Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26706 | −1.60305 | −0.801527 | − | 0.597958i | \(-0.795979\pi\) | ||||
−0.801527 | + | 0.597958i | \(0.795979\pi\) | |||||||
\(3\) | −2.69699 | −1.55711 | −0.778555 | − | 0.627576i | \(-0.784047\pi\) | ||||
−0.778555 | + | 0.627576i | \(0.784047\pi\) | |||||||
\(4\) | 3.13957 | 1.56979 | ||||||||
\(5\) | −3.90758 | −1.74752 | −0.873761 | − | 0.486355i | \(-0.838326\pi\) | ||||
−0.873761 | + | 0.486355i | \(0.838326\pi\) | |||||||
\(6\) | 6.11425 | 2.49613 | ||||||||
\(7\) | −4.79951 | −1.81404 | −0.907022 | − | 0.421083i | \(-0.861650\pi\) | ||||
−0.907022 | + | 0.421083i | \(0.861650\pi\) | |||||||
\(8\) | −2.58348 | −0.913397 | ||||||||
\(9\) | 4.27377 | 1.42459 | ||||||||
\(10\) | 8.85872 | 2.80137 | ||||||||
\(11\) | −1.38285 | −0.416944 | −0.208472 | − | 0.978028i | \(-0.566849\pi\) | ||||
−0.208472 | + | 0.978028i | \(0.566849\pi\) | |||||||
\(12\) | −8.46740 | −2.44433 | ||||||||
\(13\) | 2.27493 | 0.630952 | 0.315476 | − | 0.948934i | \(-0.397836\pi\) | ||||
0.315476 | + | 0.948934i | \(0.397836\pi\) | |||||||
\(14\) | 10.8808 | 2.90801 | ||||||||
\(15\) | 10.5387 | 2.72108 | ||||||||
\(16\) | −0.422238 | −0.105559 | ||||||||
\(17\) | 2.73391 | 0.663071 | 0.331535 | − | 0.943443i | \(-0.392433\pi\) | ||||
0.331535 | + | 0.943443i | \(0.392433\pi\) | |||||||
\(18\) | −9.68891 | −2.28370 | ||||||||
\(19\) | −4.28446 | −0.982921 | −0.491461 | − | 0.870900i | \(-0.663537\pi\) | ||||
−0.491461 | + | 0.870900i | \(0.663537\pi\) | |||||||
\(20\) | −12.2681 | −2.74323 | ||||||||
\(21\) | 12.9442 | 2.82467 | ||||||||
\(22\) | 3.13500 | 0.668384 | ||||||||
\(23\) | 6.13686 | 1.27962 | 0.639812 | − | 0.768532i | \(-0.279012\pi\) | ||||
0.639812 | + | 0.768532i | \(0.279012\pi\) | |||||||
\(24\) | 6.96762 | 1.42226 | ||||||||
\(25\) | 10.2692 | 2.05383 | ||||||||
\(26\) | −5.15740 | −1.01145 | ||||||||
\(27\) | −3.43536 | −0.661135 | ||||||||
\(28\) | −15.0684 | −2.84766 | ||||||||
\(29\) | −9.75536 | −1.81152 | −0.905762 | − | 0.423787i | \(-0.860701\pi\) | ||||
−0.905762 | + | 0.423787i | \(0.860701\pi\) | |||||||
\(30\) | −23.8919 | −4.36205 | ||||||||
\(31\) | 1.51721 | 0.272498 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(32\) | 6.12419 | 1.08261 | ||||||||
\(33\) | 3.72953 | 0.649228 | ||||||||
\(34\) | −6.19794 | −1.06294 | ||||||||
\(35\) | 18.7545 | 3.17008 | ||||||||
\(36\) | 13.4178 | 2.23630 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 9.71313 | 1.57568 | ||||||||
\(39\) | −6.13547 | −0.982461 | ||||||||
\(40\) | 10.0951 | 1.59618 | ||||||||
\(41\) | −1.14774 | −0.179247 | −0.0896236 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896236 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(42\) | −29.3454 | −4.52809 | ||||||||
\(43\) | −8.75122 | −1.33455 | −0.667274 | − | 0.744812i | \(-0.732539\pi\) | ||||
−0.667274 | + | 0.744812i | \(0.732539\pi\) | |||||||
\(44\) | −4.34154 | −0.654512 | ||||||||
\(45\) | −16.7001 | −2.48951 | ||||||||
\(46\) | −13.9126 | −2.05131 | ||||||||
\(47\) | 12.5748 | 1.83423 | 0.917113 | − | 0.398626i | \(-0.130513\pi\) | ||||
0.917113 | + | 0.398626i | \(0.130513\pi\) | |||||||
\(48\) | 1.13877 | 0.164368 | ||||||||
\(49\) | 16.0353 | 2.29076 | ||||||||
\(50\) | −23.2809 | −3.29241 | ||||||||
\(51\) | −7.37334 | −1.03247 | ||||||||
\(52\) | 7.14230 | 0.990459 | ||||||||
\(53\) | −9.73727 | −1.33752 | −0.668758 | − | 0.743480i | \(-0.733174\pi\) | ||||
−0.668758 | + | 0.743480i | \(0.733174\pi\) | |||||||
\(54\) | 7.78817 | 1.05984 | ||||||||
\(55\) | 5.40358 | 0.728619 | ||||||||
\(56\) | 12.3994 | 1.65694 | ||||||||
\(57\) | 11.5551 | 1.53052 | ||||||||
\(58\) | 22.1160 | 2.90397 | ||||||||
\(59\) | −2.87631 | −0.374463 | −0.187232 | − | 0.982316i | \(-0.559951\pi\) | ||||
−0.187232 | + | 0.982316i | \(0.559951\pi\) | |||||||
\(60\) | 33.0870 | 4.27152 | ||||||||
\(61\) | −9.93731 | −1.27234 | −0.636171 | − | 0.771548i | \(-0.719483\pi\) | ||||
−0.636171 | + | 0.771548i | \(0.719483\pi\) | |||||||
\(62\) | −3.43960 | −0.436830 | ||||||||
\(63\) | −20.5120 | −2.58427 | ||||||||
\(64\) | −13.0395 | −1.62993 | ||||||||
\(65\) | −8.88946 | −1.10260 | ||||||||
\(66\) | −8.45507 | −1.04075 | ||||||||
\(67\) | 2.26696 | 0.276953 | 0.138476 | − | 0.990366i | \(-0.455779\pi\) | ||||
0.138476 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(68\) | 8.58330 | 1.04088 | ||||||||
\(69\) | −16.5511 | −1.99251 | ||||||||
\(70\) | −42.5175 | −5.08182 | ||||||||
\(71\) | −5.98115 | −0.709832 | −0.354916 | − | 0.934898i | \(-0.615490\pi\) | ||||
−0.354916 | + | 0.934898i | \(0.615490\pi\) | |||||||
\(72\) | −11.0412 | −1.30122 | ||||||||
\(73\) | −16.5196 | −1.93347 | −0.966736 | − | 0.255775i | \(-0.917669\pi\) | ||||
−0.966736 | + | 0.255775i | \(0.917669\pi\) | |||||||
\(74\) | −2.26706 | −0.263541 | ||||||||
\(75\) | −27.6959 | −3.19805 | ||||||||
\(76\) | −13.4514 | −1.54298 | ||||||||
\(77\) | 6.63698 | 0.756355 | ||||||||
\(78\) | 13.9095 | 1.57494 | ||||||||
\(79\) | −6.45107 | −0.725802 | −0.362901 | − | 0.931828i | \(-0.618214\pi\) | ||||
−0.362901 | + | 0.931828i | \(0.618214\pi\) | |||||||
\(80\) | 1.64993 | 0.184468 | ||||||||
\(81\) | −3.55618 | −0.395131 | ||||||||
\(82\) | 2.60200 | 0.287343 | ||||||||
\(83\) | 7.49907 | 0.823130 | 0.411565 | − | 0.911380i | \(-0.364982\pi\) | ||||
0.411565 | + | 0.911380i | \(0.364982\pi\) | |||||||
\(84\) | 40.6394 | 4.43412 | ||||||||
\(85\) | −10.6830 | −1.15873 | ||||||||
\(86\) | 19.8396 | 2.13935 | ||||||||
\(87\) | 26.3101 | 2.82074 | ||||||||
\(88\) | 3.57255 | 0.380835 | ||||||||
\(89\) | 0.279679 | 0.0296460 | 0.0148230 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148230 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(90\) | 37.8602 | 3.99081 | ||||||||
\(91\) | −10.9185 | −1.14457 | ||||||||
\(92\) | 19.2671 | 2.00873 | ||||||||
\(93\) | −4.09190 | −0.424310 | ||||||||
\(94\) | −28.5079 | −2.94037 | ||||||||
\(95\) | 16.7418 | 1.71768 | ||||||||
\(96\) | −16.5169 | −1.68575 | ||||||||
\(97\) | −12.6937 | −1.28885 | −0.644426 | − | 0.764666i | \(-0.722904\pi\) | ||||
−0.644426 | + | 0.764666i | \(0.722904\pi\) | |||||||
\(98\) | −36.3530 | −3.67221 | ||||||||
\(99\) | −5.90997 | −0.593975 | ||||||||
\(100\) | 32.2408 | 3.22408 | ||||||||
\(101\) | −8.19444 | −0.815377 | −0.407689 | − | 0.913121i | \(-0.633665\pi\) | ||||
−0.407689 | + | 0.913121i | \(0.633665\pi\) | |||||||
\(102\) | 16.7158 | 1.65511 | ||||||||
\(103\) | 4.51496 | 0.444872 | 0.222436 | − | 0.974947i | \(-0.428599\pi\) | ||||
0.222436 | + | 0.974947i | \(0.428599\pi\) | |||||||
\(104\) | −5.87723 | −0.576309 | ||||||||
\(105\) | −50.5807 | −4.93617 | ||||||||
\(106\) | 22.0750 | 2.14411 | ||||||||
\(107\) | 14.8383 | 1.43447 | 0.717237 | − | 0.696830i | \(-0.245407\pi\) | ||||
0.717237 | + | 0.696830i | \(0.245407\pi\) | |||||||
\(108\) | −10.7856 | −1.03784 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −12.2503 | −1.16802 | ||||||||
\(111\) | −2.69699 | −0.255987 | ||||||||
\(112\) | 2.02654 | 0.191490 | ||||||||
\(113\) | 11.4853 | 1.08045 | 0.540224 | − | 0.841521i | \(-0.318339\pi\) | ||||
