Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.87951 | −1.66248 | −0.831242 | − | 0.555910i | \(-0.812370\pi\) | ||||
−0.831242 | + | 0.555910i | \(0.812370\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.727191 | −0.325210 | −0.162605 | − | 0.986691i | \(-0.551990\pi\) | ||||
−0.162605 | + | 0.986691i | \(0.551990\pi\) | |||||||
\(6\) | −2.87951 | −1.17555 | ||||||||
\(7\) | −4.06984 | −1.53826 | −0.769128 | − | 0.639094i | \(-0.779309\pi\) | ||||
−0.769128 | + | 0.639094i | \(0.779309\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.29156 | 1.76385 | ||||||||
\(10\) | −0.727191 | −0.229958 | ||||||||
\(11\) | 3.61815 | 1.09091 | 0.545457 | − | 0.838139i | \(-0.316356\pi\) | ||||
0.545457 | + | 0.838139i | \(0.316356\pi\) | |||||||
\(12\) | −2.87951 | −0.831242 | ||||||||
\(13\) | 1.25152 | 0.347109 | 0.173554 | − | 0.984824i | \(-0.444475\pi\) | ||||
0.173554 | + | 0.984824i | \(0.444475\pi\) | |||||||
\(14\) | −4.06984 | −1.08771 | ||||||||
\(15\) | 2.09395 | 0.540656 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.13118 | −0.516886 | −0.258443 | − | 0.966026i | \(-0.583209\pi\) | ||||
−0.258443 | + | 0.966026i | \(0.583209\pi\) | |||||||
\(18\) | 5.29156 | 1.24723 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.727191 | −0.162605 | ||||||||
\(21\) | 11.7191 | 2.55733 | ||||||||
\(22\) | 3.61815 | 0.771392 | ||||||||
\(23\) | −5.63090 | −1.17412 | −0.587062 | − | 0.809542i | \(-0.699716\pi\) | ||||
−0.587062 | + | 0.809542i | \(0.699716\pi\) | |||||||
\(24\) | −2.87951 | −0.587777 | ||||||||
\(25\) | −4.47119 | −0.894239 | ||||||||
\(26\) | 1.25152 | 0.245443 | ||||||||
\(27\) | −6.59857 | −1.26990 | ||||||||
\(28\) | −4.06984 | −0.769128 | ||||||||
\(29\) | 0.443419 | 0.0823408 | 0.0411704 | − | 0.999152i | \(-0.486891\pi\) | ||||
0.0411704 | + | 0.999152i | \(0.486891\pi\) | |||||||
\(30\) | 2.09395 | 0.382302 | ||||||||
\(31\) | 8.17728 | 1.46868 | 0.734341 | − | 0.678780i | \(-0.237491\pi\) | ||||
0.734341 | + | 0.678780i | \(0.237491\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.4185 | −1.81363 | ||||||||
\(34\) | −2.13118 | −0.365494 | ||||||||
\(35\) | 2.95955 | 0.500256 | ||||||||
\(36\) | 5.29156 | 0.881927 | ||||||||
\(37\) | 0.0414686 | 0.00681740 | 0.00340870 | − | 0.999994i | \(-0.498915\pi\) | ||||
0.00340870 | + | 0.999994i | \(0.498915\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −3.60376 | −0.577063 | ||||||||
\(40\) | −0.727191 | −0.114979 | ||||||||
\(41\) | −2.66115 | −0.415601 | −0.207801 | − | 0.978171i | \(-0.566631\pi\) | ||||
−0.207801 | + | 0.978171i | \(0.566631\pi\) | |||||||
\(42\) | 11.7191 | 1.80830 | ||||||||
\(43\) | 0.595822 | 0.0908620 | 0.0454310 | − | 0.998967i | \(-0.485534\pi\) | ||||
0.0454310 | + | 0.998967i | \(0.485534\pi\) | |||||||
\(44\) | 3.61815 | 0.545457 | ||||||||
\(45\) | −3.84798 | −0.573623 | ||||||||
\(46\) | −5.63090 | −0.830231 | ||||||||
\(47\) | 8.94221 | 1.30436 | 0.652178 | − | 0.758066i | \(-0.273856\pi\) | ||||
0.652178 | + | 0.758066i | \(0.273856\pi\) | |||||||
\(48\) | −2.87951 | −0.415621 | ||||||||
\(49\) | 9.56364 | 1.36623 | ||||||||
\(50\) | −4.47119 | −0.632322 | ||||||||
\(51\) | 6.13674 | 0.859315 | ||||||||
\(52\) | 1.25152 | 0.173554 | ||||||||
\(53\) | −5.80482 | −0.797353 | −0.398677 | − | 0.917092i | \(-0.630530\pi\) | ||||
−0.398677 | + | 0.917092i | \(0.630530\pi\) | |||||||
\(54\) | −6.59857 | −0.897952 | ||||||||
\(55\) | −2.63109 | −0.354776 | ||||||||
\(56\) | −4.06984 | −0.543856 | ||||||||
\(57\) | 2.87951 | 0.381400 | ||||||||
\(58\) | 0.443419 | 0.0582237 | ||||||||
\(59\) | 10.8913 | 1.41792 | 0.708960 | − | 0.705249i | \(-0.249165\pi\) | ||||
0.708960 | + | 0.705249i | \(0.249165\pi\) | |||||||
\(60\) | 2.09395 | 0.270328 | ||||||||
\(61\) | −6.38286 | −0.817242 | −0.408621 | − | 0.912704i | \(-0.633990\pi\) | ||||
−0.408621 | + | 0.912704i | \(0.633990\pi\) | |||||||
\(62\) | 8.17728 | 1.03852 | ||||||||
\(63\) | −21.5358 | −2.71326 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.910093 | −0.112883 | ||||||||
\(66\) | −10.4185 | −1.28243 | ||||||||
\(67\) | 11.4714 | 1.40146 | 0.700728 | − | 0.713428i | \(-0.252859\pi\) | ||||
0.700728 | + | 0.713428i | \(0.252859\pi\) | |||||||
\(68\) | −2.13118 | −0.258443 | ||||||||
\(69\) | 16.2142 | 1.95196 | ||||||||
\(70\) | 2.95955 | 0.353734 | ||||||||
\(71\) | −3.38669 | −0.401926 | −0.200963 | − | 0.979599i | \(-0.564407\pi\) | ||||
−0.200963 | + | 0.979599i | \(0.564407\pi\) | |||||||
\(72\) | 5.29156 | 0.623617 | ||||||||
\(73\) | −0.0581009 | −0.00680019 | −0.00340010 | − | 0.999994i | \(-0.501082\pi\) | ||||
−0.00340010 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(74\) | 0.0414686 | 0.00482063 | ||||||||
\(75\) | 12.8748 | 1.48666 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −14.7253 | −1.67810 | ||||||||
\(78\) | −3.60376 | −0.408045 | ||||||||
\(79\) | −2.17699 | −0.244930 | −0.122465 | − | 0.992473i | \(-0.539080\pi\) | ||||
−0.122465 | + | 0.992473i | \(0.539080\pi\) | |||||||
\(80\) | −0.727191 | −0.0813024 | ||||||||
\(81\) | 3.12595 | 0.347328 | ||||||||
\(82\) | −2.66115 | −0.293874 | ||||||||
\(83\) | 3.33356 | 0.365905 | 0.182953 | − | 0.983122i | \(-0.441434\pi\) | ||||
0.182953 | + | 0.983122i | \(0.441434\pi\) | |||||||
\(84\) | 11.7191 | 1.27866 | ||||||||
\(85\) | 1.54977 | 0.168096 | ||||||||
\(86\) | 0.595822 | 0.0642491 | ||||||||
\(87\) | −1.27683 | −0.136890 | ||||||||
\(88\) | 3.61815 | 0.385696 | ||||||||
\(89\) | 13.4876 | 1.42969 | 0.714844 | − | 0.699284i | \(-0.246498\pi\) | ||||
0.714844 | + | 0.699284i | \(0.246498\pi\) | |||||||
\(90\) | −3.84798 | −0.405612 | ||||||||
\(91\) | −5.09349 | −0.533943 | ||||||||
\(92\) | −5.63090 | −0.587062 | ||||||||
\(93\) | −23.5465 | −2.44166 | ||||||||
\(94\) | 8.94221 | 0.922319 | ||||||||
\(95\) | 0.727191 | 0.0746082 | ||||||||
\(96\) | −2.87951 | −0.293889 | ||||||||
\(97\) | −3.24683 | −0.329666 | −0.164833 | − | 0.986321i | \(-0.552709\pi\) | ||||
−0.164833 | + | 0.986321i | \(0.552709\pi\) | |||||||
\(98\) | 9.56364 | 0.966073 | ||||||||
\(99\) | 19.1457 | 1.92421 | ||||||||
\(100\) | −4.47119 | −0.447119 | ||||||||
\(101\) | 2.82422 | 0.281021 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(102\) | 6.13674 | 0.607628 | ||||||||
\(103\) | −9.44507 | −0.930651 | −0.465325 | − | 0.885140i | \(-0.654063\pi\) | ||||
−0.465325 | + | 0.885140i | \(0.654063\pi\) | |||||||
\(104\) | 1.25152 | 0.122722 | ||||||||
\(105\) | −8.52206 | −0.831668 | ||||||||
\(106\) | −5.80482 | −0.563814 | ||||||||
\(107\) | 3.86570 | 0.373712 | 0.186856 | − | 0.982387i | \(-0.440170\pi\) | ||||
0.186856 | + | 0.982387i | \(0.440170\pi\) | |||||||
\(108\) | −6.59857 | −0.634948 | ||||||||
\(109\) | 9.32825 | 0.893485 | 0.446742 | − | 0.894663i | \(-0.352584\pi\) | ||||
0.446742 | + | 0.894663i | \(0.352584\pi\) | |||||||
\(110\) | −2.63109 | −0.250864 | ||||||||
\(111\) | −0.119409 | −0.0113338 | ||||||||
\(112\) | −4.06984 | −0.384564 | ||||||||
\(113\) | −0.836958 | −0.0787344 | −0.0393672 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393672 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(114\) | 2.87951 | 0.269691 | ||||||||
