Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.44853 | 0.836311 | 0.418156 | − | 0.908375i | \(-0.362677\pi\) | ||||
0.418156 | + | 0.908375i | \(0.362677\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.26403 | −0.565289 | −0.282645 | − | 0.959225i | \(-0.591212\pi\) | ||||
−0.282645 | + | 0.959225i | \(0.591212\pi\) | |||||||
\(6\) | −1.44853 | −0.591361 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.901751 | −0.300584 | ||||||||
\(10\) | 1.26403 | 0.399720 | ||||||||
\(11\) | −3.22511 | −0.972406 | −0.486203 | − | 0.873846i | \(-0.661618\pi\) | ||||
−0.486203 | + | 0.873846i | \(0.661618\pi\) | |||||||
\(12\) | 1.44853 | 0.418156 | ||||||||
\(13\) | −2.31777 | −0.642835 | −0.321417 | − | 0.946938i | \(-0.604159\pi\) | ||||
−0.321417 | + | 0.946938i | \(0.604159\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.83098 | −0.472758 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.60165 | 0.873527 | 0.436764 | − | 0.899576i | \(-0.356125\pi\) | ||||
0.436764 | + | 0.899576i | \(0.356125\pi\) | |||||||
\(18\) | 0.901751 | 0.212545 | ||||||||
\(19\) | 5.33546 | 1.22404 | 0.612020 | − | 0.790843i | \(-0.290357\pi\) | ||||
0.612020 | + | 0.790843i | \(0.290357\pi\) | |||||||
\(20\) | −1.26403 | −0.282645 | ||||||||
\(21\) | −1.44853 | −0.316096 | ||||||||
\(22\) | 3.22511 | 0.687595 | ||||||||
\(23\) | −7.66129 | −1.59749 | −0.798745 | − | 0.601670i | \(-0.794502\pi\) | ||||
−0.798745 | + | 0.601670i | \(0.794502\pi\) | |||||||
\(24\) | −1.44853 | −0.295681 | ||||||||
\(25\) | −3.40224 | −0.680448 | ||||||||
\(26\) | 2.31777 | 0.454553 | ||||||||
\(27\) | −5.65182 | −1.08769 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.214755 | −0.0398791 | −0.0199395 | − | 0.999801i | \(-0.506347\pi\) | ||||
−0.0199395 | + | 0.999801i | \(0.506347\pi\) | |||||||
\(30\) | 1.83098 | 0.334290 | ||||||||
\(31\) | −5.47162 | −0.982732 | −0.491366 | − | 0.870953i | \(-0.663502\pi\) | ||||
−0.491366 | + | 0.870953i | \(0.663502\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.67167 | −0.813234 | ||||||||
\(34\) | −3.60165 | −0.617677 | ||||||||
\(35\) | 1.26403 | 0.213659 | ||||||||
\(36\) | −0.901751 | −0.150292 | ||||||||
\(37\) | 0.154141 | 0.0253407 | 0.0126703 | − | 0.999920i | \(-0.495967\pi\) | ||||
0.0126703 | + | 0.999920i | \(0.495967\pi\) | |||||||
\(38\) | −5.33546 | −0.865526 | ||||||||
\(39\) | −3.35737 | −0.537610 | ||||||||
\(40\) | 1.26403 | 0.199860 | ||||||||
\(41\) | 3.69908 | 0.577699 | 0.288850 | − | 0.957374i | \(-0.406727\pi\) | ||||
0.288850 | + | 0.957374i | \(0.406727\pi\) | |||||||
\(42\) | 1.44853 | 0.223514 | ||||||||
\(43\) | 7.50104 | 1.14390 | 0.571949 | − | 0.820289i | \(-0.306188\pi\) | ||||
0.571949 | + | 0.820289i | \(0.306188\pi\) | |||||||
\(44\) | −3.22511 | −0.486203 | ||||||||
\(45\) | 1.13984 | 0.169917 | ||||||||
\(46\) | 7.66129 | 1.12960 | ||||||||
\(47\) | 0.101562 | 0.0148144 | 0.00740720 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740720 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(48\) | 1.44853 | 0.209078 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.40224 | 0.481149 | ||||||||
\(51\) | 5.21710 | 0.730541 | ||||||||
\(52\) | −2.31777 | −0.321417 | ||||||||
\(53\) | 9.39083 | 1.28993 | 0.644965 | − | 0.764212i | \(-0.276872\pi\) | ||||
0.644965 | + | 0.764212i | \(0.276872\pi\) | |||||||
\(54\) | 5.65182 | 0.769115 | ||||||||
\(55\) | 4.07662 | 0.549691 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 7.72860 | 1.02368 | ||||||||
\(58\) | 0.214755 | 0.0281988 | ||||||||
\(59\) | 11.8493 | 1.54264 | 0.771322 | − | 0.636445i | \(-0.219596\pi\) | ||||
0.771322 | + | 0.636445i | \(0.219596\pi\) | |||||||
\(60\) | −1.83098 | −0.236379 | ||||||||
\(61\) | 5.95759 | 0.762792 | 0.381396 | − | 0.924412i | \(-0.375443\pi\) | ||||
0.381396 | + | 0.924412i | \(0.375443\pi\) | |||||||
\(62\) | 5.47162 | 0.694897 | ||||||||
\(63\) | 0.901751 | 0.113610 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.92972 | 0.363388 | ||||||||
\(66\) | 4.67167 | 0.575043 | ||||||||
\(67\) | −2.95438 | −0.360935 | −0.180467 | − | 0.983581i | \(-0.557761\pi\) | ||||
−0.180467 | + | 0.983581i | \(0.557761\pi\) | |||||||
\(68\) | 3.60165 | 0.436764 | ||||||||
\(69\) | −11.0976 | −1.33600 | ||||||||
\(70\) | −1.26403 | −0.151080 | ||||||||
\(71\) | 10.7018 | 1.27007 | 0.635035 | − | 0.772483i | \(-0.280986\pi\) | ||||
0.635035 | + | 0.772483i | \(0.280986\pi\) | |||||||
\(72\) | 0.901751 | 0.106272 | ||||||||
\(73\) | −15.7336 | −1.84148 | −0.920739 | − | 0.390179i | \(-0.872413\pi\) | ||||
−0.920739 | + | 0.390179i | \(0.872413\pi\) | |||||||
\(74\) | −0.154141 | −0.0179186 | ||||||||
\(75\) | −4.92826 | −0.569066 | ||||||||
\(76\) | 5.33546 | 0.612020 | ||||||||
\(77\) | 3.22511 | 0.367535 | ||||||||
\(78\) | 3.35737 | 0.380147 | ||||||||
\(79\) | −13.6695 | −1.53794 | −0.768970 | − | 0.639285i | \(-0.779230\pi\) | ||||
−0.768970 | + | 0.639285i | \(0.779230\pi\) | |||||||
\(80\) | −1.26403 | −0.141322 | ||||||||
\(81\) | −5.48159 | −0.609066 | ||||||||
\(82\) | −3.69908 | −0.408495 | ||||||||
\(83\) | −1.96725 | −0.215934 | −0.107967 | − | 0.994154i | \(-0.534434\pi\) | ||||
−0.107967 | + | 0.994154i | \(0.534434\pi\) | |||||||
\(84\) | −1.44853 | −0.158048 | ||||||||
\(85\) | −4.55257 | −0.493796 | ||||||||
\(86\) | −7.50104 | −0.808857 | ||||||||
\(87\) | −0.311080 | −0.0333513 | ||||||||
\(88\) | 3.22511 | 0.343797 | ||||||||
\(89\) | −0.350463 | −0.0371490 | −0.0185745 | − | 0.999827i | \(-0.505913\pi\) | ||||
−0.0185745 | + | 0.999827i | \(0.505913\pi\) | |||||||
\(90\) | −1.13984 | −0.120149 | ||||||||
\(91\) | 2.31777 | 0.242969 | ||||||||
\(92\) | −7.66129 | −0.798745 | ||||||||
\(93\) | −7.92583 | −0.821870 | ||||||||
\(94\) | −0.101562 | −0.0104754 | ||||||||
\(95\) | −6.74416 | −0.691936 | ||||||||
\(96\) | −1.44853 | −0.147840 | ||||||||
\(97\) | −17.6621 | −1.79332 | −0.896659 | − | 0.442723i | \(-0.854013\pi\) | ||||
−0.896659 | + | 0.442723i | \(0.854013\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 2.90824 | 0.292289 | ||||||||
\(100\) | −3.40224 | −0.340224 | ||||||||
\(101\) | 8.91473 | 0.887049 | 0.443524 | − | 0.896262i | \(-0.353728\pi\) | ||||
0.443524 | + | 0.896262i | \(0.353728\pi\) | |||||||
\(102\) | −5.21710 | −0.516570 | ||||||||
\(103\) | 9.46770 | 0.932880 | 0.466440 | − | 0.884553i | \(-0.345536\pi\) | ||||
0.466440 | + | 0.884553i | \(0.345536\pi\) | |||||||
\(104\) | 2.31777 | 0.227276 | ||||||||
\(105\) | 1.83098 | 0.178686 | ||||||||
\(106\) | −9.39083 | −0.912118 | ||||||||
\(107\) | 17.0234 | 1.64571 | 0.822856 | − | 0.568250i | \(-0.192380\pi\) | ||||
0.822856 | + | 0.568250i | \(0.192380\pi\) | |||||||
\(108\) | −5.65182 | −0.543846 | ||||||||
\(109\) | 19.5460 | 1.87217 | 0.936086 | − | 0.351773i | \(-0.114421\pi\) | ||||
0.936086 | + | 0.351773i | \(0.114421\pi\) | |||||||
\(110\) | −4.07662 | −0.388690 | ||||||||
\(111\) | 0.223279 | 0.0211927 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −14.8821 | −1.39999 | −0.699997 | − | 0.714146i | \(-0.746815\pi\) | ||||
−0.699997 | + | 0.714146i | \(0.746815\pi\) | |||||||
\(114\) | −7.72860 | −0.723849 | ||||||||
