Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.25864\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25864 | −1.59710 | −0.798548 | − | 0.601931i | \(-0.794398\pi\) | ||||
−0.798548 | + | 0.601931i | \(0.794398\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.10144 | 1.55072 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.25864 | 0.922084 | ||||||||
\(7\) | 3.65257 | 1.38054 | 0.690272 | − | 0.723550i | \(-0.257491\pi\) | ||||
0.690272 | + | 0.723550i | \(0.257491\pi\) | |||||||
\(8\) | −2.48774 | −0.879549 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.39045 | −1.62528 | −0.812640 | − | 0.582766i | \(-0.801971\pi\) | ||||
−0.812640 | + | 0.582766i | \(0.801971\pi\) | |||||||
\(12\) | −3.10144 | −0.895307 | ||||||||
\(13\) | 3.76717 | 1.04482 | 0.522412 | − | 0.852693i | \(-0.325032\pi\) | ||||
0.522412 | + | 0.852693i | \(0.325032\pi\) | |||||||
\(14\) | −8.24983 | −2.20486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.583969 | −0.145992 | ||||||||
\(17\) | −6.40426 | −1.55326 | −0.776631 | − | 0.629956i | \(-0.783073\pi\) | ||||
−0.776631 | + | 0.629956i | \(0.783073\pi\) | |||||||
\(18\) | −2.25864 | −0.532366 | ||||||||
\(19\) | −8.07640 | −1.85285 | −0.926427 | − | 0.376475i | \(-0.877136\pi\) | ||||
−0.926427 | + | 0.376475i | \(0.877136\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.65257 | −0.797057 | ||||||||
\(22\) | 12.1751 | 2.59573 | ||||||||
\(23\) | −4.76354 | −0.993268 | −0.496634 | − | 0.867960i | \(-0.665431\pi\) | ||||
−0.496634 | + | 0.867960i | \(0.665431\pi\) | |||||||
\(24\) | 2.48774 | 0.507808 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.50866 | −1.66869 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 11.3282 | 2.14083 | ||||||||
\(29\) | −3.78248 | −0.702390 | −0.351195 | − | 0.936302i | \(-0.614225\pi\) | ||||
−0.351195 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.26069 | −0.944847 | −0.472423 | − | 0.881372i | \(-0.656621\pi\) | ||||
−0.472423 | + | 0.881372i | \(0.656621\pi\) | |||||||
\(32\) | 6.29446 | 1.11271 | ||||||||
\(33\) | 5.39045 | 0.938356 | ||||||||
\(34\) | 14.4649 | 2.48071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.10144 | 0.516906 | ||||||||
\(37\) | 3.48931 | 0.573640 | 0.286820 | − | 0.957985i | \(-0.407402\pi\) | ||||
0.286820 | + | 0.957985i | \(0.407402\pi\) | |||||||
\(38\) | 18.2416 | 2.95919 | ||||||||
\(39\) | −3.76717 | −0.603230 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.70344 | 1.04690 | 0.523451 | − | 0.852056i | \(-0.324644\pi\) | ||||
0.523451 | + | 0.852056i | \(0.324644\pi\) | |||||||
\(42\) | 8.24983 | 1.27298 | ||||||||
\(43\) | 5.28901 | 0.806566 | 0.403283 | − | 0.915075i | \(-0.367869\pi\) | ||||
0.403283 | + | 0.915075i | \(0.367869\pi\) | |||||||
\(44\) | −16.7181 | −2.52035 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.7591 | 1.58634 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 0.583969 | 0.0842887 | ||||||||
\(49\) | 6.34130 | 0.905899 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.40426 | 0.896776 | ||||||||
\(52\) | 11.6836 | 1.62023 | ||||||||
\(53\) | −9.62076 | −1.32151 | −0.660756 | − | 0.750601i | \(-0.729764\pi\) | ||||
−0.660756 | + | 0.750601i | \(0.729764\pi\) | |||||||
\(54\) | 2.25864 | 0.307361 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.08666 | −1.21426 | ||||||||
\(57\) | 8.07640 | 1.06975 | ||||||||
\(58\) | 8.54325 | 1.12178 | ||||||||
\(59\) | 10.0449 | 1.30774 | 0.653870 | − | 0.756607i | \(-0.273144\pi\) | ||||
0.653870 | + | 0.756607i | \(0.273144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68111 | −0.599355 | −0.299677 | − | 0.954041i | \(-0.596879\pi\) | ||||
−0.299677 | + | 0.954041i | \(0.596879\pi\) | |||||||
\(62\) | 11.8820 | 1.50901 | ||||||||
\(63\) | 3.65257 | 0.460181 | ||||||||
\(64\) | −13.0489 | −1.63112 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.1751 | −1.49865 | ||||||||
\(67\) | 14.1087 | 1.72365 | 0.861824 | − | 0.507207i | \(-0.169322\pi\) | ||||
0.861824 | + | 0.507207i | \(0.169322\pi\) | |||||||
\(68\) | −19.8624 | −2.40867 | ||||||||
\(69\) | 4.76354 | 0.573463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0784 | 1.43344 | 0.716721 | − | 0.697360i | \(-0.245642\pi\) | ||||
0.716721 | + | 0.697360i | \(0.245642\pi\) | |||||||
\(72\) | −2.48774 | −0.293183 | ||||||||
\(73\) | −11.5541 | −1.35231 | −0.676155 | − | 0.736759i | \(-0.736355\pi\) | ||||
−0.676155 | + | 0.736759i | \(0.736355\pi\) | |||||||
\(74\) | −7.88109 | −0.916158 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −25.0484 | −2.87325 | ||||||||
\(77\) | −19.6890 | −2.24377 | ||||||||
\(78\) | 8.50866 | 0.963417 | ||||||||
\(79\) | 1.64874 | 0.185498 | 0.0927491 | − | 0.995690i | \(-0.470435\pi\) | ||||
0.0927491 | + | 0.995690i | \(0.470435\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.1406 | −1.67200 | ||||||||
\(83\) | 10.7120 | 1.17579 | 0.587895 | − | 0.808937i | \(-0.299957\pi\) | ||||
0.587895 | + | 0.808937i | \(0.299957\pi\) | |||||||
\(84\) | −11.3282 | −1.23601 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.9459 | −1.28816 | ||||||||
\(87\) | 3.78248 | 0.405525 | ||||||||
\(88\) | 13.4100 | 1.42951 | ||||||||
\(89\) | −7.50610 | −0.795645 | −0.397822 | − | 0.917462i | \(-0.630234\pi\) | ||||
−0.397822 | + | 0.917462i | \(0.630234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7599 | 1.44243 | ||||||||
\(92\) | −14.7738 | −1.54028 | ||||||||
\(93\) | 5.26069 | 0.545508 | ||||||||
\(94\) | −2.25864 | −0.232960 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.29446 | −0.642425 | ||||||||
\(97\) | 11.7481 | 1.19284 | 0.596420 | − | 0.802673i | \(-0.296589\pi\) | ||||
0.596420 | + | 0.802673i | \(0.296589\pi\) | |||||||
\(98\) | −14.3227 | −1.44681 | ||||||||
\(99\) | −5.39045 | −0.541760 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.79905 | 0.975042 | 0.487521 | − | 0.873111i | \(-0.337901\pi\) | ||||
0.487521 | + | 0.873111i | \(0.337901\pi\) | |||||||
\(102\) | −14.4649 | −1.43224 | ||||||||
\(103\) | −7.91135 | −0.779528 | −0.389764 | − | 0.920915i | \(-0.627443\pi\) | ||||
−0.389764 | + | 0.920915i | \(0.627443\pi\) | |||||||
\(104\) | −9.37174 | −0.918975 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.7298 | 2.11058 | ||||||||
\(107\) | 16.0171 | 1.54843 | 0.774217 | − | 0.632921i | \(-0.218144\pi\) | ||||
0.774217 | + | 0.632921i | \(0.218144\pi\) | |||||||
\(108\) | −3.10144 | −0.298436 | ||||||||
\(109\) | −6.27573 | −0.601106 | −0.300553 | − | 0.953765i | \(-0.597171\pi\) | ||||
−0.300553 | + | 0.953765i | \(0.597171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.48931 | −0.331191 | ||||||||
\(112\) | −2.13299 | −0.201549 | ||||||||
\(113\) | 15.5200 | 1.45999 | 0.729997 | − | 0.683450i | \(-0.239521\pi\) | ||||