\(115\) | 4.09474 | 0.381837 | ||||||||
\(116\) | 0.443419 | 0.0411704 | ||||||||
\(117\) | 6.62249 | 0.612250 | ||||||||
\(118\) | 10.8913 | 1.00262 | ||||||||
\(119\) | 8.67356 | 0.795104 | ||||||||
\(120\) | 2.09395 | 0.191151 | ||||||||
\(121\) | 2.09101 | 0.190092 | ||||||||
\(122\) | −6.38286 | −0.577877 | ||||||||
\(123\) | 7.66279 | 0.690931 | ||||||||
\(124\) | 8.17728 | 0.734341 | ||||||||
\(125\) | 6.88737 | 0.616025 | ||||||||
\(126\) | −21.5358 | −1.91857 | ||||||||
\(127\) | −3.18628 | −0.282736 | −0.141368 | − | 0.989957i | \(-0.545150\pi\) | ||||
−0.141368 | + | 0.989957i | \(0.545150\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.71567 | −0.151057 | ||||||||
\(130\) | −0.910093 | −0.0798205 | ||||||||
\(131\) | −3.63269 | −0.317389 | −0.158695 | − | 0.987328i | \(-0.550729\pi\) | ||||
−0.158695 | + | 0.987328i | \(0.550729\pi\) | |||||||
\(132\) | −10.4185 | −0.906813 | ||||||||
\(133\) | 4.06984 | 0.352900 | ||||||||
\(134\) | 11.4714 | 0.990979 | ||||||||
\(135\) | 4.79842 | 0.412983 | ||||||||
\(136\) | −2.13118 | −0.182747 | ||||||||
\(137\) | −17.3661 | −1.48368 | −0.741841 | − | 0.670576i | \(-0.766047\pi\) | ||||
−0.741841 | + | 0.670576i | \(0.766047\pi\) | |||||||
\(138\) | 16.2142 | 1.38025 | ||||||||
\(139\) | 4.12808 | 0.350139 | 0.175069 | − | 0.984556i | \(-0.443985\pi\) | ||||
0.175069 | + | 0.984556i | \(0.443985\pi\) | |||||||
\(140\) | 2.95955 | 0.250128 | ||||||||
\(141\) | −25.7492 | −2.16847 | ||||||||
\(142\) | −3.38669 | −0.284205 | ||||||||
\(143\) | 4.52818 | 0.378666 | ||||||||
\(144\) | 5.29156 | 0.440964 | ||||||||
\(145\) | −0.322450 | −0.0267780 | ||||||||
\(146\) | −0.0581009 | −0.00480846 | ||||||||
\(147\) | −27.5386 | −2.27134 | ||||||||
\(148\) | 0.0414686 | 0.00340870 | ||||||||
\(149\) | 9.75805 | 0.799411 | 0.399705 | − | 0.916644i | \(-0.369112\pi\) | ||||
0.399705 | + | 0.916644i | \(0.369112\pi\) | |||||||
\(150\) | 12.8748 | 1.05123 | ||||||||
\(151\) | 5.86077 | 0.476943 | 0.238471 | − | 0.971150i | \(-0.423354\pi\) | ||||
0.238471 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −11.2773 | −0.911712 | ||||||||
\(154\) | −14.7253 | −1.18660 | ||||||||
\(155\) | −5.94644 | −0.477630 | ||||||||
\(156\) | −3.60376 | −0.288532 | ||||||||
\(157\) | −0.0193246 | −0.00154227 | −0.000771136 | − | 1.00000i | \(-0.500245\pi\) | ||||
−0.000771136 | 1.00000i | \(0.500245\pi\) | ||||||||
\(158\) | −2.17699 | −0.173192 | ||||||||
\(159\) | 16.7150 | 1.32559 | ||||||||
\(160\) | −0.727191 | −0.0574895 | ||||||||
\(161\) | 22.9169 | 1.80610 | ||||||||
\(162\) | 3.12595 | 0.245598 | ||||||||
\(163\) | 8.32582 | 0.652129 | 0.326064 | − | 0.945348i | \(-0.394277\pi\) | ||||
0.326064 | + | 0.945348i | \(0.394277\pi\) | |||||||
\(164\) | −2.66115 | −0.207801 | ||||||||
\(165\) | 7.57623 | 0.589809 | ||||||||
\(166\) | 3.33356 | 0.258734 | ||||||||
\(167\) | −13.2062 | −1.02192 | −0.510962 | − | 0.859603i | \(-0.670711\pi\) | ||||
−0.510962 | + | 0.859603i | \(0.670711\pi\) | |||||||
\(168\) | 11.7191 | 0.904152 | ||||||||
\(169\) | −11.4337 | −0.879515 | ||||||||
\(170\) | 1.54977 | 0.118862 | ||||||||
\(171\) | −5.29156 | −0.404656 | ||||||||
\(172\) | 0.595822 | 0.0454310 | ||||||||
\(173\) | 11.3203 | 0.860664 | 0.430332 | − | 0.902671i | \(-0.358396\pi\) | ||||
0.430332 | + | 0.902671i | \(0.358396\pi\) | |||||||
\(174\) | −1.27683 | −0.0967961 | ||||||||
\(175\) | 18.1971 | 1.37557 | ||||||||
\(176\) | 3.61815 | 0.272728 | ||||||||
\(177\) | −31.3614 | −2.35727 | ||||||||
\(178\) | 13.4876 | 1.01094 | ||||||||
\(179\) | −17.2073 | −1.28613 | −0.643067 | − | 0.765810i | \(-0.722338\pi\) | ||||
−0.643067 | + | 0.765810i | \(0.722338\pi\) | |||||||
\(180\) | −3.84798 | −0.286811 | ||||||||
\(181\) | −1.10634 | −0.0822333 | −0.0411167 | − | 0.999154i | \(-0.513092\pi\) | ||||
−0.0411167 | + | 0.999154i | \(0.513092\pi\) | |||||||
\(182\) | −5.09349 | −0.377554 | ||||||||
\(183\) | 18.3795 | 1.35865 | ||||||||
\(184\) | −5.63090 | −0.415116 | ||||||||
\(185\) | −0.0301556 | −0.00221708 | ||||||||
\(186\) | −23.5465 | −1.72652 | ||||||||
\(187\) | −7.71092 | −0.563878 | ||||||||
\(188\) | 8.94221 | 0.652178 | ||||||||
\(189\) | 26.8552 | 1.95343 | ||||||||
\(190\) | 0.727191 | 0.0527560 | ||||||||
\(191\) | 17.6307 | 1.27572 | 0.637858 | − | 0.770154i | \(-0.279821\pi\) | ||||
0.637858 | + | 0.770154i | \(0.279821\pi\) | |||||||
\(192\) | −2.87951 | −0.207811 | ||||||||
\(193\) | −12.4341 | −0.895029 | −0.447514 | − | 0.894277i | \(-0.647691\pi\) | ||||
−0.447514 | + | 0.894277i | \(0.647691\pi\) | |||||||
\(194\) | −3.24683 | −0.233109 | ||||||||
\(195\) | 2.62062 | 0.187667 | ||||||||
\(196\) | 9.56364 | 0.683117 | ||||||||
\(197\) | −9.18547 | −0.654438 | −0.327219 | − | 0.944949i | \(-0.606111\pi\) | ||||
−0.327219 | + | 0.944949i | \(0.606111\pi\) | |||||||
\(198\) | 19.1457 | 1.36062 | ||||||||
\(199\) | −2.41467 | −0.171172 | −0.0855858 | − | 0.996331i | \(-0.527276\pi\) | ||||
−0.0855858 | + | 0.996331i | \(0.527276\pi\) | |||||||
\(200\) | −4.47119 | −0.316161 | ||||||||
\(201\) | −33.0320 | −2.32990 | ||||||||
\(202\) | 2.82422 | 0.198712 | ||||||||
\(203\) | −1.80465 | −0.126661 | ||||||||
\(204\) | 6.13674 | 0.429658 | ||||||||
\(205\) | 1.93516 | 0.135158 | ||||||||
\(206\) | −9.44507 | −0.658070 | ||||||||
\(207\) | −29.7963 | −2.07098 | ||||||||
\(208\) | 1.25152 | 0.0867772 | ||||||||
\(209\) | −3.61815 | −0.250273 | ||||||||
\(210\) | −8.52206 | −0.588078 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −5.80482 | −0.398677 | ||||||||
\(213\) | 9.75200 | 0.668196 | ||||||||
\(214\) | 3.86570 | 0.264254 | ||||||||
\(215\) | −0.433276 | −0.0295492 | ||||||||
\(216\) | −6.59857 | −0.448976 | ||||||||
\(217\) | −33.2803 | −2.25921 | ||||||||
\(218\) | 9.32825 | 0.631789 | ||||||||
\(219\) | 0.167302 | 0.0113052 | ||||||||
\(220\) | −2.63109 | −0.177388 | ||||||||
\(221\) | −2.66721 | −0.179416 | ||||||||
\(222\) | −0.119409 | −0.00801422 | ||||||||
\(223\) | 5.31025 | 0.355601 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(224\) | −4.06984 | −0.271928 | ||||||||
\(225\) | −23.6596 | −1.57731 | ||||||||
\(226\) | −0.836958 | −0.0556736 | ||||||||
\(227\) | 2.23883 | 0.148596 | 0.0742982 | − | 0.997236i | \(-0.476328\pi\) | ||||
0.0742982 | + | 0.997236i | \(0.476328\pi\) | |||||||
\(228\) | 2.87951 | 0.190700 | ||||||||
\(229\) | −11.3240 | −0.748311 | −0.374156 | − | 0.927366i | \(-0.622067\pi\) | ||||
−0.374156 | + | 0.927366i | \(0.622067\pi\) | |||||||
\(230\) | 4.09474 | 0.269999 | ||||||||
\(231\) | 42.4016 | 2.78982 | ||||||||
\(232\) | 0.443419 | 0.0291119 | ||||||||
\(233\) | −28.2061 | −1.84784 | −0.923921 | − | 0.382584i | \(-0.875034\pi\) | ||||
−0.923921 | + | 0.382584i | \(0.875034\pi\) | |||||||
\(234\) | 6.62249 | 0.432926 | ||||||||
\(235\) | −6.50270 | −0.424189 | ||||||||
\(236\) | 10.8913 | 0.708960 | ||||||||
\(237\) | 6.26866 | 0.407193 | ||||||||
\(238\) | 8.67356 | 0.562223 | ||||||||
\(239\) | −21.9897 | −1.42239 | −0.711197 | − | 0.702992i | \(-0.751847\pi\) | ||||
−0.711197 | + | 0.702992i | \(0.751847\pi\) | |||||||
