Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(0\) |
Dimension: | \(287\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58681 | −1.82915 | −0.914575 | − | 0.404417i | \(-0.867474\pi\) | ||||
−0.914575 | + | 0.404417i | \(0.867474\pi\) | |||||||
\(3\) | 1.99218 | 1.15019 | 0.575094 | − | 0.818088i | \(-0.304966\pi\) | ||||
0.575094 | + | 0.818088i | \(0.304966\pi\) | |||||||
\(4\) | 4.69158 | 2.34579 | ||||||||
\(5\) | 0.151026 | 0.0675408 | 0.0337704 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337704 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(6\) | −5.15340 | −2.10386 | ||||||||
\(7\) | −4.97386 | −1.87994 | −0.939972 | − | 0.341252i | \(-0.889149\pi\) | ||||
−0.939972 | + | 0.341252i | \(0.889149\pi\) | |||||||
\(8\) | −6.96259 | −2.46165 | ||||||||
\(9\) | 0.968794 | 0.322931 | ||||||||
\(10\) | −0.390675 | −0.123542 | ||||||||
\(11\) | −0.968270 | −0.291944 | −0.145972 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145972 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(12\) | 9.34648 | 2.69810 | ||||||||
\(13\) | −6.17147 | −1.71166 | −0.855829 | − | 0.517258i | \(-0.826953\pi\) | ||||
−0.855829 | + | 0.517258i | \(0.826953\pi\) | |||||||
\(14\) | 12.8664 | 3.43870 | ||||||||
\(15\) | 0.300871 | 0.0776846 | ||||||||
\(16\) | 8.62773 | 2.15693 | ||||||||
\(17\) | 3.00615 | 0.729098 | 0.364549 | − | 0.931184i | \(-0.381223\pi\) | ||||
0.364549 | + | 0.931184i | \(0.381223\pi\) | |||||||
\(18\) | −2.50608 | −0.590689 | ||||||||
\(19\) | −5.05300 | −1.15924 | −0.579619 | − | 0.814888i | \(-0.696799\pi\) | ||||
−0.579619 | + | 0.814888i | \(0.696799\pi\) | |||||||
\(20\) | 0.708549 | 0.158436 | ||||||||
\(21\) | −9.90885 | −2.16229 | ||||||||
\(22\) | 2.50473 | 0.534010 | ||||||||
\(23\) | −6.46344 | −1.34772 | −0.673860 | − | 0.738859i | \(-0.735365\pi\) | ||||
−0.673860 | + | 0.738859i | \(0.735365\pi\) | |||||||
\(24\) | −13.8708 | −2.83136 | ||||||||
\(25\) | −4.97719 | −0.995438 | ||||||||
\(26\) | 15.9644 | 3.13088 | ||||||||
\(27\) | −4.04654 | −0.778756 | ||||||||
\(28\) | −23.3353 | −4.40995 | ||||||||
\(29\) | −5.49154 | −1.01975 | −0.509877 | − | 0.860248i | \(-0.670309\pi\) | ||||
−0.509877 | + | 0.860248i | \(0.670309\pi\) | |||||||
\(30\) | −0.778296 | −0.142097 | ||||||||
\(31\) | −7.05539 | −1.26719 | −0.633593 | − | 0.773667i | \(-0.718421\pi\) | ||||
−0.633593 | + | 0.773667i | \(0.718421\pi\) | |||||||
\(32\) | −8.39310 | −1.48370 | ||||||||
\(33\) | −1.92897 | −0.335791 | ||||||||
\(34\) | −7.77633 | −1.33363 | ||||||||
\(35\) | −0.751182 | −0.126973 | ||||||||
\(36\) | 4.54517 | 0.757528 | ||||||||
\(37\) | 8.19484 | 1.34722 | 0.673612 | − | 0.739085i | \(-0.264742\pi\) | ||||
0.673612 | + | 0.739085i | \(0.264742\pi\) | |||||||
\(38\) | 13.0711 | 2.12042 | ||||||||
\(39\) | −12.2947 | −1.96873 | ||||||||
\(40\) | −1.05153 | −0.166262 | ||||||||
\(41\) | 0.0800108 | 0.0124956 | 0.00624779 | − | 0.999980i | \(-0.498011\pi\) | ||||
0.00624779 | + | 0.999980i | \(0.498011\pi\) | |||||||
\(42\) | 25.6323 | 3.95515 | ||||||||
\(43\) | −6.33730 | −0.966429 | −0.483214 | − | 0.875502i | \(-0.660531\pi\) | ||||
−0.483214 | + | 0.875502i | \(0.660531\pi\) | |||||||
\(44\) | −4.54271 | −0.684840 | ||||||||
\(45\) | 0.146313 | 0.0218110 | ||||||||
\(46\) | 16.7197 | 2.46518 | ||||||||
\(47\) | 12.4672 | 1.81852 | 0.909261 | − | 0.416226i | \(-0.136647\pi\) | ||||
0.909261 | + | 0.416226i | \(0.136647\pi\) | |||||||
\(48\) | 17.1880 | 2.48088 | ||||||||
\(49\) | 17.7393 | 2.53419 | ||||||||
\(50\) | 12.8750 | 1.82081 | ||||||||
\(51\) | 5.98880 | 0.838600 | ||||||||
\(52\) | −28.9539 | −4.01519 | ||||||||
\(53\) | −7.51380 | −1.03210 | −0.516050 | − | 0.856559i | \(-0.672598\pi\) | ||||
−0.516050 | + | 0.856559i | \(0.672598\pi\) | |||||||
\(54\) | 10.4676 | 1.42446 | ||||||||
\(55\) | −0.146234 | −0.0197182 | ||||||||
\(56\) | 34.6310 | 4.62776 | ||||||||
\(57\) | −10.0665 | −1.33334 | ||||||||
\(58\) | 14.2056 | 1.86528 | ||||||||
\(59\) | −3.40256 | −0.442975 | −0.221488 | − | 0.975163i | \(-0.571091\pi\) | ||||
−0.221488 | + | 0.975163i | \(0.571091\pi\) | |||||||
\(60\) | 1.41156 | 0.182232 | ||||||||
\(61\) | 0.430487 | 0.0551182 | 0.0275591 | − | 0.999620i | \(-0.491227\pi\) | ||||
0.0275591 | + | 0.999620i | \(0.491227\pi\) | |||||||
\(62\) | 18.2509 | 2.31787 | ||||||||
\(63\) | −4.81865 | −0.607092 | ||||||||
\(64\) | 4.45588 | 0.556985 | ||||||||
\(65\) | −0.932052 | −0.115607 | ||||||||
\(66\) | 4.98988 | 0.614211 | ||||||||
\(67\) | 14.0613 | 1.71786 | 0.858931 | − | 0.512091i | \(-0.171129\pi\) | ||||
0.858931 | + | 0.512091i | \(0.171129\pi\) | |||||||
\(68\) | 14.1036 | 1.71031 | ||||||||
\(69\) | −12.8764 | −1.55013 | ||||||||
\(70\) | 1.94316 | 0.232252 | ||||||||
\(71\) | 6.43164 | 0.763296 | 0.381648 | − | 0.924308i | \(-0.375357\pi\) | ||||
0.381648 | + | 0.924308i | \(0.375357\pi\) | |||||||
\(72\) | −6.74531 | −0.794942 | ||||||||
\(73\) | −3.94156 | −0.461325 | −0.230662 | − | 0.973034i | \(-0.574089\pi\) | ||||
−0.230662 | + | 0.973034i | \(0.574089\pi\) | |||||||
\(74\) | −21.1985 | −2.46427 | ||||||||
\(75\) | −9.91548 | −1.14494 | ||||||||
\(76\) | −23.7065 | −2.71933 | ||||||||
\(77\) | 4.81604 | 0.548839 | ||||||||
\(78\) | 31.8040 | 3.60110 | ||||||||
\(79\) | −2.73184 | −0.307356 | −0.153678 | − | 0.988121i | \(-0.549112\pi\) | ||||
−0.153678 | + | 0.988121i | \(0.549112\pi\) | |||||||
\(80\) | 1.30301 | 0.145681 | ||||||||
\(81\) | −10.9678 | −1.21865 | ||||||||
\(82\) | −0.206972 | −0.0228563 | ||||||||
\(83\) | 15.9217 | 1.74764 | 0.873819 | − | 0.486251i | \(-0.161636\pi\) | ||||
0.873819 | + | 0.486251i | \(0.161636\pi\) | |||||||
\(84\) | −46.4881 | −5.07227 | ||||||||
\(85\) | 0.454006 | 0.0492439 | ||||||||
\(86\) | 16.3934 | 1.76774 | ||||||||
\(87\) | −10.9402 | −1.17291 | ||||||||
\(88\) | 6.74167 | 0.718664 | ||||||||
\(89\) | −12.0433 | −1.27659 | −0.638293 | − | 0.769794i | \(-0.720359\pi\) | ||||
−0.638293 | + | 0.769794i | \(0.720359\pi\) | |||||||
\(90\) | −0.378483 | −0.0398956 | ||||||||
\(91\) | 30.6961 | 3.21782 | ||||||||
\(92\) | −30.3237 | −3.16147 | ||||||||
\(93\) | −14.0556 | −1.45750 | ||||||||
\(94\) | −32.2502 | −3.32635 | ||||||||
\(95\) | −0.763134 | −0.0782959 | ||||||||
\(96\) | −16.7206 | −1.70654 | ||||||||
\(97\) | −2.16350 | −0.219671 | −0.109835 | − | 0.993950i | \(-0.535032\pi\) | ||||
−0.109835 | + | 0.993950i | \(0.535032\pi\) | |||||||
\(98\) | −45.8882 | −4.63541 | ||||||||
\(99\) | −0.938054 | −0.0942779 | ||||||||
\(100\) | −23.3509 | −2.33509 | ||||||||
\(101\) | 0.313832 | 0.0312275 | 0.0156137 | − | 0.999878i | \(-0.495030\pi\) | ||||
0.0156137 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(102\) | −15.4919 | −1.53392 | ||||||||
\(103\) | 7.82414 | 0.770936 | 0.385468 | − | 0.922721i | \(-0.374040\pi\) | ||||
0.385468 | + | 0.922721i | \(0.374040\pi\) | |||||||
\(104\) | 42.9694 | 4.21350 | ||||||||
\(105\) | −1.49649 | −0.146043 | ||||||||
\(106\) | 19.4367 | 1.88786 | ||||||||
\(107\) | −1.77036 | −0.171147 | −0.0855736 | − | 0.996332i | \(-0.527272\pi\) | ||||
−0.0855736 | + | 0.996332i | \(0.527272\pi\) | |||||||
\(108\) | −18.9846 | −1.82680 | ||||||||
