Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.35 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.12255 | 0.750435 | 0.375218 | − | 0.926937i | \(-0.377568\pi\) | ||||
0.375218 | + | 0.926937i | \(0.377568\pi\) | |||||||
\(3\) | −9.87196 | −1.89986 | −0.949930 | − | 0.312463i | \(-0.898846\pi\) | ||||
−0.949930 | + | 0.312463i | \(0.898846\pi\) | |||||||
\(4\) | −3.49478 | −0.436847 | ||||||||
\(5\) | 15.5747 | 1.39304 | 0.696520 | − | 0.717537i | \(-0.254731\pi\) | ||||
0.696520 | + | 0.717537i | \(0.254731\pi\) | |||||||
\(6\) | −20.9537 | −1.42572 | ||||||||
\(7\) | 16.3831 | 0.884603 | 0.442302 | − | 0.896866i | \(-0.354162\pi\) | ||||
0.442302 | + | 0.896866i | \(0.354162\pi\) | |||||||
\(8\) | −24.3983 | −1.07826 | ||||||||
\(9\) | 70.4556 | 2.60947 | ||||||||
\(10\) | 33.0580 | 1.04539 | ||||||||
\(11\) | 42.7049 | 1.17055 | 0.585274 | − | 0.810836i | \(-0.300987\pi\) | ||||
0.585274 | + | 0.810836i | \(0.300987\pi\) | |||||||
\(12\) | 34.5003 | 0.829948 | ||||||||
\(13\) | −44.4137 | −0.947549 | −0.473774 | − | 0.880646i | \(-0.657109\pi\) | ||||
−0.473774 | + | 0.880646i | \(0.657109\pi\) | |||||||
\(14\) | 34.7739 | 0.663837 | ||||||||
\(15\) | −153.752 | −2.64658 | ||||||||
\(16\) | −23.8283 | −0.372318 | ||||||||
\(17\) | −80.6618 | −1.15079 | −0.575393 | − | 0.817877i | \(-0.695151\pi\) | ||||
−0.575393 | + | 0.817877i | \(0.695151\pi\) | |||||||
\(18\) | 149.546 | 1.95824 | ||||||||
\(19\) | −9.72641 | −0.117442 | −0.0587208 | − | 0.998274i | \(-0.518702\pi\) | ||||
−0.0587208 | + | 0.998274i | \(0.518702\pi\) | |||||||
\(20\) | −54.4300 | −0.608546 | ||||||||
\(21\) | −161.733 | −1.68062 | ||||||||
\(22\) | 90.6434 | 0.878420 | ||||||||
\(23\) | 81.9683 | 0.743111 | 0.371556 | − | 0.928411i | \(-0.378824\pi\) | ||||
0.371556 | + | 0.928411i | \(0.378824\pi\) | |||||||
\(24\) | 240.859 | 2.04854 | ||||||||
\(25\) | 117.570 | 0.940562 | ||||||||
\(26\) | −94.2703 | −0.711074 | ||||||||
\(27\) | −428.992 | −3.05776 | ||||||||
\(28\) | −57.2552 | −0.386436 | ||||||||
\(29\) | −170.553 | −1.09210 | −0.546049 | − | 0.837753i | \(-0.683869\pi\) | ||||
−0.546049 | + | 0.837753i | \(0.683869\pi\) | |||||||
\(30\) | −326.348 | −1.98609 | ||||||||
\(31\) | −115.463 | −0.668958 | −0.334479 | − | 0.942403i | \(-0.608560\pi\) | ||||
−0.334479 | + | 0.942403i | \(0.608560\pi\) | |||||||
\(32\) | 144.609 | 0.798860 | ||||||||
\(33\) | −421.581 | −2.22388 | ||||||||
\(34\) | −171.209 | −0.863590 | ||||||||
\(35\) | 255.161 | 1.23229 | ||||||||
\(36\) | −246.227 | −1.13994 | ||||||||
\(37\) | −56.3932 | −0.250567 | −0.125284 | − | 0.992121i | \(-0.539984\pi\) | ||||
−0.125284 | + | 0.992121i | \(0.539984\pi\) | |||||||
\(38\) | −20.6448 | −0.0881323 | ||||||||
\(39\) | 438.450 | 1.80021 | ||||||||
\(40\) | −379.995 | −1.50206 | ||||||||
\(41\) | 9.51295 | 0.0362359 | 0.0181180 | − | 0.999836i | \(-0.494233\pi\) | ||||
0.0181180 | + | 0.999836i | \(0.494233\pi\) | |||||||
\(42\) | −343.287 | −1.26120 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −149.244 | −0.511350 | ||||||||
\(45\) | 1097.32 | 3.63509 | ||||||||
\(46\) | 173.982 | 0.557657 | ||||||||
\(47\) | 9.55328 | 0.0296487 | 0.0148243 | − | 0.999890i | \(-0.495281\pi\) | ||||
0.0148243 | + | 0.999890i | \(0.495281\pi\) | |||||||
\(48\) | 235.232 | 0.707351 | ||||||||
\(49\) | −74.5945 | −0.217477 | ||||||||
\(50\) | 249.549 | 0.705830 | ||||||||
\(51\) | 796.290 | 2.18633 | ||||||||
\(52\) | 155.216 | 0.413934 | ||||||||
