Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6728,2,Mod(1,6728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6728 = 2^{3} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6728.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: | \(53.7233504799\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6728.1 |
$q$-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 | ||||||||
\(3\) | 2.12489 | 1.22680 | 0.613402 | − | 0.789771i | \(-0.289801\pi\) | ||||
0.613402 | + | 0.789771i | \(0.289801\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.48486 | 0.664050 | 0.332025 | − | 0.943271i | \(-0.392268\pi\) | ||||
0.332025 | + | 0.943271i | \(0.392268\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.51514 | 0.505046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.15516 | −0.951317 | −0.475658 | − | 0.879630i | \(-0.657790\pi\) | ||||
−0.475658 | + | 0.879630i | \(0.657790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.76491 | 1.87625 | 0.938124 | − | 0.346299i | \(-0.112562\pi\) | ||||
0.938124 | + | 0.346299i | \(0.112562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.15516 | 0.814659 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03028 | 0.236362 | 0.118181 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118181 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24977 | 0.886138 | 0.443069 | − | 0.896487i | \(-0.353890\pi\) | ||||
0.443069 | + | 0.896487i | \(0.353890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79518 | −0.559037 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.15516 | −0.607211 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.87511 | 0.336781 | 0.168390 | − | 0.985720i | \(-0.446143\pi\) | ||||
0.168390 | + | 0.985720i | \(0.446143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.70436 | −1.16708 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.969724 | 0.159422 | 0.0797108 | − | 0.996818i | \(-0.474600\pi\) | ||||
0.0797108 | + | 0.996818i | \(0.474600\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.3747 | 2.30179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.52982 | 1.17596 | 0.587980 | − | 0.808875i | \(-0.299923\pi\) | ||||
0.587980 | + | 0.808875i | \(0.299923\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.09461 | −0.166926 | −0.0834632 | − | 0.996511i | \(-0.526598\pi\) | ||||
−0.0834632 | + | 0.996511i | \(0.526598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.24977 | 0.335376 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.34438 | 1.36302 | 0.681509 | − | 0.731810i | \(-0.261324\pi\) | ||||
0.681509 | + | 0.731810i | \(0.261324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.24977 | −0.595087 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73463 | 0.787712 | 0.393856 | − | 0.919172i | \(-0.371141\pi\) | ||||
0.393856 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.68498 | −0.631722 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.18922 | 0.289969 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.24977 | 1.07403 | 0.537014 | − | 0.843573i | \(-0.319552\pi\) | ||||
0.537014 | + | 0.843573i | \(0.319552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4995 | 1.34433 | 0.672164 | − | 0.740402i | \(-0.265365\pi\) | ||||
0.672164 | + | 0.740402i | \(0.265365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.0450 | 1.24592 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.49954 | −0.549707 | −0.274853 | − | 0.961486i | \(-0.588629\pi\) | ||||
−0.274853 | + | 0.961486i | \(0.588629\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.03028 | 1.08712 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1892 | 1.20924 | 0.604619 | − | 0.796515i | \(-0.293325\pi\) | ||||
0.604619 | + | 0.796515i | \(0.293325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5298 | −1.34946 | −0.674732 | − | 0.738063i | \(-0.735741\pi\) | ||||
−0.674732 | + | 0.738063i | \(0.735741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.93945 | −0.685828 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0946 | 1.47326 | 0.736629 | − | 0.676297i | \(-0.236416\pi\) | ||||
0.736629 | + | 0.676297i | \(0.236416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2498 | −1.24997 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.2498 | 1.78364 | 0.891822 | − | 0.452386i | \(-0.149427\pi\) | ||||
0.891822 | + | 0.452386i | \(0.149427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.96972 | −0.322112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.5904 | −1.44058 | −0.720288 | − | 0.693675i | \(-0.755990\pi\) | ||||
−0.720288 | + | 0.693675i | \(0.755990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.98440 | 0.413163 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.52982 | 0.156956 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.96972 | 0.504599 | 0.252300 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252300 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.78051 | −0.480459 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.46927 | 0.942227 | 0.471114 | − | 0.882073i | \(-0.343852\pi\) | ||||
0.471114 | + | 0.882073i | \(0.343852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.24977 | 0.418742 | 0.209371 | − | 0.977836i | \(-0.432858\pi\) | ||||
0.209371 | + | 0.977836i | \(0.432858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.56009 | −0.634188 | −0.317094 | − | 0.948394i | \(-0.602707\pi\) | ||||
−0.317094 | + | 0.948394i | \(0.602707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9541 | −1.24078 | −0.620390 | − | 0.784293i | \(-0.713026\pi\) | ||||