\(115\) | 9.68407 | 0.903044 | ||||||||
\(116\) | −0.214755 | −0.0199395 | ||||||||
\(117\) | 2.09005 | 0.193226 | ||||||||
\(118\) | −11.8493 | −1.09081 | ||||||||
\(119\) | −3.60165 | −0.330162 | ||||||||
\(120\) | 1.83098 | 0.167145 | ||||||||
\(121\) | −0.598690 | −0.0544264 | ||||||||
\(122\) | −5.95759 | −0.539375 | ||||||||
\(123\) | 5.35824 | 0.483136 | ||||||||
\(124\) | −5.47162 | −0.491366 | ||||||||
\(125\) | 10.6206 | 0.949939 | ||||||||
\(126\) | −0.901751 | −0.0803344 | ||||||||
\(127\) | 7.87038 | 0.698383 | 0.349191 | − | 0.937051i | \(-0.386456\pi\) | ||||
0.349191 | + | 0.937051i | \(0.386456\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.8655 | 0.956654 | ||||||||
\(130\) | −2.92972 | −0.256954 | ||||||||
\(131\) | −0.0345986 | −0.00302290 | −0.00151145 | − | 0.999999i | \(-0.500481\pi\) | ||||
−0.00151145 | + | 0.999999i | \(0.500481\pi\) | |||||||
\(132\) | −4.67167 | −0.406617 | ||||||||
\(133\) | −5.33546 | −0.462643 | ||||||||
\(134\) | 2.95438 | 0.255219 | ||||||||
\(135\) | 7.14404 | 0.614861 | ||||||||
\(136\) | −3.60165 | −0.308839 | ||||||||
\(137\) | −2.39977 | −0.205026 | −0.102513 | − | 0.994732i | \(-0.532688\pi\) | ||||
−0.102513 | + | 0.994732i | \(0.532688\pi\) | |||||||
\(138\) | 11.0976 | 0.944694 | ||||||||
\(139\) | −13.1736 | −1.11737 | −0.558683 | − | 0.829381i | \(-0.688693\pi\) | ||||
−0.558683 | + | 0.829381i | \(0.688693\pi\) | |||||||
\(140\) | 1.26403 | 0.106830 | ||||||||
\(141\) | 0.147116 | 0.0123894 | ||||||||
\(142\) | −10.7018 | −0.898075 | ||||||||
\(143\) | 7.47506 | 0.625096 | ||||||||
\(144\) | −0.901751 | −0.0751459 | ||||||||
\(145\) | 0.271456 | 0.0225432 | ||||||||
\(146\) | 15.7336 | 1.30212 | ||||||||
\(147\) | 1.44853 | 0.119473 | ||||||||
\(148\) | 0.154141 | 0.0126703 | ||||||||
\(149\) | 14.8747 | 1.21859 | 0.609293 | − | 0.792945i | \(-0.291453\pi\) | ||||
0.609293 | + | 0.792945i | \(0.291453\pi\) | |||||||
\(150\) | 4.92826 | 0.402390 | ||||||||
\(151\) | 24.1404 | 1.96452 | 0.982259 | − | 0.187530i | \(-0.0600480\pi\) | ||||
0.982259 | + | 0.187530i | \(0.0600480\pi\) | |||||||
\(152\) | −5.33546 | −0.432763 | ||||||||
\(153\) | −3.24779 | −0.262568 | ||||||||
\(154\) | −3.22511 | −0.259886 | ||||||||
\(155\) | 6.91627 | 0.555528 | ||||||||
\(156\) | −3.35737 | −0.268805 | ||||||||
\(157\) | 6.06502 | 0.484041 | 0.242021 | − | 0.970271i | \(-0.422190\pi\) | ||||
0.242021 | + | 0.970271i | \(0.422190\pi\) | |||||||
\(158\) | 13.6695 | 1.08749 | ||||||||
\(159\) | 13.6029 | 1.07878 | ||||||||
\(160\) | 1.26403 | 0.0999300 | ||||||||
\(161\) | 7.66129 | 0.603794 | ||||||||
\(162\) | 5.48159 | 0.430674 | ||||||||
\(163\) | 10.5901 | 0.829477 | 0.414738 | − | 0.909941i | \(-0.363873\pi\) | ||||
0.414738 | + | 0.909941i | \(0.363873\pi\) | |||||||
\(164\) | 3.69908 | 0.288850 | ||||||||
\(165\) | 5.90512 | 0.459713 | ||||||||
\(166\) | 1.96725 | 0.152688 | ||||||||
\(167\) | 3.80166 | 0.294181 | 0.147091 | − | 0.989123i | \(-0.453009\pi\) | ||||
0.147091 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(168\) | 1.44853 | 0.111757 | ||||||||
\(169\) | −7.62793 | −0.586764 | ||||||||
\(170\) | 4.55257 | 0.349166 | ||||||||
\(171\) | −4.81126 | −0.367926 | ||||||||
\(172\) | 7.50104 | 0.571949 | ||||||||
\(173\) | 16.4571 | 1.25121 | 0.625605 | − | 0.780140i | \(-0.284852\pi\) | ||||
0.625605 | + | 0.780140i | \(0.284852\pi\) | |||||||
\(174\) | 0.311080 | 0.0235829 | ||||||||
\(175\) | 3.40224 | 0.257185 | ||||||||
\(176\) | −3.22511 | −0.243102 | ||||||||
\(177\) | 17.1641 | 1.29013 | ||||||||
\(178\) | 0.350463 | 0.0262683 | ||||||||
\(179\) | 19.1032 | 1.42784 | 0.713921 | − | 0.700227i | \(-0.246918\pi\) | ||||
0.713921 | + | 0.700227i | \(0.246918\pi\) | |||||||
\(180\) | 1.13984 | 0.0849584 | ||||||||
\(181\) | 15.4524 | 1.14857 | 0.574285 | − | 0.818655i | \(-0.305280\pi\) | ||||
0.574285 | + | 0.818655i | \(0.305280\pi\) | |||||||
\(182\) | −2.31777 | −0.171805 | ||||||||
\(183\) | 8.62977 | 0.637931 | ||||||||
\(184\) | 7.66129 | 0.564798 | ||||||||
\(185\) | −0.194839 | −0.0143248 | ||||||||
\(186\) | 7.92583 | 0.581150 | ||||||||
\(187\) | −11.6157 | −0.849423 | ||||||||
\(188\) | 0.101562 | 0.00740720 | ||||||||
\(189\) | 5.65182 | 0.411109 | ||||||||
\(190\) | 6.74416 | 0.489273 | ||||||||
\(191\) | 4.74568 | 0.343385 | 0.171692 | − | 0.985151i | \(-0.445076\pi\) | ||||
0.171692 | + | 0.985151i | \(0.445076\pi\) | |||||||
\(192\) | 1.44853 | 0.104539 | ||||||||
\(193\) | 4.37571 | 0.314970 | 0.157485 | − | 0.987521i | \(-0.449661\pi\) | ||||
0.157485 | + | 0.987521i | \(0.449661\pi\) | |||||||
\(194\) | 17.6621 | 1.26807 | ||||||||
\(195\) | 4.24380 | 0.303905 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.06798 | 0.218585 | 0.109292 | − | 0.994010i | \(-0.465142\pi\) | ||||
0.109292 | + | 0.994010i | \(0.465142\pi\) | |||||||
\(198\) | −2.90824 | −0.206680 | ||||||||
\(199\) | −26.2836 | −1.86320 | −0.931599 | − | 0.363488i | \(-0.881586\pi\) | ||||
−0.931599 | + | 0.363488i | \(0.881586\pi\) | |||||||
\(200\) | 3.40224 | 0.240575 | ||||||||
\(201\) | −4.27951 | −0.301854 | ||||||||
\(202\) | −8.91473 | −0.627238 | ||||||||
\(203\) | 0.214755 | 0.0150729 | ||||||||
\(204\) | 5.21710 | 0.365270 | ||||||||
\(205\) | −4.67573 | −0.326567 | ||||||||
\(206\) | −9.46770 | −0.659646 | ||||||||
\(207\) | 6.90858 | 0.480179 | ||||||||
\(208\) | −2.31777 | −0.160709 | ||||||||
\(209\) | −17.2074 | −1.19026 | ||||||||
\(210\) | −1.83098 | −0.126350 | ||||||||
\(211\) | −8.94228 | −0.615612 | −0.307806 | − | 0.951449i | \(-0.599595\pi\) | ||||
−0.307806 | + | 0.951449i | \(0.599595\pi\) | |||||||
\(212\) | 9.39083 | 0.644965 | ||||||||
\(213\) | 15.5019 | 1.06217 | ||||||||
\(214\) | −17.0234 | −1.16369 | ||||||||
\(215\) | −9.48150 | −0.646633 | ||||||||
\(216\) | 5.65182 | 0.384557 | ||||||||
\(217\) | 5.47162 | 0.371438 | ||||||||
\(218\) | −19.5460 | −1.32382 | ||||||||
\(219\) | −22.7906 | −1.54005 | ||||||||
\(220\) | 4.07662 | 0.274845 | ||||||||
\(221\) | −8.34780 | −0.561534 | ||||||||
\(222\) | −0.223279 | −0.0149855 | ||||||||
\(223\) | −27.0980 | −1.81461 | −0.907307 | − | 0.420470i | \(-0.861865\pi\) | ||||
−0.907307 | + | 0.420470i | \(0.861865\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.06797 | 0.204532 | ||||||||
\(226\) | 14.8821 | 0.989946 | ||||||||
\(227\) | 0.799865 | 0.0530889 | 0.0265444 | − | 0.999648i | \(-0.491550\pi\) | ||||
0.0265444 | + | 0.999648i | \(0.491550\pi\) | |||||||
\(228\) | 7.72860 | 0.511839 | ||||||||
\(229\) | −1.41408 | −0.0934453 | −0.0467227 | − | 0.998908i | \(-0.514878\pi\) | ||||
−0.0467227 | + | 0.998908i | \(0.514878\pi\) | |||||||
\(230\) | −9.68407 | −0.638549 | ||||||||
\(231\) | 4.67167 | 0.307374 | ||||||||
\(232\) | 0.214755 | 0.0140994 | ||||||||
\(233\) | 2.30009 | 0.150684 | 0.0753419 | − | 0.997158i | \(-0.475995\pi\) | ||||
0.0753419 | + | 0.997158i | \(0.475995\pi\) | |||||||
\(234\) | −2.09005 | −0.136631 | ||||||||
\(235\) | −0.128377 | −0.00837442 | ||||||||
\(236\) | 11.8493 | 0.771322 | ||||||||
\(237\) | −19.8007 | −1.28620 | ||||||||
\(238\) | 3.60165 | 0.233460 | ||||||||
\(239\) | 9.46668 | 0.612349 | 0.306174 | − | 0.951975i | \(-0.400951\pi\) | ||||
