Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53156 | −1.79008 | −0.895041 | − | 0.445984i | \(-0.852854\pi\) | ||||
−0.895041 | + | 0.445984i | \(0.852854\pi\) | |||||||
\(3\) | 1.58470 | 0.914924 | 0.457462 | − | 0.889229i | \(-0.348759\pi\) | ||||
0.457462 | + | 0.889229i | \(0.348759\pi\) | |||||||
\(4\) | 4.40878 | 2.20439 | ||||||||
\(5\) | 2.52136 | 1.12759 | 0.563793 | − | 0.825916i | \(-0.309342\pi\) | ||||
0.563793 | + | 0.825916i | \(0.309342\pi\) | |||||||
\(6\) | −4.01175 | −1.63779 | ||||||||
\(7\) | −1.30202 | −0.492117 | −0.246058 | − | 0.969255i | \(-0.579136\pi\) | ||||
−0.246058 | + | 0.969255i | \(0.579136\pi\) | |||||||
\(8\) | −6.09798 | −2.15596 | ||||||||
\(9\) | −0.488741 | −0.162914 | ||||||||
\(10\) | −6.38296 | −2.01847 | ||||||||
\(11\) | −3.27822 | −0.988422 | −0.494211 | − | 0.869342i | \(-0.664543\pi\) | ||||
−0.494211 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(12\) | 6.98658 | 2.01685 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.29614 | 0.880929 | ||||||||
\(15\) | 3.99558 | 1.03166 | ||||||||
\(16\) | 6.61981 | 1.65495 | ||||||||
\(17\) | 6.15331 | 1.49240 | 0.746199 | − | 0.665723i | \(-0.231877\pi\) | ||||
0.746199 | + | 0.665723i | \(0.231877\pi\) | |||||||
\(18\) | 1.23728 | 0.291629 | ||||||||
\(19\) | 3.28802 | 0.754323 | 0.377162 | − | 0.926147i | \(-0.376900\pi\) | ||||
0.377162 | + | 0.926147i | \(0.376900\pi\) | |||||||
\(20\) | 11.1161 | 2.48564 | ||||||||
\(21\) | −2.06330 | −0.450250 | ||||||||
\(22\) | 8.29901 | 1.76936 | ||||||||
\(23\) | −2.96765 | −0.618797 | −0.309398 | − | 0.950933i | \(-0.600128\pi\) | ||||
−0.309398 | + | 0.950933i | \(0.600128\pi\) | |||||||
\(24\) | −9.66343 | −1.97254 | ||||||||
\(25\) | 1.35725 | 0.271449 | ||||||||
\(26\) | −2.53156 | −0.496479 | ||||||||
\(27\) | −5.52859 | −1.06398 | ||||||||
\(28\) | −5.74032 | −1.08482 | ||||||||
\(29\) | −6.10366 | −1.13342 | −0.566711 | − | 0.823917i | \(-0.691784\pi\) | ||||
−0.566711 | + | 0.823917i | \(0.691784\pi\) | |||||||
\(30\) | −10.1151 | −1.84675 | ||||||||
\(31\) | 5.90133 | 1.05991 | 0.529955 | − | 0.848026i | \(-0.322209\pi\) | ||||
0.529955 | + | 0.848026i | \(0.322209\pi\) | |||||||
\(32\) | −4.56248 | −0.806539 | ||||||||
\(33\) | −5.19499 | −0.904331 | ||||||||
\(34\) | −15.5775 | −2.67151 | ||||||||
\(35\) | −3.28286 | −0.554904 | ||||||||
\(36\) | −2.15475 | −0.359125 | ||||||||
\(37\) | 1.03524 | 0.170192 | 0.0850962 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850962 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(38\) | −8.32381 | −1.35030 | ||||||||
\(39\) | 1.58470 | 0.253754 | ||||||||
\(40\) | −15.3752 | −2.43103 | ||||||||
\(41\) | −9.62322 | −1.50290 | −0.751448 | − | 0.659793i | \(-0.770644\pi\) | ||||
−0.751448 | + | 0.659793i | \(0.770644\pi\) | |||||||
\(42\) | 5.22337 | 0.805984 | ||||||||
\(43\) | −4.86241 | −0.741510 | −0.370755 | − | 0.928731i | \(-0.620901\pi\) | ||||
−0.370755 | + | 0.928731i | \(0.620901\pi\) | |||||||
\(44\) | −14.4530 | −2.17887 | ||||||||
\(45\) | −1.23229 | −0.183699 | ||||||||
\(46\) | 7.51276 | 1.10770 | ||||||||
\(47\) | −4.95938 | −0.723399 | −0.361700 | − | 0.932295i | \(-0.617803\pi\) | ||||
−0.361700 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(48\) | 10.4904 | 1.51416 | ||||||||
\(49\) | −5.30475 | −0.757821 | ||||||||
\(50\) | −3.43595 | −0.485917 | ||||||||
\(51\) | 9.75113 | 1.36543 | ||||||||
\(52\) | 4.40878 | 0.611388 | ||||||||
\(53\) | −4.95420 | −0.680512 | −0.340256 | − | 0.940333i | \(-0.610514\pi\) | ||||
−0.340256 | + | 0.940333i | \(0.610514\pi\) | |||||||
\(54\) | 13.9959 | 1.90461 | ||||||||
\(55\) | −8.26558 | −1.11453 | ||||||||
\(56\) | 7.93968 | 1.06098 | ||||||||
\(57\) | 5.21051 | 0.690149 | ||||||||
\(58\) | 15.4518 | 2.02892 | ||||||||
\(59\) | 9.49507 | 1.23615 | 0.618076 | − | 0.786118i | \(-0.287912\pi\) | ||||
0.618076 | + | 0.786118i | \(0.287912\pi\) | |||||||
\(60\) | 17.6157 | 2.27417 | ||||||||
\(61\) | −10.6112 | −1.35863 | −0.679314 | − | 0.733848i | \(-0.737723\pi\) | ||||
−0.679314 | + | 0.733848i | \(0.737723\pi\) | |||||||
\(62\) | −14.9396 | −1.89733 | ||||||||
\(63\) | 0.636350 | 0.0801725 | ||||||||
\(64\) | −1.68945 | −0.211181 | ||||||||
\(65\) | 2.52136 | 0.312736 | ||||||||
\(66\) | 13.1514 | 1.61883 | ||||||||
\(67\) | −11.3374 | −1.38508 | −0.692541 | − | 0.721378i | \(-0.743509\pi\) | ||||
−0.692541 | + | 0.721378i | \(0.743509\pi\) | |||||||
\(68\) | 27.1286 | 3.28983 | ||||||||
\(69\) | −4.70281 | −0.566152 | ||||||||
\(70\) | 8.31074 | 0.993323 | ||||||||
\(71\) | −5.71104 | −0.677776 | −0.338888 | − | 0.940827i | \(-0.610051\pi\) | ||||
−0.338888 | + | 0.940827i | \(0.610051\pi\) | |||||||
\(72\) | 2.98033 | 0.351235 | ||||||||
\(73\) | 1.14637 | 0.134172 | 0.0670861 | − | 0.997747i | \(-0.478630\pi\) | ||||
0.0670861 | + | 0.997747i | \(0.478630\pi\) | |||||||
\(74\) | −2.62077 | −0.304658 | ||||||||
\(75\) | 2.15082 | 0.248356 | ||||||||
\(76\) | 14.4962 | 1.66282 | ||||||||
\(77\) | 4.26831 | 0.486419 | ||||||||
\(78\) | −4.01175 | −0.454241 | ||||||||
\(79\) | 7.40174 | 0.832761 | 0.416380 | − | 0.909191i | \(-0.363298\pi\) | ||||
0.416380 | + | 0.909191i | \(0.363298\pi\) | |||||||
\(80\) | 16.6909 | 1.86610 | ||||||||
\(81\) | −7.29491 | −0.810546 | ||||||||
\(82\) | 24.3617 | 2.69030 | ||||||||
\(83\) | 0.278442 | 0.0305629 | 0.0152815 | − | 0.999883i | \(-0.495136\pi\) | ||||
0.0152815 | + | 0.999883i | \(0.495136\pi\) | |||||||
\(84\) | −9.09666 | −0.992527 | ||||||||
\(85\) | 15.5147 | 1.68281 | ||||||||
\(86\) | 12.3095 | 1.32736 | ||||||||
\(87\) | −9.67244 | −1.03699 | ||||||||
\(88\) | 19.9905 | 2.13100 | ||||||||
\(89\) | 2.91764 | 0.309270 | 0.154635 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154635 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(90\) | 3.11961 | 0.328836 | ||||||||
\(91\) | −1.30202 | −0.136489 | ||||||||
\(92\) | −13.0837 | −1.36407 | ||||||||
\(93\) | 9.35182 | 0.969738 | ||||||||
\(94\) | 12.5549 | 1.29494 | ||||||||
\(95\) | 8.29028 | 0.850564 | ||||||||
\(96\) | −7.23013 | −0.737922 | ||||||||
\(97\) | 4.95000 | 0.502596 | 0.251298 | − | 0.967910i | \(-0.419143\pi\) | ||||
0.251298 | + | 0.967910i | \(0.419143\pi\) | |||||||
\(98\) | 13.4293 | 1.35656 | ||||||||
\(99\) | 1.60220 | 0.161027 | ||||||||
\(100\) | 5.98381 | 0.598381 | ||||||||
\(101\) | 8.79833 | 0.875467 | 0.437733 | − | 0.899105i | \(-0.355781\pi\) | ||||
0.437733 | + | 0.899105i | \(0.355781\pi\) | |||||||
\(102\) | −24.6855 | −2.44423 | ||||||||
\(103\) | 16.0230 | 1.57879 | 0.789397 | − | 0.613883i | \(-0.210393\pi\) | ||||
0.789397 | + | 0.613883i | \(0.210393\pi\) | |||||||
\(104\) | −6.09798 | −0.597956 | ||||||||
\(105\) | −5.20233 | −0.507695 | ||||||||
\(106\) | 12.5419 | 1.21817 | ||||||||
\(107\) | −13.5858 | −1.31339 | −0.656696 | − | 0.754155i | \(-0.728047\pi\) | ||||
−0.656696 | + | 0.754155i | \(0.728047\pi\) | |||||||
\(108\) | −24.3744 | −2.34542 | ||||||||
\(109\) | 2.71223 | 0.259784 | 0.129892 | − | 0.991528i | \(-0.458537\pi\) | ||||
0.129892 | + | 0.991528i | \(0.458537\pi\) | |||||||
\(110\) | 20.9248 | 1.99510 | ||||||||
\(111\) | 1.64054 | 0.155713 | ||||||||