0.540224 | + | 0.841521i | \(0.318339\pi\) | |||||||
\(114\) | −26.1962 | −2.45350 | ||||||||
\(115\) | −23.9803 | −2.23617 | ||||||||
\(116\) | −30.6276 | −2.84370 | ||||||||
\(117\) | 9.72253 | 0.898848 | ||||||||
\(118\) | 6.52077 | 0.600285 | ||||||||
\(119\) | −13.1214 | −1.20284 | ||||||||
\(120\) | −27.2265 | −2.48543 | ||||||||
\(121\) | −9.08774 | −0.826158 | ||||||||
\(122\) | 22.5285 | 2.03963 | ||||||||
\(123\) | 3.09545 | 0.279108 | ||||||||
\(124\) | 4.76338 | 0.427764 | ||||||||
\(125\) | −20.5897 | −1.84160 | ||||||||
\(126\) | 46.5020 | 4.14273 | ||||||||
\(127\) | 2.27602 | 0.201964 | 0.100982 | − | 0.994888i | \(-0.467802\pi\) | ||||
0.100982 | + | 0.994888i | \(0.467802\pi\) | |||||||
\(128\) | 17.3129 | 1.53026 | ||||||||
\(129\) | 23.6020 | 2.07804 | ||||||||
\(130\) | 20.1530 | 1.76753 | ||||||||
\(131\) | −2.27581 | −0.198838 | −0.0994191 | − | 0.995046i | \(-0.531698\pi\) | ||||
−0.0994191 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(132\) | 11.7091 | 1.01915 | ||||||||
\(133\) | 20.5633 | 1.78306 | ||||||||
\(134\) | −5.13933 | −0.443971 | ||||||||
\(135\) | 13.4239 | 1.15535 | ||||||||
\(136\) | −7.06299 | −0.605647 | ||||||||
\(137\) | −6.84896 | −0.585146 | −0.292573 | − | 0.956243i | \(-0.594511\pi\) | ||||
−0.292573 | + | 0.956243i | \(0.594511\pi\) | |||||||
\(138\) | 37.5223 | 3.19411 | ||||||||
\(139\) | −5.59110 | −0.474231 | −0.237115 | − | 0.971481i | \(-0.576202\pi\) | ||||
−0.237115 | + | 0.971481i | \(0.576202\pi\) | |||||||
\(140\) | 58.8810 | 4.97635 | ||||||||
\(141\) | −33.9142 | −2.85609 | ||||||||
\(142\) | 13.5596 | 1.13790 | ||||||||
\(143\) | −3.14588 | −0.263071 | ||||||||
\(144\) | −1.80455 | −0.150379 | ||||||||
\(145\) | 38.1198 | 3.16568 | ||||||||
\(146\) | 37.4510 | 3.09946 | ||||||||
\(147\) | −43.2471 | −3.56696 | ||||||||
\(148\) | 3.13957 | 0.258071 | ||||||||
\(149\) | −14.4316 | −1.18228 | −0.591141 | − | 0.806568i | \(-0.701322\pi\) | ||||
−0.591141 | + | 0.806568i | \(0.701322\pi\) | |||||||
\(150\) | 62.7883 | 5.12664 | ||||||||
\(151\) | 11.3800 | 0.926089 | 0.463044 | − | 0.886335i | \(-0.346757\pi\) | ||||
0.463044 | + | 0.886335i | \(0.346757\pi\) | |||||||
\(152\) | 11.0688 | 0.897798 | ||||||||
\(153\) | 11.6841 | 0.944605 | ||||||||
\(154\) | −15.0465 | −1.21248 | ||||||||
\(155\) | −5.92860 | −0.476197 | ||||||||
\(156\) | −19.2627 | −1.54225 | ||||||||
\(157\) | −12.5949 | −1.00518 | −0.502592 | − | 0.864524i | \(-0.667620\pi\) | ||||
−0.502592 | + | 0.864524i | \(0.667620\pi\) | |||||||
\(158\) | 14.6250 | 1.16350 | ||||||||
\(159\) | 26.2614 | 2.08266 | ||||||||
\(160\) | −23.9308 | −1.89189 | ||||||||
\(161\) | −29.4539 | −2.32129 | ||||||||
\(162\) | 8.06208 | 0.633417 | ||||||||
\(163\) | −12.9150 | −1.01158 | −0.505791 | − | 0.862656i | \(-0.668799\pi\) | ||||
−0.505791 | + | 0.862656i | \(0.668799\pi\) | |||||||
\(164\) | −3.60342 | −0.281380 | ||||||||
\(165\) | −14.5734 | −1.13454 | ||||||||
\(166\) | −17.0009 | −1.31952 | ||||||||
\(167\) | −12.9607 | −1.00293 | −0.501463 | − | 0.865179i | \(-0.667205\pi\) | ||||
−0.501463 | + | 0.865179i | \(0.667205\pi\) | |||||||
\(168\) | −33.4412 | −2.58004 | ||||||||
\(169\) | −7.82470 | −0.601900 | ||||||||
\(170\) | 24.2190 | 1.85751 | ||||||||
\(171\) | −18.3108 | −1.40026 | ||||||||
\(172\) | −27.4751 | −2.09495 | ||||||||
\(173\) | −2.25143 | −0.171173 | −0.0855866 | − | 0.996331i | \(-0.527276\pi\) | ||||
−0.0855866 | + | 0.996331i | \(0.527276\pi\) | |||||||
\(174\) | −59.6467 | −4.52180 | ||||||||
\(175\) | −49.2870 | −3.72575 | ||||||||
\(176\) | 0.583890 | 0.0440124 | ||||||||
\(177\) | 7.75738 | 0.583080 | ||||||||
\(178\) | −0.634051 | −0.0475241 | ||||||||
\(179\) | −6.45763 | −0.482666 | −0.241333 | − | 0.970442i | \(-0.577585\pi\) | ||||
−0.241333 | + | 0.970442i | \(0.577585\pi\) | |||||||
\(180\) | −52.4312 | −3.90799 | ||||||||
\(181\) | −22.4584 | −1.66932 | −0.834661 | − | 0.550763i | \(-0.814337\pi\) | ||||
−0.834661 | + | 0.550763i | \(0.814337\pi\) | |||||||
\(182\) | 24.7530 | 1.83482 | ||||||||
\(183\) | 26.8009 | 1.98118 | ||||||||
\(184\) | −15.8544 | −1.16880 | ||||||||
\(185\) | −3.90758 | −0.287291 | ||||||||
\(186\) | 9.27658 | 0.680192 | ||||||||
\(187\) | −3.78058 | −0.276463 | ||||||||
\(188\) | 39.4796 | 2.87934 | ||||||||
\(189\) | 16.4880 | 1.19933 | ||||||||
\(190\) | −37.9548 | −2.75353 | ||||||||
\(191\) | 16.7988 | 1.21552 | 0.607758 | − | 0.794122i | \(-0.292069\pi\) | ||||
0.607758 | + | 0.794122i | \(0.292069\pi\) | |||||||
\(192\) | 35.1673 | 2.53798 | ||||||||
\(193\) | −9.77320 | −0.703490 | −0.351745 | − | 0.936096i | \(-0.614412\pi\) | ||||
−0.351745 | + | 0.936096i | \(0.614412\pi\) | |||||||
\(194\) | 28.7775 | 2.06610 | ||||||||
\(195\) | 23.9748 | 1.71687 | ||||||||
\(196\) | 50.3439 | 3.59599 | ||||||||
\(197\) | −25.1556 | −1.79226 | −0.896132 | − | 0.443788i | \(-0.853634\pi\) | ||||
−0.896132 | + | 0.443788i | \(0.853634\pi\) | |||||||
\(198\) | 13.3983 | 0.952174 | ||||||||
\(199\) | 18.5202 | 1.31286 | 0.656431 | − | 0.754386i | \(-0.272065\pi\) | ||||
0.656431 | + | 0.754386i | \(0.272065\pi\) | |||||||
\(200\) | −26.5302 | −1.87597 | ||||||||
\(201\) | −6.11397 | −0.431246 | ||||||||
\(202\) | 18.5773 | 1.30709 | ||||||||
\(203\) | 46.8209 | 3.28618 | ||||||||
\(204\) | −23.1491 | −1.62076 | ||||||||
\(205\) | 4.48489 | 0.313238 | ||||||||
\(206\) | −10.2357 | −0.713154 | ||||||||
\(207\) | 26.2275 | 1.82294 | ||||||||
\(208\) | −0.960561 | −0.0666029 | ||||||||
\(209\) | 5.92474 | 0.409823 | ||||||||
\(210\) | 114.669 | 7.91295 | ||||||||
\(211\) | 6.59359 | 0.453922 | 0.226961 | − | 0.973904i | \(-0.427121\pi\) | ||||
0.226961 | + | 0.973904i | \(0.427121\pi\) | |||||||
\(212\) | −30.5708 | −2.09961 | ||||||||
\(213\) | 16.1311 | 1.10529 | ||||||||
\(214\) | −33.6394 | −2.29954 | ||||||||
\(215\) | 34.1961 | 2.33215 | ||||||||
\(216\) | 8.87517 | 0.603879 | ||||||||
\(217\) | −7.28185 | −0.494324 | ||||||||
\(218\) | 2.26706 | 0.153545 | ||||||||
\(219\) | 44.5532 | 3.01063 | ||||||||
\(220\) | 16.9649 | 1.14378 | ||||||||
\(221\) | 6.21945 | 0.418365 | ||||||||
\(222\) | 6.11425 | 0.410362 | ||||||||
\(223\) | −12.3053 | −0.824024 | −0.412012 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412012 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(224\) | −29.3931 | −1.96391 | ||||||||
\(225\) | 43.8881 | 2.92587 | ||||||||
\(226\) | −26.0379 | −1.73202 | ||||||||
\(227\) | −6.59178 | −0.437512 | −0.218756 | − | 0.975780i | \(-0.570200\pi\) | ||||
−0.218756 | + | 0.975780i | \(0.570200\pi\) | |||||||
\(228\) | 36.2782 | 2.40258 | ||||||||
\(229\) | 1.40131 | 0.0926015 | 0.0463007 | − | 0.998928i | \(-0.485257\pi\) | ||||
0.0463007 | + | 0.998928i | \(0.485257\pi\) | |||||||
\(230\) | 54.3647 | 3.58470 | ||||||||
\(231\) | −17.8999 | −1.17773 | ||||||||
\(232\) | 25.2027 | 1.65464 | ||||||||
\(233\) | −9.92219 | −0.650024 | −0.325012 | − | 0.945710i | \(-0.605368\pi\) | ||||
−0.325012 | + | 0.945710i | \(0.605368\pi\) | |||||||
\(234\) | −22.0416 | −1.44090 | ||||||||
\(235\) | −49.1371 | −3.20535 | ||||||||
\(236\) | −9.03037 | −0.587827 | ||||||||