\(109\) | 14.8736 | 1.42463 | 0.712314 | − | 0.701861i | \(-0.247647\pi\) | ||||
0.712314 | + | 0.701861i | \(0.247647\pi\) | |||||||
\(110\) | 0.378279 | 0.0360675 | ||||||||
\(111\) | 16.3256 | 1.54956 | ||||||||
\(112\) | −42.9131 | −4.05491 | ||||||||
\(113\) | −0.180437 | −0.0169741 | −0.00848705 | − | 0.999964i | \(-0.502702\pi\) | ||||
−0.00848705 | + | 0.999964i | \(0.502702\pi\) | |||||||
\(114\) | 26.0401 | 2.43888 | ||||||||
\(115\) | −0.976146 | −0.0910261 | ||||||||
\(116\) | −25.7640 | −2.39212 | ||||||||
\(117\) | −5.97888 | −0.552748 | ||||||||
\(118\) | 8.80176 | 0.810268 | ||||||||
\(119\) | −14.9522 | −1.37066 | ||||||||
\(120\) | −2.09484 | −0.191232 | ||||||||
\(121\) | −10.0625 | −0.914768 | ||||||||
\(122\) | −1.11359 | −0.100819 | ||||||||
\(123\) | 0.159396 | 0.0143723 | ||||||||
\(124\) | −33.1009 | −2.97255 | ||||||||
\(125\) | −1.50681 | −0.134773 | ||||||||
\(126\) | 12.4649 | 1.11046 | ||||||||
\(127\) | −8.25832 | −0.732807 | −0.366404 | − | 0.930456i | \(-0.619411\pi\) | ||||
−0.366404 | + | 0.930456i | \(0.619411\pi\) | |||||||
\(128\) | 5.25970 | 0.464896 | ||||||||
\(129\) | −12.6251 | −1.11157 | ||||||||
\(130\) | 2.41104 | 0.211462 | ||||||||
\(131\) | 4.51551 | 0.394522 | 0.197261 | − | 0.980351i | \(-0.436795\pi\) | ||||
0.197261 | + | 0.980351i | \(0.436795\pi\) | |||||||
\(132\) | −9.04991 | −0.787694 | ||||||||
\(133\) | 25.1329 | 2.17930 | ||||||||
\(134\) | −36.3739 | −3.14223 | ||||||||
\(135\) | −0.611131 | −0.0525978 | ||||||||
\(136\) | −20.9306 | −1.79478 | ||||||||
\(137\) | 18.7466 | 1.60163 | 0.800814 | − | 0.598913i | \(-0.204400\pi\) | ||||
0.800814 | + | 0.598913i | \(0.204400\pi\) | |||||||
\(138\) | 33.3087 | 2.83542 | ||||||||
\(139\) | 12.0992 | 1.02624 | 0.513121 | − | 0.858316i | \(-0.328489\pi\) | ||||
0.513121 | + | 0.858316i | \(0.328489\pi\) | |||||||
\(140\) | −3.52423 | −0.297851 | ||||||||
\(141\) | 24.8369 | 2.09164 | ||||||||
\(142\) | −16.6374 | −1.39618 | ||||||||
\(143\) | 5.97565 | 0.499709 | ||||||||
\(144\) | 8.35849 | 0.696541 | ||||||||
\(145\) | −0.829364 | −0.0688749 | ||||||||
\(146\) | 10.1961 | 0.843832 | ||||||||
\(147\) | 35.3400 | 2.91479 | ||||||||
\(148\) | 38.4467 | 3.16030 | ||||||||
\(149\) | −18.6573 | −1.52846 | −0.764232 | − | 0.644941i | \(-0.776882\pi\) | ||||
−0.764232 | + | 0.644941i | \(0.776882\pi\) | |||||||
\(150\) | 25.6494 | 2.09427 | ||||||||
\(151\) | −18.9369 | −1.54107 | −0.770534 | − | 0.637399i | \(-0.780010\pi\) | ||||
−0.770534 | + | 0.637399i | \(0.780010\pi\) | |||||||
\(152\) | 35.1820 | 2.85363 | ||||||||
\(153\) | 2.91234 | 0.235449 | ||||||||
\(154\) | −12.4582 | −1.00391 | ||||||||
\(155\) | −1.06555 | −0.0855867 | ||||||||
\(156\) | −57.6815 | −4.61822 | ||||||||
\(157\) | 23.4623 | 1.87250 | 0.936248 | − | 0.351341i | \(-0.114274\pi\) | ||||
0.936248 | + | 0.351341i | \(0.114274\pi\) | |||||||
\(158\) | 7.06674 | 0.562200 | ||||||||
\(159\) | −14.9689 | −1.18711 | ||||||||
\(160\) | −1.26757 | −0.100211 | ||||||||
\(161\) | 32.1483 | 2.53364 | ||||||||
\(162\) | 28.3716 | 2.22909 | ||||||||
\(163\) | −11.8742 | −0.930060 | −0.465030 | − | 0.885295i | \(-0.653956\pi\) | ||||
−0.465030 | + | 0.885295i | \(0.653956\pi\) | |||||||
\(164\) | 0.375376 | 0.0293120 | ||||||||
\(165\) | −0.291324 | −0.0226796 | ||||||||
\(166\) | −41.1865 | −3.19669 | ||||||||
\(167\) | 3.72636 | 0.288355 | 0.144177 | − | 0.989552i | \(-0.453946\pi\) | ||||
0.144177 | + | 0.989552i | \(0.453946\pi\) | |||||||
\(168\) | 68.9912 | 5.32279 | ||||||||
\(169\) | 25.0871 | 1.92978 | ||||||||
\(170\) | −1.17443 | −0.0900744 | ||||||||
\(171\) | −4.89532 | −0.374354 | ||||||||
\(172\) | −29.7319 | −2.26704 | ||||||||
\(173\) | −2.59867 | −0.197573 | −0.0987867 | − | 0.995109i | \(-0.531496\pi\) | ||||
−0.0987867 | + | 0.995109i | \(0.531496\pi\) | |||||||
\(174\) | 28.3001 | 2.14542 | ||||||||
\(175\) | 24.7559 | 1.87137 | ||||||||
\(176\) | −8.35397 | −0.629704 | ||||||||
\(177\) | −6.77852 | −0.509505 | ||||||||
\(178\) | 31.1537 | 2.33507 | ||||||||
\(179\) | −9.23214 | −0.690042 | −0.345021 | − | 0.938595i | \(-0.612128\pi\) | ||||
−0.345021 | + | 0.938595i | \(0.612128\pi\) | |||||||
\(180\) | 0.686438 | 0.0511640 | ||||||||
\(181\) | 5.00108 | 0.371727 | 0.185864 | − | 0.982576i | \(-0.440492\pi\) | ||||
0.185864 | + | 0.982576i | \(0.440492\pi\) | |||||||
\(182\) | −79.4048 | −5.88588 | ||||||||
\(183\) | 0.857609 | 0.0633963 | ||||||||
\(184\) | 45.0023 | 3.31761 | ||||||||
\(185\) | 1.23763 | 0.0909926 | ||||||||
\(186\) | 36.3592 | 2.66599 | ||||||||
\(187\) | −2.91076 | −0.212856 | ||||||||
\(188\) | 58.4906 | 4.26587 | ||||||||
\(189\) | 20.1269 | 1.46402 | ||||||||
\(190\) | 1.97408 | 0.143215 | ||||||||
\(191\) | −19.0187 | −1.37615 | −0.688073 | − | 0.725642i | \(-0.741543\pi\) | ||||
−0.688073 | + | 0.725642i | \(0.741543\pi\) | |||||||
\(192\) | 8.87693 | 0.640637 | ||||||||
\(193\) | 23.6376 | 1.70147 | 0.850737 | − | 0.525592i | \(-0.176156\pi\) | ||||
0.850737 | + | 0.525592i | \(0.176156\pi\) | |||||||
\(194\) | 5.59657 | 0.401810 | ||||||||
\(195\) | −1.85682 | −0.132969 | ||||||||
\(196\) | 83.2253 | 5.94467 | ||||||||
\(197\) | −5.72476 | −0.407873 | −0.203936 | − | 0.978984i | \(-0.565374\pi\) | ||||
−0.203936 | + | 0.978984i | \(0.565374\pi\) | |||||||
\(198\) | 2.42656 | 0.172448 | ||||||||
\(199\) | −4.99872 | −0.354350 | −0.177175 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177175 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(200\) | 34.6541 | 2.45042 | ||||||||
\(201\) | 28.0127 | 1.97586 | ||||||||
\(202\) | −0.811824 | −0.0571198 | ||||||||
\(203\) | 27.3142 | 1.91708 | ||||||||
\(204\) | 28.0969 | 1.96718 | ||||||||
\(205\) | 0.0120837 | 0.000843961 0 | ||||||||
\(206\) | −20.2395 | −1.41016 | ||||||||
\(207\) | −6.26174 | −0.435221 | ||||||||
\(208\) | −53.2458 | −3.69193 | ||||||||
\(209\) | 4.89267 | 0.338433 | ||||||||
\(210\) | 3.87114 | 0.267134 | ||||||||
\(211\) | −24.0350 | −1.65463 | −0.827317 | − | 0.561735i | \(-0.810134\pi\) | ||||
−0.827317 | + | 0.561735i | \(0.810134\pi\) | |||||||
\(212\) | −35.2515 | −2.42109 | ||||||||
\(213\) | 12.8130 | 0.877933 | ||||||||
\(214\) | 4.57958 | 0.313054 | ||||||||
\(215\) | −0.957095 | −0.0652733 | ||||||||
\(216\) | 28.1744 | 1.91702 | ||||||||
\(217\) | 35.0926 | 2.38224 | ||||||||
\(218\) | −38.4750 | −2.60586 | ||||||||
\(219\) | −7.85231 | −0.530610 | ||||||||
\(220\) | −0.686067 | −0.0462546 | ||||||||
\(221\) | −18.5524 | −1.24797 | ||||||||
\(222\) | −42.2313 | −2.83438 | ||||||||
\(223\) | 8.04524 | 0.538749 | 0.269375 | − | 0.963035i | \(-0.413183\pi\) | ||||
0.269375 | + | 0.963035i | \(0.413183\pi\) | |||||||
\(224\) | 41.7461 | 2.78928 | ||||||||
\(225\) | −4.82187 | −0.321458 | ||||||||
\(226\) | 0.466756 | 0.0310482 | ||||||||
\(227\) | −6.79371 | −0.450915 | −0.225457 | − | 0.974253i | \(-0.572388\pi\) | ||||
−0.225457 | + | 0.974253i | \(0.572388\pi\) | |||||||
\(228\) | −47.2278 | −3.12774 | ||||||||
\(229\) | 8.33769 | 0.550970 | 0.275485 | − | 0.961305i | \(-0.411162\pi\) | ||||
0.275485 | + | 0.961305i | \(0.411162\pi\) | |||||||
\(230\) | 2.52510 | 0.166500 | ||||||||
\(231\) | 9.59444 | 0.631268 | ||||||||
\(232\) | 38.2353 | 2.51027 | ||||||||