−0.620390 | + | 0.784293i | \(0.713026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.06055 | 0.195579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0605522 | 0.00569627 | 0.00284814 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00284814 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.31032 | 0.588441 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2498 | 0.947592 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.04496 | −0.0949960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.0000 | 1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5748 | −1.03528 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5298 | 1.20058 | 0.600289 | − | 0.799783i | \(-0.295052\pi\) | ||||
0.600289 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.32592 | −0.204786 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.03028 | −0.788979 | −0.394489 | − | 0.918900i | \(-0.629079\pi\) | ||||
−0.394489 | + | 0.918900i | \(0.629079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.68498 | −0.403219 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.969724 | −0.0828491 | −0.0414246 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414246 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7493 | 1.42066 | 0.710329 | − | 0.703870i | \(-0.248546\pi\) | ||||
0.710329 | + | 0.703870i | \(0.248546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.8557 | 1.67215 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.3444 | −1.78491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.8742 | −1.22680 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.2947 | −1.66261 | −0.831304 | − | 0.555817i | \(-0.812405\pi\) | ||||
−0.831304 | + | 0.555817i | \(0.812405\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5601 | −1.51040 | −0.755200 | − | 0.655495i | \(-0.772460\pi\) | ||||
−0.755200 | + | 0.655495i | \(0.772460\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.03028 | −0.244983 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.78429 | 0.223639 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.03028 | −0.561077 | −0.280539 | − | 0.959843i | \(-0.590513\pi\) | ||||
−0.280539 | + | 0.959843i | \(0.590513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.1854 | 0.966368 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.9348 | 1.95304 | 0.976520 | − | 0.215426i | \(-0.0691140\pi\) | ||||
0.976520 | + | 0.215426i | \(0.0691140\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.95504 | −0.774999 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1892 | 0.788465 | 0.394233 | − | 0.919011i | \(-0.371010\pi\) | ||||
0.394233 | + | 0.919011i | \(0.371010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.7640 | 2.52031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.56101 | 0.119373 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0605522 | 0.00460370 | 0.00230185 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230185 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.5298 | 1.31762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1892 | −1.06055 | −0.530276 | − | 0.847825i | \(-0.677912\pi\) | ||||
−0.530276 | + | 0.847825i | \(0.677912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9541 | 1.26019 | 0.630095 | − | 0.776518i | \(-0.283016\pi\) | ||||
0.630095 | + | 0.776518i | \(0.283016\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.3103 | 1.64923 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.43991 | 0.105864 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.31032 | 0.461457 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.59037 | −0.549220 | −0.274610 | − | 0.961556i | \(-0.588549\pi\) | ||||
−0.274610 | + | 0.961556i | \(0.588549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4693 | 0.969539 | 0.484769 | − | 0.874642i | \(-0.338903\pi\) | ||||
0.484769 | + | 0.874642i | \(0.338903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.3444 | 1.52850 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.93945 | −0.565662 | −0.282831 | − | 0.959170i | \(-0.591274\pi\) | ||||
−0.282831 | + | 0.959170i | \(0.591274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.5601 | −1.88280 | −0.941398 | − | 0.337299i | \(-0.890487\pi\) | ||||
−0.941398 | + | 0.337299i | \(0.890487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.56101 | −0.674382 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1807 | 0.780897 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.43899 | 0.447541 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.25069 | −0.224855 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.435208 | 0.0299610 | 0.0149805 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149805 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.6509 | 1.48350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.62534 | −0.110848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.4995 | −1.65553 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5298 | −0.910114 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.12867 | −0.544336 | −0.272168 | − | 0.962250i | \(-0.587741\pi\) | ||||
−0.272168 | + | 0.962250i | \(0.587741\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.23509 | −0.282339 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.3700 | −1.94935 | −0.974676 | − | 0.223620i | \(-0.928212\pi\) | ||||
−0.974676 | + | 0.223620i | \(0.928212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.46927 | 0.625747 | 0.312873 | − | 0.949795i | \(-0.398708\pi\) | ||||
0.312873 | + | 0.949795i | \(0.398708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.20482 | 0.537515 | 0.268758 | − | 0.963208i | \(-0.413387\pi\) | ||||