\(237\) | 17.3985 | 1.13015 | ||||||||
\(238\) | 29.7471 | 1.92822 | ||||||||
\(239\) | −3.63292 | −0.234994 | −0.117497 | − | 0.993073i | \(-0.537487\pi\) | ||||
−0.117497 | + | 0.993073i | \(0.537487\pi\) | |||||||
\(240\) | −4.44985 | −0.287236 | ||||||||
\(241\) | −8.95515 | −0.576852 | −0.288426 | − | 0.957502i | \(-0.593132\pi\) | ||||
−0.288426 | + | 0.957502i | \(0.593132\pi\) | |||||||
\(242\) | 20.6025 | 1.32438 | ||||||||
\(243\) | 19.8971 | 1.27640 | ||||||||
\(244\) | −31.1989 | −1.99730 | ||||||||
\(245\) | −62.6592 | −4.00315 | ||||||||
\(246\) | −7.01758 | −0.447425 | ||||||||
\(247\) | −9.74683 | −0.620176 | ||||||||
\(248\) | −3.91967 | −0.248899 | ||||||||
\(249\) | −20.2250 | −1.28170 | ||||||||
\(250\) | 46.6782 | 2.95219 | ||||||||
\(251\) | −6.07033 | −0.383156 | −0.191578 | − | 0.981477i | \(-0.561360\pi\) | ||||
−0.191578 | + | 0.981477i | \(0.561360\pi\) | |||||||
\(252\) | −64.3989 | −4.05675 | ||||||||
\(253\) | −8.48633 | −0.533531 | ||||||||
\(254\) | −5.15988 | −0.323759 | ||||||||
\(255\) | 28.8119 | 1.80427 | ||||||||
\(256\) | −13.1704 | −0.823151 | ||||||||
\(257\) | 23.5738 | 1.47049 | 0.735246 | − | 0.677800i | \(-0.237067\pi\) | ||||
0.735246 | + | 0.677800i | \(0.237067\pi\) | |||||||
\(258\) | −53.5071 | −3.33121 | ||||||||
\(259\) | −4.79951 | −0.298227 | ||||||||
\(260\) | −27.9091 | −1.73085 | ||||||||
\(261\) | −41.6922 | −2.58068 | ||||||||
\(262\) | 5.15940 | 0.318749 | ||||||||
\(263\) | 1.47912 | 0.0912067 | 0.0456034 | − | 0.998960i | \(-0.485479\pi\) | ||||
0.0456034 | + | 0.998960i | \(0.485479\pi\) | |||||||
\(264\) | −9.63515 | −0.593003 | ||||||||
\(265\) | 38.0492 | 2.33734 | ||||||||
\(266\) | −46.6182 | −2.85835 | ||||||||
\(267\) | −0.754294 | −0.0461620 | ||||||||
\(268\) | 7.11727 | 0.434757 | ||||||||
\(269\) | 29.2441 | 1.78304 | 0.891522 | − | 0.452978i | \(-0.149638\pi\) | ||||
0.891522 | + | 0.452978i | \(0.149638\pi\) | |||||||
\(270\) | −30.4329 | −1.85209 | ||||||||
\(271\) | −5.60187 | −0.340289 | −0.170145 | − | 0.985419i | \(-0.554424\pi\) | ||||
−0.170145 | + | 0.985419i | \(0.554424\pi\) | |||||||
\(272\) | −1.15436 | −0.0699934 | ||||||||
\(273\) | 29.4472 | 1.78223 | ||||||||
\(274\) | 15.5270 | 0.938021 | ||||||||
\(275\) | −14.2007 | −0.856334 | ||||||||
\(276\) | −51.9632 | −3.12782 | ||||||||
\(277\) | −1.94784 | −0.117034 | −0.0585171 | − | 0.998286i | \(-0.518637\pi\) | ||||
−0.0585171 | + | 0.998286i | \(0.518637\pi\) | |||||||
\(278\) | 12.6754 | 0.760218 | ||||||||
\(279\) | 6.48420 | 0.388199 | ||||||||
\(280\) | −48.4517 | −2.89554 | ||||||||
\(281\) | −26.9135 | −1.60553 | −0.802763 | − | 0.596298i | \(-0.796638\pi\) | ||||
−0.802763 | + | 0.596298i | \(0.796638\pi\) | |||||||
\(282\) | 76.8856 | 4.57847 | ||||||||
\(283\) | −5.39817 | −0.320888 | −0.160444 | − | 0.987045i | \(-0.551293\pi\) | ||||
−0.160444 | + | 0.987045i | \(0.551293\pi\) | |||||||
\(284\) | −18.7782 | −1.11428 | ||||||||
\(285\) | −45.1527 | −2.67461 | ||||||||
\(286\) | 7.13190 | 0.421718 | ||||||||
\(287\) | 5.50860 | 0.325162 | ||||||||
\(288\) | 26.1734 | 1.54228 | ||||||||
\(289\) | −9.52574 | −0.560337 | ||||||||
\(290\) | −86.4200 | −5.07476 | ||||||||
\(291\) | 34.2349 | 2.00689 | ||||||||
\(292\) | −51.8644 | −3.03514 | ||||||||
\(293\) | −9.20631 | −0.537838 | −0.268919 | − | 0.963163i | \(-0.586666\pi\) | ||||
−0.268919 | + | 0.963163i | \(0.586666\pi\) | |||||||
\(294\) | 98.0438 | 5.71803 | ||||||||
\(295\) | 11.2394 | 0.654383 | ||||||||
\(296\) | −2.58348 | −0.150162 | ||||||||
\(297\) | 4.75057 | 0.275656 | ||||||||
\(298\) | 32.7173 | 1.89526 | ||||||||
\(299\) | 13.9609 | 0.807381 | ||||||||
\(300\) | −86.9532 | −5.02025 | ||||||||
\(301\) | 42.0015 | 2.42093 | ||||||||
\(302\) | −25.7991 | −1.48457 | ||||||||
\(303\) | 22.1003 | 1.26963 | ||||||||
\(304\) | 1.80906 | 0.103757 | ||||||||
\(305\) | 38.8308 | 2.22345 | ||||||||
\(306\) | −26.4886 | −1.51425 | ||||||||
\(307\) | −16.1861 | −0.923791 | −0.461896 | − | 0.886934i | \(-0.652831\pi\) | ||||
−0.461896 | + | 0.886934i | \(0.652831\pi\) | |||||||
\(308\) | 20.8373 | 1.18731 | ||||||||
\(309\) | −12.1768 | −0.692715 | ||||||||
\(310\) | 13.4405 | 0.763370 | ||||||||
\(311\) | 29.3232 | 1.66277 | 0.831384 | − | 0.555698i | \(-0.187549\pi\) | ||||
0.831384 | + | 0.555698i | \(0.187549\pi\) | |||||||
\(312\) | 15.8508 | 0.897377 | ||||||||
\(313\) | 27.9445 | 1.57952 | 0.789758 | − | 0.613418i | \(-0.210206\pi\) | ||||
0.789758 | + | 0.613418i | \(0.210206\pi\) | |||||||
\(314\) | 28.5535 | 1.61137 | ||||||||
\(315\) | 80.1523 | 4.51607 | ||||||||
\(316\) | −20.2536 | −1.13935 | ||||||||
\(317\) | 12.3817 | 0.695426 | 0.347713 | − | 0.937601i | \(-0.386958\pi\) | ||||
0.347713 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(318\) | −59.5361 | −3.33862 | ||||||||
\(319\) | 13.4902 | 0.755304 | ||||||||
\(320\) | 50.9527 | 2.84834 | ||||||||
\(321\) | −40.0188 | −2.23363 | ||||||||
\(322\) | 66.7738 | 3.72116 | ||||||||
\(323\) | −11.7133 | −0.651746 | ||||||||
\(324\) | −11.1649 | −0.620271 | ||||||||
\(325\) | 23.3616 | 1.29587 | ||||||||
\(326\) | 29.2791 | 1.62162 | ||||||||
\(327\) | 2.69699 | 0.149144 | ||||||||
\(328\) | 2.96516 | 0.163724 | ||||||||
\(329\) | −60.3530 | −3.32737 | ||||||||
\(330\) | 33.0389 | 1.81873 | ||||||||
\(331\) | −18.6325 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671120\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671120\pi\) | |||||||
\(332\) | 23.5439 | 1.29214 | ||||||||
\(333\) | 4.27377 | 0.234201 | ||||||||
\(334\) | 29.3826 | 1.60775 | ||||||||
\(335\) | −8.85831 | −0.483981 | ||||||||
\(336\) | −5.46555 | −0.298170 | ||||||||
\(337\) | −26.0497 | −1.41902 | −0.709510 | − | 0.704695i | \(-0.751084\pi\) | ||||
−0.709510 | + | 0.704695i | \(0.751084\pi\) | |||||||
\(338\) | 17.7391 | 0.964879 | ||||||||
\(339\) | −30.9758 | −1.68238 | ||||||||
\(340\) | −33.5399 | −1.81896 | ||||||||
\(341\) | −2.09806 | −0.113617 | ||||||||
\(342\) | 41.5117 | 2.24470 | ||||||||
\(343\) | −43.3650 | −2.34149 | ||||||||
\(344\) | 22.6086 | 1.21897 | ||||||||
\(345\) | 64.6746 | 3.48196 | ||||||||
\(346\) | 5.10414 | 0.274400 | ||||||||
\(347\) | −33.6303 | −1.80537 | −0.902686 | − | 0.430301i | \(-0.858408\pi\) | ||||
−0.902686 | + | 0.430301i | \(0.858408\pi\) | |||||||
\(348\) | 82.6025 | 4.42796 | ||||||||
\(349\) | 28.4304 | 1.52184 | 0.760921 | − | 0.648844i | \(-0.224747\pi\) | ||||
0.760921 | + | 0.648844i | \(0.224747\pi\) | |||||||
\(350\) | 111.737 | 5.97258 | ||||||||
\(351\) | −7.81520 | −0.417144 | ||||||||
\(352\) | −8.46882 | −0.451390 | ||||||||
\(353\) | −6.04422 | −0.321701 | −0.160851 | − | 0.986979i | \(-0.551424\pi\) | ||||
−0.160851 | + | 0.986979i | \(0.551424\pi\) | |||||||
\(354\) | −17.5865 | −0.934710 | ||||||||
\(355\) | 23.3718 | 1.24045 | ||||||||
\(356\) | 0.878073 | 0.0465378 | ||||||||
\(357\) | 35.3884 | 1.87295 | ||||||||
\(358\) | 14.6399 | 0.773740 | ||||||||
\(359\) | −15.0125 | −0.792328 | −0.396164 | − | 0.918180i | \(-0.629659\pi\) | ||||
−0.396164 | + | 0.918180i | \(0.629659\pi\) | |||||||
\(360\) | 43.1443 | 2.27391 | ||||||||