\(233\) | −11.0817 | −0.725988 | −0.362994 | − | 0.931791i | \(-0.618245\pi\) | ||||
−0.362994 | + | 0.931791i | \(0.618245\pi\) | |||||||
\(234\) | 15.4662 | 1.01106 | ||||||||
\(235\) | 1.88286 | 0.122824 | ||||||||
\(236\) | −15.9634 | −1.03913 | ||||||||
\(237\) | −5.44232 | −0.353517 | ||||||||
\(238\) | 38.6784 | 2.50715 | ||||||||
\(239\) | 19.3530 | 1.25184 | 0.625919 | − | 0.779888i | \(-0.284724\pi\) | ||||
0.625919 | + | 0.779888i | \(0.284724\pi\) | |||||||
\(240\) | 2.59583 | 0.167560 | ||||||||
\(241\) | 0.868809 | 0.0559649 | 0.0279824 | − | 0.999608i | \(-0.491092\pi\) | ||||
0.0279824 | + | 0.999608i | \(0.491092\pi\) | |||||||
\(242\) | 26.0296 | 1.67325 | ||||||||
\(243\) | −9.71030 | −0.622916 | ||||||||
\(244\) | 2.01966 | 0.129296 | ||||||||
\(245\) | 2.67909 | 0.171161 | ||||||||
\(246\) | −0.412327 | −0.0262890 | ||||||||
\(247\) | 31.1845 | 1.98422 | ||||||||
\(248\) | 49.1238 | 3.11936 | ||||||||
\(249\) | 31.7190 | 2.01011 | ||||||||
\(250\) | 3.89784 | 0.246521 | ||||||||
\(251\) | 29.4712 | 1.86021 | 0.930103 | − | 0.367299i | \(-0.119717\pi\) | ||||
0.930103 | + | 0.367299i | \(0.119717\pi\) | |||||||
\(252\) | −22.6070 | −1.42411 | ||||||||
\(253\) | 6.25836 | 0.393459 | ||||||||
\(254\) | 21.3627 | 1.34041 | ||||||||
\(255\) | 0.904463 | 0.0566397 | ||||||||
\(256\) | −22.5176 | −1.40735 | ||||||||
\(257\) | −19.3230 | −1.20534 | −0.602668 | − | 0.797992i | \(-0.705896\pi\) | ||||
−0.602668 | + | 0.797992i | \(0.705896\pi\) | |||||||
\(258\) | 32.6586 | 2.03323 | ||||||||
\(259\) | −40.7600 | −2.53271 | ||||||||
\(260\) | −4.37279 | −0.271189 | ||||||||
\(261\) | −5.32017 | −0.329310 | ||||||||
\(262\) | −11.6807 | −0.721639 | ||||||||
\(263\) | −18.6227 | −1.14833 | −0.574163 | − | 0.818741i | \(-0.694672\pi\) | ||||
−0.574163 | + | 0.818741i | \(0.694672\pi\) | |||||||
\(264\) | 13.4306 | 0.826598 | ||||||||
\(265\) | −1.13478 | −0.0697088 | ||||||||
\(266\) | −65.0141 | −3.98627 | ||||||||
\(267\) | −23.9924 | −1.46831 | ||||||||
\(268\) | 65.9697 | 4.02974 | ||||||||
\(269\) | 4.29321 | 0.261762 | 0.130881 | − | 0.991398i | \(-0.458219\pi\) | ||||
0.130881 | + | 0.991398i | \(0.458219\pi\) | |||||||
\(270\) | 1.58088 | 0.0962092 | ||||||||
\(271\) | −12.8878 | −0.782875 | −0.391438 | − | 0.920205i | \(-0.628022\pi\) | ||||
−0.391438 | + | 0.920205i | \(0.628022\pi\) | |||||||
\(272\) | 25.9362 | 1.57262 | ||||||||
\(273\) | 61.1522 | 3.70110 | ||||||||
\(274\) | −48.4938 | −2.92962 | ||||||||
\(275\) | 4.81926 | 0.290613 | ||||||||
\(276\) | −60.4104 | −3.63628 | ||||||||
\(277\) | −10.4687 | −0.629004 | −0.314502 | − | 0.949257i | \(-0.601838\pi\) | ||||
−0.314502 | + | 0.949257i | \(0.601838\pi\) | |||||||
\(278\) | −31.2984 | −1.87715 | ||||||||
\(279\) | −6.83522 | −0.409214 | ||||||||
\(280\) | 5.23017 | 0.312562 | ||||||||
\(281\) | −11.2590 | −0.671656 | −0.335828 | − | 0.941923i | \(-0.609016\pi\) | ||||
−0.335828 | + | 0.941923i | \(0.609016\pi\) | |||||||
\(282\) | −64.2482 | −3.82593 | ||||||||
\(283\) | 12.8406 | 0.763293 | 0.381646 | − | 0.924308i | \(-0.375357\pi\) | ||||
0.381646 | + | 0.924308i | \(0.375357\pi\) | |||||||
\(284\) | 30.1745 | 1.79053 | ||||||||
\(285\) | −1.52030 | −0.0900549 | ||||||||
\(286\) | −15.4579 | −0.914043 | ||||||||
\(287\) | −0.397963 | −0.0234910 | ||||||||
\(288\) | −8.13118 | −0.479134 | ||||||||
\(289\) | −7.96307 | −0.468416 | ||||||||
\(290\) | 2.14541 | 0.125983 | ||||||||
\(291\) | −4.31010 | −0.252662 | ||||||||
\(292\) | −18.4921 | −1.08217 | ||||||||
\(293\) | −5.88607 | −0.343868 | −0.171934 | − | 0.985108i | \(-0.555002\pi\) | ||||
−0.171934 | + | 0.985108i | \(0.555002\pi\) | |||||||
\(294\) | −91.4177 | −5.33159 | ||||||||
\(295\) | −0.513874 | −0.0299189 | ||||||||
\(296\) | −57.0573 | −3.31639 | ||||||||
\(297\) | 3.91814 | 0.227353 | ||||||||
\(298\) | 48.2628 | 2.79579 | ||||||||
\(299\) | 39.8889 | 2.30684 | ||||||||
\(300\) | −46.5192 | −2.68579 | ||||||||
\(301\) | 31.5208 | 1.81683 | ||||||||
\(302\) | 48.9863 | 2.81884 | ||||||||
\(303\) | 0.625212 | 0.0359175 | ||||||||
\(304\) | −43.5959 | −2.50040 | ||||||||
\(305\) | 0.0650146 | 0.00372273 | ||||||||
\(306\) | −7.53366 | −0.430671 | ||||||||
\(307\) | −8.74852 | −0.499305 | −0.249652 | − | 0.968336i | \(-0.580316\pi\) | ||||
−0.249652 | + | 0.968336i | \(0.580316\pi\) | |||||||
\(308\) | 22.5948 | 1.28746 | ||||||||
\(309\) | 15.5871 | 0.886720 | ||||||||
\(310\) | 2.75636 | 0.156551 | ||||||||
\(311\) | −19.0704 | −1.08139 | −0.540693 | − | 0.841220i | \(-0.681838\pi\) | ||||
−0.540693 | + | 0.841220i | \(0.681838\pi\) | |||||||
\(312\) | 85.6030 | 4.84631 | ||||||||
\(313\) | −6.17966 | −0.349295 | −0.174648 | − | 0.984631i | \(-0.555879\pi\) | ||||
−0.174648 | + | 0.984631i | \(0.555879\pi\) | |||||||
\(314\) | −60.6925 | −3.42507 | ||||||||
\(315\) | −0.727740 | −0.0410035 | ||||||||
\(316\) | −12.8166 | −0.720991 | ||||||||
\(317\) | 5.33981 | 0.299913 | 0.149957 | − | 0.988693i | \(-0.452087\pi\) | ||||
0.149957 | + | 0.988693i | \(0.452087\pi\) | |||||||
\(318\) | 38.7216 | 2.17140 | ||||||||
\(319\) | 5.31729 | 0.297711 | ||||||||
\(320\) | 0.672953 | 0.0376192 | ||||||||
\(321\) | −3.52688 | −0.196851 | ||||||||
\(322\) | −83.1614 | −4.63440 | ||||||||
\(323\) | −15.1901 | −0.845198 | ||||||||
\(324\) | −51.4564 | −2.85869 | ||||||||
\(325\) | 30.7166 | 1.70385 | ||||||||
\(326\) | 30.7163 | 1.70122 | ||||||||
\(327\) | 29.6308 | 1.63859 | ||||||||
\(328\) | −0.557082 | −0.0307597 | ||||||||
\(329\) | −62.0100 | −3.41872 | ||||||||
\(330\) | 0.753600 | 0.0414843 | ||||||||
\(331\) | 18.2390 | 1.00250 | 0.501252 | − | 0.865301i | \(-0.332873\pi\) | ||||
0.501252 | + | 0.865301i | \(0.332873\pi\) | |||||||
\(332\) | 74.6981 | 4.09959 | ||||||||
\(333\) | 7.93911 | 0.435061 | ||||||||
\(334\) | −9.63938 | −0.527444 | ||||||||
\(335\) | 2.12362 | 0.116026 | ||||||||
\(336\) | −85.4908 | −4.66391 | ||||||||
\(337\) | 29.5450 | 1.60942 | 0.804710 | − | 0.593668i | \(-0.202321\pi\) | ||||
0.804710 | + | 0.593668i | \(0.202321\pi\) | |||||||
\(338\) | −64.8955 | −3.52985 | ||||||||
\(339\) | −0.359464 | −0.0195234 | ||||||||
\(340\) | 2.13000 | 0.115516 | ||||||||
\(341\) | 6.83152 | 0.369948 | ||||||||
\(342\) | 12.6632 | 0.684750 | ||||||||
\(343\) | −53.4159 | −2.88419 | ||||||||
\(344\) | 44.1240 | 2.37901 | ||||||||
\(345\) | −1.94466 | −0.104697 | ||||||||
\(346\) | 6.72226 | 0.361391 | ||||||||
\(347\) | −21.9194 | −1.17669 | −0.588347 | − | 0.808608i | \(-0.700221\pi\) | ||||
−0.588347 | + | 0.808608i | \(0.700221\pi\) | |||||||
\(348\) | −51.3265 | −2.75139 | ||||||||
\(349\) | 5.27001 | 0.282097 | 0.141048 | − | 0.990003i | \(-0.454953\pi\) | ||||
0.141048 | + | 0.990003i | \(0.454953\pi\) | |||||||
\(350\) | −64.0387 | −3.42301 | ||||||||
\(351\) | 24.9731 | 1.33296 | ||||||||
\(352\) | 8.12679 | 0.433159 | ||||||||
\(353\) | −33.0100 | −1.75694 | −0.878472 | − | 0.477795i | \(-0.841436\pi\) | ||||
−0.878472 | + | 0.477795i | \(0.841436\pi\) | |||||||
\(354\) | 17.5347 | 0.931960 | ||||||||
\(355\) | 0.971344 | 0.0515536 | ||||||||
\(356\) | −56.5020 | −2.99460 | ||||||||
\(357\) | −29.7875 | −1.57652 | ||||||||
