Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35123 | −1.66257 | −0.831285 | − | 0.555846i | \(-0.812394\pi\) | ||||
−0.831285 | + | 0.555846i | \(0.812394\pi\) | |||||||
\(3\) | −2.62167 | −1.51362 | −0.756812 | − | 0.653632i | \(-0.773244\pi\) | ||||
−0.756812 | + | 0.653632i | \(0.773244\pi\) | |||||||
\(4\) | 3.52828 | 1.76414 | ||||||||
\(5\) | −1.32904 | −0.594367 | −0.297183 | − | 0.954820i | \(-0.596047\pi\) | ||||
−0.297183 | + | 0.954820i | \(0.596047\pi\) | |||||||
\(6\) | 6.16416 | 2.51651 | ||||||||
\(7\) | −2.62369 | −0.991661 | −0.495830 | − | 0.868419i | \(-0.665136\pi\) | ||||
−0.495830 | + | 0.868419i | \(0.665136\pi\) | |||||||
\(8\) | −3.59334 | −1.27044 | ||||||||
\(9\) | 3.87318 | 1.29106 | ||||||||
\(10\) | 3.12489 | 0.988177 | ||||||||
\(11\) | 0.707561 | 0.213338 | 0.106669 | − | 0.994295i | \(-0.465982\pi\) | ||||
0.106669 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(12\) | −9.25001 | −2.67025 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 6.16889 | 1.64871 | ||||||||
\(15\) | 3.48432 | 0.899648 | ||||||||
\(16\) | 1.39221 | 0.348053 | ||||||||
\(17\) | 0.107924 | 0.0261753 | 0.0130877 | − | 0.999914i | \(-0.495834\pi\) | ||||
0.0130877 | + | 0.999914i | \(0.495834\pi\) | |||||||
\(18\) | −9.10674 | −2.14648 | ||||||||
\(19\) | −5.33371 | −1.22364 | −0.611819 | − | 0.790998i | \(-0.709562\pi\) | ||||
−0.611819 | + | 0.790998i | \(0.709562\pi\) | |||||||
\(20\) | −4.68924 | −1.04855 | ||||||||
\(21\) | 6.87846 | 1.50100 | ||||||||
\(22\) | −1.66364 | −0.354689 | ||||||||
\(23\) | 5.99504 | 1.25005 | 0.625026 | − | 0.780604i | \(-0.285088\pi\) | ||||
0.625026 | + | 0.780604i | \(0.285088\pi\) | |||||||
\(24\) | 9.42058 | 1.92297 | ||||||||
\(25\) | −3.23364 | −0.646728 | ||||||||
\(26\) | −2.35123 | −0.461114 | ||||||||
\(27\) | −2.28919 | −0.440555 | ||||||||
\(28\) | −9.25711 | −1.74943 | ||||||||
\(29\) | −3.89189 | −0.722706 | −0.361353 | − | 0.932429i | \(-0.617685\pi\) | ||||
−0.361353 | + | 0.932429i | \(0.617685\pi\) | |||||||
\(30\) | −8.19244 | −1.49573 | ||||||||
\(31\) | 1.52075 | 0.273135 | 0.136568 | − | 0.990631i | \(-0.456393\pi\) | ||||
0.136568 | + | 0.990631i | \(0.456393\pi\) | |||||||
\(32\) | 3.91328 | 0.691776 | ||||||||
\(33\) | −1.85499 | −0.322913 | ||||||||
\(34\) | −0.253753 | −0.0435183 | ||||||||
\(35\) | 3.48700 | 0.589410 | ||||||||
\(36\) | 13.6657 | 2.27761 | ||||||||
\(37\) | 3.57394 | 0.587551 | 0.293776 | − | 0.955874i | \(-0.405088\pi\) | ||||
0.293776 | + | 0.955874i | \(0.405088\pi\) | |||||||
\(38\) | 12.5408 | 2.03438 | ||||||||
\(39\) | −2.62167 | −0.419804 | ||||||||
\(40\) | 4.77571 | 0.755107 | ||||||||
\(41\) | −1.34958 | −0.210769 | −0.105385 | − | 0.994432i | \(-0.533607\pi\) | ||||
−0.105385 | + | 0.994432i | \(0.533607\pi\) | |||||||
\(42\) | −16.1728 | −2.49552 | ||||||||
\(43\) | 1.37913 | 0.210315 | 0.105158 | − | 0.994456i | \(-0.466465\pi\) | ||||
0.105158 | + | 0.994456i | \(0.466465\pi\) | |||||||
\(44\) | 2.49647 | 0.376358 | ||||||||
\(45\) | −5.14763 | −0.767363 | ||||||||
\(46\) | −14.0957 | −2.07830 | ||||||||
\(47\) | −6.62813 | −0.966813 | −0.483406 | − | 0.875396i | \(-0.660601\pi\) | ||||
−0.483406 | + | 0.875396i | \(0.660601\pi\) | |||||||
\(48\) | −3.64993 | −0.526822 | ||||||||
\(49\) | −0.116260 | −0.0166086 | ||||||||
\(50\) | 7.60303 | 1.07523 | ||||||||
\(51\) | −0.282941 | −0.0396196 | ||||||||
\(52\) | 3.52828 | 0.489285 | ||||||||
\(53\) | −8.61589 | −1.18348 | −0.591742 | − | 0.806128i | \(-0.701560\pi\) | ||||
−0.591742 | + | 0.806128i | \(0.701560\pi\) | |||||||
\(54\) | 5.38242 | 0.732454 | ||||||||
\(55\) | −0.940380 | −0.126801 | ||||||||
\(56\) | 9.42781 | 1.25984 | ||||||||
\(57\) | 13.9833 | 1.85213 | ||||||||
\(58\) | 9.15073 | 1.20155 | ||||||||
\(59\) | −7.88656 | −1.02674 | −0.513372 | − | 0.858166i | \(-0.671604\pi\) | ||||
−0.513372 | + | 0.858166i | \(0.671604\pi\) | |||||||
\(60\) | 12.2937 | 1.58711 | ||||||||
\(61\) | 0.719770 | 0.0921572 | 0.0460786 | − | 0.998938i | \(-0.485328\pi\) | ||||
0.0460786 | + | 0.998938i | \(0.485328\pi\) | |||||||
\(62\) | −3.57564 | −0.454106 | ||||||||
\(63\) | −10.1620 | −1.28029 | ||||||||
\(64\) | −11.9854 | −1.49818 | ||||||||
\(65\) | −1.32904 | −0.164848 | ||||||||
\(66\) | 4.36152 | 0.536866 | ||||||||
\(67\) | 8.31103 | 1.01535 | 0.507677 | − | 0.861547i | \(-0.330504\pi\) | ||||
0.507677 | + | 0.861547i | \(0.330504\pi\) | |||||||
\(68\) | 0.380785 | 0.0461770 | ||||||||
\(69\) | −15.7170 | −1.89211 | ||||||||
\(70\) | −8.19873 | −0.979936 | ||||||||
\(71\) | 12.5153 | 1.48530 | 0.742649 | − | 0.669681i | \(-0.233569\pi\) | ||||
0.742649 | + | 0.669681i | \(0.233569\pi\) | |||||||
\(72\) | −13.9177 | −1.64021 | ||||||||
\(73\) | 8.05783 | 0.943098 | 0.471549 | − | 0.881840i | \(-0.343695\pi\) | ||||
0.471549 | + | 0.881840i | \(0.343695\pi\) | |||||||
\(74\) | −8.40314 | −0.976846 | ||||||||
\(75\) | 8.47756 | 0.978904 | ||||||||
\(76\) | −18.8188 | −2.15867 | ||||||||
\(77\) | −1.85642 | −0.211559 | ||||||||
\(78\) | 6.16416 | 0.697954 | ||||||||
\(79\) | −14.1205 | −1.58868 | −0.794340 | − | 0.607474i | \(-0.792183\pi\) | ||||
−0.794340 | + | 0.607474i | \(0.792183\pi\) | |||||||
\(80\) | −1.85031 | −0.206871 | ||||||||
\(81\) | −5.61802 | −0.624224 | ||||||||
\(82\) | 3.17317 | 0.350418 | ||||||||
\(83\) | 6.80636 | 0.747095 | 0.373547 | − | 0.927611i | \(-0.378141\pi\) | ||||
0.373547 | + | 0.927611i | \(0.378141\pi\) | |||||||
\(84\) | 24.2691 | 2.64798 | ||||||||
\(85\) | −0.143435 | −0.0155577 | ||||||||
\(86\) | −3.24265 | −0.349664 | ||||||||
\(87\) | 10.2033 | 1.09391 | ||||||||
\(88\) | −2.54251 | −0.271032 | ||||||||
\(89\) | −1.71630 | −0.181928 | −0.0909639 | − | 0.995854i | \(-0.528995\pi\) | ||||
−0.0909639 | + | 0.995854i | \(0.528995\pi\) | |||||||
\(90\) | 12.1033 | 1.27580 | ||||||||
\(91\) | −2.62369 | −0.275037 | ||||||||
\(92\) | 21.1522 | 2.20527 | ||||||||
\(93\) | −3.98692 | −0.413424 | ||||||||
\(94\) | 15.5843 | 1.60739 | ||||||||
\(95\) | 7.08874 | 0.727289 | ||||||||
\(96\) | −10.2593 | −1.04709 | ||||||||
\(97\) | −4.38469 | −0.445197 | −0.222599 | − | 0.974910i | \(-0.571454\pi\) | ||||
−0.222599 | + | 0.974910i | \(0.571454\pi\) | |||||||
\(98\) | 0.273354 | 0.0276130 | ||||||||
\(99\) | 2.74051 | 0.275432 | ||||||||
\(100\) | −11.4092 | −1.14092 | ||||||||
\(101\) | 6.80213 | 0.676837 | 0.338419 | − | 0.940996i | \(-0.390108\pi\) | ||||
0.338419 | + | 0.940996i | \(0.390108\pi\) | |||||||
\(102\) | 0.665258 | 0.0658704 | ||||||||
\(103\) | 18.1665 | 1.79000 | 0.895001 | − | 0.446065i | \(-0.147175\pi\) | ||||
0.895001 | + | 0.446065i | \(0.147175\pi\) | |||||||
\(104\) | −3.59334 | −0.352356 | ||||||||
\(105\) | −9.14178 | −0.892146 | ||||||||
\(106\) | 20.2579 | 1.96763 | ||||||||
\(107\) | −15.3751 | −1.48637 | −0.743183 | − | 0.669088i | \(-0.766685\pi\) | ||||
−0.743183 | + | 0.669088i | \(0.766685\pi\) | |||||||
\(108\) | −8.07692 | −0.777202 | ||||||||
\(109\) | 0.344652 | 0.0330117 | 0.0165058 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165058 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(110\) | 2.21105 | 0.210815 | ||||||||
\(111\) | −9.36970 | −0.889332 | ||||||||
