Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58511 | −1.82795 | −0.913976 | − | 0.405769i | \(-0.867004\pi\) | ||||
−0.913976 | + | 0.405769i | \(0.867004\pi\) | |||||||
\(3\) | −2.87890 | −1.66214 | −0.831068 | − | 0.556172i | \(-0.812270\pi\) | ||||
−0.831068 | + | 0.556172i | \(0.812270\pi\) | |||||||
\(4\) | 4.68281 | 2.34141 | ||||||||
\(5\) | −1.51557 | −0.677783 | −0.338891 | − | 0.940826i | \(-0.610052\pi\) | ||||
−0.338891 | + | 0.940826i | \(0.610052\pi\) | |||||||
\(6\) | 7.44229 | 3.03830 | ||||||||
\(7\) | 0.161489 | 0.0610373 | 0.0305186 | − | 0.999534i | \(-0.490284\pi\) | ||||
0.0305186 | + | 0.999534i | \(0.490284\pi\) | |||||||
\(8\) | −6.93538 | −2.45203 | ||||||||
\(9\) | 5.28808 | 1.76269 | ||||||||
\(10\) | 3.91792 | 1.23895 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −13.4814 | −3.89173 | ||||||||
\(13\) | −6.99617 | −1.94039 | −0.970194 | − | 0.242329i | \(-0.922089\pi\) | ||||
−0.970194 | + | 0.242329i | \(0.922089\pi\) | |||||||
\(14\) | −0.417469 | −0.111573 | ||||||||
\(15\) | 4.36317 | 1.12657 | ||||||||
\(16\) | 8.56312 | 2.14078 | ||||||||
\(17\) | −4.66254 | −1.13083 | −0.565417 | − | 0.824805i | \(-0.691285\pi\) | ||||
−0.565417 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(18\) | −13.6703 | −3.22212 | ||||||||
\(19\) | 4.03748 | 0.926261 | 0.463131 | − | 0.886290i | \(-0.346726\pi\) | ||||
0.463131 | + | 0.886290i | \(0.346726\pi\) | |||||||
\(20\) | −7.09712 | −1.58696 | ||||||||
\(21\) | −0.464912 | −0.101452 | ||||||||
\(22\) | −2.58511 | −0.551148 | ||||||||
\(23\) | 4.97780 | 1.03794 | 0.518972 | − | 0.854792i | \(-0.326315\pi\) | ||||
0.518972 | + | 0.854792i | \(0.326315\pi\) | |||||||
\(24\) | 19.9663 | 4.07560 | ||||||||
\(25\) | −2.70305 | −0.540611 | ||||||||
\(26\) | 18.0859 | 3.54694 | ||||||||
\(27\) | −6.58715 | −1.26770 | ||||||||
\(28\) | 0.756225 | 0.142913 | ||||||||
\(29\) | −1.95167 | −0.362415 | −0.181208 | − | 0.983445i | \(-0.558001\pi\) | ||||
−0.181208 | + | 0.983445i | \(0.558001\pi\) | |||||||
\(30\) | −11.2793 | −2.05931 | ||||||||
\(31\) | −0.546934 | −0.0982323 | −0.0491162 | − | 0.998793i | \(-0.515640\pi\) | ||||
−0.0491162 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(32\) | −8.26588 | −1.46121 | ||||||||
\(33\) | −2.87890 | −0.501153 | ||||||||
\(34\) | 12.0532 | 2.06711 | ||||||||
\(35\) | −0.244748 | −0.0413700 | ||||||||
\(36\) | 24.7631 | 4.12718 | ||||||||
\(37\) | −3.94217 | −0.648088 | −0.324044 | − | 0.946042i | \(-0.605043\pi\) | ||||
−0.324044 | + | 0.946042i | \(0.605043\pi\) | |||||||
\(38\) | −10.4373 | −1.69316 | ||||||||
\(39\) | 20.1413 | 3.22519 | ||||||||
\(40\) | 10.5110 | 1.66194 | ||||||||
\(41\) | 4.07011 | 0.635644 | 0.317822 | − | 0.948150i | \(-0.397048\pi\) | ||||
0.317822 | + | 0.948150i | \(0.397048\pi\) | |||||||
\(42\) | 1.20185 | 0.185450 | ||||||||
\(43\) | 5.47625 | 0.835120 | 0.417560 | − | 0.908649i | \(-0.362885\pi\) | ||||
0.417560 | + | 0.908649i | \(0.362885\pi\) | |||||||
\(44\) | 4.68281 | 0.705961 | ||||||||
\(45\) | −8.01444 | −1.19472 | ||||||||
\(46\) | −12.8682 | −1.89731 | ||||||||
\(47\) | −2.72261 | −0.397134 | −0.198567 | − | 0.980087i | \(-0.563629\pi\) | ||||
−0.198567 | + | 0.980087i | \(0.563629\pi\) | |||||||
\(48\) | −24.6524 | −3.55826 | ||||||||
\(49\) | −6.97392 | −0.996274 | ||||||||
\(50\) | 6.98770 | 0.988210 | ||||||||
\(51\) | 13.4230 | 1.87960 | ||||||||
\(52\) | −32.7618 | −4.54324 | ||||||||
\(53\) | 13.7242 | 1.88516 | 0.942581 | − | 0.333978i | \(-0.108391\pi\) | ||||
0.942581 | + | 0.333978i | \(0.108391\pi\) | |||||||
\(54\) | 17.0285 | 2.31729 | ||||||||
\(55\) | −1.51557 | −0.204359 | ||||||||
\(56\) | −1.11999 | −0.149665 | ||||||||
\(57\) | −11.6235 | −1.53957 | ||||||||
\(58\) | 5.04528 | 0.662477 | ||||||||
\(59\) | −0.114947 | −0.0149648 | −0.00748240 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748240 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(60\) | 20.4319 | 2.63775 | ||||||||
\(61\) | −2.36507 | −0.302816 | −0.151408 | − | 0.988471i | \(-0.548381\pi\) | ||||
−0.151408 | + | 0.988471i | \(0.548381\pi\) | |||||||
\(62\) | 1.41389 | 0.179564 | ||||||||
\(63\) | 0.853969 | 0.107590 | ||||||||
\(64\) | 4.24200 | 0.530250 | ||||||||
\(65\) | 10.6032 | 1.31516 | ||||||||
\(66\) | 7.44229 | 0.916083 | ||||||||
\(67\) | 4.13899 | 0.505658 | 0.252829 | − | 0.967511i | \(-0.418639\pi\) | ||||
0.252829 | + | 0.967511i | \(0.418639\pi\) | |||||||
\(68\) | −21.8338 | −2.64774 | ||||||||
\(69\) | −14.3306 | −1.72520 | ||||||||
\(70\) | 0.632702 | 0.0756224 | ||||||||
\(71\) | 5.67318 | 0.673282 | 0.336641 | − | 0.941633i | \(-0.390709\pi\) | ||||
0.336641 | + | 0.941633i | \(0.390709\pi\) | |||||||
\(72\) | −36.6748 | −4.32217 | ||||||||
\(73\) | −14.8910 | −1.74286 | −0.871430 | − | 0.490520i | \(-0.836807\pi\) | ||||
−0.871430 | + | 0.490520i | \(0.836807\pi\) | |||||||
\(74\) | 10.1909 | 1.18467 | ||||||||
\(75\) | 7.78183 | 0.898568 | ||||||||
\(76\) | 18.9068 | 2.16875 | ||||||||
\(77\) | 0.161489 | 0.0184034 | ||||||||
\(78\) | −52.0675 | −5.89549 | ||||||||
\(79\) | −7.56851 | −0.851524 | −0.425762 | − | 0.904835i | \(-0.639994\pi\) | ||||
−0.425762 | + | 0.904835i | \(0.639994\pi\) | |||||||
\(80\) | −12.9780 | −1.45098 | ||||||||
\(81\) | 3.09954 | 0.344393 | ||||||||
\(82\) | −10.5217 | −1.16193 | ||||||||
\(83\) | −9.11300 | −1.00028 | −0.500141 | − | 0.865944i | \(-0.666719\pi\) | ||||
−0.500141 | + | 0.865944i | \(0.666719\pi\) | |||||||
\(84\) | −2.17710 | −0.237541 | ||||||||
\(85\) | 7.06640 | 0.766459 | ||||||||
\(86\) | −14.1567 | −1.52656 | ||||||||
\(87\) | 5.61865 | 0.602383 | ||||||||
\(88\) | −6.93538 | −0.739314 | ||||||||
\(89\) | 10.4253 | 1.10508 | 0.552542 | − | 0.833485i | \(-0.313658\pi\) | ||||
0.552542 | + | 0.833485i | \(0.313658\pi\) | |||||||
\(90\) | 20.7182 | 2.18389 | ||||||||
\(91\) | −1.12981 | −0.118436 | ||||||||
\(92\) | 23.3101 | 2.43025 | ||||||||
\(93\) | 1.57457 | 0.163275 | ||||||||
\(94\) | 7.03827 | 0.725942 | ||||||||
\(95\) | −6.11907 | −0.627804 | ||||||||
\(96\) | 23.7967 | 2.42874 | ||||||||
\(97\) | −6.91061 | −0.701667 | −0.350833 | − | 0.936438i | \(-0.614102\pi\) | ||||
−0.350833 | + | 0.936438i | \(0.614102\pi\) | |||||||
\(98\) | 18.0284 | 1.82114 | ||||||||
\(99\) | 5.28808 | 0.531472 | ||||||||
\(100\) | −12.6579 | −1.26579 | ||||||||
\(101\) | −5.03261 | −0.500763 | −0.250382 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250382 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(102\) | −34.7000 | −3.43581 | ||||||||
\(103\) | 2.72640 | 0.268641 | 0.134320 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(104\) | 48.5211 | 4.75788 | ||||||||
\(105\) | 0.704606 | 0.0687625 | ||||||||
\(106\) | −35.4786 | −3.44598 | ||||||||
\(107\) | 13.6287 | 1.31753 | 0.658766 | − | 0.752348i | \(-0.271079\pi\) | ||||
0.658766 | + | 0.752348i | \(0.271079\pi\) | |||||||
\(108\) | −30.8464 | −2.96820 | ||||||||
\(109\) | −15.2555 | −1.46122 | −0.730608 | − | 0.682797i | \(-0.760763\pi\) | ||||
−0.730608 | + | 0.682797i | \(0.760763\pi\) | |||||||
\(110\) | 3.91792 | 0.373559 | ||||||||
\(111\) | 11.3491 | 1.07721 | ||||||||