\(361\) | −0.643441 | −0.0338653 | ||||||||
\(362\) | 50.9147 | 2.67602 | ||||||||
\(363\) | 24.5096 | 1.28642 | ||||||||
\(364\) | −34.2795 | −1.79674 | ||||||||
\(365\) | 64.5516 | 3.37879 | ||||||||
\(366\) | −60.7592 | −3.17593 | ||||||||
\(367\) | −5.74743 | −0.300013 | −0.150007 | − | 0.988685i | \(-0.547930\pi\) | ||||
−0.150007 | + | 0.988685i | \(0.547930\pi\) | |||||||
\(368\) | −2.59121 | −0.135076 | ||||||||
\(369\) | −4.90519 | −0.255354 | ||||||||
\(370\) | 8.85872 | 0.460543 | ||||||||
\(371\) | 46.7341 | 2.42631 | ||||||||
\(372\) | −12.8468 | −0.666075 | ||||||||
\(373\) | 5.73024 | 0.296700 | 0.148350 | − | 0.988935i | \(-0.452604\pi\) | ||||
0.148350 | + | 0.988935i | \(0.452604\pi\) | |||||||
\(374\) | 8.57081 | 0.443186 | ||||||||
\(375\) | 55.5303 | 2.86757 | ||||||||
\(376\) | −32.4868 | −1.67538 | ||||||||
\(377\) | −22.1927 | −1.14298 | ||||||||
\(378\) | −37.3794 | −1.92259 | ||||||||
\(379\) | 2.33628 | 0.120007 | 0.0600034 | − | 0.998198i | \(-0.480889\pi\) | ||||
0.0600034 | + | 0.998198i | \(0.480889\pi\) | |||||||
\(380\) | 52.5622 | 2.69638 | ||||||||
\(381\) | −6.13841 | −0.314480 | ||||||||
\(382\) | −38.0838 | −1.94854 | ||||||||
\(383\) | 38.8560 | 1.98545 | 0.992724 | − | 0.120415i | \(-0.0384226\pi\) | ||||
0.992724 | + | 0.120415i | \(0.0384226\pi\) | |||||||
\(384\) | −46.6927 | −2.38278 | ||||||||
\(385\) | −25.9345 | −1.32175 | ||||||||
\(386\) | 22.1564 | 1.12773 | ||||||||
\(387\) | −37.4007 | −1.90119 | ||||||||
\(388\) | −39.8528 | −2.02322 | ||||||||
\(389\) | 25.0339 | 1.26927 | 0.634633 | − | 0.772813i | \(-0.281151\pi\) | ||||
0.634633 | + | 0.772813i | \(0.281151\pi\) | |||||||
\(390\) | −54.3524 | −2.75224 | ||||||||
\(391\) | 16.7776 | 0.848481 | ||||||||
\(392\) | −41.4268 | −2.09237 | ||||||||
\(393\) | 6.13784 | 0.309613 | ||||||||
\(394\) | 57.0293 | 2.87310 | ||||||||
\(395\) | 25.2081 | 1.26836 | ||||||||
\(396\) | −18.5548 | −0.932413 | ||||||||
\(397\) | 0.770024 | 0.0386464 | 0.0193232 | − | 0.999813i | \(-0.493849\pi\) | ||||
0.0193232 | + | 0.999813i | \(0.493849\pi\) | |||||||
\(398\) | −41.9864 | −2.10459 | ||||||||
\(399\) | −55.4590 | −2.77642 | ||||||||
\(400\) | −4.33603 | −0.216802 | ||||||||
\(401\) | −28.2063 | −1.40856 | −0.704279 | − | 0.709923i | \(-0.748730\pi\) | ||||
−0.704279 | + | 0.709923i | \(0.748730\pi\) | |||||||
\(402\) | 13.8607 | 0.691311 | ||||||||
\(403\) | 3.45154 | 0.171933 | ||||||||
\(404\) | −25.7270 | −1.27997 | ||||||||
\(405\) | 13.8961 | 0.690501 | ||||||||
\(406\) | −106.146 | −5.26793 | ||||||||
\(407\) | −1.38285 | −0.0685452 | ||||||||
\(408\) | 19.0488 | 0.943059 | ||||||||
\(409\) | −39.6979 | −1.96294 | −0.981469 | − | 0.191623i | \(-0.938625\pi\) | ||||
−0.981469 | + | 0.191623i | \(0.938625\pi\) | |||||||
\(410\) | −10.1675 | −0.502138 | ||||||||
\(411\) | 18.4716 | 0.911136 | ||||||||
\(412\) | 14.1750 | 0.698354 | ||||||||
\(413\) | 13.8049 | 0.679293 | ||||||||
\(414\) | −59.4595 | −2.92227 | ||||||||
\(415\) | −29.3032 | −1.43844 | ||||||||
\(416\) | 13.9321 | 0.683078 | ||||||||
\(417\) | 15.0792 | 0.738429 | ||||||||
\(418\) | −13.4318 | −0.656969 | ||||||||
\(419\) | 13.0860 | 0.639293 | 0.319646 | − | 0.947537i | \(-0.396436\pi\) | ||||
0.319646 | + | 0.947537i | \(0.396436\pi\) | |||||||
\(420\) | −158.802 | −7.74872 | ||||||||
\(421\) | 16.8470 | 0.821071 | 0.410536 | − | 0.911845i | \(-0.365342\pi\) | ||||
0.410536 | + | 0.911845i | \(0.365342\pi\) | |||||||
\(422\) | −14.9481 | −0.727662 | ||||||||
\(423\) | 53.7420 | 2.61302 | ||||||||
\(424\) | 25.1560 | 1.22168 | ||||||||
\(425\) | 28.0750 | 1.36184 | ||||||||
\(426\) | −36.5702 | −1.77183 | ||||||||
\(427\) | 47.6942 | 2.30808 | ||||||||
\(428\) | 46.5859 | 2.25181 | ||||||||
\(429\) | 8.48441 | 0.409631 | ||||||||
\(430\) | −77.5246 | −3.73857 | ||||||||
\(431\) | −2.56848 | −0.123719 | −0.0618597 | − | 0.998085i | \(-0.519703\pi\) | ||||
−0.0618597 | + | 0.998085i | \(0.519703\pi\) | |||||||
\(432\) | 1.45054 | 0.0697891 | ||||||||
\(433\) | 9.02113 | 0.433528 | 0.216764 | − | 0.976224i | \(-0.430450\pi\) | ||||
0.216764 | + | 0.976224i | \(0.430450\pi\) | |||||||
\(434\) | 16.5084 | 0.792429 | ||||||||
\(435\) | −102.809 | −4.92931 | ||||||||
\(436\) | −3.13957 | −0.150358 | ||||||||
\(437\) | −26.2931 | −1.25777 | ||||||||
\(438\) | −101.005 | −4.82620 | ||||||||
\(439\) | −15.5195 | −0.740704 | −0.370352 | − | 0.928891i | \(-0.620763\pi\) | ||||
−0.370352 | + | 0.928891i | \(0.620763\pi\) | |||||||
\(440\) | −13.9600 | −0.665518 | ||||||||
\(441\) | 68.5312 | 3.26339 | ||||||||
\(442\) | −14.0999 | −0.670663 | ||||||||
\(443\) | −2.47284 | −0.117488 | −0.0587440 | − | 0.998273i | \(-0.518710\pi\) | ||||
−0.0587440 | + | 0.998273i | \(0.518710\pi\) | |||||||
\(444\) | −8.46740 | −0.401845 | ||||||||
\(445\) | −1.09287 | −0.0518070 | ||||||||
\(446\) | 27.8969 | 1.32096 | ||||||||
\(447\) | 38.9219 | 1.84094 | ||||||||
\(448\) | 62.5830 | 2.95677 | ||||||||
\(449\) | 0.118434 | 0.00558924 | 0.00279462 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279462 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(450\) | −99.4971 | −4.69034 | ||||||||
\(451\) | 1.58715 | 0.0747360 | ||||||||
\(452\) | 36.0590 | 1.69607 | ||||||||
\(453\) | −30.6917 | −1.44202 | ||||||||
\(454\) | 14.9440 | 0.701356 | ||||||||
\(455\) | 42.6651 | 2.00017 | ||||||||
\(456\) | −29.8525 | −1.39797 | ||||||||
\(457\) | −36.8279 | −1.72274 | −0.861369 | − | 0.507979i | \(-0.830393\pi\) | ||||
−0.861369 | + | 0.507979i | \(0.830393\pi\) | |||||||
\(458\) | −3.17687 | −0.148445 | ||||||||
\(459\) | −9.39196 | −0.438379 | ||||||||
\(460\) | −75.2877 | −3.51031 | ||||||||
\(461\) | 0.785039 | 0.0365629 | 0.0182815 | − | 0.999833i | \(-0.494181\pi\) | ||||
0.0182815 | + | 0.999833i | \(0.494181\pi\) | |||||||
\(462\) | 40.5802 | 1.88796 | ||||||||
\(463\) | 11.4484 | 0.532055 | 0.266027 | − | 0.963965i | \(-0.414289\pi\) | ||||
0.266027 | + | 0.963965i | \(0.414289\pi\) | |||||||
\(464\) | 4.11908 | 0.191224 | ||||||||
\(465\) | 15.9894 | 0.741491 | ||||||||
\(466\) | 22.4942 | 1.04202 | ||||||||
\(467\) | 37.9401 | 1.75566 | 0.877829 | − | 0.478974i | \(-0.158991\pi\) | ||||
0.877829 | + | 0.478974i | \(0.158991\pi\) | |||||||
\(468\) | 30.5246 | 1.41100 | ||||||||
\(469\) | −10.8803 | −0.502405 | ||||||||
\(470\) | 111.397 | 5.13836 | ||||||||
\(471\) | 33.9684 | 1.56518 | ||||||||
\(472\) | 7.43087 | 0.342034 | ||||||||
\(473\) | 12.1016 | 0.556432 | ||||||||
\(474\) | −39.4435 | −1.81170 | ||||||||
\(475\) | −43.9978 | −2.01876 | ||||||||
\(476\) | −41.1956 | −1.88820 | ||||||||
\(477\) | −41.6149 | −1.90541 | ||||||||
\(478\) | 8.23605 | 0.376708 | ||||||||
\(479\) | −29.8738 | −1.36497 | −0.682484 | − | 0.730901i | \(-0.739100\pi\) | ||||
−0.682484 | + | 0.730901i | \(0.739100\pi\) | |||||||
\(480\) | 64.5411 | 2.94589 | ||||||||
\(481\) | 2.27493 | 0.103728 | ||||||||
\(482\) | 20.3019 | 0.924725 | ||||||||
\(483\) | 79.4370 | 3.61451 | ||||||||
\(484\) | −28.5316 | −1.29689 | ||||||||
\(485\) | 49.6017 | 2.25230 | ||||||||
\(486\) | −45.1079 | −2.04614 | ||||||||