0.268758 | + | 0.963208i | \(0.413387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8751 | 0.905113 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.8245 | 1.80740 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.75023 | 0.242582 | 0.121291 | − | 0.992617i | \(-0.461297\pi\) | ||||
0.121291 | + | 0.992617i | \(0.461297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2947 | 1.82262 | 0.911312 | − | 0.411717i | \(-0.135071\pi\) | ||||
0.911312 | + | 0.411717i | \(0.135071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.4390 | −0.926262 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.3940 | −0.664050 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.96972 | 0.443473 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.5289 | 2.18818 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1854 | 0.769138 | 0.384569 | − | 0.923096i | \(-0.374350\pi\) | ||||
0.384569 | + | 0.923096i | \(0.374350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.4087 | −0.842999 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.31032 | −0.395168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.98532 | 0.310976 | 0.155488 | − | 0.987838i | \(-0.450305\pi\) | ||||
0.155488 | + | 0.987838i | \(0.450305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.37466 | 0.146428 | 0.0732138 | − | 0.997316i | \(-0.476674\pi\) | ||||
0.0732138 | + | 0.997316i | \(0.476674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.51514 | 0.523081 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.8780 | −1.76730 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.9385 | −1.76441 | −0.882207 | − | 0.470862i | \(-0.843943\pi\) | ||||
−0.882207 | + | 0.470862i | \(0.843943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1854 | 0.983195 | 0.491598 | − | 0.870822i | \(-0.336413\pi\) | ||||
0.491598 | + | 0.870822i | \(0.336413\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.81926 | 0.531821 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.0596 | 1.50569 | 0.752844 | − | 0.658199i | \(-0.228682\pi\) | ||||
0.752844 | + | 0.658199i | \(0.228682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.84106 | 0.170090 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2351 | −0.789539 | −0.394770 | − | 0.918780i | \(-0.629176\pi\) | ||||
−0.394770 | + | 0.918780i | \(0.629176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3103 | 1.08844 | 0.544218 | − | 0.838944i | \(-0.316826\pi\) | ||||
0.544218 | + | 0.838944i | \(0.316826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.25069 | 0.192554 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5601 | 0.619044 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.93945 | 0.463827 | 0.231914 | − | 0.972736i | \(-0.425501\pi\) | ||||
0.231914 | + | 0.972736i | \(0.425501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2498 | 0.713209 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.95504 | 0.577650 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.7493 | 1.66262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.1211 | 1.15593 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.5904 | 0.892702 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.1542 | −1.60685 | −0.803424 | − | 0.595408i | \(-0.796991\pi\) | ||||
−0.803424 | + | 0.595408i | \(0.796991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.03028 | 0.513714 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.53073 | 0.256914 | 0.128457 | − | 0.991715i | \(-0.458998\pi\) | ||||
0.128457 | + | 0.991715i | \(0.458998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.48486 | 0.310023 | 0.155011 | − | 0.987913i | \(-0.450459\pi\) | ||||
0.155011 | + | 0.987913i | \(0.450459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4390 | −1.14797 | −0.573984 | − | 0.818867i | \(-0.694603\pi\) | ||||
−0.573984 | + | 0.818867i | \(0.694603\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.9394 | −0.778024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.06055 | −0.114652 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.9092 | −1.04889 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.5260 | −1.52219 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5639 | −1.35015 | −0.675076 | − | 0.737748i | \(-0.735889\pi\) | ||||
−0.675076 | + | 0.737748i | \(0.735889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.46927 | 0.0805153 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.68120 | −0.365033 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.4995 | −1.44352 | −0.721761 | − | 0.692142i | \(-0.756667\pi\) | ||||
−0.721761 | + | 0.692142i | \(0.756667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.128666 | 0.00698820 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.91629 | −0.320385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.4087 | 0.721901 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.8704 | −1.12038 | −0.560191 | − | 0.828363i | \(-0.689272\pi\) | ||||
−0.560191 | + | 0.828363i | \(0.689272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.26445 | −0.174742 | −0.0873710 | − | 0.996176i | \(-0.527847\pi\) | ||||
−0.0873710 | + | 0.996176i | \(0.527847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.3444 | −1.13928 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.9991 | −1.64991 | −0.824957 | − | 0.565195i | \(-0.808801\pi\) | ||||
−0.824957 | + | 0.565195i | \(0.808801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1296 | 0.802995 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.03406 | 0.160131 | 0.0800657 | − | 0.996790i | \(-0.474487\pi\) | ||||