\(112\) | 1.38285 | 0.130667 | ||||||||
\(113\) | 5.26182 | 0.494990 | 0.247495 | − | 0.968889i | \(-0.420393\pi\) | ||||
0.247495 | + | 0.968889i | \(0.420393\pi\) | |||||||
\(114\) | 30.0481 | 2.81426 | ||||||||
\(115\) | −7.54419 | −0.703500 | ||||||||
\(116\) | −9.13929 | −0.848562 | ||||||||
\(117\) | −36.9963 | −3.42031 | ||||||||
\(118\) | 0.297151 | 0.0273549 | ||||||||
\(119\) | −0.752952 | −0.0690230 | ||||||||
\(120\) | −30.2603 | −2.76237 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.11397 | 0.553533 | ||||||||
\(123\) | −11.7175 | −1.05653 | ||||||||
\(124\) | −2.56119 | −0.230002 | ||||||||
\(125\) | 11.6745 | 1.04420 | ||||||||
\(126\) | −2.20761 | −0.196669 | ||||||||
\(127\) | 0.925858 | 0.0821566 | 0.0410783 | − | 0.999156i | \(-0.486921\pi\) | ||||
0.0410783 | + | 0.999156i | \(0.486921\pi\) | |||||||
\(128\) | 5.56571 | 0.491944 | ||||||||
\(129\) | −15.7656 | −1.38808 | ||||||||
\(130\) | −27.4104 | −2.40405 | ||||||||
\(131\) | 10.4749 | 0.915192 | 0.457596 | − | 0.889160i | \(-0.348711\pi\) | ||||
0.457596 | + | 0.889160i | \(0.348711\pi\) | |||||||
\(132\) | −13.4814 | −1.17340 | ||||||||
\(133\) | 0.652010 | 0.0565365 | ||||||||
\(134\) | −10.6997 | −0.924318 | ||||||||
\(135\) | 9.98328 | 0.859224 | ||||||||
\(136\) | 32.3365 | 2.77283 | ||||||||
\(137\) | −3.09197 | −0.264165 | −0.132082 | − | 0.991239i | \(-0.542166\pi\) | ||||
−0.132082 | + | 0.991239i | \(0.542166\pi\) | |||||||
\(138\) | 37.0462 | 3.15358 | ||||||||
\(139\) | 14.6916 | 1.24612 | 0.623061 | − | 0.782173i | \(-0.285889\pi\) | ||||
0.623061 | + | 0.782173i | \(0.285889\pi\) | |||||||
\(140\) | −1.14611 | −0.0968640 | ||||||||
\(141\) | 7.83814 | 0.660090 | ||||||||
\(142\) | −14.6658 | −1.23073 | ||||||||
\(143\) | −6.99617 | −0.585049 | ||||||||
\(144\) | 45.2824 | 3.77354 | ||||||||
\(145\) | 2.95788 | 0.245639 | ||||||||
\(146\) | 38.4949 | 3.18586 | ||||||||
\(147\) | 20.0772 | 1.65594 | ||||||||
\(148\) | −18.4604 | −1.51744 | ||||||||
\(149\) | 8.05954 | 0.660263 | 0.330132 | − | 0.943935i | \(-0.392907\pi\) | ||||
0.330132 | + | 0.943935i | \(0.392907\pi\) | |||||||
\(150\) | −20.1169 | −1.64254 | ||||||||
\(151\) | 7.99433 | 0.650570 | 0.325285 | − | 0.945616i | \(-0.394540\pi\) | ||||
0.325285 | + | 0.945616i | \(0.394540\pi\) | |||||||
\(152\) | −28.0014 | −2.27122 | ||||||||
\(153\) | −24.6559 | −1.99331 | ||||||||
\(154\) | −0.417469 | −0.0336406 | ||||||||
\(155\) | 0.828916 | 0.0665801 | ||||||||
\(156\) | 94.3179 | 7.55148 | ||||||||
\(157\) | −9.44993 | −0.754187 | −0.377093 | − | 0.926175i | \(-0.623076\pi\) | ||||
−0.377093 | + | 0.926175i | \(0.623076\pi\) | |||||||
\(158\) | 19.5655 | 1.55654 | ||||||||
\(159\) | −39.5106 | −3.13339 | ||||||||
\(160\) | 12.5275 | 0.990386 | ||||||||
\(161\) | 0.803862 | 0.0633532 | ||||||||
\(162\) | −8.01266 | −0.629534 | ||||||||
\(163\) | 8.41794 | 0.659344 | 0.329672 | − | 0.944096i | \(-0.393062\pi\) | ||||
0.329672 | + | 0.944096i | \(0.393062\pi\) | |||||||
\(164\) | 19.0596 | 1.48830 | ||||||||
\(165\) | 4.36317 | 0.339672 | ||||||||
\(166\) | 23.5582 | 1.82847 | ||||||||
\(167\) | −19.7872 | −1.53118 | −0.765590 | − | 0.643329i | \(-0.777553\pi\) | ||||
−0.765590 | + | 0.643329i | \(0.777553\pi\) | |||||||
\(168\) | 3.22434 | 0.248764 | ||||||||
\(169\) | 35.9464 | 2.76511 | ||||||||
\(170\) | −18.2675 | −1.40105 | ||||||||
\(171\) | 21.3505 | 1.63271 | ||||||||
\(172\) | 25.6442 | 1.95536 | ||||||||
\(173\) | −7.68459 | −0.584249 | −0.292124 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(174\) | −14.5249 | −1.10113 | ||||||||
\(175\) | −0.436515 | −0.0329974 | ||||||||
\(176\) | 8.56312 | 0.645469 | ||||||||
\(177\) | 0.330921 | 0.0248735 | ||||||||
\(178\) | −26.9507 | −2.02004 | ||||||||
\(179\) | 10.5445 | 0.788135 | 0.394067 | − | 0.919082i | \(-0.371068\pi\) | ||||
0.394067 | + | 0.919082i | \(0.371068\pi\) | |||||||
\(180\) | −37.5301 | −2.79733 | ||||||||
\(181\) | 15.0626 | 1.11959 | 0.559796 | − | 0.828630i | \(-0.310879\pi\) | ||||
0.559796 | + | 0.828630i | \(0.310879\pi\) | |||||||
\(182\) | 2.92068 | 0.216495 | ||||||||
\(183\) | 6.80880 | 0.503321 | ||||||||
\(184\) | −34.5229 | −2.54506 | ||||||||
\(185\) | 5.97462 | 0.439263 | ||||||||
\(186\) | −4.07044 | −0.298459 | ||||||||
\(187\) | −4.66254 | −0.340959 | ||||||||
\(188\) | −12.7495 | −0.929852 | ||||||||
\(189\) | −1.06376 | −0.0773769 | ||||||||
\(190\) | 15.8185 | 1.14759 | ||||||||
\(191\) | −11.1598 | −0.807496 | −0.403748 | − | 0.914870i | \(-0.632293\pi\) | ||||
−0.403748 | + | 0.914870i | \(0.632293\pi\) | |||||||
\(192\) | −12.2123 | −0.881347 | ||||||||
\(193\) | −2.87338 | −0.206830 | −0.103415 | − | 0.994638i | \(-0.532977\pi\) | ||||
−0.103415 | + | 0.994638i | \(0.532977\pi\) | |||||||
\(194\) | 17.8647 | 1.28261 | ||||||||
\(195\) | −30.5255 | −2.18598 | ||||||||
\(196\) | −32.6576 | −2.33268 | ||||||||
\(197\) | 1.34645 | 0.0959306 | 0.0479653 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479653 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(198\) | −13.6703 | −0.971505 | ||||||||
\(199\) | −9.04600 | −0.641254 | −0.320627 | − | 0.947206i | \(-0.603894\pi\) | ||||
−0.320627 | + | 0.947206i | \(0.603894\pi\) | |||||||
\(200\) | 18.7467 | 1.32559 | ||||||||
\(201\) | −11.9157 | −0.840471 | ||||||||
\(202\) | 13.0099 | 0.915371 | ||||||||
\(203\) | −0.315174 | −0.0221208 | ||||||||
\(204\) | 62.8575 | 4.40090 | ||||||||
\(205\) | −6.16853 | −0.430829 | ||||||||
\(206\) | −7.04807 | −0.491062 | ||||||||
\(207\) | 26.3230 | 1.82957 | ||||||||
\(208\) | −59.9090 | −4.15394 | ||||||||
\(209\) | 4.03748 | 0.279278 | ||||||||
\(210\) | −1.82149 | −0.125695 | ||||||||
\(211\) | 9.37452 | 0.645369 | 0.322684 | − | 0.946507i | \(-0.395415\pi\) | ||||
0.322684 | + | 0.946507i | \(0.395415\pi\) | |||||||
\(212\) | 64.2678 | 4.41393 | ||||||||
\(213\) | −16.3325 | −1.11909 | ||||||||
\(214\) | −35.2316 | −2.40838 | ||||||||
\(215\) | −8.29962 | −0.566030 | ||||||||
\(216\) | 45.6844 | 3.10843 | ||||||||
\(217\) | −0.0883242 | −0.00599583 | ||||||||
\(218\) | 39.4373 | 2.67103 | ||||||||
\(219\) | 42.8697 | 2.89687 | ||||||||
\(220\) | −7.09712 | −0.478488 | ||||||||
\(221\) | 32.6200 | 2.19426 | ||||||||
\(222\) | −29.3387 | −1.96909 | ||||||||
\(223\) | 20.9816 | 1.40503 | 0.702515 | − | 0.711668i | \(-0.252060\pi\) | ||||
0.702515 | + | 0.711668i | \(0.252060\pi\) | |||||||
\(224\) | −1.33485 | −0.0891886 | ||||||||
\(225\) | −14.2940 | −0.952931 | ||||||||
\(226\) | −13.6024 | −0.904818 | ||||||||
\(227\) | 3.20659 | 0.212829 | 0.106415 | − | 0.994322i | \(-0.466063\pi\) | ||||
0.106415 | + | 0.994322i | \(0.466063\pi\) | |||||||
\(228\) | −54.4307 | −3.60476 | ||||||||
\(229\) | 12.1614 | 0.803651 | 0.401825 | − | 0.915716i | \(-0.368376\pi\) | ||||
0.401825 | + | 0.915716i | \(0.368376\pi\) | |||||||
\(230\) | 19.5026 | 1.28596 | ||||||||
\(231\) | −0.464912 | −0.0305890 | ||||||||
\(232\) | 13.5355 | 0.888652 | ||||||||
\(233\) | 12.3003 | 0.805817 | 0.402909 | − | 0.915240i | \(-0.367999\pi\) | ||||
0.402909 | + | 0.915240i | \(0.367999\pi\) | |||||||
\(234\) | 95.6396 | 6.25216 | ||||||||