\(112\) | −3.65273 | −0.345151 | ||||||||
\(113\) | −2.04628 | −0.192498 | −0.0962489 | − | 0.995357i | \(-0.530684\pi\) | ||||
−0.0962489 | + | 0.995357i | \(0.530684\pi\) | |||||||
\(114\) | −32.8779 | −3.07929 | ||||||||
\(115\) | −7.96767 | −0.742989 | ||||||||
\(116\) | −13.7317 | −1.27496 | ||||||||
\(117\) | 3.87318 | 0.358076 | ||||||||
\(118\) | 18.5431 | 1.70703 | ||||||||
\(119\) | −0.283158 | −0.0259570 | ||||||||
\(120\) | −12.5204 | −1.14295 | ||||||||
\(121\) | −10.4994 | −0.954487 | ||||||||
\(122\) | −1.69235 | −0.153218 | ||||||||
\(123\) | 3.53816 | 0.319025 | ||||||||
\(124\) | 5.36564 | 0.481849 | ||||||||
\(125\) | 10.9429 | 0.978760 | ||||||||
\(126\) | 23.8932 | 2.12858 | ||||||||
\(127\) | 14.0584 | 1.24749 | 0.623743 | − | 0.781630i | \(-0.285611\pi\) | ||||
0.623743 | + | 0.781630i | \(0.285611\pi\) | |||||||
\(128\) | 20.3540 | 1.79905 | ||||||||
\(129\) | −3.61563 | −0.318338 | ||||||||
\(130\) | 3.12489 | 0.274071 | ||||||||
\(131\) | −15.5706 | −1.36041 | −0.680205 | − | 0.733022i | \(-0.738109\pi\) | ||||
−0.680205 | + | 0.733022i | \(0.738109\pi\) | |||||||
\(132\) | −6.54494 | −0.569664 | ||||||||
\(133\) | 13.9940 | 1.21343 | ||||||||
\(134\) | −19.5412 | −1.68810 | ||||||||
\(135\) | 3.04244 | 0.261851 | ||||||||
\(136\) | −0.387807 | −0.0332541 | ||||||||
\(137\) | −9.60707 | −0.820787 | −0.410394 | − | 0.911908i | \(-0.634609\pi\) | ||||
−0.410394 | + | 0.911908i | \(0.634609\pi\) | |||||||
\(138\) | 36.9544 | 3.14577 | ||||||||
\(139\) | −3.70004 | −0.313833 | −0.156917 | − | 0.987612i | \(-0.550155\pi\) | ||||
−0.156917 | + | 0.987612i | \(0.550155\pi\) | |||||||
\(140\) | 12.3031 | 1.03980 | ||||||||
\(141\) | 17.3768 | 1.46339 | ||||||||
\(142\) | −29.4264 | −2.46941 | ||||||||
\(143\) | 0.707561 | 0.0591692 | ||||||||
\(144\) | 5.39229 | 0.449357 | ||||||||
\(145\) | 5.17250 | 0.429553 | ||||||||
\(146\) | −18.9458 | −1.56797 | ||||||||
\(147\) | 0.304796 | 0.0251392 | ||||||||
\(148\) | 12.6099 | 1.03652 | ||||||||
\(149\) | 6.95047 | 0.569405 | 0.284703 | − | 0.958616i | \(-0.408105\pi\) | ||||
0.284703 | + | 0.958616i | \(0.408105\pi\) | |||||||
\(150\) | −19.9327 | −1.62750 | ||||||||
\(151\) | 24.5043 | 1.99413 | 0.997064 | − | 0.0765743i | \(-0.0243982\pi\) | ||||
0.997064 | + | 0.0765743i | \(0.0243982\pi\) | |||||||
\(152\) | 19.1659 | 1.55456 | ||||||||
\(153\) | 0.418007 | 0.0337939 | ||||||||
\(154\) | 4.36487 | 0.351731 | ||||||||
\(155\) | −2.02115 | −0.162342 | ||||||||
\(156\) | −9.25001 | −0.740593 | ||||||||
\(157\) | 21.4347 | 1.71067 | 0.855336 | − | 0.518073i | \(-0.173351\pi\) | ||||
0.855336 | + | 0.518073i | \(0.173351\pi\) | |||||||
\(158\) | 33.2005 | 2.64129 | ||||||||
\(159\) | 22.5881 | 1.79135 | ||||||||
\(160\) | −5.20092 | −0.411169 | ||||||||
\(161\) | −15.7291 | −1.23963 | ||||||||
\(162\) | 13.2093 | 1.03782 | ||||||||
\(163\) | 19.2620 | 1.50872 | 0.754360 | − | 0.656461i | \(-0.227948\pi\) | ||||
0.754360 | + | 0.656461i | \(0.227948\pi\) | |||||||
\(164\) | −4.76170 | −0.371826 | ||||||||
\(165\) | 2.46537 | 0.191929 | ||||||||
\(166\) | −16.0033 | −1.24210 | ||||||||
\(167\) | 8.10339 | 0.627059 | 0.313529 | − | 0.949578i | \(-0.398489\pi\) | ||||
0.313529 | + | 0.949578i | \(0.398489\pi\) | |||||||
\(168\) | −24.7167 | −1.90693 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.337249 | 0.0258658 | ||||||||
\(171\) | −20.6584 | −1.57979 | ||||||||
\(172\) | 4.86596 | 0.371026 | ||||||||
\(173\) | 20.7994 | 1.58135 | 0.790676 | − | 0.612234i | \(-0.209729\pi\) | ||||
0.790676 | + | 0.612234i | \(0.209729\pi\) | |||||||
\(174\) | −23.9902 | −1.81870 | ||||||||
\(175\) | 8.48407 | 0.641335 | ||||||||
\(176\) | 0.985074 | 0.0742528 | ||||||||
\(177\) | 20.6760 | 1.55410 | ||||||||
\(178\) | 4.03543 | 0.302468 | ||||||||
\(179\) | −19.5198 | −1.45898 | −0.729488 | − | 0.683994i | \(-0.760242\pi\) | ||||
−0.729488 | + | 0.683994i | \(0.760242\pi\) | |||||||
\(180\) | −18.1623 | −1.35374 | ||||||||
\(181\) | 5.32245 | 0.395615 | 0.197807 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197807 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(182\) | 6.16889 | 0.457269 | ||||||||
\(183\) | −1.88700 | −0.139491 | ||||||||
\(184\) | −21.5422 | −1.58811 | ||||||||
\(185\) | −4.74992 | −0.349221 | ||||||||
\(186\) | 9.37416 | 0.687347 | ||||||||
\(187\) | 0.0763625 | 0.00558418 | ||||||||
\(188\) | −23.3859 | −1.70559 | ||||||||
\(189\) | 6.00613 | 0.436882 | ||||||||
\(190\) | −16.6673 | −1.20917 | ||||||||
\(191\) | 2.86695 | 0.207445 | 0.103723 | − | 0.994606i | \(-0.466925\pi\) | ||||
0.103723 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(192\) | 31.4219 | 2.26768 | ||||||||
\(193\) | 3.14768 | 0.226575 | 0.113288 | − | 0.993562i | \(-0.463862\pi\) | ||||
0.113288 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(194\) | 10.3094 | 0.740172 | ||||||||
\(195\) | 3.48432 | 0.249518 | ||||||||
\(196\) | −0.410199 | −0.0292999 | ||||||||
\(197\) | −21.4159 | −1.52582 | −0.762911 | − | 0.646504i | \(-0.776230\pi\) | ||||
−0.762911 | + | 0.646504i | \(0.776230\pi\) | |||||||
\(198\) | −6.44357 | −0.457924 | ||||||||
\(199\) | −0.754636 | −0.0534948 | −0.0267474 | − | 0.999642i | \(-0.508515\pi\) | ||||
−0.0267474 | + | 0.999642i | \(0.508515\pi\) | |||||||
\(200\) | 11.6196 | 0.821629 | ||||||||
\(201\) | −21.7888 | −1.53687 | ||||||||
\(202\) | −15.9934 | −1.12529 | ||||||||
\(203\) | 10.2111 | 0.716679 | ||||||||
\(204\) | −0.998294 | −0.0698946 | ||||||||
\(205\) | 1.79365 | 0.125274 | ||||||||
\(206\) | −42.7137 | −2.97600 | ||||||||
\(207\) | 23.2199 | 1.61389 | ||||||||
\(208\) | 1.39221 | 0.0965325 | ||||||||
\(209\) | −3.77393 | −0.261048 | ||||||||
\(210\) | 21.4944 | 1.48326 | ||||||||
\(211\) | −26.1617 | −1.80104 | −0.900522 | − | 0.434811i | \(-0.856815\pi\) | ||||
−0.900522 | + | 0.434811i | \(0.856815\pi\) | |||||||
\(212\) | −30.3993 | −2.08783 | ||||||||
\(213\) | −32.8111 | −2.24818 | ||||||||
\(214\) | 36.1504 | 2.47119 | ||||||||
\(215\) | −1.83292 | −0.125004 | ||||||||
\(216\) | 8.22586 | 0.559699 | ||||||||
\(217\) | −3.98998 | −0.270857 | ||||||||
\(218\) | −0.810356 | −0.0548842 | ||||||||
\(219\) | −21.1250 | −1.42750 | ||||||||
\(220\) | −3.31792 | −0.223694 | ||||||||
\(221\) | 0.107924 | 0.00725973 | ||||||||
\(222\) | 22.0303 | 1.47858 | ||||||||
\(223\) | 0.967801 | 0.0648087 | 0.0324044 | − | 0.999475i | \(-0.489684\pi\) | ||||
0.0324044 | + | 0.999475i | \(0.489684\pi\) | |||||||
\(224\) | −10.2672 | −0.686007 | ||||||||
\(225\) | −12.5245 | −0.834965 | ||||||||
\(226\) | 4.81127 | 0.320041 | ||||||||
\(227\) | 14.5384 | 0.964950 | 0.482475 | − | 0.875910i | \(-0.339738\pi\) | ||||
0.482475 | + | 0.875910i | \(0.339738\pi\) | |||||||
\(228\) | 49.3369 | 3.26742 | ||||||||
\(229\) | 26.0378 | 1.72063 | 0.860315 | − | 0.509763i | \(-0.170267\pi\) | ||||
0.860315 | + | 0.509763i | \(0.170267\pi\) | |||||||
\(230\) | 18.7338 | 1.23527 | ||||||||
\(231\) | 4.86693 | 0.320220 | ||||||||
\(232\) | 13.9849 | 0.918154 | ||||||||
\(233\) | −4.89033 | −0.320376 | −0.160188 | − | 0.987086i | \(-0.551210\pi\) | ||||
−0.160188 | + | 0.987086i | \(0.551210\pi\) | |||||||