\(240\) | 2.09395 | 0.135164 | ||||||||
\(241\) | −9.92311 | −0.639203 | −0.319602 | − | 0.947552i | \(-0.603549\pi\) | ||||
−0.319602 | + | 0.947552i | \(0.603549\pi\) | |||||||
\(242\) | 2.09101 | 0.134415 | ||||||||
\(243\) | 10.7945 | 0.692468 | ||||||||
\(244\) | −6.38286 | −0.408621 | ||||||||
\(245\) | −6.95459 | −0.444313 | ||||||||
\(246\) | 7.66279 | 0.488562 | ||||||||
\(247\) | −1.25152 | −0.0796322 | ||||||||
\(248\) | 8.17728 | 0.519258 | ||||||||
\(249\) | −9.59900 | −0.608312 | ||||||||
\(250\) | 6.88737 | 0.435595 | ||||||||
\(251\) | −19.4864 | −1.22997 | −0.614986 | − | 0.788538i | \(-0.710838\pi\) | ||||
−0.614986 | + | 0.788538i | \(0.710838\pi\) | |||||||
\(252\) | −21.5358 | −1.35663 | ||||||||
\(253\) | −20.3735 | −1.28087 | ||||||||
\(254\) | −3.18628 | −0.199925 | ||||||||
\(255\) | −4.46258 | −0.279458 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.644104 | 0.0401781 | 0.0200890 | − | 0.999798i | \(-0.493605\pi\) | ||||
0.0200890 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(258\) | −1.71567 | −0.106813 | ||||||||
\(259\) | −0.168771 | −0.0104869 | ||||||||
\(260\) | −0.910093 | −0.0564416 | ||||||||
\(261\) | 2.34638 | 0.145237 | ||||||||
\(262\) | −3.63269 | −0.224428 | ||||||||
\(263\) | −0.0603677 | −0.00372243 | −0.00186121 | − | 0.999998i | \(-0.500592\pi\) | ||||
−0.00186121 | + | 0.999998i | \(0.500592\pi\) | |||||||
\(264\) | −10.4185 | −0.641214 | ||||||||
\(265\) | 4.22121 | 0.259307 | ||||||||
\(266\) | 4.06984 | 0.249538 | ||||||||
\(267\) | −38.8378 | −2.37683 | ||||||||
\(268\) | 11.4714 | 0.700728 | ||||||||
\(269\) | −9.66382 | −0.589213 | −0.294607 | − | 0.955619i | \(-0.595189\pi\) | ||||
−0.294607 | + | 0.955619i | \(0.595189\pi\) | |||||||
\(270\) | 4.79842 | 0.292023 | ||||||||
\(271\) | 8.86078 | 0.538254 | 0.269127 | − | 0.963105i | \(-0.413265\pi\) | ||||
0.269127 | + | 0.963105i | \(0.413265\pi\) | |||||||
\(272\) | −2.13118 | −0.129222 | ||||||||
\(273\) | 14.6667 | 0.887671 | ||||||||
\(274\) | −17.3661 | −1.04912 | ||||||||
\(275\) | −16.1774 | −0.975537 | ||||||||
\(276\) | 16.2142 | 0.975982 | ||||||||
\(277\) | −14.2875 | −0.858450 | −0.429225 | − | 0.903198i | \(-0.641213\pi\) | ||||
−0.429225 | + | 0.903198i | \(0.641213\pi\) | |||||||
\(278\) | 4.12808 | 0.247586 | ||||||||
\(279\) | 43.2706 | 2.59054 | ||||||||
\(280\) | 2.95955 | 0.176867 | ||||||||
\(281\) | −5.91818 | −0.353049 | −0.176524 | − | 0.984296i | \(-0.556485\pi\) | ||||
−0.176524 | + | 0.984296i | \(0.556485\pi\) | |||||||
\(282\) | −25.7492 | −1.53334 | ||||||||
\(283\) | −13.7719 | −0.818652 | −0.409326 | − | 0.912388i | \(-0.634236\pi\) | ||||
−0.409326 | + | 0.912388i | \(0.634236\pi\) | |||||||
\(284\) | −3.38669 | −0.200963 | ||||||||
\(285\) | −2.09395 | −0.124035 | ||||||||
\(286\) | 4.52818 | 0.267757 | ||||||||
\(287\) | 10.8305 | 0.639301 | ||||||||
\(288\) | 5.29156 | 0.311808 | ||||||||
\(289\) | −12.4581 | −0.732829 | ||||||||
\(290\) | −0.322450 | −0.0189349 | ||||||||
\(291\) | 9.34929 | 0.548065 | ||||||||
\(292\) | −0.0581009 | −0.00340010 | ||||||||
\(293\) | −18.6214 | −1.08787 | −0.543937 | − | 0.839126i | \(-0.683067\pi\) | ||||
−0.543937 | + | 0.839126i | \(0.683067\pi\) | |||||||
\(294\) | −27.5386 | −1.60608 | ||||||||
\(295\) | −7.92002 | −0.461122 | ||||||||
\(296\) | 0.0414686 | 0.00241031 | ||||||||
\(297\) | −23.8746 | −1.38535 | ||||||||
\(298\) | 9.75805 | 0.565269 | ||||||||
\(299\) | −7.04718 | −0.407549 | ||||||||
\(300\) | 12.8748 | 0.743329 | ||||||||
\(301\) | −2.42490 | −0.139769 | ||||||||
\(302\) | 5.86077 | 0.337249 | ||||||||
\(303\) | −8.13237 | −0.467192 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 4.64156 | 0.265775 | ||||||||
\(306\) | −11.2773 | −0.644678 | ||||||||
\(307\) | 14.2345 | 0.812408 | 0.406204 | − | 0.913782i | \(-0.366852\pi\) | ||||
0.406204 | + | 0.913782i | \(0.366852\pi\) | |||||||
\(308\) | −14.7253 | −0.839052 | ||||||||
\(309\) | 27.1972 | 1.54719 | ||||||||
\(310\) | −5.94644 | −0.337735 | ||||||||
\(311\) | 7.14179 | 0.404974 | 0.202487 | − | 0.979285i | \(-0.435098\pi\) | ||||
0.202487 | + | 0.979285i | \(0.435098\pi\) | |||||||
\(312\) | −3.60376 | −0.204023 | ||||||||
\(313\) | −28.6539 | −1.61961 | −0.809806 | − | 0.586698i | \(-0.800428\pi\) | ||||
−0.809806 | + | 0.586698i | \(0.800428\pi\) | |||||||
\(314\) | −0.0193246 | −0.00109055 | ||||||||
\(315\) | 15.6607 | 0.882379 | ||||||||
\(316\) | −2.17699 | −0.122465 | ||||||||
\(317\) | −21.7416 | −1.22113 | −0.610564 | − | 0.791967i | \(-0.709057\pi\) | ||||
−0.610564 | + | 0.791967i | \(0.709057\pi\) | |||||||
\(318\) | 16.7150 | 0.937332 | ||||||||
\(319\) | 1.60436 | 0.0898267 | ||||||||
\(320\) | −0.727191 | −0.0406512 | ||||||||
\(321\) | −11.1313 | −0.621290 | ||||||||
\(322\) | 22.9169 | 1.27711 | ||||||||
\(323\) | 2.13118 | 0.118582 | ||||||||
\(324\) | 3.12595 | 0.173664 | ||||||||
\(325\) | −5.59578 | −0.310398 | ||||||||
\(326\) | 8.32582 | 0.461125 | ||||||||
\(327\) | −26.8608 | −1.48540 | ||||||||
\(328\) | −2.66115 | −0.146937 | ||||||||
\(329\) | −36.3934 | −2.00643 | ||||||||
\(330\) | 7.57623 | 0.417058 | ||||||||
\(331\) | −30.5077 | −1.67685 | −0.838426 | − | 0.545015i | \(-0.816524\pi\) | ||||
−0.838426 | + | 0.545015i | \(0.816524\pi\) | |||||||
\(332\) | 3.33356 | 0.182953 | ||||||||
\(333\) | 0.219434 | 0.0120249 | ||||||||
\(334\) | −13.2062 | −0.722609 | ||||||||
\(335\) | −8.34191 | −0.455767 | ||||||||
\(336\) | 11.7191 | 0.639332 | ||||||||
\(337\) | −1.44029 | −0.0784574 | −0.0392287 | − | 0.999230i | \(-0.512490\pi\) | ||||
−0.0392287 | + | 0.999230i | \(0.512490\pi\) | |||||||
\(338\) | −11.4337 | −0.621911 | ||||||||
\(339\) | 2.41003 | 0.130895 | ||||||||
\(340\) | 1.54977 | 0.0840482 | ||||||||
\(341\) | 29.5866 | 1.60221 | ||||||||
\(342\) | −5.29156 | −0.286135 | ||||||||
\(343\) | −10.4336 | −0.563362 | ||||||||
\(344\) | 0.595822 | 0.0321246 | ||||||||
\(345\) | −11.7908 | −0.634798 | ||||||||
\(346\) | 11.3203 | 0.608582 | ||||||||
\(347\) | −18.2248 | −0.978360 | −0.489180 | − | 0.872183i | \(-0.662704\pi\) | ||||
−0.489180 | + | 0.872183i | \(0.662704\pi\) | |||||||
\(348\) | −1.27683 | −0.0684452 | ||||||||
\(349\) | −7.30817 | −0.391197 | −0.195599 | − | 0.980684i | \(-0.562665\pi\) | ||||
−0.195599 | + | 0.980684i | \(0.562665\pi\) | |||||||
\(350\) | 18.1971 | 0.972674 | ||||||||
\(351\) | −8.25824 | −0.440792 | ||||||||
\(352\) | 3.61815 | 0.192848 | ||||||||
\(353\) | −23.4595 | −1.24862 | −0.624312 | − | 0.781175i | \(-0.714621\pi\) | ||||
−0.624312 | + | 0.781175i | \(0.714621\pi\) | |||||||
\(354\) | −31.3614 | −1.66684 | ||||||||
\(355\) | 2.46277 | 0.130710 | ||||||||
\(356\) | 13.4876 | 0.714844 | ||||||||
\(357\) | −24.9756 | −1.32185 | ||||||||
\(358\) | −17.2073 | −0.909434 | ||||||||
\(359\) | 30.3218 | 1.60032 | 0.800161 | − | 0.599785i | \(-0.204747\pi\) | ||||
0.800161 | + | 0.599785i | \(0.204747\pi\) | |||||||
\(360\) | −3.84798 | −0.202806 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.10634 | −0.0581477 | ||||||||
\(363\) | −6.02109 | −0.316025 | ||||||||
\(364\) | −5.09349 | −0.266971 | ||||||||
\(365\) | 0.0422504 | 0.00221149 | ||||||||