0.729997 | + | 0.683450i | \(0.239521\pi\) | |||||||
\(114\) | −18.2416 | −1.70849 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.7311 | −1.08921 | ||||||||
\(117\) | 3.76717 | 0.348275 | ||||||||
\(118\) | −22.6879 | −2.08859 | ||||||||
\(119\) | −23.3920 | −2.14434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.0569 | 1.64154 | ||||||||
\(122\) | 10.5729 | 0.957227 | ||||||||
\(123\) | −6.70344 | −0.604429 | ||||||||
\(124\) | −16.3157 | −1.46519 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.24983 | −0.734954 | ||||||||
\(127\) | 16.1501 | 1.43309 | 0.716543 | − | 0.697543i | \(-0.245723\pi\) | ||||
0.716543 | + | 0.697543i | \(0.245723\pi\) | |||||||
\(128\) | 16.8839 | 1.49234 | ||||||||
\(129\) | −5.28901 | −0.465671 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0586 | 1.22831 | 0.614155 | − | 0.789186i | \(-0.289497\pi\) | ||||
0.614155 | + | 0.789186i | \(0.289497\pi\) | |||||||
\(132\) | 16.7181 | 1.45513 | ||||||||
\(133\) | −29.4997 | −2.55794 | ||||||||
\(134\) | −31.8664 | −2.75283 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.9321 | 1.36617 | ||||||||
\(137\) | −20.6494 | −1.76419 | −0.882097 | − | 0.471069i | \(-0.843868\pi\) | ||||
−0.882097 | + | 0.471069i | \(0.843868\pi\) | |||||||
\(138\) | −10.7591 | −0.915876 | ||||||||
\(139\) | −3.85467 | −0.326949 | −0.163474 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163474 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −27.2807 | −2.28935 | ||||||||
\(143\) | −20.3067 | −1.69813 | ||||||||
\(144\) | −0.583969 | −0.0486641 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26.0966 | 2.15977 | ||||||||
\(147\) | −6.34130 | −0.523021 | ||||||||
\(148\) | 10.8219 | 0.889553 | ||||||||
\(149\) | −9.31652 | −0.763239 | −0.381620 | − | 0.924319i | \(-0.624634\pi\) | ||||
−0.381620 | + | 0.924319i | \(0.624634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9014 | 0.887146 | 0.443573 | − | 0.896238i | \(-0.353711\pi\) | ||||
0.443573 | + | 0.896238i | \(0.353711\pi\) | |||||||
\(152\) | 20.0920 | 1.62968 | ||||||||
\(153\) | −6.40426 | −0.517754 | ||||||||
\(154\) | 44.4703 | 3.58352 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.6836 | −0.935439 | ||||||||
\(157\) | 8.68544 | 0.693174 | 0.346587 | − | 0.938018i | \(-0.387341\pi\) | ||||
0.346587 | + | 0.938018i | \(0.387341\pi\) | |||||||
\(158\) | −3.72391 | −0.296258 | ||||||||
\(159\) | 9.62076 | 0.762976 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.3992 | −1.37125 | ||||||||
\(162\) | −2.25864 | −0.177455 | ||||||||
\(163\) | −14.4978 | −1.13556 | −0.567778 | − | 0.823182i | \(-0.692197\pi\) | ||||
−0.567778 | + | 0.823182i | \(0.692197\pi\) | |||||||
\(164\) | 20.7903 | 1.62345 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.1944 | −1.87785 | ||||||||
\(167\) | 14.1218 | 1.09278 | 0.546388 | − | 0.837532i | \(-0.316002\pi\) | ||||
0.546388 | + | 0.837532i | \(0.316002\pi\) | |||||||
\(168\) | 9.08666 | 0.701051 | ||||||||
\(169\) | 1.19157 | 0.0916591 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.07640 | −0.617618 | ||||||||
\(172\) | 16.4035 | 1.25076 | ||||||||
\(173\) | 6.32710 | 0.481041 | 0.240520 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240520 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(174\) | −8.54325 | −0.647662 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.14785 | 0.237278 | ||||||||
\(177\) | −10.0449 | −0.755024 | ||||||||
\(178\) | 16.9535 | 1.27072 | ||||||||
\(179\) | 8.85078 | 0.661538 | 0.330769 | − | 0.943712i | \(-0.392692\pi\) | ||||
0.330769 | + | 0.943712i | \(0.392692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.6795 | 1.01679 | 0.508395 | − | 0.861124i | \(-0.330239\pi\) | ||||
0.508395 | + | 0.861124i | \(0.330239\pi\) | |||||||
\(182\) | −31.0785 | −2.30369 | ||||||||
\(183\) | 4.68111 | 0.346038 | ||||||||
\(184\) | 11.8505 | 0.873628 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.8820 | −0.871228 | ||||||||
\(187\) | 34.5218 | 2.52449 | ||||||||
\(188\) | 3.10144 | 0.226195 | ||||||||
\(189\) | −3.65257 | −0.265686 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7719 | 1.14121 | 0.570607 | − | 0.821223i | \(-0.306708\pi\) | ||||
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(192\) | 13.0489 | 0.941727 | ||||||||
\(193\) | −7.82923 | −0.563561 | −0.281780 | − | 0.959479i | \(-0.590925\pi\) | ||||
−0.281780 | + | 0.959479i | \(0.590925\pi\) | |||||||
\(194\) | −26.5347 | −1.90508 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.6671 | 1.40479 | ||||||||
\(197\) | −10.6587 | −0.759401 | −0.379701 | − | 0.925109i | \(-0.623973\pi\) | ||||
−0.379701 | + | 0.925109i | \(0.623973\pi\) | |||||||
\(198\) | 12.1751 | 0.865243 | ||||||||
\(199\) | −6.40218 | −0.453839 | −0.226919 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226919 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.1087 | −0.995149 | ||||||||
\(202\) | −22.1325 | −1.55724 | ||||||||
\(203\) | −13.8158 | −0.969679 | ||||||||
\(204\) | 19.8624 | 1.39065 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.8689 | 1.24498 | ||||||||
\(207\) | −4.76354 | −0.331089 | ||||||||
\(208\) | −2.19991 | −0.152536 | ||||||||
\(209\) | 43.5354 | 3.01141 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.13642 | 0.491291 | 0.245646 | − | 0.969360i | \(-0.421000\pi\) | ||||
0.245646 | + | 0.969360i | \(0.421000\pi\) | |||||||
\(212\) | −29.8382 | −2.04929 | ||||||||
\(213\) | −12.0784 | −0.827599 | ||||||||
\(214\) | −36.1768 | −2.47300 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.48774 | 0.169269 | ||||||||
\(217\) | −19.2150 | −1.30440 | ||||||||
\(218\) | 14.1746 | 0.960024 | ||||||||
\(219\) | 11.5541 | 0.780756 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.1259 | −1.62289 | ||||||||
\(222\) | 7.88109 | 0.528944 | ||||||||
\(223\) | 5.41572 | 0.362664 | 0.181332 | − | 0.983422i | \(-0.441959\pi\) | ||||
0.181332 | + | 0.983422i | \(0.441959\pi\) | |||||||
\(224\) | 22.9910 | 1.53615 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −35.0539 | −2.33175 | ||||||||
\(227\) | 22.8812 | 1.51868 | 0.759339 | − | 0.650695i | \(-0.225522\pi\) | ||||
0.759339 | + | 0.650695i | \(0.225522\pi\) | |||||||
\(228\) | 25.0484 | 1.65887 | ||||||||
\(229\) | 25.9203 | 1.71286 | 0.856431 | − | 0.516261i | \(-0.172677\pi\) | ||||
0.856431 | + | 0.516261i | \(0.172677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.6890 | 1.29544 | ||||||||
\(232\) | 9.40984 | 0.617786 | ||||||||
\(233\) | −1.38698 | −0.0908638 | −0.0454319 | − | 0.998967i | \(-0.514466\pi\) | ||||
−0.0454319 | + | 0.998967i | \(0.514466\pi\) | |||||||
\(234\) | −8.50866 | −0.556229 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 31.1538 | 2.02794 | ||||||||
\(237\) | −1.64874 | −0.107097 | ||||||||
\(238\) | 52.8341 | 3.42472 | ||||||||
