Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71591 | −1.92044 | −0.960219 | − | 0.279248i | \(-0.909915\pi\) | ||||
−0.960219 | + | 0.279248i | \(0.909915\pi\) | |||||||
\(3\) | −1.21901 | −0.703798 | −0.351899 | − | 0.936038i | \(-0.614464\pi\) | ||||
−0.351899 | + | 0.936038i | \(0.614464\pi\) | |||||||
\(4\) | 5.37616 | 2.68808 | ||||||||
\(5\) | 2.34595 | 1.04914 | 0.524570 | − | 0.851367i | \(-0.324226\pi\) | ||||
0.524570 | + | 0.851367i | \(0.324226\pi\) | |||||||
\(6\) | 3.31073 | 1.35160 | ||||||||
\(7\) | 3.38769 | 1.28043 | 0.640213 | − | 0.768198i | \(-0.278846\pi\) | ||||
0.640213 | + | 0.768198i | \(0.278846\pi\) | |||||||
\(8\) | −9.16936 | −3.24186 | ||||||||
\(9\) | −1.51401 | −0.504669 | ||||||||
\(10\) | −6.37139 | −2.01481 | ||||||||
\(11\) | −0.811481 | −0.244671 | −0.122335 | − | 0.992489i | \(-0.539038\pi\) | ||||
−0.122335 | + | 0.992489i | \(0.539038\pi\) | |||||||
\(12\) | −6.55362 | −1.89187 | ||||||||
\(13\) | −2.55732 | −0.709274 | −0.354637 | − | 0.935004i | \(-0.615396\pi\) | ||||
−0.354637 | + | 0.935004i | \(0.615396\pi\) | |||||||
\(14\) | −9.20065 | −2.45898 | ||||||||
\(15\) | −2.85974 | −0.738382 | ||||||||
\(16\) | 14.1508 | 3.53770 | ||||||||
\(17\) | −3.94346 | −0.956429 | −0.478215 | − | 0.878243i | \(-0.658716\pi\) | ||||
−0.478215 | + | 0.878243i | \(0.658716\pi\) | |||||||
\(18\) | 4.11191 | 0.969186 | ||||||||
\(19\) | −3.34018 | −0.766290 | −0.383145 | − | 0.923688i | \(-0.625159\pi\) | ||||
−0.383145 | + | 0.923688i | \(0.625159\pi\) | |||||||
\(20\) | 12.6122 | 2.82018 | ||||||||
\(21\) | −4.12964 | −0.901160 | ||||||||
\(22\) | 2.20391 | 0.469875 | ||||||||
\(23\) | −3.85630 | −0.804094 | −0.402047 | − | 0.915619i | \(-0.631701\pi\) | ||||
−0.402047 | + | 0.915619i | \(0.631701\pi\) | |||||||
\(24\) | 11.1776 | 2.28161 | ||||||||
\(25\) | 0.503476 | 0.100695 | ||||||||
\(26\) | 6.94546 | 1.36212 | ||||||||
\(27\) | 5.50263 | 1.05898 | ||||||||
\(28\) | 18.2128 | 3.44189 | ||||||||
\(29\) | 4.22183 | 0.783973 | 0.391987 | − | 0.919971i | \(-0.371788\pi\) | ||||
0.391987 | + | 0.919971i | \(0.371788\pi\) | |||||||
\(30\) | 7.76680 | 1.41802 | ||||||||
\(31\) | 6.07512 | 1.09112 | 0.545561 | − | 0.838071i | \(-0.316316\pi\) | ||||
0.545561 | + | 0.838071i | \(0.316316\pi\) | |||||||
\(32\) | −20.0936 | −3.55209 | ||||||||
\(33\) | 0.989206 | 0.172199 | ||||||||
\(34\) | 10.7101 | 1.83676 | ||||||||
\(35\) | 7.94734 | 1.34335 | ||||||||
\(36\) | −8.13955 | −1.35659 | ||||||||
\(37\) | 1.41221 | 0.232165 | 0.116083 | − | 0.993240i | \(-0.462966\pi\) | ||||
0.116083 | + | 0.993240i | \(0.462966\pi\) | |||||||
\(38\) | 9.07163 | 1.47161 | ||||||||
\(39\) | 3.11741 | 0.499185 | ||||||||
\(40\) | −21.5108 | −3.40116 | ||||||||
\(41\) | 2.27396 | 0.355132 | 0.177566 | − | 0.984109i | \(-0.443178\pi\) | ||||
0.177566 | + | 0.984109i | \(0.443178\pi\) | |||||||
\(42\) | 11.2157 | 1.73062 | ||||||||
\(43\) | 5.23352 | 0.798105 | 0.399052 | − | 0.916928i | \(-0.369339\pi\) | ||||
0.399052 | + | 0.916928i | \(0.369339\pi\) | |||||||
\(44\) | −4.36265 | −0.657695 | ||||||||
\(45\) | −3.55178 | −0.529469 | ||||||||
\(46\) | 10.4734 | 1.54421 | ||||||||
\(47\) | −6.02476 | −0.878801 | −0.439400 | − | 0.898291i | \(-0.644809\pi\) | ||||
−0.439400 | + | 0.898291i | \(0.644809\pi\) | |||||||
\(48\) | −17.2500 | −2.48983 | ||||||||
\(49\) | 4.47643 | 0.639490 | ||||||||
\(50\) | −1.36740 | −0.193379 | ||||||||
\(51\) | 4.80713 | 0.673133 | ||||||||
\(52\) | −13.7486 | −1.90659 | ||||||||
\(53\) | 3.81772 | 0.524404 | 0.262202 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262202 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(54\) | −14.9447 | −2.03371 | ||||||||
\(55\) | −1.90369 | −0.256694 | ||||||||
\(56\) | −31.0629 | −4.15096 | ||||||||
\(57\) | 4.07172 | 0.539313 | ||||||||
\(58\) | −11.4661 | −1.50557 | ||||||||
\(59\) | −6.50570 | −0.846970 | −0.423485 | − | 0.905903i | \(-0.639193\pi\) | ||||
−0.423485 | + | 0.905903i | \(0.639193\pi\) | |||||||
\(60\) | −15.3744 | −1.98483 | ||||||||
\(61\) | 12.0368 | 1.54116 | 0.770579 | − | 0.637344i | \(-0.219967\pi\) | ||||
0.770579 | + | 0.637344i | \(0.219967\pi\) | |||||||
\(62\) | −16.4995 | −2.09543 | ||||||||
\(63\) | −5.12898 | −0.646191 | ||||||||
\(64\) | 26.2708 | 3.28386 | ||||||||
\(65\) | −5.99935 | −0.744128 | ||||||||
\(66\) | −2.68659 | −0.330697 | ||||||||
\(67\) | 1.82591 | 0.223070 | 0.111535 | − | 0.993761i | \(-0.464423\pi\) | ||||
0.111535 | + | 0.993761i | \(0.464423\pi\) | |||||||
\(68\) | −21.2007 | −2.57096 | ||||||||
\(69\) | 4.70088 | 0.565919 | ||||||||
\(70\) | −21.5843 | −2.57981 | ||||||||
\(71\) | 0.823990 | 0.0977897 | 0.0488948 | − | 0.998804i | \(-0.484430\pi\) | ||||
0.0488948 | + | 0.998804i | \(0.484430\pi\) | |||||||
\(72\) | 13.8825 | 1.63607 | ||||||||
\(73\) | −8.93057 | −1.04524 | −0.522622 | − | 0.852564i | \(-0.675046\pi\) | ||||
−0.522622 | + | 0.852564i | \(0.675046\pi\) | |||||||
\(74\) | −3.83543 | −0.445859 | ||||||||
\(75\) | −0.613744 | −0.0708690 | ||||||||
\(76\) | −17.9574 | −2.05985 | ||||||||
\(77\) | −2.74904 | −0.313283 | ||||||||
\(78\) | −8.46661 | −0.958655 | ||||||||
\(79\) | −9.23686 | −1.03923 | −0.519614 | − | 0.854401i | \(-0.673924\pi\) | ||||
−0.519614 | + | 0.854401i | \(0.673924\pi\) | |||||||
\(80\) | 33.1971 | 3.71155 | ||||||||
\(81\) | −2.16576 | −0.240640 | ||||||||
\(82\) | −6.17586 | −0.682009 | ||||||||
\(83\) | 2.44747 | 0.268644 | 0.134322 | − | 0.990938i | \(-0.457114\pi\) | ||||
0.134322 | + | 0.990938i | \(0.457114\pi\) | |||||||
\(84\) | −22.2016 | −2.42239 | ||||||||
\(85\) | −9.25115 | −1.00343 | ||||||||
\(86\) | −14.2138 | −1.53271 | ||||||||
\(87\) | −5.14646 | −0.551759 | ||||||||
\(88\) | 7.44076 | 0.793188 | ||||||||
\(89\) | 0.485918 | 0.0515072 | 0.0257536 | − | 0.999668i | \(-0.491801\pi\) | ||||
0.0257536 | + | 0.999668i | \(0.491801\pi\) | |||||||
\(90\) | 9.64632 | 1.01681 | ||||||||
\(91\) | −8.66342 | −0.908173 | ||||||||
\(92\) | −20.7321 | −2.16147 | ||||||||
\(93\) | −7.40565 | −0.767930 | ||||||||
\(94\) | 16.3627 | 1.68768 | ||||||||
\(95\) | −7.83589 | −0.803945 | ||||||||
\(96\) | 24.4944 | 2.49995 | ||||||||
\(97\) | 12.0833 | 1.22688 | 0.613439 | − | 0.789742i | \(-0.289786\pi\) | ||||
0.613439 | + | 0.789742i | \(0.289786\pi\) | |||||||
\(98\) | −12.1576 | −1.22810 | ||||||||
\(99\) | 1.22859 | 0.123478 | ||||||||
\(100\) | 2.70677 | 0.270677 | ||||||||
\(101\) | −7.46651 | −0.742946 | −0.371473 | − | 0.928444i | \(-0.621147\pi\) | ||||
−0.371473 | + | 0.928444i | \(0.621147\pi\) | |||||||
\(102\) | −13.0557 | −1.29271 | ||||||||
\(103\) | −16.9914 | −1.67421 | −0.837105 | − | 0.547043i | \(-0.815754\pi\) | ||||
−0.837105 | + | 0.547043i | \(0.815754\pi\) | |||||||
\(104\) | 23.4490 | 2.29937 | ||||||||
\(105\) | −9.68791 | −0.945444 | ||||||||
\(106\) | −10.3686 | −1.00708 | ||||||||
\(107\) | −8.41114 | −0.813136 | −0.406568 | − | 0.913621i | \(-0.633275\pi\) | ||||
−0.406568 | + | 0.913621i | \(0.633275\pi\) | |||||||
\(108\) | 29.5831 | 2.84663 | ||||||||
\(109\) | 12.3949 | 1.18722 | 0.593609 | − | 0.804753i | \(-0.297702\pi\) | ||||
0.593609 | + | 0.804753i | \(0.297702\pi\) | |||||||