0.306174 | + | 0.951975i | \(0.400951\pi\) | |||||||
\(240\) | −1.83098 | −0.118189 | ||||||||
\(241\) | 15.2642 | 0.983254 | 0.491627 | − | 0.870806i | \(-0.336402\pi\) | ||||
0.491627 | + | 0.870806i | \(0.336402\pi\) | |||||||
\(242\) | 0.598690 | 0.0384853 | ||||||||
\(243\) | 9.01518 | 0.578324 | ||||||||
\(244\) | 5.95759 | 0.381396 | ||||||||
\(245\) | −1.26403 | −0.0807556 | ||||||||
\(246\) | −5.35824 | −0.341629 | ||||||||
\(247\) | −12.3664 | −0.786855 | ||||||||
\(248\) | 5.47162 | 0.347448 | ||||||||
\(249\) | −2.84963 | −0.180588 | ||||||||
\(250\) | −10.6206 | −0.671709 | ||||||||
\(251\) | 1.32168 | 0.0834237 | 0.0417118 | − | 0.999130i | \(-0.486719\pi\) | ||||
0.0417118 | + | 0.999130i | \(0.486719\pi\) | |||||||
\(252\) | 0.901751 | 0.0568050 | ||||||||
\(253\) | 24.7085 | 1.55341 | ||||||||
\(254\) | −7.87038 | −0.493831 | ||||||||
\(255\) | −6.59455 | −0.412967 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.58020 | −0.597597 | −0.298798 | − | 0.954316i | \(-0.596586\pi\) | ||||
−0.298798 | + | 0.954316i | \(0.596586\pi\) | |||||||
\(258\) | −10.8655 | −0.676456 | ||||||||
\(259\) | −0.154141 | −0.00957788 | ||||||||
\(260\) | 2.92972 | 0.181694 | ||||||||
\(261\) | 0.193656 | 0.0119870 | ||||||||
\(262\) | 0.0345986 | 0.00213751 | ||||||||
\(263\) | 26.9818 | 1.66377 | 0.831885 | − | 0.554947i | \(-0.187262\pi\) | ||||
0.831885 | + | 0.554947i | \(0.187262\pi\) | |||||||
\(264\) | 4.67167 | 0.287522 | ||||||||
\(265\) | −11.8703 | −0.729184 | ||||||||
\(266\) | 5.33546 | 0.327138 | ||||||||
\(267\) | −0.507657 | −0.0310681 | ||||||||
\(268\) | −2.95438 | −0.180467 | ||||||||
\(269\) | −7.60283 | −0.463553 | −0.231776 | − | 0.972769i | \(-0.574454\pi\) | ||||
−0.231776 | + | 0.972769i | \(0.574454\pi\) | |||||||
\(270\) | −7.14404 | −0.434773 | ||||||||
\(271\) | 23.1724 | 1.40763 | 0.703813 | − | 0.710386i | \(-0.251479\pi\) | ||||
0.703813 | + | 0.710386i | \(0.251479\pi\) | |||||||
\(272\) | 3.60165 | 0.218382 | ||||||||
\(273\) | 3.35737 | 0.203197 | ||||||||
\(274\) | 2.39977 | 0.144976 | ||||||||
\(275\) | 10.9726 | 0.661672 | ||||||||
\(276\) | −11.0976 | −0.667999 | ||||||||
\(277\) | 21.5203 | 1.29303 | 0.646515 | − | 0.762902i | \(-0.276226\pi\) | ||||
0.646515 | + | 0.762902i | \(0.276226\pi\) | |||||||
\(278\) | 13.1736 | 0.790098 | ||||||||
\(279\) | 4.93404 | 0.295393 | ||||||||
\(280\) | −1.26403 | −0.0755400 | ||||||||
\(281\) | −29.3424 | −1.75042 | −0.875210 | − | 0.483742i | \(-0.839277\pi\) | ||||
−0.875210 | + | 0.483742i | \(0.839277\pi\) | |||||||
\(282\) | −0.147116 | −0.00876066 | ||||||||
\(283\) | −30.0854 | −1.78839 | −0.894197 | − | 0.447674i | \(-0.852253\pi\) | ||||
−0.894197 | + | 0.447674i | \(0.852253\pi\) | |||||||
\(284\) | 10.7018 | 0.635035 | ||||||||
\(285\) | −9.76914 | −0.578674 | ||||||||
\(286\) | −7.47506 | −0.442010 | ||||||||
\(287\) | −3.69908 | −0.218350 | ||||||||
\(288\) | 0.901751 | 0.0531362 | ||||||||
\(289\) | −4.02815 | −0.236950 | ||||||||
\(290\) | −0.271456 | −0.0159405 | ||||||||
\(291\) | −25.5842 | −1.49977 | ||||||||
\(292\) | −15.7336 | −0.920739 | ||||||||
\(293\) | 19.2131 | 1.12244 | 0.561221 | − | 0.827666i | \(-0.310332\pi\) | ||||
0.561221 | + | 0.827666i | \(0.310332\pi\) | |||||||
\(294\) | −1.44853 | −0.0844802 | ||||||||
\(295\) | −14.9778 | −0.872040 | ||||||||
\(296\) | −0.154141 | −0.00895929 | ||||||||
\(297\) | 18.2277 | 1.05768 | ||||||||
\(298\) | −14.8747 | −0.861671 | ||||||||
\(299\) | 17.7571 | 1.02692 | ||||||||
\(300\) | −4.92826 | −0.284533 | ||||||||
\(301\) | −7.50104 | −0.432352 | ||||||||
\(302\) | −24.1404 | −1.38912 | ||||||||
\(303\) | 12.9133 | 0.741849 | ||||||||
\(304\) | 5.33546 | 0.306010 | ||||||||
\(305\) | −7.53055 | −0.431198 | ||||||||
\(306\) | 3.24779 | 0.185664 | ||||||||
\(307\) | −2.60073 | −0.148431 | −0.0742156 | − | 0.997242i | \(-0.523645\pi\) | ||||
−0.0742156 | + | 0.997242i | \(0.523645\pi\) | |||||||
\(308\) | 3.22511 | 0.183767 | ||||||||
\(309\) | 13.7143 | 0.780178 | ||||||||
\(310\) | −6.91627 | −0.392818 | ||||||||
\(311\) | −10.9513 | −0.620991 | −0.310495 | − | 0.950575i | \(-0.600495\pi\) | ||||
−0.310495 | + | 0.950575i | \(0.600495\pi\) | |||||||
\(312\) | 3.35737 | 0.190074 | ||||||||
\(313\) | 21.0786 | 1.19143 | 0.595717 | − | 0.803195i | \(-0.296868\pi\) | ||||
0.595717 | + | 0.803195i | \(0.296868\pi\) | |||||||
\(314\) | −6.06502 | −0.342269 | ||||||||
\(315\) | −1.13984 | −0.0642225 | ||||||||
\(316\) | −13.6695 | −0.768970 | ||||||||
\(317\) | −3.41278 | −0.191681 | −0.0958403 | − | 0.995397i | \(-0.530554\pi\) | ||||
−0.0958403 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(318\) | −13.6029 | −0.762815 | ||||||||
\(319\) | 0.692609 | 0.0387787 | ||||||||
\(320\) | −1.26403 | −0.0706612 | ||||||||
\(321\) | 24.6589 | 1.37633 | ||||||||
\(322\) | −7.66129 | −0.426947 | ||||||||
\(323\) | 19.2164 | 1.06923 | ||||||||
\(324\) | −5.48159 | −0.304533 | ||||||||
\(325\) | 7.88562 | 0.437415 | ||||||||
\(326\) | −10.5901 | −0.586529 | ||||||||
\(327\) | 28.3131 | 1.56572 | ||||||||
\(328\) | −3.69908 | −0.204248 | ||||||||
\(329\) | −0.101562 | −0.00559931 | ||||||||
\(330\) | −5.90512 | −0.325066 | ||||||||
\(331\) | 1.05122 | 0.0577806 | 0.0288903 | − | 0.999583i | \(-0.490803\pi\) | ||||
0.0288903 | + | 0.999583i | \(0.490803\pi\) | |||||||
\(332\) | −1.96725 | −0.107967 | ||||||||
\(333\) | −0.138997 | −0.00761700 | ||||||||
\(334\) | −3.80166 | −0.208018 | ||||||||
\(335\) | 3.73441 | 0.204033 | ||||||||
\(336\) | −1.44853 | −0.0790240 | ||||||||
\(337\) | 8.35437 | 0.455092 | 0.227546 | − | 0.973767i | \(-0.426930\pi\) | ||||
0.227546 | + | 0.973767i | \(0.426930\pi\) | |||||||
\(338\) | 7.62793 | 0.414905 | ||||||||
\(339\) | −21.5573 | −1.17083 | ||||||||
\(340\) | −4.55257 | −0.246898 | ||||||||
\(341\) | 17.6466 | 0.955615 | ||||||||
\(342\) | 4.81126 | 0.260163 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −7.50104 | −0.404429 | ||||||||
\(345\) | 14.0277 | 0.755226 | ||||||||
\(346\) | −16.4571 | −0.884739 | ||||||||
\(347\) | −7.54630 | −0.405107 | −0.202553 | − | 0.979271i | \(-0.564924\pi\) | ||||
−0.202553 | + | 0.979271i | \(0.564924\pi\) | |||||||
\(348\) | −0.311080 | −0.0166757 | ||||||||
\(349\) | 2.03679 | 0.109027 | 0.0545133 | − | 0.998513i | \(-0.482639\pi\) | ||||
0.0545133 | + | 0.998513i | \(0.482639\pi\) | |||||||
\(350\) | −3.40224 | −0.181857 | ||||||||
\(351\) | 13.0996 | 0.699206 | ||||||||
\(352\) | 3.22511 | 0.171899 | ||||||||
\(353\) | −29.7876 | −1.58544 | −0.792718 | − | 0.609589i | \(-0.791334\pi\) | ||||
−0.792718 | + | 0.609589i | \(0.791334\pi\) | |||||||
\(354\) | −17.1641 | −0.912260 | ||||||||
\(355\) | −13.5273 | −0.717957 | ||||||||
\(356\) | −0.350463 | −0.0185745 | ||||||||
\(357\) | −5.21710 | −0.276118 | ||||||||
\(358\) | −19.1032 | −1.00964 | ||||||||
\(359\) | 11.9211 | 0.629173 | 0.314586 | − | 0.949229i | \(-0.398134\pi\) | ||||
0.314586 | + | 0.949229i | \(0.398134\pi\) | |||||||
\(360\) | −1.13984 | −0.0600747 | ||||||||
\(361\) | 9.46716 | 0.498272 | ||||||||
\(362\) | −15.4524 | −0.812162 | ||||||||
