
−0.609084 | + | 0.793106i | \(0.708463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00068 | 0.508749 | 0.254374 | − | 0.967106i | \(-0.418130\pi\) | ||||
0.254374 | + | 0.967106i | \(0.418130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.82921 | 0.159408 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.4485 | 0.980004 | 0.490002 | − | 0.871721i | \(-0.336996\pi\) | ||||
0.490002 | + | 0.871721i | \(0.336996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.8870 | −1.61736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −48.3287 | −2.69744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −38.1533 | −2.12291 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.4615 | −1.19047 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44.8713 | −2.48139 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.26726 | 0.0698662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1209 | 0.831122 | 0.415561 | − | 0.909565i | \(-0.363585\pi\) | ||||
0.415561 | + | 0.909565i | \(0.363585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.8049 | 1.14010 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.50684 | 0.246235 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7645 | −0.695328 | −0.347664 | − | 0.937619i | \(-0.613025\pi\) | ||||
−0.347664 | + | 0.937619i | \(0.613025\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.0901 | 1.14546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.83260 | −0.478312 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4769 | 0.781678 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.22789 | −0.335298 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3748 | −0.664312 | −0.332156 | − | 0.943224i | \(-0.607776\pi\) | ||||
−0.332156 | + | 0.943224i | \(0.607776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.8885 | 1.33225 | 0.666124 | − | 0.745841i | \(-0.267952\pi\) | ||||
0.666124 | + | 0.745841i | \(0.267952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0799 | −0.804903 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.05852 | 0.482137 | 0.241068 | − | 0.970508i | \(-0.422502\pi\) | ||||
0.241068 | + | 0.970508i | \(0.422502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.89093 | −0.100360 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.7063 | 0.937116 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.5518 | 1.29580 | 0.647899 | − | 0.761727i | \(-0.275648\pi\) | ||||
0.647899 | + | 0.761727i | \(0.275648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.5377 | 1.29146 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.4798 | −1.23237 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.20384 | −0.220039 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.7211 | −1.55143 | −0.775715 | − | 0.631083i | \(-0.782611\pi\) | ||||
−0.775715 | + | 0.631083i | \(0.782611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.5237 | 1.27665 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.18743 | 0.269318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.4434 | −1.42097 | −0.710483 | − | 0.703714i | \(-0.751524\pi\) | ||||
−0.710483 | + | 0.703714i | \(0.751524\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.2642 | −0.788237 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.9848 | −1.54430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.7071 | 1.16638 | 0.583192 | − | 0.812334i | \(-0.301804\pi\) | ||||
0.583192 | + | 0.812334i | \(0.301804\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −47.3734 | −2.42701 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.6053 | −0.644101 | −0.322051 | − | 0.946722i | \(-0.604372\pi\) | ||||
−0.322051 | + | 0.946722i | \(0.604372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.98072 | 0.151911 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.7553 | −1.00422 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.1313 | 1.67982 | 0.839912 | − | 0.542723i | \(-0.182607\pi\) | ||||
0.839912 | + | 0.542723i | \(0.182607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7749 | −1.15178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.7131 | −1.90237 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.64884 | 0.233908 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3482 | 1.32238 | 0.661188 | − | 0.750220i | \(-0.270052\pi\) | ||||
0.661188 | + | 0.750220i | \(0.270052\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.2051 | −1.01152 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.9013 | −1.29345 | −0.646724 | − | 0.762724i | \(-0.723861\pi\) | ||||
−0.646724 | + | 0.762724i | \(0.723861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.16826 | −0.456704 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.27609 | 0.113100 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.9190 | 1.08648 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.24608 | −0.308849 | −0.154424 | − | 0.988005i | \(-0.549352\pi\) | ||||
−0.154424 | + | 0.988005i | \(0.549352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.1440 | 1.19094 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.70782 | 0.231657 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.827970 | 0.0406434 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.10696 | 0.348029 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.2000 | −0.889127 | −0.444564 | − | 0.895747i | \(-0.646641\pi\) | ||||
−0.444564 | + | 0.895747i | \(0.646641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.3059 | −1.57449 | −0.787247 | − | 0.616637i | \(-0.788494\pi\) | ||||