\(110\) | 5.17026 | 0.492965 | ||||||||
\(111\) | −1.72150 | −0.163397 | ||||||||
\(112\) | 47.9386 | 4.52977 | ||||||||
\(113\) | −13.7058 | −1.28934 | −0.644668 | − | 0.764462i | \(-0.723005\pi\) | ||||
−0.644668 | + | 0.764462i | \(0.723005\pi\) | |||||||
\(114\) | −11.0584 | −1.03572 | ||||||||
\(115\) | −9.04668 | −0.843608 | ||||||||
\(116\) | 22.6972 | 2.10739 | ||||||||
\(117\) | 3.87181 | 0.357949 | ||||||||
\(118\) | 17.6689 | 1.62655 | ||||||||
\(119\) | −13.3592 | −1.22464 | ||||||||
\(120\) | 26.2220 | 2.39373 | ||||||||
\(121\) | −10.3415 | −0.940136 | ||||||||
\(122\) | −32.6909 | −2.95970 | ||||||||
\(123\) | −2.77198 | −0.249941 | ||||||||
\(124\) | 32.6608 | 2.93303 | ||||||||
\(125\) | −10.5486 | −0.943497 | ||||||||
\(126\) | 13.9299 | 1.24097 | ||||||||
\(127\) | 11.4285 | 1.01411 | 0.507056 | − | 0.861913i | \(-0.330734\pi\) | ||||
0.507056 | + | 0.861913i | \(0.330734\pi\) | |||||||
\(128\) | −31.1620 | −2.75436 | ||||||||
\(129\) | −6.37973 | −0.561704 | ||||||||
\(130\) | 16.2937 | 1.42905 | ||||||||
\(131\) | 11.4683 | 1.00199 | 0.500993 | − | 0.865451i | \(-0.332968\pi\) | ||||
0.500993 | + | 0.865451i | \(0.332968\pi\) | |||||||
\(132\) | 5.31813 | 0.462884 | ||||||||
\(133\) | −11.3155 | −0.981177 | ||||||||
\(134\) | −4.95900 | −0.428392 | ||||||||
\(135\) | 12.9089 | 1.11102 | ||||||||
\(136\) | 36.1590 | 3.10061 | ||||||||
\(137\) | −1.42455 | −0.121708 | −0.0608539 | − | 0.998147i | \(-0.519382\pi\) | ||||
−0.0608539 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(138\) | −12.7672 | −1.08681 | ||||||||
\(139\) | −3.89077 | −0.330010 | −0.165005 | − | 0.986293i | \(-0.552764\pi\) | ||||
−0.165005 | + | 0.986293i | \(0.552764\pi\) | |||||||
\(140\) | 42.7262 | 3.61102 | ||||||||
\(141\) | 7.34426 | 0.618498 | ||||||||
\(142\) | −2.23788 | −0.187799 | ||||||||
\(143\) | 2.07522 | 0.173539 | ||||||||
\(144\) | −21.4244 | −1.78537 | ||||||||
\(145\) | 9.90419 | 0.822498 | ||||||||
\(146\) | 24.2546 | 2.00733 | ||||||||
\(147\) | −5.45682 | −0.450071 | ||||||||
\(148\) | 7.59226 | 0.624080 | ||||||||
\(149\) | −8.64459 | −0.708192 | −0.354096 | − | 0.935209i | \(-0.615211\pi\) | ||||
−0.354096 | + | 0.935209i | \(0.615211\pi\) | |||||||
\(150\) | 1.66687 | 0.136100 | ||||||||
\(151\) | 1.33471 | 0.108617 | 0.0543087 | − | 0.998524i | \(-0.482705\pi\) | ||||
0.0543087 | + | 0.998524i | \(0.482705\pi\) | |||||||
\(152\) | 30.6273 | 2.48420 | ||||||||
\(153\) | 5.97043 | 0.482680 | ||||||||
\(154\) | 7.46615 | 0.601640 | ||||||||
\(155\) | 14.2519 | 1.14474 | ||||||||
\(156\) | 16.7597 | 1.34185 | ||||||||
\(157\) | −13.8722 | −1.10712 | −0.553560 | − | 0.832809i | \(-0.686731\pi\) | ||||
−0.553560 | + | 0.832809i | \(0.686731\pi\) | |||||||
\(158\) | 25.0865 | 1.99577 | ||||||||
\(159\) | −4.65385 | −0.369074 | ||||||||
\(160\) | −47.1386 | −3.72664 | ||||||||
\(161\) | −13.0639 | −1.02958 | ||||||||
\(162\) | 5.88201 | 0.462135 | ||||||||
\(163\) | −7.18081 | −0.562444 | −0.281222 | − | 0.959643i | \(-0.590740\pi\) | ||||
−0.281222 | + | 0.959643i | \(0.590740\pi\) | |||||||
\(164\) | 12.2252 | 0.954625 | ||||||||
\(165\) | 2.32063 | 0.180660 | ||||||||
\(166\) | −6.64710 | −0.515915 | ||||||||
\(167\) | −8.26957 | −0.639918 | −0.319959 | − | 0.947431i | \(-0.603669\pi\) | ||||
−0.319959 | + | 0.947431i | \(0.603669\pi\) | |||||||
\(168\) | 37.8661 | 2.92143 | ||||||||
\(169\) | −6.46009 | −0.496930 | ||||||||
\(170\) | 25.1253 | 1.92702 | ||||||||
\(171\) | 5.05706 | 0.386723 | ||||||||
\(172\) | 28.1363 | 2.14537 | ||||||||
\(173\) | −6.38589 | −0.485510 | −0.242755 | − | 0.970088i | \(-0.578051\pi\) | ||||
−0.242755 | + | 0.970088i | \(0.578051\pi\) | |||||||
\(174\) | 13.9773 | 1.05962 | ||||||||
\(175\) | 1.70562 | 0.128933 | ||||||||
\(176\) | −11.4831 | −0.865573 | ||||||||
\(177\) | 7.93054 | 0.596096 | ||||||||
\(178\) | −1.31971 | −0.0989163 | ||||||||
\(179\) | −16.6674 | −1.24578 | −0.622891 | − | 0.782309i | \(-0.714042\pi\) | ||||
−0.622891 | + | 0.782309i | \(0.714042\pi\) | |||||||
\(180\) | −19.0950 | −1.42326 | ||||||||
\(181\) | 8.77818 | 0.652477 | 0.326238 | − | 0.945288i | \(-0.394219\pi\) | ||||
0.326238 | + | 0.945288i | \(0.394219\pi\) | |||||||
\(182\) | 23.5291 | 1.74409 | ||||||||
\(183\) | −14.6731 | −1.08466 | ||||||||
\(184\) | 35.3598 | 2.60676 | ||||||||
\(185\) | 3.31296 | 0.243574 | ||||||||
\(186\) | 20.1131 | 1.47476 | ||||||||
\(187\) | 3.20004 | 0.234010 | ||||||||
\(188\) | −32.3901 | −2.36229 | ||||||||
\(189\) | 18.6412 | 1.35595 | ||||||||
\(190\) | 21.2816 | 1.54393 | ||||||||
\(191\) | 2.77339 | 0.200675 | 0.100338 | − | 0.994953i | \(-0.468008\pi\) | ||||
0.100338 | + | 0.994953i | \(0.468008\pi\) | |||||||
\(192\) | −32.0245 | −2.31117 | ||||||||
\(193\) | −3.19788 | −0.230189 | −0.115094 | − | 0.993355i | \(-0.536717\pi\) | ||||
−0.115094 | + | 0.993355i | \(0.536717\pi\) | |||||||
\(194\) | −32.8173 | −2.35614 | ||||||||
\(195\) | 7.31329 | 0.523715 | ||||||||
\(196\) | 24.0660 | 1.71900 | ||||||||
\(197\) | −7.75246 | −0.552340 | −0.276170 | − | 0.961109i | \(-0.589065\pi\) | ||||
−0.276170 | + | 0.961109i | \(0.589065\pi\) | |||||||
\(198\) | −3.33673 | −0.237131 | ||||||||
\(199\) | −7.25874 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(200\) | −4.61655 | −0.326440 | ||||||||
\(201\) | −2.22580 | −0.156996 | ||||||||
\(202\) | 20.2784 | 1.42678 | ||||||||
\(203\) | 14.3022 | 1.00382 | ||||||||
\(204\) | 25.8439 | 1.80944 | ||||||||
\(205\) | 5.33458 | 0.372583 | ||||||||
\(206\) | 46.1470 | 3.21522 | ||||||||
\(207\) | 5.83847 | 0.405801 | ||||||||
\(208\) | −36.1882 | −2.50920 | ||||||||
\(209\) | 2.71049 | 0.187489 | ||||||||
\(210\) | 26.3115 | 1.81567 | ||||||||
\(211\) | 8.38241 | 0.577069 | 0.288534 | − | 0.957470i | \(-0.406832\pi\) | ||||
0.288534 | + | 0.957470i | \(0.406832\pi\) | |||||||
\(212\) | 20.5247 | 1.40964 | ||||||||
\(213\) | −1.00446 | −0.0688241 | ||||||||
\(214\) | 22.8439 | 1.56158 | ||||||||
\(215\) | 12.2776 | 0.837324 | ||||||||
\(216\) | −50.4556 | −3.43307 | ||||||||
\(217\) | 20.5806 | 1.39710 | ||||||||
\(218\) | −33.6635 | −2.27998 | ||||||||
\(219\) | 10.8865 | 0.735640 | ||||||||
\(220\) | −10.2346 | −0.690014 | ||||||||
\(221\) | 10.0847 | 0.678371 | ||||||||
\(222\) | 4.67543 | 0.313795 | ||||||||
\(223\) | 3.98109 | 0.266594 | 0.133297 | − | 0.991076i | \(-0.457444\pi\) | ||||
0.133297 | + | 0.991076i | \(0.457444\pi\) | |||||||
\(224\) | −68.0709 | −4.54818 | ||||||||
\(225\) | −0.762266 | −0.0508178 | ||||||||
\(226\) | 37.2238 | 2.47609 | ||||||||
\(227\) | −15.4613 | −1.02620 | −0.513101 | − | 0.858328i | \(-0.671503\pi\) | ||||
−0.513101 | + | 0.858328i | \(0.671503\pi\) | |||||||
\(228\) | 21.8903 | 1.44972 | ||||||||
\(229\) | 9.60886 | 0.634971 | 0.317486 | − | 0.948263i | \(-0.397161\pi\) | ||||
0.317486 | + | 0.948263i | \(0.397161\pi\) | |||||||
\(230\) | 24.5700 | 1.62010 | ||||||||
\(231\) | 3.35112 | 0.220488 | ||||||||
\(232\) | −38.7114 | −2.54153 | ||||||||
\(233\) | 23.2996 | 1.52641 | 0.763203 | − | 0.646158i | \(-0.223625\pi\) | ||||
0.763203 | + | 0.646158i | \(0.223625\pi\) | |||||||
\(234\) | −10.5155 | −0.687418 | ||||||||
