Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(1\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.426737 | −0.301748 | −0.150874 | − | 0.988553i | \(-0.548209\pi\) | ||||
−0.150874 | + | 0.988553i | \(0.548209\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.81790 | −0.908948 | ||||||||
\(5\) | −3.28382 | −1.46857 | −0.734284 | − | 0.678842i | \(-0.762482\pi\) | ||||
−0.734284 | + | 0.678842i | \(0.762482\pi\) | |||||||
\(6\) | 0.426737 | 0.174215 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.62924 | 0.576022 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.40133 | 0.443138 | ||||||||
\(11\) | −2.62788 | −0.792335 | −0.396168 | − | 0.918178i | \(-0.629660\pi\) | ||||
−0.396168 | + | 0.918178i | \(0.629660\pi\) | |||||||
\(12\) | 1.81790 | 0.524781 | ||||||||
\(13\) | 0.620243 | 0.172025 | 0.0860123 | − | 0.996294i | \(-0.472588\pi\) | ||||
0.0860123 | + | 0.996294i | \(0.472588\pi\) | |||||||
\(14\) | −0.426737 | −0.114050 | ||||||||
\(15\) | 3.28382 | 0.847878 | ||||||||
\(16\) | 2.94054 | 0.735134 | ||||||||
\(17\) | −2.07930 | −0.504304 | −0.252152 | − | 0.967688i | \(-0.581138\pi\) | ||||
−0.252152 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(18\) | −0.426737 | −0.100583 | ||||||||
\(19\) | −7.62070 | −1.74831 | −0.874154 | − | 0.485649i | \(-0.838583\pi\) | ||||
−0.874154 | + | 0.485649i | \(0.838583\pi\) | |||||||
\(20\) | 5.96964 | 1.33485 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.12141 | 0.239086 | ||||||||
\(23\) | 6.98579 | 1.45664 | 0.728319 | − | 0.685238i | \(-0.240302\pi\) | ||||
0.728319 | + | 0.685238i | \(0.240302\pi\) | |||||||
\(24\) | −1.62924 | −0.332567 | ||||||||
\(25\) | 5.78347 | 1.15669 | ||||||||
\(26\) | −0.264681 | −0.0519082 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.81790 | −0.343550 | ||||||||
\(29\) | −2.98214 | −0.553770 | −0.276885 | − | 0.960903i | \(-0.589302\pi\) | ||||
−0.276885 | + | 0.960903i | \(0.589302\pi\) | |||||||
\(30\) | −1.40133 | −0.255846 | ||||||||
\(31\) | 0.454979 | 0.0817167 | 0.0408584 | − | 0.999165i | \(-0.486991\pi\) | ||||
0.0408584 | + | 0.999165i | \(0.486991\pi\) | |||||||
\(32\) | −4.51331 | −0.797848 | ||||||||
\(33\) | 2.62788 | 0.457455 | ||||||||
\(34\) | 0.887314 | 0.152173 | ||||||||
\(35\) | −3.28382 | −0.555067 | ||||||||
\(36\) | −1.81790 | −0.302983 | ||||||||
\(37\) | −11.5815 | −1.90399 | −0.951994 | − | 0.306115i | \(-0.900971\pi\) | ||||
−0.951994 | + | 0.306115i | \(0.900971\pi\) | |||||||
\(38\) | 3.25203 | 0.527549 | ||||||||
\(39\) | −0.620243 | −0.0993184 | ||||||||
\(40\) | −5.35012 | −0.845928 | ||||||||
\(41\) | 1.52292 | 0.237840 | 0.118920 | − | 0.992904i | \(-0.462057\pi\) | ||||
0.118920 | + | 0.992904i | \(0.462057\pi\) | |||||||
\(42\) | 0.426737 | 0.0658469 | ||||||||
\(43\) | 6.91315 | 1.05425 | 0.527123 | − | 0.849789i | \(-0.323271\pi\) | ||||
0.527123 | + | 0.849789i | \(0.323271\pi\) | |||||||
\(44\) | 4.77721 | 0.720191 | ||||||||
\(45\) | −3.28382 | −0.489523 | ||||||||
\(46\) | −2.98109 | −0.439538 | ||||||||
\(47\) | 9.49134 | 1.38445 | 0.692227 | − | 0.721680i | \(-0.256630\pi\) | ||||
0.692227 | + | 0.721680i | \(0.256630\pi\) | |||||||
\(48\) | −2.94054 | −0.424430 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.46802 | −0.349030 | ||||||||
\(51\) | 2.07930 | 0.291160 | ||||||||
\(52\) | −1.12754 | −0.156361 | ||||||||
\(53\) | −5.26196 | −0.722785 | −0.361393 | − | 0.932414i | \(-0.617699\pi\) | ||||
−0.361393 | + | 0.932414i | \(0.617699\pi\) | |||||||
\(54\) | 0.426737 | 0.0580715 | ||||||||
\(55\) | 8.62948 | 1.16360 | ||||||||
\(56\) | 1.62924 | 0.217716 | ||||||||
\(57\) | 7.62070 | 1.00939 | ||||||||
\(58\) | 1.27259 | 0.167099 | ||||||||
\(59\) | −11.6791 | −1.52049 | −0.760247 | − | 0.649635i | \(-0.774922\pi\) | ||||
−0.760247 | + | 0.649635i | \(0.774922\pi\) | |||||||
\(60\) | −5.96964 | −0.770677 | ||||||||
\(61\) | 11.9493 | 1.52995 | 0.764976 | − | 0.644059i | \(-0.222751\pi\) | ||||
0.764976 | + | 0.644059i | \(0.222751\pi\) | |||||||
\(62\) | −0.194156 | −0.0246579 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −3.95508 | −0.494385 | ||||||||
\(65\) | −2.03677 | −0.252630 | ||||||||
\(66\) | −1.12141 | −0.138036 | ||||||||
\(67\) | −14.0526 | −1.71680 | −0.858400 | − | 0.512981i | \(-0.828541\pi\) | ||||
−0.858400 | + | 0.512981i | \(0.828541\pi\) | |||||||
\(68\) | 3.77995 | 0.458386 | ||||||||
\(69\) | −6.98579 | −0.840990 | ||||||||
\(70\) | 1.40133 | 0.167491 | ||||||||
\(71\) | 13.3701 | 1.58674 | 0.793369 | − | 0.608740i | \(-0.208325\pi\) | ||||
0.793369 | + | 0.608740i | \(0.208325\pi\) | |||||||
\(72\) | 1.62924 | 0.192007 | ||||||||
\(73\) | 7.88472 | 0.922836 | 0.461418 | − | 0.887183i | \(-0.347341\pi\) | ||||
0.461418 | + | 0.887183i | \(0.347341\pi\) | |||||||
\(74\) | 4.94226 | 0.574526 | ||||||||
\(75\) | −5.78347 | −0.667817 | ||||||||
\(76\) | 13.8536 | 1.58912 | ||||||||
\(77\) | −2.62788 | −0.299475 | ||||||||
\(78\) | 0.264681 | 0.0299692 | ||||||||
\(79\) | −5.65341 | −0.636058 | −0.318029 | − | 0.948081i | \(-0.603021\pi\) | ||||
−0.318029 | + | 0.948081i | \(0.603021\pi\) | |||||||
\(80\) | −9.65619 | −1.07959 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.649886 | −0.0717679 | ||||||||
\(83\) | 13.6501 | 1.49829 | 0.749146 | − | 0.662405i | \(-0.230464\pi\) | ||||
0.749146 | + | 0.662405i | \(0.230464\pi\) | |||||||
\(84\) | 1.81790 | 0.198349 | ||||||||
\(85\) | 6.82804 | 0.740605 | ||||||||
\(86\) | −2.95010 | −0.318117 | ||||||||
\(87\) | 2.98214 | 0.319719 | ||||||||
\(88\) | −4.28144 | −0.456403 | ||||||||
\(89\) | 13.9255 | 1.47610 | 0.738050 | − | 0.674746i | \(-0.235747\pi\) | ||||
0.738050 | + | 0.674746i | \(0.235747\pi\) | |||||||
\(90\) | 1.40133 | 0.147713 | ||||||||
\(91\) | 0.620243 | 0.0650192 | ||||||||
\(92\) | −12.6994 | −1.32401 | ||||||||
\(93\) | −0.454979 | −0.0471792 | ||||||||
\(94\) | −4.05030 | −0.417757 | ||||||||
\(95\) | 25.0250 | 2.56751 | ||||||||
\(96\) | 4.51331 | 0.460638 | ||||||||
\(97\) | 13.9587 | 1.41729 | 0.708643 | − | 0.705567i | \(-0.249308\pi\) | ||||
0.708643 | + | 0.705567i | \(0.249308\pi\) | |||||||
\(98\) | −0.426737 | −0.0431069 | ||||||||
\(99\) | −2.62788 | −0.264112 | ||||||||
\(100\) | −10.5137 | −1.05137 | ||||||||
\(101\) | 3.16595 | 0.315024 | 0.157512 | − | 0.987517i | \(-0.449653\pi\) | ||||
0.157512 | + | 0.987517i | \(0.449653\pi\) | |||||||
\(102\) | −0.887314 | −0.0878571 | ||||||||
\(103\) | −11.6184 | −1.14479 | −0.572397 | − | 0.819977i | \(-0.693986\pi\) | ||||
−0.572397 | + | 0.819977i | \(0.693986\pi\) | |||||||
\(104\) | 1.01052 | 0.0990900 | ||||||||
\(105\) | 3.28382 | 0.320468 | ||||||||
\(106\) | 2.24547 | 0.218099 | ||||||||
\(107\) | 15.6211 | 1.51015 | 0.755076 | − | 0.655637i | \(-0.227600\pi\) | ||||
0.755076 | + | 0.655637i | \(0.227600\pi\) | |||||||
\(108\) | 1.81790 | 0.174927 | ||||||||
\(109\) | 17.3743 | 1.66416 | 0.832080 | − | 0.554655i | \(-0.187150\pi\) | ||||
0.832080 | + | 0.554655i | \(0.187150\pi\) | |||||||
\(110\) | −3.68252 | −0.351114 | ||||||||
\(111\) | 11.5815 | 1.09927 | ||||||||
\(112\) | 2.94054 | 0.277855 | ||||||||
\(113\) | −17.5901 | −1.65474 | −0.827368 | − | 0.561660i | \(-0.810163\pi\) | ||||