\(234\) | −9.10674 | −0.595326 | ||||||||
\(235\) | 8.80908 | 0.574641 | ||||||||
\(236\) | −27.8260 | −1.81132 | ||||||||
\(237\) | 37.0193 | 2.40466 | ||||||||
\(238\) | 0.665769 | 0.0431554 | ||||||||
\(239\) | 24.9185 | 1.61184 | 0.805921 | − | 0.592024i | \(-0.201671\pi\) | ||||
0.805921 | + | 0.592024i | \(0.201671\pi\) | |||||||
\(240\) | 4.85091 | 0.313125 | ||||||||
\(241\) | 13.6432 | 0.878833 | 0.439416 | − | 0.898284i | \(-0.355185\pi\) | ||||
0.439416 | + | 0.898284i | \(0.355185\pi\) | |||||||
\(242\) | 24.6864 | 1.58690 | ||||||||
\(243\) | 21.5962 | 1.38540 | ||||||||
\(244\) | 2.53955 | 0.162578 | ||||||||
\(245\) | 0.154515 | 0.00987160 | ||||||||
\(246\) | −8.31903 | −0.530402 | ||||||||
\(247\) | −5.33371 | −0.339376 | ||||||||
\(248\) | −5.46458 | −0.347001 | ||||||||
\(249\) | −17.8441 | −1.13082 | ||||||||
\(250\) | −25.7292 | −1.62726 | ||||||||
\(251\) | 16.5467 | 1.04442 | 0.522208 | − | 0.852818i | \(-0.325108\pi\) | ||||
0.522208 | + | 0.852818i | \(0.325108\pi\) | |||||||
\(252\) | −35.8545 | −2.25862 | ||||||||
\(253\) | 4.24185 | 0.266683 | ||||||||
\(254\) | −33.0546 | −2.07403 | ||||||||
\(255\) | 0.376041 | 0.0235486 | ||||||||
\(256\) | −23.8860 | −1.49287 | ||||||||
\(257\) | −14.4629 | −0.902170 | −0.451085 | − | 0.892481i | \(-0.648963\pi\) | ||||
−0.451085 | + | 0.892481i | \(0.648963\pi\) | |||||||
\(258\) | 8.50117 | 0.529260 | ||||||||
\(259\) | −9.37689 | −0.582652 | ||||||||
\(260\) | −4.68924 | −0.290815 | ||||||||
\(261\) | −15.0740 | −0.933057 | ||||||||
\(262\) | 36.6101 | 2.26178 | ||||||||
\(263\) | 2.67360 | 0.164862 | 0.0824308 | − | 0.996597i | \(-0.473732\pi\) | ||||
0.0824308 | + | 0.996597i | \(0.473732\pi\) | |||||||
\(264\) | 6.66563 | 0.410241 | ||||||||
\(265\) | 11.4509 | 0.703423 | ||||||||
\(266\) | −32.9031 | −2.01742 | ||||||||
\(267\) | 4.49959 | 0.275371 | ||||||||
\(268\) | 29.3237 | 1.79123 | ||||||||
\(269\) | −10.5165 | −0.641203 | −0.320601 | − | 0.947214i | \(-0.603885\pi\) | ||||
−0.320601 | + | 0.947214i | \(0.603885\pi\) | |||||||
\(270\) | −7.15347 | −0.435347 | ||||||||
\(271\) | 15.3528 | 0.932617 | 0.466308 | − | 0.884622i | \(-0.345584\pi\) | ||||
0.466308 | + | 0.884622i | \(0.345584\pi\) | |||||||
\(272\) | 0.150253 | 0.00911040 | ||||||||
\(273\) | 6.87846 | 0.416303 | ||||||||
\(274\) | 22.5884 | 1.36462 | ||||||||
\(275\) | −2.28800 | −0.137971 | ||||||||
\(276\) | −55.4542 | −3.33795 | ||||||||
\(277\) | 24.8770 | 1.49471 | 0.747356 | − | 0.664424i | \(-0.231323\pi\) | ||||
0.747356 | + | 0.664424i | \(0.231323\pi\) | |||||||
\(278\) | 8.69964 | 0.521770 | ||||||||
\(279\) | 5.89015 | 0.352634 | ||||||||
\(280\) | −12.5300 | −0.748810 | ||||||||
\(281\) | 26.6898 | 1.59218 | 0.796090 | − | 0.605178i | \(-0.206898\pi\) | ||||
0.796090 | + | 0.605178i | \(0.206898\pi\) | |||||||
\(282\) | −40.8569 | −2.43299 | ||||||||
\(283\) | −0.347485 | −0.0206559 | −0.0103279 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103279 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(284\) | 44.1576 | 2.62027 | ||||||||
\(285\) | −18.5844 | −1.10084 | ||||||||
\(286\) | −1.66364 | −0.0983730 | ||||||||
\(287\) | 3.54088 | 0.209011 | ||||||||
\(288\) | 15.1568 | 0.893124 | ||||||||
\(289\) | −16.9884 | −0.999315 | ||||||||
\(290\) | −12.1617 | −0.714161 | ||||||||
\(291\) | 11.4952 | 0.673862 | ||||||||
\(292\) | 28.4303 | 1.66376 | ||||||||
\(293\) | −3.60994 | −0.210895 | −0.105447 | − | 0.994425i | \(-0.533627\pi\) | ||||
−0.105447 | + | 0.994425i | \(0.533627\pi\) | |||||||
\(294\) | −0.716647 | −0.0417957 | ||||||||
\(295\) | 10.4816 | 0.610262 | ||||||||
\(296\) | −12.8424 | −0.746448 | ||||||||
\(297\) | −1.61974 | −0.0939870 | ||||||||
\(298\) | −16.3422 | −0.946676 | ||||||||
\(299\) | 5.99504 | 0.346702 | ||||||||
\(300\) | 29.9112 | 1.72692 | ||||||||
\(301\) | −3.61840 | −0.208561 | ||||||||
\(302\) | −57.6151 | −3.31538 | ||||||||
\(303\) | −17.8330 | −1.02448 | ||||||||
\(304\) | −7.42566 | −0.425891 | ||||||||
\(305\) | −0.956607 | −0.0547751 | ||||||||
\(306\) | −0.982832 | −0.0561847 | ||||||||
\(307\) | 8.68582 | 0.495726 | 0.247863 | − | 0.968795i | \(-0.420272\pi\) | ||||
0.247863 | + | 0.968795i | \(0.420272\pi\) | |||||||
\(308\) | −6.54997 | −0.373219 | ||||||||
\(309\) | −47.6267 | −2.70939 | ||||||||
\(310\) | 4.75218 | 0.269906 | ||||||||
\(311\) | 24.5052 | 1.38956 | 0.694781 | − | 0.719221i | \(-0.255501\pi\) | ||||
0.694781 | + | 0.719221i | \(0.255501\pi\) | |||||||
\(312\) | 9.42058 | 0.533335 | ||||||||
\(313\) | −2.14430 | −0.121203 | −0.0606014 | − | 0.998162i | \(-0.519302\pi\) | ||||
−0.0606014 | + | 0.998162i | \(0.519302\pi\) | |||||||
\(314\) | −50.3978 | −2.84411 | ||||||||
\(315\) | 13.5058 | 0.760964 | ||||||||
\(316\) | −49.8211 | −2.80265 | ||||||||
\(317\) | −30.3704 | −1.70577 | −0.852886 | − | 0.522097i | \(-0.825150\pi\) | ||||
−0.852886 | + | 0.522097i | \(0.825150\pi\) | |||||||
\(318\) | −53.1097 | −2.97825 | ||||||||
\(319\) | −2.75375 | −0.154180 | ||||||||
\(320\) | 15.9292 | 0.890468 | ||||||||
\(321\) | 40.3085 | 2.24980 | ||||||||
\(322\) | 36.9828 | 2.06097 | ||||||||
\(323\) | −0.575633 | −0.0320291 | ||||||||
\(324\) | −19.8220 | −1.10122 | ||||||||
\(325\) | −3.23364 | −0.179370 | ||||||||
\(326\) | −45.2895 | −2.50835 | ||||||||
\(327\) | −0.903565 | −0.0499673 | ||||||||
\(328\) | 4.84951 | 0.267769 | ||||||||
\(329\) | 17.3902 | 0.958750 | ||||||||
\(330\) | −5.79665 | −0.319095 | ||||||||
\(331\) | 19.5857 | 1.07653 | 0.538265 | − | 0.842776i | \(-0.319080\pi\) | ||||
0.538265 | + | 0.842776i | \(0.319080\pi\) | |||||||
\(332\) | 24.0148 | 1.31798 | ||||||||
\(333\) | 13.8425 | 0.758564 | ||||||||
\(334\) | −19.0529 | −1.04253 | ||||||||
\(335\) | −11.0457 | −0.603493 | ||||||||
\(336\) | 9.57627 | 0.522428 | ||||||||
\(337\) | 5.43680 | 0.296161 | 0.148081 | − | 0.988975i | \(-0.452690\pi\) | ||||
0.148081 | + | 0.988975i | \(0.452690\pi\) | |||||||
\(338\) | −2.35123 | −0.127890 | ||||||||
\(339\) | 5.36468 | 0.291369 | ||||||||
\(340\) | −0.506080 | −0.0274460 | ||||||||
\(341\) | 1.07602 | 0.0582700 | ||||||||
\(342\) | 48.5727 | 2.62651 | ||||||||
\(343\) | 18.6708 | 1.00813 | ||||||||
\(344\) | −4.95568 | −0.267193 | ||||||||
\(345\) | 20.8886 | 1.12461 | ||||||||
\(346\) | −48.9043 | −2.62911 | ||||||||
\(347\) | 19.9788 | 1.07252 | 0.536258 | − | 0.844054i | \(-0.319837\pi\) | ||||
0.536258 | + | 0.844054i | \(0.319837\pi\) | |||||||
\(348\) | 36.0000 | 1.92980 | ||||||||
\(349\) | −31.9403 | −1.70972 | −0.854861 | − | 0.518857i | \(-0.826358\pi\) | ||||
−0.854861 | + | 0.518857i | \(0.826358\pi\) | |||||||
\(350\) | −19.9480 | −1.06626 | ||||||||
\(351\) | −2.28919 | −0.122188 | ||||||||
\(352\) | 2.76888 | 0.147582 | ||||||||
\(353\) | −32.1803 | −1.71279 | −0.856393 | − | 0.516325i | \(-0.827300\pi\) | ||||
−0.856393 | + | 0.516325i | \(0.827300\pi\) | |||||||
\(354\) | −48.6140 | −2.58381 | ||||||||
\(355\) | −16.6334 | −0.882811 | ||||||||
\(356\) | −6.05561 | −0.320946 | ||||||||
\(357\) | 0.742348 | 0.0392892 | ||||||||
\(358\) | 45.8955 | 2.42565 | ||||||||
\(359\) | 13.7843 | 0.727508 | 0.363754 | − | 0.931495i | \(-0.381495\pi\) | ||||