\(358\) | 23.8818 | 1.26219 | ||||||||
\(359\) | −19.7262 | −1.04111 | −0.520554 | − | 0.853829i | \(-0.674274\pi\) | ||||
−0.520554 | + | 0.853829i | \(0.674274\pi\) | |||||||
\(360\) | −1.01872 | −0.0536910 | ||||||||
\(361\) | 6.53282 | 0.343833 | ||||||||
\(362\) | −12.9368 | −0.679945 | ||||||||
\(363\) | −20.0462 | −1.05216 | ||||||||
\(364\) | 144.013 | 7.54833 | ||||||||
\(365\) | −0.595277 | −0.0311582 | ||||||||
\(366\) | −2.21847 | −0.115961 | ||||||||
\(367\) | −19.1526 | −0.999756 | −0.499878 | − | 0.866096i | \(-0.666622\pi\) | ||||
−0.499878 | + | 0.866096i | \(0.666622\pi\) | |||||||
\(368\) | −55.7648 | −2.90694 | ||||||||
\(369\) | 0.0775139 | 0.00403521 | ||||||||
\(370\) | −3.20152 | −0.166439 | ||||||||
\(371\) | 37.3726 | 1.94029 | ||||||||
\(372\) | −65.9431 | −3.41899 | ||||||||
\(373\) | 15.8379 | 0.820054 | 0.410027 | − | 0.912073i | \(-0.365519\pi\) | ||||
0.410027 | + | 0.912073i | \(0.365519\pi\) | |||||||
\(374\) | 7.52959 | 0.389346 | ||||||||
\(375\) | −3.00185 | −0.155015 | ||||||||
\(376\) | −86.8037 | −4.47656 | ||||||||
\(377\) | 33.8909 | 1.74547 | ||||||||
\(378\) | −52.0645 | −2.67791 | ||||||||
\(379\) | 9.25970 | 0.475639 | 0.237819 | − | 0.971309i | \(-0.423567\pi\) | ||||
0.237819 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(380\) | −3.58030 | −0.183665 | ||||||||
\(381\) | −16.4521 | −0.842866 | ||||||||
\(382\) | 49.1977 | 2.51718 | ||||||||
\(383\) | −29.6271 | −1.51387 | −0.756936 | − | 0.653489i | \(-0.773305\pi\) | ||||
−0.756936 | + | 0.653489i | \(0.773305\pi\) | |||||||
\(384\) | 10.4783 | 0.534717 | ||||||||
\(385\) | 0.727347 | 0.0370690 | ||||||||
\(386\) | −61.1460 | −3.11225 | ||||||||
\(387\) | −6.13953 | −0.312090 | ||||||||
\(388\) | −10.1502 | −0.515301 | ||||||||
\(389\) | −8.19494 | −0.415500 | −0.207750 | − | 0.978182i | \(-0.566614\pi\) | ||||
−0.207750 | + | 0.978182i | \(0.566614\pi\) | |||||||
\(390\) | 4.80323 | 0.243221 | ||||||||
\(391\) | −19.4301 | −0.982621 | ||||||||
\(392\) | −123.512 | −6.23828 | ||||||||
\(393\) | 8.99572 | 0.453774 | ||||||||
\(394\) | 14.8089 | 0.746060 | ||||||||
\(395\) | −0.412578 | −0.0207591 | ||||||||
\(396\) | −4.40095 | −0.221156 | ||||||||
\(397\) | 6.85428 | 0.344006 | 0.172003 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172003 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(398\) | 12.9307 | 0.648159 | ||||||||
\(399\) | 50.0694 | 2.50661 | ||||||||
\(400\) | −42.9419 | −2.14709 | ||||||||
\(401\) | 7.13203 | 0.356157 | 0.178078 | − | 0.984016i | \(-0.443012\pi\) | ||||
0.178078 | + | 0.984016i | \(0.443012\pi\) | |||||||
\(402\) | −72.4635 | −3.61415 | ||||||||
\(403\) | 43.5422 | 2.16899 | ||||||||
\(404\) | 1.47237 | 0.0732531 | ||||||||
\(405\) | −1.65642 | −0.0823084 | ||||||||
\(406\) | −70.6565 | −3.50662 | ||||||||
\(407\) | −7.93482 | −0.393314 | ||||||||
\(408\) | −41.6975 | −2.06434 | ||||||||
\(409\) | 32.8102 | 1.62236 | 0.811179 | − | 0.584798i | \(-0.198826\pi\) | ||||
0.811179 | + | 0.584798i | \(0.198826\pi\) | |||||||
\(410\) | −0.0312582 | −0.00154373 | ||||||||
\(411\) | 37.3466 | 1.84217 | ||||||||
\(412\) | 36.7075 | 1.80845 | ||||||||
\(413\) | 16.9239 | 0.832769 | ||||||||
\(414\) | 16.1979 | 0.796084 | ||||||||
\(415\) | 2.40459 | 0.118037 | ||||||||
\(416\) | 51.7978 | 2.53960 | ||||||||
\(417\) | 24.1039 | 1.18037 | ||||||||
\(418\) | −12.6564 | −0.619045 | ||||||||
\(419\) | 17.6200 | 0.860795 | 0.430397 | − | 0.902640i | \(-0.358373\pi\) | ||||
0.430397 | + | 0.902640i | \(0.358373\pi\) | |||||||
\(420\) | −7.02090 | −0.342585 | ||||||||
\(421\) | −37.8157 | −1.84302 | −0.921512 | − | 0.388350i | \(-0.873045\pi\) | ||||
−0.921512 | + | 0.388350i | \(0.873045\pi\) | |||||||
\(422\) | 62.1738 | 3.02657 | ||||||||
\(423\) | 12.0781 | 0.587258 | ||||||||
\(424\) | 52.3155 | 2.54066 | ||||||||
\(425\) | −14.9622 | −0.725772 | ||||||||
\(426\) | −33.1448 | −1.60587 | ||||||||
\(427\) | −2.14118 | −0.103619 | ||||||||
\(428\) | −8.30578 | −0.401475 | ||||||||
\(429\) | 11.9046 | 0.574759 | ||||||||
\(430\) | 2.47582 | 0.119395 | ||||||||
\(431\) | −17.0613 | −0.821812 | −0.410906 | − | 0.911678i | \(-0.634788\pi\) | ||||
−0.410906 | + | 0.911678i | \(0.634788\pi\) | |||||||
\(432\) | −34.9124 | −1.67972 | ||||||||
\(433\) | 35.9074 | 1.72560 | 0.862801 | − | 0.505544i | \(-0.168708\pi\) | ||||
0.862801 | + | 0.505544i | \(0.168708\pi\) | |||||||
\(434\) | −90.7777 | −4.35747 | ||||||||
\(435\) | −1.65225 | −0.0792191 | ||||||||
\(436\) | 69.7804 | 3.34187 | ||||||||
\(437\) | 32.6598 | 1.56233 | ||||||||
\(438\) | 20.3124 | 0.970565 | ||||||||
\(439\) | −17.3935 | −0.830147 | −0.415074 | − | 0.909788i | \(-0.636244\pi\) | ||||
−0.415074 | + | 0.909788i | \(0.636244\pi\) | |||||||
\(440\) | 1.01817 | 0.0485391 | ||||||||
\(441\) | 17.1857 | 0.818368 | ||||||||
\(442\) | 47.9914 | 2.28272 | ||||||||
\(443\) | 16.5288 | 0.785307 | 0.392654 | − | 0.919686i | \(-0.371557\pi\) | ||||
0.392654 | + | 0.919686i | \(0.371557\pi\) | |||||||
\(444\) | 76.5929 | 3.63494 | ||||||||
\(445\) | −1.81885 | −0.0862216 | ||||||||
\(446\) | −20.8115 | −0.985453 | ||||||||
\(447\) | −37.1687 | −1.75802 | ||||||||
\(448\) | −22.1629 | −1.04710 | ||||||||
\(449\) | −7.12487 | −0.336243 | −0.168122 | − | 0.985766i | \(-0.553770\pi\) | ||||
−0.168122 | + | 0.985766i | \(0.553770\pi\) | |||||||
\(450\) | 12.4733 | 0.587995 | ||||||||
\(451\) | −0.0774720 | −0.00364801 | ||||||||
\(452\) | −0.846534 | −0.0398176 | ||||||||
\(453\) | −37.7259 | −1.77252 | ||||||||
\(454\) | 17.5740 | 0.824790 | ||||||||
\(455\) | 4.63590 | 0.217334 | ||||||||
\(456\) | 70.0889 | 3.28221 | ||||||||
\(457\) | −1.36874 | −0.0640268 | −0.0320134 | − | 0.999487i | \(-0.510192\pi\) | ||||
−0.0320134 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(458\) | −21.5680 | −1.00781 | ||||||||
\(459\) | −12.1645 | −0.567790 | ||||||||
\(460\) | −4.57966 | −0.213528 | ||||||||
\(461\) | 17.6511 | 0.822094 | 0.411047 | − | 0.911614i | \(-0.365163\pi\) | ||||
0.411047 | + | 0.911614i | \(0.365163\pi\) | |||||||
\(462\) | −24.8190 | −1.15468 | ||||||||
\(463\) | 13.7068 | 0.637009 | 0.318505 | − | 0.947921i | \(-0.396819\pi\) | ||||
0.318505 | + | 0.947921i | \(0.396819\pi\) | |||||||
\(464\) | −47.3795 | −2.19954 | ||||||||
\(465\) | −2.12276 | −0.0984408 | ||||||||
\(466\) | 28.6663 | 1.32794 | ||||||||
\(467\) | 10.3100 | 0.477088 | 0.238544 | − | 0.971132i | \(-0.423330\pi\) | ||||
0.238544 | + | 0.971132i | \(0.423330\pi\) | |||||||
\(468\) | −28.0504 | −1.29663 | ||||||||
\(469\) | −69.9391 | −3.22949 | ||||||||
\(470\) | −4.87061 | −0.224664 | ||||||||
\(471\) | 46.7412 | 2.15372 | ||||||||
\(472\) | 23.6906 | 1.09045 | ||||||||
\(473\) | 6.13621 | 0.282143 | ||||||||
\(474\) | 14.0782 | 0.646635 | ||||||||
\(475\) | 25.1498 | 1.15395 | ||||||||
\(476\) | −70.1492 | −3.21529 | ||||||||
\(477\) | −7.27932 | −0.333297 | ||||||||
\(478\) | −50.0624 | −2.28980 | ||||||||
\(479\) | −37.8772 | −1.73066 | −0.865328 | − | 0.501206i | \(-0.832890\pi\) | ||||
−0.865328 | + | 0.501206i | \(0.832890\pi\) | |||||||
\(480\) | −2.52524 | −0.115261 | ||||||||
\(481\) | −50.5743 | −2.30599 | ||||||||
\(482\) | −2.24744 | −0.102368 | ||||||||
