Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76609 | −1.95592 | −0.977960 | − | 0.208794i | \(-0.933046\pi\) | ||||
−0.977960 | + | 0.208794i | \(0.933046\pi\) | |||||||
\(3\) | 1.72204 | 0.994219 | 0.497110 | − | 0.867688i | \(-0.334395\pi\) | ||||
0.497110 | + | 0.867688i | \(0.334395\pi\) | |||||||
\(4\) | 5.65124 | 2.82562 | ||||||||
\(5\) | 1.59310 | 0.712457 | 0.356228 | − | 0.934399i | \(-0.384063\pi\) | ||||
0.356228 | + | 0.934399i | \(0.384063\pi\) | |||||||
\(6\) | −4.76331 | −1.94461 | ||||||||
\(7\) | 4.82706 | 1.82446 | 0.912229 | − | 0.409681i | \(-0.134360\pi\) | ||||
0.912229 | + | 0.409681i | \(0.134360\pi\) | |||||||
\(8\) | −10.0996 | −3.57076 | ||||||||
\(9\) | −0.0345853 | −0.0115284 | ||||||||
\(10\) | −4.40666 | −1.39351 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 9.73165 | 2.80929 | ||||||||
\(13\) | −4.55724 | −1.26395 | −0.631975 | − | 0.774989i | \(-0.717756\pi\) | ||||
−0.631975 | + | 0.774989i | \(0.717756\pi\) | |||||||
\(14\) | −13.3521 | −3.56849 | ||||||||
\(15\) | 2.74338 | 0.708338 | ||||||||
\(16\) | 16.6340 | 4.15851 | ||||||||
\(17\) | −7.55927 | −1.83339 | −0.916696 | − | 0.399584i | \(-0.869154\pi\) | ||||
−0.916696 | + | 0.399584i | \(0.869154\pi\) | |||||||
\(18\) | 0.0956660 | 0.0225487 | ||||||||
\(19\) | 3.61389 | 0.829084 | 0.414542 | − | 0.910030i | \(-0.363942\pi\) | ||||
0.414542 | + | 0.910030i | \(0.363942\pi\) | |||||||
\(20\) | 9.00300 | 2.01313 | ||||||||
\(21\) | 8.31238 | 1.81391 | ||||||||
\(22\) | 2.76609 | 0.589732 | ||||||||
\(23\) | 7.11636 | 1.48386 | 0.741932 | − | 0.670475i | \(-0.233910\pi\) | ||||
0.741932 | + | 0.670475i | \(0.233910\pi\) | |||||||
\(24\) | −17.3920 | −3.55012 | ||||||||
\(25\) | −2.46203 | −0.492406 | ||||||||
\(26\) | 12.6057 | 2.47218 | ||||||||
\(27\) | −5.22567 | −1.00568 | ||||||||
\(28\) | 27.2789 | 5.15522 | ||||||||
\(29\) | 4.19876 | 0.779690 | 0.389845 | − | 0.920880i | \(-0.372529\pi\) | ||||
0.389845 | + | 0.920880i | \(0.372529\pi\) | |||||||
\(30\) | −7.58843 | −1.38545 | ||||||||
\(31\) | 5.25576 | 0.943962 | 0.471981 | − | 0.881609i | \(-0.343539\pi\) | ||||
0.471981 | + | 0.881609i | \(0.343539\pi\) | |||||||
\(32\) | −25.8119 | −4.56294 | ||||||||
\(33\) | −1.72204 | −0.299768 | ||||||||
\(34\) | 20.9096 | 3.58597 | ||||||||
\(35\) | 7.69000 | 1.29985 | ||||||||
\(36\) | −0.195450 | −0.0325750 | ||||||||
\(37\) | 3.75063 | 0.616600 | 0.308300 | − | 0.951289i | \(-0.400240\pi\) | ||||
0.308300 | + | 0.951289i | \(0.400240\pi\) | |||||||
\(38\) | −9.99634 | −1.62162 | ||||||||
\(39\) | −7.84774 | −1.25664 | ||||||||
\(40\) | −16.0898 | −2.54401 | ||||||||
\(41\) | −4.11901 | −0.643281 | −0.321641 | − | 0.946862i | \(-0.604234\pi\) | ||||
−0.321641 | + | 0.946862i | \(0.604234\pi\) | |||||||
\(42\) | −22.9928 | −3.54786 | ||||||||
\(43\) | 7.79370 | 1.18853 | 0.594264 | − | 0.804270i | \(-0.297444\pi\) | ||||
0.594264 | + | 0.804270i | \(0.297444\pi\) | |||||||
\(44\) | −5.65124 | −0.851956 | ||||||||
\(45\) | −0.0550979 | −0.00821351 | ||||||||
\(46\) | −19.6845 | −2.90232 | ||||||||
\(47\) | 7.98049 | 1.16407 | 0.582037 | − | 0.813162i | \(-0.302256\pi\) | ||||
0.582037 | + | 0.813162i | \(0.302256\pi\) | |||||||
\(48\) | 28.6444 | 4.13447 | ||||||||
\(49\) | 16.3005 | 2.32865 | ||||||||
\(50\) | 6.81019 | 0.963106 | ||||||||
\(51\) | −13.0174 | −1.82279 | ||||||||
\(52\) | −25.7540 | −3.57144 | ||||||||
\(53\) | 7.83066 | 1.07562 | 0.537812 | − | 0.843065i | \(-0.319251\pi\) | ||||
0.537812 | + | 0.843065i | \(0.319251\pi\) | |||||||
\(54\) | 14.4547 | 1.96703 | ||||||||
\(55\) | −1.59310 | −0.214814 | ||||||||
\(56\) | −48.7516 | −6.51471 | ||||||||
\(57\) | 6.22326 | 0.824291 | ||||||||
\(58\) | −11.6141 | −1.52501 | ||||||||
\(59\) | −3.96160 | −0.515756 | −0.257878 | − | 0.966177i | \(-0.583023\pi\) | ||||
−0.257878 | + | 0.966177i | \(0.583023\pi\) | |||||||
\(60\) | 15.5035 | 2.00149 | ||||||||
\(61\) | −9.41072 | −1.20492 | −0.602460 | − | 0.798149i | \(-0.705813\pi\) | ||||
−0.602460 | + | 0.798149i | \(0.705813\pi\) | |||||||
\(62\) | −14.5379 | −1.84631 | ||||||||
\(63\) | −0.166945 | −0.0210331 | ||||||||
\(64\) | 38.1299 | 4.76623 | ||||||||
\(65\) | −7.26014 | −0.900510 | ||||||||
\(66\) | 4.76331 | 0.586323 | ||||||||
\(67\) | −6.42278 | −0.784668 | −0.392334 | − | 0.919823i | \(-0.628332\pi\) | ||||
−0.392334 | + | 0.919823i | \(0.628332\pi\) | |||||||
\(68\) | −42.7193 | −5.18047 | ||||||||
\(69\) | 12.2546 | 1.47529 | ||||||||
\(70\) | −21.2712 | −2.54240 | ||||||||
\(71\) | −5.79611 | −0.687872 | −0.343936 | − | 0.938993i | \(-0.611760\pi\) | ||||
−0.343936 | + | 0.938993i | \(0.611760\pi\) | |||||||
\(72\) | 0.349299 | 0.0411653 | ||||||||
\(73\) | 4.61959 | 0.540682 | 0.270341 | − | 0.962765i | \(-0.412864\pi\) | ||||
0.270341 | + | 0.962765i | \(0.412864\pi\) | |||||||
\(74\) | −10.3746 | −1.20602 | ||||||||
\(75\) | −4.23971 | −0.489559 | ||||||||
\(76\) | 20.4230 | 2.34268 | ||||||||
\(77\) | −4.82706 | −0.550095 | ||||||||
\(78\) | 21.7075 | 2.45789 | ||||||||
\(79\) | 11.8018 | 1.32780 | 0.663902 | − | 0.747820i | \(-0.268899\pi\) | ||||
0.663902 | + | 0.747820i | \(0.268899\pi\) | |||||||
\(80\) | 26.4997 | 2.96276 | ||||||||
\(81\) | −8.89505 | −0.988339 | ||||||||
\(82\) | 11.3935 | 1.25821 | ||||||||
\(83\) | 13.1657 | 1.44513 | 0.722563 | − | 0.691305i | \(-0.242964\pi\) | ||||
0.722563 | + | 0.691305i | \(0.242964\pi\) | |||||||
\(84\) | 46.9753 | 5.12542 | ||||||||
\(85\) | −12.0427 | −1.30621 | ||||||||
\(86\) | −21.5580 | −2.32466 | ||||||||
\(87\) | 7.23042 | 0.775183 | ||||||||
\(88\) | 10.0996 | 1.07663 | ||||||||
\(89\) | 2.28499 | 0.242208 | 0.121104 | − | 0.992640i | \(-0.461356\pi\) | ||||
0.121104 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(90\) | 0.152406 | 0.0160650 | ||||||||
\(91\) | −21.9981 | −2.30602 | ||||||||
\(92\) | 40.2163 | 4.19284 | ||||||||
\(93\) | 9.05062 | 0.938505 | ||||||||
\(94\) | −22.0747 | −2.27684 | ||||||||
\(95\) | 5.75730 | 0.590686 | ||||||||
\(96\) | −44.4490 | −4.53656 | ||||||||
\(97\) | −4.21485 | −0.427953 | −0.213977 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213977 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(98\) | −45.0887 | −4.55464 | ||||||||
\(99\) | 0.0345853 | 0.00347595 | ||||||||
\(100\) | −13.9135 | −1.39135 | ||||||||
\(101\) | 1.74584 | 0.173718 | 0.0868588 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868588 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(102\) | 36.0071 | 3.56524 | ||||||||
\(103\) | 8.98750 | 0.885565 | 0.442782 | − | 0.896629i | \(-0.353991\pi\) | ||||
0.442782 | + | 0.896629i | \(0.353991\pi\) | |||||||
\(104\) | 46.0265 | 4.51327 | ||||||||
\(105\) | 13.2425 | 1.29233 | ||||||||
\(106\) | −21.6603 | −2.10383 | ||||||||
\(107\) | −19.0131 | −1.83807 | −0.919034 | − | 0.394178i | \(-0.871029\pi\) | ||||
−0.919034 | + | 0.394178i | \(0.871029\pi\) | |||||||
\(108\) | −29.5315 | −2.84167 | ||||||||
\(109\) | 10.9149 | 1.04546 | 0.522728 | − | 0.852500i | \(-0.324914\pi\) | ||||
0.522728 | + | 0.852500i | \(0.324914\pi\) | |||||||
\(110\) | 4.40666 | 0.420158 | ||||||||
\(111\) | 6.45873 | 0.613036 | ||||||||