\(235\) | −14.1338 | −0.921985 | ||||||||
\(236\) | −34.9757 | −2.27673 | ||||||||
\(237\) | 11.2599 | 0.731406 | ||||||||
\(238\) | 36.2824 | 2.35184 | ||||||||
\(239\) | −29.9454 | −1.93700 | −0.968502 | − | 0.249005i | \(-0.919896\pi\) | ||||
−0.968502 | + | 0.249005i | \(0.919896\pi\) | |||||||
\(240\) | −40.4677 | −2.61218 | ||||||||
\(241\) | 9.68595 | 0.623927 | 0.311964 | − | 0.950094i | \(-0.399013\pi\) | ||||
0.311964 | + | 0.950094i | \(0.399013\pi\) | |||||||
\(242\) | 28.0866 | 1.80547 | ||||||||
\(243\) | −13.8678 | −0.889620 | ||||||||
\(244\) | 64.7120 | 4.14276 | ||||||||
\(245\) | 10.5015 | 0.670914 | ||||||||
\(246\) | 7.52845 | 0.479997 | ||||||||
\(247\) | 8.54192 | 0.543509 | ||||||||
\(248\) | −55.7049 | −3.53727 | ||||||||
\(249\) | −2.98349 | −0.189071 | ||||||||
\(250\) | 28.6491 | 1.81193 | ||||||||
\(251\) | 10.5555 | 0.666255 | 0.333128 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333128 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(252\) | −27.5743 | −1.73701 | ||||||||
\(253\) | 3.12931 | 0.196738 | ||||||||
\(254\) | −31.0387 | −1.94754 | ||||||||
\(255\) | 11.2773 | 0.706211 | ||||||||
\(256\) | 32.0914 | 2.00571 | ||||||||
\(257\) | −16.2583 | −1.01417 | −0.507084 | − | 0.861897i | \(-0.669277\pi\) | ||||
−0.507084 | + | 0.861897i | \(0.669277\pi\) | |||||||
\(258\) | 17.3268 | 1.07872 | ||||||||
\(259\) | 4.78411 | 0.297270 | ||||||||
\(260\) | −32.2535 | −2.00028 | ||||||||
\(261\) | −6.39187 | −0.395647 | ||||||||
\(262\) | −31.1468 | −1.92425 | ||||||||
\(263\) | 8.35083 | 0.514934 | 0.257467 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257467 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(264\) | −9.07038 | −0.558243 | ||||||||
\(265\) | 8.95617 | 0.550173 | ||||||||
\(266\) | 30.7318 | 1.88429 | ||||||||
\(267\) | −0.592340 | −0.0362506 | ||||||||
\(268\) | 9.81638 | 0.599631 | ||||||||
\(269\) | −3.76939 | −0.229824 | −0.114912 | − | 0.993376i | \(-0.536659\pi\) | ||||
−0.114912 | + | 0.993376i | \(0.536659\pi\) | |||||||
\(270\) | −35.0594 | −2.13365 | ||||||||
\(271\) | −25.1946 | −1.53046 | −0.765231 | − | 0.643756i | \(-0.777375\pi\) | ||||
−0.765231 | + | 0.643756i | \(0.777375\pi\) | |||||||
\(272\) | −55.8032 | −3.38357 | ||||||||
\(273\) | 10.5608 | 0.639170 | ||||||||
\(274\) | 3.86896 | 0.233732 | ||||||||
\(275\) | −0.408561 | −0.0246372 | ||||||||
\(276\) | 25.2727 | 1.52124 | ||||||||
\(277\) | 0.668286 | 0.0401534 | 0.0200767 | − | 0.999798i | \(-0.493609\pi\) | ||||
0.0200767 | + | 0.999798i | \(0.493609\pi\) | |||||||
\(278\) | 10.5670 | 0.633765 | ||||||||
\(279\) | −9.19777 | −0.550656 | ||||||||
\(280\) | −72.8720 | −4.35494 | ||||||||
\(281\) | −18.2233 | −1.08711 | −0.543556 | − | 0.839373i | \(-0.682922\pi\) | ||||
−0.543556 | + | 0.839373i | \(0.682922\pi\) | |||||||
\(282\) | −19.9463 | −1.18779 | ||||||||
\(283\) | −25.1313 | −1.49390 | −0.746949 | − | 0.664881i | \(-0.768482\pi\) | ||||
−0.746949 | + | 0.664881i | \(0.768482\pi\) | |||||||
\(284\) | 4.42991 | 0.262867 | ||||||||
\(285\) | 9.55205 | 0.565815 | ||||||||
\(286\) | −5.63611 | −0.333270 | ||||||||
\(287\) | 7.70345 | 0.454720 | ||||||||
\(288\) | 30.4219 | 1.79263 | ||||||||
\(289\) | −1.44913 | −0.0852427 | ||||||||
\(290\) | −26.8989 | −1.57956 | ||||||||
\(291\) | −14.7298 | −0.863474 | ||||||||
\(292\) | −48.0122 | −2.80970 | ||||||||
\(293\) | −8.18796 | −0.478346 | −0.239173 | − | 0.970977i | \(-0.576876\pi\) | ||||
−0.239173 | + | 0.970977i | \(0.576876\pi\) | |||||||
\(294\) | 14.8202 | 0.864334 | ||||||||
\(295\) | −15.2620 | −0.888591 | ||||||||
\(296\) | −12.9490 | −0.752647 | ||||||||
\(297\) | −4.46528 | −0.259102 | ||||||||
\(298\) | 23.4779 | 1.36004 | ||||||||
\(299\) | 9.86181 | 0.570323 | ||||||||
\(300\) | −3.29959 | −0.190502 | ||||||||
\(301\) | 17.7295 | 1.02191 | ||||||||
\(302\) | −3.62496 | −0.208593 | ||||||||
\(303\) | 9.10178 | 0.522884 | ||||||||
\(304\) | −47.2663 | −2.71091 | ||||||||
\(305\) | 28.2378 | 1.61689 | ||||||||
\(306\) | −16.2151 | −0.926958 | ||||||||
\(307\) | 22.3341 | 1.27468 | 0.637338 | − | 0.770585i | \(-0.280036\pi\) | ||||
0.637338 | + | 0.770585i | \(0.280036\pi\) | |||||||
\(308\) | −14.7793 | −0.842129 | ||||||||
\(309\) | 20.7127 | 1.17830 | ||||||||
\(310\) | −38.7069 | −2.19840 | ||||||||
\(311\) | 32.7851 | 1.85907 | 0.929536 | − | 0.368731i | \(-0.120208\pi\) | ||||
0.929536 | + | 0.368731i | \(0.120208\pi\) | |||||||
\(312\) | −28.5847 | −1.61829 | ||||||||
\(313\) | −20.3797 | −1.15193 | −0.575964 | − | 0.817475i | \(-0.695373\pi\) | ||||
−0.575964 | + | 0.817475i | \(0.695373\pi\) | |||||||
\(314\) | 37.6756 | 2.12616 | ||||||||
\(315\) | −12.0323 | −0.677945 | ||||||||
\(316\) | −49.6589 | −2.79353 | ||||||||
\(317\) | −28.8608 | −1.62099 | −0.810493 | − | 0.585748i | \(-0.800801\pi\) | ||||
−0.810493 | + | 0.585748i | \(0.800801\pi\) | |||||||
\(318\) | 12.6394 | 0.708784 | ||||||||
\(319\) | −3.42593 | −0.191815 | ||||||||
\(320\) | 61.6301 | 3.44522 | ||||||||
\(321\) | 10.2533 | 0.572283 | ||||||||
\(322\) | 35.4805 | 1.97725 | ||||||||
\(323\) | 13.1719 | 0.732902 | ||||||||
\(324\) | −11.6435 | −0.646861 | ||||||||
\(325\) | −1.28755 | −0.0714205 | ||||||||
\(326\) | 19.5024 | 1.08014 | ||||||||
\(327\) | −15.1096 | −0.835562 | ||||||||
\(328\) | −20.8507 | −1.15129 | ||||||||
\(329\) | −20.4100 | −1.12524 | ||||||||
\(330\) | −6.30261 | −0.346947 | ||||||||
\(331\) | 24.9883 | 1.37348 | 0.686741 | − | 0.726902i | \(-0.259041\pi\) | ||||
0.686741 | + | 0.726902i | \(0.259041\pi\) | |||||||
\(332\) | 13.1580 | 0.722138 | ||||||||
\(333\) | −2.13809 | −0.117167 | ||||||||
\(334\) | 22.4594 | 1.22892 | ||||||||
\(335\) | 4.28348 | 0.234032 | ||||||||
\(336\) | −58.4377 | −3.18804 | ||||||||
\(337\) | −25.5893 | −1.39394 | −0.696970 | − | 0.717101i | \(-0.745469\pi\) | ||||
−0.696970 | + | 0.717101i | \(0.745469\pi\) | |||||||
\(338\) | 17.5450 | 0.954324 | ||||||||
\(339\) | 16.7076 | 0.907432 | ||||||||
\(340\) | −49.7357 | −2.69730 | ||||||||
\(341\) | −4.92984 | −0.266966 | ||||||||
\(342\) | −13.7345 | −0.742677 | ||||||||
\(343\) | −8.54908 | −0.461607 | ||||||||
\(344\) | −47.9881 | −2.58734 | ||||||||
\(345\) | 11.0280 | 0.593729 | ||||||||
\(346\) | 17.3435 | 0.932392 | ||||||||
\(347\) | −7.41665 | −0.398146 | −0.199073 | − | 0.979985i | \(-0.563793\pi\) | ||||
−0.199073 | + | 0.979985i | \(0.563793\pi\) | |||||||
\(348\) | −27.6682 | −1.48317 | ||||||||
\(349\) | −26.1150 | −1.39790 | −0.698951 | − | 0.715170i | \(-0.746349\pi\) | ||||
−0.698951 | + | 0.715170i | \(0.746349\pi\) | |||||||
\(350\) | −4.63231 | −0.247607 | ||||||||
\(351\) | −14.0720 | −0.751109 | ||||||||
\(352\) | 16.3056 | 0.869091 | ||||||||
\(353\) | −9.23587 | −0.491576 | −0.245788 | − | 0.969324i | \(-0.579047\pi\) | ||||
−0.245788 | + | 0.969324i | \(0.579047\pi\) | |||||||
\(354\) | −21.5386 | −1.14476 | ||||||||
\(355\) | 1.93304 | 0.102595 | ||||||||
\(356\) | 2.61237 | 0.138456 | ||||||||
\(357\) | 16.2851 | 0.861896 | ||||||||
\(358\) | 45.2672 | 2.39245 | ||||||||
\(359\) | −7.16788 | −0.378306 | −0.189153 | − | 0.981948i | \(-0.560574\pi\) | ||||
