Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23657 | −1.58149 | −0.790747 | − | 0.612143i | \(-0.790308\pi\) | ||||
−0.790747 | + | 0.612143i | \(0.790308\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.00224 | 1.50112 | ||||||||
\(5\) | −0.453557 | −0.202837 | −0.101418 | − | 0.994844i | \(-0.532338\pi\) | ||||
−0.101418 | + | 0.994844i | \(0.532338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23602 | 0.845137 | 0.422568 | − | 0.906331i | \(-0.361129\pi\) | ||||
0.422568 | + | 0.906331i | \(0.361129\pi\) | |||||||
\(8\) | −2.24159 | −0.792521 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.01441 | 0.320785 | ||||||||
\(11\) | −2.98485 | −0.899967 | −0.449983 | − | 0.893037i | \(-0.648570\pi\) | ||||
−0.449983 | + | 0.893037i | \(0.648570\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.660563 | 0.183207 | 0.0916036 | − | 0.995796i | \(-0.470801\pi\) | ||||
0.0916036 | + | 0.995796i | \(0.470801\pi\) | |||||||
\(14\) | −5.00102 | −1.33658 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.991020 | −0.247755 | ||||||||
\(17\) | −2.90682 | −0.705008 | −0.352504 | − | 0.935810i | \(-0.614670\pi\) | ||||
−0.352504 | + | 0.935810i | \(0.614670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.95647 | 1.36651 | 0.683254 | − | 0.730181i | \(-0.260564\pi\) | ||||
0.683254 | + | 0.730181i | \(0.260564\pi\) | |||||||
\(20\) | −1.36169 | −0.304483 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.67583 | 1.42329 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79429 | −0.958857 | ||||||||
\(26\) | −1.47739 | −0.289741 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.71308 | 1.26865 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.21096 | 0.217495 | 0.108748 | − | 0.994069i | \(-0.465316\pi\) | ||||
0.108748 | + | 0.994069i | \(0.465316\pi\) | |||||||
\(32\) | 6.69966 | 1.18434 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.50131 | 1.11497 | ||||||||
\(35\) | −1.01416 | −0.171425 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.58687 | −0.425278 | −0.212639 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212639 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(38\) | −13.3221 | −2.16112 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.01669 | 0.160753 | ||||||||
\(41\) | −4.93674 | −0.770989 | −0.385494 | − | 0.922710i | \(-0.625969\pi\) | ||||
−0.385494 | + | 0.922710i | \(0.625969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.83954 | 0.738023 | 0.369012 | − | 0.929425i | \(-0.379696\pi\) | ||||
0.369012 | + | 0.929425i | \(0.379696\pi\) | |||||||
\(44\) | −8.96125 | −1.35096 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.23657 | 0.329764 | ||||||||
\(47\) | 3.25072 | 0.474167 | 0.237083 | − | 0.971489i | \(-0.423809\pi\) | ||||
0.237083 | + | 0.971489i | \(0.423809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00021 | −0.285744 | ||||||||
\(50\) | 10.7228 | 1.51643 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.98317 | 0.275016 | ||||||||
\(53\) | −11.3487 | −1.55886 | −0.779432 | − | 0.626487i | \(-0.784492\pi\) | ||||
−0.779432 | + | 0.626487i | \(0.784492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35380 | 0.182546 | ||||||||
\(56\) | −5.01224 | −0.669789 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.23657 | −0.293676 | ||||||||
\(59\) | 9.01149 | 1.17320 | 0.586598 | − | 0.809878i | \(-0.300467\pi\) | ||||
0.586598 | + | 0.809878i | \(0.300467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.99942 | −0.896184 | −0.448092 | − | 0.893987i | \(-0.647896\pi\) | ||||
−0.448092 | + | 0.893987i | \(0.647896\pi\) | |||||||
\(62\) | −2.70840 | −0.343967 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0022 | −1.62528 | ||||||||
\(65\) | −0.299603 | −0.0371612 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.10792 | 0.624031 | 0.312016 | − | 0.950077i | \(-0.398996\pi\) | ||||
0.312016 | + | 0.950077i | \(0.398996\pi\) | |||||||
\(68\) | −8.72699 | −1.05830 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.26825 | 0.271107 | ||||||||
\(71\) | 6.78368 | 0.805075 | 0.402537 | − | 0.915404i | \(-0.368128\pi\) | ||||
0.402537 | + | 0.915404i | \(0.368128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.70604 | −0.433759 | −0.216879 | − | 0.976198i | \(-0.569588\pi\) | ||||
−0.216879 | + | 0.976198i | \(0.569588\pi\) | |||||||
\(74\) | 5.78571 | 0.672575 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.8828 | 2.05130 | ||||||||
\(77\) | −6.67419 | −0.760595 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.99775 | 1.12483 | 0.562417 | − | 0.826854i | \(-0.309872\pi\) | ||||
0.562417 | + | 0.826854i | \(0.309872\pi\) | |||||||
\(80\) | 0.449484 | 0.0502539 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.0414 | 1.21931 | ||||||||
\(83\) | 9.24765 | 1.01506 | 0.507531 | − | 0.861634i | \(-0.330558\pi\) | ||||
0.507531 | + | 0.861634i | \(0.330558\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31841 | 0.143002 | ||||||||
\(86\) | −10.8240 | −1.16718 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.69081 | 0.713243 | ||||||||
\(89\) | −6.86790 | −0.727996 | −0.363998 | − | 0.931400i | \(-0.618589\pi\) | ||||
−0.363998 | + | 0.931400i | \(0.618589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.47703 | 0.154835 | ||||||||
\(92\) | −3.00224 | −0.313006 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.27047 | −0.749892 | ||||||||
\(95\) | −2.70160 | −0.277178 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0800 | 1.63268 | 0.816340 | − | 0.577571i | \(-0.195999\pi\) | ||||
0.816340 | + | 0.577571i | \(0.195999\pi\) | |||||||
\(98\) | 4.47360 | 0.451902 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.3936 | −1.43936 | ||||||||
\(101\) | 5.32290 | 0.529649 | 0.264824 | − | 0.964297i | \(-0.414686\pi\) | ||||
0.264824 | + | 0.964297i | \(0.414686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.88241 | 0.875210 | 0.437605 | − | 0.899167i | \(-0.355827\pi\) | ||||
0.437605 | + | 0.899167i | \(0.355827\pi\) | |||||||
\(104\) | −1.48071 | −0.145196 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.3822 | 2.46533 | ||||||||
\(107\) | −9.48454 | −0.916905 | −0.458452 | − | 0.888719i | \(-0.651596\pi\) | ||||
−0.458452 | + | 0.888719i | \(0.651596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.68396 | 0.352860 | 0.176430 | − | 0.984313i | \(-0.443545\pi\) | ||||
0.176430 | + | 0.984313i | \(0.443545\pi\) | |||||||
\(110\) | −3.02787 | −0.288696 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.21594 | −0.209387 | ||||||||
\(113\) | −0.789297 | −0.0742508 | −0.0371254 | − | 0.999311i | \(-0.511820\pi\) | ||||
