Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82541 | −1.29076 | −0.645381 | − | 0.763861i | \(-0.723301\pi\) | ||||
−0.645381 | + | 0.763861i | \(0.723301\pi\) | |||||||
\(3\) | 0.572536 | 0.330554 | 0.165277 | − | 0.986247i | \(-0.447148\pi\) | ||||
0.165277 | + | 0.986247i | \(0.447148\pi\) | |||||||
\(4\) | 1.33213 | 0.666065 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.04512 | −0.426666 | ||||||||
\(7\) | −3.97729 | −1.50327 | −0.751636 | − | 0.659578i | \(-0.770735\pi\) | ||||
−0.751636 | + | 0.659578i | \(0.770735\pi\) | |||||||
\(8\) | 1.21914 | 0.431030 | ||||||||
\(9\) | −2.67220 | −0.890734 | ||||||||
\(10\) | −1.82541 | −0.577246 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.762693 | 0.220171 | ||||||||
\(13\) | −5.95658 | −1.65206 | −0.826028 | − | 0.563628i | \(-0.809405\pi\) | ||||
−0.826028 | + | 0.563628i | \(0.809405\pi\) | |||||||
\(14\) | 7.26019 | 1.94037 | ||||||||
\(15\) | 0.572536 | 0.147828 | ||||||||
\(16\) | −4.88969 | −1.22242 | ||||||||
\(17\) | 0.0624446 | 0.0151450 | 0.00757252 | − | 0.999971i | \(-0.497590\pi\) | ||||
0.00757252 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(18\) | 4.87787 | 1.14973 | ||||||||
\(19\) | 7.47082 | 1.71392 | 0.856962 | − | 0.515380i | \(-0.172349\pi\) | ||||
0.856962 | + | 0.515380i | \(0.172349\pi\) | |||||||
\(20\) | 1.33213 | 0.297873 | ||||||||
\(21\) | −2.27714 | −0.496913 | ||||||||
\(22\) | −1.82541 | −0.389179 | ||||||||
\(23\) | −4.78206 | −0.997129 | −0.498564 | − | 0.866853i | \(-0.666139\pi\) | ||||
−0.498564 | + | 0.866853i | \(0.666139\pi\) | |||||||
\(24\) | 0.698000 | 0.142479 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 10.8732 | 2.13241 | ||||||||
\(27\) | −3.24754 | −0.624990 | ||||||||
\(28\) | −5.29826 | −1.00128 | ||||||||
\(29\) | 0.732323 | 0.135989 | 0.0679945 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679945 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(30\) | −1.04512 | −0.190811 | ||||||||
\(31\) | 2.17635 | 0.390883 | 0.195442 | − | 0.980715i | \(-0.437386\pi\) | ||||
0.195442 | + | 0.980715i | \(0.437386\pi\) | |||||||
\(32\) | 6.48743 | 1.14683 | ||||||||
\(33\) | 0.572536 | 0.0996658 | ||||||||
\(34\) | −0.113987 | −0.0195486 | ||||||||
\(35\) | −3.97729 | −0.672284 | ||||||||
\(36\) | −3.55972 | −0.593287 | ||||||||
\(37\) | −6.76150 | −1.11158 | −0.555792 | − | 0.831322i | \(-0.687585\pi\) | ||||
−0.555792 | + | 0.831322i | \(0.687585\pi\) | |||||||
\(38\) | −13.6373 | −2.21227 | ||||||||
\(39\) | −3.41036 | −0.546094 | ||||||||
\(40\) | 1.21914 | 0.192762 | ||||||||
\(41\) | −7.30658 | −1.14110 | −0.570548 | − | 0.821264i | \(-0.693269\pi\) | ||||
−0.570548 | + | 0.821264i | \(0.693269\pi\) | |||||||
\(42\) | 4.15672 | 0.641396 | ||||||||
\(43\) | −0.257853 | −0.0393222 | −0.0196611 | − | 0.999807i | \(-0.506259\pi\) | ||||
−0.0196611 | + | 0.999807i | \(0.506259\pi\) | |||||||
\(44\) | 1.33213 | 0.200826 | ||||||||
\(45\) | −2.67220 | −0.398348 | ||||||||
\(46\) | 8.72923 | 1.28706 | ||||||||
\(47\) | 4.16410 | 0.607396 | 0.303698 | − | 0.952768i | \(-0.401779\pi\) | ||||
0.303698 | + | 0.952768i | \(0.401779\pi\) | |||||||
\(48\) | −2.79952 | −0.404077 | ||||||||
\(49\) | 8.81880 | 1.25983 | ||||||||
\(50\) | −1.82541 | −0.258152 | ||||||||
\(51\) | 0.0357518 | 0.00500625 | ||||||||
\(52\) | −7.93494 | −1.10038 | ||||||||
\(53\) | −10.8555 | −1.49111 | −0.745557 | − | 0.666442i | \(-0.767816\pi\) | ||||
−0.745557 | + | 0.666442i | \(0.767816\pi\) | |||||||
\(54\) | 5.92810 | 0.806713 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −4.84886 | −0.647956 | ||||||||
\(57\) | 4.27732 | 0.566544 | ||||||||
\(58\) | −1.33679 | −0.175529 | ||||||||
\(59\) | −2.87196 | −0.373897 | −0.186949 | − | 0.982370i | \(-0.559860\pi\) | ||||
−0.186949 | + | 0.982370i | \(0.559860\pi\) | |||||||
\(60\) | 0.762693 | 0.0984633 | ||||||||
\(61\) | −2.48748 | −0.318489 | −0.159245 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159245 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(62\) | −3.97273 | −0.504537 | ||||||||
\(63\) | 10.6281 | 1.33902 | ||||||||
\(64\) | −2.06285 | −0.257856 | ||||||||
\(65\) | −5.95658 | −0.738822 | ||||||||
\(66\) | −1.04512 | −0.128645 | ||||||||
\(67\) | 6.77358 | 0.827525 | 0.413762 | − | 0.910385i | \(-0.364214\pi\) | ||||
0.413762 | + | 0.910385i | \(0.364214\pi\) | |||||||
\(68\) | 0.0831843 | 0.0100876 | ||||||||
\(69\) | −2.73790 | −0.329605 | ||||||||
\(70\) | 7.26019 | 0.867758 | ||||||||
\(71\) | −11.3027 | −1.34139 | −0.670694 | − | 0.741734i | \(-0.734004\pi\) | ||||
−0.670694 | + | 0.741734i | \(0.734004\pi\) | |||||||
\(72\) | −3.25778 | −0.383933 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 12.3425 | 1.43479 | ||||||||
\(75\) | 0.572536 | 0.0661108 | ||||||||
\(76\) | 9.95211 | 1.14158 | ||||||||
\(77\) | −3.97729 | −0.453254 | ||||||||
\(78\) | 6.22531 | 0.704877 | ||||||||
\(79\) | 16.8072 | 1.89095 | 0.945477 | − | 0.325689i | \(-0.105596\pi\) | ||||
0.945477 | + | 0.325689i | \(0.105596\pi\) | |||||||
\(80\) | −4.88969 | −0.546684 | ||||||||
\(81\) | 6.15727 | 0.684141 | ||||||||
\(82\) | 13.3375 | 1.47288 | ||||||||
\(83\) | 4.36026 | 0.478601 | 0.239300 | − | 0.970946i | \(-0.423082\pi\) | ||||
0.239300 | + | 0.970946i | \(0.423082\pi\) | |||||||
\(84\) | −3.03345 | −0.330976 | ||||||||
\(85\) | 0.0624446 | 0.00677307 | ||||||||
\(86\) | 0.470688 | 0.0507556 | ||||||||
\(87\) | 0.419281 | 0.0449517 | ||||||||
\(88\) | 1.21914 | 0.129960 | ||||||||
\(89\) | −7.39881 | −0.784272 | −0.392136 | − | 0.919907i | \(-0.628264\pi\) | ||||
−0.392136 | + | 0.919907i | \(0.628264\pi\) | |||||||
\(90\) | 4.87787 | 0.514173 | ||||||||
\(91\) | 23.6910 | 2.48349 | ||||||||
\(92\) | −6.37033 | −0.664153 | ||||||||
\(93\) | 1.24604 | 0.129208 | ||||||||
\(94\) | −7.60119 | −0.784003 | ||||||||
\(95\) | 7.47082 | 0.766490 | ||||||||
\(96\) | 3.71429 | 0.379088 | ||||||||
\(97\) | −6.04749 | −0.614029 | −0.307015 | − | 0.951705i | \(-0.599330\pi\) | ||||
−0.307015 | + | 0.951705i | \(0.599330\pi\) | |||||||
\(98\) | −16.0979 | −1.62614 | ||||||||
\(99\) | −2.67220 | −0.268566 | ||||||||
\(100\) | 1.33213 | 0.133213 | ||||||||
\(101\) | −0.909194 | −0.0904682 | −0.0452341 | − | 0.998976i | \(-0.514403\pi\) | ||||
−0.0452341 | + | 0.998976i | \(0.514403\pi\) | |||||||
\(102\) | −0.0652618 | −0.00646188 | ||||||||
\(103\) | −4.44462 | −0.437942 | −0.218971 | − | 0.975731i | \(-0.570270\pi\) | ||||
−0.218971 | + | 0.975731i | \(0.570270\pi\) | |||||||
\(104\) | −7.26188 | −0.712086 | ||||||||
\(105\) | −2.27714 | −0.222226 | ||||||||
\(106\) | 19.8157 | 1.92467 | ||||||||
\(107\) | 0.851123 | 0.0822812 | 0.0411406 | − | 0.999153i | \(-0.486901\pi\) | ||||
0.0411406 | + | 0.999153i | \(0.486901\pi\) | |||||||
\(108\) | −4.32615 | −0.416284 | ||||||||
\(109\) | 6.65383 | 0.637321 | 0.318661 | − | 0.947869i | \(-0.396767\pi\) | ||||
0.318661 | + | 0.947869i | \(0.396767\pi\) | |||||||
\(110\) | −1.82541 | −0.174046 | ||||||||
\(111\) | −3.87120 | −0.367438 | ||||||||
\(112\) | 19.4477 | 1.83763 | ||||||||
\(113\) | 19.6307 | 1.84670 | 0.923349 | − | 0.383963i | \(-0.125441\pi\) | ||||
0.923349 | + | 0.383963i | \(0.125441\pi\) | |||||||