\(239\) | −20.8507 | −1.34872 | −0.674361 | − | 0.738402i | \(-0.735581\pi\) | ||||
−0.674361 | + | 0.738402i | \(0.735581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2621 | −1.24078 | −0.620389 | − | 0.784294i | \(-0.713025\pi\) | ||||
−0.620389 | + | 0.784294i | \(0.713025\pi\) | |||||||
\(242\) | −40.7840 | −2.62169 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.5182 | −0.929430 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.1406 | 0.965332 | ||||||||
\(247\) | −30.4252 | −1.93591 | ||||||||
\(248\) | 13.0872 | 0.831040 | ||||||||
\(249\) | −10.7120 | −0.678843 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0252 | 0.632784 | 0.316392 | − | 0.948629i | \(-0.397529\pi\) | ||||
0.316392 | + | 0.948629i | \(0.397529\pi\) | |||||||
\(252\) | 11.3282 | 0.713611 | ||||||||
\(253\) | 25.6776 | 1.61434 | ||||||||
\(254\) | −36.4771 | −2.28878 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.0367 | −0.752293 | ||||||||
\(257\) | −11.1976 | −0.698488 | −0.349244 | − | 0.937032i | \(-0.613562\pi\) | ||||
−0.349244 | + | 0.937032i | \(0.613562\pi\) | |||||||
\(258\) | 11.9459 | 0.743722 | ||||||||
\(259\) | 12.7450 | 0.791935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.78248 | −0.234130 | ||||||||
\(262\) | −31.7534 | −1.96173 | ||||||||
\(263\) | 0.764798 | 0.0471595 | 0.0235797 | − | 0.999722i | \(-0.492494\pi\) | ||||
0.0235797 | + | 0.999722i | \(0.492494\pi\) | |||||||
\(264\) | −13.4100 | −0.825331 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 66.6290 | 4.08528 | ||||||||
\(267\) | 7.50610 | 0.459366 | ||||||||
\(268\) | 43.7571 | 2.67289 | ||||||||
\(269\) | 2.34969 | 0.143263 | 0.0716316 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716316 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8548 | −0.963111 | −0.481556 | − | 0.876416i | \(-0.659928\pi\) | ||||
−0.481556 | + | 0.876416i | \(0.659928\pi\) | |||||||
\(272\) | 3.73989 | 0.226764 | ||||||||
\(273\) | −13.7599 | −0.832785 | ||||||||
\(274\) | 46.6394 | 2.81759 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.7738 | 0.889280 | ||||||||
\(277\) | 17.8932 | 1.07510 | 0.537548 | − | 0.843233i | \(-0.319351\pi\) | ||||
0.537548 | + | 0.843233i | \(0.319351\pi\) | |||||||
\(278\) | 8.70630 | 0.522169 | ||||||||
\(279\) | −5.26069 | −0.314949 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7136 | −1.29533 | −0.647663 | − | 0.761927i | \(-0.724253\pi\) | ||||
−0.647663 | + | 0.761927i | \(0.724253\pi\) | |||||||
\(282\) | 2.25864 | 0.134500 | ||||||||
\(283\) | 14.5961 | 0.867648 | 0.433824 | − | 0.900998i | \(-0.357164\pi\) | ||||
0.433824 | + | 0.900998i | \(0.357164\pi\) | |||||||
\(284\) | 37.4604 | 2.22286 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 45.8655 | 2.71208 | ||||||||
\(287\) | 24.4848 | 1.44529 | ||||||||
\(288\) | 6.29446 | 0.370904 | ||||||||
\(289\) | 24.0145 | 1.41262 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7481 | −0.688686 | ||||||||
\(292\) | −35.8344 | −2.09705 | ||||||||
\(293\) | −6.51441 | −0.380576 | −0.190288 | − | 0.981728i | \(-0.560942\pi\) | ||||
−0.190288 | + | 0.981728i | \(0.560942\pi\) | |||||||
\(294\) | 14.3227 | 0.835316 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.68051 | −0.504545 | ||||||||
\(297\) | 5.39045 | 0.312785 | ||||||||
\(298\) | 21.0426 | 1.21897 | ||||||||
\(299\) | −17.9451 | −1.03779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.3185 | 1.11350 | ||||||||
\(302\) | −24.6224 | −1.41686 | ||||||||
\(303\) | −9.79905 | −0.562941 | ||||||||
\(304\) | 4.71637 | 0.270502 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.4649 | 0.826903 | ||||||||
\(307\) | 30.2614 | 1.72711 | 0.863555 | − | 0.504254i | \(-0.168233\pi\) | ||||
0.863555 | + | 0.504254i | \(0.168233\pi\) | |||||||
\(308\) | −61.0642 | −3.47945 | ||||||||
\(309\) | 7.91135 | 0.450061 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.8690 | −0.843145 | −0.421572 | − | 0.906795i | \(-0.638522\pi\) | ||||
−0.421572 | + | 0.906795i | \(0.638522\pi\) | |||||||
\(312\) | 9.37174 | 0.530571 | ||||||||
\(313\) | 19.0799 | 1.07846 | 0.539231 | − | 0.842158i | \(-0.318715\pi\) | ||||
0.539231 | + | 0.842158i | \(0.318715\pi\) | |||||||
\(314\) | −19.6172 | −1.10707 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.11347 | 0.287655 | ||||||||
\(317\) | −11.9688 | −0.672234 | −0.336117 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336117 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(318\) | −21.7298 | −1.21855 | ||||||||
\(319\) | 20.3893 | 1.14158 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.0171 | −0.893989 | ||||||||
\(322\) | 39.2984 | 2.19002 | ||||||||
\(323\) | 51.7234 | 2.87797 | ||||||||
\(324\) | 3.10144 | 0.172302 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.7453 | 1.81359 | ||||||||
\(327\) | 6.27573 | 0.347049 | ||||||||
\(328\) | −16.6764 | −0.920802 | ||||||||
\(329\) | 3.65257 | 0.201373 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0901 | −0.884390 | −0.442195 | − | 0.896919i | \(-0.645800\pi\) | ||||
−0.442195 | + | 0.896919i | \(0.645800\pi\) | |||||||
\(332\) | 33.2224 | 1.82332 | ||||||||
\(333\) | 3.48931 | 0.191213 | ||||||||
\(334\) | −31.8960 | −1.74527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.13299 | 0.116364 | ||||||||
\(337\) | −9.68906 | −0.527797 | −0.263898 | − | 0.964550i | \(-0.585008\pi\) | ||||
−0.263898 | + | 0.964550i | \(0.585008\pi\) | |||||||
\(338\) | −2.69132 | −0.146388 | ||||||||
\(339\) | −15.5200 | −0.842928 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3574 | 1.53564 | ||||||||
\(342\) | 18.2416 | 0.986395 | ||||||||
\(343\) | −2.40596 | −0.129910 | ||||||||
\(344\) | −13.1577 | −0.709415 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2906 | −0.768268 | ||||||||
\(347\) | 3.87840 | 0.208203 | 0.104102 | − | 0.994567i | \(-0.466803\pi\) | ||||
0.104102 | + | 0.994567i | \(0.466803\pi\) | |||||||
\(348\) | 11.7311 | 0.628855 | ||||||||
\(349\) | −26.0674 | −1.39536 | −0.697679 | − | 0.716411i | \(-0.745784\pi\) | ||||
−0.697679 | + | 0.716411i | \(0.745784\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.76717 | −0.201077 | ||||||||
\(352\) | −33.9299 | −1.80847 | ||||||||
\(353\) | 32.9876 | 1.75575 | 0.877877 | − | 0.478886i | \(-0.158959\pi\) | ||||
0.877877 | + | 0.478886i | \(0.158959\pi\) | |||||||
\(354\) | 22.6879 | 1.20585 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −23.2797 | −1.23382 | ||||||||
\(357\) | 23.3920 | 1.23804 | ||||||||
\(358\) | −19.9907 | −1.05654 | ||||||||
\(359\) | −0.425406 | −0.0224520 | −0.0112260 | − | 0.999937i | \(-0.503573\pi\) | ||||
−0.0112260 | + | 0.999937i | \(0.503573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.2283 | 2.43307 | ||||||||
\(362\) | −30.8970 | −1.62391 | ||||||||