\(487\) | −0.0302710 | −0.00137171 | −0.000685855 | − | 1.00000i | \(-0.500218\pi\) | ||||
−0.000685855 | 1.00000i | \(0.500218\pi\) | ||||||||
\(488\) | 25.6728 | 1.16215 | ||||||||
\(489\) | 34.8317 | 1.57514 | ||||||||
\(490\) | 142.052 | 6.41726 | ||||||||
\(491\) | −25.4346 | −1.14785 | −0.573923 | − | 0.818909i | \(-0.694579\pi\) | ||||
−0.573923 | + | 0.818909i | \(0.694579\pi\) | |||||||
\(492\) | 9.71839 | 0.438139 | ||||||||
\(493\) | −26.6703 | −1.20117 | ||||||||
\(494\) | 22.0967 | 0.994176 | ||||||||
\(495\) | 23.0937 | 1.03798 | ||||||||
\(496\) | −0.640622 | −0.0287648 | ||||||||
\(497\) | 28.7066 | 1.28767 | ||||||||
\(498\) | 45.8512 | 2.05464 | ||||||||
\(499\) | 1.05251 | 0.0471169 | 0.0235584 | − | 0.999722i | \(-0.492500\pi\) | ||||
0.0235584 | + | 0.999722i | \(0.492500\pi\) | |||||||
\(500\) | −64.6429 | −2.89092 | ||||||||
\(501\) | 34.9548 | 1.56167 | ||||||||
\(502\) | 13.7618 | 0.614219 | ||||||||
\(503\) | 13.6643 | 0.609259 | 0.304630 | − | 0.952471i | \(-0.401467\pi\) | ||||
0.304630 | + | 0.952471i | \(0.401467\pi\) | |||||||
\(504\) | 52.9923 | 2.36047 | ||||||||
\(505\) | 32.0204 | 1.42489 | ||||||||
\(506\) | 19.2390 | 0.855280 | ||||||||
\(507\) | 21.1032 | 0.937224 | ||||||||
\(508\) | 7.14572 | 0.317040 | ||||||||
\(509\) | −6.02784 | −0.267179 | −0.133590 | − | 0.991037i | \(-0.542650\pi\) | ||||
−0.133590 | + | 0.991037i | \(0.542650\pi\) | |||||||
\(510\) | −65.3184 | −2.89235 | ||||||||
\(511\) | 79.2860 | 3.50740 | ||||||||
\(512\) | −4.76755 | −0.210698 | ||||||||
\(513\) | 14.7186 | 0.649844 | ||||||||
\(514\) | −53.4432 | −2.35728 | ||||||||
\(515\) | −17.6426 | −0.777424 | ||||||||
\(516\) | 74.1001 | 3.26207 | ||||||||
\(517\) | −17.3891 | −0.764770 | ||||||||
\(518\) | 10.8808 | 0.478074 | ||||||||
\(519\) | 6.07210 | 0.266535 | ||||||||
\(520\) | 22.9657 | 1.00711 | ||||||||
\(521\) | 4.47223 | 0.195932 | 0.0979661 | − | 0.995190i | \(-0.468766\pi\) | ||||
0.0979661 | + | 0.995190i | \(0.468766\pi\) | |||||||
\(522\) | 94.5188 | 4.13697 | ||||||||
\(523\) | −15.2839 | −0.668316 | −0.334158 | − | 0.942517i | \(-0.608452\pi\) | ||||
−0.334158 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(524\) | −7.14506 | −0.312133 | ||||||||
\(525\) | 132.927 | 5.80140 | ||||||||
\(526\) | −3.35327 | −0.146209 | ||||||||
\(527\) | 4.14791 | 0.180686 | ||||||||
\(528\) | −1.57475 | −0.0685321 | ||||||||
\(529\) | 14.6610 | 0.637436 | ||||||||
\(530\) | −86.2598 | −3.74689 | ||||||||
\(531\) | −12.2927 | −0.533457 | ||||||||
\(532\) | 64.5599 | 2.79903 | ||||||||
\(533\) | −2.61103 | −0.113096 | ||||||||
\(534\) | 1.71003 | 0.0740003 | ||||||||
\(535\) | −57.9819 | −2.50677 | ||||||||
\(536\) | −5.85663 | −0.252968 | ||||||||
\(537\) | 17.4162 | 0.751564 | ||||||||
\(538\) | −66.2982 | −2.85832 | ||||||||
\(539\) | −22.1743 | −0.955117 | ||||||||
\(540\) | 42.1454 | 1.81365 | ||||||||
\(541\) | 15.9178 | 0.684362 | 0.342181 | − | 0.939634i | \(-0.388834\pi\) | ||||
0.342181 | + | 0.939634i | \(0.388834\pi\) | |||||||
\(542\) | 12.6998 | 0.545503 | ||||||||
\(543\) | 60.5703 | 2.59932 | ||||||||
\(544\) | 16.7430 | 0.717850 | ||||||||
\(545\) | 3.90758 | 0.167382 | ||||||||
\(546\) | −66.7587 | −2.85701 | ||||||||
\(547\) | −43.0374 | −1.84015 | −0.920073 | − | 0.391747i | \(-0.871871\pi\) | ||||
−0.920073 | + | 0.391747i | \(0.871871\pi\) | |||||||
\(548\) | −21.5028 | −0.918553 | ||||||||
\(549\) | −42.4698 | −1.81257 | ||||||||
\(550\) | 32.1938 | 1.37275 | ||||||||
\(551\) | 41.7964 | 1.78059 | ||||||||
\(552\) | 42.7593 | 1.81996 | ||||||||
\(553\) | 30.9620 | 1.31664 | ||||||||
\(554\) | 4.41587 | 0.187612 | ||||||||
\(555\) | 10.5387 | 0.447344 | ||||||||
\(556\) | −17.5536 | −0.744441 | ||||||||
\(557\) | 28.7849 | 1.21966 | 0.609829 | − | 0.792533i | \(-0.291238\pi\) | ||||
0.609829 | + | 0.792533i | \(0.291238\pi\) | |||||||
\(558\) | −14.7001 | −0.622304 | ||||||||
\(559\) | −19.9084 | −0.842035 | ||||||||
\(560\) | −7.91885 | −0.334632 | ||||||||
\(561\) | 10.1962 | 0.430484 | ||||||||
\(562\) | 61.0146 | 2.57375 | ||||||||
\(563\) | −5.09060 | −0.214543 | −0.107272 | − | 0.994230i | \(-0.534211\pi\) | ||||
−0.107272 | + | 0.994230i | \(0.534211\pi\) | |||||||
\(564\) | −106.476 | −4.48345 | ||||||||
\(565\) | −44.8798 | −1.88811 | ||||||||
\(566\) | 12.2380 | 0.514401 | ||||||||
\(567\) | 17.0679 | 0.716785 | ||||||||
\(568\) | 15.4522 | 0.648358 | ||||||||
\(569\) | 44.7274 | 1.87507 | 0.937536 | − | 0.347889i | \(-0.113101\pi\) | ||||
0.937536 | + | 0.347889i | \(0.113101\pi\) | |||||||
\(570\) | 102.364 | 4.28755 | ||||||||
\(571\) | 36.7979 | 1.53994 | 0.769972 | − | 0.638077i | \(-0.220270\pi\) | ||||
0.769972 | + | 0.638077i | \(0.220270\pi\) | |||||||
\(572\) | −9.87670 | −0.412966 | ||||||||
\(573\) | −45.3061 | −1.89269 | ||||||||
\(574\) | −12.4883 | −0.521253 | ||||||||
\(575\) | 63.0205 | 2.62814 | ||||||||
\(576\) | −55.7277 | −2.32199 | ||||||||
\(577\) | −21.9204 | −0.912556 | −0.456278 | − | 0.889837i | \(-0.650818\pi\) | ||||
−0.456278 | + | 0.889837i | \(0.650818\pi\) | |||||||
\(578\) | 21.5954 | 0.898252 | ||||||||
\(579\) | 26.3583 | 1.09541 | ||||||||
\(580\) | 119.680 | 4.96944 | ||||||||
\(581\) | −35.9919 | −1.49319 | ||||||||
\(582\) | −77.6126 | −3.21715 | ||||||||
\(583\) | 13.4652 | 0.557670 | ||||||||
\(584\) | 42.6780 | 1.76603 | ||||||||
\(585\) | −37.9916 | −1.57076 | ||||||||
\(586\) | 20.8713 | 0.862185 | ||||||||
\(587\) | −21.2708 | −0.877938 | −0.438969 | − | 0.898502i | \(-0.644656\pi\) | ||||
−0.438969 | + | 0.898502i | \(0.644656\pi\) | |||||||
\(588\) | −135.777 | −5.59936 | ||||||||
\(589\) | −6.50040 | −0.267844 | ||||||||
\(590\) | −25.4804 | −1.04901 | ||||||||
\(591\) | 67.8445 | 2.79075 | ||||||||
\(592\) | −0.422238 | −0.0173539 | ||||||||
\(593\) | 15.9520 | 0.655070 | 0.327535 | − | 0.944839i | \(-0.393782\pi\) | ||||
0.327535 | + | 0.944839i | \(0.393782\pi\) | |||||||
\(594\) | −10.7698 | −0.441892 | ||||||||
\(595\) | 51.2730 | 2.10199 | ||||||||
\(596\) | −45.3090 | −1.85593 | ||||||||
\(597\) | −49.9489 | −2.04427 | ||||||||
\(598\) | −31.6503 | −1.29428 | ||||||||
\(599\) | −30.0794 | −1.22901 | −0.614506 | − | 0.788912i | \(-0.710645\pi\) | ||||
−0.614506 | + | 0.788912i | \(0.710645\pi\) | |||||||
\(600\) | 71.5517 | 2.92109 | ||||||||
\(601\) | −20.3443 | −0.829861 | −0.414930 | − | 0.909853i | \(-0.636194\pi\) | ||||
−0.414930 | + | 0.909853i | \(0.636194\pi\) | |||||||
\(602\) | −95.2201 | −3.88088 | ||||||||
\(603\) | 9.68846 | 0.394545 | ||||||||
\(604\) | 35.7282 | 1.45376 | ||||||||
\(605\) | 35.5110 | 1.44373 | ||||||||
\(606\) | −50.1029 | −2.03529 | ||||||||
\(607\) | −20.3111 | −0.824402 | −0.412201 | − | 0.911093i | \(-0.635240\pi\) | ||||
−0.412201 | + | 0.911093i | \(0.635240\pi\) | |||||||
\(608\) | −26.2388 | −1.06413 | ||||||||
\(609\) | −126.276 | −5.11695 | ||||||||
\(610\) | −88.0319 | −3.56431 | ||||||||
\(611\) | 28.6068 | 1.15731 | ||||||||
\(612\) | 36.6831 | 1.48283 | ||||||||
\(613\) | 36.1412 | 1.45973 | 0.729864 | − | 0.683592i | \(-0.239583\pi\) | ||||
0.729864 | + | 0.683592i | \(0.239583\pi\) | |||||||
\(614\) | 36.6950 | 1.48089 | ||||||||
