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: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 | ||||||||
\(3\) | −2.35248 | −1.35820 | −0.679102 | − | 0.734044i | \(-0.737631\pi\) | ||||
−0.679102 | + | 0.734044i | \(0.737631\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.260869 | 0.116664 | 0.0583321 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583321 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(6\) | 2.35248 | 0.960396 | ||||||||
\(7\) | 1.92119 | 0.726142 | 0.363071 | − | 0.931762i | \(-0.381728\pi\) | ||||
0.363071 | + | 0.931762i | \(0.381728\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.53416 | 0.844719 | ||||||||
\(10\) | −0.260869 | −0.0824941 | ||||||||
\(11\) | −1.27745 | −0.385166 | −0.192583 | − | 0.981281i | \(-0.561686\pi\) | ||||
−0.192583 | + | 0.981281i | \(0.561686\pi\) | |||||||
\(12\) | −2.35248 | −0.679102 | ||||||||
\(13\) | −3.40018 | −0.943041 | −0.471520 | − | 0.881855i | \(-0.656295\pi\) | ||||
−0.471520 | + | 0.881855i | \(0.656295\pi\) | |||||||
\(14\) | −1.92119 | −0.513460 | ||||||||
\(15\) | −0.613689 | −0.158454 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.10774 | −0.268667 | −0.134334 | − | 0.990936i | \(-0.542889\pi\) | ||||
−0.134334 | + | 0.990936i | \(0.542889\pi\) | |||||||
\(18\) | −2.53416 | −0.597307 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.260869 | 0.0583321 | ||||||||
\(21\) | −4.51956 | −0.986249 | ||||||||
\(22\) | 1.27745 | 0.272353 | ||||||||
\(23\) | −3.07239 | −0.640638 | −0.320319 | − | 0.947310i | \(-0.603790\pi\) | ||||
−0.320319 | + | 0.947310i | \(0.603790\pi\) | |||||||
\(24\) | 2.35248 | 0.480198 | ||||||||
\(25\) | −4.93195 | −0.986389 | ||||||||
\(26\) | 3.40018 | 0.666830 | ||||||||
\(27\) | 1.09588 | 0.210903 | ||||||||
\(28\) | 1.92119 | 0.363071 | ||||||||
\(29\) | 6.82956 | 1.26822 | 0.634109 | − | 0.773244i | \(-0.281367\pi\) | ||||
0.634109 | + | 0.773244i | \(0.281367\pi\) | |||||||
\(30\) | 0.613689 | 0.112044 | ||||||||
\(31\) | 0.607752 | 0.109155 | 0.0545777 | − | 0.998510i | \(-0.482619\pi\) | ||||
0.0545777 | + | 0.998510i | \(0.482619\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.00517 | 0.523134 | ||||||||
\(34\) | 1.10774 | 0.189976 | ||||||||
\(35\) | 0.501179 | 0.0847148 | ||||||||
\(36\) | 2.53416 | 0.422360 | ||||||||
\(37\) | −2.11494 | −0.347694 | −0.173847 | − | 0.984773i | \(-0.555620\pi\) | ||||
−0.173847 | + | 0.984773i | \(0.555620\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 7.99886 | 1.28084 | ||||||||
\(40\) | −0.260869 | −0.0412470 | ||||||||
\(41\) | 8.27764 | 1.29275 | 0.646375 | − | 0.763020i | \(-0.276284\pi\) | ||||
0.646375 | + | 0.763020i | \(0.276284\pi\) | |||||||
\(42\) | 4.51956 | 0.697383 | ||||||||
\(43\) | 7.68294 | 1.17164 | 0.585819 | − | 0.810442i | \(-0.300773\pi\) | ||||
0.585819 | + | 0.810442i | \(0.300773\pi\) | |||||||
\(44\) | −1.27745 | −0.192583 | ||||||||
\(45\) | 0.661084 | 0.0985485 | ||||||||
\(46\) | 3.07239 | 0.452999 | ||||||||
\(47\) | 4.68145 | 0.682860 | 0.341430 | − | 0.939907i | \(-0.389089\pi\) | ||||
0.341430 | + | 0.939907i | \(0.389089\pi\) | |||||||
\(48\) | −2.35248 | −0.339551 | ||||||||
\(49\) | −3.30903 | −0.472718 | ||||||||
\(50\) | 4.93195 | 0.697483 | ||||||||
\(51\) | 2.60594 | 0.364905 | ||||||||
\(52\) | −3.40018 | −0.471520 | ||||||||
\(53\) | −6.26629 | −0.860741 | −0.430371 | − | 0.902652i | \(-0.641617\pi\) | ||||
−0.430371 | + | 0.902652i | \(0.641617\pi\) | |||||||
\(54\) | −1.09588 | −0.149131 | ||||||||
\(55\) | −0.333247 | −0.0449351 | ||||||||
\(56\) | −1.92119 | −0.256730 | ||||||||
\(57\) | −2.35248 | −0.311593 | ||||||||
\(58\) | −6.82956 | −0.896765 | ||||||||
\(59\) | −10.3205 | −1.34362 | −0.671810 | − | 0.740724i | \(-0.734483\pi\) | ||||
−0.671810 | + | 0.740724i | \(0.734483\pi\) | |||||||
\(60\) | −0.613689 | −0.0792269 | ||||||||
\(61\) | 8.15631 | 1.04431 | 0.522155 | − | 0.852851i | \(-0.325128\pi\) | ||||
0.522155 | + | 0.852851i | \(0.325128\pi\) | |||||||
\(62\) | −0.607752 | −0.0771846 | ||||||||
\(63\) | 4.86860 | 0.613386 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.887002 | −0.110019 | ||||||||
\(66\) | −3.00517 | −0.369911 | ||||||||
\(67\) | 3.25511 | 0.397675 | 0.198837 | − | 0.980032i | \(-0.436283\pi\) | ||||
0.198837 | + | 0.980032i | \(0.436283\pi\) | |||||||
\(68\) | −1.10774 | −0.134334 | ||||||||
\(69\) | 7.22773 | 0.870117 | ||||||||
\(70\) | −0.501179 | −0.0599024 | ||||||||
\(71\) | 5.61654 | 0.666561 | 0.333281 | − | 0.942828i | \(-0.391844\pi\) | ||||
0.333281 | + | 0.942828i | \(0.391844\pi\) | |||||||
\(72\) | −2.53416 | −0.298653 | ||||||||
\(73\) | −9.62094 | −1.12605 | −0.563023 | − | 0.826441i | \(-0.690362\pi\) | ||||
−0.563023 | + | 0.826441i | \(0.690362\pi\) | |||||||
\(74\) | 2.11494 | 0.245857 | ||||||||
\(75\) | 11.6023 | 1.33972 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −2.45422 | −0.279685 | ||||||||
\(78\) | −7.99886 | −0.905692 | ||||||||
\(79\) | 6.10531 | 0.686901 | 0.343451 | − | 0.939171i | \(-0.388404\pi\) | ||||
0.343451 | + | 0.939171i | \(0.388404\pi\) | |||||||
\(80\) | 0.260869 | 0.0291661 | ||||||||
\(81\) | −10.1805 | −1.13117 | ||||||||
\(82\) | −8.27764 | −0.914112 | ||||||||
\(83\) | −9.09858 | −0.998699 | −0.499349 | − | 0.866401i | \(-0.666428\pi\) | ||||
−0.499349 | + | 0.866401i | \(0.666428\pi\) | |||||||
\(84\) | −4.51956 | −0.493124 | ||||||||
\(85\) | −0.288976 | −0.0313439 | ||||||||
\(86\) | −7.68294 | −0.828473 | ||||||||
\(87\) | −16.0664 | −1.72250 | ||||||||
\(88\) | 1.27745 | 0.136177 | ||||||||
\(89\) | 14.7652 | 1.56510 | 0.782552 | − | 0.622585i | \(-0.213917\pi\) | ||||
0.782552 | + | 0.622585i | \(0.213917\pi\) | |||||||
\(90\) | −0.661084 | −0.0696843 | ||||||||
\(91\) | −6.53240 | −0.684781 | ||||||||
\(92\) | −3.07239 | −0.320319 | ||||||||
\(93\) | −1.42972 | −0.148255 | ||||||||
\(94\) | −4.68145 | −0.482855 | ||||||||
\(95\) | 0.260869 | 0.0267646 | ||||||||
\(96\) | 2.35248 | 0.240099 | ||||||||
\(97\) | −15.9686 | −1.62137 | −0.810683 | − | 0.585486i | \(-0.800904\pi\) | ||||
−0.810683 | + | 0.585486i | \(0.800904\pi\) | |||||||
\(98\) | 3.30903 | 0.334262 | ||||||||
\(99\) | −3.23726 | −0.325357 | ||||||||
\(100\) | −4.93195 | −0.493195 | ||||||||
\(101\) | −7.00502 | −0.697025 | −0.348513 | − | 0.937304i | \(-0.613313\pi\) | ||||
−0.348513 | + | 0.937304i | \(0.613313\pi\) | |||||||
\(102\) | −2.60594 | −0.258027 | ||||||||
\(103\) | −0.752391 | −0.0741353 | −0.0370677 | − | 0.999313i | \(-0.511802\pi\) | ||||
−0.0370677 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(104\) | 3.40018 | 0.333415 | ||||||||
\(105\) | −1.17901 | −0.115060 | ||||||||
\(106\) | 6.26629 | 0.608636 | ||||||||
\(107\) | −8.46676 | −0.818513 | −0.409256 | − | 0.912419i | \(-0.634212\pi\) | ||||
−0.409256 | + | 0.912419i | \(0.634212\pi\) | |||||||
\(108\) | 1.09588 | 0.105451 | ||||||||
\(109\) | 9.56375 | 0.916041 | 0.458021 | − | 0.888942i | \(-0.348559\pi\) | ||||
0.458021 | + | 0.888942i | \(0.348559\pi\) | |||||||
\(110\) | 0.333247 | 0.0317739 | ||||||||
\(111\) | 4.97536 | 0.472240 | ||||||||
\(112\) | 1.92119 | 0.181535 | ||||||||