\(112\) | 80.2935 | 7.58702 | ||||||||
\(113\) | 9.81947 | 0.923738 | 0.461869 | − | 0.886948i | \(-0.347179\pi\) | ||||
0.461869 | + | 0.886948i | \(0.347179\pi\) | |||||||
\(114\) | −17.2141 | −1.61225 | ||||||||
\(115\) | 11.3371 | 1.05719 | ||||||||
\(116\) | 23.7282 | 2.20311 | ||||||||
\(117\) | 0.157613 | 0.0145714 | ||||||||
\(118\) | 10.9581 | 1.00878 | ||||||||
\(119\) | −36.4891 | −3.34495 | ||||||||
\(120\) | −27.7072 | −2.52931 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 26.0309 | 2.35672 | ||||||||
\(123\) | −7.09309 | −0.639562 | ||||||||
\(124\) | 29.7016 | 2.66728 | ||||||||
\(125\) | −11.8878 | −1.06327 | ||||||||
\(126\) | 0.461786 | 0.0411391 | ||||||||
\(127\) | 17.1760 | 1.52413 | 0.762063 | − | 0.647503i | \(-0.224187\pi\) | ||||
0.762063 | + | 0.647503i | \(0.224187\pi\) | |||||||
\(128\) | −53.8468 | −4.75943 | ||||||||
\(129\) | 13.4210 | 1.18166 | ||||||||
\(130\) | 20.0822 | 1.76132 | ||||||||
\(131\) | 6.49876 | 0.567799 | 0.283900 | − | 0.958854i | \(-0.408372\pi\) | ||||
0.283900 | + | 0.958854i | \(0.408372\pi\) | |||||||
\(132\) | −9.73165 | −0.847031 | ||||||||
\(133\) | 17.4445 | 1.51263 | ||||||||
\(134\) | 17.7660 | 1.53475 | ||||||||
\(135\) | −8.32502 | −0.716504 | ||||||||
\(136\) | 76.3460 | 6.54661 | ||||||||
\(137\) | 10.1562 | 0.867703 | 0.433852 | − | 0.900984i | \(-0.357154\pi\) | ||||
0.433852 | + | 0.900984i | \(0.357154\pi\) | |||||||
\(138\) | −33.8974 | −2.88554 | ||||||||
\(139\) | 12.0892 | 1.02540 | 0.512698 | − | 0.858569i | \(-0.328646\pi\) | ||||
0.512698 | + | 0.858569i | \(0.328646\pi\) | |||||||
\(140\) | 43.4580 | 3.67287 | ||||||||
\(141\) | 13.7427 | 1.15734 | ||||||||
\(142\) | 16.0326 | 1.34542 | ||||||||
\(143\) | 4.55724 | 0.381095 | ||||||||
\(144\) | −0.575293 | −0.0479411 | ||||||||
\(145\) | 6.68905 | 0.555495 | ||||||||
\(146\) | −12.7782 | −1.05753 | ||||||||
\(147\) | 28.0701 | 2.31518 | ||||||||
\(148\) | 21.1957 | 1.74228 | ||||||||
\(149\) | −17.4041 | −1.42580 | −0.712901 | − | 0.701264i | \(-0.752619\pi\) | ||||
−0.712901 | + | 0.701264i | \(0.752619\pi\) | |||||||
\(150\) | 11.7274 | 0.957538 | ||||||||
\(151\) | −17.3696 | −1.41352 | −0.706759 | − | 0.707455i | \(-0.749843\pi\) | ||||
−0.706759 | + | 0.707455i | \(0.749843\pi\) | |||||||
\(152\) | −36.4990 | −2.96046 | ||||||||
\(153\) | 0.261440 | 0.0211361 | ||||||||
\(154\) | 13.3521 | 1.07594 | ||||||||
\(155\) | 8.37296 | 0.672532 | ||||||||
\(156\) | −44.3494 | −3.55080 | ||||||||
\(157\) | 0.302820 | 0.0241677 | 0.0120839 | − | 0.999927i | \(-0.496153\pi\) | ||||
0.0120839 | + | 0.999927i | \(0.496153\pi\) | |||||||
\(158\) | −32.6447 | −2.59708 | ||||||||
\(159\) | 13.4847 | 1.06941 | ||||||||
\(160\) | −41.1209 | −3.25090 | ||||||||
\(161\) | 34.3511 | 2.70725 | ||||||||
\(162\) | 24.6045 | 1.93311 | ||||||||
\(163\) | 23.2004 | 1.81720 | 0.908599 | − | 0.417669i | \(-0.137153\pi\) | ||||
0.908599 | + | 0.417669i | \(0.137153\pi\) | |||||||
\(164\) | −23.2775 | −1.81767 | ||||||||
\(165\) | −2.74338 | −0.213572 | ||||||||
\(166\) | −36.4176 | −2.82655 | ||||||||
\(167\) | −8.25517 | −0.638804 | −0.319402 | − | 0.947619i | \(-0.603482\pi\) | ||||
−0.319402 | + | 0.947619i | \(0.603482\pi\) | |||||||
\(168\) | −83.9521 | −6.47705 | ||||||||
\(169\) | 7.76842 | 0.597571 | ||||||||
\(170\) | 33.3111 | 2.55485 | ||||||||
\(171\) | −0.124988 | −0.00955804 | ||||||||
\(172\) | 44.0440 | 3.35833 | ||||||||
\(173\) | −12.3052 | −0.935546 | −0.467773 | − | 0.883849i | \(-0.654944\pi\) | ||||
−0.467773 | + | 0.883849i | \(0.654944\pi\) | |||||||
\(174\) | −20.0000 | −1.51620 | ||||||||
\(175\) | −11.8844 | −0.898373 | ||||||||
\(176\) | −16.6340 | −1.25384 | ||||||||
\(177\) | −6.82202 | −0.512774 | ||||||||
\(178\) | −6.32048 | −0.473740 | ||||||||
\(179\) | −2.93838 | −0.219625 | −0.109812 | − | 0.993952i | \(-0.535025\pi\) | ||||
−0.109812 | + | 0.993952i | \(0.535025\pi\) | |||||||
\(180\) | −0.311371 | −0.0232083 | ||||||||
\(181\) | 20.5463 | 1.52720 | 0.763599 | − | 0.645691i | \(-0.223430\pi\) | ||||
0.763599 | + | 0.645691i | \(0.223430\pi\) | |||||||
\(182\) | 60.8486 | 4.51040 | ||||||||
\(183\) | −16.2056 | −1.19795 | ||||||||
\(184\) | −71.8727 | −5.29853 | ||||||||
\(185\) | 5.97514 | 0.439301 | ||||||||
\(186\) | −25.0348 | −1.83564 | ||||||||
\(187\) | 7.55927 | 0.552789 | ||||||||
\(188\) | 45.0997 | 3.28923 | ||||||||
\(189\) | −25.2246 | −1.83482 | ||||||||
\(190\) | −15.9252 | −1.15533 | ||||||||
\(191\) | −2.29237 | −0.165870 | −0.0829352 | − | 0.996555i | \(-0.526429\pi\) | ||||
−0.0829352 | + | 0.996555i | \(0.526429\pi\) | |||||||
\(192\) | 65.6611 | 4.73868 | ||||||||
\(193\) | 4.85074 | 0.349164 | 0.174582 | − | 0.984643i | \(-0.444143\pi\) | ||||
0.174582 | + | 0.984643i | \(0.444143\pi\) | |||||||
\(194\) | 11.6586 | 0.837042 | ||||||||
\(195\) | −12.5022 | −0.895304 | ||||||||
\(196\) | 92.1181 | 6.57987 | ||||||||
\(197\) | 24.7690 | 1.76472 | 0.882360 | − | 0.470575i | \(-0.155953\pi\) | ||||
0.882360 | + | 0.470575i | \(0.155953\pi\) | |||||||
\(198\) | −0.0956660 | −0.00679869 | ||||||||
\(199\) | −6.01960 | −0.426718 | −0.213359 | − | 0.976974i | \(-0.568440\pi\) | ||||
−0.213359 | + | 0.976974i | \(0.568440\pi\) | |||||||
\(200\) | 24.8656 | 1.75826 | ||||||||
\(201\) | −11.0603 | −0.780132 | ||||||||
\(202\) | −4.82915 | −0.339778 | ||||||||
\(203\) | 20.2677 | 1.42251 | ||||||||
\(204\) | −73.5642 | −5.15052 | ||||||||
\(205\) | −6.56200 | −0.458310 | ||||||||
\(206\) | −24.8602 | −1.73209 | ||||||||
\(207\) | −0.246122 | −0.0171066 | ||||||||
\(208\) | −75.8052 | −5.25615 | ||||||||
\(209\) | −3.61389 | −0.249978 | ||||||||
\(210\) | −36.6298 | −2.52770 | ||||||||
\(211\) | −18.6808 | −1.28604 | −0.643021 | − | 0.765848i | \(-0.722319\pi\) | ||||
−0.643021 | + | 0.765848i | \(0.722319\pi\) | |||||||
\(212\) | 44.2530 | 3.03931 | ||||||||
\(213\) | −9.98113 | −0.683895 | ||||||||
\(214\) | 52.5920 | 3.59511 | ||||||||
\(215\) | 12.4161 | 0.846774 | ||||||||
\(216\) | 52.7774 | 3.59105 | ||||||||
\(217\) | 25.3699 | 1.72222 | ||||||||
\(218\) | −30.1915 | −2.04483 | ||||||||
\(219\) | 7.95511 | 0.537556 | ||||||||
\(220\) | −9.00300 | −0.606982 | ||||||||
\(221\) | 34.4494 | 2.31732 | ||||||||
\(222\) | −17.8654 | −1.19905 | ||||||||
\(223\) | 14.5378 | 0.973523 | 0.486762 | − | 0.873535i | \(-0.338178\pi\) | ||||
0.486762 | + | 0.873535i | \(0.338178\pi\) | |||||||
\(224\) | −124.596 | −8.32489 | ||||||||
\(225\) | 0.0851500 | 0.00567667 | ||||||||
\(226\) | −27.1615 | −1.80676 | ||||||||
\(227\) | 0.885115 | 0.0587472 | 0.0293736 | − | 0.999569i | \(-0.490649\pi\) | ||||
0.0293736 | + | 0.999569i | \(0.490649\pi\) | |||||||
\(228\) | 35.1691 | 2.32913 | ||||||||
\(229\) | −17.3684 | −1.14774 | −0.573868 | − | 0.818948i | \(-0.694558\pi\) | ||||
−0.573868 | + | 0.818948i | \(0.694558\pi\) | |||||||
\(230\) | −31.3594 | −2.06778 | ||||||||
\(231\) | −8.31238 | −0.546915 | ||||||||
\(232\) | −42.4060 | −2.78409 | ||||||||
\(233\) | 12.8875 | 0.844287 | 0.422143 | − | 0.906529i | \(-0.361278\pi\) | ||||
0.422143 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(234\) | −0.435973 | −0.0285004 | ||||||||
