Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47225 | −1.74815 | −0.874073 | − | 0.485794i | \(-0.838530\pi\) | ||||
−0.874073 | + | 0.485794i | \(0.838530\pi\) | |||||||
\(3\) | −1.54593 | −0.892542 | −0.446271 | − | 0.894898i | \(-0.647248\pi\) | ||||
−0.446271 | + | 0.894898i | \(0.647248\pi\) | |||||||
\(4\) | 4.11203 | 2.05602 | ||||||||
\(5\) | 3.04029 | 1.35966 | 0.679830 | − | 0.733370i | \(-0.262054\pi\) | ||||
0.679830 | + | 0.733370i | \(0.262054\pi\) | |||||||
\(6\) | 3.82192 | 1.56029 | ||||||||
\(7\) | −2.57940 | −0.974923 | −0.487462 | − | 0.873144i | \(-0.662077\pi\) | ||||
−0.487462 | + | 0.873144i | \(0.662077\pi\) | |||||||
\(8\) | −5.22147 | −1.84607 | ||||||||
\(9\) | −0.610108 | −0.203369 | ||||||||
\(10\) | −7.51637 | −2.37688 | ||||||||
\(11\) | 0.679395 | 0.204845 | 0.102423 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102423 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(12\) | −6.35690 | −1.83508 | ||||||||
\(13\) | −3.89012 | −1.07892 | −0.539462 | − | 0.842010i | \(-0.681372\pi\) | ||||
−0.539462 | + | 0.842010i | \(0.681372\pi\) | |||||||
\(14\) | 6.37694 | 1.70431 | ||||||||
\(15\) | −4.70007 | −1.21355 | ||||||||
\(16\) | 4.68474 | 1.17118 | ||||||||
\(17\) | 0.0690897 | 0.0167567 | 0.00837836 | − | 0.999965i | \(-0.497333\pi\) | ||||
0.00837836 | + | 0.999965i | \(0.497333\pi\) | |||||||
\(18\) | 1.50834 | 0.355519 | ||||||||
\(19\) | −6.13331 | −1.40708 | −0.703539 | − | 0.710657i | \(-0.748398\pi\) | ||||
−0.703539 | + | 0.710657i | \(0.748398\pi\) | |||||||
\(20\) | 12.5018 | 2.79548 | ||||||||
\(21\) | 3.98757 | 0.870160 | ||||||||
\(22\) | −1.67964 | −0.358100 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 8.07202 | 1.64769 | ||||||||
\(25\) | 4.24337 | 0.848674 | ||||||||
\(26\) | 9.61735 | 1.88612 | ||||||||
\(27\) | 5.58097 | 1.07406 | ||||||||
\(28\) | −10.6066 | −2.00446 | ||||||||
\(29\) | 4.44649 | 0.825692 | 0.412846 | − | 0.910801i | \(-0.364535\pi\) | ||||
0.412846 | + | 0.910801i | \(0.364535\pi\) | |||||||
\(30\) | 11.6198 | 2.12147 | ||||||||
\(31\) | −10.6549 | −1.91368 | −0.956839 | − | 0.290620i | \(-0.906139\pi\) | ||||
−0.956839 | + | 0.290620i | \(0.906139\pi\) | |||||||
\(32\) | −1.13890 | −0.201332 | ||||||||
\(33\) | −1.05030 | −0.182833 | ||||||||
\(34\) | −0.170807 | −0.0292932 | ||||||||
\(35\) | −7.84214 | −1.32556 | ||||||||
\(36\) | −2.50878 | −0.418130 | ||||||||
\(37\) | −2.59587 | −0.426758 | −0.213379 | − | 0.976970i | \(-0.568447\pi\) | ||||
−0.213379 | + | 0.976970i | \(0.568447\pi\) | |||||||
\(38\) | 15.1631 | 2.45978 | ||||||||
\(39\) | 6.01384 | 0.962985 | ||||||||
\(40\) | −15.8748 | −2.51003 | ||||||||
\(41\) | 3.98215 | 0.621908 | 0.310954 | − | 0.950425i | \(-0.399352\pi\) | ||||
0.310954 | + | 0.950425i | \(0.399352\pi\) | |||||||
\(42\) | −9.85829 | −1.52117 | ||||||||
\(43\) | 4.63146 | 0.706290 | 0.353145 | − | 0.935569i | \(-0.385112\pi\) | ||||
0.353145 | + | 0.935569i | \(0.385112\pi\) | |||||||
\(44\) | 2.79370 | 0.421165 | ||||||||
\(45\) | −1.85491 | −0.276513 | ||||||||
\(46\) | 2.47225 | 0.364514 | ||||||||
\(47\) | 1.84738 | 0.269468 | 0.134734 | − | 0.990882i | \(-0.456982\pi\) | ||||
0.134734 | + | 0.990882i | \(0.456982\pi\) | |||||||
\(48\) | −7.24226 | −1.04533 | ||||||||
\(49\) | −0.346673 | −0.0495247 | ||||||||
\(50\) | −10.4907 | −1.48361 | ||||||||
\(51\) | −0.106808 | −0.0149561 | ||||||||
\(52\) | −15.9963 | −2.21829 | ||||||||
\(53\) | −0.186508 | −0.0256188 | −0.0128094 | − | 0.999918i | \(-0.504077\pi\) | ||||
−0.0128094 | + | 0.999918i | \(0.504077\pi\) | |||||||
\(54\) | −13.7976 | −1.87761 | ||||||||
\(55\) | 2.06556 | 0.278520 | ||||||||
\(56\) | 13.4683 | 1.79978 | ||||||||
\(57\) | 9.48166 | 1.25588 | ||||||||
\(58\) | −10.9928 | −1.44343 | ||||||||
\(59\) | −1.79713 | −0.233966 | −0.116983 | − | 0.993134i | \(-0.537322\pi\) | ||||
−0.116983 | + | 0.993134i | \(0.537322\pi\) | |||||||
\(60\) | −19.3268 | −2.49508 | ||||||||
\(61\) | −13.9350 | −1.78419 | −0.892094 | − | 0.451849i | \(-0.850765\pi\) | ||||
−0.892094 | + | 0.451849i | \(0.850765\pi\) | |||||||
\(62\) | 26.3416 | 3.34539 | ||||||||
\(63\) | 1.57371 | 0.198269 | ||||||||
\(64\) | −6.55382 | −0.819227 | ||||||||
\(65\) | −11.8271 | −1.46697 | ||||||||
\(66\) | 2.59660 | 0.319619 | ||||||||
\(67\) | 0.579508 | 0.0707982 | 0.0353991 | − | 0.999373i | \(-0.488730\pi\) | ||||
0.0353991 | + | 0.999373i | \(0.488730\pi\) | |||||||
\(68\) | 0.284099 | 0.0344521 | ||||||||
\(69\) | 1.54593 | 0.186108 | ||||||||
\(70\) | 19.3878 | 2.31728 | ||||||||
\(71\) | −11.4021 | −1.35318 | −0.676591 | − | 0.736359i | \(-0.736543\pi\) | ||||
−0.676591 | + | 0.736359i | \(0.736543\pi\) | |||||||
\(72\) | 3.18566 | 0.375434 | ||||||||
\(73\) | −0.353462 | −0.0413696 | −0.0206848 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206848 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(74\) | 6.41764 | 0.746035 | ||||||||
\(75\) | −6.55994 | −0.757477 | ||||||||
\(76\) | −25.2204 | −2.89297 | ||||||||
\(77\) | −1.75244 | −0.199709 | ||||||||
\(78\) | −14.8677 | −1.68344 | ||||||||
\(79\) | −8.28701 | −0.932361 | −0.466181 | − | 0.884690i | \(-0.654370\pi\) | ||||
−0.466181 | + | 0.884690i | \(0.654370\pi\) | |||||||
\(80\) | 14.2430 | 1.59241 | ||||||||
\(81\) | −6.79745 | −0.755272 | ||||||||
\(82\) | −9.84488 | −1.08719 | ||||||||
\(83\) | 1.38251 | 0.151750 | 0.0758749 | − | 0.997117i | \(-0.475825\pi\) | ||||
0.0758749 | + | 0.997117i | \(0.475825\pi\) | |||||||
\(84\) | 16.3970 | 1.78906 | ||||||||
\(85\) | 0.210053 | 0.0227834 | ||||||||
\(86\) | −11.4501 | −1.23470 | ||||||||
\(87\) | −6.87395 | −0.736964 | ||||||||
\(88\) | −3.54745 | −0.378159 | ||||||||
\(89\) | 4.90655 | 0.520093 | 0.260046 | − | 0.965596i | \(-0.416262\pi\) | ||||
0.260046 | + | 0.965596i | \(0.416262\pi\) | |||||||
\(90\) | 4.58579 | 0.483385 | ||||||||
\(91\) | 10.0342 | 1.05187 | ||||||||
\(92\) | −4.11203 | −0.428709 | ||||||||
\(93\) | 16.4717 | 1.70804 | ||||||||
\(94\) | −4.56719 | −0.471070 | ||||||||
\(95\) | −18.6471 | −1.91315 | ||||||||
\(96\) | 1.76066 | 0.179697 | ||||||||
\(97\) | −8.39976 | −0.852867 | −0.426433 | − | 0.904519i | \(-0.640230\pi\) | ||||
−0.426433 | + | 0.904519i | \(0.640230\pi\) | |||||||
\(98\) | 0.857062 | 0.0865764 | ||||||||
\(99\) | −0.414504 | −0.0416593 | ||||||||
\(100\) | 17.4489 | 1.74489 | ||||||||
\(101\) | 12.8871 | 1.28232 | 0.641159 | − | 0.767408i | \(-0.278454\pi\) | ||||
0.641159 | + | 0.767408i | \(0.278454\pi\) | |||||||
\(102\) | 0.264056 | 0.0261454 | ||||||||
\(103\) | −7.15738 | −0.705237 | −0.352619 | − | 0.935767i | \(-0.614709\pi\) | ||||
−0.352619 | + | 0.935767i | \(0.614709\pi\) | |||||||
\(104\) | 20.3121 | 1.99177 | ||||||||
\(105\) | 12.1234 | 1.18312 | ||||||||
\(106\) | 0.461094 | 0.0447854 | ||||||||
\(107\) | −3.21772 | −0.311069 | −0.155534 | − | 0.987830i | \(-0.549710\pi\) | ||||
−0.155534 | + | 0.987830i | \(0.549710\pi\) | |||||||
\(108\) | 22.9491 | 2.20828 | ||||||||
\(109\) | −5.47802 | −0.524700 | −0.262350 | − | 0.964973i | \(-0.584497\pi\) | ||||
−0.262350 | + | 0.964973i | \(0.584497\pi\) | |||||||
\(110\) | −5.10659 | −0.486894 | ||||||||