0.0800657 | + | 0.996790i | \(0.474487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9385 | −0.944133 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.22041 | −0.116541 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.1202 | −0.896112 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9092 | 0.882652 | 0.441326 | − | 0.897347i | \(-0.354508\pi\) | ||||
0.441326 | + | 0.897347i | \(0.354508\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4087 | 0.593914 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5757 | 0.651145 | 0.325572 | − | 0.945517i | \(-0.394443\pi\) | ||||
0.325572 | + | 0.945517i | \(0.394443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.5951 | −1.27008 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4087 | 0.688759 | 0.344380 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344380 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.7493 | 1.47287 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0606 | 0.922851 | 0.461426 | − | 0.887179i | \(-0.347338\pi\) | ||||
0.461426 | + | 0.887179i | \(0.347338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.65848 | −0.0843055 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0293595 | −0.00148858 | −0.000744292 | − | 1.00000i | \(-0.500237\pi\) | ||||
−0.000744292 | 1.00000i | \(0.500237\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.49954 | −0.429840 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.1883 | −0.967922 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.4437 | 0.978318 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.1055 | −1.31020 | −0.655099 | − | 0.755543i | \(-0.727373\pi\) | ||||
−0.655099 | + | 0.755543i | \(0.727373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.2645 | 0.962021 | 0.481010 | − | 0.876715i | \(-0.340270\pi\) | ||||
0.481010 | + | 0.876715i | \(0.340270\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6850 | 0.631884 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.7044 | −0.830046 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.05964 | −0.151661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.4986 | −0.964145 | −0.482072 | − | 0.876131i | \(-0.660116\pi\) | ||||
−0.482072 | + | 0.876131i | \(0.660116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.06055 | −0.101640 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.1287 | 1.18443 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.5904 | 1.74287 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.2489 | −1.62431 | −0.812156 | − | 0.583440i | \(-0.801706\pi\) | ||||
−0.812156 | + | 0.583440i | \(0.801706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.93945 | −0.191997 | −0.0959985 | − | 0.995381i | \(-0.530604\pi\) | ||||
−0.0959985 | + | 0.995381i | \(0.530604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.1580 | 0.688387 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.59037 | 0.271173 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −45.3544 | −2.18973 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.3700 | 0.836681 | 0.418341 | − | 0.908290i | \(-0.362612\pi\) | ||||
0.418341 | + | 0.908290i | \(0.362612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5298 | 0.746315 | 0.373158 | − | 0.927768i | \(-0.378275\pi\) | ||||
0.373158 | + | 0.927768i | \(0.378275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.37844 | 0.209449 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.87042 | 0.423362 | 0.211681 | − | 0.977339i | \(-0.432106\pi\) | ||||
0.211681 | + | 0.977339i | \(0.432106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6060 | −0.505046 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.09083 | 0.146850 | 0.0734248 | − | 0.997301i | \(-0.476607\pi\) | ||||
0.0734248 | + | 0.997301i | \(0.476607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.1798 | −0.956615 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.1240 | −2.03969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9385 | −0.799379 | −0.399689 | − | 0.916651i | \(-0.630882\pi\) | ||||
−0.399689 | + | 0.916651i | \(0.630882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.7578 | −1.11871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.4381 | −1.85296 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9991 | 0.514515 | 0.257258 | − | 0.966343i | \(-0.417181\pi\) | ||||
0.257258 | + | 0.966343i | \(0.417181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.31032 | 0.294541 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1202 | 1.07681 | 0.538407 | − | 0.842685i | \(-0.319026\pi\) | ||||
0.538407 | + | 0.842685i | \(0.319026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.870417 | −0.0404517 | −0.0202259 | − | 0.999795i | \(-0.506439\pi\) | ||||
−0.0202259 | + | 0.999795i | \(0.506439\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.91629 | 0.274361 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.2148 | −0.657782 | −0.328891 | − | 0.944368i | \(-0.606675\pi\) | ||||
−0.328891 | + | 0.944368i | \(0.606675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9385 | −0.688331 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.45367 | 0.158800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.87981 | −0.132135 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.68876 | 0.397831 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.56479 | 0.162879 | 0.0814397 | − | 0.996678i | \(-0.474048\pi\) | ||||
0.0814397 | + | 0.996678i | \(0.474048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.56009 | 0.299115 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.37935 | 0.335079 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.49954 | −0.385151 | −0.192575 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192575 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.9835 | 2.39600 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.595068 | 0.0268550 | 0.0134275 | − | 0.999910i | \(-0.495726\pi\) | ||||
