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: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 | ||||||||
\(3\) | −1.90367 | −1.09908 | −0.549542 | − | 0.835466i | \(-0.685198\pi\) | ||||
−0.549542 | + | 0.835466i | \(0.685198\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.72741 | −1.66695 | −0.833474 | − | 0.552558i | \(-0.813652\pi\) | ||||
−0.833474 | + | 0.552558i | \(0.813652\pi\) | |||||||
\(6\) | 1.90367 | 0.777170 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.623956 | 0.207985 | ||||||||
\(10\) | 3.72741 | 1.17871 | ||||||||
\(11\) | 2.91306 | 0.878320 | 0.439160 | − | 0.898409i | \(-0.355276\pi\) | ||||
0.439160 | + | 0.898409i | \(0.355276\pi\) | |||||||
\(12\) | −1.90367 | −0.549542 | ||||||||
\(13\) | 0.858424 | 0.238084 | 0.119042 | − | 0.992889i | \(-0.462018\pi\) | ||||
0.119042 | + | 0.992889i | \(0.462018\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 7.09576 | 1.83212 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.98075 | 0.722938 | 0.361469 | − | 0.932384i | \(-0.382275\pi\) | ||||
0.361469 | + | 0.932384i | \(0.382275\pi\) | |||||||
\(18\) | −0.623956 | −0.147068 | ||||||||
\(19\) | −1.77524 | −0.407267 | −0.203634 | − | 0.979047i | \(-0.565275\pi\) | ||||
−0.203634 | + | 0.979047i | \(0.565275\pi\) | |||||||
\(20\) | −3.72741 | −0.833474 | ||||||||
\(21\) | −1.90367 | −0.415415 | ||||||||
\(22\) | −2.91306 | −0.621066 | ||||||||
\(23\) | 7.03281 | 1.46644 | 0.733221 | − | 0.679991i | \(-0.238016\pi\) | ||||
0.733221 | + | 0.679991i | \(0.238016\pi\) | |||||||
\(24\) | 1.90367 | 0.388585 | ||||||||
\(25\) | 8.89359 | 1.77872 | ||||||||
\(26\) | −0.858424 | −0.168351 | ||||||||
\(27\) | 4.52320 | 0.870491 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 7.80533 | 1.44941 | 0.724707 | − | 0.689057i | \(-0.241975\pi\) | ||||
0.724707 | + | 0.689057i | \(0.241975\pi\) | |||||||
\(30\) | −7.09576 | −1.29550 | ||||||||
\(31\) | 0.802592 | 0.144150 | 0.0720749 | − | 0.997399i | \(-0.477038\pi\) | ||||
0.0720749 | + | 0.997399i | \(0.477038\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.54550 | −0.965347 | ||||||||
\(34\) | −2.98075 | −0.511194 | ||||||||
\(35\) | −3.72741 | −0.630047 | ||||||||
\(36\) | 0.623956 | 0.103993 | ||||||||
\(37\) | 0.206301 | 0.0339156 | 0.0169578 | − | 0.999856i | \(-0.494602\pi\) | ||||
0.0169578 | + | 0.999856i | \(0.494602\pi\) | |||||||
\(38\) | 1.77524 | 0.287982 | ||||||||
\(39\) | −1.63416 | −0.261674 | ||||||||
\(40\) | 3.72741 | 0.589355 | ||||||||
\(41\) | 4.82573 | 0.753652 | 0.376826 | − | 0.926284i | \(-0.377015\pi\) | ||||
0.376826 | + | 0.926284i | \(0.377015\pi\) | |||||||
\(42\) | 1.90367 | 0.293742 | ||||||||
\(43\) | 1.00633 | 0.153464 | 0.0767318 | − | 0.997052i | \(-0.475551\pi\) | ||||
0.0767318 | + | 0.997052i | \(0.475551\pi\) | |||||||
\(44\) | 2.91306 | 0.439160 | ||||||||
\(45\) | −2.32574 | −0.346701 | ||||||||
\(46\) | −7.03281 | −1.03693 | ||||||||
\(47\) | −5.24240 | −0.764683 | −0.382341 | − | 0.924021i | \(-0.624882\pi\) | ||||
−0.382341 | + | 0.924021i | \(0.624882\pi\) | |||||||
\(48\) | −1.90367 | −0.274771 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.89359 | −1.25774 | ||||||||
\(51\) | −5.67436 | −0.794569 | ||||||||
\(52\) | 0.858424 | 0.119042 | ||||||||
\(53\) | −9.66754 | −1.32794 | −0.663969 | − | 0.747760i | \(-0.731129\pi\) | ||||
−0.663969 | + | 0.747760i | \(0.731129\pi\) | |||||||
\(54\) | −4.52320 | −0.615530 | ||||||||
\(55\) | −10.8582 | −1.46411 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.37946 | 0.447621 | ||||||||
\(58\) | −7.80533 | −1.02489 | ||||||||
\(59\) | −5.01202 | −0.652510 | −0.326255 | − | 0.945282i | \(-0.605787\pi\) | ||||
−0.326255 | + | 0.945282i | \(0.605787\pi\) | |||||||
\(60\) | 7.09576 | 0.916058 | ||||||||
\(61\) | −11.9098 | −1.52490 | −0.762450 | − | 0.647047i | \(-0.776004\pi\) | ||||
−0.762450 | + | 0.647047i | \(0.776004\pi\) | |||||||
\(62\) | −0.802592 | −0.101929 | ||||||||
\(63\) | 0.623956 | 0.0786110 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.19970 | −0.396874 | ||||||||
\(66\) | 5.54550 | 0.682604 | ||||||||
\(67\) | 8.51127 | 1.03982 | 0.519908 | − | 0.854222i | \(-0.325966\pi\) | ||||
0.519908 | + | 0.854222i | \(0.325966\pi\) | |||||||
\(68\) | 2.98075 | 0.361469 | ||||||||
\(69\) | −13.3881 | −1.61174 | ||||||||
\(70\) | 3.72741 | 0.445511 | ||||||||
\(71\) | 12.7885 | 1.51771 | 0.758857 | − | 0.651257i | \(-0.225758\pi\) | ||||
0.758857 | + | 0.651257i | \(0.225758\pi\) | |||||||
\(72\) | −0.623956 | −0.0735339 | ||||||||
\(73\) | −0.847830 | −0.0992310 | −0.0496155 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496155 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(74\) | −0.206301 | −0.0239820 | ||||||||
\(75\) | −16.9305 | −1.95496 | ||||||||
\(76\) | −1.77524 | −0.203634 | ||||||||
\(77\) | 2.91306 | 0.331974 | ||||||||
\(78\) | 1.63416 | 0.185032 | ||||||||
\(79\) | 2.38319 | 0.268130 | 0.134065 | − | 0.990973i | \(-0.457197\pi\) | ||||
0.134065 | + | 0.990973i | \(0.457197\pi\) | |||||||
\(80\) | −3.72741 | −0.416737 | ||||||||
\(81\) | −10.4825 | −1.16473 | ||||||||
\(82\) | −4.82573 | −0.532912 | ||||||||
\(83\) | −1.46787 | −0.161120 | −0.0805600 | − | 0.996750i | \(-0.525671\pi\) | ||||
−0.0805600 | + | 0.996750i | \(0.525671\pi\) | |||||||
\(84\) | −1.90367 | −0.207707 | ||||||||
\(85\) | −11.1105 | −1.20510 | ||||||||
\(86\) | −1.00633 | −0.108515 | ||||||||
\(87\) | −14.8588 | −1.59303 | ||||||||
\(88\) | −2.91306 | −0.310533 | ||||||||
\(89\) | 8.13689 | 0.862509 | 0.431254 | − | 0.902230i | \(-0.358071\pi\) | ||||
0.431254 | + | 0.902230i | \(0.358071\pi\) | |||||||
\(90\) | 2.32574 | 0.245154 | ||||||||
\(91\) | 0.858424 | 0.0899873 | ||||||||
\(92\) | 7.03281 | 0.733221 | ||||||||
\(93\) | −1.52787 | −0.158433 | ||||||||
\(94\) | 5.24240 | 0.540712 | ||||||||
\(95\) | 6.61704 | 0.678894 | ||||||||
\(96\) | 1.90367 | 0.194292 | ||||||||
\(97\) | 14.3308 | 1.45508 | 0.727538 | − | 0.686067i | \(-0.240664\pi\) | ||||
0.727538 | + | 0.686067i | \(0.240664\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.81762 | 0.182678 | ||||||||
\(100\) | 8.89359 | 0.889359 | ||||||||
\(101\) | 14.4359 | 1.43643 | 0.718214 | − | 0.695823i | \(-0.244960\pi\) | ||||
0.718214 | + | 0.695823i | \(0.244960\pi\) | |||||||
\(102\) | 5.67436 | 0.561845 | ||||||||
\(103\) | −9.76032 | −0.961713 | −0.480857 | − | 0.876799i | \(-0.659674\pi\) | ||||
−0.480857 | + | 0.876799i | \(0.659674\pi\) | |||||||
\(104\) | −0.858424 | −0.0841754 | ||||||||
\(105\) | 7.09576 | 0.692475 | ||||||||
\(106\) | 9.66754 | 0.938994 | ||||||||
\(107\) | −7.84253 | −0.758166 | −0.379083 | − | 0.925363i | \(-0.623761\pi\) | ||||
−0.379083 | + | 0.925363i | \(0.623761\pi\) | |||||||
\(108\) | 4.52320 | 0.435245 | ||||||||
\(109\) | −1.09655 | −0.105031 | −0.0525154 | − | 0.998620i | \(-0.516724\pi\) | ||||
−0.0525154 | + | 0.998620i | \(0.516724\pi\) | |||||||
\(110\) | 10.8582 | 1.03529 | ||||||||
\(111\) | −0.392728 | −0.0372761 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 19.6638 | 1.84982 | 0.924909 | − | 0.380188i | \(-0.124141\pi\) | ||||