\(111\) | 4.01302 | 0.380899 | ||||||||
\(112\) | −12.0838 | −1.14181 | ||||||||
\(113\) | 15.2001 | 1.42991 | 0.714953 | − | 0.699173i | \(-0.246448\pi\) | ||||
0.714953 | + | 0.699173i | \(0.246448\pi\) | |||||||
\(114\) | −23.4410 | −2.19545 | ||||||||
\(115\) | −3.04029 | −0.283509 | ||||||||
\(116\) | 18.2841 | 1.69764 | ||||||||
\(117\) | 2.37339 | 0.219420 | ||||||||
\(118\) | 4.44296 | 0.409008 | ||||||||
\(119\) | −0.178210 | −0.0163365 | ||||||||
\(120\) | 24.5413 | 2.24030 | ||||||||
\(121\) | −10.5384 | −0.958038 | ||||||||
\(122\) | 34.4507 | 3.11902 | ||||||||
\(123\) | −6.15612 | −0.555079 | ||||||||
\(124\) | −43.8133 | −3.93455 | ||||||||
\(125\) | −2.30037 | −0.205752 | ||||||||
\(126\) | −3.89062 | −0.346604 | ||||||||
\(127\) | −3.33793 | −0.296194 | −0.148097 | − | 0.988973i | \(-0.547315\pi\) | ||||
−0.148097 | + | 0.988973i | \(0.547315\pi\) | |||||||
\(128\) | 18.4805 | 1.63346 | ||||||||
\(129\) | −7.15990 | −0.630394 | ||||||||
\(130\) | 29.2395 | 2.56448 | ||||||||
\(131\) | −17.7441 | −1.55031 | −0.775154 | − | 0.631772i | \(-0.782328\pi\) | ||||
−0.775154 | + | 0.631772i | \(0.782328\pi\) | |||||||
\(132\) | −4.31885 | −0.375908 | ||||||||
\(133\) | 15.8203 | 1.37179 | ||||||||
\(134\) | −1.43269 | −0.123766 | ||||||||
\(135\) | 16.9678 | 1.46035 | ||||||||
\(136\) | −0.360750 | −0.0309341 | ||||||||
\(137\) | 11.2773 | 0.963489 | 0.481744 | − | 0.876312i | \(-0.340003\pi\) | ||||
0.481744 | + | 0.876312i | \(0.340003\pi\) | |||||||
\(138\) | −3.82192 | −0.325344 | ||||||||
\(139\) | 3.12741 | 0.265264 | 0.132632 | − | 0.991165i | \(-0.457657\pi\) | ||||
0.132632 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(140\) | −32.2471 | −2.72538 | ||||||||
\(141\) | −2.85592 | −0.240512 | ||||||||
\(142\) | 28.1889 | 2.36556 | ||||||||
\(143\) | −2.64293 | −0.221013 | ||||||||
\(144\) | −2.85819 | −0.238183 | ||||||||
\(145\) | 13.5186 | 1.12266 | ||||||||
\(146\) | 0.873848 | 0.0723202 | ||||||||
\(147\) | 0.535931 | 0.0442028 | ||||||||
\(148\) | −10.6743 | −0.877421 | ||||||||
\(149\) | −10.0497 | −0.823300 | −0.411650 | − | 0.911342i | \(-0.635047\pi\) | ||||
−0.411650 | + | 0.911342i | \(0.635047\pi\) | |||||||
\(150\) | 16.2178 | 1.32418 | ||||||||
\(151\) | 13.3876 | 1.08947 | 0.544733 | − | 0.838609i | \(-0.316631\pi\) | ||||
0.544733 | + | 0.838609i | \(0.316631\pi\) | |||||||
\(152\) | 32.0249 | 2.59756 | ||||||||
\(153\) | −0.0421522 | −0.00340780 | ||||||||
\(154\) | 4.33246 | 0.349120 | ||||||||
\(155\) | −32.3940 | −2.60195 | ||||||||
\(156\) | 24.7291 | 1.97991 | ||||||||
\(157\) | 15.1877 | 1.21211 | 0.606055 | − | 0.795423i | \(-0.292751\pi\) | ||||
0.606055 | + | 0.795423i | \(0.292751\pi\) | |||||||
\(158\) | 20.4876 | 1.62990 | ||||||||
\(159\) | 0.288328 | 0.0228659 | ||||||||
\(160\) | −3.46260 | −0.273742 | ||||||||
\(161\) | 2.57940 | 0.203286 | ||||||||
\(162\) | 16.8050 | 1.32033 | ||||||||
\(163\) | −0.574585 | −0.0450049 | −0.0225025 | − | 0.999747i | \(-0.507163\pi\) | ||||
−0.0225025 | + | 0.999747i | \(0.507163\pi\) | |||||||
\(164\) | 16.3747 | 1.27865 | ||||||||
\(165\) | −3.19321 | −0.248591 | ||||||||
\(166\) | −3.41790 | −0.265281 | ||||||||
\(167\) | −5.09417 | −0.394199 | −0.197099 | − | 0.980383i | \(-0.563152\pi\) | ||||
−0.197099 | + | 0.980383i | \(0.563152\pi\) | |||||||
\(168\) | −20.8210 | −1.60638 | ||||||||
\(169\) | 2.13301 | 0.164078 | ||||||||
\(170\) | −0.519304 | −0.0398288 | ||||||||
\(171\) | 3.74198 | 0.286156 | ||||||||
\(172\) | 19.0447 | 1.45214 | ||||||||
\(173\) | 1.41115 | 0.107288 | 0.0536440 | − | 0.998560i | \(-0.482916\pi\) | ||||
0.0536440 | + | 0.998560i | \(0.482916\pi\) | |||||||
\(174\) | 16.9941 | 1.28832 | ||||||||
\(175\) | −10.9454 | −0.827392 | ||||||||
\(176\) | 3.18279 | 0.239912 | ||||||||
\(177\) | 2.77823 | 0.208825 | ||||||||
\(178\) | −12.1302 | −0.909198 | ||||||||
\(179\) | 24.8613 | 1.85822 | 0.929110 | − | 0.369804i | \(-0.120575\pi\) | ||||
0.929110 | + | 0.369804i | \(0.120575\pi\) | |||||||
\(180\) | −7.62743 | −0.568515 | ||||||||
\(181\) | 1.80062 | 0.133839 | 0.0669197 | − | 0.997758i | \(-0.478683\pi\) | ||||
0.0669197 | + | 0.997758i | \(0.478683\pi\) | |||||||
\(182\) | −24.8070 | −1.83882 | ||||||||
\(183\) | 21.5424 | 1.59246 | ||||||||
\(184\) | 5.22147 | 0.384932 | ||||||||
\(185\) | −7.89219 | −0.580245 | ||||||||
\(186\) | −40.7222 | −2.98590 | ||||||||
\(187\) | 0.0469392 | 0.00343254 | ||||||||
\(188\) | 7.59649 | 0.554031 | ||||||||
\(189\) | −14.3956 | −1.04712 | ||||||||
\(190\) | 46.1002 | 3.34446 | ||||||||
\(191\) | 6.39159 | 0.462479 | 0.231240 | − | 0.972897i | \(-0.425722\pi\) | ||||
0.231240 | + | 0.972897i | \(0.425722\pi\) | |||||||
\(192\) | 10.1317 | 0.731194 | ||||||||
\(193\) | 1.27887 | 0.0920553 | 0.0460276 | − | 0.998940i | \(-0.485344\pi\) | ||||
0.0460276 | + | 0.998940i | \(0.485344\pi\) | |||||||
\(194\) | 20.7663 | 1.49094 | ||||||||
\(195\) | 18.2838 | 1.30933 | ||||||||
\(196\) | −1.42553 | −0.101824 | ||||||||
\(197\) | −1.50570 | −0.107277 | −0.0536385 | − | 0.998560i | \(-0.517082\pi\) | ||||
−0.0536385 | + | 0.998560i | \(0.517082\pi\) | |||||||
\(198\) | 1.02476 | 0.0728265 | ||||||||
\(199\) | 12.5661 | 0.890784 | 0.445392 | − | 0.895336i | \(-0.353064\pi\) | ||||
0.445392 | + | 0.895336i | \(0.353064\pi\) | |||||||
\(200\) | −22.1566 | −1.56671 | ||||||||
\(201\) | −0.895878 | −0.0631904 | ||||||||
\(202\) | −31.8603 | −2.24168 | ||||||||
\(203\) | −11.4693 | −0.804986 | ||||||||
\(204\) | −0.439197 | −0.0307499 | ||||||||
\(205\) | 12.1069 | 0.845583 | ||||||||
\(206\) | 17.6948 | 1.23286 | ||||||||
\(207\) | 0.610108 | 0.0424054 | ||||||||
\(208\) | −18.2242 | −1.26362 | ||||||||
\(209\) | −4.16694 | −0.288234 | ||||||||
\(210\) | −29.9721 | −2.06827 | ||||||||
\(211\) | 0.479113 | 0.0329835 | 0.0164917 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164917 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(212\) | −0.766926 | −0.0526727 | ||||||||
\(213\) | 17.6268 | 1.20777 | ||||||||
\(214\) | 7.95502 | 0.543794 | ||||||||
\(215\) | 14.0810 | 0.960314 | ||||||||
\(216\) | −29.1409 | −1.98278 | ||||||||
\(217\) | 27.4833 | 1.86569 | ||||||||
\(218\) | 13.5431 | 0.917252 | ||||||||
\(219\) | 0.546427 | 0.0369241 | ||||||||
\(220\) | 8.49365 | 0.572642 | ||||||||
\(221\) | −0.268767 | −0.0180792 | ||||||||
\(222\) | −9.92120 | −0.665867 | ||||||||
\(223\) | 23.1372 | 1.54938 | 0.774691 | − | 0.632340i | \(-0.217905\pi\) | ||||
0.774691 | + | 0.632340i | \(0.217905\pi\) | |||||||
\(224\) | 2.93769 | 0.196283 | ||||||||
\(225\) | −2.58891 | −0.172594 | ||||||||
\(226\) | −37.5785 | −2.49968 | ||||||||
\(227\) | 1.69490 | 0.112495 | 0.0562473 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562473 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(228\) | 38.9889 | 2.58210 | ||||||||
\(229\) | −13.8097 | −0.912572 | −0.456286 | − | 0.889833i | \(-0.650821\pi\) | ||||
−0.456286 | + | 0.889833i | \(0.650821\pi\) | |||||||
\(230\) | 7.51637 | 0.495615 | ||||||||
\(231\) | 2.70914 | 0.178248 | ||||||||
\(232\) | −23.2172 | −1.52428 | ||||||||
\(233\) | 24.3195 | 1.59322 | 0.796611 | − | 0.604493i | \(-0.206624\pi\) | ||||