\(114\) | −7.80786 | −0.731273 | ||||||||
\(115\) | −4.78206 | −0.445930 | ||||||||
\(116\) | 0.975550 | 0.0905775 | ||||||||
\(117\) | 15.9172 | 1.47154 | ||||||||
\(118\) | 5.24251 | 0.482612 | ||||||||
\(119\) | −0.248360 | −0.0227671 | ||||||||
\(120\) | 0.698000 | 0.0637184 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.54068 | 0.411094 | ||||||||
\(123\) | −4.18329 | −0.377194 | ||||||||
\(124\) | 2.89918 | 0.260354 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −19.4007 | −1.72835 | ||||||||
\(127\) | −2.12927 | −0.188942 | −0.0944709 | − | 0.995528i | \(-0.530116\pi\) | ||||
−0.0944709 | + | 0.995528i | \(0.530116\pi\) | |||||||
\(128\) | −9.20930 | −0.813995 | ||||||||
\(129\) | −0.147630 | −0.0129981 | ||||||||
\(130\) | 10.8732 | 0.953643 | ||||||||
\(131\) | 18.4138 | 1.60882 | 0.804409 | − | 0.594075i | \(-0.202482\pi\) | ||||
0.804409 | + | 0.594075i | \(0.202482\pi\) | |||||||
\(132\) | 0.762693 | 0.0663839 | ||||||||
\(133\) | −29.7136 | −2.57649 | ||||||||
\(134\) | −12.3646 | −1.06814 | ||||||||
\(135\) | −3.24754 | −0.279504 | ||||||||
\(136\) | 0.0761285 | 0.00652796 | ||||||||
\(137\) | 10.3749 | 0.886390 | 0.443195 | − | 0.896425i | \(-0.353845\pi\) | ||||
0.443195 | + | 0.896425i | \(0.353845\pi\) | |||||||
\(138\) | 4.99780 | 0.425441 | ||||||||
\(139\) | −3.80781 | −0.322975 | −0.161487 | − | 0.986875i | \(-0.551629\pi\) | ||||
−0.161487 | + | 0.986875i | \(0.551629\pi\) | |||||||
\(140\) | −5.29826 | −0.447785 | ||||||||
\(141\) | 2.38410 | 0.200777 | ||||||||
\(142\) | 20.6322 | 1.73141 | ||||||||
\(143\) | −5.95658 | −0.498114 | ||||||||
\(144\) | 13.0662 | 1.08885 | ||||||||
\(145\) | 0.732323 | 0.0608161 | ||||||||
\(146\) | −1.82541 | −0.151072 | ||||||||
\(147\) | 5.04908 | 0.416441 | ||||||||
\(148\) | −9.00720 | −0.740387 | ||||||||
\(149\) | −3.31198 | −0.271328 | −0.135664 | − | 0.990755i | \(-0.543317\pi\) | ||||
−0.135664 | + | 0.990755i | \(0.543317\pi\) | |||||||
\(150\) | −1.04512 | −0.0853333 | ||||||||
\(151\) | 9.71443 | 0.790549 | 0.395275 | − | 0.918563i | \(-0.370649\pi\) | ||||
0.395275 | + | 0.918563i | \(0.370649\pi\) | |||||||
\(152\) | 9.10795 | 0.738752 | ||||||||
\(153\) | −0.166865 | −0.0134902 | ||||||||
\(154\) | 7.26019 | 0.585042 | ||||||||
\(155\) | 2.17635 | 0.174808 | ||||||||
\(156\) | −4.54304 | −0.363734 | ||||||||
\(157\) | 10.4139 | 0.831121 | 0.415561 | − | 0.909566i | \(-0.363585\pi\) | ||||
0.415561 | + | 0.909566i | \(0.363585\pi\) | |||||||
\(158\) | −30.6800 | −2.44077 | ||||||||
\(159\) | −6.21515 | −0.492894 | ||||||||
\(160\) | 6.48743 | 0.512876 | ||||||||
\(161\) | 19.0196 | 1.49896 | ||||||||
\(162\) | −11.2396 | −0.883063 | ||||||||
\(163\) | −13.6348 | −1.06796 | −0.533979 | − | 0.845498i | \(-0.679304\pi\) | ||||
−0.533979 | + | 0.845498i | \(0.679304\pi\) | |||||||
\(164\) | −9.73332 | −0.760045 | ||||||||
\(165\) | 0.572536 | 0.0445719 | ||||||||
\(166\) | −7.95927 | −0.617760 | ||||||||
\(167\) | 25.1067 | 1.94282 | 0.971409 | − | 0.237413i | \(-0.0762994\pi\) | ||||
0.971409 | + | 0.237413i | \(0.0762994\pi\) | |||||||
\(168\) | −2.77615 | −0.214184 | ||||||||
\(169\) | 22.4808 | 1.72929 | ||||||||
\(170\) | −0.113987 | −0.00874241 | ||||||||
\(171\) | −19.9635 | −1.52665 | ||||||||
\(172\) | −0.343494 | −0.0261912 | ||||||||
\(173\) | 9.43336 | 0.717205 | 0.358602 | − | 0.933490i | \(-0.383253\pi\) | ||||
0.358602 | + | 0.933490i | \(0.383253\pi\) | |||||||
\(174\) | −0.765361 | −0.0580219 | ||||||||
\(175\) | −3.97729 | −0.300655 | ||||||||
\(176\) | −4.88969 | −0.368574 | ||||||||
\(177\) | −1.64430 | −0.123593 | ||||||||
\(178\) | 13.5059 | 1.01231 | ||||||||
\(179\) | −23.4176 | −1.75032 | −0.875158 | − | 0.483838i | \(-0.839243\pi\) | ||||
−0.875158 | + | 0.483838i | \(0.839243\pi\) | |||||||
\(180\) | −3.55972 | −0.265326 | ||||||||
\(181\) | −4.13000 | −0.306980 | −0.153490 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153490 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(182\) | −43.2458 | −3.20560 | ||||||||
\(183\) | −1.42417 | −0.105278 | ||||||||
\(184\) | −5.82999 | −0.429792 | ||||||||
\(185\) | −6.76150 | −0.497115 | ||||||||
\(186\) | −2.27453 | −0.166777 | ||||||||
\(187\) | 0.0624446 | 0.00456640 | ||||||||
\(188\) | 5.54712 | 0.404565 | ||||||||
\(189\) | 12.9164 | 0.939530 | ||||||||
\(190\) | −13.6373 | −0.989356 | ||||||||
\(191\) | 14.7414 | 1.06665 | 0.533324 | − | 0.845911i | \(-0.320943\pi\) | ||||
0.533324 | + | 0.845911i | \(0.320943\pi\) | |||||||
\(192\) | −1.18106 | −0.0852354 | ||||||||
\(193\) | −7.91989 | −0.570086 | −0.285043 | − | 0.958515i | \(-0.592008\pi\) | ||||
−0.285043 | + | 0.958515i | \(0.592008\pi\) | |||||||
\(194\) | 11.0392 | 0.792565 | ||||||||
\(195\) | −3.41036 | −0.244221 | ||||||||
\(196\) | 11.7478 | 0.839128 | ||||||||
\(197\) | −19.2554 | −1.37189 | −0.685944 | − | 0.727655i | \(-0.740610\pi\) | ||||
−0.685944 | + | 0.727655i | \(0.740610\pi\) | |||||||
\(198\) | 4.87787 | 0.346655 | ||||||||
\(199\) | −6.98322 | −0.495027 | −0.247514 | − | 0.968884i | \(-0.579614\pi\) | ||||
−0.247514 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(200\) | 1.21914 | 0.0862060 | ||||||||
\(201\) | 3.87812 | 0.273542 | ||||||||
\(202\) | 1.65965 | 0.116773 | ||||||||
\(203\) | −2.91266 | −0.204428 | ||||||||
\(204\) | 0.0476261 | 0.00333449 | ||||||||
\(205\) | −7.30658 | −0.510314 | ||||||||
\(206\) | 8.11327 | 0.565278 | ||||||||
\(207\) | 12.7786 | 0.888176 | ||||||||
\(208\) | 29.1258 | 2.01951 | ||||||||
\(209\) | 7.47082 | 0.516767 | ||||||||
\(210\) | 4.15672 | 0.286841 | ||||||||
\(211\) | −7.69662 | −0.529857 | −0.264929 | − | 0.964268i | \(-0.585348\pi\) | ||||
−0.264929 | + | 0.964268i | \(0.585348\pi\) | |||||||
\(212\) | −14.4609 | −0.993179 | ||||||||
\(213\) | −6.47123 | −0.443401 | ||||||||
\(214\) | −1.55365 | −0.106205 | ||||||||
\(215\) | −0.257853 | −0.0175854 | ||||||||
\(216\) | −3.95920 | −0.269389 | ||||||||
\(217\) | −8.65595 | −0.587604 | ||||||||
\(218\) | −12.1460 | −0.822630 | ||||||||
\(219\) | 0.572536 | 0.0386884 | ||||||||
\(220\) | 1.33213 | 0.0898122 | ||||||||
\(221\) | −0.371956 | −0.0250205 | ||||||||
\(222\) | 7.06654 | 0.474275 | ||||||||
\(223\) | −3.51587 | −0.235440 | −0.117720 | − | 0.993047i | \(-0.537559\pi\) | ||||
−0.117720 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(224\) | −25.8023 | −1.72399 | ||||||||
\(225\) | −2.67220 | −0.178147 | ||||||||
\(226\) | −35.8341 | −2.38365 | ||||||||
\(227\) | 19.5537 | 1.29782 | 0.648912 | − | 0.760863i | \(-0.275224\pi\) | ||||
0.648912 | + | 0.760863i | \(0.275224\pi\) | |||||||
\(228\) | 5.69794 | 0.377355 | ||||||||
\(229\) | 13.8127 | 0.912768 | 0.456384 | − | 0.889783i | \(-0.349144\pi\) | ||||
0.456384 | + | 0.889783i | \(0.349144\pi\) | |||||||
\(230\) | 8.72923 | 0.575589 | ||||||||
\(231\) | −2.27714 | −0.149825 | ||||||||
\(232\) | 0.892802 | 0.0586153 | ||||||||
\(233\) | 10.8144 | 0.708473 | 0.354237 | − | 0.935156i | \(-0.384741\pi\) | ||||
0.354237 | + | 0.935156i | \(0.384741\pi\) | |||||||
\(234\) | −29.0554 | −1.89941 | ||||||||
\(235\) | 4.16410 | 0.271636 | ||||||||
\(236\) | −3.82583 | −0.249040 | ||||||||