\(53\) | 254.029 | 0.658370 | 0.329185 | − | 0.944265i | \(-0.393226\pi\) | ||||
0.329185 | + | 0.944265i | \(0.393226\pi\) | |||||||
\(54\) | −910.558 | −2.29465 | ||||||||
\(55\) | 665.115 | 1.63062 | ||||||||
\(56\) | −399.719 | −0.953833 | ||||||||
\(57\) | 96.0187 | 0.223123 | ||||||||
\(58\) | −362.007 | −0.819549 | ||||||||
\(59\) | 288.741 | 0.637133 | 0.318566 | − | 0.947901i | \(-0.396799\pi\) | ||||
0.318566 | + | 0.947901i | \(0.396799\pi\) | |||||||
\(60\) | 537.331 | 1.15615 | ||||||||
\(61\) | 67.9815 | 0.142691 | 0.0713454 | − | 0.997452i | \(-0.477271\pi\) | ||||
0.0713454 | + | 0.997452i | \(0.477271\pi\) | |||||||
\(62\) | −245.075 | −0.502009 | ||||||||
\(63\) | 1154.28 | 2.30834 | ||||||||
\(64\) | 497.567 | 0.971810 | ||||||||
\(65\) | −691.728 | −1.31997 | ||||||||
\(66\) | −894.828 | −1.66887 | ||||||||
\(67\) | 273.745 | 0.499153 | 0.249577 | − | 0.968355i | \(-0.419709\pi\) | ||||
0.249577 | + | 0.968355i | \(0.419709\pi\) | |||||||
\(68\) | 281.895 | 0.502717 | ||||||||
\(69\) | −809.187 | −1.41181 | ||||||||
\(70\) | 541.592 | 0.924752 | ||||||||
\(71\) | 113.470 | 0.189668 | 0.0948339 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948339 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(72\) | −1718.99 | −2.81369 | ||||||||
\(73\) | 908.508 | 1.45661 | 0.728307 | − | 0.685251i | \(-0.240307\pi\) | ||||
0.728307 | + | 0.685251i | \(0.240307\pi\) | |||||||
\(74\) | −119.698 | −0.188035 | ||||||||
\(75\) | −1160.65 | −1.78694 | ||||||||
\(76\) | 33.9916 | 0.0513040 | ||||||||
\(77\) | 699.638 | 1.03547 | ||||||||
\(78\) | 930.632 | 1.35094 | ||||||||
\(79\) | −798.537 | −1.13725 | −0.568623 | − | 0.822598i | \(-0.692524\pi\) | ||||
−0.568623 | + | 0.822598i | \(0.692524\pi\) | |||||||
\(80\) | −371.118 | −0.518653 | ||||||||
\(81\) | 2332.69 | 3.19985 | ||||||||
\(82\) | 20.1917 | 0.0271927 | ||||||||
\(83\) | −1273.00 | −1.68349 | −0.841744 | − | 0.539878i | \(-0.818471\pi\) | ||||
−0.841744 | + | 0.539878i | \(0.818471\pi\) | |||||||
\(84\) | 565.221 | 0.734175 | ||||||||
\(85\) | −1256.28 | −1.60309 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1683.69 | 2.07483 | ||||||||
\(88\) | −1041.93 | −1.26215 | ||||||||
\(89\) | −1394.34 | −1.66067 | −0.830335 | − | 0.557265i | \(-0.811851\pi\) | ||||
−0.830335 | + | 0.557265i | \(0.811851\pi\) | |||||||
\(90\) | 2329.12 | 2.72790 | ||||||||
\(91\) | −727.633 | −0.838205 | ||||||||
\(92\) | −286.461 | −0.324626 | ||||||||
\(93\) | 1139.84 | 1.27093 | ||||||||
\(94\) | 20.2773 | 0.0222494 | ||||||||
\(95\) | −151.486 | −0.163601 | ||||||||
\(96\) | −1427.58 | −1.51772 | ||||||||
\(97\) | 253.183 | 0.265018 | 0.132509 | − | 0.991182i | \(-0.457697\pi\) | ||||
0.132509 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(98\) | −158.331 | −0.163202 | ||||||||
\(99\) | 3008.80 | 3.05450 | ||||||||
\(100\) | −410.882 | −0.410882 | ||||||||
\(101\) | 623.621 | 0.614383 | 0.307191 | − | 0.951648i | \(-0.400611\pi\) | ||||
0.307191 | + | 0.951648i | \(0.400611\pi\) | |||||||
\(102\) | 1690.17 | 1.64070 | ||||||||
\(103\) | −1534.71 | −1.46815 | −0.734076 | − | 0.679067i | \(-0.762385\pi\) | ||||
−0.734076 | + | 0.679067i | \(0.762385\pi\) | |||||||
\(104\) | 1083.62 | 1.02170 | ||||||||
\(105\) | −2518.94 | −2.34117 | ||||||||
\(106\) | 539.190 | 0.494064 | ||||||||
\(107\) | 978.902 | 0.884430 | 0.442215 | − | 0.896909i | \(-0.354193\pi\) | ||||
0.442215 | + | 0.896909i | \(0.354193\pi\) | |||||||
\(108\) | 1499.23 | 1.33577 | ||||||||