0.796611 | + | 0.604493i | \(0.206624\pi\) | |||||||
\(234\) | −5.86762 | −0.383578 | ||||||||
\(235\) | 5.61658 | 0.366385 | ||||||||
\(236\) | −7.38986 | −0.481039 | ||||||||
\(237\) | 12.8111 | 0.832171 | ||||||||
\(238\) | 0.440581 | 0.0285586 | ||||||||
\(239\) | −19.7790 | −1.27940 | −0.639698 | − | 0.768626i | \(-0.720941\pi\) | ||||
−0.639698 | + | 0.768626i | \(0.720941\pi\) | |||||||
\(240\) | −22.0186 | −1.42129 | ||||||||
\(241\) | 4.76696 | 0.307067 | 0.153533 | − | 0.988143i | \(-0.450935\pi\) | ||||
0.153533 | + | 0.988143i | \(0.450935\pi\) | |||||||
\(242\) | 26.0536 | 1.67479 | ||||||||
\(243\) | −6.23454 | −0.399946 | ||||||||
\(244\) | −57.3010 | −3.66832 | ||||||||
\(245\) | −1.05399 | −0.0673367 | ||||||||
\(246\) | 15.2195 | 0.970359 | ||||||||
\(247\) | 23.8593 | 1.51813 | ||||||||
\(248\) | 55.6343 | 3.53278 | ||||||||
\(249\) | −2.13725 | −0.135443 | ||||||||
\(250\) | 5.68710 | 0.359684 | ||||||||
\(251\) | −11.4296 | −0.721430 | −0.360715 | − | 0.932676i | \(-0.617467\pi\) | ||||
−0.360715 | + | 0.932676i | \(0.617467\pi\) | |||||||
\(252\) | 6.47116 | 0.407645 | ||||||||
\(253\) | −0.679395 | −0.0427132 | ||||||||
\(254\) | 8.25221 | 0.517790 | ||||||||
\(255\) | −0.324727 | −0.0203352 | ||||||||
\(256\) | −32.5808 | −2.03630 | ||||||||
\(257\) | 2.45900 | 0.153388 | 0.0766940 | − | 0.997055i | \(-0.475564\pi\) | ||||
0.0766940 | + | 0.997055i | \(0.475564\pi\) | |||||||
\(258\) | 17.7011 | 1.10202 | ||||||||
\(259\) | 6.69579 | 0.416056 | ||||||||
\(260\) | −48.6334 | −3.01611 | ||||||||
\(261\) | −2.71284 | −0.167920 | ||||||||
\(262\) | 43.8679 | 2.71017 | ||||||||
\(263\) | −16.4584 | −1.01487 | −0.507435 | − | 0.861690i | \(-0.669406\pi\) | ||||
−0.507435 | + | 0.861690i | \(0.669406\pi\) | |||||||
\(264\) | 5.48409 | 0.337523 | ||||||||
\(265\) | −0.567038 | −0.0348329 | ||||||||
\(266\) | −39.1117 | −2.39810 | ||||||||
\(267\) | −7.58516 | −0.464205 | ||||||||
\(268\) | 2.38296 | 0.145562 | ||||||||
\(269\) | 6.84890 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(270\) | −41.9486 | −2.55291 | ||||||||
\(271\) | −23.1940 | −1.40894 | −0.704468 | − | 0.709736i | \(-0.748814\pi\) | ||||
−0.704468 | + | 0.709736i | \(0.748814\pi\) | |||||||
\(272\) | 0.323667 | 0.0196252 | ||||||||
\(273\) | −15.5121 | −0.938837 | ||||||||
\(274\) | −27.8804 | −1.68432 | ||||||||
\(275\) | 2.88293 | 0.173847 | ||||||||
\(276\) | 6.35690 | 0.382641 | ||||||||
\(277\) | 0.652386 | 0.0391981 | 0.0195990 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0195990 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(278\) | −7.73175 | −0.463719 | ||||||||
\(279\) | 6.50064 | 0.389183 | ||||||||
\(280\) | 40.9475 | 2.44708 | ||||||||
\(281\) | 5.89657 | 0.351760 | 0.175880 | − | 0.984412i | \(-0.443723\pi\) | ||||
0.175880 | + | 0.984412i | \(0.443723\pi\) | |||||||
\(282\) | 7.06055 | 0.420449 | ||||||||
\(283\) | −22.5163 | −1.33846 | −0.669228 | − | 0.743057i | \(-0.733375\pi\) | ||||
−0.669228 | + | 0.743057i | \(0.733375\pi\) | |||||||
\(284\) | −46.8858 | −2.78216 | ||||||||
\(285\) | 28.8270 | 1.70756 | ||||||||
\(286\) | 6.53398 | 0.386363 | ||||||||
\(287\) | −10.2716 | −0.606312 | ||||||||
\(288\) | 0.694854 | 0.0409447 | ||||||||
\(289\) | −16.9952 | −0.999719 | ||||||||
\(290\) | −33.4214 | −1.96257 | ||||||||
\(291\) | 12.9854 | 0.761219 | ||||||||
\(292\) | −1.45345 | −0.0850566 | ||||||||
\(293\) | −1.41555 | −0.0826972 | −0.0413486 | − | 0.999145i | \(-0.513165\pi\) | ||||
−0.0413486 | + | 0.999145i | \(0.513165\pi\) | |||||||
\(294\) | −1.32496 | −0.0772730 | ||||||||
\(295\) | −5.46380 | −0.318115 | ||||||||
\(296\) | 13.5542 | 0.787825 | ||||||||
\(297\) | 3.79168 | 0.220016 | ||||||||
\(298\) | 24.8453 | 1.43925 | ||||||||
\(299\) | 3.89012 | 0.224971 | ||||||||
\(300\) | −26.9747 | −1.55738 | ||||||||
\(301\) | −11.9464 | −0.688579 | ||||||||
\(302\) | −33.0975 | −1.90455 | ||||||||
\(303\) | −19.9226 | −1.14452 | ||||||||
\(304\) | −28.7329 | −1.64795 | ||||||||
\(305\) | −42.3663 | −2.42589 | ||||||||
\(306\) | 0.104211 | 0.00595734 | ||||||||
\(307\) | −11.1987 | −0.639143 | −0.319571 | − | 0.947562i | \(-0.603539\pi\) | ||||
−0.319571 | + | 0.947562i | \(0.603539\pi\) | |||||||
\(308\) | −7.20607 | −0.410604 | ||||||||
\(309\) | 11.0648 | 0.629454 | ||||||||
\(310\) | 80.0862 | 4.54859 | ||||||||
\(311\) | −17.3211 | −0.982190 | −0.491095 | − | 0.871106i | \(-0.663403\pi\) | ||||
−0.491095 | + | 0.871106i | \(0.663403\pi\) | |||||||
\(312\) | −31.4011 | −1.77774 | ||||||||
\(313\) | −8.69105 | −0.491247 | −0.245624 | − | 0.969365i | \(-0.578993\pi\) | ||||
−0.245624 | + | 0.969365i | \(0.578993\pi\) | |||||||
\(314\) | −37.5478 | −2.11895 | ||||||||
\(315\) | 4.78455 | 0.269579 | ||||||||
\(316\) | −34.0764 | −1.91695 | ||||||||
\(317\) | 22.6414 | 1.27167 | 0.635835 | − | 0.771825i | \(-0.280656\pi\) | ||||
0.635835 | + | 0.771825i | \(0.280656\pi\) | |||||||
\(318\) | −0.712818 | −0.0399729 | ||||||||
\(319\) | 3.02092 | 0.169139 | ||||||||
\(320\) | −19.9255 | −1.11387 | ||||||||
\(321\) | 4.97436 | 0.277642 | ||||||||
\(322\) | −6.37694 | −0.355373 | ||||||||
\(323\) | −0.423749 | −0.0235780 | ||||||||
\(324\) | −27.9513 | −1.55285 | ||||||||
\(325\) | −16.5072 | −0.915655 | ||||||||
\(326\) | 1.42052 | 0.0786752 | ||||||||
\(327\) | 8.46863 | 0.468316 | ||||||||
\(328\) | −20.7927 | −1.14808 | ||||||||
\(329\) | −4.76514 | −0.262711 | ||||||||
\(330\) | 7.89441 | 0.434573 | ||||||||
\(331\) | 32.6386 | 1.79398 | 0.896990 | − | 0.442051i | \(-0.145749\pi\) | ||||
0.896990 | + | 0.442051i | \(0.145749\pi\) | |||||||
\(332\) | 5.68491 | 0.312000 | ||||||||
\(333\) | 1.58376 | 0.0867894 | ||||||||
\(334\) | 12.5941 | 0.689117 | ||||||||
\(335\) | 1.76187 | 0.0962615 | ||||||||
\(336\) | 18.6807 | 1.01912 | ||||||||
\(337\) | 2.59253 | 0.141224 | 0.0706121 | − | 0.997504i | \(-0.477505\pi\) | ||||
0.0706121 | + | 0.997504i | \(0.477505\pi\) | |||||||
\(338\) | −5.27335 | −0.286832 | ||||||||
\(339\) | −23.4983 | −1.27625 | ||||||||
\(340\) | 0.863744 | 0.0468431 | ||||||||
\(341\) | −7.23889 | −0.392008 | ||||||||
\(342\) | −9.25112 | −0.500243 | ||||||||
\(343\) | 18.9500 | 1.02321 | ||||||||
\(344\) | −24.1830 | −1.30386 | ||||||||
\(345\) | 4.70007 | 0.253043 | ||||||||
\(346\) | −3.48872 | −0.187555 | ||||||||
\(347\) | −31.8239 | −1.70840 | −0.854198 | − | 0.519947i | \(-0.825952\pi\) | ||||
−0.854198 | + | 0.519947i | \(0.825952\pi\) | |||||||
\(348\) | −28.2659 | −1.51521 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 27.0597 | 1.44640 | ||||||||
\(351\) | −21.7106 | −1.15883 | ||||||||
\(352\) | −0.773766 | −0.0412419 | ||||||||
\(353\) | 23.1930 | 1.23444 | 0.617219 | − | 0.786792i | \(-0.288259\pi\) | ||||
0.617219 | + | 0.786792i | \(0.288259\pi\) | |||||||
\(354\) | −6.86849 | −0.365056 | ||||||||
\(355\) | −34.6657 | −1.83987 | ||||||||
\(356\) | 20.1759 | 1.06932 | ||||||||
\(357\) | 0.275500 | 0.0145810 | ||||||||
\(358\) | −61.4634 | −3.24844 | ||||||||
\(359\) | 7.50850 | 0.396284 | 0.198142 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198142 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(360\) | 9.68534 | 0.510462 | ||||||||