−0.0371254 | + | 0.999311i | \(0.511820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.453557 | 0.0422944 | ||||||||
\(116\) | 3.00224 | 0.278751 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.1548 | −1.85540 | ||||||||
\(119\) | −6.49972 | −0.595828 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.09066 | −0.190060 | ||||||||
\(122\) | 15.6547 | 1.41731 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.63561 | 0.326487 | ||||||||
\(125\) | 4.44227 | 0.397329 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.73448 | 0.863796 | 0.431898 | − | 0.901923i | \(-0.357844\pi\) | ||||
0.431898 | + | 0.901923i | \(0.357844\pi\) | |||||||
\(128\) | 15.6810 | 1.38602 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.670083 | 0.0587702 | ||||||||
\(131\) | 4.79840 | 0.419238 | 0.209619 | − | 0.977783i | \(-0.432778\pi\) | ||||
0.209619 | + | 0.977783i | \(0.432778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.3188 | 1.15489 | ||||||||
\(134\) | −11.4242 | −0.986901 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.51590 | 0.558734 | ||||||||
\(137\) | 10.5960 | 0.905274 | 0.452637 | − | 0.891695i | \(-0.350483\pi\) | ||||
0.452637 | + | 0.891695i | \(0.350483\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.96119 | 0.420803 | 0.210401 | − | 0.977615i | \(-0.432523\pi\) | ||||
0.210401 | + | 0.977615i | \(0.432523\pi\) | |||||||
\(140\) | −3.04477 | −0.257330 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.1722 | −1.27322 | ||||||||
\(143\) | −1.97168 | −0.164880 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.453557 | −0.0376659 | ||||||||
\(146\) | 8.28881 | 0.685987 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.76641 | −0.638395 | ||||||||
\(149\) | 4.11712 | 0.337287 | 0.168644 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168644 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2586 | 1.40449 | 0.702244 | − | 0.711936i | \(-0.252182\pi\) | ||||
0.702244 | + | 0.711936i | \(0.252182\pi\) | |||||||
\(152\) | −13.3520 | −1.08299 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.9273 | 1.20288 | ||||||||
\(155\) | −0.549241 | −0.0441161 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.8082 | −1.42125 | −0.710625 | − | 0.703571i | \(-0.751588\pi\) | ||||
−0.710625 | + | 0.703571i | \(0.751588\pi\) | |||||||
\(158\) | −22.3607 | −1.77892 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.03868 | −0.240229 | ||||||||
\(161\) | −2.23602 | −0.176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0763 | −0.789241 | −0.394620 | − | 0.918844i | \(-0.629124\pi\) | ||||
−0.394620 | + | 0.918844i | \(0.629124\pi\) | |||||||
\(164\) | −14.8213 | −1.15735 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.6830 | −1.60531 | ||||||||
\(167\) | 18.2564 | 1.41272 | 0.706361 | − | 0.707852i | \(-0.250336\pi\) | ||||
0.706361 | + | 0.707852i | \(0.250336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5637 | −0.966435 | ||||||||
\(170\) | −2.94872 | −0.226156 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.5295 | 1.10786 | ||||||||
\(173\) | −10.6770 | −0.811756 | −0.405878 | − | 0.913927i | \(-0.633034\pi\) | ||||
−0.405878 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7201 | −0.810365 | ||||||||
\(176\) | 2.95805 | 0.222971 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.3605 | 1.15132 | ||||||||
\(179\) | −10.0442 | −0.750740 | −0.375370 | − | 0.926875i | \(-0.622484\pi\) | ||||
−0.375370 | + | 0.926875i | \(0.622484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.44665 | −0.330517 | −0.165259 | − | 0.986250i | \(-0.552846\pi\) | ||||
−0.165259 | + | 0.986250i | \(0.552846\pi\) | |||||||
\(182\) | −3.30349 | −0.244871 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.24159 | 0.165252 | ||||||||
\(185\) | 1.17329 | 0.0862622 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.67644 | 0.634484 | ||||||||
\(188\) | 9.75946 | 0.711782 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.04232 | 0.438356 | ||||||||
\(191\) | −10.1295 | −0.732944 | −0.366472 | − | 0.930429i | \(-0.619435\pi\) | ||||
−0.366472 | + | 0.930429i | \(0.619435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.54906 | 0.471412 | 0.235706 | − | 0.971824i | \(-0.424260\pi\) | ||||
0.235706 | + | 0.971824i | \(0.424260\pi\) | |||||||
\(194\) | −35.9641 | −2.58207 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00511 | −0.428936 | ||||||||
\(197\) | 14.8397 | 1.05728 | 0.528641 | − | 0.848845i | \(-0.322702\pi\) | ||||
0.528641 | + | 0.848845i | \(0.322702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.83719 | 0.342899 | 0.171450 | − | 0.985193i | \(-0.445155\pi\) | ||||
0.171450 | + | 0.985193i | \(0.445155\pi\) | |||||||
\(200\) | 10.7468 | 0.759914 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.9050 | −0.837636 | ||||||||
\(203\) | 2.23602 | 0.156938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.23909 | 0.156385 | ||||||||
\(206\) | −19.8661 | −1.38414 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.654631 | −0.0453905 | ||||||||
\(209\) | −17.7792 | −1.22981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8458 | 1.50393 | 0.751965 | − | 0.659203i | \(-0.229106\pi\) | ||||
0.751965 | + | 0.659203i | \(0.229106\pi\) | |||||||
\(212\) | −34.0716 | −2.34004 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.2128 | 1.45008 | ||||||||
\(215\) | −2.19501 | −0.149698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.70774 | 0.183813 | ||||||||
\(218\) | −8.23944 | −0.558045 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.06444 | 0.274025 | ||||||||
\(221\) | −1.92014 | −0.129163 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0488 | −1.40953 | −0.704766 | − | 0.709440i | \(-0.748948\pi\) | ||||
−0.704766 | + | 0.709440i | \(0.748948\pi\) | |||||||
\(224\) | 14.9806 | 1.00093 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.76532 | 0.117427 | ||||||||
\(227\) | −4.78355 | −0.317495 | −0.158748 | − | 0.987319i | \(-0.550746\pi\) | ||||
−0.158748 | + | 0.987319i | \(0.550746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.9948 | 1.32130 | 0.660648 | − | 0.750696i | \(-0.270281\pi\) | ||||
0.660648 | + | 0.750696i | \(0.270281\pi\) | |||||||
\(230\) | −1.01441 | −0.0668883 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.24159 | −0.147167 | ||||||||
\(233\) | −2.20911 | −0.144724 | −0.0723618 | − | 0.997378i | \(-0.523054\pi\) | ||||
−0.0723618 | + | 0.997378i | \(0.523054\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.47439 | −0.0961785 | ||||||||