\(235\) | 4.12631 | 0.269171 | ||||||||
\(236\) | −0.538274 | −0.0350387 | ||||||||
\(237\) | 21.7890 | 1.41535 | ||||||||
\(238\) | 1.94647 | 0.126171 | ||||||||
\(239\) | 18.9956 | 1.22872 | 0.614360 | − | 0.789026i | \(-0.289414\pi\) | ||||
0.614360 | + | 0.789026i | \(0.289414\pi\) | |||||||
\(240\) | 37.3624 | 2.41173 | ||||||||
\(241\) | 22.0061 | 1.41754 | 0.708769 | − | 0.705440i | \(-0.249251\pi\) | ||||
0.708769 | + | 0.705440i | \(0.249251\pi\) | |||||||
\(242\) | −2.58511 | −0.166177 | ||||||||
\(243\) | 10.8382 | 0.695271 | ||||||||
\(244\) | −11.0752 | −0.709016 | ||||||||
\(245\) | 10.5695 | 0.675257 | ||||||||
\(246\) | 30.2909 | 1.93128 | ||||||||
\(247\) | −28.2469 | −1.79731 | ||||||||
\(248\) | 3.79320 | 0.240868 | ||||||||
\(249\) | 26.2354 | 1.66260 | ||||||||
\(250\) | −30.1799 | −1.90875 | ||||||||
\(251\) | −19.7167 | −1.24451 | −0.622253 | − | 0.782816i | \(-0.713783\pi\) | ||||
−0.622253 | + | 0.782816i | \(0.713783\pi\) | |||||||
\(252\) | 3.99898 | 0.251912 | ||||||||
\(253\) | 4.97780 | 0.312952 | ||||||||
\(254\) | −2.39345 | −0.150178 | ||||||||
\(255\) | −20.3435 | −1.27396 | ||||||||
\(256\) | −22.8720 | −1.42950 | ||||||||
\(257\) | 3.09154 | 0.192845 | 0.0964225 | − | 0.995340i | \(-0.469260\pi\) | ||||
0.0964225 | + | 0.995340i | \(0.469260\pi\) | |||||||
\(258\) | 40.7558 | 2.53735 | ||||||||
\(259\) | −0.636618 | −0.0395575 | ||||||||
\(260\) | 49.6527 | 3.07933 | ||||||||
\(261\) | −10.3206 | −0.638827 | ||||||||
\(262\) | −27.0787 | −1.67293 | ||||||||
\(263\) | 21.5974 | 1.33175 | 0.665876 | − | 0.746062i | \(-0.268058\pi\) | ||||
0.665876 | + | 0.746062i | \(0.268058\pi\) | |||||||
\(264\) | 19.9663 | 1.22884 | ||||||||
\(265\) | −20.7999 | −1.27773 | ||||||||
\(266\) | −1.68552 | −0.103346 | ||||||||
\(267\) | −30.0135 | −1.83680 | ||||||||
\(268\) | 19.3821 | 1.18395 | ||||||||
\(269\) | 13.3903 | 0.816419 | 0.408210 | − | 0.912888i | \(-0.366153\pi\) | ||||
0.408210 | + | 0.912888i | \(0.366153\pi\) | |||||||
\(270\) | −25.8079 | −1.57062 | ||||||||
\(271\) | −6.57861 | −0.399622 | −0.199811 | − | 0.979834i | \(-0.564033\pi\) | ||||
−0.199811 | + | 0.979834i | \(0.564033\pi\) | |||||||
\(272\) | −39.9259 | −2.42086 | ||||||||
\(273\) | 3.25261 | 0.196857 | ||||||||
\(274\) | 7.99308 | 0.482880 | ||||||||
\(275\) | −2.70305 | −0.163000 | ||||||||
\(276\) | −67.1075 | −4.03940 | ||||||||
\(277\) | −22.2248 | −1.33536 | −0.667678 | − | 0.744450i | \(-0.732712\pi\) | ||||
−0.667678 | + | 0.744450i | \(0.732712\pi\) | |||||||
\(278\) | −37.9794 | −2.27785 | ||||||||
\(279\) | −2.89223 | −0.173153 | ||||||||
\(280\) | 1.69742 | 0.101440 | ||||||||
\(281\) | −10.1465 | −0.605288 | −0.302644 | − | 0.953104i | \(-0.597869\pi\) | ||||
−0.302644 | + | 0.953104i | \(0.597869\pi\) | |||||||
\(282\) | −20.2625 | −1.20661 | ||||||||
\(283\) | 2.43092 | 0.144503 | 0.0722515 | − | 0.997386i | \(-0.476982\pi\) | ||||
0.0722515 | + | 0.997386i | \(0.476982\pi\) | |||||||
\(284\) | 26.5664 | 1.57643 | ||||||||
\(285\) | 17.6162 | 1.04349 | ||||||||
\(286\) | 18.0859 | 1.06944 | ||||||||
\(287\) | 0.657280 | 0.0387980 | ||||||||
\(288\) | −43.7106 | −2.57567 | ||||||||
\(289\) | 4.73932 | 0.278784 | ||||||||
\(290\) | −7.64646 | −0.449016 | ||||||||
\(291\) | 19.8950 | 1.16626 | ||||||||
\(292\) | −69.7318 | −4.08074 | ||||||||
\(293\) | 8.83366 | 0.516068 | 0.258034 | − | 0.966136i | \(-0.416925\pi\) | ||||
0.258034 | + | 0.966136i | \(0.416925\pi\) | |||||||
\(294\) | −51.9019 | −3.02698 | ||||||||
\(295\) | 0.174210 | 0.0101429 | ||||||||
\(296\) | 27.3404 | 1.58913 | ||||||||
\(297\) | −6.58715 | −0.382225 | ||||||||
\(298\) | −20.8348 | −1.20693 | ||||||||
\(299\) | −34.8255 | −2.01401 | ||||||||
\(300\) | 36.4409 | 2.10391 | ||||||||
\(301\) | 0.884356 | 0.0509735 | ||||||||
\(302\) | −20.6663 | −1.18921 | ||||||||
\(303\) | 14.4884 | 0.832336 | ||||||||
\(304\) | 34.5734 | 1.98292 | ||||||||
\(305\) | 3.58442 | 0.205243 | ||||||||
\(306\) | 63.7383 | 3.64368 | ||||||||
\(307\) | 20.7216 | 1.18265 | 0.591323 | − | 0.806434i | \(-0.298606\pi\) | ||||
0.591323 | + | 0.806434i | \(0.298606\pi\) | |||||||
\(308\) | 0.756225 | 0.0430899 | ||||||||
\(309\) | −7.84905 | −0.446517 | ||||||||
\(310\) | −2.14284 | −0.121705 | ||||||||
\(311\) | 3.17697 | 0.180149 | 0.0900747 | − | 0.995935i | \(-0.471289\pi\) | ||||
0.0900747 | + | 0.995935i | \(0.471289\pi\) | |||||||
\(312\) | −139.687 | −7.90825 | ||||||||
\(313\) | 32.6979 | 1.84819 | 0.924096 | − | 0.382160i | \(-0.124820\pi\) | ||||
0.924096 | + | 0.382160i | \(0.124820\pi\) | |||||||
\(314\) | 24.4291 | 1.37862 | ||||||||
\(315\) | −1.29425 | −0.0729226 | ||||||||
\(316\) | −35.4419 | −1.99376 | ||||||||
\(317\) | 1.74848 | 0.0982045 | 0.0491022 | − | 0.998794i | \(-0.484364\pi\) | ||||
0.0491022 | + | 0.998794i | \(0.484364\pi\) | |||||||
\(318\) | 102.139 | 5.72769 | ||||||||
\(319\) | −1.95167 | −0.109272 | ||||||||
\(320\) | −6.42904 | −0.359394 | ||||||||
\(321\) | −39.2356 | −2.18992 | ||||||||
\(322\) | −2.07808 | −0.115807 | ||||||||
\(323\) | −18.8249 | −1.04745 | ||||||||
\(324\) | 14.5146 | 0.806364 | ||||||||
\(325\) | 18.9110 | 1.04899 | ||||||||
\(326\) | −21.7613 | −1.20525 | ||||||||
\(327\) | 43.9192 | 2.42874 | ||||||||
\(328\) | −28.2278 | −1.55862 | ||||||||
\(329\) | −0.439674 | −0.0242400 | ||||||||
\(330\) | −11.2793 | −0.620905 | ||||||||
\(331\) | 13.6593 | 0.750782 | 0.375391 | − | 0.926866i | \(-0.377508\pi\) | ||||
0.375391 | + | 0.926866i | \(0.377508\pi\) | |||||||
\(332\) | −42.6745 | −2.34207 | ||||||||
\(333\) | −20.8465 | −1.14238 | ||||||||
\(334\) | 51.1522 | 2.79892 | ||||||||
\(335\) | −6.27291 | −0.342726 | ||||||||
\(336\) | −3.98110 | −0.217187 | ||||||||
\(337\) | 29.2215 | 1.59180 | 0.795898 | − | 0.605431i | \(-0.206999\pi\) | ||||
0.795898 | + | 0.605431i | \(0.206999\pi\) | |||||||
\(338\) | −92.9255 | −5.05448 | ||||||||
\(339\) | −15.1483 | −0.822741 | ||||||||
\(340\) | 33.0907 | 1.79459 | ||||||||
\(341\) | −0.546934 | −0.0296182 | ||||||||
\(342\) | −55.1935 | −2.98452 | ||||||||
\(343\) | −2.25664 | −0.121847 | ||||||||
\(344\) | −37.9799 | −2.04774 | ||||||||
\(345\) | 21.7190 | 1.16931 | ||||||||
\(346\) | 19.8655 | 1.06798 | ||||||||
\(347\) | 5.25371 | 0.282034 | 0.141017 | − | 0.990007i | \(-0.454963\pi\) | ||||
0.141017 | + | 0.990007i | \(0.454963\pi\) | |||||||
\(348\) | 26.3111 | 1.41042 | ||||||||
\(349\) | −29.1507 | −1.56040 | −0.780200 | − | 0.625531i | \(-0.784882\pi\) | ||||
−0.780200 | + | 0.625531i | \(0.784882\pi\) | |||||||
\(350\) | 1.12844 | 0.0603177 | ||||||||
\(351\) | 46.0848 | 2.45983 | ||||||||
\(352\) | −8.26588 | −0.440573 | ||||||||
\(353\) | −11.8078 | −0.628467 | −0.314234 | − | 0.949346i | \(-0.601748\pi\) | ||||
−0.314234 | + | 0.949346i | \(0.601748\pi\) | |||||||
\(354\) | −0.855467 | −0.0454676 | ||||||||
\(355\) | −8.59809 | −0.456339 | ||||||||
\(356\) | 48.8199 | 2.58745 | ||||||||
\(357\) | 2.16768 | 0.114726 | ||||||||
\(358\) | −27.2588 | −1.44067 | ||||||||
\(359\) | −37.5797 | −1.98338 | −0.991689 | − | 0.128656i | \(-0.958934\pi\) | ||||
−0.991689 | + | 0.128656i | \(0.958934\pi\) | |||||||