\(237\) | 9.62271 | 0.625062 | ||||||||
\(238\) | 0.453359 | 0.0293869 | ||||||||
\(239\) | 11.5352 | 0.746150 | 0.373075 | − | 0.927801i | \(-0.378303\pi\) | ||||
0.373075 | + | 0.927801i | \(0.378303\pi\) | |||||||
\(240\) | −2.79952 | −0.180709 | ||||||||
\(241\) | 20.2550 | 1.30474 | 0.652369 | − | 0.757902i | \(-0.273775\pi\) | ||||
0.652369 | + | 0.757902i | \(0.273775\pi\) | |||||||
\(242\) | −1.82541 | −0.117342 | ||||||||
\(243\) | 13.2679 | 0.851135 | ||||||||
\(244\) | −3.31365 | −0.212135 | ||||||||
\(245\) | 8.81880 | 0.563412 | ||||||||
\(246\) | 7.63622 | 0.486868 | ||||||||
\(247\) | −44.5005 | −2.83150 | ||||||||
\(248\) | 2.65326 | 0.168482 | ||||||||
\(249\) | 2.49641 | 0.158203 | ||||||||
\(250\) | −1.82541 | −0.115449 | ||||||||
\(251\) | 6.58326 | 0.415532 | 0.207766 | − | 0.978179i | \(-0.433381\pi\) | ||||
0.207766 | + | 0.978179i | \(0.433381\pi\) | |||||||
\(252\) | 14.1580 | 0.891872 | ||||||||
\(253\) | −4.78206 | −0.300646 | ||||||||
\(254\) | 3.88679 | 0.243879 | ||||||||
\(255\) | 0.0357518 | 0.00223886 | ||||||||
\(256\) | 20.9365 | 1.30853 | ||||||||
\(257\) | 30.9555 | 1.93095 | 0.965475 | − | 0.260495i | \(-0.0838858\pi\) | ||||
0.965475 | + | 0.260495i | \(0.0838858\pi\) | |||||||
\(258\) | 0.269486 | 0.0167775 | ||||||||
\(259\) | 26.8924 | 1.67101 | ||||||||
\(260\) | −7.93494 | −0.492104 | ||||||||
\(261\) | −1.95691 | −0.121130 | ||||||||
\(262\) | −33.6127 | −2.07660 | ||||||||
\(263\) | −22.2645 | −1.37289 | −0.686444 | − | 0.727182i | \(-0.740829\pi\) | ||||
−0.686444 | + | 0.727182i | \(0.740829\pi\) | |||||||
\(264\) | 0.698000 | 0.0429589 | ||||||||
\(265\) | −10.8555 | −0.666846 | ||||||||
\(266\) | 54.2395 | 3.32564 | ||||||||
\(267\) | −4.23609 | −0.259244 | ||||||||
\(268\) | 9.02330 | 0.551185 | ||||||||
\(269\) | 1.82765 | 0.111434 | 0.0557168 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557168 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(270\) | 5.92810 | 0.360773 | ||||||||
\(271\) | 3.99725 | 0.242816 | 0.121408 | − | 0.992603i | \(-0.461259\pi\) | ||||
0.121408 | + | 0.992603i | \(0.461259\pi\) | |||||||
\(272\) | −0.305335 | −0.0185136 | ||||||||
\(273\) | 13.5640 | 0.820928 | ||||||||
\(274\) | −18.9385 | −1.14412 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −3.64725 | −0.219538 | ||||||||
\(277\) | 3.93518 | 0.236442 | 0.118221 | − | 0.992987i | \(-0.462281\pi\) | ||||
0.118221 | + | 0.992987i | \(0.462281\pi\) | |||||||
\(278\) | 6.95083 | 0.416883 | ||||||||
\(279\) | −5.81564 | −0.348173 | ||||||||
\(280\) | −4.84886 | −0.289775 | ||||||||
\(281\) | 5.31105 | 0.316830 | 0.158415 | − | 0.987373i | \(-0.449362\pi\) | ||||
0.158415 | + | 0.987373i | \(0.449362\pi\) | |||||||
\(282\) | −4.35196 | −0.259155 | ||||||||
\(283\) | −7.08081 | −0.420911 | −0.210455 | − | 0.977603i | \(-0.567495\pi\) | ||||
−0.210455 | + | 0.977603i | \(0.567495\pi\) | |||||||
\(284\) | −15.0567 | −0.893452 | ||||||||
\(285\) | 4.27732 | 0.253366 | ||||||||
\(286\) | 10.8732 | 0.642946 | ||||||||
\(287\) | 29.0604 | 1.71538 | ||||||||
\(288\) | −17.3357 | −1.02152 | ||||||||
\(289\) | −16.9961 | −0.999771 | ||||||||
\(290\) | −1.33679 | −0.0784991 | ||||||||
\(291\) | −3.46241 | −0.202970 | ||||||||
\(292\) | 1.33213 | 0.0779571 | ||||||||
\(293\) | −4.56834 | −0.266885 | −0.133443 | − | 0.991057i | \(-0.542603\pi\) | ||||
−0.133443 | + | 0.991057i | \(0.542603\pi\) | |||||||
\(294\) | −9.21666 | −0.537526 | ||||||||
\(295\) | −2.87196 | −0.167212 | ||||||||
\(296\) | −8.24319 | −0.479126 | ||||||||
\(297\) | −3.24754 | −0.188442 | ||||||||
\(298\) | 6.04572 | 0.350219 | ||||||||
\(299\) | 28.4847 | 1.64731 | ||||||||
\(300\) | 0.762693 | 0.0440341 | ||||||||
\(301\) | 1.02555 | 0.0591120 | ||||||||
\(302\) | −17.7328 | −1.02041 | ||||||||
\(303\) | −0.520547 | −0.0299046 | ||||||||
\(304\) | −36.5300 | −2.09514 | ||||||||
\(305\) | −2.48748 | −0.142433 | ||||||||
\(306\) | 0.304597 | 0.0174126 | ||||||||
\(307\) | −22.1111 | −1.26194 | −0.630972 | − | 0.775805i | \(-0.717344\pi\) | ||||
−0.630972 | + | 0.775805i | \(0.717344\pi\) | |||||||
\(308\) | −5.29826 | −0.301897 | ||||||||
\(309\) | −2.54471 | −0.144763 | ||||||||
\(310\) | −3.97273 | −0.225636 | ||||||||
\(311\) | −5.55131 | −0.314786 | −0.157393 | − | 0.987536i | \(-0.550309\pi\) | ||||
−0.157393 | + | 0.987536i | \(0.550309\pi\) | |||||||
\(312\) | −4.15769 | −0.235383 | ||||||||
\(313\) | −29.5115 | −1.66809 | −0.834045 | − | 0.551697i | \(-0.813981\pi\) | ||||
−0.834045 | + | 0.551697i | \(0.813981\pi\) | |||||||
\(314\) | −19.0097 | −1.07278 | ||||||||
\(315\) | 10.6281 | 0.598826 | ||||||||
\(316\) | 22.3893 | 1.25950 | ||||||||
\(317\) | −5.42841 | −0.304890 | −0.152445 | − | 0.988312i | \(-0.548715\pi\) | ||||
−0.152445 | + | 0.988312i | \(0.548715\pi\) | |||||||
\(318\) | 11.3452 | 0.636208 | ||||||||
\(319\) | 0.732323 | 0.0410022 | ||||||||
\(320\) | −2.06285 | −0.115317 | ||||||||
\(321\) | 0.487299 | 0.0271984 | ||||||||
\(322\) | −34.7187 | −1.93479 | ||||||||
\(323\) | 0.466512 | 0.0259574 | ||||||||
\(324\) | 8.20229 | 0.455683 | ||||||||
\(325\) | −5.95658 | −0.330411 | ||||||||
\(326\) | 24.8891 | 1.37848 | ||||||||
\(327\) | 3.80956 | 0.210669 | ||||||||
\(328\) | −8.90773 | −0.491847 | ||||||||
\(329\) | −16.5618 | −0.913081 | ||||||||
\(330\) | −1.04512 | −0.0575317 | ||||||||
\(331\) | 19.6653 | 1.08090 | 0.540452 | − | 0.841375i | \(-0.318253\pi\) | ||||
0.540452 | + | 0.841375i | \(0.318253\pi\) | |||||||
\(332\) | 5.80844 | 0.318779 | ||||||||
\(333\) | 18.0681 | 0.990125 | ||||||||
\(334\) | −45.8302 | −2.50771 | ||||||||
\(335\) | 6.77358 | 0.370080 | ||||||||
\(336\) | 11.1345 | 0.607437 | ||||||||
\(337\) | 0.894802 | 0.0487430 | 0.0243715 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243715 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(338\) | −41.0367 | −2.23210 | ||||||||
\(339\) | 11.2393 | 0.610433 | ||||||||
\(340\) | 0.0831843 | 0.00451130 | ||||||||
\(341\) | 2.17635 | 0.117856 | ||||||||
\(342\) | 36.4417 | 1.97054 | ||||||||
\(343\) | −7.23388 | −0.390593 | ||||||||
\(344\) | −0.314358 | −0.0169490 | ||||||||
\(345\) | −2.73790 | −0.147404 | ||||||||
\(346\) | −17.2198 | −0.925741 | ||||||||
\(347\) | 31.9613 | 1.71577 | 0.857885 | − | 0.513842i | \(-0.171778\pi\) | ||||
0.857885 | + | 0.513842i | \(0.171778\pi\) | |||||||
\(348\) | 0.558538 | 0.0299408 | ||||||||
\(349\) | 11.9587 | 0.640134 | 0.320067 | − | 0.947395i | \(-0.396295\pi\) | ||||
0.320067 | + | 0.947395i | \(0.396295\pi\) | |||||||
\(350\) | 7.26019 | 0.388073 | ||||||||
\(351\) | 19.3442 | 1.03252 | ||||||||
\(352\) | 6.48743 | 0.345781 | ||||||||
\(353\) | −24.1558 | −1.28568 | −0.642841 | − | 0.766000i | \(-0.722244\pi\) | ||||
−0.642841 | + | 0.766000i | \(0.722244\pi\) | |||||||
\(354\) | 3.00153 | 0.159529 | ||||||||
\(355\) | −11.3027 | −0.599887 | ||||||||
\(356\) | −9.85618 | −0.522376 | ||||||||
\(357\) | −0.142195 | −0.00752576 | ||||||||
\(358\) | 42.7468 | 2.25924 | ||||||||
\(359\) | 11.1170 | 0.586734 | 0.293367 | − | 0.956000i | \(-0.405224\pi\) | ||||
0.293367 | + | 0.956000i | \(0.405224\pi\) | |||||||
\(360\) | −3.25778 | −0.171700 | ||||||||