\(361\) | 18.6175 | 0.979869 | ||||||||
\(362\) | −4.45160 | −0.233971 | ||||||||
\(363\) | 16.2916 | 0.855089 | ||||||||
\(364\) | 41.2609 | 2.16266 | ||||||||
\(365\) | −1.07463 | −0.0562486 | ||||||||
\(366\) | −53.2583 | −2.78386 | ||||||||
\(367\) | 6.90912 | 0.360653 | 0.180327 | − | 0.983607i | \(-0.442285\pi\) | ||||
0.180327 | + | 0.983607i | \(0.442285\pi\) | |||||||
\(368\) | −4.68474 | −0.244209 | ||||||||
\(369\) | −2.42954 | −0.126477 | ||||||||
\(370\) | 19.5115 | 1.01435 | ||||||||
\(371\) | 0.481079 | 0.0249764 | ||||||||
\(372\) | 67.7322 | 3.51175 | ||||||||
\(373\) | 10.4648 | 0.541846 | 0.270923 | − | 0.962601i | \(-0.412671\pi\) | ||||
0.270923 | + | 0.962601i | \(0.412671\pi\) | |||||||
\(374\) | −0.116046 | −0.00600058 | ||||||||
\(375\) | 3.55621 | 0.183642 | ||||||||
\(376\) | −9.64605 | −0.497457 | ||||||||
\(377\) | −17.2974 | −0.890859 | ||||||||
\(378\) | 35.5895 | 1.83052 | ||||||||
\(379\) | −16.5540 | −0.850323 | −0.425161 | − | 0.905118i | \(-0.639783\pi\) | ||||
−0.425161 | + | 0.905118i | \(0.639783\pi\) | |||||||
\(380\) | −76.6773 | −3.93346 | ||||||||
\(381\) | 5.16020 | 0.264365 | ||||||||
\(382\) | −15.8016 | −0.808481 | ||||||||
\(383\) | 24.6934 | 1.26177 | 0.630887 | − | 0.775874i | \(-0.282691\pi\) | ||||
0.630887 | + | 0.775874i | \(0.282691\pi\) | |||||||
\(384\) | −28.5695 | −1.45793 | ||||||||
\(385\) | −5.32792 | −0.271536 | ||||||||
\(386\) | −3.16170 | −0.160926 | ||||||||
\(387\) | −2.82569 | −0.143638 | ||||||||
\(388\) | −34.5401 | −1.75351 | ||||||||
\(389\) | 14.9837 | 0.759706 | 0.379853 | − | 0.925047i | \(-0.375975\pi\) | ||||
0.379853 | + | 0.925047i | \(0.375975\pi\) | |||||||
\(390\) | −45.2022 | −2.28890 | ||||||||
\(391\) | −0.0690897 | −0.00349402 | ||||||||
\(392\) | 1.81014 | 0.0914260 | ||||||||
\(393\) | 27.4311 | 1.38371 | ||||||||
\(394\) | 3.72248 | 0.187536 | ||||||||
\(395\) | −25.1949 | −1.26769 | ||||||||
\(396\) | −1.70445 | −0.0856521 | ||||||||
\(397\) | −3.60294 | −0.180827 | −0.0904133 | − | 0.995904i | \(-0.528819\pi\) | ||||
−0.0904133 | + | 0.995904i | \(0.528819\pi\) | |||||||
\(398\) | −31.0665 | −1.55722 | ||||||||
\(399\) | −24.4570 | −1.22438 | ||||||||
\(400\) | 19.8791 | 0.993954 | ||||||||
\(401\) | −0.636892 | −0.0318049 | −0.0159024 | − | 0.999874i | \(-0.505062\pi\) | ||||
−0.0159024 | + | 0.999874i | \(0.505062\pi\) | |||||||
\(402\) | 2.21484 | 0.110466 | ||||||||
\(403\) | 41.4488 | 2.06471 | ||||||||
\(404\) | 52.9923 | 2.63647 | ||||||||
\(405\) | −20.6662 | −1.02691 | ||||||||
\(406\) | 28.3550 | 1.40723 | ||||||||
\(407\) | −1.76362 | −0.0874194 | ||||||||
\(408\) | 0.557694 | 0.0276099 | ||||||||
\(409\) | 13.4174 | 0.663449 | 0.331724 | − | 0.943376i | \(-0.392370\pi\) | ||||
0.331724 | + | 0.943376i | \(0.392370\pi\) | |||||||
\(410\) | −29.9313 | −1.47820 | ||||||||
\(411\) | −17.4340 | −0.859954 | ||||||||
\(412\) | −29.4314 | −1.44998 | ||||||||
\(413\) | 4.63553 | 0.228099 | ||||||||
\(414\) | −1.50834 | −0.0741309 | ||||||||
\(415\) | 4.20322 | 0.206328 | ||||||||
\(416\) | 4.43047 | 0.217222 | ||||||||
\(417\) | −4.83475 | −0.236759 | ||||||||
\(418\) | 10.3017 | 0.503874 | ||||||||
\(419\) | 21.7682 | 1.06345 | 0.531723 | − | 0.846918i | \(-0.321545\pi\) | ||||
0.531723 | + | 0.846918i | \(0.321545\pi\) | |||||||
\(420\) | 49.8517 | 2.43252 | ||||||||
\(421\) | −3.99597 | −0.194752 | −0.0973759 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973759 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(422\) | −1.18449 | −0.0576600 | ||||||||
\(423\) | −1.12710 | −0.0548015 | ||||||||
\(424\) | 0.973846 | 0.0472941 | ||||||||
\(425\) | 0.293173 | 0.0142210 | ||||||||
\(426\) | −43.5780 | −2.11136 | ||||||||
\(427\) | 35.9439 | 1.73945 | ||||||||
\(428\) | −13.2314 | −0.639562 | ||||||||
\(429\) | 4.08578 | 0.197263 | ||||||||
\(430\) | −34.8117 | −1.67877 | ||||||||
\(431\) | 4.74019 | 0.228327 | 0.114163 | − | 0.993462i | \(-0.463581\pi\) | ||||
0.114163 | + | 0.993462i | \(0.463581\pi\) | |||||||
\(432\) | 26.1454 | 1.25792 | ||||||||
\(433\) | −31.4135 | −1.50964 | −0.754818 | − | 0.655934i | \(-0.772275\pi\) | ||||
−0.754818 | + | 0.655934i | \(0.772275\pi\) | |||||||
\(434\) | −67.9457 | −3.26150 | ||||||||
\(435\) | −20.8988 | −1.00202 | ||||||||
\(436\) | −22.5258 | −1.07879 | ||||||||
\(437\) | 6.13331 | 0.293396 | ||||||||
\(438\) | −1.35091 | −0.0645488 | ||||||||
\(439\) | −22.3705 | −1.06768 | −0.533842 | − | 0.845584i | \(-0.679252\pi\) | ||||
−0.533842 | + | 0.845584i | \(0.679252\pi\) | |||||||
\(440\) | −10.7853 | −0.514167 | ||||||||
\(441\) | 0.211508 | 0.0100718 | ||||||||
\(442\) | 0.664460 | 0.0316051 | ||||||||
\(443\) | −29.2151 | −1.38805 | −0.694026 | − | 0.719950i | \(-0.744165\pi\) | ||||
−0.694026 | + | 0.719950i | \(0.744165\pi\) | |||||||
\(444\) | 16.5017 | 0.783135 | ||||||||
\(445\) | 14.9173 | 0.707149 | ||||||||
\(446\) | −57.2010 | −2.70855 | ||||||||
\(447\) | 15.5360 | 0.734830 | ||||||||
\(448\) | 16.9049 | 0.798683 | ||||||||
\(449\) | 0.269793 | 0.0127323 | 0.00636617 | − | 0.999980i | \(-0.497974\pi\) | ||||
0.00636617 | + | 0.999980i | \(0.497974\pi\) | |||||||
\(450\) | 6.40045 | 0.301720 | ||||||||
\(451\) | 2.70546 | 0.127395 | ||||||||
\(452\) | 62.5033 | 2.93991 | ||||||||
\(453\) | −20.6962 | −0.972395 | ||||||||
\(454\) | −4.19023 | −0.196657 | ||||||||
\(455\) | 30.5068 | 1.43018 | ||||||||
\(456\) | −49.5082 | −2.31843 | ||||||||
\(457\) | −16.7244 | −0.782336 | −0.391168 | − | 0.920319i | \(-0.627929\pi\) | ||||
−0.391168 | + | 0.920319i | \(0.627929\pi\) | |||||||
\(458\) | 34.1411 | 1.59531 | ||||||||
\(459\) | 0.385587 | 0.0179977 | ||||||||
\(460\) | −12.5018 | −0.582898 | ||||||||
\(461\) | 9.73918 | 0.453599 | 0.226800 | − | 0.973941i | \(-0.427174\pi\) | ||||
0.226800 | + | 0.973941i | \(0.427174\pi\) | |||||||
\(462\) | −6.69767 | −0.311604 | ||||||||
\(463\) | 4.90615 | 0.228008 | 0.114004 | − | 0.993480i | \(-0.463632\pi\) | ||||
0.114004 | + | 0.993480i | \(0.463632\pi\) | |||||||
\(464\) | 20.8306 | 0.967037 | ||||||||
\(465\) | 50.0788 | 2.32235 | ||||||||
\(466\) | −60.1238 | −2.78518 | ||||||||
\(467\) | −2.11896 | −0.0980537 | −0.0490268 | − | 0.998797i | \(-0.515612\pi\) | ||||
−0.0490268 | + | 0.998797i | \(0.515612\pi\) | |||||||
\(468\) | 9.75946 | 0.451131 | ||||||||
\(469\) | −1.49479 | −0.0690228 | ||||||||
\(470\) | −13.8856 | −0.640495 | ||||||||
\(471\) | −23.4791 | −1.08186 | ||||||||
\(472\) | 9.38367 | 0.431918 | ||||||||
\(473\) | 3.14659 | 0.144680 | ||||||||
\(474\) | −31.6723 | −1.45476 | ||||||||
\(475\) | −26.0259 | −1.19415 | ||||||||
\(476\) | −0.732806 | −0.0335881 | ||||||||
\(477\) | 0.113790 | 0.00521008 | ||||||||
\(478\) | 48.8987 | 2.23657 | ||||||||
\(479\) | −4.18487 | −0.191211 | −0.0956057 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956057 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(480\) | 5.35293 | 0.244327 | ||||||||
\(481\) | 10.0982 | 0.460439 | ||||||||
\(482\) | −11.7851 | −0.536798 | ||||||||
\(483\) | −3.98757 | −0.181441 | ||||||||
\(484\) | −43.3343 | −1.96974 | ||||||||
\(485\) | −25.5377 | −1.15961 | ||||||||
\(486\) | 15.4133 | 0.699164 | ||||||||