\(366\) | 18.3795 | 0.960712 | ||||||||
\(367\) | −12.2097 | −0.637339 | −0.318670 | − | 0.947866i | \(-0.603236\pi\) | ||||
−0.318670 | + | 0.947866i | \(0.603236\pi\) | |||||||
\(368\) | −5.63090 | −0.293531 | ||||||||
\(369\) | −14.0816 | −0.733060 | ||||||||
\(370\) | −0.0301556 | −0.00156772 | ||||||||
\(371\) | 23.6247 | 1.22653 | ||||||||
\(372\) | −23.5465 | −1.22083 | ||||||||
\(373\) | 31.6590 | 1.63924 | 0.819621 | − | 0.572906i | \(-0.194184\pi\) | ||||
0.819621 | + | 0.572906i | \(0.194184\pi\) | |||||||
\(374\) | −7.71092 | −0.398722 | ||||||||
\(375\) | −19.8322 | −1.02413 | ||||||||
\(376\) | 8.94221 | 0.461159 | ||||||||
\(377\) | 0.554947 | 0.0285812 | ||||||||
\(378\) | 26.8552 | 1.38128 | ||||||||
\(379\) | −0.430657 | −0.0221213 | −0.0110607 | − | 0.999939i | \(-0.503521\pi\) | ||||
−0.0110607 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(380\) | 0.727191 | 0.0373041 | ||||||||
\(381\) | 9.17491 | 0.470045 | ||||||||
\(382\) | 17.6307 | 0.902067 | ||||||||
\(383\) | −7.69215 | −0.393050 | −0.196525 | − | 0.980499i | \(-0.562966\pi\) | ||||
−0.196525 | + | 0.980499i | \(0.562966\pi\) | |||||||
\(384\) | −2.87951 | −0.146944 | ||||||||
\(385\) | 10.7081 | 0.545736 | ||||||||
\(386\) | −12.4341 | −0.632881 | ||||||||
\(387\) | 3.15283 | 0.160267 | ||||||||
\(388\) | −3.24683 | −0.164833 | ||||||||
\(389\) | −3.32939 | −0.168807 | −0.0844034 | − | 0.996432i | \(-0.526898\pi\) | ||||
−0.0844034 | + | 0.996432i | \(0.526898\pi\) | |||||||
\(390\) | 2.62062 | 0.132700 | ||||||||
\(391\) | 12.0004 | 0.606889 | ||||||||
\(392\) | 9.56364 | 0.483037 | ||||||||
\(393\) | 10.4604 | 0.527655 | ||||||||
\(394\) | −9.18547 | −0.462757 | ||||||||
\(395\) | 1.58309 | 0.0796538 | ||||||||
\(396\) | 19.1457 | 0.962106 | ||||||||
\(397\) | 31.1952 | 1.56564 | 0.782821 | − | 0.622247i | \(-0.213780\pi\) | ||||
0.782821 | + | 0.622247i | \(0.213780\pi\) | |||||||
\(398\) | −2.41467 | −0.121037 | ||||||||
\(399\) | −11.7191 | −0.586691 | ||||||||
\(400\) | −4.47119 | −0.223560 | ||||||||
\(401\) | −22.8724 | −1.14219 | −0.571097 | − | 0.820883i | \(-0.693482\pi\) | ||||
−0.571097 | + | 0.820883i | \(0.693482\pi\) | |||||||
\(402\) | −33.0320 | −1.64749 | ||||||||
\(403\) | 10.2340 | 0.509793 | ||||||||
\(404\) | 2.82422 | 0.140510 | ||||||||
\(405\) | −2.27317 | −0.112955 | ||||||||
\(406\) | −1.80465 | −0.0895631 | ||||||||
\(407\) | 0.150040 | 0.00743719 | ||||||||
\(408\) | 6.13674 | 0.303814 | ||||||||
\(409\) | 15.5779 | 0.770276 | 0.385138 | − | 0.922859i | \(-0.374154\pi\) | ||||
0.385138 | + | 0.922859i | \(0.374154\pi\) | |||||||
\(410\) | 1.93516 | 0.0955708 | ||||||||
\(411\) | 50.0057 | 2.46660 | ||||||||
\(412\) | −9.44507 | −0.465325 | ||||||||
\(413\) | −44.3257 | −2.18113 | ||||||||
\(414\) | −29.7963 | −1.46441 | ||||||||
\(415\) | −2.42413 | −0.118996 | ||||||||
\(416\) | 1.25152 | 0.0613608 | ||||||||
\(417\) | −11.8868 | −0.582100 | ||||||||
\(418\) | −3.61815 | −0.176970 | ||||||||
\(419\) | 22.7946 | 1.11359 | 0.556795 | − | 0.830650i | \(-0.312031\pi\) | ||||
0.556795 | + | 0.830650i | \(0.312031\pi\) | |||||||
\(420\) | −8.52206 | −0.415834 | ||||||||
\(421\) | −3.48327 | −0.169764 | −0.0848822 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848822 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 47.3183 | 2.30069 | ||||||||
\(424\) | −5.80482 | −0.281907 | ||||||||
\(425\) | 9.52890 | 0.462220 | ||||||||
\(426\) | 9.75200 | 0.472486 | ||||||||
\(427\) | 25.9773 | 1.25713 | ||||||||
\(428\) | 3.86570 | 0.186856 | ||||||||
\(429\) | −13.0389 | −0.629526 | ||||||||
\(430\) | −0.433276 | −0.0208944 | ||||||||
\(431\) | −13.5984 | −0.655014 | −0.327507 | − | 0.944849i | \(-0.606208\pi\) | ||||
−0.327507 | + | 0.944849i | \(0.606208\pi\) | |||||||
\(432\) | −6.59857 | −0.317474 | ||||||||
\(433\) | 18.4255 | 0.885474 | 0.442737 | − | 0.896652i | \(-0.354008\pi\) | ||||
0.442737 | + | 0.896652i | \(0.354008\pi\) | |||||||
\(434\) | −33.2803 | −1.59750 | ||||||||
\(435\) | 0.928498 | 0.0445181 | ||||||||
\(436\) | 9.32825 | 0.446742 | ||||||||
\(437\) | 5.63090 | 0.269363 | ||||||||
\(438\) | 0.167302 | 0.00799399 | ||||||||
\(439\) | −6.20274 | −0.296041 | −0.148020 | − | 0.988984i | \(-0.547290\pi\) | ||||
−0.148020 | + | 0.988984i | \(0.547290\pi\) | |||||||
\(440\) | −2.63109 | −0.125432 | ||||||||
\(441\) | 50.6066 | 2.40984 | ||||||||
\(442\) | −2.66721 | −0.126866 | ||||||||
\(443\) | 28.2064 | 1.34013 | 0.670064 | − | 0.742303i | \(-0.266267\pi\) | ||||
0.670064 | + | 0.742303i | \(0.266267\pi\) | |||||||
\(444\) | −0.119409 | −0.00566691 | ||||||||
\(445\) | −9.80810 | −0.464948 | ||||||||
\(446\) | 5.31025 | 0.251448 | ||||||||
\(447\) | −28.0984 | −1.32901 | ||||||||
\(448\) | −4.06984 | −0.192282 | ||||||||
\(449\) | 5.81064 | 0.274221 | 0.137111 | − | 0.990556i | \(-0.456218\pi\) | ||||
0.137111 | + | 0.990556i | \(0.456218\pi\) | |||||||
\(450\) | −23.6596 | −1.11532 | ||||||||
\(451\) | −9.62843 | −0.453385 | ||||||||
\(452\) | −0.836958 | −0.0393672 | ||||||||
\(453\) | −16.8761 | −0.792910 | ||||||||
\(454\) | 2.23883 | 0.105074 | ||||||||
\(455\) | 3.70394 | 0.173643 | ||||||||
\(456\) | 2.87951 | 0.134845 | ||||||||
\(457\) | 10.2851 | 0.481115 | 0.240557 | − | 0.970635i | \(-0.422670\pi\) | ||||
0.240557 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(458\) | −11.3240 | −0.529136 | ||||||||
\(459\) | 14.0627 | 0.656392 | ||||||||
\(460\) | 4.09474 | 0.190918 | ||||||||
\(461\) | −33.1091 | −1.54205 | −0.771023 | − | 0.636808i | \(-0.780255\pi\) | ||||
−0.771023 | + | 0.636808i | \(0.780255\pi\) | |||||||
\(462\) | 42.4016 | 1.97270 | ||||||||
\(463\) | 5.33782 | 0.248070 | 0.124035 | − | 0.992278i | \(-0.460417\pi\) | ||||
0.124035 | + | 0.992278i | \(0.460417\pi\) | |||||||
\(464\) | 0.443419 | 0.0205852 | ||||||||
\(465\) | 17.1228 | 0.794052 | ||||||||
\(466\) | −28.2061 | −1.30662 | ||||||||
\(467\) | −1.53163 | −0.0708753 | −0.0354377 | − | 0.999372i | \(-0.511283\pi\) | ||||
−0.0354377 | + | 0.999372i | \(0.511283\pi\) | |||||||
\(468\) | 6.62249 | 0.306125 | ||||||||
\(469\) | −46.6869 | −2.15580 | ||||||||
\(470\) | −6.50270 | −0.299947 | ||||||||
\(471\) | 0.0556453 | 0.00256400 | ||||||||
\(472\) | 10.8913 | 0.501311 | ||||||||
\(473\) | 2.15577 | 0.0991225 | ||||||||
\(474\) | 6.26866 | 0.287929 | ||||||||
\(475\) | 4.47119 | 0.205152 | ||||||||
\(476\) | 8.67356 | 0.397552 | ||||||||
\(477\) | −30.7166 | −1.40641 | ||||||||
\(478\) | −21.9897 | −1.00578 | ||||||||
\(479\) | 3.56502 | 0.162890 | 0.0814449 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814449 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(480\) | 2.09395 | 0.0955754 | ||||||||
\(481\) | 0.0518988 | 0.00236638 | ||||||||
\(482\) | −9.92311 | −0.451985 | ||||||||
\(483\) | −65.9894 | −3.00262 | ||||||||
\(484\) | 2.09101 | 0.0950461 | ||||||||
\(485\) | 2.36107 | 0.107211 | ||||||||
\(486\) | 10.7945 | 0.489649 | ||||||||
\(487\) | −10.4722 | −0.474539 | −0.237270 | − | 0.971444i | \(-0.576253\pi\) | ||||
−0.237270 | + | 0.971444i | \(0.576253\pi\) | |||||||
\(488\) | −6.38286 | −0.288939 | ||||||||