\(109\) | −615.263 | −0.540656 | −0.270328 | − | 0.962768i | \(-0.587132\pi\) | ||||
−0.270328 | + | 0.962768i | \(0.587132\pi\) | |||||||
\(110\) | 1411.74 | 1.22367 | ||||||||
\(111\) | 556.712 | 0.476043 | ||||||||
\(112\) | −390.381 | −0.329353 | ||||||||
\(113\) | 1889.47 | 1.57298 | 0.786488 | − | 0.617605i | \(-0.211897\pi\) | ||||
0.786488 | + | 0.617605i | \(0.211897\pi\) | |||||||
\(114\) | 203.805 | 0.167439 | ||||||||
\(115\) | 1276.63 | 1.03518 | ||||||||
\(116\) | 596.044 | 0.477080 | ||||||||
\(117\) | −3129.19 | −2.47260 | ||||||||
\(118\) | 612.867 | 0.478127 | ||||||||
\(119\) | −1321.49 | −1.01799 | ||||||||
\(120\) | 3751.29 | 2.85370 | ||||||||
\(121\) | 492.710 | 0.370181 | ||||||||
\(122\) | 144.294 | 0.107080 | ||||||||
\(123\) | −93.9115 | −0.0688432 | ||||||||
\(124\) | 403.516 | 0.292232 | ||||||||
\(125\) | −115.717 | −0.0828002 | ||||||||
\(126\) | 2450.02 | 1.73226 | ||||||||
\(127\) | −333.272 | −0.232859 | −0.116430 | − | 0.993199i | \(-0.537145\pi\) | ||||
−0.116430 | + | 0.993199i | \(0.537145\pi\) | |||||||
\(128\) | −100.762 | −0.0695797 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1468.23 | −0.990554 | ||||||||
\(131\) | 1298.39 | 0.865959 | 0.432979 | − | 0.901404i | \(-0.357462\pi\) | ||||
0.432979 | + | 0.901404i | \(0.357462\pi\) | |||||||
\(132\) | 1473.33 | 0.971493 | ||||||||
\(133\) | −159.349 | −0.103889 | ||||||||
\(134\) | 581.038 | 0.374582 | ||||||||
\(135\) | −6681.41 | −4.25959 | ||||||||
\(136\) | 1968.01 | 1.24085 | ||||||||
\(137\) | −1989.18 | −1.24049 | −0.620245 | − | 0.784408i | \(-0.712967\pi\) | ||||
−0.620245 | + | 0.784408i | \(0.712967\pi\) | |||||||
\(138\) | −1717.54 | −1.05947 | ||||||||
\(139\) | −1554.18 | −0.948374 | −0.474187 | − | 0.880424i | \(-0.657258\pi\) | ||||
−0.474187 | + | 0.880424i | \(0.657258\pi\) | |||||||
\(140\) | −891.731 | −0.538322 | ||||||||
\(141\) | −94.3096 | −0.0563284 | ||||||||
\(142\) | 240.846 | 0.142333 | ||||||||
\(143\) | −1896.68 | −1.10915 | ||||||||
\(144\) | −1678.84 | −0.971550 | ||||||||
\(145\) | −2656.30 | −1.52134 | ||||||||
\(146\) | 1928.36 | 1.09309 | ||||||||
\(147\) | 736.394 | 0.413175 | ||||||||
\(148\) | 197.082 | 0.109460 | ||||||||
\(149\) | 2018.71 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(150\) | −2463.54 | −1.34098 | ||||||||
\(151\) | −219.429 | −0.118258 | −0.0591289 | − | 0.998250i | \(-0.518832\pi\) | ||||
−0.0591289 | + | 0.998250i | \(0.518832\pi\) | |||||||
\(152\) | 237.307 | 0.126633 | ||||||||
\(153\) | −5683.08 | −3.00294 | ||||||||
\(154\) | 1485.02 | 0.777053 | ||||||||
\(155\) | −1798.29 | −0.931885 | ||||||||
\(156\) | −1532.28 | −0.786416 | ||||||||
\(157\) | 2441.15 | 1.24092 | 0.620462 | − | 0.784236i | \(-0.286945\pi\) | ||||
0.620462 | + | 0.784236i | \(0.286945\pi\) | |||||||
\(158\) | −1694.94 | −0.853430 | ||||||||
\(159\) | −2507.77 | −1.25081 | ||||||||
\(160\) | 2252.24 | 1.11284 | ||||||||
\(161\) | 1342.89 | 0.657359 | ||||||||
\(162\) | 4951.26 | 2.40128 | ||||||||
\(163\) | −2934.10 | −1.40992 | −0.704959 | − | 0.709248i | \(-0.749035\pi\) | ||||
−0.704959 | + | 0.709248i | \(0.749035\pi\) | |||||||
\(164\) | −33.2456 | −0.0158296 | ||||||||
\(165\) | −6565.99 | −3.09795 | ||||||||
\(166\) | −2702.00 | −1.26335 | ||||||||
\(167\) | −4127.64 | −1.91261 | −0.956306 | − | 0.292368i | \(-0.905557\pi\) | ||||
−0.956306 | + | 0.292368i | \(0.905557\pi\) | |||||||
\(168\) | 3946.01 | 1.81215 | ||||||||
\(169\) | −224.427 | −0.102152 | ||||||||
\(170\) | −2666.52 | −1.20302 | ||||||||