0.363754 | + | 0.931495i | \(0.381495\pi\) | |||||||
\(360\) | 18.4972 | 0.974888 | ||||||||
\(361\) | 9.44848 | 0.497289 | ||||||||
\(362\) | −12.5143 | −0.657738 | ||||||||
\(363\) | 27.5259 | 1.44474 | ||||||||
\(364\) | −9.25711 | −0.485205 | ||||||||
\(365\) | −10.7092 | −0.560546 | ||||||||
\(366\) | 4.43678 | 0.231914 | ||||||||
\(367\) | 23.0347 | 1.20240 | 0.601202 | − | 0.799097i | \(-0.294689\pi\) | ||||
0.601202 | + | 0.799097i | \(0.294689\pi\) | |||||||
\(368\) | 8.34636 | 0.435084 | ||||||||
\(369\) | −5.22717 | −0.272115 | ||||||||
\(370\) | 11.1682 | 0.580604 | ||||||||
\(371\) | 22.6054 | 1.17361 | ||||||||
\(372\) | −14.0670 | −0.729338 | ||||||||
\(373\) | −8.73331 | −0.452194 | −0.226097 | − | 0.974105i | \(-0.572597\pi\) | ||||
−0.226097 | + | 0.974105i | \(0.572597\pi\) | |||||||
\(374\) | −0.179546 | −0.00928409 | ||||||||
\(375\) | −28.6887 | −1.48148 | ||||||||
\(376\) | 23.8172 | 1.22828 | ||||||||
\(377\) | −3.89189 | −0.200443 | ||||||||
\(378\) | −14.1218 | −0.726346 | ||||||||
\(379\) | −5.20921 | −0.267579 | −0.133789 | − | 0.991010i | \(-0.542715\pi\) | ||||
−0.133789 | + | 0.991010i | \(0.542715\pi\) | |||||||
\(380\) | 25.0111 | 1.28304 | ||||||||
\(381\) | −36.8567 | −1.88822 | ||||||||
\(382\) | −6.74087 | −0.344893 | ||||||||
\(383\) | −16.9776 | −0.867517 | −0.433758 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433758 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(384\) | −53.3615 | −2.72309 | ||||||||
\(385\) | 2.46726 | 0.125743 | ||||||||
\(386\) | −7.40092 | −0.376697 | ||||||||
\(387\) | 5.34161 | 0.271529 | ||||||||
\(388\) | −15.4704 | −0.785391 | ||||||||
\(389\) | 1.03217 | 0.0523330 | 0.0261665 | − | 0.999658i | \(-0.491670\pi\) | ||||
0.0261665 | + | 0.999658i | \(0.491670\pi\) | |||||||
\(390\) | −8.19244 | −0.414840 | ||||||||
\(391\) | 0.647006 | 0.0327205 | ||||||||
\(392\) | 0.417763 | 0.0211002 | ||||||||
\(393\) | 40.8210 | 2.05915 | ||||||||
\(394\) | 50.3538 | 2.53679 | ||||||||
\(395\) | 18.7668 | 0.944258 | ||||||||
\(396\) | 9.66929 | 0.485900 | ||||||||
\(397\) | 4.58914 | 0.230322 | 0.115161 | − | 0.993347i | \(-0.463262\pi\) | ||||
0.115161 | + | 0.993347i | \(0.463262\pi\) | |||||||
\(398\) | 1.77432 | 0.0889388 | ||||||||
\(399\) | −36.6877 | −1.83668 | ||||||||
\(400\) | −4.50191 | −0.225096 | ||||||||
\(401\) | −10.4623 | −0.522461 | −0.261231 | − | 0.965276i | \(-0.584128\pi\) | ||||
−0.261231 | + | 0.965276i | \(0.584128\pi\) | |||||||
\(402\) | 51.2305 | 2.55515 | ||||||||
\(403\) | 1.52075 | 0.0757541 | ||||||||
\(404\) | 23.9998 | 1.19404 | ||||||||
\(405\) | 7.46660 | 0.371018 | ||||||||
\(406\) | −24.0087 | −1.19153 | ||||||||
\(407\) | 2.52878 | 0.125347 | ||||||||
\(408\) | 1.01670 | 0.0503343 | ||||||||
\(409\) | 5.84104 | 0.288821 | 0.144411 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144411 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(410\) | −4.21729 | −0.208277 | ||||||||
\(411\) | 25.1866 | 1.24236 | ||||||||
\(412\) | 64.0966 | 3.15782 | ||||||||
\(413\) | 20.6919 | 1.01818 | ||||||||
\(414\) | −54.5952 | −2.68321 | ||||||||
\(415\) | −9.04595 | −0.444048 | ||||||||
\(416\) | 3.91328 | 0.191864 | ||||||||
\(417\) | 9.70030 | 0.475026 | ||||||||
\(418\) | 8.87337 | 0.434011 | ||||||||
\(419\) | 3.37716 | 0.164985 | 0.0824926 | − | 0.996592i | \(-0.473712\pi\) | ||||
0.0824926 | + | 0.996592i | \(0.473712\pi\) | |||||||
\(420\) | −32.2548 | −1.57387 | ||||||||
\(421\) | −3.42403 | −0.166877 | −0.0834384 | − | 0.996513i | \(-0.526590\pi\) | ||||
−0.0834384 | + | 0.996513i | \(0.526590\pi\) | |||||||
\(422\) | 61.5121 | 2.99436 | ||||||||
\(423\) | −25.6719 | −1.24821 | ||||||||
\(424\) | 30.9599 | 1.50354 | ||||||||
\(425\) | −0.348986 | −0.0169283 | ||||||||
\(426\) | 77.1466 | 3.73776 | ||||||||
\(427\) | −1.88845 | −0.0913887 | ||||||||
\(428\) | −54.2477 | −2.62216 | ||||||||
\(429\) | −1.85499 | −0.0895600 | ||||||||
\(430\) | 4.30962 | 0.207829 | ||||||||
\(431\) | −19.8333 | −0.955337 | −0.477669 | − | 0.878540i | \(-0.658518\pi\) | ||||
−0.477669 | + | 0.878540i | \(0.658518\pi\) | |||||||
\(432\) | −3.18704 | −0.153337 | ||||||||
\(433\) | −1.21486 | −0.0583827 | −0.0291913 | − | 0.999574i | \(-0.509293\pi\) | ||||
−0.0291913 | + | 0.999574i | \(0.509293\pi\) | |||||||
\(434\) | 9.38136 | 0.450320 | ||||||||
\(435\) | −13.5606 | −0.650181 | ||||||||
\(436\) | 1.21603 | 0.0582372 | ||||||||
\(437\) | −31.9758 | −1.52961 | ||||||||
\(438\) | 49.6698 | 2.37331 | ||||||||
\(439\) | 10.5353 | 0.502824 | 0.251412 | − | 0.967880i | \(-0.419105\pi\) | ||||
0.251412 | + | 0.967880i | \(0.419105\pi\) | |||||||
\(440\) | 3.37911 | 0.161093 | ||||||||
\(441\) | −0.450297 | −0.0214427 | ||||||||
\(442\) | −0.253753 | −0.0120698 | ||||||||
\(443\) | −2.53327 | −0.120359 | −0.0601796 | − | 0.998188i | \(-0.519167\pi\) | ||||
−0.0601796 | + | 0.998188i | \(0.519167\pi\) | |||||||
\(444\) | −33.0589 | −1.56891 | ||||||||
\(445\) | 2.28104 | 0.108132 | ||||||||
\(446\) | −2.27552 | −0.107749 | ||||||||
\(447\) | −18.2219 | −0.861866 | ||||||||
\(448\) | 31.4460 | 1.48569 | ||||||||
\(449\) | 11.6762 | 0.551032 | 0.275516 | − | 0.961297i | \(-0.411151\pi\) | ||||
0.275516 | + | 0.961297i | \(0.411151\pi\) | |||||||
\(450\) | 29.4479 | 1.38819 | ||||||||
\(451\) | −0.954910 | −0.0449650 | ||||||||
\(452\) | −7.21985 | −0.339593 | ||||||||
\(453\) | −64.2422 | −3.01836 | ||||||||
\(454\) | −34.1832 | −1.60430 | ||||||||
\(455\) | 3.48700 | 0.163473 | ||||||||
\(456\) | −50.2467 | −2.35301 | ||||||||
\(457\) | −4.01990 | −0.188043 | −0.0940214 | − | 0.995570i | \(-0.529972\pi\) | ||||
−0.0940214 | + | 0.995570i | \(0.529972\pi\) | |||||||
\(458\) | −61.2210 | −2.86067 | ||||||||
\(459\) | −0.247058 | −0.0115317 | ||||||||
\(460\) | −28.1122 | −1.31074 | ||||||||
\(461\) | 13.9221 | 0.648415 | 0.324208 | − | 0.945986i | \(-0.394902\pi\) | ||||
0.324208 | + | 0.945986i | \(0.394902\pi\) | |||||||
\(462\) | −11.4433 | −0.532389 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | −5.41834 | −0.251540 | ||||||||
\(465\) | 5.29879 | 0.245726 | ||||||||
\(466\) | 11.4983 | 0.532648 | ||||||||
\(467\) | −32.3287 | −1.49599 | −0.747997 | − | 0.663702i | \(-0.768985\pi\) | ||||
−0.747997 | + | 0.663702i | \(0.768985\pi\) | |||||||
\(468\) | 13.6657 | 0.631696 | ||||||||
\(469\) | −21.8056 | −1.00689 | ||||||||
\(470\) | −20.7122 | −0.955382 | ||||||||
\(471\) | −56.1947 | −2.58932 | ||||||||
\(472\) | 28.3391 | 1.30441 | ||||||||
\(473\) | 0.975817 | 0.0448681 | ||||||||
\(474\) | −87.0410 | −3.99792 | ||||||||
\(475\) | 17.2473 | 0.791361 | ||||||||
\(476\) | −0.999061 | −0.0457919 | ||||||||
\(477\) | −33.3709 | −1.52795 | ||||||||
\(478\) | −58.5890 | −2.67980 | ||||||||
\(479\) | −15.2818 | −0.698244 | −0.349122 | − | 0.937077i | \(-0.613520\pi\) | ||||
−0.349122 | + | 0.937077i | \(0.613520\pi\) | |||||||
\(480\) | 13.6351 | 0.622355 | ||||||||
\(481\) | 3.57394 | 0.162957 | ||||||||
\(482\) | −32.0782 | −1.46112 | ||||||||
\(483\) | 41.2366 | 1.87633 | ||||||||
\(484\) | −37.0447 | −1.68385 | ||||||||
\(485\) | 5.82744 | 0.264610 | ||||||||
\(486\) | −50.7776 | −2.30332 | ||||||||