\(489\) | −23.9743 | −1.08415 | ||||||||
\(490\) | −6.95459 | −0.314176 | ||||||||
\(491\) | −12.1043 | −0.546258 | −0.273129 | − | 0.961977i | \(-0.588059\pi\) | ||||
−0.273129 | + | 0.961977i | \(0.588059\pi\) | |||||||
\(492\) | 7.66279 | 0.345465 | ||||||||
\(493\) | −0.945004 | −0.0425608 | ||||||||
\(494\) | −1.25152 | −0.0563085 | ||||||||
\(495\) | −13.9226 | −0.625773 | ||||||||
\(496\) | 8.17728 | 0.367171 | ||||||||
\(497\) | 13.7833 | 0.618266 | ||||||||
\(498\) | −9.59900 | −0.430142 | ||||||||
\(499\) | −2.11949 | −0.0948813 | −0.0474407 | − | 0.998874i | \(-0.515107\pi\) | ||||
−0.0474407 | + | 0.998874i | \(0.515107\pi\) | |||||||
\(500\) | 6.88737 | 0.308012 | ||||||||
\(501\) | 38.0273 | 1.69893 | ||||||||
\(502\) | −19.4864 | −0.869721 | ||||||||
\(503\) | 9.18172 | 0.409393 | 0.204696 | − | 0.978826i | \(-0.434379\pi\) | ||||
0.204696 | + | 0.978826i | \(0.434379\pi\) | |||||||
\(504\) | −21.5358 | −0.959283 | ||||||||
\(505\) | −2.05375 | −0.0913906 | ||||||||
\(506\) | −20.3735 | −0.905710 | ||||||||
\(507\) | 32.9234 | 1.46218 | ||||||||
\(508\) | −3.18628 | −0.141368 | ||||||||
\(509\) | −27.0872 | −1.20062 | −0.600310 | − | 0.799768i | \(-0.704956\pi\) | ||||
−0.600310 | + | 0.799768i | \(0.704956\pi\) | |||||||
\(510\) | −4.46258 | −0.197606 | ||||||||
\(511\) | 0.236462 | 0.0104604 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.59857 | 0.291334 | ||||||||
\(514\) | 0.644104 | 0.0284102 | ||||||||
\(515\) | 6.86837 | 0.302657 | ||||||||
\(516\) | −1.71567 | −0.0755283 | ||||||||
\(517\) | 32.3543 | 1.42294 | ||||||||
\(518\) | −0.168771 | −0.00741536 | ||||||||
\(519\) | −32.5968 | −1.43084 | ||||||||
\(520\) | −0.910093 | −0.0399102 | ||||||||
\(521\) | 13.3292 | 0.583962 | 0.291981 | − | 0.956424i | \(-0.405686\pi\) | ||||
0.291981 | + | 0.956424i | \(0.405686\pi\) | |||||||
\(522\) | 2.34638 | 0.102698 | ||||||||
\(523\) | −13.2761 | −0.580524 | −0.290262 | − | 0.956947i | \(-0.593743\pi\) | ||||
−0.290262 | + | 0.956947i | \(0.593743\pi\) | |||||||
\(524\) | −3.63269 | −0.158695 | ||||||||
\(525\) | −52.3986 | −2.28686 | ||||||||
\(526\) | −0.0603677 | −0.00263216 | ||||||||
\(527\) | −17.4272 | −0.759142 | ||||||||
\(528\) | −10.4185 | −0.453407 | ||||||||
\(529\) | 8.70707 | 0.378568 | ||||||||
\(530\) | 4.22121 | 0.183358 | ||||||||
\(531\) | 57.6318 | 2.50101 | ||||||||
\(532\) | 4.06984 | 0.176450 | ||||||||
\(533\) | −3.33048 | −0.144259 | ||||||||
\(534\) | −38.8378 | −1.68068 | ||||||||
\(535\) | −2.81111 | −0.121535 | ||||||||
\(536\) | 11.4714 | 0.495490 | ||||||||
\(537\) | 49.5485 | 2.13818 | ||||||||
\(538\) | −9.66382 | −0.416637 | ||||||||
\(539\) | 34.6027 | 1.49044 | ||||||||
\(540\) | 4.79842 | 0.206491 | ||||||||
\(541\) | −13.0079 | −0.559254 | −0.279627 | − | 0.960109i | \(-0.590211\pi\) | ||||
−0.279627 | + | 0.960109i | \(0.590211\pi\) | |||||||
\(542\) | 8.86078 | 0.380603 | ||||||||
\(543\) | 3.18570 | 0.136712 | ||||||||
\(544\) | −2.13118 | −0.0913734 | ||||||||
\(545\) | −6.78342 | −0.290570 | ||||||||
\(546\) | 14.6667 | 0.627678 | ||||||||
\(547\) | −41.0881 | −1.75680 | −0.878401 | − | 0.477925i | \(-0.841389\pi\) | ||||
−0.878401 | + | 0.477925i | \(0.841389\pi\) | |||||||
\(548\) | −17.3661 | −0.741841 | ||||||||
\(549\) | −33.7753 | −1.44150 | ||||||||
\(550\) | −16.1774 | −0.689809 | ||||||||
\(551\) | −0.443419 | −0.0188903 | ||||||||
\(552\) | 16.2142 | 0.690123 | ||||||||
\(553\) | 8.86001 | 0.376766 | ||||||||
\(554\) | −14.2875 | −0.607016 | ||||||||
\(555\) | 0.0868333 | 0.00368587 | ||||||||
\(556\) | 4.12808 | 0.175069 | ||||||||
\(557\) | 0.106449 | 0.00451039 | 0.00225519 | − | 0.999997i | \(-0.499282\pi\) | ||||
0.00225519 | + | 0.999997i | \(0.499282\pi\) | |||||||
\(558\) | 43.2706 | 1.83179 | ||||||||
\(559\) | 0.745682 | 0.0315390 | ||||||||
\(560\) | 2.95955 | 0.125064 | ||||||||
\(561\) | 22.2036 | 0.937439 | ||||||||
\(562\) | −5.91818 | −0.249643 | ||||||||
\(563\) | 1.13878 | 0.0479937 | 0.0239969 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239969 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(564\) | −25.7492 | −1.08424 | ||||||||
\(565\) | 0.608629 | 0.0256052 | ||||||||
\(566\) | −13.7719 | −0.578874 | ||||||||
\(567\) | −12.7222 | −0.534280 | ||||||||
\(568\) | −3.38669 | −0.142102 | ||||||||
\(569\) | −10.9775 | −0.460199 | −0.230099 | − | 0.973167i | \(-0.573905\pi\) | ||||
−0.230099 | + | 0.973167i | \(0.573905\pi\) | |||||||
\(570\) | −2.09395 | −0.0877060 | ||||||||
\(571\) | −0.745682 | −0.0312058 | −0.0156029 | − | 0.999878i | \(-0.504967\pi\) | ||||
−0.0156029 | + | 0.999878i | \(0.504967\pi\) | |||||||
\(572\) | 4.52818 | 0.189333 | ||||||||
\(573\) | −50.7678 | −2.12086 | ||||||||
\(574\) | 10.8305 | 0.452054 | ||||||||
\(575\) | 25.1769 | 1.04995 | ||||||||
\(576\) | 5.29156 | 0.220482 | ||||||||
\(577\) | −20.6012 | −0.857640 | −0.428820 | − | 0.903390i | \(-0.641071\pi\) | ||||
−0.428820 | + | 0.903390i | \(0.641071\pi\) | |||||||
\(578\) | −12.4581 | −0.518188 | ||||||||
\(579\) | 35.8042 | 1.48797 | ||||||||
\(580\) | −0.322450 | −0.0133890 | ||||||||
\(581\) | −13.5671 | −0.562856 | ||||||||
\(582\) | 9.34929 | 0.387540 | ||||||||
\(583\) | −21.0027 | −0.869843 | ||||||||
\(584\) | −0.0581009 | −0.00240423 | ||||||||
\(585\) | −4.81582 | −0.199110 | ||||||||
\(586\) | −18.6214 | −0.769243 | ||||||||
\(587\) | 32.2233 | 1.33000 | 0.664999 | − | 0.746844i | \(-0.268432\pi\) | ||||
0.664999 | + | 0.746844i | \(0.268432\pi\) | |||||||
\(588\) | −27.5386 | −1.13567 | ||||||||
\(589\) | −8.17728 | −0.336939 | ||||||||
\(590\) | −7.92002 | −0.326062 | ||||||||
\(591\) | 26.4496 | 1.08799 | ||||||||
\(592\) | 0.0414686 | 0.00170435 | ||||||||
\(593\) | −10.3355 | −0.424430 | −0.212215 | − | 0.977223i | \(-0.568068\pi\) | ||||
−0.212215 | + | 0.977223i | \(0.568068\pi\) | |||||||
\(594\) | −23.8746 | −0.979588 | ||||||||
\(595\) | −6.30733 | −0.258575 | ||||||||
\(596\) | 9.75805 | 0.399705 | ||||||||
\(597\) | 6.95307 | 0.284570 | ||||||||
\(598\) | −7.04718 | −0.288181 | ||||||||
\(599\) | −15.9956 | −0.653562 | −0.326781 | − | 0.945100i | \(-0.605964\pi\) | ||||
−0.326781 | + | 0.945100i | \(0.605964\pi\) | |||||||
\(600\) | 12.8748 | 0.525613 | ||||||||
\(601\) | 39.0766 | 1.59397 | 0.796983 | − | 0.604002i | \(-0.206428\pi\) | ||||
0.796983 | + | 0.604002i | \(0.206428\pi\) | |||||||
\(602\) | −2.42490 | −0.0988316 | ||||||||
\(603\) | 60.7017 | 2.47196 | ||||||||
\(604\) | 5.86077 | 0.238471 | ||||||||
\(605\) | −1.52057 | −0.0618198 | ||||||||
\(606\) | −8.13237 | −0.330355 | ||||||||
\(607\) | −11.8746 | −0.481975 | −0.240988 | − | 0.970528i | \(-0.577471\pi\) | ||||
−0.240988 | + | 0.970528i | \(0.577471\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 5.19649 | 0.210572 | ||||||||
\(610\) | 4.64156 | 0.187931 | ||||||||
\(611\) | 11.1913 | 0.452753 | ||||||||
\(612\) | −11.2773 | −0.455856 | ||||||||
\(613\) | −43.5432 | −1.75869 | −0.879346 | − | 0.476184i | \(-0.842020\pi\) | ||||
−0.879346 | + | 0.476184i | \(0.842020\pi\) | |||||||
\(614\) | 14.2345 | 0.574459 | ||||||||
\(615\) | −5.57231 | −0.224697 | ||||||||
\(616\) | −14.7253 | −0.593300 | ||||||||