\(235\) | 12.7137 | 0.829352 | ||||||||
\(236\) | −22.3879 | −1.45733 | ||||||||
\(237\) | 20.3231 | 1.32013 | ||||||||
\(238\) | 100.932 | 6.54245 | ||||||||
\(239\) | 12.3926 | 0.801611 | 0.400805 | − | 0.916163i | \(-0.368730\pi\) | ||||
0.400805 | + | 0.916163i | \(0.368730\pi\) | |||||||
\(240\) | 45.6335 | 2.94563 | ||||||||
\(241\) | 20.5053 | 1.32086 | 0.660431 | − | 0.750887i | \(-0.270374\pi\) | ||||
0.660431 | + | 0.750887i | \(0.270374\pi\) | |||||||
\(242\) | −2.76609 | −0.177811 | ||||||||
\(243\) | 0.359403 | 0.0230557 | ||||||||
\(244\) | −53.1822 | −3.40464 | ||||||||
\(245\) | 25.9684 | 1.65906 | ||||||||
\(246\) | 19.6201 | 1.25093 | ||||||||
\(247\) | −16.4694 | −1.04792 | ||||||||
\(248\) | −53.0813 | −3.37067 | ||||||||
\(249\) | 22.6719 | 1.43677 | ||||||||
\(250\) | 32.8826 | 2.07968 | ||||||||
\(251\) | 21.9081 | 1.38283 | 0.691413 | − | 0.722460i | \(-0.256989\pi\) | ||||
0.691413 | + | 0.722460i | \(0.256989\pi\) | |||||||
\(252\) | −0.943448 | −0.0594317 | ||||||||
\(253\) | −7.11636 | −0.447402 | ||||||||
\(254\) | −47.5104 | −2.98107 | ||||||||
\(255\) | −20.7380 | −1.29866 | ||||||||
\(256\) | 72.6851 | 4.54282 | ||||||||
\(257\) | −8.39655 | −0.523762 | −0.261881 | − | 0.965100i | \(-0.584343\pi\) | ||||
−0.261881 | + | 0.965100i | \(0.584343\pi\) | |||||||
\(258\) | −37.1238 | −2.31122 | ||||||||
\(259\) | 18.1045 | 1.12496 | ||||||||
\(260\) | −41.0288 | −2.54450 | ||||||||
\(261\) | −0.145215 | −0.00898861 | ||||||||
\(262\) | −17.9761 | −1.11057 | ||||||||
\(263\) | 19.2483 | 1.18690 | 0.593449 | − | 0.804871i | \(-0.297766\pi\) | ||||
0.593449 | + | 0.804871i | \(0.297766\pi\) | |||||||
\(264\) | 17.3920 | 1.07040 | ||||||||
\(265\) | 12.4750 | 0.766336 | ||||||||
\(266\) | −48.2530 | −2.95858 | ||||||||
\(267\) | 3.93484 | 0.240808 | ||||||||
\(268\) | −36.2967 | −2.21717 | ||||||||
\(269\) | 5.16367 | 0.314834 | 0.157417 | − | 0.987532i | \(-0.449683\pi\) | ||||
0.157417 | + | 0.987532i | \(0.449683\pi\) | |||||||
\(270\) | 23.0277 | 1.40142 | ||||||||
\(271\) | 4.84737 | 0.294457 | 0.147228 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147228 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(272\) | −125.741 | −7.62418 | ||||||||
\(273\) | −37.8815 | −2.29269 | ||||||||
\(274\) | −28.0929 | −1.69716 | ||||||||
\(275\) | 2.46203 | 0.148466 | ||||||||
\(276\) | 69.2539 | 4.16860 | ||||||||
\(277\) | −7.08095 | −0.425453 | −0.212726 | − | 0.977112i | \(-0.568234\pi\) | ||||
−0.212726 | + | 0.977112i | \(0.568234\pi\) | |||||||
\(278\) | −33.4399 | −2.00559 | ||||||||
\(279\) | −0.181772 | −0.0108824 | ||||||||
\(280\) | −77.6663 | −4.64145 | ||||||||
\(281\) | −1.78300 | −0.106365 | −0.0531826 | − | 0.998585i | \(-0.516937\pi\) | ||||
−0.0531826 | + | 0.998585i | \(0.516937\pi\) | |||||||
\(282\) | −38.0135 | −2.26367 | ||||||||
\(283\) | −17.0872 | −1.01573 | −0.507863 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507863 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(284\) | −32.7552 | −1.94366 | ||||||||
\(285\) | 9.91428 | 0.587271 | ||||||||
\(286\) | −12.6057 | −0.745392 | ||||||||
\(287\) | −19.8827 | −1.17364 | ||||||||
\(288\) | 0.892712 | 0.0526035 | ||||||||
\(289\) | 40.1426 | 2.36133 | ||||||||
\(290\) | −18.5025 | −1.08650 | ||||||||
\(291\) | −7.25814 | −0.425479 | ||||||||
\(292\) | 26.1064 | 1.52776 | ||||||||
\(293\) | −16.1209 | −0.941791 | −0.470896 | − | 0.882189i | \(-0.656069\pi\) | ||||
−0.470896 | + | 0.882189i | \(0.656069\pi\) | |||||||
\(294\) | −77.6444 | −4.52831 | ||||||||
\(295\) | −6.31123 | −0.367454 | ||||||||
\(296\) | −37.8801 | −2.20173 | ||||||||
\(297\) | 5.22567 | 0.303224 | ||||||||
\(298\) | 48.1414 | 2.78876 | ||||||||
\(299\) | −32.4310 | −1.87553 | ||||||||
\(300\) | −23.9596 | −1.38331 | ||||||||
\(301\) | 37.6206 | 2.16842 | ||||||||
\(302\) | 48.0458 | 2.76473 | ||||||||
\(303\) | 3.00640 | 0.172713 | ||||||||
\(304\) | 60.1136 | 3.44775 | ||||||||
\(305\) | −14.9922 | −0.858453 | ||||||||
\(306\) | −0.723165 | −0.0413406 | ||||||||
\(307\) | −15.5729 | −0.888790 | −0.444395 | − | 0.895831i | \(-0.646581\pi\) | ||||
−0.444395 | + | 0.895831i | \(0.646581\pi\) | |||||||
\(308\) | −27.2789 | −1.55436 | ||||||||
\(309\) | 15.4768 | 0.880445 | ||||||||
\(310\) | −23.1603 | −1.31542 | ||||||||
\(311\) | −0.941881 | −0.0534092 | −0.0267046 | − | 0.999643i | \(-0.508501\pi\) | ||||
−0.0267046 | + | 0.999643i | \(0.508501\pi\) | |||||||
\(312\) | 79.2594 | 4.48718 | ||||||||
\(313\) | 2.75976 | 0.155991 | 0.0779955 | − | 0.996954i | \(-0.475148\pi\) | ||||
0.0779955 | + | 0.996954i | \(0.475148\pi\) | |||||||
\(314\) | −0.837628 | −0.0472701 | ||||||||
\(315\) | −0.265961 | −0.0149852 | ||||||||
\(316\) | 66.6946 | 3.75187 | ||||||||
\(317\) | 0.839880 | 0.0471724 | 0.0235862 | − | 0.999722i | \(-0.492492\pi\) | ||||
0.0235862 | + | 0.999722i | \(0.492492\pi\) | |||||||
\(318\) | −37.2999 | −2.09167 | ||||||||
\(319\) | −4.19876 | −0.235085 | ||||||||
\(320\) | 60.7447 | 3.39573 | ||||||||
\(321\) | −32.7413 | −1.82744 | ||||||||
\(322\) | −95.0182 | −5.29516 | ||||||||
\(323\) | −27.3184 | −1.52004 | ||||||||
\(324\) | −50.2680 | −2.79267 | ||||||||
\(325\) | 11.2200 | 0.622376 | ||||||||
\(326\) | −64.1744 | −3.55429 | ||||||||
\(327\) | 18.7958 | 1.03941 | ||||||||
\(328\) | 41.6005 | 2.29701 | ||||||||
\(329\) | 38.5223 | 2.12380 | ||||||||
\(330\) | 7.58843 | 0.417729 | ||||||||
\(331\) | −33.7289 | −1.85391 | −0.926954 | − | 0.375176i | \(-0.877582\pi\) | ||||
−0.926954 | + | 0.375176i | \(0.877582\pi\) | |||||||
\(332\) | 74.4027 | 4.08338 | ||||||||
\(333\) | −0.129717 | −0.00710843 | ||||||||
\(334\) | 22.8345 | 1.24945 | ||||||||
\(335\) | −10.2321 | −0.559042 | ||||||||
\(336\) | 138.268 | 7.54316 | ||||||||
\(337\) | 20.7409 | 1.12983 | 0.564916 | − | 0.825149i | \(-0.308909\pi\) | ||||
0.564916 | + | 0.825149i | \(0.308909\pi\) | |||||||
\(338\) | −21.4881 | −1.16880 | ||||||||
\(339\) | 16.9095 | 0.918398 | ||||||||
\(340\) | −68.0561 | −3.69086 | ||||||||
\(341\) | −5.25576 | −0.284615 | ||||||||
\(342\) | 0.345727 | 0.0186948 | ||||||||
\(343\) | 44.8942 | 2.42406 | ||||||||
\(344\) | −78.7136 | −4.24395 | ||||||||
\(345\) | 19.5229 | 1.05108 | ||||||||
\(346\) | 34.0372 | 1.82985 | ||||||||
\(347\) | −16.8679 | −0.905518 | −0.452759 | − | 0.891633i | \(-0.649560\pi\) | ||||
−0.452759 | + | 0.891633i | \(0.649560\pi\) | |||||||
\(348\) | 40.8609 | 2.19037 | ||||||||
\(349\) | −3.92387 | −0.210040 | −0.105020 | − | 0.994470i | \(-0.533491\pi\) | ||||
−0.105020 | + | 0.994470i | \(0.533491\pi\) | |||||||
\(350\) | 32.8732 | 1.75715 | ||||||||
\(351\) | 23.8146 | 1.27113 | ||||||||
\(352\) | 25.8119 | 1.37578 | ||||||||
\(353\) | 14.1778 | 0.754611 | 0.377305 | − | 0.926089i | \(-0.376851\pi\) | ||||
0.377305 | + | 0.926089i | \(0.376851\pi\) | |||||||
\(354\) | 18.8703 | 1.00295 | ||||||||
\(355\) | −9.23379 | −0.490079 | ||||||||
\(356\) | 12.9130 | 0.684389 | ||||||||
\(357\) | −62.8356 | −3.32561 | ||||||||
\(358\) | 8.12780 | 0.429568 | ||||||||
\(359\) | −23.3064 | −1.23007 | −0.615033 | − | 0.788501i | \(-0.710857\pi\) | ||||