0.924909 | + | 0.380188i | \(0.124141\pi\) | |||||||
\(114\) | −3.37946 | −0.316516 | ||||||||
\(115\) | −26.2142 | −2.44448 | ||||||||
\(116\) | 7.80533 | 0.724707 | ||||||||
\(117\) | 0.535618 | 0.0495179 | ||||||||
\(118\) | 5.01202 | 0.461394 | ||||||||
\(119\) | 2.98075 | 0.273245 | ||||||||
\(120\) | −7.09576 | −0.647751 | ||||||||
\(121\) | −2.51409 | −0.228554 | ||||||||
\(122\) | 11.9098 | 1.07827 | ||||||||
\(123\) | −9.18659 | −0.828327 | ||||||||
\(124\) | 0.802592 | 0.0720749 | ||||||||
\(125\) | −14.5130 | −1.29808 | ||||||||
\(126\) | −0.623956 | −0.0555864 | ||||||||
\(127\) | −19.8079 | −1.75767 | −0.878833 | − | 0.477130i | \(-0.841677\pi\) | ||||
−0.878833 | + | 0.477130i | \(0.841677\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.91572 | −0.168669 | ||||||||
\(130\) | 3.19970 | 0.280632 | ||||||||
\(131\) | −14.2456 | −1.24465 | −0.622324 | − | 0.782760i | \(-0.713811\pi\) | ||||
−0.622324 | + | 0.782760i | \(0.713811\pi\) | |||||||
\(132\) | −5.54550 | −0.482674 | ||||||||
\(133\) | −1.77524 | −0.153933 | ||||||||
\(134\) | −8.51127 | −0.735262 | ||||||||
\(135\) | −16.8598 | −1.45106 | ||||||||
\(136\) | −2.98075 | −0.255597 | ||||||||
\(137\) | −9.57973 | −0.818452 | −0.409226 | − | 0.912433i | \(-0.634201\pi\) | ||||
−0.409226 | + | 0.912433i | \(0.634201\pi\) | |||||||
\(138\) | 13.3881 | 1.13967 | ||||||||
\(139\) | −7.95766 | −0.674960 | −0.337480 | − | 0.941333i | \(-0.609575\pi\) | ||||
−0.337480 | + | 0.941333i | \(0.609575\pi\) | |||||||
\(140\) | −3.72741 | −0.315024 | ||||||||
\(141\) | 9.97980 | 0.840451 | ||||||||
\(142\) | −12.7885 | −1.07319 | ||||||||
\(143\) | 2.50064 | 0.209114 | ||||||||
\(144\) | 0.623956 | 0.0519963 | ||||||||
\(145\) | −29.0937 | −2.41610 | ||||||||
\(146\) | 0.847830 | 0.0701669 | ||||||||
\(147\) | −1.90367 | −0.157012 | ||||||||
\(148\) | 0.206301 | 0.0169578 | ||||||||
\(149\) | −4.14942 | −0.339934 | −0.169967 | − | 0.985450i | \(-0.554366\pi\) | ||||
−0.169967 | + | 0.985450i | \(0.554366\pi\) | |||||||
\(150\) | 16.9305 | 1.38237 | ||||||||
\(151\) | 14.6540 | 1.19253 | 0.596263 | − | 0.802789i | \(-0.296652\pi\) | ||||
0.596263 | + | 0.802789i | \(0.296652\pi\) | |||||||
\(152\) | 1.77524 | 0.143991 | ||||||||
\(153\) | 1.85985 | 0.150360 | ||||||||
\(154\) | −2.91306 | −0.234741 | ||||||||
\(155\) | −2.99159 | −0.240290 | ||||||||
\(156\) | −1.63416 | −0.130837 | ||||||||
\(157\) | 3.06225 | 0.244394 | 0.122197 | − | 0.992506i | \(-0.461006\pi\) | ||||
0.122197 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(158\) | −2.38319 | −0.189597 | ||||||||
\(159\) | 18.4038 | 1.45952 | ||||||||
\(160\) | 3.72741 | 0.294678 | ||||||||
\(161\) | 7.03281 | 0.554263 | ||||||||
\(162\) | 10.4825 | 0.823587 | ||||||||
\(163\) | 0.739064 | 0.0578880 | 0.0289440 | − | 0.999581i | \(-0.490786\pi\) | ||||
0.0289440 | + | 0.999581i | \(0.490786\pi\) | |||||||
\(164\) | 4.82573 | 0.376826 | ||||||||
\(165\) | 20.6704 | 1.60918 | ||||||||
\(166\) | 1.46787 | 0.113929 | ||||||||
\(167\) | −11.7550 | −0.909627 | −0.454814 | − | 0.890587i | \(-0.650294\pi\) | ||||
−0.454814 | + | 0.890587i | \(0.650294\pi\) | |||||||
\(168\) | 1.90367 | 0.146871 | ||||||||
\(169\) | −12.2631 | −0.943316 | ||||||||
\(170\) | 11.1105 | 0.852135 | ||||||||
\(171\) | −1.10767 | −0.0847056 | ||||||||
\(172\) | 1.00633 | 0.0767318 | ||||||||
\(173\) | −0.571790 | −0.0434724 | −0.0217362 | − | 0.999764i | \(-0.506919\pi\) | ||||
−0.0217362 | + | 0.999764i | \(0.506919\pi\) | |||||||
\(174\) | 14.8588 | 1.12644 | ||||||||
\(175\) | 8.89359 | 0.672293 | ||||||||
\(176\) | 2.91306 | 0.219580 | ||||||||
\(177\) | 9.54123 | 0.717163 | ||||||||
\(178\) | −8.13689 | −0.609886 | ||||||||
\(179\) | −15.1293 | −1.13082 | −0.565409 | − | 0.824811i | \(-0.691282\pi\) | ||||
−0.565409 | + | 0.824811i | \(0.691282\pi\) | |||||||
\(180\) | −2.32574 | −0.173350 | ||||||||
\(181\) | 6.97258 | 0.518267 | 0.259134 | − | 0.965841i | \(-0.416563\pi\) | ||||
0.259134 | + | 0.965841i | \(0.416563\pi\) | |||||||
\(182\) | −0.858424 | −0.0636306 | ||||||||
\(183\) | 22.6724 | 1.67599 | ||||||||
\(184\) | −7.03281 | −0.518465 | ||||||||
\(185\) | −0.768967 | −0.0565356 | ||||||||
\(186\) | 1.52787 | 0.112029 | ||||||||
\(187\) | 8.68309 | 0.634971 | ||||||||
\(188\) | −5.24240 | −0.382341 | ||||||||
\(189\) | 4.52320 | 0.329015 | ||||||||
\(190\) | −6.61704 | −0.480051 | ||||||||
\(191\) | 27.2529 | 1.97195 | 0.985976 | − | 0.166888i | \(-0.0533719\pi\) | ||||
0.985976 | + | 0.166888i | \(0.0533719\pi\) | |||||||
\(192\) | −1.90367 | −0.137385 | ||||||||
\(193\) | −4.63269 | −0.333468 | −0.166734 | − | 0.986002i | \(-0.553322\pi\) | ||||
−0.166734 | + | 0.986002i | \(0.553322\pi\) | |||||||
\(194\) | −14.3308 | −1.02889 | ||||||||
\(195\) | 6.09117 | 0.436198 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 14.2844 | 1.01772 | 0.508860 | − | 0.860849i | \(-0.330067\pi\) | ||||
0.508860 | + | 0.860849i | \(0.330067\pi\) | |||||||
\(198\) | −1.81762 | −0.129173 | ||||||||
\(199\) | 3.98333 | 0.282370 | 0.141185 | − | 0.989983i | \(-0.454909\pi\) | ||||
0.141185 | + | 0.989983i | \(0.454909\pi\) | |||||||
\(200\) | −8.89359 | −0.628872 | ||||||||
\(201\) | −16.2026 | −1.14285 | ||||||||
\(202\) | −14.4359 | −1.01571 | ||||||||
\(203\) | 7.80533 | 0.547827 | ||||||||
\(204\) | −5.67436 | −0.397285 | ||||||||
\(205\) | −17.9875 | −1.25630 | ||||||||
\(206\) | 9.76032 | 0.680034 | ||||||||
\(207\) | 4.38816 | 0.304998 | ||||||||
\(208\) | 0.858424 | 0.0595210 | ||||||||
\(209\) | −5.17137 | −0.357711 | ||||||||
\(210\) | −7.09576 | −0.489654 | ||||||||
\(211\) | 5.02415 | 0.345877 | 0.172938 | − | 0.984933i | \(-0.444674\pi\) | ||||
0.172938 | + | 0.984933i | \(0.444674\pi\) | |||||||
\(212\) | −9.66754 | −0.663969 | ||||||||
\(213\) | −24.3450 | −1.66809 | ||||||||
\(214\) | 7.84253 | 0.536104 | ||||||||
\(215\) | −3.75100 | −0.255816 | ||||||||
\(216\) | −4.52320 | −0.307765 | ||||||||
\(217\) | 0.802592 | 0.0544835 | ||||||||
\(218\) | 1.09655 | 0.0742680 | ||||||||
\(219\) | 1.61399 | 0.109063 | ||||||||
\(220\) | −10.8582 | −0.732057 | ||||||||
\(221\) | 2.55875 | 0.172120 | ||||||||
\(222\) | 0.392728 | 0.0263582 | ||||||||
\(223\) | 1.21846 | 0.0815941 | 0.0407970 | − | 0.999167i | \(-0.487010\pi\) | ||||
0.0407970 | + | 0.999167i | \(0.487010\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 5.54921 | 0.369947 | ||||||||
\(226\) | −19.6638 | −1.30802 | ||||||||
\(227\) | −11.2629 | −0.747543 | −0.373771 | − | 0.927521i | \(-0.621936\pi\) | ||||
−0.373771 | + | 0.927521i | \(0.621936\pi\) | |||||||
\(228\) | 3.37946 | 0.223811 | ||||||||
\(229\) | −1.13912 | −0.0752754 | −0.0376377 | − | 0.999291i | \(-0.511983\pi\) | ||||
−0.0376377 | + | 0.999291i | \(0.511983\pi\) | |||||||
\(230\) | 26.2142 | 1.72851 | ||||||||
\(231\) | −5.54550 | −0.364867 | ||||||||
\(232\) | −7.80533 | −0.512445 | ||||||||
\(233\) | −17.3780 | −1.13847 | −0.569235 | − | 0.822175i | \(-0.692761\pi\) | ||||
−0.569235 | + | 0.822175i | \(0.692761\pi\) | |||||||
\(234\) | −0.535618 | −0.0350145 | ||||||||
\(235\) | 19.5406 | 1.27469 | ||||||||
\(236\) | −5.01202 | −0.326255 | ||||||||