−0.827368 | + | 0.561660i | \(0.810163\pi\) | |||||||
\(114\) | −3.25203 | −0.304581 | ||||||||
\(115\) | −22.9401 | −2.13917 | ||||||||
\(116\) | 5.42122 | 0.503348 | ||||||||
\(117\) | 0.620243 | 0.0573415 | ||||||||
\(118\) | 4.98391 | 0.458807 | ||||||||
\(119\) | −2.07930 | −0.190609 | ||||||||
\(120\) | 5.35012 | 0.488397 | ||||||||
\(121\) | −4.09425 | −0.372205 | ||||||||
\(122\) | −5.09921 | −0.461661 | ||||||||
\(123\) | −1.52292 | −0.137317 | ||||||||
\(124\) | −0.827105 | −0.0742762 | ||||||||
\(125\) | −2.57276 | −0.230115 | ||||||||
\(126\) | −0.426737 | −0.0380167 | ||||||||
\(127\) | 6.69394 | 0.593991 | 0.296996 | − | 0.954879i | \(-0.404015\pi\) | ||||
0.296996 | + | 0.954879i | \(0.404015\pi\) | |||||||
\(128\) | 10.7144 | 0.947028 | ||||||||
\(129\) | −6.91315 | −0.608669 | ||||||||
\(130\) | 0.869163 | 0.0762307 | ||||||||
\(131\) | 6.48167 | 0.566306 | 0.283153 | − | 0.959075i | \(-0.408620\pi\) | ||||
0.283153 | + | 0.959075i | \(0.408620\pi\) | |||||||
\(132\) | −4.77721 | −0.415803 | ||||||||
\(133\) | −7.62070 | −0.660798 | ||||||||
\(134\) | 5.99677 | 0.518042 | ||||||||
\(135\) | 3.28382 | 0.282626 | ||||||||
\(136\) | −3.38767 | −0.290490 | ||||||||
\(137\) | 16.6599 | 1.42335 | 0.711675 | − | 0.702509i | \(-0.247937\pi\) | ||||
0.711675 | + | 0.702509i | \(0.247937\pi\) | |||||||
\(138\) | 2.98109 | 0.253767 | ||||||||
\(139\) | −2.96473 | −0.251465 | −0.125733 | − | 0.992064i | \(-0.540128\pi\) | ||||
−0.125733 | + | 0.992064i | \(0.540128\pi\) | |||||||
\(140\) | 5.96964 | 0.504527 | ||||||||
\(141\) | −9.49134 | −0.799315 | ||||||||
\(142\) | −5.70551 | −0.478796 | ||||||||
\(143\) | −1.62992 | −0.136301 | ||||||||
\(144\) | 2.94054 | 0.245045 | ||||||||
\(145\) | 9.79281 | 0.813249 | ||||||||
\(146\) | −3.36470 | −0.278464 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 21.0540 | 1.73063 | ||||||||
\(149\) | −8.99353 | −0.736779 | −0.368389 | − | 0.929672i | \(-0.620091\pi\) | ||||
−0.368389 | + | 0.929672i | \(0.620091\pi\) | |||||||
\(150\) | 2.46802 | 0.201513 | ||||||||
\(151\) | −2.92212 | −0.237799 | −0.118899 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118899 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(152\) | −12.4159 | −1.00706 | ||||||||
\(153\) | −2.07930 | −0.168101 | ||||||||
\(154\) | 1.12141 | 0.0903660 | ||||||||
\(155\) | −1.49407 | −0.120007 | ||||||||
\(156\) | 1.12754 | 0.0902753 | ||||||||
\(157\) | 16.8307 | 1.34323 | 0.671616 | − | 0.740899i | \(-0.265600\pi\) | ||||
0.671616 | + | 0.740899i | \(0.265600\pi\) | |||||||
\(158\) | 2.41252 | 0.191930 | ||||||||
\(159\) | 5.26196 | 0.417300 | ||||||||
\(160\) | 14.8209 | 1.17169 | ||||||||
\(161\) | 6.98579 | 0.550557 | ||||||||
\(162\) | −0.426737 | −0.0335276 | ||||||||
\(163\) | −22.5177 | −1.76373 | −0.881863 | − | 0.471507i | \(-0.843710\pi\) | ||||
−0.881863 | + | 0.471507i | \(0.843710\pi\) | |||||||
\(164\) | −2.76851 | −0.216184 | ||||||||
\(165\) | −8.62948 | −0.671804 | ||||||||
\(166\) | −5.82499 | −0.452107 | ||||||||
\(167\) | 8.01819 | 0.620467 | 0.310233 | − | 0.950660i | \(-0.399593\pi\) | ||||
0.310233 | + | 0.950660i | \(0.399593\pi\) | |||||||
\(168\) | −1.62924 | −0.125698 | ||||||||
\(169\) | −12.6153 | −0.970408 | ||||||||
\(170\) | −2.91378 | −0.223476 | ||||||||
\(171\) | −7.62070 | −0.582769 | ||||||||
\(172\) | −12.5674 | −0.958254 | ||||||||
\(173\) | 12.0798 | 0.918412 | 0.459206 | − | 0.888330i | \(-0.348134\pi\) | ||||
0.459206 | + | 0.888330i | \(0.348134\pi\) | |||||||
\(174\) | −1.27259 | −0.0964748 | ||||||||
\(175\) | 5.78347 | 0.437189 | ||||||||
\(176\) | −7.72737 | −0.582473 | ||||||||
\(177\) | 11.6791 | 0.877857 | ||||||||
\(178\) | −5.94252 | −0.445411 | ||||||||
\(179\) | −10.9759 | −0.820379 | −0.410190 | − | 0.912000i | \(-0.634537\pi\) | ||||
−0.410190 | + | 0.912000i | \(0.634537\pi\) | |||||||
\(180\) | 5.96964 | 0.444951 | ||||||||
\(181\) | −5.82133 | −0.432696 | −0.216348 | − | 0.976316i | \(-0.569415\pi\) | ||||
−0.216348 | + | 0.976316i | \(0.569415\pi\) | |||||||
\(182\) | −0.264681 | −0.0196194 | ||||||||
\(183\) | −11.9493 | −0.883318 | ||||||||
\(184\) | 11.3815 | 0.839055 | ||||||||
\(185\) | 38.0316 | 2.79614 | ||||||||
\(186\) | 0.194156 | 0.0142362 | ||||||||
\(187\) | 5.46415 | 0.399578 | ||||||||
\(188\) | −17.2543 | −1.25840 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −10.6791 | −0.774742 | ||||||||
\(191\) | 10.4215 | 0.754075 | 0.377037 | − | 0.926198i | \(-0.376943\pi\) | ||||
0.377037 | + | 0.926198i | \(0.376943\pi\) | |||||||
\(192\) | 3.95508 | 0.285433 | ||||||||
\(193\) | 1.61781 | 0.116453 | 0.0582263 | − | 0.998303i | \(-0.481456\pi\) | ||||
0.0582263 | + | 0.998303i | \(0.481456\pi\) | |||||||
\(194\) | −5.95667 | −0.427664 | ||||||||
\(195\) | 2.03677 | 0.145856 | ||||||||
\(196\) | −1.81790 | −0.129850 | ||||||||
\(197\) | −6.35580 | −0.452832 | −0.226416 | − | 0.974031i | \(-0.572701\pi\) | ||||
−0.226416 | + | 0.974031i | \(0.572701\pi\) | |||||||
\(198\) | 1.12141 | 0.0796953 | ||||||||
\(199\) | −10.4643 | −0.741795 | −0.370897 | − | 0.928674i | \(-0.620950\pi\) | ||||
−0.370897 | + | 0.928674i | \(0.620950\pi\) | |||||||
\(200\) | 9.42263 | 0.666281 | ||||||||
\(201\) | 14.0526 | 0.991195 | ||||||||
\(202\) | −1.35103 | −0.0950581 | ||||||||
\(203\) | −2.98214 | −0.209305 | ||||||||
\(204\) | −3.77995 | −0.264649 | ||||||||
\(205\) | −5.00100 | −0.349285 | ||||||||
\(206\) | 4.95800 | 0.345440 | ||||||||
\(207\) | 6.98579 | 0.485546 | ||||||||
\(208\) | 1.82385 | 0.126461 | ||||||||
\(209\) | 20.0263 | 1.38525 | ||||||||
\(210\) | −1.40133 | −0.0967007 | ||||||||
\(211\) | −16.7420 | −1.15257 | −0.576285 | − | 0.817249i | \(-0.695498\pi\) | ||||
−0.576285 | + | 0.817249i | \(0.695498\pi\) | |||||||
\(212\) | 9.56569 | 0.656974 | ||||||||
\(213\) | −13.3701 | −0.916104 | ||||||||
\(214\) | −6.66612 | −0.455686 | ||||||||
\(215\) | −22.7015 | −1.54823 | ||||||||
\(216\) | −1.62924 | −0.110856 | ||||||||
\(217\) | 0.454979 | 0.0308860 | ||||||||
\(218\) | −7.41427 | −0.502158 | ||||||||
\(219\) | −7.88472 | −0.532800 | ||||||||
\(220\) | −15.6875 | −1.05765 | ||||||||
\(221\) | −1.28967 | −0.0867527 | ||||||||
\(222\) | −4.94226 | −0.331703 | ||||||||
\(223\) | 9.81900 | 0.657529 | 0.328764 | − | 0.944412i | \(-0.393368\pi\) | ||||
0.328764 | + | 0.944412i | \(0.393368\pi\) | |||||||
\(224\) | −4.51331 | −0.301558 | ||||||||
\(225\) | 5.78347 | 0.385564 | ||||||||
\(226\) | 7.50634 | 0.499314 | ||||||||
\(227\) | 18.1308 | 1.20338 | 0.601692 | − | 0.798728i | \(-0.294494\pi\) | ||||
0.601692 | + | 0.798728i | \(0.294494\pi\) | |||||||
\(228\) | −13.8536 | −0.917479 | ||||||||
\(229\) | 16.5276 | 1.09218 | 0.546088 | − | 0.837728i | \(-0.316116\pi\) | ||||
0.546088 | + | 0.837728i | \(0.316116\pi\) | |||||||
\(230\) | 9.78937 | 0.645492 | ||||||||
\(231\) | 2.62788 | 0.172902 | ||||||||
\(232\) | −4.85861 | −0.318984 | ||||||||
\(233\) | −15.6411 | −1.02468 | −0.512340 | − | 0.858783i | \(-0.671221\pi\) | ||||
−0.512340 | + | 0.858783i | \(0.671221\pi\) | |||||||
\(234\) | −0.264681 | −0.0173027 | ||||||||
\(235\) | −31.1678 | −2.03317 | ||||||||