\(487\) | −29.7596 | −1.34854 | −0.674268 | − | 0.738487i | \(-0.735541\pi\) | ||||
−0.674268 | + | 0.738487i | \(0.735541\pi\) | |||||||
\(488\) | −2.58638 | −0.117080 | ||||||||
\(489\) | −50.4988 | −2.28363 | ||||||||
\(490\) | −0.363300 | −0.0164122 | ||||||||
\(491\) | 0.814690 | 0.0367665 | 0.0183832 | − | 0.999831i | \(-0.494148\pi\) | ||||
0.0183832 | + | 0.999831i | \(0.494148\pi\) | |||||||
\(492\) | 12.4836 | 0.562806 | ||||||||
\(493\) | −0.420027 | −0.0189171 | ||||||||
\(494\) | 12.5408 | 0.564237 | ||||||||
\(495\) | −3.64226 | −0.163707 | ||||||||
\(496\) | 2.11721 | 0.0950655 | ||||||||
\(497\) | −32.8363 | −1.47291 | ||||||||
\(498\) | 41.9555 | 1.88007 | ||||||||
\(499\) | 13.8712 | 0.620962 | 0.310481 | − | 0.950580i | \(-0.399510\pi\) | ||||
0.310481 | + | 0.950580i | \(0.399510\pi\) | |||||||
\(500\) | 38.6096 | 1.72667 | ||||||||
\(501\) | −21.2444 | −0.949132 | ||||||||
\(502\) | −38.9050 | −1.73642 | ||||||||
\(503\) | −11.4522 | −0.510627 | −0.255313 | − | 0.966858i | \(-0.582179\pi\) | ||||
−0.255313 | + | 0.966858i | \(0.582179\pi\) | |||||||
\(504\) | 36.5156 | 1.62653 | ||||||||
\(505\) | −9.04034 | −0.402290 | ||||||||
\(506\) | −9.97357 | −0.443379 | ||||||||
\(507\) | −2.62167 | −0.116433 | ||||||||
\(508\) | 49.6022 | 2.20074 | ||||||||
\(509\) | 14.5997 | 0.647120 | 0.323560 | − | 0.946208i | \(-0.395120\pi\) | ||||
0.323560 | + | 0.946208i | \(0.395120\pi\) | |||||||
\(510\) | −0.884158 | −0.0391512 | ||||||||
\(511\) | −21.1412 | −0.935233 | ||||||||
\(512\) | 15.4535 | 0.682955 | ||||||||
\(513\) | 12.2099 | 0.539080 | ||||||||
\(514\) | 34.0056 | 1.49992 | ||||||||
\(515\) | −24.1441 | −1.06392 | ||||||||
\(516\) | −12.7570 | −0.561594 | ||||||||
\(517\) | −4.68981 | −0.206257 | ||||||||
\(518\) | 22.0472 | 0.968700 | ||||||||
\(519\) | −54.5294 | −2.39357 | ||||||||
\(520\) | 4.77571 | 0.209429 | ||||||||
\(521\) | −20.0474 | −0.878293 | −0.439147 | − | 0.898415i | \(-0.644719\pi\) | ||||
−0.439147 | + | 0.898415i | \(0.644719\pi\) | |||||||
\(522\) | 35.4424 | 1.55127 | ||||||||
\(523\) | −6.94031 | −0.303479 | −0.151739 | − | 0.988421i | \(-0.548487\pi\) | ||||
−0.151739 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(524\) | −54.9375 | −2.39995 | ||||||||
\(525\) | −22.2425 | −0.970741 | ||||||||
\(526\) | −6.28626 | −0.274094 | ||||||||
\(527\) | 0.164125 | 0.00714940 | ||||||||
\(528\) | −2.58254 | −0.112391 | ||||||||
\(529\) | 12.9405 | 0.562630 | ||||||||
\(530\) | −26.9237 | −1.16949 | ||||||||
\(531\) | −30.5461 | −1.32559 | ||||||||
\(532\) | 49.3748 | 2.14067 | ||||||||
\(533\) | −1.34958 | −0.0584568 | ||||||||
\(534\) | −10.5796 | −0.457823 | ||||||||
\(535\) | 20.4342 | 0.883447 | ||||||||
\(536\) | −29.8644 | −1.28995 | ||||||||
\(537\) | 51.1745 | 2.20834 | ||||||||
\(538\) | 24.7267 | 1.06604 | ||||||||
\(539\) | −0.0822612 | −0.00354324 | ||||||||
\(540\) | 10.7346 | 0.461943 | ||||||||
\(541\) | −45.4324 | −1.95329 | −0.976645 | − | 0.214858i | \(-0.931071\pi\) | ||||
−0.976645 | + | 0.214858i | \(0.931071\pi\) | |||||||
\(542\) | −36.0980 | −1.55054 | ||||||||
\(543\) | −13.9537 | −0.598812 | ||||||||
\(544\) | 0.422335 | 0.0181075 | ||||||||
\(545\) | −0.458058 | −0.0196210 | ||||||||
\(546\) | −16.1728 | −0.692133 | ||||||||
\(547\) | −24.8677 | −1.06327 | −0.531633 | − | 0.846975i | \(-0.678421\pi\) | ||||
−0.531633 | + | 0.846975i | \(0.678421\pi\) | |||||||
\(548\) | −33.8965 | −1.44798 | ||||||||
\(549\) | 2.78780 | 0.118980 | ||||||||
\(550\) | 5.37961 | 0.229387 | ||||||||
\(551\) | 20.7582 | 0.884330 | ||||||||
\(552\) | 56.4767 | 2.40381 | ||||||||
\(553\) | 37.0478 | 1.57543 | ||||||||
\(554\) | −58.4914 | −2.48506 | ||||||||
\(555\) | 12.4527 | 0.528589 | ||||||||
\(556\) | −13.0548 | −0.553646 | ||||||||
\(557\) | −41.3128 | −1.75048 | −0.875239 | − | 0.483691i | \(-0.839296\pi\) | ||||
−0.875239 | + | 0.483691i | \(0.839296\pi\) | |||||||
\(558\) | −13.8491 | −0.586279 | ||||||||
\(559\) | 1.37913 | 0.0583309 | ||||||||
\(560\) | 4.85464 | 0.205146 | ||||||||
\(561\) | −0.200198 | −0.00845235 | ||||||||
\(562\) | −62.7539 | −2.64711 | ||||||||
\(563\) | −1.83339 | −0.0772683 | −0.0386342 | − | 0.999253i | \(-0.512301\pi\) | ||||
−0.0386342 | + | 0.999253i | \(0.512301\pi\) | |||||||
\(564\) | 61.3103 | 2.58163 | ||||||||
\(565\) | 2.71960 | 0.114414 | ||||||||
\(566\) | 0.817018 | 0.0343418 | ||||||||
\(567\) | 14.7399 | 0.619019 | ||||||||
\(568\) | −44.9719 | −1.88698 | ||||||||
\(569\) | 9.05523 | 0.379615 | 0.189807 | − | 0.981821i | \(-0.439214\pi\) | ||||
0.189807 | + | 0.981821i | \(0.439214\pi\) | |||||||
\(570\) | 43.6961 | 1.83023 | ||||||||
\(571\) | 42.9181 | 1.79607 | 0.898033 | − | 0.439929i | \(-0.144996\pi\) | ||||
0.898033 | + | 0.439929i | \(0.144996\pi\) | |||||||
\(572\) | 2.49647 | 0.104383 | ||||||||
\(573\) | −7.51622 | −0.313995 | ||||||||
\(574\) | −8.32542 | −0.347496 | ||||||||
\(575\) | −19.3858 | −0.808444 | ||||||||
\(576\) | −46.4217 | −1.93424 | ||||||||
\(577\) | 27.9436 | 1.16331 | 0.581654 | − | 0.813436i | \(-0.302406\pi\) | ||||
0.581654 | + | 0.813436i | \(0.302406\pi\) | |||||||
\(578\) | 39.9435 | 1.66143 | ||||||||
\(579\) | −8.25220 | −0.342950 | ||||||||
\(580\) | 18.2500 | 0.757791 | ||||||||
\(581\) | −17.8578 | −0.740865 | ||||||||
\(582\) | −27.0279 | −1.12034 | ||||||||
\(583\) | −6.09627 | −0.252482 | ||||||||
\(584\) | −28.9545 | −1.19815 | ||||||||
\(585\) | −5.14763 | −0.212828 | ||||||||
\(586\) | 8.48780 | 0.350628 | ||||||||
\(587\) | −1.21353 | −0.0500876 | −0.0250438 | − | 0.999686i | \(-0.507973\pi\) | ||||
−0.0250438 | + | 0.999686i | \(0.507973\pi\) | |||||||
\(588\) | 1.07541 | 0.0443491 | ||||||||
\(589\) | −8.11125 | −0.334218 | ||||||||
\(590\) | −24.6446 | −1.01460 | ||||||||
\(591\) | 56.1456 | 2.30952 | ||||||||
\(592\) | 4.97567 | 0.204499 | ||||||||
\(593\) | −22.0297 | −0.904652 | −0.452326 | − | 0.891853i | \(-0.649406\pi\) | ||||
−0.452326 | + | 0.891853i | \(0.649406\pi\) | |||||||
\(594\) | 3.80839 | 0.156260 | ||||||||
\(595\) | 0.376329 | 0.0154280 | ||||||||
\(596\) | 24.5232 | 1.00451 | ||||||||
\(597\) | 1.97841 | 0.0809710 | ||||||||
\(598\) | −14.0957 | −0.576417 | ||||||||
\(599\) | −0.369341 | −0.0150909 | −0.00754543 | − | 0.999972i | \(-0.502402\pi\) | ||||
−0.00754543 | + | 0.999972i | \(0.502402\pi\) | |||||||
\(600\) | −30.4628 | −1.24364 | ||||||||
\(601\) | −17.7828 | −0.725375 | −0.362688 | − | 0.931911i | \(-0.618141\pi\) | ||||
−0.362688 | + | 0.931911i | \(0.618141\pi\) | |||||||
\(602\) | 8.50770 | 0.346748 | ||||||||
\(603\) | 32.1901 | 1.31088 | ||||||||
\(604\) | 86.4579 | 3.51792 | ||||||||
\(605\) | 13.9541 | 0.567315 | ||||||||
\(606\) | 41.9294 | 1.70327 | ||||||||
\(607\) | −2.58727 | −0.105014 | −0.0525071 | − | 0.998621i | \(-0.516721\pi\) | ||||
−0.0525071 | + | 0.998621i | \(0.516721\pi\) | |||||||
\(608\) | −20.8723 | −0.846483 | ||||||||
\(609\) | −26.7702 | −1.08478 | ||||||||
\(610\) | 2.24920 | 0.0910676 | ||||||||
\(611\) | −6.62813 | −0.268146 | ||||||||
\(612\) | 1.47485 | 0.0596172 | ||||||||
\(613\) | −25.0800 | −1.01297 | −0.506486 | − | 0.862248i | \(-0.669056\pi\) | ||||
−0.506486 | + | 0.862248i | \(0.669056\pi\) | |||||||