\(112\) | −8.61912 | −0.814430 | ||||||||
\(113\) | −15.1376 | −1.42402 | −0.712012 | − | 0.702168i | \(-0.752216\pi\) | ||||
−0.712012 | + | 0.702168i | \(0.752216\pi\) | |||||||
\(114\) | −13.1907 | −1.23542 | ||||||||
\(115\) | −7.48250 | −0.697746 | ||||||||
\(116\) | −26.9097 | −2.49850 | ||||||||
\(117\) | −0.488741 | −0.0451841 | ||||||||
\(118\) | −24.0373 | −2.21281 | ||||||||
\(119\) | −8.01173 | −0.734434 | ||||||||
\(120\) | −24.3650 | −2.22421 | ||||||||
\(121\) | −0.253247 | −0.0230225 | ||||||||
\(122\) | 26.8629 | 2.43205 | ||||||||
\(123\) | −15.2499 | −1.37504 | ||||||||
\(124\) | 26.0177 | 2.33646 | ||||||||
\(125\) | −9.18468 | −0.821503 | ||||||||
\(126\) | −1.61096 | −0.143515 | ||||||||
\(127\) | −18.9486 | −1.68142 | −0.840710 | − | 0.541486i | \(-0.817862\pi\) | ||||
−0.840710 | + | 0.541486i | \(0.817862\pi\) | |||||||
\(128\) | 13.4019 | 1.18457 | ||||||||
\(129\) | −7.70543 | −0.678425 | ||||||||
\(130\) | −6.38296 | −0.559823 | ||||||||
\(131\) | 5.95941 | 0.520676 | 0.260338 | − | 0.965517i | \(-0.416166\pi\) | ||||
0.260338 | + | 0.965517i | \(0.416166\pi\) | |||||||
\(132\) | −22.9036 | −1.99350 | ||||||||
\(133\) | −4.28106 | −0.371215 | ||||||||
\(134\) | 28.7013 | 2.47941 | ||||||||
\(135\) | −13.9396 | −1.19973 | ||||||||
\(136\) | −37.5227 | −3.21755 | ||||||||
\(137\) | 0.427389 | 0.0365143 | 0.0182571 | − | 0.999833i | \(-0.494188\pi\) | ||||
0.0182571 | + | 0.999833i | \(0.494188\pi\) | |||||||
\(138\) | 11.9054 | 1.01346 | ||||||||
\(139\) | 11.5591 | 0.980433 | 0.490217 | − | 0.871601i | \(-0.336918\pi\) | ||||
0.490217 | + | 0.871601i | \(0.336918\pi\) | |||||||
\(140\) | −14.4734 | −1.22323 | ||||||||
\(141\) | −7.85910 | −0.661856 | ||||||||
\(142\) | 14.4578 | 1.21327 | ||||||||
\(143\) | −3.27822 | −0.274139 | ||||||||
\(144\) | −3.23537 | −0.269614 | ||||||||
\(145\) | −15.3895 | −1.27803 | ||||||||
\(146\) | −2.90210 | −0.240179 | ||||||||
\(147\) | −8.40641 | −0.693349 | ||||||||
\(148\) | 4.56415 | 0.375171 | ||||||||
\(149\) | 13.8656 | 1.13591 | 0.567956 | − | 0.823059i | \(-0.307734\pi\) | ||||
0.567956 | + | 0.823059i | \(0.307734\pi\) | |||||||
\(150\) | −5.44493 | −0.444577 | ||||||||
\(151\) | −5.26975 | −0.428846 | −0.214423 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214423 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(152\) | −20.0503 | −1.62629 | ||||||||
\(153\) | −3.00737 | −0.243132 | ||||||||
\(154\) | −10.8055 | −0.870730 | ||||||||
\(155\) | 14.8794 | 1.19514 | ||||||||
\(156\) | 6.98658 | 0.559374 | ||||||||
\(157\) | −20.9960 | −1.67566 | −0.837830 | − | 0.545931i | \(-0.816176\pi\) | ||||
−0.837830 | + | 0.545931i | \(0.816176\pi\) | |||||||
\(158\) | −18.7379 | −1.49071 | ||||||||
\(159\) | −7.85090 | −0.622617 | ||||||||
\(160\) | −11.5036 | −0.909442 | ||||||||
\(161\) | 3.86393 | 0.304520 | ||||||||
\(162\) | 18.4675 | 1.45094 | ||||||||
\(163\) | 5.71746 | 0.447826 | 0.223913 | − | 0.974609i | \(-0.428117\pi\) | ||||
0.223913 | + | 0.974609i | \(0.428117\pi\) | |||||||
\(164\) | −42.4267 | −3.31297 | ||||||||
\(165\) | −13.0984 | −1.01971 | ||||||||
\(166\) | −0.704891 | −0.0547101 | ||||||||
\(167\) | 11.1526 | 0.863013 | 0.431506 | − | 0.902110i | \(-0.357982\pi\) | ||||
0.431506 | + | 0.902110i | \(0.357982\pi\) | |||||||
\(168\) | 12.5820 | 0.970720 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −39.2764 | −3.01236 | ||||||||
\(171\) | −1.60699 | −0.122889 | ||||||||
\(172\) | −21.4373 | −1.63458 | ||||||||
\(173\) | −2.20850 | −0.167909 | −0.0839546 | − | 0.996470i | \(-0.526755\pi\) | ||||
−0.0839546 | + | 0.996470i | \(0.526755\pi\) | |||||||
\(174\) | 24.4863 | 1.85630 | ||||||||
\(175\) | −1.76716 | −0.133585 | ||||||||
\(176\) | −21.7012 | −1.63579 | ||||||||
\(177\) | 15.0468 | 1.13099 | ||||||||
\(178\) | −7.38618 | −0.553618 | ||||||||
\(179\) | −17.5090 | −1.30869 | −0.654343 | − | 0.756198i | \(-0.727055\pi\) | ||||
−0.654343 | + | 0.756198i | \(0.727055\pi\) | |||||||
\(180\) | −5.43290 | −0.404945 | ||||||||
\(181\) | 3.83182 | 0.284817 | 0.142408 | − | 0.989808i | \(-0.454515\pi\) | ||||
0.142408 | + | 0.989808i | \(0.454515\pi\) | |||||||
\(182\) | 3.29614 | 0.244326 | ||||||||
\(183\) | −16.8156 | −1.24304 | ||||||||
\(184\) | 18.0966 | 1.33410 | ||||||||
\(185\) | 2.61021 | 0.191907 | ||||||||
\(186\) | −23.6747 | −1.73591 | ||||||||
\(187\) | −20.1719 | −1.47512 | ||||||||
\(188\) | −21.8648 | −1.59466 | ||||||||
\(189\) | 7.19833 | 0.523602 | ||||||||
\(190\) | −20.9873 | −1.52258 | ||||||||
\(191\) | −19.8680 | −1.43760 | −0.718801 | − | 0.695216i | \(-0.755309\pi\) | ||||
−0.718801 | + | 0.695216i | \(0.755309\pi\) | |||||||
\(192\) | −2.67726 | −0.193215 | ||||||||
\(193\) | 20.4710 | 1.47353 | 0.736767 | − | 0.676147i | \(-0.236352\pi\) | ||||
0.736767 | + | 0.676147i | \(0.236352\pi\) | |||||||
\(194\) | −12.5312 | −0.899688 | ||||||||
\(195\) | 3.99558 | 0.286130 | ||||||||
\(196\) | −23.3875 | −1.67053 | ||||||||
\(197\) | −3.75443 | −0.267492 | −0.133746 | − | 0.991016i | \(-0.542701\pi\) | ||||
−0.133746 | + | 0.991016i | \(0.542701\pi\) | |||||||
\(198\) | −4.05606 | −0.288252 | ||||||||
\(199\) | 8.59980 | 0.609624 | 0.304812 | − | 0.952413i | \(-0.401406\pi\) | ||||
0.304812 | + | 0.952413i | \(0.401406\pi\) | |||||||
\(200\) | −8.27646 | −0.585234 | ||||||||
\(201\) | −17.9663 | −1.26725 | ||||||||
\(202\) | −22.2735 | −1.56716 | ||||||||
\(203\) | 7.94708 | 0.557776 | ||||||||
\(204\) | 42.9906 | 3.00994 | ||||||||
\(205\) | −24.2636 | −1.69464 | ||||||||
\(206\) | −40.5632 | −2.82617 | ||||||||
\(207\) | 1.45041 | 0.100810 | ||||||||
\(208\) | 6.61981 | 0.459001 | ||||||||
\(209\) | −10.7789 | −0.745590 | ||||||||
\(210\) | 13.1700 | 0.908816 | ||||||||
\(211\) | −10.3719 | −0.714033 | −0.357016 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357016 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(212\) | −21.8420 | −1.50012 | ||||||||
\(213\) | −9.05026 | −0.620114 | ||||||||
\(214\) | 34.3933 | 2.35108 | ||||||||
\(215\) | −12.2599 | −0.836116 | ||||||||
\(216\) | 33.7132 | 2.29389 | ||||||||
\(217\) | −7.68365 | −0.521600 | ||||||||
\(218\) | −6.86616 | −0.465035 | ||||||||
\(219\) | 1.81664 | 0.122757 | ||||||||
\(220\) | −36.4411 | −2.45686 | ||||||||
\(221\) | 6.15331 | 0.413917 | ||||||||
\(222\) | −4.15312 | −0.278739 | ||||||||
\(223\) | −0.413981 | −0.0277222 | −0.0138611 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138611 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(224\) | 5.94043 | 0.396912 | ||||||||
\(225\) | −0.663342 | −0.0442228 | ||||||||
\(226\) | 38.3216 | 2.54912 | ||||||||
\(227\) | −8.45863 | −0.561419 | −0.280710 | − | 0.959793i | \(-0.590570\pi\) | ||||
−0.280710 | + | 0.959793i | \(0.590570\pi\) | |||||||
\(228\) | 22.9720 | 1.52136 | ||||||||
\(229\) | 15.0190 | 0.992481 | 0.496241 | − | 0.868185i | \(-0.334713\pi\) | ||||
0.496241 | + | 0.868185i | \(0.334713\pi\) | |||||||
\(230\) | 18.9424 | 1.24902 | ||||||||
\(231\) | 6.76397 | 0.445037 | ||||||||
\(232\) | 37.2200 | 2.44361 | ||||||||
\(233\) | −11.0128 | −0.721470 | −0.360735 | − | 0.932668i | \(-0.617474\pi\) | ||||