\(236\) | 27.0547 | 1.76111 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.5371 | 0.942299 | ||||||||
\(239\) | −0.518959 | −0.0335687 | −0.0167843 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167843 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2652 | −0.983318 | −0.491659 | − | 0.870788i | \(-0.663609\pi\) | ||||
−0.491659 | + | 0.870788i | \(0.663609\pi\) | |||||||
\(242\) | 4.67590 | 0.300578 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −21.0140 | −1.34528 | ||||||||
\(245\) | 0.907208 | 0.0579594 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.93462 | 0.250354 | ||||||||
\(248\) | −2.71448 | −0.172370 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.93544 | −0.628373 | ||||||||
\(251\) | 5.84986 | 0.369240 | 0.184620 | − | 0.982810i | \(-0.440895\pi\) | ||||
0.184620 | + | 0.982810i | \(0.440895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.98485 | 0.187656 | ||||||||
\(254\) | −21.7718 | −1.36609 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.06731 | −0.566707 | ||||||||
\(257\) | 20.4478 | 1.27550 | 0.637751 | − | 0.770243i | \(-0.279865\pi\) | ||||
0.637751 | + | 0.770243i | \(0.279865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.78429 | −0.359418 | ||||||||
\(260\) | −0.899481 | −0.0557835 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.7320 | −0.663022 | ||||||||
\(263\) | −1.65230 | −0.101885 | −0.0509426 | − | 0.998702i | \(-0.516223\pi\) | ||||
−0.0509426 | + | 0.998702i | \(0.516223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.14728 | 0.316195 | ||||||||
\(266\) | −29.7884 | −1.82645 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.3352 | 0.936747 | ||||||||
\(269\) | −15.5998 | −0.951137 | −0.475568 | − | 0.879679i | \(-0.657758\pi\) | ||||
−0.475568 | + | 0.879679i | \(0.657758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71144 | 0.225454 | 0.112727 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112727 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(272\) | 2.88072 | 0.174669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.6986 | −1.43169 | ||||||||
\(275\) | 14.3102 | 0.862940 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.7396 | −1.90705 | −0.953523 | − | 0.301320i | \(-0.902573\pi\) | ||||
−0.953523 | + | 0.301320i | \(0.902573\pi\) | |||||||
\(278\) | −11.0960 | −0.665497 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.27334 | 0.135858 | ||||||||
\(281\) | 16.7174 | 0.997276 | 0.498638 | − | 0.866810i | \(-0.333834\pi\) | ||||
0.498638 | + | 0.866810i | \(0.333834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1798 | 0.605128 | 0.302564 | − | 0.953129i | \(-0.402157\pi\) | ||||
0.302564 | + | 0.953129i | \(0.402157\pi\) | |||||||
\(284\) | 20.3663 | 1.20851 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.40981 | 0.260757 | ||||||||
\(287\) | −11.0386 | −0.651591 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.55038 | −0.502963 | ||||||||
\(290\) | 1.01441 | 0.0595683 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1264 | −0.651125 | ||||||||
\(293\) | 4.30025 | 0.251223 | 0.125612 | − | 0.992079i | \(-0.459911\pi\) | ||||
0.125612 | + | 0.992079i | \(0.459911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.08723 | −0.237967 | ||||||||
\(296\) | 5.79869 | 0.337042 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.20822 | −0.533418 | ||||||||
\(299\) | −0.660563 | −0.0382013 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8213 | 0.623731 | ||||||||
\(302\) | −38.6001 | −2.22119 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.90298 | −0.338559 | ||||||||
\(305\) | 3.17464 | 0.181779 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.72908 | 0.441122 | 0.220561 | − | 0.975373i | \(-0.429211\pi\) | ||||
0.220561 | + | 0.975373i | \(0.429211\pi\) | |||||||
\(308\) | −20.0376 | −1.14175 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.22842 | 0.0697693 | ||||||||
\(311\) | −8.91470 | −0.505506 | −0.252753 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252753 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.83299 | −0.499270 | −0.249635 | − | 0.968340i | \(-0.580311\pi\) | ||||
−0.249635 | + | 0.968340i | \(0.580311\pi\) | |||||||
\(314\) | 39.8293 | 2.24770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.0157 | 1.68851 | ||||||||
\(317\) | 8.44890 | 0.474538 | 0.237269 | − | 0.971444i | \(-0.423748\pi\) | ||||
0.237269 | + | 0.971444i | \(0.423748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.98485 | −0.167120 | ||||||||
\(320\) | 5.89725 | 0.329666 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.00102 | 0.278696 | ||||||||
\(323\) | −17.3144 | −0.963399 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.16693 | −0.175670 | ||||||||
\(326\) | 22.5365 | 1.24818 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.0661 | 0.611025 | ||||||||
\(329\) | 7.26869 | 0.400736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.42025 | 0.187994 | 0.0939969 | − | 0.995572i | \(-0.470036\pi\) | ||||
0.0939969 | + | 0.995572i | \(0.470036\pi\) | |||||||
\(332\) | 27.7637 | 1.52373 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −40.8317 | −2.23421 | ||||||||
\(335\) | −2.31673 | −0.126577 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1876 | 0.609429 | 0.304714 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304714 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(338\) | 28.0995 | 1.52841 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.95819 | 0.214663 | ||||||||
\(341\) | −3.61454 | −0.195739 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1247 | −1.08663 | ||||||||
\(344\) | −10.8483 | −0.584899 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.8798 | 1.28379 | ||||||||
\(347\) | 1.74483 | 0.0936673 | 0.0468337 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468337 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.3270 | 1.03455 | 0.517275 | − | 0.855820i | \(-0.326947\pi\) | ||||
0.517275 | + | 0.855820i | \(0.326947\pi\) | |||||||
\(350\) | 23.9763 | 1.28159 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.9975 | −1.06587 | ||||||||
\(353\) | 29.0440 | 1.54586 | 0.772928 | − | 0.634494i | \(-0.218791\pi\) | ||||
0.772928 | + | 0.634494i | \(0.218791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.07679 | −0.163299 | ||||||||
\(356\) | −20.6191 | −1.09281 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.4646 | 1.18729 | ||||||||
\(359\) | 16.7914 | 0.886214 | 0.443107 | − | 0.896469i | \(-0.353876\pi\) | ||||
0.443107 | + | 0.896469i | \(0.353876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4795 | 0.867344 | ||||||||