\(363\) | −18.0569 | −0.947742 | ||||||||
\(364\) | 42.6753 | 2.23680 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5729 | −0.552655 | ||||||||
\(367\) | −1.97076 | −0.102873 | −0.0514365 | − | 0.998676i | \(-0.516380\pi\) | ||||
−0.0514365 | + | 0.998676i | \(0.516380\pi\) | |||||||
\(368\) | 2.78176 | 0.145009 | ||||||||
\(369\) | 6.70344 | 0.348967 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.1405 | −1.82441 | ||||||||
\(372\) | 16.3157 | 0.845928 | ||||||||
\(373\) | 3.91613 | 0.202770 | 0.101385 | − | 0.994847i | \(-0.467673\pi\) | ||||
0.101385 | + | 0.994847i | \(0.467673\pi\) | |||||||
\(374\) | −77.9722 | −4.03185 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.48774 | −0.128295 | ||||||||
\(377\) | −14.2493 | −0.733874 | ||||||||
\(378\) | 8.24983 | 0.424326 | ||||||||
\(379\) | −6.09374 | −0.313014 | −0.156507 | − | 0.987677i | \(-0.550023\pi\) | ||||
−0.156507 | + | 0.987677i | \(0.550023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.1501 | −0.827393 | ||||||||
\(382\) | −35.6230 | −1.82263 | ||||||||
\(383\) | −27.9056 | −1.42591 | −0.712956 | − | 0.701209i | \(-0.752644\pi\) | ||||
−0.712956 | + | 0.701209i | \(0.752644\pi\) | |||||||
\(384\) | −16.8839 | −0.861603 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.6834 | 0.900061 | ||||||||
\(387\) | 5.28901 | 0.268855 | ||||||||
\(388\) | 36.4360 | 1.84976 | ||||||||
\(389\) | 7.08100 | 0.359021 | 0.179511 | − | 0.983756i | \(-0.442549\pi\) | ||||
0.179511 | + | 0.983756i | \(0.442549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.5070 | 1.54280 | ||||||||
\(392\) | −15.7755 | −0.796783 | ||||||||
\(393\) | −14.0586 | −0.709165 | ||||||||
\(394\) | 24.0741 | 1.21284 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.7181 | −0.840117 | ||||||||
\(397\) | 12.8045 | 0.642637 | 0.321319 | − | 0.946971i | \(-0.395874\pi\) | ||||
0.321319 | + | 0.946971i | \(0.395874\pi\) | |||||||
\(398\) | 14.4602 | 0.724824 | ||||||||
\(399\) | 29.4997 | 1.47683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.9986 | 0.898808 | 0.449404 | − | 0.893329i | \(-0.351636\pi\) | ||||
0.449404 | + | 0.893329i | \(0.351636\pi\) | |||||||
\(402\) | 31.8664 | 1.58935 | ||||||||
\(403\) | −19.8179 | −0.987200 | ||||||||
\(404\) | 30.3911 | 1.51202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.2049 | 1.54867 | ||||||||
\(407\) | −18.8090 | −0.932326 | ||||||||
\(408\) | −15.9321 | −0.788759 | ||||||||
\(409\) | 28.9900 | 1.43346 | 0.716731 | − | 0.697350i | \(-0.245637\pi\) | ||||
0.716731 | + | 0.697350i | \(0.245637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.6494 | 1.01856 | ||||||||
\(412\) | −24.5365 | −1.20883 | ||||||||
\(413\) | 36.6899 | 1.80539 | ||||||||
\(414\) | 10.7591 | 0.528781 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 23.7123 | 1.16259 | ||||||||
\(417\) | 3.85467 | 0.188764 | ||||||||
\(418\) | −98.3306 | −4.80951 | ||||||||
\(419\) | −0.494504 | −0.0241581 | −0.0120791 | − | 0.999927i | \(-0.503845\pi\) | ||||
−0.0120791 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.4814 | −1.19315 | −0.596575 | − | 0.802557i | \(-0.703472\pi\) | ||||
−0.596575 | + | 0.802557i | \(0.703472\pi\) | |||||||
\(422\) | −16.1186 | −0.784640 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 23.9340 | 1.16234 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 27.2807 | 1.32175 | ||||||||
\(427\) | −17.0981 | −0.827435 | ||||||||
\(428\) | 49.6761 | 2.40118 | ||||||||
\(429\) | 20.3067 | 0.980418 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.5802 | 0.991311 | 0.495656 | − | 0.868519i | \(-0.334928\pi\) | ||||
0.495656 | + | 0.868519i | \(0.334928\pi\) | |||||||
\(432\) | 0.583969 | 0.0280962 | ||||||||
\(433\) | −10.8674 | −0.522254 | −0.261127 | − | 0.965304i | \(-0.584094\pi\) | ||||
−0.261127 | + | 0.965304i | \(0.584094\pi\) | |||||||
\(434\) | 43.3998 | 2.08326 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.4638 | −0.932145 | ||||||||
\(437\) | 38.4723 | 1.84038 | ||||||||
\(438\) | −26.0966 | −1.24694 | ||||||||
\(439\) | −4.05108 | −0.193347 | −0.0966737 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966737 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.34130 | 0.301966 | ||||||||
\(442\) | 54.4917 | 2.59191 | ||||||||
\(443\) | 19.8347 | 0.942376 | 0.471188 | − | 0.882033i | \(-0.343825\pi\) | ||||
0.471188 | + | 0.882033i | \(0.343825\pi\) | |||||||
\(444\) | −10.8219 | −0.513584 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.2321 | −0.579209 | ||||||||
\(447\) | 9.31652 | 0.440656 | ||||||||
\(448\) | −47.6622 | −2.25183 | ||||||||
\(449\) | −12.3888 | −0.584663 | −0.292331 | − | 0.956317i | \(-0.594431\pi\) | ||||
−0.292331 | + | 0.956317i | \(0.594431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.1346 | −1.70151 | ||||||||
\(452\) | 48.1341 | 2.26404 | ||||||||
\(453\) | −10.9014 | −0.512194 | ||||||||
\(454\) | −51.6803 | −2.42548 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.0920 | −0.940894 | ||||||||
\(457\) | −0.726902 | −0.0340030 | −0.0170015 | − | 0.999855i | \(-0.505412\pi\) | ||||
−0.0170015 | + | 0.999855i | \(0.505412\pi\) | |||||||
\(458\) | −58.5445 | −2.73561 | ||||||||
\(459\) | 6.40426 | 0.298925 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.78513 | −0.269440 | −0.134720 | − | 0.990884i | \(-0.543014\pi\) | ||||
−0.134720 | + | 0.990884i | \(0.543014\pi\) | |||||||
\(462\) | −44.4703 | −2.06894 | ||||||||
\(463\) | 23.2529 | 1.08066 | 0.540328 | − | 0.841455i | \(-0.318300\pi\) | ||||
0.540328 | + | 0.841455i | \(0.318300\pi\) | |||||||
\(464\) | 2.20885 | 0.102544 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.13267 | 0.145118 | ||||||||
\(467\) | −19.5028 | −0.902481 | −0.451241 | − | 0.892402i | \(-0.649018\pi\) | ||||
−0.451241 | + | 0.892402i | \(0.649018\pi\) | |||||||
\(468\) | 11.6836 | 0.540076 | ||||||||
\(469\) | 51.5330 | 2.37957 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.68544 | −0.400204 | ||||||||
\(472\) | −24.9892 | −1.15022 | ||||||||
\(473\) | −28.5101 | −1.31090 | ||||||||
\(474\) | 3.72391 | 0.171045 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −72.5489 | −3.32527 | ||||||||
\(477\) | −9.62076 | −0.440504 | ||||||||
\(478\) | 47.0942 | 2.15404 | ||||||||
\(479\) | 15.9371 | 0.728185 | 0.364093 | − | 0.931363i | \(-0.381379\pi\) | ||||
0.364093 | + | 0.931363i | \(0.381379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1448 | 0.599353 | ||||||||
\(482\) | 43.5060 | 1.98164 | ||||||||
\(483\) | 17.3992 | 0.791691 | ||||||||
\(484\) | 56.0023 | 2.54556 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.25864 | 0.102454 | ||||||||
\(487\) | 21.5979 | 0.978695 | 0.489347 | − | 0.872089i | \(-0.337235\pi\) | ||||
0.489347 | + | 0.872089i | \(0.337235\pi\) | |||||||