−0.360735 | + | 0.932668i | \(0.617474\pi\) | |||||||
\(234\) | 1.23728 | 0.0808832 | ||||||||
\(235\) | −12.5044 | −0.815695 | ||||||||
\(236\) | 41.8617 | 2.72496 | ||||||||
\(237\) | 11.7295 | 0.761913 | ||||||||
\(238\) | 20.2822 | 1.31470 | ||||||||
\(239\) | −7.75889 | −0.501881 | −0.250940 | − | 0.968003i | \(-0.580740\pi\) | ||||
−0.250940 | + | 0.968003i | \(0.580740\pi\) | |||||||
\(240\) | 26.4500 | 1.70734 | ||||||||
\(241\) | −1.70878 | −0.110072 | −0.0550361 | − | 0.998484i | \(-0.517527\pi\) | ||||
−0.0550361 | + | 0.998484i | \(0.517527\pi\) | |||||||
\(242\) | 0.641110 | 0.0412121 | ||||||||
\(243\) | 5.02556 | 0.322390 | ||||||||
\(244\) | −46.7826 | −2.99495 | ||||||||
\(245\) | −13.3752 | −0.854508 | ||||||||
\(246\) | 38.6059 | 2.46143 | ||||||||
\(247\) | 3.28802 | 0.209212 | ||||||||
\(248\) | −35.9862 | −2.28513 | ||||||||
\(249\) | 0.441245 | 0.0279628 | ||||||||
\(250\) | 23.2516 | 1.47056 | ||||||||
\(251\) | −9.89275 | −0.624425 | −0.312212 | − | 0.950012i | \(-0.601070\pi\) | ||||
−0.312212 | + | 0.950012i | \(0.601070\pi\) | |||||||
\(252\) | 2.80553 | 0.176732 | ||||||||
\(253\) | 9.72861 | 0.611632 | ||||||||
\(254\) | 47.9696 | 3.00988 | ||||||||
\(255\) | 24.5861 | 1.53964 | ||||||||
\(256\) | −30.5487 | −1.90930 | ||||||||
\(257\) | 17.6107 | 1.09853 | 0.549263 | − | 0.835650i | \(-0.314909\pi\) | ||||
0.549263 | + | 0.835650i | \(0.314909\pi\) | |||||||
\(258\) | 19.5067 | 1.21444 | ||||||||
\(259\) | −1.34790 | −0.0837546 | ||||||||
\(260\) | 11.1161 | 0.689393 | ||||||||
\(261\) | 2.98311 | 0.184650 | ||||||||
\(262\) | −15.0866 | −0.932053 | ||||||||
\(263\) | 22.2385 | 1.37129 | 0.685643 | − | 0.727938i | \(-0.259521\pi\) | ||||
0.685643 | + | 0.727938i | \(0.259521\pi\) | |||||||
\(264\) | 31.6789 | 1.94970 | ||||||||
\(265\) | −12.4913 | −0.767336 | ||||||||
\(266\) | 10.8378 | 0.664506 | ||||||||
\(267\) | 4.62358 | 0.282958 | ||||||||
\(268\) | −49.9841 | −3.05326 | ||||||||
\(269\) | 15.3883 | 0.938243 | 0.469121 | − | 0.883134i | \(-0.344571\pi\) | ||||
0.469121 | + | 0.883134i | \(0.344571\pi\) | |||||||
\(270\) | 35.2888 | 2.14761 | ||||||||
\(271\) | 2.79478 | 0.169771 | 0.0848854 | − | 0.996391i | \(-0.472948\pi\) | ||||
0.0848854 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(272\) | 40.7337 | 2.46985 | ||||||||
\(273\) | −2.06330 | −0.124877 | ||||||||
\(274\) | −1.08196 | −0.0653636 | ||||||||
\(275\) | −4.44936 | −0.268306 | ||||||||
\(276\) | −20.7337 | −1.24802 | ||||||||
\(277\) | −12.5434 | −0.753660 | −0.376830 | − | 0.926282i | \(-0.622986\pi\) | ||||
−0.376830 | + | 0.926282i | \(0.622986\pi\) | |||||||
\(278\) | −29.2626 | −1.75506 | ||||||||
\(279\) | −2.88422 | −0.172674 | ||||||||
\(280\) | 20.0188 | 1.19635 | ||||||||
\(281\) | −21.3972 | −1.27645 | −0.638225 | − | 0.769850i | \(-0.720331\pi\) | ||||
−0.638225 | + | 0.769850i | \(0.720331\pi\) | |||||||
\(282\) | 19.8958 | 1.18478 | ||||||||
\(283\) | 26.6561 | 1.58454 | 0.792269 | − | 0.610172i | \(-0.208899\pi\) | ||||
0.792269 | + | 0.610172i | \(0.208899\pi\) | |||||||
\(284\) | −25.1787 | −1.49408 | ||||||||
\(285\) | 13.1376 | 0.778202 | ||||||||
\(286\) | 8.29901 | 0.490731 | ||||||||
\(287\) | 12.5296 | 0.739600 | ||||||||
\(288\) | 2.22987 | 0.131396 | ||||||||
\(289\) | 20.8633 | 1.22725 | ||||||||
\(290\) | 38.9594 | 2.28778 | ||||||||
\(291\) | 7.84424 | 0.459837 | ||||||||
\(292\) | 5.05409 | 0.295768 | ||||||||
\(293\) | −18.3636 | −1.07281 | −0.536405 | − | 0.843961i | \(-0.680218\pi\) | ||||
−0.536405 | + | 0.843961i | \(0.680218\pi\) | |||||||
\(294\) | 21.2813 | 1.24115 | ||||||||
\(295\) | 23.9405 | 1.39387 | ||||||||
\(296\) | −6.31287 | −0.366928 | ||||||||
\(297\) | 18.1240 | 1.05166 | ||||||||
\(298\) | −35.1015 | −2.03338 | ||||||||
\(299\) | −2.96765 | −0.171623 | ||||||||
\(300\) | 9.48251 | 0.547473 | ||||||||
\(301\) | 6.33095 | 0.364910 | ||||||||
\(302\) | 13.3407 | 0.767670 | ||||||||
\(303\) | 13.9427 | 0.800986 | ||||||||
\(304\) | 21.7661 | 1.24837 | ||||||||
\(305\) | −26.7547 | −1.53197 | ||||||||
\(306\) | 7.61334 | 0.435226 | ||||||||
\(307\) | 6.74483 | 0.384948 | 0.192474 | − | 0.981302i | \(-0.438349\pi\) | ||||
0.192474 | + | 0.981302i | \(0.438349\pi\) | |||||||
\(308\) | 18.8181 | 1.07226 | ||||||||
\(309\) | 25.3916 | 1.44448 | ||||||||
\(310\) | −37.6680 | −2.13940 | ||||||||
\(311\) | −9.20685 | −0.522072 | −0.261036 | − | 0.965329i | \(-0.584064\pi\) | ||||
−0.261036 | + | 0.965329i | \(0.584064\pi\) | |||||||
\(312\) | −9.66343 | −0.547084 | ||||||||
\(313\) | −27.6556 | −1.56319 | −0.781594 | − | 0.623788i | \(-0.785593\pi\) | ||||
−0.781594 | + | 0.623788i | \(0.785593\pi\) | |||||||
\(314\) | 53.1525 | 2.99957 | ||||||||
\(315\) | 1.60447 | 0.0904014 | ||||||||
\(316\) | 32.6327 | 1.83573 | ||||||||
\(317\) | −22.6176 | −1.27033 | −0.635167 | − | 0.772375i | \(-0.719069\pi\) | ||||
−0.635167 | + | 0.772375i | \(0.719069\pi\) | |||||||
\(318\) | 19.8750 | 1.11454 | ||||||||
\(319\) | 20.0092 | 1.12030 | ||||||||
\(320\) | −4.25970 | −0.238125 | ||||||||
\(321\) | −21.5294 | −1.20165 | ||||||||
\(322\) | −9.78176 | −0.545116 | ||||||||
\(323\) | 20.2322 | 1.12575 | ||||||||
\(324\) | −32.1617 | −1.78676 | ||||||||
\(325\) | 1.35725 | 0.0752865 | ||||||||
\(326\) | −14.4741 | −0.801645 | ||||||||
\(327\) | 4.29805 | 0.237683 | ||||||||
\(328\) | 58.6822 | 3.24018 | ||||||||
\(329\) | 6.45720 | 0.355997 | ||||||||
\(330\) | 33.1594 | 1.82537 | ||||||||
\(331\) | 0.913956 | 0.0502356 | 0.0251178 | − | 0.999684i | \(-0.492004\pi\) | ||||
0.0251178 | + | 0.999684i | \(0.492004\pi\) | |||||||
\(332\) | 1.22759 | 0.0673727 | ||||||||
\(333\) | −0.505964 | −0.0277266 | ||||||||
\(334\) | −28.2334 | −1.54486 | ||||||||
\(335\) | −28.5856 | −1.56180 | ||||||||
\(336\) | −13.6587 | −0.745142 | ||||||||
\(337\) | 5.39849 | 0.294074 | 0.147037 | − | 0.989131i | \(-0.453026\pi\) | ||||
0.147037 | + | 0.989131i | \(0.453026\pi\) | |||||||
\(338\) | −2.53156 | −0.137699 | ||||||||
\(339\) | −23.9884 | −1.30287 | ||||||||
\(340\) | 68.4010 | 3.70956 | ||||||||
\(341\) | −19.3459 | −1.04764 | ||||||||
\(342\) | 4.06818 | 0.219982 | ||||||||
\(343\) | 16.0210 | 0.865053 | ||||||||
\(344\) | 29.6508 | 1.59867 | ||||||||
\(345\) | −11.8575 | −0.638385 | ||||||||
\(346\) | 5.59095 | 0.300571 | ||||||||
\(347\) | 2.67063 | 0.143367 | 0.0716835 | − | 0.997427i | \(-0.477163\pi\) | ||||
0.0716835 | + | 0.997427i | \(0.477163\pi\) | |||||||
\(348\) | −42.6437 | −2.28594 | ||||||||
\(349\) | −20.8591 | −1.11656 | −0.558281 | − | 0.829652i | \(-0.688539\pi\) | ||||
−0.558281 | + | 0.829652i | \(0.688539\pi\) | |||||||
\(350\) | 4.47367 | 0.239128 | ||||||||
\(351\) | −5.52859 | −0.295094 | ||||||||
\(352\) | 14.9568 | 0.797201 | ||||||||
\(353\) | 5.04211 | 0.268365 | 0.134182 | − | 0.990957i | \(-0.457159\pi\) | ||||
0.134182 | + | 0.990957i | \(0.457159\pi\) | |||||||
\(354\) | −38.0918 | −2.02456 | ||||||||
\(355\) | −14.3996 | −0.764250 | ||||||||
\(356\) | 12.8633 | 0.681752 | ||||||||
\(357\) | −12.6962 | −0.671952 | ||||||||
\(358\) | 44.3251 | 2.34266 | ||||||||
\(359\) | 8.30102 | 0.438111 | 0.219055 | − | 0.975712i | \(-0.429702\pi\) | ||||