−0.189153 | + | 0.981948i | \(0.560574\pi\) | |||||||
\(360\) | 32.5676 | 1.71646 | ||||||||
\(361\) | −7.84320 | −0.412800 | ||||||||
\(362\) | −23.8407 | −1.25304 | ||||||||
\(363\) | 12.6064 | 0.661666 | ||||||||
\(364\) | −46.5760 | −2.44124 | ||||||||
\(365\) | −20.9507 | −1.09661 | ||||||||
\(366\) | 39.8507 | 2.08303 | ||||||||
\(367\) | −16.6788 | −0.870627 | −0.435314 | − | 0.900279i | \(-0.643363\pi\) | ||||
−0.435314 | + | 0.900279i | \(0.643363\pi\) | |||||||
\(368\) | −54.5698 | −2.84465 | ||||||||
\(369\) | −3.44278 | −0.179224 | ||||||||
\(370\) | −8.99771 | −0.467769 | ||||||||
\(371\) | 12.9332 | 0.671460 | ||||||||
\(372\) | −39.8140 | −2.06426 | ||||||||
\(373\) | 1.81236 | 0.0938404 | 0.0469202 | − | 0.998899i | \(-0.485059\pi\) | ||||
0.0469202 | + | 0.998899i | \(0.485059\pi\) | |||||||
\(374\) | −8.69102 | −0.449402 | ||||||||
\(375\) | 12.8589 | 0.664031 | ||||||||
\(376\) | 55.2431 | 2.84895 | ||||||||
\(377\) | −10.7966 | −0.556052 | ||||||||
\(378\) | −50.6278 | −2.60401 | ||||||||
\(379\) | 25.4938 | 1.30953 | 0.654766 | − | 0.755832i | \(-0.272767\pi\) | ||||
0.654766 | + | 0.755832i | \(0.272767\pi\) | |||||||
\(380\) | −42.1270 | −2.16107 | ||||||||
\(381\) | −13.9314 | −0.713729 | ||||||||
\(382\) | −7.53227 | −0.385384 | ||||||||
\(383\) | −6.27741 | −0.320761 | −0.160380 | − | 0.987055i | \(-0.551272\pi\) | ||||
−0.160380 | + | 0.987055i | \(0.551272\pi\) | |||||||
\(384\) | 37.9869 | 1.93851 | ||||||||
\(385\) | −6.44912 | −0.328677 | ||||||||
\(386\) | 8.68516 | 0.442063 | ||||||||
\(387\) | −7.92359 | −0.402779 | ||||||||
\(388\) | 64.9621 | 3.29795 | ||||||||
\(389\) | −12.0484 | −0.610876 | −0.305438 | − | 0.952212i | \(-0.598803\pi\) | ||||
−0.305438 | + | 0.952212i | \(0.598803\pi\) | |||||||
\(390\) | −19.8622 | −1.00576 | ||||||||
\(391\) | 15.2072 | 0.769059 | ||||||||
\(392\) | −41.0460 | −2.07313 | ||||||||
\(393\) | −13.9800 | −0.705196 | ||||||||
\(394\) | 21.0550 | 1.06074 | ||||||||
\(395\) | −21.6692 | −1.09030 | ||||||||
\(396\) | 6.60509 | 0.331918 | ||||||||
\(397\) | −11.8731 | −0.595891 | −0.297946 | − | 0.954583i | \(-0.596301\pi\) | ||||
−0.297946 | + | 0.954583i | \(0.596301\pi\) | |||||||
\(398\) | 19.7141 | 0.988177 | ||||||||
\(399\) | 13.7937 | 0.690550 | ||||||||
\(400\) | 7.12460 | 0.356230 | ||||||||
\(401\) | −17.8025 | −0.889015 | −0.444507 | − | 0.895775i | \(-0.646621\pi\) | ||||
−0.444507 | + | 0.895775i | \(0.646621\pi\) | |||||||
\(402\) | 6.04508 | 0.301501 | ||||||||
\(403\) | −15.5360 | −0.773905 | ||||||||
\(404\) | −40.1412 | −1.99710 | ||||||||
\(405\) | −5.08077 | −0.252465 | ||||||||
\(406\) | −38.8436 | −1.92777 | ||||||||
\(407\) | −1.14598 | −0.0568041 | ||||||||
\(408\) | −44.0783 | −2.18220 | ||||||||
\(409\) | −1.46512 | −0.0724455 | −0.0362227 | − | 0.999344i | \(-0.511533\pi\) | ||||
−0.0362227 | + | 0.999344i | \(0.511533\pi\) | |||||||
\(410\) | −14.4882 | −0.715523 | ||||||||
\(411\) | 1.73655 | 0.0856576 | ||||||||
\(412\) | −91.3484 | −4.50041 | ||||||||
\(413\) | −22.0393 | −1.08448 | ||||||||
\(414\) | −15.8567 | −0.779316 | ||||||||
\(415\) | 5.74163 | 0.281846 | ||||||||
\(416\) | 51.3859 | 2.51940 | ||||||||
\(417\) | 4.74290 | 0.232261 | ||||||||
\(418\) | −7.36145 | −0.360060 | ||||||||
\(419\) | 8.61860 | 0.421046 | 0.210523 | − | 0.977589i | \(-0.432483\pi\) | ||||
0.210523 | + | 0.977589i | \(0.432483\pi\) | |||||||
\(420\) | −52.0838 | −2.54143 | ||||||||
\(421\) | −25.3563 | −1.23579 | −0.617896 | − | 0.786260i | \(-0.712015\pi\) | ||||
−0.617896 | + | 0.786260i | \(0.712015\pi\) | |||||||
\(422\) | −22.7659 | −1.10822 | ||||||||
\(423\) | 9.12152 | 0.443504 | ||||||||
\(424\) | −35.0060 | −1.70004 | ||||||||
\(425\) | −1.98544 | −0.0963079 | ||||||||
\(426\) | 2.72801 | 0.132172 | ||||||||
\(427\) | 40.7770 | 1.97334 | ||||||||
\(428\) | −45.2197 | −2.18578 | ||||||||
\(429\) | −2.52972 | −0.122136 | ||||||||
\(430\) | −33.3448 | −1.60803 | ||||||||
\(431\) | 25.5312 | 1.22980 | 0.614898 | − | 0.788607i | \(-0.289197\pi\) | ||||
0.614898 | + | 0.788607i | \(0.289197\pi\) | |||||||
\(432\) | 77.8668 | 3.74637 | ||||||||
\(433\) | −19.5854 | −0.941213 | −0.470606 | − | 0.882343i | \(-0.655965\pi\) | ||||
−0.470606 | + | 0.882343i | \(0.655965\pi\) | |||||||
\(434\) | −55.8950 | −2.68305 | ||||||||
\(435\) | −12.0733 | −0.578872 | ||||||||
\(436\) | 66.6372 | 3.19134 | ||||||||
\(437\) | 12.8807 | 0.616169 | ||||||||
\(438\) | −29.5667 | −1.41275 | ||||||||
\(439\) | 24.5900 | 1.17362 | 0.586808 | − | 0.809726i | \(-0.300384\pi\) | ||||
0.586808 | + | 0.809726i | \(0.300384\pi\) | |||||||
\(440\) | 17.4556 | 0.832165 | ||||||||
\(441\) | −6.77734 | −0.322731 | ||||||||
\(442\) | −27.3891 | −1.30277 | ||||||||
\(443\) | −36.7053 | −1.74392 | −0.871960 | − | 0.489578i | \(-0.837151\pi\) | ||||
−0.871960 | + | 0.489578i | \(0.837151\pi\) | |||||||
\(444\) | −9.25506 | −0.439226 | ||||||||
\(445\) | 1.13994 | 0.0540382 | ||||||||
\(446\) | −10.8123 | −0.511977 | ||||||||
\(447\) | 10.5379 | 0.498424 | ||||||||
\(448\) | 88.9974 | 4.20473 | ||||||||
\(449\) | −6.66992 | −0.314773 | −0.157387 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157387 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(450\) | 2.07025 | 0.0975924 | ||||||||
\(451\) | −1.84527 | −0.0868904 | ||||||||
\(452\) | −73.6849 | −3.46584 | ||||||||
\(453\) | −1.62703 | −0.0764446 | ||||||||
\(454\) | 41.9915 | 1.97076 | ||||||||
\(455\) | −20.3239 | −0.952801 | ||||||||
\(456\) | −37.3351 | −1.74838 | ||||||||
\(457\) | 4.35542 | 0.203738 | 0.101869 | − | 0.994798i | \(-0.467518\pi\) | ||||
0.101869 | + | 0.994798i | \(0.467518\pi\) | |||||||
\(458\) | −26.0968 | −1.21942 | ||||||||
\(459\) | −21.6994 | −1.01284 | ||||||||
\(460\) | −48.6365 | −2.26769 | ||||||||
\(461\) | 14.8966 | 0.693806 | 0.346903 | − | 0.937901i | \(-0.387233\pi\) | ||||
0.346903 | + | 0.937901i | \(0.387233\pi\) | |||||||
\(462\) | −9.10134 | −0.423433 | ||||||||
\(463\) | 13.6012 | 0.632103 | 0.316052 | − | 0.948742i | \(-0.397643\pi\) | ||||
0.316052 | + | 0.948742i | \(0.397643\pi\) | |||||||
\(464\) | 59.7423 | 2.77347 | ||||||||
\(465\) | −17.3733 | −0.805666 | ||||||||
\(466\) | −63.2796 | −2.93137 | ||||||||
\(467\) | −30.9495 | −1.43217 | −0.716087 | − | 0.698011i | \(-0.754069\pi\) | ||||
−0.716087 | + | 0.698011i | \(0.754069\pi\) | |||||||
\(468\) | 20.8155 | 0.962196 | ||||||||
\(469\) | 6.18560 | 0.285625 | ||||||||
\(470\) | 38.3860 | 1.77062 | ||||||||
\(471\) | 16.9104 | 0.779189 | ||||||||
\(472\) | 59.6531 | 2.74576 | ||||||||
\(473\) | −4.24690 | −0.195273 | ||||||||
\(474\) | −30.5808 | −1.40462 | ||||||||
\(475\) | −1.68170 | −0.0771617 | ||||||||
\(476\) | −71.8213 | −3.29192 | ||||||||
\(477\) | −5.78005 | −0.264650 | ||||||||
\(478\) | 81.3289 | 3.71990 | ||||||||
\(479\) | −2.77895 | −0.126974 | −0.0634868 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634868 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(480\) | 57.4626 | 2.62280 | ||||||||
\(481\) | −3.61147 | −0.164669 | ||||||||
\(482\) | −26.3062 | −1.19821 | ||||||||
\(483\) | 15.9251 | 0.724618 | ||||||||
\(484\) | −55.5976 | −2.52716 | ||||||||