\(363\) | −0.867223 | −0.0455174 | ||||||||
\(364\) | 2.31777 | 0.121484 | ||||||||
\(365\) | 19.8877 | 1.04097 | ||||||||
\(366\) | −8.62977 | −0.451085 | ||||||||
\(367\) | 35.9106 | 1.87452 | 0.937260 | − | 0.348632i | \(-0.113354\pi\) | ||||
0.937260 | + | 0.348632i | \(0.113354\pi\) | |||||||
\(368\) | −7.66129 | −0.399372 | ||||||||
\(369\) | −3.33565 | −0.173647 | ||||||||
\(370\) | 0.194839 | 0.0101292 | ||||||||
\(371\) | −9.39083 | −0.487548 | ||||||||
\(372\) | −7.92583 | −0.410935 | ||||||||
\(373\) | 1.76229 | 0.0912480 | 0.0456240 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456240 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(374\) | 11.6157 | 0.600633 | ||||||||
\(375\) | 15.3844 | 0.794445 | ||||||||
\(376\) | −0.101562 | −0.00523768 | ||||||||
\(377\) | 0.497754 | 0.0256356 | ||||||||
\(378\) | −5.65182 | −0.290698 | ||||||||
\(379\) | −6.08120 | −0.312370 | −0.156185 | − | 0.987728i | \(-0.549920\pi\) | ||||
−0.156185 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(380\) | −6.74416 | −0.345968 | ||||||||
\(381\) | 11.4005 | 0.584065 | ||||||||
\(382\) | −4.74568 | −0.242810 | ||||||||
\(383\) | −10.3380 | −0.528248 | −0.264124 | − | 0.964489i | \(-0.585083\pi\) | ||||
−0.264124 | + | 0.964489i | \(0.585083\pi\) | |||||||
\(384\) | −1.44853 | −0.0739202 | ||||||||
\(385\) | −4.07662 | −0.207764 | ||||||||
\(386\) | −4.37571 | −0.222718 | ||||||||
\(387\) | −6.76407 | −0.343837 | ||||||||
\(388\) | −17.6621 | −0.896659 | ||||||||
\(389\) | −29.5639 | −1.49895 | −0.749474 | − | 0.662033i | \(-0.769694\pi\) | ||||
−0.749474 | + | 0.662033i | \(0.769694\pi\) | |||||||
\(390\) | −4.24380 | −0.214893 | ||||||||
\(391\) | −27.5933 | −1.39545 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −0.0501173 | −0.00252808 | ||||||||
\(394\) | −3.06798 | −0.154563 | ||||||||
\(395\) | 17.2786 | 0.869381 | ||||||||
\(396\) | 2.90824 | 0.146145 | ||||||||
\(397\) | −2.23532 | −0.112188 | −0.0560938 | − | 0.998426i | \(-0.517865\pi\) | ||||
−0.0560938 | + | 0.998426i | \(0.517865\pi\) | |||||||
\(398\) | 26.2836 | 1.31748 | ||||||||
\(399\) | −7.72860 | −0.386914 | ||||||||
\(400\) | −3.40224 | −0.170112 | ||||||||
\(401\) | 11.2737 | 0.562979 | 0.281490 | − | 0.959564i | \(-0.409171\pi\) | ||||
0.281490 | + | 0.959564i | \(0.409171\pi\) | |||||||
\(402\) | 4.27951 | 0.213443 | ||||||||
\(403\) | 12.6820 | 0.631734 | ||||||||
\(404\) | 8.91473 | 0.443524 | ||||||||
\(405\) | 6.92887 | 0.344298 | ||||||||
\(406\) | −0.214755 | −0.0106581 | ||||||||
\(407\) | −0.497123 | −0.0246414 | ||||||||
\(408\) | −5.21710 | −0.258285 | ||||||||
\(409\) | 32.5916 | 1.61155 | 0.805777 | − | 0.592220i | \(-0.201748\pi\) | ||||
0.805777 | + | 0.592220i | \(0.201748\pi\) | |||||||
\(410\) | 4.67573 | 0.230918 | ||||||||
\(411\) | −3.47615 | −0.171466 | ||||||||
\(412\) | 9.46770 | 0.466440 | ||||||||
\(413\) | −11.8493 | −0.583065 | ||||||||
\(414\) | −6.90858 | −0.339538 | ||||||||
\(415\) | 2.48666 | 0.122065 | ||||||||
\(416\) | 2.31777 | 0.113638 | ||||||||
\(417\) | −19.0823 | −0.934466 | ||||||||
\(418\) | 17.2074 | 0.841643 | ||||||||
\(419\) | 16.8439 | 0.822880 | 0.411440 | − | 0.911437i | \(-0.365026\pi\) | ||||
0.411440 | + | 0.911437i | \(0.365026\pi\) | |||||||
\(420\) | 1.83098 | 0.0893428 | ||||||||
\(421\) | −0.753904 | −0.0367430 | −0.0183715 | − | 0.999831i | \(-0.505848\pi\) | ||||
−0.0183715 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(422\) | 8.94228 | 0.435304 | ||||||||
\(423\) | −0.0915840 | −0.00445297 | ||||||||
\(424\) | −9.39083 | −0.456059 | ||||||||
\(425\) | −12.2537 | −0.594390 | ||||||||
\(426\) | −15.5019 | −0.751070 | ||||||||
\(427\) | −5.95759 | −0.288308 | ||||||||
\(428\) | 17.0234 | 0.822856 | ||||||||
\(429\) | 10.8279 | 0.522775 | ||||||||
\(430\) | 9.48150 | 0.457239 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −5.65182 | −0.271923 | ||||||||
\(433\) | −13.5708 | −0.652171 | −0.326086 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326086 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(434\) | −5.47162 | −0.262646 | ||||||||
\(435\) | 0.393213 | 0.0188531 | ||||||||
\(436\) | 19.5460 | 0.936086 | ||||||||
\(437\) | −40.8765 | −1.95539 | ||||||||
\(438\) | 22.7906 | 1.08898 | ||||||||
\(439\) | −10.6671 | −0.509114 | −0.254557 | − | 0.967058i | \(-0.581930\pi\) | ||||
−0.254557 | + | 0.967058i | \(0.581930\pi\) | |||||||
\(440\) | −4.07662 | −0.194345 | ||||||||
\(441\) | −0.901751 | −0.0429405 | ||||||||
\(442\) | 8.34780 | 0.397064 | ||||||||
\(443\) | 10.5775 | 0.502553 | 0.251277 | − | 0.967915i | \(-0.419150\pi\) | ||||
0.251277 | + | 0.967915i | \(0.419150\pi\) | |||||||
\(444\) | 0.223279 | 0.0105964 | ||||||||
\(445\) | 0.442994 | 0.0209999 | ||||||||
\(446\) | 27.0980 | 1.28313 | ||||||||
\(447\) | 21.5466 | 1.01912 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −22.5821 | −1.06572 | −0.532859 | − | 0.846204i | \(-0.678882\pi\) | ||||
−0.532859 | + | 0.846204i | \(0.678882\pi\) | |||||||
\(450\) | −3.06797 | −0.144626 | ||||||||
\(451\) | −11.9299 | −0.561758 | ||||||||
\(452\) | −14.8821 | −0.699997 | ||||||||
\(453\) | 34.9682 | 1.64295 | ||||||||
\(454\) | −0.799865 | −0.0375395 | ||||||||
\(455\) | −2.92972 | −0.137348 | ||||||||
\(456\) | −7.72860 | −0.361925 | ||||||||
\(457\) | −4.14872 | −0.194069 | −0.0970345 | − | 0.995281i | \(-0.530936\pi\) | ||||
−0.0970345 | + | 0.995281i | \(0.530936\pi\) | |||||||
\(458\) | 1.41408 | 0.0660758 | ||||||||
\(459\) | −20.3558 | −0.950129 | ||||||||
\(460\) | 9.68407 | 0.451522 | ||||||||
\(461\) | 25.6956 | 1.19676 | 0.598382 | − | 0.801211i | \(-0.295811\pi\) | ||||
0.598382 | + | 0.801211i | \(0.295811\pi\) | |||||||
\(462\) | −4.67167 | −0.217346 | ||||||||
\(463\) | 19.0380 | 0.884773 | 0.442386 | − | 0.896825i | \(-0.354132\pi\) | ||||
0.442386 | + | 0.896825i | \(0.354132\pi\) | |||||||
\(464\) | −0.214755 | −0.00996977 | ||||||||
\(465\) | 10.0184 | 0.464594 | ||||||||
\(466\) | −2.30009 | −0.106549 | ||||||||
\(467\) | −2.34262 | −0.108404 | −0.0542018 | − | 0.998530i | \(-0.517261\pi\) | ||||
−0.0542018 | + | 0.998530i | \(0.517261\pi\) | |||||||
\(468\) | 2.09005 | 0.0966128 | ||||||||
\(469\) | 2.95438 | 0.136420 | ||||||||
\(470\) | 0.128377 | 0.00592161 | ||||||||
\(471\) | 8.78538 | 0.404809 | ||||||||
\(472\) | −11.8493 | −0.545407 | ||||||||
\(473\) | −24.1916 | −1.11233 | ||||||||
\(474\) | 19.8007 | 0.909478 | ||||||||
\(475\) | −18.1525 | −0.832895 | ||||||||
\(476\) | −3.60165 | −0.165081 | ||||||||
\(477\) | −8.46819 | −0.387732 | ||||||||
\(478\) | −9.46668 | −0.432996 | ||||||||
\(479\) | 6.41867 | 0.293277 | 0.146638 | − | 0.989190i | \(-0.453155\pi\) | ||||
0.146638 | + | 0.989190i | \(0.453155\pi\) | |||||||
\(480\) | 1.83098 | 0.0835726 | ||||||||
\(481\) | −0.357265 | −0.0162899 | ||||||||
\(482\) | −15.2642 | −0.695266 | ||||||||
\(483\) | 11.0976 | 0.504960 | ||||||||
\(484\) | −0.598690 | −0.0272132 | ||||||||
\(485\) | 22.3254 | 1.01374 | ||||||||
\(486\) | −9.01518 | −0.408937 | ||||||||
\(487\) | −0.883066 | −0.0400155 | −0.0200078 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200078 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(488\) | −5.95759 | −0.269688 | ||||||||