−0.787247 | + | 0.616637i | \(0.788494\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.68855 | −0.227965 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.9083 | −1.30525 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7287 | −0.664380 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −55.0464 | −2.65766 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.185919 | −0.00895541 | −0.00447771 | − | 0.999990i | \(-0.501425\pi\) | ||||
−0.00447771 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.0172 | −1.77893 | −0.889466 | − | 0.457001i | \(-0.848923\pi\) | ||||
−0.889466 | + | 0.457001i | \(0.848923\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.2805 | −0.492911 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.9890 | 1.24322 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.94313 | 0.188195 | 0.0940976 | − | 0.995563i | \(-0.470003\pi\) | ||||
0.0940976 | + | 0.995563i | \(0.470003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0409 | −1.14481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0303 | 1.33176 | 0.665880 | − | 0.746059i | \(-0.268056\pi\) | ||||
0.665880 | + | 0.746059i | \(0.268056\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.27122 | 0.202475 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.3188 | 1.38673 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.5884 | 1.53794 | 0.768972 | − | 0.639283i | \(-0.220769\pi\) | ||||
0.768972 | + | 0.639283i | \(0.220769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.8370 | 1.21662 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 36.8738 | 1.73248 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.09399 | 0.145048 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.9238 | 1.30622 | 0.653109 | − | 0.757264i | \(-0.273464\pi\) | ||||
0.653109 | + | 0.757264i | \(0.273464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.9071 | −0.882507 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.81442 | −0.177655 | −0.0888277 | − | 0.996047i | \(-0.528312\pi\) | ||||
−0.0888277 | + | 0.996047i | \(0.528312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.0068 | −1.06922 | −0.534608 | − | 0.845100i | \(-0.679541\pi\) | ||||
−0.534608 | + | 0.845100i | \(0.679541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.14340 | −0.145771 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.4133 | −1.45364 | −0.726818 | − | 0.686831i | \(-0.759001\pi\) | ||||
−0.726818 | + | 0.686831i | \(0.759001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.72803 | 0.403023 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6183 | 0.581421 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.8132 | −0.956994 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.7058 | 1.40888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.1922 | −0.878752 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.6004 | 0.667111 | 0.333556 | − | 0.942730i | \(-0.391751\pi\) | ||||
0.333556 | + | 0.942730i | \(0.391751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7520 | 1.03740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0610 | −0.548796 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0300 | −0.455439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2262 | 1.50562 | 0.752811 | − | 0.658236i | \(-0.228697\pi\) | ||||
0.752811 | + | 0.658236i | \(0.228697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.832997 | −0.0376694 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3052 | 1.59330 | 0.796650 | − | 0.604441i | \(-0.206604\pi\) | ||||
0.796650 | + | 0.604441i | \(0.206604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.5949 | −1.69319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.0279 | −0.495668 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.66201 | −0.164264 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.4340 | 0.825219 | 0.412610 | − | 0.910908i | \(-0.364617\pi\) | ||||
0.412610 | + | 0.910908i | \(0.364617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 59.5126 | 2.65883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.6382 | −1.23233 | −0.616164 | − | 0.787618i | \(-0.711314\pi\) | ||||
−0.616164 | + | 0.787618i | \(0.711314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.02172 | 0.356962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.2141 | −0.986563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.79650 | 0.168277 | 0.0841384 | − | 0.996454i | \(-0.473186\pi\) | ||||
0.0841384 | + | 0.996454i | \(0.473186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.14123 | −0.360147 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.5754 | 0.952575 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.20280 | −0.141132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.93962 | −0.217244 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 65.6874 | 2.88336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0365 | −1.09687 | −0.548434 | − | 0.836194i | \(-0.684776\pi\) | ||||
−0.548434 | + | 0.836194i | \(0.684776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.85749 | −0.343584 | −0.171792 | − | 0.985133i | \(-0.554956\pi\) | ||||
−0.171792 | + | 0.985133i | \(0.554956\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.2500 | −0.621921 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.4951 | −0.500736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.48639 | −0.325495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.4178 | −0.755868 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.8188 | 1.16165 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.5882 | −0.457770 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.05930 | −0.347784 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.3283 | −1.09097 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.3188 | −1.34650 | −0.673250 | − | 0.739415i | \(-0.735102\pi\) | ||||