−0.615033 | + | 0.788501i | \(0.710857\pi\) | |||||||
\(360\) | 0.556469 | 0.0293285 | ||||||||
\(361\) | −5.93978 | −0.312620 | ||||||||
\(362\) | −56.8330 | −2.98708 | ||||||||
\(363\) | 1.72204 | 0.0903836 | ||||||||
\(364\) | −124.316 | −6.51595 | ||||||||
\(365\) | 7.35947 | 0.385212 | ||||||||
\(366\) | 44.8262 | 2.34310 | ||||||||
\(367\) | −7.01716 | −0.366293 | −0.183146 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183146 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(368\) | 118.374 | 6.17066 | ||||||||
\(369\) | 0.142457 | 0.00741603 | ||||||||
\(370\) | −16.5278 | −0.859237 | ||||||||
\(371\) | 37.7991 | 1.96243 | ||||||||
\(372\) | 51.1472 | 2.65186 | ||||||||
\(373\) | 8.36997 | 0.433381 | 0.216690 | − | 0.976240i | \(-0.430474\pi\) | ||||
0.216690 | + | 0.976240i | \(0.430474\pi\) | |||||||
\(374\) | −20.9096 | −1.08121 | ||||||||
\(375\) | −20.4712 | −1.05713 | ||||||||
\(376\) | −80.6002 | −4.15664 | ||||||||
\(377\) | −19.1348 | −0.985490 | ||||||||
\(378\) | 69.7735 | 3.58876 | ||||||||
\(379\) | −16.1453 | −0.829330 | −0.414665 | − | 0.909974i | \(-0.636101\pi\) | ||||
−0.414665 | + | 0.909974i | \(0.636101\pi\) | |||||||
\(380\) | 32.5359 | 1.66905 | ||||||||
\(381\) | 29.5778 | 1.51531 | ||||||||
\(382\) | 6.34090 | 0.324429 | ||||||||
\(383\) | 12.5513 | 0.641342 | 0.320671 | − | 0.947191i | \(-0.396092\pi\) | ||||
0.320671 | + | 0.947191i | \(0.396092\pi\) | |||||||
\(384\) | −92.7262 | −4.73191 | ||||||||
\(385\) | −7.69000 | −0.391919 | ||||||||
\(386\) | −13.4176 | −0.682936 | ||||||||
\(387\) | −0.269547 | −0.0137019 | ||||||||
\(388\) | −23.8191 | −1.20923 | ||||||||
\(389\) | −11.2319 | −0.569480 | −0.284740 | − | 0.958605i | \(-0.591907\pi\) | ||||
−0.284740 | + | 0.958605i | \(0.591907\pi\) | |||||||
\(390\) | 34.5823 | 1.75114 | ||||||||
\(391\) | −53.7945 | −2.72051 | ||||||||
\(392\) | −164.630 | −8.31505 | ||||||||
\(393\) | 11.1911 | 0.564517 | ||||||||
\(394\) | −68.5133 | −3.45165 | ||||||||
\(395\) | 18.8014 | 0.946002 | ||||||||
\(396\) | 0.195450 | 0.00982172 | ||||||||
\(397\) | −32.6597 | −1.63914 | −0.819572 | − | 0.572977i | \(-0.805789\pi\) | ||||
−0.819572 | + | 0.572977i | \(0.805789\pi\) | |||||||
\(398\) | 16.6507 | 0.834626 | ||||||||
\(399\) | 30.0401 | 1.50388 | ||||||||
\(400\) | −40.9534 | −2.04767 | ||||||||
\(401\) | 30.0508 | 1.50066 | 0.750332 | − | 0.661062i | \(-0.229894\pi\) | ||||
0.750332 | + | 0.661062i | \(0.229894\pi\) | |||||||
\(402\) | 30.5937 | 1.52587 | ||||||||
\(403\) | −23.9517 | −1.19312 | ||||||||
\(404\) | 9.86617 | 0.490860 | ||||||||
\(405\) | −14.1707 | −0.704148 | ||||||||
\(406\) | −56.0622 | −2.78232 | ||||||||
\(407\) | −3.75063 | −0.185912 | ||||||||
\(408\) | 131.471 | 6.50877 | ||||||||
\(409\) | 18.3382 | 0.906764 | 0.453382 | − | 0.891316i | \(-0.350217\pi\) | ||||
0.453382 | + | 0.891316i | \(0.350217\pi\) | |||||||
\(410\) | 18.1511 | 0.896417 | ||||||||
\(411\) | 17.4894 | 0.862687 | ||||||||
\(412\) | 50.7905 | 2.50227 | ||||||||
\(413\) | −19.1229 | −0.940975 | ||||||||
\(414\) | 0.680794 | 0.0334592 | ||||||||
\(415\) | 20.9743 | 1.02959 | ||||||||
\(416\) | 117.631 | 5.76733 | ||||||||
\(417\) | 20.8181 | 1.01947 | ||||||||
\(418\) | 9.99634 | 0.488937 | ||||||||
\(419\) | −12.5393 | −0.612586 | −0.306293 | − | 0.951937i | \(-0.599089\pi\) | ||||
−0.306293 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(420\) | 74.8364 | 3.65164 | ||||||||
\(421\) | 17.8853 | 0.871676 | 0.435838 | − | 0.900025i | \(-0.356452\pi\) | ||||
0.435838 | + | 0.900025i | \(0.356452\pi\) | |||||||
\(422\) | 51.6729 | 2.51540 | ||||||||
\(423\) | −0.276008 | −0.0134200 | ||||||||
\(424\) | −79.0869 | −3.84080 | ||||||||
\(425\) | 18.6111 | 0.902773 | ||||||||
\(426\) | 27.6087 | 1.33764 | ||||||||
\(427\) | −45.4261 | −2.19832 | ||||||||
\(428\) | −107.448 | −5.19368 | ||||||||
\(429\) | 7.84774 | 0.378892 | ||||||||
\(430\) | −34.3441 | −1.65622 | ||||||||
\(431\) | −35.0836 | −1.68992 | −0.844960 | − | 0.534830i | \(-0.820376\pi\) | ||||
−0.844960 | + | 0.534830i | \(0.820376\pi\) | |||||||
\(432\) | −86.9240 | −4.18213 | ||||||||
\(433\) | −35.3433 | −1.69849 | −0.849244 | − | 0.528000i | \(-0.822942\pi\) | ||||
−0.849244 | + | 0.528000i | \(0.822942\pi\) | |||||||
\(434\) | −70.1753 | −3.36852 | ||||||||
\(435\) | 11.5188 | 0.552284 | ||||||||
\(436\) | 61.6826 | 2.95406 | ||||||||
\(437\) | 25.7178 | 1.23025 | ||||||||
\(438\) | −22.0045 | −1.05142 | ||||||||
\(439\) | −6.90256 | −0.329441 | −0.164721 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164721 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(440\) | 16.0898 | 0.767049 | ||||||||
\(441\) | −0.563759 | −0.0268456 | ||||||||
\(442\) | −95.2901 | −4.53249 | ||||||||
\(443\) | 15.7400 | 0.747830 | 0.373915 | − | 0.927463i | \(-0.378015\pi\) | ||||
0.373915 | + | 0.927463i | \(0.378015\pi\) | |||||||
\(444\) | 36.4998 | 1.73221 | ||||||||
\(445\) | 3.64022 | 0.172563 | ||||||||
\(446\) | −40.2128 | −1.90413 | ||||||||
\(447\) | −29.9706 | −1.41756 | ||||||||
\(448\) | 184.055 | 8.69579 | ||||||||
\(449\) | 15.5572 | 0.734188 | 0.367094 | − | 0.930184i | \(-0.380353\pi\) | ||||
0.367094 | + | 0.930184i | \(0.380353\pi\) | |||||||
\(450\) | −0.235532 | −0.0111031 | ||||||||
\(451\) | 4.11901 | 0.193957 | ||||||||
\(452\) | 55.4922 | 2.61013 | ||||||||
\(453\) | −29.9111 | −1.40535 | ||||||||
\(454\) | −2.44831 | −0.114905 | ||||||||
\(455\) | −35.0452 | −1.64294 | ||||||||
\(456\) | −62.8527 | −2.94335 | ||||||||
\(457\) | −36.8348 | −1.72306 | −0.861530 | − | 0.507706i | \(-0.830494\pi\) | ||||
−0.861530 | + | 0.507706i | \(0.830494\pi\) | |||||||
\(458\) | 48.0425 | 2.24488 | ||||||||
\(459\) | 39.5023 | 1.84381 | ||||||||
\(460\) | 64.0686 | 2.98721 | ||||||||
\(461\) | −1.51664 | −0.0706370 | −0.0353185 | − | 0.999376i | \(-0.511245\pi\) | ||||
−0.0353185 | + | 0.999376i | \(0.511245\pi\) | |||||||
\(462\) | 22.9928 | 1.06972 | ||||||||
\(463\) | 14.1808 | 0.659038 | 0.329519 | − | 0.944149i | \(-0.393113\pi\) | ||||
0.329519 | + | 0.944149i | \(0.393113\pi\) | |||||||
\(464\) | 69.8423 | 3.24235 | ||||||||
\(465\) | 14.4185 | 0.668644 | ||||||||
\(466\) | −35.6479 | −1.65136 | ||||||||
\(467\) | 16.6273 | 0.769418 | 0.384709 | − | 0.923038i | \(-0.374302\pi\) | ||||
0.384709 | + | 0.923038i | \(0.374302\pi\) | |||||||
\(468\) | 0.890712 | 0.0411732 | ||||||||
\(469\) | −31.0032 | −1.43159 | ||||||||
\(470\) | −35.1673 | −1.62215 | ||||||||
\(471\) | 0.521468 | 0.0240280 | ||||||||
\(472\) | 40.0107 | 1.84164 | ||||||||
\(473\) | −7.79370 | −0.358355 | ||||||||
\(474\) | −56.2155 | −2.58206 | ||||||||
\(475\) | −8.89751 | −0.408246 | ||||||||
\(476\) | −206.208 | −9.45155 | ||||||||
\(477\) | −0.270826 | −0.0124003 | ||||||||
\(478\) | −34.2790 | −1.56789 | ||||||||
\(479\) | 6.21708 | 0.284065 | 0.142033 | − | 0.989862i | \(-0.454636\pi\) | ||||
0.142033 | + | 0.989862i | \(0.454636\pi\) | |||||||
\(480\) | −70.8118 | −3.23210 | ||||||||
\(481\) | −17.0925 | −0.779352 | ||||||||
\(482\) | −56.7194 | −2.58350 | ||||||||
\(483\) | 59.1539 | 2.69160 | ||||||||