\(361\) | 36.8131 | 1.93753 | ||||||||
\(362\) | 7.53895 | 0.396238 | ||||||||
\(363\) | 0.572536 | 0.0300504 | ||||||||
\(364\) | 31.5595 | 1.65417 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 2.59970 | 0.135889 | ||||||||
\(367\) | −23.1866 | −1.21033 | −0.605167 | − | 0.796099i | \(-0.706893\pi\) | ||||
−0.605167 | + | 0.796099i | \(0.706893\pi\) | |||||||
\(368\) | 23.3828 | 1.21891 | ||||||||
\(369\) | 19.5247 | 1.01641 | ||||||||
\(370\) | 12.3425 | 0.641657 | ||||||||
\(371\) | 43.1753 | 2.24155 | ||||||||
\(372\) | 1.65989 | 0.0860610 | ||||||||
\(373\) | 25.8037 | 1.33607 | 0.668034 | − | 0.744131i | \(-0.267136\pi\) | ||||
0.668034 | + | 0.744131i | \(0.267136\pi\) | |||||||
\(374\) | −0.113987 | −0.00589413 | ||||||||
\(375\) | 0.572536 | 0.0295657 | ||||||||
\(376\) | 5.07660 | 0.261806 | ||||||||
\(377\) | −4.36214 | −0.224661 | ||||||||
\(378\) | −23.5778 | −1.21271 | ||||||||
\(379\) | 6.12477 | 0.314608 | 0.157304 | − | 0.987550i | \(-0.449720\pi\) | ||||
0.157304 | + | 0.987550i | \(0.449720\pi\) | |||||||
\(380\) | 9.95211 | 0.510532 | ||||||||
\(381\) | −1.21908 | −0.0624555 | ||||||||
\(382\) | −26.9091 | −1.37679 | ||||||||
\(383\) | −33.0109 | −1.68678 | −0.843389 | − | 0.537303i | \(-0.819443\pi\) | ||||
−0.843389 | + | 0.537303i | \(0.819443\pi\) | |||||||
\(384\) | −5.27266 | −0.269069 | ||||||||
\(385\) | −3.97729 | −0.202701 | ||||||||
\(386\) | 14.4571 | 0.735846 | ||||||||
\(387\) | 0.689035 | 0.0350256 | ||||||||
\(388\) | −8.05604 | −0.408984 | ||||||||
\(389\) | −4.29868 | −0.217952 | −0.108976 | − | 0.994044i | \(-0.534757\pi\) | ||||
−0.108976 | + | 0.994044i | \(0.534757\pi\) | |||||||
\(390\) | 6.22531 | 0.315231 | ||||||||
\(391\) | −0.298614 | −0.0151015 | ||||||||
\(392\) | 10.7513 | 0.543024 | ||||||||
\(393\) | 10.5426 | 0.531802 | ||||||||
\(394\) | 35.1490 | 1.77078 | ||||||||
\(395\) | 16.8072 | 0.845660 | ||||||||
\(396\) | −3.55972 | −0.178883 | ||||||||
\(397\) | 8.96942 | 0.450162 | 0.225081 | − | 0.974340i | \(-0.427735\pi\) | ||||
0.225081 | + | 0.974340i | \(0.427735\pi\) | |||||||
\(398\) | 12.7473 | 0.638962 | ||||||||
\(399\) | −17.0121 | −0.851670 | ||||||||
\(400\) | −4.88969 | −0.244484 | ||||||||
\(401\) | 16.7718 | 0.837544 | 0.418772 | − | 0.908091i | \(-0.362461\pi\) | ||||
0.418772 | + | 0.908091i | \(0.362461\pi\) | |||||||
\(402\) | −7.07917 | −0.353077 | ||||||||
\(403\) | −12.9636 | −0.645762 | ||||||||
\(404\) | −1.21116 | −0.0602577 | ||||||||
\(405\) | 6.15727 | 0.305957 | ||||||||
\(406\) | 5.31680 | 0.263868 | ||||||||
\(407\) | −6.76150 | −0.335155 | ||||||||
\(408\) | 0.0435863 | 0.00215784 | ||||||||
\(409\) | 31.2333 | 1.54439 | 0.772194 | − | 0.635387i | \(-0.219160\pi\) | ||||
0.772194 | + | 0.635387i | \(0.219160\pi\) | |||||||
\(410\) | 13.3375 | 0.658694 | ||||||||
\(411\) | 5.94002 | 0.293000 | ||||||||
\(412\) | −5.92082 | −0.291698 | ||||||||
\(413\) | 11.4226 | 0.562070 | ||||||||
\(414\) | −23.3263 | −1.14642 | ||||||||
\(415\) | 4.36026 | 0.214037 | ||||||||
\(416\) | −38.6428 | −1.89462 | ||||||||
\(417\) | −2.18011 | −0.106761 | ||||||||
\(418\) | −13.6373 | −0.667023 | ||||||||
\(419\) | 26.8418 | 1.31131 | 0.655655 | − | 0.755061i | \(-0.272393\pi\) | ||||
0.655655 | + | 0.755061i | \(0.272393\pi\) | |||||||
\(420\) | −3.03345 | −0.148017 | ||||||||
\(421\) | −19.5493 | −0.952775 | −0.476387 | − | 0.879235i | \(-0.658054\pi\) | ||||
−0.476387 | + | 0.879235i | \(0.658054\pi\) | |||||||
\(422\) | 14.0495 | 0.683919 | ||||||||
\(423\) | −11.1273 | −0.541028 | ||||||||
\(424\) | −13.2343 | −0.642715 | ||||||||
\(425\) | 0.0624446 | 0.00302901 | ||||||||
\(426\) | 11.8127 | 0.572325 | ||||||||
\(427\) | 9.89342 | 0.478776 | ||||||||
\(428\) | 1.13381 | 0.0548047 | ||||||||
\(429\) | −3.41036 | −0.164654 | ||||||||
\(430\) | 0.470688 | 0.0226986 | ||||||||
\(431\) | 12.2264 | 0.588924 | 0.294462 | − | 0.955663i | \(-0.404860\pi\) | ||||
0.294462 | + | 0.955663i | \(0.404860\pi\) | |||||||
\(432\) | 15.8795 | 0.764001 | ||||||||
\(433\) | 27.9346 | 1.34245 | 0.671226 | − | 0.741253i | \(-0.265768\pi\) | ||||
0.671226 | + | 0.741253i | \(0.265768\pi\) | |||||||
\(434\) | 15.8007 | 0.758457 | ||||||||
\(435\) | 0.419281 | 0.0201030 | ||||||||
\(436\) | 8.86377 | 0.424498 | ||||||||
\(437\) | −35.7259 | −1.70900 | ||||||||
\(438\) | −1.04512 | −0.0499375 | ||||||||
\(439\) | 25.5208 | 1.21804 | 0.609020 | − | 0.793155i | \(-0.291563\pi\) | ||||
0.609020 | + | 0.793155i | \(0.291563\pi\) | |||||||
\(440\) | 1.21914 | 0.0581201 | ||||||||
\(441\) | −23.5656 | −1.12217 | ||||||||
\(442\) | 0.678973 | 0.0322954 | ||||||||
\(443\) | 25.0811 | 1.19164 | 0.595819 | − | 0.803119i | \(-0.296828\pi\) | ||||
0.595819 | + | 0.803119i | \(0.296828\pi\) | |||||||
\(444\) | −5.15695 | −0.244738 | ||||||||
\(445\) | −7.39881 | −0.350737 | ||||||||
\(446\) | 6.41792 | 0.303897 | ||||||||
\(447\) | −1.89623 | −0.0896884 | ||||||||
\(448\) | 8.20454 | 0.387628 | ||||||||
\(449\) | 18.2120 | 0.859477 | 0.429738 | − | 0.902953i | \(-0.358606\pi\) | ||||
0.429738 | + | 0.902953i | \(0.358606\pi\) | |||||||
\(450\) | 4.87787 | 0.229945 | ||||||||
\(451\) | −7.30658 | −0.344054 | ||||||||
\(452\) | 26.1506 | 1.23002 | ||||||||
\(453\) | 5.56186 | 0.261319 | ||||||||
\(454\) | −35.6936 | −1.67518 | ||||||||
\(455\) | 23.6910 | 1.11065 | ||||||||
\(456\) | 5.21463 | 0.244198 | ||||||||
\(457\) | 36.5873 | 1.71148 | 0.855740 | − | 0.517406i | \(-0.173102\pi\) | ||||
0.855740 | + | 0.517406i | \(0.173102\pi\) | |||||||
\(458\) | −25.2139 | −1.17817 | ||||||||
\(459\) | −0.202791 | −0.00946549 | ||||||||
\(460\) | −6.37033 | −0.297018 | ||||||||
\(461\) | −23.3861 | −1.08920 | −0.544599 | − | 0.838696i | \(-0.683318\pi\) | ||||
−0.544599 | + | 0.838696i | \(0.683318\pi\) | |||||||
\(462\) | 4.15672 | 0.193388 | ||||||||
\(463\) | −8.83736 | −0.410707 | −0.205354 | − | 0.978688i | \(-0.565834\pi\) | ||||
−0.205354 | + | 0.978688i | \(0.565834\pi\) | |||||||
\(464\) | −3.58083 | −0.166236 | ||||||||
\(465\) | 1.24604 | 0.0577836 | ||||||||
\(466\) | −19.7407 | −0.914470 | ||||||||
\(467\) | 12.9354 | 0.598577 | 0.299288 | − | 0.954163i | \(-0.403251\pi\) | ||||
0.299288 | + | 0.954163i | \(0.403251\pi\) | |||||||
\(468\) | 21.2038 | 0.980144 | ||||||||
\(469\) | −26.9405 | −1.24400 | ||||||||
\(470\) | −7.60119 | −0.350617 | ||||||||
\(471\) | 5.96235 | 0.274730 | ||||||||
\(472\) | −3.50131 | −0.161161 | ||||||||
\(473\) | −0.257853 | −0.0118561 | ||||||||
\(474\) | −17.5654 | −0.806806 | ||||||||
\(475\) | 7.47082 | 0.342785 | ||||||||
\(476\) | −0.330848 | −0.0151644 | ||||||||
\(477\) | 29.0080 | 1.32819 | ||||||||
\(478\) | −21.0565 | −0.963102 | ||||||||
\(479\) | 4.01427 | 0.183417 | 0.0917084 | − | 0.995786i | \(-0.470767\pi\) | ||||
0.0917084 | + | 0.995786i | \(0.470767\pi\) | |||||||
\(480\) | 3.71429 | 0.169533 | ||||||||
\(481\) | 40.2754 | 1.83640 | ||||||||
\(482\) | −36.9737 | −1.68411 | ||||||||
\(483\) | 10.8894 | 0.495486 | ||||||||
\(484\) | 1.33213 | 0.0605514 | ||||||||
\(485\) | −6.04749 | −0.274602 | ||||||||
\(486\) | −24.2194 | −1.09861 | ||||||||
\(487\) | 30.9263 | 1.40140 | 0.700702 | − | 0.713454i | \(-0.252870\pi\) | ||||