−0.673250 | + | 0.739415i | \(0.735102\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.7918 | −0.763518 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.83077 | −0.421104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8022 | 0.846680 | 0.423340 | − | 0.905971i | \(-0.360858\pi\) | ||||
0.423340 | + | 0.905971i | \(0.360858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 50.7930 | 2.16779 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.9005 | 1.82762 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00302 | 0.382847 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.80065 | 0.331119 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.6734 | −0.791219 | −0.395609 | − | 0.918419i | \(-0.629467\pi\) | ||||
−0.395609 | + | 0.918419i | \(0.629467\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6042 | −0.913760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −69.0170 | −2.91390 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.5253 | −1.49721 | −0.748606 | − | 0.663015i | \(-0.769276\pi\) | ||||
−0.748606 | + | 0.663015i | \(0.769276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.62060 | 0.194390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.40791 | 0.185115 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.4668 | 1.73838 | 0.869189 | − | 0.494479i | \(-0.164641\pi\) | ||||
0.869189 | + | 0.494479i | \(0.164641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2739 | 0.555497 | 0.277749 | − | 0.960654i | \(-0.410412\pi\) | ||||
0.277749 | + | 0.960654i | \(0.410412\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.5552 | −2.27908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.3292 | 0.764381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.2957 | −1.71916 | −0.859582 | − | 0.510998i | \(-0.829276\pi\) | ||||
−0.859582 | + | 0.510998i | \(0.829276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.23772 | 0.300790 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.60346 | 0.0665227 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.2200 | −0.837426 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.4470 | −0.473276 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.1014 | −1.36624 | −0.683120 | − | 0.730306i | \(-0.739378\pi\) | ||||
−0.683120 | + | 0.730306i | \(0.739378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1174 | 0.540493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.80624 | 0.362240 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0175 | 0.822019 | 0.411010 | − | 0.911631i | \(-0.365176\pi\) | ||||
0.411010 | + | 0.911631i | \(0.365176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.87924 | 0.159033 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.4541 | −2.02402 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.05800 | 0.370100 | 0.185050 | − | 0.982729i | \(-0.440755\pi\) | ||||
0.185050 | + | 0.982729i | \(0.440755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.8148 | −1.42013 | −0.710063 | − | 0.704138i | \(-0.751334\pi\) | ||||
−0.710063 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.2916 | −1.31502 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.14416 | −0.209140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.844938 | −0.0342950 | −0.0171475 | − | 0.999853i | \(-0.505458\pi\) | ||||
−0.0171475 | + | 0.999853i | \(0.505458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.9093 | −0.806767 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.12734 | −0.207430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.5701 | −1.15393 | −0.576967 | − | 0.816768i | \(-0.695764\pi\) | ||||
−0.576967 | + | 0.816768i | \(0.695764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.19501 | 0.370779 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2245 | −0.492138 | −0.246069 | − | 0.969252i | \(-0.579139\pi\) | ||||
−0.246069 | + | 0.969252i | \(0.579139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.67031 | −0.147522 | −0.0737611 | − | 0.997276i | \(-0.523500\pi\) | ||||
−0.0737611 | + | 0.997276i | \(0.523500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.8790 | 0.516816 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.27171 | 0.331399 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9237 | 0.796948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 78.7571 | 3.14525 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.5264 | 1.13742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.1861 | −1.55997 | −0.779987 | − | 0.625796i | \(-0.784774\pi\) | ||||
−0.779987 | + | 0.625796i | \(0.784774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 54.9386 | 2.18361 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3789 | −0.411876 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.2909 | −1.04168 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5485 | 0.535972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5893 | −0.418252 | −0.209126 | − | 0.977889i | \(-0.567062\pi\) | ||||
−0.209126 | + | 0.977889i | \(0.567062\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3806 | −0.488242 | −0.244121 | − | 0.969745i | \(-0.578499\pi\) | ||||
−0.244121 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.40713 | −0.291656 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.1900 | −1.69797 | −0.848986 | − | 0.528415i | \(-0.822787\pi\) | ||||
−0.848986 | + | 0.528415i | \(0.822787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.3505 | −0.720322 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.08755 | −0.238590 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.6056 | 0.532427 | 0.266213 | − | 0.963914i | \(-0.414227\pi\) | ||||
