Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.35617\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.35617 | −0.782987 | −0.391494 | − | 0.920181i | \(-0.628041\pi\) | ||||
−0.391494 | + | 0.920181i | \(0.628041\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.14574 | 0.512392 | 0.256196 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256196 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(6\) | −1.35617 | −0.553656 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.16079 | −0.386931 | ||||||||
\(10\) | 1.14574 | 0.362316 | ||||||||
\(11\) | −4.90404 | −1.47862 | −0.739311 | − | 0.673364i | \(-0.764849\pi\) | ||||
−0.739311 | + | 0.673364i | \(0.764849\pi\) | |||||||
\(12\) | −1.35617 | −0.391494 | ||||||||
\(13\) | 3.53472 | 0.980354 | 0.490177 | − | 0.871623i | \(-0.336932\pi\) | ||||
0.490177 | + | 0.871623i | \(0.336932\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.55383 | −0.401196 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.10525 | −0.510598 | −0.255299 | − | 0.966862i | \(-0.582174\pi\) | ||||
−0.255299 | + | 0.966862i | \(0.582174\pi\) | |||||||
\(18\) | −1.16079 | −0.273601 | ||||||||
\(19\) | 2.64080 | 0.605841 | 0.302921 | − | 0.953016i | \(-0.402038\pi\) | ||||
0.302921 | + | 0.953016i | \(0.402038\pi\) | |||||||
\(20\) | 1.14574 | 0.256196 | ||||||||
\(21\) | 1.35617 | 0.295941 | ||||||||
\(22\) | −4.90404 | −1.04554 | ||||||||
\(23\) | 1.73014 | 0.360759 | 0.180379 | − | 0.983597i | \(-0.442267\pi\) | ||||
0.180379 | + | 0.983597i | \(0.442267\pi\) | |||||||
\(24\) | −1.35617 | −0.276828 | ||||||||
\(25\) | −3.68727 | −0.737455 | ||||||||
\(26\) | 3.53472 | 0.693215 | ||||||||
\(27\) | 5.64276 | 1.08595 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.92505 | −0.357473 | −0.178736 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178736 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(30\) | −1.55383 | −0.283688 | ||||||||
\(31\) | 7.14408 | 1.28311 | 0.641557 | − | 0.767075i | \(-0.278289\pi\) | ||||
0.641557 | + | 0.767075i | \(0.278289\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.65073 | 1.15774 | ||||||||
\(34\) | −2.10525 | −0.361048 | ||||||||
\(35\) | −1.14574 | −0.193666 | ||||||||
\(36\) | −1.16079 | −0.193465 | ||||||||
\(37\) | 11.0555 | 1.81752 | 0.908758 | − | 0.417324i | \(-0.137032\pi\) | ||||
0.908758 | + | 0.417324i | \(0.137032\pi\) | |||||||
\(38\) | 2.64080 | 0.428394 | ||||||||
\(39\) | −4.79369 | −0.767605 | ||||||||
\(40\) | 1.14574 | 0.181158 | ||||||||
\(41\) | −7.53470 | −1.17672 | −0.588361 | − | 0.808598i | \(-0.700227\pi\) | ||||
−0.588361 | + | 0.808598i | \(0.700227\pi\) | |||||||
\(42\) | 1.35617 | 0.209262 | ||||||||
\(43\) | 2.28457 | 0.348394 | 0.174197 | − | 0.984711i | \(-0.444267\pi\) | ||||
0.174197 | + | 0.984711i | \(0.444267\pi\) | |||||||
\(44\) | −4.90404 | −0.739311 | ||||||||
\(45\) | −1.32997 | −0.198260 | ||||||||
\(46\) | 1.73014 | 0.255095 | ||||||||
\(47\) | 3.23302 | 0.471585 | 0.235792 | − | 0.971803i | \(-0.424231\pi\) | ||||
0.235792 | + | 0.971803i | \(0.424231\pi\) | |||||||
\(48\) | −1.35617 | −0.195747 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.68727 | −0.521459 | ||||||||
\(51\) | 2.85509 | 0.399792 | ||||||||
\(52\) | 3.53472 | 0.490177 | ||||||||
\(53\) | −13.5297 | −1.85844 | −0.929222 | − | 0.369521i | \(-0.879522\pi\) | ||||
−0.929222 | + | 0.369521i | \(0.879522\pi\) | |||||||
\(54\) | 5.64276 | 0.767882 | ||||||||
\(55\) | −5.61876 | −0.757634 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.58138 | −0.474366 | ||||||||
\(58\) | −1.92505 | −0.252771 | ||||||||
\(59\) | −3.53770 | −0.460569 | −0.230285 | − | 0.973123i | \(-0.573966\pi\) | ||||
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(60\) | −1.55383 | −0.200598 | ||||||||
\(61\) | −0.0973943 | −0.0124701 | −0.00623503 | − | 0.999981i | \(-0.501985\pi\) | ||||
−0.00623503 | + | 0.999981i | \(0.501985\pi\) | |||||||
\(62\) | 7.14408 | 0.907299 | ||||||||
\(63\) | 1.16079 | 0.146246 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.04988 | 0.502325 | ||||||||
\(66\) | 6.65073 | 0.818648 | ||||||||
\(67\) | −11.6421 | −1.42231 | −0.711155 | − | 0.703035i | \(-0.751828\pi\) | ||||
−0.711155 | + | 0.703035i | \(0.751828\pi\) | |||||||
\(68\) | −2.10525 | −0.255299 | ||||||||
\(69\) | −2.34637 | −0.282470 | ||||||||
\(70\) | −1.14574 | −0.136942 | ||||||||
\(71\) | −6.82158 | −0.809572 | −0.404786 | − | 0.914411i | \(-0.632654\pi\) | ||||
−0.404786 | + | 0.914411i | \(0.632654\pi\) | |||||||
\(72\) | −1.16079 | −0.136801 | ||||||||
\(73\) | −5.06332 | −0.592617 | −0.296309 | − | 0.955092i | \(-0.595756\pi\) | ||||
−0.296309 | + | 0.955092i | \(0.595756\pi\) | |||||||
\(74\) | 11.0555 | 1.28518 | ||||||||
\(75\) | 5.00058 | 0.577418 | ||||||||
\(76\) | 2.64080 | 0.302921 | ||||||||
\(77\) | 4.90404 | 0.558867 | ||||||||
\(78\) | −4.79369 | −0.542779 | ||||||||
\(79\) | −2.22286 | −0.250091 | −0.125046 | − | 0.992151i | \(-0.539908\pi\) | ||||
−0.125046 | + | 0.992151i | \(0.539908\pi\) | |||||||
\(80\) | 1.14574 | 0.128098 | ||||||||
\(81\) | −4.17018 | −0.463353 | ||||||||
\(82\) | −7.53470 | −0.832068 | ||||||||
\(83\) | −7.91650 | −0.868949 | −0.434475 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434475 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(84\) | 1.35617 | 0.147971 | ||||||||
\(85\) | −2.41208 | −0.261626 | ||||||||
\(86\) | 2.28457 | 0.246352 | ||||||||
\(87\) | 2.61070 | 0.279896 | ||||||||
\(88\) | −4.90404 | −0.522772 | ||||||||
\(89\) | 0.879303 | 0.0932059 | 0.0466030 | − | 0.998913i | \(-0.485160\pi\) | ||||
0.0466030 | + | 0.998913i | \(0.485160\pi\) | |||||||
\(90\) | −1.32997 | −0.140191 | ||||||||
\(91\) | −3.53472 | −0.370539 | ||||||||
\(92\) | 1.73014 | 0.180379 | ||||||||
\(93\) | −9.68861 | −1.00466 | ||||||||
\(94\) | 3.23302 | 0.333461 | ||||||||
\(95\) | 3.02568 | 0.310428 | ||||||||
\(96\) | −1.35617 | −0.138414 | ||||||||
\(97\) | −11.1767 | −1.13482 | −0.567409 | − | 0.823436i | \(-0.692054\pi\) | ||||
−0.567409 | + | 0.823436i | \(0.692054\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 5.69257 | 0.572125 | ||||||||
\(100\) | −3.68727 | −0.368727 | ||||||||
\(101\) | −8.30764 | −0.826641 | −0.413321 | − | 0.910586i | \(-0.635631\pi\) | ||||
−0.413321 | + | 0.910586i | \(0.635631\pi\) | |||||||
\(102\) | 2.85509 | 0.282696 | ||||||||
\(103\) | 3.16645 | 0.312000 | 0.156000 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.156000 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(104\) | 3.53472 | 0.346608 | ||||||||
\(105\) | 1.55383 | 0.151638 | ||||||||
\(106\) | −13.5297 | −1.31412 | ||||||||
\(107\) | −7.29957 | −0.705676 | −0.352838 | − | 0.935684i | \(-0.614783\pi\) | ||||
−0.352838 | + | 0.935684i | \(0.614783\pi\) | |||||||
\(108\) | 5.64276 | 0.542975 | ||||||||
\(109\) | −4.21108 | −0.403348 | −0.201674 | − | 0.979453i | \(-0.564638\pi\) | ||||
−0.201674 | + | 0.979453i | \(0.564638\pi\) | |||||||
\(110\) | −5.61876 | −0.535728 | ||||||||
\(111\) | −14.9932 | −1.42309 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.5188 | −1.64803 | −0.824014 | − | 0.566569i | \(-0.808270\pi\) | ||||