\(487\) | 17.8966 | 0.810973 | 0.405487 | − | 0.914101i | \(-0.367102\pi\) | ||||
0.405487 | + | 0.914101i | \(0.367102\pi\) | |||||||
\(488\) | 72.7610 | 3.29374 | ||||||||
\(489\) | 0.888266 | 0.0401688 | ||||||||
\(490\) | 2.60572 | 0.117714 | ||||||||
\(491\) | −2.31772 | −0.104597 | −0.0522987 | − | 0.998631i | \(-0.516655\pi\) | ||||
−0.0522987 | + | 0.998631i | \(0.516655\pi\) | |||||||
\(492\) | −25.3142 | −1.14125 | ||||||||
\(493\) | 0.307207 | 0.0138359 | ||||||||
\(494\) | −58.9862 | −2.65391 | ||||||||
\(495\) | −1.26021 | −0.0566424 | ||||||||
\(496\) | −49.9154 | −2.24127 | ||||||||
\(497\) | 29.4107 | 1.31925 | ||||||||
\(498\) | 5.28383 | 0.236774 | ||||||||
\(499\) | −6.34103 | −0.283864 | −0.141932 | − | 0.989876i | \(-0.545331\pi\) | ||||
−0.141932 | + | 0.989876i | \(0.545331\pi\) | |||||||
\(500\) | −9.45920 | −0.423028 | ||||||||
\(501\) | 7.87522 | 0.351839 | ||||||||
\(502\) | 28.2568 | 1.26116 | ||||||||
\(503\) | 15.7946 | 0.704247 | 0.352123 | − | 0.935954i | \(-0.385460\pi\) | ||||
0.352123 | + | 0.935954i | \(0.385460\pi\) | |||||||
\(504\) | −8.21711 | −0.366019 | ||||||||
\(505\) | 39.1807 | 1.74352 | ||||||||
\(506\) | 1.67964 | 0.0746690 | ||||||||
\(507\) | −3.29748 | −0.146446 | ||||||||
\(508\) | −13.7257 | −0.608979 | ||||||||
\(509\) | 35.4472 | 1.57117 | 0.785584 | − | 0.618755i | \(-0.212362\pi\) | ||||
0.785584 | + | 0.618755i | \(0.212362\pi\) | |||||||
\(510\) | 0.802806 | 0.0355488 | ||||||||
\(511\) | 0.911722 | 0.0403322 | ||||||||
\(512\) | 43.5870 | 1.92629 | ||||||||
\(513\) | −34.2298 | −1.51128 | ||||||||
\(514\) | −6.07926 | −0.268145 | ||||||||
\(515\) | −21.7605 | −0.958883 | ||||||||
\(516\) | −29.4417 | −1.29610 | ||||||||
\(517\) | 1.25510 | 0.0551993 | ||||||||
\(518\) | −16.5537 | −0.727327 | ||||||||
\(519\) | −2.18154 | −0.0957589 | ||||||||
\(520\) | 61.7548 | 2.70813 | ||||||||
\(521\) | 24.9491 | 1.09304 | 0.546520 | − | 0.837446i | \(-0.315952\pi\) | ||||
0.546520 | + | 0.837446i | \(0.315952\pi\) | |||||||
\(522\) | 6.70681 | 0.293549 | ||||||||
\(523\) | −20.8717 | −0.912657 | −0.456329 | − | 0.889811i | \(-0.650836\pi\) | ||||
−0.456329 | + | 0.889811i | \(0.650836\pi\) | |||||||
\(524\) | −72.9642 | −3.18746 | ||||||||
\(525\) | 16.9208 | 0.738482 | ||||||||
\(526\) | 40.6894 | 1.77414 | ||||||||
\(527\) | −0.736144 | −0.0320670 | ||||||||
\(528\) | −4.92036 | −0.214131 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 1.40186 | 0.0608930 | ||||||||
\(531\) | 1.09644 | 0.0475816 | ||||||||
\(532\) | 65.0535 | 2.82043 | ||||||||
\(533\) | −15.4910 | −0.670991 | ||||||||
\(534\) | 18.7524 | 0.811497 | ||||||||
\(535\) | −9.78281 | −0.422948 | ||||||||
\(536\) | −3.02589 | −0.130698 | ||||||||
\(537\) | −38.4337 | −1.65854 | ||||||||
\(538\) | −16.9322 | −0.729999 | ||||||||
\(539\) | −0.235528 | −0.0101449 | ||||||||
\(540\) | 69.7720 | 3.00251 | ||||||||
\(541\) | 27.8464 | 1.19721 | 0.598604 | − | 0.801045i | \(-0.295722\pi\) | ||||
0.598604 | + | 0.801045i | \(0.295722\pi\) | |||||||
\(542\) | 57.3414 | 2.46303 | ||||||||
\(543\) | −2.78363 | −0.119457 | ||||||||
\(544\) | −0.0786865 | −0.00337366 | ||||||||
\(545\) | −16.6548 | −0.713413 | ||||||||
\(546\) | 38.3499 | 1.64122 | ||||||||
\(547\) | −30.9979 | −1.32537 | −0.662687 | − | 0.748896i | \(-0.730584\pi\) | ||||
−0.662687 | + | 0.748896i | \(0.730584\pi\) | |||||||
\(548\) | 46.3728 | 1.98095 | ||||||||
\(549\) | 8.50183 | 0.362849 | ||||||||
\(550\) | −7.12732 | −0.303910 | ||||||||
\(551\) | −27.2717 | −1.16181 | ||||||||
\(552\) | −8.07202 | −0.343568 | ||||||||
\(553\) | 21.3755 | 0.908980 | ||||||||
\(554\) | −1.61286 | −0.0685240 | ||||||||
\(555\) | 12.2008 | 0.517893 | ||||||||
\(556\) | 12.8600 | 0.545386 | ||||||||
\(557\) | 30.9356 | 1.31078 | 0.655392 | − | 0.755289i | \(-0.272504\pi\) | ||||
0.655392 | + | 0.755289i | \(0.272504\pi\) | |||||||
\(558\) | −16.0712 | −0.680349 | ||||||||
\(559\) | −18.0169 | −0.762034 | ||||||||
\(560\) | −36.7384 | −1.55248 | ||||||||
\(561\) | −0.0725647 | −0.00306368 | ||||||||
\(562\) | −14.5778 | −0.614928 | ||||||||
\(563\) | 22.5371 | 0.949826 | 0.474913 | − | 0.880033i | \(-0.342480\pi\) | ||||
0.474913 | + | 0.880033i | \(0.342480\pi\) | |||||||
\(564\) | −11.7436 | −0.494496 | ||||||||
\(565\) | 46.2128 | 1.94419 | ||||||||
\(566\) | 55.6660 | 2.33982 | ||||||||
\(567\) | 17.5334 | 0.736332 | ||||||||
\(568\) | 59.5358 | 2.49807 | ||||||||
\(569\) | −25.1604 | −1.05478 | −0.527390 | − | 0.849624i | \(-0.676829\pi\) | ||||
−0.527390 | + | 0.849624i | \(0.676829\pi\) | |||||||
\(570\) | −71.2676 | −2.98507 | ||||||||
\(571\) | −13.3839 | −0.560099 | −0.280049 | − | 0.959986i | \(-0.590351\pi\) | ||||
−0.280049 | + | 0.959986i | \(0.590351\pi\) | |||||||
\(572\) | −10.8678 | −0.454406 | ||||||||
\(573\) | −9.88094 | −0.412782 | ||||||||
\(574\) | 25.3939 | 1.05992 | ||||||||
\(575\) | −4.24337 | −0.176961 | ||||||||
\(576\) | 3.99853 | 0.166606 | ||||||||
\(577\) | −11.4045 | −0.474776 | −0.237388 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237388 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(578\) | 42.0165 | 1.74766 | ||||||||
\(579\) | −1.97704 | −0.0821632 | ||||||||
\(580\) | 55.5890 | 2.30821 | ||||||||
\(581\) | −3.56604 | −0.147944 | ||||||||
\(582\) | −32.1032 | −1.33072 | ||||||||
\(583\) | −0.126713 | −0.00524790 | ||||||||
\(584\) | 1.84559 | 0.0763712 | ||||||||
\(585\) | 7.21580 | 0.298337 | ||||||||
\(586\) | 3.49959 | 0.144567 | ||||||||
\(587\) | −22.0438 | −0.909847 | −0.454923 | − | 0.890531i | \(-0.650333\pi\) | ||||
−0.454923 | + | 0.890531i | \(0.650333\pi\) | |||||||
\(588\) | 2.20376 | 0.0908817 | ||||||||
\(589\) | 65.3498 | 2.69269 | ||||||||
\(590\) | 13.5079 | 0.556111 | ||||||||
\(591\) | 2.32771 | 0.0957492 | ||||||||
\(592\) | −12.1609 | −0.499812 | ||||||||
\(593\) | 12.0502 | 0.494843 | 0.247421 | − | 0.968908i | \(-0.420417\pi\) | ||||
0.247421 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(594\) | −9.37400 | −0.384620 | ||||||||
\(595\) | −0.541811 | −0.0222121 | ||||||||
\(596\) | −41.3245 | −1.69272 | ||||||||
\(597\) | −19.4262 | −0.795062 | ||||||||
\(598\) | −9.61735 | −0.393283 | ||||||||
\(599\) | −33.3908 | −1.36431 | −0.682156 | − | 0.731207i | \(-0.738957\pi\) | ||||
−0.682156 | + | 0.731207i | \(0.738957\pi\) | |||||||
\(600\) | 34.2526 | 1.39836 | ||||||||
\(601\) | 36.2767 | 1.47976 | 0.739878 | − | 0.672741i | \(-0.234883\pi\) | ||||
0.739878 | + | 0.672741i | \(0.234883\pi\) | |||||||
\(602\) | 29.5345 | 1.20374 | ||||||||
\(603\) | −0.353562 | −0.0143982 | ||||||||
\(604\) | 55.0502 | 2.23996 | ||||||||
\(605\) | −32.0399 | −1.30261 | ||||||||
\(606\) | 49.2537 | 2.00079 | ||||||||
\(607\) | 15.6845 | 0.636613 | 0.318307 | − | 0.947988i | \(-0.396886\pi\) | ||||
0.318307 | + | 0.947988i | \(0.396886\pi\) | |||||||
\(608\) | 6.98525 | 0.283289 | ||||||||
\(609\) | 17.7307 | 0.718484 | ||||||||
\(610\) | 104.740 | 4.24081 | ||||||||
\(611\) | −7.18653 | −0.290736 | ||||||||
\(612\) | −0.173331 | −0.00700649 | ||||||||
\(613\) | −11.7294 | −0.473747 | −0.236874 | − | 0.971540i | \(-0.576123\pi\) | ||||
−0.236874 | + | 0.971540i | \(0.576123\pi\) | |||||||