\(237\) | −4.53681 | −0.294697 | ||||||||
\(238\) | −2.98075 | −0.193213 | ||||||||
\(239\) | 18.0333 | 1.16648 | 0.583239 | − | 0.812301i | \(-0.301785\pi\) | ||||
0.583239 | + | 0.812301i | \(0.301785\pi\) | |||||||
\(240\) | 7.09576 | 0.458029 | ||||||||
\(241\) | −0.947127 | −0.0610098 | −0.0305049 | − | 0.999535i | \(-0.509712\pi\) | ||||
−0.0305049 | + | 0.999535i | \(0.509712\pi\) | |||||||
\(242\) | 2.51409 | 0.161612 | ||||||||
\(243\) | 6.38569 | 0.409642 | ||||||||
\(244\) | −11.9098 | −0.762450 | ||||||||
\(245\) | −3.72741 | −0.238136 | ||||||||
\(246\) | 9.18659 | 0.585715 | ||||||||
\(247\) | −1.52391 | −0.0969639 | ||||||||
\(248\) | −0.802592 | −0.0509646 | ||||||||
\(249\) | 2.79434 | 0.177084 | ||||||||
\(250\) | 14.5130 | 0.917884 | ||||||||
\(251\) | 2.98951 | 0.188696 | 0.0943480 | − | 0.995539i | \(-0.469923\pi\) | ||||
0.0943480 | + | 0.995539i | \(0.469923\pi\) | |||||||
\(252\) | 0.623956 | 0.0393055 | ||||||||
\(253\) | 20.4870 | 1.28801 | ||||||||
\(254\) | 19.8079 | 1.24286 | ||||||||
\(255\) | 21.1507 | 1.32451 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.3344 | 0.769401 | 0.384700 | − | 0.923042i | \(-0.374305\pi\) | ||||
0.384700 | + | 0.923042i | \(0.374305\pi\) | |||||||
\(258\) | 1.91572 | 0.119267 | ||||||||
\(259\) | 0.206301 | 0.0128189 | ||||||||
\(260\) | −3.19970 | −0.198437 | ||||||||
\(261\) | 4.87018 | 0.301457 | ||||||||
\(262\) | 14.2456 | 0.880099 | ||||||||
\(263\) | 20.4794 | 1.26282 | 0.631408 | − | 0.775451i | \(-0.282477\pi\) | ||||
0.631408 | + | 0.775451i | \(0.282477\pi\) | |||||||
\(264\) | 5.54550 | 0.341302 | ||||||||
\(265\) | 36.0349 | 2.21361 | ||||||||
\(266\) | 1.77524 | 0.108847 | ||||||||
\(267\) | −15.4899 | −0.947969 | ||||||||
\(268\) | 8.51127 | 0.519908 | ||||||||
\(269\) | 13.2997 | 0.810896 | 0.405448 | − | 0.914118i | \(-0.367115\pi\) | ||||
0.405448 | + | 0.914118i | \(0.367115\pi\) | |||||||
\(270\) | 16.8598 | 1.02606 | ||||||||
\(271\) | −19.3315 | −1.17430 | −0.587152 | − | 0.809477i | \(-0.699751\pi\) | ||||
−0.587152 | + | 0.809477i | \(0.699751\pi\) | |||||||
\(272\) | 2.98075 | 0.180734 | ||||||||
\(273\) | −1.63416 | −0.0989036 | ||||||||
\(274\) | 9.57973 | 0.578733 | ||||||||
\(275\) | 25.9076 | 1.56228 | ||||||||
\(276\) | −13.3881 | −0.805871 | ||||||||
\(277\) | 15.0762 | 0.905838 | 0.452919 | − | 0.891552i | \(-0.350383\pi\) | ||||
0.452919 | + | 0.891552i | \(0.350383\pi\) | |||||||
\(278\) | 7.95766 | 0.477269 | ||||||||
\(279\) | 0.500782 | 0.0299810 | ||||||||
\(280\) | 3.72741 | 0.222755 | ||||||||
\(281\) | −13.5077 | −0.805803 | −0.402901 | − | 0.915243i | \(-0.631998\pi\) | ||||
−0.402901 | + | 0.915243i | \(0.631998\pi\) | |||||||
\(282\) | −9.97980 | −0.594288 | ||||||||
\(283\) | 9.66089 | 0.574281 | 0.287140 | − | 0.957889i | \(-0.407295\pi\) | ||||
0.287140 | + | 0.957889i | \(0.407295\pi\) | |||||||
\(284\) | 12.7885 | 0.758857 | ||||||||
\(285\) | −12.5967 | −0.746161 | ||||||||
\(286\) | −2.50064 | −0.147866 | ||||||||
\(287\) | 4.82573 | 0.284854 | ||||||||
\(288\) | −0.623956 | −0.0367669 | ||||||||
\(289\) | −8.11514 | −0.477361 | ||||||||
\(290\) | 29.0937 | 1.70844 | ||||||||
\(291\) | −27.2812 | −1.59925 | ||||||||
\(292\) | −0.847830 | −0.0496155 | ||||||||
\(293\) | −23.7302 | −1.38633 | −0.693167 | − | 0.720777i | \(-0.743785\pi\) | ||||
−0.693167 | + | 0.720777i | \(0.743785\pi\) | |||||||
\(294\) | 1.90367 | 0.111024 | ||||||||
\(295\) | 18.6819 | 1.08770 | ||||||||
\(296\) | −0.206301 | −0.0119910 | ||||||||
\(297\) | 13.1764 | 0.764570 | ||||||||
\(298\) | 4.14942 | 0.240369 | ||||||||
\(299\) | 6.03713 | 0.349136 | ||||||||
\(300\) | −16.9305 | −0.977481 | ||||||||
\(301\) | 1.00633 | 0.0580038 | ||||||||
\(302\) | −14.6540 | −0.843243 | ||||||||
\(303\) | −27.4812 | −1.57875 | ||||||||
\(304\) | −1.77524 | −0.101817 | ||||||||
\(305\) | 44.3929 | 2.54193 | ||||||||
\(306\) | −1.85985 | −0.106321 | ||||||||
\(307\) | −19.0227 | −1.08568 | −0.542841 | − | 0.839835i | \(-0.682651\pi\) | ||||
−0.542841 | + | 0.839835i | \(0.682651\pi\) | |||||||
\(308\) | 2.91306 | 0.165987 | ||||||||
\(309\) | 18.5804 | 1.05700 | ||||||||
\(310\) | 2.99159 | 0.169911 | ||||||||
\(311\) | 31.3009 | 1.77491 | 0.887456 | − | 0.460892i | \(-0.152470\pi\) | ||||
0.887456 | + | 0.460892i | \(0.152470\pi\) | |||||||
\(312\) | 1.63416 | 0.0925158 | ||||||||
\(313\) | 24.9640 | 1.41105 | 0.705526 | − | 0.708684i | \(-0.250711\pi\) | ||||
0.705526 | + | 0.708684i | \(0.250711\pi\) | |||||||
\(314\) | −3.06225 | −0.172813 | ||||||||
\(315\) | −2.32574 | −0.131041 | ||||||||
\(316\) | 2.38319 | 0.134065 | ||||||||
\(317\) | 22.9749 | 1.29040 | 0.645201 | − | 0.764013i | \(-0.276774\pi\) | ||||
0.645201 | + | 0.764013i | \(0.276774\pi\) | |||||||
\(318\) | −18.4038 | −1.03203 | ||||||||
\(319\) | 22.7374 | 1.27305 | ||||||||
\(320\) | −3.72741 | −0.208369 | ||||||||
\(321\) | 14.9296 | 0.833288 | ||||||||
\(322\) | −7.03281 | −0.391923 | ||||||||
\(323\) | −5.29154 | −0.294429 | ||||||||
\(324\) | −10.4825 | −0.582364 | ||||||||
\(325\) | 7.63448 | 0.423485 | ||||||||
\(326\) | −0.739064 | −0.0409330 | ||||||||
\(327\) | 2.08748 | 0.115438 | ||||||||
\(328\) | −4.82573 | −0.266456 | ||||||||
\(329\) | −5.24240 | −0.289023 | ||||||||
\(330\) | −20.6704 | −1.13787 | ||||||||
\(331\) | −14.7306 | −0.809667 | −0.404834 | − | 0.914390i | \(-0.632671\pi\) | ||||
−0.404834 | + | 0.914390i | \(0.632671\pi\) | |||||||
\(332\) | −1.46787 | −0.0805600 | ||||||||
\(333\) | 0.128722 | 0.00705394 | ||||||||
\(334\) | 11.7550 | 0.643204 | ||||||||
\(335\) | −31.7250 | −1.73332 | ||||||||
\(336\) | −1.90367 | −0.103854 | ||||||||
\(337\) | 0.881637 | 0.0480258 | 0.0240129 | − | 0.999712i | \(-0.492356\pi\) | ||||
0.0240129 | + | 0.999712i | \(0.492356\pi\) | |||||||
\(338\) | 12.2631 | 0.667025 | ||||||||
\(339\) | −37.4334 | −2.03311 | ||||||||
\(340\) | −11.1105 | −0.602550 | ||||||||
\(341\) | 2.33800 | 0.126610 | ||||||||
\(342\) | 1.10767 | 0.0598959 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.00633 | −0.0542576 | ||||||||
\(345\) | 49.9031 | 2.68669 | ||||||||
\(346\) | 0.571790 | 0.0307396 | ||||||||
\(347\) | 34.3470 | 1.84385 | 0.921923 | − | 0.387373i | \(-0.126617\pi\) | ||||
0.921923 | + | 0.387373i | \(0.126617\pi\) | |||||||
\(348\) | −14.8588 | −0.796514 | ||||||||
\(349\) | −8.66725 | −0.463947 | −0.231974 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231974 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(350\) | −8.89359 | −0.475383 | ||||||||
\(351\) | 3.88283 | 0.207250 | ||||||||
\(352\) | −2.91306 | −0.155267 | ||||||||
\(353\) | 18.3899 | 0.978794 | 0.489397 | − | 0.872061i | \(-0.337217\pi\) | ||||
0.489397 | + | 0.872061i | \(0.337217\pi\) | |||||||
\(354\) | −9.54123 | −0.507111 | ||||||||
\(355\) | −47.6679 | −2.52995 | ||||||||
\(356\) | 8.13689 | 0.431254 | ||||||||
\(357\) | −5.67436 | −0.300319 | ||||||||
\(358\) | 15.1293 | 0.799609 | ||||||||
\(359\) | −0.178842 | −0.00943891 | −0.00471945 | − | 0.999989i | \(-0.501502\pi\) | ||||
−0.00471945 | + | 0.999989i | \(0.501502\pi\) | |||||||
\(360\) | 2.32574 | 0.122577 | ||||||||