−0.824014 | + | 0.566569i | \(0.808270\pi\) | |||||||
\(114\) | −3.58138 | −0.335427 | ||||||||
\(115\) | 1.98229 | 0.184850 | ||||||||
\(116\) | −1.92505 | −0.178736 | ||||||||
\(117\) | −4.10307 | −0.379329 | ||||||||
\(118\) | −3.53770 | −0.325672 | ||||||||
\(119\) | 2.10525 | 0.192988 | ||||||||
\(120\) | −1.55383 | −0.141844 | ||||||||
\(121\) | 13.0496 | 1.18633 | ||||||||
\(122\) | −0.0973943 | −0.00881766 | ||||||||
\(123\) | 10.2184 | 0.921359 | ||||||||
\(124\) | 7.14408 | 0.641557 | ||||||||
\(125\) | −9.95338 | −0.890257 | ||||||||
\(126\) | 1.16079 | 0.103412 | ||||||||
\(127\) | 3.66020 | 0.324791 | 0.162395 | − | 0.986726i | \(-0.448078\pi\) | ||||
0.162395 | + | 0.986726i | \(0.448078\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.09828 | −0.272788 | ||||||||
\(130\) | 4.04988 | 0.355198 | ||||||||
\(131\) | −10.5257 | −0.919633 | −0.459816 | − | 0.888014i | \(-0.652085\pi\) | ||||
−0.459816 | + | 0.888014i | \(0.652085\pi\) | |||||||
\(132\) | 6.65073 | 0.578871 | ||||||||
\(133\) | −2.64080 | −0.228986 | ||||||||
\(134\) | −11.6421 | −1.00573 | ||||||||
\(135\) | 6.46515 | 0.556431 | ||||||||
\(136\) | −2.10525 | −0.180524 | ||||||||
\(137\) | 1.21489 | 0.103795 | 0.0518977 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518977 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(138\) | −2.34637 | −0.199736 | ||||||||
\(139\) | 11.0518 | 0.937402 | 0.468701 | − | 0.883357i | \(-0.344722\pi\) | ||||
0.468701 | + | 0.883357i | \(0.344722\pi\) | |||||||
\(140\) | −1.14574 | −0.0968329 | ||||||||
\(141\) | −4.38454 | −0.369245 | ||||||||
\(142\) | −6.82158 | −0.572454 | ||||||||
\(143\) | −17.3344 | −1.44957 | ||||||||
\(144\) | −1.16079 | −0.0967327 | ||||||||
\(145\) | −2.20561 | −0.183166 | ||||||||
\(146\) | −5.06332 | −0.419044 | ||||||||
\(147\) | −1.35617 | −0.111855 | ||||||||
\(148\) | 11.0555 | 0.908758 | ||||||||
\(149\) | −11.2710 | −0.923353 | −0.461677 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461677 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(150\) | 5.00058 | 0.408296 | ||||||||
\(151\) | 7.32966 | 0.596480 | 0.298240 | − | 0.954491i | \(-0.403600\pi\) | ||||
0.298240 | + | 0.954491i | \(0.403600\pi\) | |||||||
\(152\) | 2.64080 | 0.214197 | ||||||||
\(153\) | 2.44376 | 0.197566 | ||||||||
\(154\) | 4.90404 | 0.395179 | ||||||||
\(155\) | 8.18528 | 0.657457 | ||||||||
\(156\) | −4.79369 | −0.383802 | ||||||||
\(157\) | −7.75216 | −0.618689 | −0.309345 | − | 0.950950i | \(-0.600110\pi\) | ||||
−0.309345 | + | 0.950950i | \(0.600110\pi\) | |||||||
\(158\) | −2.22286 | −0.176841 | ||||||||
\(159\) | 18.3486 | 1.45514 | ||||||||
\(160\) | 1.14574 | 0.0905789 | ||||||||
\(161\) | −1.73014 | −0.136354 | ||||||||
\(162\) | −4.17018 | −0.327640 | ||||||||
\(163\) | −1.26861 | −0.0993650 | −0.0496825 | − | 0.998765i | \(-0.515821\pi\) | ||||
−0.0496825 | + | 0.998765i | \(0.515821\pi\) | |||||||
\(164\) | −7.53470 | −0.588361 | ||||||||
\(165\) | 7.62002 | 0.593218 | ||||||||
\(166\) | −7.91650 | −0.614440 | ||||||||
\(167\) | −11.9633 | −0.925748 | −0.462874 | − | 0.886424i | \(-0.653182\pi\) | ||||
−0.462874 | + | 0.886424i | \(0.653182\pi\) | |||||||
\(168\) | 1.35617 | 0.104631 | ||||||||
\(169\) | −0.505775 | −0.0389057 | ||||||||
\(170\) | −2.41208 | −0.184998 | ||||||||
\(171\) | −3.06542 | −0.234419 | ||||||||
\(172\) | 2.28457 | 0.174197 | ||||||||
\(173\) | −9.93833 | −0.755598 | −0.377799 | − | 0.925888i | \(-0.623319\pi\) | ||||
−0.377799 | + | 0.925888i | \(0.623319\pi\) | |||||||
\(174\) | 2.61070 | 0.197917 | ||||||||
\(175\) | 3.68727 | 0.278732 | ||||||||
\(176\) | −4.90404 | −0.369656 | ||||||||
\(177\) | 4.79773 | 0.360620 | ||||||||
\(178\) | 0.879303 | 0.0659065 | ||||||||
\(179\) | 7.38368 | 0.551882 | 0.275941 | − | 0.961175i | \(-0.411011\pi\) | ||||
0.275941 | + | 0.961175i | \(0.411011\pi\) | |||||||
\(180\) | −1.32997 | −0.0991301 | ||||||||
\(181\) | 1.04317 | 0.0775384 | 0.0387692 | − | 0.999248i | \(-0.487656\pi\) | ||||
0.0387692 | + | 0.999248i | \(0.487656\pi\) | |||||||
\(182\) | −3.53472 | −0.262011 | ||||||||
\(183\) | 0.132084 | 0.00976390 | ||||||||
\(184\) | 1.73014 | 0.127547 | ||||||||
\(185\) | 12.6668 | 0.931280 | ||||||||
\(186\) | −9.68861 | −0.710404 | ||||||||
\(187\) | 10.3242 | 0.754982 | ||||||||
\(188\) | 3.23302 | 0.235792 | ||||||||
\(189\) | −5.64276 | −0.410450 | ||||||||
\(190\) | 3.02568 | 0.219506 | ||||||||
\(191\) | 13.1926 | 0.954586 | 0.477293 | − | 0.878744i | \(-0.341618\pi\) | ||||
0.477293 | + | 0.878744i | \(0.341618\pi\) | |||||||
\(192\) | −1.35617 | −0.0978734 | ||||||||
\(193\) | 18.1763 | 1.30836 | 0.654180 | − | 0.756339i | \(-0.273014\pi\) | ||||
0.654180 | + | 0.756339i | \(0.273014\pi\) | |||||||
\(194\) | −11.1767 | −0.802437 | ||||||||
\(195\) | −5.49233 | −0.393314 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 16.3826 | 1.16721 | 0.583606 | − | 0.812037i | \(-0.301641\pi\) | ||||
0.583606 | + | 0.812037i | \(0.301641\pi\) | |||||||
\(198\) | 5.69257 | 0.404553 | ||||||||
\(199\) | −5.79459 | −0.410767 | −0.205384 | − | 0.978682i | \(-0.565844\pi\) | ||||
−0.205384 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(200\) | −3.68727 | −0.260730 | ||||||||
\(201\) | 15.7887 | 1.11365 | ||||||||
\(202\) | −8.30764 | −0.584523 | ||||||||
\(203\) | 1.92505 | 0.135112 | ||||||||
\(204\) | 2.85509 | 0.199896 | ||||||||
\(205\) | −8.63282 | −0.602943 | ||||||||
\(206\) | 3.16645 | 0.220617 | ||||||||
\(207\) | −2.00833 | −0.139589 | ||||||||
\(208\) | 3.53472 | 0.245089 | ||||||||
\(209\) | −12.9506 | −0.895811 | ||||||||
\(210\) | 1.55383 | 0.107224 | ||||||||
\(211\) | 9.91695 | 0.682711 | 0.341355 | − | 0.939934i | \(-0.389114\pi\) | ||||
0.341355 | + | 0.939934i | \(0.389114\pi\) | |||||||
\(212\) | −13.5297 | −0.929222 | ||||||||
\(213\) | 9.25124 | 0.633885 | ||||||||
\(214\) | −7.29957 | −0.498988 | ||||||||
\(215\) | 2.61753 | 0.178514 | ||||||||
\(216\) | 5.64276 | 0.383941 | ||||||||
\(217\) | −7.14408 | −0.484972 | ||||||||
\(218\) | −4.21108 | −0.285210 | ||||||||
\(219\) | 6.86675 | 0.464012 | ||||||||
\(220\) | −5.61876 | −0.378817 | ||||||||
\(221\) | −7.44147 | −0.500567 | ||||||||
\(222\) | −14.9932 | −1.00628 | ||||||||
\(223\) | −8.88501 | −0.594984 | −0.297492 | − | 0.954724i | \(-0.596150\pi\) | ||||
−0.297492 | + | 0.954724i | \(0.596150\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.28016 | 0.285344 | ||||||||
\(226\) | −17.5188 | −1.16533 | ||||||||
\(227\) | −19.6178 | −1.30208 | −0.651040 | − | 0.759043i | \(-0.725667\pi\) | ||||
−0.651040 | + | 0.759043i | \(0.725667\pi\) | |||||||
\(228\) | −3.58138 | −0.237183 | ||||||||
\(229\) | −9.04766 | −0.597886 | −0.298943 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298943 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(230\) | 1.98229 | 0.130709 | ||||||||
\(231\) | −6.65073 | −0.437586 | ||||||||
\(232\) | −1.92505 | −0.126386 | ||||||||
\(233\) | −12.4968 | −0.818693 | −0.409346 | − | 0.912379i | \(-0.634243\pi\) | ||||
−0.409346 | + | 0.912379i | \(0.634243\pi\) | |||||||
\(234\) | −4.10307 | −0.268226 | ||||||||
\(235\) | 3.70421 | 0.241636 | ||||||||