\(614\) | 27.6860 | 1.11731 | ||||||||
\(615\) | −18.7164 | −0.754718 | ||||||||
\(616\) | 9.15030 | 0.368676 | ||||||||
\(617\) | 15.6739 | 0.631007 | 0.315504 | − | 0.948924i | \(-0.397827\pi\) | ||||
0.315504 | + | 0.948924i | \(0.397827\pi\) | |||||||
\(618\) | −27.3549 | −1.10038 | ||||||||
\(619\) | 17.5260 | 0.704429 | 0.352214 | − | 0.935919i | \(-0.385429\pi\) | ||||
0.352214 | + | 0.935919i | \(0.385429\pi\) | |||||||
\(620\) | −133.205 | −5.34965 | ||||||||
\(621\) | −5.58097 | −0.223956 | ||||||||
\(622\) | 42.8222 | 1.71701 | ||||||||
\(623\) | −12.6560 | −0.507051 | ||||||||
\(624\) | 28.1733 | 1.12783 | ||||||||
\(625\) | −28.2107 | −1.12843 | ||||||||
\(626\) | 21.4865 | 0.858772 | ||||||||
\(627\) | 6.44179 | 0.257260 | ||||||||
\(628\) | 62.4523 | 2.49212 | ||||||||
\(629\) | −0.179348 | −0.00715106 | ||||||||
\(630\) | −11.8286 | −0.471263 | ||||||||
\(631\) | 23.5801 | 0.938708 | 0.469354 | − | 0.883010i | \(-0.344487\pi\) | ||||
0.469354 | + | 0.883010i | \(0.344487\pi\) | |||||||
\(632\) | 43.2704 | 1.72120 | ||||||||
\(633\) | −0.740674 | −0.0294391 | ||||||||
\(634\) | −55.9753 | −2.22306 | ||||||||
\(635\) | −10.1483 | −0.402723 | ||||||||
\(636\) | 1.18561 | 0.0470126 | ||||||||
\(637\) | 1.34860 | 0.0534334 | ||||||||
\(638\) | −7.46848 | −0.295680 | ||||||||
\(639\) | 6.95652 | 0.275196 | ||||||||
\(640\) | 56.1861 | 2.22095 | ||||||||
\(641\) | −13.5642 | −0.535755 | −0.267878 | − | 0.963453i | \(-0.586322\pi\) | ||||
−0.267878 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(642\) | −12.2979 | −0.485359 | ||||||||
\(643\) | 43.0671 | 1.69840 | 0.849201 | − | 0.528070i | \(-0.177084\pi\) | ||||
0.849201 | + | 0.528070i | \(0.177084\pi\) | |||||||
\(644\) | 10.6066 | 0.417958 | ||||||||
\(645\) | −21.7682 | −0.857121 | ||||||||
\(646\) | 1.04761 | 0.0412178 | ||||||||
\(647\) | −9.91026 | −0.389613 | −0.194806 | − | 0.980842i | \(-0.562408\pi\) | ||||
−0.194806 | + | 0.980842i | \(0.562408\pi\) | |||||||
\(648\) | 35.4927 | 1.39428 | ||||||||
\(649\) | −1.22096 | −0.0479270 | ||||||||
\(650\) | 40.8100 | 1.60070 | ||||||||
\(651\) | −42.4872 | −1.66520 | ||||||||
\(652\) | −2.36271 | −0.0925309 | ||||||||
\(653\) | 38.9583 | 1.52456 | 0.762278 | − | 0.647249i | \(-0.224081\pi\) | ||||
0.762278 | + | 0.647249i | \(0.224081\pi\) | |||||||
\(654\) | −20.9366 | −0.818685 | ||||||||
\(655\) | −53.9472 | −2.10789 | ||||||||
\(656\) | 18.6553 | 0.728368 | ||||||||
\(657\) | 0.215650 | 0.00841331 | ||||||||
\(658\) | 11.7806 | 0.459257 | ||||||||
\(659\) | 2.59903 | 0.101244 | 0.0506219 | − | 0.998718i | \(-0.483880\pi\) | ||||
0.0506219 | + | 0.998718i | \(0.483880\pi\) | |||||||
\(660\) | −13.1306 | −0.511107 | ||||||||
\(661\) | 13.5362 | 0.526496 | 0.263248 | − | 0.964728i | \(-0.415206\pi\) | ||||
0.263248 | + | 0.964728i | \(0.415206\pi\) | |||||||
\(662\) | −80.6908 | −3.13614 | ||||||||
\(663\) | 0.415495 | 0.0161365 | ||||||||
\(664\) | −7.21872 | −0.280141 | ||||||||
\(665\) | 48.0983 | 1.86517 | ||||||||
\(666\) | −3.91545 | −0.151721 | ||||||||
\(667\) | −4.44649 | −0.172169 | ||||||||
\(668\) | −20.9474 | −0.810479 | ||||||||
\(669\) | −35.7684 | −1.38289 | ||||||||
\(670\) | −4.35580 | −0.168279 | ||||||||
\(671\) | −9.46735 | −0.365483 | ||||||||
\(672\) | −4.54146 | −0.175191 | ||||||||
\(673\) | 34.7451 | 1.33932 | 0.669662 | − | 0.742666i | \(-0.266439\pi\) | ||||
0.669662 | + | 0.742666i | \(0.266439\pi\) | |||||||
\(674\) | −6.40939 | −0.246881 | ||||||||
\(675\) | 23.6821 | 0.911525 | ||||||||
\(676\) | 8.77101 | 0.337347 | ||||||||
\(677\) | −12.9411 | −0.497367 | −0.248683 | − | 0.968585i | \(-0.579998\pi\) | ||||
−0.248683 | + | 0.968585i | \(0.579998\pi\) | |||||||
\(678\) | 58.0936 | 2.23107 | ||||||||
\(679\) | 21.6664 | 0.831479 | ||||||||
\(680\) | −1.09679 | −0.0420598 | ||||||||
\(681\) | −2.62020 | −0.100406 | ||||||||
\(682\) | 17.8964 | 0.685287 | ||||||||
\(683\) | −37.6943 | −1.44233 | −0.721166 | − | 0.692763i | \(-0.756393\pi\) | ||||
−0.721166 | + | 0.692763i | \(0.756393\pi\) | |||||||
\(684\) | 15.3871 | 0.588342 | ||||||||
\(685\) | 34.2864 | 1.31002 | ||||||||
\(686\) | −46.8493 | −1.78871 | ||||||||
\(687\) | 21.3488 | 0.814508 | ||||||||
\(688\) | 21.6971 | 0.827196 | ||||||||
\(689\) | 0.725537 | 0.0276408 | ||||||||
\(690\) | −11.6198 | −0.442357 | ||||||||
\(691\) | −12.6084 | −0.479648 | −0.239824 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239824 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(692\) | 5.80270 | 0.220586 | ||||||||
\(693\) | 1.06917 | 0.0406146 | ||||||||
\(694\) | 78.6767 | 2.98653 | ||||||||
\(695\) | 9.50824 | 0.360668 | ||||||||
\(696\) | 35.8921 | 1.36049 | ||||||||
\(697\) | 0.275126 | 0.0104211 | ||||||||
\(698\) | −2.47225 | −0.0935761 | ||||||||
\(699\) | −37.5961 | −1.42202 | ||||||||
\(700\) | −45.0077 | −1.70113 | ||||||||
\(701\) | −7.00099 | −0.264424 | −0.132212 | − | 0.991221i | \(-0.542208\pi\) | ||||
−0.132212 | + | 0.991221i | \(0.542208\pi\) | |||||||
\(702\) | 53.6741 | 2.02580 | ||||||||
\(703\) | 15.9213 | 0.600482 | ||||||||
\(704\) | −4.45263 | −0.167815 | ||||||||
\(705\) | −8.68282 | −0.327014 | ||||||||
\(706\) | −57.3389 | −2.15798 | ||||||||
\(707\) | −33.2411 | −1.25016 | ||||||||
\(708\) | 11.4242 | 0.429347 | ||||||||
\(709\) | −16.7033 | −0.627305 | −0.313653 | − | 0.949538i | \(-0.601553\pi\) | ||||
−0.313653 | + | 0.949538i | \(0.601553\pi\) | |||||||
\(710\) | 85.7025 | 3.21636 | ||||||||
\(711\) | 5.05597 | 0.189614 | ||||||||
\(712\) | −25.6194 | −0.960127 | ||||||||
\(713\) | 10.6549 | 0.399029 | ||||||||
\(714\) | −0.681106 | −0.0254898 | ||||||||
\(715\) | −8.03527 | −0.300502 | ||||||||
\(716\) | 102.230 | 3.82053 | ||||||||
\(717\) | 30.5769 | 1.14191 | ||||||||
\(718\) | −18.5629 | −0.692762 | ||||||||
\(719\) | −26.8149 | −1.00003 | −0.500014 | − | 0.866017i | \(-0.666672\pi\) | ||||
−0.500014 | + | 0.866017i | \(0.666672\pi\) | |||||||
\(720\) | −8.68974 | −0.323848 | ||||||||
\(721\) | 18.4618 | 0.687552 | ||||||||
\(722\) | −46.0272 | −1.71295 | ||||||||
\(723\) | −7.36937 | −0.274070 | ||||||||
\(724\) | 7.40422 | 0.275176 | ||||||||
\(725\) | 18.8681 | 0.700743 | ||||||||
\(726\) | −40.2770 | −1.49482 | ||||||||
\(727\) | 26.6700 | 0.989136 | 0.494568 | − | 0.869139i | \(-0.335326\pi\) | ||||
0.494568 | + | 0.869139i | \(0.335326\pi\) | |||||||
\(728\) | −52.3932 | −1.94182 | ||||||||
\(729\) | 30.0305 | 1.11224 | ||||||||
\(730\) | 2.65675 | 0.0983308 | ||||||||
\(731\) | 0.319986 | 0.0118351 | ||||||||
\(732\) | 88.5832 | 3.27413 | ||||||||
\(733\) | −39.1691 | −1.44674 | −0.723371 | − | 0.690460i | \(-0.757408\pi\) | ||||
−0.723371 | + | 0.690460i | \(0.757408\pi\) | |||||||
\(734\) | −17.0811 | −0.630474 | ||||||||
\(735\) | 1.62939 | 0.0601008 | ||||||||
\(736\) | 1.13890 | 0.0419805 | ||||||||
\(737\) | 0.393715 | 0.0145027 | ||||||||
\(738\) | 6.00644 | 0.221100 | ||||||||
\(739\) | 13.2423 | 0.487127 | 0.243564 | − | 0.969885i | \(-0.421684\pi\) | ||||
0.243564 | + | 0.969885i | \(0.421684\pi\) | |||||||
\(740\) | −32.4529 | −1.19299 | ||||||||
\(741\) | −36.8848 | −1.35500 | ||||||||
\(742\) | −1.18935 | −0.0436624 | ||||||||