\(614\) | −20.4224 | −0.824179 | ||||||||
\(615\) | −4.70237 | −0.189618 | ||||||||
\(616\) | 6.67075 | 0.268772 | ||||||||
\(617\) | 29.7439 | 1.19745 | 0.598723 | − | 0.800956i | \(-0.295675\pi\) | ||||
0.598723 | + | 0.800956i | \(0.295675\pi\) | |||||||
\(618\) | 111.981 | 4.50455 | ||||||||
\(619\) | −46.6537 | −1.87517 | −0.937585 | − | 0.347757i | \(-0.886943\pi\) | ||||
−0.937585 | + | 0.347757i | \(0.886943\pi\) | |||||||
\(620\) | −7.13118 | −0.286395 | ||||||||
\(621\) | −13.7238 | −0.550717 | ||||||||
\(622\) | −57.6173 | −2.31025 | ||||||||
\(623\) | 4.50305 | 0.180411 | ||||||||
\(624\) | −3.64993 | −0.146114 | ||||||||
\(625\) | 1.62464 | 0.0649855 | ||||||||
\(626\) | 5.04174 | 0.201508 | ||||||||
\(627\) | 9.89401 | 0.395129 | ||||||||
\(628\) | 75.6275 | 3.01787 | ||||||||
\(629\) | 0.385712 | 0.0153793 | ||||||||
\(630\) | −31.7552 | −1.26516 | ||||||||
\(631\) | 11.4475 | 0.455720 | 0.227860 | − | 0.973694i | \(-0.426827\pi\) | ||||
0.227860 | + | 0.973694i | \(0.426827\pi\) | |||||||
\(632\) | 50.7398 | 2.01832 | ||||||||
\(633\) | 68.5874 | 2.72610 | ||||||||
\(634\) | 71.4078 | 2.83597 | ||||||||
\(635\) | −18.6843 | −0.741464 | ||||||||
\(636\) | 79.6971 | 3.16019 | ||||||||
\(637\) | −0.116260 | −0.00460640 | ||||||||
\(638\) | 6.47470 | 0.256336 | ||||||||
\(639\) | 48.4742 | 1.91761 | ||||||||
\(640\) | −27.0513 | −1.06930 | ||||||||
\(641\) | −29.4859 | −1.16462 | −0.582311 | − | 0.812966i | \(-0.697851\pi\) | ||||
−0.582311 | + | 0.812966i | \(0.697851\pi\) | |||||||
\(642\) | −94.7746 | −3.74045 | ||||||||
\(643\) | 14.7596 | 0.582061 | 0.291031 | − | 0.956714i | \(-0.406002\pi\) | ||||
0.291031 | + | 0.956714i | \(0.406002\pi\) | |||||||
\(644\) | −55.4967 | −2.18688 | ||||||||
\(645\) | 4.80533 | 0.189210 | ||||||||
\(646\) | 1.35345 | 0.0532506 | ||||||||
\(647\) | 2.91165 | 0.114469 | 0.0572344 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572344 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(648\) | 20.1875 | 0.793039 | ||||||||
\(649\) | −5.58022 | −0.219043 | ||||||||
\(650\) | 7.60303 | 0.298216 | ||||||||
\(651\) | 10.4604 | 0.409977 | ||||||||
\(652\) | 67.9619 | 2.66159 | ||||||||
\(653\) | −49.8023 | −1.94891 | −0.974457 | − | 0.224575i | \(-0.927901\pi\) | ||||
−0.974457 | + | 0.224575i | \(0.927901\pi\) | |||||||
\(654\) | 2.12449 | 0.0830741 | ||||||||
\(655\) | 20.6940 | 0.808582 | ||||||||
\(656\) | −1.87890 | −0.0733588 | ||||||||
\(657\) | 31.2094 | 1.21760 | ||||||||
\(658\) | −40.8883 | −1.59399 | ||||||||
\(659\) | −23.8814 | −0.930288 | −0.465144 | − | 0.885235i | \(-0.653998\pi\) | ||||
−0.465144 | + | 0.885235i | \(0.653998\pi\) | |||||||
\(660\) | 8.69852 | 0.338589 | ||||||||
\(661\) | 29.0768 | 1.13096 | 0.565479 | − | 0.824763i | \(-0.308691\pi\) | ||||
0.565479 | + | 0.824763i | \(0.308691\pi\) | |||||||
\(662\) | −46.0506 | −1.78981 | ||||||||
\(663\) | −0.282941 | −0.0109885 | ||||||||
\(664\) | −24.4576 | −0.949138 | ||||||||
\(665\) | −18.5986 | −0.721224 | ||||||||
\(666\) | −32.5469 | −1.26117 | ||||||||
\(667\) | −23.3320 | −0.903420 | ||||||||
\(668\) | 28.5910 | 1.10622 | ||||||||
\(669\) | −2.53726 | −0.0980961 | ||||||||
\(670\) | 25.9711 | 1.00335 | ||||||||
\(671\) | 0.509281 | 0.0196606 | ||||||||
\(672\) | 26.9173 | 1.03836 | ||||||||
\(673\) | −21.5051 | −0.828963 | −0.414481 | − | 0.910058i | \(-0.636037\pi\) | ||||
−0.414481 | + | 0.910058i | \(0.636037\pi\) | |||||||
\(674\) | −12.7832 | −0.492389 | ||||||||
\(675\) | 7.40243 | 0.284920 | ||||||||
\(676\) | 3.52828 | 0.135703 | ||||||||
\(677\) | 16.2930 | 0.626190 | 0.313095 | − | 0.949722i | \(-0.398634\pi\) | ||||
0.313095 | + | 0.949722i | \(0.398634\pi\) | |||||||
\(678\) | −12.6136 | −0.484422 | ||||||||
\(679\) | 11.5040 | 0.441485 | ||||||||
\(680\) | 0.515412 | 0.0197652 | ||||||||
\(681\) | −38.1151 | −1.46057 | ||||||||
\(682\) | −2.52998 | −0.0968780 | ||||||||
\(683\) | −49.2052 | −1.88279 | −0.941393 | − | 0.337312i | \(-0.890482\pi\) | ||||
−0.941393 | + | 0.337312i | \(0.890482\pi\) | |||||||
\(684\) | −72.8888 | −2.78697 | ||||||||
\(685\) | 12.7682 | 0.487849 | ||||||||
\(686\) | −43.8995 | −1.67609 | ||||||||
\(687\) | −68.2628 | −2.60439 | ||||||||
\(688\) | 1.92004 | 0.0732008 | ||||||||
\(689\) | −8.61589 | −0.328239 | ||||||||
\(690\) | −49.1140 | −1.86974 | ||||||||
\(691\) | 36.5844 | 1.39174 | 0.695868 | − | 0.718169i | \(-0.255020\pi\) | ||||
0.695868 | + | 0.718169i | \(0.255020\pi\) | |||||||
\(692\) | 73.3863 | 2.78973 | ||||||||
\(693\) | −7.19024 | −0.273135 | ||||||||
\(694\) | −46.9746 | −1.78313 | ||||||||
\(695\) | 4.91752 | 0.186532 | ||||||||
\(696\) | −36.6639 | −1.38974 | ||||||||
\(697\) | −0.145652 | −0.00551695 | ||||||||
\(698\) | 75.0989 | 2.84253 | ||||||||
\(699\) | 12.8209 | 0.484930 | ||||||||
\(700\) | 29.9342 | 1.13141 | ||||||||
\(701\) | −38.2776 | −1.44573 | −0.722863 | − | 0.690991i | \(-0.757174\pi\) | ||||
−0.722863 | + | 0.690991i | \(0.757174\pi\) | |||||||
\(702\) | 5.38242 | 0.203146 | ||||||||
\(703\) | −19.0623 | −0.718950 | ||||||||
\(704\) | −8.48042 | −0.319618 | ||||||||
\(705\) | −23.0946 | −0.869791 | ||||||||
\(706\) | 75.6633 | 2.84763 | ||||||||
\(707\) | −17.8467 | −0.671193 | ||||||||
\(708\) | 72.9508 | 2.74166 | ||||||||
\(709\) | −26.1524 | −0.982174 | −0.491087 | − | 0.871111i | \(-0.663400\pi\) | ||||
−0.491087 | + | 0.871111i | \(0.663400\pi\) | |||||||
\(710\) | 39.1090 | 1.46774 | ||||||||
\(711\) | −54.6912 | −2.05108 | ||||||||
\(712\) | 6.16727 | 0.231128 | ||||||||
\(713\) | 9.11697 | 0.341433 | ||||||||
\(714\) | −1.74543 | −0.0653211 | ||||||||
\(715\) | −0.940380 | −0.0351682 | ||||||||
\(716\) | −68.8713 | −2.57384 | ||||||||
\(717\) | −65.3281 | −2.43972 | ||||||||
\(718\) | −32.4101 | −1.20953 | ||||||||
\(719\) | −13.1714 | −0.491211 | −0.245606 | − | 0.969370i | \(-0.578987\pi\) | ||||
−0.245606 | + | 0.969370i | \(0.578987\pi\) | |||||||
\(720\) | −7.16659 | −0.267083 | ||||||||
\(721\) | −47.6633 | −1.77507 | ||||||||
\(722\) | −22.2156 | −0.826777 | ||||||||
\(723\) | −35.7679 | −1.33022 | ||||||||
\(724\) | 18.7791 | 0.697921 | ||||||||
\(725\) | 12.5850 | 0.467394 | ||||||||
\(726\) | −64.7197 | −2.40197 | ||||||||
\(727\) | 42.1627 | 1.56373 | 0.781863 | − | 0.623450i | \(-0.214269\pi\) | ||||
0.781863 | + | 0.623450i | \(0.214269\pi\) | |||||||
\(728\) | 9.42781 | 0.349418 | ||||||||
\(729\) | −39.7642 | −1.47275 | ||||||||
\(730\) | 25.1798 | 0.931947 | ||||||||
\(731\) | 0.148841 | 0.00550507 | ||||||||
\(732\) | −6.65788 | −0.246082 | ||||||||
\(733\) | −22.4940 | −0.830836 | −0.415418 | − | 0.909631i | \(-0.636365\pi\) | ||||
−0.415418 | + | 0.909631i | \(0.636365\pi\) | |||||||
\(734\) | −54.1600 | −1.99908 | ||||||||
\(735\) | −0.405088 | −0.0149419 | ||||||||
\(736\) | 23.4602 | 0.864756 | ||||||||
\(737\) | 5.88056 | 0.216613 | ||||||||
\(738\) | 12.2903 | 0.452411 | ||||||||
\(739\) | −16.8143 | −0.618525 | −0.309263 | − | 0.950977i | \(-0.600082\pi\) | ||||
−0.309263 | + | 0.950977i | \(0.600082\pi\) | |||||||
\(740\) | −16.7591 | −0.616075 | ||||||||
\(741\) | 13.9833 | 0.513688 | ||||||||
\(742\) | −53.1505 | −1.95122 | ||||||||