\(483\) | 64.0452 | 2.91416 | ||||||||
\(484\) | −47.2088 | −2.14585 | ||||||||
\(485\) | −0.326745 | −0.0148367 | ||||||||
\(486\) | 25.1187 | 1.13941 | ||||||||
\(487\) | −12.1461 | −0.550391 | −0.275196 | − | 0.961388i | \(-0.588743\pi\) | ||||
−0.275196 | + | 0.961388i | \(0.588743\pi\) | |||||||
\(488\) | −2.99730 | −0.135682 | ||||||||
\(489\) | −23.6556 | −1.06974 | ||||||||
\(490\) | −6.93030 | −0.313079 | ||||||||
\(491\) | −26.3989 | −1.19136 | −0.595682 | − | 0.803221i | \(-0.703118\pi\) | ||||
−0.595682 | + | 0.803221i | \(0.703118\pi\) | |||||||
\(492\) | 0.747819 | 0.0337143 | ||||||||
\(493\) | −16.5084 | −0.743500 | ||||||||
\(494\) | −80.6682 | −3.62943 | ||||||||
\(495\) | −0.141670 | −0.00636761 | ||||||||
\(496\) | −60.8720 | −2.73323 | ||||||||
\(497\) | −31.9901 | −1.43495 | ||||||||
\(498\) | −82.0511 | −3.67680 | ||||||||
\(499\) | −16.6196 | −0.743997 | −0.371999 | − | 0.928233i | \(-0.621327\pi\) | ||||
−0.371999 | + | 0.928233i | \(0.621327\pi\) | |||||||
\(500\) | −7.06933 | −0.316150 | ||||||||
\(501\) | 7.42360 | 0.331662 | ||||||||
\(502\) | −76.2364 | −3.40260 | ||||||||
\(503\) | −3.29795 | −0.147048 | −0.0735241 | − | 0.997293i | \(-0.523425\pi\) | ||||
−0.0735241 | + | 0.997293i | \(0.523425\pi\) | |||||||
\(504\) | 33.5503 | 1.49445 | ||||||||
\(505\) | 0.0473968 | 0.00210913 | ||||||||
\(506\) | −16.1892 | −0.719696 | ||||||||
\(507\) | 49.9781 | 2.21960 | ||||||||
\(508\) | −38.7445 | −1.71901 | ||||||||
\(509\) | −38.2183 | −1.69400 | −0.846999 | − | 0.531595i | \(-0.821593\pi\) | ||||
−0.846999 | + | 0.531595i | \(0.821593\pi\) | |||||||
\(510\) | −2.33967 | −0.103602 | ||||||||
\(511\) | 19.6048 | 0.867264 | ||||||||
\(512\) | 47.7293 | 2.10936 | ||||||||
\(513\) | 20.4471 | 0.902764 | ||||||||
\(514\) | 49.9849 | 2.20474 | ||||||||
\(515\) | 1.18165 | 0.0520696 | ||||||||
\(516\) | −59.2314 | −2.60752 | ||||||||
\(517\) | −12.0716 | −0.530907 | ||||||||
\(518\) | 105.438 | 4.63270 | ||||||||
\(519\) | −5.17703 | −0.227246 | ||||||||
\(520\) | 6.48949 | 0.284583 | ||||||||
\(521\) | 22.0306 | 0.965180 | 0.482590 | − | 0.875846i | \(-0.339696\pi\) | ||||
0.482590 | + | 0.875846i | \(0.339696\pi\) | |||||||
\(522\) | 13.7623 | 0.602357 | ||||||||
\(523\) | 38.2309 | 1.67172 | 0.835861 | − | 0.548942i | \(-0.184969\pi\) | ||||
0.835861 | + | 0.548942i | \(0.184969\pi\) | |||||||
\(524\) | 21.1848 | 0.925464 | ||||||||
\(525\) | 49.3182 | 2.15242 | ||||||||
\(526\) | 48.1734 | 2.10046 | ||||||||
\(527\) | −21.2096 | −0.923903 | ||||||||
\(528\) | −16.6426 | −0.724278 | ||||||||
\(529\) | 18.7761 | 0.816351 | ||||||||
\(530\) | 2.93545 | 0.127508 | ||||||||
\(531\) | −3.29638 | −0.143051 | ||||||||
\(532\) | 117.913 | 5.11218 | ||||||||
\(533\) | −0.493784 | −0.0213882 | ||||||||
\(534\) | 62.0638 | 2.68576 | ||||||||
\(535\) | −0.267370 | −0.0115594 | ||||||||
\(536\) | −97.9031 | −4.22877 | ||||||||
\(537\) | −18.3921 | −0.793678 | ||||||||
\(538\) | −11.1057 | −0.478801 | ||||||||
\(539\) | −17.1764 | −0.739842 | ||||||||
\(540\) | −2.86717 | −0.123383 | ||||||||
\(541\) | −35.2959 | −1.51749 | −0.758744 | − | 0.651389i | \(-0.774186\pi\) | ||||
−0.758744 | + | 0.651389i | \(0.774186\pi\) | |||||||
\(542\) | 33.3382 | 1.43200 | ||||||||
\(543\) | 9.96306 | 0.427556 | ||||||||
\(544\) | −25.2309 | −1.08177 | ||||||||
\(545\) | 2.24629 | 0.0962205 | ||||||||
\(546\) | −158.189 | −6.76986 | ||||||||
\(547\) | −32.7415 | −1.39992 | −0.699962 | − | 0.714180i | \(-0.746800\pi\) | ||||
−0.699962 | + | 0.714180i | \(0.746800\pi\) | |||||||
\(548\) | 87.9510 | 3.75708 | ||||||||
\(549\) | 0.417053 | 0.0177994 | ||||||||
\(550\) | −12.4665 | −0.531574 | ||||||||
\(551\) | 27.7488 | 1.18214 | ||||||||
\(552\) | 89.6528 | 3.81588 | ||||||||
\(553\) | 13.5878 | 0.577812 | ||||||||
\(554\) | 27.0806 | 1.15054 | ||||||||
\(555\) | 2.46559 | 0.104659 | ||||||||
\(556\) | 56.7644 | 2.40735 | ||||||||
\(557\) | 27.7016 | 1.17375 | 0.586876 | − | 0.809677i | \(-0.300357\pi\) | ||||
0.586876 | + | 0.809677i | \(0.300357\pi\) | |||||||
\(558\) | 17.6814 | 0.748513 | ||||||||
\(559\) | 39.1105 | 1.65420 | ||||||||
\(560\) | −6.48099 | −0.273872 | ||||||||
\(561\) | −5.79877 | −0.244824 | ||||||||
\(562\) | 29.1249 | 1.22856 | ||||||||
\(563\) | 13.9198 | 0.586649 | 0.293325 | − | 0.956013i | \(-0.405238\pi\) | ||||
0.293325 | + | 0.956013i | \(0.405238\pi\) | |||||||
\(564\) | 116.524 | 4.90655 | ||||||||
\(565\) | −0.0272507 | −0.00114644 | ||||||||
\(566\) | −33.2161 | −1.39618 | ||||||||
\(567\) | 54.5524 | 2.29099 | ||||||||
\(568\) | −44.7809 | −1.87896 | ||||||||
\(569\) | −36.3945 | −1.52574 | −0.762869 | − | 0.646553i | \(-0.776210\pi\) | ||||
−0.762869 | + | 0.646553i | \(0.776210\pi\) | |||||||
\(570\) | 3.93273 | 0.164724 | ||||||||
\(571\) | −45.4291 | −1.90115 | −0.950574 | − | 0.310498i | \(-0.899504\pi\) | ||||
−0.950574 | + | 0.310498i | \(0.899504\pi\) | |||||||
\(572\) | 28.0352 | 1.17221 | ||||||||
\(573\) | −37.8887 | −1.58282 | ||||||||
\(574\) | 1.02945 | 0.0429685 | ||||||||
\(575\) | 32.1698 | 1.34157 | ||||||||
\(576\) | 4.31683 | 0.179868 | ||||||||
\(577\) | −31.5444 | −1.31321 | −0.656605 | − | 0.754235i | \(-0.728008\pi\) | ||||
−0.656605 | + | 0.754235i | \(0.728008\pi\) | |||||||
\(578\) | 20.5989 | 0.856803 | ||||||||
\(579\) | 47.0905 | 1.95701 | ||||||||
\(580\) | −3.89102 | −0.161566 | ||||||||
\(581\) | −79.1926 | −3.28546 | ||||||||
\(582\) | 11.1494 | 0.462157 | ||||||||
\(583\) | 7.27538 | 0.301316 | ||||||||
\(584\) | 27.4435 | 1.13562 | ||||||||
\(585\) | −0.902966 | −0.0373330 | ||||||||
\(586\) | 15.2261 | 0.628986 | ||||||||
\(587\) | −5.50999 | −0.227421 | −0.113711 | − | 0.993514i | \(-0.536274\pi\) | ||||
−0.113711 | + | 0.993514i | \(0.536274\pi\) | |||||||
\(588\) | 165.800 | 6.83748 | ||||||||
\(589\) | 35.6509 | 1.46897 | ||||||||
\(590\) | 1.32929 | 0.0547261 | ||||||||
\(591\) | −11.4048 | −0.469130 | ||||||||
\(592\) | 70.7029 | 2.90587 | ||||||||
\(593\) | 14.6019 | 0.599628 | 0.299814 | − | 0.953998i | \(-0.403075\pi\) | ||||
0.299814 | + | 0.953998i | \(0.403075\pi\) | |||||||
\(594\) | −10.1355 | −0.415863 | ||||||||
\(595\) | −2.25816 | −0.0925757 | ||||||||
\(596\) | −87.5321 | −3.58545 | ||||||||
\(597\) | −9.95836 | −0.407569 | ||||||||
\(598\) | −103.185 | −4.21955 | ||||||||
\(599\) | 20.5528 | 0.839765 | 0.419882 | − | 0.907579i | \(-0.362071\pi\) | ||||
0.419882 | + | 0.907579i | \(0.362071\pi\) | |||||||
\(600\) | 69.0374 | 2.81844 | ||||||||
\(601\) | −3.79199 | −0.154678 | −0.0773392 | − | 0.997005i | \(-0.524642\pi\) | ||||
−0.0773392 | + | 0.997005i | \(0.524642\pi\) | |||||||
\(602\) | −81.5384 | −3.32326 | ||||||||
\(603\) | 13.6225 | 0.554751 | ||||||||
\(604\) | −88.8441 | −3.61502 | ||||||||
\(605\) | −1.51969 | −0.0617842 | ||||||||
\(606\) | −1.61730 | −0.0656984 | ||||||||
\(607\) | −33.8412 | −1.37357 | −0.686786 | − | 0.726860i | \(-0.740979\pi\) | ||||
−0.686786 | + | 0.726860i | \(0.740979\pi\) | |||||||
\(608\) | 42.4103 | 1.71997 | ||||||||
\(609\) | 54.4148 | 2.20500 | ||||||||
\(610\) | −0.168180 | −0.00680943 | ||||||||
\(611\) | −76.9408 | −3.11269 | ||||||||
\(612\) | 13.6635 | 0.552312 | ||||||||