\(488\) | 11.6454 | 0.527162 | ||||||||
\(489\) | 14.4978 | 0.655613 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5726 | −0.883298 | −0.441649 | − | 0.897188i | \(-0.645606\pi\) | ||||
−0.441649 | + | 0.897188i | \(0.645606\pi\) | |||||||
\(492\) | −20.7903 | −0.937299 | ||||||||
\(493\) | 24.2240 | 1.09099 | ||||||||
\(494\) | 68.7194 | 3.09183 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.07208 | 0.137940 | ||||||||
\(497\) | 44.1173 | 1.97893 | ||||||||
\(498\) | 24.1944 | 1.08418 | ||||||||
\(499\) | −30.3032 | −1.35656 | −0.678278 | − | 0.734805i | \(-0.737274\pi\) | ||||
−0.678278 | + | 0.734805i | \(0.737274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.1218 | −0.630915 | ||||||||
\(502\) | −22.6432 | −1.01062 | ||||||||
\(503\) | −23.6646 | −1.05515 | −0.527577 | − | 0.849507i | \(-0.676899\pi\) | ||||
−0.527577 | + | 0.849507i | \(0.676899\pi\) | |||||||
\(504\) | −9.08666 | −0.404752 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −57.9964 | −2.57825 | ||||||||
\(507\) | −1.19157 | −0.0529194 | ||||||||
\(508\) | 50.0884 | 2.22231 | ||||||||
\(509\) | 12.2650 | 0.543638 | 0.271819 | − | 0.962348i | \(-0.412375\pi\) | ||||
0.271819 | + | 0.962348i | \(0.412375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.2024 | −1.86692 | ||||||||
\(512\) | −6.58130 | −0.290855 | ||||||||
\(513\) | 8.07640 | 0.356582 | ||||||||
\(514\) | 25.2913 | 1.11555 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.4035 | −0.722125 | ||||||||
\(517\) | −5.39045 | −0.237072 | ||||||||
\(518\) | −28.7863 | −1.26480 | ||||||||
\(519\) | −6.32710 | −0.277729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7739 | −1.30442 | −0.652210 | − | 0.758038i | \(-0.726158\pi\) | ||||
−0.652210 | + | 0.758038i | \(0.726158\pi\) | |||||||
\(522\) | 8.54325 | 0.373928 | ||||||||
\(523\) | 36.9743 | 1.61677 | 0.808386 | − | 0.588653i | \(-0.200342\pi\) | ||||
0.808386 | + | 0.588653i | \(0.200342\pi\) | |||||||
\(524\) | 43.6020 | 1.90476 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.72740 | −0.0753182 | ||||||||
\(527\) | 33.6908 | 1.46759 | ||||||||
\(528\) | −3.14785 | −0.136993 | ||||||||
\(529\) | −0.308648 | −0.0134195 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0449 | 0.435914 | ||||||||
\(532\) | −91.4913 | −3.96665 | ||||||||
\(533\) | 25.2530 | 1.09383 | ||||||||
\(534\) | −16.9535 | −0.733652 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.0987 | −1.51603 | ||||||||
\(537\) | −8.85078 | −0.381939 | ||||||||
\(538\) | −5.30710 | −0.228805 | ||||||||
\(539\) | −34.1824 | −1.47234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3797 | 0.747212 | 0.373606 | − | 0.927587i | \(-0.378121\pi\) | ||||
0.373606 | + | 0.927587i | \(0.378121\pi\) | |||||||
\(542\) | 35.8102 | 1.53818 | ||||||||
\(543\) | −13.6795 | −0.587044 | ||||||||
\(544\) | −40.3113 | −1.72833 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 31.0785 | 1.33004 | ||||||||
\(547\) | 3.14180 | 0.134334 | 0.0671668 | − | 0.997742i | \(-0.478604\pi\) | ||||
0.0671668 | + | 0.997742i | \(0.478604\pi\) | |||||||
\(548\) | −64.0426 | −2.73577 | ||||||||
\(549\) | −4.68111 | −0.199785 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.5489 | 1.30143 | ||||||||
\(552\) | −11.8505 | −0.504389 | ||||||||
\(553\) | 6.02216 | 0.256088 | ||||||||
\(554\) | −40.4141 | −1.71703 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.9550 | −0.507005 | ||||||||
\(557\) | −4.70436 | −0.199330 | −0.0996650 | − | 0.995021i | \(-0.531777\pi\) | ||||
−0.0996650 | + | 0.995021i | \(0.531777\pi\) | |||||||
\(558\) | 11.8820 | 0.503004 | ||||||||
\(559\) | 19.9246 | 0.842721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.5218 | −1.45751 | ||||||||
\(562\) | 49.0432 | 2.06876 | ||||||||
\(563\) | 9.19564 | 0.387550 | 0.193775 | − | 0.981046i | \(-0.437927\pi\) | ||||
0.193775 | + | 0.981046i | \(0.437927\pi\) | |||||||
\(564\) | −3.10144 | −0.130594 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.9673 | −1.38572 | ||||||||
\(567\) | 3.65257 | 0.153394 | ||||||||
\(568\) | −30.0479 | −1.26078 | ||||||||
\(569\) | 4.54858 | 0.190686 | 0.0953432 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953432 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.85447 | −0.370548 | −0.185274 | − | 0.982687i | \(-0.559317\pi\) | ||||
−0.185274 | + | 0.982687i | \(0.559317\pi\) | |||||||
\(572\) | −62.9800 | −2.63333 | ||||||||
\(573\) | −15.7719 | −0.658881 | ||||||||
\(574\) | −55.3023 | −2.30827 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.0489 | −0.543706 | ||||||||
\(577\) | −8.34516 | −0.347414 | −0.173707 | − | 0.984797i | \(-0.555575\pi\) | ||||
−0.173707 | + | 0.984797i | \(0.555575\pi\) | |||||||
\(578\) | −54.2401 | −2.25609 | ||||||||
\(579\) | 7.82923 | 0.325372 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.1262 | 1.62323 | ||||||||
\(582\) | 26.5347 | 1.09990 | ||||||||
\(583\) | 51.8602 | 2.14783 | ||||||||
\(584\) | 28.7437 | 1.18942 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7137 | 0.607817 | ||||||||
\(587\) | −18.7043 | −0.772010 | −0.386005 | − | 0.922497i | \(-0.626145\pi\) | ||||
−0.386005 | + | 0.922497i | \(0.626145\pi\) | |||||||
\(588\) | −19.6671 | −0.811058 | ||||||||
\(589\) | 42.4874 | 1.75066 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.6587 | 0.438440 | ||||||||
\(592\) | −2.03765 | −0.0837470 | ||||||||
\(593\) | −19.5188 | −0.801542 | −0.400771 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400771 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(594\) | −12.1751 | −0.499548 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.8946 | −1.18357 | ||||||||
\(597\) | 6.40218 | 0.262024 | ||||||||
\(598\) | 40.5314 | 1.65745 | ||||||||
\(599\) | −10.2208 | −0.417610 | −0.208805 | − | 0.977957i | \(-0.566957\pi\) | ||||
−0.208805 | + | 0.977957i | \(0.566957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.3384 | −0.951992 | −0.475996 | − | 0.879448i | \(-0.657912\pi\) | ||||
−0.475996 | + | 0.879448i | \(0.657912\pi\) | |||||||
\(602\) | −43.6335 | −1.77837 | ||||||||
\(603\) | 14.1087 | 0.574550 | ||||||||
\(604\) | 33.8101 | 1.37571 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.1325 | 0.899071 | ||||||||
\(607\) | −31.6937 | −1.28641 | −0.643204 | − | 0.765695i | \(-0.722395\pi\) | ||||
−0.643204 | + | 0.765695i | \(0.722395\pi\) | |||||||
\(608\) | −50.8366 | −2.06169 | ||||||||
\(609\) | 13.8158 | 0.559845 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.76717 | 0.152403 | ||||||||
\(612\) | −19.8624 | −0.802890 | ||||||||
\(613\) | −34.6718 | −1.40038 | −0.700191 | − | 0.713955i | \(-0.746902\pi\) | ||||
−0.700191 | + | 0.713955i | \(0.746902\pi\) | |||||||
\(614\) | −68.3495 | −2.75836 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.9811 | 1.97351 | ||||||||