\(362\) | 9.94525 | 0.522711 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.43441 | 0.232426 | ||||||||
\(365\) | 1.68090 | 0.0879823 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.56298 | 0.133787 | 0.0668933 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668933 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(368\) | 0.991020 | 0.0516605 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.62415 | −0.136423 | ||||||||
\(371\) | −25.3759 | −1.31745 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8875 | 0.615512 | 0.307756 | − | 0.951465i | \(-0.400422\pi\) | ||||
0.307756 | + | 0.951465i | \(0.400422\pi\) | |||||||
\(374\) | −19.4055 | −1.00343 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.28678 | −0.375787 | ||||||||
\(377\) | 0.660563 | 0.0340207 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1944 | −0.523652 | −0.261826 | − | 0.965115i | \(-0.584325\pi\) | ||||
−0.261826 | + | 0.965115i | \(0.584325\pi\) | |||||||
\(380\) | −8.11086 | −0.416078 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.6553 | 1.15915 | ||||||||
\(383\) | −9.63108 | −0.492125 | −0.246063 | − | 0.969254i | \(-0.579137\pi\) | ||||
−0.246063 | + | 0.969254i | \(0.579137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.02713 | 0.154277 | ||||||||
\(386\) | −14.6474 | −0.745535 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 48.2762 | 2.45085 | ||||||||
\(389\) | 33.0169 | 1.67402 | 0.837012 | − | 0.547184i | \(-0.184300\pi\) | ||||
0.837012 | + | 0.547184i | \(0.184300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.90682 | 0.147004 | ||||||||
\(392\) | 4.48364 | 0.226458 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.1900 | −1.67209 | ||||||||
\(395\) | −4.53455 | −0.228158 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.6212 | −1.53683 | −0.768416 | − | 0.639951i | \(-0.778955\pi\) | ||||
−0.768416 | + | 0.639951i | \(0.778955\pi\) | |||||||
\(398\) | −10.8187 | −0.542293 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.75123 | 0.237562 | ||||||||
\(401\) | 9.63167 | 0.480983 | 0.240491 | − | 0.970651i | \(-0.422691\pi\) | ||||
0.240491 | + | 0.970651i | \(0.422691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.799917 | 0.0398467 | ||||||||
\(404\) | 15.9806 | 0.795067 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.00102 | −0.248196 | ||||||||
\(407\) | 7.72142 | 0.382736 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.8897 | −1.03293 | −0.516464 | − | 0.856309i | \(-0.672752\pi\) | ||||
−0.516464 | + | 0.856309i | \(0.672752\pi\) | |||||||
\(410\) | −5.00788 | −0.247322 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.6672 | 1.31380 | ||||||||
\(413\) | 20.1499 | 0.991511 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.19434 | −0.205892 | ||||||||
\(416\) | 4.42555 | 0.216980 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 39.7644 | 1.94494 | ||||||||
\(419\) | −35.6859 | −1.74337 | −0.871686 | − | 0.490065i | \(-0.836973\pi\) | ||||
−0.871686 | + | 0.490065i | \(0.836973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.67002 | 0.471288 | 0.235644 | − | 0.971839i | \(-0.424280\pi\) | ||||
0.235644 | + | 0.971839i | \(0.424280\pi\) | |||||||
\(422\) | −48.8597 | −2.37846 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.4391 | 1.23543 | ||||||||
\(425\) | 13.9361 | 0.676002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6509 | −0.757398 | ||||||||
\(428\) | −28.4749 | −1.37639 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.90929 | 0.236747 | ||||||||
\(431\) | 14.4851 | 0.697721 | 0.348860 | − | 0.937175i | \(-0.386569\pi\) | ||||
0.348860 | + | 0.937175i | \(0.386569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7872 | −0.758684 | −0.379342 | − | 0.925256i | \(-0.623850\pi\) | ||||
−0.379342 | + | 0.925256i | \(0.623850\pi\) | |||||||
\(434\) | −6.05605 | −0.290700 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0602 | 0.529685 | ||||||||
\(437\) | −5.95647 | −0.284937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.56024 | 0.169921 | 0.0849605 | − | 0.996384i | \(-0.472924\pi\) | ||||
0.0849605 | + | 0.996384i | \(0.472924\pi\) | |||||||
\(440\) | −3.03466 | −0.144672 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.29453 | 0.204270 | ||||||||
\(443\) | 13.7694 | 0.654205 | 0.327102 | − | 0.944989i | \(-0.393928\pi\) | ||||
0.327102 | + | 0.944989i | \(0.393928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.11499 | 0.147665 | ||||||||
\(446\) | 47.0771 | 2.22916 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.0732 | −1.37358 | ||||||||
\(449\) | 22.2348 | 1.04933 | 0.524663 | − | 0.851310i | \(-0.324191\pi\) | ||||
0.524663 | + | 0.851310i | \(0.324191\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.7354 | 0.693864 | ||||||||
\(452\) | −2.36966 | −0.111459 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.6987 | 0.502117 | ||||||||
\(455\) | −0.669919 | −0.0314063 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6394 | 1.05903 | 0.529513 | − | 0.848302i | \(-0.322375\pi\) | ||||
0.529513 | + | 0.848302i | \(0.322375\pi\) | |||||||
\(458\) | −44.7199 | −2.08962 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.36169 | 0.0634891 | ||||||||
\(461\) | 7.28173 | 0.339144 | 0.169572 | − | 0.985518i | \(-0.445761\pi\) | ||||
0.169572 | + | 0.985518i | \(0.445761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2864 | −0.663946 | −0.331973 | − | 0.943289i | \(-0.607714\pi\) | ||||
−0.331973 | + | 0.943289i | \(0.607714\pi\) | |||||||
\(464\) | −0.991020 | −0.0460069 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.94083 | 0.228879 | ||||||||
\(467\) | 38.3371 | 1.77403 | 0.887015 | − | 0.461742i | \(-0.152775\pi\) | ||||
0.887015 | + | 0.461742i | \(0.152775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4214 | 0.527392 | ||||||||
\(470\) | 3.29757 | 0.152106 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.2000 | −0.929783 | ||||||||
\(473\) | −14.4453 | −0.664197 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.5570 | −1.31029 | ||||||||
\(476\) | −19.5137 | −0.894411 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.16069 | 0.0530887 | ||||||||
\(479\) | 21.0038 | 0.959688 | 0.479844 | − | 0.877354i | \(-0.340693\pi\) | ||||
0.479844 | + | 0.877354i | \(0.340693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70879 | −0.0779141 | ||||||||
\(482\) | 34.1417 | 1.55511 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.27666 | −0.285303 | ||||||||