\(617\) | −40.7667 | −1.64121 | −0.820603 | − | 0.571499i | \(-0.806362\pi\) | ||||
−0.820603 | + | 0.571499i | \(0.806362\pi\) | |||||||
\(618\) | 27.1972 | 1.09403 | ||||||||
\(619\) | 18.8604 | 0.758064 | 0.379032 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379032 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(620\) | −5.94644 | −0.238815 | ||||||||
\(621\) | 37.1559 | 1.49102 | ||||||||
\(622\) | 7.14179 | 0.286360 | ||||||||
\(623\) | −54.8926 | −2.19923 | ||||||||
\(624\) | −3.60376 | −0.144266 | ||||||||
\(625\) | 17.3475 | 0.693901 | ||||||||
\(626\) | −28.6539 | −1.14524 | ||||||||
\(627\) | 10.4185 | 0.416074 | ||||||||
\(628\) | −0.0193246 | −0.000771136 0 | ||||||||
\(629\) | −0.0883769 | −0.00352382 | ||||||||
\(630\) | 15.6607 | 0.623936 | ||||||||
\(631\) | 11.6827 | 0.465080 | 0.232540 | − | 0.972587i | \(-0.425296\pi\) | ||||
0.232540 | + | 0.972587i | \(0.425296\pi\) | |||||||
\(632\) | −2.17699 | −0.0865960 | ||||||||
\(633\) | −2.87951 | −0.114450 | ||||||||
\(634\) | −21.7416 | −0.863467 | ||||||||
\(635\) | 2.31703 | 0.0919486 | ||||||||
\(636\) | 16.7150 | 0.662794 | ||||||||
\(637\) | 11.9691 | 0.474232 | ||||||||
\(638\) | 1.60436 | 0.0635171 | ||||||||
\(639\) | −17.9209 | −0.708939 | ||||||||
\(640\) | −0.727191 | −0.0287448 | ||||||||
\(641\) | −35.7350 | −1.41145 | −0.705723 | − | 0.708487i | \(-0.749378\pi\) | ||||
−0.705723 | + | 0.708487i | \(0.749378\pi\) | |||||||
\(642\) | −11.1313 | −0.439318 | ||||||||
\(643\) | −46.6155 | −1.83834 | −0.919168 | − | 0.393867i | \(-0.871137\pi\) | ||||
−0.919168 | + | 0.393867i | \(0.871137\pi\) | |||||||
\(644\) | 22.9169 | 0.903052 | ||||||||
\(645\) | 1.24762 | 0.0491251 | ||||||||
\(646\) | 2.13118 | 0.0838500 | ||||||||
\(647\) | 16.3173 | 0.641501 | 0.320751 | − | 0.947164i | \(-0.396065\pi\) | ||||
0.320751 | + | 0.947164i | \(0.396065\pi\) | |||||||
\(648\) | 3.12595 | 0.122799 | ||||||||
\(649\) | 39.4062 | 1.54683 | ||||||||
\(650\) | −5.59578 | −0.219485 | ||||||||
\(651\) | 95.8308 | 3.75590 | ||||||||
\(652\) | 8.32582 | 0.326064 | ||||||||
\(653\) | 27.1392 | 1.06204 | 0.531019 | − | 0.847360i | \(-0.321809\pi\) | ||||
0.531019 | + | 0.847360i | \(0.321809\pi\) | |||||||
\(654\) | −26.8608 | −1.05034 | ||||||||
\(655\) | 2.64166 | 0.103218 | ||||||||
\(656\) | −2.66115 | −0.103900 | ||||||||
\(657\) | −0.307444 | −0.0119945 | ||||||||
\(658\) | −36.3934 | −1.41876 | ||||||||
\(659\) | −7.66391 | −0.298544 | −0.149272 | − | 0.988796i | \(-0.547693\pi\) | ||||
−0.149272 | + | 0.988796i | \(0.547693\pi\) | |||||||
\(660\) | 7.57623 | 0.294905 | ||||||||
\(661\) | 23.2412 | 0.903976 | 0.451988 | − | 0.892024i | \(-0.350715\pi\) | ||||
0.451988 | + | 0.892024i | \(0.350715\pi\) | |||||||
\(662\) | −30.5077 | −1.18571 | ||||||||
\(663\) | 7.68024 | 0.298276 | ||||||||
\(664\) | 3.33356 | 0.129367 | ||||||||
\(665\) | −2.95955 | −0.114767 | ||||||||
\(666\) | 0.219434 | 0.00850289 | ||||||||
\(667\) | −2.49685 | −0.0966784 | ||||||||
\(668\) | −13.2062 | −0.510962 | ||||||||
\(669\) | −15.2909 | −0.591181 | ||||||||
\(670\) | −8.34191 | −0.322276 | ||||||||
\(671\) | −23.0942 | −0.891540 | ||||||||
\(672\) | 11.7191 | 0.452076 | ||||||||
\(673\) | 25.5452 | 0.984696 | 0.492348 | − | 0.870399i | \(-0.336139\pi\) | ||||
0.492348 | + | 0.870399i | \(0.336139\pi\) | |||||||
\(674\) | −1.44029 | −0.0554778 | ||||||||
\(675\) | 29.5035 | 1.13559 | ||||||||
\(676\) | −11.4337 | −0.439758 | ||||||||
\(677\) | 22.6780 | 0.871585 | 0.435792 | − | 0.900047i | \(-0.356468\pi\) | ||||
0.435792 | + | 0.900047i | \(0.356468\pi\) | |||||||
\(678\) | 2.41003 | 0.0925566 | ||||||||
\(679\) | 13.2141 | 0.507111 | ||||||||
\(680\) | 1.54977 | 0.0594311 | ||||||||
\(681\) | −6.44673 | −0.247039 | ||||||||
\(682\) | 29.5866 | 1.13293 | ||||||||
\(683\) | −13.8440 | −0.529726 | −0.264863 | − | 0.964286i | \(-0.585327\pi\) | ||||
−0.264863 | + | 0.964286i | \(0.585327\pi\) | |||||||
\(684\) | −5.29156 | −0.202328 | ||||||||
\(685\) | 12.6284 | 0.482508 | ||||||||
\(686\) | −10.4336 | −0.398357 | ||||||||
\(687\) | 32.6076 | 1.24406 | ||||||||
\(688\) | 0.595822 | 0.0227155 | ||||||||
\(689\) | −7.26484 | −0.276768 | ||||||||
\(690\) | −11.7908 | −0.448870 | ||||||||
\(691\) | −23.2928 | −0.886100 | −0.443050 | − | 0.896497i | \(-0.646104\pi\) | ||||
−0.443050 | + | 0.896497i | \(0.646104\pi\) | |||||||
\(692\) | 11.3203 | 0.430332 | ||||||||
\(693\) | −77.9199 | −2.95993 | ||||||||
\(694\) | −18.2248 | −0.691805 | ||||||||
\(695\) | −3.00190 | −0.113869 | ||||||||
\(696\) | −1.27683 | −0.0483980 | ||||||||
\(697\) | 5.67137 | 0.214819 | ||||||||
\(698\) | −7.30817 | −0.276618 | ||||||||
\(699\) | 81.2196 | 3.07201 | ||||||||
\(700\) | 18.1971 | 0.687784 | ||||||||
\(701\) | −10.8702 | −0.410563 | −0.205281 | − | 0.978703i | \(-0.565811\pi\) | ||||
−0.205281 | + | 0.978703i | \(0.565811\pi\) | |||||||
\(702\) | −8.25824 | −0.311687 | ||||||||
\(703\) | −0.0414686 | −0.00156402 | ||||||||
\(704\) | 3.61815 | 0.136364 | ||||||||
\(705\) | 18.7246 | 0.705208 | ||||||||
\(706\) | −23.4595 | −0.882911 | ||||||||
\(707\) | −11.4941 | −0.432282 | ||||||||
\(708\) | −31.3614 | −1.17864 | ||||||||
\(709\) | 8.42575 | 0.316436 | 0.158218 | − | 0.987404i | \(-0.449425\pi\) | ||||
0.158218 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(710\) | 2.46277 | 0.0924261 | ||||||||
\(711\) | −11.5197 | −0.432022 | ||||||||
\(712\) | 13.4876 | 0.505471 | ||||||||
\(713\) | −46.0455 | −1.72442 | ||||||||
\(714\) | −24.9756 | −0.934687 | ||||||||
\(715\) | −3.29286 | −0.123146 | ||||||||
\(716\) | −17.2073 | −0.643067 | ||||||||
\(717\) | 63.3195 | 2.36471 | ||||||||
\(718\) | 30.3218 | 1.13160 | ||||||||
\(719\) | −19.2836 | −0.719157 | −0.359578 | − | 0.933115i | \(-0.617079\pi\) | ||||
−0.359578 | + | 0.933115i | \(0.617079\pi\) | |||||||
\(720\) | −3.84798 | −0.143406 | ||||||||
\(721\) | 38.4400 | 1.43158 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 28.5737 | 1.06267 | ||||||||
\(724\) | −1.10634 | −0.0411167 | ||||||||
\(725\) | −1.98261 | −0.0736323 | ||||||||
\(726\) | −6.02109 | −0.223464 | ||||||||
\(727\) | 16.1273 | 0.598128 | 0.299064 | − | 0.954233i | \(-0.403326\pi\) | ||||
0.299064 | + | 0.954233i | \(0.403326\pi\) | |||||||
\(728\) | −5.09349 | −0.188777 | ||||||||
\(729\) | −40.4607 | −1.49855 | ||||||||
\(730\) | 0.0422504 | 0.00156376 | ||||||||
\(731\) | −1.26980 | −0.0469653 | ||||||||
\(732\) | 18.3795 | 0.679326 | ||||||||
\(733\) | 15.4925 | 0.572227 | 0.286113 | − | 0.958196i | \(-0.407637\pi\) | ||||
0.286113 | + | 0.958196i | \(0.407637\pi\) | |||||||
\(734\) | −12.2097 | −0.450667 | ||||||||
\(735\) | 20.0258 | 0.738663 | ||||||||
\(736\) | −5.63090 | −0.207558 | ||||||||
\(737\) | 41.5053 | 1.52887 | ||||||||
\(738\) | −14.0816 | −0.518352 | ||||||||
\(739\) | −42.0235 | −1.54586 | −0.772929 | − | 0.634492i | \(-0.781209\pi\) | ||||
−0.772929 | + | 0.634492i | \(0.781209\pi\) | |||||||
\(740\) | −0.0301556 | −0.00110854 | ||||||||
\(741\) | 3.60376 | 0.132387 | ||||||||
\(742\) | 23.6247 | 0.867290 | ||||||||
\(743\) | −12.5997 | −0.462237 | −0.231119 | − | 0.972926i | \(-0.574239\pi\) | ||||