\(361\) | −15.8485 | −0.834133 | ||||||||
\(362\) | −6.97258 | −0.366470 | ||||||||
\(363\) | 4.78599 | 0.251200 | ||||||||
\(364\) | 0.858424 | 0.0449937 | ||||||||
\(365\) | 3.16021 | 0.165413 | ||||||||
\(366\) | −22.6724 | −1.18511 | ||||||||
\(367\) | −24.7090 | −1.28980 | −0.644899 | − | 0.764268i | \(-0.723100\pi\) | ||||
−0.644899 | + | 0.764268i | \(0.723100\pi\) | |||||||
\(368\) | 7.03281 | 0.366610 | ||||||||
\(369\) | 3.01104 | 0.156748 | ||||||||
\(370\) | 0.768967 | 0.0399767 | ||||||||
\(371\) | −9.66754 | −0.501914 | ||||||||
\(372\) | −1.52787 | −0.0792163 | ||||||||
\(373\) | 2.66705 | 0.138095 | 0.0690474 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690474 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(374\) | −8.68309 | −0.448992 | ||||||||
\(375\) | 27.6280 | 1.42670 | ||||||||
\(376\) | 5.24240 | 0.270356 | ||||||||
\(377\) | 6.70029 | 0.345082 | ||||||||
\(378\) | −4.52320 | −0.232648 | ||||||||
\(379\) | 6.15096 | 0.315953 | 0.157977 | − | 0.987443i | \(-0.449503\pi\) | ||||
0.157977 | + | 0.987443i | \(0.449503\pi\) | |||||||
\(380\) | 6.61704 | 0.339447 | ||||||||
\(381\) | 37.7076 | 1.93182 | ||||||||
\(382\) | −27.2529 | −1.39438 | ||||||||
\(383\) | −2.38838 | −0.122040 | −0.0610202 | − | 0.998137i | \(-0.519435\pi\) | ||||
−0.0610202 | + | 0.998137i | \(0.519435\pi\) | |||||||
\(384\) | 1.90367 | 0.0971462 | ||||||||
\(385\) | −10.8582 | −0.553383 | ||||||||
\(386\) | 4.63269 | 0.235798 | ||||||||
\(387\) | 0.627904 | 0.0319181 | ||||||||
\(388\) | 14.3308 | 0.727538 | ||||||||
\(389\) | −33.9102 | −1.71932 | −0.859658 | − | 0.510871i | \(-0.829323\pi\) | ||||
−0.859658 | + | 0.510871i | \(0.829323\pi\) | |||||||
\(390\) | −6.09117 | −0.308438 | ||||||||
\(391\) | 20.9630 | 1.06015 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 27.1190 | 1.36797 | ||||||||
\(394\) | −14.2844 | −0.719637 | ||||||||
\(395\) | −8.88314 | −0.446959 | ||||||||
\(396\) | 1.81762 | 0.0913388 | ||||||||
\(397\) | 2.76592 | 0.138818 | 0.0694089 | − | 0.997588i | \(-0.477889\pi\) | ||||
0.0694089 | + | 0.997588i | \(0.477889\pi\) | |||||||
\(398\) | −3.98333 | −0.199666 | ||||||||
\(399\) | 3.37946 | 0.169185 | ||||||||
\(400\) | 8.89359 | 0.444680 | ||||||||
\(401\) | 28.3809 | 1.41728 | 0.708638 | − | 0.705572i | \(-0.249310\pi\) | ||||
0.708638 | + | 0.705572i | \(0.249310\pi\) | |||||||
\(402\) | 16.2026 | 0.808114 | ||||||||
\(403\) | 0.688964 | 0.0343198 | ||||||||
\(404\) | 14.4359 | 0.718214 | ||||||||
\(405\) | 39.0728 | 1.94154 | ||||||||
\(406\) | −7.80533 | −0.387372 | ||||||||
\(407\) | 0.600966 | 0.0297888 | ||||||||
\(408\) | 5.67436 | 0.280923 | ||||||||
\(409\) | −10.5586 | −0.522091 | −0.261046 | − | 0.965326i | \(-0.584067\pi\) | ||||
−0.261046 | + | 0.965326i | \(0.584067\pi\) | |||||||
\(410\) | 17.9875 | 0.888338 | ||||||||
\(411\) | 18.2366 | 0.899547 | ||||||||
\(412\) | −9.76032 | −0.480857 | ||||||||
\(413\) | −5.01202 | −0.246626 | ||||||||
\(414\) | −4.38816 | −0.215666 | ||||||||
\(415\) | 5.47136 | 0.268579 | ||||||||
\(416\) | −0.858424 | −0.0420877 | ||||||||
\(417\) | 15.1488 | 0.741838 | ||||||||
\(418\) | 5.17137 | 0.252940 | ||||||||
\(419\) | 31.6464 | 1.54603 | 0.773015 | − | 0.634388i | \(-0.218748\pi\) | ||||
0.773015 | + | 0.634388i | \(0.218748\pi\) | |||||||
\(420\) | 7.09576 | 0.346237 | ||||||||
\(421\) | 27.7514 | 1.35252 | 0.676260 | − | 0.736663i | \(-0.263599\pi\) | ||||
0.676260 | + | 0.736663i | \(0.263599\pi\) | |||||||
\(422\) | −5.02415 | −0.244572 | ||||||||
\(423\) | −3.27103 | −0.159043 | ||||||||
\(424\) | 9.66754 | 0.469497 | ||||||||
\(425\) | 26.5096 | 1.28590 | ||||||||
\(426\) | 24.3450 | 1.17952 | ||||||||
\(427\) | −11.9098 | −0.576358 | ||||||||
\(428\) | −7.84253 | −0.379083 | ||||||||
\(429\) | −4.76039 | −0.229834 | ||||||||
\(430\) | 3.75100 | 0.180889 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 4.52320 | 0.217623 | ||||||||
\(433\) | −28.9055 | −1.38911 | −0.694555 | − | 0.719440i | \(-0.744399\pi\) | ||||
−0.694555 | + | 0.719440i | \(0.744399\pi\) | |||||||
\(434\) | −0.802592 | −0.0385257 | ||||||||
\(435\) | 55.3847 | 2.65549 | ||||||||
\(436\) | −1.09655 | −0.0525154 | ||||||||
\(437\) | −12.4849 | −0.597234 | ||||||||
\(438\) | −1.61399 | −0.0771193 | ||||||||
\(439\) | 22.2721 | 1.06299 | 0.531495 | − | 0.847062i | \(-0.321631\pi\) | ||||
0.531495 | + | 0.847062i | \(0.321631\pi\) | |||||||
\(440\) | 10.8582 | 0.517643 | ||||||||
\(441\) | 0.623956 | 0.0297122 | ||||||||
\(442\) | −2.55875 | −0.121707 | ||||||||
\(443\) | 2.32911 | 0.110659 | 0.0553297 | − | 0.998468i | \(-0.482379\pi\) | ||||
0.0553297 | + | 0.998468i | \(0.482379\pi\) | |||||||
\(444\) | −0.392728 | −0.0186380 | ||||||||
\(445\) | −30.3295 | −1.43776 | ||||||||
\(446\) | −1.21846 | −0.0576957 | ||||||||
\(447\) | 7.89912 | 0.373616 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 0.956283 | 0.0451298 | 0.0225649 | − | 0.999745i | \(-0.492817\pi\) | ||||
0.0225649 | + | 0.999745i | \(0.492817\pi\) | |||||||
\(450\) | −5.54921 | −0.261592 | ||||||||
\(451\) | 14.0576 | 0.661948 | ||||||||
\(452\) | 19.6638 | 0.924909 | ||||||||
\(453\) | −27.8964 | −1.31069 | ||||||||
\(454\) | 11.2629 | 0.528592 | ||||||||
\(455\) | −3.19970 | −0.150004 | ||||||||
\(456\) | −3.37946 | −0.158258 | ||||||||
\(457\) | −34.0425 | −1.59244 | −0.796220 | − | 0.605007i | \(-0.793170\pi\) | ||||
−0.796220 | + | 0.605007i | \(0.793170\pi\) | |||||||
\(458\) | 1.13912 | 0.0532278 | ||||||||
\(459\) | 13.4825 | 0.629311 | ||||||||
\(460\) | −26.2142 | −1.22224 | ||||||||
\(461\) | 33.0036 | 1.53713 | 0.768565 | − | 0.639772i | \(-0.220971\pi\) | ||||
0.768565 | + | 0.639772i | \(0.220971\pi\) | |||||||
\(462\) | 5.54550 | 0.258000 | ||||||||
\(463\) | −31.5144 | −1.46460 | −0.732298 | − | 0.680984i | \(-0.761552\pi\) | ||||
−0.732298 | + | 0.680984i | \(0.761552\pi\) | |||||||
\(464\) | 7.80533 | 0.362353 | ||||||||
\(465\) | 5.69500 | 0.264099 | ||||||||
\(466\) | 17.3780 | 0.805020 | ||||||||
\(467\) | 28.8027 | 1.33283 | 0.666414 | − | 0.745582i | \(-0.267828\pi\) | ||||
0.666414 | + | 0.745582i | \(0.267828\pi\) | |||||||
\(468\) | 0.535618 | 0.0247590 | ||||||||
\(469\) | 8.51127 | 0.393014 | ||||||||
\(470\) | −19.5406 | −0.901340 | ||||||||
\(471\) | −5.82951 | −0.268610 | ||||||||
\(472\) | 5.01202 | 0.230697 | ||||||||
\(473\) | 2.93149 | 0.134790 | ||||||||
\(474\) | 4.53681 | 0.208383 | ||||||||
\(475\) | −15.7882 | −0.724414 | ||||||||
\(476\) | 2.98075 | 0.136622 | ||||||||
\(477\) | −6.03211 | −0.276192 | ||||||||
\(478\) | −18.0333 | −0.824824 | ||||||||
\(479\) | 3.08293 | 0.140863 | 0.0704313 | − | 0.997517i | \(-0.477562\pi\) | ||||
0.0704313 | + | 0.997517i | \(0.477562\pi\) | |||||||
\(480\) | −7.09576 | −0.323876 | ||||||||
\(481\) | 0.177093 | 0.00807476 | ||||||||
\(482\) | 0.947127 | 0.0431405 | ||||||||
\(483\) | −13.3881 | −0.609181 | ||||||||
\(484\) | −2.51409 | −0.114277 | ||||||||
\(485\) | −53.4169 | −2.42554 | ||||||||
\(486\) | −6.38569 | −0.289661 | ||||||||
\(487\) | −2.47113 | −0.111977 | −0.0559887 | − | 0.998431i | \(-0.517831\pi\) | ||||
−0.0559887 | + | 0.998431i | \(0.517831\pi\) | |||||||