\(360\) | 55.5832 | 2.92949 | ||||||||
\(361\) | −2.69877 | −0.142040 | ||||||||
\(362\) | −38.9385 | −2.04656 | ||||||||
\(363\) | −2.87890 | −0.151103 | ||||||||
\(364\) | −5.29068 | −0.277307 | ||||||||
\(365\) | 22.5683 | 1.18128 | ||||||||
\(366\) | −17.6015 | −0.920047 | ||||||||
\(367\) | 21.8766 | 1.14195 | 0.570975 | − | 0.820967i | \(-0.306565\pi\) | ||||
0.570975 | + | 0.820967i | \(0.306565\pi\) | |||||||
\(368\) | 42.6255 | 2.22201 | ||||||||
\(369\) | 21.5231 | 1.12045 | ||||||||
\(370\) | −15.4451 | −0.802951 | ||||||||
\(371\) | 2.21631 | 0.115065 | ||||||||
\(372\) | 7.37342 | 0.382294 | ||||||||
\(373\) | −16.3409 | −0.846100 | −0.423050 | − | 0.906106i | \(-0.639041\pi\) | ||||
−0.423050 | + | 0.906106i | \(0.639041\pi\) | |||||||
\(374\) | 12.0532 | 0.623257 | ||||||||
\(375\) | −33.6097 | −1.73560 | ||||||||
\(376\) | 18.8824 | 0.973783 | ||||||||
\(377\) | 13.6542 | 0.703226 | ||||||||
\(378\) | 2.74993 | 0.141441 | ||||||||
\(379\) | 23.9542 | 1.23044 | 0.615222 | − | 0.788354i | \(-0.289066\pi\) | ||||
0.615222 | + | 0.788354i | \(0.289066\pi\) | |||||||
\(380\) | −28.6545 | −1.46994 | ||||||||
\(381\) | −2.66545 | −0.136555 | ||||||||
\(382\) | 28.8494 | 1.47606 | ||||||||
\(383\) | 9.53268 | 0.487097 | 0.243549 | − | 0.969889i | \(-0.421688\pi\) | ||||
0.243549 | + | 0.969889i | \(0.421688\pi\) | |||||||
\(384\) | −16.0231 | −0.817677 | ||||||||
\(385\) | −0.244748 | −0.0124735 | ||||||||
\(386\) | 7.42801 | 0.378076 | ||||||||
\(387\) | 28.9588 | 1.47206 | ||||||||
\(388\) | −32.3611 | −1.64289 | ||||||||
\(389\) | 17.4434 | 0.884417 | 0.442209 | − | 0.896912i | \(-0.354195\pi\) | ||||
0.442209 | + | 0.896912i | \(0.354195\pi\) | |||||||
\(390\) | 78.9119 | 3.99586 | ||||||||
\(391\) | −23.2092 | −1.17374 | ||||||||
\(392\) | 48.3668 | 2.44289 | ||||||||
\(393\) | −30.1561 | −1.52117 | ||||||||
\(394\) | −3.48073 | −0.175357 | ||||||||
\(395\) | 11.4706 | 0.577148 | ||||||||
\(396\) | 24.7631 | 1.24439 | ||||||||
\(397\) | −21.0785 | −1.05790 | −0.528950 | − | 0.848653i | \(-0.677414\pi\) | ||||
−0.528950 | + | 0.848653i | \(0.677414\pi\) | |||||||
\(398\) | 23.3849 | 1.17218 | ||||||||
\(399\) | −1.87707 | −0.0939712 | ||||||||
\(400\) | −23.1466 | −1.15733 | ||||||||
\(401\) | −8.79432 | −0.439167 | −0.219584 | − | 0.975594i | \(-0.570470\pi\) | ||||
−0.219584 | + | 0.975594i | \(0.570470\pi\) | |||||||
\(402\) | 30.8035 | 1.53634 | ||||||||
\(403\) | 3.82645 | 0.190609 | ||||||||
\(404\) | −23.5668 | −1.17249 | ||||||||
\(405\) | −4.69756 | −0.233424 | ||||||||
\(406\) | 0.814759 | 0.0404358 | ||||||||
\(407\) | −3.94217 | −0.195406 | ||||||||
\(408\) | −93.0937 | −4.60882 | ||||||||
\(409\) | −22.7627 | −1.12554 | −0.562772 | − | 0.826612i | \(-0.690265\pi\) | ||||
−0.562772 | + | 0.826612i | \(0.690265\pi\) | |||||||
\(410\) | 15.9463 | 0.787534 | ||||||||
\(411\) | 8.90147 | 0.439077 | ||||||||
\(412\) | 12.7672 | 0.628997 | ||||||||
\(413\) | −0.0185627 | −0.000913411 0 | ||||||||
\(414\) | −68.0479 | −3.34437 | ||||||||
\(415\) | 13.8114 | 0.677974 | ||||||||
\(416\) | 57.8295 | 2.83532 | ||||||||
\(417\) | −42.2956 | −2.07122 | ||||||||
\(418\) | −10.4373 | −0.510507 | ||||||||
\(419\) | −7.39567 | −0.361302 | −0.180651 | − | 0.983547i | \(-0.557820\pi\) | ||||
−0.180651 | + | 0.983547i | \(0.557820\pi\) | |||||||
\(420\) | 3.29954 | 0.161001 | ||||||||
\(421\) | 14.3276 | 0.698285 | 0.349143 | − | 0.937070i | \(-0.386473\pi\) | ||||
0.349143 | + | 0.937070i | \(0.386473\pi\) | |||||||
\(422\) | −24.2342 | −1.17970 | ||||||||
\(423\) | −14.3974 | −0.700025 | ||||||||
\(424\) | −95.1824 | −4.62247 | ||||||||
\(425\) | 12.6031 | 0.611341 | ||||||||
\(426\) | 42.2214 | 2.04564 | ||||||||
\(427\) | −0.381934 | −0.0184831 | ||||||||
\(428\) | 63.8205 | 3.08488 | ||||||||
\(429\) | 20.1413 | 0.972431 | ||||||||
\(430\) | 21.4555 | 1.03467 | ||||||||
\(431\) | 8.81640 | 0.424671 | 0.212336 | − | 0.977197i | \(-0.431893\pi\) | ||||
0.212336 | + | 0.977197i | \(0.431893\pi\) | |||||||
\(432\) | −56.4066 | −2.71386 | ||||||||
\(433\) | −13.3556 | −0.641829 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(434\) | 0.228328 | 0.0109601 | ||||||||
\(435\) | −8.51545 | −0.408285 | ||||||||
\(436\) | −71.4388 | −3.42130 | ||||||||
\(437\) | 20.0978 | 0.961406 | ||||||||
\(438\) | −110.823 | −5.29534 | ||||||||
\(439\) | 1.22712 | 0.0585675 | 0.0292837 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292837 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(440\) | 10.5110 | 0.501094 | ||||||||
\(441\) | −36.8786 | −1.75613 | ||||||||
\(442\) | −84.3263 | −4.01099 | ||||||||
\(443\) | −34.7240 | −1.64979 | −0.824894 | − | 0.565288i | \(-0.808765\pi\) | ||||
−0.824894 | + | 0.565288i | \(0.808765\pi\) | |||||||
\(444\) | 53.1458 | 2.52219 | ||||||||
\(445\) | −15.8003 | −0.749006 | ||||||||
\(446\) | −54.2398 | −2.56833 | ||||||||
\(447\) | −23.2026 | −1.09745 | ||||||||
\(448\) | 0.685038 | 0.0323650 | ||||||||
\(449\) | −11.6811 | −0.551266 | −0.275633 | − | 0.961263i | \(-0.588887\pi\) | ||||
−0.275633 | + | 0.961263i | \(0.588887\pi\) | |||||||
\(450\) | 36.9515 | 1.74191 | ||||||||
\(451\) | 4.07011 | 0.191654 | ||||||||
\(452\) | 24.6401 | 1.15897 | ||||||||
\(453\) | −23.0149 | −1.08133 | ||||||||
\(454\) | −8.28941 | −0.389041 | ||||||||
\(455\) | 1.71230 | 0.0802739 | ||||||||
\(456\) | 80.6134 | 3.77507 | ||||||||
\(457\) | −2.17391 | −0.101691 | −0.0508456 | − | 0.998707i | \(-0.516192\pi\) | ||||
−0.0508456 | + | 0.998707i | \(0.516192\pi\) | |||||||
\(458\) | −31.4387 | −1.46903 | ||||||||
\(459\) | 30.7129 | 1.43356 | ||||||||
\(460\) | −35.3281 | −1.64718 | ||||||||
\(461\) | 1.29809 | 0.0604579 | 0.0302290 | − | 0.999543i | \(-0.490376\pi\) | ||||
0.0302290 | + | 0.999543i | \(0.490376\pi\) | |||||||
\(462\) | 1.20185 | 0.0559152 | ||||||||
\(463\) | −2.86111 | −0.132967 | −0.0664834 | − | 0.997788i | \(-0.521178\pi\) | ||||
−0.0664834 | + | 0.997788i | \(0.521178\pi\) | |||||||
\(464\) | −16.7123 | −0.775851 | ||||||||
\(465\) | −2.38637 | −0.110665 | ||||||||
\(466\) | −31.7976 | −1.47299 | ||||||||
\(467\) | 0.427463 | 0.0197806 | 0.00989032 | − | 0.999951i | \(-0.496852\pi\) | ||||
0.00989032 | + | 0.999951i | \(0.496852\pi\) | |||||||
\(468\) | −173.247 | −8.00833 | ||||||||
\(469\) | 0.668403 | 0.0308640 | ||||||||
\(470\) | −10.6670 | −0.492031 | ||||||||
\(471\) | 27.2054 | 1.25356 | ||||||||
\(472\) | 0.797200 | 0.0366941 | ||||||||
\(473\) | 5.47625 | 0.251798 | ||||||||
\(474\) | −56.3271 | −2.58719 | ||||||||
\(475\) | −10.9135 | −0.500747 | ||||||||
\(476\) | −3.52593 | −0.161611 | ||||||||
\(477\) | 72.5746 | 3.32296 | ||||||||
\(478\) | −49.1057 | −2.24604 | ||||||||
\(479\) | 14.1486 | 0.646468 | 0.323234 | − | 0.946319i | \(-0.395230\pi\) | ||||
0.323234 | + | 0.946319i | \(0.395230\pi\) | |||||||
\(480\) | −36.0654 | −1.64615 | ||||||||
\(481\) | 27.5801 | 1.25754 | ||||||||
\(482\) | −56.8883 | −2.59119 | ||||||||
\(483\) | −2.31424 | −0.105302 | ||||||||
\(484\) | 4.68281 | 0.212855 | ||||||||
\(485\) | 10.4735 | 0.475577 | ||||||||
\(486\) | −28.0180 | −1.27092 | ||||||||