\(489\) | 15.3400 | 0.693701 | ||||||||
\(490\) | 1.26403 | 0.0571029 | ||||||||
\(491\) | −22.4448 | −1.01292 | −0.506460 | − | 0.862263i | \(-0.669046\pi\) | ||||
−0.506460 | + | 0.862263i | \(0.669046\pi\) | |||||||
\(492\) | 5.35824 | 0.241568 | ||||||||
\(493\) | −0.773473 | −0.0348355 | ||||||||
\(494\) | 12.3664 | 0.556390 | ||||||||
\(495\) | −3.67609 | −0.165228 | ||||||||
\(496\) | −5.47162 | −0.245683 | ||||||||
\(497\) | −10.7018 | −0.480041 | ||||||||
\(498\) | 2.84963 | 0.127695 | ||||||||
\(499\) | 19.9212 | 0.891796 | 0.445898 | − | 0.895084i | \(-0.352884\pi\) | ||||
0.445898 | + | 0.895084i | \(0.352884\pi\) | |||||||
\(500\) | 10.6206 | 0.474970 | ||||||||
\(501\) | 5.50683 | 0.246027 | ||||||||
\(502\) | −1.32168 | −0.0589895 | ||||||||
\(503\) | 3.31834 | 0.147958 | 0.0739788 | − | 0.997260i | \(-0.476430\pi\) | ||||
0.0739788 | + | 0.997260i | \(0.476430\pi\) | |||||||
\(504\) | −0.901751 | −0.0401672 | ||||||||
\(505\) | −11.2684 | −0.501439 | ||||||||
\(506\) | −24.7085 | −1.09843 | ||||||||
\(507\) | −11.0493 | −0.490717 | ||||||||
\(508\) | 7.87038 | 0.349191 | ||||||||
\(509\) | 23.8167 | 1.05566 | 0.527829 | − | 0.849351i | \(-0.323006\pi\) | ||||
0.527829 | + | 0.849351i | \(0.323006\pi\) | |||||||
\(510\) | 6.59455 | 0.292012 | ||||||||
\(511\) | 15.7336 | 0.696013 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −30.1551 | −1.33138 | ||||||||
\(514\) | 9.58020 | 0.422565 | ||||||||
\(515\) | −11.9674 | −0.527347 | ||||||||
\(516\) | 10.8655 | 0.478327 | ||||||||
\(517\) | −0.327549 | −0.0144056 | ||||||||
\(518\) | 0.154141 | 0.00677259 | ||||||||
\(519\) | 23.8386 | 1.04640 | ||||||||
\(520\) | −2.92972 | −0.128477 | ||||||||
\(521\) | 21.2943 | 0.932920 | 0.466460 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466460 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(522\) | −0.193656 | −0.00847609 | ||||||||
\(523\) | −0.989607 | −0.0432725 | −0.0216362 | − | 0.999766i | \(-0.506888\pi\) | ||||
−0.0216362 | + | 0.999766i | \(0.506888\pi\) | |||||||
\(524\) | −0.0345986 | −0.00151145 | ||||||||
\(525\) | 4.92826 | 0.215087 | ||||||||
\(526\) | −26.9818 | −1.17646 | ||||||||
\(527\) | −19.7068 | −0.858443 | ||||||||
\(528\) | −4.67167 | −0.203309 | ||||||||
\(529\) | 35.6954 | 1.55197 | ||||||||
\(530\) | 11.8703 | 0.515611 | ||||||||
\(531\) | −10.6851 | −0.463694 | ||||||||
\(532\) | −5.33546 | −0.231322 | ||||||||
\(533\) | −8.57363 | −0.371365 | ||||||||
\(534\) | 0.507657 | 0.0219685 | ||||||||
\(535\) | −21.5180 | −0.930303 | ||||||||
\(536\) | 2.95438 | 0.127610 | ||||||||
\(537\) | 27.6716 | 1.19412 | ||||||||
\(538\) | 7.60283 | 0.327781 | ||||||||
\(539\) | −3.22511 | −0.138915 | ||||||||
\(540\) | 7.14404 | 0.307431 | ||||||||
\(541\) | 29.7230 | 1.27789 | 0.638947 | − | 0.769251i | \(-0.279370\pi\) | ||||
0.638947 | + | 0.769251i | \(0.279370\pi\) | |||||||
\(542\) | −23.1724 | −0.995341 | ||||||||
\(543\) | 22.3834 | 0.960563 | ||||||||
\(544\) | −3.60165 | −0.154419 | ||||||||
\(545\) | −24.7067 | −1.05832 | ||||||||
\(546\) | −3.35737 | −0.143682 | ||||||||
\(547\) | −18.7571 | −0.801997 | −0.400998 | − | 0.916079i | \(-0.631337\pi\) | ||||
−0.400998 | + | 0.916079i | \(0.631337\pi\) | |||||||
\(548\) | −2.39977 | −0.102513 | ||||||||
\(549\) | −5.37227 | −0.229283 | ||||||||
\(550\) | −10.9726 | −0.467872 | ||||||||
\(551\) | −1.14582 | −0.0488135 | ||||||||
\(552\) | 11.0976 | 0.472347 | ||||||||
\(553\) | 13.6695 | 0.581287 | ||||||||
\(554\) | −21.5203 | −0.914310 | ||||||||
\(555\) | −0.282230 | −0.0119800 | ||||||||
\(556\) | −13.1736 | −0.558683 | ||||||||
\(557\) | −3.12542 | −0.132428 | −0.0662142 | − | 0.997805i | \(-0.521092\pi\) | ||||
−0.0662142 | + | 0.997805i | \(0.521092\pi\) | |||||||
\(558\) | −4.93404 | −0.208875 | ||||||||
\(559\) | −17.3857 | −0.735337 | ||||||||
\(560\) | 1.26403 | 0.0534148 | ||||||||
\(561\) | −16.8257 | −0.710382 | ||||||||
\(562\) | 29.3424 | 1.23773 | ||||||||
\(563\) | 32.6668 | 1.37674 | 0.688371 | − | 0.725359i | \(-0.258326\pi\) | ||||
0.688371 | + | 0.725359i | \(0.258326\pi\) | |||||||
\(564\) | 0.147116 | 0.00619472 | ||||||||
\(565\) | 18.8114 | 0.791402 | ||||||||
\(566\) | 30.0854 | 1.26459 | ||||||||
\(567\) | 5.48159 | 0.230205 | ||||||||
\(568\) | −10.7018 | −0.449037 | ||||||||
\(569\) | 12.7210 | 0.533293 | 0.266647 | − | 0.963794i | \(-0.414084\pi\) | ||||
0.266647 | + | 0.963794i | \(0.414084\pi\) | |||||||
\(570\) | 9.76914 | 0.409184 | ||||||||
\(571\) | −7.60141 | −0.318109 | −0.159055 | − | 0.987270i | \(-0.550845\pi\) | ||||
−0.159055 | + | 0.987270i | \(0.550845\pi\) | |||||||
\(572\) | 7.47506 | 0.312548 | ||||||||
\(573\) | 6.87427 | 0.287177 | ||||||||
\(574\) | 3.69908 | 0.154397 | ||||||||
\(575\) | 26.0655 | 1.08701 | ||||||||
\(576\) | −0.901751 | −0.0375730 | ||||||||
\(577\) | 13.7678 | 0.573159 | 0.286579 | − | 0.958056i | \(-0.407482\pi\) | ||||
0.286579 | + | 0.958056i | \(0.407482\pi\) | |||||||
\(578\) | 4.02815 | 0.167549 | ||||||||
\(579\) | 6.33836 | 0.263413 | ||||||||
\(580\) | 0.271456 | 0.0112716 | ||||||||
\(581\) | 1.96725 | 0.0816154 | ||||||||
\(582\) | 25.5842 | 1.06050 | ||||||||
\(583\) | −30.2864 | −1.25434 | ||||||||
\(584\) | 15.7336 | 0.651061 | ||||||||
\(585\) | −2.64188 | −0.109228 | ||||||||
\(586\) | −19.2131 | −0.793687 | ||||||||
\(587\) | −20.6386 | −0.851844 | −0.425922 | − | 0.904760i | \(-0.640050\pi\) | ||||
−0.425922 | + | 0.904760i | \(0.640050\pi\) | |||||||
\(588\) | 1.44853 | 0.0597365 | ||||||||
\(589\) | −29.1936 | −1.20290 | ||||||||
\(590\) | 14.9778 | 0.616626 | ||||||||
\(591\) | 4.44408 | 0.182805 | ||||||||
\(592\) | 0.154141 | 0.00633517 | ||||||||
\(593\) | 39.6214 | 1.62706 | 0.813528 | − | 0.581525i | \(-0.197544\pi\) | ||||
0.813528 | + | 0.581525i | \(0.197544\pi\) | |||||||
\(594\) | −18.2277 | −0.747892 | ||||||||
\(595\) | 4.55257 | 0.186637 | ||||||||
\(596\) | 14.8747 | 0.609293 | ||||||||
\(597\) | −38.0727 | −1.55821 | ||||||||
\(598\) | −17.7571 | −0.726143 | ||||||||
\(599\) | −12.5956 | −0.514643 | −0.257321 | − | 0.966326i | \(-0.582840\pi\) | ||||
−0.257321 | + | 0.966326i | \(0.582840\pi\) | |||||||
\(600\) | 4.92826 | 0.201195 | ||||||||
\(601\) | −18.3882 | −0.750072 | −0.375036 | − | 0.927010i | \(-0.622370\pi\) | ||||
−0.375036 | + | 0.927010i | \(0.622370\pi\) | |||||||
\(602\) | 7.50104 | 0.305719 | ||||||||
\(603\) | 2.66411 | 0.108491 | ||||||||
\(604\) | 24.1404 | 0.982259 | ||||||||
\(605\) | 0.756760 | 0.0307667 | ||||||||
\(606\) | −12.9133 | −0.524566 | ||||||||
\(607\) | −23.2820 | −0.944988 | −0.472494 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472494 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(608\) | −5.33546 | −0.216382 | ||||||||
\(609\) | 0.311080 | 0.0126056 | ||||||||
\(610\) | 7.53055 | 0.304903 | ||||||||
\(611\) | −0.235398 | −0.00952320 | ||||||||
\(612\) | −3.24779 | −0.131284 | ||||||||
\(613\) | −27.5399 | −1.11233 | −0.556163 | − | 0.831073i | \(-0.687727\pi\) | ||||
−0.556163 | + | 0.831073i | \(0.687727\pi\) | |||||||
\(614\) | 2.60073 | 0.104957 | ||||||||
\(615\) | −6.77295 | −0.273112 | ||||||||