\(236\) | −3.53770 | −0.230285 | ||||||||
\(237\) | 3.01459 | 0.195818 | ||||||||
\(238\) | 2.10525 | 0.136463 | ||||||||
\(239\) | −20.7502 | −1.34222 | −0.671109 | − | 0.741359i | \(-0.734182\pi\) | ||||
−0.671109 | + | 0.741359i | \(0.734182\pi\) | |||||||
\(240\) | −1.55383 | −0.100299 | ||||||||
\(241\) | 8.41356 | 0.541965 | 0.270982 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270982 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(242\) | 13.0496 | 0.838859 | ||||||||
\(243\) | −11.2728 | −0.723149 | ||||||||
\(244\) | −0.0973943 | −0.00623503 | ||||||||
\(245\) | 1.14574 | 0.0731988 | ||||||||
\(246\) | 10.2184 | 0.651499 | ||||||||
\(247\) | 9.33448 | 0.593939 | ||||||||
\(248\) | 7.14408 | 0.453650 | ||||||||
\(249\) | 10.7362 | 0.680376 | ||||||||
\(250\) | −9.95338 | −0.629507 | ||||||||
\(251\) | 28.7022 | 1.81167 | 0.905834 | − | 0.423633i | \(-0.139245\pi\) | ||||
0.905834 | + | 0.423633i | \(0.139245\pi\) | |||||||
\(252\) | 1.16079 | 0.0731231 | ||||||||
\(253\) | −8.48466 | −0.533426 | ||||||||
\(254\) | 3.66020 | 0.229662 | ||||||||
\(255\) | 3.27119 | 0.204850 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.6139 | −1.66013 | −0.830065 | − | 0.557667i | \(-0.811697\pi\) | ||||
−0.830065 | + | 0.557667i | \(0.811697\pi\) | |||||||
\(258\) | −3.09828 | −0.192890 | ||||||||
\(259\) | −11.0555 | −0.686956 | ||||||||
\(260\) | 4.04988 | 0.251163 | ||||||||
\(261\) | 2.23458 | 0.138317 | ||||||||
\(262\) | −10.5257 | −0.650279 | ||||||||
\(263\) | −11.6978 | −0.721320 | −0.360660 | − | 0.932697i | \(-0.617448\pi\) | ||||
−0.360660 | + | 0.932697i | \(0.617448\pi\) | |||||||
\(264\) | 6.65073 | 0.409324 | ||||||||
\(265\) | −15.5015 | −0.952252 | ||||||||
\(266\) | −2.64080 | −0.161918 | ||||||||
\(267\) | −1.19249 | −0.0729790 | ||||||||
\(268\) | −11.6421 | −0.711155 | ||||||||
\(269\) | 16.0908 | 0.981074 | 0.490537 | − | 0.871420i | \(-0.336801\pi\) | ||||
0.490537 | + | 0.871420i | \(0.336801\pi\) | |||||||
\(270\) | 6.46515 | 0.393456 | ||||||||
\(271\) | 2.84989 | 0.173118 | 0.0865591 | − | 0.996247i | \(-0.472413\pi\) | ||||
0.0865591 | + | 0.996247i | \(0.472413\pi\) | |||||||
\(272\) | −2.10525 | −0.127650 | ||||||||
\(273\) | 4.79369 | 0.290127 | ||||||||
\(274\) | 1.21489 | 0.0733944 | ||||||||
\(275\) | 18.0825 | 1.09042 | ||||||||
\(276\) | −2.34637 | −0.141235 | ||||||||
\(277\) | 8.72327 | 0.524131 | 0.262065 | − | 0.965050i | \(-0.415596\pi\) | ||||
0.262065 | + | 0.965050i | \(0.415596\pi\) | |||||||
\(278\) | 11.0518 | 0.662843 | ||||||||
\(279\) | −8.29280 | −0.496477 | ||||||||
\(280\) | −1.14574 | −0.0684712 | ||||||||
\(281\) | −23.6016 | −1.40796 | −0.703978 | − | 0.710222i | \(-0.748595\pi\) | ||||
−0.703978 | + | 0.710222i | \(0.748595\pi\) | |||||||
\(282\) | −4.38454 | −0.261096 | ||||||||
\(283\) | 29.8859 | 1.77653 | 0.888265 | − | 0.459332i | \(-0.151911\pi\) | ||||
0.888265 | + | 0.459332i | \(0.151911\pi\) | |||||||
\(284\) | −6.82158 | −0.404786 | ||||||||
\(285\) | −4.10334 | −0.243061 | ||||||||
\(286\) | −17.3344 | −1.02500 | ||||||||
\(287\) | 7.53470 | 0.444759 | ||||||||
\(288\) | −1.16079 | −0.0684004 | ||||||||
\(289\) | −12.5679 | −0.739289 | ||||||||
\(290\) | −2.20561 | −0.129518 | ||||||||
\(291\) | 15.1575 | 0.888548 | ||||||||
\(292\) | −5.06332 | −0.296309 | ||||||||
\(293\) | 23.3294 | 1.36292 | 0.681458 | − | 0.731857i | \(-0.261346\pi\) | ||||
0.681458 | + | 0.731857i | \(0.261346\pi\) | |||||||
\(294\) | −1.35617 | −0.0790937 | ||||||||
\(295\) | −4.05329 | −0.235992 | ||||||||
\(296\) | 11.0555 | 0.642589 | ||||||||
\(297\) | −27.6723 | −1.60571 | ||||||||
\(298\) | −11.2710 | −0.652909 | ||||||||
\(299\) | 6.11555 | 0.353671 | ||||||||
\(300\) | 5.00058 | 0.288709 | ||||||||
\(301\) | −2.28457 | −0.131681 | ||||||||
\(302\) | 7.32966 | 0.421775 | ||||||||
\(303\) | 11.2666 | 0.647249 | ||||||||
\(304\) | 2.64080 | 0.151460 | ||||||||
\(305\) | −0.111589 | −0.00638955 | ||||||||
\(306\) | 2.44376 | 0.139700 | ||||||||
\(307\) | −11.0714 | −0.631877 | −0.315939 | − | 0.948780i | \(-0.602319\pi\) | ||||
−0.315939 | + | 0.948780i | \(0.602319\pi\) | |||||||
\(308\) | 4.90404 | 0.279433 | ||||||||
\(309\) | −4.29426 | −0.244292 | ||||||||
\(310\) | 8.18528 | 0.464893 | ||||||||
\(311\) | −20.0417 | −1.13646 | −0.568231 | − | 0.822869i | \(-0.692372\pi\) | ||||
−0.568231 | + | 0.822869i | \(0.692372\pi\) | |||||||
\(312\) | −4.79369 | −0.271389 | ||||||||
\(313\) | −14.6082 | −0.825705 | −0.412853 | − | 0.910798i | \(-0.635468\pi\) | ||||
−0.412853 | + | 0.910798i | \(0.635468\pi\) | |||||||
\(314\) | −7.75216 | −0.437479 | ||||||||
\(315\) | 1.32997 | 0.0749353 | ||||||||
\(316\) | −2.22286 | −0.125046 | ||||||||
\(317\) | −4.45017 | −0.249947 | −0.124973 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124973 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(318\) | 18.3486 | 1.02894 | ||||||||
\(319\) | 9.44051 | 0.528567 | ||||||||
\(320\) | 1.14574 | 0.0640490 | ||||||||
\(321\) | 9.89948 | 0.552535 | ||||||||
\(322\) | −1.73014 | −0.0964168 | ||||||||
\(323\) | −5.55955 | −0.309342 | ||||||||
\(324\) | −4.17018 | −0.231677 | ||||||||
\(325\) | −13.0335 | −0.722967 | ||||||||
\(326\) | −1.26861 | −0.0702617 | ||||||||
\(327\) | 5.71095 | 0.315816 | ||||||||
\(328\) | −7.53470 | −0.416034 | ||||||||
\(329\) | −3.23302 | −0.178242 | ||||||||
\(330\) | 7.62002 | 0.419468 | ||||||||
\(331\) | 33.9755 | 1.86746 | 0.933730 | − | 0.357978i | \(-0.116534\pi\) | ||||
0.933730 | + | 0.357978i | \(0.116534\pi\) | |||||||
\(332\) | −7.91650 | −0.434475 | ||||||||
\(333\) | −12.8332 | −0.703253 | ||||||||
\(334\) | −11.9633 | −0.654602 | ||||||||
\(335\) | −13.3389 | −0.728780 | ||||||||
\(336\) | 1.35617 | 0.0739853 | ||||||||
\(337\) | −19.5007 | −1.06227 | −0.531136 | − | 0.847286i | \(-0.678235\pi\) | ||||
−0.531136 | + | 0.847286i | \(0.678235\pi\) | |||||||
\(338\) | −0.505775 | −0.0275105 | ||||||||
\(339\) | 23.7585 | 1.29039 | ||||||||
\(340\) | −2.41208 | −0.130813 | ||||||||
\(341\) | −35.0348 | −1.89724 | ||||||||
\(342\) | −3.06542 | −0.165759 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.28457 | 0.123176 | ||||||||
\(345\) | −2.68833 | −0.144735 | ||||||||
\(346\) | −9.93833 | −0.534288 | ||||||||
\(347\) | 22.6747 | 1.21724 | 0.608620 | − | 0.793462i | \(-0.291723\pi\) | ||||
0.608620 | + | 0.793462i | \(0.291723\pi\) | |||||||
\(348\) | 2.61070 | 0.139948 | ||||||||
\(349\) | 2.46440 | 0.131916 | 0.0659582 | − | 0.997822i | \(-0.478990\pi\) | ||||
0.0659582 | + | 0.997822i | \(0.478990\pi\) | |||||||
\(350\) | 3.68727 | 0.197093 | ||||||||
\(351\) | 19.9456 | 1.06461 | ||||||||
\(352\) | −4.90404 | −0.261386 | ||||||||
\(353\) | 14.1125 | 0.751135 | 0.375567 | − | 0.926795i | \(-0.377448\pi\) | ||||
0.375567 | + | 0.926795i | \(0.377448\pi\) | |||||||
\(354\) | 4.79773 | 0.254997 | ||||||||
\(355\) | −7.81577 | −0.414818 | ||||||||
\(356\) | 0.879303 | 0.0466030 | ||||||||
\(357\) | −2.85509 | −0.151107 | ||||||||
\(358\) | 7.38368 | 0.390240 | ||||||||
\(359\) | 25.0089 | 1.31992 | 0.659960 | − | 0.751301i | \(-0.270573\pi\) | ||||
0.659960 | + | 0.751301i | \(0.270573\pi\) | |||||||