\(113\) | 18.0481 | 1.69782 | 0.848911 | − | 0.528536i | \(-0.177259\pi\) | ||||
0.848911 | + | 0.528536i | \(0.177259\pi\) | |||||||
\(114\) | 2.35248 | 0.220330 | ||||||||
\(115\) | −0.801492 | −0.0747395 | ||||||||
\(116\) | 6.82956 | 0.634109 | ||||||||
\(117\) | −8.61660 | −0.796605 | ||||||||
\(118\) | 10.3205 | 0.950082 | ||||||||
\(119\) | −2.12819 | −0.195090 | ||||||||
\(120\) | 0.613689 | 0.0560219 | ||||||||
\(121\) | −9.36812 | −0.851647 | ||||||||
\(122\) | −8.15631 | −0.738438 | ||||||||
\(123\) | −19.4730 | −1.75582 | ||||||||
\(124\) | 0.607752 | 0.0545777 | ||||||||
\(125\) | −2.59094 | −0.231741 | ||||||||
\(126\) | −4.86860 | −0.433729 | ||||||||
\(127\) | 10.2252 | 0.907336 | 0.453668 | − | 0.891171i | \(-0.350115\pi\) | ||||
0.453668 | + | 0.891171i | \(0.350115\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −18.0740 | −1.59132 | ||||||||
\(130\) | 0.887002 | 0.0777953 | ||||||||
\(131\) | 8.84956 | 0.773190 | 0.386595 | − | 0.922250i | \(-0.373651\pi\) | ||||
0.386595 | + | 0.922250i | \(0.373651\pi\) | |||||||
\(132\) | 3.00517 | 0.261567 | ||||||||
\(133\) | 1.92119 | 0.166588 | ||||||||
\(134\) | −3.25511 | −0.281199 | ||||||||
\(135\) | 0.285882 | 0.0246048 | ||||||||
\(136\) | 1.10774 | 0.0949882 | ||||||||
\(137\) | −14.1680 | −1.21046 | −0.605228 | − | 0.796052i | \(-0.706918\pi\) | ||||
−0.605228 | + | 0.796052i | \(0.706918\pi\) | |||||||
\(138\) | −7.22773 | −0.615266 | ||||||||
\(139\) | −15.4875 | −1.31363 | −0.656815 | − | 0.754051i | \(-0.728097\pi\) | ||||
−0.656815 | + | 0.754051i | \(0.728097\pi\) | |||||||
\(140\) | 0.501179 | 0.0423574 | ||||||||
\(141\) | −11.0130 | −0.927464 | ||||||||
\(142\) | −5.61654 | −0.471330 | ||||||||
\(143\) | 4.34356 | 0.363227 | ||||||||
\(144\) | 2.53416 | 0.211180 | ||||||||
\(145\) | 1.78162 | 0.147956 | ||||||||
\(146\) | 9.62094 | 0.796235 | ||||||||
\(147\) | 7.78442 | 0.642048 | ||||||||
\(148\) | −2.11494 | −0.173847 | ||||||||
\(149\) | 7.77181 | 0.636692 | 0.318346 | − | 0.947975i | \(-0.396873\pi\) | ||||
0.318346 | + | 0.947975i | \(0.396873\pi\) | |||||||
\(150\) | −11.6023 | −0.947324 | ||||||||
\(151\) | −14.1832 | −1.15421 | −0.577104 | − | 0.816670i | \(-0.695817\pi\) | ||||
−0.577104 | + | 0.816670i | \(0.695817\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −2.80720 | −0.226948 | ||||||||
\(154\) | 2.45422 | 0.197767 | ||||||||
\(155\) | 0.158544 | 0.0127345 | ||||||||
\(156\) | 7.99886 | 0.640421 | ||||||||
\(157\) | 16.1341 | 1.28764 | 0.643821 | − | 0.765176i | \(-0.277348\pi\) | ||||
0.643821 | + | 0.765176i | \(0.277348\pi\) | |||||||
\(158\) | −6.10531 | −0.485713 | ||||||||
\(159\) | 14.7413 | 1.16906 | ||||||||
\(160\) | −0.260869 | −0.0206235 | ||||||||
\(161\) | −5.90265 | −0.465194 | ||||||||
\(162\) | 10.1805 | 0.799857 | ||||||||
\(163\) | 1.35846 | 0.106403 | 0.0532013 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532013 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(164\) | 8.27764 | 0.646375 | ||||||||
\(165\) | 0.783957 | 0.0610310 | ||||||||
\(166\) | 9.09858 | 0.706186 | ||||||||
\(167\) | 4.78613 | 0.370362 | 0.185181 | − | 0.982704i | \(-0.440713\pi\) | ||||
0.185181 | + | 0.982704i | \(0.440713\pi\) | |||||||
\(168\) | 4.51956 | 0.348692 | ||||||||
\(169\) | −1.43876 | −0.110674 | ||||||||
\(170\) | 0.288976 | 0.0221635 | ||||||||
\(171\) | 2.53416 | 0.193792 | ||||||||
\(172\) | 7.68294 | 0.585819 | ||||||||
\(173\) | 13.6294 | 1.03623 | 0.518113 | − | 0.855312i | \(-0.326635\pi\) | ||||
0.518113 | + | 0.855312i | \(0.326635\pi\) | |||||||
\(174\) | 16.0664 | 1.21799 | ||||||||
\(175\) | −9.47521 | −0.716258 | ||||||||
\(176\) | −1.27745 | −0.0962914 | ||||||||
\(177\) | 24.2788 | 1.82491 | ||||||||
\(178\) | −14.7652 | −1.10670 | ||||||||
\(179\) | −14.3320 | −1.07122 | −0.535612 | − | 0.844464i | \(-0.679919\pi\) | ||||
−0.535612 | + | 0.844464i | \(0.679919\pi\) | |||||||
\(180\) | 0.661084 | 0.0492743 | ||||||||
\(181\) | 20.8693 | 1.55120 | 0.775602 | − | 0.631222i | \(-0.217446\pi\) | ||||
0.775602 | + | 0.631222i | \(0.217446\pi\) | |||||||
\(182\) | 6.53240 | 0.484213 | ||||||||
\(183\) | −19.1876 | −1.41839 | ||||||||
\(184\) | 3.07239 | 0.226500 | ||||||||
\(185\) | −0.551723 | −0.0405635 | ||||||||
\(186\) | 1.42972 | 0.104832 | ||||||||
\(187\) | 1.41509 | 0.103481 | ||||||||
\(188\) | 4.68145 | 0.341430 | ||||||||
\(189\) | 2.10540 | 0.153145 | ||||||||
\(190\) | −0.260869 | −0.0189254 | ||||||||
\(191\) | 2.26218 | 0.163685 | 0.0818426 | − | 0.996645i | \(-0.473920\pi\) | ||||
0.0818426 | + | 0.996645i | \(0.473920\pi\) | |||||||
\(192\) | −2.35248 | −0.169776 | ||||||||
\(193\) | 2.55163 | 0.183670 | 0.0918352 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918352 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(194\) | 15.9686 | 1.14648 | ||||||||
\(195\) | 2.08665 | 0.149428 | ||||||||
\(196\) | −3.30903 | −0.236359 | ||||||||
\(197\) | 1.57928 | 0.112519 | 0.0562596 | − | 0.998416i | \(-0.482083\pi\) | ||||
0.0562596 | + | 0.998416i | \(0.482083\pi\) | |||||||
\(198\) | 3.23726 | 0.230062 | ||||||||
\(199\) | −14.2060 | −1.00704 | −0.503519 | − | 0.863984i | \(-0.667962\pi\) | ||||
−0.503519 | + | 0.863984i | \(0.667962\pi\) | |||||||
\(200\) | 4.93195 | 0.348741 | ||||||||
\(201\) | −7.65758 | −0.540124 | ||||||||
\(202\) | 7.00502 | 0.492871 | ||||||||
\(203\) | 13.1209 | 0.920906 | ||||||||
\(204\) | 2.60594 | 0.182453 | ||||||||
\(205\) | 2.15938 | 0.150818 | ||||||||
\(206\) | 0.752391 | 0.0524216 | ||||||||
\(207\) | −7.78592 | −0.541159 | ||||||||
\(208\) | −3.40018 | −0.235760 | ||||||||
\(209\) | −1.27745 | −0.0883631 | ||||||||
\(210\) | 1.17901 | 0.0813597 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −6.26629 | −0.430371 | ||||||||
\(213\) | −13.2128 | −0.905326 | ||||||||
\(214\) | 8.46676 | 0.578776 | ||||||||
\(215\) | 2.00424 | 0.136688 | ||||||||
\(216\) | −1.09588 | −0.0745654 | ||||||||
\(217\) | 1.16761 | 0.0792624 | ||||||||
\(218\) | −9.56375 | −0.647739 | ||||||||
\(219\) | 22.6331 | 1.52940 | ||||||||
\(220\) | −0.333247 | −0.0224675 | ||||||||
\(221\) | 3.76653 | 0.253364 | ||||||||
\(222\) | −4.97536 | −0.333924 | ||||||||
\(223\) | −12.2039 | −0.817235 | −0.408617 | − | 0.912706i | \(-0.633989\pi\) | ||||
−0.408617 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(224\) | −1.92119 | −0.128365 | ||||||||
\(225\) | −12.4983 | −0.833222 | ||||||||
\(226\) | −18.0481 | −1.20054 | ||||||||
\(227\) | 10.0676 | 0.668213 | 0.334107 | − | 0.942535i | \(-0.391565\pi\) | ||||
0.334107 | + | 0.942535i | \(0.391565\pi\) | |||||||
\(228\) | −2.35248 | −0.155797 | ||||||||
\(229\) | 24.6235 | 1.62717 | 0.813583 | − | 0.581449i | \(-0.197514\pi\) | ||||
0.813583 | + | 0.581449i | \(0.197514\pi\) | |||||||
\(230\) | 0.801492 | 0.0528488 | ||||||||
\(231\) | 5.77351 | 0.379869 | ||||||||
\(232\) | −6.82956 | −0.448383 | ||||||||
\(233\) | 5.42237 | 0.355231 | 0.177616 | − | 0.984100i | \(-0.443162\pi\) | ||||
0.177616 | + | 0.984100i | \(0.443162\pi\) | |||||||
\(234\) | 8.61660 | 0.563285 | ||||||||
\(235\) | 1.22125 | 0.0796654 | ||||||||
\(236\) | −10.3205 | −0.671810 | ||||||||
\(237\) | −14.3626 | −0.932952 | ||||||||
\(238\) | 2.12819 | 0.137950 | ||||||||