\(616\) | −3.22511 | −0.129943 | ||||||||
\(617\) | −8.33362 | −0.335499 | −0.167749 | − | 0.985830i | \(-0.553650\pi\) | ||||
−0.167749 | + | 0.985830i | \(0.553650\pi\) | |||||||
\(618\) | −13.7143 | −0.551669 | ||||||||
\(619\) | 47.6877 | 1.91673 | 0.958366 | − | 0.285542i | \(-0.0921737\pi\) | ||||
0.958366 | + | 0.285542i | \(0.0921737\pi\) | |||||||
\(620\) | 6.91627 | 0.277764 | ||||||||
\(621\) | 43.3002 | 1.73758 | ||||||||
\(622\) | 10.9513 | 0.439107 | ||||||||
\(623\) | 0.350463 | 0.0140410 | ||||||||
\(624\) | −3.35737 | −0.134402 | ||||||||
\(625\) | 3.58643 | 0.143457 | ||||||||
\(626\) | −21.0786 | −0.842471 | ||||||||
\(627\) | −24.9255 | −0.995430 | ||||||||
\(628\) | 6.06502 | 0.242021 | ||||||||
\(629\) | 0.555163 | 0.0221358 | ||||||||
\(630\) | 1.13984 | 0.0454122 | ||||||||
\(631\) | 9.06920 | 0.361039 | 0.180520 | − | 0.983571i | \(-0.442222\pi\) | ||||
0.180520 | + | 0.983571i | \(0.442222\pi\) | |||||||
\(632\) | 13.6695 | 0.543744 | ||||||||
\(633\) | −12.9532 | −0.514843 | ||||||||
\(634\) | 3.41278 | 0.135539 | ||||||||
\(635\) | −9.94836 | −0.394789 | ||||||||
\(636\) | 13.6029 | 0.539391 | ||||||||
\(637\) | −2.31777 | −0.0918335 | ||||||||
\(638\) | −0.692609 | −0.0274206 | ||||||||
\(639\) | −9.65036 | −0.381762 | ||||||||
\(640\) | 1.26403 | 0.0499650 | ||||||||
\(641\) | −8.20148 | −0.323939 | −0.161969 | − | 0.986796i | \(-0.551785\pi\) | ||||
−0.161969 | + | 0.986796i | \(0.551785\pi\) | |||||||
\(642\) | −24.6589 | −0.973210 | ||||||||
\(643\) | 38.6839 | 1.52554 | 0.762772 | − | 0.646667i | \(-0.223838\pi\) | ||||
0.762772 | + | 0.646667i | \(0.223838\pi\) | |||||||
\(644\) | 7.66129 | 0.301897 | ||||||||
\(645\) | −13.7343 | −0.540786 | ||||||||
\(646\) | −19.2164 | −0.756061 | ||||||||
\(647\) | 14.5250 | 0.571038 | 0.285519 | − | 0.958373i | \(-0.407834\pi\) | ||||
0.285519 | + | 0.958373i | \(0.407834\pi\) | |||||||
\(648\) | 5.48159 | 0.215337 | ||||||||
\(649\) | −38.2152 | −1.50008 | ||||||||
\(650\) | −7.88562 | −0.309299 | ||||||||
\(651\) | 7.92583 | 0.310638 | ||||||||
\(652\) | 10.5901 | 0.414738 | ||||||||
\(653\) | 33.1727 | 1.29815 | 0.649074 | − | 0.760725i | \(-0.275157\pi\) | ||||
0.649074 | + | 0.760725i | \(0.275157\pi\) | |||||||
\(654\) | −28.3131 | −1.10713 | ||||||||
\(655\) | 0.0437336 | 0.00170881 | ||||||||
\(656\) | 3.69908 | 0.144425 | ||||||||
\(657\) | 14.1878 | 0.553518 | ||||||||
\(658\) | 0.101562 | 0.00395931 | ||||||||
\(659\) | 2.38108 | 0.0927539 | 0.0463769 | − | 0.998924i | \(-0.485232\pi\) | ||||
0.0463769 | + | 0.998924i | \(0.485232\pi\) | |||||||
\(660\) | 5.90512 | 0.229856 | ||||||||
\(661\) | −35.0387 | −1.36285 | −0.681423 | − | 0.731890i | \(-0.738639\pi\) | ||||
−0.681423 | + | 0.731890i | \(0.738639\pi\) | |||||||
\(662\) | −1.05122 | −0.0408570 | ||||||||
\(663\) | −12.0921 | −0.469617 | ||||||||
\(664\) | 1.96725 | 0.0763442 | ||||||||
\(665\) | 6.74416 | 0.261527 | ||||||||
\(666\) | 0.138997 | 0.00538603 | ||||||||
\(667\) | 1.64530 | 0.0637064 | ||||||||
\(668\) | 3.80166 | 0.147091 | ||||||||
\(669\) | −39.2523 | −1.51758 | ||||||||
\(670\) | −3.73441 | −0.144273 | ||||||||
\(671\) | −19.2139 | −0.741743 | ||||||||
\(672\) | 1.44853 | 0.0558784 | ||||||||
\(673\) | −23.1260 | −0.891440 | −0.445720 | − | 0.895172i | \(-0.647052\pi\) | ||||
−0.445720 | + | 0.895172i | \(0.647052\pi\) | |||||||
\(674\) | −8.35437 | −0.321798 | ||||||||
\(675\) | 19.2288 | 0.740118 | ||||||||
\(676\) | −7.62793 | −0.293382 | ||||||||
\(677\) | −1.52519 | −0.0586177 | −0.0293089 | − | 0.999570i | \(-0.509331\pi\) | ||||
−0.0293089 | + | 0.999570i | \(0.509331\pi\) | |||||||
\(678\) | 21.5573 | 0.827903 | ||||||||
\(679\) | 17.6621 | 0.677810 | ||||||||
\(680\) | 4.55257 | 0.174583 | ||||||||
\(681\) | 1.15863 | 0.0443988 | ||||||||
\(682\) | −17.6466 | −0.675722 | ||||||||
\(683\) | −29.1688 | −1.11611 | −0.558057 | − | 0.829803i | \(-0.688453\pi\) | ||||
−0.558057 | + | 0.829803i | \(0.688453\pi\) | |||||||
\(684\) | −4.81126 | −0.183963 | ||||||||
\(685\) | 3.03337 | 0.115899 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −2.04835 | −0.0781494 | ||||||||
\(688\) | 7.50104 | 0.285974 | ||||||||
\(689\) | −21.7658 | −0.829211 | ||||||||
\(690\) | −14.0277 | −0.534025 | ||||||||
\(691\) | −30.5639 | −1.16271 | −0.581353 | − | 0.813652i | \(-0.697476\pi\) | ||||
−0.581353 | + | 0.813652i | \(0.697476\pi\) | |||||||
\(692\) | 16.4571 | 0.625605 | ||||||||
\(693\) | −2.90824 | −0.110475 | ||||||||
\(694\) | 7.54630 | 0.286454 | ||||||||
\(695\) | 16.6517 | 0.631636 | ||||||||
\(696\) | 0.311080 | 0.0117915 | ||||||||
\(697\) | 13.3228 | 0.504636 | ||||||||
\(698\) | −2.03679 | −0.0770935 | ||||||||
\(699\) | 3.33175 | 0.126018 | ||||||||
\(700\) | 3.40224 | 0.128593 | ||||||||
\(701\) | 35.7765 | 1.35126 | 0.675629 | − | 0.737242i | \(-0.263872\pi\) | ||||
0.675629 | + | 0.737242i | \(0.263872\pi\) | |||||||
\(702\) | −13.0996 | −0.494414 | ||||||||
\(703\) | 0.822416 | 0.0310180 | ||||||||
\(704\) | −3.22511 | −0.121551 | ||||||||
\(705\) | −0.185959 | −0.00700362 | ||||||||
\(706\) | 29.7876 | 1.12107 | ||||||||
\(707\) | −8.91473 | −0.335273 | ||||||||
\(708\) | 17.1641 | 0.645065 | ||||||||
\(709\) | −46.5856 | −1.74956 | −0.874779 | − | 0.484523i | \(-0.838993\pi\) | ||||
−0.874779 | + | 0.484523i | \(0.838993\pi\) | |||||||
\(710\) | 13.5273 | 0.507672 | ||||||||
\(711\) | 12.3265 | 0.462280 | ||||||||
\(712\) | 0.350463 | 0.0131342 | ||||||||
\(713\) | 41.9197 | 1.56990 | ||||||||
\(714\) | 5.21710 | 0.195245 | ||||||||
\(715\) | −9.44867 | −0.353360 | ||||||||
\(716\) | 19.1032 | 0.713921 | ||||||||
\(717\) | 13.7128 | 0.512114 | ||||||||
\(718\) | −11.9211 | −0.444892 | ||||||||
\(719\) | 22.9733 | 0.856760 | 0.428380 | − | 0.903599i | \(-0.359084\pi\) | ||||
0.428380 | + | 0.903599i | \(0.359084\pi\) | |||||||
\(720\) | 1.13984 | 0.0424792 | ||||||||
\(721\) | −9.46770 | −0.352596 | ||||||||
\(722\) | −9.46716 | −0.352331 | ||||||||
\(723\) | 22.1107 | 0.822306 | ||||||||
\(724\) | 15.4524 | 0.574285 | ||||||||
\(725\) | 0.730649 | 0.0271356 | ||||||||
\(726\) | 0.867223 | 0.0321856 | ||||||||
\(727\) | −45.7342 | −1.69619 | −0.848094 | − | 0.529846i | \(-0.822250\pi\) | ||||
−0.848094 | + | 0.529846i | \(0.822250\pi\) | |||||||
\(728\) | −2.31777 | −0.0859024 | ||||||||
\(729\) | 29.5036 | 1.09272 | ||||||||
\(730\) | −19.8877 | −0.736076 | ||||||||
\(731\) | 27.0161 | 0.999225 | ||||||||
\(732\) | 8.62977 | 0.318966 | ||||||||
\(733\) | 16.4772 | 0.608599 | 0.304299 | − | 0.952576i | \(-0.401578\pi\) | ||||
0.304299 | + | 0.952576i | \(0.401578\pi\) | |||||||
\(734\) | −35.9106 | −1.32549 | ||||||||
\(735\) | −1.83098 | −0.0675368 | ||||||||
\(736\) | 7.66129 | 0.282399 | ||||||||
\(737\) | 9.52818 | 0.350975 | ||||||||
\(738\) | 3.33565 | 0.122787 | ||||||||
\(739\) | 7.07809 | 0.260372 | 0.130186 | − | 0.991490i | \(-0.458443\pi\) | ||||
0.130186 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(740\) | −0.194839 | −0.00716241 | ||||||||
\(741\) | −17.9131 | −0.658055 | ||||||||
\(742\) | 9.39083 | 0.344748 | ||||||||
\(743\) | 37.7294 | 1.38416 | 0.692078 | − | 0.721823i | \(-0.256695\pi\) | ||||