\(485\) | 28.3469 | 1.28717 | ||||||||
\(486\) | 37.6637 | 1.70846 | ||||||||
\(487\) | 3.88132 | 0.175880 | 0.0879398 | − | 0.996126i | \(-0.471972\pi\) | ||||
0.0879398 | + | 0.996126i | \(0.471972\pi\) | |||||||
\(488\) | −110.370 | −4.99622 | ||||||||
\(489\) | 8.75350 | 0.395847 | ||||||||
\(490\) | −28.5210 | −1.28845 | ||||||||
\(491\) | 14.4734 | 0.653174 | 0.326587 | − | 0.945167i | \(-0.394101\pi\) | ||||
0.326587 | + | 0.945167i | \(0.394101\pi\) | |||||||
\(492\) | −14.9026 | −0.671862 | ||||||||
\(493\) | −16.6486 | −0.749815 | ||||||||
\(494\) | −23.1991 | −1.04378 | ||||||||
\(495\) | 2.88220 | 0.129545 | ||||||||
\(496\) | 85.9679 | 3.86007 | ||||||||
\(497\) | 2.79142 | 0.125212 | ||||||||
\(498\) | 8.10290 | 0.363100 | ||||||||
\(499\) | −8.48380 | −0.379787 | −0.189894 | − | 0.981805i | \(-0.560814\pi\) | ||||
−0.189894 | + | 0.981805i | \(0.560814\pi\) | |||||||
\(500\) | −56.7111 | −2.53620 | ||||||||
\(501\) | 10.0807 | 0.450373 | ||||||||
\(502\) | −28.6677 | −1.27950 | ||||||||
\(503\) | 20.1722 | 0.899432 | 0.449716 | − | 0.893172i | \(-0.351525\pi\) | ||||
0.449716 | + | 0.893172i | \(0.351525\pi\) | |||||||
\(504\) | 47.0295 | 2.09486 | ||||||||
\(505\) | −17.5161 | −0.779455 | ||||||||
\(506\) | −8.49893 | −0.377824 | ||||||||
\(507\) | 7.87494 | 0.349738 | ||||||||
\(508\) | 61.4413 | 2.72602 | ||||||||
\(509\) | 44.6181 | 1.97766 | 0.988832 | − | 0.149035i | \(-0.0476167\pi\) | ||||
0.988832 | + | 0.149035i | \(0.0476167\pi\) | |||||||
\(510\) | −30.6281 | −1.35623 | ||||||||
\(511\) | −30.2540 | −1.33836 | ||||||||
\(512\) | −24.8334 | −1.09749 | ||||||||
\(513\) | −18.3798 | −0.811487 | ||||||||
\(514\) | 44.1562 | 1.94765 | ||||||||
\(515\) | −39.8609 | −1.75648 | ||||||||
\(516\) | −34.2985 | −1.50991 | ||||||||
\(517\) | 4.88897 | 0.215017 | ||||||||
\(518\) | −12.9932 | −0.570889 | ||||||||
\(519\) | 7.78448 | 0.341701 | ||||||||
\(520\) | 55.0102 | 2.41236 | ||||||||
\(521\) | 12.6560 | 0.554469 | 0.277234 | − | 0.960802i | \(-0.410582\pi\) | ||||
0.277234 | + | 0.960802i | \(0.410582\pi\) | |||||||
\(522\) | 17.3598 | 0.759816 | ||||||||
\(523\) | 36.0828 | 1.57779 | 0.788896 | − | 0.614527i | \(-0.210653\pi\) | ||||
0.788896 | + | 0.614527i | \(0.210653\pi\) | |||||||
\(524\) | 61.6553 | 2.69342 | ||||||||
\(525\) | −2.07917 | −0.0907425 | ||||||||
\(526\) | −22.6801 | −0.988899 | ||||||||
\(527\) | −23.9570 | −1.04358 | ||||||||
\(528\) | 13.9981 | 0.609188 | ||||||||
\(529\) | −8.12895 | −0.353433 | ||||||||
\(530\) | −24.3241 | −1.05657 | ||||||||
\(531\) | 9.84968 | 0.427440 | ||||||||
\(532\) | −60.8339 | −2.63748 | ||||||||
\(533\) | −5.81524 | −0.251886 | ||||||||
\(534\) | 1.60874 | 0.0696171 | ||||||||
\(535\) | −19.7321 | −0.853093 | ||||||||
\(536\) | −16.7424 | −0.723161 | ||||||||
\(537\) | 20.3178 | 0.876778 | ||||||||
\(538\) | 10.2373 | 0.441362 | ||||||||
\(539\) | −3.63253 | −0.156464 | ||||||||
\(540\) | 69.4004 | 2.98652 | ||||||||
\(541\) | 23.3384 | 1.00339 | 0.501697 | − | 0.865043i | \(-0.332709\pi\) | ||||
0.501697 | + | 0.865043i | \(0.332709\pi\) | |||||||
\(542\) | 68.4262 | 2.93916 | ||||||||
\(543\) | −10.7007 | −0.459212 | ||||||||
\(544\) | 79.2384 | 3.39732 | ||||||||
\(545\) | 29.0779 | 1.24556 | ||||||||
\(546\) | −28.6822 | −1.22749 | ||||||||
\(547\) | 1.81438 | 0.0775772 | 0.0387886 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387886 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(548\) | −7.65863 | −0.327160 | ||||||||
\(549\) | −18.2238 | −0.777775 | ||||||||
\(550\) | 1.10962 | 0.0473142 | ||||||||
\(551\) | −14.1017 | −0.600751 | ||||||||
\(552\) | −43.1041 | −1.83463 | ||||||||
\(553\) | −31.2916 | −1.33065 | ||||||||
\(554\) | −1.81500 | −0.0771121 | ||||||||
\(555\) | −4.03855 | −0.171427 | ||||||||
\(556\) | −20.9174 | −0.887095 | ||||||||
\(557\) | −24.1043 | −1.02133 | −0.510666 | − | 0.859779i | \(-0.670601\pi\) | ||||
−0.510666 | + | 0.859779i | \(0.670601\pi\) | |||||||
\(558\) | 24.9803 | 1.05750 | ||||||||
\(559\) | −13.3838 | −0.566075 | ||||||||
\(560\) | 112.461 | 4.75236 | ||||||||
\(561\) | −3.90089 | −0.164696 | ||||||||
\(562\) | 49.4929 | 2.08773 | ||||||||
\(563\) | 25.3282 | 1.06746 | 0.533729 | − | 0.845655i | \(-0.320790\pi\) | ||||
0.533729 | + | 0.845655i | \(0.320790\pi\) | |||||||
\(564\) | 39.4839 | 1.66257 | ||||||||
\(565\) | −32.1532 | −1.35270 | ||||||||
\(566\) | 68.2542 | 2.86894 | ||||||||
\(567\) | −7.33692 | −0.308122 | ||||||||
\(568\) | −7.55546 | −0.317020 | ||||||||
\(569\) | 32.5865 | 1.36610 | 0.683048 | − | 0.730373i | \(-0.260654\pi\) | ||||
0.683048 | + | 0.730373i | \(0.260654\pi\) | |||||||
\(570\) | −25.9425 | −1.08661 | ||||||||
\(571\) | 31.9431 | 1.33678 | 0.668388 | − | 0.743813i | \(-0.266984\pi\) | ||||
0.668388 | + | 0.743813i | \(0.266984\pi\) | |||||||
\(572\) | 11.1567 | 0.466486 | ||||||||
\(573\) | −3.38080 | −0.141235 | ||||||||
\(574\) | −20.9219 | −0.873262 | ||||||||
\(575\) | −1.94155 | −0.0809684 | ||||||||
\(576\) | −39.7742 | −1.65726 | ||||||||
\(577\) | −17.2713 | −0.719015 | −0.359507 | − | 0.933142i | \(-0.617055\pi\) | ||||
−0.359507 | + | 0.933142i | \(0.617055\pi\) | |||||||
\(578\) | 3.93569 | 0.163703 | ||||||||
\(579\) | 3.89826 | 0.162006 | ||||||||
\(580\) | 53.2466 | 2.21094 | ||||||||
\(581\) | 8.29125 | 0.343979 | ||||||||
\(582\) | 40.0047 | 1.65825 | ||||||||
\(583\) | −3.09800 | −0.128306 | ||||||||
\(584\) | 81.8876 | 3.38853 | ||||||||
\(585\) | 9.08306 | 0.375538 | ||||||||
\(586\) | 22.2378 | 0.918634 | ||||||||
\(587\) | 14.1067 | 0.582247 | 0.291124 | − | 0.956685i | \(-0.405971\pi\) | ||||
0.291124 | + | 0.956685i | \(0.405971\pi\) | |||||||
\(588\) | −29.3368 | −1.20983 | ||||||||
\(589\) | −20.2920 | −0.836116 | ||||||||
\(590\) | 41.4503 | 1.70648 | ||||||||
\(591\) | 9.45035 | 0.388736 | ||||||||
\(592\) | 19.9839 | 0.821332 | ||||||||
\(593\) | 0.125965 | 0.00517275 | 0.00258638 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258638 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(594\) | 12.1273 | 0.497589 | ||||||||
\(595\) | −31.3400 | −1.28482 | ||||||||
\(596\) | −46.4747 | −1.90368 | ||||||||
\(597\) | 8.84850 | 0.362145 | ||||||||
\(598\) | −26.7838 | −1.09527 | ||||||||
\(599\) | −8.70627 | −0.355728 | −0.177864 | − | 0.984055i | \(-0.556919\pi\) | ||||
−0.177864 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(600\) | 5.62764 | 0.229747 | ||||||||
\(601\) | 45.0940 | 1.83942 | 0.919712 | − | 0.392594i | \(-0.128422\pi\) | ||||
0.919712 | + | 0.392594i | \(0.128422\pi\) | |||||||
\(602\) | −48.1518 | −1.96252 | ||||||||
\(603\) | −2.76444 | −0.112577 | ||||||||
\(604\) | 7.17563 | 0.291972 | ||||||||
\(605\) | −24.2606 | −0.986335 | ||||||||
\(606\) | −24.7196 | −1.00417 | ||||||||
\(607\) | 39.5949 | 1.60711 | 0.803555 | − | 0.595231i | \(-0.202939\pi\) | ||||
0.803555 | + | 0.595231i | \(0.202939\pi\) | |||||||
\(608\) | 67.1163 | 2.72193 | ||||||||
\(609\) | −17.4346 | −0.706486 | ||||||||
\(610\) | −76.6913 | −3.10514 | ||||||||
\(611\) | 15.4073 | 0.623311 | ||||||||
\(612\) | 32.0980 | 1.29748 | ||||||||
\(613\) | −45.7881 | −1.84937 | −0.924683 | − | 0.380738i | \(-0.875670\pi\) | ||||