\(743\) | 0.846604 | 0.0310589 | 0.0155294 | − | 0.999879i | \(-0.495057\pi\) | ||||
0.0155294 | + | 0.999879i | \(0.495057\pi\) | |||||||
\(744\) | −86.0066 | −3.15315 | ||||||||
\(745\) | −30.5539 | −1.11941 | ||||||||
\(746\) | −25.8716 | −0.947226 | ||||||||
\(747\) | −0.843478 | −0.0308612 | ||||||||
\(748\) | 0.193016 | 0.00705735 | ||||||||
\(749\) | 8.29980 | 0.303268 | ||||||||
\(750\) | −8.79184 | −0.321033 | ||||||||
\(751\) | 49.8816 | 1.82021 | 0.910103 | − | 0.414382i | \(-0.136002\pi\) | ||||
0.910103 | + | 0.414382i | \(0.136002\pi\) | |||||||
\(752\) | 8.65449 | 0.315597 | ||||||||
\(753\) | 17.6693 | 0.643906 | ||||||||
\(754\) | 42.7634 | 1.55735 | ||||||||
\(755\) | 40.7022 | 1.48130 | ||||||||
\(756\) | −59.1950 | −2.15290 | ||||||||
\(757\) | 22.4527 | 0.816056 | 0.408028 | − | 0.912969i | \(-0.366217\pi\) | ||||
0.408028 | + | 0.912969i | \(0.366217\pi\) | |||||||
\(758\) | 40.9257 | 1.48649 | ||||||||
\(759\) | 1.05030 | 0.0381233 | ||||||||
\(760\) | 97.3651 | 3.53180 | ||||||||
\(761\) | 30.5909 | 1.10892 | 0.554459 | − | 0.832211i | \(-0.312925\pi\) | ||||
0.554459 | + | 0.832211i | \(0.312925\pi\) | |||||||
\(762\) | −12.7573 | −0.462149 | ||||||||
\(763\) | 14.1300 | 0.511542 | ||||||||
\(764\) | 26.2824 | 0.950864 | ||||||||
\(765\) | −0.128155 | −0.00463345 | ||||||||
\(766\) | −61.0484 | −2.20577 | ||||||||
\(767\) | 6.99105 | 0.252432 | ||||||||
\(768\) | 50.3676 | 1.81748 | ||||||||
\(769\) | −14.8896 | −0.536931 | −0.268466 | − | 0.963289i | \(-0.586517\pi\) | ||||
−0.268466 | + | 0.963289i | \(0.586517\pi\) | |||||||
\(770\) | 13.1719 | 0.474684 | ||||||||
\(771\) | −3.80143 | −0.136905 | ||||||||
\(772\) | 5.25876 | 0.189267 | ||||||||
\(773\) | 29.1942 | 1.05004 | 0.525021 | − | 0.851089i | \(-0.324058\pi\) | ||||
0.525021 | + | 0.851089i | \(0.324058\pi\) | |||||||
\(774\) | 6.98581 | 0.251100 | ||||||||
\(775\) | −45.2127 | −1.62409 | ||||||||
\(776\) | 43.8591 | 1.57445 | ||||||||
\(777\) | −10.3512 | −0.371347 | ||||||||
\(778\) | −37.0436 | −1.32808 | ||||||||
\(779\) | −24.4238 | −0.875073 | ||||||||
\(780\) | 75.1837 | 2.69201 | ||||||||
\(781\) | −7.74654 | −0.277193 | ||||||||
\(782\) | 0.170807 | 0.00610805 | ||||||||
\(783\) | 24.8157 | 0.886840 | ||||||||
\(784\) | −1.62407 | −0.0580025 | ||||||||
\(785\) | 46.1750 | 1.64806 | ||||||||
\(786\) | −67.8165 | −2.41894 | ||||||||
\(787\) | 40.8189 | 1.45504 | 0.727518 | − | 0.686089i | \(-0.240674\pi\) | ||||
0.727518 | + | 0.686089i | \(0.240674\pi\) | |||||||
\(788\) | −6.19150 | −0.220563 | ||||||||
\(789\) | 25.4435 | 0.905814 | ||||||||
\(790\) | 62.2882 | 2.21611 | ||||||||
\(791\) | −39.2072 | −1.39405 | ||||||||
\(792\) | 2.16432 | 0.0769059 | ||||||||
\(793\) | 54.2086 | 1.92500 | ||||||||
\(794\) | 8.90738 | 0.316111 | ||||||||
\(795\) | 0.876600 | 0.0310898 | ||||||||
\(796\) | 51.6720 | 1.83147 | ||||||||
\(797\) | −2.65134 | −0.0939151 | −0.0469576 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469576 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(798\) | 60.4639 | 2.14040 | ||||||||
\(799\) | 0.127635 | 0.00451540 | ||||||||
\(800\) | −4.83279 | −0.170865 | ||||||||
\(801\) | −2.99352 | −0.105771 | ||||||||
\(802\) | 1.57456 | 0.0555996 | ||||||||
\(803\) | −0.240141 | −0.00847438 | ||||||||
\(804\) | −3.68388 | −0.129920 | ||||||||
\(805\) | 7.84214 | 0.276399 | ||||||||
\(806\) | −102.472 | −3.60942 | ||||||||
\(807\) | −10.5879 | −0.372712 | ||||||||
\(808\) | −67.2899 | −2.36725 | ||||||||
\(809\) | −38.1588 | −1.34159 | −0.670796 | − | 0.741642i | \(-0.734047\pi\) | ||||
−0.670796 | + | 0.741642i | \(0.734047\pi\) | |||||||
\(810\) | 51.0921 | 1.79519 | ||||||||
\(811\) | 0.414288 | 0.0145476 | 0.00727381 | − | 0.999974i | \(-0.497685\pi\) | ||||
0.00727381 | + | 0.999974i | \(0.497685\pi\) | |||||||
\(812\) | −47.1621 | −1.65506 | ||||||||
\(813\) | 35.8563 | 1.25753 | ||||||||
\(814\) | 4.36011 | 0.152822 | ||||||||
\(815\) | −1.74690 | −0.0611914 | ||||||||
\(816\) | −0.500366 | −0.0175163 | ||||||||
\(817\) | −28.4062 | −0.993806 | ||||||||
\(818\) | −33.1713 | −1.15981 | ||||||||
\(819\) | −6.12193 | −0.213918 | ||||||||
\(820\) | 49.7840 | 1.73853 | ||||||||
\(821\) | 18.0568 | 0.630187 | 0.315093 | − | 0.949061i | \(-0.397964\pi\) | ||||
0.315093 | + | 0.949061i | \(0.397964\pi\) | |||||||
\(822\) | 43.1011 | 1.50333 | ||||||||
\(823\) | 21.3426 | 0.743957 | 0.371979 | − | 0.928241i | \(-0.378679\pi\) | ||||
0.371979 | + | 0.928241i | \(0.378679\pi\) | |||||||
\(824\) | 37.3721 | 1.30192 | ||||||||
\(825\) | −4.45680 | −0.155166 | ||||||||
\(826\) | −11.4602 | −0.398751 | ||||||||
\(827\) | 15.2881 | 0.531621 | 0.265810 | − | 0.964025i | \(-0.414361\pi\) | ||||
0.265810 | + | 0.964025i | \(0.414361\pi\) | |||||||
\(828\) | 2.50878 | 0.0871862 | ||||||||
\(829\) | 4.06554 | 0.141202 | 0.0706010 | − | 0.997505i | \(-0.477508\pi\) | ||||
0.0706010 | + | 0.997505i | \(0.477508\pi\) | |||||||
\(830\) | −10.3914 | −0.360692 | ||||||||
\(831\) | −1.00854 | −0.0349859 | ||||||||
\(832\) | 25.4951 | 0.883884 | ||||||||
\(833\) | −0.0239515 | −0.000829871 0 | ||||||||
\(834\) | 11.9527 | 0.413889 | ||||||||
\(835\) | −15.4878 | −0.535976 | ||||||||
\(836\) | −17.1346 | −0.592613 | ||||||||
\(837\) | −59.4647 | −2.05540 | ||||||||
\(838\) | −53.8165 | −1.85906 | ||||||||
\(839\) | −10.0183 | −0.345869 | −0.172934 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172934 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(840\) | −63.3019 | −2.18412 | ||||||||
\(841\) | −9.22876 | −0.318233 | ||||||||
\(842\) | 9.87905 | 0.340454 | ||||||||
\(843\) | −9.11568 | −0.313961 | ||||||||
\(844\) | 1.97013 | 0.0678146 | ||||||||
\(845\) | 6.48498 | 0.223090 | ||||||||
\(846\) | 2.78648 | 0.0958011 | ||||||||
\(847\) | 27.1829 | 0.934014 | ||||||||
\(848\) | −0.873740 | −0.0300044 | ||||||||
\(849\) | 34.8086 | 1.19463 | ||||||||
\(850\) | −0.724798 | −0.0248604 | ||||||||
\(851\) | 2.59587 | 0.0889852 | ||||||||
\(852\) | 72.4821 | 2.48320 | ||||||||
\(853\) | 49.8617 | 1.70723 | 0.853616 | − | 0.520903i | \(-0.174405\pi\) | ||||
0.853616 | + | 0.520903i | \(0.174405\pi\) | |||||||
\(854\) | −88.8624 | −3.04081 | ||||||||
\(855\) | 11.3767 | 0.389075 | ||||||||
\(856\) | 16.8012 | 0.574255 | ||||||||
\(857\) | −30.0651 | −1.02700 | −0.513502 | − | 0.858089i | \(-0.671652\pi\) | ||||
−0.513502 | + | 0.858089i | \(0.671652\pi\) | |||||||
\(858\) | −10.1011 | −0.344845 | ||||||||
\(859\) | −36.5435 | −1.24685 | −0.623423 | − | 0.781884i | \(-0.714259\pi\) | ||||
−0.623423 | + | 0.781884i | \(0.714259\pi\) | |||||||
\(860\) | 57.9014 | 1.97442 | ||||||||
\(861\) | 15.8791 | 0.541159 | ||||||||
\(862\) | −11.7189 | −0.399149 | ||||||||
\(863\) | 5.47399 | 0.186337 | 0.0931685 | − | 0.995650i | \(-0.470300\pi\) | ||||
0.0931685 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(864\) | −6.35618 | −0.216242 | ||||||||
\(865\) | 4.29031 | 0.145875 | ||||||||
\(866\) | 77.6621 | 2.63907 | ||||||||
\(867\) | 26.2734 | 0.892291 | ||||||||
\(868\) | 113.012 | 3.83588 | ||||||||
\(869\) | −5.63015 | −0.190990 | ||||||||
\(870\) | 51.6671 | 1.75168 | ||||||||
\(871\) | −2.25436 | −0.0763859 | ||||||||