−0.231119 | + | 0.972926i | \(0.574239\pi\) | |||||||
\(744\) | −23.5465 | −0.863258 | ||||||||
\(745\) | −7.09597 | −0.259976 | ||||||||
\(746\) | 31.6590 | 1.15912 | ||||||||
\(747\) | 17.6397 | 0.645404 | ||||||||
\(748\) | −7.71092 | −0.281939 | ||||||||
\(749\) | −15.7328 | −0.574865 | ||||||||
\(750\) | −19.8322 | −0.724171 | ||||||||
\(751\) | 22.2269 | 0.811071 | 0.405536 | − | 0.914079i | \(-0.367085\pi\) | ||||
0.405536 | + | 0.914079i | \(0.367085\pi\) | |||||||
\(752\) | 8.94221 | 0.326089 | ||||||||
\(753\) | 56.1113 | 2.04481 | ||||||||
\(754\) | 0.554947 | 0.0202100 | ||||||||
\(755\) | −4.26190 | −0.155106 | ||||||||
\(756\) | 26.8552 | 0.976713 | ||||||||
\(757\) | 16.6377 | 0.604708 | 0.302354 | − | 0.953196i | \(-0.402228\pi\) | ||||
0.302354 | + | 0.953196i | \(0.402228\pi\) | |||||||
\(758\) | −0.430657 | −0.0156422 | ||||||||
\(759\) | 58.6655 | 2.12942 | ||||||||
\(760\) | 0.727191 | 0.0263780 | ||||||||
\(761\) | 2.68070 | 0.0971751 | 0.0485876 | − | 0.998819i | \(-0.484528\pi\) | ||||
0.0485876 | + | 0.998819i | \(0.484528\pi\) | |||||||
\(762\) | 9.17491 | 0.332372 | ||||||||
\(763\) | −37.9645 | −1.37441 | ||||||||
\(764\) | 17.6307 | 0.637858 | ||||||||
\(765\) | 8.20072 | 0.296498 | ||||||||
\(766\) | −7.69215 | −0.277929 | ||||||||
\(767\) | 13.6306 | 0.492173 | ||||||||
\(768\) | −2.87951 | −0.103905 | ||||||||
\(769\) | 9.33180 | 0.336513 | 0.168257 | − | 0.985743i | \(-0.446186\pi\) | ||||
0.168257 | + | 0.985743i | \(0.446186\pi\) | |||||||
\(770\) | 10.7081 | 0.385894 | ||||||||
\(771\) | −1.85470 | −0.0667955 | ||||||||
\(772\) | −12.4341 | −0.447514 | ||||||||
\(773\) | 30.6134 | 1.10109 | 0.550544 | − | 0.834806i | \(-0.314420\pi\) | ||||
0.550544 | + | 0.834806i | \(0.314420\pi\) | |||||||
\(774\) | 3.15283 | 0.113326 | ||||||||
\(775\) | −36.5622 | −1.31335 | ||||||||
\(776\) | −3.24683 | −0.116555 | ||||||||
\(777\) | 0.485977 | 0.0174343 | ||||||||
\(778\) | −3.32939 | −0.119364 | ||||||||
\(779\) | 2.66115 | 0.0953455 | ||||||||
\(780\) | 2.62062 | 0.0938333 | ||||||||
\(781\) | −12.2536 | −0.438467 | ||||||||
\(782\) | 12.0004 | 0.429135 | ||||||||
\(783\) | −2.92593 | −0.104564 | ||||||||
\(784\) | 9.56364 | 0.341558 | ||||||||
\(785\) | 0.0140527 | 0.000501562 0 | ||||||||
\(786\) | 10.4604 | 0.373108 | ||||||||
\(787\) | −44.4661 | −1.58504 | −0.792522 | − | 0.609843i | \(-0.791232\pi\) | ||||
−0.792522 | + | 0.609843i | \(0.791232\pi\) | |||||||
\(788\) | −9.18547 | −0.327219 | ||||||||
\(789\) | 0.173829 | 0.00618848 | ||||||||
\(790\) | 1.58309 | 0.0563237 | ||||||||
\(791\) | 3.40629 | 0.121114 | ||||||||
\(792\) | 19.1457 | 0.680312 | ||||||||
\(793\) | −7.98827 | −0.283672 | ||||||||
\(794\) | 31.1952 | 1.10708 | ||||||||
\(795\) | −12.1550 | −0.431094 | ||||||||
\(796\) | −2.41467 | −0.0855858 | ||||||||
\(797\) | −26.0737 | −0.923579 | −0.461789 | − | 0.886990i | \(-0.652792\pi\) | ||||
−0.461789 | + | 0.886990i | \(0.652792\pi\) | |||||||
\(798\) | −11.7191 | −0.414853 | ||||||||
\(799\) | −19.0574 | −0.674203 | ||||||||
\(800\) | −4.47119 | −0.158081 | ||||||||
\(801\) | 71.3708 | 2.52176 | ||||||||
\(802\) | −22.8724 | −0.807653 | ||||||||
\(803\) | −0.210218 | −0.00741842 | ||||||||
\(804\) | −33.0320 | −1.16495 | ||||||||
\(805\) | −16.6650 | −0.587363 | ||||||||
\(806\) | 10.2340 | 0.360478 | ||||||||
\(807\) | 27.8270 | 0.979558 | ||||||||
\(808\) | 2.82422 | 0.0993558 | ||||||||
\(809\) | 56.0474 | 1.97052 | 0.985260 | − | 0.171061i | \(-0.0547196\pi\) | ||||
0.985260 | + | 0.171061i | \(0.0547196\pi\) | |||||||
\(810\) | −2.27317 | −0.0798709 | ||||||||
\(811\) | 17.3713 | 0.609990 | 0.304995 | − | 0.952354i | \(-0.401345\pi\) | ||||
0.304995 | + | 0.952354i | \(0.401345\pi\) | |||||||
\(812\) | −1.80465 | −0.0633307 | ||||||||
\(813\) | −25.5147 | −0.894839 | ||||||||
\(814\) | 0.150040 | 0.00525889 | ||||||||
\(815\) | −6.05446 | −0.212079 | ||||||||
\(816\) | 6.13674 | 0.214829 | ||||||||
\(817\) | −0.595822 | −0.0208452 | ||||||||
\(818\) | 15.5779 | 0.544667 | ||||||||
\(819\) | −26.9525 | −0.941797 | ||||||||
\(820\) | 1.93516 | 0.0675788 | ||||||||
\(821\) | 23.8709 | 0.833100 | 0.416550 | − | 0.909113i | \(-0.363239\pi\) | ||||
0.416550 | + | 0.909113i | \(0.363239\pi\) | |||||||
\(822\) | 50.0057 | 1.74415 | ||||||||
\(823\) | 30.6630 | 1.06885 | 0.534423 | − | 0.845217i | \(-0.320529\pi\) | ||||
0.534423 | + | 0.845217i | \(0.320529\pi\) | |||||||
\(824\) | −9.44507 | −0.329035 | ||||||||
\(825\) | 46.5831 | 1.62181 | ||||||||
\(826\) | −44.3257 | −1.54229 | ||||||||
\(827\) | −3.72261 | −0.129448 | −0.0647239 | − | 0.997903i | \(-0.520617\pi\) | ||||
−0.0647239 | + | 0.997903i | \(0.520617\pi\) | |||||||
\(828\) | −29.7963 | −1.03549 | ||||||||
\(829\) | 30.8489 | 1.07143 | 0.535714 | − | 0.844400i | \(-0.320043\pi\) | ||||
0.535714 | + | 0.844400i | \(0.320043\pi\) | |||||||
\(830\) | −2.42413 | −0.0841429 | ||||||||
\(831\) | 41.1408 | 1.42716 | ||||||||
\(832\) | 1.25152 | 0.0433886 | ||||||||
\(833\) | −20.3818 | −0.706187 | ||||||||
\(834\) | −11.8868 | −0.411607 | ||||||||
\(835\) | 9.60341 | 0.332340 | ||||||||
\(836\) | −3.61815 | −0.125136 | ||||||||
\(837\) | −53.9584 | −1.86507 | ||||||||
\(838\) | 22.7946 | 0.787427 | ||||||||
\(839\) | −1.73237 | −0.0598079 | −0.0299039 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299039 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(840\) | −8.52206 | −0.294039 | ||||||||
\(841\) | −28.8034 | −0.993220 | ||||||||
\(842\) | −3.48327 | −0.120042 | ||||||||
\(843\) | 17.0414 | 0.586938 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | 8.31449 | 0.286027 | ||||||||
\(846\) | 47.3183 | 1.62684 | ||||||||
\(847\) | −8.51010 | −0.292411 | ||||||||
\(848\) | −5.80482 | −0.199338 | ||||||||
\(849\) | 39.6562 | 1.36100 | ||||||||
\(850\) | 9.52890 | 0.326839 | ||||||||
\(851\) | −0.233506 | −0.00800447 | ||||||||
\(852\) | 9.75200 | 0.334098 | ||||||||
\(853\) | 17.7543 | 0.607895 | 0.303948 | − | 0.952689i | \(-0.401695\pi\) | ||||
0.303948 | + | 0.952689i | \(0.401695\pi\) | |||||||
\(854\) | 25.9773 | 0.888923 | ||||||||
\(855\) | 3.84798 | 0.131598 | ||||||||
\(856\) | 3.86570 | 0.132127 | ||||||||
\(857\) | −30.0164 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(858\) | −13.0389 | −0.445142 | ||||||||
\(859\) | 20.4155 | 0.696568 | 0.348284 | − | 0.937389i | \(-0.386765\pi\) | ||||
0.348284 | + | 0.937389i | \(0.386765\pi\) | |||||||
\(860\) | −0.433276 | −0.0147746 | ||||||||
\(861\) | −31.1864 | −1.06283 | ||||||||
\(862\) | −13.5984 | −0.463165 | ||||||||
\(863\) | 38.7224 | 1.31813 | 0.659063 | − | 0.752088i | \(-0.270953\pi\) | ||||
0.659063 | + | 0.752088i | \(0.270953\pi\) | |||||||
\(864\) | −6.59857 | −0.224488 | ||||||||
\(865\) | −8.23200 | −0.279896 | ||||||||
\(866\) | 18.4255 | 0.626124 | ||||||||
\(867\) | 35.8732 | 1.21832 | ||||||||
\(868\) | −33.2803 | −1.12961 | ||||||||
\(869\) | −7.87667 | −0.267198 | ||||||||
\(870\) | 0.928498 | 0.0314790 | ||||||||
\(871\) | 14.3567 | 0.486458 | ||||||||
\(872\) | 9.32825 | 0.315895 | ||||||||
\(873\) | −17.1808 | −0.581483 | ||||||||