\(743\) | 18.4612 | 0.677277 | 0.338638 | − | 0.940917i | \(-0.390034\pi\) | ||||
0.338638 | + | 0.940917i | \(0.390034\pi\) | |||||||
\(744\) | 14.3264 | 0.525230 | ||||||||
\(745\) | −9.23749 | −0.338435 | ||||||||
\(746\) | 20.5340 | 0.751804 | ||||||||
\(747\) | 26.3622 | 0.964544 | ||||||||
\(748\) | 0.269428 | 0.00985128 | ||||||||
\(749\) | 40.3395 | 1.47397 | ||||||||
\(750\) | 67.4536 | 2.46306 | ||||||||
\(751\) | −28.9175 | −1.05521 | −0.527607 | − | 0.849489i | \(-0.676910\pi\) | ||||
−0.527607 | + | 0.849489i | \(0.676910\pi\) | |||||||
\(752\) | −9.22776 | −0.336502 | ||||||||
\(753\) | −43.3800 | −1.58085 | ||||||||
\(754\) | 9.15073 | 0.333250 | ||||||||
\(755\) | −32.5672 | −1.18524 | ||||||||
\(756\) | 21.1913 | 0.770721 | ||||||||
\(757\) | 34.6847 | 1.26064 | 0.630319 | − | 0.776336i | \(-0.282924\pi\) | ||||
0.630319 | + | 0.776336i | \(0.282924\pi\) | |||||||
\(758\) | 12.2480 | 0.444869 | ||||||||
\(759\) | −11.1208 | −0.403658 | ||||||||
\(760\) | −25.4723 | −0.923977 | ||||||||
\(761\) | 0.409172 | 0.0148325 | 0.00741623 | − | 0.999972i | \(-0.497639\pi\) | ||||
0.00741623 | + | 0.999972i | \(0.497639\pi\) | |||||||
\(762\) | 86.6585 | 3.13931 | ||||||||
\(763\) | −0.904259 | −0.0327364 | ||||||||
\(764\) | 10.1154 | 0.365963 | ||||||||
\(765\) | −0.555551 | −0.0200860 | ||||||||
\(766\) | 39.9183 | 1.44231 | ||||||||
\(767\) | −7.88656 | −0.284767 | ||||||||
\(768\) | 62.6213 | 2.25965 | ||||||||
\(769\) | 10.0799 | 0.363490 | 0.181745 | − | 0.983346i | \(-0.441825\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441825\pi\) | |||||||
\(770\) | −5.80110 | −0.209057 | ||||||||
\(771\) | 37.9170 | 1.36555 | ||||||||
\(772\) | 11.1059 | 0.399710 | ||||||||
\(773\) | −10.3448 | −0.372076 | −0.186038 | − | 0.982543i | \(-0.559565\pi\) | ||||
−0.186038 | + | 0.982543i | \(0.559565\pi\) | |||||||
\(774\) | −12.5594 | −0.451437 | ||||||||
\(775\) | −4.91757 | −0.176644 | ||||||||
\(776\) | 15.7557 | 0.565596 | ||||||||
\(777\) | 24.5832 | 0.881916 | ||||||||
\(778\) | −2.42686 | −0.0870073 | ||||||||
\(779\) | 7.19827 | 0.257905 | ||||||||
\(780\) | 12.2937 | 0.440184 | ||||||||
\(781\) | 8.85536 | 0.316870 | ||||||||
\(782\) | −1.52126 | −0.0544002 | ||||||||
\(783\) | 8.90929 | 0.318392 | ||||||||
\(784\) | −0.161859 | −0.00578067 | ||||||||
\(785\) | −28.4876 | −1.01677 | ||||||||
\(786\) | −95.9797 | −3.42348 | ||||||||
\(787\) | −29.8489 | −1.06400 | −0.531998 | − | 0.846745i | \(-0.678559\pi\) | ||||
−0.531998 | + | 0.846745i | \(0.678559\pi\) | |||||||
\(788\) | −75.5614 | −2.69176 | ||||||||
\(789\) | −7.00932 | −0.249538 | ||||||||
\(790\) | −44.1250 | −1.56990 | ||||||||
\(791\) | 5.36880 | 0.190893 | ||||||||
\(792\) | −9.84759 | −0.349919 | ||||||||
\(793\) | 0.719770 | 0.0255598 | ||||||||
\(794\) | −10.7901 | −0.382927 | ||||||||
\(795\) | −30.0205 | −1.06472 | ||||||||
\(796\) | −2.66257 | −0.0943723 | ||||||||
\(797\) | −34.9895 | −1.23939 | −0.619697 | − | 0.784842i | \(-0.712744\pi\) | ||||
−0.619697 | + | 0.784842i | \(0.712744\pi\) | |||||||
\(798\) | 86.2612 | 3.05362 | ||||||||
\(799\) | −0.715332 | −0.0253066 | ||||||||
\(800\) | −12.6541 | −0.447391 | ||||||||
\(801\) | −6.64755 | −0.234880 | ||||||||
\(802\) | 24.5992 | 0.868628 | ||||||||
\(803\) | 5.70140 | 0.201198 | ||||||||
\(804\) | −76.8771 | −2.71125 | ||||||||
\(805\) | 20.9047 | 0.736793 | ||||||||
\(806\) | −3.57564 | −0.125946 | ||||||||
\(807\) | 27.5709 | 0.970540 | ||||||||
\(808\) | −24.4424 | −0.859881 | ||||||||
\(809\) | −32.6961 | −1.14953 | −0.574766 | − | 0.818318i | \(-0.694907\pi\) | ||||
−0.574766 | + | 0.818318i | \(0.694907\pi\) | |||||||
\(810\) | −17.5557 | −0.616844 | ||||||||
\(811\) | 4.92204 | 0.172836 | 0.0864181 | − | 0.996259i | \(-0.472458\pi\) | ||||
0.0864181 | + | 0.996259i | \(0.472458\pi\) | |||||||
\(812\) | 36.0277 | 1.26432 | ||||||||
\(813\) | −40.2501 | −1.41163 | ||||||||
\(814\) | −5.94573 | −0.208398 | ||||||||
\(815\) | −25.6001 | −0.896732 | ||||||||
\(816\) | −0.393913 | −0.0137897 | ||||||||
\(817\) | −7.35588 | −0.257349 | ||||||||
\(818\) | −13.7336 | −0.480185 | ||||||||
\(819\) | −10.1620 | −0.355090 | ||||||||
\(820\) | 6.32851 | 0.221001 | ||||||||
\(821\) | −23.2833 | −0.812593 | −0.406296 | − | 0.913741i | \(-0.633180\pi\) | ||||
−0.406296 | + | 0.913741i | \(0.633180\pi\) | |||||||
\(822\) | −59.2195 | −2.06552 | ||||||||
\(823\) | −31.9014 | −1.11201 | −0.556006 | − | 0.831178i | \(-0.687667\pi\) | ||||
−0.556006 | + | 0.831178i | \(0.687667\pi\) | |||||||
\(824\) | −65.2786 | −2.27409 | ||||||||
\(825\) | 5.99839 | 0.208837 | ||||||||
\(826\) | −48.6514 | −1.69280 | ||||||||
\(827\) | 52.8324 | 1.83716 | 0.918582 | − | 0.395231i | \(-0.129335\pi\) | ||||
0.918582 | + | 0.395231i | \(0.129335\pi\) | |||||||
\(828\) | 81.9262 | 2.84713 | ||||||||
\(829\) | −27.2027 | −0.944789 | −0.472394 | − | 0.881387i | \(-0.656610\pi\) | ||||
−0.472394 | + | 0.881387i | \(0.656610\pi\) | |||||||
\(830\) | 21.2691 | 0.738262 | ||||||||
\(831\) | −65.2193 | −2.26243 | ||||||||
\(832\) | −11.9854 | −0.415520 | ||||||||
\(833\) | −0.0125472 | −0.000434735 0 | ||||||||
\(834\) | −22.8076 | −0.789764 | ||||||||
\(835\) | −10.7698 | −0.372703 | ||||||||
\(836\) | −13.3155 | −0.460525 | ||||||||
\(837\) | −3.48129 | −0.120331 | ||||||||
\(838\) | −7.94049 | −0.274300 | ||||||||
\(839\) | 13.4158 | 0.463165 | 0.231583 | − | 0.972815i | \(-0.425610\pi\) | ||||
0.231583 | + | 0.972815i | \(0.425610\pi\) | |||||||
\(840\) | 32.8495 | 1.13342 | ||||||||
\(841\) | −13.8532 | −0.477696 | ||||||||
\(842\) | 8.05067 | 0.277445 | ||||||||
\(843\) | −69.9720 | −2.40996 | ||||||||
\(844\) | −92.3058 | −3.17729 | ||||||||
\(845\) | −1.32904 | −0.0457205 | ||||||||
\(846\) | 60.3607 | 2.07524 | ||||||||
\(847\) | 27.5470 | 0.946528 | ||||||||
\(848\) | −11.9951 | −0.411915 | ||||||||
\(849\) | 0.910994 | 0.0312652 | ||||||||
\(850\) | 0.820547 | 0.0281445 | ||||||||
\(851\) | 21.4259 | 0.734470 | ||||||||
\(852\) | −115.767 | −3.96611 | ||||||||
\(853\) | 19.9257 | 0.682243 | 0.341122 | − | 0.940019i | \(-0.389193\pi\) | ||||
0.341122 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(854\) | 4.44019 | 0.151940 | ||||||||
\(855\) | 27.4560 | 0.938974 | ||||||||
\(856\) | 55.2480 | 1.88834 | ||||||||
\(857\) | 15.0050 | 0.512560 | 0.256280 | − | 0.966603i | \(-0.417503\pi\) | ||||
0.256280 | + | 0.966603i | \(0.417503\pi\) | |||||||
\(858\) | 4.36152 | 0.148900 | ||||||||
\(859\) | −35.5168 | −1.21182 | −0.605909 | − | 0.795534i | \(-0.707190\pi\) | ||||
−0.605909 | + | 0.795534i | \(0.707190\pi\) | |||||||
\(860\) | −6.46707 | −0.220525 | ||||||||
\(861\) | −9.28303 | −0.316365 | ||||||||
\(862\) | 46.6327 | 1.58832 | ||||||||
\(863\) | 28.8239 | 0.981177 | 0.490589 | − | 0.871391i | \(-0.336782\pi\) | ||||
0.490589 | + | 0.871391i | \(0.336782\pi\) | |||||||
\(864\) | −8.95825 | −0.304766 | ||||||||
\(865\) | −27.6434 | −0.939903 | ||||||||
\(866\) | 2.85643 | 0.0970653 | ||||||||
\(867\) | 44.5379 | 1.51259 | ||||||||
\(868\) | −14.0778 | −0.477831 | ||||||||
\(869\) | −9.99110 | −0.338925 | ||||||||
\(870\) | 31.8841 | 1.08097 | ||||||||
\(871\) | 8.31103 | 0.281609 | ||||||||