\(239\) | 9.09339 | 0.588203 | 0.294101 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294101 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(240\) | −0.613689 | −0.0396135 | ||||||||
\(241\) | 14.2414 | 0.917372 | 0.458686 | − | 0.888598i | \(-0.348320\pi\) | ||||
0.458686 | + | 0.888598i | \(0.348320\pi\) | |||||||
\(242\) | 9.36812 | 0.602206 | ||||||||
\(243\) | 20.6618 | 1.32546 | ||||||||
\(244\) | 8.15631 | 0.522155 | ||||||||
\(245\) | −0.863223 | −0.0551493 | ||||||||
\(246\) | 19.4730 | 1.24155 | ||||||||
\(247\) | −3.40018 | −0.216348 | ||||||||
\(248\) | −0.607752 | −0.0385923 | ||||||||
\(249\) | 21.4042 | 1.35644 | ||||||||
\(250\) | 2.59094 | 0.163865 | ||||||||
\(251\) | 0.637031 | 0.0402090 | 0.0201045 | − | 0.999798i | \(-0.493600\pi\) | ||||
0.0201045 | + | 0.999798i | \(0.493600\pi\) | |||||||
\(252\) | 4.86860 | 0.306693 | ||||||||
\(253\) | 3.92483 | 0.246752 | ||||||||
\(254\) | −10.2252 | −0.641584 | ||||||||
\(255\) | 0.679810 | 0.0425714 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.3218 | −1.57953 | −0.789764 | − | 0.613411i | \(-0.789797\pi\) | ||||
−0.789764 | + | 0.613411i | \(0.789797\pi\) | |||||||
\(258\) | 18.0740 | 1.12524 | ||||||||
\(259\) | −4.06321 | −0.252475 | ||||||||
\(260\) | −0.887002 | −0.0550096 | ||||||||
\(261\) | 17.3072 | 1.07129 | ||||||||
\(262\) | −8.84956 | −0.546728 | ||||||||
\(263\) | 6.84138 | 0.421858 | 0.210929 | − | 0.977501i | \(-0.432351\pi\) | ||||
0.210929 | + | 0.977501i | \(0.432351\pi\) | |||||||
\(264\) | −3.00517 | −0.184956 | ||||||||
\(265\) | −1.63468 | −0.100418 | ||||||||
\(266\) | −1.92119 | −0.117796 | ||||||||
\(267\) | −34.7347 | −2.12573 | ||||||||
\(268\) | 3.25511 | 0.198837 | ||||||||
\(269\) | −2.84734 | −0.173605 | −0.0868027 | − | 0.996226i | \(-0.527665\pi\) | ||||
−0.0868027 | + | 0.996226i | \(0.527665\pi\) | |||||||
\(270\) | −0.285882 | −0.0173982 | ||||||||
\(271\) | −8.49718 | −0.516167 | −0.258084 | − | 0.966123i | \(-0.583091\pi\) | ||||
−0.258084 | + | 0.966123i | \(0.583091\pi\) | |||||||
\(272\) | −1.10774 | −0.0671668 | ||||||||
\(273\) | 15.3673 | 0.930073 | ||||||||
\(274\) | 14.1680 | 0.855922 | ||||||||
\(275\) | 6.30032 | 0.379923 | ||||||||
\(276\) | 7.22773 | 0.435058 | ||||||||
\(277\) | −18.3442 | −1.10219 | −0.551097 | − | 0.834441i | \(-0.685791\pi\) | ||||
−0.551097 | + | 0.834441i | \(0.685791\pi\) | |||||||
\(278\) | 15.4875 | 0.928877 | ||||||||
\(279\) | 1.54014 | 0.0922058 | ||||||||
\(280\) | −0.501179 | −0.0299512 | ||||||||
\(281\) | 4.52281 | 0.269808 | 0.134904 | − | 0.990859i | \(-0.456927\pi\) | ||||
0.134904 | + | 0.990859i | \(0.456927\pi\) | |||||||
\(282\) | 11.0130 | 0.655816 | ||||||||
\(283\) | −27.0942 | −1.61058 | −0.805291 | − | 0.592880i | \(-0.797991\pi\) | ||||
−0.805291 | + | 0.592880i | \(0.797991\pi\) | |||||||
\(284\) | 5.61654 | 0.333281 | ||||||||
\(285\) | −0.613689 | −0.0363518 | ||||||||
\(286\) | −4.34356 | −0.256840 | ||||||||
\(287\) | 15.9029 | 0.938719 | ||||||||
\(288\) | −2.53416 | −0.149327 | ||||||||
\(289\) | −15.7729 | −0.927818 | ||||||||
\(290\) | −1.78162 | −0.104620 | ||||||||
\(291\) | 37.5658 | 2.20215 | ||||||||
\(292\) | −9.62094 | −0.563023 | ||||||||
\(293\) | 6.12466 | 0.357806 | 0.178903 | − | 0.983867i | \(-0.442745\pi\) | ||||
0.178903 | + | 0.983867i | \(0.442745\pi\) | |||||||
\(294\) | −7.78442 | −0.453997 | ||||||||
\(295\) | −2.69231 | −0.156752 | ||||||||
\(296\) | 2.11494 | 0.122928 | ||||||||
\(297\) | −1.39994 | −0.0812326 | ||||||||
\(298\) | −7.77181 | −0.450209 | ||||||||
\(299\) | 10.4467 | 0.604147 | ||||||||
\(300\) | 11.6023 | 0.669859 | ||||||||
\(301\) | 14.7604 | 0.850775 | ||||||||
\(302\) | 14.1832 | 0.816149 | ||||||||
\(303\) | 16.4792 | 0.946703 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 2.12773 | 0.121834 | ||||||||
\(306\) | 2.80720 | 0.160477 | ||||||||
\(307\) | −0.937760 | −0.0535208 | −0.0267604 | − | 0.999642i | \(-0.508519\pi\) | ||||
−0.0267604 | + | 0.999642i | \(0.508519\pi\) | |||||||
\(308\) | −2.45422 | −0.139842 | ||||||||
\(309\) | 1.76998 | 0.100691 | ||||||||
\(310\) | −0.158544 | −0.00900468 | ||||||||
\(311\) | −4.22138 | −0.239373 | −0.119686 | − | 0.992812i | \(-0.538189\pi\) | ||||
−0.119686 | + | 0.992812i | \(0.538189\pi\) | |||||||
\(312\) | −7.99886 | −0.452846 | ||||||||
\(313\) | 27.4989 | 1.55433 | 0.777165 | − | 0.629297i | \(-0.216657\pi\) | ||||
0.777165 | + | 0.629297i | \(0.216657\pi\) | |||||||
\(314\) | −16.1341 | −0.910501 | ||||||||
\(315\) | 1.27007 | 0.0715602 | ||||||||
\(316\) | 6.10531 | 0.343451 | ||||||||
\(317\) | −0.195660 | −0.0109894 | −0.00549468 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549468 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(318\) | −14.7413 | −0.826652 | ||||||||
\(319\) | −8.72442 | −0.488474 | ||||||||
\(320\) | 0.260869 | 0.0145830 | ||||||||
\(321\) | 19.9179 | 1.11171 | ||||||||
\(322\) | 5.90265 | 0.328942 | ||||||||
\(323\) | −1.10774 | −0.0616365 | ||||||||
\(324\) | −10.1805 | −0.565584 | ||||||||
\(325\) | 16.7695 | 0.930205 | ||||||||
\(326\) | −1.35846 | −0.0752381 | ||||||||
\(327\) | −22.4985 | −1.24417 | ||||||||
\(328\) | −8.27764 | −0.457056 | ||||||||
\(329\) | 8.99396 | 0.495853 | ||||||||
\(330\) | −0.783957 | −0.0431554 | ||||||||
\(331\) | −34.5165 | −1.89720 | −0.948599 | − | 0.316481i | \(-0.897498\pi\) | ||||
−0.948599 | + | 0.316481i | \(0.897498\pi\) | |||||||
\(332\) | −9.09858 | −0.499349 | ||||||||
\(333\) | −5.35960 | −0.293704 | ||||||||
\(334\) | −4.78613 | −0.261886 | ||||||||
\(335\) | 0.849158 | 0.0463944 | ||||||||
\(336\) | −4.51956 | −0.246562 | ||||||||
\(337\) | −17.0826 | −0.930546 | −0.465273 | − | 0.885167i | \(-0.654044\pi\) | ||||
−0.465273 | + | 0.885167i | \(0.654044\pi\) | |||||||
\(338\) | 1.43876 | 0.0782585 | ||||||||
\(339\) | −42.4578 | −2.30599 | ||||||||
\(340\) | −0.288976 | −0.0156719 | ||||||||
\(341\) | −0.776373 | −0.0420430 | ||||||||
\(342\) | −2.53416 | −0.137032 | ||||||||
\(343\) | −19.8056 | −1.06940 | ||||||||
\(344\) | −7.68294 | −0.414237 | ||||||||
\(345\) | 1.88549 | 0.101512 | ||||||||
\(346\) | −13.6294 | −0.732723 | ||||||||
\(347\) | −15.2489 | −0.818601 | −0.409301 | − | 0.912400i | \(-0.634227\pi\) | ||||
−0.409301 | + | 0.912400i | \(0.634227\pi\) | |||||||
\(348\) | −16.0664 | −0.861249 | ||||||||
\(349\) | −12.7235 | −0.681072 | −0.340536 | − | 0.940231i | \(-0.610609\pi\) | ||||
−0.340536 | + | 0.940231i | \(0.610609\pi\) | |||||||
\(350\) | 9.47521 | 0.506471 | ||||||||
\(351\) | −3.72620 | −0.198890 | ||||||||
\(352\) | 1.27745 | 0.0680883 | ||||||||
\(353\) | −7.28527 | −0.387756 | −0.193878 | − | 0.981026i | \(-0.562107\pi\) | ||||
−0.193878 | + | 0.981026i | \(0.562107\pi\) | |||||||
\(354\) | −24.2788 | −1.29041 | ||||||||
\(355\) | 1.46518 | 0.0777638 | ||||||||
\(356\) | 14.7652 | 0.782552 | ||||||||
\(357\) | 5.00651 | 0.264973 | ||||||||
\(358\) | 14.3320 | 0.757470 | ||||||||
\(359\) | −18.7403 | −0.989077 | −0.494538 | − | 0.869156i | \(-0.664663\pi\) | ||||
−0.494538 | + | 0.869156i | \(0.664663\pi\) | |||||||
\(360\) | −0.661084 | −0.0348422 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −20.8693 | −1.09687 | ||||||||