\(613\) | 7.81334 | 0.315578 | 0.157789 | − | 0.987473i | \(-0.449563\pi\) | ||||
0.157789 | + | 0.987473i | \(0.449563\pi\) | |||||||
\(614\) | 22.6308 | 0.913303 | ||||||||
\(615\) | 0.0240729 | 0.000970714 0 | ||||||||
\(616\) | −33.5321 | −1.35105 | ||||||||
\(617\) | 10.3077 | 0.414973 | 0.207487 | − | 0.978238i | \(-0.433472\pi\) | ||||
0.207487 | + | 0.978238i | \(0.433472\pi\) | |||||||
\(618\) | −40.3209 | −1.62194 | ||||||||
\(619\) | 25.6000 | 1.02895 | 0.514475 | − | 0.857505i | \(-0.327987\pi\) | ||||
0.514475 | + | 0.857505i | \(0.327987\pi\) | |||||||
\(620\) | −4.99909 | −0.200768 | ||||||||
\(621\) | 26.1545 | 1.04955 | ||||||||
\(622\) | 49.3316 | 1.97802 | ||||||||
\(623\) | 59.9016 | 2.39991 | ||||||||
\(624\) | −106.075 | −4.24641 | ||||||||
\(625\) | 24.6584 | 0.986336 | ||||||||
\(626\) | 15.9856 | 0.638913 | ||||||||
\(627\) | 9.74709 | 0.389261 | ||||||||
\(628\) | 110.075 | 4.39248 | ||||||||
\(629\) | 24.6349 | 0.982259 | ||||||||
\(630\) | 1.88252 | 0.0750015 | ||||||||
\(631\) | 15.6003 | 0.621038 | 0.310519 | − | 0.950567i | \(-0.399497\pi\) | ||||
0.310519 | + | 0.950567i | \(0.399497\pi\) | |||||||
\(632\) | 19.0207 | 0.756601 | ||||||||
\(633\) | −47.8820 | −1.90314 | ||||||||
\(634\) | −13.8131 | −0.548587 | ||||||||
\(635\) | −1.24722 | −0.0494944 | ||||||||
\(636\) | −70.2275 | −2.78470 | ||||||||
\(637\) | −109.478 | −4.33767 | ||||||||
\(638\) | −13.7548 | −0.544558 | ||||||||
\(639\) | 6.23094 | 0.246492 | ||||||||
\(640\) | 0.794350 | 0.0313994 | ||||||||
\(641\) | 39.1275 | 1.54544 | 0.772722 | − | 0.634745i | \(-0.218895\pi\) | ||||
0.772722 | + | 0.634745i | \(0.218895\pi\) | |||||||
\(642\) | 9.12337 | 0.360071 | ||||||||
\(643\) | 43.3090 | 1.70794 | 0.853971 | − | 0.520321i | \(-0.174188\pi\) | ||||
0.853971 | + | 0.520321i | \(0.174188\pi\) | |||||||
\(644\) | 150.826 | 5.94338 | ||||||||
\(645\) | −1.90671 | −0.0750766 | ||||||||
\(646\) | 39.2938 | 1.54599 | ||||||||
\(647\) | −34.3027 | −1.34858 | −0.674289 | − | 0.738468i | \(-0.735550\pi\) | ||||
−0.674289 | + | 0.738468i | \(0.735550\pi\) | |||||||
\(648\) | 76.3644 | 2.99988 | ||||||||
\(649\) | 3.29459 | 0.129324 | ||||||||
\(650\) | −79.4580 | −3.11660 | ||||||||
\(651\) | 69.9108 | 2.74002 | ||||||||
\(652\) | −55.7087 | −2.18172 | ||||||||
\(653\) | −14.7413 | −0.576871 | −0.288436 | − | 0.957499i | \(-0.593135\pi\) | ||||
−0.288436 | + | 0.957499i | \(0.593135\pi\) | |||||||
\(654\) | −76.6493 | −2.99722 | ||||||||
\(655\) | 0.681958 | 0.0266463 | ||||||||
\(656\) | 0.690311 | 0.0269521 | ||||||||
\(657\) | −3.81856 | −0.148976 | ||||||||
\(658\) | 160.408 | 6.25335 | ||||||||
\(659\) | −8.39053 | −0.326849 | −0.163424 | − | 0.986556i | \(-0.552254\pi\) | ||||
−0.163424 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(660\) | −1.36677 | −0.0532015 | ||||||||
\(661\) | 12.7159 | 0.494591 | 0.247296 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247296 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(662\) | −47.1807 | −1.83373 | ||||||||
\(663\) | −36.9597 | −1.43540 | ||||||||
\(664\) | −110.857 | −4.30207 | ||||||||
\(665\) | 3.79572 | 0.147192 | ||||||||
\(666\) | −20.5370 | −0.795791 | ||||||||
\(667\) | 35.4942 | 1.37434 | ||||||||
\(668\) | 17.4825 | 0.676419 | ||||||||
\(669\) | 16.0276 | 0.619663 | ||||||||
\(670\) | −5.49340 | −0.212229 | ||||||||
\(671\) | −0.416828 | −0.0160915 | ||||||||
\(672\) | 83.1659 | 3.20820 | ||||||||
\(673\) | 12.7901 | 0.493020 | 0.246510 | − | 0.969140i | \(-0.420716\pi\) | ||||
0.246510 | + | 0.969140i | \(0.420716\pi\) | |||||||
\(674\) | −76.4273 | −2.94387 | ||||||||
\(675\) | 20.1404 | 0.775204 | ||||||||
\(676\) | 117.698 | 4.52684 | ||||||||
\(677\) | 20.0158 | 0.769270 | 0.384635 | − | 0.923069i | \(-0.374327\pi\) | ||||
0.384635 | + | 0.923069i | \(0.374327\pi\) | |||||||
\(678\) | 0.929864 | 0.0357112 | ||||||||
\(679\) | 10.7610 | 0.412968 | ||||||||
\(680\) | −3.16106 | −0.121221 | ||||||||
\(681\) | −13.5343 | −0.518636 | ||||||||
\(682\) | −17.6718 | −0.676690 | ||||||||
\(683\) | −32.0046 | −1.22462 | −0.612312 | − | 0.790616i | \(-0.709760\pi\) | ||||
−0.612312 | + | 0.790616i | \(0.709760\pi\) | |||||||
\(684\) | −22.9667 | −0.878155 | ||||||||
\(685\) | 2.83122 | 0.108175 | ||||||||
\(686\) | 138.177 | 5.27561 | ||||||||
\(687\) | 16.6102 | 0.633719 | ||||||||
\(688\) | −54.6765 | −2.08452 | ||||||||
\(689\) | 46.3712 | 1.76660 | ||||||||
\(690\) | 5.03047 | 0.191507 | ||||||||
\(691\) | −50.7021 | −1.92880 | −0.964399 | − | 0.264453i | \(-0.914809\pi\) | ||||
−0.964399 | + | 0.264453i | \(0.914809\pi\) | |||||||
\(692\) | −12.1919 | −0.463465 | ||||||||
\(693\) | 4.66575 | 0.177237 | ||||||||
\(694\) | 56.7013 | 2.15235 | ||||||||
\(695\) | 1.82729 | 0.0693132 | ||||||||
\(696\) | 76.1718 | 2.88728 | ||||||||
\(697\) | 0.240524 | 0.00911050 | ||||||||
\(698\) | −13.6325 | −0.515998 | ||||||||
\(699\) | −22.0768 | −0.835022 | ||||||||
\(700\) | 116.144 | 4.38983 | ||||||||
\(701\) | −25.6171 | −0.967543 | −0.483771 | − | 0.875194i | \(-0.660733\pi\) | ||||
−0.483771 | + | 0.875194i | \(0.660733\pi\) | |||||||
\(702\) | −64.6006 | −2.43819 | ||||||||
\(703\) | −41.4086 | −1.56175 | ||||||||
\(704\) | −4.31449 | −0.162609 | ||||||||
\(705\) | 3.75101 | 0.141271 | ||||||||
\(706\) | 85.3904 | 3.21371 | ||||||||
\(707\) | −1.56096 | −0.0587059 | ||||||||
\(708\) | −31.8019 | −1.19519 | ||||||||
\(709\) | 23.4172 | 0.879450 | 0.439725 | − | 0.898132i | \(-0.355076\pi\) | ||||
0.439725 | + | 0.898132i | \(0.355076\pi\) | |||||||
\(710\) | −2.51268 | −0.0942992 | ||||||||
\(711\) | −2.64659 | −0.0992548 | ||||||||
\(712\) | 83.8524 | 3.14250 | ||||||||
\(713\) | 45.6021 | 1.70781 | ||||||||
\(714\) | 77.0545 | 2.88369 | ||||||||
\(715\) | 0.902478 | 0.0337508 | ||||||||
\(716\) | −43.3133 | −1.61869 | ||||||||
\(717\) | 38.5546 | 1.43985 | ||||||||
\(718\) | 51.0278 | 1.90434 | ||||||||
\(719\) | −0.169207 | −0.00631036 | −0.00315518 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315518 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(720\) | 1.26235 | 0.0470449 | ||||||||
\(721\) | −38.9162 | −1.44932 | ||||||||
\(722\) | −16.8992 | −0.628922 | ||||||||
\(723\) | 1.73083 | 0.0643701 | ||||||||
\(724\) | 23.4629 | 0.871993 | ||||||||
\(725\) | 27.3324 | 1.01510 | ||||||||
\(726\) | 51.8558 | 1.92455 | ||||||||
\(727\) | −5.76002 | −0.213627 | −0.106814 | − | 0.994279i | \(-0.534065\pi\) | ||||
−0.106814 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(728\) | −213.724 | −7.92114 | ||||||||
\(729\) | 13.5588 | 0.502176 | ||||||||
\(730\) | 1.53987 | 0.0569931 | ||||||||
\(731\) | −19.0509 | −0.704621 | ||||||||
\(732\) | 4.02354 | 0.148714 | ||||||||
\(733\) | −11.7182 | −0.432820 | −0.216410 | − | 0.976303i | \(-0.569435\pi\) | ||||
−0.216410 | + | 0.976303i | \(0.569435\pi\) | |||||||
\(734\) | 49.5440 | 1.82870 | ||||||||
\(735\) | 5.33725 | 0.196867 | ||||||||
\(736\) | 54.2483 | 1.99962 | ||||||||
\(737\) | −13.6151 | −0.501520 | ||||||||
\(738\) | −0.200514 | −0.00738101 | ||||||||
\(739\) | 24.9178 | 0.916617 | 0.458309 | − | 0.888793i | \(-0.348455\pi\) | ||||
0.458309 | + | 0.888793i | \(0.348455\pi\) | |||||||
\(740\) | 5.80645 | 0.213449 | ||||||||