0.266213 | + | 0.963914i | \(0.414227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.26249 | −0.322842 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.1206 | 1.17512 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.6391 | −1.58307 | −0.791537 | − | 0.611122i | \(-0.790719\pi\) | ||||
−0.791537 | + | 0.611122i | \(0.790719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1381 | 1.71677 | 0.858386 | − | 0.513004i | \(-0.171467\pi\) | ||||
0.858386 | + | 0.513004i | \(0.171467\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −71.6398 | −2.78226 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.42670 | −0.171660 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.6086 | 0.991568 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.5248 | 1.68276 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.5130 | 2.06585 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.743820 | −0.0286721 | −0.0143361 | − | 0.999897i | \(-0.504563\pi\) | ||||
−0.0143361 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.2164 | 0.585680 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.58028 | −0.291334 | −0.145667 | − | 0.989334i | \(-0.546533\pi\) | ||||
−0.145667 | + | 0.989334i | \(0.546533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.4243 | −0.745436 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.5374 | 1.93660 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0378 | 1.14937 | 0.574683 | − | 0.818376i | \(-0.305126\pi\) | ||||
0.574683 | + | 0.818376i | \(0.305126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.28967 | 0.202108 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.56600 | −0.212356 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.9884 | −0.799594 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.9733 | −1.52065 | −0.760327 | − | 0.649540i | \(-0.774961\pi\) | ||||
−0.760327 | + | 0.649540i | \(0.774961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.3569 | −0.811280 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.55705 | 0.0590623 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.6254 | 1.27365 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 62.5982 | 2.36768 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.7114 | 0.933335 | 0.466668 | − | 0.884433i | \(-0.345454\pi\) | ||||
0.466668 | + | 0.884433i | \(0.345454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.5522 | −1.22773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.75794 | −0.0662079 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5350 | 0.584253 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.9783 | −1.65164 | −0.825820 | − | 0.563933i | \(-0.809288\pi\) | ||||
−0.825820 | + | 0.563933i | \(0.809288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.3090 | −1.24918 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.83017 | 0.293242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0600 | −0.451019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.73867 | 0.289006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6486 | −1.10571 | −0.552853 | − | 0.833279i | \(-0.686461\pi\) | ||||
−0.552853 | + | 0.833279i | \(0.686461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.20260 | −0.230997 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 53.5782 | 1.99260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.2563 | 1.12369 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0626388 | 0.00232314 | 0.00116157 | − | 0.999999i | \(-0.499630\pi\) | ||||
0.00116157 | + | 0.999999i | \(0.499630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.6612 | −1.58004 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.0873 | −1.00186 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.0615 | 1.18422 | 0.592109 | − | 0.805858i | \(-0.298296\pi\) | ||||
0.592109 | + | 0.805858i | \(0.298296\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.01398 | −0.332486 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.0208 | −1.25317 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.65515 | −0.171243 | −0.0856213 | − | 0.996328i | \(-0.527288\pi\) | ||||
−0.0856213 | + | 0.996328i | \(0.527288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 81.7500 | 3.00316 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.7053 | 1.38327 | 0.691636 | − | 0.722246i | \(-0.256890\pi\) | ||||
0.691636 | + | 0.722246i | \(0.256890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.42340 | 0.235335 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.93241 | −0.217056 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.5054 | −0.749250 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.20433 | −0.226399 | −0.113200 | − | 0.993572i | \(-0.536110\pi\) | ||||
−0.113200 | + | 0.993572i | \(0.536110\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −48.2569 | −1.75858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.07860 | 0.294010 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0028 | −0.617978 | −0.308989 | − | 0.951066i | \(-0.599991\pi\) | ||||
−0.308989 | + | 0.951066i | \(0.599991\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.0125 | 1.70644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6918 | 0.387578 | 0.193789 | − | 0.981043i | \(-0.437922\pi\) | ||||
0.193789 | + | 0.981043i | \(0.437922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.0384 | −0.689237 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.3522 | −0.518906 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.0479 | −0.687780 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.7270 | −1.57684 | −0.788418 | − | 0.615139i | \(-0.789100\pi\) | ||||