\(484\) | 5.65124 | 0.256875 | ||||||||
\(485\) | −6.71469 | −0.304898 | ||||||||
\(486\) | −0.994140 | −0.0450951 | ||||||||
\(487\) | −28.6906 | −1.30009 | −0.650047 | − | 0.759894i | \(-0.725251\pi\) | ||||
−0.650047 | + | 0.759894i | \(0.725251\pi\) | |||||||
\(488\) | 95.0450 | 4.30248 | ||||||||
\(489\) | 39.9520 | 1.80669 | ||||||||
\(490\) | −71.8308 | −3.24499 | ||||||||
\(491\) | 1.38426 | 0.0624706 | 0.0312353 | − | 0.999512i | \(-0.490056\pi\) | ||||
0.0312353 | + | 0.999512i | \(0.490056\pi\) | |||||||
\(492\) | −40.0848 | −1.80716 | ||||||||
\(493\) | −31.7396 | −1.42948 | ||||||||
\(494\) | 45.5557 | 2.04965 | ||||||||
\(495\) | 0.0550979 | 0.00247647 | ||||||||
\(496\) | 87.4244 | 3.92547 | ||||||||
\(497\) | −27.9782 | −1.25499 | ||||||||
\(498\) | −62.7124 | −2.81021 | ||||||||
\(499\) | 11.4918 | 0.514444 | 0.257222 | − | 0.966352i | \(-0.417193\pi\) | ||||
0.257222 | + | 0.966352i | \(0.417193\pi\) | |||||||
\(500\) | −67.1806 | −3.00441 | ||||||||
\(501\) | −14.2157 | −0.635111 | ||||||||
\(502\) | −60.5997 | −2.70470 | ||||||||
\(503\) | −11.1348 | −0.496478 | −0.248239 | − | 0.968699i | \(-0.579852\pi\) | ||||
−0.248239 | + | 0.968699i | \(0.579852\pi\) | |||||||
\(504\) | 1.68609 | 0.0751044 | ||||||||
\(505\) | 2.78130 | 0.123766 | ||||||||
\(506\) | 19.6845 | 0.875082 | ||||||||
\(507\) | 13.3775 | 0.594116 | ||||||||
\(508\) | 97.0658 | 4.30660 | ||||||||
\(509\) | −9.78466 | −0.433697 | −0.216849 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216849 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(510\) | 57.3630 | 2.54008 | ||||||||
\(511\) | 22.2990 | 0.986452 | ||||||||
\(512\) | −93.3599 | −4.12596 | ||||||||
\(513\) | −18.8850 | −0.833794 | ||||||||
\(514\) | 23.2256 | 1.02444 | ||||||||
\(515\) | 14.3180 | 0.630926 | ||||||||
\(516\) | 75.8455 | 3.33891 | ||||||||
\(517\) | −7.98049 | −0.350982 | ||||||||
\(518\) | −50.0787 | −2.20033 | ||||||||
\(519\) | −21.1900 | −0.930138 | ||||||||
\(520\) | 73.3249 | 3.21551 | ||||||||
\(521\) | −5.79636 | −0.253943 | −0.126972 | − | 0.991906i | \(-0.540526\pi\) | ||||
−0.126972 | + | 0.991906i | \(0.540526\pi\) | |||||||
\(522\) | 0.401679 | 0.0175810 | ||||||||
\(523\) | 17.1372 | 0.749358 | 0.374679 | − | 0.927155i | \(-0.377753\pi\) | ||||
0.374679 | + | 0.927155i | \(0.377753\pi\) | |||||||
\(524\) | 36.7261 | 1.60439 | ||||||||
\(525\) | −20.4653 | −0.893180 | ||||||||
\(526\) | −53.2424 | −2.32148 | ||||||||
\(527\) | −39.7297 | −1.73065 | ||||||||
\(528\) | −28.6444 | −1.24659 | ||||||||
\(529\) | 27.6426 | 1.20185 | ||||||||
\(530\) | −34.5070 | −1.49889 | ||||||||
\(531\) | 0.137013 | 0.00594586 | ||||||||
\(532\) | 98.5829 | 4.27411 | ||||||||
\(533\) | 18.7713 | 0.813076 | ||||||||
\(534\) | −10.8841 | −0.471001 | ||||||||
\(535\) | −30.2898 | −1.30954 | ||||||||
\(536\) | 64.8678 | 2.80186 | ||||||||
\(537\) | −5.06000 | −0.218355 | ||||||||
\(538\) | −14.2831 | −0.615790 | ||||||||
\(539\) | −16.3005 | −0.702113 | ||||||||
\(540\) | −47.0467 | −2.02457 | ||||||||
\(541\) | 16.0419 | 0.689696 | 0.344848 | − | 0.938659i | \(-0.387931\pi\) | ||||
0.344848 | + | 0.938659i | \(0.387931\pi\) | |||||||
\(542\) | −13.4082 | −0.575933 | ||||||||
\(543\) | 35.3816 | 1.51837 | ||||||||
\(544\) | 195.119 | 8.36566 | ||||||||
\(545\) | 17.3885 | 0.744841 | ||||||||
\(546\) | 104.784 | 4.48432 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 57.3951 | 2.45180 | ||||||||
\(549\) | 0.325473 | 0.0138908 | ||||||||
\(550\) | −6.81019 | −0.290387 | ||||||||
\(551\) | 15.1739 | 0.646429 | ||||||||
\(552\) | −123.768 | −5.26790 | ||||||||
\(553\) | 56.9679 | 2.42252 | ||||||||
\(554\) | 19.5865 | 0.832151 | ||||||||
\(555\) | 10.2894 | 0.436761 | ||||||||
\(556\) | 68.3192 | 2.89738 | ||||||||
\(557\) | 19.7295 | 0.835967 | 0.417983 | − | 0.908455i | \(-0.362737\pi\) | ||||
0.417983 | + | 0.908455i | \(0.362737\pi\) | |||||||
\(558\) | 0.502797 | 0.0212851 | ||||||||
\(559\) | −35.5177 | −1.50224 | ||||||||
\(560\) | 127.916 | 5.40542 | ||||||||
\(561\) | 13.0174 | 0.549593 | ||||||||
\(562\) | 4.93195 | 0.208042 | ||||||||
\(563\) | −26.2904 | −1.10801 | −0.554005 | − | 0.832513i | \(-0.686901\pi\) | ||||
−0.554005 | + | 0.832513i | \(0.686901\pi\) | |||||||
\(564\) | 77.6633 | 3.27022 | ||||||||
\(565\) | 15.6434 | 0.658123 | ||||||||
\(566\) | 47.2646 | 1.98668 | ||||||||
\(567\) | −42.9369 | −1.80318 | ||||||||
\(568\) | 58.5387 | 2.45623 | ||||||||
\(569\) | −28.2588 | −1.18467 | −0.592336 | − | 0.805691i | \(-0.701794\pi\) | ||||
−0.592336 | + | 0.805691i | \(0.701794\pi\) | |||||||
\(570\) | −27.4238 | −1.14866 | ||||||||
\(571\) | −5.14097 | −0.215143 | −0.107571 | − | 0.994197i | \(-0.534307\pi\) | ||||
−0.107571 | + | 0.994197i | \(0.534307\pi\) | |||||||
\(572\) | 25.7540 | 1.07683 | ||||||||
\(573\) | −3.94755 | −0.164911 | ||||||||
\(574\) | 54.9973 | 2.29554 | ||||||||
\(575\) | −17.5207 | −0.730663 | ||||||||
\(576\) | −1.31873 | −0.0549472 | ||||||||
\(577\) | 21.2285 | 0.883754 | 0.441877 | − | 0.897076i | \(-0.354313\pi\) | ||||
0.441877 | + | 0.897076i | \(0.354313\pi\) | |||||||
\(578\) | −111.038 | −4.61857 | ||||||||
\(579\) | 8.35315 | 0.347145 | ||||||||
\(580\) | 37.8014 | 1.56962 | ||||||||
\(581\) | 63.5518 | 2.63657 | ||||||||
\(582\) | 20.0766 | 0.832203 | ||||||||
\(583\) | −7.83066 | −0.324313 | ||||||||
\(584\) | −46.6562 | −1.93065 | ||||||||
\(585\) | 0.251094 | 0.0103815 | ||||||||
\(586\) | 44.5917 | 1.84207 | ||||||||
\(587\) | 41.4487 | 1.71077 | 0.855386 | − | 0.517992i | \(-0.173320\pi\) | ||||
0.855386 | + | 0.517992i | \(0.173320\pi\) | |||||||
\(588\) | 158.631 | 6.54183 | ||||||||
\(589\) | 18.9937 | 0.782624 | ||||||||
\(590\) | 17.4574 | 0.718710 | ||||||||
\(591\) | 42.6532 | 1.75452 | ||||||||
\(592\) | 62.3881 | 2.56414 | ||||||||
\(593\) | 12.9625 | 0.532308 | 0.266154 | − | 0.963931i | \(-0.414247\pi\) | ||||
0.266154 | + | 0.963931i | \(0.414247\pi\) | |||||||
\(594\) | −14.4547 | −0.593082 | ||||||||
\(595\) | −58.1308 | −2.38313 | ||||||||
\(596\) | −98.3550 | −4.02878 | ||||||||
\(597\) | −10.3660 | −0.424251 | ||||||||
\(598\) | 89.7069 | 3.66839 | ||||||||
\(599\) | −39.0427 | −1.59524 | −0.797621 | − | 0.603158i | \(-0.793909\pi\) | ||||
−0.797621 | + | 0.603158i | \(0.793909\pi\) | |||||||
\(600\) | 42.8195 | 1.74810 | ||||||||
\(601\) | −23.4330 | −0.955850 | −0.477925 | − | 0.878401i | \(-0.658611\pi\) | ||||
−0.477925 | + | 0.878401i | \(0.658611\pi\) | |||||||
\(602\) | −104.062 | −4.24125 | ||||||||
\(603\) | 0.222134 | 0.00904599 | ||||||||
\(604\) | −98.1597 | −3.99406 | ||||||||
\(605\) | 1.59310 | 0.0647688 | ||||||||
\(606\) | −8.31598 | −0.337814 | ||||||||
\(607\) | 44.1869 | 1.79349 | 0.896746 | − | 0.442545i | \(-0.145924\pi\) | ||||
0.896746 | + | 0.442545i | \(0.145924\pi\) | |||||||
\(608\) | −93.2814 | −3.78306 | ||||||||
\(609\) | 34.9017 | 1.41429 | ||||||||
\(610\) | 41.4698 | 1.67906 | ||||||||
\(611\) | −36.3690 | −1.47133 | ||||||||
\(612\) | 1.47746 | 0.0597227 | ||||||||
\(613\) | −6.92238 | −0.279592 | −0.139796 | − | 0.990180i | \(-0.544645\pi\) | ||||
−0.139796 | + | 0.990180i | \(0.544645\pi\) | |||||||