\(236\) | 21.2314 | 1.38205 | ||||||||
\(237\) | 5.65341 | 0.367228 | ||||||||
\(238\) | 0.887314 | 0.0575160 | ||||||||
\(239\) | −24.7485 | −1.60085 | −0.800424 | − | 0.599434i | \(-0.795393\pi\) | ||||
−0.800424 | + | 0.599434i | \(0.795393\pi\) | |||||||
\(240\) | 9.65619 | 0.623304 | ||||||||
\(241\) | −26.4849 | −1.70604 | −0.853022 | − | 0.521874i | \(-0.825233\pi\) | ||||
−0.853022 | + | 0.521874i | \(0.825233\pi\) | |||||||
\(242\) | 1.74717 | 0.112312 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −21.7226 | −1.39065 | ||||||||
\(245\) | −3.28382 | −0.209795 | ||||||||
\(246\) | 0.649886 | 0.0414352 | ||||||||
\(247\) | −4.72669 | −0.300752 | ||||||||
\(248\) | 0.741269 | 0.0470706 | ||||||||
\(249\) | −13.6501 | −0.865039 | ||||||||
\(250\) | 1.09789 | 0.0694367 | ||||||||
\(251\) | 9.59598 | 0.605693 | 0.302847 | − | 0.953039i | \(-0.402063\pi\) | ||||
0.302847 | + | 0.953039i | \(0.402063\pi\) | |||||||
\(252\) | −1.81790 | −0.114517 | ||||||||
\(253\) | −18.3578 | −1.15415 | ||||||||
\(254\) | −2.85655 | −0.179236 | ||||||||
\(255\) | −6.82804 | −0.427589 | ||||||||
\(256\) | 3.33793 | 0.208621 | ||||||||
\(257\) | 14.8391 | 0.925639 | 0.462819 | − | 0.886453i | \(-0.346838\pi\) | ||||
0.462819 | + | 0.886453i | \(0.346838\pi\) | |||||||
\(258\) | 2.95010 | 0.183665 | ||||||||
\(259\) | −11.5815 | −0.719640 | ||||||||
\(260\) | 3.70263 | 0.229627 | ||||||||
\(261\) | −2.98214 | −0.184590 | ||||||||
\(262\) | −2.76597 | −0.170882 | ||||||||
\(263\) | 16.6847 | 1.02882 | 0.514412 | − | 0.857543i | \(-0.328010\pi\) | ||||
0.514412 | + | 0.857543i | \(0.328010\pi\) | |||||||
\(264\) | 4.28144 | 0.263504 | ||||||||
\(265\) | 17.2793 | 1.06146 | ||||||||
\(266\) | 3.25203 | 0.199395 | ||||||||
\(267\) | −13.9255 | −0.852227 | ||||||||
\(268\) | 25.5462 | 1.56048 | ||||||||
\(269\) | −7.78161 | −0.474453 | −0.237227 | − | 0.971454i | \(-0.576238\pi\) | ||||
−0.237227 | + | 0.971454i | \(0.576238\pi\) | |||||||
\(270\) | −1.40133 | −0.0852820 | ||||||||
\(271\) | 20.1007 | 1.22103 | 0.610514 | − | 0.792005i | \(-0.290963\pi\) | ||||
0.610514 | + | 0.792005i | \(0.290963\pi\) | |||||||
\(272\) | −6.11425 | −0.370731 | ||||||||
\(273\) | −0.620243 | −0.0375388 | ||||||||
\(274\) | −7.10939 | −0.429494 | ||||||||
\(275\) | −15.1982 | −0.916489 | ||||||||
\(276\) | 12.6994 | 0.764416 | ||||||||
\(277\) | −17.9552 | −1.07882 | −0.539412 | − | 0.842042i | \(-0.681353\pi\) | ||||
−0.539412 | + | 0.842042i | \(0.681353\pi\) | |||||||
\(278\) | 1.26516 | 0.0758793 | ||||||||
\(279\) | 0.454979 | 0.0272389 | ||||||||
\(280\) | −5.35012 | −0.319731 | ||||||||
\(281\) | 1.71727 | 0.102444 | 0.0512219 | − | 0.998687i | \(-0.483688\pi\) | ||||
0.0512219 | + | 0.998687i | \(0.483688\pi\) | |||||||
\(282\) | 4.05030 | 0.241192 | ||||||||
\(283\) | −6.52811 | −0.388056 | −0.194028 | − | 0.980996i | \(-0.562155\pi\) | ||||
−0.194028 | + | 0.980996i | \(0.562155\pi\) | |||||||
\(284\) | −24.3054 | −1.44226 | ||||||||
\(285\) | −25.0250 | −1.48235 | ||||||||
\(286\) | 0.695549 | 0.0411287 | ||||||||
\(287\) | 1.52292 | 0.0898952 | ||||||||
\(288\) | −4.51331 | −0.265949 | ||||||||
\(289\) | −12.6765 | −0.745677 | ||||||||
\(290\) | −4.17895 | −0.245397 | ||||||||
\(291\) | −13.9587 | −0.818271 | ||||||||
\(292\) | −14.3336 | −0.838810 | ||||||||
\(293\) | 3.35466 | 0.195981 | 0.0979907 | − | 0.995187i | \(-0.468758\pi\) | ||||
0.0979907 | + | 0.995187i | \(0.468758\pi\) | |||||||
\(294\) | 0.426737 | 0.0248878 | ||||||||
\(295\) | 38.3521 | 2.23295 | ||||||||
\(296\) | −18.8690 | −1.09674 | ||||||||
\(297\) | 2.62788 | 0.152485 | ||||||||
\(298\) | 3.83787 | 0.222322 | ||||||||
\(299\) | 4.33289 | 0.250577 | ||||||||
\(300\) | 10.5137 | 0.607011 | ||||||||
\(301\) | 6.91315 | 0.398467 | ||||||||
\(302\) | 1.24698 | 0.0717555 | ||||||||
\(303\) | −3.16595 | −0.181879 | ||||||||
\(304\) | −22.4089 | −1.28524 | ||||||||
\(305\) | −39.2393 | −2.24684 | ||||||||
\(306\) | 0.887314 | 0.0507243 | ||||||||
\(307\) | 6.88211 | 0.392783 | 0.196391 | − | 0.980526i | \(-0.437078\pi\) | ||||
0.196391 | + | 0.980526i | \(0.437078\pi\) | |||||||
\(308\) | 4.77721 | 0.272207 | ||||||||
\(309\) | 11.6184 | 0.660947 | ||||||||
\(310\) | 0.637575 | 0.0362118 | ||||||||
\(311\) | 7.00933 | 0.397463 | 0.198731 | − | 0.980054i | \(-0.436318\pi\) | ||||
0.198731 | + | 0.980054i | \(0.436318\pi\) | |||||||
\(312\) | −1.01052 | −0.0572096 | ||||||||
\(313\) | −9.50269 | −0.537124 | −0.268562 | − | 0.963262i | \(-0.586548\pi\) | ||||
−0.268562 | + | 0.963262i | \(0.586548\pi\) | |||||||
\(314\) | −7.18226 | −0.405318 | ||||||||
\(315\) | −3.28382 | −0.185022 | ||||||||
\(316\) | 10.2773 | 0.578144 | ||||||||
\(317\) | −7.82025 | −0.439229 | −0.219615 | − | 0.975587i | \(-0.570480\pi\) | ||||
−0.219615 | + | 0.975587i | \(0.570480\pi\) | |||||||
\(318\) | −2.24547 | −0.125920 | ||||||||
\(319\) | 7.83670 | 0.438771 | ||||||||
\(320\) | 12.9878 | 0.726038 | ||||||||
\(321\) | −15.6211 | −0.871887 | ||||||||
\(322\) | −2.98109 | −0.166130 | ||||||||
\(323\) | 15.8457 | 0.881679 | ||||||||
\(324\) | −1.81790 | −0.100994 | ||||||||
\(325\) | 3.58716 | 0.198980 | ||||||||
\(326\) | 9.60915 | 0.532201 | ||||||||
\(327\) | −17.3743 | −0.960804 | ||||||||
\(328\) | 2.48120 | 0.137001 | ||||||||
\(329\) | 9.49134 | 0.523274 | ||||||||
\(330\) | 3.68252 | 0.202716 | ||||||||
\(331\) | 7.32951 | 0.402866 | 0.201433 | − | 0.979502i | \(-0.435440\pi\) | ||||
0.201433 | + | 0.979502i | \(0.435440\pi\) | |||||||
\(332\) | −24.8144 | −1.36187 | ||||||||
\(333\) | −11.5815 | −0.634663 | ||||||||
\(334\) | −3.42166 | −0.187225 | ||||||||
\(335\) | 46.1462 | 2.52124 | ||||||||
\(336\) | −2.94054 | −0.160419 | ||||||||
\(337\) | 3.95415 | 0.215396 | 0.107698 | − | 0.994184i | \(-0.465652\pi\) | ||||
0.107698 | + | 0.994184i | \(0.465652\pi\) | |||||||
\(338\) | 5.38341 | 0.292819 | ||||||||
\(339\) | 17.5901 | 0.955363 | ||||||||
\(340\) | −12.4127 | −0.673171 | ||||||||
\(341\) | −1.19563 | −0.0647470 | ||||||||
\(342\) | 3.25203 | 0.175850 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.2632 | 0.607269 | ||||||||
\(345\) | 22.9401 | 1.23505 | ||||||||
\(346\) | −5.15491 | −0.277130 | ||||||||
\(347\) | 6.80849 | 0.365499 | 0.182749 | − | 0.983160i | \(-0.441500\pi\) | ||||
0.182749 | + | 0.983160i | \(0.441500\pi\) | |||||||
\(348\) | −5.42122 | −0.290608 | ||||||||
\(349\) | −0.0826098 | −0.00442200 | −0.00221100 | − | 0.999998i | \(-0.500704\pi\) | ||||
−0.00221100 | + | 0.999998i | \(0.500704\pi\) | |||||||
\(350\) | −2.46802 | −0.131921 | ||||||||
\(351\) | −0.620243 | −0.0331061 | ||||||||
\(352\) | 11.8604 | 0.632163 | ||||||||
\(353\) | −20.3722 | −1.08430 | −0.542151 | − | 0.840281i | \(-0.682390\pi\) | ||||
−0.542151 | + | 0.840281i | \(0.682390\pi\) | |||||||
\(354\) | −4.98391 | −0.264892 | ||||||||
\(355\) | −43.9050 | −2.33023 | ||||||||
\(356\) | −25.3151 | −1.34170 | ||||||||
\(357\) | 2.07930 | 0.110048 | ||||||||
\(358\) | 4.68383 | 0.247548 | ||||||||
\(359\) | −6.69510 | −0.353354 | −0.176677 | − | 0.984269i | \(-0.556535\pi\) | ||||
−0.176677 | + | 0.984269i | \(0.556535\pi\) | |||||||