0.219055 | + | 0.975712i | \(0.429702\pi\) | |||||||
\(360\) | 7.51448 | 0.396048 | ||||||||
\(361\) | −8.18893 | −0.430996 | ||||||||
\(362\) | −9.70046 | −0.509845 | ||||||||
\(363\) | −0.401319 | −0.0210638 | ||||||||
\(364\) | −5.74032 | −0.300875 | ||||||||
\(365\) | 2.89040 | 0.151291 | ||||||||
\(366\) | 42.5696 | 2.22515 | ||||||||
\(367\) | −0.0265580 | −0.00138631 | −0.000693157 | − | 1.00000i | \(-0.500221\pi\) | ||||
−0.000693157 | 1.00000i | \(0.500221\pi\) | ||||||||
\(368\) | −19.6452 | −1.02408 | ||||||||
\(369\) | 4.70326 | 0.244842 | ||||||||
\(370\) | −6.60790 | −0.343528 | ||||||||
\(371\) | 6.45047 | 0.334892 | ||||||||
\(372\) | 41.2301 | 2.13768 | ||||||||
\(373\) | 15.1984 | 0.786941 | 0.393471 | − | 0.919337i | \(-0.371274\pi\) | ||||
0.393471 | + | 0.919337i | \(0.371274\pi\) | |||||||
\(374\) | 51.0664 | 2.64058 | ||||||||
\(375\) | −14.5549 | −0.751613 | ||||||||
\(376\) | 30.2422 | 1.55962 | ||||||||
\(377\) | −6.10366 | −0.314354 | ||||||||
\(378\) | −18.2230 | −0.937289 | ||||||||
\(379\) | 3.70468 | 0.190297 | 0.0951484 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951484 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(380\) | 36.5500 | 1.87498 | ||||||||
\(381\) | −30.0278 | −1.53837 | ||||||||
\(382\) | 50.2971 | 2.57342 | ||||||||
\(383\) | −18.4802 | −0.944294 | −0.472147 | − | 0.881520i | \(-0.656521\pi\) | ||||
−0.472147 | + | 0.881520i | \(0.656521\pi\) | |||||||
\(384\) | 21.2379 | 1.08379 | ||||||||
\(385\) | 10.7619 | 0.548479 | ||||||||
\(386\) | −51.8235 | −2.63775 | ||||||||
\(387\) | 2.37646 | 0.120802 | ||||||||
\(388\) | 21.8235 | 1.10792 | ||||||||
\(389\) | −18.7853 | −0.952450 | −0.476225 | − | 0.879323i | \(-0.657995\pi\) | ||||
−0.476225 | + | 0.879323i | \(0.657995\pi\) | |||||||
\(390\) | −10.1151 | −0.512196 | ||||||||
\(391\) | −18.2608 | −0.923491 | ||||||||
\(392\) | 32.3482 | 1.63383 | ||||||||
\(393\) | 9.44386 | 0.476380 | ||||||||
\(394\) | 9.50454 | 0.478832 | ||||||||
\(395\) | 18.6624 | 0.939009 | ||||||||
\(396\) | 7.06376 | 0.354967 | ||||||||
\(397\) | 24.9735 | 1.25339 | 0.626693 | − | 0.779267i | \(-0.284408\pi\) | ||||
0.626693 | + | 0.779267i | \(0.284408\pi\) | |||||||
\(398\) | −21.7709 | −1.09128 | ||||||||
\(399\) | −6.78418 | −0.339634 | ||||||||
\(400\) | 8.98472 | 0.449236 | ||||||||
\(401\) | −29.4822 | −1.47227 | −0.736136 | − | 0.676834i | \(-0.763351\pi\) | ||||
−0.736136 | + | 0.676834i | \(0.763351\pi\) | |||||||
\(402\) | 45.4827 | 2.26847 | ||||||||
\(403\) | 5.90133 | 0.293966 | ||||||||
\(404\) | 38.7899 | 1.92987 | ||||||||
\(405\) | −18.3931 | −0.913960 | ||||||||
\(406\) | −20.1185 | −0.998464 | ||||||||
\(407\) | −3.39375 | −0.168222 | ||||||||
\(408\) | −59.4621 | −2.94381 | ||||||||
\(409\) | −7.46081 | −0.368913 | −0.184457 | − | 0.982841i | \(-0.559053\pi\) | ||||
−0.184457 | + | 0.982841i | \(0.559053\pi\) | |||||||
\(410\) | 61.4247 | 3.03355 | ||||||||
\(411\) | 0.677281 | 0.0334078 | ||||||||
\(412\) | 70.6420 | 3.48028 | ||||||||
\(413\) | −12.3628 | −0.608331 | ||||||||
\(414\) | −3.67179 | −0.180459 | ||||||||
\(415\) | 0.702051 | 0.0344623 | ||||||||
\(416\) | −4.56248 | −0.223694 | ||||||||
\(417\) | 18.3177 | 0.897022 | ||||||||
\(418\) | 27.2873 | 1.33467 | ||||||||
\(419\) | −12.0711 | −0.589714 | −0.294857 | − | 0.955541i | \(-0.595272\pi\) | ||||
−0.294857 | + | 0.955541i | \(0.595272\pi\) | |||||||
\(420\) | −22.9359 | −1.11916 | ||||||||
\(421\) | −18.1762 | −0.885853 | −0.442927 | − | 0.896558i | \(-0.646060\pi\) | ||||
−0.442927 | + | 0.896558i | \(0.646060\pi\) | |||||||
\(422\) | 26.2571 | 1.27818 | ||||||||
\(423\) | 2.42385 | 0.117852 | ||||||||
\(424\) | 30.2106 | 1.46716 | ||||||||
\(425\) | 8.35156 | 0.405110 | ||||||||
\(426\) | 22.9113 | 1.11005 | ||||||||
\(427\) | 13.8160 | 0.668604 | ||||||||
\(428\) | −59.8970 | −2.89523 | ||||||||
\(429\) | −5.19499 | −0.250816 | ||||||||
\(430\) | 31.0366 | 1.49672 | ||||||||
\(431\) | 15.3464 | 0.739209 | 0.369605 | − | 0.929189i | \(-0.379493\pi\) | ||||
0.369605 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(432\) | −36.5982 | −1.76083 | ||||||||
\(433\) | 8.61489 | 0.414005 | 0.207003 | − | 0.978340i | \(-0.433629\pi\) | ||||
0.207003 | + | 0.978340i | \(0.433629\pi\) | |||||||
\(434\) | 19.4516 | 0.933707 | ||||||||
\(435\) | −24.3877 | −1.16930 | ||||||||
\(436\) | 11.9576 | 0.572666 | ||||||||
\(437\) | −9.75768 | −0.466773 | ||||||||
\(438\) | −4.59894 | −0.219746 | ||||||||
\(439\) | −23.0496 | −1.10010 | −0.550048 | − | 0.835133i | \(-0.685390\pi\) | ||||
−0.550048 | + | 0.835133i | \(0.685390\pi\) | |||||||
\(440\) | 50.4033 | 2.40288 | ||||||||
\(441\) | 2.59265 | 0.123459 | ||||||||
\(442\) | −15.5775 | −0.740944 | ||||||||
\(443\) | −9.92838 | −0.471712 | −0.235856 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235856 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(444\) | 7.23279 | 0.343253 | ||||||||
\(445\) | 7.35643 | 0.348728 | ||||||||
\(446\) | 1.04802 | 0.0496251 | ||||||||
\(447\) | 21.9727 | 1.03927 | ||||||||
\(448\) | 2.19969 | 0.103926 | ||||||||
\(449\) | −34.2024 | −1.61411 | −0.807056 | − | 0.590474i | \(-0.798941\pi\) | ||||
−0.807056 | + | 0.590474i | \(0.798941\pi\) | |||||||
\(450\) | 1.67929 | 0.0791624 | ||||||||
\(451\) | 31.5471 | 1.48549 | ||||||||
\(452\) | −66.7383 | −3.13911 | ||||||||
\(453\) | −8.35095 | −0.392362 | ||||||||
\(454\) | 21.4135 | 1.00499 | ||||||||
\(455\) | −3.28286 | −0.153903 | ||||||||
\(456\) | −31.7736 | −1.48793 | ||||||||
\(457\) | 8.64468 | 0.404381 | 0.202190 | − | 0.979346i | \(-0.435194\pi\) | ||||
0.202190 | + | 0.979346i | \(0.435194\pi\) | |||||||
\(458\) | −38.0214 | −1.77662 | ||||||||
\(459\) | −34.0191 | −1.58788 | ||||||||
\(460\) | −32.9887 | −1.53811 | ||||||||
\(461\) | 10.5227 | 0.490093 | 0.245046 | − | 0.969511i | \(-0.421197\pi\) | ||||
0.245046 | + | 0.969511i | \(0.421197\pi\) | |||||||
\(462\) | −17.1234 | −0.796652 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | −40.4051 | −1.87576 | ||||||||
\(465\) | 23.5793 | 1.09346 | ||||||||
\(466\) | 27.8794 | 1.29149 | ||||||||
\(467\) | −31.2892 | −1.44789 | −0.723946 | − | 0.689856i | \(-0.757674\pi\) | ||||
−0.723946 | + | 0.689856i | \(0.757674\pi\) | |||||||
\(468\) | −2.15475 | −0.0996034 | ||||||||
\(469\) | 14.7615 | 0.681623 | ||||||||
\(470\) | 31.6555 | 1.46016 | ||||||||
\(471\) | −33.2722 | −1.53310 | ||||||||
\(472\) | −57.9007 | −2.66509 | ||||||||
\(473\) | 15.9401 | 0.732925 | ||||||||
\(474\) | −29.6939 | −1.36389 | ||||||||
\(475\) | 4.46265 | 0.204761 | ||||||||
\(476\) | −35.3220 | −1.61898 | ||||||||
\(477\) | 2.42132 | 0.110865 | ||||||||
\(478\) | 19.6421 | 0.898408 | ||||||||
\(479\) | −1.87421 | −0.0856349 | −0.0428175 | − | 0.999083i | \(-0.513633\pi\) | ||||
−0.0428175 | + | 0.999083i | \(0.513633\pi\) | |||||||
\(480\) | −18.2298 | −0.832071 | ||||||||
\(481\) | 1.03524 | 0.0472029 | ||||||||
\(482\) | 4.32587 | 0.197038 | ||||||||
\(483\) | 6.12315 | 0.278613 | ||||||||
\(484\) | −1.11651 | −0.0507505 | ||||||||
\(485\) | 12.4807 | 0.566720 | ||||||||
\(486\) | −12.7225 | −0.577104 | ||||||||