−0.924683 | + | 0.380738i | \(0.875670\pi\) | |||||||
\(614\) | −60.6574 | −2.44793 | ||||||||
\(615\) | −6.50293 | −0.262223 | ||||||||
\(616\) | 25.2070 | 1.01562 | ||||||||
\(617\) | −31.0597 | −1.25042 | −0.625209 | − | 0.780458i | \(-0.714986\pi\) | ||||
−0.625209 | + | 0.780458i | \(0.714986\pi\) | |||||||
\(618\) | −56.2538 | −2.26286 | ||||||||
\(619\) | −37.0714 | −1.49003 | −0.745013 | − | 0.667050i | \(-0.767557\pi\) | ||||
−0.745013 | + | 0.667050i | \(0.767557\pi\) | |||||||
\(620\) | 76.6206 | 3.07716 | ||||||||
\(621\) | −21.2198 | −0.851522 | ||||||||
\(622\) | −89.0413 | −3.57023 | ||||||||
\(623\) | 1.64614 | 0.0659511 | ||||||||
\(624\) | 44.1139 | 1.76597 | ||||||||
\(625\) | −27.2639 | −1.09056 | ||||||||
\(626\) | 55.3494 | 2.21221 | ||||||||
\(627\) | −3.30412 | −0.131954 | ||||||||
\(628\) | −74.5791 | −2.97603 | ||||||||
\(629\) | −5.56898 | −0.222050 | ||||||||
\(630\) | 32.6787 | 1.30195 | ||||||||
\(631\) | 29.9595 | 1.19267 | 0.596334 | − | 0.802737i | \(-0.296624\pi\) | ||||
0.596334 | + | 0.802737i | \(0.296624\pi\) | |||||||
\(632\) | 84.6961 | 3.36903 | ||||||||
\(633\) | −10.2183 | −0.406139 | ||||||||
\(634\) | 78.3834 | 3.11300 | ||||||||
\(635\) | 26.8106 | 1.06395 | ||||||||
\(636\) | −25.0198 | −0.992101 | ||||||||
\(637\) | −11.4477 | −0.453573 | ||||||||
\(638\) | 9.30452 | 0.368369 | ||||||||
\(639\) | −1.24753 | −0.0493514 | ||||||||
\(640\) | −73.1044 | −2.88970 | ||||||||
\(641\) | 24.9439 | 0.985225 | 0.492612 | − | 0.870249i | \(-0.336042\pi\) | ||||
0.492612 | + | 0.870249i | \(0.336042\pi\) | |||||||
\(642\) | −27.8470 | −1.09903 | ||||||||
\(643\) | 7.70102 | 0.303699 | 0.151849 | − | 0.988404i | \(-0.451477\pi\) | ||||
0.151849 | + | 0.988404i | \(0.451477\pi\) | |||||||
\(644\) | −70.2339 | −2.76760 | ||||||||
\(645\) | −14.9665 | −0.589307 | ||||||||
\(646\) | −35.7736 | −1.40749 | ||||||||
\(647\) | −14.5983 | −0.573918 | −0.286959 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286959 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(648\) | 19.8586 | 0.780121 | ||||||||
\(649\) | 5.27925 | 0.207229 | ||||||||
\(650\) | 3.49687 | 0.137159 | ||||||||
\(651\) | −25.0880 | −0.983277 | ||||||||
\(652\) | −38.6052 | −1.51190 | ||||||||
\(653\) | 35.9508 | 1.40686 | 0.703431 | − | 0.710764i | \(-0.251650\pi\) | ||||
0.703431 | + | 0.710764i | \(0.251650\pi\) | |||||||
\(654\) | 41.0362 | 1.60464 | ||||||||
\(655\) | 26.9040 | 1.05122 | ||||||||
\(656\) | 32.1783 | 1.25635 | ||||||||
\(657\) | 13.5209 | 0.527502 | ||||||||
\(658\) | 55.4317 | 2.16095 | ||||||||
\(659\) | −23.4272 | −0.912596 | −0.456298 | − | 0.889827i | \(-0.650825\pi\) | ||||
−0.456298 | + | 0.889827i | \(0.650825\pi\) | |||||||
\(660\) | 12.4761 | 0.485630 | ||||||||
\(661\) | −17.0585 | −0.663499 | −0.331749 | − | 0.943368i | \(-0.607639\pi\) | ||||
−0.331749 | + | 0.943368i | \(0.607639\pi\) | |||||||
\(662\) | −67.8660 | −2.63769 | ||||||||
\(663\) | −12.2934 | −0.477436 | ||||||||
\(664\) | −22.4417 | −0.870907 | ||||||||
\(665\) | −26.5455 | −1.02939 | ||||||||
\(666\) | 5.80686 | 0.225011 | ||||||||
\(667\) | −16.2806 | −0.630388 | ||||||||
\(668\) | −44.4586 | −1.72015 | ||||||||
\(669\) | −4.85300 | −0.187628 | ||||||||
\(670\) | −11.6336 | −0.449444 | ||||||||
\(671\) | −9.76766 | −0.377076 | ||||||||
\(672\) | 82.9794 | 3.20100 | ||||||||
\(673\) | 46.6597 | 1.79860 | 0.899300 | − | 0.437332i | \(-0.144077\pi\) | ||||
0.899300 | + | 0.437332i | \(0.144077\pi\) | |||||||
\(674\) | 69.4983 | 2.67697 | ||||||||
\(675\) | 2.77044 | 0.106634 | ||||||||
\(676\) | −34.7305 | −1.33579 | ||||||||
\(677\) | −27.9266 | −1.07331 | −0.536653 | − | 0.843803i | \(-0.680311\pi\) | ||||
−0.536653 | + | 0.843803i | \(0.680311\pi\) | |||||||
\(678\) | −45.3763 | −1.74267 | ||||||||
\(679\) | 40.9346 | 1.57093 | ||||||||
\(680\) | 84.8272 | 3.25297 | ||||||||
\(681\) | 18.8475 | 0.722239 | ||||||||
\(682\) | 13.3890 | 0.512691 | ||||||||
\(683\) | −38.5106 | −1.47357 | −0.736783 | − | 0.676129i | \(-0.763656\pi\) | ||||
−0.736783 | + | 0.676129i | \(0.763656\pi\) | |||||||
\(684\) | 27.1876 | 1.03954 | ||||||||
\(685\) | −3.34193 | −0.127688 | ||||||||
\(686\) | 23.2185 | 0.886487 | ||||||||
\(687\) | −11.7133 | −0.446891 | ||||||||
\(688\) | 74.0587 | 2.82346 | ||||||||
\(689\) | −9.76314 | −0.371946 | ||||||||
\(690\) | −29.9511 | −1.14022 | ||||||||
\(691\) | 11.8064 | 0.449137 | 0.224569 | − | 0.974458i | \(-0.427903\pi\) | ||||
0.224569 | + | 0.974458i | \(0.427903\pi\) | |||||||
\(692\) | −34.3316 | −1.30509 | ||||||||
\(693\) | 4.16207 | 0.158104 | ||||||||
\(694\) | 20.1429 | 0.764616 | ||||||||
\(695\) | −9.12754 | −0.346227 | ||||||||
\(696\) | 47.1898 | 1.78872 | ||||||||
\(697\) | −8.96725 | −0.339659 | ||||||||
\(698\) | 70.9259 | 2.68458 | ||||||||
\(699\) | −28.4025 | −1.07428 | ||||||||
\(700\) | 9.16969 | 0.346582 | ||||||||
\(701\) | −36.4154 | −1.37539 | −0.687695 | − | 0.726000i | \(-0.741377\pi\) | ||||
−0.687695 | + | 0.726000i | \(0.741377\pi\) | |||||||
\(702\) | 38.2183 | 1.44246 | ||||||||
\(703\) | −4.71702 | −0.177906 | ||||||||
\(704\) | −21.3183 | −0.803463 | ||||||||
\(705\) | 17.2292 | 0.648891 | ||||||||
\(706\) | 25.0838 | 0.944040 | ||||||||
\(707\) | −25.2942 | −0.951287 | ||||||||
\(708\) | 42.6359 | 1.60235 | ||||||||
\(709\) | 22.1543 | 0.832022 | 0.416011 | − | 0.909360i | \(-0.363428\pi\) | ||||
0.416011 | + | 0.909360i | \(0.363428\pi\) | |||||||
\(710\) | −5.24996 | −0.197028 | ||||||||
\(711\) | 13.9847 | 0.524466 | ||||||||
\(712\) | −4.45555 | −0.166979 | ||||||||
\(713\) | −23.4275 | −0.877366 | ||||||||
\(714\) | −44.2287 | −1.65522 | ||||||||
\(715\) | 4.86836 | 0.182066 | ||||||||
\(716\) | −89.6068 | −3.34876 | ||||||||
\(717\) | 36.5038 | 1.36326 | ||||||||
\(718\) | 19.4673 | 0.726514 | ||||||||
\(719\) | 36.2655 | 1.35247 | 0.676237 | − | 0.736684i | \(-0.263610\pi\) | ||||
0.676237 | + | 0.736684i | \(0.263610\pi\) | |||||||
\(720\) | −50.2606 | −1.87310 | ||||||||
\(721\) | −57.5615 | −2.14370 | ||||||||
\(722\) | 21.3014 | 0.792757 | ||||||||
\(723\) | −11.8073 | −0.439118 | ||||||||
\(724\) | 47.1929 | 1.75391 | ||||||||
\(725\) | 2.12559 | 0.0789424 | ||||||||
\(726\) | −34.2379 | −1.27069 | ||||||||
\(727\) | −48.6385 | −1.80390 | −0.901952 | − | 0.431837i | \(-0.857866\pi\) | ||||
−0.901952 | + | 0.431837i | \(0.857866\pi\) | |||||||
\(728\) | 79.4380 | 2.94417 | ||||||||
\(729\) | 23.4023 | 0.866753 | ||||||||
\(730\) | 56.9001 | 2.10597 | ||||||||
\(731\) | −20.6382 | −0.763331 | ||||||||
\(732\) | −78.8848 | −2.91566 | ||||||||
\(733\) | −15.1688 | −0.560271 | −0.280135 | − | 0.959960i | \(-0.590379\pi\) | ||||
−0.280135 | + | 0.959960i | \(0.590379\pi\) | |||||||
\(734\) | 45.2982 | 1.67199 | ||||||||
\(735\) | −12.8014 | −0.472188 | ||||||||
\(736\) | 77.4871 | 2.85621 | ||||||||
\(737\) | −1.48169 | −0.0545787 | ||||||||
\(738\) | 9.35029 | 0.344189 | ||||||||
\(739\) | −31.0650 | −1.14275 | −0.571373 | − | 0.820691i | \(-0.693589\pi\) | ||||
−0.571373 | + | 0.820691i | \(0.693589\pi\) | |||||||
\(740\) | 17.8110 | 0.654747 | ||||||||
\(741\) | −10.4127 | −0.382521 | ||||||||