\(360\) | −1.32997 | −0.0700956 | ||||||||
\(361\) | −12.0262 | −0.632956 | ||||||||
\(362\) | 1.04317 | 0.0548279 | ||||||||
\(363\) | −17.6975 | −0.928878 | ||||||||
\(364\) | −3.53472 | −0.185270 | ||||||||
\(365\) | −5.80126 | −0.303652 | ||||||||
\(366\) | 0.132084 | 0.00690412 | ||||||||
\(367\) | −19.9683 | −1.04234 | −0.521170 | − | 0.853453i | \(-0.674504\pi\) | ||||
−0.521170 | + | 0.853453i | \(0.674504\pi\) | |||||||
\(368\) | 1.73014 | 0.0901897 | ||||||||
\(369\) | 8.74622 | 0.455310 | ||||||||
\(370\) | 12.6668 | 0.658514 | ||||||||
\(371\) | 13.5297 | 0.702426 | ||||||||
\(372\) | −9.68861 | −0.502331 | ||||||||
\(373\) | −13.6918 | −0.708934 | −0.354467 | − | 0.935069i | \(-0.615338\pi\) | ||||
−0.354467 | + | 0.935069i | \(0.615338\pi\) | |||||||
\(374\) | 10.3242 | 0.533853 | ||||||||
\(375\) | 13.4985 | 0.697060 | ||||||||
\(376\) | 3.23302 | 0.166730 | ||||||||
\(377\) | −6.80450 | −0.350450 | ||||||||
\(378\) | −5.64276 | −0.290232 | ||||||||
\(379\) | 4.21371 | 0.216444 | 0.108222 | − | 0.994127i | \(-0.465484\pi\) | ||||
0.108222 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(380\) | 3.02568 | 0.155214 | ||||||||
\(381\) | −4.96387 | −0.254307 | ||||||||
\(382\) | 13.1926 | 0.674994 | ||||||||
\(383\) | 18.0865 | 0.924179 | 0.462089 | − | 0.886833i | \(-0.347100\pi\) | ||||
0.462089 | + | 0.886833i | \(0.347100\pi\) | |||||||
\(384\) | −1.35617 | −0.0692070 | ||||||||
\(385\) | 5.61876 | 0.286359 | ||||||||
\(386\) | 18.1763 | 0.925150 | ||||||||
\(387\) | −2.65191 | −0.134804 | ||||||||
\(388\) | −11.1767 | −0.567409 | ||||||||
\(389\) | 25.5220 | 1.29402 | 0.647008 | − | 0.762483i | \(-0.276020\pi\) | ||||
0.647008 | + | 0.762483i | \(0.276020\pi\) | |||||||
\(390\) | −5.49233 | −0.278115 | ||||||||
\(391\) | −3.64238 | −0.184203 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 14.2746 | 0.720061 | ||||||||
\(394\) | 16.3826 | 0.825344 | ||||||||
\(395\) | −2.54683 | −0.128145 | ||||||||
\(396\) | 5.69257 | 0.286062 | ||||||||
\(397\) | −17.1808 | −0.862278 | −0.431139 | − | 0.902285i | \(-0.641888\pi\) | ||||
−0.431139 | + | 0.902285i | \(0.641888\pi\) | |||||||
\(398\) | −5.79459 | −0.290456 | ||||||||
\(399\) | 3.58138 | 0.179293 | ||||||||
\(400\) | −3.68727 | −0.184364 | ||||||||
\(401\) | 15.8302 | 0.790520 | 0.395260 | − | 0.918569i | \(-0.370654\pi\) | ||||
0.395260 | + | 0.918569i | \(0.370654\pi\) | |||||||
\(402\) | 15.7887 | 0.787470 | ||||||||
\(403\) | 25.2523 | 1.25791 | ||||||||
\(404\) | −8.30764 | −0.413321 | ||||||||
\(405\) | −4.77795 | −0.237418 | ||||||||
\(406\) | 1.92505 | 0.0955386 | ||||||||
\(407\) | −54.2166 | −2.68742 | ||||||||
\(408\) | 2.85509 | 0.141348 | ||||||||
\(409\) | −26.5689 | −1.31375 | −0.656874 | − | 0.754000i | \(-0.728122\pi\) | ||||
−0.656874 | + | 0.754000i | \(0.728122\pi\) | |||||||
\(410\) | −8.63282 | −0.426345 | ||||||||
\(411\) | −1.64761 | −0.0812705 | ||||||||
\(412\) | 3.16645 | 0.156000 | ||||||||
\(413\) | 3.53770 | 0.174079 | ||||||||
\(414\) | −2.00833 | −0.0987041 | ||||||||
\(415\) | −9.07028 | −0.445242 | ||||||||
\(416\) | 3.53472 | 0.173304 | ||||||||
\(417\) | −14.9882 | −0.733974 | ||||||||
\(418\) | −12.9506 | −0.633434 | ||||||||
\(419\) | 2.73493 | 0.133610 | 0.0668049 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668049 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(420\) | 1.55383 | 0.0758189 | ||||||||
\(421\) | −16.8138 | −0.819455 | −0.409728 | − | 0.912208i | \(-0.634376\pi\) | ||||
−0.409728 | + | 0.912208i | \(0.634376\pi\) | |||||||
\(422\) | 9.91695 | 0.482750 | ||||||||
\(423\) | −3.75287 | −0.182471 | ||||||||
\(424\) | −13.5297 | −0.657059 | ||||||||
\(425\) | 7.76264 | 0.376543 | ||||||||
\(426\) | 9.25124 | 0.448224 | ||||||||
\(427\) | 0.0973943 | 0.00471324 | ||||||||
\(428\) | −7.29957 | −0.352838 | ||||||||
\(429\) | 23.5084 | 1.13500 | ||||||||
\(430\) | 2.61753 | 0.126229 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 5.64276 | 0.271487 | ||||||||
\(433\) | 11.5140 | 0.553329 | 0.276664 | − | 0.960967i | \(-0.410771\pi\) | ||||
0.276664 | + | 0.960967i | \(0.410771\pi\) | |||||||
\(434\) | −7.14408 | −0.342927 | ||||||||
\(435\) | 2.99119 | 0.143417 | ||||||||
\(436\) | −4.21108 | −0.201674 | ||||||||
\(437\) | 4.56895 | 0.218563 | ||||||||
\(438\) | 6.86675 | 0.328106 | ||||||||
\(439\) | −9.27411 | −0.442629 | −0.221314 | − | 0.975203i | \(-0.571035\pi\) | ||||
−0.221314 | + | 0.975203i | \(0.571035\pi\) | |||||||
\(440\) | −5.61876 | −0.267864 | ||||||||
\(441\) | −1.16079 | −0.0552758 | ||||||||
\(442\) | −7.44147 | −0.353955 | ||||||||
\(443\) | 29.7255 | 1.41230 | 0.706151 | − | 0.708061i | \(-0.250430\pi\) | ||||
0.706151 | + | 0.708061i | \(0.250430\pi\) | |||||||
\(444\) | −14.9932 | −0.711546 | ||||||||
\(445\) | 1.00745 | 0.0477579 | ||||||||
\(446\) | −8.88501 | −0.420717 | ||||||||
\(447\) | 15.2854 | 0.722974 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 13.5470 | 0.639323 | 0.319661 | − | 0.947532i | \(-0.396431\pi\) | ||||
0.319661 | + | 0.947532i | \(0.396431\pi\) | |||||||
\(450\) | 4.28016 | 0.201769 | ||||||||
\(451\) | 36.9504 | 1.73993 | ||||||||
\(452\) | −17.5188 | −0.824014 | ||||||||
\(453\) | −9.94030 | −0.467036 | ||||||||
\(454\) | −19.6178 | −0.920710 | ||||||||
\(455\) | −4.04988 | −0.189861 | ||||||||
\(456\) | −3.58138 | −0.167714 | ||||||||
\(457\) | −4.06347 | −0.190081 | −0.0950406 | − | 0.995473i | \(-0.530298\pi\) | ||||
−0.0950406 | + | 0.995473i | \(0.530298\pi\) | |||||||
\(458\) | −9.04766 | −0.422769 | ||||||||
\(459\) | −11.8794 | −0.554484 | ||||||||
\(460\) | 1.98229 | 0.0924249 | ||||||||
\(461\) | −28.8537 | −1.34385 | −0.671925 | − | 0.740619i | \(-0.734532\pi\) | ||||
−0.671925 | + | 0.740619i | \(0.734532\pi\) | |||||||
\(462\) | −6.65073 | −0.309420 | ||||||||
\(463\) | 2.43037 | 0.112949 | 0.0564744 | − | 0.998404i | \(-0.482014\pi\) | ||||
0.0564744 | + | 0.998404i | \(0.482014\pi\) | |||||||
\(464\) | −1.92505 | −0.0893681 | ||||||||
\(465\) | −11.1007 | −0.514781 | ||||||||
\(466\) | −12.4968 | −0.578903 | ||||||||
\(467\) | 3.04652 | 0.140976 | 0.0704880 | − | 0.997513i | \(-0.477544\pi\) | ||||
0.0704880 | + | 0.997513i | \(0.477544\pi\) | |||||||
\(468\) | −4.10307 | −0.189665 | ||||||||
\(469\) | 11.6421 | 0.537583 | ||||||||
\(470\) | 3.70421 | 0.170863 | ||||||||
\(471\) | 10.5133 | 0.484426 | ||||||||
\(472\) | −3.53770 | −0.162836 | ||||||||
\(473\) | −11.2036 | −0.515143 | ||||||||
\(474\) | 3.01459 | 0.138464 | ||||||||
\(475\) | −9.73736 | −0.446781 | ||||||||
\(476\) | 2.10525 | 0.0964940 | ||||||||
\(477\) | 15.7052 | 0.719090 | ||||||||
\(478\) | −20.7502 | −0.949091 | ||||||||
\(479\) | −27.7072 | −1.26597 | −0.632986 | − | 0.774163i | \(-0.718171\pi\) | ||||
−0.632986 | + | 0.774163i | \(0.718171\pi\) | |||||||
\(480\) | −1.55383 | −0.0709221 | ||||||||
\(481\) | 39.0781 | 1.78181 | ||||||||
\(482\) | 8.41356 | 0.383227 | ||||||||
\(483\) | 2.34637 | 0.106763 | ||||||||
\(484\) | 13.0496 | 0.593163 | ||||||||
\(485\) | −12.8056 | −0.581471 | ||||||||
\(486\) | −11.2728 | −0.511344 | ||||||||