\(615\) | −12.0957 | −0.487747 | ||||||||
\(616\) | −17.1465 | −0.690852 | ||||||||
\(617\) | −13.2986 | −0.535383 | −0.267691 | − | 0.963505i | \(-0.586261\pi\) | ||||
−0.267691 | + | 0.963505i | \(0.586261\pi\) | |||||||
\(618\) | 27.6056 | 1.11046 | ||||||||
\(619\) | −7.63434 | −0.306850 | −0.153425 | − | 0.988160i | \(-0.549030\pi\) | ||||
−0.153425 | + | 0.988160i | \(0.549030\pi\) | |||||||
\(620\) | −18.6133 | −0.747527 | ||||||||
\(621\) | −21.0823 | −0.846004 | ||||||||
\(622\) | −66.4776 | −2.66551 | ||||||||
\(623\) | −1.34232 | −0.0537791 | ||||||||
\(624\) | 2.59063 | 0.103708 | ||||||||
\(625\) | 29.1101 | 1.16440 | ||||||||
\(626\) | −63.3519 | −2.53205 | ||||||||
\(627\) | −15.9790 | −0.638140 | ||||||||
\(628\) | −39.5427 | −1.57792 | ||||||||
\(629\) | 2.73391 | 0.109008 | ||||||||
\(630\) | −181.710 | −7.23951 | ||||||||
\(631\) | −35.6061 | −1.41746 | −0.708729 | − | 0.705481i | \(-0.750731\pi\) | ||||
−0.708729 | + | 0.705481i | \(0.750731\pi\) | |||||||
\(632\) | 16.6662 | 0.662945 | ||||||||
\(633\) | −17.7829 | −0.706806 | ||||||||
\(634\) | −28.0701 | −1.11481 | ||||||||
\(635\) | −8.89373 | −0.352937 | ||||||||
\(636\) | 82.4494 | 3.26933 | ||||||||
\(637\) | 36.4791 | 1.44536 | ||||||||
\(638\) | −30.5830 | −1.21079 | ||||||||
\(639\) | −25.5621 | −1.01122 | ||||||||
\(640\) | −67.6514 | −2.67416 | ||||||||
\(641\) | −17.9187 | −0.707745 | −0.353873 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353873 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(642\) | 90.7251 | 3.58064 | ||||||||
\(643\) | 7.99908 | 0.315453 | 0.157726 | − | 0.987483i | \(-0.449584\pi\) | ||||
0.157726 | + | 0.987483i | \(0.449584\pi\) | |||||||
\(644\) | −92.4726 | −3.64393 | ||||||||
\(645\) | −92.2266 | −3.63142 | ||||||||
\(646\) | 26.5548 | 1.04479 | ||||||||
\(647\) | −18.6325 | −0.732521 | −0.366260 | − | 0.930512i | \(-0.619362\pi\) | ||||
−0.366260 | + | 0.930512i | \(0.619362\pi\) | |||||||
\(648\) | 9.18731 | 0.360912 | ||||||||
\(649\) | 3.97749 | 0.156130 | ||||||||
\(650\) | −52.9623 | −2.07735 | ||||||||
\(651\) | 19.6391 | 0.769717 | ||||||||
\(652\) | −40.5476 | −1.58797 | ||||||||
\(653\) | −1.83131 | −0.0716648 | −0.0358324 | − | 0.999358i | \(-0.511408\pi\) | ||||
−0.0358324 | + | 0.999358i | \(0.511408\pi\) | |||||||
\(654\) | −6.11425 | −0.239086 | ||||||||
\(655\) | 8.89290 | 0.347474 | ||||||||
\(656\) | 0.484620 | 0.0189212 | ||||||||
\(657\) | −70.6010 | −2.75441 | ||||||||
\(658\) | 136.824 | 5.33395 | ||||||||
\(659\) | −6.29243 | −0.245118 | −0.122559 | − | 0.992461i | \(-0.539110\pi\) | ||||
−0.122559 | + | 0.992461i | \(0.539110\pi\) | |||||||
\(660\) | −45.7543 | −1.78098 | ||||||||
\(661\) | 21.7758 | 0.846979 | 0.423489 | − | 0.905901i | \(-0.360805\pi\) | ||||
0.423489 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(662\) | 42.2411 | 1.64175 | ||||||||
\(663\) | −16.7738 | −0.651441 | ||||||||
\(664\) | −19.3737 | −0.751845 | ||||||||
\(665\) | −80.3527 | −3.11594 | ||||||||
\(666\) | −9.68891 | −0.375438 | ||||||||
\(667\) | −59.8672 | −2.31807 | ||||||||
\(668\) | −40.6909 | −1.57438 | ||||||||
\(669\) | 33.1873 | 1.28310 | ||||||||
\(670\) | 20.0823 | 0.775849 | ||||||||
\(671\) | 13.7418 | 0.530495 | ||||||||
\(672\) | 79.2731 | 3.05802 | ||||||||
\(673\) | 3.07068 | 0.118366 | 0.0591831 | − | 0.998247i | \(-0.481150\pi\) | ||||
0.0591831 | + | 0.998247i | \(0.481150\pi\) | |||||||
\(674\) | 59.0564 | 2.27477 | ||||||||
\(675\) | −35.2783 | −1.35786 | ||||||||
\(676\) | −24.5662 | −0.944854 | ||||||||
\(677\) | −3.24960 | −0.124892 | −0.0624462 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624462 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(678\) | 70.2242 | 2.69694 | ||||||||
\(679\) | 60.9237 | 2.33804 | ||||||||
\(680\) | 27.5992 | 1.05838 | ||||||||
\(681\) | 17.7780 | 0.681254 | ||||||||
\(682\) | 4.75644 | 0.182134 | ||||||||
\(683\) | −40.0227 | −1.53143 | −0.765714 | − | 0.643182i | \(-0.777614\pi\) | ||||
−0.765714 | + | 0.643182i | \(0.777614\pi\) | |||||||
\(684\) | −57.4880 | −2.19811 | ||||||||
\(685\) | 26.7628 | 1.02256 | ||||||||
\(686\) | 98.3110 | 3.75353 | ||||||||
\(687\) | −3.77934 | −0.144191 | ||||||||
\(688\) | 3.69510 | 0.140874 | ||||||||
\(689\) | −22.1516 | −0.843909 | ||||||||
\(690\) | −146.621 | −5.58178 | ||||||||
\(691\) | 4.10442 | 0.156139 | 0.0780697 | − | 0.996948i | \(-0.475124\pi\) | ||||
0.0780697 | + | 0.996948i | \(0.475124\pi\) | |||||||
\(692\) | −7.06853 | −0.268705 | ||||||||
\(693\) | 28.3650 | 1.07750 | ||||||||
\(694\) | 76.2421 | 2.89411 | ||||||||
\(695\) | 21.8477 | 0.828729 | ||||||||
\(696\) | −67.9716 | −2.57646 | ||||||||
\(697\) | −3.13782 | −0.118854 | ||||||||
\(698\) | −64.4534 | −2.43960 | ||||||||
\(699\) | 26.7601 | 1.01216 | ||||||||
\(700\) | −154.740 | −5.84862 | ||||||||
\(701\) | −41.9022 | −1.58262 | −0.791312 | − | 0.611413i | \(-0.790602\pi\) | ||||
−0.791312 | + | 0.611413i | \(0.790602\pi\) | |||||||
\(702\) | 17.7175 | 0.668705 | ||||||||
\(703\) | −4.28446 | −0.161591 | ||||||||
\(704\) | 18.0316 | 0.679590 | ||||||||
\(705\) | 132.522 | 4.99109 | ||||||||
\(706\) | 13.7026 | 0.515705 | ||||||||
\(707\) | 39.3293 | 1.47913 | ||||||||
\(708\) | 24.3548 | 0.915311 | ||||||||
\(709\) | −11.0237 | −0.414004 | −0.207002 | − | 0.978340i | \(-0.566371\pi\) | ||||
−0.207002 | + | 0.978340i | \(0.566371\pi\) | |||||||
\(710\) | −52.9853 | −1.98850 | ||||||||
\(711\) | −27.5704 | −1.03397 | ||||||||
\(712\) | −0.722545 | −0.0270785 | ||||||||
\(713\) | 9.31088 | 0.348695 | ||||||||
\(714\) | −80.2277 | −3.00245 | ||||||||
\(715\) | 12.2928 | 0.459723 | ||||||||
\(716\) | −20.2742 | −0.757682 | ||||||||
\(717\) | 9.79796 | 0.365911 | ||||||||
\(718\) | 34.0342 | 1.27015 | ||||||||
\(719\) | −28.1282 | −1.04900 | −0.524502 | − | 0.851409i | \(-0.675749\pi\) | ||||
−0.524502 | + | 0.851409i | \(0.675749\pi\) | |||||||
\(720\) | 7.05142 | 0.262791 | ||||||||
\(721\) | −21.6696 | −0.807018 | ||||||||
\(722\) | 1.45872 | 0.0542880 | ||||||||
\(723\) | 24.1520 | 0.898222 | ||||||||
\(724\) | −70.5099 | −2.62048 | ||||||||
\(725\) | −100.179 | −3.72057 | ||||||||
\(726\) | −55.5647 | −2.06220 | ||||||||
\(727\) | −12.6327 | −0.468522 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(728\) | 28.2078 | 1.04545 | ||||||||
\(729\) | −42.9937 | −1.59236 | ||||||||
\(730\) | −146.343 | −5.41638 | ||||||||
\(731\) | −23.9250 | −0.884900 | ||||||||
\(732\) | 84.1432 | 3.11002 | ||||||||
\(733\) | 29.0669 | 1.07361 | 0.536805 | − | 0.843707i | \(-0.319631\pi\) | ||||
0.536805 | + | 0.843707i | \(0.319631\pi\) | |||||||
\(734\) | 13.0298 | 0.480938 | ||||||||
\(735\) | 168.991 | 6.23334 | ||||||||
\(736\) | 37.5833 | 1.38534 | ||||||||
\(737\) | −3.13485 | −0.115474 | ||||||||
\(738\) | 11.1204 | 0.409346 | ||||||||
\(739\) | 23.0222 | 0.846887 | 0.423444 | − | 0.905922i | \(-0.360821\pi\) | ||||
0.423444 | + | 0.905922i | \(0.360821\pi\) | |||||||
\(740\) | −12.2681 | −0.450985 | ||||||||
\(741\) | 26.2871 | 0.965682 | ||||||||
\(742\) | −105.949 | −3.88952 | ||||||||
\(743\) | −37.0672 | −1.35986 | −0.679931 | − | 0.733276i | \(-0.737990\pi\) | ||||