\(742\) | −35.1255 | −1.28950 | ||||||||
\(743\) | 53.8252 | 1.97465 | 0.987327 | − | 0.158696i | \(-0.0507290\pi\) | ||||
0.987327 | + | 0.158696i | \(0.0507290\pi\) | |||||||
\(744\) | 67.9050 | 2.48952 | ||||||||
\(745\) | −20.2798 | −0.742993 | ||||||||
\(746\) | −4.92220 | −0.180215 | ||||||||
\(747\) | −3.70548 | −0.135577 | ||||||||
\(748\) | 17.2040 | 0.629039 | ||||||||
\(749\) | −28.4943 | −1.04116 | ||||||||
\(750\) | −34.9236 | −1.27523 | ||||||||
\(751\) | −24.3647 | −0.889080 | −0.444540 | − | 0.895759i | \(-0.646633\pi\) | ||||
−0.444540 | + | 0.895759i | \(0.646633\pi\) | |||||||
\(752\) | −85.2552 | −3.10894 | ||||||||
\(753\) | −12.8673 | −0.468909 | ||||||||
\(754\) | 29.3225 | 1.06786 | ||||||||
\(755\) | 3.13117 | 0.113955 | ||||||||
\(756\) | 100.218 | 3.64490 | ||||||||
\(757\) | −21.2877 | −0.773715 | −0.386857 | − | 0.922140i | \(-0.626439\pi\) | ||||
−0.386857 | + | 0.922140i | \(0.626439\pi\) | |||||||
\(758\) | −69.2390 | −2.51487 | ||||||||
\(759\) | −3.81467 | −0.138464 | ||||||||
\(760\) | 71.8501 | 2.60628 | ||||||||
\(761\) | 5.15064 | 0.186710 | 0.0933552 | − | 0.995633i | \(-0.470241\pi\) | ||||
0.0933552 | + | 0.995633i | \(0.470241\pi\) | |||||||
\(762\) | 37.8365 | 1.37067 | ||||||||
\(763\) | 41.9901 | 1.52014 | ||||||||
\(764\) | 14.9102 | 0.539432 | ||||||||
\(765\) | 14.0063 | 0.506399 | ||||||||
\(766\) | 17.0489 | 0.616001 | ||||||||
\(767\) | 16.6372 | 0.600734 | ||||||||
\(768\) | −39.1199 | −1.41162 | ||||||||
\(769\) | −10.3093 | −0.371762 | −0.185881 | − | 0.982572i | \(-0.559514\pi\) | ||||
−0.185881 | + | 0.982572i | \(0.559514\pi\) | |||||||
\(770\) | 17.5152 | 0.631205 | ||||||||
\(771\) | 19.8191 | 0.713769 | ||||||||
\(772\) | −17.1923 | −0.618766 | ||||||||
\(773\) | 40.4102 | 1.45345 | 0.726727 | − | 0.686927i | \(-0.241041\pi\) | ||||
0.726727 | + | 0.686927i | \(0.241041\pi\) | |||||||
\(774\) | 21.5198 | 0.773512 | ||||||||
\(775\) | 3.05868 | 0.109871 | ||||||||
\(776\) | −110.797 | −3.97736 | ||||||||
\(777\) | −5.83190 | −0.209218 | ||||||||
\(778\) | 32.7223 | 1.17315 | ||||||||
\(779\) | −7.59542 | −0.272134 | ||||||||
\(780\) | 39.3174 | 1.40779 | ||||||||
\(781\) | −0.668652 | −0.0239263 | ||||||||
\(782\) | −41.3013 | −1.47693 | ||||||||
\(783\) | 23.2312 | 0.830214 | ||||||||
\(784\) | 63.3451 | 2.26233 | ||||||||
\(785\) | −32.5434 | −1.16152 | ||||||||
\(786\) | 37.9683 | 1.35428 | ||||||||
\(787\) | −19.6957 | −0.702075 | −0.351037 | − | 0.936361i | \(-0.614171\pi\) | ||||
−0.351037 | + | 0.936361i | \(0.614171\pi\) | |||||||
\(788\) | −41.6785 | −1.48474 | ||||||||
\(789\) | −10.1798 | −0.362409 | ||||||||
\(790\) | 58.8516 | 2.09385 | ||||||||
\(791\) | −46.4311 | −1.65090 | ||||||||
\(792\) | −11.2654 | −0.400297 | ||||||||
\(793\) | −30.7821 | −1.09310 | ||||||||
\(794\) | 32.2461 | 1.14437 | ||||||||
\(795\) | −10.9177 | −0.387210 | ||||||||
\(796\) | −39.0242 | −1.38318 | ||||||||
\(797\) | 3.49397 | 0.123763 | 0.0618813 | − | 0.998084i | \(-0.480290\pi\) | ||||
0.0618813 | + | 0.998084i | \(0.480290\pi\) | |||||||
\(798\) | −37.4625 | −1.32616 | ||||||||
\(799\) | 23.7584 | 0.840511 | ||||||||
\(800\) | −10.1167 | −0.357678 | ||||||||
\(801\) | −0.735683 | −0.0259941 | ||||||||
\(802\) | 48.3500 | 1.70730 | ||||||||
\(803\) | 7.24699 | 0.255741 | ||||||||
\(804\) | −11.9663 | −0.422019 | ||||||||
\(805\) | −30.6473 | −1.08018 | ||||||||
\(806\) | 42.1945 | 1.48624 | ||||||||
\(807\) | 4.59493 | 0.161749 | ||||||||
\(808\) | 68.4632 | 2.40853 | ||||||||
\(809\) | 23.6320 | 0.830855 | 0.415428 | − | 0.909626i | \(-0.363632\pi\) | ||||
0.415428 | + | 0.909626i | \(0.363632\pi\) | |||||||
\(810\) | 13.7989 | 0.484844 | ||||||||
\(811\) | −11.2573 | −0.395296 | −0.197648 | − | 0.980273i | \(-0.563330\pi\) | ||||
−0.197648 | + | 0.980273i | \(0.563330\pi\) | |||||||
\(812\) | 76.8911 | 2.69835 | ||||||||
\(813\) | 30.7125 | 1.07713 | ||||||||
\(814\) | 3.11237 | 0.109089 | ||||||||
\(815\) | −16.8458 | −0.590083 | ||||||||
\(816\) | 68.0248 | 2.38134 | ||||||||
\(817\) | −17.4809 | −0.611580 | ||||||||
\(818\) | 3.97913 | 0.139127 | ||||||||
\(819\) | 13.1165 | 0.458327 | ||||||||
\(820\) | 28.6796 | 1.00154 | ||||||||
\(821\) | −7.41175 | −0.258672 | −0.129336 | − | 0.991601i | \(-0.541285\pi\) | ||||
−0.129336 | + | 0.991601i | \(0.541285\pi\) | |||||||
\(822\) | −4.71631 | −0.164500 | ||||||||
\(823\) | −7.51069 | −0.261806 | −0.130903 | − | 0.991395i | \(-0.541788\pi\) | ||||
−0.130903 | + | 0.991395i | \(0.541788\pi\) | |||||||
\(824\) | 155.800 | 5.42755 | ||||||||
\(825\) | 0.498041 | 0.0173396 | ||||||||
\(826\) | 59.8567 | 2.08268 | ||||||||
\(827\) | −10.4117 | −0.362050 | −0.181025 | − | 0.983478i | \(-0.557942\pi\) | ||||
−0.181025 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(828\) | 31.3886 | 1.09083 | ||||||||
\(829\) | −54.9525 | −1.90858 | −0.954290 | − | 0.298882i | \(-0.903386\pi\) | ||||
−0.954290 | + | 0.298882i | \(0.903386\pi\) | |||||||
\(830\) | −15.5938 | −0.541267 | ||||||||
\(831\) | −0.814649 | −0.0282599 | ||||||||
\(832\) | −67.1831 | −2.32915 | ||||||||
\(833\) | −17.6526 | −0.611627 | ||||||||
\(834\) | −12.8813 | −0.446042 | ||||||||
\(835\) | −19.4000 | −0.671364 | ||||||||
\(836\) | 14.5720 | 0.503985 | ||||||||
\(837\) | 33.4291 | 1.15548 | ||||||||
\(838\) | −23.4074 | −0.808594 | ||||||||
\(839\) | −24.3022 | −0.839005 | −0.419503 | − | 0.907754i | \(-0.637795\pi\) | ||||
−0.419503 | + | 0.907754i | \(0.637795\pi\) | |||||||
\(840\) | 88.8320 | 3.06499 | ||||||||
\(841\) | −11.1762 | −0.385386 | ||||||||
\(842\) | 68.8655 | 2.37326 | ||||||||
\(843\) | 22.2145 | 0.765106 | ||||||||
\(844\) | 45.0652 | 1.55121 | ||||||||
\(845\) | −15.1550 | −0.521349 | ||||||||
\(846\) | −24.7732 | −0.851721 | ||||||||
\(847\) | −35.0338 | −1.20377 | ||||||||
\(848\) | 54.0238 | 1.85518 | ||||||||
\(849\) | 30.6353 | 1.05140 | ||||||||
\(850\) | 5.39227 | 0.184953 | ||||||||
\(851\) | −5.44589 | −0.186683 | ||||||||
\(852\) | −5.40012 | −0.185005 | ||||||||
\(853\) | 19.5618 | 0.669783 | 0.334891 | − | 0.942257i | \(-0.391300\pi\) | ||||
0.334891 | + | 0.942257i | \(0.391300\pi\) | |||||||
\(854\) | −110.747 | −3.78967 | ||||||||
\(855\) | 11.8636 | 0.405726 | ||||||||
\(856\) | 77.1248 | 2.63607 | ||||||||
\(857\) | −31.5568 | −1.07796 | −0.538980 | − | 0.842319i | \(-0.681190\pi\) | ||||
−0.538980 | + | 0.842319i | \(0.681190\pi\) | |||||||
\(858\) | 6.87049 | 0.234555 | ||||||||
\(859\) | −9.57504 | −0.326696 | −0.163348 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163348 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(860\) | 66.0063 | 2.25080 | ||||||||
\(861\) | −9.39061 | −0.320031 | ||||||||
\(862\) | −69.3405 | −2.36175 | ||||||||
\(863\) | 3.59312 | 0.122311 | 0.0611557 | − | 0.998128i | \(-0.480521\pi\) | ||||
0.0611557 | + | 0.998128i | \(0.480521\pi\) | |||||||
\(864\) | −110.568 | −3.76160 | ||||||||
\(865\) | −14.9810 | −0.509368 | ||||||||
\(866\) | 53.1921 | 1.80754 | ||||||||
\(867\) | 1.76650 | 0.0599936 | ||||||||
\(868\) | 110.645 | 3.75552 | ||||||||
\(869\) | 7.49554 | 0.254269 | ||||||||
\(870\) | 32.7901 | 1.11169 | ||||||||
\(871\) | −4.66944 | −0.158218 | ||||||||