\(485\) | −7.29322 | −0.331168 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2968 | 1.05568 | 0.527839 | − | 0.849345i | \(-0.323003\pi\) | ||||
0.527839 | + | 0.849345i | \(0.323003\pi\) | |||||||
\(488\) | 15.6898 | 0.710245 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.02903 | −0.0916624 | ||||||||
\(491\) | 7.19117 | 0.324533 | 0.162266 | − | 0.986747i | \(-0.448120\pi\) | ||||
0.162266 | + | 0.986747i | \(0.448120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.90682 | −0.130917 | ||||||||
\(494\) | −8.80006 | −0.395933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20009 | −0.0538856 | ||||||||
\(497\) | 15.1685 | 0.680398 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7979 | −1.11011 | −0.555053 | − | 0.831815i | \(-0.687302\pi\) | ||||
−0.555053 | + | 0.831815i | \(0.687302\pi\) | |||||||
\(500\) | 13.3368 | 0.596439 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.0836 | −0.583950 | ||||||||
\(503\) | −42.0808 | −1.87629 | −0.938145 | − | 0.346243i | \(-0.887457\pi\) | ||||
−0.938145 | + | 0.346243i | \(0.887457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.41424 | −0.107432 | ||||||||
\(506\) | −6.67583 | −0.296777 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.2253 | 1.29666 | ||||||||
\(509\) | 22.7171 | 1.00692 | 0.503459 | − | 0.864019i | \(-0.332061\pi\) | ||||
0.503459 | + | 0.864019i | \(0.332061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.28678 | −0.366585 | ||||||||
\(512\) | −11.0824 | −0.489778 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.7330 | −2.01720 | ||||||||
\(515\) | −4.02868 | −0.177525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70293 | −0.426734 | ||||||||
\(518\) | 12.9370 | 0.568418 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.671586 | 0.0294510 | ||||||||
\(521\) | −26.9094 | −1.17892 | −0.589462 | − | 0.807796i | \(-0.700660\pi\) | ||||
−0.589462 | + | 0.807796i | \(0.700660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.4973 | 1.15865 | 0.579323 | − | 0.815098i | \(-0.303317\pi\) | ||||
0.579323 | + | 0.815098i | \(0.303317\pi\) | |||||||
\(524\) | 14.4060 | 0.629327 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.69548 | 0.161131 | ||||||||
\(527\) | −3.52005 | −0.153336 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −11.5123 | −0.500061 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 39.9863 | 1.73362 | ||||||||
\(533\) | −3.26102 | −0.141251 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.30178 | 0.185982 | ||||||||
\(536\) | −11.4498 | −0.494558 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.8901 | 1.50422 | ||||||||
\(539\) | 5.97032 | 0.257160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7935 | 0.807994 | 0.403997 | − | 0.914760i | \(-0.367621\pi\) | ||||
0.403997 | + | 0.914760i | \(0.367621\pi\) | |||||||
\(542\) | −8.30089 | −0.356554 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.4747 | −0.834972 | ||||||||
\(545\) | −1.67089 | −0.0715729 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.46597 | 0.233708 | 0.116854 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116854 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(548\) | 31.8117 | 1.35893 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −32.0058 | −1.36473 | ||||||||
\(551\) | 5.95647 | 0.253754 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.3552 | 0.950639 | ||||||||
\(554\) | 70.9878 | 3.01598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.8947 | 0.631676 | ||||||||
\(557\) | 2.16854 | 0.0918841 | 0.0459420 | − | 0.998944i | \(-0.485371\pi\) | ||||
0.0459420 | + | 0.998944i | \(0.485371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.19682 | 0.135211 | ||||||||
\(560\) | 1.00506 | 0.0424714 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −37.3896 | −1.57719 | ||||||||
\(563\) | 39.9355 | 1.68308 | 0.841540 | − | 0.540194i | \(-0.181649\pi\) | ||||
0.841540 | + | 0.540194i | \(0.181649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.357991 | 0.0150608 | ||||||||
\(566\) | −22.7679 | −0.957006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.2062 | −0.638038 | ||||||||
\(569\) | −5.04467 | −0.211484 | −0.105742 | − | 0.994394i | \(-0.533722\pi\) | ||||
−0.105742 | + | 0.994394i | \(0.533722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9257 | −0.499076 | −0.249538 | − | 0.968365i | \(-0.580279\pi\) | ||||
−0.249538 | + | 0.968365i | \(0.580279\pi\) | |||||||
\(572\) | −5.91947 | −0.247506 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.6887 | 1.03049 | ||||||||
\(575\) | 4.79429 | 0.199936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7255 | 0.987704 | 0.493852 | − | 0.869546i | \(-0.335588\pi\) | ||||
0.493852 | + | 0.869546i | \(0.335588\pi\) | |||||||
\(578\) | 19.1235 | 0.795433 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.36169 | −0.0565411 | ||||||||
\(581\) | 20.6780 | 0.857866 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8742 | 1.40293 | ||||||||
\(584\) | 8.30741 | 0.343763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.61781 | −0.397308 | ||||||||
\(587\) | 38.7609 | 1.59983 | 0.799916 | − | 0.600112i | \(-0.204877\pi\) | ||||
0.799916 | + | 0.600112i | \(0.204877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.21306 | 0.297209 | ||||||||
\(590\) | 9.14136 | 0.376344 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.56364 | 0.105365 | ||||||||
\(593\) | 13.5642 | 0.557016 | 0.278508 | − | 0.960434i | \(-0.410160\pi\) | ||||
0.278508 | + | 0.960434i | \(0.410160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.94799 | 0.120856 | ||||||||
\(596\) | 12.3606 | 0.506310 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.47739 | 0.0604152 | ||||||||
\(599\) | 30.4692 | 1.24494 | 0.622469 | − | 0.782645i | \(-0.286130\pi\) | ||||
0.622469 | + | 0.782645i | \(0.286130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9846 | 0.774397 | 0.387199 | − | 0.921996i | \(-0.373443\pi\) | ||||
0.387199 | + | 0.921996i | \(0.373443\pi\) | |||||||
\(602\) | −24.2026 | −0.986426 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.8146 | 2.10831 | ||||||||
\(605\) | 0.948232 | 0.0385511 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.3484 | 1.47534 | 0.737669 | − | 0.675163i | \(-0.235927\pi\) | ||||
0.737669 | + | 0.675163i | \(0.235927\pi\) | |||||||
\(608\) | 39.9063 | 1.61842 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.10030 | −0.287483 | ||||||||
\(611\) | 2.14731 | 0.0868708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.882083 | 0.0356270 | 0.0178135 | − | 0.999841i | \(-0.494329\pi\) | ||||