−0.679931 | + | 0.733276i | \(0.737990\pi\) | |||||||
\(744\) | 10.5713 | 0.387563 | ||||||||
\(745\) | 56.3926 | 2.06607 | ||||||||
\(746\) | −12.9908 | −0.475627 | ||||||||
\(747\) | 32.0493 | 1.17262 | ||||||||
\(748\) | −11.8694 | −0.433988 | ||||||||
\(749\) | −71.2166 | −2.60220 | ||||||||
\(750\) | −125.891 | −4.59688 | ||||||||
\(751\) | −1.41819 | −0.0517505 | −0.0258753 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258753 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(752\) | −5.30957 | −0.193620 | ||||||||
\(753\) | 16.3716 | 0.596615 | ||||||||
\(754\) | 50.3123 | 1.83227 | ||||||||
\(755\) | −44.4681 | −1.61836 | ||||||||
\(756\) | 51.7654 | 1.88269 | ||||||||
\(757\) | −0.0199105 | −0.000723659 0 | −0.000361830 | − | 1.00000i | \(-0.500115\pi\) | ||||
−0.000361830 | 1.00000i | \(0.500115\pi\) | ||||||||
\(758\) | −5.29650 | −0.192378 | ||||||||
\(759\) | 22.8876 | 0.830767 | ||||||||
\(760\) | −43.2522 | −1.56892 | ||||||||
\(761\) | 21.1444 | 0.766484 | 0.383242 | − | 0.923648i | \(-0.374808\pi\) | ||||
0.383242 | + | 0.923648i | \(0.374808\pi\) | |||||||
\(762\) | 13.9162 | 0.504129 | ||||||||
\(763\) | 4.79951 | 0.173754 | ||||||||
\(764\) | 52.7409 | 1.90810 | ||||||||
\(765\) | −45.6566 | −1.65072 | ||||||||
\(766\) | −88.0889 | −3.18278 | ||||||||
\(767\) | −6.54339 | −0.236268 | ||||||||
\(768\) | 35.5205 | 1.28174 | ||||||||
\(769\) | −7.28020 | −0.262531 | −0.131265 | − | 0.991347i | \(-0.541904\pi\) | ||||
−0.131265 | + | 0.991347i | \(0.541904\pi\) | |||||||
\(770\) | 58.7952 | 2.11883 | ||||||||
\(771\) | −63.5783 | −2.28972 | ||||||||
\(772\) | −30.6836 | −1.10433 | ||||||||
\(773\) | −18.8747 | −0.678877 | −0.339438 | − | 0.940628i | \(-0.610237\pi\) | ||||
−0.339438 | + | 0.940628i | \(0.610237\pi\) | |||||||
\(774\) | 84.7897 | 3.04770 | ||||||||
\(775\) | 15.5805 | 0.559667 | ||||||||
\(776\) | 32.7939 | 1.17723 | ||||||||
\(777\) | 12.9442 | 0.464372 | ||||||||
\(778\) | −56.7533 | −2.03470 | ||||||||
\(779\) | 4.91745 | 0.176186 | ||||||||
\(780\) | 75.2706 | 2.69512 | ||||||||
\(781\) | 8.27101 | 0.295960 | ||||||||
\(782\) | −38.0359 | −1.36016 | ||||||||
\(783\) | 33.5131 | 1.19766 | ||||||||
\(784\) | −6.77071 | −0.241811 | ||||||||
\(785\) | 49.2157 | 1.75658 | ||||||||
\(786\) | −13.9149 | −0.496327 | ||||||||
\(787\) | −34.8376 | −1.24183 | −0.620914 | − | 0.783879i | \(-0.713238\pi\) | ||||
−0.620914 | + | 0.783879i | \(0.713238\pi\) | |||||||
\(788\) | −78.9778 | −2.81347 | ||||||||
\(789\) | −3.98919 | −0.142019 | ||||||||
\(790\) | −57.1482 | −2.03324 | ||||||||
\(791\) | −55.1239 | −1.95998 | ||||||||
\(792\) | 15.2683 | 0.542535 | ||||||||
\(793\) | −22.6067 | −0.802786 | ||||||||
\(794\) | −1.74569 | −0.0619523 | ||||||||
\(795\) | −102.618 | −3.63950 | ||||||||
\(796\) | 58.1455 | 2.06091 | ||||||||
\(797\) | 15.4218 | 0.546270 | 0.273135 | − | 0.961976i | \(-0.411939\pi\) | ||||
0.273135 | + | 0.961976i | \(0.411939\pi\) | |||||||
\(798\) | 125.729 | 4.45076 | ||||||||
\(799\) | 34.3784 | 1.21622 | ||||||||
\(800\) | 62.8904 | 2.22351 | ||||||||
\(801\) | 1.19529 | 0.0422334 | ||||||||
\(802\) | 63.9455 | 2.25800 | ||||||||
\(803\) | 22.8441 | 0.806150 | ||||||||
\(804\) | −19.1952 | −0.676964 | ||||||||
\(805\) | 115.093 | 4.05651 | ||||||||
\(806\) | −7.82485 | −0.275618 | ||||||||
\(807\) | −78.8711 | −2.77639 | ||||||||
\(808\) | 21.1701 | 0.744763 | ||||||||
\(809\) | −25.0283 | −0.879947 | −0.439973 | − | 0.898011i | \(-0.645012\pi\) | ||||
−0.439973 | + | 0.898011i | \(0.645012\pi\) | |||||||
\(810\) | −31.5032 | −1.10691 | ||||||||
\(811\) | −46.7655 | −1.64216 | −0.821080 | − | 0.570813i | \(-0.806628\pi\) | ||||
−0.821080 | + | 0.570813i | \(0.806628\pi\) | |||||||
\(812\) | 146.998 | 5.15860 | ||||||||
\(813\) | 15.1082 | 0.529868 | ||||||||
\(814\) | 3.13500 | 0.109882 | ||||||||
\(815\) | 50.4664 | 1.76776 | ||||||||
\(816\) | 3.11330 | 0.108987 | ||||||||
\(817\) | 37.4942 | 1.31176 | ||||||||
\(818\) | 89.9977 | 3.14670 | ||||||||
\(819\) | −46.6634 | −1.63055 | ||||||||
\(820\) | 14.0806 | 0.491717 | ||||||||
\(821\) | −4.93802 | −0.172338 | −0.0861690 | − | 0.996281i | \(-0.527463\pi\) | ||||
−0.0861690 | + | 0.996281i | \(0.527463\pi\) | |||||||
\(822\) | −41.8762 | −1.46060 | ||||||||
\(823\) | −10.0634 | −0.350788 | −0.175394 | − | 0.984498i | \(-0.556120\pi\) | ||||
−0.175394 | + | 0.984498i | \(0.556120\pi\) | |||||||
\(824\) | −11.6643 | −0.406345 | ||||||||
\(825\) | 38.2992 | 1.33341 | ||||||||
\(826\) | −31.2965 | −1.08894 | ||||||||
\(827\) | −8.66040 | −0.301152 | −0.150576 | − | 0.988598i | \(-0.548113\pi\) | ||||
−0.150576 | + | 0.988598i | \(0.548113\pi\) | |||||||
\(828\) | 82.3432 | 2.86162 | ||||||||
\(829\) | −34.4007 | −1.19478 | −0.597392 | − | 0.801949i | \(-0.703797\pi\) | ||||
−0.597392 | + | 0.801949i | \(0.703797\pi\) | |||||||
\(830\) | 66.4322 | 2.30590 | ||||||||
\(831\) | 5.25331 | 0.182235 | ||||||||
\(832\) | −29.6638 | −1.02841 | ||||||||
\(833\) | 43.8390 | 1.51893 | ||||||||
\(834\) | −34.1854 | −1.18374 | ||||||||
\(835\) | 50.6448 | 1.75264 | ||||||||
\(836\) | 18.6012 | 0.643334 | ||||||||
\(837\) | −5.21215 | −0.180158 | ||||||||
\(838\) | −29.6668 | −1.02482 | ||||||||
\(839\) | 15.1294 | 0.522324 | 0.261162 | − | 0.965295i | \(-0.415894\pi\) | ||||
0.261162 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(840\) | 130.674 | 4.50868 | ||||||||
\(841\) | 66.1670 | 2.28162 | ||||||||
\(842\) | −38.1931 | −1.31622 | ||||||||
\(843\) | 72.5856 | 2.49998 | ||||||||
\(844\) | 20.7011 | 0.712560 | ||||||||
\(845\) | 30.5756 | 1.05183 | ||||||||
\(846\) | −121.836 | −4.18882 | ||||||||
\(847\) | 43.6167 | 1.49869 | ||||||||
\(848\) | 4.11145 | 0.141188 | ||||||||
\(849\) | 14.5588 | 0.499658 | ||||||||
\(850\) | −63.6478 | −2.18310 | ||||||||
\(851\) | 6.13686 | 0.210369 | ||||||||
\(852\) | 50.6448 | 1.73506 | ||||||||
\(853\) | 2.12121 | 0.0726288 | 0.0363144 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363144 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(854\) | −108.126 | −3.69999 | ||||||||
\(855\) | 71.5509 | 2.44699 | ||||||||
\(856\) | −38.3344 | −1.31024 | ||||||||
\(857\) | −25.4613 | −0.869742 | −0.434871 | − | 0.900493i | \(-0.643206\pi\) | ||||
−0.434871 | + | 0.900493i | \(0.643206\pi\) | |||||||
\(858\) | −19.2347 | −0.656661 | ||||||||
\(859\) | −15.7319 | −0.536765 | −0.268383 | − | 0.963312i | \(-0.586489\pi\) | ||||
−0.268383 | + | 0.963312i | \(0.586489\pi\) | |||||||
\(860\) | 107.361 | 3.66098 | ||||||||
\(861\) | −14.8567 | −0.506313 | ||||||||
\(862\) | 5.82290 | 0.198329 | ||||||||
\(863\) | −3.88810 | −0.132353 | −0.0661763 | − | 0.997808i | \(-0.521080\pi\) | ||||
−0.0661763 | + | 0.997808i | \(0.521080\pi\) | |||||||
\(864\) | −21.0388 | −0.715755 | ||||||||
\(865\) | 8.79765 | 0.299129 | ||||||||
\(866\) | −20.4515 | −0.694969 | ||||||||
\(867\) | 25.6908 | 0.872507 | ||||||||
\(868\) | −22.8619 | −0.775982 | ||||||||
\(869\) | 8.92084 | 0.302619 | ||||||||
\(870\) | 233.074 | 7.90196 | ||||||||
\(871\) | 5.15717 | 0.174744 | ||||||||
\(872\) | 2.58348 | 0.0874876 | ||||||||