\(872\) | −113.654 | −3.84879 | ||||||||
\(873\) | −18.2943 | −0.619167 | ||||||||
\(874\) | −34.9829 | −1.18331 | ||||||||
\(875\) | −35.7354 | −1.20808 | ||||||||
\(876\) | 58.5275 | 1.97746 | ||||||||
\(877\) | 22.4987 | 0.759727 | 0.379863 | − | 0.925043i | \(-0.375971\pi\) | ||||
0.379863 | + | 0.925043i | \(0.375971\pi\) | |||||||
\(878\) | −66.7841 | −2.25386 | ||||||||
\(879\) | 9.98124 | 0.336659 | ||||||||
\(880\) | −26.9388 | −0.908107 | ||||||||
\(881\) | −7.18161 | −0.241955 | −0.120977 | − | 0.992655i | \(-0.538603\pi\) | ||||
−0.120977 | + | 0.992655i | \(0.538603\pi\) | |||||||
\(882\) | 18.4066 | 0.619784 | ||||||||
\(883\) | −5.02831 | −0.169216 | −0.0846080 | − | 0.996414i | \(-0.526964\pi\) | ||||
−0.0846080 | + | 0.996414i | \(0.526964\pi\) | |||||||
\(884\) | 54.2170 | 1.82352 | ||||||||
\(885\) | 18.6046 | 0.625388 | ||||||||
\(886\) | 99.6881 | 3.34909 | ||||||||
\(887\) | 31.8830 | 1.07053 | 0.535263 | − | 0.844686i | \(-0.320213\pi\) | ||||
0.535263 | + | 0.844686i | \(0.320213\pi\) | |||||||
\(888\) | 15.7850 | 0.529711 | ||||||||
\(889\) | 38.7160 | 1.29849 | ||||||||
\(890\) | −3.09597 | −0.103777 | ||||||||
\(891\) | 1.75747 | 0.0588776 | ||||||||
\(892\) | 21.4030 | 0.716626 | ||||||||
\(893\) | 20.1238 | 0.673416 | ||||||||
\(894\) | −28.6199 | −0.957193 | ||||||||
\(895\) | −39.1009 | −1.30700 | ||||||||
\(896\) | −105.567 | −3.52675 | ||||||||
\(897\) | −12.0217 | −0.401392 | ||||||||
\(898\) | 18.1149 | 0.604502 | ||||||||
\(899\) | 25.6481 | 0.855411 | ||||||||
\(900\) | −4.09807 | −0.136602 | ||||||||
\(901\) | −15.0550 | −0.501555 | ||||||||
\(902\) | 5.01159 | 0.166868 | ||||||||
\(903\) | −21.6125 | −0.719220 | ||||||||
\(904\) | 125.674 | 4.17985 | ||||||||
\(905\) | 20.5932 | 0.684540 | ||||||||
\(906\) | 4.41887 | 0.146807 | ||||||||
\(907\) | 0.764286 | 0.0253777 | 0.0126889 | − | 0.999919i | \(-0.495961\pi\) | ||||
0.0126889 | + | 0.999919i | \(0.495961\pi\) | |||||||
\(908\) | −83.1225 | −2.75852 | ||||||||
\(909\) | 11.3044 | 0.374942 | ||||||||
\(910\) | 55.1980 | 1.82979 | ||||||||
\(911\) | 42.5702 | 1.41041 | 0.705207 | − | 0.709001i | \(-0.250854\pi\) | ||||
0.705207 | + | 0.709001i | \(0.250854\pi\) | |||||||
\(912\) | 57.6182 | 1.90793 | ||||||||
\(913\) | −1.98607 | −0.0657294 | ||||||||
\(914\) | −11.8289 | −0.391266 | ||||||||
\(915\) | −34.4222 | −1.13796 | ||||||||
\(916\) | 51.6588 | 1.70686 | ||||||||
\(917\) | 38.8509 | 1.28297 | ||||||||
\(918\) | 58.9336 | 1.94510 | ||||||||
\(919\) | 38.8369 | 1.28111 | 0.640556 | − | 0.767912i | \(-0.278704\pi\) | ||||
0.640556 | + | 0.767912i | \(0.278704\pi\) | |||||||
\(920\) | 82.9523 | 2.73486 | ||||||||
\(921\) | −27.2256 | −0.897113 | ||||||||
\(922\) | −40.4579 | −1.33241 | ||||||||
\(923\) | −2.10721 | −0.0693597 | ||||||||
\(924\) | 18.0162 | 0.592689 | ||||||||
\(925\) | 0.711012 | 0.0233779 | ||||||||
\(926\) | −36.9398 | −1.21392 | ||||||||
\(927\) | 25.7251 | 0.844922 | ||||||||
\(928\) | −84.8318 | −2.78474 | ||||||||
\(929\) | −5.84638 | −0.191813 | −0.0959067 | − | 0.995390i | \(-0.530575\pi\) | ||||
−0.0959067 | + | 0.995390i | \(0.530575\pi\) | |||||||
\(930\) | 47.1842 | 1.54723 | ||||||||
\(931\) | −14.9521 | −0.490034 | ||||||||
\(932\) | 125.262 | 4.10311 | ||||||||
\(933\) | −39.9655 | −1.30841 | ||||||||
\(934\) | 84.0561 | 2.75040 | ||||||||
\(935\) | 7.50713 | 0.245510 | ||||||||
\(936\) | −35.5020 | −1.16042 | ||||||||
\(937\) | −44.3789 | −1.44980 | −0.724898 | − | 0.688856i | \(-0.758113\pi\) | ||||
−0.724898 | + | 0.688856i | \(0.758113\pi\) | |||||||
\(938\) | −16.7995 | −0.548524 | ||||||||
\(939\) | 24.8431 | 0.810724 | ||||||||
\(940\) | −75.9855 | −2.47837 | ||||||||
\(941\) | −31.3992 | −1.02359 | −0.511793 | − | 0.859109i | \(-0.671019\pi\) | ||||
−0.511793 | + | 0.859109i | \(0.671019\pi\) | |||||||
\(942\) | −45.9270 | −1.49638 | ||||||||
\(943\) | −8.76905 | −0.285560 | ||||||||
\(944\) | −92.0610 | −2.99633 | ||||||||
\(945\) | 43.7313 | 1.42258 | ||||||||
\(946\) | 11.5342 | 0.375009 | ||||||||
\(947\) | −0.0640227 | −0.00208046 | −0.00104023 | − | 0.999999i | \(-0.500331\pi\) | ||||
−0.00104023 | + | 0.999999i | \(0.500331\pi\) | |||||||
\(948\) | 60.5349 | 1.96608 | ||||||||
\(949\) | 22.8384 | 0.741365 | ||||||||
\(950\) | 4.56735 | 0.148184 | ||||||||
\(951\) | 35.1817 | 1.14085 | ||||||||
\(952\) | 122.495 | 3.97010 | ||||||||
\(953\) | 27.1203 | 0.878512 | 0.439256 | − | 0.898362i | \(-0.355242\pi\) | ||||
0.439256 | + | 0.898362i | \(0.355242\pi\) | |||||||
\(954\) | 15.6981 | 0.508244 | ||||||||
\(955\) | 6.50622 | 0.210536 | ||||||||
\(956\) | −160.991 | −5.20683 | ||||||||
\(957\) | 4.17625 | 0.134999 | ||||||||
\(958\) | 7.54739 | 0.243845 | ||||||||
\(959\) | −4.82594 | −0.155838 | ||||||||
\(960\) | −75.1278 | −2.42474 | ||||||||
\(961\) | 5.90703 | 0.190549 | ||||||||
\(962\) | 9.80843 | 0.316236 | ||||||||
\(963\) | 12.7345 | 0.410364 | ||||||||
\(964\) | 52.0733 | 1.67717 | ||||||||
\(965\) | −7.50207 | −0.241500 | ||||||||
\(966\) | −43.2512 | −1.39158 | ||||||||
\(967\) | 17.8100 | 0.572731 | 0.286365 | − | 0.958120i | \(-0.407553\pi\) | ||||
0.286365 | + | 0.958120i | \(0.407553\pi\) | |||||||
\(968\) | 94.8249 | 3.04779 | ||||||||
\(969\) | −16.0567 | −0.515815 | ||||||||
\(970\) | −76.9877 | −2.47193 | ||||||||
\(971\) | 5.44421 | 0.174713 | 0.0873565 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873565 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(972\) | −74.5556 | −2.39137 | ||||||||
\(973\) | −13.1807 | −0.422554 | ||||||||
\(974\) | −10.5413 | −0.337766 | ||||||||
\(975\) | 1.56954 | 0.0502656 | ||||||||
\(976\) | 170.331 | 5.45216 | ||||||||
\(977\) | −8.84834 | −0.283084 | −0.141542 | − | 0.989932i | \(-0.545206\pi\) | ||||
−0.141542 | + | 0.989932i | \(0.545206\pi\) | |||||||
\(978\) | −23.7737 | −0.760200 | ||||||||
\(979\) | −0.394313 | −0.0126023 | ||||||||
\(980\) | 56.4576 | 1.80347 | ||||||||
\(981\) | −18.7660 | −0.599152 | ||||||||
\(982\) | −39.3084 | −1.25438 | ||||||||
\(983\) | 46.5123 | 1.48351 | 0.741756 | − | 0.670670i | \(-0.233993\pi\) | ||||
0.741756 | + | 0.670670i | \(0.233993\pi\) | |||||||
\(984\) | 25.4173 | 0.810274 | ||||||||
\(985\) | −18.1869 | −0.579482 | ||||||||
\(986\) | 45.2161 | 1.43997 | ||||||||
\(987\) | 24.8800 | 0.791941 | ||||||||
\(988\) | 45.9228 | 1.46100 | ||||||||
\(989\) | −20.1820 | −0.641751 | ||||||||
\(990\) | −7.82781 | −0.248784 | ||||||||
\(991\) | 32.6179 | 1.03614 | 0.518071 | − | 0.855337i | \(-0.326650\pi\) | ||||
0.518071 | + | 0.855337i | \(0.326650\pi\) | |||||||
\(992\) | −122.071 | −3.87576 | ||||||||
\(993\) | −30.4611 | −0.966653 | ||||||||
\(994\) | −7.58125 | −0.240463 | ||||||||
\(995\) | −17.0286 | −0.539844 | ||||||||
\(996\) | −16.0398 | −0.508239 | ||||||||
\(997\) | 44.1410 | 1.39796 | 0.698980 | − | 0.715141i | \(-0.253637\pi\) | ||||
0.698980 | + | 0.715141i | \(0.253637\pi\) | |||||||
\(998\) | 23.0412 | 0.729358 | ||||||||
\(999\) | 7.77086 | 0.245859 |
(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 | 4003.2.a.b.1.4 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.4 | ✓ | 152 | 1.1 | even | 1 | trivial |