\(487\) | −17.3031 | −0.784076 | −0.392038 | − | 0.919949i | \(-0.628230\pi\) | ||||
−0.392038 | + | 0.919949i | \(0.628230\pi\) | |||||||
\(488\) | 16.4027 | 0.742513 | ||||||||
\(489\) | −24.2344 | −1.09592 | ||||||||
\(490\) | −27.3232 | −1.23434 | ||||||||
\(491\) | 8.70093 | 0.392667 | 0.196334 | − | 0.980537i | \(-0.437096\pi\) | ||||
0.196334 | + | 0.980537i | \(0.437096\pi\) | |||||||
\(492\) | −54.8706 | −2.47376 | ||||||||
\(493\) | 9.09973 | 0.409831 | ||||||||
\(494\) | 73.0214 | 3.28539 | ||||||||
\(495\) | −8.01444 | −0.360222 | ||||||||
\(496\) | −4.68346 | −0.210294 | ||||||||
\(497\) | 0.916159 | 0.0410953 | ||||||||
\(498\) | −67.8216 | −3.03916 | ||||||||
\(499\) | −16.8790 | −0.755606 | −0.377803 | − | 0.925886i | \(-0.623320\pi\) | ||||
−0.377803 | + | 0.925886i | \(0.623320\pi\) | |||||||
\(500\) | 54.6695 | 2.44490 | ||||||||
\(501\) | 56.9654 | 2.54503 | ||||||||
\(502\) | 50.9699 | 2.27490 | ||||||||
\(503\) | −31.8644 | −1.42076 | −0.710382 | − | 0.703816i | \(-0.751478\pi\) | ||||
−0.710382 | + | 0.703816i | \(0.751478\pi\) | |||||||
\(504\) | −5.92260 | −0.263814 | ||||||||
\(505\) | 7.62726 | 0.339409 | ||||||||
\(506\) | −12.8682 | −0.572060 | ||||||||
\(507\) | −103.486 | −4.59598 | ||||||||
\(508\) | 4.33562 | 0.192362 | ||||||||
\(509\) | 19.5984 | 0.868684 | 0.434342 | − | 0.900748i | \(-0.356981\pi\) | ||||
0.434342 | + | 0.900748i | \(0.356981\pi\) | |||||||
\(510\) | 52.5902 | 2.32873 | ||||||||
\(511\) | −2.40474 | −0.106379 | ||||||||
\(512\) | 47.9953 | 2.12111 | ||||||||
\(513\) | −26.5955 | −1.17422 | ||||||||
\(514\) | −7.99198 | −0.352511 | ||||||||
\(515\) | −4.13205 | −0.182080 | ||||||||
\(516\) | −73.8273 | −3.25006 | ||||||||
\(517\) | −2.72261 | −0.119740 | ||||||||
\(518\) | 1.64573 | 0.0723093 | ||||||||
\(519\) | 22.1232 | 0.971100 | ||||||||
\(520\) | −73.5370 | −3.22481 | ||||||||
\(521\) | −43.8426 | −1.92078 | −0.960389 | − | 0.278662i | \(-0.910109\pi\) | ||||
−0.960389 | + | 0.278662i | \(0.910109\pi\) | |||||||
\(522\) | 26.6798 | 1.16774 | ||||||||
\(523\) | −9.32950 | −0.407950 | −0.203975 | − | 0.978976i | \(-0.565386\pi\) | ||||
−0.203975 | + | 0.978976i | \(0.565386\pi\) | |||||||
\(524\) | 49.0518 | 2.14284 | ||||||||
\(525\) | 1.25668 | 0.0548462 | ||||||||
\(526\) | −55.8317 | −2.43438 | ||||||||
\(527\) | 2.55011 | 0.111084 | ||||||||
\(528\) | −24.6524 | −1.07286 | ||||||||
\(529\) | 1.77849 | 0.0773258 | ||||||||
\(530\) | 53.7702 | 2.33563 | ||||||||
\(531\) | −0.607848 | −0.0263783 | ||||||||
\(532\) | 3.05324 | 0.132375 | ||||||||
\(533\) | −28.4752 | −1.23340 | ||||||||
\(534\) | 77.5884 | 3.35758 | ||||||||
\(535\) | −20.6552 | −0.893000 | ||||||||
\(536\) | −28.7054 | −1.23989 | ||||||||
\(537\) | −30.3567 | −1.30999 | ||||||||
\(538\) | −34.6154 | −1.49237 | ||||||||
\(539\) | −6.97392 | −0.300388 | ||||||||
\(540\) | 46.7498 | 2.01179 | ||||||||
\(541\) | 5.07859 | 0.218345 | 0.109173 | − | 0.994023i | \(-0.465180\pi\) | ||||
0.109173 | + | 0.994023i | \(0.465180\pi\) | |||||||
\(542\) | 17.0065 | 0.730490 | ||||||||
\(543\) | −43.3637 | −1.86091 | ||||||||
\(544\) | 38.5400 | 1.65239 | ||||||||
\(545\) | 23.1208 | 0.990386 | ||||||||
\(546\) | −8.40836 | −0.359845 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −14.4791 | −0.618517 | ||||||||
\(549\) | −12.5067 | −0.533772 | ||||||||
\(550\) | 6.98770 | 0.297957 | ||||||||
\(551\) | −7.87981 | −0.335691 | ||||||||
\(552\) | 99.3881 | 4.23024 | ||||||||
\(553\) | −1.22223 | −0.0519747 | ||||||||
\(554\) | 57.4535 | 2.44097 | ||||||||
\(555\) | −17.2003 | −0.730114 | ||||||||
\(556\) | 68.7979 | 2.91768 | ||||||||
\(557\) | 38.7081 | 1.64012 | 0.820058 | − | 0.572280i | \(-0.193941\pi\) | ||||
0.820058 | + | 0.572280i | \(0.193941\pi\) | |||||||
\(558\) | 7.47675 | 0.316516 | ||||||||
\(559\) | −38.3128 | −1.62046 | ||||||||
\(560\) | −2.09581 | −0.0885641 | ||||||||
\(561\) | 13.4230 | 0.566720 | ||||||||
\(562\) | 26.2298 | 1.10644 | ||||||||
\(563\) | 13.0177 | 0.548632 | 0.274316 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274316 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(564\) | 36.7045 | 1.54554 | ||||||||
\(565\) | −7.97464 | −0.335496 | ||||||||
\(566\) | −6.28420 | −0.264144 | ||||||||
\(567\) | 0.500543 | 0.0210208 | ||||||||
\(568\) | −39.3456 | −1.65091 | ||||||||
\(569\) | −1.88665 | −0.0790925 | −0.0395462 | − | 0.999218i | \(-0.512591\pi\) | ||||
−0.0395462 | + | 0.999218i | \(0.512591\pi\) | |||||||
\(570\) | −45.5399 | −1.90746 | ||||||||
\(571\) | −0.986817 | −0.0412970 | −0.0206485 | − | 0.999787i | \(-0.506573\pi\) | ||||
−0.0206485 | + | 0.999787i | \(0.506573\pi\) | |||||||
\(572\) | −32.7618 | −1.36984 | ||||||||
\(573\) | 32.1280 | 1.34217 | ||||||||
\(574\) | −1.69914 | −0.0709209 | ||||||||
\(575\) | −13.4553 | −0.561123 | ||||||||
\(576\) | 22.4320 | 0.934667 | ||||||||
\(577\) | 15.2056 | 0.633019 | 0.316510 | − | 0.948589i | \(-0.397489\pi\) | ||||
0.316510 | + | 0.948589i | \(0.397489\pi\) | |||||||
\(578\) | −12.2517 | −0.509603 | ||||||||
\(579\) | 8.27217 | 0.343780 | ||||||||
\(580\) | 13.8512 | 0.575140 | ||||||||
\(581\) | −1.47165 | −0.0610545 | ||||||||
\(582\) | −51.4308 | −2.13188 | ||||||||
\(583\) | 13.7242 | 0.568398 | ||||||||
\(584\) | 103.275 | 4.27354 | ||||||||
\(585\) | 56.0704 | 2.31823 | ||||||||
\(586\) | −22.8360 | −0.943347 | ||||||||
\(587\) | −14.1367 | −0.583484 | −0.291742 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291742 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(588\) | 94.0180 | 3.87724 | ||||||||
\(589\) | −2.20824 | −0.0909888 | ||||||||
\(590\) | −0.450352 | −0.0185407 | ||||||||
\(591\) | −3.87630 | −0.159450 | ||||||||
\(592\) | −33.7572 | −1.38741 | ||||||||
\(593\) | 33.4461 | 1.37347 | 0.686733 | − | 0.726910i | \(-0.259044\pi\) | ||||
0.686733 | + | 0.726910i | \(0.259044\pi\) | |||||||
\(594\) | 17.0285 | 0.698690 | ||||||||
\(595\) | 1.14115 | 0.0467826 | ||||||||
\(596\) | 37.7413 | 1.54595 | ||||||||
\(597\) | 26.0425 | 1.06585 | ||||||||
\(598\) | 90.0280 | 3.68152 | ||||||||
\(599\) | 31.4078 | 1.28329 | 0.641645 | − | 0.767002i | \(-0.278252\pi\) | ||||
0.641645 | + | 0.767002i | \(0.278252\pi\) | |||||||
\(600\) | −53.9699 | −2.20331 | ||||||||
\(601\) | −34.3757 | −1.40222 | −0.701108 | − | 0.713055i | \(-0.747311\pi\) | ||||
−0.701108 | + | 0.713055i | \(0.747311\pi\) | |||||||
\(602\) | −2.28616 | −0.0931770 | ||||||||
\(603\) | 21.8873 | 0.891319 | ||||||||
\(604\) | 37.4360 | 1.52325 | ||||||||
\(605\) | −1.51557 | −0.0616166 | ||||||||
\(606\) | −37.4541 | −1.52147 | ||||||||
\(607\) | −17.9097 | −0.726931 | −0.363466 | − | 0.931608i | \(-0.618407\pi\) | ||||
−0.363466 | + | 0.931608i | \(0.618407\pi\) | |||||||
\(608\) | −33.3733 | −1.35347 | ||||||||
\(609\) | 0.907354 | 0.0367678 | ||||||||
\(610\) | −9.26614 | −0.375175 | ||||||||
\(611\) | 19.0479 | 0.770594 | ||||||||
\(612\) | −115.459 | −4.66715 | ||||||||
\(613\) | 16.8330 | 0.679879 | 0.339939 | − | 0.940447i | \(-0.389593\pi\) | ||||
0.339939 | + | 0.940447i | \(0.389593\pi\) | |||||||
\(614\) | −53.5678 | −2.16182 | ||||||||
\(615\) | 17.7586 | 0.716096 | ||||||||