\(487\) | 5.29140 | 0.239776 | 0.119888 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119888 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(488\) | −0.0973943 | −0.00440883 | ||||||||
\(489\) | 1.72045 | 0.0778016 | ||||||||
\(490\) | 1.14574 | 0.0517594 | ||||||||
\(491\) | 3.44552 | 0.155494 | 0.0777472 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777472 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(492\) | 10.2184 | 0.460679 | ||||||||
\(493\) | 4.05271 | 0.182525 | ||||||||
\(494\) | 9.33448 | 0.419978 | ||||||||
\(495\) | 6.52222 | 0.293152 | ||||||||
\(496\) | 7.14408 | 0.320779 | ||||||||
\(497\) | 6.82158 | 0.305989 | ||||||||
\(498\) | 10.7362 | 0.481099 | ||||||||
\(499\) | −11.1979 | −0.501289 | −0.250645 | − | 0.968079i | \(-0.580643\pi\) | ||||
−0.250645 | + | 0.968079i | \(0.580643\pi\) | |||||||
\(500\) | −9.95338 | −0.445129 | ||||||||
\(501\) | 16.2243 | 0.724849 | ||||||||
\(502\) | 28.7022 | 1.28104 | ||||||||
\(503\) | 8.65536 | 0.385923 | 0.192962 | − | 0.981206i | \(-0.438191\pi\) | ||||
0.192962 | + | 0.981206i | \(0.438191\pi\) | |||||||
\(504\) | 1.16079 | 0.0517058 | ||||||||
\(505\) | −9.51842 | −0.423564 | ||||||||
\(506\) | −8.48466 | −0.377189 | ||||||||
\(507\) | 0.685918 | 0.0304627 | ||||||||
\(508\) | 3.66020 | 0.162395 | ||||||||
\(509\) | −26.7644 | −1.18631 | −0.593157 | − | 0.805087i | \(-0.702118\pi\) | ||||
−0.593157 | + | 0.805087i | \(0.702118\pi\) | |||||||
\(510\) | 3.27119 | 0.144851 | ||||||||
\(511\) | 5.06332 | 0.223988 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 14.9014 | 0.657913 | ||||||||
\(514\) | −26.6139 | −1.17389 | ||||||||
\(515\) | 3.62794 | 0.159866 | ||||||||
\(516\) | −3.09828 | −0.136394 | ||||||||
\(517\) | −15.8549 | −0.697296 | ||||||||
\(518\) | −11.0555 | −0.485751 | ||||||||
\(519\) | 13.4781 | 0.591623 | ||||||||
\(520\) | 4.04988 | 0.177599 | ||||||||
\(521\) | −12.1340 | −0.531602 | −0.265801 | − | 0.964028i | \(-0.585636\pi\) | ||||
−0.265801 | + | 0.964028i | \(0.585636\pi\) | |||||||
\(522\) | 2.23458 | 0.0978050 | ||||||||
\(523\) | −34.4822 | −1.50780 | −0.753901 | − | 0.656988i | \(-0.771830\pi\) | ||||
−0.753901 | + | 0.656988i | \(0.771830\pi\) | |||||||
\(524\) | −10.5257 | −0.459816 | ||||||||
\(525\) | −5.00058 | −0.218243 | ||||||||
\(526\) | −11.6978 | −0.510050 | ||||||||
\(527\) | −15.0401 | −0.655156 | ||||||||
\(528\) | 6.65073 | 0.289436 | ||||||||
\(529\) | −20.0066 | −0.869853 | ||||||||
\(530\) | −15.5015 | −0.673344 | ||||||||
\(531\) | 4.10654 | 0.178208 | ||||||||
\(532\) | −2.64080 | −0.114493 | ||||||||
\(533\) | −26.6330 | −1.15360 | ||||||||
\(534\) | −1.19249 | −0.0516040 | ||||||||
\(535\) | −8.36343 | −0.361582 | ||||||||
\(536\) | −11.6421 | −0.502863 | ||||||||
\(537\) | −10.0136 | −0.432117 | ||||||||
\(538\) | 16.0908 | 0.693724 | ||||||||
\(539\) | −4.90404 | −0.211232 | ||||||||
\(540\) | 6.46515 | 0.278216 | ||||||||
\(541\) | 40.3882 | 1.73643 | 0.868213 | − | 0.496192i | \(-0.165269\pi\) | ||||
0.868213 | + | 0.496192i | \(0.165269\pi\) | |||||||
\(542\) | 2.84989 | 0.122413 | ||||||||
\(543\) | −1.41472 | −0.0607116 | ||||||||
\(544\) | −2.10525 | −0.0902619 | ||||||||
\(545\) | −4.82481 | −0.206672 | ||||||||
\(546\) | 4.79369 | 0.205151 | ||||||||
\(547\) | 29.2613 | 1.25112 | 0.625562 | − | 0.780175i | \(-0.284870\pi\) | ||||
0.625562 | + | 0.780175i | \(0.284870\pi\) | |||||||
\(548\) | 1.21489 | 0.0518977 | ||||||||
\(549\) | 0.113055 | 0.00482505 | ||||||||
\(550\) | 18.0825 | 0.771042 | ||||||||
\(551\) | −5.08367 | −0.216572 | ||||||||
\(552\) | −2.34637 | −0.0998681 | ||||||||
\(553\) | 2.22286 | 0.0945257 | ||||||||
\(554\) | 8.72327 | 0.370616 | ||||||||
\(555\) | −17.1783 | −0.729180 | ||||||||
\(556\) | 11.0518 | 0.468701 | ||||||||
\(557\) | −15.1914 | −0.643681 | −0.321841 | − | 0.946794i | \(-0.604302\pi\) | ||||
−0.321841 | + | 0.946794i | \(0.604302\pi\) | |||||||
\(558\) | −8.29280 | −0.351062 | ||||||||
\(559\) | 8.07531 | 0.341549 | ||||||||
\(560\) | −1.14574 | −0.0484165 | ||||||||
\(561\) | −14.0014 | −0.591142 | ||||||||
\(562\) | −23.6016 | −0.995575 | ||||||||
\(563\) | −29.1446 | −1.22830 | −0.614149 | − | 0.789190i | \(-0.710501\pi\) | ||||
−0.614149 | + | 0.789190i | \(0.710501\pi\) | |||||||
\(564\) | −4.38454 | −0.184622 | ||||||||
\(565\) | −20.0720 | −0.844436 | ||||||||
\(566\) | 29.8859 | 1.25620 | ||||||||
\(567\) | 4.17018 | 0.175131 | ||||||||
\(568\) | −6.82158 | −0.286227 | ||||||||
\(569\) | 20.7375 | 0.869363 | 0.434682 | − | 0.900584i | \(-0.356861\pi\) | ||||
0.434682 | + | 0.900584i | \(0.356861\pi\) | |||||||
\(570\) | −4.10334 | −0.171870 | ||||||||
\(571\) | 30.7830 | 1.28823 | 0.644114 | − | 0.764929i | \(-0.277226\pi\) | ||||
0.644114 | + | 0.764929i | \(0.277226\pi\) | |||||||
\(572\) | −17.3344 | −0.724787 | ||||||||
\(573\) | −17.8915 | −0.747429 | ||||||||
\(574\) | 7.53470 | 0.314492 | ||||||||
\(575\) | −6.37949 | −0.266043 | ||||||||
\(576\) | −1.16079 | −0.0483664 | ||||||||
\(577\) | 13.2893 | 0.553240 | 0.276620 | − | 0.960979i | \(-0.410786\pi\) | ||||
0.276620 | + | 0.960979i | \(0.410786\pi\) | |||||||
\(578\) | −12.5679 | −0.522756 | ||||||||
\(579\) | −24.6502 | −1.02443 | ||||||||
\(580\) | −2.20561 | −0.0915830 | ||||||||
\(581\) | 7.91650 | 0.328432 | ||||||||
\(582\) | 15.1575 | 0.628298 | ||||||||
\(583\) | 66.3501 | 2.74794 | ||||||||
\(584\) | −5.06332 | −0.209522 | ||||||||
\(585\) | −4.70107 | −0.194365 | ||||||||
\(586\) | 23.3294 | 0.963728 | ||||||||
\(587\) | 9.51557 | 0.392750 | 0.196375 | − | 0.980529i | \(-0.437083\pi\) | ||||
0.196375 | + | 0.980529i | \(0.437083\pi\) | |||||||
\(588\) | −1.35617 | −0.0559277 | ||||||||
\(589\) | 18.8661 | 0.777364 | ||||||||
\(590\) | −4.05329 | −0.166871 | ||||||||
\(591\) | −22.2177 | −0.913913 | ||||||||
\(592\) | 11.0555 | 0.454379 | ||||||||
\(593\) | −25.1462 | −1.03263 | −0.516316 | − | 0.856398i | \(-0.672697\pi\) | ||||
−0.516316 | + | 0.856398i | \(0.672697\pi\) | |||||||
\(594\) | −27.6723 | −1.13541 | ||||||||
\(595\) | 2.41208 | 0.0988855 | ||||||||
\(596\) | −11.2710 | −0.461677 | ||||||||
\(597\) | 7.85847 | 0.321626 | ||||||||
\(598\) | 6.11555 | 0.250083 | ||||||||
\(599\) | 29.9202 | 1.22251 | 0.611253 | − | 0.791436i | \(-0.290666\pi\) | ||||
0.611253 | + | 0.791436i | \(0.290666\pi\) | |||||||
\(600\) | 5.00058 | 0.204148 | ||||||||
\(601\) | 32.4455 | 1.32348 | 0.661739 | − | 0.749734i | \(-0.269819\pi\) | ||||
0.661739 | + | 0.749734i | \(0.269819\pi\) | |||||||
\(602\) | −2.28457 | −0.0931122 | ||||||||
\(603\) | 13.5141 | 0.550336 | ||||||||
\(604\) | 7.32966 | 0.298240 | ||||||||
\(605\) | 14.9515 | 0.607863 | ||||||||
\(606\) | 11.2666 | 0.457674 | ||||||||
\(607\) | −22.3150 | −0.905736 | −0.452868 | − | 0.891577i | \(-0.649599\pi\) | ||||
−0.452868 | + | 0.891577i | \(0.649599\pi\) | |||||||
\(608\) | 2.64080 | 0.107099 | ||||||||
\(609\) | −2.61070 | −0.105791 | ||||||||
\(610\) | −0.111589 | −0.00451810 | ||||||||
\(611\) | 11.4278 | 0.462320 | ||||||||
\(612\) | 2.44376 | 0.0987832 | ||||||||
\(613\) | −38.9110 | −1.57160 | −0.785799 | − | 0.618481i | \(-0.787748\pi\) | ||||
−0.785799 | + | 0.618481i | \(0.787748\pi\) | |||||||
\(614\) | −11.0714 | −0.446805 | ||||||||