\(363\) | 22.0383 | 1.15671 | ||||||||
\(364\) | −6.53240 | −0.342391 | ||||||||
\(365\) | −2.50981 | −0.131369 | ||||||||
\(366\) | 19.1876 | 1.00295 | ||||||||
\(367\) | −3.72876 | −0.194640 | −0.0973199 | − | 0.995253i | \(-0.531027\pi\) | ||||
−0.0973199 | + | 0.995253i | \(0.531027\pi\) | |||||||
\(368\) | −3.07239 | −0.160159 | ||||||||
\(369\) | 20.9768 | 1.09201 | ||||||||
\(370\) | 0.551723 | 0.0286827 | ||||||||
\(371\) | −12.0387 | −0.625020 | ||||||||
\(372\) | −1.42972 | −0.0741277 | ||||||||
\(373\) | −4.37335 | −0.226443 | −0.113222 | − | 0.993570i | \(-0.536117\pi\) | ||||
−0.113222 | + | 0.993570i | \(0.536117\pi\) | |||||||
\(374\) | −1.41509 | −0.0731724 | ||||||||
\(375\) | 6.09513 | 0.314751 | ||||||||
\(376\) | −4.68145 | −0.241428 | ||||||||
\(377\) | −23.2217 | −1.19598 | ||||||||
\(378\) | −2.10540 | −0.108290 | ||||||||
\(379\) | 25.3048 | 1.29982 | 0.649909 | − | 0.760012i | \(-0.274807\pi\) | ||||
0.649909 | + | 0.760012i | \(0.274807\pi\) | |||||||
\(380\) | 0.260869 | 0.0133823 | ||||||||
\(381\) | −24.0545 | −1.23235 | ||||||||
\(382\) | −2.26218 | −0.115743 | ||||||||
\(383\) | −2.70412 | −0.138174 | −0.0690870 | − | 0.997611i | \(-0.522009\pi\) | ||||
−0.0690870 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(384\) | 2.35248 | 0.120049 | ||||||||
\(385\) | −0.640232 | −0.0326292 | ||||||||
\(386\) | −2.55163 | −0.129875 | ||||||||
\(387\) | 19.4698 | 0.989705 | ||||||||
\(388\) | −15.9686 | −0.810683 | ||||||||
\(389\) | 34.9492 | 1.77199 | 0.885997 | − | 0.463691i | \(-0.153475\pi\) | ||||
0.885997 | + | 0.463691i | \(0.153475\pi\) | |||||||
\(390\) | −2.08665 | −0.105662 | ||||||||
\(391\) | 3.40342 | 0.172118 | ||||||||
\(392\) | 3.30903 | 0.167131 | ||||||||
\(393\) | −20.8184 | −1.05015 | ||||||||
\(394\) | −1.57928 | −0.0795631 | ||||||||
\(395\) | 1.59269 | 0.0801368 | ||||||||
\(396\) | −3.23726 | −0.162678 | ||||||||
\(397\) | −11.7872 | −0.591585 | −0.295792 | − | 0.955252i | \(-0.595584\pi\) | ||||
−0.295792 | + | 0.955252i | \(0.595584\pi\) | |||||||
\(398\) | 14.2060 | 0.712084 | ||||||||
\(399\) | −4.51956 | −0.226261 | ||||||||
\(400\) | −4.93195 | −0.246597 | ||||||||
\(401\) | −13.0075 | −0.649562 | −0.324781 | − | 0.945789i | \(-0.605291\pi\) | ||||
−0.324781 | + | 0.945789i | \(0.605291\pi\) | |||||||
\(402\) | 7.65758 | 0.381925 | ||||||||
\(403\) | −2.06647 | −0.102938 | ||||||||
\(404\) | −7.00502 | −0.348513 | ||||||||
\(405\) | −2.65578 | −0.131967 | ||||||||
\(406\) | −13.1209 | −0.651179 | ||||||||
\(407\) | 2.70173 | 0.133920 | ||||||||
\(408\) | −2.60594 | −0.129013 | ||||||||
\(409\) | 15.7308 | 0.777836 | 0.388918 | − | 0.921272i | \(-0.372849\pi\) | ||||
0.388918 | + | 0.921272i | \(0.372849\pi\) | |||||||
\(410\) | −2.15938 | −0.106644 | ||||||||
\(411\) | 33.3300 | 1.64405 | ||||||||
\(412\) | −0.752391 | −0.0370677 | ||||||||
\(413\) | −19.8277 | −0.975658 | ||||||||
\(414\) | 7.78592 | 0.382657 | ||||||||
\(415\) | −2.37354 | −0.116512 | ||||||||
\(416\) | 3.40018 | 0.166708 | ||||||||
\(417\) | 36.4340 | 1.78418 | ||||||||
\(418\) | 1.27745 | 0.0624821 | ||||||||
\(419\) | 14.2628 | 0.696781 | 0.348391 | − | 0.937349i | \(-0.386728\pi\) | ||||
0.348391 | + | 0.937349i | \(0.386728\pi\) | |||||||
\(420\) | −1.17901 | −0.0575300 | ||||||||
\(421\) | 26.9049 | 1.31126 | 0.655632 | − | 0.755080i | \(-0.272402\pi\) | ||||
0.655632 | + | 0.755080i | \(0.272402\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 11.8635 | 0.576825 | ||||||||
\(424\) | 6.26629 | 0.304318 | ||||||||
\(425\) | 5.46333 | 0.265011 | ||||||||
\(426\) | 13.2128 | 0.640162 | ||||||||
\(427\) | 15.6698 | 0.758316 | ||||||||
\(428\) | −8.46676 | −0.409256 | ||||||||
\(429\) | −10.2181 | −0.493336 | ||||||||
\(430\) | −2.00424 | −0.0966532 | ||||||||
\(431\) | 24.0999 | 1.16085 | 0.580424 | − | 0.814314i | \(-0.302887\pi\) | ||||
0.580424 | + | 0.814314i | \(0.302887\pi\) | |||||||
\(432\) | 1.09588 | 0.0527257 | ||||||||
\(433\) | 1.04175 | 0.0500635 | 0.0250317 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250317 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(434\) | −1.16761 | −0.0560469 | ||||||||
\(435\) | −4.19123 | −0.200954 | ||||||||
\(436\) | 9.56375 | 0.458021 | ||||||||
\(437\) | −3.07239 | −0.146972 | ||||||||
\(438\) | −22.6331 | −1.08145 | ||||||||
\(439\) | −25.8422 | −1.23338 | −0.616691 | − | 0.787205i | \(-0.711527\pi\) | ||||
−0.616691 | + | 0.787205i | \(0.711527\pi\) | |||||||
\(440\) | 0.333247 | 0.0158869 | ||||||||
\(441\) | −8.38560 | −0.399314 | ||||||||
\(442\) | −3.76653 | −0.179156 | ||||||||
\(443\) | 39.4514 | 1.87439 | 0.937196 | − | 0.348803i | \(-0.113412\pi\) | ||||
0.937196 | + | 0.348803i | \(0.113412\pi\) | |||||||
\(444\) | 4.97536 | 0.236120 | ||||||||
\(445\) | 3.85178 | 0.182592 | ||||||||
\(446\) | 12.2039 | 0.577872 | ||||||||
\(447\) | −18.2830 | −0.864757 | ||||||||
\(448\) | 1.92119 | 0.0907677 | ||||||||
\(449\) | 12.7735 | 0.602817 | 0.301408 | − | 0.953495i | \(-0.402543\pi\) | ||||
0.301408 | + | 0.953495i | \(0.402543\pi\) | |||||||
\(450\) | 12.4983 | 0.589177 | ||||||||
\(451\) | −10.5743 | −0.497923 | ||||||||
\(452\) | 18.0481 | 0.848911 | ||||||||
\(453\) | 33.3656 | 1.56765 | ||||||||
\(454\) | −10.0676 | −0.472498 | ||||||||
\(455\) | −1.70410 | −0.0798895 | ||||||||
\(456\) | 2.35248 | 0.110165 | ||||||||
\(457\) | −16.5672 | −0.774980 | −0.387490 | − | 0.921874i | \(-0.626658\pi\) | ||||
−0.387490 | + | 0.921874i | \(0.626658\pi\) | |||||||
\(458\) | −24.6235 | −1.15058 | ||||||||
\(459\) | −1.21396 | −0.0566627 | ||||||||
\(460\) | −0.801492 | −0.0373697 | ||||||||
\(461\) | −10.0959 | −0.470214 | −0.235107 | − | 0.971969i | \(-0.575544\pi\) | ||||
−0.235107 | + | 0.971969i | \(0.575544\pi\) | |||||||
\(462\) | −5.77351 | −0.268608 | ||||||||
\(463\) | −28.6478 | −1.33138 | −0.665688 | − | 0.746230i | \(-0.731862\pi\) | ||||
−0.665688 | + | 0.746230i | \(0.731862\pi\) | |||||||
\(464\) | 6.82956 | 0.317054 | ||||||||
\(465\) | −0.372971 | −0.0172961 | ||||||||
\(466\) | −5.42237 | −0.251186 | ||||||||
\(467\) | −4.52317 | −0.209307 | −0.104654 | − | 0.994509i | \(-0.533373\pi\) | ||||
−0.104654 | + | 0.994509i | \(0.533373\pi\) | |||||||
\(468\) | −8.61660 | −0.398302 | ||||||||
\(469\) | 6.25369 | 0.288768 | ||||||||
\(470\) | −1.22125 | −0.0563319 | ||||||||
\(471\) | −37.9552 | −1.74888 | ||||||||
\(472\) | 10.3205 | 0.475041 | ||||||||
\(473\) | −9.81458 | −0.451275 | ||||||||
\(474\) | 14.3626 | 0.659697 | ||||||||
\(475\) | −4.93195 | −0.226293 | ||||||||
\(476\) | −2.12819 | −0.0975452 | ||||||||
\(477\) | −15.8798 | −0.727085 | ||||||||
\(478\) | −9.09339 | −0.415922 | ||||||||
\(479\) | 17.8331 | 0.814815 | 0.407408 | − | 0.913246i | \(-0.366433\pi\) | ||||
0.407408 | + | 0.913246i | \(0.366433\pi\) | |||||||
\(480\) | 0.613689 | 0.0280110 | ||||||||
\(481\) | 7.19119 | 0.327890 | ||||||||
\(482\) | −14.2414 | −0.648680 | ||||||||
\(483\) | 13.8859 | 0.631828 | ||||||||
\(484\) | −9.36812 | −0.425824 | ||||||||
\(485\) | −4.16571 | −0.189155 | ||||||||
\(486\) | −20.6618 | −0.937238 | ||||||||
\(487\) | −4.14484 | −0.187821 | −0.0939103 | − | 0.995581i | \(-0.529937\pi\) | ||||