\(741\) | 62.1252 | 2.28222 | ||||||||
\(742\) | −96.6757 | −3.54908 | ||||||||
\(743\) | 37.3941 | 1.37186 | 0.685928 | − | 0.727669i | \(-0.259396\pi\) | ||||
0.685928 | + | 0.727669i | \(0.259396\pi\) | |||||||
\(744\) | 97.8636 | 3.58785 | ||||||||
\(745\) | −2.81773 | −0.103234 | ||||||||
\(746\) | −40.9695 | −1.50000 | ||||||||
\(747\) | 15.4249 | 0.564367 | ||||||||
\(748\) | −13.6561 | −0.499315 | ||||||||
\(749\) | 8.80553 | 0.321747 | ||||||||
\(750\) | 7.76520 | 0.283545 | ||||||||
\(751\) | 34.6167 | 1.26318 | 0.631590 | − | 0.775303i | \(-0.282403\pi\) | ||||
0.631590 | + | 0.775303i | \(0.282403\pi\) | |||||||
\(752\) | 107.563 | 3.92243 | ||||||||
\(753\) | 58.7120 | 2.13959 | ||||||||
\(754\) | −87.6692 | −3.19272 | ||||||||
\(755\) | −2.85997 | −0.104085 | ||||||||
\(756\) | 94.4269 | 3.43427 | ||||||||
\(757\) | 7.41207 | 0.269396 | 0.134698 | − | 0.990887i | \(-0.456994\pi\) | ||||
0.134698 | + | 0.990887i | \(0.456994\pi\) | |||||||
\(758\) | −23.9531 | −0.870014 | ||||||||
\(759\) | 12.4678 | 0.452552 | ||||||||
\(760\) | 5.31339 | 0.192737 | ||||||||
\(761\) | 9.61285 | 0.348465 | 0.174233 | − | 0.984705i | \(-0.444256\pi\) | ||||
0.174233 | + | 0.984705i | \(0.444256\pi\) | |||||||
\(762\) | 42.5584 | 1.54173 | ||||||||
\(763\) | −73.9790 | −2.67822 | ||||||||
\(764\) | −89.2277 | −3.22814 | ||||||||
\(765\) | 0.439838 | 0.0159024 | ||||||||
\(766\) | 76.6395 | 2.76910 | ||||||||
\(767\) | 20.9988 | 0.758222 | ||||||||
\(768\) | −44.8591 | −1.61871 | ||||||||
\(769\) | 38.0448 | 1.37193 | 0.685965 | − | 0.727634i | \(-0.259380\pi\) | ||||
0.685965 | + | 0.727634i | \(0.259380\pi\) | |||||||
\(770\) | −1.88151 | −0.0678048 | ||||||||
\(771\) | −38.4950 | −1.38636 | ||||||||
\(772\) | 110.898 | 3.99130 | ||||||||
\(773\) | −24.3451 | −0.875634 | −0.437817 | − | 0.899064i | \(-0.644248\pi\) | ||||
−0.437817 | + | 0.899064i | \(0.644248\pi\) | |||||||
\(774\) | 15.8818 | 0.570859 | ||||||||
\(775\) | 35.1160 | 1.26141 | ||||||||
\(776\) | 15.0636 | 0.540751 | ||||||||
\(777\) | −81.2015 | −2.91309 | ||||||||
\(778\) | 21.1987 | 0.760011 | ||||||||
\(779\) | −0.404294 | −0.0144854 | ||||||||
\(780\) | −8.71140 | −0.311918 | ||||||||
\(781\) | −6.22757 | −0.222840 | ||||||||
\(782\) | 50.2618 | 1.79736 | ||||||||
\(783\) | 22.2217 | 0.794139 | ||||||||
\(784\) | 153.050 | 5.46607 | ||||||||
\(785\) | 3.54341 | 0.126470 | ||||||||
\(786\) | −23.2702 | −0.830020 | ||||||||
\(787\) | 34.9320 | 1.24519 | 0.622596 | − | 0.782543i | \(-0.286078\pi\) | ||||
0.622596 | + | 0.782543i | \(0.286078\pi\) | |||||||
\(788\) | −26.8582 | −0.956782 | ||||||||
\(789\) | −37.0998 | −1.32079 | ||||||||
\(790\) | 1.06726 | 0.0379714 | ||||||||
\(791\) | 0.897470 | 0.0319103 | ||||||||
\(792\) | 6.53128 | 0.232079 | ||||||||
\(793\) | −2.65674 | −0.0943436 | ||||||||
\(794\) | −17.7307 | −0.629239 | ||||||||
\(795\) | −2.26068 | −0.0801782 | ||||||||
\(796\) | −23.4519 | −0.831229 | ||||||||
\(797\) | −4.40735 | −0.156116 | −0.0780581 | − | 0.996949i | \(-0.524872\pi\) | ||||
−0.0780581 | + | 0.996949i | \(0.524872\pi\) | |||||||
\(798\) | −129.520 | −4.58496 | ||||||||
\(799\) | 37.4781 | 1.32588 | ||||||||
\(800\) | 41.7741 | 1.47694 | ||||||||
\(801\) | −11.6675 | −0.412249 | ||||||||
\(802\) | −18.4492 | −0.651464 | ||||||||
\(803\) | 3.81649 | 0.134681 | ||||||||
\(804\) | 131.424 | 4.63496 | ||||||||
\(805\) | 4.85522 | 0.171124 | ||||||||
\(806\) | −112.635 | −3.96741 | ||||||||
\(807\) | 8.55286 | 0.301075 | ||||||||
\(808\) | −2.18509 | −0.0768711 | ||||||||
\(809\) | 14.2117 | 0.499658 | 0.249829 | − | 0.968290i | \(-0.419626\pi\) | ||||
0.249829 | + | 0.968290i | \(0.419626\pi\) | |||||||
\(810\) | 4.28485 | 0.150554 | ||||||||
\(811\) | 15.4198 | 0.541463 | 0.270731 | − | 0.962655i | \(-0.412734\pi\) | ||||
0.270731 | + | 0.962655i | \(0.412734\pi\) | |||||||
\(812\) | 128.146 | 4.49706 | ||||||||
\(813\) | −25.6748 | −0.900454 | ||||||||
\(814\) | 20.5259 | 0.719431 | ||||||||
\(815\) | −1.79331 | −0.0628170 | ||||||||
\(816\) | 51.6697 | 1.80880 | ||||||||
\(817\) | 32.0224 | 1.12032 | ||||||||
\(818\) | −84.8736 | −2.96754 | ||||||||
\(819\) | 29.7381 | 1.03914 | ||||||||
\(820\) | 0.0566915 | 0.00197975 | ||||||||
\(821\) | −7.63569 | −0.266487 | −0.133244 | − | 0.991083i | \(-0.542539\pi\) | ||||
−0.133244 | + | 0.991083i | \(0.542539\pi\) | |||||||
\(822\) | −96.6086 | −3.36961 | ||||||||
\(823\) | 7.03484 | 0.245219 | 0.122610 | − | 0.992455i | \(-0.460874\pi\) | ||||
0.122610 | + | 0.992455i | \(0.460874\pi\) | |||||||
\(824\) | −54.4763 | −1.89777 | ||||||||
\(825\) | 9.60086 | 0.334259 | ||||||||
\(826\) | −43.7788 | −1.52326 | ||||||||
\(827\) | 11.6860 | 0.406361 | 0.203181 | − | 0.979141i | \(-0.434872\pi\) | ||||
0.203181 | + | 0.979141i | \(0.434872\pi\) | |||||||
\(828\) | −29.3774 | −1.02094 | ||||||||
\(829\) | 10.9805 | 0.381368 | 0.190684 | − | 0.981651i | \(-0.438929\pi\) | ||||
0.190684 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(830\) | −6.22023 | −0.215907 | ||||||||
\(831\) | −20.8556 | −0.723473 | ||||||||
\(832\) | −27.4993 | −0.953368 | ||||||||
\(833\) | 53.3270 | 1.84767 | ||||||||
\(834\) | −62.3521 | −2.15908 | ||||||||
\(835\) | 0.562777 | 0.0194757 | ||||||||
\(836\) | 22.9543 | 0.793892 | ||||||||
\(837\) | 28.5499 | 0.986829 | ||||||||
\(838\) | −45.5796 | −1.57452 | ||||||||
\(839\) | 12.1386 | 0.419073 | 0.209536 | − | 0.977801i | \(-0.432805\pi\) | ||||
0.209536 | + | 0.977801i | \(0.432805\pi\) | |||||||
\(840\) | 10.4195 | 0.359505 | ||||||||
\(841\) | 1.15700 | 0.0398965 | ||||||||
\(842\) | 97.8219 | 3.37117 | ||||||||
\(843\) | −22.4300 | −0.772531 | ||||||||
\(844\) | −112.762 | −3.88142 | ||||||||
\(845\) | 3.78880 | 0.130339 | ||||||||
\(846\) | −31.2437 | −1.07418 | ||||||||
\(847\) | 50.0493 | 1.71971 | ||||||||
\(848\) | −64.8270 | −2.22617 | ||||||||
\(849\) | 25.5808 | 0.877930 | ||||||||
\(850\) | 38.7043 | 1.32755 | ||||||||
\(851\) | −52.9669 | −1.81568 | ||||||||
\(852\) | 60.1132 | 2.05944 | ||||||||
\(853\) | 21.1229 | 0.723235 | 0.361617 | − | 0.932327i | \(-0.382225\pi\) | ||||
0.361617 | + | 0.932327i | \(0.382225\pi\) | |||||||
\(854\) | 5.53883 | 0.189535 | ||||||||
\(855\) | −0.739319 | −0.0252842 | ||||||||
\(856\) | 12.3263 | 0.421304 | ||||||||
\(857\) | 3.55034 | 0.121277 | 0.0606387 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606387 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(858\) | −30.7949 | −1.05132 | ||||||||
\(859\) | −20.8298 | −0.710703 | −0.355352 | − | 0.934733i | \(-0.615639\pi\) | ||||
−0.355352 | + | 0.934733i | \(0.615639\pi\) | |||||||
\(860\) | −4.49028 | −0.153117 | ||||||||
\(861\) | −0.792814 | −0.0270190 | ||||||||
\(862\) | 44.1342 | 1.50322 | ||||||||
\(863\) | −1.77956 | −0.0605769 | −0.0302885 | − | 0.999541i | \(-0.509643\pi\) | ||||
−0.0302885 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(864\) | 33.9630 | 1.15544 | ||||||||
\(865\) | −0.392466 | −0.0133443 | ||||||||
\(866\) | −92.8857 | −3.15638 | ||||||||
\(867\) | −15.8639 | −0.538766 | ||||||||
\(868\) | 164.639 | 5.58823 | ||||||||
\(869\) | 2.64516 | 0.0897308 | ||||||||
\(870\) | 4.27404 | 0.144904 | ||||||||