0.0134275 | + | 0.999910i | \(0.495726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.09839 | −0.319049 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.24885 | 0.414036 | 0.207018 | − | 0.978337i | \(-0.433624\pi\) | ||||
0.207018 | + | 0.978337i | \(0.433624\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6509 | 0.967292 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.314104 | −0.0140052 | −0.00700260 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700260 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0606 | 0.625686 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 69.6197 | 3.09192 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.11399 | 0.0493766 | 0.0246883 | − | 0.999695i | \(-0.492141\pi\) | ||||
0.0246883 | + | 0.999695i | \(0.492141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.25069 | −0.143521 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.31032 | 0.278066 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.4830 | −1.29666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.128666 | 0.00564783 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1358 | 0.487868 | 0.243934 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243934 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.49954 | −0.196751 | −0.0983756 | − | 0.995149i | \(-0.531365\pi\) | ||||
−0.0983756 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.75023 | −0.163363 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.93945 | −0.214759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4995 | 0.542434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 50.9385 | 2.20639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.74083 | −0.421133 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.1505 | −1.30109 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.0861 | 0.951317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6509 | −0.844859 | −0.422430 | − | 0.906396i | \(-0.638823\pi\) | ||||
−0.422430 | + | 0.906396i | \(0.638823\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.0256 | 1.54601 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.2351 | −0.823941 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.93945 | −0.0829248 | −0.0414624 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414624 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9083 | 0.678948 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.05964 | 0.129874 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.0587 | −1.61260 | −0.806300 | − | 0.591507i | \(-0.798533\pi\) | ||||
−0.806300 | + | 0.591507i | \(0.798533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.40493 | −0.313195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4087 | 0.566116 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.1845 | −1.90430 | −0.952150 | − | 0.305630i | \(-0.901133\pi\) | ||||
−0.952150 | + | 0.305630i | \(0.901133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0899116 | 0.00378261 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.4986 | 1.32049 | 0.660246 | − | 0.751050i | \(-0.270452\pi\) | ||||
0.660246 | + | 0.751050i | \(0.270452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.6206 | 0.695552 | 0.347776 | − | 0.937578i | \(-0.386937\pi\) | ||||
0.347776 | + | 0.937578i | \(0.386937\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.1287 | −0.673785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.8789 | −0.495384 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.43991 | 0.143205 | 0.0716026 | − | 0.997433i | \(-0.477189\pi\) | ||||
0.0716026 | + | 0.997433i | \(0.477189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.6206 | 1.18943 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0937 | −0.749364 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.2195 | 0.629249 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.93097 | 0.286072 | 0.143036 | − | 0.989718i | \(-0.454314\pi\) | ||||
0.143036 | + | 0.989718i | \(0.454314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.93189 | 0.0796020 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.8704 | −0.693956 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.6041 | −1.29783 | −0.648913 | − | 0.760863i | \(-0.724776\pi\) | ||||
−0.648913 | + | 0.760863i | \(0.724776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −56.4372 | −2.30982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.6547 | 1.29338 | 0.646688 | − | 0.762755i | \(-0.276154\pi\) | ||||
0.646688 | + | 0.762755i | \(0.276154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0303 | −0.776261 | −0.388131 | − | 0.921604i | \(-0.626879\pi\) | ||||
−0.388131 | + | 0.921604i | \(0.626879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.81743 | −0.277627 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.55162 | −0.0630821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.3141 | −0.986879 | −0.493440 | − | 0.869780i | \(-0.664261\pi\) | ||||
−0.493440 | + | 0.869780i | \(0.664261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.2139 | 2.55736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.07615 | −0.326193 | −0.163096 | − | 0.986610i | \(-0.552148\pi\) | ||||
−0.163096 | + | 0.986610i | \(0.552148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.7578 | 0.958007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.9697 | −0.683175 | −0.341588 | − | 0.939850i | \(-0.610965\pi\) | ||||