0.700702 | + | 0.713454i | \(0.252870\pi\) | |||||||
\(488\) | −3.03258 | −0.137278 | ||||||||
\(489\) | −7.80641 | −0.353018 | ||||||||
\(490\) | −16.0979 | −0.727231 | ||||||||
\(491\) | 10.0248 | 0.452411 | 0.226206 | − | 0.974080i | \(-0.427368\pi\) | ||||
0.226206 | + | 0.974080i | \(0.427368\pi\) | |||||||
\(492\) | −5.57268 | −0.251236 | ||||||||
\(493\) | 0.0457296 | 0.00205956 | ||||||||
\(494\) | 81.2318 | 3.65479 | ||||||||
\(495\) | −2.67220 | −0.120107 | ||||||||
\(496\) | −10.6417 | −0.477825 | ||||||||
\(497\) | 44.9542 | 2.01647 | ||||||||
\(498\) | −4.55697 | −0.204203 | ||||||||
\(499\) | −30.4536 | −1.36329 | −0.681645 | − | 0.731683i | \(-0.738735\pi\) | ||||
−0.681645 | + | 0.731683i | \(0.738735\pi\) | |||||||
\(500\) | 1.33213 | 0.0595747 | ||||||||
\(501\) | 14.3745 | 0.642206 | ||||||||
\(502\) | −12.0172 | −0.536353 | ||||||||
\(503\) | −16.2335 | −0.723814 | −0.361907 | − | 0.932214i | \(-0.617874\pi\) | ||||
−0.361907 | + | 0.932214i | \(0.617874\pi\) | |||||||
\(504\) | 12.9571 | 0.577156 | ||||||||
\(505\) | −0.909194 | −0.0404586 | ||||||||
\(506\) | 8.72923 | 0.388062 | ||||||||
\(507\) | 12.8711 | 0.571624 | ||||||||
\(508\) | −2.83646 | −0.125848 | ||||||||
\(509\) | 32.5441 | 1.44249 | 0.721245 | − | 0.692680i | \(-0.243570\pi\) | ||||
0.721245 | + | 0.692680i | \(0.243570\pi\) | |||||||
\(510\) | −0.0652618 | −0.00288984 | ||||||||
\(511\) | −3.97729 | −0.175945 | ||||||||
\(512\) | −19.7991 | −0.875005 | ||||||||
\(513\) | −24.2618 | −1.07118 | ||||||||
\(514\) | −56.5065 | −2.49240 | ||||||||
\(515\) | −4.44462 | −0.195853 | ||||||||
\(516\) | −0.196663 | −0.00865759 | ||||||||
\(517\) | 4.16410 | 0.183137 | ||||||||
\(518\) | −49.0897 | −2.15688 | ||||||||
\(519\) | 5.40094 | 0.237075 | ||||||||
\(520\) | −7.26188 | −0.318455 | ||||||||
\(521\) | −26.2947 | −1.15199 | −0.575995 | − | 0.817453i | \(-0.695385\pi\) | ||||
−0.575995 | + | 0.817453i | \(0.695385\pi\) | |||||||
\(522\) | 3.57218 | 0.156350 | ||||||||
\(523\) | −30.2378 | −1.32221 | −0.661103 | − | 0.750295i | \(-0.729911\pi\) | ||||
−0.661103 | + | 0.750295i | \(0.729911\pi\) | |||||||
\(524\) | 24.5296 | 1.07158 | ||||||||
\(525\) | −2.27714 | −0.0993826 | ||||||||
\(526\) | 40.6419 | 1.77207 | ||||||||
\(527\) | 0.135901 | 0.00591994 | ||||||||
\(528\) | −2.79952 | −0.121834 | ||||||||
\(529\) | −0.131891 | −0.00573437 | ||||||||
\(530\) | 19.8157 | 0.860740 | ||||||||
\(531\) | 7.67446 | 0.333043 | ||||||||
\(532\) | −39.5824 | −1.71611 | ||||||||
\(533\) | 43.5222 | 1.88516 | ||||||||
\(534\) | 7.73261 | 0.334623 | ||||||||
\(535\) | 0.851123 | 0.0367973 | ||||||||
\(536\) | 8.25792 | 0.356688 | ||||||||
\(537\) | −13.4074 | −0.578574 | ||||||||
\(538\) | −3.33621 | −0.143834 | ||||||||
\(539\) | 8.81880 | 0.379853 | ||||||||
\(540\) | −4.32615 | −0.186168 | ||||||||
\(541\) | −2.56772 | −0.110395 | −0.0551974 | − | 0.998475i | \(-0.517579\pi\) | ||||
−0.0551974 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(542\) | −7.29663 | −0.313417 | ||||||||
\(543\) | −2.36457 | −0.101474 | ||||||||
\(544\) | 0.405105 | 0.0173687 | ||||||||
\(545\) | 6.65383 | 0.285019 | ||||||||
\(546\) | −24.7598 | −1.05962 | ||||||||
\(547\) | 39.2263 | 1.67720 | 0.838598 | − | 0.544751i | \(-0.183376\pi\) | ||||
0.838598 | + | 0.544751i | \(0.183376\pi\) | |||||||
\(548\) | 13.8208 | 0.590393 | ||||||||
\(549\) | 6.64705 | 0.283689 | ||||||||
\(550\) | −1.82541 | −0.0778358 | ||||||||
\(551\) | 5.47105 | 0.233075 | ||||||||
\(552\) | −3.33788 | −0.142070 | ||||||||
\(553\) | −66.8469 | −2.84262 | ||||||||
\(554\) | −7.18333 | −0.305190 | ||||||||
\(555\) | −3.87120 | −0.164323 | ||||||||
\(556\) | −5.07251 | −0.215122 | ||||||||
\(557\) | −15.4127 | −0.653058 | −0.326529 | − | 0.945187i | \(-0.605879\pi\) | ||||
−0.326529 | + | 0.945187i | \(0.605879\pi\) | |||||||
\(558\) | 10.6159 | 0.449409 | ||||||||
\(559\) | 1.53592 | 0.0649625 | ||||||||
\(560\) | 19.4477 | 0.821815 | ||||||||
\(561\) | 0.0357518 | 0.00150944 | ||||||||
\(562\) | −9.69485 | −0.408953 | ||||||||
\(563\) | −18.1899 | −0.766614 | −0.383307 | − | 0.923621i | \(-0.625215\pi\) | ||||
−0.383307 | + | 0.923621i | \(0.625215\pi\) | |||||||
\(564\) | 3.17593 | 0.133731 | ||||||||
\(565\) | 19.6307 | 0.825868 | ||||||||
\(566\) | 12.9254 | 0.543295 | ||||||||
\(567\) | −24.4892 | −1.02845 | ||||||||
\(568\) | −13.7796 | −0.578179 | ||||||||
\(569\) | −5.28963 | −0.221753 | −0.110876 | − | 0.993834i | \(-0.535366\pi\) | ||||
−0.110876 | + | 0.993834i | \(0.535366\pi\) | |||||||
\(570\) | −7.80786 | −0.327035 | ||||||||
\(571\) | 19.3654 | 0.810419 | 0.405209 | − | 0.914224i | \(-0.367199\pi\) | ||||
0.405209 | + | 0.914224i | \(0.367199\pi\) | |||||||
\(572\) | −7.93494 | −0.331776 | ||||||||
\(573\) | 8.43998 | 0.352585 | ||||||||
\(574\) | −53.0472 | −2.21415 | ||||||||
\(575\) | −4.78206 | −0.199426 | ||||||||
\(576\) | 5.51235 | 0.229681 | ||||||||
\(577\) | 2.29948 | 0.0957285 | 0.0478642 | − | 0.998854i | \(-0.484759\pi\) | ||||
0.0478642 | + | 0.998854i | \(0.484759\pi\) | |||||||
\(578\) | 31.0249 | 1.29047 | ||||||||
\(579\) | −4.53443 | −0.188444 | ||||||||
\(580\) | 0.975550 | 0.0405075 | ||||||||
\(581\) | −17.3420 | −0.719467 | ||||||||
\(582\) | 6.32032 | 0.261986 | ||||||||
\(583\) | −10.8555 | −0.449588 | ||||||||
\(584\) | 1.21914 | 0.0504482 | ||||||||
\(585\) | 15.9172 | 0.658094 | ||||||||
\(586\) | 8.33910 | 0.344485 | ||||||||
\(587\) | −26.0625 | −1.07571 | −0.537857 | − | 0.843036i | \(-0.680766\pi\) | ||||
−0.537857 | + | 0.843036i | \(0.680766\pi\) | |||||||
\(588\) | 6.72604 | 0.277377 | ||||||||
\(589\) | 16.2591 | 0.669944 | ||||||||
\(590\) | 5.24251 | 0.215831 | ||||||||
\(591\) | −11.0244 | −0.453483 | ||||||||
\(592\) | 33.0616 | 1.35882 | ||||||||
\(593\) | −17.4884 | −0.718162 | −0.359081 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359081 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(594\) | 5.92810 | 0.243233 | ||||||||
\(595\) | −0.248360 | −0.0101818 | ||||||||
\(596\) | −4.41198 | −0.180722 | ||||||||
\(597\) | −3.99815 | −0.163633 | ||||||||
\(598\) | −51.9963 | −2.12629 | ||||||||
\(599\) | 2.78712 | 0.113878 | 0.0569392 | − | 0.998378i | \(-0.481866\pi\) | ||||
0.0569392 | + | 0.998378i | \(0.481866\pi\) | |||||||
\(600\) | 0.698000 | 0.0284957 | ||||||||
\(601\) | 8.31497 | 0.339175 | 0.169587 | − | 0.985515i | \(-0.445756\pi\) | ||||
0.169587 | + | 0.985515i | \(0.445756\pi\) | |||||||
\(602\) | −1.87206 | −0.0762995 | ||||||||
\(603\) | −18.1004 | −0.737104 | ||||||||
\(604\) | 12.9409 | 0.526557 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0.950212 | 0.0385997 | ||||||||
\(607\) | −24.6354 | −0.999921 | −0.499960 | − | 0.866048i | \(-0.666652\pi\) | ||||
−0.499960 | + | 0.866048i | \(0.666652\pi\) | |||||||
\(608\) | 48.4664 | 1.96557 | ||||||||
\(609\) | −1.66760 | −0.0675746 | ||||||||
\(610\) | 4.54068 | 0.183847 | ||||||||
\(611\) | −24.8037 | −1.00345 | ||||||||
\(612\) | −0.222285 | −0.00898535 | ||||||||
\(613\) | 22.5277 | 0.909886 | 0.454943 | − | 0.890521i | \(-0.349660\pi\) | ||||
0.454943 | + | 0.890521i | \(0.349660\pi\) | |||||||
\(614\) | 40.3618 | 1.62887 | ||||||||