\(487\) | 8.24621 | 0.373671 | 0.186836 | − | 0.982391i | \(-0.440177\pi\) | ||||
0.186836 | + | 0.982391i | \(0.440177\pi\) | |||||||
\(488\) | 64.7070 | 2.92915 | ||||||||
\(489\) | 9.06044 | 0.409727 | ||||||||
\(490\) | 33.8600 | 1.52964 | ||||||||
\(491\) | −11.6867 | −0.527413 | −0.263706 | − | 0.964603i | \(-0.584945\pi\) | ||||
−0.263706 | + | 0.964603i | \(0.584945\pi\) | |||||||
\(492\) | −67.2334 | −3.03112 | ||||||||
\(493\) | −37.5577 | −1.69151 | ||||||||
\(494\) | −8.32381 | −0.374506 | ||||||||
\(495\) | 4.03972 | 0.181572 | ||||||||
\(496\) | 39.0657 | 1.75410 | ||||||||
\(497\) | 7.43588 | 0.333545 | ||||||||
\(498\) | −1.11704 | −0.0500556 | ||||||||
\(499\) | 26.7137 | 1.19587 | 0.597935 | − | 0.801544i | \(-0.295988\pi\) | ||||
0.597935 | + | 0.801544i | \(0.295988\pi\) | |||||||
\(500\) | −40.4933 | −1.81092 | ||||||||
\(501\) | 17.6734 | 0.789591 | ||||||||
\(502\) | 25.0441 | 1.11777 | ||||||||
\(503\) | 4.23133 | 0.188666 | 0.0943328 | − | 0.995541i | \(-0.469928\pi\) | ||||
0.0943328 | + | 0.995541i | \(0.469928\pi\) | |||||||
\(504\) | −3.88044 | −0.172849 | ||||||||
\(505\) | 22.1837 | 0.987164 | ||||||||
\(506\) | −24.6285 | −1.09487 | ||||||||
\(507\) | 1.58470 | 0.0703788 | ||||||||
\(508\) | −83.5404 | −3.70651 | ||||||||
\(509\) | −30.5529 | −1.35423 | −0.677116 | − | 0.735876i | \(-0.736771\pi\) | ||||
−0.677116 | + | 0.735876i | \(0.736771\pi\) | |||||||
\(510\) | −62.2411 | −2.75608 | ||||||||
\(511\) | −1.49259 | −0.0660284 | ||||||||
\(512\) | 50.5321 | 2.23323 | ||||||||
\(513\) | −18.1781 | −0.802583 | ||||||||
\(514\) | −44.5825 | −1.96645 | ||||||||
\(515\) | 40.3997 | 1.78023 | ||||||||
\(516\) | −33.9716 | −1.49552 | ||||||||
\(517\) | 16.2579 | 0.715024 | ||||||||
\(518\) | 3.41229 | 0.149928 | ||||||||
\(519\) | −3.49980 | −0.153624 | ||||||||
\(520\) | −15.3752 | −0.674246 | ||||||||
\(521\) | 30.5614 | 1.33892 | 0.669460 | − | 0.742848i | \(-0.266526\pi\) | ||||
0.669460 | + | 0.742848i | \(0.266526\pi\) | |||||||
\(522\) | −7.55191 | −0.330538 | ||||||||
\(523\) | 9.60674 | 0.420074 | 0.210037 | − | 0.977693i | \(-0.432642\pi\) | ||||
0.210037 | + | 0.977693i | \(0.432642\pi\) | |||||||
\(524\) | 26.2738 | 1.14777 | ||||||||
\(525\) | −2.80041 | −0.122220 | ||||||||
\(526\) | −56.2981 | −2.45471 | ||||||||
\(527\) | 36.3127 | 1.58181 | ||||||||
\(528\) | −34.3898 | −1.49662 | ||||||||
\(529\) | −14.1931 | −0.617091 | ||||||||
\(530\) | 31.6225 | 1.37359 | ||||||||
\(531\) | −4.64062 | −0.201386 | ||||||||
\(532\) | −18.8743 | −0.818304 | ||||||||
\(533\) | −9.62322 | −0.416828 | ||||||||
\(534\) | −11.7049 | −0.506518 | ||||||||
\(535\) | −34.2547 | −1.48096 | ||||||||
\(536\) | 69.1351 | 2.98618 | ||||||||
\(537\) | −27.7465 | −1.19735 | ||||||||
\(538\) | −38.9564 | −1.67953 | ||||||||
\(539\) | 17.3901 | 0.749047 | ||||||||
\(540\) | −61.4565 | −2.64467 | ||||||||
\(541\) | −12.9675 | −0.557515 | −0.278757 | − | 0.960362i | \(-0.589923\pi\) | ||||
−0.278757 | + | 0.960362i | \(0.589923\pi\) | |||||||
\(542\) | −7.07515 | −0.303904 | ||||||||
\(543\) | 6.07226 | 0.260586 | ||||||||
\(544\) | −28.0743 | −1.20368 | ||||||||
\(545\) | 6.83850 | 0.292929 | ||||||||
\(546\) | 5.22337 | 0.223540 | ||||||||
\(547\) | 13.6969 | 0.585635 | 0.292818 | − | 0.956168i | \(-0.405407\pi\) | ||||
0.292818 | + | 0.956168i | \(0.405407\pi\) | |||||||
\(548\) | 1.88426 | 0.0804918 | ||||||||
\(549\) | 5.18614 | 0.221339 | ||||||||
\(550\) | 11.2638 | 0.480291 | ||||||||
\(551\) | −20.0690 | −0.854966 | ||||||||
\(552\) | 28.6776 | 1.22060 | ||||||||
\(553\) | −9.63720 | −0.409816 | ||||||||
\(554\) | 31.7543 | 1.34911 | ||||||||
\(555\) | 4.13639 | 0.175580 | ||||||||
\(556\) | 50.9617 | 2.16126 | ||||||||
\(557\) | −42.1488 | −1.78590 | −0.892951 | − | 0.450154i | \(-0.851369\pi\) | ||||
−0.892951 | + | 0.450154i | \(0.851369\pi\) | |||||||
\(558\) | 7.30157 | 0.309100 | ||||||||
\(559\) | −4.86241 | −0.205658 | ||||||||
\(560\) | −21.7319 | −0.918340 | ||||||||
\(561\) | −31.9664 | −1.34962 | ||||||||
\(562\) | 54.1683 | 2.28495 | ||||||||
\(563\) | 24.9588 | 1.05189 | 0.525945 | − | 0.850519i | \(-0.323712\pi\) | ||||
0.525945 | + | 0.850519i | \(0.323712\pi\) | |||||||
\(564\) | −34.6491 | −1.45899 | ||||||||
\(565\) | −38.1673 | −1.60571 | ||||||||
\(566\) | −67.4814 | −2.83645 | ||||||||
\(567\) | 9.49811 | 0.398883 | ||||||||
\(568\) | 34.8258 | 1.46126 | ||||||||
\(569\) | 12.5376 | 0.525604 | 0.262802 | − | 0.964850i | \(-0.415353\pi\) | ||||
0.262802 | + | 0.964850i | \(0.415353\pi\) | |||||||
\(570\) | −33.2585 | −1.39304 | ||||||||
\(571\) | −17.3840 | −0.727499 | −0.363749 | − | 0.931497i | \(-0.618504\pi\) | ||||
−0.363749 | + | 0.931497i | \(0.618504\pi\) | |||||||
\(572\) | −14.4530 | −0.604310 | ||||||||
\(573\) | −31.4848 | −1.31530 | ||||||||
\(574\) | −31.7195 | −1.32394 | ||||||||
\(575\) | −4.02783 | −0.167972 | ||||||||
\(576\) | 0.825702 | 0.0344042 | ||||||||
\(577\) | 16.4738 | 0.685813 | 0.342907 | − | 0.939370i | \(-0.388589\pi\) | ||||
0.342907 | + | 0.939370i | \(0.388589\pi\) | |||||||
\(578\) | −52.8165 | −2.19688 | ||||||||
\(579\) | 32.4403 | 1.34817 | ||||||||
\(580\) | −67.8490 | −2.81728 | ||||||||
\(581\) | −0.362536 | −0.0150405 | ||||||||
\(582\) | −19.8581 | −0.823147 | ||||||||
\(583\) | 16.2410 | 0.672633 | ||||||||
\(584\) | −6.99052 | −0.289270 | ||||||||
\(585\) | −1.23229 | −0.0509489 | ||||||||
\(586\) | 46.4884 | 1.92042 | ||||||||
\(587\) | 23.0296 | 0.950533 | 0.475267 | − | 0.879842i | \(-0.342352\pi\) | ||||
0.475267 | + | 0.879842i | \(0.342352\pi\) | |||||||
\(588\) | −37.0620 | −1.52841 | ||||||||
\(589\) | 19.4037 | 0.799516 | ||||||||
\(590\) | −60.6067 | −2.49514 | ||||||||
\(591\) | −5.94962 | −0.244735 | ||||||||
\(592\) | 6.85309 | 0.281660 | ||||||||
\(593\) | 34.4420 | 1.41436 | 0.707181 | − | 0.707032i | \(-0.249966\pi\) | ||||
0.707181 | + | 0.707032i | \(0.249966\pi\) | |||||||
\(594\) | −45.8818 | −1.88256 | ||||||||
\(595\) | −20.2004 | −0.828137 | ||||||||
\(596\) | 61.1303 | 2.50400 | ||||||||
\(597\) | 13.6281 | 0.557759 | ||||||||
\(598\) | 7.51276 | 0.307220 | ||||||||
\(599\) | −30.9935 | −1.26636 | −0.633181 | − | 0.774004i | \(-0.718251\pi\) | ||||
−0.633181 | + | 0.774004i | \(0.718251\pi\) | |||||||
\(600\) | −13.1157 | −0.535445 | ||||||||
\(601\) | −14.0568 | −0.573388 | −0.286694 | − | 0.958022i | \(-0.592556\pi\) | ||||
−0.286694 | + | 0.958022i | \(0.592556\pi\) | |||||||
\(602\) | −16.0272 | −0.653218 | ||||||||
\(603\) | 5.54104 | 0.225649 | ||||||||
\(604\) | −23.2332 | −0.945346 | ||||||||
\(605\) | −0.638527 | −0.0259598 | ||||||||
\(606\) | −35.2967 | −1.43383 | ||||||||
\(607\) | 34.1866 | 1.38759 | 0.693796 | − | 0.720171i | \(-0.255937\pi\) | ||||
0.693796 | + | 0.720171i | \(0.255937\pi\) | |||||||
\(608\) | −15.0015 | −0.608392 | ||||||||
\(609\) | 12.5937 | 0.510323 | ||||||||
\(610\) | 67.7311 | 2.74235 | ||||||||
\(611\) | −4.95938 | −0.200635 | ||||||||
\(612\) | −13.2589 | −0.535958 | ||||||||
\(613\) | −33.3711 | −1.34785 | −0.673923 | − | 0.738801i | \(-0.735392\pi\) | ||||
−0.673923 | + | 0.738801i | \(0.735392\pi\) | |||||||
\(614\) | −17.0749 | −0.689088 | ||||||||