\(171\) | −685.280 | −0.306460 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −803.747 | −0.353224 | −0.176612 | − | 0.984281i | \(-0.556514\pi\) | ||||
−0.176612 | + | 0.984281i | \(0.556514\pi\) | |||||||
\(174\) | 3573.72 | 1.55703 | ||||||||
\(175\) | 1926.16 | 0.832024 | ||||||||
\(176\) | −1017.59 | −0.435815 | ||||||||
\(177\) | −2850.44 | −1.21046 | ||||||||
\(178\) | −2959.55 | −1.24622 | ||||||||
\(179\) | −3352.74 | −1.39998 | −0.699988 | − | 0.714155i | \(-0.746811\pi\) | ||||
−0.699988 | + | 0.714155i | \(0.746811\pi\) | |||||||
\(180\) | −3834.90 | −1.58798 | ||||||||
\(181\) | −4226.02 | −1.73546 | −0.867728 | − | 0.497040i | \(-0.834420\pi\) | ||||
−0.867728 | + | 0.497040i | \(0.834420\pi\) | |||||||
\(182\) | −1544.44 | −0.629018 | ||||||||
\(183\) | −671.111 | −0.271093 | ||||||||
\(184\) | −1999.88 | −0.801268 | ||||||||
\(185\) | −878.306 | −0.349050 | ||||||||
\(186\) | 2419.37 | 0.953748 | ||||||||
\(187\) | −3444.66 | −1.34705 | ||||||||
\(188\) | −33.3866 | −0.0129519 | ||||||||
\(189\) | −7028.21 | −2.70491 | ||||||||
\(190\) | −321.536 | −0.122772 | ||||||||
\(191\) | 3645.85 | 1.38118 | 0.690588 | − | 0.723249i | \(-0.257352\pi\) | ||||
0.690588 | + | 0.723249i | \(0.257352\pi\) | |||||||
\(192\) | −4911.96 | −1.84630 | ||||||||
\(193\) | 3201.57 | 1.19406 | 0.597032 | − | 0.802218i | \(-0.296347\pi\) | ||||
0.597032 | + | 0.802218i | \(0.296347\pi\) | |||||||
\(194\) | 537.393 | 0.198879 | ||||||||
\(195\) | 6828.71 | 2.50776 | ||||||||
\(196\) | 260.691 | 0.0950041 | ||||||||
\(197\) | 92.9451 | 0.0336145 | 0.0168073 | − | 0.999859i | \(-0.494650\pi\) | ||||
0.0168073 | + | 0.999859i | \(0.494650\pi\) | |||||||
\(198\) | 6386.33 | 2.29221 | ||||||||
\(199\) | 97.0214 | 0.0345611 | 0.0172806 | − | 0.999851i | \(-0.494499\pi\) | ||||
0.0172806 | + | 0.999851i | \(0.494499\pi\) | |||||||
\(200\) | −2868.51 | −1.01417 | ||||||||
\(201\) | −2702.40 | −0.948321 | ||||||||
\(202\) | 1323.67 | 0.461054 | ||||||||
\(203\) | −2794.18 | −0.966074 | ||||||||
\(204\) | −2782.86 | −0.955093 | ||||||||
\(205\) | 148.161 | 0.0504781 | ||||||||
\(206\) | −3257.51 | −1.10175 | ||||||||
\(207\) | 5775.12 | 1.93912 | ||||||||
\(208\) | 1058.30 | 0.352789 | ||||||||
\(209\) | −415.365 | −0.137471 | ||||||||
\(210\) | −5346.58 | −1.75690 | ||||||||
\(211\) | −106.820 | −0.0348522 | −0.0174261 | − | 0.999848i | \(-0.505547\pi\) | ||||
−0.0174261 | + | 0.999848i | \(0.505547\pi\) | |||||||
\(212\) | −887.776 | −0.287607 | ||||||||
\(213\) | −1120.17 | −0.360342 | ||||||||
\(214\) | 2077.77 | 0.663708 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 10466.7 | 3.29706 | ||||||||
\(217\) | −1891.63 | −0.591762 | ||||||||
\(218\) | −1305.93 | −0.405727 | ||||||||
\(219\) | −8968.76 | −2.76736 | ||||||||
\(220\) | −2324.43 | −0.712331 | ||||||||
\(221\) | 3582.48 | 1.09043 | ||||||||
\(222\) | 1181.65 | 0.357239 | ||||||||
\(223\) | 3792.84 | 1.13896 | 0.569478 | − | 0.822006i | \(-0.307145\pi\) | ||||
0.569478 | + | 0.822006i | \(0.307145\pi\) | |||||||
\(224\) | 2369.14 | 0.706675 | ||||||||
\(225\) | 8283.48 | 2.45436 | ||||||||
\(226\) | 4010.50 | 1.18042 | ||||||||
\(227\) | −2142.14 | −0.626339 | −0.313170 | − | 0.949697i | \(-0.601391\pi\) | ||||
−0.313170 | + | 0.949697i | \(0.601391\pi\) | |||||||
\(228\) | −335.564 | −0.0974705 | ||||||||
\(229\) | −866.711 | −0.250104 | −0.125052 | − | 0.992150i | \(-0.539910\pi\) | ||||
−0.125052 | + | 0.992150i | \(0.539910\pi\) | |||||||