\(615\) | −4.18329 | −0.168686 | ||||||||
\(616\) | −4.84886 | −0.195366 | ||||||||
\(617\) | 6.83978 | 0.275359 | 0.137680 | − | 0.990477i | \(-0.456036\pi\) | ||||
0.137680 | + | 0.990477i | \(0.456036\pi\) | |||||||
\(618\) | 4.64514 | 0.186855 | ||||||||
\(619\) | 18.7575 | 0.753929 | 0.376965 | − | 0.926228i | \(-0.376968\pi\) | ||||
0.376965 | + | 0.926228i | \(0.376968\pi\) | |||||||
\(620\) | 2.89918 | 0.116434 | ||||||||
\(621\) | 15.5299 | 0.623195 | ||||||||
\(622\) | 10.1334 | 0.406314 | ||||||||
\(623\) | 29.4272 | 1.17897 | ||||||||
\(624\) | 16.6756 | 0.667558 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 53.8707 | 2.15311 | ||||||||
\(627\) | 4.27732 | 0.170820 | ||||||||
\(628\) | 13.8727 | 0.553581 | ||||||||
\(629\) | −0.422219 | −0.0168350 | ||||||||
\(630\) | −19.4007 | −0.772942 | ||||||||
\(631\) | −26.5216 | −1.05581 | −0.527903 | − | 0.849305i | \(-0.677022\pi\) | ||||
−0.527903 | + | 0.849305i | \(0.677022\pi\) | |||||||
\(632\) | 20.4902 | 0.815058 | ||||||||
\(633\) | −4.40660 | −0.175146 | ||||||||
\(634\) | 9.90909 | 0.393540 | ||||||||
\(635\) | −2.12927 | −0.0844973 | ||||||||
\(636\) | −8.27940 | −0.328299 | ||||||||
\(637\) | −52.5298 | −2.08131 | ||||||||
\(638\) | −1.33679 | −0.0529241 | ||||||||
\(639\) | 30.2032 | 1.19482 | ||||||||
\(640\) | −9.20930 | −0.364030 | ||||||||
\(641\) | 25.1651 | 0.993962 | 0.496981 | − | 0.867761i | \(-0.334442\pi\) | ||||
0.496981 | + | 0.867761i | \(0.334442\pi\) | |||||||
\(642\) | −0.889522 | −0.0351066 | ||||||||
\(643\) | 22.4622 | 0.885824 | 0.442912 | − | 0.896565i | \(-0.353945\pi\) | ||||
0.442912 | + | 0.896565i | \(0.353945\pi\) | |||||||
\(644\) | 25.3366 | 0.998403 | ||||||||
\(645\) | −0.147630 | −0.00581293 | ||||||||
\(646\) | −0.851577 | −0.0335048 | ||||||||
\(647\) | 27.1996 | 1.06933 | 0.534663 | − | 0.845065i | \(-0.320438\pi\) | ||||
0.534663 | + | 0.845065i | \(0.320438\pi\) | |||||||
\(648\) | 7.50656 | 0.294885 | ||||||||
\(649\) | −2.87196 | −0.112734 | ||||||||
\(650\) | 10.8732 | 0.426482 | ||||||||
\(651\) | −4.95585 | −0.194235 | ||||||||
\(652\) | −18.1633 | −0.711330 | ||||||||
\(653\) | 30.0406 | 1.17558 | 0.587790 | − | 0.809014i | \(-0.299998\pi\) | ||||
0.587790 | + | 0.809014i | \(0.299998\pi\) | |||||||
\(654\) | −6.95402 | −0.271924 | ||||||||
\(655\) | 18.4138 | 0.719486 | ||||||||
\(656\) | 35.7269 | 1.39490 | ||||||||
\(657\) | −2.67220 | −0.104253 | ||||||||
\(658\) | 30.2321 | 1.17857 | ||||||||
\(659\) | 0.302425 | 0.0117808 | 0.00589040 | − | 0.999983i | \(-0.498125\pi\) | ||||
0.00589040 | + | 0.999983i | \(0.498125\pi\) | |||||||
\(660\) | 0.762693 | 0.0296878 | ||||||||
\(661\) | 8.75991 | 0.340721 | 0.170360 | − | 0.985382i | \(-0.445507\pi\) | ||||
0.170360 | + | 0.985382i | \(0.445507\pi\) | |||||||
\(662\) | −35.8973 | −1.39519 | ||||||||
\(663\) | −0.212958 | −0.00827061 | ||||||||
\(664\) | 5.31575 | 0.206291 | ||||||||
\(665\) | −29.7136 | −1.15224 | ||||||||
\(666\) | −32.9817 | −1.27802 | ||||||||
\(667\) | −3.50201 | −0.135598 | ||||||||
\(668\) | 33.4455 | 1.29404 | ||||||||
\(669\) | −2.01297 | −0.0778257 | ||||||||
\(670\) | −12.3646 | −0.477685 | ||||||||
\(671\) | −2.48748 | −0.0960281 | ||||||||
\(672\) | −14.7728 | −0.569872 | ||||||||
\(673\) | 12.7795 | 0.492615 | 0.246307 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246307 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(674\) | −1.63338 | −0.0629156 | ||||||||
\(675\) | −3.24754 | −0.124998 | ||||||||
\(676\) | 29.9474 | 1.15182 | ||||||||
\(677\) | 34.1423 | 1.31220 | 0.656098 | − | 0.754675i | \(-0.272206\pi\) | ||||
0.656098 | + | 0.754675i | \(0.272206\pi\) | |||||||
\(678\) | −20.5163 | −0.787924 | ||||||||
\(679\) | 24.0526 | 0.923053 | ||||||||
\(680\) | 0.0761285 | 0.00291939 | ||||||||
\(681\) | 11.1952 | 0.429001 | ||||||||
\(682\) | −3.97273 | −0.152124 | ||||||||
\(683\) | −43.5086 | −1.66481 | −0.832405 | − | 0.554168i | \(-0.813037\pi\) | ||||
−0.832405 | + | 0.554168i | \(0.813037\pi\) | |||||||
\(684\) | −26.5940 | −1.01685 | ||||||||
\(685\) | 10.3749 | 0.396406 | ||||||||
\(686\) | 13.2048 | 0.504162 | ||||||||
\(687\) | 7.90827 | 0.301719 | ||||||||
\(688\) | 1.26082 | 0.0480683 | ||||||||
\(689\) | 64.6614 | 2.46340 | ||||||||
\(690\) | 4.99780 | 0.190263 | ||||||||
\(691\) | −49.1993 | −1.87163 | −0.935815 | − | 0.352493i | \(-0.885334\pi\) | ||||
−0.935815 | + | 0.352493i | \(0.885334\pi\) | |||||||
\(692\) | 12.5665 | 0.477705 | ||||||||
\(693\) | 10.6281 | 0.403729 | ||||||||
\(694\) | −58.3425 | −2.21465 | ||||||||
\(695\) | −3.80781 | −0.144439 | ||||||||
\(696\) | 0.511161 | 0.0193755 | ||||||||
\(697\) | −0.456257 | −0.0172819 | ||||||||
\(698\) | −21.8295 | −0.826260 | ||||||||
\(699\) | 6.19162 | 0.234189 | ||||||||
\(700\) | −5.29826 | −0.200256 | ||||||||
\(701\) | −9.77682 | −0.369266 | −0.184633 | − | 0.982808i | \(-0.559110\pi\) | ||||
−0.184633 | + | 0.982808i | \(0.559110\pi\) | |||||||
\(702\) | −35.3112 | −1.33274 | ||||||||
\(703\) | −50.5139 | −1.90517 | ||||||||
\(704\) | −2.06285 | −0.0777466 | ||||||||
\(705\) | 2.38410 | 0.0897903 | ||||||||
\(706\) | 44.0942 | 1.65951 | ||||||||
\(707\) | 3.61612 | 0.135998 | ||||||||
\(708\) | −2.19042 | −0.0823212 | ||||||||
\(709\) | −28.7367 | −1.07923 | −0.539615 | − | 0.841912i | \(-0.681430\pi\) | ||||
−0.539615 | + | 0.841912i | \(0.681430\pi\) | |||||||
\(710\) | 20.6322 | 0.774311 | ||||||||
\(711\) | −44.9121 | −1.68434 | ||||||||
\(712\) | −9.02016 | −0.338045 | ||||||||
\(713\) | −10.4074 | −0.389761 | ||||||||
\(714\) | 0.259565 | 0.00971396 | ||||||||
\(715\) | −5.95658 | −0.222763 | ||||||||
\(716\) | −31.1953 | −1.16582 | ||||||||
\(717\) | 6.60432 | 0.246643 | ||||||||
\(718\) | −20.2931 | −0.757334 | ||||||||
\(719\) | −13.2386 | −0.493715 | −0.246858 | − | 0.969052i | \(-0.579398\pi\) | ||||
−0.246858 | + | 0.969052i | \(0.579398\pi\) | |||||||
\(720\) | 13.0662 | 0.486950 | ||||||||
\(721\) | 17.6775 | 0.658345 | ||||||||
\(722\) | −67.1991 | −2.50089 | ||||||||
\(723\) | 11.5967 | 0.431286 | ||||||||
\(724\) | −5.50170 | −0.204469 | ||||||||
\(725\) | 0.732323 | 0.0271978 | ||||||||
\(726\) | −1.04512 | −0.0387879 | ||||||||
\(727\) | 34.8059 | 1.29088 | 0.645439 | − | 0.763812i | \(-0.276675\pi\) | ||||
0.645439 | + | 0.763812i | \(0.276675\pi\) | |||||||
\(728\) | 28.8826 | 1.07046 | ||||||||
\(729\) | −10.8755 | −0.402795 | ||||||||
\(730\) | −1.82541 | −0.0675615 | ||||||||
\(731\) | −0.0161015 | −0.000595536 0 | ||||||||
\(732\) | −1.89719 | −0.0701220 | ||||||||
\(733\) | −5.28451 | −0.195188 | −0.0975939 | − | 0.995226i | \(-0.531115\pi\) | ||||
−0.0975939 | + | 0.995226i | \(0.531115\pi\) | |||||||
\(734\) | 42.3252 | 1.56225 | ||||||||
\(735\) | 5.04908 | 0.186238 | ||||||||
\(736\) | −31.0233 | −1.14353 | ||||||||
\(737\) | 6.77358 | 0.249508 | ||||||||
\(738\) | −35.6406 | −1.31195 | ||||||||
\(739\) | 30.0845 | 1.10668 | 0.553338 | − | 0.832957i | \(-0.313354\pi\) | ||||
0.553338 | + | 0.832957i | \(0.313354\pi\) | |||||||
\(740\) | −9.00720 | −0.331111 | ||||||||
\(741\) | −25.4782 | −0.935963 | ||||||||
\(742\) | −78.8127 | −2.89331 | ||||||||
\(743\) | −17.0901 | −0.626977 | −0.313488 | − | 0.949592i | \(-0.601498\pi\) | ||||