\(616\) | −1.11999 | −0.0451257 | ||||||||
\(617\) | 41.4502 | 1.66872 | 0.834360 | − | 0.551219i | \(-0.185837\pi\) | ||||
0.834360 | + | 0.551219i | \(0.185837\pi\) | |||||||
\(618\) | 20.2907 | 0.816211 | ||||||||
\(619\) | −26.6160 | −1.06979 | −0.534894 | − | 0.844919i | \(-0.679649\pi\) | ||||
−0.534894 | + | 0.844919i | \(0.679649\pi\) | |||||||
\(620\) | 3.88166 | 0.155891 | ||||||||
\(621\) | −32.7895 | −1.31580 | ||||||||
\(622\) | −8.21283 | −0.329305 | ||||||||
\(623\) | 1.68358 | 0.0674513 | ||||||||
\(624\) | 172.472 | 6.90442 | ||||||||
\(625\) | −4.17823 | −0.167129 | ||||||||
\(626\) | −84.5277 | −3.37841 | ||||||||
\(627\) | −11.6235 | −0.464198 | ||||||||
\(628\) | −44.2523 | −1.76586 | ||||||||
\(629\) | 18.3805 | 0.732879 | ||||||||
\(630\) | 3.34578 | 0.133299 | ||||||||
\(631\) | −44.0330 | −1.75293 | −0.876463 | − | 0.481468i | \(-0.840104\pi\) | ||||
−0.876463 | + | 0.481468i | \(0.840104\pi\) | |||||||
\(632\) | 52.4905 | 2.08796 | ||||||||
\(633\) | −26.9883 | −1.07269 | ||||||||
\(634\) | −4.52002 | −0.179513 | ||||||||
\(635\) | −1.40320 | −0.0556843 | ||||||||
\(636\) | −185.021 | −7.33655 | ||||||||
\(637\) | 48.7907 | 1.93316 | ||||||||
\(638\) | 5.04528 | 0.199744 | ||||||||
\(639\) | 30.0002 | 1.18679 | ||||||||
\(640\) | −8.43521 | −0.333431 | ||||||||
\(641\) | −20.5714 | −0.812521 | −0.406260 | − | 0.913757i | \(-0.633167\pi\) | ||||
−0.406260 | + | 0.913757i | \(0.633167\pi\) | |||||||
\(642\) | 101.428 | 4.00306 | ||||||||
\(643\) | 43.0152 | 1.69635 | 0.848177 | − | 0.529713i | \(-0.177700\pi\) | ||||
0.848177 | + | 0.529713i | \(0.177700\pi\) | |||||||
\(644\) | 3.76434 | 0.148336 | ||||||||
\(645\) | 23.8938 | 0.940818 | ||||||||
\(646\) | 48.6646 | 1.91468 | ||||||||
\(647\) | −7.20143 | −0.283117 | −0.141559 | − | 0.989930i | \(-0.545211\pi\) | ||||
−0.141559 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(648\) | −21.4965 | −0.844461 | ||||||||
\(649\) | −0.114947 | −0.00451206 | ||||||||
\(650\) | −48.8872 | −1.91751 | ||||||||
\(651\) | 0.254277 | 0.00996589 | ||||||||
\(652\) | 39.4196 | 1.54379 | ||||||||
\(653\) | 0.250362 | 0.00979742 | 0.00489871 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489871 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(654\) | −113.536 | −4.43961 | ||||||||
\(655\) | −15.8754 | −0.620301 | ||||||||
\(656\) | 34.8528 | 1.36077 | ||||||||
\(657\) | −78.7448 | −3.07213 | ||||||||
\(658\) | 1.13661 | 0.0443095 | ||||||||
\(659\) | −5.67795 | −0.221182 | −0.110591 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110591 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(660\) | 20.4319 | 0.795311 | ||||||||
\(661\) | −24.6075 | −0.957122 | −0.478561 | − | 0.878054i | \(-0.658841\pi\) | ||||
−0.478561 | + | 0.878054i | \(0.658841\pi\) | |||||||
\(662\) | −35.3108 | −1.37239 | ||||||||
\(663\) | −93.9097 | −3.64715 | ||||||||
\(664\) | 63.2021 | 2.45272 | ||||||||
\(665\) | −0.988166 | −0.0383194 | ||||||||
\(666\) | 53.8905 | 2.08822 | ||||||||
\(667\) | −9.71500 | −0.376166 | ||||||||
\(668\) | −92.6598 | −3.58512 | ||||||||
\(669\) | −60.4039 | −2.33535 | ||||||||
\(670\) | 16.2162 | 0.626486 | ||||||||
\(671\) | −2.36507 | −0.0913025 | ||||||||
\(672\) | 3.84291 | 0.148243 | ||||||||
\(673\) | −27.7457 | −1.06952 | −0.534758 | − | 0.845005i | \(-0.679597\pi\) | ||||
−0.534758 | + | 0.845005i | \(0.679597\pi\) | |||||||
\(674\) | −75.5409 | −2.90973 | ||||||||
\(675\) | 17.8054 | 0.685331 | ||||||||
\(676\) | 168.330 | 6.47424 | ||||||||
\(677\) | 47.0005 | 1.80638 | 0.903188 | − | 0.429245i | \(-0.141220\pi\) | ||||
0.903188 | + | 0.429245i | \(0.141220\pi\) | |||||||
\(678\) | 39.1600 | 1.50393 | ||||||||
\(679\) | −1.11599 | −0.0428278 | ||||||||
\(680\) | −49.0082 | −1.87938 | ||||||||
\(681\) | −9.23147 | −0.353751 | ||||||||
\(682\) | 1.41389 | 0.0541406 | ||||||||
\(683\) | 16.5936 | 0.634937 | 0.317469 | − | 0.948269i | \(-0.397167\pi\) | ||||
0.317469 | + | 0.948269i | \(0.397167\pi\) | |||||||
\(684\) | 99.9804 | 3.82285 | ||||||||
\(685\) | 4.68608 | 0.179046 | ||||||||
\(686\) | 5.83368 | 0.222731 | ||||||||
\(687\) | −35.0116 | −1.33578 | ||||||||
\(688\) | 46.8938 | 1.78781 | ||||||||
\(689\) | −96.0167 | −3.65795 | ||||||||
\(690\) | −56.1461 | −2.13744 | ||||||||
\(691\) | 38.5825 | 1.46775 | 0.733874 | − | 0.679285i | \(-0.237710\pi\) | ||||
0.733874 | + | 0.679285i | \(0.237710\pi\) | |||||||
\(692\) | −35.9855 | −1.36796 | ||||||||
\(693\) | 0.853969 | 0.0324396 | ||||||||
\(694\) | −13.5814 | −0.515544 | ||||||||
\(695\) | −22.2661 | −0.844600 | ||||||||
\(696\) | −38.9675 | −1.47706 | ||||||||
\(697\) | −18.9771 | −0.718808 | ||||||||
\(698\) | 75.3578 | 2.85233 | ||||||||
\(699\) | −35.4113 | −1.33938 | ||||||||
\(700\) | −2.04412 | −0.0772604 | ||||||||
\(701\) | −2.14089 | −0.0808603 | −0.0404302 | − | 0.999182i | \(-0.512873\pi\) | ||||
−0.0404302 | + | 0.999182i | \(0.512873\pi\) | |||||||
\(702\) | −119.135 | −4.49645 | ||||||||
\(703\) | −15.9164 | −0.600299 | ||||||||
\(704\) | 4.24200 | 0.159876 | ||||||||
\(705\) | −11.8792 | −0.447398 | ||||||||
\(706\) | 30.5246 | 1.14881 | ||||||||
\(707\) | −0.812714 | −0.0305652 | ||||||||
\(708\) | 1.54964 | 0.0582390 | ||||||||
\(709\) | 25.9461 | 0.974428 | 0.487214 | − | 0.873283i | \(-0.338013\pi\) | ||||
0.487214 | + | 0.873283i | \(0.338013\pi\) | |||||||
\(710\) | 22.2270 | 0.834166 | ||||||||
\(711\) | −40.0229 | −1.50098 | ||||||||
\(712\) | −72.3037 | −2.70969 | ||||||||
\(713\) | −2.72253 | −0.101960 | ||||||||
\(714\) | −5.60369 | −0.209713 | ||||||||
\(715\) | 10.6032 | 0.396536 | ||||||||
\(716\) | 49.3781 | 1.84534 | ||||||||
\(717\) | −54.6864 | −2.04230 | ||||||||
\(718\) | 97.1477 | 3.62552 | ||||||||
\(719\) | 1.93803 | 0.0722765 | 0.0361382 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361382 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(720\) | −68.6286 | −2.55764 | ||||||||
\(721\) | 0.440286 | 0.0163971 | ||||||||
\(722\) | 6.97663 | 0.259643 | ||||||||
\(723\) | −63.3535 | −2.35614 | ||||||||
\(724\) | 70.5352 | 2.62142 | ||||||||
\(725\) | 5.27546 | 0.195926 | ||||||||
\(726\) | 7.44229 | 0.276209 | ||||||||
\(727\) | −36.5797 | −1.35667 | −0.678333 | − | 0.734754i | \(-0.737297\pi\) | ||||
−0.678333 | + | 0.734754i | \(0.737297\pi\) | |||||||
\(728\) | 7.83565 | 0.290408 | ||||||||
\(729\) | −40.5007 | −1.50003 | ||||||||
\(730\) | −58.3417 | −2.15932 | ||||||||
\(731\) | −25.5332 | −0.944381 | ||||||||
\(732\) | 31.8844 | 1.17848 | ||||||||
\(733\) | −14.3156 | −0.528761 | −0.264380 | − | 0.964419i | \(-0.585167\pi\) | ||||
−0.264380 | + | 0.964419i | \(0.585167\pi\) | |||||||
\(734\) | −56.5536 | −2.08743 | ||||||||
\(735\) | −30.4284 | −1.12237 | ||||||||
\(736\) | −41.1459 | −1.51666 | ||||||||
\(737\) | 4.13899 | 0.152461 | ||||||||
\(738\) | −55.6396 | −2.04812 | ||||||||
\(739\) | 32.2885 | 1.18775 | 0.593876 | − | 0.804557i | \(-0.297597\pi\) | ||||
0.593876 | + | 0.804557i | \(0.297597\pi\) | |||||||
\(740\) | 27.9780 | 1.02849 | ||||||||
\(741\) | 81.3200 | 2.98737 | ||||||||
\(742\) | −5.72942 | −0.210334 | ||||||||