\(617\) | 45.0825 | 1.81495 | 0.907476 | − | 0.420104i | \(-0.138006\pi\) | ||||
0.907476 | + | 0.420104i | \(0.138006\pi\) | |||||||
\(618\) | −17.8689 | −0.718791 | ||||||||
\(619\) | 15.5285 | 0.624141 | 0.312071 | − | 0.950059i | \(-0.398977\pi\) | ||||
0.312071 | + | 0.950059i | \(0.398977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.76354 | 0.191154 | ||||||||
\(622\) | 33.5837 | 1.34658 | ||||||||
\(623\) | −27.4166 | −1.09842 | ||||||||
\(624\) | 2.19991 | 0.0880669 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −43.0947 | −1.72241 | ||||||||
\(627\) | −43.5354 | −1.73864 | ||||||||
\(628\) | 26.9373 | 1.07492 | ||||||||
\(629\) | −22.3465 | −0.891012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8534 | 0.471878 | 0.235939 | − | 0.971768i | \(-0.424183\pi\) | ||||
0.235939 | + | 0.971768i | \(0.424183\pi\) | |||||||
\(632\) | −4.10165 | −0.163155 | ||||||||
\(633\) | −7.13642 | −0.283647 | ||||||||
\(634\) | 27.0331 | 1.07362 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 29.8382 | 1.18316 | ||||||||
\(637\) | 23.8887 | 0.946506 | ||||||||
\(638\) | −46.0519 | −1.82321 | ||||||||
\(639\) | 12.0784 | 0.477814 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3123 | 0.446807 | 0.223404 | − | 0.974726i | \(-0.428283\pi\) | ||||
0.223404 | + | 0.974726i | \(0.428283\pi\) | |||||||
\(642\) | 36.1768 | 1.42779 | ||||||||
\(643\) | −3.71679 | −0.146576 | −0.0732879 | − | 0.997311i | \(-0.523349\pi\) | ||||
−0.0732879 | + | 0.997311i | \(0.523349\pi\) | |||||||
\(644\) | −53.9625 | −2.12642 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −116.824 | −4.59639 | ||||||||
\(647\) | 20.9097 | 0.822047 | 0.411023 | − | 0.911625i | \(-0.365171\pi\) | ||||
0.411023 | + | 0.911625i | \(0.365171\pi\) | |||||||
\(648\) | −2.48774 | −0.0977277 | ||||||||
\(649\) | −54.1467 | −2.12545 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.2150 | 0.753097 | ||||||||
\(652\) | −44.9640 | −1.76093 | ||||||||
\(653\) | −31.2980 | −1.22479 | −0.612393 | − | 0.790553i | \(-0.709793\pi\) | ||||
−0.612393 | + | 0.790553i | \(0.709793\pi\) | |||||||
\(654\) | −14.1746 | −0.554270 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.91461 | −0.152840 | ||||||||
\(657\) | −11.5541 | −0.450770 | ||||||||
\(658\) | −8.24983 | −0.321612 | ||||||||
\(659\) | 11.6158 | 0.452487 | 0.226243 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.93633 | −0.386478 | −0.193239 | − | 0.981152i | \(-0.561899\pi\) | ||||
−0.193239 | + | 0.981152i | \(0.561899\pi\) | |||||||
\(662\) | 36.3416 | 1.41246 | ||||||||
\(663\) | 24.1259 | 0.936974 | ||||||||
\(664\) | −26.6486 | −1.03417 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.88109 | −0.305386 | ||||||||
\(667\) | 18.0180 | 0.697661 | ||||||||
\(668\) | 43.7978 | 1.69459 | ||||||||
\(669\) | −5.41572 | −0.209384 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.2333 | 0.974119 | ||||||||
\(672\) | −22.9910 | −0.886896 | ||||||||
\(673\) | −22.5946 | −0.870957 | −0.435479 | − | 0.900199i | \(-0.643421\pi\) | ||||
−0.435479 | + | 0.900199i | \(0.643421\pi\) | |||||||
\(674\) | 21.8841 | 0.842943 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.69557 | 0.142137 | ||||||||
\(677\) | 30.0102 | 1.15338 | 0.576692 | − | 0.816962i | \(-0.304343\pi\) | ||||
0.576692 | + | 0.816962i | \(0.304343\pi\) | |||||||
\(678\) | 35.0539 | 1.34624 | ||||||||
\(679\) | 42.9108 | 1.64677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.8812 | −0.876809 | ||||||||
\(682\) | −64.0491 | −2.45257 | ||||||||
\(683\) | −2.71242 | −0.103788 | −0.0518939 | − | 0.998653i | \(-0.516526\pi\) | ||||
−0.0518939 | + | 0.998653i | \(0.516526\pi\) | |||||||
\(684\) | −25.0484 | −0.957751 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.43419 | 0.207479 | ||||||||
\(687\) | −25.9203 | −0.988921 | ||||||||
\(688\) | −3.08862 | −0.117753 | ||||||||
\(689\) | −36.2430 | −1.38075 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4120 | 0.472174 | 0.236087 | − | 0.971732i | \(-0.424135\pi\) | ||||
0.236087 | + | 0.971732i | \(0.424135\pi\) | |||||||
\(692\) | 19.6231 | 0.745958 | ||||||||
\(693\) | −19.6890 | −0.747923 | ||||||||
\(694\) | −8.75989 | −0.332521 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.40984 | −0.356679 | ||||||||
\(697\) | −42.9306 | −1.62611 | ||||||||
\(698\) | 58.8768 | 2.22852 | ||||||||
\(699\) | 1.38698 | 0.0524603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.1760 | 1.44189 | 0.720943 | − | 0.692994i | \(-0.243709\pi\) | ||||
0.720943 | + | 0.692994i | \(0.243709\pi\) | |||||||
\(702\) | 8.50866 | 0.321139 | ||||||||
\(703\) | −28.1811 | −1.06287 | ||||||||
\(704\) | 70.3396 | 2.65102 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −74.5070 | −2.80411 | ||||||||
\(707\) | 35.7918 | 1.34609 | ||||||||
\(708\) | −31.1538 | −1.17083 | ||||||||
\(709\) | −21.2535 | −0.798194 | −0.399097 | − | 0.916909i | \(-0.630676\pi\) | ||||
−0.399097 | + | 0.916909i | \(0.630676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.64874 | 0.0618327 | ||||||||
\(712\) | 18.6732 | 0.699809 | ||||||||
\(713\) | 25.0595 | 0.938486 | ||||||||
\(714\) | −52.8341 | −1.97727 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.4501 | 1.02586 | ||||||||
\(717\) | 20.8507 | 0.778685 | ||||||||
\(718\) | 0.960836 | 0.0358581 | ||||||||
\(719\) | 25.3271 | 0.944543 | 0.472272 | − | 0.881453i | \(-0.343434\pi\) | ||||
0.472272 | + | 0.881453i | \(0.343434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.8968 | −1.07617 | ||||||||
\(722\) | −104.413 | −3.88584 | ||||||||
\(723\) | 19.2621 | 0.716364 | ||||||||
\(724\) | 42.4261 | 1.57675 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 40.7840 | 1.51363 | ||||||||
\(727\) | −38.4277 | −1.42521 | −0.712603 | − | 0.701567i | \(-0.752484\pi\) | ||||
−0.712603 | + | 0.701567i | \(0.752484\pi\) | |||||||
\(728\) | −34.2310 | −1.26868 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.8722 | −1.25281 | ||||||||
\(732\) | 14.5182 | 0.536607 | ||||||||
\(733\) | 39.9589 | 1.47592 | 0.737959 | − | 0.674846i | \(-0.235790\pi\) | ||||
0.737959 | + | 0.674846i | \(0.235790\pi\) | |||||||
\(734\) | 4.45123 | 0.164298 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.9839 | −1.10522 | ||||||||
\(737\) | −76.0520 | −2.80141 | ||||||||
\(738\) | −15.1406 | −0.557335 | ||||||||
\(739\) | 6.27640 | 0.230881 | 0.115441 | − | 0.993314i | \(-0.463172\pi\) | ||||
0.115441 | + | 0.993314i | \(0.463172\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.4252 | 1.11770 | ||||||||
\(742\) | 79.3696 | 2.91375 | ||||||||
\(743\) | 18.5595 | 0.680882 | 0.340441 | − | 0.940266i | \(-0.389424\pi\) | ||||
0.340441 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(744\) | −13.0872 | −0.479801 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.84511 | −0.323843 | ||||||||