\(488\) | 11.9098 | 0.539133 | ||||||||
\(489\) | −1.40693 | −0.0636237 | ||||||||
\(490\) | 3.72741 | 0.168387 | ||||||||
\(491\) | −33.8624 | −1.52819 | −0.764095 | − | 0.645104i | \(-0.776814\pi\) | ||||
−0.764095 | + | 0.645104i | \(0.776814\pi\) | |||||||
\(492\) | −9.18659 | −0.414163 | ||||||||
\(493\) | 23.2657 | 1.04784 | ||||||||
\(494\) | 1.52391 | 0.0685638 | ||||||||
\(495\) | −6.77501 | −0.304514 | ||||||||
\(496\) | 0.802592 | 0.0360374 | ||||||||
\(497\) | 12.7885 | 0.573642 | ||||||||
\(498\) | −2.79434 | −0.125218 | ||||||||
\(499\) | 36.8515 | 1.64970 | 0.824850 | − | 0.565352i | \(-0.191259\pi\) | ||||
0.824850 | + | 0.565352i | \(0.191259\pi\) | |||||||
\(500\) | −14.5130 | −0.649042 | ||||||||
\(501\) | 22.3776 | 0.999756 | ||||||||
\(502\) | −2.98951 | −0.133428 | ||||||||
\(503\) | 6.27919 | 0.279975 | 0.139988 | − | 0.990153i | \(-0.455294\pi\) | ||||
0.139988 | + | 0.990153i | \(0.455294\pi\) | |||||||
\(504\) | −0.623956 | −0.0277932 | ||||||||
\(505\) | −53.8086 | −2.39445 | ||||||||
\(506\) | −20.4870 | −0.910757 | ||||||||
\(507\) | 23.3449 | 1.03678 | ||||||||
\(508\) | −19.8079 | −0.878833 | ||||||||
\(509\) | 38.1696 | 1.69184 | 0.845918 | − | 0.533313i | \(-0.179053\pi\) | ||||
0.845918 | + | 0.533313i | \(0.179053\pi\) | |||||||
\(510\) | −21.1507 | −0.936567 | ||||||||
\(511\) | −0.847830 | −0.0375058 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.02976 | −0.354522 | ||||||||
\(514\) | −12.3344 | −0.544048 | ||||||||
\(515\) | 36.3807 | 1.60313 | ||||||||
\(516\) | −1.91572 | −0.0843347 | ||||||||
\(517\) | −15.2714 | −0.671636 | ||||||||
\(518\) | −0.206301 | −0.00906433 | ||||||||
\(519\) | 1.08850 | 0.0477798 | ||||||||
\(520\) | 3.19970 | 0.140316 | ||||||||
\(521\) | −11.6956 | −0.512392 | −0.256196 | − | 0.966625i | \(-0.582469\pi\) | ||||
−0.256196 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(522\) | −4.87018 | −0.213162 | ||||||||
\(523\) | −28.5438 | −1.24813 | −0.624066 | − | 0.781372i | \(-0.714520\pi\) | ||||
−0.624066 | + | 0.781372i | \(0.714520\pi\) | |||||||
\(524\) | −14.2456 | −0.622324 | ||||||||
\(525\) | −16.9305 | −0.738906 | ||||||||
\(526\) | −20.4794 | −0.892946 | ||||||||
\(527\) | 2.39233 | 0.104211 | ||||||||
\(528\) | −5.54550 | −0.241337 | ||||||||
\(529\) | 26.4604 | 1.15045 | ||||||||
\(530\) | −36.0349 | −1.56526 | ||||||||
\(531\) | −3.12728 | −0.135712 | ||||||||
\(532\) | −1.77524 | −0.0769663 | ||||||||
\(533\) | 4.14252 | 0.179432 | ||||||||
\(534\) | 15.4899 | 0.670316 | ||||||||
\(535\) | 29.2323 | 1.26382 | ||||||||
\(536\) | −8.51127 | −0.367631 | ||||||||
\(537\) | 28.8012 | 1.24286 | ||||||||
\(538\) | −13.2997 | −0.573390 | ||||||||
\(539\) | 2.91306 | 0.125474 | ||||||||
\(540\) | −16.8598 | −0.725532 | ||||||||
\(541\) | 12.6694 | 0.544699 | 0.272349 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272349 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(542\) | 19.3315 | 0.830358 | ||||||||
\(543\) | −13.2735 | −0.569619 | ||||||||
\(544\) | −2.98075 | −0.127799 | ||||||||
\(545\) | 4.08731 | 0.175081 | ||||||||
\(546\) | 1.63416 | 0.0699354 | ||||||||
\(547\) | −35.0361 | −1.49804 | −0.749019 | − | 0.662549i | \(-0.769475\pi\) | ||||
−0.749019 | + | 0.662549i | \(0.769475\pi\) | |||||||
\(548\) | −9.57973 | −0.409226 | ||||||||
\(549\) | −7.43121 | −0.317157 | ||||||||
\(550\) | −25.9076 | −1.10470 | ||||||||
\(551\) | −13.8563 | −0.590299 | ||||||||
\(552\) | 13.3881 | 0.569837 | ||||||||
\(553\) | 2.38319 | 0.101344 | ||||||||
\(554\) | −15.0762 | −0.640524 | ||||||||
\(555\) | 1.46386 | 0.0621373 | ||||||||
\(556\) | −7.95766 | −0.337480 | ||||||||
\(557\) | 40.1089 | 1.69947 | 0.849734 | − | 0.527212i | \(-0.176763\pi\) | ||||
0.849734 | + | 0.527212i | \(0.176763\pi\) | |||||||
\(558\) | −0.500782 | −0.0211998 | ||||||||
\(559\) | 0.863856 | 0.0365372 | ||||||||
\(560\) | −3.72741 | −0.157512 | ||||||||
\(561\) | −16.5297 | −0.697886 | ||||||||
\(562\) | 13.5077 | 0.569789 | ||||||||
\(563\) | −17.8295 | −0.751423 | −0.375711 | − | 0.926737i | \(-0.622602\pi\) | ||||
−0.375711 | + | 0.926737i | \(0.622602\pi\) | |||||||
\(564\) | 9.97980 | 0.420225 | ||||||||
\(565\) | −73.2952 | −3.08355 | ||||||||
\(566\) | −9.66089 | −0.406078 | ||||||||
\(567\) | −10.4825 | −0.440226 | ||||||||
\(568\) | −12.7885 | −0.536593 | ||||||||
\(569\) | 2.69928 | 0.113160 | 0.0565799 | − | 0.998398i | \(-0.481980\pi\) | ||||
0.0565799 | + | 0.998398i | \(0.481980\pi\) | |||||||
\(570\) | 12.5967 | 0.527616 | ||||||||
\(571\) | 41.9535 | 1.75570 | 0.877849 | − | 0.478937i | \(-0.158978\pi\) | ||||
0.877849 | + | 0.478937i | \(0.158978\pi\) | |||||||
\(572\) | 2.50064 | 0.104557 | ||||||||
\(573\) | −51.8805 | −2.16734 | ||||||||
\(574\) | −4.82573 | −0.201422 | ||||||||
\(575\) | 62.5469 | 2.60839 | ||||||||
\(576\) | 0.623956 | 0.0259981 | ||||||||
\(577\) | −11.2451 | −0.468138 | −0.234069 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234069 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(578\) | 8.11514 | 0.337545 | ||||||||
\(579\) | 8.81910 | 0.366509 | ||||||||
\(580\) | −29.0937 | −1.20805 | ||||||||
\(581\) | −1.46787 | −0.0608976 | ||||||||
\(582\) | 27.2812 | 1.13084 | ||||||||
\(583\) | −28.1621 | −1.16636 | ||||||||
\(584\) | 0.847830 | 0.0350835 | ||||||||
\(585\) | −1.99647 | −0.0825439 | ||||||||
\(586\) | 23.7302 | 0.980286 | ||||||||
\(587\) | 11.7812 | 0.486263 | 0.243132 | − | 0.969993i | \(-0.421825\pi\) | ||||
0.243132 | + | 0.969993i | \(0.421825\pi\) | |||||||
\(588\) | −1.90367 | −0.0785060 | ||||||||
\(589\) | −1.42479 | −0.0587075 | ||||||||
\(590\) | −18.6819 | −0.769120 | ||||||||
\(591\) | −27.1927 | −1.11856 | ||||||||
\(592\) | 0.206301 | 0.00847890 | ||||||||
\(593\) | 9.12303 | 0.374638 | 0.187319 | − | 0.982299i | \(-0.440020\pi\) | ||||
0.187319 | + | 0.982299i | \(0.440020\pi\) | |||||||
\(594\) | −13.1764 | −0.540632 | ||||||||
\(595\) | −11.1105 | −0.455485 | ||||||||
\(596\) | −4.14942 | −0.169967 | ||||||||
\(597\) | −7.58293 | −0.310349 | ||||||||
\(598\) | −6.03713 | −0.246877 | ||||||||
\(599\) | −21.8588 | −0.893128 | −0.446564 | − | 0.894752i | \(-0.647352\pi\) | ||||
−0.446564 | + | 0.894752i | \(0.647352\pi\) | |||||||
\(600\) | 16.9305 | 0.691183 | ||||||||
\(601\) | 0.758674 | 0.0309470 | 0.0154735 | − | 0.999880i | \(-0.495074\pi\) | ||||
0.0154735 | + | 0.999880i | \(0.495074\pi\) | |||||||
\(602\) | −1.00633 | −0.0410149 | ||||||||
\(603\) | 5.31065 | 0.216267 | ||||||||
\(604\) | 14.6540 | 0.596263 | ||||||||
\(605\) | 9.37105 | 0.380987 | ||||||||
\(606\) | 27.4812 | 1.11635 | ||||||||
\(607\) | −5.45318 | −0.221338 | −0.110669 | − | 0.993857i | \(-0.535299\pi\) | ||||
−0.110669 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(608\) | 1.77524 | 0.0719954 | ||||||||
\(609\) | −14.8588 | −0.602108 | ||||||||
\(610\) | −44.3929 | −1.79742 | ||||||||
\(611\) | −4.50020 | −0.182059 | ||||||||
\(612\) | 1.85985 | 0.0751802 | ||||||||
\(613\) | 4.43417 | 0.179094 | 0.0895472 | − | 0.995983i | \(-0.471458\pi\) | ||||
0.0895472 | + | 0.995983i | \(0.471458\pi\) | |||||||
\(614\) | 19.0227 | 0.767693 | ||||||||