0.692078 | + | 0.721823i | \(0.256695\pi\) | |||||||
\(744\) | 7.92583 | 0.290575 | ||||||||
\(745\) | −18.8021 | −0.688854 | ||||||||
\(746\) | −1.76229 | −0.0645221 | ||||||||
\(747\) | 1.77397 | 0.0649063 | ||||||||
\(748\) | −11.6157 | −0.424712 | ||||||||
\(749\) | −17.0234 | −0.622020 | ||||||||
\(750\) | −15.3844 | −0.561757 | ||||||||
\(751\) | −22.3861 | −0.816879 | −0.408439 | − | 0.912785i | \(-0.633927\pi\) | ||||
−0.408439 | + | 0.912785i | \(0.633927\pi\) | |||||||
\(752\) | 0.101562 | 0.00370360 | ||||||||
\(753\) | 1.91450 | 0.0697682 | ||||||||
\(754\) | −0.497754 | −0.0181271 | ||||||||
\(755\) | −30.5141 | −1.11052 | ||||||||
\(756\) | 5.65182 | 0.205555 | ||||||||
\(757\) | −39.3845 | −1.43146 | −0.715728 | − | 0.698379i | \(-0.753905\pi\) | ||||
−0.715728 | + | 0.698379i | \(0.753905\pi\) | |||||||
\(758\) | 6.08120 | 0.220879 | ||||||||
\(759\) | 35.7911 | 1.29913 | ||||||||
\(760\) | 6.74416 | 0.244636 | ||||||||
\(761\) | −4.36983 | −0.158406 | −0.0792031 | − | 0.996858i | \(-0.525238\pi\) | ||||
−0.0792031 | + | 0.996858i | \(0.525238\pi\) | |||||||
\(762\) | −11.4005 | −0.412997 | ||||||||
\(763\) | −19.5460 | −0.707614 | ||||||||
\(764\) | 4.74568 | 0.171692 | ||||||||
\(765\) | 4.10529 | 0.148427 | ||||||||
\(766\) | 10.3380 | 0.373527 | ||||||||
\(767\) | −27.4639 | −0.991665 | ||||||||
\(768\) | 1.44853 | 0.0522694 | ||||||||
\(769\) | 1.36858 | 0.0493524 | 0.0246762 | − | 0.999695i | \(-0.492145\pi\) | ||||
0.0246762 | + | 0.999695i | \(0.492145\pi\) | |||||||
\(770\) | 4.07662 | 0.146911 | ||||||||
\(771\) | −13.8772 | −0.499777 | ||||||||
\(772\) | 4.37571 | 0.157485 | ||||||||
\(773\) | −33.0732 | −1.18956 | −0.594781 | − | 0.803888i | \(-0.702761\pi\) | ||||
−0.594781 | + | 0.803888i | \(0.702761\pi\) | |||||||
\(774\) | 6.76407 | 0.243129 | ||||||||
\(775\) | 18.6158 | 0.668698 | ||||||||
\(776\) | 17.6621 | 0.634033 | ||||||||
\(777\) | −0.223279 | −0.00801009 | ||||||||
\(778\) | 29.5639 | 1.05992 | ||||||||
\(779\) | 19.7363 | 0.707126 | ||||||||
\(780\) | 4.24380 | 0.151953 | ||||||||
\(781\) | −34.5144 | −1.23502 | ||||||||
\(782\) | 27.5933 | 0.986733 | ||||||||
\(783\) | 1.21376 | 0.0433762 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.66634 | −0.273623 | ||||||||
\(786\) | 0.0501173 | 0.00178762 | ||||||||
\(787\) | −16.8755 | −0.601547 | −0.300773 | − | 0.953696i | \(-0.597245\pi\) | ||||
−0.300773 | + | 0.953696i | \(0.597245\pi\) | |||||||
\(788\) | 3.06798 | 0.109292 | ||||||||
\(789\) | 39.0841 | 1.39143 | ||||||||
\(790\) | −17.2786 | −0.614745 | ||||||||
\(791\) | 14.8821 | 0.529148 | ||||||||
\(792\) | −2.90824 | −0.103340 | ||||||||
\(793\) | −13.8083 | −0.490349 | ||||||||
\(794\) | 2.23532 | 0.0793286 | ||||||||
\(795\) | −17.1945 | −0.609824 | ||||||||
\(796\) | −26.2836 | −0.931599 | ||||||||
\(797\) | −22.6911 | −0.803761 | −0.401881 | − | 0.915692i | \(-0.631643\pi\) | ||||
−0.401881 | + | 0.915692i | \(0.631643\pi\) | |||||||
\(798\) | 7.72860 | 0.273589 | ||||||||
\(799\) | 0.365792 | 0.0129408 | ||||||||
\(800\) | 3.40224 | 0.120287 | ||||||||
\(801\) | 0.316030 | 0.0111664 | ||||||||
\(802\) | −11.2737 | −0.398087 | ||||||||
\(803\) | 50.7425 | 1.79066 | ||||||||
\(804\) | −4.27951 | −0.150927 | ||||||||
\(805\) | −9.68407 | −0.341319 | ||||||||
\(806\) | −12.6820 | −0.446704 | ||||||||
\(807\) | −11.0130 | −0.387674 | ||||||||
\(808\) | −8.91473 | −0.313619 | ||||||||
\(809\) | 18.2557 | 0.641835 | 0.320917 | − | 0.947107i | \(-0.396009\pi\) | ||||
0.320917 | + | 0.947107i | \(0.396009\pi\) | |||||||
\(810\) | −6.92887 | −0.243456 | ||||||||
\(811\) | 10.7230 | 0.376535 | 0.188267 | − | 0.982118i | \(-0.439713\pi\) | ||||
0.188267 | + | 0.982118i | \(0.439713\pi\) | |||||||
\(812\) | 0.214755 | 0.00753644 | ||||||||
\(813\) | 33.5660 | 1.17721 | ||||||||
\(814\) | 0.497123 | 0.0174241 | ||||||||
\(815\) | −13.3861 | −0.468895 | ||||||||
\(816\) | 5.21710 | 0.182635 | ||||||||
\(817\) | 40.0215 | 1.40017 | ||||||||
\(818\) | −32.5916 | −1.13954 | ||||||||
\(819\) | −2.09005 | −0.0730324 | ||||||||
\(820\) | −4.67573 | −0.163284 | ||||||||
\(821\) | 25.1558 | 0.877942 | 0.438971 | − | 0.898501i | \(-0.355343\pi\) | ||||
0.438971 | + | 0.898501i | \(0.355343\pi\) | |||||||
\(822\) | 3.47615 | 0.121245 | ||||||||
\(823\) | −22.6642 | −0.790025 | −0.395012 | − | 0.918676i | \(-0.629260\pi\) | ||||
−0.395012 | + | 0.918676i | \(0.629260\pi\) | |||||||
\(824\) | −9.46770 | −0.329823 | ||||||||
\(825\) | 15.8942 | 0.553363 | ||||||||
\(826\) | 11.8493 | 0.412289 | ||||||||
\(827\) | −46.7646 | −1.62617 | −0.813083 | − | 0.582148i | \(-0.802212\pi\) | ||||
−0.813083 | + | 0.582148i | \(0.802212\pi\) | |||||||
\(828\) | 6.90858 | 0.240090 | ||||||||
\(829\) | −3.07344 | −0.106745 | −0.0533725 | − | 0.998575i | \(-0.516997\pi\) | ||||
−0.0533725 | + | 0.998575i | \(0.516997\pi\) | |||||||
\(830\) | −2.48666 | −0.0863132 | ||||||||
\(831\) | 31.1729 | 1.08137 | ||||||||
\(832\) | −2.31777 | −0.0803543 | ||||||||
\(833\) | 3.60165 | 0.124790 | ||||||||
\(834\) | 19.0823 | 0.660768 | ||||||||
\(835\) | −4.80540 | −0.166298 | ||||||||
\(836\) | −17.2074 | −0.595132 | ||||||||
\(837\) | 30.9246 | 1.06891 | ||||||||
\(838\) | −16.8439 | −0.581864 | ||||||||
\(839\) | 20.3451 | 0.702391 | 0.351196 | − | 0.936302i | \(-0.385775\pi\) | ||||
0.351196 | + | 0.936302i | \(0.385775\pi\) | |||||||
\(840\) | −1.83098 | −0.0631749 | ||||||||
\(841\) | −28.9539 | −0.998410 | ||||||||
\(842\) | 0.753904 | 0.0259812 | ||||||||
\(843\) | −42.5034 | −1.46390 | ||||||||
\(844\) | −8.94228 | −0.307806 | ||||||||
\(845\) | 9.64190 | 0.331691 | ||||||||
\(846\) | 0.0915840 | 0.00314872 | ||||||||
\(847\) | 0.598690 | 0.0205712 | ||||||||
\(848\) | 9.39083 | 0.322482 | ||||||||
\(849\) | −43.5798 | −1.49565 | ||||||||
\(850\) | 12.2537 | 0.420297 | ||||||||
\(851\) | −1.18092 | −0.0404815 | ||||||||
\(852\) | 15.5019 | 0.531087 | ||||||||
\(853\) | 6.13553 | 0.210076 | 0.105038 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105038 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(854\) | 5.95759 | 0.203865 | ||||||||
\(855\) | 6.08156 | 0.207985 | ||||||||
\(856\) | −17.0234 | −0.581847 | ||||||||
\(857\) | 32.3955 | 1.10661 | 0.553305 | − | 0.832979i | \(-0.313366\pi\) | ||||
0.553305 | + | 0.832979i | \(0.313366\pi\) | |||||||
\(858\) | −10.8279 | −0.369658 | ||||||||
\(859\) | 21.0123 | 0.716929 | 0.358465 | − | 0.933543i | \(-0.383300\pi\) | ||||
0.358465 | + | 0.933543i | \(0.383300\pi\) | |||||||
\(860\) | −9.48150 | −0.323317 | ||||||||
\(861\) | −5.35824 | −0.182608 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 8.12612 | 0.276616 | 0.138308 | − | 0.990389i | \(-0.455834\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(864\) | 5.65182 | 0.192279 | ||||||||
\(865\) | −20.8022 | −0.707296 | ||||||||
\(866\) | 13.5708 | 0.461155 | ||||||||
\(867\) | −5.83491 | −0.198164 | ||||||||
\(868\) | 5.47162 | 0.185719 | ||||||||
\(869\) | 44.0856 | 1.49550 | ||||||||
\(870\) | −0.393213 | −0.0133312 | ||||||||
\(871\) | 6.84758 | 0.232021 | ||||||||
\(872\) | −19.5460 | −0.661912 | ||||||||