\(872\) | 28.6034 | 0.968632 | ||||||||
\(873\) | 5.12476 | 0.173447 | ||||||||
\(874\) | −15.1631 | −0.512899 | ||||||||
\(875\) | 5.93359 | 0.200592 | ||||||||
\(876\) | 2.24693 | 0.0759166 | ||||||||
\(877\) | 29.2603 | 0.988051 | 0.494026 | − | 0.869447i | \(-0.335525\pi\) | ||||
0.494026 | + | 0.869447i | \(0.335525\pi\) | |||||||
\(878\) | 55.3054 | 1.86647 | ||||||||
\(879\) | 2.18833 | 0.0738107 | ||||||||
\(880\) | 9.67660 | 0.326198 | ||||||||
\(881\) | 59.0302 | 1.98878 | 0.994389 | − | 0.105784i | \(-0.0337352\pi\) | ||||
0.994389 | + | 0.105784i | \(0.0337352\pi\) | |||||||
\(882\) | −0.522900 | −0.0176070 | ||||||||
\(883\) | −7.71437 | −0.259609 | −0.129805 | − | 0.991540i | \(-0.541435\pi\) | ||||
−0.129805 | + | 0.991540i | \(0.541435\pi\) | |||||||
\(884\) | −1.10518 | −0.0371712 | ||||||||
\(885\) | 8.44664 | 0.283931 | ||||||||
\(886\) | 72.2271 | 2.42652 | ||||||||
\(887\) | 48.6186 | 1.63245 | 0.816226 | − | 0.577733i | \(-0.196062\pi\) | ||||
0.816226 | + | 0.577733i | \(0.196062\pi\) | |||||||
\(888\) | −20.9539 | −0.703166 | ||||||||
\(889\) | 8.60988 | 0.288766 | ||||||||
\(890\) | −36.8794 | −1.23620 | ||||||||
\(891\) | −4.61815 | −0.154714 | ||||||||
\(892\) | 95.1409 | 3.18555 | ||||||||
\(893\) | −11.3306 | −0.379163 | ||||||||
\(894\) | −38.4090 | −1.28459 | ||||||||
\(895\) | 75.5856 | 2.52655 | ||||||||
\(896\) | −47.6687 | −1.59250 | ||||||||
\(897\) | −6.01384 | −0.200796 | ||||||||
\(898\) | −0.666997 | −0.0222580 | ||||||||
\(899\) | −47.3769 | −1.58011 | ||||||||
\(900\) | −10.6457 | −0.354856 | ||||||||
\(901\) | −0.0128858 | −0.000429287 0 | ||||||||
\(902\) | −6.68857 | −0.222705 | ||||||||
\(903\) | 18.4683 | 0.614585 | ||||||||
\(904\) | −79.3670 | −2.63971 | ||||||||
\(905\) | 5.47442 | 0.181976 | ||||||||
\(906\) | 51.1663 | 1.69989 | ||||||||
\(907\) | −5.51377 | −0.183082 | −0.0915408 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915408 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(908\) | 6.96949 | 0.231291 | ||||||||
\(909\) | −7.86254 | −0.260784 | ||||||||
\(910\) | −75.4206 | −2.50017 | ||||||||
\(911\) | 28.2552 | 0.936137 | 0.468068 | − | 0.883692i | \(-0.344950\pi\) | ||||
0.468068 | + | 0.883692i | \(0.344950\pi\) | |||||||
\(912\) | 44.4191 | 1.47086 | ||||||||
\(913\) | 0.939268 | 0.0310852 | ||||||||
\(914\) | 41.3470 | 1.36764 | ||||||||
\(915\) | 65.4953 | 2.16521 | ||||||||
\(916\) | −56.7860 | −1.87626 | ||||||||
\(917\) | 45.7692 | 1.51143 | ||||||||
\(918\) | −0.953269 | −0.0314626 | ||||||||
\(919\) | 41.0091 | 1.35276 | 0.676382 | − | 0.736551i | \(-0.263547\pi\) | ||||
0.676382 | + | 0.736551i | \(0.263547\pi\) | |||||||
\(920\) | 15.8748 | 0.523377 | ||||||||
\(921\) | 17.3124 | 0.570461 | ||||||||
\(922\) | −24.0777 | −0.792957 | ||||||||
\(923\) | 44.3556 | 1.45998 | ||||||||
\(924\) | 11.1401 | 0.366481 | ||||||||
\(925\) | −11.0152 | −0.362178 | ||||||||
\(926\) | −12.1292 | −0.398592 | ||||||||
\(927\) | 4.36677 | 0.143424 | ||||||||
\(928\) | −5.06412 | −0.166238 | ||||||||
\(929\) | −52.2165 | −1.71317 | −0.856584 | − | 0.516008i | \(-0.827418\pi\) | ||||
−0.856584 | + | 0.516008i | \(0.827418\pi\) | |||||||
\(930\) | −123.807 | −4.05981 | ||||||||
\(931\) | 2.12625 | 0.0696851 | ||||||||
\(932\) | 100.002 | 3.27569 | ||||||||
\(933\) | 26.7772 | 0.876646 | ||||||||
\(934\) | 5.23860 | 0.171412 | ||||||||
\(935\) | 0.142709 | 0.00466708 | ||||||||
\(936\) | −12.3926 | −0.405065 | ||||||||
\(937\) | −39.0391 | −1.27535 | −0.637676 | − | 0.770304i | \(-0.720104\pi\) | ||||
−0.637676 | + | 0.770304i | \(0.720104\pi\) | |||||||
\(938\) | 3.69549 | 0.120662 | ||||||||
\(939\) | 13.4357 | 0.438459 | ||||||||
\(940\) | 23.0955 | 0.753293 | ||||||||
\(941\) | −18.3020 | −0.596627 | −0.298314 | − | 0.954468i | \(-0.596424\pi\) | ||||
−0.298314 | + | 0.954468i | \(0.596424\pi\) | |||||||
\(942\) | 58.0462 | 1.89125 | ||||||||
\(943\) | −3.98215 | −0.129677 | ||||||||
\(944\) | −8.41908 | −0.274018 | ||||||||
\(945\) | −43.7667 | −1.42373 | ||||||||
\(946\) | −7.77916 | −0.252922 | ||||||||
\(947\) | 33.0394 | 1.07364 | 0.536819 | − | 0.843698i | \(-0.319626\pi\) | ||||
0.536819 | + | 0.843698i | \(0.319626\pi\) | |||||||
\(948\) | 52.6797 | 1.71096 | ||||||||
\(949\) | 1.37501 | 0.0446347 | ||||||||
\(950\) | 64.3426 | 2.08755 | ||||||||
\(951\) | −35.0020 | −1.13502 | ||||||||
\(952\) | 0.930521 | 0.0301583 | ||||||||
\(953\) | −29.5717 | −0.957920 | −0.478960 | − | 0.877837i | \(-0.658986\pi\) | ||||
−0.478960 | + | 0.877837i | \(0.658986\pi\) | |||||||
\(954\) | −0.281317 | −0.00910798 | ||||||||
\(955\) | 19.4323 | 0.628814 | ||||||||
\(956\) | −81.3318 | −2.63046 | ||||||||
\(957\) | −4.67013 | −0.150964 | ||||||||
\(958\) | 10.3460 | 0.334266 | ||||||||
\(959\) | −29.0888 | −0.939328 | ||||||||
\(960\) | 30.8034 | 0.994175 | ||||||||
\(961\) | 82.5270 | 2.66216 | ||||||||
\(962\) | −24.9654 | −0.804915 | ||||||||
\(963\) | 1.96316 | 0.0632618 | ||||||||
\(964\) | 19.6019 | 0.631334 | ||||||||
\(965\) | 3.88815 | 0.125164 | ||||||||
\(966\) | 9.85829 | 0.317185 | ||||||||
\(967\) | −17.5092 | −0.563057 | −0.281529 | − | 0.959553i | \(-0.590841\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590841\pi\) | |||||||
\(968\) | 55.0261 | 1.76861 | ||||||||
\(969\) | 0.655085 | 0.0210444 | ||||||||
\(970\) | 63.1357 | 2.02716 | ||||||||
\(971\) | 60.1243 | 1.92948 | 0.964741 | − | 0.263201i | \(-0.0847783\pi\) | ||||
0.964741 | + | 0.263201i | \(0.0847783\pi\) | |||||||
\(972\) | −25.6366 | −0.822295 | ||||||||
\(973\) | −8.06686 | −0.258612 | ||||||||
\(974\) | −44.2449 | −1.41770 | ||||||||
\(975\) | 25.5190 | 0.817261 | ||||||||
\(976\) | −65.2816 | −2.08961 | ||||||||
\(977\) | 31.5216 | 1.00846 | 0.504232 | − | 0.863568i | \(-0.331776\pi\) | ||||
0.504232 | + | 0.863568i | \(0.331776\pi\) | |||||||
\(978\) | −2.19602 | −0.0702209 | ||||||||
\(979\) | 3.33349 | 0.106539 | ||||||||
\(980\) | −4.33402 | −0.138445 | ||||||||
\(981\) | 3.34218 | 0.106708 | ||||||||
\(982\) | 5.72999 | 0.182851 | ||||||||
\(983\) | 5.40376 | 0.172353 | 0.0861765 | − | 0.996280i | \(-0.472535\pi\) | ||||
0.0861765 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(984\) | 32.1440 | 1.02471 | ||||||||
\(985\) | −4.57778 | −0.145860 | ||||||||
\(986\) | −0.759492 | −0.0241872 | ||||||||
\(987\) | 7.36657 | 0.234480 | ||||||||
\(988\) | 98.1102 | 3.12130 | ||||||||
\(989\) | −4.63146 | −0.147272 | ||||||||
\(990\) | 3.11557 | 0.0990192 | ||||||||
\(991\) | 52.9995 | 1.68358 | 0.841792 | − | 0.539802i | \(-0.181501\pi\) | ||||
0.841792 | + | 0.539802i | \(0.181501\pi\) | |||||||
\(992\) | 12.1349 | 0.385284 | ||||||||
\(993\) | −50.4569 | −1.60120 | ||||||||
\(994\) | −72.7106 | −2.30624 | ||||||||
\(995\) | 38.2045 | 1.21116 | ||||||||
\(996\) | −8.78846 | −0.278473 | ||||||||
\(997\) | −12.3012 | −0.389584 | −0.194792 | − | 0.980845i | \(-0.562403\pi\) | ||||
−0.194792 | + | 0.980845i | \(0.562403\pi\) | |||||||
\(998\) | 15.6766 | 0.496235 | ||||||||
\(999\) | −14.4874 | −0.458362 |
(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 | 8027.2.a.e.1.15 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.e.1.15 | ✓ | 169 | 1.1 | even | 1 | trivial |