\(743\) | −43.3774 | −1.59136 | −0.795682 | − | 0.605715i | \(-0.792887\pi\) | ||||
−0.795682 | + | 0.605715i | \(0.792887\pi\) | |||||||
\(744\) | −10.9202 | −0.400356 | ||||||||
\(745\) | −12.2148 | −0.447515 | ||||||||
\(746\) | 42.2431 | 1.54663 | ||||||||
\(747\) | −48.1903 | −1.76319 | ||||||||
\(748\) | −21.8338 | −0.798324 | ||||||||
\(749\) | 2.20088 | 0.0804186 | ||||||||
\(750\) | 86.8850 | 3.17259 | ||||||||
\(751\) | 5.03165 | 0.183607 | 0.0918037 | − | 0.995777i | \(-0.470737\pi\) | ||||
0.0918037 | + | 0.995777i | \(0.470737\pi\) | |||||||
\(752\) | −23.3141 | −0.850176 | ||||||||
\(753\) | 56.7624 | 2.06854 | ||||||||
\(754\) | −35.2976 | −1.28546 | ||||||||
\(755\) | −12.1160 | −0.440945 | ||||||||
\(756\) | −4.98137 | −0.181171 | ||||||||
\(757\) | −43.1143 | −1.56702 | −0.783509 | − | 0.621381i | \(-0.786572\pi\) | ||||
−0.783509 | + | 0.621381i | \(0.786572\pi\) | |||||||
\(758\) | −61.9243 | −2.24919 | ||||||||
\(759\) | −14.3306 | −0.520168 | ||||||||
\(760\) | 42.4381 | 1.53939 | ||||||||
\(761\) | −15.4426 | −0.559793 | −0.279896 | − | 0.960030i | \(-0.590300\pi\) | ||||
−0.279896 | + | 0.960030i | \(0.590300\pi\) | |||||||
\(762\) | 6.89050 | 0.249617 | ||||||||
\(763\) | −2.46361 | −0.0891886 | ||||||||
\(764\) | −52.2594 | −1.89068 | ||||||||
\(765\) | 37.3677 | 1.35103 | ||||||||
\(766\) | −24.6431 | −0.890390 | ||||||||
\(767\) | 0.804187 | 0.0290375 | ||||||||
\(768\) | 65.8462 | 2.37602 | ||||||||
\(769\) | −52.1705 | −1.88132 | −0.940658 | − | 0.339356i | \(-0.889791\pi\) | ||||
−0.940658 | + | 0.339356i | \(0.889791\pi\) | |||||||
\(770\) | 0.632702 | 0.0228010 | ||||||||
\(771\) | −8.90024 | −0.320534 | ||||||||
\(772\) | −13.4555 | −0.484274 | ||||||||
\(773\) | −37.7145 | −1.35650 | −0.678249 | − | 0.734833i | \(-0.737261\pi\) | ||||
−0.678249 | + | 0.734833i | \(0.737261\pi\) | |||||||
\(774\) | −74.8619 | −2.69085 | ||||||||
\(775\) | 1.47839 | 0.0531054 | ||||||||
\(776\) | 47.9277 | 1.72051 | ||||||||
\(777\) | 1.83276 | 0.0657500 | ||||||||
\(778\) | −45.0933 | −1.61667 | ||||||||
\(779\) | 16.4330 | 0.588773 | ||||||||
\(780\) | −142.945 | −5.11826 | ||||||||
\(781\) | 5.67318 | 0.203002 | ||||||||
\(782\) | 59.9985 | 2.14554 | ||||||||
\(783\) | 12.8559 | 0.459433 | ||||||||
\(784\) | −59.7185 | −2.13280 | ||||||||
\(785\) | 14.3220 | 0.511175 | ||||||||
\(786\) | 77.9569 | 2.78063 | ||||||||
\(787\) | −51.9526 | −1.85191 | −0.925955 | − | 0.377633i | \(-0.876738\pi\) | ||||
−0.925955 | + | 0.377633i | \(0.876738\pi\) | |||||||
\(788\) | 6.30518 | 0.224613 | ||||||||
\(789\) | −62.1768 | −2.21355 | ||||||||
\(790\) | −29.6528 | −1.05500 | ||||||||
\(791\) | 0.849729 | 0.0302129 | ||||||||
\(792\) | −36.6748 | −1.30318 | ||||||||
\(793\) | 16.5464 | 0.587581 | ||||||||
\(794\) | 54.4904 | 1.93379 | ||||||||
\(795\) | 59.8810 | 2.12376 | ||||||||
\(796\) | −42.3607 | −1.50144 | ||||||||
\(797\) | −21.6111 | −0.765506 | −0.382753 | − | 0.923851i | \(-0.625024\pi\) | ||||
−0.382753 | + | 0.923851i | \(0.625024\pi\) | |||||||
\(798\) | 4.85245 | 0.171775 | ||||||||
\(799\) | 12.6943 | 0.449092 | ||||||||
\(800\) | 22.3431 | 0.789948 | ||||||||
\(801\) | 55.1300 | 1.94792 | ||||||||
\(802\) | 22.7343 | 0.802777 | ||||||||
\(803\) | −14.8910 | −0.525492 | ||||||||
\(804\) | −55.7992 | −1.96789 | ||||||||
\(805\) | −1.21831 | −0.0429397 | ||||||||
\(806\) | −9.89180 | −0.348424 | ||||||||
\(807\) | −38.5493 | −1.35700 | ||||||||
\(808\) | 34.9031 | 1.22789 | ||||||||
\(809\) | −40.3141 | −1.41737 | −0.708684 | − | 0.705526i | \(-0.750711\pi\) | ||||
−0.708684 | + | 0.705526i | \(0.750711\pi\) | |||||||
\(810\) | 12.1437 | 0.426687 | ||||||||
\(811\) | −49.2849 | −1.73063 | −0.865313 | − | 0.501232i | \(-0.832880\pi\) | ||||
−0.865313 | + | 0.501232i | \(0.832880\pi\) | |||||||
\(812\) | −1.47590 | −0.0517939 | ||||||||
\(813\) | 18.9392 | 0.664226 | ||||||||
\(814\) | 10.1909 | 0.357192 | ||||||||
\(815\) | −12.7580 | −0.446892 | ||||||||
\(816\) | 114.943 | 4.02380 | ||||||||
\(817\) | 22.1102 | 0.773539 | ||||||||
\(818\) | 58.8442 | 2.05744 | ||||||||
\(819\) | −5.97451 | −0.208766 | ||||||||
\(820\) | −28.8861 | −1.00875 | ||||||||
\(821\) | −6.67849 | −0.233081 | −0.116540 | − | 0.993186i | \(-0.537180\pi\) | ||||
−0.116540 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(822\) | −23.0113 | −0.802612 | ||||||||
\(823\) | −54.4162 | −1.89683 | −0.948415 | − | 0.317033i | \(-0.897313\pi\) | ||||
−0.948415 | + | 0.317033i | \(0.897313\pi\) | |||||||
\(824\) | −18.9086 | −0.658714 | ||||||||
\(825\) | 7.78183 | 0.270928 | ||||||||
\(826\) | 0.0479867 | 0.00166967 | ||||||||
\(827\) | 3.10943 | 0.108125 | 0.0540627 | − | 0.998538i | \(-0.482783\pi\) | ||||
0.0540627 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(828\) | 123.266 | 4.28378 | ||||||||
\(829\) | 19.2971 | 0.670216 | 0.335108 | − | 0.942180i | \(-0.391227\pi\) | ||||
0.335108 | + | 0.942180i | \(0.391227\pi\) | |||||||
\(830\) | −35.7040 | −1.23930 | ||||||||
\(831\) | 63.9829 | 2.21954 | ||||||||
\(832\) | −29.6777 | −1.02889 | ||||||||
\(833\) | 32.5162 | 1.12662 | ||||||||
\(834\) | 109.339 | 3.78610 | ||||||||
\(835\) | 29.9889 | 1.03781 | ||||||||
\(836\) | 18.9068 | 0.653904 | ||||||||
\(837\) | 3.60274 | 0.124529 | ||||||||
\(838\) | 19.1186 | 0.660443 | ||||||||
\(839\) | −14.9063 | −0.514622 | −0.257311 | − | 0.966329i | \(-0.582837\pi\) | ||||
−0.257311 | + | 0.966329i | \(0.582837\pi\) | |||||||
\(840\) | −4.88671 | −0.168608 | ||||||||
\(841\) | −25.1910 | −0.868655 | ||||||||
\(842\) | −37.0385 | −1.27643 | ||||||||
\(843\) | 29.2107 | 1.00607 | ||||||||
\(844\) | 43.8991 | 1.51107 | ||||||||
\(845\) | −54.4792 | −1.87414 | ||||||||
\(846\) | 37.2189 | 1.27961 | ||||||||
\(847\) | 0.161489 | 0.00554884 | ||||||||
\(848\) | 117.522 | 4.03572 | ||||||||
\(849\) | −6.99837 | −0.240183 | ||||||||
\(850\) | −32.5805 | −1.11750 | ||||||||
\(851\) | −19.6233 | −0.672678 | ||||||||
\(852\) | −76.4822 | −2.62024 | ||||||||
\(853\) | −46.4502 | −1.59043 | −0.795213 | − | 0.606330i | \(-0.792641\pi\) | ||||
−0.795213 | + | 0.606330i | \(0.792641\pi\) | |||||||
\(854\) | 0.987342 | 0.0337862 | ||||||||
\(855\) | −32.3581 | −1.10662 | ||||||||
\(856\) | −94.5199 | −3.23062 | ||||||||
\(857\) | 49.7322 | 1.69882 | 0.849409 | − | 0.527734i | \(-0.176958\pi\) | ||||
0.849409 | + | 0.527734i | \(0.176958\pi\) | |||||||
\(858\) | −52.0675 | −1.77756 | ||||||||
\(859\) | 17.6664 | 0.602770 | 0.301385 | − | 0.953502i | \(-0.402551\pi\) | ||||
0.301385 | + | 0.953502i | \(0.402551\pi\) | |||||||
\(860\) | −38.8656 | −1.32531 | ||||||||
\(861\) | −1.89225 | −0.0644875 | ||||||||
\(862\) | −22.7914 | −0.776278 | ||||||||
\(863\) | 26.3017 | 0.895320 | 0.447660 | − | 0.894204i | \(-0.352257\pi\) | ||||
0.447660 | + | 0.894204i | \(0.352257\pi\) | |||||||
\(864\) | 54.4486 | 1.85238 | ||||||||
\(865\) | 11.6465 | 0.395994 | ||||||||
\(866\) | 34.5258 | 1.17323 | ||||||||
\(867\) | −13.6440 | −0.463376 | ||||||||
\(868\) | −0.413606 | −0.0140387 | ||||||||
\(869\) | −7.56851 | −0.256744 | ||||||||
\(870\) | 22.0134 | 0.746325 | ||||||||
\(871\) | −28.9570 | −0.981172 | ||||||||
\(872\) | 105.803 | 3.58294 | ||||||||