\(615\) | 11.7076 | 0.472096 | ||||||||
\(616\) | 4.90404 | 0.197589 | ||||||||
\(617\) | 23.5506 | 0.948113 | 0.474057 | − | 0.880494i | \(-0.342789\pi\) | ||||
0.474057 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(618\) | −4.29426 | −0.172741 | ||||||||
\(619\) | −20.8450 | −0.837829 | −0.418915 | − | 0.908026i | \(-0.637589\pi\) | ||||
−0.418915 | + | 0.908026i | \(0.637589\pi\) | |||||||
\(620\) | 8.18528 | 0.328729 | ||||||||
\(621\) | 9.76275 | 0.391766 | ||||||||
\(622\) | −20.0417 | −0.803600 | ||||||||
\(623\) | −0.879303 | −0.0352285 | ||||||||
\(624\) | −4.79369 | −0.191901 | ||||||||
\(625\) | 7.03236 | 0.281294 | ||||||||
\(626\) | −14.6082 | −0.583862 | ||||||||
\(627\) | 17.5632 | 0.701408 | ||||||||
\(628\) | −7.75216 | −0.309345 | ||||||||
\(629\) | −23.2746 | −0.928020 | ||||||||
\(630\) | 1.32997 | 0.0529873 | ||||||||
\(631\) | −29.1169 | −1.15913 | −0.579563 | − | 0.814928i | \(-0.696777\pi\) | ||||
−0.579563 | + | 0.814928i | \(0.696777\pi\) | |||||||
\(632\) | −2.22286 | −0.0884207 | ||||||||
\(633\) | −13.4491 | −0.534554 | ||||||||
\(634\) | −4.45017 | −0.176739 | ||||||||
\(635\) | 4.19365 | 0.166420 | ||||||||
\(636\) | 18.3486 | 0.727569 | ||||||||
\(637\) | 3.53472 | 0.140051 | ||||||||
\(638\) | 9.44051 | 0.373753 | ||||||||
\(639\) | 7.91844 | 0.313248 | ||||||||
\(640\) | 1.14574 | 0.0452894 | ||||||||
\(641\) | −43.4277 | −1.71529 | −0.857645 | − | 0.514242i | \(-0.828073\pi\) | ||||
−0.857645 | + | 0.514242i | \(0.828073\pi\) | |||||||
\(642\) | 9.89948 | 0.390701 | ||||||||
\(643\) | −2.95223 | −0.116425 | −0.0582123 | − | 0.998304i | \(-0.518540\pi\) | ||||
−0.0582123 | + | 0.998304i | \(0.518540\pi\) | |||||||
\(644\) | −1.73014 | −0.0681770 | ||||||||
\(645\) | −3.54983 | −0.139774 | ||||||||
\(646\) | −5.55955 | −0.218738 | ||||||||
\(647\) | 15.2926 | 0.601213 | 0.300607 | − | 0.953748i | \(-0.402811\pi\) | ||||
0.300607 | + | 0.953748i | \(0.402811\pi\) | |||||||
\(648\) | −4.17018 | −0.163820 | ||||||||
\(649\) | 17.3490 | 0.681008 | ||||||||
\(650\) | −13.0335 | −0.511215 | ||||||||
\(651\) | 9.68861 | 0.379727 | ||||||||
\(652\) | −1.26861 | −0.0496825 | ||||||||
\(653\) | 31.9240 | 1.24928 | 0.624640 | − | 0.780913i | \(-0.285246\pi\) | ||||
0.624640 | + | 0.780913i | \(0.285246\pi\) | |||||||
\(654\) | 5.71095 | 0.223316 | ||||||||
\(655\) | −12.0597 | −0.471212 | ||||||||
\(656\) | −7.53470 | −0.294181 | ||||||||
\(657\) | 5.87747 | 0.229302 | ||||||||
\(658\) | −3.23302 | −0.126036 | ||||||||
\(659\) | −31.4421 | −1.22481 | −0.612406 | − | 0.790544i | \(-0.709798\pi\) | ||||
−0.612406 | + | 0.790544i | \(0.709798\pi\) | |||||||
\(660\) | 7.62002 | 0.296609 | ||||||||
\(661\) | 7.09662 | 0.276027 | 0.138013 | − | 0.990430i | \(-0.455928\pi\) | ||||
0.138013 | + | 0.990430i | \(0.455928\pi\) | |||||||
\(662\) | 33.9755 | 1.32049 | ||||||||
\(663\) | 10.0919 | 0.391938 | ||||||||
\(664\) | −7.91650 | −0.307220 | ||||||||
\(665\) | −3.02568 | −0.117331 | ||||||||
\(666\) | −12.8332 | −0.497275 | ||||||||
\(667\) | −3.33060 | −0.128961 | ||||||||
\(668\) | −11.9633 | −0.462874 | ||||||||
\(669\) | 12.0496 | 0.465865 | ||||||||
\(670\) | −13.3389 | −0.515325 | ||||||||
\(671\) | 0.477625 | 0.0184385 | ||||||||
\(672\) | 1.35617 | 0.0523155 | ||||||||
\(673\) | −31.2657 | −1.20520 | −0.602602 | − | 0.798042i | \(-0.705869\pi\) | ||||
−0.602602 | + | 0.798042i | \(0.705869\pi\) | |||||||
\(674\) | −19.5007 | −0.751140 | ||||||||
\(675\) | −20.8064 | −0.800839 | ||||||||
\(676\) | −0.505775 | −0.0194529 | ||||||||
\(677\) | 29.0329 | 1.11582 | 0.557912 | − | 0.829900i | \(-0.311603\pi\) | ||||
0.557912 | + | 0.829900i | \(0.311603\pi\) | |||||||
\(678\) | 23.7585 | 0.912440 | ||||||||
\(679\) | 11.1767 | 0.428921 | ||||||||
\(680\) | −2.41208 | −0.0924989 | ||||||||
\(681\) | 26.6052 | 1.01951 | ||||||||
\(682\) | −35.0348 | −1.34155 | ||||||||
\(683\) | −44.7310 | −1.71159 | −0.855793 | − | 0.517319i | \(-0.826930\pi\) | ||||
−0.855793 | + | 0.517319i | \(0.826930\pi\) | |||||||
\(684\) | −3.06542 | −0.117209 | ||||||||
\(685\) | 1.39196 | 0.0531839 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 12.2702 | 0.468137 | ||||||||
\(688\) | 2.28457 | 0.0870985 | ||||||||
\(689\) | −47.8236 | −1.82193 | ||||||||
\(690\) | −2.68833 | −0.102343 | ||||||||
\(691\) | 8.20859 | 0.312270 | 0.156135 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156135 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(692\) | −9.93833 | −0.377799 | ||||||||
\(693\) | −5.69257 | −0.216243 | ||||||||
\(694\) | 22.6747 | 0.860719 | ||||||||
\(695\) | 12.6625 | 0.480317 | ||||||||
\(696\) | 2.61070 | 0.0989583 | ||||||||
\(697\) | 15.8624 | 0.600833 | ||||||||
\(698\) | 2.46440 | 0.0932790 | ||||||||
\(699\) | 16.9478 | 0.641026 | ||||||||
\(700\) | 3.68727 | 0.139366 | ||||||||
\(701\) | −11.0094 | −0.415819 | −0.207910 | − | 0.978148i | \(-0.566666\pi\) | ||||
−0.207910 | + | 0.978148i | \(0.566666\pi\) | |||||||
\(702\) | 19.9456 | 0.752796 | ||||||||
\(703\) | 29.1954 | 1.10113 | ||||||||
\(704\) | −4.90404 | −0.184828 | ||||||||
\(705\) | −5.02355 | −0.189198 | ||||||||
\(706\) | 14.1125 | 0.531133 | ||||||||
\(707\) | 8.30764 | 0.312441 | ||||||||
\(708\) | 4.79773 | 0.180310 | ||||||||
\(709\) | −52.0900 | −1.95628 | −0.978141 | − | 0.207943i | \(-0.933323\pi\) | ||||
−0.978141 | + | 0.207943i | \(0.933323\pi\) | |||||||
\(710\) | −7.81577 | −0.293321 | ||||||||
\(711\) | 2.58028 | 0.0967681 | ||||||||
\(712\) | 0.879303 | 0.0329533 | ||||||||
\(713\) | 12.3602 | 0.462895 | ||||||||
\(714\) | −2.85509 | −0.106849 | ||||||||
\(715\) | −19.8607 | −0.742750 | ||||||||
\(716\) | 7.38368 | 0.275941 | ||||||||
\(717\) | 28.1409 | 1.05094 | ||||||||
\(718\) | 25.0089 | 0.933325 | ||||||||
\(719\) | −9.74203 | −0.363316 | −0.181658 | − | 0.983362i | \(-0.558146\pi\) | ||||
−0.181658 | + | 0.983362i | \(0.558146\pi\) | |||||||
\(720\) | −1.32997 | −0.0495650 | ||||||||
\(721\) | −3.16645 | −0.117925 | ||||||||
\(722\) | −12.0262 | −0.447568 | ||||||||
\(723\) | −11.4102 | −0.424352 | ||||||||
\(724\) | 1.04317 | 0.0387692 | ||||||||
\(725\) | 7.09818 | 0.263620 | ||||||||
\(726\) | −17.6975 | −0.656816 | ||||||||
\(727\) | 18.2819 | 0.678038 | 0.339019 | − | 0.940779i | \(-0.389905\pi\) | ||||
0.339019 | + | 0.940779i | \(0.389905\pi\) | |||||||
\(728\) | −3.53472 | −0.131005 | ||||||||
\(729\) | 27.7984 | 1.02957 | ||||||||
\(730\) | −5.80126 | −0.214714 | ||||||||
\(731\) | −4.80960 | −0.177889 | ||||||||
\(732\) | 0.132084 | 0.00488195 | ||||||||
\(733\) | −13.6652 | −0.504736 | −0.252368 | − | 0.967631i | \(-0.581209\pi\) | ||||
−0.252368 | + | 0.967631i | \(0.581209\pi\) | |||||||
\(734\) | −19.9683 | −0.737045 | ||||||||
\(735\) | −1.55383 | −0.0573137 | ||||||||
\(736\) | 1.73014 | 0.0637737 | ||||||||
\(737\) | 57.0934 | 2.10306 | ||||||||
\(738\) | 8.74622 | 0.321953 | ||||||||
\(739\) | 46.1911 | 1.69917 | 0.849584 | − | 0.527453i | \(-0.176853\pi\) | ||||
0.849584 | + | 0.527453i | \(0.176853\pi\) | |||||||
\(740\) | 12.6668 | 0.465640 | ||||||||
\(741\) | −12.6592 | −0.465047 | ||||||||
\(742\) | 13.5297 | 0.496690 | ||||||||