\(873\) | 15.9268 | 0.539042 | ||||||||
\(874\) | 40.8765 | 1.38267 | ||||||||
\(875\) | −10.6206 | −0.359043 | ||||||||
\(876\) | −22.7906 | −0.770024 | ||||||||
\(877\) | 39.3833 | 1.32988 | 0.664940 | − | 0.746896i | \(-0.268457\pi\) | ||||
0.664940 | + | 0.746896i | \(0.268457\pi\) | |||||||
\(878\) | 10.6671 | 0.359998 | ||||||||
\(879\) | 27.8308 | 0.938711 | ||||||||
\(880\) | 4.07662 | 0.137423 | ||||||||
\(881\) | −13.7834 | −0.464375 | −0.232187 | − | 0.972671i | \(-0.574588\pi\) | ||||
−0.232187 | + | 0.972671i | \(0.574588\pi\) | |||||||
\(882\) | 0.901751 | 0.0303635 | ||||||||
\(883\) | 42.7783 | 1.43960 | 0.719802 | − | 0.694179i | \(-0.244232\pi\) | ||||
0.719802 | + | 0.694179i | \(0.244232\pi\) | |||||||
\(884\) | −8.34780 | −0.280767 | ||||||||
\(885\) | −21.6958 | −0.729297 | ||||||||
\(886\) | −10.5775 | −0.355359 | ||||||||
\(887\) | 19.9689 | 0.670489 | 0.335244 | − | 0.942131i | \(-0.391181\pi\) | ||||
0.335244 | + | 0.942131i | \(0.391181\pi\) | |||||||
\(888\) | −0.223279 | −0.00749275 | ||||||||
\(889\) | −7.87038 | −0.263964 | ||||||||
\(890\) | −0.442994 | −0.0148492 | ||||||||
\(891\) | 17.6787 | 0.592259 | ||||||||
\(892\) | −27.0980 | −0.907307 | ||||||||
\(893\) | 0.541882 | 0.0181334 | ||||||||
\(894\) | −21.5466 | −0.720625 | ||||||||
\(895\) | −24.1470 | −0.807144 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 25.7218 | 0.858826 | ||||||||
\(898\) | 22.5821 | 0.753576 | ||||||||
\(899\) | 1.17506 | 0.0391904 | ||||||||
\(900\) | 3.06797 | 0.102266 | ||||||||
\(901\) | 33.8224 | 1.12679 | ||||||||
\(902\) | 11.9299 | 0.397223 | ||||||||
\(903\) | −10.8655 | −0.361581 | ||||||||
\(904\) | 14.8821 | 0.494973 | ||||||||
\(905\) | −19.5323 | −0.649275 | ||||||||
\(906\) | −34.9682 | −1.16174 | ||||||||
\(907\) | −29.8320 | −0.990554 | −0.495277 | − | 0.868735i | \(-0.664933\pi\) | ||||
−0.495277 | + | 0.868735i | \(0.664933\pi\) | |||||||
\(908\) | 0.799865 | 0.0265444 | ||||||||
\(909\) | −8.03887 | −0.266632 | ||||||||
\(910\) | 2.92972 | 0.0971194 | ||||||||
\(911\) | 13.0430 | 0.432134 | 0.216067 | − | 0.976379i | \(-0.430677\pi\) | ||||
0.216067 | + | 0.976379i | \(0.430677\pi\) | |||||||
\(912\) | 7.72860 | 0.255919 | ||||||||
\(913\) | 6.34460 | 0.209976 | ||||||||
\(914\) | 4.14872 | 0.137228 | ||||||||
\(915\) | −10.9083 | −0.360616 | ||||||||
\(916\) | −1.41408 | −0.0467227 | ||||||||
\(917\) | 0.0345986 | 0.00114255 | ||||||||
\(918\) | 20.3558 | 0.671843 | ||||||||
\(919\) | −51.8241 | −1.70952 | −0.854760 | − | 0.519024i | \(-0.826295\pi\) | ||||
−0.854760 | + | 0.519024i | \(0.826295\pi\) | |||||||
\(920\) | −9.68407 | −0.319274 | ||||||||
\(921\) | −3.76724 | −0.124135 | ||||||||
\(922\) | −25.6956 | −0.846240 | ||||||||
\(923\) | −24.8043 | −0.816445 | ||||||||
\(924\) | 4.67167 | 0.153687 | ||||||||
\(925\) | −0.524426 | −0.0172430 | ||||||||
\(926\) | −19.0380 | −0.625629 | ||||||||
\(927\) | −8.53751 | −0.280409 | ||||||||
\(928\) | 0.214755 | 0.00704969 | ||||||||
\(929\) | 20.6123 | 0.676266 | 0.338133 | − | 0.941098i | \(-0.390205\pi\) | ||||
0.338133 | + | 0.941098i | \(0.390205\pi\) | |||||||
\(930\) | −10.0184 | −0.328518 | ||||||||
\(931\) | 5.33546 | 0.174863 | ||||||||
\(932\) | 2.30009 | 0.0753419 | ||||||||
\(933\) | −15.8633 | −0.519341 | ||||||||
\(934\) | 2.34262 | 0.0766529 | ||||||||
\(935\) | 14.6825 | 0.480170 | ||||||||
\(936\) | −2.09005 | −0.0683156 | ||||||||
\(937\) | −10.7696 | −0.351829 | −0.175914 | − | 0.984405i | \(-0.556288\pi\) | ||||
−0.175914 | + | 0.984405i | \(0.556288\pi\) | |||||||
\(938\) | −2.95438 | −0.0964638 | ||||||||
\(939\) | 30.5331 | 0.996409 | ||||||||
\(940\) | −0.128377 | −0.00418721 | ||||||||
\(941\) | −31.6617 | −1.03214 | −0.516070 | − | 0.856546i | \(-0.672606\pi\) | ||||
−0.516070 | + | 0.856546i | \(0.672606\pi\) | |||||||
\(942\) | −8.78538 | −0.286243 | ||||||||
\(943\) | −28.3397 | −0.922869 | ||||||||
\(944\) | 11.8493 | 0.385661 | ||||||||
\(945\) | −7.14404 | −0.232396 | ||||||||
\(946\) | 24.1916 | 0.786538 | ||||||||
\(947\) | −29.7484 | −0.966693 | −0.483346 | − | 0.875429i | \(-0.660579\pi\) | ||||
−0.483346 | + | 0.875429i | \(0.660579\pi\) | |||||||
\(948\) | −19.8007 | −0.643098 | ||||||||
\(949\) | 36.4669 | 1.18377 | ||||||||
\(950\) | 18.1525 | 0.588946 | ||||||||
\(951\) | −4.94352 | −0.160305 | ||||||||
\(952\) | 3.60165 | 0.116730 | ||||||||
\(953\) | −14.4958 | −0.469565 | −0.234783 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234783 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(954\) | 8.46819 | 0.274168 | ||||||||
\(955\) | −5.99866 | −0.194112 | ||||||||
\(956\) | 9.46668 | 0.306174 | ||||||||
\(957\) | 1.00327 | 0.0324310 | ||||||||
\(958\) | −6.41867 | −0.207378 | ||||||||
\(959\) | 2.39977 | 0.0774927 | ||||||||
\(960\) | −1.83098 | −0.0590947 | ||||||||
\(961\) | −1.06136 | −0.0342376 | ||||||||
\(962\) | 0.357265 | 0.0115187 | ||||||||
\(963\) | −15.3508 | −0.494674 | ||||||||
\(964\) | 15.2642 | 0.491627 | ||||||||
\(965\) | −5.53101 | −0.178049 | ||||||||
\(966\) | −11.0976 | −0.357061 | ||||||||
\(967\) | 19.6733 | 0.632649 | 0.316325 | − | 0.948651i | \(-0.397551\pi\) | ||||
0.316325 | + | 0.948651i | \(0.397551\pi\) | |||||||
\(968\) | 0.598690 | 0.0192426 | ||||||||
\(969\) | 27.8357 | 0.894210 | ||||||||
\(970\) | −22.3254 | −0.716825 | ||||||||
\(971\) | 50.1679 | 1.60996 | 0.804982 | − | 0.593299i | \(-0.202175\pi\) | ||||
0.804982 | + | 0.593299i | \(0.202175\pi\) | |||||||
\(972\) | 9.01518 | 0.289162 | ||||||||
\(973\) | 13.1736 | 0.422325 | ||||||||
\(974\) | 0.883066 | 0.0282952 | ||||||||
\(975\) | 11.4226 | 0.365815 | ||||||||
\(976\) | 5.95759 | 0.190698 | ||||||||
\(977\) | 46.9127 | 1.50087 | 0.750435 | − | 0.660944i | \(-0.229844\pi\) | ||||
0.750435 | + | 0.660944i | \(0.229844\pi\) | |||||||
\(978\) | −15.3400 | −0.490521 | ||||||||
\(979\) | 1.13028 | 0.0361239 | ||||||||
\(980\) | −1.26403 | −0.0403778 | ||||||||
\(981\) | −17.6257 | −0.562744 | ||||||||
\(982\) | 22.4448 | 0.716243 | ||||||||
\(983\) | 34.9309 | 1.11412 | 0.557062 | − | 0.830471i | \(-0.311929\pi\) | ||||
0.557062 | + | 0.830471i | \(0.311929\pi\) | |||||||
\(984\) | −5.35824 | −0.170814 | ||||||||
\(985\) | −3.87801 | −0.123564 | ||||||||
\(986\) | 0.773473 | 0.0246324 | ||||||||
\(987\) | −0.147116 | −0.00468277 | ||||||||
\(988\) | −12.3664 | −0.393427 | ||||||||
\(989\) | −57.4676 | −1.82736 | ||||||||
\(990\) | 3.67609 | 0.116834 | ||||||||
\(991\) | 32.8605 | 1.04385 | 0.521924 | − | 0.852992i | \(-0.325214\pi\) | ||||
0.521924 | + | 0.852992i | \(0.325214\pi\) | |||||||
\(992\) | 5.47162 | 0.173724 | ||||||||
\(993\) | 1.52273 | 0.0483225 | ||||||||
\(994\) | 10.7018 | 0.339440 | ||||||||
\(995\) | 33.2232 | 1.05325 | ||||||||
\(996\) | −2.84963 | −0.0902941 | ||||||||
\(997\) | 31.3910 | 0.994163 | 0.497081 | − | 0.867704i | \(-0.334405\pi\) | ||||
0.497081 | + | 0.867704i | \(0.334405\pi\) | |||||||
\(998\) | −19.9212 | −0.630595 | ||||||||
\(999\) | −0.871179 | −0.0275629 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6034.2.a.n.1.16 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.16 | ✓ | 24 | 1.1 | even | 1 | trivial |