0.0178135 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(614\) | −17.2866 | −0.697631 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.9608 | 0.602788 | ||||||||
\(617\) | −1.04758 | −0.0421742 | −0.0210871 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210871 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.9392 | −1.08278 | −0.541389 | − | 0.840772i | \(-0.682101\pi\) | ||||
−0.541389 | + | 0.840772i | \(0.682101\pi\) | |||||||
\(620\) | −1.64895 | −0.0662236 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.9383 | 0.799454 | ||||||||
\(623\) | −15.3568 | −0.615256 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9566 | 0.878264 | ||||||||
\(626\) | 19.7556 | 0.789592 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −53.4646 | −2.13347 | ||||||||
\(629\) | 7.51957 | 0.299825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5512 | −1.05698 | −0.528492 | − | 0.848938i | \(-0.677242\pi\) | ||||
−0.528492 | + | 0.848938i | \(0.677242\pi\) | |||||||
\(632\) | −22.4108 | −0.891455 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.8966 | −0.750478 | ||||||||
\(635\) | −4.41514 | −0.175210 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.32126 | −0.0523503 | ||||||||
\(638\) | 6.67583 | 0.264299 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.11225 | −0.281136 | ||||||||
\(641\) | −4.68929 | −0.185216 | −0.0926080 | − | 0.995703i | \(-0.529520\pi\) | ||||
−0.0926080 | + | 0.995703i | \(0.529520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.6616 | −0.617634 | −0.308817 | − | 0.951122i | \(-0.599933\pi\) | ||||
−0.308817 | + | 0.951122i | \(0.599933\pi\) | |||||||
\(644\) | −6.71308 | −0.264532 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.7249 | 1.52361 | ||||||||
\(647\) | −37.3920 | −1.47003 | −0.735015 | − | 0.678050i | \(-0.762825\pi\) | ||||
−0.735015 | + | 0.678050i | \(0.762825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.8980 | −1.05584 | ||||||||
\(650\) | 7.08305 | 0.277820 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.2517 | −1.18475 | ||||||||
\(653\) | −5.61580 | −0.219763 | −0.109882 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109882 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.17635 | −0.0850370 | ||||||||
\(656\) | 4.89240 | 0.191016 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.2569 | −0.633761 | ||||||||
\(659\) | 22.2009 | 0.864825 | 0.432412 | − | 0.901676i | \(-0.357663\pi\) | ||||
0.432412 | + | 0.901676i | \(0.357663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6255 | 0.880028 | 0.440014 | − | 0.897991i | \(-0.354973\pi\) | ||||
0.440014 | + | 0.897991i | \(0.354973\pi\) | |||||||
\(662\) | −7.64962 | −0.297311 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.7294 | −0.804458 | ||||||||
\(665\) | −6.04084 | −0.234254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 54.8101 | 2.12067 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.18153 | 0.200180 | ||||||||
\(671\) | 20.8922 | 0.806536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6175 | −0.833294 | −0.416647 | − | 0.909068i | \(-0.636795\pi\) | ||||
−0.416647 | + | 0.909068i | \(0.636795\pi\) | |||||||
\(674\) | −25.0219 | −0.963807 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.7192 | −1.45074 | ||||||||
\(677\) | 17.2957 | 0.664729 | 0.332365 | − | 0.943151i | \(-0.392154\pi\) | ||||
0.332365 | + | 0.943151i | \(0.392154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.9553 | 1.37984 | ||||||||
\(680\) | −2.95533 | −0.113332 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.08418 | 0.309559 | ||||||||
\(683\) | 30.8022 | 1.17862 | 0.589308 | − | 0.807909i | \(-0.299401\pi\) | ||||
0.589308 | + | 0.807909i | \(0.299401\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.80587 | −0.183623 | ||||||||
\(686\) | 45.0102 | 1.71850 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.79608 | −0.182849 | ||||||||
\(689\) | −7.49653 | −0.285595 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.3225 | −0.887230 | −0.443615 | − | 0.896217i | \(-0.646304\pi\) | ||||
−0.443615 | + | 0.896217i | \(0.646304\pi\) | |||||||
\(692\) | −32.0549 | −1.21854 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.90243 | −0.148134 | ||||||||
\(695\) | −2.25018 | −0.0853543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.3502 | 0.543553 | ||||||||
\(698\) | −43.2261 | −1.63613 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −32.1844 | −1.21646 | ||||||||
\(701\) | −14.4108 | −0.544287 | −0.272143 | − | 0.962257i | \(-0.587732\pi\) | ||||
−0.272143 | + | 0.962257i | \(0.587732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4086 | −0.581146 | ||||||||
\(704\) | 38.8097 | 1.46270 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −64.9589 | −2.44476 | ||||||||
\(707\) | 11.9021 | 0.447625 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.3763 | −0.953026 | −0.476513 | − | 0.879168i | \(-0.658099\pi\) | ||||
−0.476513 | + | 0.879168i | \(0.658099\pi\) | |||||||
\(710\) | 6.88145 | 0.258256 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.3950 | 0.576952 | ||||||||
\(713\) | −1.21096 | −0.0453509 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.894271 | 0.0334438 | ||||||||
\(716\) | −30.1552 | −1.12695 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −37.5550 | −1.40154 | ||||||||
\(719\) | 2.41527 | 0.0900742 | 0.0450371 | − | 0.998985i | \(-0.485659\pi\) | ||||
0.0450371 | + | 0.998985i | \(0.485659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8613 | 0.739672 | ||||||||
\(722\) | −36.8576 | −1.37170 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.3499 | −0.496147 | ||||||||
\(725\) | −4.79429 | −0.178055 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.7792 | 1.17863 | 0.589313 | − | 0.807905i | \(-0.299398\pi\) | ||||
0.589313 | + | 0.807905i | \(0.299398\pi\) | |||||||
\(728\) | −3.31090 | −0.122710 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.75945 | −0.139143 | ||||||||
\(731\) | −14.0677 | −0.520313 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.3148 | 0.787279 | 0.393639 | − | 0.919265i | \(-0.371216\pi\) | ||||
0.393639 | + | 0.919265i | \(0.371216\pi\) | |||||||
\(734\) | −5.73229 | −0.211583 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.69966 | −0.246953 | ||||||||
\(737\) | −15.2464 | −0.561607 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.18650 | 0.264360 | 0.132180 | − | 0.991226i | \(-0.457802\pi\) | ||||
0.132180 | + | 0.991226i | \(0.457802\pi\) | |||||||
\(740\) | 3.52251 | 0.129490 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 56.7551 | 2.08354 | ||||||||