\(615\) | −38.4504 | −1.55047 | ||||||||
\(616\) | −26.0280 | −1.04870 | ||||||||
\(617\) | −16.9920 | −0.684073 | −0.342037 | − | 0.939687i | \(-0.611117\pi\) | ||||
−0.342037 | + | 0.939687i | \(0.611117\pi\) | |||||||
\(618\) | −64.2803 | −2.58573 | ||||||||
\(619\) | 30.4093 | 1.22225 | 0.611127 | − | 0.791533i | \(-0.290716\pi\) | ||||
0.611127 | + | 0.791533i | \(0.290716\pi\) | |||||||
\(620\) | 65.6000 | 2.63456 | ||||||||
\(621\) | 16.4069 | 0.658386 | ||||||||
\(622\) | 23.3077 | 0.934552 | ||||||||
\(623\) | −3.79883 | −0.152197 | ||||||||
\(624\) | 10.4904 | 0.419951 | ||||||||
\(625\) | −29.9441 | −1.19776 | ||||||||
\(626\) | 70.0118 | 2.79823 | ||||||||
\(627\) | −17.0812 | −0.682158 | ||||||||
\(628\) | −92.5667 | −3.69381 | ||||||||
\(629\) | 6.37016 | 0.253995 | ||||||||
\(630\) | −4.06180 | −0.161826 | ||||||||
\(631\) | 29.6555 | 1.18057 | 0.590284 | − | 0.807196i | \(-0.299016\pi\) | ||||
0.590284 | + | 0.807196i | \(0.299016\pi\) | |||||||
\(632\) | −45.1356 | −1.79540 | ||||||||
\(633\) | −16.4363 | −0.653286 | ||||||||
\(634\) | 57.2579 | 2.27400 | ||||||||
\(635\) | −47.7763 | −1.89594 | ||||||||
\(636\) | −34.6129 | −1.37249 | ||||||||
\(637\) | −5.30475 | −0.210182 | ||||||||
\(638\) | −50.6544 | −2.00543 | ||||||||
\(639\) | 2.79122 | 0.110419 | ||||||||
\(640\) | 33.7910 | 1.33570 | ||||||||
\(641\) | −15.3970 | −0.608147 | −0.304073 | − | 0.952649i | \(-0.598347\pi\) | ||||
−0.304073 | + | 0.952649i | \(0.598347\pi\) | |||||||
\(642\) | 54.5029 | 2.15106 | ||||||||
\(643\) | −33.5617 | −1.32355 | −0.661773 | − | 0.749705i | \(-0.730196\pi\) | ||||
−0.661773 | + | 0.749705i | \(0.730196\pi\) | |||||||
\(644\) | 17.0352 | 0.671282 | ||||||||
\(645\) | −19.4282 | −0.764983 | ||||||||
\(646\) | −51.2190 | −2.01518 | ||||||||
\(647\) | 45.5985 | 1.79266 | 0.896330 | − | 0.443387i | \(-0.146223\pi\) | ||||
0.896330 | + | 0.443387i | \(0.146223\pi\) | |||||||
\(648\) | 44.4842 | 1.74750 | ||||||||
\(649\) | −31.1270 | −1.22184 | ||||||||
\(650\) | −3.43595 | −0.134769 | ||||||||
\(651\) | −12.1762 | −0.477225 | ||||||||
\(652\) | 25.2071 | 0.987185 | ||||||||
\(653\) | −0.363681 | −0.0142320 | −0.00711598 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711598 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(654\) | −10.8808 | −0.425472 | ||||||||
\(655\) | 15.0258 | 0.587107 | ||||||||
\(656\) | −63.7039 | −2.48722 | ||||||||
\(657\) | −0.560277 | −0.0218585 | ||||||||
\(658\) | −16.3468 | −0.637264 | ||||||||
\(659\) | −38.9169 | −1.51599 | −0.757994 | − | 0.652261i | \(-0.773820\pi\) | ||||
−0.757994 | + | 0.652261i | \(0.773820\pi\) | |||||||
\(660\) | −57.7481 | −2.24784 | ||||||||
\(661\) | 6.02900 | 0.234501 | 0.117250 | − | 0.993102i | \(-0.462592\pi\) | ||||
0.117250 | + | 0.993102i | \(0.462592\pi\) | |||||||
\(662\) | −2.31373 | −0.0899258 | ||||||||
\(663\) | 9.75113 | 0.378702 | ||||||||
\(664\) | −1.69793 | −0.0658925 | ||||||||
\(665\) | −10.7941 | −0.418577 | ||||||||
\(666\) | 1.28088 | 0.0496330 | ||||||||
\(667\) | 18.1135 | 0.701357 | ||||||||
\(668\) | 49.1693 | 1.90242 | ||||||||
\(669\) | −0.656034 | −0.0253637 | ||||||||
\(670\) | 72.3661 | 2.79575 | ||||||||
\(671\) | 34.7860 | 1.34290 | ||||||||
\(672\) | 9.41377 | 0.363144 | ||||||||
\(673\) | 9.77621 | 0.376845 | 0.188423 | − | 0.982088i | \(-0.439663\pi\) | ||||
0.188423 | + | 0.982088i | \(0.439663\pi\) | |||||||
\(674\) | −13.6666 | −0.526417 | ||||||||
\(675\) | −7.50366 | −0.288816 | ||||||||
\(676\) | 4.40878 | 0.169569 | ||||||||
\(677\) | −3.00224 | −0.115385 | −0.0576927 | − | 0.998334i | \(-0.518374\pi\) | ||||
−0.0576927 | + | 0.998334i | \(0.518374\pi\) | |||||||
\(678\) | 60.7281 | 2.33225 | ||||||||
\(679\) | −6.44499 | −0.247336 | ||||||||
\(680\) | −94.6083 | −3.62806 | ||||||||
\(681\) | −13.4044 | −0.513656 | ||||||||
\(682\) | 48.9752 | 1.87536 | ||||||||
\(683\) | −40.7988 | −1.56112 | −0.780561 | − | 0.625079i | \(-0.785067\pi\) | ||||
−0.780561 | + | 0.625079i | \(0.785067\pi\) | |||||||
\(684\) | −7.08487 | −0.270897 | ||||||||
\(685\) | 1.07760 | 0.0411730 | ||||||||
\(686\) | −40.5581 | −1.54852 | ||||||||
\(687\) | 23.8005 | 0.908045 | ||||||||
\(688\) | −32.1882 | −1.22716 | ||||||||
\(689\) | −4.95420 | −0.188740 | ||||||||
\(690\) | 30.0179 | 1.14276 | ||||||||
\(691\) | 43.7463 | 1.66419 | 0.832095 | − | 0.554634i | \(-0.187142\pi\) | ||||
0.832095 | + | 0.554634i | \(0.187142\pi\) | |||||||
\(692\) | −9.73680 | −0.370138 | ||||||||
\(693\) | −2.08610 | −0.0792443 | ||||||||
\(694\) | −6.76086 | −0.256639 | ||||||||
\(695\) | 29.1447 | 1.10552 | ||||||||
\(696\) | 58.9823 | 2.23572 | ||||||||
\(697\) | −59.2147 | −2.24292 | ||||||||
\(698\) | 52.8060 | 1.99874 | ||||||||
\(699\) | −17.4519 | −0.660091 | ||||||||
\(700\) | −7.79103 | −0.294473 | ||||||||
\(701\) | 5.73694 | 0.216681 | 0.108341 | − | 0.994114i | \(-0.465446\pi\) | ||||
0.108341 | + | 0.994114i | \(0.465446\pi\) | |||||||
\(702\) | 13.9959 | 0.528243 | ||||||||
\(703\) | 3.40389 | 0.128380 | ||||||||
\(704\) | 5.53839 | 0.208736 | ||||||||
\(705\) | −19.8156 | −0.746299 | ||||||||
\(706\) | −12.7644 | −0.480395 | ||||||||
\(707\) | −11.4556 | −0.430832 | ||||||||
\(708\) | 66.3380 | 2.49314 | ||||||||
\(709\) | 8.08547 | 0.303656 | 0.151828 | − | 0.988407i | \(-0.451484\pi\) | ||||
0.151828 | + | 0.988407i | \(0.451484\pi\) | |||||||
\(710\) | 36.4534 | 1.36807 | ||||||||
\(711\) | −3.61753 | −0.135668 | ||||||||
\(712\) | −17.7917 | −0.666773 | ||||||||
\(713\) | −17.5131 | −0.655869 | ||||||||
\(714\) | 32.1410 | 1.20285 | ||||||||
\(715\) | −8.26558 | −0.309115 | ||||||||
\(716\) | −77.1936 | −2.88486 | ||||||||
\(717\) | −12.2955 | −0.459183 | ||||||||
\(718\) | −21.0145 | −0.784254 | ||||||||
\(719\) | −5.29478 | −0.197462 | −0.0987310 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987310 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(720\) | −8.15752 | −0.304013 | ||||||||
\(721\) | −20.8623 | −0.776951 | ||||||||
\(722\) | 20.7307 | 0.771518 | ||||||||
\(723\) | −2.70789 | −0.100708 | ||||||||
\(724\) | 16.8936 | 0.627847 | ||||||||
\(725\) | −8.28417 | −0.307667 | ||||||||
\(726\) | 1.01596 | 0.0377059 | ||||||||
\(727\) | −37.8024 | −1.40201 | −0.701006 | − | 0.713155i | \(-0.747265\pi\) | ||||
−0.701006 | + | 0.713155i | \(0.747265\pi\) | |||||||
\(728\) | 7.93968 | 0.294264 | ||||||||
\(729\) | 29.8487 | 1.10551 | ||||||||
\(730\) | −7.31722 | −0.270823 | ||||||||
\(731\) | −29.9199 | −1.10663 | ||||||||
\(732\) | −74.1362 | −2.74015 | ||||||||
\(733\) | −16.2336 | −0.599601 | −0.299800 | − | 0.954002i | \(-0.596920\pi\) | ||||
−0.299800 | + | 0.954002i | \(0.596920\pi\) | |||||||
\(734\) | 0.0672330 | 0.00248162 | ||||||||
\(735\) | −21.1956 | −0.781810 | ||||||||
\(736\) | 13.5398 | 0.499084 | ||||||||
\(737\) | 37.1665 | 1.36905 | ||||||||
\(738\) | −11.9066 | −0.438287 | ||||||||
\(739\) | −2.21135 | −0.0813460 | −0.0406730 | − | 0.999173i | \(-0.512950\pi\) | ||||
−0.0406730 | + | 0.999173i | \(0.512950\pi\) | |||||||
\(740\) | 11.5079 | 0.423037 | ||||||||
\(741\) | 5.21051 | 0.191413 | ||||||||
\(742\) | −16.3297 | −0.599483 | ||||||||