−0.0939103 | + | 0.995581i | \(0.529937\pi\) | |||||||
\(488\) | −8.15631 | −0.369219 | ||||||||
\(489\) | −3.19575 | −0.144517 | ||||||||
\(490\) | 0.863223 | 0.0389965 | ||||||||
\(491\) | −5.88427 | −0.265553 | −0.132777 | − | 0.991146i | \(-0.542389\pi\) | ||||
−0.132777 | + | 0.991146i | \(0.542389\pi\) | |||||||
\(492\) | −19.4730 | −0.877909 | ||||||||
\(493\) | −7.56540 | −0.340729 | ||||||||
\(494\) | 3.40018 | 0.152981 | ||||||||
\(495\) | −0.844501 | −0.0379575 | ||||||||
\(496\) | 0.607752 | 0.0272889 | ||||||||
\(497\) | 10.7904 | 0.484018 | ||||||||
\(498\) | −21.4042 | −0.959146 | ||||||||
\(499\) | −36.0493 | −1.61379 | −0.806894 | − | 0.590696i | \(-0.798853\pi\) | ||||
−0.806894 | + | 0.590696i | \(0.798853\pi\) | |||||||
\(500\) | −2.59094 | −0.115870 | ||||||||
\(501\) | −11.2593 | −0.503027 | ||||||||
\(502\) | −0.637031 | −0.0284321 | ||||||||
\(503\) | −2.90375 | −0.129472 | −0.0647358 | − | 0.997902i | \(-0.520620\pi\) | ||||
−0.0647358 | + | 0.997902i | \(0.520620\pi\) | |||||||
\(504\) | −4.86860 | −0.216865 | ||||||||
\(505\) | −1.82739 | −0.0813179 | ||||||||
\(506\) | −3.92483 | −0.174480 | ||||||||
\(507\) | 3.38466 | 0.150318 | ||||||||
\(508\) | 10.2252 | 0.453668 | ||||||||
\(509\) | 24.5593 | 1.08857 | 0.544287 | − | 0.838899i | \(-0.316800\pi\) | ||||
0.544287 | + | 0.838899i | \(0.316800\pi\) | |||||||
\(510\) | −0.679810 | −0.0301025 | ||||||||
\(511\) | −18.4837 | −0.817669 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.09588 | 0.0483844 | ||||||||
\(514\) | 25.3218 | 1.11690 | ||||||||
\(515\) | −0.196276 | −0.00864894 | ||||||||
\(516\) | −18.0740 | −0.795662 | ||||||||
\(517\) | −5.98032 | −0.263014 | ||||||||
\(518\) | 4.06321 | 0.178527 | ||||||||
\(519\) | −32.0630 | −1.40741 | ||||||||
\(520\) | 0.887002 | 0.0388976 | ||||||||
\(521\) | −33.9573 | −1.48770 | −0.743848 | − | 0.668349i | \(-0.767001\pi\) | ||||
−0.743848 | + | 0.668349i | \(0.767001\pi\) | |||||||
\(522\) | −17.3072 | −0.757515 | ||||||||
\(523\) | −1.89668 | −0.0829361 | −0.0414680 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414680 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(524\) | 8.84956 | 0.386595 | ||||||||
\(525\) | 22.2902 | 0.972825 | ||||||||
\(526\) | −6.84138 | −0.298298 | ||||||||
\(527\) | −0.673233 | −0.0293265 | ||||||||
\(528\) | 3.00517 | 0.130783 | ||||||||
\(529\) | −13.5604 | −0.589583 | ||||||||
\(530\) | 1.63468 | 0.0710060 | ||||||||
\(531\) | −26.1539 | −1.13498 | ||||||||
\(532\) | 1.92119 | 0.0832942 | ||||||||
\(533\) | −28.1455 | −1.21912 | ||||||||
\(534\) | 34.7347 | 1.50312 | ||||||||
\(535\) | −2.20872 | −0.0954912 | ||||||||
\(536\) | −3.25511 | −0.140599 | ||||||||
\(537\) | 33.7158 | 1.45494 | ||||||||
\(538\) | 2.84734 | 0.122758 | ||||||||
\(539\) | 4.22712 | 0.182075 | ||||||||
\(540\) | 0.285882 | 0.0123024 | ||||||||
\(541\) | −22.7791 | −0.979352 | −0.489676 | − | 0.871904i | \(-0.662885\pi\) | ||||
−0.489676 | + | 0.871904i | \(0.662885\pi\) | |||||||
\(542\) | 8.49718 | 0.364985 | ||||||||
\(543\) | −49.0946 | −2.10685 | ||||||||
\(544\) | 1.10774 | 0.0474941 | ||||||||
\(545\) | 2.49489 | 0.106869 | ||||||||
\(546\) | −15.3673 | −0.657661 | ||||||||
\(547\) | −39.2160 | −1.67675 | −0.838377 | − | 0.545091i | \(-0.816495\pi\) | ||||
−0.838377 | + | 0.545091i | \(0.816495\pi\) | |||||||
\(548\) | −14.1680 | −0.605228 | ||||||||
\(549\) | 20.6694 | 0.882148 | ||||||||
\(550\) | −6.30032 | −0.268646 | ||||||||
\(551\) | 6.82956 | 0.290949 | ||||||||
\(552\) | −7.22773 | −0.307633 | ||||||||
\(553\) | 11.7295 | 0.498788 | ||||||||
\(554\) | 18.3442 | 0.779369 | ||||||||
\(555\) | 1.29792 | 0.0550935 | ||||||||
\(556\) | −15.4875 | −0.656815 | ||||||||
\(557\) | −38.2604 | −1.62114 | −0.810572 | − | 0.585639i | \(-0.800844\pi\) | ||||
−0.810572 | + | 0.585639i | \(0.800844\pi\) | |||||||
\(558\) | −1.54014 | −0.0651993 | ||||||||
\(559\) | −26.1234 | −1.10490 | ||||||||
\(560\) | 0.501179 | 0.0211787 | ||||||||
\(561\) | −3.32896 | −0.140549 | ||||||||
\(562\) | −4.52281 | −0.190783 | ||||||||
\(563\) | −15.9228 | −0.671067 | −0.335534 | − | 0.942028i | \(-0.608917\pi\) | ||||
−0.335534 | + | 0.942028i | \(0.608917\pi\) | |||||||
\(564\) | −11.0130 | −0.463732 | ||||||||
\(565\) | 4.70819 | 0.198075 | ||||||||
\(566\) | 27.0942 | 1.13885 | ||||||||
\(567\) | −19.5587 | −0.821389 | ||||||||
\(568\) | −5.61654 | −0.235665 | ||||||||
\(569\) | −21.0733 | −0.883440 | −0.441720 | − | 0.897153i | \(-0.645632\pi\) | ||||
−0.441720 | + | 0.897153i | \(0.645632\pi\) | |||||||
\(570\) | 0.613689 | 0.0257046 | ||||||||
\(571\) | −20.6849 | −0.865635 | −0.432818 | − | 0.901482i | \(-0.642481\pi\) | ||||
−0.432818 | + | 0.901482i | \(0.642481\pi\) | |||||||
\(572\) | 4.34356 | 0.181613 | ||||||||
\(573\) | −5.32172 | −0.222318 | ||||||||
\(574\) | −15.9029 | −0.663775 | ||||||||
\(575\) | 15.1529 | 0.631918 | ||||||||
\(576\) | 2.53416 | 0.105590 | ||||||||
\(577\) | −31.2389 | −1.30049 | −0.650245 | − | 0.759724i | \(-0.725334\pi\) | ||||
−0.650245 | + | 0.759724i | \(0.725334\pi\) | |||||||
\(578\) | 15.7729 | 0.656066 | ||||||||
\(579\) | −6.00266 | −0.249462 | ||||||||
\(580\) | 1.78162 | 0.0739778 | ||||||||
\(581\) | −17.4801 | −0.725197 | ||||||||
\(582\) | −37.5658 | −1.55715 | ||||||||
\(583\) | 8.00487 | 0.331528 | ||||||||
\(584\) | 9.62094 | 0.398117 | ||||||||
\(585\) | −2.24780 | −0.0929353 | ||||||||
\(586\) | −6.12466 | −0.253007 | ||||||||
\(587\) | −33.3143 | −1.37503 | −0.687513 | − | 0.726172i | \(-0.741298\pi\) | ||||
−0.687513 | + | 0.726172i | \(0.741298\pi\) | |||||||
\(588\) | 7.78442 | 0.321024 | ||||||||
\(589\) | 0.607752 | 0.0250420 | ||||||||
\(590\) | 2.69231 | 0.110841 | ||||||||
\(591\) | −3.71523 | −0.152824 | ||||||||
\(592\) | −2.11494 | −0.0869236 | ||||||||
\(593\) | 5.37232 | 0.220615 | 0.110307 | − | 0.993898i | \(-0.464816\pi\) | ||||
0.110307 | + | 0.993898i | \(0.464816\pi\) | |||||||
\(594\) | 1.39994 | 0.0574401 | ||||||||
\(595\) | −0.555178 | −0.0227601 | ||||||||
\(596\) | 7.77181 | 0.318346 | ||||||||
\(597\) | 33.4194 | 1.36776 | ||||||||
\(598\) | −10.4467 | −0.427197 | ||||||||
\(599\) | −9.98759 | −0.408082 | −0.204041 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204041 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(600\) | −11.6023 | −0.473662 | ||||||||
\(601\) | −12.6366 | −0.515457 | −0.257728 | − | 0.966217i | \(-0.582974\pi\) | ||||
−0.257728 | + | 0.966217i | \(0.582974\pi\) | |||||||
\(602\) | −14.7604 | −0.601589 | ||||||||
\(603\) | 8.24896 | 0.335924 | ||||||||
\(604\) | −14.1832 | −0.577104 | ||||||||
\(605\) | −2.44385 | −0.0993568 | ||||||||
\(606\) | −16.4792 | −0.669420 | ||||||||
\(607\) | −16.3279 | −0.662731 | −0.331365 | − | 0.943503i | \(-0.607509\pi\) | ||||
−0.331365 | + | 0.943503i | \(0.607509\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −30.8666 | −1.25078 | ||||||||
\(610\) | −2.12773 | −0.0861493 | ||||||||
\(611\) | −15.9178 | −0.643965 | ||||||||
\(612\) | −2.80720 | −0.113474 | ||||||||
\(613\) | −27.2397 | −1.10020 | −0.550100 | − | 0.835099i | \(-0.685411\pi\) | ||||
−0.550100 | + | 0.835099i | \(0.685411\pi\) | |||||||