\(743\) | 47.3808 | 1.73823 | 0.869117 | − | 0.494606i | \(-0.164688\pi\) | ||||
0.869117 | + | 0.494606i | \(0.164688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.86735 | −0.0684144 | ||||||||
\(746\) | −26.5872 | −0.973428 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 26.0488 | 0.952438 | ||||||||
\(749\) | −21.2076 | −0.774910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.17198 | 0.188728 | 0.0943641 | − | 0.995538i | \(-0.469918\pi\) | ||||
0.0943641 | + | 0.995538i | \(0.469918\pi\) | |||||||
\(752\) | −3.22153 | −0.117477 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.47739 | −0.0538035 | ||||||||
\(755\) | −7.82778 | −0.284882 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.36910 | 0.0861063 | 0.0430532 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430532 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(758\) | 22.8005 | 0.828153 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.05587 | 0.219670 | ||||||||
\(761\) | −25.8371 | −0.936593 | −0.468297 | − | 0.883571i | \(-0.655132\pi\) | ||||
−0.468297 | + | 0.883571i | \(0.655132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.23742 | 0.298215 | ||||||||
\(764\) | −30.4112 | −1.10024 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5406 | 0.778293 | ||||||||
\(767\) | 5.95266 | 0.214938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.7704 | 1.54234 | 0.771170 | − | 0.636629i | \(-0.219672\pi\) | ||||
0.771170 | + | 0.636629i | \(0.219672\pi\) | |||||||
\(770\) | −6.77038 | −0.243988 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.6619 | 0.707646 | ||||||||
\(773\) | −4.78538 | −0.172118 | −0.0860591 | − | 0.996290i | \(-0.527427\pi\) | ||||
−0.0860591 | + | 0.996290i | \(0.527427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.80570 | −0.208547 | ||||||||
\(776\) | −36.0448 | −1.29393 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −73.8446 | −2.64746 | ||||||||
\(779\) | −29.4055 | −1.05356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2483 | −0.724540 | ||||||||
\(782\) | −6.50131 | −0.232486 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.98225 | 0.0707945 | ||||||||
\(785\) | 8.07704 | 0.288282 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5741 | 1.48196 | 0.740978 | − | 0.671529i | \(-0.234362\pi\) | ||||
0.740978 | + | 0.671529i | \(0.234362\pi\) | |||||||
\(788\) | 44.5523 | 1.58711 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.1418 | 0.360830 | ||||||||
\(791\) | −1.76488 | −0.0627521 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.62356 | −0.164187 | ||||||||
\(794\) | 68.4864 | 2.43049 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.5224 | 0.514734 | ||||||||
\(797\) | 8.27869 | 0.293246 | 0.146623 | − | 0.989192i | \(-0.453160\pi\) | ||||
0.146623 | + | 0.989192i | \(0.453160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.44928 | −0.334291 | ||||||||
\(800\) | −32.1201 | −1.13562 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.5419 | −0.760671 | ||||||||
\(803\) | 11.0620 | 0.390369 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.01416 | 0.0357446 | ||||||||
\(806\) | −1.78907 | −0.0630173 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.9318 | −0.419758 | ||||||||
\(809\) | 47.8198 | 1.68125 | 0.840627 | − | 0.541614i | \(-0.182187\pi\) | ||||
0.840627 | + | 0.541614i | \(0.182187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.1665 | −1.62112 | −0.810562 | − | 0.585653i | \(-0.800838\pi\) | ||||
−0.810562 | + | 0.585653i | \(0.800838\pi\) | |||||||
\(812\) | 6.71308 | 0.235583 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.2695 | −0.605295 | ||||||||
\(815\) | 4.57020 | 0.160087 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.8266 | 1.00851 | ||||||||
\(818\) | 46.7212 | 1.63357 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.72230 | 0.234753 | ||||||||
\(821\) | −7.48770 | −0.261323 | −0.130661 | − | 0.991427i | \(-0.541710\pi\) | ||||
−0.130661 | + | 0.991427i | \(0.541710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.5952 | 1.55449 | 0.777245 | − | 0.629198i | \(-0.216616\pi\) | ||||
0.777245 | + | 0.629198i | \(0.216616\pi\) | |||||||
\(824\) | −19.9107 | −0.693622 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.0666 | −1.56807 | ||||||||
\(827\) | 27.9479 | 0.971842 | 0.485921 | − | 0.874003i | \(-0.338484\pi\) | ||||
0.485921 | + | 0.874003i | \(0.338484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.6817 | 0.405723 | 0.202862 | − | 0.979207i | \(-0.434976\pi\) | ||||
0.202862 | + | 0.979207i | \(0.434976\pi\) | |||||||
\(830\) | 9.38093 | 0.325617 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.58878 | −0.297762 | ||||||||
\(833\) | 5.81425 | 0.201452 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.28032 | −0.286552 | ||||||||
\(836\) | −53.3774 | −1.84610 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 79.8140 | 2.75713 | ||||||||
\(839\) | 0.687980 | 0.0237517 | 0.0118759 | − | 0.999929i | \(-0.496220\pi\) | ||||
0.0118759 | + | 0.999929i | \(0.496220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −21.6277 | −0.745339 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 65.5865 | 2.25758 | ||||||||
\(845\) | 5.69834 | 0.196029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.67475 | −0.160626 | ||||||||
\(848\) | 11.2468 | 0.386216 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −31.1692 | −1.06909 | ||||||||
\(851\) | 2.58687 | 0.0886767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.2306 | 1.68562 | 0.842812 | − | 0.538208i | \(-0.180898\pi\) | ||||
0.842812 | + | 0.538208i | \(0.180898\pi\) | |||||||
\(854\) | 35.0042 | 1.19782 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.2604 | 0.726666 | ||||||||
\(857\) | 46.7516 | 1.59701 | 0.798503 | − | 0.601991i | \(-0.205626\pi\) | ||||
0.798503 | + | 0.601991i | \(0.205626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6789 | 0.603196 | 0.301598 | − | 0.953435i | \(-0.402480\pi\) | ||||
0.301598 | + | 0.953435i | \(0.402480\pi\) | |||||||
\(860\) | −6.58995 | −0.224716 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.3968 | −1.10344 | ||||||||
\(863\) | 56.7921 | 1.93323 | 0.966613 | − | 0.256242i | \(-0.0824843\pi\) | ||||
0.966613 | + | 0.256242i | \(0.0824843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.84262 | 0.164654 | ||||||||
\(866\) | 35.3092 | 1.19985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.12929 | 0.275926 | ||||||||
\(869\) | −29.8418 | −1.01231 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.37410 | 0.114327 | ||||||||