−0.341588 | + | 0.939850i | \(0.610965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3737 | 0.939470 | 0.469735 | − | 0.882807i | \(-0.344349\pi\) | ||||
0.469735 | + | 0.882807i | \(0.344349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.4087 | −0.538073 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.21102 | −0.128441 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.90734 | −0.275853 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.93945 | −0.0773308 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.75023 | −0.149294 | −0.0746471 | − | 0.997210i | \(-0.523783\pi\) | ||||
−0.0746471 | + | 0.997210i | \(0.523783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.924768 | 0.0367562 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0899 | 0.797244 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.3544 | −1.87625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.4381 | 0.610721 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.5592 | −1.16752 | −0.583759 | − | 0.811927i | \(-0.698419\pi\) | ||||
−0.583759 | + | 0.811927i | \(0.698419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.4995 | 1.75489 | 0.877445 | − | 0.479677i | \(-0.159246\pi\) | ||||
0.877445 | + | 0.479677i | \(0.159246\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.45367 | −0.135988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.80986 | −0.267723 | −0.133862 | − | 0.991000i | \(-0.542738\pi\) | ||||
−0.133862 | + | 0.991000i | \(0.542738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0294 | −1.02174 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.1514 | −0.436387 | −0.218194 | − | 0.975905i | \(-0.570016\pi\) | ||||
−0.218194 | + | 0.975905i | \(0.570016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.4087 | −0.523922 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.4693 | −0.681541 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.2526 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9991 | 1.51689 | 0.758444 | − | 0.651738i | \(-0.225960\pi\) | ||||
0.758444 | + | 0.651738i | \(0.225960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.7493 | −1.11653 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2725 | −0.667793 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.1277 | −1.27888 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1443 | −0.391033 | −0.195516 | − | 0.980700i | \(-0.562638\pi\) | ||||
−0.195516 | + | 0.980700i | \(0.562638\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.81926 | 0.339453 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.4986 | −1.82552 | −0.912760 | − | 0.408496i | \(-0.866053\pi\) | ||||
−0.912760 | + | 0.408496i | \(0.866053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −62.4078 | −2.39147 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.43991 | −0.0550965 | −0.0275482 | − | 0.999620i | \(-0.508770\pi\) | ||||
−0.0275482 | + | 0.999620i | \(0.508770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.43991 | −0.0550160 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1211 | 0.767668 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.7943 | 1.47794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.9385 | 1.02479 | 0.512395 | − | 0.858750i | \(-0.328758\pi\) | ||||
0.512395 | + | 0.858750i | \(0.328758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.8704 | 0.943389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0596 | −0.570424 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.4343 | 0.659425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3250 | 0.654356 | 0.327178 | − | 0.944963i | \(-0.393902\pi\) | ||||
0.327178 | + | 0.944963i | \(0.393902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.999083 | 0.0376811 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.4830 | 1.11040 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0837106 | 0.00314382 | 0.00157191 | − | 0.999999i | \(-0.499500\pi\) | ||||
0.00157191 | + | 0.999999i | \(0.499500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.8401 | 0.744063 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.96881 | 0.298434 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.6935 | −1.18527 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.96881 | 0.297601 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.4305 | 0.724636 | 0.362318 | − | 0.932055i | \(-0.381985\pi\) | ||||
0.362318 | + | 0.932055i | \(0.381985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 60.1231 | 2.23600 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.2876 | 1.08622 | 0.543109 | − | 0.839662i | \(-0.317247\pi\) | ||||
0.543109 | + | 0.839662i | \(0.317247\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.06811 | 0.113634 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.18922 | 0.0809712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7115 | −0.801932 | −0.400966 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400966 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.0861 | −0.814659 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.1968 | 0.522945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.37466 | −0.234496 | −0.117248 | − | 0.993103i | \(-0.537407\pi\) | ||||
−0.117248 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.8099 | 0.544054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.4693 | 1.00775 | 0.503875 | − | 0.863777i | \(-0.331907\pi\) | ||||
0.503875 | + | 0.863777i | \(0.331907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.1349 | −1.10406 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.6206 | 0.900822 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.0890 | 1.79128 | 0.895641 | − | 0.444777i | \(-0.146717\pi\) | ||||