\(230\) | 2709.71 | 0.776839 | ||||||||
\(231\) | −6906.80 | −1.96725 | ||||||||
\(232\) | 4161.19 | 1.17757 | ||||||||
\(233\) | −2698.47 | −0.758724 | −0.379362 | − | 0.925248i | \(-0.623856\pi\) | ||||
−0.379362 | + | 0.925248i | \(0.623856\pi\) | |||||||
\(234\) | −6641.87 | −1.85552 | ||||||||
\(235\) | 148.789 | 0.0413018 | ||||||||
\(236\) | −1009.08 | −0.278330 | ||||||||
\(237\) | 7883.13 | 2.16061 | ||||||||
\(238\) | −2804.93 | −0.763935 | ||||||||
\(239\) | −1856.90 | −0.502564 | −0.251282 | − | 0.967914i | \(-0.580852\pi\) | ||||
−0.251282 | + | 0.967914i | \(0.580852\pi\) | |||||||
\(240\) | 3663.66 | 0.985369 | ||||||||
\(241\) | 4891.12 | 1.30732 | 0.653661 | − | 0.756788i | \(-0.273232\pi\) | ||||
0.653661 | + | 0.756788i | \(0.273232\pi\) | |||||||
\(242\) | 1045.80 | 0.277796 | ||||||||
\(243\) | −11445.5 | −3.02151 | ||||||||
\(244\) | −237.580 | −0.0623341 | ||||||||
\(245\) | −1161.78 | −0.302954 | ||||||||
\(246\) | −199.332 | −0.0516623 | ||||||||
\(247\) | 431.985 | 0.111282 | ||||||||
\(248\) | 2817.09 | 0.721311 | ||||||||
\(249\) | 12567.0 | 3.19839 | ||||||||
\(250\) | −245.615 | −0.0621362 | ||||||||
\(251\) | −5679.81 | −1.42831 | −0.714156 | − | 0.699987i | \(-0.753189\pi\) | ||||
−0.714156 | + | 0.699987i | \(0.753189\pi\) | |||||||
\(252\) | −4033.95 | −1.00839 | ||||||||
\(253\) | 3500.45 | 0.869847 | ||||||||
\(254\) | −707.387 | −0.174746 | ||||||||
\(255\) | 12402.0 | 3.04565 | ||||||||
\(256\) | −4194.41 | −1.02403 | ||||||||
\(257\) | 3095.65 | 0.751366 | 0.375683 | − | 0.926748i | \(-0.377408\pi\) | ||||
0.375683 | + | 0.926748i | \(0.377408\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −923.895 | −0.221653 | ||||||||
\(260\) | 2417.43 | 0.576627 | ||||||||
\(261\) | −12016.4 | −2.84980 | ||||||||
\(262\) | 2755.89 | 0.649846 | ||||||||
\(263\) | −2790.13 | −0.654170 | −0.327085 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327085 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(264\) | 10285.8 | 2.39792 | ||||||||
\(265\) | 3956.42 | 0.917136 | ||||||||
\(266\) | −338.225 | −0.0779622 | ||||||||
\(267\) | 13764.9 | 3.15504 | ||||||||
\(268\) | −956.678 | −0.218054 | ||||||||
\(269\) | −8193.14 | −1.85704 | −0.928521 | − | 0.371279i | \(-0.878919\pi\) | ||||
−0.928521 | + | 0.371279i | \(0.878919\pi\) | |||||||
\(270\) | −14181.6 | −3.19654 | ||||||||
\(271\) | −4239.14 | −0.950218 | −0.475109 | − | 0.879927i | \(-0.657591\pi\) | ||||
−0.475109 | + | 0.879927i | \(0.657591\pi\) | |||||||
\(272\) | 1922.04 | 0.428458 | ||||||||
\(273\) | 7183.16 | 1.59247 | ||||||||
\(274\) | −4222.14 | −0.930907 | ||||||||
\(275\) | 5020.83 | 1.10097 | ||||||||
\(276\) | 2827.93 | 0.616744 | ||||||||
\(277\) | 8528.69 | 1.84996 | 0.924981 | − | 0.380014i | \(-0.124081\pi\) | ||||
0.924981 | + | 0.380014i | \(0.124081\pi\) | |||||||
\(278\) | −3298.83 | −0.711693 | ||||||||
\(279\) | −8134.99 | −1.74562 | ||||||||
\(280\) | −6225.48 | −1.32873 | ||||||||
\(281\) | −1287.15 | −0.273257 | −0.136628 | − | 0.990622i | \(-0.543627\pi\) | ||||
−0.136628 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(282\) | −200.177 | −0.0422708 | ||||||||
\(283\) | −8974.14 | −1.88501 | −0.942504 | − | 0.334194i | \(-0.891536\pi\) | ||||
−0.942504 | + | 0.334194i | \(0.891536\pi\) | |||||||
\(284\) | −396.552 | −0.0828558 | ||||||||
\(285\) | 1495.46 | 0.310819 | ||||||||
\(286\) | −4025.80 | −0.832345 | ||||||||
\(287\) | 155.851 | 0.0320544 | ||||||||
\(288\) | 10188.5 | 2.08460 | ||||||||