−0.313488 | + | 0.949592i | \(0.601498\pi\) | |||||||
\(744\) | 1.51909 | 0.0556926 | ||||||||
\(745\) | −3.31198 | −0.121341 | ||||||||
\(746\) | −47.1025 | −1.72454 | ||||||||
\(747\) | −11.6515 | −0.426306 | ||||||||
\(748\) | 0.0831843 | 0.00304152 | ||||||||
\(749\) | −3.38516 | −0.123691 | ||||||||
\(750\) | −1.04512 | −0.0381622 | ||||||||
\(751\) | 4.79269 | 0.174888 | 0.0874439 | − | 0.996169i | \(-0.472130\pi\) | ||||
0.0874439 | + | 0.996169i | \(0.472130\pi\) | |||||||
\(752\) | −20.3611 | −0.742494 | ||||||||
\(753\) | 3.76916 | 0.137356 | ||||||||
\(754\) | 7.96270 | 0.289984 | ||||||||
\(755\) | 9.71443 | 0.353544 | ||||||||
\(756\) | 17.2063 | 0.625788 | ||||||||
\(757\) | −1.66572 | −0.0605415 | −0.0302707 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302707 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(758\) | −11.1802 | −0.406084 | ||||||||
\(759\) | −2.73790 | −0.0993796 | ||||||||
\(760\) | 9.10795 | 0.330380 | ||||||||
\(761\) | 16.3328 | 0.592064 | 0.296032 | − | 0.955178i | \(-0.404336\pi\) | ||||
0.296032 | + | 0.955178i | \(0.404336\pi\) | |||||||
\(762\) | 2.22533 | 0.0806151 | ||||||||
\(763\) | −26.4642 | −0.958068 | ||||||||
\(764\) | 19.6374 | 0.710458 | ||||||||
\(765\) | −0.166865 | −0.00603300 | ||||||||
\(766\) | 60.2585 | 2.17723 | ||||||||
\(767\) | 17.1070 | 0.617700 | ||||||||
\(768\) | 11.9869 | 0.432540 | ||||||||
\(769\) | −8.43323 | −0.304110 | −0.152055 | − | 0.988372i | \(-0.548589\pi\) | ||||
−0.152055 | + | 0.988372i | \(0.548589\pi\) | |||||||
\(770\) | 7.26019 | 0.261639 | ||||||||
\(771\) | 17.7231 | 0.638283 | ||||||||
\(772\) | −10.5503 | −0.379715 | ||||||||
\(773\) | 15.7987 | 0.568239 | 0.284119 | − | 0.958789i | \(-0.408299\pi\) | ||||
0.284119 | + | 0.958789i | \(0.408299\pi\) | |||||||
\(774\) | −1.25777 | −0.0452097 | ||||||||
\(775\) | 2.17635 | 0.0781767 | ||||||||
\(776\) | −7.37271 | −0.264665 | ||||||||
\(777\) | 15.3969 | 0.552360 | ||||||||
\(778\) | 7.84686 | 0.281324 | ||||||||
\(779\) | −54.5862 | −1.95575 | ||||||||
\(780\) | −4.54304 | −0.162667 | ||||||||
\(781\) | −11.3027 | −0.404444 | ||||||||
\(782\) | 0.545093 | 0.0194925 | ||||||||
\(783\) | −2.37825 | −0.0849917 | ||||||||
\(784\) | −43.1212 | −1.54004 | ||||||||
\(785\) | 10.4139 | 0.371689 | ||||||||
\(786\) | −19.2445 | −0.686429 | ||||||||
\(787\) | −25.2856 | −0.901334 | −0.450667 | − | 0.892692i | \(-0.648814\pi\) | ||||
−0.450667 | + | 0.892692i | \(0.648814\pi\) | |||||||
\(788\) | −25.6507 | −0.913767 | ||||||||
\(789\) | −12.7472 | −0.453814 | ||||||||
\(790\) | −30.6800 | −1.09155 | ||||||||
\(791\) | −78.0767 | −2.77609 | ||||||||
\(792\) | −3.25778 | −0.115760 | ||||||||
\(793\) | 14.8169 | 0.526162 | ||||||||
\(794\) | −16.3729 | −0.581052 | ||||||||
\(795\) | −6.21515 | −0.220429 | ||||||||
\(796\) | −9.30256 | −0.329721 | ||||||||
\(797\) | 14.5872 | 0.516704 | 0.258352 | − | 0.966051i | \(-0.416821\pi\) | ||||
0.258352 | + | 0.966051i | \(0.416821\pi\) | |||||||
\(798\) | 31.0541 | 1.09930 | ||||||||
\(799\) | 0.260025 | 0.00919903 | ||||||||
\(800\) | 6.48743 | 0.229365 | ||||||||
\(801\) | 19.7711 | 0.698578 | ||||||||
\(802\) | −30.6155 | −1.08107 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 5.16616 | 0.182197 | ||||||||
\(805\) | 19.0196 | 0.670354 | ||||||||
\(806\) | 23.6639 | 0.833524 | ||||||||
\(807\) | 1.04639 | 0.0368348 | ||||||||
\(808\) | −1.10843 | −0.0389945 | ||||||||
\(809\) | −30.7364 | −1.08064 | −0.540318 | − | 0.841461i | \(-0.681696\pi\) | ||||
−0.540318 | + | 0.841461i | \(0.681696\pi\) | |||||||
\(810\) | −11.2396 | −0.394918 | ||||||||
\(811\) | −45.9306 | −1.61284 | −0.806421 | − | 0.591341i | \(-0.798599\pi\) | ||||
−0.806421 | + | 0.591341i | \(0.798599\pi\) | |||||||
\(812\) | −3.88004 | −0.136163 | ||||||||
\(813\) | 2.28857 | 0.0802637 | ||||||||
\(814\) | 12.3425 | 0.432605 | ||||||||
\(815\) | −13.6348 | −0.477605 | ||||||||
\(816\) | −0.174815 | −0.00611975 | ||||||||
\(817\) | −1.92637 | −0.0673952 | ||||||||
\(818\) | −57.0137 | −1.99344 | ||||||||
\(819\) | −63.3071 | −2.21213 | ||||||||
\(820\) | −9.73332 | −0.339902 | ||||||||
\(821\) | −36.1425 | −1.26138 | −0.630690 | − | 0.776035i | \(-0.717228\pi\) | ||||
−0.630690 | + | 0.776035i | \(0.717228\pi\) | |||||||
\(822\) | −10.8430 | −0.378193 | ||||||||
\(823\) | −50.0757 | −1.74553 | −0.872765 | − | 0.488141i | \(-0.837675\pi\) | ||||
−0.872765 | + | 0.488141i | \(0.837675\pi\) | |||||||
\(824\) | −5.41860 | −0.188766 | ||||||||
\(825\) | 0.572536 | 0.0199332 | ||||||||
\(826\) | −20.8510 | −0.725498 | ||||||||
\(827\) | 12.2115 | 0.424635 | 0.212318 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212318 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(828\) | 17.0228 | 0.591584 | ||||||||
\(829\) | −5.31050 | −0.184441 | −0.0922206 | − | 0.995739i | \(-0.529396\pi\) | ||||
−0.0922206 | + | 0.995739i | \(0.529396\pi\) | |||||||
\(830\) | −7.95927 | −0.276270 | ||||||||
\(831\) | 2.25303 | 0.0781569 | ||||||||
\(832\) | 12.2875 | 0.425993 | ||||||||
\(833\) | 0.550686 | 0.0190801 | ||||||||
\(834\) | 3.97960 | 0.137802 | ||||||||
\(835\) | 25.1067 | 0.868854 | ||||||||
\(836\) | 9.95211 | 0.344201 | ||||||||
\(837\) | −7.06778 | −0.244298 | ||||||||
\(838\) | −48.9974 | −1.69259 | ||||||||
\(839\) | −7.69701 | −0.265730 | −0.132865 | − | 0.991134i | \(-0.542418\pi\) | ||||
−0.132865 | + | 0.991134i | \(0.542418\pi\) | |||||||
\(840\) | −2.77615 | −0.0957861 | ||||||||
\(841\) | −28.4637 | −0.981507 | ||||||||
\(842\) | 35.6855 | 1.22981 | ||||||||
\(843\) | 3.04077 | 0.104730 | ||||||||
\(844\) | −10.2529 | −0.352920 | ||||||||
\(845\) | 22.4808 | 0.773363 | ||||||||
\(846\) | 20.3119 | 0.698338 | ||||||||
\(847\) | −3.97729 | −0.136661 | ||||||||
\(848\) | 53.0799 | 1.82277 | ||||||||
\(849\) | −4.05402 | −0.139134 | ||||||||
\(850\) | −0.113987 | −0.00390973 | ||||||||
\(851\) | 32.3339 | 1.10839 | ||||||||
\(852\) | −8.62052 | −0.295334 | ||||||||
\(853\) | −33.6697 | −1.15283 | −0.576414 | − | 0.817158i | \(-0.695549\pi\) | ||||
−0.576414 | + | 0.817158i | \(0.695549\pi\) | |||||||
\(854\) | −18.0596 | −0.617986 | ||||||||
\(855\) | −19.9635 | −0.682739 | ||||||||
\(856\) | 1.03764 | 0.0354657 | ||||||||
\(857\) | −20.3732 | −0.695936 | −0.347968 | − | 0.937506i | \(-0.613128\pi\) | ||||
−0.347968 | + | 0.937506i | \(0.613128\pi\) | |||||||
\(858\) | 6.22531 | 0.212528 | ||||||||
\(859\) | −46.9767 | −1.60282 | −0.801411 | − | 0.598113i | \(-0.795917\pi\) | ||||
−0.801411 | + | 0.598113i | \(0.795917\pi\) | |||||||
\(860\) | −0.343494 | −0.0117130 | ||||||||
\(861\) | 16.6381 | 0.567026 | ||||||||
\(862\) | −22.3182 | −0.760161 | ||||||||
\(863\) | 10.4335 | 0.355159 | 0.177580 | − | 0.984106i | \(-0.443173\pi\) | ||||
0.177580 | + | 0.984106i | \(0.443173\pi\) | |||||||
\(864\) | −21.0682 | −0.716754 | ||||||||
\(865\) | 9.43336 | 0.320744 | ||||||||
\(866\) | −50.9922 | −1.73279 | ||||||||
\(867\) | −9.73089 | −0.330478 | ||||||||
\(868\) | −11.5309 | −0.391383 | ||||||||
\(869\) | 16.8072 | 0.570144 | ||||||||
\(870\) | −0.765361 | −0.0259482 | ||||||||
\(871\) | −40.3473 | −1.36712 | ||||||||