0.895641 | + | 0.444777i | \(0.146717\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.8927 | 0.943581 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.5592 | −1.00298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.2413 | 1.28087 | 0.640433 | − | 0.768014i | \(-0.278755\pi\) | ||||
0.640433 | + | 0.768014i | \(0.278755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.4920 | −1.03419 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0596 | −0.908411 | −0.454206 | − | 0.890897i | \(-0.650077\pi\) | ||||
−0.454206 | + | 0.890897i | \(0.650077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.49954 | −0.162681 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.8089 | 2.01514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6803 | 1.07030 | 0.535149 | − | 0.844758i | \(-0.320255\pi\) | ||||
0.535149 | + | 0.844758i | \(0.320255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5932 | 0.381506 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.5298 | −0.846309 | −0.423154 | − | 0.906058i | \(-0.639077\pi\) | ||||
−0.423154 | + | 0.906058i | \(0.639077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.24129 | −0.188273 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.75779 | 0.277952 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.1486 | −1.15037 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4390 | −0.372584 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.7484 | −1.48817 | −0.744085 | − | 0.668085i | \(-0.767114\pi\) | ||||
−0.744085 | + | 0.668085i | \(0.767114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.04587 | 0.179638 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.0284 | 2.52229 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.0937 | 0.641717 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.50046 | −0.194836 | −0.0974181 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974181 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6888 | −0.661161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.5913 | −0.727557 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.3784 | 1.28377 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −61.4911 | −2.16459 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.1505 | −1.41162 | −0.705808 | − | 0.708404i | \(-0.749416\pi\) | ||||
−0.705808 | + | 0.708404i | \(0.749416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0606 | 0.493733 | 0.246866 | − | 0.969050i | \(-0.420599\pi\) | ||||
0.246866 | + | 0.969050i | \(0.420599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.3922 | 1.20619 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.0247 | 1.29692 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.12775 | −0.0394550 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.1131 | −1.05095 | −0.525477 | − | 0.850808i | \(-0.676113\pi\) | ||||
−0.525477 | + | 0.850808i | \(0.676113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.5895 | −1.69372 | −0.846861 | − | 0.531814i | \(-0.821510\pi\) | ||||
−0.846861 | + | 0.531814i | \(0.821510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.7399 | 0.652440 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.0029 | −1.07808 | −0.539038 | − | 0.842282i | \(-0.681212\pi\) | ||||
−0.539038 | + | 0.842282i | \(0.681212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.6206 | 1.61920 | 0.809601 | − | 0.586981i | \(-0.199684\pi\) | ||||
0.809601 | + | 0.586981i | \(0.199684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.2489 | 1.84718 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.0000 | 0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1296 | 0.523581 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.91629 | −0.204497 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.09553 | −0.141393 | −0.0706966 | − | 0.997498i | \(-0.522522\pi\) | ||||
−0.0706966 | + | 0.997498i | \(0.522522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.1231 | −0.968609 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.6500 | 1.67361 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.9073 | 1.33530 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.12110 | 0.141270 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.0606 | 0.960775 | 0.480388 | − | 0.877056i | \(-0.340496\pi\) | ||||
0.480388 | + | 0.877056i | \(0.340496\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.31789 | 0.0792700 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.60597 | 0.328134 | 0.164067 | − | 0.986449i | \(-0.447539\pi\) | ||||
0.164067 | + | 0.986449i | \(0.447539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.96594 | −0.305914 | −0.152957 | − | 0.988233i | \(-0.548880\pi\) | ||||
−0.152957 | + | 0.988233i | \(0.548880\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.4911 | −1.54853 | −0.774267 | − | 0.632859i | \(-0.781881\pi\) | ||||
−0.774267 | + | 0.632859i | \(0.781881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0899116 | 0.00305709 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.6235 | −0.938144 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.3156 | −1.40154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.4390 | −1.03139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.52982 | 0.254846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.2654 | −1.15706 | −0.578530 | − | 0.815661i | \(-0.696373\pi\) | ||||
−0.578530 | + | 0.815661i | \(0.696373\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.8704 | 0.569025 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4995 | 0.758029 | 0.379014 | − | 0.925391i | \(-0.376263\pi\) | ||||