\(289\) | 1593.32 | 0.324308 | ||||||||
\(290\) | −5638.14 | −1.14167 | ||||||||
\(291\) | −2499.41 | −0.503498 | ||||||||
\(292\) | −3175.03 | −0.636318 | ||||||||
\(293\) | 1173.60 | 0.234002 | 0.117001 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.117001 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(294\) | 1563.03 | 0.310061 | ||||||||
\(295\) | 4497.04 | 0.887552 | ||||||||
\(296\) | 1375.90 | 0.270177 | ||||||||
\(297\) | −18320.1 | −3.57925 | ||||||||
\(298\) | 4284.81 | 0.832928 | ||||||||
\(299\) | −3640.51 | −0.704134 | ||||||||
\(300\) | 4056.21 | 0.780617 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −465.750 | −0.0887447 | ||||||||
\(303\) | −6156.37 | −1.16724 | ||||||||
\(304\) | 231.764 | 0.0437256 | ||||||||
\(305\) | 1058.79 | 0.198774 | ||||||||
\(306\) | −12062.6 | −2.25351 | ||||||||
\(307\) | −8027.77 | −1.49241 | −0.746204 | − | 0.665718i | \(-0.768126\pi\) | ||||
−0.746204 | + | 0.665718i | \(0.768126\pi\) | |||||||
\(308\) | −2445.08 | −0.452342 | ||||||||
\(309\) | 15150.6 | 2.78928 | ||||||||
\(310\) | −3816.97 | −0.699320 | ||||||||
\(311\) | 5900.91 | 1.07592 | 0.537958 | − | 0.842972i | \(-0.319196\pi\) | ||||
0.537958 | + | 0.842972i | \(0.319196\pi\) | |||||||
\(312\) | −10697.4 | −1.94109 | ||||||||
\(313\) | −7645.72 | −1.38071 | −0.690354 | − | 0.723471i | \(-0.742545\pi\) | ||||
−0.690354 | + | 0.723471i | \(0.742545\pi\) | |||||||
\(314\) | 5181.47 | 0.931234 | ||||||||
\(315\) | 17977.5 | 3.21562 | ||||||||
\(316\) | 2790.71 | 0.496803 | ||||||||
\(317\) | 8873.30 | 1.57216 | 0.786079 | − | 0.618126i | \(-0.212108\pi\) | ||||
0.786079 | + | 0.618126i | \(0.212108\pi\) | |||||||
\(318\) | −5322.87 | −0.938653 | ||||||||
\(319\) | −7283.45 | −1.27835 | ||||||||
\(320\) | 7749.44 | 1.35377 | ||||||||
\(321\) | −9663.68 | −1.68029 | ||||||||
\(322\) | 2850.36 | 0.493305 | ||||||||
\(323\) | 784.549 | 0.135150 | ||||||||
\(324\) | −8152.24 | −1.39785 | ||||||||
\(325\) | −5221.72 | −0.891228 | ||||||||
\(326\) | −6227.78 | −1.05805 | ||||||||
\(327\) | 6073.85 | 1.02717 | ||||||||
\(328\) | −232.099 | −0.0390718 | ||||||||
\(329\) | 156.512 | 0.0262273 | ||||||||
\(330\) | −13936.6 | −2.32481 | ||||||||
\(331\) | −3998.27 | −0.663943 | −0.331971 | − | 0.943289i | \(-0.607714\pi\) | ||||
−0.331971 | + | 0.943289i | \(0.607714\pi\) | |||||||
\(332\) | 4448.84 | 0.735426 | ||||||||
\(333\) | −3973.22 | −0.653847 | ||||||||
\(334\) | −8761.12 | −1.43529 | ||||||||
\(335\) | 4263.49 | 0.695341 | ||||||||
\(336\) | 3853.83 | 0.625725 | ||||||||
\(337\) | 3151.54 | 0.509423 | 0.254711 | − | 0.967017i | \(-0.418020\pi\) | ||||
0.254711 | + | 0.967017i | \(0.418020\pi\) | |||||||
\(338\) | −476.359 | −0.0766583 | ||||||||
\(339\) | −18652.8 | −2.98844 | ||||||||
\(340\) | 4390.42 | 0.700306 | ||||||||
\(341\) | −4930.82 | −0.783047 | ||||||||
\(342\) | −1454.54 | −0.229978 | ||||||||
\(343\) | −6841.49 | −1.07698 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12602.8 | −1.96670 | ||||||||
\(346\) | −1705.99 | −0.265072 | ||||||||
\(347\) | 2639.21 | 0.408300 | 0.204150 | − | 0.978940i | \(-0.434557\pi\) | ||||
0.204150 | + | 0.978940i | \(0.434557\pi\) | |||||||
\(348\) | −5884.12 | −0.906386 | ||||||||
\(349\) | −8673.47 | −1.33032 | −0.665158 | − | 0.746702i | \(-0.731636\pi\) | ||||
−0.665158 | + | 0.746702i | \(0.731636\pi\) | |||||||
\(350\) | 4088.38 | 0.624380 | ||||||||
\(351\) | 19053.1 | 2.89738 | ||||||||
\(352\) | 6175.52 | 0.935104 | ||||||||