\(360\) | −5.35012 | −0.281976 | ||||||||
\(361\) | 39.0750 | 2.05658 | ||||||||
\(362\) | 2.48418 | 0.130565 | ||||||||
\(363\) | 4.09425 | 0.214893 | ||||||||
\(364\) | −1.12754 | −0.0590990 | ||||||||
\(365\) | −25.8920 | −1.35525 | ||||||||
\(366\) | 5.09921 | 0.266540 | ||||||||
\(367\) | 11.6423 | 0.607723 | 0.303862 | − | 0.952716i | \(-0.401724\pi\) | ||||
0.303862 | + | 0.952716i | \(0.401724\pi\) | |||||||
\(368\) | 20.5420 | 1.07082 | ||||||||
\(369\) | 1.52292 | 0.0792801 | ||||||||
\(370\) | −16.2295 | −0.843730 | ||||||||
\(371\) | −5.26196 | −0.273187 | ||||||||
\(372\) | 0.827105 | 0.0428834 | ||||||||
\(373\) | 32.1923 | 1.66686 | 0.833428 | − | 0.552628i | \(-0.186375\pi\) | ||||
0.833428 | + | 0.552628i | \(0.186375\pi\) | |||||||
\(374\) | −2.33175 | −0.120572 | ||||||||
\(375\) | 2.57276 | 0.132857 | ||||||||
\(376\) | 15.4636 | 0.797476 | ||||||||
\(377\) | −1.84965 | −0.0952620 | ||||||||
\(378\) | 0.426737 | 0.0219490 | ||||||||
\(379\) | −27.0679 | −1.39038 | −0.695191 | − | 0.718825i | \(-0.744680\pi\) | ||||
−0.695191 | + | 0.718825i | \(0.744680\pi\) | |||||||
\(380\) | −45.4928 | −2.33373 | ||||||||
\(381\) | −6.69394 | −0.342941 | ||||||||
\(382\) | −4.44725 | −0.227541 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | −10.7144 | −0.546767 | ||||||||
\(385\) | 8.62948 | 0.439799 | ||||||||
\(386\) | −0.690379 | −0.0351394 | ||||||||
\(387\) | 6.91315 | 0.351415 | ||||||||
\(388\) | −25.3754 | −1.28824 | ||||||||
\(389\) | −14.3758 | −0.728883 | −0.364442 | − | 0.931226i | \(-0.618740\pi\) | ||||
−0.364442 | + | 0.931226i | \(0.618740\pi\) | |||||||
\(390\) | −0.869163 | −0.0440118 | ||||||||
\(391\) | −14.5255 | −0.734588 | ||||||||
\(392\) | 1.62924 | 0.0822889 | ||||||||
\(393\) | −6.48167 | −0.326957 | ||||||||
\(394\) | 2.71226 | 0.136641 | ||||||||
\(395\) | 18.5648 | 0.934095 | ||||||||
\(396\) | 4.77721 | 0.240064 | ||||||||
\(397\) | 35.7020 | 1.79183 | 0.895917 | − | 0.444221i | \(-0.146520\pi\) | ||||
0.895917 | + | 0.444221i | \(0.146520\pi\) | |||||||
\(398\) | 4.46550 | 0.223836 | ||||||||
\(399\) | 7.62070 | 0.381512 | ||||||||
\(400\) | 17.0065 | 0.850324 | ||||||||
\(401\) | 1.27616 | 0.0637282 | 0.0318641 | − | 0.999492i | \(-0.489856\pi\) | ||||
0.0318641 | + | 0.999492i | \(0.489856\pi\) | |||||||
\(402\) | −5.99677 | −0.299092 | ||||||||
\(403\) | 0.282198 | 0.0140573 | ||||||||
\(404\) | −5.75537 | −0.286341 | ||||||||
\(405\) | −3.28382 | −0.163174 | ||||||||
\(406\) | 1.27259 | 0.0631576 | ||||||||
\(407\) | 30.4348 | 1.50860 | ||||||||
\(408\) | 3.38767 | 0.167715 | ||||||||
\(409\) | −22.4511 | −1.11014 | −0.555068 | − | 0.831805i | \(-0.687308\pi\) | ||||
−0.555068 | + | 0.831805i | \(0.687308\pi\) | |||||||
\(410\) | 2.13411 | 0.105396 | ||||||||
\(411\) | −16.6599 | −0.821771 | ||||||||
\(412\) | 21.1210 | 1.04056 | ||||||||
\(413\) | −11.6791 | −0.574692 | ||||||||
\(414\) | −2.98109 | −0.146513 | ||||||||
\(415\) | −44.8244 | −2.20034 | ||||||||
\(416\) | −2.79935 | −0.137249 | ||||||||
\(417\) | 2.96473 | 0.145184 | ||||||||
\(418\) | −8.54595 | −0.417996 | ||||||||
\(419\) | −26.2976 | −1.28472 | −0.642360 | − | 0.766403i | \(-0.722044\pi\) | ||||
−0.642360 | + | 0.766403i | \(0.722044\pi\) | |||||||
\(420\) | −5.96964 | −0.291289 | ||||||||
\(421\) | −26.2791 | −1.28077 | −0.640383 | − | 0.768056i | \(-0.721224\pi\) | ||||
−0.640383 | + | 0.768056i | \(0.721224\pi\) | |||||||
\(422\) | 7.14444 | 0.347786 | ||||||||
\(423\) | 9.49134 | 0.461485 | ||||||||
\(424\) | −8.57297 | −0.416340 | ||||||||
\(425\) | −12.0256 | −0.583325 | ||||||||
\(426\) | 5.70551 | 0.276433 | ||||||||
\(427\) | 11.9493 | 0.578267 | ||||||||
\(428\) | −28.3976 | −1.37265 | ||||||||
\(429\) | 1.62992 | 0.0786935 | ||||||||
\(430\) | 9.68758 | 0.467177 | ||||||||
\(431\) | −3.41779 | −0.164629 | −0.0823145 | − | 0.996606i | \(-0.526231\pi\) | ||||
−0.0823145 | + | 0.996606i | \(0.526231\pi\) | |||||||
\(432\) | −2.94054 | −0.141477 | ||||||||
\(433\) | −4.37913 | −0.210448 | −0.105224 | − | 0.994449i | \(-0.533556\pi\) | ||||
−0.105224 | + | 0.994449i | \(0.533556\pi\) | |||||||
\(434\) | −0.194156 | −0.00931981 | ||||||||
\(435\) | −9.79281 | −0.469529 | ||||||||
\(436\) | −31.5848 | −1.51264 | ||||||||
\(437\) | −53.2366 | −2.54665 | ||||||||
\(438\) | 3.36470 | 0.160772 | ||||||||
\(439\) | −35.7233 | −1.70498 | −0.852490 | − | 0.522744i | \(-0.824908\pi\) | ||||
−0.852490 | + | 0.522744i | \(0.824908\pi\) | |||||||
\(440\) | 14.0595 | 0.670258 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.550350 | 0.0261775 | ||||||||
\(443\) | −33.0415 | −1.56985 | −0.784925 | − | 0.619591i | \(-0.787298\pi\) | ||||
−0.784925 | + | 0.619591i | \(0.787298\pi\) | |||||||
\(444\) | −21.0540 | −0.999178 | ||||||||
\(445\) | −45.7288 | −2.16775 | ||||||||
\(446\) | −4.19013 | −0.198408 | ||||||||
\(447\) | 8.99353 | 0.425379 | ||||||||
\(448\) | −3.95508 | −0.186860 | ||||||||
\(449\) | 30.5096 | 1.43984 | 0.719919 | − | 0.694058i | \(-0.244179\pi\) | ||||
0.719919 | + | 0.694058i | \(0.244179\pi\) | |||||||
\(450\) | −2.46802 | −0.116343 | ||||||||
\(451\) | −4.00205 | −0.188449 | ||||||||
\(452\) | 31.9770 | 1.50407 | ||||||||
\(453\) | 2.92212 | 0.137293 | ||||||||
\(454\) | −7.73708 | −0.363119 | ||||||||
\(455\) | −2.03677 | −0.0954851 | ||||||||
\(456\) | 12.4159 | 0.581429 | ||||||||
\(457\) | −21.2143 | −0.992361 | −0.496180 | − | 0.868219i | \(-0.665265\pi\) | ||||
−0.496180 | + | 0.868219i | \(0.665265\pi\) | |||||||
\(458\) | −7.05295 | −0.329563 | ||||||||
\(459\) | 2.07930 | 0.0970534 | ||||||||
\(460\) | 41.7026 | 1.94440 | ||||||||
\(461\) | 15.1654 | 0.706322 | 0.353161 | − | 0.935563i | \(-0.385107\pi\) | ||||
0.353161 | + | 0.935563i | \(0.385107\pi\) | |||||||
\(462\) | −1.12141 | −0.0521728 | ||||||||
\(463\) | 31.7926 | 1.47753 | 0.738765 | − | 0.673964i | \(-0.235410\pi\) | ||||
0.738765 | + | 0.673964i | \(0.235410\pi\) | |||||||
\(464\) | −8.76909 | −0.407095 | ||||||||
\(465\) | 1.49407 | 0.0692858 | ||||||||
\(466\) | 6.67462 | 0.309196 | ||||||||
\(467\) | −5.27539 | −0.244116 | −0.122058 | − | 0.992523i | \(-0.538949\pi\) | ||||
−0.122058 | + | 0.992523i | \(0.538949\pi\) | |||||||
\(468\) | −1.12754 | −0.0521205 | ||||||||
\(469\) | −14.0526 | −0.648889 | ||||||||
\(470\) | 13.3005 | 0.613505 | ||||||||
\(471\) | −16.8307 | −0.775516 | ||||||||
\(472\) | −19.0281 | −0.875838 | ||||||||
\(473\) | −18.1669 | −0.835316 | ||||||||
\(474\) | −2.41252 | −0.110811 | ||||||||
\(475\) | −44.0740 | −2.02226 | ||||||||
\(476\) | 3.77995 | 0.173254 | ||||||||
\(477\) | −5.26196 | −0.240928 | ||||||||
\(478\) | 10.5611 | 0.483054 | ||||||||
\(479\) | −31.7950 | −1.45275 | −0.726375 | − | 0.687298i | \(-0.758796\pi\) | ||||
−0.726375 | + | 0.687298i | \(0.758796\pi\) | |||||||
\(480\) | −14.8209 | −0.676478 | ||||||||
\(481\) | −7.18336 | −0.327533 | ||||||||
\(482\) | 11.3021 | 0.514797 | ||||||||
\(483\) | −6.98579 | −0.317864 | ||||||||
\(484\) | 7.44293 | 0.338315 | ||||||||
\(485\) | −45.8377 | −2.08138 | ||||||||
\(486\) | 0.426737 | 0.0193572 | ||||||||
\(487\) | 0.555760 | 0.0251839 | 0.0125919 | − | 0.999921i | \(-0.495992\pi\) | ||||