\(743\) | 34.6343 | 1.27061 | 0.635305 | − | 0.772262i | \(-0.280874\pi\) | ||||
0.635305 | + | 0.772262i | \(0.280874\pi\) | |||||||
\(744\) | −57.0271 | −2.09072 | ||||||||
\(745\) | 34.9601 | 1.28084 | ||||||||
\(746\) | −38.4755 | −1.40869 | ||||||||
\(747\) | −0.136086 | −0.00497912 | ||||||||
\(748\) | −88.9337 | −3.25174 | ||||||||
\(749\) | 17.6890 | 0.646342 | ||||||||
\(750\) | 36.8466 | 1.34545 | ||||||||
\(751\) | 4.65075 | 0.169708 | 0.0848541 | − | 0.996393i | \(-0.472958\pi\) | ||||
0.0848541 | + | 0.996393i | \(0.472958\pi\) | |||||||
\(752\) | −32.8301 | −1.19719 | ||||||||
\(753\) | −15.6770 | −0.571301 | ||||||||
\(754\) | 15.4518 | 0.562720 | ||||||||
\(755\) | −13.2869 | −0.483561 | ||||||||
\(756\) | 31.7359 | 1.15422 | ||||||||
\(757\) | −26.1708 | −0.951194 | −0.475597 | − | 0.879663i | \(-0.657768\pi\) | ||||
−0.475597 | + | 0.879663i | \(0.657768\pi\) | |||||||
\(758\) | −9.37862 | −0.340647 | ||||||||
\(759\) | 15.4169 | 0.559597 | ||||||||
\(760\) | −50.5539 | −1.83378 | ||||||||
\(761\) | −14.7165 | −0.533472 | −0.266736 | − | 0.963770i | \(-0.585945\pi\) | ||||
−0.266736 | + | 0.963770i | \(0.585945\pi\) | |||||||
\(762\) | 76.0171 | 2.75381 | ||||||||
\(763\) | −3.53137 | −0.127844 | ||||||||
\(764\) | −87.5939 | −3.16904 | ||||||||
\(765\) | −7.58267 | −0.274152 | ||||||||
\(766\) | 46.7837 | 1.69036 | ||||||||
\(767\) | 9.49507 | 0.342847 | ||||||||
\(768\) | −48.4105 | −1.74686 | ||||||||
\(769\) | 46.8720 | 1.69025 | 0.845124 | − | 0.534571i | \(-0.179527\pi\) | ||||
0.845124 | + | 0.534571i | \(0.179527\pi\) | |||||||
\(770\) | −27.2445 | −0.981822 | ||||||||
\(771\) | 27.9076 | 1.00507 | ||||||||
\(772\) | 90.2521 | 3.24825 | ||||||||
\(773\) | 3.30443 | 0.118852 | 0.0594260 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594260 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(774\) | −6.01613 | −0.216245 | ||||||||
\(775\) | 8.00957 | 0.287712 | ||||||||
\(776\) | −30.1850 | −1.08358 | ||||||||
\(777\) | −2.13601 | −0.0766291 | ||||||||
\(778\) | 47.5560 | 1.70496 | ||||||||
\(779\) | −31.6414 | −1.13367 | ||||||||
\(780\) | 17.6157 | 0.630742 | ||||||||
\(781\) | 18.7221 | 0.669928 | ||||||||
\(782\) | 46.2284 | 1.65312 | ||||||||
\(783\) | 33.7446 | 1.20594 | ||||||||
\(784\) | −35.1164 | −1.25416 | ||||||||
\(785\) | −52.9384 | −1.88945 | ||||||||
\(786\) | −23.9077 | −0.852758 | ||||||||
\(787\) | 26.6451 | 0.949796 | 0.474898 | − | 0.880041i | \(-0.342485\pi\) | ||||
0.474898 | + | 0.880041i | \(0.342485\pi\) | |||||||
\(788\) | −16.5524 | −0.589657 | ||||||||
\(789\) | 35.2413 | 1.25462 | ||||||||
\(790\) | −47.2450 | −1.68090 | ||||||||
\(791\) | 19.7094 | 0.700786 | ||||||||
\(792\) | −9.77018 | −0.347168 | ||||||||
\(793\) | −10.6112 | −0.376816 | ||||||||
\(794\) | −63.2219 | −2.24366 | ||||||||
\(795\) | −19.7949 | −0.702054 | ||||||||
\(796\) | 37.9147 | 1.34385 | ||||||||
\(797\) | −31.2303 | −1.10623 | −0.553117 | − | 0.833104i | \(-0.686562\pi\) | ||||
−0.553117 | + | 0.833104i | \(0.686562\pi\) | |||||||
\(798\) | 17.1745 | 0.607972 | ||||||||
\(799\) | −30.5166 | −1.07960 | ||||||||
\(800\) | −6.19241 | −0.218935 | ||||||||
\(801\) | −1.42597 | −0.0503842 | ||||||||
\(802\) | 74.6359 | 2.63549 | ||||||||
\(803\) | −3.75805 | −0.132619 | ||||||||
\(804\) | −79.2096 | −2.79351 | ||||||||
\(805\) | 9.74235 | 0.343373 | ||||||||
\(806\) | −14.9396 | −0.526224 | ||||||||
\(807\) | 24.3858 | 0.858421 | ||||||||
\(808\) | −53.6520 | −1.88747 | ||||||||
\(809\) | −28.5723 | −1.00455 | −0.502274 | − | 0.864709i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864709i | \(0.667503\pi\) | |||||||
\(810\) | 46.5631 | 1.63606 | ||||||||
\(811\) | −16.1813 | −0.568202 | −0.284101 | − | 0.958794i | \(-0.591695\pi\) | ||||
−0.284101 | + | 0.958794i | \(0.591695\pi\) | |||||||
\(812\) | 35.0370 | 1.22956 | ||||||||
\(813\) | 4.42887 | 0.155327 | ||||||||
\(814\) | 8.59147 | 0.301131 | ||||||||
\(815\) | 14.4158 | 0.504962 | ||||||||
\(816\) | 64.5506 | 2.25972 | ||||||||
\(817\) | −15.9877 | −0.559338 | ||||||||
\(818\) | 18.8875 | 0.660385 | ||||||||
\(819\) | 0.636350 | 0.0222359 | ||||||||
\(820\) | −106.973 | −3.73566 | ||||||||
\(821\) | −20.7759 | −0.725084 | −0.362542 | − | 0.931967i | \(-0.618091\pi\) | ||||
−0.362542 | + | 0.931967i | \(0.618091\pi\) | |||||||
\(822\) | −1.71458 | −0.0598027 | ||||||||
\(823\) | 18.7526 | 0.653675 | 0.326837 | − | 0.945081i | \(-0.394017\pi\) | ||||
0.326837 | + | 0.945081i | \(0.394017\pi\) | |||||||
\(824\) | −97.7079 | −3.40382 | ||||||||
\(825\) | −7.05088 | −0.245480 | ||||||||
\(826\) | 31.2970 | 1.08896 | ||||||||
\(827\) | −39.8210 | −1.38471 | −0.692357 | − | 0.721555i | \(-0.743427\pi\) | ||||
−0.692357 | + | 0.721555i | \(0.743427\pi\) | |||||||
\(828\) | 6.39454 | 0.222226 | ||||||||
\(829\) | 11.6907 | 0.406035 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(830\) | −1.77728 | −0.0616904 | ||||||||
\(831\) | −19.8775 | −0.689542 | ||||||||
\(832\) | −1.68945 | −0.0585711 | ||||||||
\(833\) | −32.6418 | −1.13097 | ||||||||
\(834\) | −46.3723 | −1.60574 | ||||||||
\(835\) | 28.1196 | 0.973121 | ||||||||
\(836\) | −47.5217 | −1.64357 | ||||||||
\(837\) | −32.6261 | −1.12772 | ||||||||
\(838\) | 30.5588 | 1.05564 | ||||||||
\(839\) | −49.7658 | −1.71810 | −0.859052 | − | 0.511888i | \(-0.828946\pi\) | ||||
−0.859052 | + | 0.511888i | \(0.828946\pi\) | |||||||
\(840\) | 31.7237 | 1.09457 | ||||||||
\(841\) | 8.25467 | 0.284644 | ||||||||
\(842\) | 46.0141 | 1.58575 | ||||||||
\(843\) | −33.9081 | −1.16786 | ||||||||
\(844\) | −45.7276 | −1.57401 | ||||||||
\(845\) | 2.52136 | 0.0867374 | ||||||||
\(846\) | −6.13611 | −0.210964 | ||||||||
\(847\) | 0.329733 | 0.0113297 | ||||||||
\(848\) | −32.7959 | −1.12622 | ||||||||
\(849\) | 42.2417 | 1.44973 | ||||||||
\(850\) | −21.1425 | −0.725181 | ||||||||
\(851\) | −3.07223 | −0.105315 | ||||||||
\(852\) | −39.9006 | −1.36697 | ||||||||
\(853\) | 41.3980 | 1.41744 | 0.708721 | − | 0.705489i | \(-0.249273\pi\) | ||||
0.708721 | + | 0.705489i | \(0.249273\pi\) | |||||||
\(854\) | −34.9760 | −1.19686 | ||||||||
\(855\) | −4.05179 | −0.138568 | ||||||||
\(856\) | 82.8461 | 2.83162 | ||||||||
\(857\) | −8.15091 | −0.278430 | −0.139215 | − | 0.990262i | \(-0.544458\pi\) | ||||
−0.139215 | + | 0.990262i | \(0.544458\pi\) | |||||||
\(858\) | 13.1514 | 0.448982 | ||||||||
\(859\) | 4.70562 | 0.160554 | 0.0802768 | − | 0.996773i | \(-0.474420\pi\) | ||||
0.0802768 | + | 0.996773i | \(0.474420\pi\) | |||||||
\(860\) | −54.0511 | −1.84313 | ||||||||
\(861\) | 19.8556 | 0.676678 | ||||||||
\(862\) | −38.8502 | −1.32324 | ||||||||
\(863\) | −0.500265 | −0.0170292 | −0.00851462 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851462 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(864\) | 25.2241 | 0.858140 | ||||||||
\(865\) | −5.56842 | −0.189332 | ||||||||
\(866\) | −21.8091 | −0.741103 | ||||||||
\(867\) | 33.0619 | 1.12284 | ||||||||
\(868\) | −33.8755 | −1.14981 | ||||||||
\(869\) | −24.2646 | −0.823119 | ||||||||
\(870\) | 61.7388 | 2.09314 | ||||||||
\(871\) | −11.3374 | −0.384153 | ||||||||
\(872\) | −16.5391 | −0.560084 | ||||||||