\(873\) | −54.2501 | −1.83609 | ||||||||
\(874\) | 59.6081 | 2.01627 | ||||||||
\(875\) | 98.8205 | 3.34074 | ||||||||
\(876\) | 139.878 | 4.72604 | ||||||||
\(877\) | 9.84333 | 0.332386 | 0.166193 | − | 0.986093i | \(-0.446853\pi\) | ||||
0.166193 | + | 0.986093i | \(0.446853\pi\) | |||||||
\(878\) | 35.1836 | 1.18739 | ||||||||
\(879\) | 24.8294 | 0.837473 | ||||||||
\(880\) | −2.28160 | −0.0769126 | ||||||||
\(881\) | −27.6161 | −0.930410 | −0.465205 | − | 0.885203i | \(-0.654019\pi\) | ||||
−0.465205 | + | 0.885203i | \(0.654019\pi\) | |||||||
\(882\) | −155.364 | −5.23139 | ||||||||
\(883\) | 18.4095 | 0.619529 | 0.309765 | − | 0.950813i | \(-0.399750\pi\) | ||||
0.309765 | + | 0.950813i | \(0.399750\pi\) | |||||||
\(884\) | 19.5264 | 0.656744 | ||||||||
\(885\) | −30.3126 | −1.01895 | ||||||||
\(886\) | 5.60607 | 0.188340 | ||||||||
\(887\) | −23.9276 | −0.803412 | −0.401706 | − | 0.915769i | \(-0.631583\pi\) | ||||
−0.401706 | + | 0.915769i | \(0.631583\pi\) | |||||||
\(888\) | 6.96762 | 0.233818 | ||||||||
\(889\) | −10.9238 | −0.366372 | ||||||||
\(890\) | 2.47760 | 0.0830494 | ||||||||
\(891\) | 4.91765 | 0.164748 | ||||||||
\(892\) | −38.6334 | −1.29354 | ||||||||
\(893\) | −53.8763 | −1.80290 | ||||||||
\(894\) | −88.2384 | −2.95113 | ||||||||
\(895\) | 25.2337 | 0.843470 | ||||||||
\(896\) | −83.0932 | −2.77595 | ||||||||
\(897\) | −37.6525 | −1.25718 | ||||||||
\(898\) | −0.268497 | −0.00895985 | ||||||||
\(899\) | −14.8009 | −0.493637 | ||||||||
\(900\) | 137.790 | 4.59300 | ||||||||
\(901\) | −26.6208 | −0.886868 | ||||||||
\(902\) | −3.59817 | −0.119806 | ||||||||
\(903\) | −113.278 | −3.76965 | ||||||||
\(904\) | −29.6721 | −0.986878 | ||||||||
\(905\) | 87.7581 | 2.91718 | ||||||||
\(906\) | 69.5800 | 2.31164 | ||||||||
\(907\) | 33.0950 | 1.09890 | 0.549451 | − | 0.835526i | \(-0.314837\pi\) | ||||
0.549451 | + | 0.835526i | \(0.314837\pi\) | |||||||
\(908\) | −20.6954 | −0.686800 | ||||||||
\(909\) | −35.0212 | −1.16158 | ||||||||
\(910\) | −96.7243 | −3.20638 | ||||||||
\(911\) | −44.7060 | −1.48118 | −0.740588 | − | 0.671959i | \(-0.765453\pi\) | ||||
−0.740588 | + | 0.671959i | \(0.765453\pi\) | |||||||
\(912\) | −4.87902 | −0.161561 | ||||||||
\(913\) | −10.3701 | −0.343199 | ||||||||
\(914\) | 83.4912 | 2.76164 | ||||||||
\(915\) | −104.726 | −3.46215 | ||||||||
\(916\) | 4.39953 | 0.145364 | ||||||||
\(917\) | 10.9228 | 0.360701 | ||||||||
\(918\) | 21.2922 | 0.702746 | ||||||||
\(919\) | −18.3157 | −0.604179 | −0.302090 | − | 0.953280i | \(-0.597684\pi\) | ||||
−0.302090 | + | 0.953280i | \(0.597684\pi\) | |||||||
\(920\) | 61.9525 | 2.04251 | ||||||||
\(921\) | 43.6539 | 1.43844 | ||||||||
\(922\) | −1.77973 | −0.0586124 | ||||||||
\(923\) | −13.6067 | −0.447869 | ||||||||
\(924\) | −56.1980 | −1.84878 | ||||||||
\(925\) | 10.2692 | 0.337648 | ||||||||
\(926\) | −25.9543 | −0.852913 | ||||||||
\(927\) | 19.2959 | 0.633761 | ||||||||
\(928\) | −59.7437 | −1.96118 | ||||||||
\(929\) | 8.47775 | 0.278146 | 0.139073 | − | 0.990282i | \(-0.455588\pi\) | ||||
0.139073 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(930\) | −36.2490 | −1.18865 | ||||||||
\(931\) | −68.7025 | −2.25163 | ||||||||
\(932\) | −31.1514 | −1.02040 | ||||||||
\(933\) | −79.0846 | −2.58911 | ||||||||
\(934\) | −86.0126 | −2.81442 | ||||||||
\(935\) | 14.7729 | 0.483126 | ||||||||
\(936\) | −25.1179 | −0.821005 | ||||||||
\(937\) | −48.0495 | −1.56971 | −0.784855 | − | 0.619680i | \(-0.787263\pi\) | ||||
−0.784855 | + | 0.619680i | \(0.787263\pi\) | |||||||
\(938\) | 24.6663 | 0.805382 | ||||||||
\(939\) | −75.3661 | −2.45948 | ||||||||
\(940\) | −154.269 | −5.03172 | ||||||||
\(941\) | 36.3086 | 1.18363 | 0.591813 | − | 0.806076i | \(-0.298413\pi\) | ||||
0.591813 | + | 0.806076i | \(0.298413\pi\) | |||||||
\(942\) | −77.0085 | −2.50907 | ||||||||
\(943\) | −7.04353 | −0.229369 | ||||||||
\(944\) | 1.21449 | 0.0395281 | ||||||||
\(945\) | −64.4283 | −2.09585 | ||||||||
\(946\) | −27.4351 | −0.891991 | ||||||||
\(947\) | 4.69074 | 0.152429 | 0.0762144 | − | 0.997091i | \(-0.475717\pi\) | ||||
0.0762144 | + | 0.997091i | \(0.475717\pi\) | |||||||
\(948\) | 54.6238 | 1.77410 | ||||||||
\(949\) | −37.5809 | −1.21993 | ||||||||
\(950\) | 99.7458 | 3.23618 | ||||||||
\(951\) | −33.3934 | −1.08285 | ||||||||
\(952\) | 33.8989 | 1.09867 | ||||||||
\(953\) | 58.8275 | 1.90561 | 0.952805 | − | 0.303582i | \(-0.0981828\pi\) | ||||
0.952805 | + | 0.303582i | \(0.0981828\pi\) | |||||||
\(954\) | 94.3435 | 3.05448 | ||||||||
\(955\) | −65.6425 | −2.12414 | ||||||||
\(956\) | −11.4058 | −0.368890 | ||||||||
\(957\) | −36.3829 | −1.17609 | ||||||||
\(958\) | 67.7257 | 2.18812 | ||||||||
\(959\) | 32.8716 | 1.06148 | ||||||||
\(960\) | −137.419 | −4.43518 | ||||||||
\(961\) | −28.6981 | −0.925745 | ||||||||
\(962\) | −5.15740 | −0.166281 | ||||||||
\(963\) | 63.4156 | 2.04354 | ||||||||
\(964\) | −28.1153 | −0.905533 | ||||||||
\(965\) | 38.1895 | 1.22937 | ||||||||
\(966\) | −180.089 | −5.79426 | ||||||||
\(967\) | −28.7247 | −0.923725 | −0.461862 | − | 0.886952i | \(-0.652819\pi\) | ||||
−0.461862 | + | 0.886952i | \(0.652819\pi\) | |||||||
\(968\) | 23.4780 | 0.754610 | ||||||||
\(969\) | 31.5907 | 1.01484 | ||||||||
\(970\) | −112.450 | −3.61056 | ||||||||
\(971\) | 41.6689 | 1.33722 | 0.668609 | − | 0.743614i | \(-0.266890\pi\) | ||||
0.668609 | + | 0.743614i | \(0.266890\pi\) | |||||||
\(972\) | 62.4683 | 2.00367 | ||||||||
\(973\) | 26.8345 | 0.860276 | ||||||||
\(974\) | 0.0686262 | 0.00219893 | ||||||||
\(975\) | −63.0062 | −2.01781 | ||||||||
\(976\) | 4.19591 | 0.134308 | ||||||||
\(977\) | −53.4803 | −1.71099 | −0.855493 | − | 0.517814i | \(-0.826746\pi\) | ||||
−0.855493 | + | 0.517814i | \(0.826746\pi\) | |||||||
\(978\) | −78.9656 | −2.52504 | ||||||||
\(979\) | −0.386754 | −0.0123607 | ||||||||
\(980\) | −196.723 | −6.28408 | ||||||||
\(981\) | −4.27377 | −0.136451 | ||||||||
\(982\) | 57.6617 | 1.84006 | ||||||||
\(983\) | −6.75920 | −0.215585 | −0.107793 | − | 0.994173i | \(-0.534378\pi\) | ||||
−0.107793 | + | 0.994173i | \(0.534378\pi\) | |||||||
\(984\) | −7.99703 | −0.254936 | ||||||||
\(985\) | 98.2976 | 3.13202 | ||||||||
\(986\) | 60.4632 | 1.92554 | ||||||||
\(987\) | 162.772 | 5.18108 | ||||||||
\(988\) | −30.6009 | −0.973543 | ||||||||
\(989\) | −53.7050 | −1.70772 | ||||||||
\(990\) | −52.3548 | −1.66395 | ||||||||
\(991\) | −58.2238 | −1.84954 | −0.924770 | − | 0.380525i | \(-0.875743\pi\) | ||||
−0.924770 | + | 0.380525i | \(0.875743\pi\) | |||||||
\(992\) | 9.29167 | 0.295011 | ||||||||
\(993\) | 50.2518 | 1.59469 | ||||||||
\(994\) | −65.0796 | −2.06420 | ||||||||
\(995\) | −72.3691 | −2.29426 | ||||||||
\(996\) | −63.4977 | −2.01200 | ||||||||
\(997\) | 39.0144 | 1.23560 | 0.617800 | − | 0.786336i | \(-0.288024\pi\) | ||||
0.617800 | + | 0.786336i | \(0.288024\pi\) | |||||||
\(998\) | −2.38611 | −0.0755310 | ||||||||
\(999\) | −3.43536 | −0.108690 |
(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 | 4033.2.a.f.1.10 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.10 | ✓ | 85 | 1.1 | even | 1 | trivial |