\(614\) | 0.937760 | 0.0378449 | ||||||||
\(615\) | −5.07990 | −0.204841 | ||||||||
\(616\) | 2.45422 | 0.0988835 | ||||||||
\(617\) | 4.60100 | 0.185229 | 0.0926147 | − | 0.995702i | \(-0.470478\pi\) | ||||
0.0926147 | + | 0.995702i | \(0.470478\pi\) | |||||||
\(618\) | −1.76998 | −0.0711992 | ||||||||
\(619\) | 12.2323 | 0.491656 | 0.245828 | − | 0.969314i | \(-0.420940\pi\) | ||||
0.245828 | + | 0.969314i | \(0.420940\pi\) | |||||||
\(620\) | 0.158544 | 0.00636727 | ||||||||
\(621\) | −3.36698 | −0.135112 | ||||||||
\(622\) | 4.22138 | 0.169262 | ||||||||
\(623\) | 28.3667 | 1.13649 | ||||||||
\(624\) | 7.99886 | 0.320211 | ||||||||
\(625\) | 23.9838 | 0.959354 | ||||||||
\(626\) | −27.4989 | −1.09908 | ||||||||
\(627\) | 3.00517 | 0.120015 | ||||||||
\(628\) | 16.1341 | 0.643821 | ||||||||
\(629\) | 2.34281 | 0.0934141 | ||||||||
\(630\) | −1.27007 | −0.0506007 | ||||||||
\(631\) | −22.5929 | −0.899407 | −0.449704 | − | 0.893178i | \(-0.648470\pi\) | ||||
−0.449704 | + | 0.893178i | \(0.648470\pi\) | |||||||
\(632\) | −6.10531 | −0.242856 | ||||||||
\(633\) | −2.35248 | −0.0935027 | ||||||||
\(634\) | 0.195660 | 0.00777066 | ||||||||
\(635\) | 2.66743 | 0.105854 | ||||||||
\(636\) | 14.7413 | 0.584531 | ||||||||
\(637\) | 11.2513 | 0.445793 | ||||||||
\(638\) | 8.72442 | 0.345403 | ||||||||
\(639\) | 14.2332 | 0.563057 | ||||||||
\(640\) | −0.260869 | −0.0103118 | ||||||||
\(641\) | 12.2383 | 0.483384 | 0.241692 | − | 0.970353i | \(-0.422298\pi\) | ||||
0.241692 | + | 0.970353i | \(0.422298\pi\) | |||||||
\(642\) | −19.9179 | −0.786096 | ||||||||
\(643\) | 21.9274 | 0.864733 | 0.432366 | − | 0.901698i | \(-0.357679\pi\) | ||||
0.432366 | + | 0.901698i | \(0.357679\pi\) | |||||||
\(644\) | −5.90265 | −0.232597 | ||||||||
\(645\) | −4.71494 | −0.185651 | ||||||||
\(646\) | 1.10774 | 0.0435836 | ||||||||
\(647\) | 15.3001 | 0.601507 | 0.300754 | − | 0.953702i | \(-0.402762\pi\) | ||||
0.300754 | + | 0.953702i | \(0.402762\pi\) | |||||||
\(648\) | 10.1805 | 0.399928 | ||||||||
\(649\) | 13.1840 | 0.517516 | ||||||||
\(650\) | −16.7695 | −0.657755 | ||||||||
\(651\) | −2.74677 | −0.107654 | ||||||||
\(652\) | 1.35846 | 0.0532013 | ||||||||
\(653\) | 42.2023 | 1.65150 | 0.825752 | − | 0.564033i | \(-0.190751\pi\) | ||||
0.825752 | + | 0.564033i | \(0.190751\pi\) | |||||||
\(654\) | 22.4985 | 0.879762 | ||||||||
\(655\) | 2.30858 | 0.0902036 | ||||||||
\(656\) | 8.27764 | 0.323187 | ||||||||
\(657\) | −24.3810 | −0.951193 | ||||||||
\(658\) | −8.99396 | −0.350621 | ||||||||
\(659\) | 1.65894 | 0.0646232 | 0.0323116 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323116 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(660\) | 0.783957 | 0.0305155 | ||||||||
\(661\) | −12.8553 | −0.500013 | −0.250006 | − | 0.968244i | \(-0.580433\pi\) | ||||
−0.250006 | + | 0.968244i | \(0.580433\pi\) | |||||||
\(662\) | 34.5165 | 1.34152 | ||||||||
\(663\) | −8.86068 | −0.344120 | ||||||||
\(664\) | 9.09858 | 0.353093 | ||||||||
\(665\) | 0.501179 | 0.0194349 | ||||||||
\(666\) | 5.35960 | 0.207680 | ||||||||
\(667\) | −20.9831 | −0.812468 | ||||||||
\(668\) | 4.78613 | 0.185181 | ||||||||
\(669\) | 28.7095 | 1.10997 | ||||||||
\(670\) | −0.849158 | −0.0328058 | ||||||||
\(671\) | −10.4193 | −0.402232 | ||||||||
\(672\) | 4.51956 | 0.174346 | ||||||||
\(673\) | 20.8663 | 0.804338 | 0.402169 | − | 0.915565i | \(-0.368256\pi\) | ||||
0.402169 | + | 0.915565i | \(0.368256\pi\) | |||||||
\(674\) | 17.0826 | 0.657996 | ||||||||
\(675\) | −5.40484 | −0.208032 | ||||||||
\(676\) | −1.43876 | −0.0553371 | ||||||||
\(677\) | −28.8138 | −1.10740 | −0.553702 | − | 0.832715i | \(-0.686785\pi\) | ||||
−0.553702 | + | 0.832715i | \(0.686785\pi\) | |||||||
\(678\) | 42.4578 | 1.63058 | ||||||||
\(679\) | −30.6787 | −1.17734 | ||||||||
\(680\) | 0.288976 | 0.0110817 | ||||||||
\(681\) | −23.6839 | −0.907570 | ||||||||
\(682\) | 0.776373 | 0.0297289 | ||||||||
\(683\) | −14.5589 | −0.557082 | −0.278541 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278541 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(684\) | 2.53416 | 0.0968960 | ||||||||
\(685\) | −3.69600 | −0.141217 | ||||||||
\(686\) | 19.8056 | 0.756181 | ||||||||
\(687\) | −57.9262 | −2.21002 | ||||||||
\(688\) | 7.68294 | 0.292909 | ||||||||
\(689\) | 21.3065 | 0.811714 | ||||||||
\(690\) | −1.88549 | −0.0717795 | ||||||||
\(691\) | −10.6470 | −0.405029 | −0.202515 | − | 0.979279i | \(-0.564911\pi\) | ||||
−0.202515 | + | 0.979279i | \(0.564911\pi\) | |||||||
\(692\) | 13.6294 | 0.518113 | ||||||||
\(693\) | −6.21939 | −0.236255 | ||||||||
\(694\) | 15.2489 | 0.578839 | ||||||||
\(695\) | −4.04020 | −0.153254 | ||||||||
\(696\) | 16.0664 | 0.608995 | ||||||||
\(697\) | −9.16950 | −0.347320 | ||||||||
\(698\) | 12.7235 | 0.481591 | ||||||||
\(699\) | −12.7560 | −0.482477 | ||||||||
\(700\) | −9.47521 | −0.358129 | ||||||||
\(701\) | −44.0785 | −1.66482 | −0.832411 | − | 0.554158i | \(-0.813040\pi\) | ||||
−0.832411 | + | 0.554158i | \(0.813040\pi\) | |||||||
\(702\) | 3.72620 | 0.140636 | ||||||||
\(703\) | −2.11494 | −0.0797665 | ||||||||
\(704\) | −1.27745 | −0.0481457 | ||||||||
\(705\) | −2.87296 | −0.108202 | ||||||||
\(706\) | 7.28527 | 0.274185 | ||||||||
\(707\) | −13.4580 | −0.506139 | ||||||||
\(708\) | 24.2788 | 0.912455 | ||||||||
\(709\) | −7.03195 | −0.264090 | −0.132045 | − | 0.991244i | \(-0.542154\pi\) | ||||
−0.132045 | + | 0.991244i | \(0.542154\pi\) | |||||||
\(710\) | −1.46518 | −0.0549873 | ||||||||
\(711\) | 15.4718 | 0.580239 | ||||||||
\(712\) | −14.7652 | −0.553348 | ||||||||
\(713\) | −1.86725 | −0.0699291 | ||||||||
\(714\) | −5.00651 | −0.187364 | ||||||||
\(715\) | 1.13310 | 0.0423756 | ||||||||
\(716\) | −14.3320 | −0.535612 | ||||||||
\(717\) | −21.3920 | −0.798899 | ||||||||
\(718\) | 18.7403 | 0.699383 | ||||||||
\(719\) | 15.1298 | 0.564248 | 0.282124 | − | 0.959378i | \(-0.408961\pi\) | ||||
0.282124 | + | 0.959378i | \(0.408961\pi\) | |||||||
\(720\) | 0.661084 | 0.0246371 | ||||||||
\(721\) | −1.44549 | −0.0538327 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −33.5027 | −1.24598 | ||||||||
\(724\) | 20.8693 | 0.775602 | ||||||||
\(725\) | −33.6830 | −1.25096 | ||||||||
\(726\) | −22.0383 | −0.817918 | ||||||||
\(727\) | −40.7784 | −1.51239 | −0.756193 | − | 0.654348i | \(-0.772943\pi\) | ||||
−0.756193 | + | 0.654348i | \(0.772943\pi\) | |||||||
\(728\) | 6.53240 | 0.242107 | ||||||||
\(729\) | −18.0649 | −0.669071 | ||||||||
\(730\) | 2.50981 | 0.0928921 | ||||||||
\(731\) | −8.51073 | −0.314781 | ||||||||
\(732\) | −19.1876 | −0.709193 | ||||||||
\(733\) | −6.24079 | −0.230509 | −0.115254 | − | 0.993336i | \(-0.536768\pi\) | ||||
−0.115254 | + | 0.993336i | \(0.536768\pi\) | |||||||
\(734\) | 3.72876 | 0.137631 | ||||||||
\(735\) | 2.03071 | 0.0749040 | ||||||||
\(736\) | 3.07239 | 0.113250 | ||||||||
\(737\) | −4.15824 | −0.153171 | ||||||||
\(738\) | −20.9768 | −0.772168 | ||||||||
\(739\) | 2.23701 | 0.0822898 | 0.0411449 | − | 0.999153i | \(-0.486899\pi\) | ||||
0.0411449 | + | 0.999153i | \(0.486899\pi\) | |||||||
\(740\) | −0.551723 | −0.0202817 | ||||||||
\(741\) | 7.99886 | 0.293845 | ||||||||