\(615\) | 34.2422 | 1.38078 | ||||||||
\(616\) | −2.91306 | −0.117370 | ||||||||
\(617\) | 30.6054 | 1.23213 | 0.616064 | − | 0.787696i | \(-0.288726\pi\) | ||||
0.616064 | + | 0.787696i | \(0.288726\pi\) | |||||||
\(618\) | −18.5804 | −0.747414 | ||||||||
\(619\) | 45.1412 | 1.81438 | 0.907189 | − | 0.420722i | \(-0.138223\pi\) | ||||
0.907189 | + | 0.420722i | \(0.138223\pi\) | |||||||
\(620\) | −2.99159 | −0.120145 | ||||||||
\(621\) | 31.8108 | 1.27652 | ||||||||
\(622\) | −31.3009 | −1.25505 | ||||||||
\(623\) | 8.13689 | 0.325998 | ||||||||
\(624\) | −1.63416 | −0.0654186 | ||||||||
\(625\) | 9.62804 | 0.385122 | ||||||||
\(626\) | −24.9640 | −0.997764 | ||||||||
\(627\) | 9.84458 | 0.393155 | ||||||||
\(628\) | 3.06225 | 0.122197 | ||||||||
\(629\) | 0.614930 | 0.0245189 | ||||||||
\(630\) | 2.32574 | 0.0926596 | ||||||||
\(631\) | 35.9418 | 1.43082 | 0.715410 | − | 0.698704i | \(-0.246240\pi\) | ||||
0.715410 | + | 0.698704i | \(0.246240\pi\) | |||||||
\(632\) | −2.38319 | −0.0947983 | ||||||||
\(633\) | −9.56432 | −0.380147 | ||||||||
\(634\) | −22.9749 | −0.912452 | ||||||||
\(635\) | 73.8321 | 2.92994 | ||||||||
\(636\) | 18.4038 | 0.729758 | ||||||||
\(637\) | 0.858424 | 0.0340120 | ||||||||
\(638\) | −22.7374 | −0.900182 | ||||||||
\(639\) | 7.97944 | 0.315662 | ||||||||
\(640\) | 3.72741 | 0.147339 | ||||||||
\(641\) | 30.6669 | 1.21127 | 0.605635 | − | 0.795742i | \(-0.292919\pi\) | ||||
0.605635 | + | 0.795742i | \(0.292919\pi\) | |||||||
\(642\) | −14.9296 | −0.589224 | ||||||||
\(643\) | 1.10669 | 0.0436436 | 0.0218218 | − | 0.999762i | \(-0.493053\pi\) | ||||
0.0218218 | + | 0.999762i | \(0.493053\pi\) | |||||||
\(644\) | 7.03281 | 0.277131 | ||||||||
\(645\) | 7.14066 | 0.281163 | ||||||||
\(646\) | 5.29154 | 0.208193 | ||||||||
\(647\) | 40.0622 | 1.57501 | 0.787505 | − | 0.616309i | \(-0.211373\pi\) | ||||
0.787505 | + | 0.616309i | \(0.211373\pi\) | |||||||
\(648\) | 10.4825 | 0.411793 | ||||||||
\(649\) | −14.6003 | −0.573113 | ||||||||
\(650\) | −7.63448 | −0.299449 | ||||||||
\(651\) | −1.52787 | −0.0598819 | ||||||||
\(652\) | 0.739064 | 0.0289440 | ||||||||
\(653\) | −29.3311 | −1.14781 | −0.573907 | − | 0.818921i | \(-0.694573\pi\) | ||||
−0.573907 | + | 0.818921i | \(0.694573\pi\) | |||||||
\(654\) | −2.08748 | −0.0816268 | ||||||||
\(655\) | 53.0994 | 2.07476 | ||||||||
\(656\) | 4.82573 | 0.188413 | ||||||||
\(657\) | −0.529008 | −0.0206386 | ||||||||
\(658\) | 5.24240 | 0.204370 | ||||||||
\(659\) | −18.9021 | −0.736322 | −0.368161 | − | 0.929762i | \(-0.620012\pi\) | ||||
−0.368161 | + | 0.929762i | \(0.620012\pi\) | |||||||
\(660\) | 20.6704 | 0.804592 | ||||||||
\(661\) | −34.9014 | −1.35751 | −0.678753 | − | 0.734367i | \(-0.737479\pi\) | ||||
−0.678753 | + | 0.734367i | \(0.737479\pi\) | |||||||
\(662\) | 14.7306 | 0.572521 | ||||||||
\(663\) | −4.87101 | −0.189174 | ||||||||
\(664\) | 1.46787 | 0.0569645 | ||||||||
\(665\) | 6.61704 | 0.256598 | ||||||||
\(666\) | −0.128722 | −0.00498789 | ||||||||
\(667\) | 54.8934 | 2.12548 | ||||||||
\(668\) | −11.7550 | −0.454814 | ||||||||
\(669\) | −2.31954 | −0.0896787 | ||||||||
\(670\) | 31.7250 | 1.22564 | ||||||||
\(671\) | −34.6941 | −1.33935 | ||||||||
\(672\) | 1.90367 | 0.0734356 | ||||||||
\(673\) | 2.18760 | 0.0843258 | 0.0421629 | − | 0.999111i | \(-0.486575\pi\) | ||||
0.0421629 | + | 0.999111i | \(0.486575\pi\) | |||||||
\(674\) | −0.881637 | −0.0339594 | ||||||||
\(675\) | 40.2275 | 1.54836 | ||||||||
\(676\) | −12.2631 | −0.471658 | ||||||||
\(677\) | −26.7315 | −1.02737 | −0.513687 | − | 0.857978i | \(-0.671721\pi\) | ||||
−0.513687 | + | 0.857978i | \(0.671721\pi\) | |||||||
\(678\) | 37.4334 | 1.43762 | ||||||||
\(679\) | 14.3308 | 0.549967 | ||||||||
\(680\) | 11.1105 | 0.426067 | ||||||||
\(681\) | 21.4408 | 0.821612 | ||||||||
\(682\) | −2.33800 | −0.0895266 | ||||||||
\(683\) | 9.82778 | 0.376049 | 0.188025 | − | 0.982164i | \(-0.439792\pi\) | ||||
0.188025 | + | 0.982164i | \(0.439792\pi\) | |||||||
\(684\) | −1.10767 | −0.0423528 | ||||||||
\(685\) | 35.7076 | 1.36432 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 2.16852 | 0.0827340 | ||||||||
\(688\) | 1.00633 | 0.0383659 | ||||||||
\(689\) | −8.29885 | −0.316161 | ||||||||
\(690\) | −49.9031 | −1.89978 | ||||||||
\(691\) | 33.1081 | 1.25949 | 0.629746 | − | 0.776801i | \(-0.283159\pi\) | ||||
0.629746 | + | 0.776801i | \(0.283159\pi\) | |||||||
\(692\) | −0.571790 | −0.0217362 | ||||||||
\(693\) | 1.81762 | 0.0690456 | ||||||||
\(694\) | −34.3470 | −1.30380 | ||||||||
\(695\) | 29.6615 | 1.12512 | ||||||||
\(696\) | 14.8588 | 0.563220 | ||||||||
\(697\) | 14.3843 | 0.544843 | ||||||||
\(698\) | 8.66725 | 0.328060 | ||||||||
\(699\) | 33.0820 | 1.25127 | ||||||||
\(700\) | 8.89359 | 0.336146 | ||||||||
\(701\) | −44.4148 | −1.67752 | −0.838761 | − | 0.544499i | \(-0.816720\pi\) | ||||
−0.838761 | + | 0.544499i | \(0.816720\pi\) | |||||||
\(702\) | −3.88283 | −0.146548 | ||||||||
\(703\) | −0.366232 | −0.0138127 | ||||||||
\(704\) | 2.91306 | 0.109790 | ||||||||
\(705\) | −37.1988 | −1.40099 | ||||||||
\(706\) | −18.3899 | −0.692112 | ||||||||
\(707\) | 14.4359 | 0.542919 | ||||||||
\(708\) | 9.54123 | 0.358581 | ||||||||
\(709\) | −36.7461 | −1.38003 | −0.690014 | − | 0.723796i | \(-0.742396\pi\) | ||||
−0.690014 | + | 0.723796i | \(0.742396\pi\) | |||||||
\(710\) | 47.6679 | 1.78895 | ||||||||
\(711\) | 1.48701 | 0.0557671 | ||||||||
\(712\) | −8.13689 | −0.304943 | ||||||||
\(713\) | 5.64447 | 0.211387 | ||||||||
\(714\) | 5.67436 | 0.212358 | ||||||||
\(715\) | −9.32091 | −0.348582 | ||||||||
\(716\) | −15.1293 | −0.565409 | ||||||||
\(717\) | −34.3294 | −1.28206 | ||||||||
\(718\) | 0.178842 | 0.00667432 | ||||||||
\(719\) | 11.4609 | 0.427419 | 0.213709 | − | 0.976897i | \(-0.431445\pi\) | ||||
0.213709 | + | 0.976897i | \(0.431445\pi\) | |||||||
\(720\) | −2.32574 | −0.0866752 | ||||||||
\(721\) | −9.76032 | −0.363493 | ||||||||
\(722\) | 15.8485 | 0.589821 | ||||||||
\(723\) | 1.80302 | 0.0670549 | ||||||||
\(724\) | 6.97258 | 0.259134 | ||||||||
\(725\) | 69.4175 | 2.57810 | ||||||||
\(726\) | −4.78599 | −0.177625 | ||||||||
\(727\) | −31.9309 | −1.18425 | −0.592125 | − | 0.805846i | \(-0.701711\pi\) | ||||
−0.592125 | + | 0.805846i | \(0.701711\pi\) | |||||||
\(728\) | −0.858424 | −0.0318153 | ||||||||
\(729\) | 19.2914 | 0.714496 | ||||||||
\(730\) | −3.16021 | −0.116965 | ||||||||
\(731\) | 2.99961 | 0.110945 | ||||||||
\(732\) | 22.6724 | 0.837996 | ||||||||
\(733\) | −38.7241 | −1.43031 | −0.715153 | − | 0.698968i | \(-0.753643\pi\) | ||||
−0.715153 | + | 0.698968i | \(0.753643\pi\) | |||||||
\(734\) | 24.7090 | 0.912024 | ||||||||
\(735\) | 7.09576 | 0.261731 | ||||||||
\(736\) | −7.03281 | −0.259233 | ||||||||
\(737\) | 24.7938 | 0.913292 | ||||||||
\(738\) | −3.01104 | −0.110838 | ||||||||
\(739\) | 17.7540 | 0.653092 | 0.326546 | − | 0.945181i | \(-0.394115\pi\) | ||||
0.326546 | + | 0.945181i | \(0.394115\pi\) | |||||||
\(740\) | −0.768967 | −0.0282678 | ||||||||
\(741\) | 2.90101 | 0.106571 | ||||||||
\(742\) | 9.66754 | 0.354907 | ||||||||