0.0125919 | + | 0.999921i | \(0.495992\pi\) | |||||||
\(488\) | 19.4682 | 0.881286 | ||||||||
\(489\) | 22.5177 | 1.01829 | ||||||||
\(490\) | 1.40133 | 0.0633055 | ||||||||
\(491\) | 14.4832 | 0.653616 | 0.326808 | − | 0.945091i | \(-0.394027\pi\) | ||||
0.326808 | + | 0.945091i | \(0.394027\pi\) | |||||||
\(492\) | 2.76851 | 0.124814 | ||||||||
\(493\) | 6.20076 | 0.279268 | ||||||||
\(494\) | 2.01705 | 0.0907514 | ||||||||
\(495\) | 8.62948 | 0.387866 | ||||||||
\(496\) | 1.33788 | 0.0600727 | ||||||||
\(497\) | 13.3701 | 0.599731 | ||||||||
\(498\) | 5.82499 | 0.261024 | ||||||||
\(499\) | 18.7250 | 0.838245 | 0.419123 | − | 0.907930i | \(-0.362338\pi\) | ||||
0.419123 | + | 0.907930i | \(0.362338\pi\) | |||||||
\(500\) | 4.67701 | 0.209162 | ||||||||
\(501\) | −8.01819 | −0.358227 | ||||||||
\(502\) | −4.09496 | −0.182767 | ||||||||
\(503\) | −6.01096 | −0.268016 | −0.134008 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134008 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(504\) | 1.62924 | 0.0725720 | ||||||||
\(505\) | −10.3964 | −0.462635 | ||||||||
\(506\) | 7.83395 | 0.348262 | ||||||||
\(507\) | 12.6153 | 0.560265 | ||||||||
\(508\) | −12.1689 | −0.539907 | ||||||||
\(509\) | 6.89192 | 0.305479 | 0.152739 | − | 0.988266i | \(-0.451190\pi\) | ||||
0.152739 | + | 0.988266i | \(0.451190\pi\) | |||||||
\(510\) | 2.91378 | 0.129024 | ||||||||
\(511\) | 7.88472 | 0.348799 | ||||||||
\(512\) | −22.8532 | −1.00998 | ||||||||
\(513\) | 7.62070 | 0.336462 | ||||||||
\(514\) | −6.33240 | −0.279310 | ||||||||
\(515\) | 38.1527 | 1.68121 | ||||||||
\(516\) | 12.5674 | 0.553248 | ||||||||
\(517\) | −24.9421 | −1.09695 | ||||||||
\(518\) | 4.94226 | 0.217150 | ||||||||
\(519\) | −12.0798 | −0.530246 | ||||||||
\(520\) | −3.31838 | −0.145520 | ||||||||
\(521\) | −34.9933 | −1.53308 | −0.766541 | − | 0.642195i | \(-0.778024\pi\) | ||||
−0.766541 | + | 0.642195i | \(0.778024\pi\) | |||||||
\(522\) | 1.27259 | 0.0556997 | ||||||||
\(523\) | −40.8787 | −1.78750 | −0.893750 | − | 0.448566i | \(-0.851935\pi\) | ||||
−0.893750 | + | 0.448566i | \(0.851935\pi\) | |||||||
\(524\) | −11.7830 | −0.514743 | ||||||||
\(525\) | −5.78347 | −0.252411 | ||||||||
\(526\) | −7.11999 | −0.310446 | ||||||||
\(527\) | −0.946039 | −0.0412101 | ||||||||
\(528\) | 7.72737 | 0.336291 | ||||||||
\(529\) | 25.8012 | 1.12179 | ||||||||
\(530\) | −7.37372 | −0.320294 | ||||||||
\(531\) | −11.6791 | −0.506831 | ||||||||
\(532\) | 13.8536 | 0.600631 | ||||||||
\(533\) | 0.944581 | 0.0409144 | ||||||||
\(534\) | 5.94252 | 0.257158 | ||||||||
\(535\) | −51.2970 | −2.21776 | ||||||||
\(536\) | −22.8950 | −0.988915 | ||||||||
\(537\) | 10.9759 | 0.473646 | ||||||||
\(538\) | 3.32070 | 0.143166 | ||||||||
\(539\) | −2.62788 | −0.113191 | ||||||||
\(540\) | −5.96964 | −0.256892 | ||||||||
\(541\) | −41.8318 | −1.79849 | −0.899244 | − | 0.437448i | \(-0.855883\pi\) | ||||
−0.899244 | + | 0.437448i | \(0.855883\pi\) | |||||||
\(542\) | −8.57769 | −0.368443 | ||||||||
\(543\) | 5.82133 | 0.249817 | ||||||||
\(544\) | 9.38452 | 0.402358 | ||||||||
\(545\) | −57.0542 | −2.44393 | ||||||||
\(546\) | 0.264681 | 0.0113273 | ||||||||
\(547\) | 4.79672 | 0.205093 | 0.102546 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102546 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(548\) | −30.2859 | −1.29375 | ||||||||
\(549\) | 11.9493 | 0.509984 | ||||||||
\(550\) | 6.48565 | 0.276549 | ||||||||
\(551\) | 22.7260 | 0.968160 | ||||||||
\(552\) | −11.3815 | −0.484429 | ||||||||
\(553\) | −5.65341 | −0.240407 | ||||||||
\(554\) | 7.66215 | 0.325533 | ||||||||
\(555\) | −38.0316 | −1.61435 | ||||||||
\(556\) | 5.38957 | 0.228569 | ||||||||
\(557\) | −22.6413 | −0.959343 | −0.479672 | − | 0.877448i | \(-0.659244\pi\) | ||||
−0.479672 | + | 0.877448i | \(0.659244\pi\) | |||||||
\(558\) | −0.194156 | −0.00821930 | ||||||||
\(559\) | 4.28784 | 0.181356 | ||||||||
\(560\) | −9.65619 | −0.408048 | ||||||||
\(561\) | −5.46415 | −0.230696 | ||||||||
\(562\) | −0.732823 | −0.0309123 | ||||||||
\(563\) | −36.8755 | −1.55412 | −0.777058 | − | 0.629429i | \(-0.783289\pi\) | ||||
−0.777058 | + | 0.629429i | \(0.783289\pi\) | |||||||
\(564\) | 17.2543 | 0.726536 | ||||||||
\(565\) | 57.7627 | 2.43009 | ||||||||
\(566\) | 2.78578 | 0.117095 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 21.7831 | 0.913997 | ||||||||
\(569\) | −27.4885 | −1.15238 | −0.576190 | − | 0.817316i | \(-0.695461\pi\) | ||||
−0.576190 | + | 0.817316i | \(0.695461\pi\) | |||||||
\(570\) | 10.6791 | 0.447298 | ||||||||
\(571\) | −32.7613 | −1.37102 | −0.685510 | − | 0.728064i | \(-0.740421\pi\) | ||||
−0.685510 | + | 0.728064i | \(0.740421\pi\) | |||||||
\(572\) | 2.96303 | 0.123891 | ||||||||
\(573\) | −10.4215 | −0.435365 | ||||||||
\(574\) | −0.649886 | −0.0271257 | ||||||||
\(575\) | 40.4021 | 1.68488 | ||||||||
\(576\) | −3.95508 | −0.164795 | ||||||||
\(577\) | −25.6633 | −1.06838 | −0.534189 | − | 0.845365i | \(-0.679383\pi\) | ||||
−0.534189 | + | 0.845365i | \(0.679383\pi\) | |||||||
\(578\) | 5.40954 | 0.225007 | ||||||||
\(579\) | −1.61781 | −0.0672339 | ||||||||
\(580\) | −17.8023 | −0.739201 | ||||||||
\(581\) | 13.6501 | 0.566301 | ||||||||
\(582\) | 5.95667 | 0.246912 | ||||||||
\(583\) | 13.8278 | 0.572688 | ||||||||
\(584\) | 12.8461 | 0.531574 | ||||||||
\(585\) | −2.03677 | −0.0842099 | ||||||||
\(586\) | −1.43156 | −0.0591371 | ||||||||
\(587\) | 22.0720 | 0.911008 | 0.455504 | − | 0.890234i | \(-0.349459\pi\) | ||||
0.455504 | + | 0.890234i | \(0.349459\pi\) | |||||||
\(588\) | 1.81790 | 0.0749688 | ||||||||
\(589\) | −3.46726 | −0.142866 | ||||||||
\(590\) | −16.3663 | −0.673789 | ||||||||
\(591\) | 6.35580 | 0.261443 | ||||||||
\(592\) | −34.0559 | −1.39969 | ||||||||
\(593\) | 28.2075 | 1.15834 | 0.579172 | − | 0.815205i | \(-0.303376\pi\) | ||||
0.579172 | + | 0.815205i | \(0.303376\pi\) | |||||||
\(594\) | −1.12141 | −0.0460121 | ||||||||
\(595\) | 6.82804 | 0.279922 | ||||||||
\(596\) | 16.3493 | 0.669693 | ||||||||
\(597\) | 10.4643 | 0.428276 | ||||||||
\(598\) | −1.84900 | −0.0756114 | ||||||||
\(599\) | −10.0612 | −0.411090 | −0.205545 | − | 0.978648i | \(-0.565897\pi\) | ||||
−0.205545 | + | 0.978648i | \(0.565897\pi\) | |||||||
\(600\) | −9.42263 | −0.384677 | ||||||||
\(601\) | 3.79228 | 0.154690 | 0.0773452 | − | 0.997004i | \(-0.475356\pi\) | ||||
0.0773452 | + | 0.997004i | \(0.475356\pi\) | |||||||
\(602\) | −2.95010 | −0.120237 | ||||||||
\(603\) | −14.0526 | −0.572267 | ||||||||
\(604\) | 5.31211 | 0.216147 | ||||||||
\(605\) | 13.4448 | 0.546608 | ||||||||
\(606\) | 1.35103 | 0.0548818 | ||||||||
\(607\) | −0.700709 | −0.0284409 | −0.0142205 | − | 0.999899i | \(-0.504527\pi\) | ||||
−0.0142205 | + | 0.999899i | \(0.504527\pi\) | |||||||
\(608\) | 34.3946 | 1.39488 | ||||||||
\(609\) | 2.98214 | 0.120842 | ||||||||
\(610\) | 16.7449 | 0.677980 | ||||||||
\(611\) | 5.88694 | 0.238160 | ||||||||
\(612\) | 3.77995 | 0.152795 | ||||||||
\(613\) | −2.33635 | −0.0943642 | −0.0471821 | − | 0.998886i | \(-0.515024\pi\) | ||||
−0.0471821 | + | 0.998886i | \(0.515024\pi\) | |||||||
\(614\) | −2.93685 | −0.118522 | ||||||||