\(742\) | 12.0387 | 0.441956 | ||||||||
\(743\) | 24.5252 | 0.899744 | 0.449872 | − | 0.893093i | \(-0.351470\pi\) | ||||
0.449872 | + | 0.893093i | \(0.351470\pi\) | |||||||
\(744\) | 1.42972 | 0.0524162 | ||||||||
\(745\) | 2.02743 | 0.0742791 | ||||||||
\(746\) | 4.37335 | 0.160120 | ||||||||
\(747\) | −23.0572 | −0.843620 | ||||||||
\(748\) | 1.41509 | 0.0517407 | ||||||||
\(749\) | −16.2663 | −0.594356 | ||||||||
\(750\) | −6.09513 | −0.222563 | ||||||||
\(751\) | −7.36045 | −0.268587 | −0.134293 | − | 0.990942i | \(-0.542876\pi\) | ||||
−0.134293 | + | 0.990942i | \(0.542876\pi\) | |||||||
\(752\) | 4.68145 | 0.170715 | ||||||||
\(753\) | −1.49860 | −0.0546121 | ||||||||
\(754\) | 23.2217 | 0.845686 | ||||||||
\(755\) | −3.69995 | −0.134655 | ||||||||
\(756\) | 2.10540 | 0.0765727 | ||||||||
\(757\) | 21.6621 | 0.787322 | 0.393661 | − | 0.919256i | \(-0.371208\pi\) | ||||
0.393661 | + | 0.919256i | \(0.371208\pi\) | |||||||
\(758\) | −25.3048 | −0.919110 | ||||||||
\(759\) | −9.23307 | −0.335139 | ||||||||
\(760\) | −0.260869 | −0.00946272 | ||||||||
\(761\) | −36.3814 | −1.31883 | −0.659413 | − | 0.751781i | \(-0.729195\pi\) | ||||
−0.659413 | + | 0.751781i | \(0.729195\pi\) | |||||||
\(762\) | 24.0545 | 0.871402 | ||||||||
\(763\) | 18.3738 | 0.665176 | ||||||||
\(764\) | 2.26218 | 0.0818426 | ||||||||
\(765\) | −0.732311 | −0.0264768 | ||||||||
\(766\) | 2.70412 | 0.0977038 | ||||||||
\(767\) | 35.0917 | 1.26709 | ||||||||
\(768\) | −2.35248 | −0.0848878 | ||||||||
\(769\) | −27.9419 | −1.00761 | −0.503804 | − | 0.863818i | \(-0.668067\pi\) | ||||
−0.503804 | + | 0.863818i | \(0.668067\pi\) | |||||||
\(770\) | 0.640232 | 0.0230723 | ||||||||
\(771\) | 59.5689 | 2.14532 | ||||||||
\(772\) | 2.55163 | 0.0918352 | ||||||||
\(773\) | 26.6740 | 0.959396 | 0.479698 | − | 0.877434i | \(-0.340746\pi\) | ||||
0.479698 | + | 0.877434i | \(0.340746\pi\) | |||||||
\(774\) | −19.4698 | −0.699827 | ||||||||
\(775\) | −2.99740 | −0.107670 | ||||||||
\(776\) | 15.9686 | 0.573239 | ||||||||
\(777\) | 9.55861 | 0.342913 | ||||||||
\(778\) | −34.9492 | −1.25299 | ||||||||
\(779\) | 8.27764 | 0.296577 | ||||||||
\(780\) | 2.08665 | 0.0747142 | ||||||||
\(781\) | −7.17485 | −0.256736 | ||||||||
\(782\) | −3.40342 | −0.121706 | ||||||||
\(783\) | 7.48440 | 0.267471 | ||||||||
\(784\) | −3.30903 | −0.118180 | ||||||||
\(785\) | 4.20889 | 0.150222 | ||||||||
\(786\) | 20.8184 | 0.742568 | ||||||||
\(787\) | 1.42482 | 0.0507894 | 0.0253947 | − | 0.999678i | \(-0.491916\pi\) | ||||
0.0253947 | + | 0.999678i | \(0.491916\pi\) | |||||||
\(788\) | 1.57928 | 0.0562596 | ||||||||
\(789\) | −16.0942 | −0.572969 | ||||||||
\(790\) | −1.59269 | −0.0566653 | ||||||||
\(791\) | 34.6738 | 1.23286 | ||||||||
\(792\) | 3.23726 | 0.115031 | ||||||||
\(793\) | −27.7330 | −0.984826 | ||||||||
\(794\) | 11.7872 | 0.418314 | ||||||||
\(795\) | 3.84555 | 0.136388 | ||||||||
\(796\) | −14.2060 | −0.503519 | ||||||||
\(797\) | −17.6910 | −0.626648 | −0.313324 | − | 0.949646i | \(-0.601443\pi\) | ||||
−0.313324 | + | 0.949646i | \(0.601443\pi\) | |||||||
\(798\) | 4.51956 | 0.159991 | ||||||||
\(799\) | −5.18585 | −0.183462 | ||||||||
\(800\) | 4.93195 | 0.174371 | ||||||||
\(801\) | 37.4173 | 1.32207 | ||||||||
\(802\) | 13.0075 | 0.459309 | ||||||||
\(803\) | 12.2903 | 0.433714 | ||||||||
\(804\) | −7.65758 | −0.270062 | ||||||||
\(805\) | −1.53982 | −0.0542715 | ||||||||
\(806\) | 2.06647 | 0.0727882 | ||||||||
\(807\) | 6.69831 | 0.235792 | ||||||||
\(808\) | 7.00502 | 0.246436 | ||||||||
\(809\) | −47.9866 | −1.68712 | −0.843560 | − | 0.537035i | \(-0.819544\pi\) | ||||
−0.843560 | + | 0.537035i | \(0.819544\pi\) | |||||||
\(810\) | 2.65578 | 0.0933147 | ||||||||
\(811\) | −32.0232 | −1.12449 | −0.562243 | − | 0.826972i | \(-0.690061\pi\) | ||||
−0.562243 | + | 0.826972i | \(0.690061\pi\) | |||||||
\(812\) | 13.1209 | 0.460453 | ||||||||
\(813\) | 19.9894 | 0.701061 | ||||||||
\(814\) | −2.70173 | −0.0946957 | ||||||||
\(815\) | 0.354380 | 0.0124134 | ||||||||
\(816\) | 2.60594 | 0.0912263 | ||||||||
\(817\) | 7.68294 | 0.268792 | ||||||||
\(818\) | −15.7308 | −0.550013 | ||||||||
\(819\) | −16.5541 | −0.578448 | ||||||||
\(820\) | 2.15938 | 0.0754088 | ||||||||
\(821\) | 3.46136 | 0.120802 | 0.0604011 | − | 0.998174i | \(-0.480762\pi\) | ||||
0.0604011 | + | 0.998174i | \(0.480762\pi\) | |||||||
\(822\) | −33.3300 | −1.16252 | ||||||||
\(823\) | −39.5412 | −1.37832 | −0.689160 | − | 0.724609i | \(-0.742020\pi\) | ||||
−0.689160 | + | 0.724609i | \(0.742020\pi\) | |||||||
\(824\) | 0.752391 | 0.0262108 | ||||||||
\(825\) | −14.8214 | −0.516014 | ||||||||
\(826\) | 19.8277 | 0.689894 | ||||||||
\(827\) | 4.35419 | 0.151410 | 0.0757051 | − | 0.997130i | \(-0.475879\pi\) | ||||
0.0757051 | + | 0.997130i | \(0.475879\pi\) | |||||||
\(828\) | −7.78592 | −0.270580 | ||||||||
\(829\) | −13.3865 | −0.464932 | −0.232466 | − | 0.972605i | \(-0.574679\pi\) | ||||
−0.232466 | + | 0.972605i | \(0.574679\pi\) | |||||||
\(830\) | 2.37354 | 0.0823867 | ||||||||
\(831\) | 43.1543 | 1.49700 | ||||||||
\(832\) | −3.40018 | −0.117880 | ||||||||
\(833\) | 3.66555 | 0.127004 | ||||||||
\(834\) | −36.4340 | −1.26161 | ||||||||
\(835\) | 1.24855 | 0.0432080 | ||||||||
\(836\) | −1.27745 | −0.0441815 | ||||||||
\(837\) | 0.666025 | 0.0230212 | ||||||||
\(838\) | −14.2628 | −0.492699 | ||||||||
\(839\) | −9.23750 | −0.318914 | −0.159457 | − | 0.987205i | \(-0.550974\pi\) | ||||
−0.159457 | + | 0.987205i | \(0.550974\pi\) | |||||||
\(840\) | 1.17901 | 0.0406798 | ||||||||
\(841\) | 17.6429 | 0.608376 | ||||||||
\(842\) | −26.9049 | −0.927204 | ||||||||
\(843\) | −10.6398 | −0.366455 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | −0.375329 | −0.0129117 | ||||||||
\(846\) | −11.8635 | −0.407877 | ||||||||
\(847\) | −17.9979 | −0.618417 | ||||||||
\(848\) | −6.26629 | −0.215185 | ||||||||
\(849\) | 63.7385 | 2.18750 | ||||||||
\(850\) | −5.46333 | −0.187391 | ||||||||
\(851\) | 6.49793 | 0.222746 | ||||||||
\(852\) | −13.2128 | −0.452663 | ||||||||
\(853\) | −17.9724 | −0.615363 | −0.307681 | − | 0.951489i | \(-0.599553\pi\) | ||||
−0.307681 | + | 0.951489i | \(0.599553\pi\) | |||||||
\(854\) | −15.6698 | −0.536211 | ||||||||
\(855\) | 0.661084 | 0.0226086 | ||||||||
\(856\) | 8.46676 | 0.289388 | ||||||||
\(857\) | 33.2828 | 1.13692 | 0.568460 | − | 0.822711i | \(-0.307539\pi\) | ||||
0.568460 | + | 0.822711i | \(0.307539\pi\) | |||||||
\(858\) | 10.2181 | 0.348842 | ||||||||
\(859\) | 2.23081 | 0.0761144 | 0.0380572 | − | 0.999276i | \(-0.487883\pi\) | ||||
0.0380572 | + | 0.999276i | \(0.487883\pi\) | |||||||
\(860\) | 2.00424 | 0.0683441 | ||||||||
\(861\) | −37.4113 | −1.27497 | ||||||||
\(862\) | −24.0999 | −0.820844 | ||||||||
\(863\) | −42.7327 | −1.45464 | −0.727319 | − | 0.686299i | \(-0.759234\pi\) | ||||
−0.727319 | + | 0.686299i | \(0.759234\pi\) | |||||||
\(864\) | −1.09588 | −0.0372827 | ||||||||
\(865\) | 3.55550 | 0.120891 | ||||||||
\(866\) | −1.04175 | −0.0354002 | ||||||||
\(867\) | 37.1054 | 1.26017 | ||||||||
\(868\) | 1.16761 | 0.0396312 | ||||||||
\(869\) | −7.79923 | −0.264571 | ||||||||
\(870\) | 4.19123 | 0.142096 | ||||||||
\(871\) | −11.0680 | −0.375024 | ||||||||