\(743\) | 2.73788 | 0.100443 | 0.0502215 | − | 0.998738i | \(-0.484007\pi\) | ||||
0.0502215 | + | 0.998738i | \(0.484007\pi\) | |||||||
\(744\) | −9.68861 | −0.355202 | ||||||||
\(745\) | −12.9136 | −0.473119 | ||||||||
\(746\) | −13.6918 | −0.501292 | ||||||||
\(747\) | 9.18942 | 0.336223 | ||||||||
\(748\) | 10.3242 | 0.377491 | ||||||||
\(749\) | 7.29957 | 0.266720 | ||||||||
\(750\) | 13.4985 | 0.492896 | ||||||||
\(751\) | 15.9346 | 0.581463 | 0.290732 | − | 0.956805i | \(-0.406101\pi\) | ||||
0.290732 | + | 0.956805i | \(0.406101\pi\) | |||||||
\(752\) | 3.23302 | 0.117896 | ||||||||
\(753\) | −38.9252 | −1.41851 | ||||||||
\(754\) | −6.80450 | −0.247805 | ||||||||
\(755\) | 8.39791 | 0.305631 | ||||||||
\(756\) | −5.64276 | −0.205225 | ||||||||
\(757\) | 37.2259 | 1.35300 | 0.676500 | − | 0.736443i | \(-0.263496\pi\) | ||||
0.676500 | + | 0.736443i | \(0.263496\pi\) | |||||||
\(758\) | 4.21371 | 0.153049 | ||||||||
\(759\) | 11.5067 | 0.417666 | ||||||||
\(760\) | 3.02568 | 0.109753 | ||||||||
\(761\) | 48.6629 | 1.76403 | 0.882015 | − | 0.471221i | \(-0.156187\pi\) | ||||
0.882015 | + | 0.471221i | \(0.156187\pi\) | |||||||
\(762\) | −4.96387 | −0.179822 | ||||||||
\(763\) | 4.21108 | 0.152451 | ||||||||
\(764\) | 13.1926 | 0.477293 | ||||||||
\(765\) | 2.79992 | 0.101231 | ||||||||
\(766\) | 18.0865 | 0.653493 | ||||||||
\(767\) | −12.5048 | −0.451521 | ||||||||
\(768\) | −1.35617 | −0.0489367 | ||||||||
\(769\) | 23.3698 | 0.842736 | 0.421368 | − | 0.906890i | \(-0.361550\pi\) | ||||
0.421368 | + | 0.906890i | \(0.361550\pi\) | |||||||
\(770\) | 5.61876 | 0.202486 | ||||||||
\(771\) | 36.0931 | 1.29986 | ||||||||
\(772\) | 18.1763 | 0.654180 | ||||||||
\(773\) | −7.11128 | −0.255775 | −0.127887 | − | 0.991789i | \(-0.540820\pi\) | ||||
−0.127887 | + | 0.991789i | \(0.540820\pi\) | |||||||
\(774\) | −2.65191 | −0.0953211 | ||||||||
\(775\) | −26.3422 | −0.946239 | ||||||||
\(776\) | −11.1767 | −0.401219 | ||||||||
\(777\) | 14.9932 | 0.537878 | ||||||||
\(778\) | 25.5220 | 0.915008 | ||||||||
\(779\) | −19.8976 | −0.712907 | ||||||||
\(780\) | −5.49233 | −0.196657 | ||||||||
\(781\) | 33.4533 | 1.19705 | ||||||||
\(782\) | −3.64238 | −0.130251 | ||||||||
\(783\) | −10.8626 | −0.388197 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −8.88197 | −0.317011 | ||||||||
\(786\) | 14.2746 | 0.509160 | ||||||||
\(787\) | 1.24229 | 0.0442829 | 0.0221414 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221414 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(788\) | 16.3826 | 0.583606 | ||||||||
\(789\) | 15.8643 | 0.564784 | ||||||||
\(790\) | −2.54683 | −0.0906120 | ||||||||
\(791\) | 17.5188 | 0.622896 | ||||||||
\(792\) | 5.69257 | 0.202277 | ||||||||
\(793\) | −0.344261 | −0.0122251 | ||||||||
\(794\) | −17.1808 | −0.609723 | ||||||||
\(795\) | 21.0228 | 0.745601 | ||||||||
\(796\) | −5.79459 | −0.205384 | ||||||||
\(797\) | −40.4081 | −1.43133 | −0.715663 | − | 0.698445i | \(-0.753876\pi\) | ||||
−0.715663 | + | 0.698445i | \(0.753876\pi\) | |||||||
\(798\) | 3.58138 | 0.126780 | ||||||||
\(799\) | −6.80632 | −0.240790 | ||||||||
\(800\) | −3.68727 | −0.130365 | ||||||||
\(801\) | −1.02069 | −0.0360643 | ||||||||
\(802\) | 15.8302 | 0.558982 | ||||||||
\(803\) | 24.8307 | 0.876257 | ||||||||
\(804\) | 15.7887 | 0.556826 | ||||||||
\(805\) | −1.98229 | −0.0698666 | ||||||||
\(806\) | 25.2523 | 0.889475 | ||||||||
\(807\) | −21.8219 | −0.768169 | ||||||||
\(808\) | −8.30764 | −0.292262 | ||||||||
\(809\) | 42.1841 | 1.48312 | 0.741558 | − | 0.670889i | \(-0.234087\pi\) | ||||
0.741558 | + | 0.670889i | \(0.234087\pi\) | |||||||
\(810\) | −4.77795 | −0.167880 | ||||||||
\(811\) | −44.2422 | −1.55355 | −0.776776 | − | 0.629777i | \(-0.783146\pi\) | ||||
−0.776776 | + | 0.629777i | \(0.783146\pi\) | |||||||
\(812\) | 1.92505 | 0.0675560 | ||||||||
\(813\) | −3.86494 | −0.135549 | ||||||||
\(814\) | −54.2166 | −1.90029 | ||||||||
\(815\) | −1.45350 | −0.0509138 | ||||||||
\(816\) | 2.85509 | 0.0999480 | ||||||||
\(817\) | 6.03310 | 0.211071 | ||||||||
\(818\) | −26.5689 | −0.928960 | ||||||||
\(819\) | 4.10307 | 0.143373 | ||||||||
\(820\) | −8.63282 | −0.301471 | ||||||||
\(821\) | −7.90394 | −0.275850 | −0.137925 | − | 0.990443i | \(-0.544043\pi\) | ||||
−0.137925 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(822\) | −1.64761 | −0.0574669 | ||||||||
\(823\) | −22.5714 | −0.786789 | −0.393394 | − | 0.919370i | \(-0.628699\pi\) | ||||
−0.393394 | + | 0.919370i | \(0.628699\pi\) | |||||||
\(824\) | 3.16645 | 0.110309 | ||||||||
\(825\) | −24.5231 | −0.853783 | ||||||||
\(826\) | 3.53770 | 0.123092 | ||||||||
\(827\) | −14.5987 | −0.507648 | −0.253824 | − | 0.967250i | \(-0.581688\pi\) | ||||
−0.253824 | + | 0.967250i | \(0.581688\pi\) | |||||||
\(828\) | −2.00833 | −0.0697944 | ||||||||
\(829\) | −37.1226 | −1.28932 | −0.644660 | − | 0.764469i | \(-0.723001\pi\) | ||||
−0.644660 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(830\) | −9.07028 | −0.314834 | ||||||||
\(831\) | −11.8303 | −0.410388 | ||||||||
\(832\) | 3.53472 | 0.122544 | ||||||||
\(833\) | −2.10525 | −0.0729426 | ||||||||
\(834\) | −14.9882 | −0.518998 | ||||||||
\(835\) | −13.7069 | −0.474345 | ||||||||
\(836\) | −12.9506 | −0.447905 | ||||||||
\(837\) | 40.3123 | 1.39340 | ||||||||
\(838\) | 2.73493 | 0.0944765 | ||||||||
\(839\) | 44.5317 | 1.53740 | 0.768702 | − | 0.639607i | \(-0.220903\pi\) | ||||
0.768702 | + | 0.639607i | \(0.220903\pi\) | |||||||
\(840\) | 1.55383 | 0.0536121 | ||||||||
\(841\) | −25.2942 | −0.872213 | ||||||||
\(842\) | −16.8138 | −0.579442 | ||||||||
\(843\) | 32.0079 | 1.10241 | ||||||||
\(844\) | 9.91695 | 0.341355 | ||||||||
\(845\) | −0.579488 | −0.0199350 | ||||||||
\(846\) | −3.75287 | −0.129026 | ||||||||
\(847\) | −13.0496 | −0.448389 | ||||||||
\(848\) | −13.5297 | −0.464611 | ||||||||
\(849\) | −40.5304 | −1.39100 | ||||||||
\(850\) | 7.76264 | 0.266256 | ||||||||
\(851\) | 19.1276 | 0.655685 | ||||||||
\(852\) | 9.25124 | 0.316942 | ||||||||
\(853\) | 28.3695 | 0.971352 | 0.485676 | − | 0.874139i | \(-0.338574\pi\) | ||||
0.485676 | + | 0.874139i | \(0.338574\pi\) | |||||||
\(854\) | 0.0973943 | 0.00333276 | ||||||||
\(855\) | −3.51219 | −0.120114 | ||||||||
\(856\) | −7.29957 | −0.249494 | ||||||||
\(857\) | 44.9274 | 1.53469 | 0.767346 | − | 0.641233i | \(-0.221577\pi\) | ||||
0.767346 | + | 0.641233i | \(0.221577\pi\) | |||||||
\(858\) | 23.5084 | 0.802565 | ||||||||
\(859\) | 9.47658 | 0.323337 | 0.161668 | − | 0.986845i | \(-0.448312\pi\) | ||||
0.161668 | + | 0.986845i | \(0.448312\pi\) | |||||||
\(860\) | 2.61753 | 0.0892570 | ||||||||
\(861\) | −10.2184 | −0.348241 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | 53.9640 | 1.83696 | 0.918478 | − | 0.395472i | \(-0.129419\pi\) | ||||
0.918478 | + | 0.395472i | \(0.129419\pi\) | |||||||
\(864\) | 5.64276 | 0.191971 | ||||||||
\(865\) | −11.3868 | −0.387162 | ||||||||
\(866\) | 11.5140 | 0.391263 | ||||||||
\(867\) | 17.0443 | 0.578854 | ||||||||
\(868\) | −7.14408 | −0.242486 | ||||||||
\(869\) | 10.9010 | 0.369791 | ||||||||
\(870\) | 2.99119 | 0.101411 | ||||||||
\(871\) | −41.1516 | −1.39437 | ||||||||
\(872\) | −4.21108 | −0.142605 | ||||||||