\(615\) | 5.00100 | 0.201660 | ||||||||
\(616\) | −4.28144 | −0.172504 | ||||||||
\(617\) | 5.63267 | 0.226763 | 0.113381 | − | 0.993552i | \(-0.463832\pi\) | ||||
0.113381 | + | 0.993552i | \(0.463832\pi\) | |||||||
\(618\) | −4.95800 | −0.199440 | ||||||||
\(619\) | 12.6129 | 0.506957 | 0.253478 | − | 0.967341i | \(-0.418425\pi\) | ||||
0.253478 | + | 0.967341i | \(0.418425\pi\) | |||||||
\(620\) | 2.71606 | 0.109080 | ||||||||
\(621\) | −6.98579 | −0.280330 | ||||||||
\(622\) | −2.99114 | −0.119934 | ||||||||
\(623\) | 13.9255 | 0.557913 | ||||||||
\(624\) | −1.82385 | −0.0730124 | ||||||||
\(625\) | −20.4689 | −0.818754 | ||||||||
\(626\) | 4.05515 | 0.162076 | ||||||||
\(627\) | −20.0263 | −0.799772 | ||||||||
\(628\) | −30.5964 | −1.22093 | ||||||||
\(629\) | 24.0814 | 0.960190 | ||||||||
\(630\) | 1.40133 | 0.0558302 | ||||||||
\(631\) | −16.6390 | −0.662386 | −0.331193 | − | 0.943563i | \(-0.607451\pi\) | ||||
−0.331193 | + | 0.943563i | \(0.607451\pi\) | |||||||
\(632\) | −9.21074 | −0.366384 | ||||||||
\(633\) | 16.7420 | 0.665436 | ||||||||
\(634\) | 3.33719 | 0.132537 | ||||||||
\(635\) | −21.9817 | −0.872317 | ||||||||
\(636\) | −9.56569 | −0.379304 | ||||||||
\(637\) | 0.620243 | 0.0245749 | ||||||||
\(638\) | −3.34421 | −0.132399 | ||||||||
\(639\) | 13.3701 | 0.528913 | ||||||||
\(640\) | −35.1841 | −1.39077 | ||||||||
\(641\) | −9.32823 | −0.368443 | −0.184221 | − | 0.982885i | \(-0.558976\pi\) | ||||
−0.184221 | + | 0.982885i | \(0.558976\pi\) | |||||||
\(642\) | 6.66612 | 0.263091 | ||||||||
\(643\) | 33.5044 | 1.32128 | 0.660642 | − | 0.750701i | \(-0.270284\pi\) | ||||
0.660642 | + | 0.750701i | \(0.270284\pi\) | |||||||
\(644\) | −12.6994 | −0.500428 | ||||||||
\(645\) | 22.7015 | 0.893872 | ||||||||
\(646\) | −6.76195 | −0.266045 | ||||||||
\(647\) | −28.9348 | −1.13754 | −0.568772 | − | 0.822495i | \(-0.692581\pi\) | ||||
−0.568772 | + | 0.822495i | \(0.692581\pi\) | |||||||
\(648\) | 1.62924 | 0.0640025 | ||||||||
\(649\) | 30.6913 | 1.20474 | ||||||||
\(650\) | −1.53077 | −0.0600418 | ||||||||
\(651\) | −0.454979 | −0.0178321 | ||||||||
\(652\) | 40.9349 | 1.60313 | ||||||||
\(653\) | 35.8792 | 1.40406 | 0.702031 | − | 0.712147i | \(-0.252277\pi\) | ||||
0.702031 | + | 0.712147i | \(0.252277\pi\) | |||||||
\(654\) | 7.41427 | 0.289921 | ||||||||
\(655\) | −21.2846 | −0.831659 | ||||||||
\(656\) | 4.47820 | 0.174844 | ||||||||
\(657\) | 7.88472 | 0.307612 | ||||||||
\(658\) | −4.05030 | −0.157897 | ||||||||
\(659\) | 17.7897 | 0.692987 | 0.346493 | − | 0.938052i | \(-0.387372\pi\) | ||||
0.346493 | + | 0.938052i | \(0.387372\pi\) | |||||||
\(660\) | 15.6875 | 0.610635 | ||||||||
\(661\) | −11.1418 | −0.433367 | −0.216684 | − | 0.976242i | \(-0.569524\pi\) | ||||
−0.216684 | + | 0.976242i | \(0.569524\pi\) | |||||||
\(662\) | −3.12777 | −0.121564 | ||||||||
\(663\) | 1.28967 | 0.0500867 | ||||||||
\(664\) | 22.2392 | 0.863049 | ||||||||
\(665\) | 25.0250 | 0.970427 | ||||||||
\(666\) | 4.94226 | 0.191509 | ||||||||
\(667\) | −20.8326 | −0.806642 | ||||||||
\(668\) | −14.5762 | −0.563972 | ||||||||
\(669\) | −9.81900 | −0.379624 | ||||||||
\(670\) | −19.6923 | −0.760780 | ||||||||
\(671\) | −31.4013 | −1.21223 | ||||||||
\(672\) | 4.51331 | 0.174105 | ||||||||
\(673\) | 49.9492 | 1.92540 | 0.962700 | − | 0.270572i | \(-0.0872129\pi\) | ||||
0.962700 | + | 0.270572i | \(0.0872129\pi\) | |||||||
\(674\) | −1.68738 | −0.0649955 | ||||||||
\(675\) | −5.78347 | −0.222606 | ||||||||
\(676\) | 22.9333 | 0.882050 | ||||||||
\(677\) | 20.5892 | 0.791306 | 0.395653 | − | 0.918400i | \(-0.370518\pi\) | ||||
0.395653 | + | 0.918400i | \(0.370518\pi\) | |||||||
\(678\) | −7.50634 | −0.288279 | ||||||||
\(679\) | 13.9587 | 0.535684 | ||||||||
\(680\) | 11.1245 | 0.426605 | ||||||||
\(681\) | −18.1308 | −0.694774 | ||||||||
\(682\) | 0.510220 | 0.0195373 | ||||||||
\(683\) | 26.0306 | 0.996032 | 0.498016 | − | 0.867168i | \(-0.334062\pi\) | ||||
0.498016 | + | 0.867168i | \(0.334062\pi\) | |||||||
\(684\) | 13.8536 | 0.529707 | ||||||||
\(685\) | −54.7080 | −2.09029 | ||||||||
\(686\) | −0.426737 | −0.0162929 | ||||||||
\(687\) | −16.5276 | −0.630568 | ||||||||
\(688\) | 20.3284 | 0.775012 | ||||||||
\(689\) | −3.26369 | −0.124337 | ||||||||
\(690\) | −9.78937 | −0.372675 | ||||||||
\(691\) | −21.3915 | −0.813770 | −0.406885 | − | 0.913479i | \(-0.633385\pi\) | ||||
−0.406885 | + | 0.913479i | \(0.633385\pi\) | |||||||
\(692\) | −21.9599 | −0.834789 | ||||||||
\(693\) | −2.62788 | −0.0998248 | ||||||||
\(694\) | −2.90543 | −0.110289 | ||||||||
\(695\) | 9.73564 | 0.369294 | ||||||||
\(696\) | 4.85861 | 0.184165 | ||||||||
\(697\) | −3.16661 | −0.119944 | ||||||||
\(698\) | 0.0352527 | 0.00133433 | ||||||||
\(699\) | 15.6411 | 0.591600 | ||||||||
\(700\) | −10.5137 | −0.397382 | ||||||||
\(701\) | −4.65980 | −0.175998 | −0.0879991 | − | 0.996121i | \(-0.528047\pi\) | ||||
−0.0879991 | + | 0.996121i | \(0.528047\pi\) | |||||||
\(702\) | 0.264681 | 0.00998973 | ||||||||
\(703\) | 88.2592 | 3.32876 | ||||||||
\(704\) | 10.3935 | 0.391718 | ||||||||
\(705\) | 31.1678 | 1.17385 | ||||||||
\(706\) | 8.69356 | 0.327186 | ||||||||
\(707\) | 3.16595 | 0.119068 | ||||||||
\(708\) | −21.2314 | −0.797926 | ||||||||
\(709\) | −28.3389 | −1.06429 | −0.532145 | − | 0.846653i | \(-0.678614\pi\) | ||||
−0.532145 | + | 0.846653i | \(0.678614\pi\) | |||||||
\(710\) | 18.7359 | 0.703145 | ||||||||
\(711\) | −5.65341 | −0.212019 | ||||||||
\(712\) | 22.6879 | 0.850266 | ||||||||
\(713\) | 3.17839 | 0.119032 | ||||||||
\(714\) | −0.887314 | −0.0332069 | ||||||||
\(715\) | 5.35238 | 0.200168 | ||||||||
\(716\) | 19.9531 | 0.745682 | ||||||||
\(717\) | 24.7485 | 0.924251 | ||||||||
\(718\) | 2.85705 | 0.106624 | ||||||||
\(719\) | −33.3346 | −1.24317 | −0.621585 | − | 0.783346i | \(-0.713511\pi\) | ||||
−0.621585 | + | 0.783346i | \(0.713511\pi\) | |||||||
\(720\) | −9.65619 | −0.359865 | ||||||||
\(721\) | −11.6184 | −0.432692 | ||||||||
\(722\) | −16.6748 | −0.620570 | ||||||||
\(723\) | 26.4849 | 0.984986 | ||||||||
\(724\) | 10.5826 | 0.393298 | ||||||||
\(725\) | −17.2471 | −0.640542 | ||||||||
\(726\) | −1.74717 | −0.0648435 | ||||||||
\(727\) | −0.668594 | −0.0247968 | −0.0123984 | − | 0.999923i | \(-0.503947\pi\) | ||||
−0.0123984 | + | 0.999923i | \(0.503947\pi\) | |||||||
\(728\) | 1.01052 | 0.0374525 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.0491 | 0.408944 | ||||||||
\(731\) | −14.3745 | −0.531661 | ||||||||
\(732\) | 21.7226 | 0.802890 | ||||||||
\(733\) | −8.29214 | −0.306277 | −0.153139 | − | 0.988205i | \(-0.548938\pi\) | ||||
−0.153139 | + | 0.988205i | \(0.548938\pi\) | |||||||
\(734\) | −4.96820 | −0.183380 | ||||||||
\(735\) | 3.28382 | 0.121125 | ||||||||
\(736\) | −31.5290 | −1.16217 | ||||||||
\(737\) | 36.9286 | 1.36028 | ||||||||
\(738\) | −0.649886 | −0.0239226 | ||||||||
\(739\) | −12.3459 | −0.454151 | −0.227076 | − | 0.973877i | \(-0.572916\pi\) | ||||
−0.227076 | + | 0.973877i | \(0.572916\pi\) | |||||||
\(740\) | −69.1375 | −2.54154 | ||||||||
\(741\) | 4.72669 | 0.173639 | ||||||||
\(742\) | 2.24547 | 0.0824338 | ||||||||