\(872\) | −8.25793 | −0.279649 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.3221 | 0.450625 | ||||||||
\(875\) | 9.93301 | 0.335797 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.4597 | −1.26492 | −0.632462 | − | 0.774591i | \(-0.717956\pi\) | ||||
−0.632462 | + | 0.774591i | \(0.717956\pi\) | |||||||
\(878\) | −7.96272 | −0.268729 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.34164 | −0.0452268 | ||||||||
\(881\) | −11.5175 | −0.388035 | −0.194018 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194018 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.51176 | −0.118180 | −0.0590900 | − | 0.998253i | \(-0.518820\pi\) | ||||
−0.0590900 | + | 0.998253i | \(0.518820\pi\) | |||||||
\(884\) | −5.76473 | −0.193889 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.7963 | −1.03462 | ||||||||
\(887\) | −16.0468 | −0.538800 | −0.269400 | − | 0.963028i | \(-0.586825\pi\) | ||||
−0.269400 | + | 0.963028i | \(0.586825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.7665 | 0.730025 | ||||||||
\(890\) | −6.96688 | −0.233530 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −63.1936 | −2.11588 | ||||||||
\(893\) | 19.3628 | 0.647953 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.55562 | 0.152278 | ||||||||
\(896\) | 35.0632 | 1.17138 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −49.7297 | −1.65950 | ||||||||
\(899\) | 1.21096 | 0.0403879 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.9887 | 1.09901 | ||||||||
\(902\) | −32.9568 | −1.09734 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.76928 | 0.0588453 | ||||||||
\(905\) | 2.01681 | 0.0670411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.5760 | 1.11487 | 0.557436 | − | 0.830220i | \(-0.311785\pi\) | ||||
0.557436 | + | 0.830220i | \(0.311785\pi\) | |||||||
\(908\) | −14.3614 | −0.476599 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.49832 | 0.0496688 | ||||||||
\(911\) | 37.9612 | 1.25771 | 0.628855 | − | 0.777523i | \(-0.283524\pi\) | ||||
0.628855 | + | 0.777523i | \(0.283524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.6029 | −0.913522 | ||||||||
\(914\) | −50.6346 | −1.67484 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 60.0294 | 1.98343 | ||||||||
\(917\) | 10.7293 | 0.354314 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.7984 | −0.719062 | −0.359531 | − | 0.933133i | \(-0.617063\pi\) | ||||
−0.359531 | + | 0.933133i | \(0.617063\pi\) | |||||||
\(920\) | −1.01669 | −0.0335192 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.2861 | −0.536354 | ||||||||
\(923\) | 4.48105 | 0.147495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.4022 | 0.407781 | ||||||||
\(926\) | 31.9526 | 1.05003 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.69966 | 0.219927 | ||||||||
\(929\) | 26.7546 | 0.877790 | 0.438895 | − | 0.898538i | \(-0.355370\pi\) | ||||
0.438895 | + | 0.898538i | \(0.355370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.9142 | −0.390471 | ||||||||
\(932\) | −6.63228 | −0.217248 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −85.7436 | −2.80562 | ||||||||
\(935\) | −3.93526 | −0.128697 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0999 | 0.689305 | 0.344652 | − | 0.938730i | \(-0.387997\pi\) | ||||
0.344652 | + | 0.938730i | \(0.387997\pi\) | |||||||
\(938\) | −25.5448 | −0.834066 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.42647 | −0.144376 | ||||||||
\(941\) | 20.5081 | 0.668545 | 0.334273 | − | 0.942476i | \(-0.391509\pi\) | ||||
0.334273 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.93674 | 0.160762 | ||||||||
\(944\) | −8.93057 | −0.290665 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.3080 | 1.05042 | ||||||||
\(947\) | 58.6897 | 1.90716 | 0.953580 | − | 0.301141i | \(-0.0973675\pi\) | ||||
0.953580 | + | 0.301141i | \(0.0973675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.44807 | −0.0794677 | ||||||||
\(950\) | 63.8698 | 2.07221 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.5697 | 0.472206 | ||||||||
\(953\) | −22.6328 | −0.733149 | −0.366574 | − | 0.930389i | \(-0.619469\pi\) | ||||
−0.366574 | + | 0.930389i | \(0.619469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.59430 | 0.148668 | ||||||||
\(956\) | −1.55804 | −0.0503907 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −46.9764 | −1.51774 | ||||||||
\(959\) | 23.6928 | 0.765080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5336 | −0.952696 | ||||||||
\(962\) | 3.82183 | 0.123221 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −45.8298 | −1.47608 | ||||||||
\(965\) | −2.97037 | −0.0956197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.9635 | 1.63887 | 0.819437 | − | 0.573169i | \(-0.194286\pi\) | ||||
0.819437 | + | 0.573169i | \(0.194286\pi\) | |||||||
\(968\) | 4.68639 | 0.150626 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.3118 | 0.523740 | ||||||||
\(971\) | −23.2567 | −0.746344 | −0.373172 | − | 0.927762i | \(-0.621730\pi\) | ||||
−0.373172 | + | 0.927762i | \(0.621730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0933 | 0.355636 | ||||||||
\(974\) | −52.1048 | −1.66955 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.93657 | 0.222034 | ||||||||
\(977\) | −48.6497 | −1.55644 | −0.778221 | − | 0.627990i | \(-0.783878\pi\) | ||||
−0.778221 | + | 0.627990i | \(0.783878\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.4997 | 0.655173 | ||||||||
\(980\) | 2.72366 | 0.0870041 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.0835 | −0.513247 | ||||||||
\(983\) | −15.9161 | −0.507646 | −0.253823 | − | 0.967251i | \(-0.581688\pi\) | ||||
−0.253823 | + | 0.967251i | \(0.581688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.73064 | −0.214456 | ||||||||
\(986\) | 6.50131 | 0.207044 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.8127 | 0.375812 | ||||||||
\(989\) | −4.83954 | −0.153889 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.6468 | 0.560570 | 0.280285 | − | 0.959917i | \(-0.409571\pi\) | ||||
0.280285 | + | 0.959917i | \(0.409571\pi\) | |||||||
\(992\) | 8.11304 | 0.257589 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.9253 | −1.07605 | ||||||||
\(995\) | −2.19394 | −0.0695526 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2198 | −0.893730 | −0.446865 | − | 0.894601i | \(-0.647460\pi\) | ||||
−0.446865 | + | 0.894601i | \(0.647460\pi\) | |||||||
\(998\) | 55.4622 | 1.75563 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.w.1.5 | yes | 30 | |
3.2 | odd | 2 | 6003.2.a.v.1.26 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.26 | ✓ | 30 | 3.2 | odd | 2 | ||
6003.2.a.w.1.5 | yes | 30 | 1.1 | even | 1 | trivial |