\(353\) | −799.760 | −0.120586 | −0.0602931 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602931 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(354\) | −6050.20 | −0.908374 | ||||||||
\(355\) | 1767.26 | 0.264215 | ||||||||
\(356\) | 4872.90 | 0.725459 | ||||||||
\(357\) | 13045.7 | 1.93404 | ||||||||
\(358\) | −7116.36 | −1.05059 | ||||||||
\(359\) | −6892.85 | −1.01334 | −0.506672 | − | 0.862139i | \(-0.669125\pi\) | ||||
−0.506672 | + | 0.862139i | \(0.669125\pi\) | |||||||
\(360\) | −26772.8 | −3.91958 | ||||||||
\(361\) | −6764.40 | −0.986207 | ||||||||
\(362\) | −8969.94 | −1.30235 | ||||||||
\(363\) | −4864.02 | −0.703291 | ||||||||
\(364\) | 2542.91 | 0.366167 | ||||||||
\(365\) | 14149.7 | 2.02912 | ||||||||
\(366\) | −1424.47 | −0.203437 | ||||||||
\(367\) | 10785.9 | 1.53412 | 0.767058 | − | 0.641578i | \(-0.221720\pi\) | ||||
0.767058 | + | 0.641578i | \(0.221720\pi\) | |||||||
\(368\) | −1953.17 | −0.276673 | ||||||||
\(369\) | 670.241 | 0.0945565 | ||||||||
\(370\) | −1864.25 | −0.261940 | ||||||||
\(371\) | 4161.79 | 0.582397 | ||||||||
\(372\) | −3983.49 | −0.555200 | ||||||||
\(373\) | 2319.02 | 0.321916 | 0.160958 | − | 0.986961i | \(-0.448542\pi\) | ||||
0.160958 | + | 0.986961i | \(0.448542\pi\) | |||||||
\(374\) | −7311.46 | −1.01087 | ||||||||
\(375\) | 1142.35 | 0.157309 | ||||||||
\(376\) | −233.083 | −0.0319690 | ||||||||
\(377\) | 7574.88 | 1.03482 | ||||||||
\(378\) | −14917.7 | −2.02986 | ||||||||
\(379\) | −9170.77 | −1.24293 | −0.621466 | − | 0.783441i | \(-0.713462\pi\) | ||||
−0.621466 | + | 0.783441i | \(0.713462\pi\) | |||||||
\(380\) | 529.408 | 0.0714686 | ||||||||
\(381\) | 3290.05 | 0.442400 | ||||||||
\(382\) | 7738.50 | 1.03648 | ||||||||
\(383\) | 6403.02 | 0.854253 | 0.427127 | − | 0.904192i | \(-0.359526\pi\) | ||||
0.427127 | + | 0.904192i | \(0.359526\pi\) | |||||||
\(384\) | 994.720 | 0.132192 | ||||||||
\(385\) | 10896.6 | 1.44245 | ||||||||
\(386\) | 6795.50 | 0.896067 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −884.817 | −0.115773 | ||||||||
\(389\) | 7196.53 | 0.937991 | 0.468995 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468995 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(390\) | 14494.3 | 1.88191 | ||||||||
\(391\) | −6611.71 | −0.855162 | ||||||||
\(392\) | 1819.98 | 0.234497 | ||||||||
\(393\) | −12817.6 | −1.64520 | ||||||||
\(394\) | 197.281 | 0.0252255 | ||||||||
\(395\) | −12436.9 | −1.58423 | ||||||||
\(396\) | −10515.1 | −1.33435 | ||||||||
\(397\) | 10186.1 | 1.28773 | 0.643863 | − | 0.765141i | \(-0.277331\pi\) | ||||
0.643863 | + | 0.765141i | \(0.277331\pi\) | |||||||
\(398\) | 205.933 | 0.0259359 | ||||||||
\(399\) | 1573.08 | 0.197375 | ||||||||
\(400\) | −2801.50 | −0.350188 | ||||||||
\(401\) | 4639.83 | 0.577810 | 0.288905 | − | 0.957358i | \(-0.406709\pi\) | ||||
0.288905 | + | 0.957358i | \(0.406709\pi\) | |||||||
\(402\) | −5735.98 | −0.711654 | ||||||||
\(403\) | 5128.12 | 0.633870 | ||||||||
\(404\) | −2179.42 | −0.268391 | ||||||||
\(405\) | 36330.9 | 4.45752 | ||||||||
\(406\) | −5930.79 | −0.724976 | ||||||||
\(407\) | −2408.27 | −0.293301 | ||||||||
\(408\) | −19428.1 | −2.35743 | ||||||||
\(409\) | −9793.28 | −1.18398 | −0.591988 | − | 0.805947i | \(-0.701657\pi\) | ||||
−0.591988 | + | 0.805947i | \(0.701657\pi\) | |||||||
\(410\) | 314.479 | 0.0378806 | ||||||||
\(411\) | 19637.1 | 2.35676 | ||||||||
\(412\) | 5363.48 | 0.641358 | ||||||||
\(413\) | 4730.46 | 0.563610 | ||||||||
\(414\) | 12258.0 | 1.45519 | ||||||||