0.379014 | + | 0.925391i | \(0.376263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.5592 | 1.06205 | 0.531025 | − | 0.847356i | \(-0.321807\pi\) | ||||
0.531025 | + | 0.847356i | \(0.321807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.0294 | 0.874967 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.6841 | −0.593773 | −0.296886 | − | 0.954913i | \(-0.595948\pi\) | ||||
−0.296886 | + | 0.954913i | \(0.595948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.4948 | 1.18912 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.62729 | 0.322165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0690 | −0.704260 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 61.0890 | 2.03970 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4693 | −0.382097 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.1745 | 0.836830 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.03028 | −0.0342098 | −0.0171049 | − | 0.999854i | \(-0.505445\pi\) | ||||
−0.0171049 | + | 0.999854i | \(0.505445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.3472 | 0.475868 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3056 | 0.705887 | 0.352943 | − | 0.935645i | \(-0.385181\pi\) | ||||
0.352943 | + | 0.935645i | \(0.385181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.2707 | −1.69681 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.1277 | 1.09517 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.1883 | 0.632964 | 0.316482 | − | 0.948599i | \(-0.397498\pi\) | ||||
0.316482 | + | 0.948599i | \(0.397498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −59.8245 | −1.97129 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.9291 | 2.26883 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.71056 | −0.0891226 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.43899 | 0.211484 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.18166 | −0.137196 | −0.0685979 | − | 0.997644i | \(-0.521853\pi\) | ||||
−0.0685979 | + | 0.997644i | \(0.521853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.21193 | −0.236362 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.62729 | 0.315183 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.36996 | 0.306430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.1807 | −1.47599 | −0.737995 | − | 0.674806i | \(-0.764227\pi\) | ||||
−0.737995 | + | 0.674806i | \(0.764227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6547 | 0.380337 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0752 | −0.556637 | −0.278318 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278318 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.3359 | −1.63570 | −0.817849 | − | 0.575434i | \(-0.804833\pi\) | ||||
−0.817849 | + | 0.575434i | \(0.804833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.9982 | −2.53193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.4305 | −1.40833 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.94657 | 0.289808 | 0.144904 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144904 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.2707 | −0.364710 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4839 | −0.886579 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.93945 | −0.320294 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0000 | 0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.5327 | −1.43207 | −0.716037 | − | 0.698062i | \(-0.754046\pi\) | ||||
−0.716037 | + | 0.698062i | \(0.754046\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.37844 | −0.140656 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0294 | 1.34879 | 0.674393 | − | 0.738372i | \(-0.264405\pi\) | ||||
0.674393 | + | 0.738372i | \(0.264405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −40.1798 | −1.28678 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.3931 | −0.492469 | −0.246235 | − | 0.969210i | \(-0.579193\pi\) | ||||
−0.246235 | + | 0.969210i | \(0.579193\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.8798 | 1.37044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.6273 | −0.626651 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7153 | −1.07535 | −0.537675 | − | 0.843152i | \(-0.680697\pi\) | ||||
−0.537675 | + | 0.843152i | \(0.680697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.7890 | −0.375628 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.65184 | −0.147920 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.3094 | −0.740448 | −0.370224 | − | 0.928943i | \(-0.620719\pi\) | ||||
−0.370224 | + | 0.928943i | \(0.620719\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −52.1954 | −1.65637 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.4381 | −1.25027 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.02936 | 0.127611 | 0.0638055 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638055 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.05964 | −0.0968026 |
(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 | 6728.2.a.j.1.3 | 3 | ||
29.28 | even | 2 | 232.2.a.d.1.1 | ✓ | 3 | ||
87.86 | odd | 2 | 2088.2.a.s.1.2 | 3 | |||
116.115 | odd | 2 | 464.2.a.j.1.3 | 3 | |||
145.144 | even | 2 | 5800.2.a.p.1.3 | 3 | |||
232.115 | odd | 2 | 1856.2.a.y.1.1 | 3 | |||
232.173 | even | 2 | 1856.2.a.x.1.3 | 3 | |||
348.347 | even | 2 | 4176.2.a.bu.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.a.d.1.1 | ✓ | 3 | 29.28 | even | 2 | ||
464.2.a.j.1.3 | 3 | 116.115 | odd | 2 | |||
1856.2.a.x.1.3 | 3 | 232.173 | even | 2 | |||
1856.2.a.y.1.1 | 3 | 232.115 | odd | 2 | |||
2088.2.a.s.1.2 | 3 | 87.86 | odd | 2 | |||
4176.2.a.bu.1.2 | 3 | 348.347 | even | 2 | |||
5800.2.a.p.1.3 | 3 | 145.144 | even | 2 | |||
6728.2.a.j.1.3 | 3 | 1.1 | even | 1 | trivial |