\(874\) | 5.63090 | 0.190468 | ||||||||
\(875\) | −28.0305 | −0.947604 | ||||||||
\(876\) | 0.167302 | 0.00565261 | ||||||||
\(877\) | 8.77146 | 0.296191 | 0.148096 | − | 0.988973i | \(-0.452686\pi\) | ||||
0.148096 | + | 0.988973i | \(0.452686\pi\) | |||||||
\(878\) | −6.20274 | −0.209332 | ||||||||
\(879\) | 53.6205 | 1.80857 | ||||||||
\(880\) | −2.63109 | −0.0886939 | ||||||||
\(881\) | 34.1193 | 1.14951 | 0.574754 | − | 0.818326i | \(-0.305098\pi\) | ||||
0.574754 | + | 0.818326i | \(0.305098\pi\) | |||||||
\(882\) | 50.6066 | 1.70401 | ||||||||
\(883\) | 9.55329 | 0.321494 | 0.160747 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160747 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(884\) | −2.66721 | −0.0897079 | ||||||||
\(885\) | 22.8058 | 0.766607 | ||||||||
\(886\) | 28.2064 | 0.947614 | ||||||||
\(887\) | −46.7395 | −1.56936 | −0.784680 | − | 0.619901i | \(-0.787173\pi\) | ||||
−0.784680 | + | 0.619901i | \(0.787173\pi\) | |||||||
\(888\) | −0.119409 | −0.00400711 | ||||||||
\(889\) | 12.9677 | 0.434921 | ||||||||
\(890\) | −9.80810 | −0.328768 | ||||||||
\(891\) | 11.3102 | 0.378905 | ||||||||
\(892\) | 5.31025 | 0.177800 | ||||||||
\(893\) | −8.94221 | −0.299240 | ||||||||
\(894\) | −28.0984 | −0.939750 | ||||||||
\(895\) | 12.5130 | 0.418263 | ||||||||
\(896\) | −4.06984 | −0.135964 | ||||||||
\(897\) | 20.2924 | 0.677544 | ||||||||
\(898\) | 5.81064 | 0.193904 | ||||||||
\(899\) | 3.62596 | 0.120933 | ||||||||
\(900\) | −23.6596 | −0.788653 | ||||||||
\(901\) | 12.3711 | 0.412141 | ||||||||
\(902\) | −9.62843 | −0.320592 | ||||||||
\(903\) | 6.98252 | 0.232364 | ||||||||
\(904\) | −0.836958 | −0.0278368 | ||||||||
\(905\) | 0.804518 | 0.0267431 | ||||||||
\(906\) | −16.8761 | −0.560672 | ||||||||
\(907\) | −12.2840 | −0.407885 | −0.203942 | − | 0.978983i | \(-0.565376\pi\) | ||||
−0.203942 | + | 0.978983i | \(0.565376\pi\) | |||||||
\(908\) | 2.23883 | 0.0742982 | ||||||||
\(909\) | 14.9445 | 0.495679 | ||||||||
\(910\) | 3.70394 | 0.122784 | ||||||||
\(911\) | −26.7451 | −0.886106 | −0.443053 | − | 0.896495i | \(-0.646105\pi\) | ||||
−0.443053 | + | 0.896495i | \(0.646105\pi\) | |||||||
\(912\) | 2.87951 | 0.0953500 | ||||||||
\(913\) | 12.0613 | 0.399171 | ||||||||
\(914\) | 10.2851 | 0.340199 | ||||||||
\(915\) | −13.3654 | −0.441847 | ||||||||
\(916\) | −11.3240 | −0.374156 | ||||||||
\(917\) | 14.7845 | 0.488226 | ||||||||
\(918\) | 14.0627 | 0.464139 | ||||||||
\(919\) | 2.88795 | 0.0952646 | 0.0476323 | − | 0.998865i | \(-0.484832\pi\) | ||||
0.0476323 | + | 0.998865i | \(0.484832\pi\) | |||||||
\(920\) | 4.09474 | 0.135000 | ||||||||
\(921\) | −40.9885 | −1.35062 | ||||||||
\(922\) | −33.1091 | −1.09039 | ||||||||
\(923\) | −4.23851 | −0.139512 | ||||||||
\(924\) | 42.4016 | 1.39491 | ||||||||
\(925\) | −0.185414 | −0.00609638 | ||||||||
\(926\) | 5.33782 | 0.175412 | ||||||||
\(927\) | −49.9792 | −1.64153 | ||||||||
\(928\) | 0.443419 | 0.0145559 | ||||||||
\(929\) | −11.4850 | −0.376810 | −0.188405 | − | 0.982091i | \(-0.560332\pi\) | ||||
−0.188405 | + | 0.982091i | \(0.560332\pi\) | |||||||
\(930\) | 17.1228 | 0.561480 | ||||||||
\(931\) | −9.56364 | −0.313436 | ||||||||
\(932\) | −28.2061 | −0.923921 | ||||||||
\(933\) | −20.5648 | −0.673263 | ||||||||
\(934\) | −1.53163 | −0.0501164 | ||||||||
\(935\) | 5.60731 | 0.183379 | ||||||||
\(936\) | 6.62249 | 0.216463 | ||||||||
\(937\) | 30.1168 | 0.983872 | 0.491936 | − | 0.870631i | \(-0.336289\pi\) | ||||
0.491936 | + | 0.870631i | \(0.336289\pi\) | |||||||
\(938\) | −46.6869 | −1.52438 | ||||||||
\(939\) | 82.5090 | 2.69258 | ||||||||
\(940\) | −6.50270 | −0.212095 | ||||||||
\(941\) | −25.0710 | −0.817292 | −0.408646 | − | 0.912693i | \(-0.633999\pi\) | ||||
−0.408646 | + | 0.912693i | \(0.633999\pi\) | |||||||
\(942\) | 0.0556453 | 0.00181302 | ||||||||
\(943\) | 14.9847 | 0.487968 | ||||||||
\(944\) | 10.8913 | 0.354480 | ||||||||
\(945\) | −19.5288 | −0.635273 | ||||||||
\(946\) | 2.15577 | 0.0700902 | ||||||||
\(947\) | −52.8944 | −1.71884 | −0.859419 | − | 0.511272i | \(-0.829174\pi\) | ||||
−0.859419 | + | 0.511272i | \(0.829174\pi\) | |||||||
\(948\) | 6.26866 | 0.203596 | ||||||||
\(949\) | −0.0727143 | −0.00236041 | ||||||||
\(950\) | 4.47119 | 0.145065 | ||||||||
\(951\) | 62.6050 | 2.03011 | ||||||||
\(952\) | 8.67356 | 0.281112 | ||||||||
\(953\) | −12.0514 | −0.390382 | −0.195191 | − | 0.980765i | \(-0.562533\pi\) | ||||
−0.195191 | + | 0.980765i | \(0.562533\pi\) | |||||||
\(954\) | −30.7166 | −0.994486 | ||||||||
\(955\) | −12.8209 | −0.414875 | ||||||||
\(956\) | −21.9897 | −0.711197 | ||||||||
\(957\) | −4.61976 | −0.149335 | ||||||||
\(958\) | 3.56502 | 0.115181 | ||||||||
\(959\) | 70.6772 | 2.28228 | ||||||||
\(960\) | 2.09395 | 0.0675820 | ||||||||
\(961\) | 35.8679 | 1.15703 | ||||||||
\(962\) | 0.0518988 | 0.00167328 | ||||||||
\(963\) | 20.4556 | 0.659173 | ||||||||
\(964\) | −9.92311 | −0.319602 | ||||||||
\(965\) | 9.04199 | 0.291072 | ||||||||
\(966\) | −65.9894 | −2.12317 | ||||||||
\(967\) | −9.90806 | −0.318622 | −0.159311 | − | 0.987228i | \(-0.550927\pi\) | ||||
−0.159311 | + | 0.987228i | \(0.550927\pi\) | |||||||
\(968\) | 2.09101 | 0.0672077 | ||||||||
\(969\) | −6.13674 | −0.197140 | ||||||||
\(970\) | 2.36107 | 0.0758094 | ||||||||
\(971\) | −1.45812 | −0.0467932 | −0.0233966 | − | 0.999726i | \(-0.507448\pi\) | ||||
−0.0233966 | + | 0.999726i | \(0.507448\pi\) | |||||||
\(972\) | 10.7945 | 0.346234 | ||||||||
\(973\) | −16.8006 | −0.538604 | ||||||||
\(974\) | −10.4722 | −0.335550 | ||||||||
\(975\) | 16.1131 | 0.516032 | ||||||||
\(976\) | −6.38286 | −0.204310 | ||||||||
\(977\) | 4.69463 | 0.150195 | 0.0750973 | − | 0.997176i | \(-0.476073\pi\) | ||||
0.0750973 | + | 0.997176i | \(0.476073\pi\) | |||||||
\(978\) | −23.9743 | −0.766612 | ||||||||
\(979\) | 48.8003 | 1.55967 | ||||||||
\(980\) | −6.95459 | −0.222156 | ||||||||
\(981\) | 49.3610 | 1.57598 | ||||||||
\(982\) | −12.1043 | −0.386263 | ||||||||
\(983\) | −39.8447 | −1.27085 | −0.635424 | − | 0.772163i | \(-0.719175\pi\) | ||||
−0.635424 | + | 0.772163i | \(0.719175\pi\) | |||||||
\(984\) | 7.66279 | 0.244281 | ||||||||
\(985\) | 6.67959 | 0.212830 | ||||||||
\(986\) | −0.945004 | −0.0300950 | ||||||||
\(987\) | 104.795 | 3.33566 | ||||||||
\(988\) | −1.25152 | −0.0398161 | ||||||||
\(989\) | −3.35501 | −0.106683 | ||||||||
\(990\) | −13.9226 | −0.442488 | ||||||||
\(991\) | −47.9852 | −1.52430 | −0.762150 | − | 0.647400i | \(-0.775856\pi\) | ||||
−0.762150 | + | 0.647400i | \(0.775856\pi\) | |||||||
\(992\) | 8.17728 | 0.259629 | ||||||||
\(993\) | 87.8471 | 2.78774 | ||||||||
\(994\) | 13.7833 | 0.437180 | ||||||||
\(995\) | 1.75593 | 0.0556667 | ||||||||
\(996\) | −9.59900 | −0.304156 | ||||||||
\(997\) | 7.25910 | 0.229898 | 0.114949 | − | 0.993371i | \(-0.463330\pi\) | ||||
0.114949 | + | 0.993371i | \(0.463330\pi\) | |||||||
\(998\) | −2.11949 | −0.0670912 | ||||||||
\(999\) | −0.273634 | −0.00865739 |
(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 | 8018.2.a.e.1.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.e.1.3 | ✓ | 32 | 1.1 | even | 1 | trivial |