\(872\) | −1.23845 | −0.0419393 | ||||||||
\(873\) | −16.9827 | −0.574776 | ||||||||
\(874\) | 75.1825 | 2.54309 | ||||||||
\(875\) | −28.7107 | −0.970598 | ||||||||
\(876\) | −74.5350 | −2.51830 | ||||||||
\(877\) | 18.5733 | 0.627174 | 0.313587 | − | 0.949559i | \(-0.398469\pi\) | ||||
0.313587 | + | 0.949559i | \(0.398469\pi\) | |||||||
\(878\) | −24.7710 | −0.835981 | ||||||||
\(879\) | 9.46409 | 0.319216 | ||||||||
\(880\) | −1.30921 | −0.0441334 | ||||||||
\(881\) | 17.5796 | 0.592273 | 0.296137 | − | 0.955146i | \(-0.404302\pi\) | ||||
0.296137 | + | 0.955146i | \(0.404302\pi\) | |||||||
\(882\) | 1.05875 | 0.0356500 | ||||||||
\(883\) | 17.5269 | 0.589826 | 0.294913 | − | 0.955524i | \(-0.404709\pi\) | ||||
0.294913 | + | 0.955524i | \(0.404709\pi\) | |||||||
\(884\) | 0.380785 | 0.0128072 | ||||||||
\(885\) | −27.4793 | −0.923708 | ||||||||
\(886\) | 5.95630 | 0.200106 | ||||||||
\(887\) | 35.8634 | 1.20417 | 0.602087 | − | 0.798431i | \(-0.294336\pi\) | ||||
0.602087 | + | 0.798431i | \(0.294336\pi\) | |||||||
\(888\) | 33.6685 | 1.12984 | ||||||||
\(889\) | −36.8850 | −1.23708 | ||||||||
\(890\) | −5.36326 | −0.179777 | ||||||||
\(891\) | −3.97509 | −0.133171 | ||||||||
\(892\) | 3.41467 | 0.114332 | ||||||||
\(893\) | 35.3526 | 1.18303 | ||||||||
\(894\) | 42.8438 | 1.43291 | ||||||||
\(895\) | 25.9426 | 0.867167 | ||||||||
\(896\) | −53.4025 | −1.78405 | ||||||||
\(897\) | −15.7170 | −0.524777 | ||||||||
\(898\) | −27.4533 | −0.916129 | ||||||||
\(899\) | −5.91860 | −0.197396 | ||||||||
\(900\) | −44.1899 | −1.47300 | ||||||||
\(901\) | −0.929858 | −0.0309781 | ||||||||
\(902\) | 2.24521 | 0.0747574 | ||||||||
\(903\) | 9.48628 | 0.315684 | ||||||||
\(904\) | 7.35299 | 0.244557 | ||||||||
\(905\) | −7.07378 | −0.235140 | ||||||||
\(906\) | 151.048 | 5.01824 | ||||||||
\(907\) | 28.5273 | 0.947235 | 0.473617 | − | 0.880731i | \(-0.342948\pi\) | ||||
0.473617 | + | 0.880731i | \(0.342948\pi\) | |||||||
\(908\) | 51.2957 | 1.70231 | ||||||||
\(909\) | 26.3459 | 0.873838 | ||||||||
\(910\) | −8.19873 | −0.271785 | ||||||||
\(911\) | −29.6322 | −0.981760 | −0.490880 | − | 0.871227i | \(-0.663325\pi\) | ||||
−0.490880 | + | 0.871227i | \(0.663325\pi\) | |||||||
\(912\) | 19.4677 | 0.644639 | ||||||||
\(913\) | 4.81591 | 0.159383 | ||||||||
\(914\) | 9.45170 | 0.312635 | ||||||||
\(915\) | 2.50791 | 0.0829090 | ||||||||
\(916\) | 91.8689 | 3.03543 | ||||||||
\(917\) | 40.8524 | 1.34906 | ||||||||
\(918\) | 0.580890 | 0.0191722 | ||||||||
\(919\) | −10.6593 | −0.351619 | −0.175810 | − | 0.984424i | \(-0.556254\pi\) | ||||
−0.175810 | + | 0.984424i | \(0.556254\pi\) | |||||||
\(920\) | 28.6306 | 0.943922 | ||||||||
\(921\) | −22.7714 | −0.750343 | ||||||||
\(922\) | −32.7340 | −1.07804 | ||||||||
\(923\) | 12.5153 | 0.411947 | ||||||||
\(924\) | 17.1719 | 0.564914 | ||||||||
\(925\) | −11.5568 | −0.379986 | ||||||||
\(926\) | −2.35123 | −0.0772662 | ||||||||
\(927\) | 70.3622 | 2.31100 | ||||||||
\(928\) | −15.2300 | −0.499951 | ||||||||
\(929\) | −51.3170 | −1.68366 | −0.841828 | − | 0.539747i | \(-0.818520\pi\) | ||||
−0.841828 | + | 0.539747i | \(0.818520\pi\) | |||||||
\(930\) | −12.4587 | −0.408536 | ||||||||
\(931\) | 0.620098 | 0.0203229 | ||||||||
\(932\) | −17.2545 | −0.565189 | ||||||||
\(933\) | −64.2447 | −2.10328 | ||||||||
\(934\) | 76.0123 | 2.48720 | ||||||||
\(935\) | −0.101489 | −0.00331905 | ||||||||
\(936\) | −13.9177 | −0.454913 | ||||||||
\(937\) | 54.0810 | 1.76675 | 0.883374 | − | 0.468668i | \(-0.155266\pi\) | ||||
0.883374 | + | 0.468668i | \(0.155266\pi\) | |||||||
\(938\) | 51.2699 | 1.67402 | ||||||||
\(939\) | 5.62165 | 0.183456 | ||||||||
\(940\) | 31.0809 | 1.01375 | ||||||||
\(941\) | 48.0503 | 1.56640 | 0.783198 | − | 0.621772i | \(-0.213587\pi\) | ||||
0.783198 | + | 0.621772i | \(0.213587\pi\) | |||||||
\(942\) | 132.127 | 4.30492 | ||||||||
\(943\) | −8.09079 | −0.263472 | ||||||||
\(944\) | −10.9798 | −0.357361 | ||||||||
\(945\) | −7.98241 | −0.259668 | ||||||||
\(946\) | −2.29437 | −0.0745964 | ||||||||
\(947\) | −8.03466 | −0.261091 | −0.130546 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130546 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(948\) | 130.615 | 4.24217 | ||||||||
\(949\) | 8.05783 | 0.261568 | ||||||||
\(950\) | −40.5524 | −1.31569 | ||||||||
\(951\) | 79.6213 | 2.58190 | ||||||||
\(952\) | 1.01748 | 0.0329768 | ||||||||
\(953\) | 52.2712 | 1.69323 | 0.846615 | − | 0.532206i | \(-0.178637\pi\) | ||||
0.846615 | + | 0.532206i | \(0.178637\pi\) | |||||||
\(954\) | 78.4626 | 2.54032 | ||||||||
\(955\) | −3.81031 | −0.123299 | ||||||||
\(956\) | 87.9194 | 2.84352 | ||||||||
\(957\) | 7.21944 | 0.233371 | ||||||||
\(958\) | 35.9311 | 1.16088 | ||||||||
\(959\) | 25.2060 | 0.813943 | ||||||||
\(960\) | −41.7611 | −1.34783 | ||||||||
\(961\) | −28.6873 | −0.925397 | ||||||||
\(962\) | −8.40314 | −0.270928 | ||||||||
\(963\) | −59.5505 | −1.91899 | ||||||||
\(964\) | 48.1369 | 1.55038 | ||||||||
\(965\) | −4.18341 | −0.134669 | ||||||||
\(966\) | −96.9568 | −3.11953 | ||||||||
\(967\) | −56.0172 | −1.80139 | −0.900695 | − | 0.434451i | \(-0.856942\pi\) | ||||
−0.900695 | + | 0.434451i | \(0.856942\pi\) | |||||||
\(968\) | 37.7278 | 1.21262 | ||||||||
\(969\) | 1.50912 | 0.0484800 | ||||||||
\(970\) | −13.7017 | −0.439934 | ||||||||
\(971\) | −16.4988 | −0.529472 | −0.264736 | − | 0.964321i | \(-0.585285\pi\) | ||||
−0.264736 | + | 0.964321i | \(0.585285\pi\) | |||||||
\(972\) | 76.1975 | 2.44404 | ||||||||
\(973\) | 9.70775 | 0.311216 | ||||||||
\(974\) | 69.9716 | 2.24204 | ||||||||
\(975\) | 8.47756 | 0.271499 | ||||||||
\(976\) | 1.00207 | 0.0320756 | ||||||||
\(977\) | 5.29964 | 0.169550 | 0.0847752 | − | 0.996400i | \(-0.472983\pi\) | ||||
0.0847752 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(978\) | 118.734 | 3.79670 | ||||||||
\(979\) | −1.21439 | −0.0388121 | ||||||||
\(980\) | 0.545172 | 0.0174149 | ||||||||
\(981\) | 1.33490 | 0.0426200 | ||||||||
\(982\) | −1.91552 | −0.0611268 | ||||||||
\(983\) | 27.6712 | 0.882575 | 0.441288 | − | 0.897366i | \(-0.354522\pi\) | ||||
0.441288 | + | 0.897366i | \(0.354522\pi\) | |||||||
\(984\) | −12.7138 | −0.405302 | ||||||||
\(985\) | 28.4627 | 0.906897 | ||||||||
\(986\) | 0.987580 | 0.0314510 | ||||||||
\(987\) | −45.5913 | −1.45119 | ||||||||
\(988\) | −18.8188 | −0.598707 | ||||||||
\(989\) | 8.26793 | 0.262905 | ||||||||
\(990\) | 8.56379 | 0.272175 | ||||||||
\(991\) | 24.6785 | 0.783938 | 0.391969 | − | 0.919978i | \(-0.371794\pi\) | ||||
0.391969 | + | 0.919978i | \(0.371794\pi\) | |||||||
\(992\) | 5.95112 | 0.188948 | ||||||||
\(993\) | −51.3474 | −1.62946 | ||||||||
\(994\) | 77.2058 | 2.44882 | ||||||||
\(995\) | 1.00295 | 0.0317955 | ||||||||
\(996\) | −62.9589 | −1.99493 | ||||||||
\(997\) | −53.6541 | −1.69924 | −0.849621 | − | 0.527393i | \(-0.823170\pi\) | ||||
−0.849621 | + | 0.527393i | \(0.823170\pi\) | |||||||
\(998\) | −32.6145 | −1.03239 | ||||||||
\(999\) | −8.18143 | −0.258849 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6019.2.a.b.1.10 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.b.1.10 | ✓ | 101 | 1.1 | even | 1 | trivial |