−0.788418 | + | 0.615139i | \(0.789100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −71.4112 | −2.57181 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.33581 | 0.335786 | 0.167893 | − | 0.985805i | \(-0.446304\pi\) | ||||
0.167893 | + | 0.985805i | \(0.446304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.25128 | 0.332316 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.1069 | 0.541956 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.3708 | −1.37478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.2741 | 0.510767 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.2595 | 0.759754 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.76452 | 0.0986699 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.74366 | 0.0978009 | 0.0489004 | − | 0.998804i | \(-0.484428\pi\) | ||||
0.0489004 | + | 0.998804i | \(0.484428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 69.5523 | 2.47613 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.94833 | 0.318166 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.5466 | 1.97252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.19600 | −0.255216 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0420 | 0.780768 | 0.390384 | − | 0.920652i | \(-0.372342\pi\) | ||||
0.390384 | + | 0.920652i | \(0.372342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.42865 | −0.227429 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.6033 | −1.08132 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.7336 | 1.11985 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.64243 | −0.0931333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.6395 | −1.21937 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8320 | 0.451148 | 0.225574 | − | 0.974226i | \(-0.427574\pi\) | ||||
0.225574 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.0735 | 1.89878 | 0.949389 | − | 0.314103i | \(-0.101704\pi\) | ||||
0.949389 | + | 0.314103i | \(0.101704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.6546 | 1.11017 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.182500 | −0.00639269 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.9100 | 1.08140 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.1685 | −0.774629 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.1134 | 1.71407 | 0.857034 | − | 0.515259i | \(-0.172304\pi\) | ||||
0.857034 | + | 0.515259i | \(0.172304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.7671 | 1.38619 | 0.693097 | − | 0.720844i | \(-0.256246\pi\) | ||||
0.693097 | + | 0.720844i | \(0.256246\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 55.5448 | 1.93382 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.50468 | 0.295737 | 0.147868 | − | 0.989007i | \(-0.452759\pi\) | ||||
0.147868 | + | 0.989007i | \(0.452759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.0456 | −1.39084 | −0.695420 | − | 0.718603i | \(-0.744782\pi\) | ||||
−0.695420 | + | 0.718603i | \(0.744782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.4581 | −1.36879 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.9634 | −1.14211 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.0385 | 0.451216 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.50040 | 0.224687 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2491 | −1.04431 | −0.522157 | − | 0.852849i | \(-0.674873\pi\) | ||||
−0.522157 | + | 0.852849i | \(0.674873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2725 | 0.457672 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.4175 | −1.35761 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.86685 | −0.167425 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.96226 | −0.342307 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 80.3715 | 2.75834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.4314 | −0.666098 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.8735 | 0.543497 | 0.271749 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271749 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.3777 | 0.560106 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.3549 | −0.592833 | −0.296417 | − | 0.955059i | \(-0.595792\pi\) | ||||
−0.296417 | + | 0.955059i | \(0.595792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.29543 | 0.0441995 | 0.0220998 | − | 0.999756i | \(-0.492965\pi\) | ||||
0.0220998 | + | 0.999756i | \(0.492965\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.8072 | 0.606868 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.7197 | −1.79460 | −0.897300 | − | 0.441422i | \(-0.854474\pi\) | ||||
−0.897300 | + | 0.441422i | \(0.854474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.3913 | 0.489320 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.1518 | −1.49947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.0927 | −1.19044 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.3137 | −1.19656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 71.8652 | 2.43227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.47642 | −0.218943 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.5598 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.1953 | 0.816086 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.4313 | 1.66538 | 0.832692 | − | 0.553736i | \(-0.186799\pi\) | ||||
0.832692 | + | 0.553736i | \(0.186799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2964 | −1.28878 | −0.644388 | − | 0.764699i | \(-0.722888\pi\) | ||||