\(747\) | 10.7120 | 0.391930 | ||||||||
\(748\) | 107.067 | 3.91476 | ||||||||
\(749\) | 58.5037 | 2.13768 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.3145 | 1.69004 | 0.845019 | − | 0.534736i | \(-0.179589\pi\) | ||||
0.845019 | + | 0.534736i | \(0.179589\pi\) | |||||||
\(752\) | −0.583969 | −0.0212952 | ||||||||
\(753\) | −10.0252 | −0.365338 | ||||||||
\(754\) | 32.1839 | 1.17207 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.3282 | −0.412003 | ||||||||
\(757\) | 28.8540 | 1.04872 | 0.524358 | − | 0.851498i | \(-0.324305\pi\) | ||||
0.524358 | + | 0.851498i | \(0.324305\pi\) | |||||||
\(758\) | 13.7635 | 0.499914 | ||||||||
\(759\) | −25.6776 | −0.932039 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.16914 | 0.0786313 | 0.0393156 | − | 0.999227i | \(-0.487482\pi\) | ||||
0.0393156 | + | 0.999227i | \(0.487482\pi\) | |||||||
\(762\) | 36.4771 | 1.32143 | ||||||||
\(763\) | −22.9226 | −0.829852 | ||||||||
\(764\) | 48.9155 | 1.76970 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 63.0287 | 2.27732 | ||||||||
\(767\) | 37.8410 | 1.36636 | ||||||||
\(768\) | 12.0367 | 0.434337 | ||||||||
\(769\) | −30.4385 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1976 | 0.403272 | ||||||||
\(772\) | −24.2819 | −0.873923 | ||||||||
\(773\) | −0.878615 | −0.0316016 | −0.0158008 | − | 0.999875i | \(-0.505030\pi\) | ||||
−0.0158008 | + | 0.999875i | \(0.505030\pi\) | |||||||
\(774\) | −11.9459 | −0.429388 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29.2262 | −1.04916 | ||||||||
\(777\) | −12.7450 | −0.457224 | ||||||||
\(778\) | −15.9934 | −0.573391 | ||||||||
\(779\) | −54.1397 | −1.93976 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.1080 | −2.32975 | ||||||||
\(782\) | −68.9041 | −2.46401 | ||||||||
\(783\) | 3.78248 | 0.135175 | ||||||||
\(784\) | −3.70312 | −0.132254 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 31.7534 | 1.13260 | ||||||||
\(787\) | 17.9038 | 0.638202 | 0.319101 | − | 0.947721i | \(-0.396619\pi\) | ||||
0.319101 | + | 0.947721i | \(0.396619\pi\) | |||||||
\(788\) | −33.0573 | −1.17762 | ||||||||
\(789\) | −0.764798 | −0.0272275 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.6878 | 2.01559 | ||||||||
\(792\) | 13.4100 | 0.476505 | ||||||||
\(793\) | −17.6345 | −0.626221 | ||||||||
\(794\) | −28.9206 | −1.02635 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.8560 | −0.703776 | ||||||||
\(797\) | 2.03099 | 0.0719413 | 0.0359707 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359707 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(798\) | −66.6290 | −2.35864 | ||||||||
\(799\) | −6.40426 | −0.226566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.50610 | −0.265215 | ||||||||
\(802\) | −40.6523 | −1.43548 | ||||||||
\(803\) | 62.2820 | 2.19788 | ||||||||
\(804\) | −43.7571 | −1.54320 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 44.7614 | 1.57665 | ||||||||
\(807\) | −2.34969 | −0.0827130 | ||||||||
\(808\) | −24.3775 | −0.857598 | ||||||||
\(809\) | −3.21240 | −0.112942 | −0.0564710 | − | 0.998404i | \(-0.517985\pi\) | ||||
−0.0564710 | + | 0.998404i | \(0.517985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.93628 | 0.103107 | 0.0515533 | − | 0.998670i | \(-0.483583\pi\) | ||||
0.0515533 | + | 0.998670i | \(0.483583\pi\) | |||||||
\(812\) | −42.8488 | −1.50370 | ||||||||
\(813\) | 15.8548 | 0.556053 | ||||||||
\(814\) | 42.4826 | 1.48901 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.73989 | −0.130922 | ||||||||
\(817\) | −42.7162 | −1.49445 | ||||||||
\(818\) | −65.4778 | −2.28938 | ||||||||
\(819\) | 13.7599 | 0.480809 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8856 | −0.484611 | −0.242305 | − | 0.970200i | \(-0.577904\pi\) | ||||
−0.242305 | + | 0.970200i | \(0.577904\pi\) | |||||||
\(822\) | −46.6394 | −1.62673 | ||||||||
\(823\) | −10.2213 | −0.356294 | −0.178147 | − | 0.984004i | \(-0.557010\pi\) | ||||
−0.178147 | + | 0.984004i | \(0.557010\pi\) | |||||||
\(824\) | 19.6814 | 0.685634 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −82.8691 | −2.88339 | ||||||||
\(827\) | 27.1692 | 0.944765 | 0.472383 | − | 0.881394i | \(-0.343394\pi\) | ||||
0.472383 | + | 0.881394i | \(0.343394\pi\) | |||||||
\(828\) | −14.7738 | −0.513426 | ||||||||
\(829\) | −7.41476 | −0.257525 | −0.128763 | − | 0.991675i | \(-0.541101\pi\) | ||||
−0.128763 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.8932 | −0.620707 | ||||||||
\(832\) | −49.1576 | −1.70423 | ||||||||
\(833\) | −40.6113 | −1.40710 | ||||||||
\(834\) | −8.70630 | −0.301474 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 135.022 | 4.66984 | ||||||||
\(837\) | 5.26069 | 0.181836 | ||||||||
\(838\) | 1.11691 | 0.0385829 | ||||||||
\(839\) | 6.99598 | 0.241528 | 0.120764 | − | 0.992681i | \(-0.461466\pi\) | ||||
0.120764 | + | 0.992681i | \(0.461466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.6928 | −0.506649 | ||||||||
\(842\) | 55.2946 | 1.90558 | ||||||||
\(843\) | 21.7136 | 0.747857 | ||||||||
\(844\) | 22.1331 | 0.761854 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.25864 | −0.0776535 | ||||||||
\(847\) | 65.9542 | 2.26621 | ||||||||
\(848\) | 5.61823 | 0.192931 | ||||||||
\(849\) | −14.5961 | −0.500937 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.6215 | −0.569778 | ||||||||
\(852\) | −37.4604 | −1.28337 | ||||||||
\(853\) | −25.3316 | −0.867338 | −0.433669 | − | 0.901072i | \(-0.642781\pi\) | ||||
−0.433669 | + | 0.901072i | \(0.642781\pi\) | |||||||
\(854\) | 38.6184 | 1.32149 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.8465 | −1.36192 | ||||||||
\(857\) | 11.2384 | 0.383898 | 0.191949 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191949 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(858\) | −45.8655 | −1.56582 | ||||||||
\(859\) | −41.7711 | −1.42521 | −0.712605 | − | 0.701566i | \(-0.752485\pi\) | ||||
−0.712605 | + | 0.701566i | \(0.752485\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.4848 | −0.834441 | ||||||||
\(862\) | −46.4831 | −1.58322 | ||||||||
\(863\) | −30.0343 | −1.02238 | −0.511190 | − | 0.859468i | \(-0.670795\pi\) | ||||
−0.511190 | + | 0.859468i | \(0.670795\pi\) | |||||||
\(864\) | −6.29446 | −0.214142 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.5455 | 0.834090 | ||||||||
\(867\) | −24.0145 | −0.815577 | ||||||||
\(868\) | −59.5942 | −2.02276 | ||||||||
\(869\) | −8.88746 | −0.301487 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.1498 | 1.80091 | ||||||||
\(872\) | 15.6124 | 0.528702 | ||||||||
\(873\) | 11.7481 | 0.397613 | ||||||||
\(874\) | −86.8949 | −2.93926 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.8344 | 1.21073 | ||||||||