\(871\) | −86.7790 | −2.94039 | ||||||||
\(872\) | −103.558 | −3.50693 | ||||||||
\(873\) | −2.09599 | −0.0709385 | ||||||||
\(874\) | −84.4846 | −2.85773 | ||||||||
\(875\) | 7.49468 | 0.253367 | ||||||||
\(876\) | −36.8397 | −1.24470 | ||||||||
\(877\) | 25.2856 | 0.853836 | 0.426918 | − | 0.904290i | \(-0.359599\pi\) | ||||
0.426918 | + | 0.904290i | \(0.359599\pi\) | |||||||
\(878\) | 44.9937 | 1.51846 | ||||||||
\(879\) | −11.7261 | −0.395513 | ||||||||
\(880\) | −1.26167 | −0.0425307 | ||||||||
\(881\) | 53.0433 | 1.78707 | 0.893537 | − | 0.448989i | \(-0.148216\pi\) | ||||
0.893537 | + | 0.448989i | \(0.148216\pi\) | |||||||
\(882\) | −44.4562 | −1.49692 | ||||||||
\(883\) | 20.4028 | 0.686609 | 0.343305 | − | 0.939224i | \(-0.388454\pi\) | ||||
0.343305 | + | 0.939224i | \(0.388454\pi\) | |||||||
\(884\) | −87.0398 | −2.92747 | ||||||||
\(885\) | −1.02373 | −0.0344123 | ||||||||
\(886\) | −42.7569 | −1.43644 | ||||||||
\(887\) | 27.4801 | 0.922690 | 0.461345 | − | 0.887221i | \(-0.347367\pi\) | ||||
0.461345 | + | 0.887221i | \(0.347367\pi\) | |||||||
\(888\) | −113.669 | −3.81447 | ||||||||
\(889\) | 41.0757 | 1.37764 | ||||||||
\(890\) | 4.70501 | 0.157712 | ||||||||
\(891\) | 10.6198 | 0.355777 | ||||||||
\(892\) | 37.7449 | 1.26379 | ||||||||
\(893\) | −62.9966 | −2.10810 | ||||||||
\(894\) | 96.1484 | 3.21568 | ||||||||
\(895\) | −1.39429 | −0.0466060 | ||||||||
\(896\) | −26.1610 | −0.873978 | ||||||||
\(897\) | 79.4661 | 2.65330 | ||||||||
\(898\) | 18.4307 | 0.615040 | ||||||||
\(899\) | 38.7450 | 1.29222 | ||||||||
\(900\) | −22.6222 | −0.754072 | ||||||||
\(901\) | −22.5876 | −0.752502 | ||||||||
\(902\) | 0.200405 | 0.00667276 | ||||||||
\(903\) | 62.7953 | 2.08970 | ||||||||
\(904\) | 1.25631 | 0.0417842 | ||||||||
\(905\) | 0.755292 | 0.0251067 | ||||||||
\(906\) | 97.5896 | 3.24220 | ||||||||
\(907\) | −46.8641 | −1.55610 | −0.778048 | − | 0.628204i | \(-0.783790\pi\) | ||||
−0.778048 | + | 0.628204i | \(0.783790\pi\) | |||||||
\(908\) | −31.8732 | −1.05775 | ||||||||
\(909\) | 0.304039 | 0.0100843 | ||||||||
\(910\) | −11.9922 | −0.397537 | ||||||||
\(911\) | −5.05152 | −0.167364 | −0.0836822 | − | 0.996492i | \(-0.526668\pi\) | ||||
−0.0836822 | + | 0.996492i | \(0.526668\pi\) | |||||||
\(912\) | −86.8511 | −2.87593 | ||||||||
\(913\) | −15.4166 | −0.510213 | ||||||||
\(914\) | 3.54066 | 0.117115 | ||||||||
\(915\) | 0.129521 | 0.00428183 | ||||||||
\(916\) | 39.1169 | 1.29246 | ||||||||
\(917\) | −22.4595 | −0.741678 | ||||||||
\(918\) | 31.4672 | 1.03857 | ||||||||
\(919\) | −49.9846 | −1.64884 | −0.824419 | − | 0.565979i | \(-0.808498\pi\) | ||||
−0.824419 | + | 0.565979i | \(0.808498\pi\) | |||||||
\(920\) | 6.79650 | 0.224074 | ||||||||
\(921\) | −17.4287 | −0.574294 | ||||||||
\(922\) | −45.6600 | −1.50373 | ||||||||
\(923\) | −39.6927 | −1.30650 | ||||||||
\(924\) | 45.0130 | 1.48082 | ||||||||
\(925\) | −40.7873 | −1.34108 | ||||||||
\(926\) | −35.4569 | −1.16518 | ||||||||
\(927\) | 7.57998 | 0.248959 | ||||||||
\(928\) | 46.0910 | 1.51301 | ||||||||
\(929\) | 23.3799 | 0.767071 | 0.383536 | − | 0.923526i | \(-0.374706\pi\) | ||||
0.383536 | + | 0.923526i | \(0.374706\pi\) | |||||||
\(930\) | 5.49118 | 0.180063 | ||||||||
\(931\) | −89.6368 | −2.93773 | ||||||||
\(932\) | −51.9907 | −1.70301 | ||||||||
\(933\) | −37.9918 | −1.24380 | ||||||||
\(934\) | −26.6699 | −0.872665 | ||||||||
\(935\) | −0.439600 | −0.0143765 | ||||||||
\(936\) | 41.6285 | 1.36067 | ||||||||
\(937\) | −38.6593 | −1.26294 | −0.631472 | − | 0.775399i | \(-0.717549\pi\) | ||||
−0.631472 | + | 0.775399i | \(0.717549\pi\) | |||||||
\(938\) | 180.919 | 5.90721 | ||||||||
\(939\) | −12.3110 | −0.401755 | ||||||||
\(940\) | 8.83359 | 0.288120 | ||||||||
\(941\) | −38.6825 | −1.26101 | −0.630506 | − | 0.776184i | \(-0.717153\pi\) | ||||
−0.630506 | + | 0.776184i | \(0.717153\pi\) | |||||||
\(942\) | −120.911 | −3.93948 | ||||||||
\(943\) | −0.517145 | −0.0168405 | ||||||||
\(944\) | −29.3563 | −0.955468 | ||||||||
\(945\) | 3.03968 | 0.0988809 | ||||||||
\(946\) | −15.8732 | −0.516082 | ||||||||
\(947\) | 1.52713 | 0.0496250 | 0.0248125 | − | 0.999692i | \(-0.492101\pi\) | ||||
0.0248125 | + | 0.999692i | \(0.492101\pi\) | |||||||
\(948\) | −25.5331 | −0.829275 | ||||||||
\(949\) | 24.3252 | 0.789630 | ||||||||
\(950\) | −65.0576 | −2.11075 | ||||||||
\(951\) | 10.6379 | 0.344957 | ||||||||
\(952\) | 104.106 | 3.37409 | ||||||||
\(953\) | −6.44281 | −0.208703 | −0.104352 | − | 0.994540i | \(-0.533277\pi\) | ||||
−0.104352 | + | 0.994540i | \(0.533277\pi\) | |||||||
\(954\) | 18.8302 | 0.609650 | ||||||||
\(955\) | −2.87232 | −0.0929459 | ||||||||
\(956\) | 90.7959 | 2.93655 | ||||||||
\(957\) | 10.5930 | 0.342424 | ||||||||
\(958\) | 97.9812 | 3.16563 | ||||||||
\(959\) | −93.2430 | −3.01097 | ||||||||
\(960\) | 1.34064 | 0.0432691 | ||||||||
\(961\) | 18.7786 | 0.605760 | ||||||||
\(962\) | 130.826 | 4.21800 | ||||||||
\(963\) | −1.71511 | −0.0552688 | ||||||||
\(964\) | 4.07608 | 0.131282 | ||||||||
\(965\) | 3.56989 | 0.114919 | ||||||||
\(966\) | −165.673 | −5.33043 | ||||||||
\(967\) | −21.2147 | −0.682217 | −0.341109 | − | 0.940024i | \(-0.610802\pi\) | ||||
−0.341109 | + | 0.940024i | \(0.610802\pi\) | |||||||
\(968\) | 70.0607 | 2.25184 | ||||||||
\(969\) | −30.2614 | −0.972137 | ||||||||
\(970\) | 0.845227 | 0.0271386 | ||||||||
\(971\) | 32.7107 | 1.04974 | 0.524868 | − | 0.851184i | \(-0.324115\pi\) | ||||
0.524868 | + | 0.851184i | \(0.324115\pi\) | |||||||
\(972\) | −45.5566 | −1.46123 | ||||||||
\(973\) | −60.1799 | −1.92928 | ||||||||
\(974\) | 31.4196 | 1.00675 | ||||||||
\(975\) | 61.1931 | 1.95975 | ||||||||
\(976\) | 3.71412 | 0.118886 | ||||||||
\(977\) | 33.8823 | 1.08399 | 0.541995 | − | 0.840382i | \(-0.317669\pi\) | ||||
0.541995 | + | 0.840382i | \(0.317669\pi\) | |||||||
\(978\) | 61.1925 | 1.95672 | ||||||||
\(979\) | 11.6611 | 0.372692 | ||||||||
\(980\) | 12.5692 | 0.401508 | ||||||||
\(981\) | 14.4094 | 0.460057 | ||||||||
\(982\) | 68.2888 | 2.17918 | ||||||||
\(983\) | −33.8288 | −1.07897 | −0.539485 | − | 0.841995i | \(-0.681381\pi\) | ||||
−0.539485 | + | 0.841995i | \(0.681381\pi\) | |||||||
\(984\) | −1.10981 | −0.0353794 | ||||||||
\(985\) | −0.864587 | −0.0275480 | ||||||||
\(986\) | 42.7040 | 1.35997 | ||||||||
\(987\) | −123.535 | −3.93217 | ||||||||
\(988\) | 146.304 | 4.65456 | ||||||||
\(989\) | 40.9607 | 1.30248 | ||||||||
\(990\) | 0.366474 | 0.0116473 | ||||||||
\(991\) | 13.6248 | 0.432806 | 0.216403 | − | 0.976304i | \(-0.430568\pi\) | ||||
0.216403 | + | 0.976304i | \(0.430568\pi\) | |||||||
\(992\) | 59.2166 | 1.88013 | ||||||||
\(993\) | 36.3353 | 1.15307 | ||||||||
\(994\) | 82.7523 | 2.62474 | ||||||||
\(995\) | −0.754935 | −0.0239331 | ||||||||
\(996\) | 148.812 | 4.71530 | ||||||||
\(997\) | 45.8380 | 1.45170 | 0.725852 | − | 0.687851i | \(-0.241446\pi\) | ||||
0.725852 | + | 0.687851i | \(0.241446\pi\) | |||||||
\(998\) | 42.9918 | 1.36088 | ||||||||
\(999\) | −33.1607 | −1.04916 |
(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 | 6047.2.a.b.1.16 | ✓ | 287 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.b.1.16 | ✓ | 287 | 1.1 | even | 1 | trivial |