\(873\) | 12.9738 | 0.439096 | ||||||||
\(874\) | 4.56895 | 0.154547 | ||||||||
\(875\) | 9.95338 | 0.336486 | ||||||||
\(876\) | 6.86675 | 0.232006 | ||||||||
\(877\) | −52.3417 | −1.76745 | −0.883726 | − | 0.468004i | \(-0.844973\pi\) | ||||
−0.883726 | + | 0.468004i | \(0.844973\pi\) | |||||||
\(878\) | −9.27411 | −0.312986 | ||||||||
\(879\) | −31.6387 | −1.06715 | ||||||||
\(880\) | −5.61876 | −0.189408 | ||||||||
\(881\) | −49.3253 | −1.66181 | −0.830907 | − | 0.556412i | \(-0.812178\pi\) | ||||
−0.830907 | + | 0.556412i | \(0.812178\pi\) | |||||||
\(882\) | −1.16079 | −0.0390859 | ||||||||
\(883\) | −15.2043 | −0.511665 | −0.255833 | − | 0.966721i | \(-0.582350\pi\) | ||||
−0.255833 | + | 0.966721i | \(0.582350\pi\) | |||||||
\(884\) | −7.44147 | −0.250284 | ||||||||
\(885\) | 5.49697 | 0.184779 | ||||||||
\(886\) | 29.7255 | 0.998648 | ||||||||
\(887\) | 7.79135 | 0.261608 | 0.130804 | − | 0.991408i | \(-0.458244\pi\) | ||||
0.130804 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(888\) | −14.9932 | −0.503139 | ||||||||
\(889\) | −3.66020 | −0.122759 | ||||||||
\(890\) | 1.00745 | 0.0337700 | ||||||||
\(891\) | 20.4507 | 0.685125 | ||||||||
\(892\) | −8.88501 | −0.297492 | ||||||||
\(893\) | 8.53777 | 0.285706 | ||||||||
\(894\) | 15.2854 | 0.511220 | ||||||||
\(895\) | 8.45980 | 0.282780 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −8.29375 | −0.276920 | ||||||||
\(898\) | 13.5470 | 0.452070 | ||||||||
\(899\) | −13.7527 | −0.458678 | ||||||||
\(900\) | 4.28016 | 0.142672 | ||||||||
\(901\) | 28.4834 | 0.948919 | ||||||||
\(902\) | 36.9504 | 1.23032 | ||||||||
\(903\) | 3.09828 | 0.103104 | ||||||||
\(904\) | −17.5188 | −0.582666 | ||||||||
\(905\) | 1.19521 | 0.0397300 | ||||||||
\(906\) | −9.94030 | −0.330244 | ||||||||
\(907\) | 26.0447 | 0.864799 | 0.432400 | − | 0.901682i | \(-0.357667\pi\) | ||||
0.432400 | + | 0.901682i | \(0.357667\pi\) | |||||||
\(908\) | −19.6178 | −0.651040 | ||||||||
\(909\) | 9.64345 | 0.319853 | ||||||||
\(910\) | −4.04988 | −0.134252 | ||||||||
\(911\) | 30.4713 | 1.00956 | 0.504779 | − | 0.863248i | \(-0.331574\pi\) | ||||
0.504779 | + | 0.863248i | \(0.331574\pi\) | |||||||
\(912\) | −3.58138 | −0.118591 | ||||||||
\(913\) | 38.8228 | 1.28485 | ||||||||
\(914\) | −4.06347 | −0.134408 | ||||||||
\(915\) | 0.151334 | 0.00500294 | ||||||||
\(916\) | −9.04766 | −0.298943 | ||||||||
\(917\) | 10.5257 | 0.347589 | ||||||||
\(918\) | −11.8794 | −0.392079 | ||||||||
\(919\) | −26.8941 | −0.887155 | −0.443578 | − | 0.896236i | \(-0.646291\pi\) | ||||
−0.443578 | + | 0.896236i | \(0.646291\pi\) | |||||||
\(920\) | 1.98229 | 0.0653543 | ||||||||
\(921\) | 15.0147 | 0.494752 | ||||||||
\(922\) | −28.8537 | −0.950245 | ||||||||
\(923\) | −24.1123 | −0.793667 | ||||||||
\(924\) | −6.65073 | −0.218793 | ||||||||
\(925\) | −40.7647 | −1.34034 | ||||||||
\(926\) | 2.43037 | 0.0798669 | ||||||||
\(927\) | −3.67560 | −0.120722 | ||||||||
\(928\) | −1.92505 | −0.0631928 | ||||||||
\(929\) | 45.3528 | 1.48798 | 0.743988 | − | 0.668193i | \(-0.232932\pi\) | ||||
0.743988 | + | 0.668193i | \(0.232932\pi\) | |||||||
\(930\) | −11.1007 | −0.364005 | ||||||||
\(931\) | 2.64080 | 0.0865488 | ||||||||
\(932\) | −12.4968 | −0.409346 | ||||||||
\(933\) | 27.1801 | 0.889835 | ||||||||
\(934\) | 3.04652 | 0.0996851 | ||||||||
\(935\) | 11.8289 | 0.386847 | ||||||||
\(936\) | −4.10307 | −0.134113 | ||||||||
\(937\) | −30.3138 | −0.990308 | −0.495154 | − | 0.868805i | \(-0.664888\pi\) | ||||
−0.495154 | + | 0.868805i | \(0.664888\pi\) | |||||||
\(938\) | 11.6421 | 0.380129 | ||||||||
\(939\) | 19.8113 | 0.646517 | ||||||||
\(940\) | 3.70421 | 0.120818 | ||||||||
\(941\) | −49.2076 | −1.60412 | −0.802061 | − | 0.597241i | \(-0.796263\pi\) | ||||
−0.802061 | + | 0.597241i | \(0.796263\pi\) | |||||||
\(942\) | 10.5133 | 0.342541 | ||||||||
\(943\) | −13.0361 | −0.424513 | ||||||||
\(944\) | −3.53770 | −0.115142 | ||||||||
\(945\) | −6.46515 | −0.210311 | ||||||||
\(946\) | −11.2036 | −0.364261 | ||||||||
\(947\) | 15.8750 | 0.515867 | 0.257934 | − | 0.966163i | \(-0.416958\pi\) | ||||
0.257934 | + | 0.966163i | \(0.416958\pi\) | |||||||
\(948\) | 3.01459 | 0.0979092 | ||||||||
\(949\) | −17.8974 | −0.580975 | ||||||||
\(950\) | −9.73736 | −0.315922 | ||||||||
\(951\) | 6.03521 | 0.195705 | ||||||||
\(952\) | 2.10525 | 0.0682316 | ||||||||
\(953\) | 27.9330 | 0.904838 | 0.452419 | − | 0.891806i | \(-0.350561\pi\) | ||||
0.452419 | + | 0.891806i | \(0.350561\pi\) | |||||||
\(954\) | 15.7052 | 0.508473 | ||||||||
\(955\) | 15.1154 | 0.489122 | ||||||||
\(956\) | −20.7502 | −0.671109 | ||||||||
\(957\) | −12.8030 | −0.413861 | ||||||||
\(958\) | −27.7072 | −0.895177 | ||||||||
\(959\) | −1.21489 | −0.0392310 | ||||||||
\(960\) | −1.55383 | −0.0501495 | ||||||||
\(961\) | 20.0379 | 0.646384 | ||||||||
\(962\) | 39.0781 | 1.25993 | ||||||||
\(963\) | 8.47329 | 0.273048 | ||||||||
\(964\) | 8.41356 | 0.270982 | ||||||||
\(965\) | 20.8254 | 0.670393 | ||||||||
\(966\) | 2.34637 | 0.0754932 | ||||||||
\(967\) | 12.3904 | 0.398448 | 0.199224 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199224 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(968\) | 13.0496 | 0.419429 | ||||||||
\(969\) | 7.53971 | 0.242211 | ||||||||
\(970\) | −12.8056 | −0.411162 | ||||||||
\(971\) | −11.8212 | −0.379359 | −0.189680 | − | 0.981846i | \(-0.560745\pi\) | ||||
−0.189680 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(972\) | −11.2728 | −0.361575 | ||||||||
\(973\) | −11.0518 | −0.354305 | ||||||||
\(974\) | 5.29140 | 0.169547 | ||||||||
\(975\) | 17.6757 | 0.566074 | ||||||||
\(976\) | −0.0973943 | −0.00311752 | ||||||||
\(977\) | 56.8405 | 1.81849 | 0.909245 | − | 0.416261i | \(-0.136660\pi\) | ||||
0.909245 | + | 0.416261i | \(0.136660\pi\) | |||||||
\(978\) | 1.72045 | 0.0550140 | ||||||||
\(979\) | −4.31213 | −0.137816 | ||||||||
\(980\) | 1.14574 | 0.0365994 | ||||||||
\(981\) | 4.88819 | 0.156068 | ||||||||
\(982\) | 3.44552 | 0.109951 | ||||||||
\(983\) | 5.39585 | 0.172101 | 0.0860504 | − | 0.996291i | \(-0.472575\pi\) | ||||
0.0860504 | + | 0.996291i | \(0.472575\pi\) | |||||||
\(984\) | 10.2184 | 0.325749 | ||||||||
\(985\) | 18.7703 | 0.598070 | ||||||||
\(986\) | 4.05271 | 0.129065 | ||||||||
\(987\) | 4.38454 | 0.139561 | ||||||||
\(988\) | 9.33448 | 0.296969 | ||||||||
\(989\) | 3.95262 | 0.125686 | ||||||||
\(990\) | 6.52222 | 0.207290 | ||||||||
\(991\) | −44.6814 | −1.41935 | −0.709676 | − | 0.704528i | \(-0.751159\pi\) | ||||
−0.709676 | + | 0.704528i | \(0.751159\pi\) | |||||||
\(992\) | 7.14408 | 0.226825 | ||||||||
\(993\) | −46.0766 | −1.46220 | ||||||||
\(994\) | 6.82158 | 0.216367 | ||||||||
\(995\) | −6.63910 | −0.210474 | ||||||||
\(996\) | 10.7362 | 0.340188 | ||||||||
\(997\) | 17.0680 | 0.540548 | 0.270274 | − | 0.962783i | \(-0.412886\pi\) | ||||
0.270274 | + | 0.962783i | \(0.412886\pi\) | |||||||
\(998\) | −11.1979 | −0.354465 | ||||||||
\(999\) | 62.3836 | 1.97373 |
(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 | 6034.2.a.l.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.l.1.8 | ✓ | 20 | 1.1 | even | 1 | trivial |