\(877\) | −8.46607 | −0.285879 | −0.142939 | − | 0.989731i | \(-0.545655\pi\) | ||||
−0.142939 | + | 0.989731i | \(0.545655\pi\) | |||||||
\(878\) | 9.14991 | 0.308794 | ||||||||
\(879\) | 6.51441 | 0.219726 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.4949 | −0.420965 | −0.210482 | − | 0.977598i | \(-0.567503\pi\) | ||||
−0.210482 | + | 0.977598i | \(0.567503\pi\) | |||||||
\(882\) | −14.3227 | −0.482270 | ||||||||
\(883\) | −8.80299 | −0.296244 | −0.148122 | − | 0.988969i | \(-0.547323\pi\) | ||||
−0.148122 | + | 0.988969i | \(0.547323\pi\) | |||||||
\(884\) | −74.8250 | −2.51664 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44.7994 | −1.50507 | ||||||||
\(887\) | −56.7788 | −1.90645 | −0.953223 | − | 0.302269i | \(-0.902256\pi\) | ||||
−0.953223 | + | 0.302269i | \(0.902256\pi\) | |||||||
\(888\) | 8.68051 | 0.291299 | ||||||||
\(889\) | 58.9893 | 1.97844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.39045 | −0.180587 | ||||||||
\(892\) | 16.7965 | 0.562389 | ||||||||
\(893\) | −8.07640 | −0.270266 | ||||||||
\(894\) | −21.0426 | −0.703771 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 61.6697 | 2.06024 | ||||||||
\(897\) | 17.9451 | 0.599169 | ||||||||
\(898\) | 27.9817 | 0.933763 | ||||||||
\(899\) | 19.8985 | 0.663651 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.6138 | 2.05265 | ||||||||
\(902\) | 81.6148 | 2.71748 | ||||||||
\(903\) | −19.3185 | −0.642879 | ||||||||
\(904\) | −38.6096 | −1.28414 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.6224 | 0.818024 | ||||||||
\(907\) | −39.1164 | −1.29884 | −0.649419 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649419 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(908\) | 70.9645 | 2.35504 | ||||||||
\(909\) | 9.79905 | 0.325014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.2215 | 0.669969 | 0.334984 | − | 0.942224i | \(-0.391269\pi\) | ||||
0.334984 | + | 0.942224i | \(0.391269\pi\) | |||||||
\(912\) | −4.71637 | −0.156175 | ||||||||
\(913\) | −57.7422 | −1.91099 | ||||||||
\(914\) | 1.64181 | 0.0543061 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 80.3902 | 2.65617 | ||||||||
\(917\) | 51.3502 | 1.69573 | ||||||||
\(918\) | −14.4649 | −0.477413 | ||||||||
\(919\) | −30.6670 | −1.01161 | −0.505806 | − | 0.862647i | \(-0.668805\pi\) | ||||
−0.505806 | + | 0.862647i | \(0.668805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.2614 | −0.997148 | ||||||||
\(922\) | 13.0665 | 0.430322 | ||||||||
\(923\) | 45.5014 | 1.49770 | ||||||||
\(924\) | 61.0642 | 2.00886 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.5199 | −1.72591 | ||||||||
\(927\) | −7.91135 | −0.259843 | ||||||||
\(928\) | −23.8087 | −0.781558 | ||||||||
\(929\) | 17.3908 | 0.570573 | 0.285286 | − | 0.958442i | \(-0.407911\pi\) | ||||
0.285286 | + | 0.958442i | \(0.407911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51.2149 | −1.67850 | ||||||||
\(932\) | −4.30162 | −0.140904 | ||||||||
\(933\) | 14.8690 | 0.486790 | ||||||||
\(934\) | 44.0497 | 1.44135 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.37174 | −0.306325 | ||||||||
\(937\) | −25.7353 | −0.840736 | −0.420368 | − | 0.907354i | \(-0.638099\pi\) | ||||
−0.420368 | + | 0.907354i | \(0.638099\pi\) | |||||||
\(938\) | −116.394 | −3.80041 | ||||||||
\(939\) | −19.0799 | −0.622651 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.20220 | 0.169587 | 0.0847934 | − | 0.996399i | \(-0.472977\pi\) | ||||
0.0847934 | + | 0.996399i | \(0.472977\pi\) | |||||||
\(942\) | 19.6172 | 0.639164 | ||||||||
\(943\) | −31.9322 | −1.03985 | ||||||||
\(944\) | −5.86594 | −0.190920 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64.3940 | 2.09363 | ||||||||
\(947\) | 15.3966 | 0.500323 | 0.250162 | − | 0.968204i | \(-0.419516\pi\) | ||||
0.250162 | + | 0.968204i | \(0.419516\pi\) | |||||||
\(948\) | −5.11347 | −0.166078 | ||||||||
\(949\) | −43.5264 | −1.41293 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.9688 | 0.388115 | ||||||||
\(952\) | 58.1933 | 1.88606 | ||||||||
\(953\) | −25.8939 | −0.838785 | −0.419393 | − | 0.907805i | \(-0.637757\pi\) | ||||
−0.419393 | + | 0.907805i | \(0.637757\pi\) | |||||||
\(954\) | 21.7298 | 0.703528 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −64.6672 | −2.09149 | ||||||||
\(957\) | −20.3893 | −0.659092 | ||||||||
\(958\) | −35.9961 | −1.16298 | ||||||||
\(959\) | −75.4233 | −2.43554 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.32519 | −0.107264 | ||||||||
\(962\) | −29.6894 | −0.957225 | ||||||||
\(963\) | 16.0171 | 0.516145 | ||||||||
\(964\) | −59.7400 | −1.92410 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −39.2984 | −1.26441 | ||||||||
\(967\) | −59.1183 | −1.90112 | −0.950559 | − | 0.310545i | \(-0.899488\pi\) | ||||
−0.950559 | + | 0.310545i | \(0.899488\pi\) | |||||||
\(968\) | −44.9209 | −1.44381 | ||||||||
\(969\) | −51.7234 | −1.66159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.55439 | −0.210340 | −0.105170 | − | 0.994454i | \(-0.533539\pi\) | ||||
−0.105170 | + | 0.994454i | \(0.533539\pi\) | |||||||
\(972\) | −3.10144 | −0.0994786 | ||||||||
\(973\) | −14.0795 | −0.451367 | ||||||||
\(974\) | −48.7818 | −1.56307 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.73362 | 0.0875012 | ||||||||
\(977\) | 12.4405 | 0.398007 | 0.199004 | − | 0.979999i | \(-0.436229\pi\) | ||||
0.199004 | + | 0.979999i | \(0.436229\pi\) | |||||||
\(978\) | −32.7453 | −1.04708 | ||||||||
\(979\) | 40.4612 | 1.29315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.27573 | −0.200369 | ||||||||
\(982\) | 44.2073 | 1.41071 | ||||||||
\(983\) | 11.5633 | 0.368812 | 0.184406 | − | 0.982850i | \(-0.440964\pi\) | ||||
0.184406 | + | 0.982850i | \(0.440964\pi\) | |||||||
\(984\) | 16.6764 | 0.531625 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −54.7132 | −1.74242 | ||||||||
\(987\) | −3.65257 | −0.116263 | ||||||||
\(988\) | −94.3617 | −3.00205 | ||||||||
\(989\) | −25.1944 | −0.801136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5006 | −0.333562 | −0.166781 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166781 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(992\) | −33.1132 | −1.05134 | ||||||||
\(993\) | 16.0901 | 0.510603 | ||||||||
\(994\) | −99.6448 | −3.16054 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −33.2224 | −1.05269 | ||||||||
\(997\) | 31.0404 | 0.983059 | 0.491529 | − | 0.870861i | \(-0.336438\pi\) | ||||
0.491529 | + | 0.870861i | \(0.336438\pi\) | |||||||
\(998\) | 68.4438 | 2.16655 | ||||||||
\(999\) | −3.48931 | −0.110397 |
(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 | 3525.2.a.be.1.1 | yes | 8 | |
5.4 | even | 2 | 3525.2.a.bd.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.bd.1.8 | ✓ | 8 | 5.4 | even | 2 | ||
3525.2.a.be.1.1 | yes | 8 | 1.1 | even | 1 | trivial |