\(743\) | −6.16383 | −0.226129 | −0.113064 | − | 0.993588i | \(-0.536067\pi\) | ||||
−0.113064 | + | 0.993588i | \(0.536067\pi\) | |||||||
\(744\) | 1.52787 | 0.0560144 | ||||||||
\(745\) | 15.4666 | 0.566652 | ||||||||
\(746\) | −2.66705 | −0.0976478 | ||||||||
\(747\) | −0.915887 | −0.0335106 | ||||||||
\(748\) | 8.68309 | 0.317485 | ||||||||
\(749\) | −7.84253 | −0.286560 | ||||||||
\(750\) | −27.6280 | −1.00883 | ||||||||
\(751\) | 43.1997 | 1.57638 | 0.788189 | − | 0.615433i | \(-0.211019\pi\) | ||||
0.788189 | + | 0.615433i | \(0.211019\pi\) | |||||||
\(752\) | −5.24240 | −0.191171 | ||||||||
\(753\) | −5.69103 | −0.207393 | ||||||||
\(754\) | −6.70029 | −0.244010 | ||||||||
\(755\) | −54.6215 | −1.98788 | ||||||||
\(756\) | 4.52320 | 0.164507 | ||||||||
\(757\) | 10.9375 | 0.397529 | 0.198765 | − | 0.980047i | \(-0.436307\pi\) | ||||
0.198765 | + | 0.980047i | \(0.436307\pi\) | |||||||
\(758\) | −6.15096 | −0.223413 | ||||||||
\(759\) | −39.0004 | −1.41563 | ||||||||
\(760\) | −6.61704 | −0.240025 | ||||||||
\(761\) | 30.2068 | 1.09500 | 0.547498 | − | 0.836807i | \(-0.315580\pi\) | ||||
0.547498 | + | 0.836807i | \(0.315580\pi\) | |||||||
\(762\) | −37.7076 | −1.36600 | ||||||||
\(763\) | −1.09655 | −0.0396979 | ||||||||
\(764\) | 27.2529 | 0.985976 | ||||||||
\(765\) | −6.93244 | −0.250643 | ||||||||
\(766\) | 2.38838 | 0.0862957 | ||||||||
\(767\) | −4.30244 | −0.155352 | ||||||||
\(768\) | −1.90367 | −0.0686927 | ||||||||
\(769\) | −10.1063 | −0.364443 | −0.182222 | − | 0.983257i | \(-0.558329\pi\) | ||||
−0.182222 | + | 0.983257i | \(0.558329\pi\) | |||||||
\(770\) | 10.8582 | 0.391301 | ||||||||
\(771\) | −23.4807 | −0.845636 | ||||||||
\(772\) | −4.63269 | −0.166734 | ||||||||
\(773\) | −15.4312 | −0.555022 | −0.277511 | − | 0.960722i | \(-0.589509\pi\) | ||||
−0.277511 | + | 0.960722i | \(0.589509\pi\) | |||||||
\(774\) | −0.627904 | −0.0225695 | ||||||||
\(775\) | 7.13793 | 0.256402 | ||||||||
\(776\) | −14.3308 | −0.514447 | ||||||||
\(777\) | −0.392728 | −0.0140890 | ||||||||
\(778\) | 33.9102 | 1.21574 | ||||||||
\(779\) | −8.56681 | −0.306938 | ||||||||
\(780\) | 6.09117 | 0.218099 | ||||||||
\(781\) | 37.2536 | 1.33304 | ||||||||
\(782\) | −20.9630 | −0.749636 | ||||||||
\(783\) | 35.3051 | 1.26170 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.4143 | −0.407393 | ||||||||
\(786\) | −27.1190 | −0.967302 | ||||||||
\(787\) | −13.5513 | −0.483051 | −0.241525 | − | 0.970395i | \(-0.577648\pi\) | ||||
−0.241525 | + | 0.970395i | \(0.577648\pi\) | |||||||
\(788\) | 14.2844 | 0.508860 | ||||||||
\(789\) | −38.9861 | −1.38794 | ||||||||
\(790\) | 8.88314 | 0.316048 | ||||||||
\(791\) | 19.6638 | 0.699166 | ||||||||
\(792\) | −1.81762 | −0.0645863 | ||||||||
\(793\) | −10.2237 | −0.363054 | ||||||||
\(794\) | −2.76592 | −0.0981590 | ||||||||
\(795\) | −68.5985 | −2.43294 | ||||||||
\(796\) | 3.98333 | 0.141185 | ||||||||
\(797\) | −16.6848 | −0.591006 | −0.295503 | − | 0.955342i | \(-0.595487\pi\) | ||||
−0.295503 | + | 0.955342i | \(0.595487\pi\) | |||||||
\(798\) | −3.37946 | −0.119632 | ||||||||
\(799\) | −15.6263 | −0.552818 | ||||||||
\(800\) | −8.89359 | −0.314436 | ||||||||
\(801\) | 5.07706 | 0.179389 | ||||||||
\(802\) | −28.3809 | −1.00217 | ||||||||
\(803\) | −2.46978 | −0.0871566 | ||||||||
\(804\) | −16.2026 | −0.571423 | ||||||||
\(805\) | −26.2142 | −0.923928 | ||||||||
\(806\) | −0.688964 | −0.0242677 | ||||||||
\(807\) | −25.3182 | −0.891243 | ||||||||
\(808\) | −14.4359 | −0.507854 | ||||||||
\(809\) | 3.25257 | 0.114354 | 0.0571771 | − | 0.998364i | \(-0.481790\pi\) | ||||
0.0571771 | + | 0.998364i | \(0.481790\pi\) | |||||||
\(810\) | −39.0728 | −1.37288 | ||||||||
\(811\) | 0.948085 | 0.0332918 | 0.0166459 | − | 0.999861i | \(-0.494701\pi\) | ||||
0.0166459 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(812\) | 7.80533 | 0.273913 | ||||||||
\(813\) | 36.8007 | 1.29066 | ||||||||
\(814\) | −0.600966 | −0.0210638 | ||||||||
\(815\) | −2.75480 | −0.0964963 | ||||||||
\(816\) | −5.67436 | −0.198642 | ||||||||
\(817\) | −1.78647 | −0.0625007 | ||||||||
\(818\) | 10.5586 | 0.369174 | ||||||||
\(819\) | 0.535618 | 0.0187160 | ||||||||
\(820\) | −17.9875 | −0.628150 | ||||||||
\(821\) | −11.4265 | −0.398787 | −0.199394 | − | 0.979919i | \(-0.563897\pi\) | ||||
−0.199394 | + | 0.979919i | \(0.563897\pi\) | |||||||
\(822\) | −18.2366 | −0.636076 | ||||||||
\(823\) | 13.2382 | 0.461456 | 0.230728 | − | 0.973018i | \(-0.425889\pi\) | ||||
0.230728 | + | 0.973018i | \(0.425889\pi\) | |||||||
\(824\) | 9.76032 | 0.340017 | ||||||||
\(825\) | −49.3194 | −1.71708 | ||||||||
\(826\) | 5.01202 | 0.174391 | ||||||||
\(827\) | −28.2114 | −0.981005 | −0.490503 | − | 0.871440i | \(-0.663187\pi\) | ||||
−0.490503 | + | 0.871440i | \(0.663187\pi\) | |||||||
\(828\) | 4.38816 | 0.152499 | ||||||||
\(829\) | 12.5306 | 0.435206 | 0.217603 | − | 0.976037i | \(-0.430176\pi\) | ||||
0.217603 | + | 0.976037i | \(0.430176\pi\) | |||||||
\(830\) | −5.47136 | −0.189914 | ||||||||
\(831\) | −28.7000 | −0.995592 | ||||||||
\(832\) | 0.858424 | 0.0297605 | ||||||||
\(833\) | 2.98075 | 0.103277 | ||||||||
\(834\) | −15.1488 | −0.524559 | ||||||||
\(835\) | 43.8156 | 1.51630 | ||||||||
\(836\) | −5.17137 | −0.178856 | ||||||||
\(837\) | 3.63029 | 0.125481 | ||||||||
\(838\) | −31.6464 | −1.09321 | ||||||||
\(839\) | 12.0597 | 0.416346 | 0.208173 | − | 0.978092i | \(-0.433248\pi\) | ||||
0.208173 | + | 0.978092i | \(0.433248\pi\) | |||||||
\(840\) | −7.09576 | −0.244827 | ||||||||
\(841\) | 31.9232 | 1.10080 | ||||||||
\(842\) | −27.7514 | −0.956377 | ||||||||
\(843\) | 25.7142 | 0.885645 | ||||||||
\(844\) | 5.02415 | 0.172938 | ||||||||
\(845\) | 45.7096 | 1.57246 | ||||||||
\(846\) | 3.27103 | 0.112460 | ||||||||
\(847\) | −2.51409 | −0.0863852 | ||||||||
\(848\) | −9.66754 | −0.331985 | ||||||||
\(849\) | −18.3911 | −0.631182 | ||||||||
\(850\) | −26.5096 | −0.909271 | ||||||||
\(851\) | 1.45087 | 0.0497352 | ||||||||
\(852\) | −24.3450 | −0.834047 | ||||||||
\(853\) | −57.6635 | −1.97436 | −0.987180 | − | 0.159608i | \(-0.948977\pi\) | ||||
−0.987180 | + | 0.159608i | \(0.948977\pi\) | |||||||
\(854\) | 11.9098 | 0.407547 | ||||||||
\(855\) | 4.12874 | 0.141200 | ||||||||
\(856\) | 7.84253 | 0.268052 | ||||||||
\(857\) | −40.1915 | −1.37292 | −0.686458 | − | 0.727170i | \(-0.740835\pi\) | ||||
−0.686458 | + | 0.727170i | \(0.740835\pi\) | |||||||
\(858\) | 4.76039 | 0.162517 | ||||||||
\(859\) | −3.52290 | −0.120200 | −0.0601000 | − | 0.998192i | \(-0.519142\pi\) | ||||
−0.0601000 | + | 0.998192i | \(0.519142\pi\) | |||||||
\(860\) | −3.75100 | −0.127908 | ||||||||
\(861\) | −9.18659 | −0.313078 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | 32.9820 | 1.12272 | 0.561360 | − | 0.827572i | \(-0.310278\pi\) | ||||
0.561360 | + | 0.827572i | \(0.310278\pi\) | |||||||
\(864\) | −4.52320 | −0.153882 | ||||||||
\(865\) | 2.13130 | 0.0724663 | ||||||||
\(866\) | 28.9055 | 0.982249 | ||||||||
\(867\) | 15.4485 | 0.524660 | ||||||||
\(868\) | 0.802592 | 0.0272417 | ||||||||
\(869\) | 6.94238 | 0.235504 | ||||||||
\(870\) | −55.3847 | −1.87772 | ||||||||
\(871\) | 7.30628 | 0.247564 | ||||||||