\(873\) | −36.5439 | −1.23682 | ||||||||
\(874\) | −51.9550 | −1.75740 | ||||||||
\(875\) | 1.88531 | 0.0637351 | ||||||||
\(876\) | 200.751 | 6.78275 | ||||||||
\(877\) | 41.9397 | 1.41620 | 0.708102 | − | 0.706111i | \(-0.249552\pi\) | ||||
0.708102 | + | 0.706111i | \(0.249552\pi\) | |||||||
\(878\) | −3.17226 | −0.107059 | ||||||||
\(879\) | −25.4313 | −0.857775 | ||||||||
\(880\) | −12.9780 | −0.437488 | ||||||||
\(881\) | 54.7979 | 1.84619 | 0.923094 | − | 0.384574i | \(-0.125652\pi\) | ||||
0.923094 | + | 0.384574i | \(0.125652\pi\) | |||||||
\(882\) | 95.3355 | 3.21011 | ||||||||
\(883\) | −32.4485 | −1.09198 | −0.545990 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545990 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(884\) | 152.753 | 5.13765 | ||||||||
\(885\) | −0.501533 | −0.0168588 | ||||||||
\(886\) | 89.7655 | 3.01573 | ||||||||
\(887\) | −2.47299 | −0.0830347 | −0.0415174 | − | 0.999138i | \(-0.513219\pi\) | ||||
−0.0415174 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(888\) | −78.7104 | −2.64135 | ||||||||
\(889\) | 0.149516 | 0.00501461 | ||||||||
\(890\) | 40.8456 | 1.36915 | ||||||||
\(891\) | 3.09954 | 0.103838 | ||||||||
\(892\) | 98.2529 | 3.28975 | ||||||||
\(893\) | −10.9925 | −0.367850 | ||||||||
\(894\) | 59.9815 | 2.00608 | ||||||||
\(895\) | −15.9809 | −0.534184 | ||||||||
\(896\) | 0.898803 | 0.0300269 | ||||||||
\(897\) | 100.259 | 3.34756 | ||||||||
\(898\) | 30.1970 | 1.00769 | ||||||||
\(899\) | 1.06743 | 0.0356009 | ||||||||
\(900\) | −66.9360 | −2.23120 | ||||||||
\(901\) | −63.9896 | −2.13180 | ||||||||
\(902\) | −10.5217 | −0.350334 | ||||||||
\(903\) | −2.54598 | −0.0847248 | ||||||||
\(904\) | −36.4927 | −1.21373 | ||||||||
\(905\) | −22.8284 | −0.758840 | ||||||||
\(906\) | 59.4961 | 1.97663 | ||||||||
\(907\) | 49.8744 | 1.65605 | 0.828026 | − | 0.560690i | \(-0.189464\pi\) | ||||
0.828026 | + | 0.560690i | \(0.189464\pi\) | |||||||
\(908\) | 15.0159 | 0.498319 | ||||||||
\(909\) | −26.6128 | −0.882692 | ||||||||
\(910\) | −4.42649 | −0.146737 | ||||||||
\(911\) | −49.5070 | −1.64024 | −0.820120 | − | 0.572192i | \(-0.806093\pi\) | ||||
−0.820120 | + | 0.572192i | \(0.806093\pi\) | |||||||
\(912\) | −99.5335 | −3.29588 | ||||||||
\(913\) | −9.11300 | −0.301596 | ||||||||
\(914\) | 5.61980 | 0.185887 | ||||||||
\(915\) | −10.3192 | −0.341142 | ||||||||
\(916\) | 56.9498 | 1.88167 | ||||||||
\(917\) | 1.69158 | 0.0558609 | ||||||||
\(918\) | −79.3963 | −2.62047 | ||||||||
\(919\) | −44.3554 | −1.46315 | −0.731574 | − | 0.681762i | \(-0.761214\pi\) | ||||
−0.731574 | + | 0.681762i | \(0.761214\pi\) | |||||||
\(920\) | 52.3218 | 1.72500 | ||||||||
\(921\) | −59.6556 | −1.96572 | ||||||||
\(922\) | −3.35570 | −0.110514 | ||||||||
\(923\) | −39.6905 | −1.30643 | ||||||||
\(924\) | −2.17710 | −0.0716213 | ||||||||
\(925\) | 10.6559 | 0.350363 | ||||||||
\(926\) | 7.39629 | 0.243057 | ||||||||
\(927\) | 14.4174 | 0.473531 | ||||||||
\(928\) | 16.1322 | 0.529566 | ||||||||
\(929\) | −10.8535 | −0.356091 | −0.178046 | − | 0.984022i | \(-0.556977\pi\) | ||||
−0.178046 | + | 0.984022i | \(0.556977\pi\) | |||||||
\(930\) | 6.16903 | 0.202291 | ||||||||
\(931\) | −28.1571 | −0.922810 | ||||||||
\(932\) | 57.5999 | 1.88675 | ||||||||
\(933\) | −9.14619 | −0.299433 | ||||||||
\(934\) | −1.10504 | −0.0361581 | ||||||||
\(935\) | 7.06640 | 0.231096 | ||||||||
\(936\) | 256.583 | 8.38669 | ||||||||
\(937\) | 38.0257 | 1.24225 | 0.621123 | − | 0.783713i | \(-0.286677\pi\) | ||||
0.621123 | + | 0.783713i | \(0.286677\pi\) | |||||||
\(938\) | −1.72790 | −0.0564178 | ||||||||
\(939\) | −94.1340 | −3.07195 | ||||||||
\(940\) | 19.3227 | 0.630238 | ||||||||
\(941\) | −24.8764 | −0.810947 | −0.405474 | − | 0.914107i | \(-0.632893\pi\) | ||||
−0.405474 | + | 0.914107i | \(0.632893\pi\) | |||||||
\(942\) | −70.3291 | −2.29145 | ||||||||
\(943\) | 20.2602 | 0.659763 | ||||||||
\(944\) | −0.984303 | −0.0320363 | ||||||||
\(945\) | 1.61219 | 0.0524447 | ||||||||
\(946\) | −14.1567 | −0.460275 | ||||||||
\(947\) | −40.0294 | −1.30078 | −0.650391 | − | 0.759600i | \(-0.725395\pi\) | ||||
−0.650391 | + | 0.759600i | \(0.725395\pi\) | |||||||
\(948\) | 102.034 | 3.31391 | ||||||||
\(949\) | 104.180 | 3.38183 | ||||||||
\(950\) | 28.2127 | 0.915341 | ||||||||
\(951\) | −5.03371 | −0.163229 | ||||||||
\(952\) | 5.22201 | 0.169246 | ||||||||
\(953\) | 17.9403 | 0.581144 | 0.290572 | − | 0.956853i | \(-0.406154\pi\) | ||||
0.290572 | + | 0.956853i | \(0.406154\pi\) | |||||||
\(954\) | −187.614 | −6.07421 | ||||||||
\(955\) | 16.9135 | 0.547307 | ||||||||
\(956\) | 88.9527 | 2.87694 | ||||||||
\(957\) | 5.61865 | 0.181625 | ||||||||
\(958\) | −36.5758 | −1.18171 | ||||||||
\(959\) | −0.499320 | −0.0161239 | ||||||||
\(960\) | 18.5086 | 0.597361 | ||||||||
\(961\) | −30.7009 | −0.990350 | ||||||||
\(962\) | −71.2976 | −2.29873 | ||||||||
\(963\) | 72.0694 | 2.32240 | ||||||||
\(964\) | 103.051 | 3.31903 | ||||||||
\(965\) | 4.35480 | 0.140186 | ||||||||
\(966\) | 5.98258 | 0.192486 | ||||||||
\(967\) | 51.1550 | 1.64503 | 0.822516 | − | 0.568742i | \(-0.192570\pi\) | ||||
0.822516 | + | 0.568742i | \(0.192570\pi\) | |||||||
\(968\) | −6.93538 | −0.222912 | ||||||||
\(969\) | 54.1951 | 1.74100 | ||||||||
\(970\) | −27.0752 | −0.869332 | ||||||||
\(971\) | −16.8976 | −0.542269 | −0.271134 | − | 0.962542i | \(-0.587399\pi\) | ||||
−0.271134 | + | 0.962542i | \(0.587399\pi\) | |||||||
\(972\) | 50.7533 | 1.62791 | ||||||||
\(973\) | 2.37253 | 0.0760599 | ||||||||
\(974\) | 44.7304 | 1.43325 | ||||||||
\(975\) | −54.4430 | −1.74357 | ||||||||
\(976\) | −20.2524 | −0.648263 | ||||||||
\(977\) | 27.2904 | 0.873098 | 0.436549 | − | 0.899681i | \(-0.356201\pi\) | ||||
0.436549 | + | 0.899681i | \(0.356201\pi\) | |||||||
\(978\) | 62.6487 | 2.00329 | ||||||||
\(979\) | 10.4253 | 0.333195 | ||||||||
\(980\) | 49.4948 | 1.58105 | ||||||||
\(981\) | −80.6725 | −2.57567 | ||||||||
\(982\) | −22.4929 | −0.717777 | ||||||||
\(983\) | 5.15037 | 0.164271 | 0.0821356 | − | 0.996621i | \(-0.473826\pi\) | ||||
0.0821356 | + | 0.996621i | \(0.473826\pi\) | |||||||
\(984\) | 81.2650 | 2.59063 | ||||||||
\(985\) | −2.04064 | −0.0650201 | ||||||||
\(986\) | −23.5238 | −0.749152 | ||||||||
\(987\) | 1.26578 | 0.0402901 | ||||||||
\(988\) | −132.275 | −4.20823 | ||||||||
\(989\) | 27.2597 | 0.866807 | ||||||||
\(990\) | 20.7182 | 0.658469 | ||||||||
\(991\) | 3.83886 | 0.121946 | 0.0609728 | − | 0.998139i | \(-0.480580\pi\) | ||||
0.0609728 | + | 0.998139i | \(0.480580\pi\) | |||||||
\(992\) | 4.52089 | 0.143538 | ||||||||
\(993\) | −39.3238 | −1.24790 | ||||||||
\(994\) | −2.36837 | −0.0751203 | ||||||||
\(995\) | 13.7098 | 0.434631 | ||||||||
\(996\) | 122.856 | 3.89283 | ||||||||
\(997\) | 36.0307 | 1.14110 | 0.570551 | − | 0.821262i | \(-0.306730\pi\) | ||||
0.570551 | + | 0.821262i | \(0.306730\pi\) | |||||||
\(998\) | 43.6340 | 1.38121 | ||||||||
\(999\) | 25.9676 | 0.821580 |
(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 | 6017.2.a.c.1.7 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.7 | ✓ | 106 | 1.1 | even | 1 | trivial |