\(614\) | 43.0759 | 1.73840 | ||||||||
\(615\) | −11.3000 | −0.455660 | ||||||||
\(616\) | 48.7516 | 1.96426 | ||||||||
\(617\) | 8.10349 | 0.326234 | 0.163117 | − | 0.986607i | \(-0.447845\pi\) | ||||
0.163117 | + | 0.986607i | \(0.447845\pi\) | |||||||
\(618\) | −42.8102 | −1.72208 | ||||||||
\(619\) | 1.83586 | 0.0737895 | 0.0368948 | − | 0.999319i | \(-0.488253\pi\) | ||||
0.0368948 | + | 0.999319i | \(0.488253\pi\) | |||||||
\(620\) | 47.3176 | 1.90032 | ||||||||
\(621\) | −37.1878 | −1.49229 | ||||||||
\(622\) | 2.60533 | 0.104464 | ||||||||
\(623\) | 11.0298 | 0.441899 | ||||||||
\(624\) | −130.539 | −5.22576 | ||||||||
\(625\) | −6.62828 | −0.265131 | ||||||||
\(626\) | −7.63374 | −0.305106 | ||||||||
\(627\) | −6.22326 | −0.248533 | ||||||||
\(628\) | 1.71131 | 0.0682887 | ||||||||
\(629\) | −28.3520 | −1.13047 | ||||||||
\(630\) | 0.735671 | 0.0293098 | ||||||||
\(631\) | −32.5986 | −1.29773 | −0.648864 | − | 0.760904i | \(-0.724756\pi\) | ||||
−0.648864 | + | 0.760904i | \(0.724756\pi\) | |||||||
\(632\) | −119.194 | −4.74127 | ||||||||
\(633\) | −32.1691 | −1.27861 | ||||||||
\(634\) | −2.32318 | −0.0922653 | ||||||||
\(635\) | 27.3631 | 1.08587 | ||||||||
\(636\) | 76.2053 | 3.02174 | ||||||||
\(637\) | −74.2854 | −2.94329 | ||||||||
\(638\) | 11.6141 | 0.459808 | ||||||||
\(639\) | 0.200460 | 0.00793009 | ||||||||
\(640\) | −85.7834 | −3.39088 | ||||||||
\(641\) | 27.7925 | 1.09774 | 0.548868 | − | 0.835909i | \(-0.315059\pi\) | ||||
0.548868 | + | 0.835909i | \(0.315059\pi\) | |||||||
\(642\) | 90.5654 | 3.57433 | ||||||||
\(643\) | 15.5759 | 0.614252 | 0.307126 | − | 0.951669i | \(-0.400633\pi\) | ||||
0.307126 | + | 0.951669i | \(0.400633\pi\) | |||||||
\(644\) | 194.126 | 7.64965 | ||||||||
\(645\) | 21.3811 | 0.841879 | ||||||||
\(646\) | 75.5651 | 2.97307 | ||||||||
\(647\) | −44.8356 | −1.76267 | −0.881335 | − | 0.472492i | \(-0.843355\pi\) | ||||
−0.881335 | + | 0.472492i | \(0.843355\pi\) | |||||||
\(648\) | 89.8368 | 3.52912 | ||||||||
\(649\) | 3.96160 | 0.155506 | ||||||||
\(650\) | −31.0356 | −1.21732 | ||||||||
\(651\) | 43.6879 | 1.71226 | ||||||||
\(652\) | 131.111 | 5.13471 | ||||||||
\(653\) | −33.8941 | −1.32638 | −0.663190 | − | 0.748451i | \(-0.730798\pi\) | ||||
−0.663190 | + | 0.748451i | \(0.730798\pi\) | |||||||
\(654\) | −51.9909 | −2.03301 | ||||||||
\(655\) | 10.3532 | 0.404532 | ||||||||
\(656\) | −68.5157 | −2.67509 | ||||||||
\(657\) | −0.159770 | −0.00623322 | ||||||||
\(658\) | −106.556 | −4.15399 | ||||||||
\(659\) | 22.7738 | 0.887140 | 0.443570 | − | 0.896240i | \(-0.353712\pi\) | ||||
0.443570 | + | 0.896240i | \(0.353712\pi\) | |||||||
\(660\) | −15.5035 | −0.603473 | ||||||||
\(661\) | −8.05202 | −0.313187 | −0.156594 | − | 0.987663i | \(-0.550051\pi\) | ||||
−0.156594 | + | 0.987663i | \(0.550051\pi\) | |||||||
\(662\) | 93.2971 | 3.62609 | ||||||||
\(663\) | 59.3232 | 2.30392 | ||||||||
\(664\) | −132.969 | −5.16021 | ||||||||
\(665\) | 27.7908 | 1.07768 | ||||||||
\(666\) | 0.358808 | 0.0139035 | ||||||||
\(667\) | 29.8799 | 1.15695 | ||||||||
\(668\) | −46.6520 | −1.80502 | ||||||||
\(669\) | 25.0346 | 0.967895 | ||||||||
\(670\) | 28.3030 | 1.09344 | ||||||||
\(671\) | 9.41072 | 0.363297 | ||||||||
\(672\) | −214.558 | −8.27676 | ||||||||
\(673\) | −12.2755 | −0.473187 | −0.236593 | − | 0.971609i | \(-0.576031\pi\) | ||||
−0.236593 | + | 0.971609i | \(0.576031\pi\) | |||||||
\(674\) | −57.3713 | −2.20986 | ||||||||
\(675\) | 12.8657 | 0.495203 | ||||||||
\(676\) | 43.9012 | 1.68851 | ||||||||
\(677\) | 17.2430 | 0.662701 | 0.331350 | − | 0.943508i | \(-0.392496\pi\) | ||||
0.331350 | + | 0.943508i | \(0.392496\pi\) | |||||||
\(678\) | −46.7732 | −1.79631 | ||||||||
\(679\) | −20.3453 | −0.780783 | ||||||||
\(680\) | 121.627 | 4.66418 | ||||||||
\(681\) | 1.52420 | 0.0584075 | ||||||||
\(682\) | 14.5379 | 0.556684 | ||||||||
\(683\) | 3.01755 | 0.115464 | 0.0577318 | − | 0.998332i | \(-0.481613\pi\) | ||||
0.0577318 | + | 0.998332i | \(0.481613\pi\) | |||||||
\(684\) | −0.706335 | −0.0270074 | ||||||||
\(685\) | 16.1799 | 0.618201 | ||||||||
\(686\) | −124.181 | −4.74126 | ||||||||
\(687\) | −29.9090 | −1.14110 | ||||||||
\(688\) | 129.641 | 4.94250 | ||||||||
\(689\) | −35.6862 | −1.35954 | ||||||||
\(690\) | −54.0020 | −2.05582 | ||||||||
\(691\) | −19.5725 | −0.744572 | −0.372286 | − | 0.928118i | \(-0.621426\pi\) | ||||
−0.372286 | + | 0.928118i | \(0.621426\pi\) | |||||||
\(692\) | −69.5396 | −2.64350 | ||||||||
\(693\) | 0.166945 | 0.00634173 | ||||||||
\(694\) | 46.6582 | 1.77112 | ||||||||
\(695\) | 19.2594 | 0.730551 | ||||||||
\(696\) | −73.0247 | −2.76800 | ||||||||
\(697\) | 31.1367 | 1.17939 | ||||||||
\(698\) | 10.8538 | 0.410821 | ||||||||
\(699\) | 22.1927 | 0.839406 | ||||||||
\(700\) | −67.1614 | −2.53846 | ||||||||
\(701\) | 38.2218 | 1.44362 | 0.721810 | − | 0.692092i | \(-0.243311\pi\) | ||||
0.721810 | + | 0.692092i | \(0.243311\pi\) | |||||||
\(702\) | −65.8733 | −2.48623 | ||||||||
\(703\) | 13.5544 | 0.511213 | ||||||||
\(704\) | −38.1299 | −1.43707 | ||||||||
\(705\) | 21.8935 | 0.824558 | ||||||||
\(706\) | −39.2172 | −1.47596 | ||||||||
\(707\) | 8.42728 | 0.316941 | ||||||||
\(708\) | −38.5529 | −1.44891 | ||||||||
\(709\) | −46.0209 | −1.72835 | −0.864175 | − | 0.503191i | \(-0.832159\pi\) | ||||
−0.864175 | + | 0.503191i | \(0.832159\pi\) | |||||||
\(710\) | 25.5415 | 0.958555 | ||||||||
\(711\) | −0.408168 | −0.0153075 | ||||||||
\(712\) | −23.0776 | −0.864869 | ||||||||
\(713\) | 37.4019 | 1.40071 | ||||||||
\(714\) | 173.809 | 6.50463 | ||||||||
\(715\) | 7.26014 | 0.271514 | ||||||||
\(716\) | −16.6055 | −0.620575 | ||||||||
\(717\) | 21.3405 | 0.796977 | ||||||||
\(718\) | 64.4676 | 2.40591 | ||||||||
\(719\) | 20.9429 | 0.781038 | 0.390519 | − | 0.920595i | \(-0.372296\pi\) | ||||
0.390519 | + | 0.920595i | \(0.372296\pi\) | |||||||
\(720\) | −0.916500 | −0.0341559 | ||||||||
\(721\) | 43.3832 | 1.61568 | ||||||||
\(722\) | 16.4300 | 0.611460 | ||||||||
\(723\) | 35.3109 | 1.31323 | ||||||||
\(724\) | 116.112 | 4.31528 | ||||||||
\(725\) | −10.3375 | −0.383924 | ||||||||
\(726\) | −4.76331 | −0.176783 | ||||||||
\(727\) | −15.5958 | −0.578416 | −0.289208 | − | 0.957266i | \(-0.593392\pi\) | ||||
−0.289208 | + | 0.957266i | \(0.593392\pi\) | |||||||
\(728\) | 222.173 | 8.23427 | ||||||||
\(729\) | 27.3040 | 1.01126 | ||||||||
\(730\) | −20.3569 | −0.753444 | ||||||||
\(731\) | −58.9147 | −2.17904 | ||||||||
\(732\) | −91.5818 | −3.38496 | ||||||||
\(733\) | 43.1501 | 1.59378 | 0.796892 | − | 0.604121i | \(-0.206476\pi\) | ||||
0.796892 | + | 0.604121i | \(0.206476\pi\) | |||||||
\(734\) | 19.4101 | 0.716439 | ||||||||
\(735\) | 44.7185 | 1.64947 | ||||||||
\(736\) | −183.687 | −6.77078 | ||||||||
\(737\) | 6.42278 | 0.236586 | ||||||||
\(738\) | −0.394049 | −0.0145051 | ||||||||
\(739\) | 4.44706 | 0.163588 | 0.0817939 | − | 0.996649i | \(-0.473935\pi\) | ||||
0.0817939 | + | 0.996649i | \(0.473935\pi\) | |||||||
\(740\) | 33.7669 | 1.24130 | ||||||||
\(741\) | −28.3609 | −1.04186 | ||||||||
\(742\) | −104.556 | −3.83836 | ||||||||