\(872\) | 1.09655 | 0.0371340 | ||||||||
\(873\) | 8.94181 | 0.302634 | ||||||||
\(874\) | 12.4849 | 0.422308 | ||||||||
\(875\) | −14.5130 | −0.490630 | ||||||||
\(876\) | 1.61399 | 0.0545316 | ||||||||
\(877\) | 22.7575 | 0.768467 | 0.384234 | − | 0.923236i | \(-0.374466\pi\) | ||||
0.384234 | + | 0.923236i | \(0.374466\pi\) | |||||||
\(878\) | −22.2721 | −0.751647 | ||||||||
\(879\) | 45.1745 | 1.52370 | ||||||||
\(880\) | −10.8582 | −0.366029 | ||||||||
\(881\) | 31.7901 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(882\) | −0.623956 | −0.0210097 | ||||||||
\(883\) | −8.08296 | −0.272013 | −0.136007 | − | 0.990708i | \(-0.543427\pi\) | ||||
−0.136007 | + | 0.990708i | \(0.543427\pi\) | |||||||
\(884\) | 2.55875 | 0.0860600 | ||||||||
\(885\) | −35.5641 | −1.19547 | ||||||||
\(886\) | −2.32911 | −0.0782480 | ||||||||
\(887\) | −12.8923 | −0.432881 | −0.216440 | − | 0.976296i | \(-0.569445\pi\) | ||||
−0.216440 | + | 0.976296i | \(0.569445\pi\) | |||||||
\(888\) | 0.392728 | 0.0131791 | ||||||||
\(889\) | −19.8079 | −0.664335 | ||||||||
\(890\) | 30.3295 | 1.01665 | ||||||||
\(891\) | −30.5363 | −1.02300 | ||||||||
\(892\) | 1.21846 | 0.0407970 | ||||||||
\(893\) | 9.30651 | 0.311430 | ||||||||
\(894\) | −7.89912 | −0.264186 | ||||||||
\(895\) | 56.3931 | 1.88501 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −11.4927 | −0.383730 | ||||||||
\(898\) | −0.956283 | −0.0319116 | ||||||||
\(899\) | 6.26450 | 0.208933 | ||||||||
\(900\) | 5.54921 | 0.184974 | ||||||||
\(901\) | −28.8165 | −0.960017 | ||||||||
\(902\) | −14.0576 | −0.468068 | ||||||||
\(903\) | −1.91572 | −0.0637510 | ||||||||
\(904\) | −19.6638 | −0.654009 | ||||||||
\(905\) | −25.9897 | −0.863925 | ||||||||
\(906\) | 27.8964 | 0.926795 | ||||||||
\(907\) | −52.9811 | −1.75921 | −0.879605 | − | 0.475706i | \(-0.842193\pi\) | ||||
−0.879605 | + | 0.475706i | \(0.842193\pi\) | |||||||
\(908\) | −11.2629 | −0.373771 | ||||||||
\(909\) | 9.00737 | 0.298756 | ||||||||
\(910\) | 3.19970 | 0.106069 | ||||||||
\(911\) | 11.8761 | 0.393472 | 0.196736 | − | 0.980457i | \(-0.436966\pi\) | ||||
0.196736 | + | 0.980457i | \(0.436966\pi\) | |||||||
\(912\) | 3.37946 | 0.111905 | ||||||||
\(913\) | −4.27600 | −0.141515 | ||||||||
\(914\) | 34.0425 | 1.12603 | ||||||||
\(915\) | −84.5094 | −2.79379 | ||||||||
\(916\) | −1.13912 | −0.0376377 | ||||||||
\(917\) | −14.2456 | −0.470433 | ||||||||
\(918\) | −13.4825 | −0.444990 | ||||||||
\(919\) | 46.7794 | 1.54311 | 0.771555 | − | 0.636162i | \(-0.219479\pi\) | ||||
0.771555 | + | 0.636162i | \(0.219479\pi\) | |||||||
\(920\) | 26.2142 | 0.864255 | ||||||||
\(921\) | 36.2129 | 1.19326 | ||||||||
\(922\) | −33.0036 | −1.08691 | ||||||||
\(923\) | 10.9779 | 0.361343 | ||||||||
\(924\) | −5.54550 | −0.182434 | ||||||||
\(925\) | 1.83475 | 0.0603263 | ||||||||
\(926\) | 31.5144 | 1.03563 | ||||||||
\(927\) | −6.09001 | −0.200022 | ||||||||
\(928\) | −7.80533 | −0.256223 | ||||||||
\(929\) | 23.9724 | 0.786507 | 0.393254 | − | 0.919430i | \(-0.371349\pi\) | ||||
0.393254 | + | 0.919430i | \(0.371349\pi\) | |||||||
\(930\) | −5.69500 | −0.186746 | ||||||||
\(931\) | −1.77524 | −0.0581811 | ||||||||
\(932\) | −17.3780 | −0.569235 | ||||||||
\(933\) | −59.5866 | −1.95078 | ||||||||
\(934\) | −28.8027 | −0.942452 | ||||||||
\(935\) | −32.3655 | −1.05846 | ||||||||
\(936\) | −0.535618 | −0.0175072 | ||||||||
\(937\) | 10.5748 | 0.345465 | 0.172732 | − | 0.984969i | \(-0.444740\pi\) | ||||
0.172732 | + | 0.984969i | \(0.444740\pi\) | |||||||
\(938\) | −8.51127 | −0.277903 | ||||||||
\(939\) | −47.5233 | −1.55086 | ||||||||
\(940\) | 19.5406 | 0.637344 | ||||||||
\(941\) | −46.0615 | −1.50156 | −0.750781 | − | 0.660551i | \(-0.770323\pi\) | ||||
−0.750781 | + | 0.660551i | \(0.770323\pi\) | |||||||
\(942\) | 5.82951 | 0.189936 | ||||||||
\(943\) | 33.9384 | 1.10519 | ||||||||
\(944\) | −5.01202 | −0.163127 | ||||||||
\(945\) | −16.8598 | −0.548450 | ||||||||
\(946\) | −2.93149 | −0.0953110 | ||||||||
\(947\) | 19.3816 | 0.629816 | 0.314908 | − | 0.949122i | \(-0.398026\pi\) | ||||
0.314908 | + | 0.949122i | \(0.398026\pi\) | |||||||
\(948\) | −4.53681 | −0.147349 | ||||||||
\(949\) | −0.727798 | −0.0236253 | ||||||||
\(950\) | 15.7882 | 0.512238 | ||||||||
\(951\) | −43.7367 | −1.41826 | ||||||||
\(952\) | −2.98075 | −0.0966066 | ||||||||
\(953\) | −1.46579 | −0.0474814 | −0.0237407 | − | 0.999718i | \(-0.507558\pi\) | ||||
−0.0237407 | + | 0.999718i | \(0.507558\pi\) | |||||||
\(954\) | 6.03211 | 0.195297 | ||||||||
\(955\) | −101.583 | −3.28714 | ||||||||
\(956\) | 18.0333 | 0.583239 | ||||||||
\(957\) | −43.2845 | −1.39919 | ||||||||
\(958\) | −3.08293 | −0.0996049 | ||||||||
\(959\) | −9.57973 | −0.309346 | ||||||||
\(960\) | 7.09576 | 0.229015 | ||||||||
\(961\) | −30.3558 | −0.979221 | ||||||||
\(962\) | −0.177093 | −0.00570972 | ||||||||
\(963\) | −4.89339 | −0.157687 | ||||||||
\(964\) | −0.947127 | −0.0305049 | ||||||||
\(965\) | 17.2679 | 0.555874 | ||||||||
\(966\) | 13.3881 | 0.430756 | ||||||||
\(967\) | −17.6070 | −0.566204 | −0.283102 | − | 0.959090i | \(-0.591363\pi\) | ||||
−0.283102 | + | 0.959090i | \(0.591363\pi\) | |||||||
\(968\) | 2.51409 | 0.0808059 | ||||||||
\(969\) | 10.0733 | 0.323602 | ||||||||
\(970\) | 53.4169 | 1.71511 | ||||||||
\(971\) | −20.3946 | −0.654493 | −0.327246 | − | 0.944939i | \(-0.606121\pi\) | ||||
−0.327246 | + | 0.944939i | \(0.606121\pi\) | |||||||
\(972\) | 6.38569 | 0.204821 | ||||||||
\(973\) | −7.95766 | −0.255111 | ||||||||
\(974\) | 2.47113 | 0.0791800 | ||||||||
\(975\) | −14.5335 | −0.465445 | ||||||||
\(976\) | −11.9098 | −0.381225 | ||||||||
\(977\) | −14.6917 | −0.470029 | −0.235015 | − | 0.971992i | \(-0.575514\pi\) | ||||
−0.235015 | + | 0.971992i | \(0.575514\pi\) | |||||||
\(978\) | 1.40693 | 0.0449888 | ||||||||
\(979\) | 23.7032 | 0.757559 | ||||||||
\(980\) | −3.72741 | −0.119068 | ||||||||
\(981\) | −0.684201 | −0.0218449 | ||||||||
\(982\) | 33.8624 | 1.08059 | ||||||||
\(983\) | −29.0008 | −0.924982 | −0.462491 | − | 0.886624i | \(-0.653044\pi\) | ||||
−0.462491 | + | 0.886624i | \(0.653044\pi\) | |||||||
\(984\) | 9.18659 | 0.292858 | ||||||||
\(985\) | −53.2438 | −1.69649 | ||||||||
\(986\) | −23.2657 | −0.740932 | ||||||||
\(987\) | 9.97980 | 0.317660 | ||||||||
\(988\) | −1.52391 | −0.0484819 | ||||||||
\(989\) | 7.07731 | 0.225045 | ||||||||
\(990\) | 6.77501 | 0.215324 | ||||||||
\(991\) | 20.1901 | 0.641361 | 0.320680 | − | 0.947187i | \(-0.396088\pi\) | ||||
0.320680 | + | 0.947187i | \(0.396088\pi\) | |||||||
\(992\) | −0.802592 | −0.0254823 | ||||||||
\(993\) | 28.0422 | 0.889892 | ||||||||
\(994\) | −12.7885 | −0.405626 | ||||||||
\(995\) | −14.8475 | −0.470697 | ||||||||
\(996\) | 2.79434 | 0.0885422 | ||||||||
\(997\) | 23.5371 | 0.745428 | 0.372714 | − | 0.927946i | \(-0.378427\pi\) | ||||
0.372714 | + | 0.927946i | \(0.378427\pi\) | |||||||
\(998\) | −36.8515 | −1.16651 | ||||||||
\(999\) | 0.933139 | 0.0295232 |
(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.p.1.6 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.6 | ✓ | 27 | 1.1 | even | 1 | trivial |