\(872\) | −9.56375 | −0.323869 | ||||||||
\(873\) | −40.4669 | −1.36960 | ||||||||
\(874\) | 3.07239 | 0.103925 | ||||||||
\(875\) | −4.97769 | −0.168276 | ||||||||
\(876\) | 22.6331 | 0.764700 | ||||||||
\(877\) | 1.55882 | 0.0526375 | 0.0263187 | − | 0.999654i | \(-0.491622\pi\) | ||||
0.0263187 | + | 0.999654i | \(0.491622\pi\) | |||||||
\(878\) | 25.8422 | 0.872132 | ||||||||
\(879\) | −14.4081 | −0.485974 | ||||||||
\(880\) | −0.333247 | −0.0112338 | ||||||||
\(881\) | 8.71614 | 0.293654 | 0.146827 | − | 0.989162i | \(-0.453094\pi\) | ||||
0.146827 | + | 0.989162i | \(0.453094\pi\) | |||||||
\(882\) | 8.38560 | 0.282358 | ||||||||
\(883\) | 10.2592 | 0.345251 | 0.172625 | − | 0.984988i | \(-0.444775\pi\) | ||||
0.172625 | + | 0.984988i | \(0.444775\pi\) | |||||||
\(884\) | 3.76653 | 0.126682 | ||||||||
\(885\) | 6.33360 | 0.212902 | ||||||||
\(886\) | −39.4514 | −1.32540 | ||||||||
\(887\) | −35.4155 | −1.18913 | −0.594567 | − | 0.804046i | \(-0.702677\pi\) | ||||
−0.594567 | + | 0.804046i | \(0.702677\pi\) | |||||||
\(888\) | −4.97536 | −0.166962 | ||||||||
\(889\) | 19.6445 | 0.658855 | ||||||||
\(890\) | −3.85178 | −0.129112 | ||||||||
\(891\) | 13.0051 | 0.435687 | ||||||||
\(892\) | −12.2039 | −0.408617 | ||||||||
\(893\) | 4.68145 | 0.156659 | ||||||||
\(894\) | 18.2830 | 0.611476 | ||||||||
\(895\) | −3.73878 | −0.124974 | ||||||||
\(896\) | −1.92119 | −0.0641825 | ||||||||
\(897\) | −24.5756 | −0.820556 | ||||||||
\(898\) | −12.7735 | −0.426256 | ||||||||
\(899\) | 4.15068 | 0.138433 | ||||||||
\(900\) | −12.4983 | −0.416611 | ||||||||
\(901\) | 6.94144 | 0.231253 | ||||||||
\(902\) | 10.5743 | 0.352085 | ||||||||
\(903\) | −34.7235 | −1.15553 | ||||||||
\(904\) | −18.0481 | −0.600271 | ||||||||
\(905\) | 5.44416 | 0.180970 | ||||||||
\(906\) | −33.3656 | −1.10850 | ||||||||
\(907\) | −4.97424 | −0.165167 | −0.0825834 | − | 0.996584i | \(-0.526317\pi\) | ||||
−0.0825834 | + | 0.996584i | \(0.526317\pi\) | |||||||
\(908\) | 10.0676 | 0.334107 | ||||||||
\(909\) | −17.7518 | −0.588791 | ||||||||
\(910\) | 1.70410 | 0.0564904 | ||||||||
\(911\) | −36.7726 | −1.21833 | −0.609166 | − | 0.793043i | \(-0.708496\pi\) | ||||
−0.609166 | + | 0.793043i | \(0.708496\pi\) | |||||||
\(912\) | −2.35248 | −0.0778984 | ||||||||
\(913\) | 11.6230 | 0.384664 | ||||||||
\(914\) | 16.5672 | 0.547993 | ||||||||
\(915\) | −5.00544 | −0.165475 | ||||||||
\(916\) | 24.6235 | 0.813583 | ||||||||
\(917\) | 17.0017 | 0.561445 | ||||||||
\(918\) | 1.21396 | 0.0400666 | ||||||||
\(919\) | 14.6531 | 0.483361 | 0.241681 | − | 0.970356i | \(-0.422301\pi\) | ||||
0.241681 | + | 0.970356i | \(0.422301\pi\) | |||||||
\(920\) | 0.801492 | 0.0264244 | ||||||||
\(921\) | 2.20606 | 0.0726922 | ||||||||
\(922\) | 10.0959 | 0.332492 | ||||||||
\(923\) | −19.0973 | −0.628594 | ||||||||
\(924\) | 5.77351 | 0.189935 | ||||||||
\(925\) | 10.4308 | 0.342962 | ||||||||
\(926\) | 28.6478 | 0.941425 | ||||||||
\(927\) | −1.90668 | −0.0626235 | ||||||||
\(928\) | −6.82956 | −0.224191 | ||||||||
\(929\) | 54.9285 | 1.80215 | 0.901073 | − | 0.433668i | \(-0.142781\pi\) | ||||
0.901073 | + | 0.433668i | \(0.142781\pi\) | |||||||
\(930\) | 0.372971 | 0.0122302 | ||||||||
\(931\) | −3.30903 | −0.108449 | ||||||||
\(932\) | 5.42237 | 0.177616 | ||||||||
\(933\) | 9.93071 | 0.325117 | ||||||||
\(934\) | 4.52317 | 0.148003 | ||||||||
\(935\) | 0.369153 | 0.0120726 | ||||||||
\(936\) | 8.61660 | 0.281642 | ||||||||
\(937\) | 12.9787 | 0.423995 | 0.211998 | − | 0.977270i | \(-0.432003\pi\) | ||||
0.211998 | + | 0.977270i | \(0.432003\pi\) | |||||||
\(938\) | −6.25369 | −0.204190 | ||||||||
\(939\) | −64.6906 | −2.11110 | ||||||||
\(940\) | 1.22125 | 0.0398327 | ||||||||
\(941\) | 57.8262 | 1.88508 | 0.942540 | − | 0.334094i | \(-0.108430\pi\) | ||||
0.942540 | + | 0.334094i | \(0.108430\pi\) | |||||||
\(942\) | 37.9552 | 1.23665 | ||||||||
\(943\) | −25.4321 | −0.828184 | ||||||||
\(944\) | −10.3205 | −0.335905 | ||||||||
\(945\) | 0.549234 | 0.0178666 | ||||||||
\(946\) | 9.81458 | 0.319099 | ||||||||
\(947\) | 55.3981 | 1.80019 | 0.900097 | − | 0.435689i | \(-0.143495\pi\) | ||||
0.900097 | + | 0.435689i | \(0.143495\pi\) | |||||||
\(948\) | −14.3626 | −0.466476 | ||||||||
\(949\) | 32.7129 | 1.06191 | ||||||||
\(950\) | 4.93195 | 0.160013 | ||||||||
\(951\) | 0.460286 | 0.0149258 | ||||||||
\(952\) | 2.12819 | 0.0689749 | ||||||||
\(953\) | 2.77078 | 0.0897544 | 0.0448772 | − | 0.998993i | \(-0.485710\pi\) | ||||
0.0448772 | + | 0.998993i | \(0.485710\pi\) | |||||||
\(954\) | 15.8798 | 0.514127 | ||||||||
\(955\) | 0.590132 | 0.0190962 | ||||||||
\(956\) | 9.09339 | 0.294101 | ||||||||
\(957\) | 20.5240 | 0.663448 | ||||||||
\(958\) | −17.8331 | −0.576161 | ||||||||
\(959\) | −27.2195 | −0.878962 | ||||||||
\(960\) | −0.613689 | −0.0198067 | ||||||||
\(961\) | −30.6306 | −0.988085 | ||||||||
\(962\) | −7.19119 | −0.231853 | ||||||||
\(963\) | −21.4561 | −0.691414 | ||||||||
\(964\) | 14.2414 | 0.458686 | ||||||||
\(965\) | 0.665642 | 0.0214278 | ||||||||
\(966\) | −13.8859 | −0.446770 | ||||||||
\(967\) | 13.2949 | 0.427534 | 0.213767 | − | 0.976885i | \(-0.431427\pi\) | ||||
0.213767 | + | 0.976885i | \(0.431427\pi\) | |||||||
\(968\) | 9.36812 | 0.301103 | ||||||||
\(969\) | 2.60594 | 0.0837150 | ||||||||
\(970\) | 4.16571 | 0.133753 | ||||||||
\(971\) | −50.1208 | −1.60845 | −0.804227 | − | 0.594322i | \(-0.797420\pi\) | ||||
−0.804227 | + | 0.594322i | \(0.797420\pi\) | |||||||
\(972\) | 20.6618 | 0.662728 | ||||||||
\(973\) | −29.7544 | −0.953882 | ||||||||
\(974\) | 4.14484 | 0.132809 | ||||||||
\(975\) | −39.4499 | −1.26341 | ||||||||
\(976\) | 8.15631 | 0.261077 | ||||||||
\(977\) | −26.5437 | −0.849209 | −0.424605 | − | 0.905379i | \(-0.639587\pi\) | ||||
−0.424605 | + | 0.905379i | \(0.639587\pi\) | |||||||
\(978\) | 3.19575 | 0.102189 | ||||||||
\(979\) | −18.8618 | −0.602825 | ||||||||
\(980\) | −0.863223 | −0.0275747 | ||||||||
\(981\) | 24.2361 | 0.773798 | ||||||||
\(982\) | 5.88427 | 0.187775 | ||||||||
\(983\) | 11.2401 | 0.358505 | 0.179253 | − | 0.983803i | \(-0.442632\pi\) | ||||
0.179253 | + | 0.983803i | \(0.442632\pi\) | |||||||
\(984\) | 19.4730 | 0.620776 | ||||||||
\(985\) | 0.411986 | 0.0131270 | ||||||||
\(986\) | 7.56540 | 0.240931 | ||||||||
\(987\) | −21.1581 | −0.673470 | ||||||||
\(988\) | −3.40018 | −0.108174 | ||||||||
\(989\) | −23.6050 | −0.750595 | ||||||||
\(990\) | 0.844501 | 0.0268400 | ||||||||
\(991\) | −17.8389 | −0.566671 | −0.283335 | − | 0.959021i | \(-0.591441\pi\) | ||||
−0.283335 | + | 0.959021i | \(0.591441\pi\) | |||||||
\(992\) | −0.607752 | −0.0192961 | ||||||||
\(993\) | 81.1993 | 2.57678 | ||||||||
\(994\) | −10.7904 | −0.342252 | ||||||||
\(995\) | −3.70591 | −0.117485 | ||||||||
\(996\) | 21.4042 | 0.678218 | ||||||||
\(997\) | 44.3938 | 1.40597 | 0.702983 | − | 0.711207i | \(-0.251851\pi\) | ||||
0.702983 | + | 0.711207i | \(0.251851\pi\) | |||||||
\(998\) | 36.0493 | 1.14112 | ||||||||
\(999\) | −2.31773 | −0.0733297 |
(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.g.1.8 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.g.1.8 | ✓ | 34 | 1.1 | even | 1 | trivial |