\(743\) | −13.6476 | −0.500682 | −0.250341 | − | 0.968158i | \(-0.580543\pi\) | ||||
−0.250341 | + | 0.968158i | \(0.580543\pi\) | |||||||
\(744\) | −91.4080 | −3.35118 | ||||||||
\(745\) | −27.7266 | −1.01582 | ||||||||
\(746\) | −23.1521 | −0.847657 | ||||||||
\(747\) | −0.455341 | −0.0166601 | ||||||||
\(748\) | 42.7193 | 1.56197 | ||||||||
\(749\) | −91.7775 | −3.35348 | ||||||||
\(750\) | 56.6251 | 2.06766 | ||||||||
\(751\) | 30.8658 | 1.12631 | 0.563154 | − | 0.826352i | \(-0.309588\pi\) | ||||
0.563154 | + | 0.826352i | \(0.309588\pi\) | |||||||
\(752\) | 132.748 | 4.84081 | ||||||||
\(753\) | 37.7265 | 1.37483 | ||||||||
\(754\) | 52.9284 | 1.92754 | ||||||||
\(755\) | −27.6715 | −1.00707 | ||||||||
\(756\) | −142.550 | −5.18451 | ||||||||
\(757\) | 16.7802 | 0.609885 | 0.304942 | − | 0.952371i | \(-0.401363\pi\) | ||||
0.304942 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(758\) | 44.6594 | 1.62210 | ||||||||
\(759\) | −12.2546 | −0.444815 | ||||||||
\(760\) | −58.1467 | −2.10920 | ||||||||
\(761\) | 16.6043 | 0.601904 | 0.300952 | − | 0.953639i | \(-0.402696\pi\) | ||||
0.300952 | + | 0.953639i | \(0.402696\pi\) | |||||||
\(762\) | −81.8147 | −2.96383 | ||||||||
\(763\) | 52.6868 | 1.90739 | ||||||||
\(764\) | −12.9548 | −0.468686 | ||||||||
\(765\) | 0.416500 | 0.0150586 | ||||||||
\(766\) | −34.7180 | −1.25441 | ||||||||
\(767\) | 18.0539 | 0.651890 | ||||||||
\(768\) | 125.167 | 4.51656 | ||||||||
\(769\) | 42.5253 | 1.53350 | 0.766752 | − | 0.641944i | \(-0.221872\pi\) | ||||
0.766752 | + | 0.641944i | \(0.221872\pi\) | |||||||
\(770\) | 21.2712 | 0.766561 | ||||||||
\(771\) | −14.4592 | −0.520734 | ||||||||
\(772\) | 27.4127 | 0.986604 | ||||||||
\(773\) | 5.04172 | 0.181338 | 0.0906691 | − | 0.995881i | \(-0.471099\pi\) | ||||
0.0906691 | + | 0.995881i | \(0.471099\pi\) | |||||||
\(774\) | 0.745592 | 0.0267997 | ||||||||
\(775\) | −12.9398 | −0.464812 | ||||||||
\(776\) | 42.5685 | 1.52812 | ||||||||
\(777\) | 31.1767 | 1.11846 | ||||||||
\(778\) | 31.0684 | 1.11386 | ||||||||
\(779\) | −14.8857 | −0.533334 | ||||||||
\(780\) | −70.6532 | −2.52979 | ||||||||
\(781\) | 5.79611 | 0.207401 | ||||||||
\(782\) | 148.800 | 5.32109 | ||||||||
\(783\) | −21.9413 | −0.784120 | ||||||||
\(784\) | 271.143 | 9.68369 | ||||||||
\(785\) | 0.482424 | 0.0172184 | ||||||||
\(786\) | −30.9556 | −1.10415 | ||||||||
\(787\) | 0.739039 | 0.0263439 | 0.0131719 | − | 0.999913i | \(-0.495807\pi\) | ||||
0.0131719 | + | 0.999913i | \(0.495807\pi\) | |||||||
\(788\) | 139.976 | 4.98643 | ||||||||
\(789\) | 33.1462 | 1.18004 | ||||||||
\(790\) | −52.0064 | −1.85030 | ||||||||
\(791\) | 47.3992 | 1.68532 | ||||||||
\(792\) | −0.349299 | −0.0124118 | ||||||||
\(793\) | 42.8869 | 1.52296 | ||||||||
\(794\) | 90.3396 | 3.20603 | ||||||||
\(795\) | 21.4825 | 0.761905 | ||||||||
\(796\) | −34.0182 | −1.20574 | ||||||||
\(797\) | 27.8065 | 0.984956 | 0.492478 | − | 0.870325i | \(-0.336091\pi\) | ||||
0.492478 | + | 0.870325i | \(0.336091\pi\) | |||||||
\(798\) | −83.0934 | −2.94148 | ||||||||
\(799\) | −60.3267 | −2.13421 | ||||||||
\(800\) | 63.5496 | 2.24682 | ||||||||
\(801\) | −0.0790271 | −0.00279228 | ||||||||
\(802\) | −83.1230 | −2.93518 | ||||||||
\(803\) | −4.61959 | −0.163022 | ||||||||
\(804\) | −62.5043 | −2.20436 | ||||||||
\(805\) | 54.7248 | 1.92880 | ||||||||
\(806\) | 66.2526 | 2.33365 | ||||||||
\(807\) | 8.89203 | 0.313014 | ||||||||
\(808\) | −17.6324 | −0.620305 | ||||||||
\(809\) | 17.3056 | 0.608433 | 0.304216 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304216 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(810\) | 39.1974 | 1.37726 | ||||||||
\(811\) | 15.6310 | 0.548879 | 0.274439 | − | 0.961604i | \(-0.411508\pi\) | ||||
0.274439 | + | 0.961604i | \(0.411508\pi\) | |||||||
\(812\) | 114.537 | 4.01948 | ||||||||
\(813\) | 8.34735 | 0.292754 | ||||||||
\(814\) | 10.3746 | 0.363629 | ||||||||
\(815\) | 36.9606 | 1.29467 | ||||||||
\(816\) | −216.531 | −7.58010 | ||||||||
\(817\) | 28.1656 | 0.985389 | ||||||||
\(818\) | −50.7250 | −1.77356 | ||||||||
\(819\) | 0.760810 | 0.0265849 | ||||||||
\(820\) | −37.0834 | −1.29501 | ||||||||
\(821\) | −46.9309 | −1.63790 | −0.818950 | − | 0.573864i | \(-0.805444\pi\) | ||||
−0.818950 | + | 0.573864i | \(0.805444\pi\) | |||||||
\(822\) | −48.3771 | −1.68735 | ||||||||
\(823\) | 40.1087 | 1.39810 | 0.699051 | − | 0.715072i | \(-0.253606\pi\) | ||||
0.699051 | + | 0.715072i | \(0.253606\pi\) | |||||||
\(824\) | −90.7706 | −3.16214 | ||||||||
\(825\) | 4.23971 | 0.147608 | ||||||||
\(826\) | 52.8955 | 1.84047 | ||||||||
\(827\) | 9.72155 | 0.338051 | 0.169026 | − | 0.985612i | \(-0.445938\pi\) | ||||
0.169026 | + | 0.985612i | \(0.445938\pi\) | |||||||
\(828\) | −1.39089 | −0.0483368 | ||||||||
\(829\) | 27.9566 | 0.970973 | 0.485487 | − | 0.874244i | \(-0.338642\pi\) | ||||
0.485487 | + | 0.874244i | \(0.338642\pi\) | |||||||
\(830\) | −58.0169 | −2.01379 | ||||||||
\(831\) | −12.1937 | −0.422993 | ||||||||
\(832\) | −173.767 | −6.02428 | ||||||||
\(833\) | −123.220 | −4.26932 | ||||||||
\(834\) | −57.5848 | −1.99400 | ||||||||
\(835\) | −13.1513 | −0.455120 | ||||||||
\(836\) | −20.4230 | −0.706343 | ||||||||
\(837\) | −27.4649 | −0.949325 | ||||||||
\(838\) | 34.6848 | 1.19817 | ||||||||
\(839\) | −49.4330 | −1.70662 | −0.853308 | − | 0.521407i | \(-0.825407\pi\) | ||||
−0.853308 | + | 0.521407i | \(0.825407\pi\) | |||||||
\(840\) | −133.744 | −4.61462 | ||||||||
\(841\) | −11.3704 | −0.392083 | ||||||||
\(842\) | −49.4723 | −1.70493 | ||||||||
\(843\) | −3.07040 | −0.105750 | ||||||||
\(844\) | −105.570 | −3.63387 | ||||||||
\(845\) | 12.3759 | 0.425743 | ||||||||
\(846\) | 0.763462 | 0.0262483 | ||||||||
\(847\) | 4.82706 | 0.165860 | ||||||||
\(848\) | 130.255 | 4.47299 | ||||||||
\(849\) | −29.4247 | −1.00985 | ||||||||
\(850\) | −51.4800 | −1.76575 | ||||||||
\(851\) | 26.6909 | 0.914951 | ||||||||
\(852\) | −56.4057 | −1.93243 | ||||||||
\(853\) | −15.2840 | −0.523314 | −0.261657 | − | 0.965161i | \(-0.584269\pi\) | ||||
−0.261657 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(854\) | 125.653 | 4.29974 | ||||||||
\(855\) | −0.199118 | −0.00680969 | ||||||||
\(856\) | 192.026 | 6.56331 | ||||||||
\(857\) | −53.8381 | −1.83908 | −0.919538 | − | 0.393001i | \(-0.871437\pi\) | ||||
−0.919538 | + | 0.393001i | \(0.871437\pi\) | |||||||
\(858\) | −21.7075 | −0.741083 | ||||||||
\(859\) | −10.7928 | −0.368245 | −0.184123 | − | 0.982903i | \(-0.558944\pi\) | ||||
−0.184123 | + | 0.982903i | \(0.558944\pi\) | |||||||
\(860\) | 70.1666 | 2.39266 | ||||||||
\(861\) | −34.2388 | −1.16685 | ||||||||
\(862\) | 97.0444 | 3.30535 | ||||||||
\(863\) | −54.4143 | −1.85228 | −0.926142 | − | 0.377174i | \(-0.876896\pi\) | ||||
−0.926142 | + | 0.377174i | \(0.876896\pi\) | |||||||
\(864\) | 134.884 | 4.58886 | ||||||||
\(865\) | −19.6034 | −0.666536 | ||||||||
\(866\) | 97.7626 | 3.32211 | ||||||||
\(867\) | 69.1271 | 2.34768 | ||||||||
\(868\) | 143.371 | 4.86634 | ||||||||
\(869\) | −11.8018 | −0.400348 | ||||||||
\(870\) | −31.8620 | −1.08022 | ||||||||
\(871\) | 29.2701 | 0.991781 | ||||||||
\(872\) | −110.236 | −3.73307 | ||||||||