\(872\) | 8.11193 | 0.274705 | ||||||||
\(873\) | 16.1601 | 0.546937 | ||||||||
\(874\) | 65.2145 | 2.20591 | ||||||||
\(875\) | −3.97729 | −0.134457 | ||||||||
\(876\) | 0.762693 | 0.0257690 | ||||||||
\(877\) | 0.873478 | 0.0294953 | 0.0147476 | − | 0.999891i | \(-0.495306\pi\) | ||||
0.0147476 | + | 0.999891i | \(0.495306\pi\) | |||||||
\(878\) | −46.5859 | −1.57220 | ||||||||
\(879\) | −2.61554 | −0.0882199 | ||||||||
\(880\) | −4.88969 | −0.164831 | ||||||||
\(881\) | 13.2800 | 0.447414 | 0.223707 | − | 0.974656i | \(-0.428184\pi\) | ||||
0.223707 | + | 0.974656i | \(0.428184\pi\) | |||||||
\(882\) | 43.0170 | 1.44846 | ||||||||
\(883\) | 21.7634 | 0.732397 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(884\) | −0.495494 | −0.0166653 | ||||||||
\(885\) | −1.64430 | −0.0552726 | ||||||||
\(886\) | −45.7833 | −1.53812 | ||||||||
\(887\) | −58.2019 | −1.95423 | −0.977115 | − | 0.212714i | \(-0.931770\pi\) | ||||
−0.977115 | + | 0.212714i | \(0.931770\pi\) | |||||||
\(888\) | −4.71953 | −0.158377 | ||||||||
\(889\) | 8.46870 | 0.284031 | ||||||||
\(890\) | 13.5059 | 0.452718 | ||||||||
\(891\) | 6.15727 | 0.206276 | ||||||||
\(892\) | −4.68360 | −0.156819 | ||||||||
\(893\) | 31.1092 | 1.04103 | ||||||||
\(894\) | 3.46139 | 0.115766 | ||||||||
\(895\) | −23.4176 | −0.782765 | ||||||||
\(896\) | 36.6280 | 1.22366 | ||||||||
\(897\) | 16.3085 | 0.544526 | ||||||||
\(898\) | −33.2444 | −1.10938 | ||||||||
\(899\) | 1.59379 | 0.0531558 | ||||||||
\(900\) | −3.55972 | −0.118657 | ||||||||
\(901\) | −0.677865 | −0.0225830 | ||||||||
\(902\) | 13.3375 | 0.444091 | ||||||||
\(903\) | 0.587167 | 0.0195397 | ||||||||
\(904\) | 23.9325 | 0.795982 | ||||||||
\(905\) | −4.13000 | −0.137286 | ||||||||
\(906\) | −10.1527 | −0.337301 | ||||||||
\(907\) | −11.4799 | −0.381183 | −0.190591 | − | 0.981669i | \(-0.561041\pi\) | ||||
−0.190591 | + | 0.981669i | \(0.561041\pi\) | |||||||
\(908\) | 26.0481 | 0.864436 | ||||||||
\(909\) | 2.42955 | 0.0805831 | ||||||||
\(910\) | −43.2458 | −1.43359 | ||||||||
\(911\) | 24.0459 | 0.796676 | 0.398338 | − | 0.917239i | \(-0.369587\pi\) | ||||
0.398338 | + | 0.917239i | \(0.369587\pi\) | |||||||
\(912\) | −20.9147 | −0.692556 | ||||||||
\(913\) | 4.36026 | 0.144304 | ||||||||
\(914\) | −66.7869 | −2.20911 | ||||||||
\(915\) | −1.42417 | −0.0470817 | ||||||||
\(916\) | 18.4003 | 0.607963 | ||||||||
\(917\) | −73.2368 | −2.41849 | ||||||||
\(918\) | 0.370178 | 0.0122177 | ||||||||
\(919\) | −11.0686 | −0.365120 | −0.182560 | − | 0.983195i | \(-0.558438\pi\) | ||||
−0.182560 | + | 0.983195i | \(0.558438\pi\) | |||||||
\(920\) | −5.82999 | −0.192209 | ||||||||
\(921\) | −12.6594 | −0.417141 | ||||||||
\(922\) | 42.6893 | 1.40590 | ||||||||
\(923\) | 67.3256 | 2.21605 | ||||||||
\(924\) | −3.03345 | −0.0997931 | ||||||||
\(925\) | −6.76150 | −0.222317 | ||||||||
\(926\) | 16.1318 | 0.530125 | ||||||||
\(927\) | 11.8769 | 0.390089 | ||||||||
\(928\) | 4.75089 | 0.155956 | ||||||||
\(929\) | 58.5645 | 1.92144 | 0.960720 | − | 0.277519i | \(-0.0895123\pi\) | ||||
0.960720 | + | 0.277519i | \(0.0895123\pi\) | |||||||
\(930\) | −2.27453 | −0.0745849 | ||||||||
\(931\) | 65.8836 | 2.15925 | ||||||||
\(932\) | 14.4062 | 0.471889 | ||||||||
\(933\) | −3.17833 | −0.104054 | ||||||||
\(934\) | −23.6124 | −0.772620 | ||||||||
\(935\) | 0.0624446 | 0.00204216 | ||||||||
\(936\) | 19.4052 | 0.634279 | ||||||||
\(937\) | 34.5295 | 1.12803 | 0.564016 | − | 0.825764i | \(-0.309256\pi\) | ||||
0.564016 | + | 0.825764i | \(0.309256\pi\) | |||||||
\(938\) | 49.1775 | 1.60570 | ||||||||
\(939\) | −16.8964 | −0.551394 | ||||||||
\(940\) | 5.54712 | 0.180927 | ||||||||
\(941\) | −51.2421 | −1.67045 | −0.835223 | − | 0.549912i | \(-0.814661\pi\) | ||||
−0.835223 | + | 0.549912i | \(0.814661\pi\) | |||||||
\(942\) | −10.8837 | −0.354611 | ||||||||
\(943\) | 34.9405 | 1.13782 | ||||||||
\(944\) | 14.0430 | 0.457060 | ||||||||
\(945\) | 12.9164 | 0.420171 | ||||||||
\(946\) | 0.470688 | 0.0153034 | ||||||||
\(947\) | 16.8563 | 0.547755 | 0.273878 | − | 0.961765i | \(-0.411694\pi\) | ||||
0.273878 | + | 0.961765i | \(0.411694\pi\) | |||||||
\(948\) | 12.8187 | 0.416332 | ||||||||
\(949\) | −5.95658 | −0.193359 | ||||||||
\(950\) | −13.6373 | −0.442453 | ||||||||
\(951\) | −3.10796 | −0.100783 | ||||||||
\(952\) | −0.302785 | −0.00981331 | ||||||||
\(953\) | 52.1860 | 1.69047 | 0.845234 | − | 0.534396i | \(-0.179461\pi\) | ||||
0.845234 | + | 0.534396i | \(0.179461\pi\) | |||||||
\(954\) | −52.9516 | −1.71437 | ||||||||
\(955\) | 14.7414 | 0.477020 | ||||||||
\(956\) | 15.3664 | 0.496985 | ||||||||
\(957\) | 0.419281 | 0.0135534 | ||||||||
\(958\) | −7.32770 | −0.236747 | ||||||||
\(959\) | −41.2640 | −1.33249 | ||||||||
\(960\) | −1.18106 | −0.0381184 | ||||||||
\(961\) | −26.2635 | −0.847210 | ||||||||
\(962\) | −73.5192 | −2.37035 | ||||||||
\(963\) | −2.27437 | −0.0732907 | ||||||||
\(964\) | 26.9823 | 0.869041 | ||||||||
\(965\) | −7.91989 | −0.254950 | ||||||||
\(966\) | −19.8777 | −0.639554 | ||||||||
\(967\) | 8.20198 | 0.263758 | 0.131879 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131879 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(968\) | 1.21914 | 0.0391845 | ||||||||
\(969\) | 0.267095 | 0.00858033 | ||||||||
\(970\) | 11.0392 | 0.354446 | ||||||||
\(971\) | 1.02351 | 0.0328460 | 0.0164230 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164230 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(972\) | 17.6746 | 0.566912 | ||||||||
\(973\) | 15.1448 | 0.485519 | ||||||||
\(974\) | −56.4532 | −1.80888 | ||||||||
\(975\) | −3.41036 | −0.109219 | ||||||||
\(976\) | 12.1630 | 0.389328 | ||||||||
\(977\) | −36.7427 | −1.17550 | −0.587752 | − | 0.809041i | \(-0.699987\pi\) | ||||
−0.587752 | + | 0.809041i | \(0.699987\pi\) | |||||||
\(978\) | 14.2499 | 0.455662 | ||||||||
\(979\) | −7.39881 | −0.236467 | ||||||||
\(980\) | 11.7478 | 0.375269 | ||||||||
\(981\) | −17.7804 | −0.567684 | ||||||||
\(982\) | −18.2993 | −0.583955 | ||||||||
\(983\) | −7.17396 | −0.228814 | −0.114407 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114407 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(984\) | −5.10000 | −0.162582 | ||||||||
\(985\) | −19.2554 | −0.613527 | ||||||||
\(986\) | −0.0834753 | −0.00265840 | ||||||||
\(987\) | −9.48223 | −0.301823 | ||||||||
\(988\) | −59.2805 | −1.88596 | ||||||||
\(989\) | 1.23307 | 0.0392093 | ||||||||
\(990\) | 4.87787 | 0.155029 | ||||||||
\(991\) | 4.28532 | 0.136128 | 0.0680639 | − | 0.997681i | \(-0.478318\pi\) | ||||
0.0680639 | + | 0.997681i | \(0.478318\pi\) | |||||||
\(992\) | 14.1189 | 0.448275 | ||||||||
\(993\) | 11.2591 | 0.357297 | ||||||||
\(994\) | −82.0600 | −2.60279 | ||||||||
\(995\) | −6.98322 | −0.221383 | ||||||||
\(996\) | 3.32554 | 0.105374 | ||||||||
\(997\) | 8.99158 | 0.284766 | 0.142383 | − | 0.989812i | \(-0.454523\pi\) | ||||
0.142383 | + | 0.989812i | \(0.454523\pi\) | |||||||
\(998\) | 55.5903 | 1.75968 | ||||||||
\(999\) | 21.9582 | 0.694728 |
(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 | 4015.2.a.h.1.9 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.9 | ✓ | 37 | 1.1 | even | 1 | trivial |