\(873\) | −2.41927 | −0.0818797 | ||||||||
\(874\) | 24.7021 | 0.835562 | ||||||||
\(875\) | 11.9586 | 0.404276 | ||||||||
\(876\) | 8.00919 | 0.270605 | ||||||||
\(877\) | 3.98318 | 0.134503 | 0.0672513 | − | 0.997736i | \(-0.478577\pi\) | ||||
0.0672513 | + | 0.997736i | \(0.478577\pi\) | |||||||
\(878\) | 58.3513 | 1.96926 | ||||||||
\(879\) | −29.1006 | −0.981540 | ||||||||
\(880\) | −54.7165 | −1.84449 | ||||||||
\(881\) | −40.3454 | −1.35927 | −0.679636 | − | 0.733550i | \(-0.737862\pi\) | ||||
−0.679636 | + | 0.733550i | \(0.737862\pi\) | |||||||
\(882\) | −6.56343 | −0.221002 | ||||||||
\(883\) | 43.8163 | 1.47454 | 0.737268 | − | 0.675600i | \(-0.236115\pi\) | ||||
0.737268 | + | 0.675600i | \(0.236115\pi\) | |||||||
\(884\) | 27.1286 | 0.912434 | ||||||||
\(885\) | 37.9383 | 1.27528 | ||||||||
\(886\) | 25.1343 | 0.844402 | ||||||||
\(887\) | 44.4188 | 1.49144 | 0.745719 | − | 0.666260i | \(-0.232106\pi\) | ||||
0.745719 | + | 0.666260i | \(0.232106\pi\) | |||||||
\(888\) | −10.0040 | −0.335711 | ||||||||
\(889\) | 24.6715 | 0.827455 | ||||||||
\(890\) | −18.6232 | −0.624252 | ||||||||
\(891\) | 23.9144 | 0.801161 | ||||||||
\(892\) | −1.82515 | −0.0611107 | ||||||||
\(893\) | −16.3065 | −0.545677 | ||||||||
\(894\) | −55.6252 | −1.86038 | ||||||||
\(895\) | −44.1466 | −1.47566 | ||||||||
\(896\) | −17.4495 | −0.582947 | ||||||||
\(897\) | −4.70281 | −0.157022 | ||||||||
\(898\) | 86.5854 | 2.88939 | ||||||||
\(899\) | −36.0197 | −1.20133 | ||||||||
\(900\) | −2.92453 | −0.0974843 | ||||||||
\(901\) | −30.4848 | −1.01559 | ||||||||
\(902\) | −79.8633 | −2.65916 | ||||||||
\(903\) | 10.0326 | 0.333865 | ||||||||
\(904\) | 92.3086 | 3.07014 | ||||||||
\(905\) | 9.66138 | 0.321155 | ||||||||
\(906\) | 21.1409 | 0.702360 | ||||||||
\(907\) | −27.5521 | −0.914851 | −0.457426 | − | 0.889248i | \(-0.651228\pi\) | ||||
−0.457426 | + | 0.889248i | \(0.651228\pi\) | |||||||
\(908\) | −37.2923 | −1.23759 | ||||||||
\(909\) | −4.30010 | −0.142625 | ||||||||
\(910\) | 8.31074 | 0.275498 | ||||||||
\(911\) | −44.8641 | −1.48641 | −0.743207 | − | 0.669062i | \(-0.766696\pi\) | ||||
−0.743207 | + | 0.669062i | \(0.766696\pi\) | |||||||
\(912\) | 34.4926 | 1.14216 | ||||||||
\(913\) | −0.912794 | −0.0302091 | ||||||||
\(914\) | −21.8845 | −0.723875 | ||||||||
\(915\) | −42.3980 | −1.40164 | ||||||||
\(916\) | 66.2154 | 2.18782 | ||||||||
\(917\) | −7.75927 | −0.256234 | ||||||||
\(918\) | 86.1214 | 2.84243 | ||||||||
\(919\) | 9.92251 | 0.327313 | 0.163657 | − | 0.986517i | \(-0.447671\pi\) | ||||
0.163657 | + | 0.986517i | \(0.447671\pi\) | |||||||
\(920\) | 45.6281 | 1.50431 | ||||||||
\(921\) | 10.6885 | 0.352198 | ||||||||
\(922\) | −26.6389 | −0.877306 | ||||||||
\(923\) | −5.71104 | −0.187981 | ||||||||
\(924\) | 29.8209 | 0.981035 | ||||||||
\(925\) | 1.40508 | 0.0461986 | ||||||||
\(926\) | −2.53156 | −0.0831921 | ||||||||
\(927\) | −7.83110 | −0.257207 | ||||||||
\(928\) | 27.8478 | 0.914149 | ||||||||
\(929\) | 12.3501 | 0.405194 | 0.202597 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202597 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(930\) | −59.6923 | −1.95739 | ||||||||
\(931\) | −17.4421 | −0.571642 | ||||||||
\(932\) | −48.5529 | −1.59040 | ||||||||
\(933\) | −14.5900 | −0.477657 | ||||||||
\(934\) | 79.2105 | 2.59185 | ||||||||
\(935\) | −50.8607 | −1.66332 | ||||||||
\(936\) | 2.98033 | 0.0974151 | ||||||||
\(937\) | 32.0670 | 1.04758 | 0.523791 | − | 0.851847i | \(-0.324517\pi\) | ||||
0.523791 | + | 0.851847i | \(0.324517\pi\) | |||||||
\(938\) | −37.3696 | −1.22016 | ||||||||
\(939\) | −43.8257 | −1.43020 | ||||||||
\(940\) | −55.1290 | −1.79811 | ||||||||
\(941\) | 38.5802 | 1.25768 | 0.628839 | − | 0.777536i | \(-0.283531\pi\) | ||||
0.628839 | + | 0.777536i | \(0.283531\pi\) | |||||||
\(942\) | 84.2305 | 2.74438 | ||||||||
\(943\) | 28.5583 | 0.929987 | ||||||||
\(944\) | 62.8555 | 2.04577 | ||||||||
\(945\) | 18.1496 | 0.590406 | ||||||||
\(946\) | −40.3532 | −1.31199 | ||||||||
\(947\) | −50.0756 | −1.62724 | −0.813620 | − | 0.581397i | \(-0.802506\pi\) | ||||
−0.813620 | + | 0.581397i | \(0.802506\pi\) | |||||||
\(948\) | 51.7128 | 1.67955 | ||||||||
\(949\) | 1.14637 | 0.0372127 | ||||||||
\(950\) | −11.2975 | −0.366538 | ||||||||
\(951\) | −35.8421 | −1.16226 | ||||||||
\(952\) | 48.8553 | 1.58341 | ||||||||
\(953\) | 11.5351 | 0.373659 | 0.186830 | − | 0.982392i | \(-0.440179\pi\) | ||||
0.186830 | + | 0.982392i | \(0.440179\pi\) | |||||||
\(954\) | −6.12971 | −0.198457 | ||||||||
\(955\) | −50.0945 | −1.62102 | ||||||||
\(956\) | −34.2073 | −1.10634 | ||||||||
\(957\) | 31.7084 | 1.02499 | ||||||||
\(958\) | 4.74468 | 0.153294 | ||||||||
\(959\) | −0.556468 | −0.0179693 | ||||||||
\(960\) | −6.75033 | −0.217866 | ||||||||
\(961\) | 3.82574 | 0.123411 | ||||||||
\(962\) | −2.62077 | −0.0844970 | ||||||||
\(963\) | 6.63995 | 0.213969 | ||||||||
\(964\) | −7.53364 | −0.242642 | ||||||||
\(965\) | 51.6147 | 1.66154 | ||||||||
\(966\) | −15.5011 | −0.498740 | ||||||||
\(967\) | −27.2112 | −0.875054 | −0.437527 | − | 0.899205i | \(-0.644146\pi\) | ||||
−0.437527 | + | 0.899205i | \(0.644146\pi\) | |||||||
\(968\) | 1.54429 | 0.0496355 | ||||||||
\(969\) | 32.0619 | 1.02998 | ||||||||
\(970\) | −31.5957 | −1.01448 | ||||||||
\(971\) | 50.1971 | 1.61090 | 0.805450 | − | 0.592663i | \(-0.201923\pi\) | ||||
0.805450 | + | 0.592663i | \(0.201923\pi\) | |||||||
\(972\) | 22.1566 | 0.710674 | ||||||||
\(973\) | −15.0502 | −0.482488 | ||||||||
\(974\) | −20.8758 | −0.668902 | ||||||||
\(975\) | 2.15082 | 0.0688815 | ||||||||
\(976\) | −70.2443 | −2.24846 | ||||||||
\(977\) | 45.4587 | 1.45435 | 0.727176 | − | 0.686451i | \(-0.240832\pi\) | ||||
0.727176 | + | 0.686451i | \(0.240832\pi\) | |||||||
\(978\) | −22.9370 | −0.733445 | ||||||||
\(979\) | −9.56469 | −0.305689 | ||||||||
\(980\) | −58.9682 | −1.88367 | ||||||||
\(981\) | −1.32558 | −0.0423224 | ||||||||
\(982\) | 29.5855 | 0.944111 | ||||||||
\(983\) | 48.4752 | 1.54612 | 0.773060 | − | 0.634333i | \(-0.218725\pi\) | ||||
0.773060 | + | 0.634333i | \(0.218725\pi\) | |||||||
\(984\) | 92.9934 | 2.96452 | ||||||||
\(985\) | −9.46625 | −0.301620 | ||||||||
\(986\) | 95.0795 | 3.02795 | ||||||||
\(987\) | 10.2327 | 0.325710 | ||||||||
\(988\) | 14.4962 | 0.461185 | ||||||||
\(989\) | 14.4299 | 0.458844 | ||||||||
\(990\) | −10.2268 | −0.325029 | ||||||||
\(991\) | 17.3311 | 0.550541 | 0.275271 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275271 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(992\) | −26.9247 | −0.854860 | ||||||||
\(993\) | 1.44834 | 0.0459618 | ||||||||
\(994\) | −18.8244 | −0.597073 | ||||||||
\(995\) | 21.6832 | 0.687403 | ||||||||
\(996\) | 1.94535 | 0.0616409 | ||||||||
\(997\) | 59.0950 | 1.87156 | 0.935778 | − | 0.352589i | \(-0.114699\pi\) | ||||
0.935778 | + | 0.352589i | \(0.114699\pi\) | |||||||
\(998\) | −67.6273 | −2.14071 | ||||||||
\(999\) | −5.72342 | −0.181081 |
(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 | 6019.2.a.b.1.6 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.b.1.6 | ✓ | 101 | 1.1 | even | 1 | trivial |