\(873\) | 0.145772 | 0.00493363 | ||||||||
\(874\) | −71.1376 | −2.40626 | ||||||||
\(875\) | −57.3830 | −1.93990 | ||||||||
\(876\) | 44.9562 | 1.51893 | ||||||||
\(877\) | −14.2199 | −0.480171 | −0.240086 | − | 0.970752i | \(-0.577176\pi\) | ||||
−0.240086 | + | 0.970752i | \(0.577176\pi\) | |||||||
\(878\) | 19.0931 | 0.644361 | ||||||||
\(879\) | −27.7607 | −0.936347 | ||||||||
\(880\) | −26.4997 | −0.893304 | ||||||||
\(881\) | 7.21423 | 0.243054 | 0.121527 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121527 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(882\) | 1.55941 | 0.0525079 | ||||||||
\(883\) | −39.1720 | −1.31824 | −0.659122 | − | 0.752036i | \(-0.729072\pi\) | ||||
−0.659122 | + | 0.752036i | \(0.729072\pi\) | |||||||
\(884\) | 194.682 | 6.54786 | ||||||||
\(885\) | −10.8682 | −0.365330 | ||||||||
\(886\) | −43.5382 | −1.46270 | ||||||||
\(887\) | 46.6889 | 1.56766 | 0.783829 | − | 0.620976i | \(-0.213264\pi\) | ||||
0.783829 | + | 0.620976i | \(0.213264\pi\) | |||||||
\(888\) | −65.2309 | −2.18901 | ||||||||
\(889\) | 82.9097 | 2.78070 | ||||||||
\(890\) | −10.0692 | −0.337519 | ||||||||
\(891\) | 8.89505 | 0.297995 | ||||||||
\(892\) | 82.1566 | 2.75081 | ||||||||
\(893\) | 28.8406 | 0.965115 | ||||||||
\(894\) | 82.9013 | 2.77263 | ||||||||
\(895\) | −4.68113 | −0.156473 | ||||||||
\(896\) | −259.922 | −8.68337 | ||||||||
\(897\) | −55.8473 | −1.86469 | ||||||||
\(898\) | −43.0325 | −1.43601 | ||||||||
\(899\) | 22.0677 | 0.735998 | ||||||||
\(900\) | 0.481203 | 0.0160401 | ||||||||
\(901\) | −59.1941 | −1.97204 | ||||||||
\(902\) | −11.3935 | −0.379363 | ||||||||
\(903\) | 64.7842 | 2.15588 | ||||||||
\(904\) | −99.1732 | −3.29845 | ||||||||
\(905\) | 32.7324 | 1.08806 | ||||||||
\(906\) | 82.7367 | 2.74874 | ||||||||
\(907\) | 26.0115 | 0.863696 | 0.431848 | − | 0.901946i | \(-0.357862\pi\) | ||||
0.431848 | + | 0.901946i | \(0.357862\pi\) | |||||||
\(908\) | 5.00200 | 0.165997 | ||||||||
\(909\) | −0.0603804 | −0.00200269 | ||||||||
\(910\) | 96.9380 | 3.21346 | ||||||||
\(911\) | 38.4828 | 1.27499 | 0.637496 | − | 0.770454i | \(-0.279970\pi\) | ||||
0.637496 | + | 0.770454i | \(0.279970\pi\) | |||||||
\(912\) | 103.518 | 3.42782 | ||||||||
\(913\) | −13.1657 | −0.435722 | ||||||||
\(914\) | 101.888 | 3.37017 | ||||||||
\(915\) | −25.8172 | −0.853490 | ||||||||
\(916\) | −98.1529 | −3.24306 | ||||||||
\(917\) | 31.3699 | 1.03593 | ||||||||
\(918\) | −109.267 | −3.60634 | ||||||||
\(919\) | −30.2143 | −0.996679 | −0.498339 | − | 0.866982i | \(-0.666057\pi\) | ||||
−0.498339 | + | 0.866982i | \(0.666057\pi\) | |||||||
\(920\) | −114.501 | −3.77497 | ||||||||
\(921\) | −26.8170 | −0.883652 | ||||||||
\(922\) | 4.19516 | 0.138160 | ||||||||
\(923\) | 26.4143 | 0.869436 | ||||||||
\(924\) | −46.9753 | −1.54537 | ||||||||
\(925\) | −9.23416 | −0.303617 | ||||||||
\(926\) | −39.2254 | −1.28903 | ||||||||
\(927\) | −0.310835 | −0.0102092 | ||||||||
\(928\) | −108.378 | −3.55768 | ||||||||
\(929\) | −44.5084 | −1.46027 | −0.730137 | − | 0.683301i | \(-0.760544\pi\) | ||||
−0.730137 | + | 0.683301i | \(0.760544\pi\) | |||||||
\(930\) | −39.8830 | −1.30781 | ||||||||
\(931\) | 58.9083 | 1.93064 | ||||||||
\(932\) | 72.8302 | 2.38563 | ||||||||
\(933\) | −1.62196 | −0.0531004 | ||||||||
\(934\) | −45.9925 | −1.50492 | ||||||||
\(935\) | 12.0427 | 0.393838 | ||||||||
\(936\) | −1.59184 | −0.0520309 | ||||||||
\(937\) | −35.5029 | −1.15983 | −0.579915 | − | 0.814677i | \(-0.696914\pi\) | ||||
−0.579915 | + | 0.814677i | \(0.696914\pi\) | |||||||
\(938\) | 85.7575 | 2.80008 | ||||||||
\(939\) | 4.75241 | 0.155089 | ||||||||
\(940\) | 71.8483 | 2.34343 | ||||||||
\(941\) | −7.83018 | −0.255256 | −0.127628 | − | 0.991822i | \(-0.540736\pi\) | ||||
−0.127628 | + | 0.991822i | \(0.540736\pi\) | |||||||
\(942\) | −1.44243 | −0.0469968 | ||||||||
\(943\) | −29.3124 | −0.954542 | ||||||||
\(944\) | −65.8973 | −2.14477 | ||||||||
\(945\) | −40.1854 | −1.30723 | ||||||||
\(946\) | 21.5580 | 0.700912 | ||||||||
\(947\) | 18.2581 | 0.593309 | 0.296654 | − | 0.954985i | \(-0.404129\pi\) | ||||
0.296654 | + | 0.954985i | \(0.404129\pi\) | |||||||
\(948\) | 114.851 | 3.73018 | ||||||||
\(949\) | −21.0526 | −0.683395 | ||||||||
\(950\) | 24.6113 | 0.798495 | ||||||||
\(951\) | 1.44631 | 0.0468997 | ||||||||
\(952\) | 368.527 | 11.9440 | ||||||||
\(953\) | 8.61510 | 0.279070 | 0.139535 | − | 0.990217i | \(-0.455439\pi\) | ||||
0.139535 | + | 0.990217i | \(0.455439\pi\) | |||||||
\(954\) | 0.749128 | 0.0242539 | ||||||||
\(955\) | −3.65198 | −0.118175 | ||||||||
\(956\) | 70.0336 | 2.26505 | ||||||||
\(957\) | −7.23042 | −0.233726 | ||||||||
\(958\) | −17.1970 | −0.555609 | ||||||||
\(959\) | 49.0246 | 1.58309 | ||||||||
\(960\) | 104.605 | 3.37610 | ||||||||
\(961\) | −3.37700 | −0.108936 | ||||||||
\(962\) | 47.2794 | 1.52435 | ||||||||
\(963\) | 0.657575 | 0.0211901 | ||||||||
\(964\) | 115.880 | 3.73225 | ||||||||
\(965\) | 7.72771 | 0.248764 | ||||||||
\(966\) | −163.625 | −5.26455 | ||||||||
\(967\) | −15.1217 | −0.486280 | −0.243140 | − | 0.969991i | \(-0.578177\pi\) | ||||
−0.243140 | + | 0.969991i | \(0.578177\pi\) | |||||||
\(968\) | −10.0996 | −0.324615 | ||||||||
\(969\) | −47.0433 | −1.51125 | ||||||||
\(970\) | 18.5734 | 0.596356 | ||||||||
\(971\) | −18.3217 | −0.587972 | −0.293986 | − | 0.955810i | \(-0.594982\pi\) | ||||
−0.293986 | + | 0.955810i | \(0.594982\pi\) | |||||||
\(972\) | 2.03107 | 0.0651467 | ||||||||
\(973\) | 58.3555 | 1.87079 | ||||||||
\(974\) | 79.3606 | 2.54288 | ||||||||
\(975\) | 19.3214 | 0.618778 | ||||||||
\(976\) | −156.538 | −5.01066 | ||||||||
\(977\) | 25.9350 | 0.829734 | 0.414867 | − | 0.909882i | \(-0.363828\pi\) | ||||
0.414867 | + | 0.909882i | \(0.363828\pi\) | |||||||
\(978\) | −110.511 | −3.53375 | ||||||||
\(979\) | −2.28499 | −0.0730286 | ||||||||
\(980\) | 146.754 | 4.68787 | ||||||||
\(981\) | −0.377494 | −0.0120525 | ||||||||
\(982\) | −3.82898 | −0.122188 | ||||||||
\(983\) | −32.8735 | −1.04850 | −0.524251 | − | 0.851564i | \(-0.675655\pi\) | ||||
−0.524251 | + | 0.851564i | \(0.675655\pi\) | |||||||
\(984\) | 71.6377 | 2.28373 | ||||||||
\(985\) | 39.4596 | 1.25729 | ||||||||
\(986\) | 87.7944 | 2.79594 | ||||||||
\(987\) | 66.3369 | 2.11153 | ||||||||
\(988\) | −93.0723 | −2.96103 | ||||||||
\(989\) | 55.4628 | 1.76361 | ||||||||
\(990\) | −0.152406 | −0.00484377 | ||||||||
\(991\) | −48.3428 | −1.53566 | −0.767829 | − | 0.640655i | \(-0.778663\pi\) | ||||
−0.767829 | + | 0.640655i | \(0.778663\pi\) | |||||||
\(992\) | −135.661 | −4.30724 | ||||||||
\(993\) | −58.0824 | −1.84319 | ||||||||
\(994\) | 77.3901 | 2.45467 | ||||||||
\(995\) | −9.58983 | −0.304018 | ||||||||
\(996\) | 128.124 | 4.05977 | ||||||||
\(997\) | 27.9591 | 0.885473 | 0.442736 | − | 0.896652i | \(-0.354008\pi\) | ||||
0.442736 | + | 0.896652i | \(0.354008\pi\) | |||||||
\(998\) | −31.7874 | −1.00621 | ||||||||
\(999\) | −19.5996 | −0.620103 |
(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 | 6017.2.a.f.1.1 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.f.1.1 | ✓ | 121 | 1.1 | even | 1 | trivial |