\(743\) | −14.6361 | −0.536947 | −0.268474 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268474 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(744\) | −0.741269 | −0.0271762 | ||||||||
\(745\) | 29.5331 | 1.08201 | ||||||||
\(746\) | −13.7377 | −0.502971 | ||||||||
\(747\) | 13.6501 | 0.499430 | ||||||||
\(748\) | −9.93325 | −0.363196 | ||||||||
\(749\) | 15.6211 | 0.570784 | ||||||||
\(750\) | −1.09789 | −0.0400893 | ||||||||
\(751\) | 31.8082 | 1.16070 | 0.580349 | − | 0.814368i | \(-0.302916\pi\) | ||||
0.580349 | + | 0.814368i | \(0.302916\pi\) | |||||||
\(752\) | 27.9096 | 1.01776 | ||||||||
\(753\) | −9.59598 | −0.349697 | ||||||||
\(754\) | 0.789315 | 0.0287452 | ||||||||
\(755\) | 9.59572 | 0.349224 | ||||||||
\(756\) | 1.81790 | 0.0661162 | ||||||||
\(757\) | −3.59738 | −0.130749 | −0.0653745 | − | 0.997861i | \(-0.520824\pi\) | ||||
−0.0653745 | + | 0.997861i | \(0.520824\pi\) | |||||||
\(758\) | 11.5509 | 0.419546 | ||||||||
\(759\) | 18.3578 | 0.666346 | ||||||||
\(760\) | 40.7716 | 1.47894 | ||||||||
\(761\) | 44.5049 | 1.61330 | 0.806651 | − | 0.591028i | \(-0.201278\pi\) | ||||
0.806651 | + | 0.591028i | \(0.201278\pi\) | |||||||
\(762\) | 2.85655 | 0.103482 | ||||||||
\(763\) | 17.3743 | 0.628994 | ||||||||
\(764\) | −18.9452 | −0.685414 | ||||||||
\(765\) | 6.82804 | 0.246868 | ||||||||
\(766\) | −0.426737 | −0.0154186 | ||||||||
\(767\) | −7.24390 | −0.261562 | ||||||||
\(768\) | −3.33793 | −0.120447 | ||||||||
\(769\) | −15.9647 | −0.575703 | −0.287851 | − | 0.957675i | \(-0.592941\pi\) | ||||
−0.287851 | + | 0.957675i | \(0.592941\pi\) | |||||||
\(770\) | −3.68252 | −0.132709 | ||||||||
\(771\) | −14.8391 | −0.534418 | ||||||||
\(772\) | −2.94101 | −0.105849 | ||||||||
\(773\) | 25.3571 | 0.912030 | 0.456015 | − | 0.889972i | \(-0.349276\pi\) | ||||
0.456015 | + | 0.889972i | \(0.349276\pi\) | |||||||
\(774\) | −2.95010 | −0.106039 | ||||||||
\(775\) | 2.63136 | 0.0945212 | ||||||||
\(776\) | 22.7419 | 0.816388 | ||||||||
\(777\) | 11.5815 | 0.415484 | ||||||||
\(778\) | 6.13469 | 0.219939 | ||||||||
\(779\) | −11.6057 | −0.415818 | ||||||||
\(780\) | −3.70263 | −0.132575 | ||||||||
\(781\) | −35.1350 | −1.25723 | ||||||||
\(782\) | 6.19858 | 0.221661 | ||||||||
\(783\) | 2.98214 | 0.106573 | ||||||||
\(784\) | 2.94054 | 0.105019 | ||||||||
\(785\) | −55.2688 | −1.97263 | ||||||||
\(786\) | 2.76597 | 0.0986588 | ||||||||
\(787\) | −32.7435 | −1.16718 | −0.583590 | − | 0.812048i | \(-0.698352\pi\) | ||||
−0.583590 | + | 0.812048i | \(0.698352\pi\) | |||||||
\(788\) | 11.5542 | 0.411601 | ||||||||
\(789\) | −16.6847 | −0.593992 | ||||||||
\(790\) | −7.92227 | −0.281862 | ||||||||
\(791\) | −17.5901 | −0.625432 | ||||||||
\(792\) | −4.28144 | −0.152134 | ||||||||
\(793\) | 7.41148 | 0.263189 | ||||||||
\(794\) | −15.2354 | −0.540683 | ||||||||
\(795\) | −17.2793 | −0.612834 | ||||||||
\(796\) | 19.0230 | 0.674253 | ||||||||
\(797\) | −8.12071 | −0.287650 | −0.143825 | − | 0.989603i | \(-0.545940\pi\) | ||||
−0.143825 | + | 0.989603i | \(0.545940\pi\) | |||||||
\(798\) | −3.25203 | −0.115121 | ||||||||
\(799\) | −19.7353 | −0.698186 | ||||||||
\(800\) | −26.1026 | −0.922865 | ||||||||
\(801\) | 13.9255 | 0.492033 | ||||||||
\(802\) | −0.544583 | −0.0192299 | ||||||||
\(803\) | −20.7201 | −0.731196 | ||||||||
\(804\) | −25.5462 | −0.900944 | ||||||||
\(805\) | −22.9401 | −0.808531 | ||||||||
\(806\) | −0.120424 | −0.00424176 | ||||||||
\(807\) | 7.78161 | 0.273926 | ||||||||
\(808\) | 5.15809 | 0.181461 | ||||||||
\(809\) | 40.3439 | 1.41842 | 0.709208 | − | 0.705000i | \(-0.249053\pi\) | ||||
0.709208 | + | 0.705000i | \(0.249053\pi\) | |||||||
\(810\) | 1.40133 | 0.0492376 | ||||||||
\(811\) | 35.4070 | 1.24331 | 0.621653 | − | 0.783292i | \(-0.286461\pi\) | ||||
0.621653 | + | 0.783292i | \(0.286461\pi\) | |||||||
\(812\) | 5.42122 | 0.190248 | ||||||||
\(813\) | −20.1007 | −0.704961 | ||||||||
\(814\) | −12.9877 | −0.455217 | ||||||||
\(815\) | 73.9442 | 2.59015 | ||||||||
\(816\) | 6.11425 | 0.214042 | ||||||||
\(817\) | −52.6830 | −1.84315 | ||||||||
\(818\) | 9.58072 | 0.334982 | ||||||||
\(819\) | 0.620243 | 0.0216731 | ||||||||
\(820\) | 9.09129 | 0.317482 | ||||||||
\(821\) | 8.31790 | 0.290297 | 0.145148 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145148 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(822\) | 7.10939 | 0.247968 | ||||||||
\(823\) | 42.7277 | 1.48940 | 0.744698 | − | 0.667402i | \(-0.232594\pi\) | ||||
0.744698 | + | 0.667402i | \(0.232594\pi\) | |||||||
\(824\) | −18.9291 | −0.659427 | ||||||||
\(825\) | 15.1982 | 0.529135 | ||||||||
\(826\) | 4.98391 | 0.173413 | ||||||||
\(827\) | −9.83244 | −0.341908 | −0.170954 | − | 0.985279i | \(-0.554685\pi\) | ||||
−0.170954 | + | 0.985279i | \(0.554685\pi\) | |||||||
\(828\) | −12.6994 | −0.441336 | ||||||||
\(829\) | −3.96124 | −0.137580 | −0.0687898 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687898 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(830\) | 19.1282 | 0.663950 | ||||||||
\(831\) | 17.9552 | 0.622859 | ||||||||
\(832\) | −2.45311 | −0.0850463 | ||||||||
\(833\) | −2.07930 | −0.0720435 | ||||||||
\(834\) | −1.26516 | −0.0438089 | ||||||||
\(835\) | −26.3303 | −0.911198 | ||||||||
\(836\) | −36.4057 | −1.25912 | ||||||||
\(837\) | −0.454979 | −0.0157264 | ||||||||
\(838\) | 11.2221 | 0.387662 | ||||||||
\(839\) | −36.4922 | −1.25985 | −0.629925 | − | 0.776656i | \(-0.716914\pi\) | ||||
−0.629925 | + | 0.776656i | \(0.716914\pi\) | |||||||
\(840\) | 5.35012 | 0.184597 | ||||||||
\(841\) | −20.1068 | −0.693339 | ||||||||
\(842\) | 11.2143 | 0.386469 | ||||||||
\(843\) | −1.71727 | −0.0591460 | ||||||||
\(844\) | 30.4353 | 1.04763 | ||||||||
\(845\) | 41.4264 | 1.42511 | ||||||||
\(846\) | −4.05030 | −0.139252 | ||||||||
\(847\) | −4.09425 | −0.140680 | ||||||||
\(848\) | −15.4730 | −0.531344 | ||||||||
\(849\) | 6.52811 | 0.224044 | ||||||||
\(850\) | 5.13175 | 0.176017 | ||||||||
\(851\) | −80.9060 | −2.77342 | ||||||||
\(852\) | 24.3054 | 0.832691 | ||||||||
\(853\) | −47.9076 | −1.64032 | −0.820162 | − | 0.572132i | \(-0.806117\pi\) | ||||
−0.820162 | + | 0.572132i | \(0.806117\pi\) | |||||||
\(854\) | −5.09921 | −0.174491 | ||||||||
\(855\) | 25.0250 | 0.855837 | ||||||||
\(856\) | 25.4505 | 0.869881 | ||||||||
\(857\) | −4.41416 | −0.150785 | −0.0753925 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753925 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(858\) | −0.695549 | −0.0237456 | ||||||||
\(859\) | 8.86569 | 0.302493 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(860\) | 41.2690 | 1.40726 | ||||||||
\(861\) | −1.52292 | −0.0519010 | ||||||||
\(862\) | 1.45850 | 0.0496765 | ||||||||
\(863\) | 35.3044 | 1.20178 | 0.600888 | − | 0.799333i | \(-0.294814\pi\) | ||||
0.600888 | + | 0.799333i | \(0.294814\pi\) | |||||||
\(864\) | 4.51331 | 0.153546 | ||||||||
\(865\) | −39.6680 | −1.34875 | ||||||||
\(866\) | 1.86874 | 0.0635023 | ||||||||
\(867\) | 12.6765 | 0.430517 | ||||||||
\(868\) | −0.827105 | −0.0280738 | ||||||||
\(869\) | 14.8565 | 0.503971 | ||||||||
\(870\) | 4.17895 | 0.141680 | ||||||||
\(871\) | −8.71604 | −0.295332 | ||||||||
\(872\) | 28.3069 | 0.958593 | ||||||||