−0.644388 | + | 0.764699i | \(0.722888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.53069 | −0.219527 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.55771 | −0.186610 | −0.0933048 | − | 0.995638i | \(-0.529743\pi\) | ||||
−0.0933048 | + | 0.995638i | \(0.529743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.1000 | −0.674134 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.1815 | −0.575603 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.33589 | 0.245486 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76570 | −0.0590207 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.7991 | 1.62935 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9254 | 0.431086 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3152 | −0.876686 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.3448 | −0.477364 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.89796 | −0.129573 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.1142 | −1.73042 | −0.865211 | − | 0.501408i | \(-0.832816\pi\) | ||||
−0.865211 | + | 0.501408i | \(0.832816\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −57.4757 | −1.90635 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.7911 | −0.523182 | −0.261591 | − | 0.965179i | \(-0.584247\pi\) | ||||
−0.261591 | + | 0.965179i | \(0.584247\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.25010 | −0.206848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.0445 | 0.629592 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.0013 | −0.528408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.71169 | −0.155424 | −0.0777121 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777121 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.8596 | 2.20310 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8165 | 0.487692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.9580 | −0.754854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.9481 | 0.753716 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.7630 | −1.86233 | −0.931166 | − | 0.364595i | \(-0.881208\pi\) | ||||
−0.931166 | + | 0.364595i | \(0.881208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.6154 | 1.23279 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57.7125 | 1.88942 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.1208 | −0.494503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.7475 | −1.42917 | −0.714585 | − | 0.699549i | \(-0.753384\pi\) | ||||
−0.714585 | + | 0.699549i | \(0.753384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.1801 | −0.789088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.5133 | −1.80968 | −0.904840 | − | 0.425751i | \(-0.860010\pi\) | ||||
−0.904840 | + | 0.425751i | \(0.860010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.9047 | −0.745879 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.19367 | −0.0713602 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.0500 | −0.554051 | −0.277026 | − | 0.960863i | \(-0.589349\pi\) | ||||
−0.277026 | + | 0.960863i | \(0.589349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.9395 | 1.06926 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −46.8749 | −1.52002 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0861 | −1.16894 | −0.584471 | − | 0.811414i | \(-0.698698\pi\) | ||||
−0.584471 | + | 0.811414i | \(0.698698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9524 | −0.386771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 77.6042 | 2.50859 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2441 | 0.330798 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0479 | −0.872512 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 75.8649 | 2.44471 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.58570 | 0.0510455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.3465 | −0.750773 | −0.375386 | − | 0.926868i | \(-0.622490\pi\) | ||||
−0.375386 | + | 0.926868i | \(0.622490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 102.498 | 3.29271 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6416 | 0.694511 | 0.347255 | − | 0.937771i | \(-0.387114\pi\) | ||||
0.347255 | + | 0.937771i | \(0.387114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.01541 | 0.0966696 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57.6557 | 1.84646 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.8412 | −1.56257 | −0.781284 | − | 0.624176i | \(-0.785435\pi\) | ||||
−0.781284 | + | 0.624176i | \(0.785435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.2421 | −1.03046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 70.4376 | 2.24890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.8726 | 0.570046 | 0.285023 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285023 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.92934 | 0.0614739 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.40446 | −0.108365 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.4511 | 0.586711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.0939 | 1.78188 | 0.890941 | − | 0.454120i | \(-0.150046\pi\) | ||||
0.890941 | + | 0.454120i | \(0.150046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.6220 | −1.28910 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.8348 | −0.343486 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.5691 | −0.398066 | −0.199033 | − | 0.979993i | \(-0.563780\pi\) | ||||
−0.199033 | + | 0.979993i | \(0.563780\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.1314 | −0.510375 |
(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 | 8012.2.a.a.1.11 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8012.2.a.a.1.11 | ✓ | 79 | 1.1 | even | 1 | trivial |