\(873\) | 13.9587 | 0.472429 | ||||||||
\(874\) | 22.7180 | 0.768448 | ||||||||
\(875\) | −2.57276 | −0.0869751 | ||||||||
\(876\) | 14.3336 | 0.484287 | ||||||||
\(877\) | 32.4427 | 1.09551 | 0.547757 | − | 0.836638i | \(-0.315482\pi\) | ||||
0.547757 | + | 0.836638i | \(0.315482\pi\) | |||||||
\(878\) | 15.2444 | 0.514475 | ||||||||
\(879\) | −3.35466 | −0.113150 | ||||||||
\(880\) | 25.3753 | 0.855401 | ||||||||
\(881\) | −5.11150 | −0.172211 | −0.0861054 | − | 0.996286i | \(-0.527442\pi\) | ||||
−0.0861054 | + | 0.996286i | \(0.527442\pi\) | |||||||
\(882\) | −0.426737 | −0.0143690 | ||||||||
\(883\) | 15.9059 | 0.535277 | 0.267638 | − | 0.963519i | \(-0.413757\pi\) | ||||
0.267638 | + | 0.963519i | \(0.413757\pi\) | |||||||
\(884\) | 2.34449 | 0.0788537 | ||||||||
\(885\) | −38.3521 | −1.28919 | ||||||||
\(886\) | 14.1000 | 0.473700 | ||||||||
\(887\) | 12.3203 | 0.413674 | 0.206837 | − | 0.978375i | \(-0.433683\pi\) | ||||
0.206837 | + | 0.978375i | \(0.433683\pi\) | |||||||
\(888\) | 18.8690 | 0.633203 | ||||||||
\(889\) | 6.69394 | 0.224508 | ||||||||
\(890\) | 19.5142 | 0.654116 | ||||||||
\(891\) | −2.62788 | −0.0880372 | ||||||||
\(892\) | −17.8499 | −0.597659 | ||||||||
\(893\) | −72.3306 | −2.42045 | ||||||||
\(894\) | −3.83787 | −0.128358 | ||||||||
\(895\) | 36.0429 | 1.20478 | ||||||||
\(896\) | 10.7144 | 0.357943 | ||||||||
\(897\) | −4.33289 | −0.144671 | ||||||||
\(898\) | −13.0196 | −0.434469 | ||||||||
\(899\) | −1.35681 | −0.0452522 | ||||||||
\(900\) | −10.5137 | −0.350458 | ||||||||
\(901\) | 10.9412 | 0.364504 | ||||||||
\(902\) | 1.70782 | 0.0568643 | ||||||||
\(903\) | −6.91315 | −0.230055 | ||||||||
\(904\) | −28.6584 | −0.953165 | ||||||||
\(905\) | 19.1162 | 0.635444 | ||||||||
\(906\) | −1.24698 | −0.0414280 | ||||||||
\(907\) | −14.2200 | −0.472167 | −0.236083 | − | 0.971733i | \(-0.575864\pi\) | ||||
−0.236083 | + | 0.971733i | \(0.575864\pi\) | |||||||
\(908\) | −32.9599 | −1.09381 | ||||||||
\(909\) | 3.16595 | 0.105008 | ||||||||
\(910\) | 0.869163 | 0.0288125 | ||||||||
\(911\) | 40.8990 | 1.35504 | 0.677522 | − | 0.735503i | \(-0.263054\pi\) | ||||
0.677522 | + | 0.735503i | \(0.263054\pi\) | |||||||
\(912\) | 22.4089 | 0.742034 | ||||||||
\(913\) | −35.8708 | −1.18715 | ||||||||
\(914\) | 9.05290 | 0.299443 | ||||||||
\(915\) | 39.2393 | 1.29721 | ||||||||
\(916\) | −30.0455 | −0.992731 | ||||||||
\(917\) | 6.48167 | 0.214044 | ||||||||
\(918\) | −0.887314 | −0.0292857 | ||||||||
\(919\) | 38.6145 | 1.27377 | 0.636887 | − | 0.770957i | \(-0.280222\pi\) | ||||
0.636887 | + | 0.770957i | \(0.280222\pi\) | |||||||
\(920\) | −37.3748 | −1.23221 | ||||||||
\(921\) | −6.88211 | −0.226773 | ||||||||
\(922\) | −6.47163 | −0.213132 | ||||||||
\(923\) | 8.29272 | 0.272958 | ||||||||
\(924\) | −4.77721 | −0.157159 | ||||||||
\(925\) | −66.9813 | −2.20233 | ||||||||
\(926\) | −13.5671 | −0.445842 | ||||||||
\(927\) | −11.6184 | −0.381598 | ||||||||
\(928\) | 13.4593 | 0.441824 | ||||||||
\(929\) | −5.47883 | −0.179754 | −0.0898772 | − | 0.995953i | \(-0.528647\pi\) | ||||
−0.0898772 | + | 0.995953i | \(0.528647\pi\) | |||||||
\(930\) | −0.637575 | −0.0209069 | ||||||||
\(931\) | −7.62070 | −0.249758 | ||||||||
\(932\) | 28.4338 | 0.931381 | ||||||||
\(933\) | −7.00933 | −0.229475 | ||||||||
\(934\) | 2.25120 | 0.0736616 | ||||||||
\(935\) | −17.9433 | −0.586808 | ||||||||
\(936\) | 1.01052 | 0.0330300 | ||||||||
\(937\) | −33.8209 | −1.10488 | −0.552441 | − | 0.833552i | \(-0.686303\pi\) | ||||
−0.552441 | + | 0.833552i | \(0.686303\pi\) | |||||||
\(938\) | 5.99677 | 0.195801 | ||||||||
\(939\) | 9.50269 | 0.310109 | ||||||||
\(940\) | 56.6599 | 1.84804 | ||||||||
\(941\) | 21.1606 | 0.689816 | 0.344908 | − | 0.938637i | \(-0.387910\pi\) | ||||
0.344908 | + | 0.938637i | \(0.387910\pi\) | |||||||
\(942\) | 7.18226 | 0.234011 | ||||||||
\(943\) | 10.6388 | 0.346447 | ||||||||
\(944\) | −34.3429 | −1.11777 | ||||||||
\(945\) | 3.28382 | 0.106823 | ||||||||
\(946\) | 7.75249 | 0.252055 | ||||||||
\(947\) | 18.4744 | 0.600337 | 0.300168 | − | 0.953886i | \(-0.402957\pi\) | ||||
0.300168 | + | 0.953886i | \(0.402957\pi\) | |||||||
\(948\) | −10.2773 | −0.333791 | ||||||||
\(949\) | 4.89044 | 0.158750 | ||||||||
\(950\) | 18.8080 | 0.610213 | ||||||||
\(951\) | 7.82025 | 0.253589 | ||||||||
\(952\) | −3.38767 | −0.109795 | ||||||||
\(953\) | −8.52192 | −0.276052 | −0.138026 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138026 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(954\) | 2.24547 | 0.0726998 | ||||||||
\(955\) | −34.2224 | −1.10741 | ||||||||
\(956\) | 44.9902 | 1.45509 | ||||||||
\(957\) | −7.83670 | −0.253325 | ||||||||
\(958\) | 13.5681 | 0.438365 | ||||||||
\(959\) | 16.6599 | 0.537976 | ||||||||
\(960\) | −12.9878 | −0.419178 | ||||||||
\(961\) | −30.7930 | −0.993322 | ||||||||
\(962\) | 3.06540 | 0.0988325 | ||||||||
\(963\) | 15.6211 | 0.503384 | ||||||||
\(964\) | 48.1469 | 1.55071 | ||||||||
\(965\) | −5.31259 | −0.171018 | ||||||||
\(966\) | 2.98109 | 0.0959151 | ||||||||
\(967\) | 2.15984 | 0.0694557 | 0.0347278 | − | 0.999397i | \(-0.488944\pi\) | ||||
0.0347278 | + | 0.999397i | \(0.488944\pi\) | |||||||
\(968\) | −6.67051 | −0.214398 | ||||||||
\(969\) | −15.8457 | −0.509038 | ||||||||
\(970\) | 19.5606 | 0.628054 | ||||||||
\(971\) | −31.2026 | −1.00134 | −0.500670 | − | 0.865638i | \(-0.666913\pi\) | ||||
−0.500670 | + | 0.865638i | \(0.666913\pi\) | |||||||
\(972\) | 1.81790 | 0.0583090 | ||||||||
\(973\) | −2.96473 | −0.0950449 | ||||||||
\(974\) | −0.237163 | −0.00759919 | ||||||||
\(975\) | −3.58716 | −0.114881 | ||||||||
\(976\) | 35.1374 | 1.12472 | ||||||||
\(977\) | −25.1859 | −0.805768 | −0.402884 | − | 0.915251i | \(-0.631992\pi\) | ||||
−0.402884 | + | 0.915251i | \(0.631992\pi\) | |||||||
\(978\) | −9.60915 | −0.307267 | ||||||||
\(979\) | −36.5945 | −1.16957 | ||||||||
\(980\) | 5.96964 | 0.190693 | ||||||||
\(981\) | 17.3743 | 0.554720 | ||||||||
\(982\) | −6.18050 | −0.197228 | ||||||||
\(983\) | −41.0778 | −1.31018 | −0.655089 | − | 0.755552i | \(-0.727369\pi\) | ||||
−0.655089 | + | 0.755552i | \(0.727369\pi\) | |||||||
\(984\) | −2.48120 | −0.0790977 | ||||||||
\(985\) | 20.8713 | 0.665015 | ||||||||
\(986\) | −2.64609 | −0.0842688 | ||||||||
\(987\) | −9.49134 | −0.302113 | ||||||||
\(988\) | 8.59262 | 0.273368 | ||||||||
\(989\) | 48.2938 | 1.53565 | ||||||||
\(990\) | −3.68252 | −0.117038 | ||||||||
\(991\) | −22.6102 | −0.718235 | −0.359118 | − | 0.933292i | \(-0.616922\pi\) | ||||
−0.359118 | + | 0.933292i | \(0.616922\pi\) | |||||||
\(992\) | −2.05346 | −0.0651975 | ||||||||
\(993\) | −7.32951 | −0.232595 | ||||||||
\(994\) | −5.70551 | −0.180968 | ||||||||
\(995\) | 34.3629 | 1.08938 | ||||||||
\(996\) | 24.8144 | 0.786275 | ||||||||
\(997\) | 39.2121 | 1.24186 | 0.620930 | − | 0.783866i | \(-0.286755\pi\) | ||||
0.620930 | + | 0.783866i | \(0.286755\pi\) | |||||||
\(998\) | −7.99064 | −0.252939 | ||||||||
\(999\) | 11.5815 | 0.366423 |
(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 | 8043.2.a.o.1.19 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.o.1.19 | ✓ | 41 | 1.1 | even | 1 | trivial |