\(415\) | −19826.5 | −2.34517 | ||||||||
\(416\) | −6422.62 | −0.756959 | ||||||||
\(417\) | 15342.8 | 1.80178 | ||||||||
\(418\) | −881.635 | −0.103163 | ||||||||
\(419\) | 10390.7 | 1.21150 | 0.605748 | − | 0.795657i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795657i | \(0.292874\pi\) | |||||||
\(420\) | 8803.13 | 1.02274 | ||||||||
\(421\) | 1278.81 | 0.148041 | 0.0740206 | − | 0.997257i | \(-0.476417\pi\) | ||||
0.0740206 | + | 0.997257i | \(0.476417\pi\) | |||||||
\(422\) | −226.732 | −0.0261543 | ||||||||
\(423\) | 673.082 | 0.0773673 | ||||||||
\(424\) | −6197.87 | −0.709895 | ||||||||
\(425\) | −9483.42 | −1.08238 | ||||||||
\(426\) | −2377.62 | −0.270414 | ||||||||
\(427\) | 1113.75 | 0.126225 | ||||||||
\(428\) | −3421.04 | −0.386361 | ||||||||
\(429\) | 18724.0 | 2.10723 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8345.12 | −0.932646 | −0.466323 | − | 0.884615i | \(-0.654422\pi\) | ||||
−0.466323 | + | 0.884615i | \(0.654422\pi\) | |||||||
\(432\) | 10222.2 | 1.13846 | ||||||||
\(433\) | 8533.68 | 0.947119 | 0.473560 | − | 0.880762i | \(-0.342969\pi\) | ||||
0.473560 | + | 0.880762i | \(0.342969\pi\) | |||||||
\(434\) | −4015.09 | −0.444079 | ||||||||
\(435\) | 26222.9 | 2.89033 | ||||||||
\(436\) | 2150.21 | 0.236184 | ||||||||
\(437\) | −797.257 | −0.0872722 | ||||||||
\(438\) | −19036.6 | −2.07673 | ||||||||
\(439\) | −14123.5 | −1.53549 | −0.767744 | − | 0.640756i | \(-0.778621\pi\) | ||||
−0.767744 | + | 0.640756i | \(0.778621\pi\) | |||||||
\(440\) | −16227.6 | −1.75823 | ||||||||
\(441\) | −5255.60 | −0.567499 | ||||||||
\(442\) | 7604.01 | 0.818293 | ||||||||
\(443\) | 6033.41 | 0.647079 | 0.323539 | − | 0.946215i | \(-0.395127\pi\) | ||||
0.323539 | + | 0.946215i | \(0.395127\pi\) | |||||||
\(444\) | −1945.58 | −0.207958 | ||||||||
\(445\) | −21716.4 | −2.31338 | ||||||||
\(446\) | 8050.49 | 0.854713 | ||||||||
\(447\) | −19928.6 | −2.10871 | ||||||||
\(448\) | 8151.68 | 0.859667 | ||||||||
\(449\) | −15345.6 | −1.61293 | −0.806464 | − | 0.591284i | \(-0.798621\pi\) | ||||
−0.806464 | + | 0.591284i | \(0.798621\pi\) | |||||||
\(450\) | 17582.1 | 1.84184 | ||||||||
\(451\) | 406.250 | 0.0424159 | ||||||||
\(452\) | −6603.28 | −0.687150 | ||||||||
\(453\) | 2166.20 | 0.224673 | ||||||||
\(454\) | −4546.81 | −0.470027 | ||||||||
\(455\) | −11332.6 | −1.16765 | ||||||||
\(456\) | −2342.69 | −0.240584 | ||||||||
\(457\) | −16460.5 | −1.68488 | −0.842439 | − | 0.538792i | \(-0.818881\pi\) | ||||
−0.842439 | + | 0.538792i | \(0.818881\pi\) | |||||||
\(458\) | −1839.64 | −0.187687 | ||||||||
\(459\) | 34603.3 | 3.51883 | ||||||||
\(460\) | −4461.53 | −0.452217 | ||||||||
\(461\) | −1574.00 | −0.159021 | −0.0795103 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795103 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(462\) | −14660.0 | −1.47629 | ||||||||
\(463\) | −10676.6 | −1.07167 | −0.535834 | − | 0.844323i | \(-0.680003\pi\) | ||||
−0.535834 | + | 0.844323i | \(0.680003\pi\) | |||||||
\(464\) | 4063.99 | 0.406608 | ||||||||
\(465\) | 17752.7 | 1.77045 | ||||||||
\(466\) | −5727.64 | −0.569373 | ||||||||
\(467\) | −6834.42 | −0.677215 | −0.338607 | − | 0.940928i | \(-0.609956\pi\) | ||||
−0.338607 | + | 0.940928i | \(0.609956\pi\) | |||||||
\(468\) | 10935.8 | 1.08015 | ||||||||
\(469\) | 4484.79 | 0.441553 | ||||||||
\(470\) | 315.812 | 0.0309943 | ||||||||
\(471\) | −24099.0 | −2.35758 | ||||||||
\(472\) | −7044.77 | −0.686995 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 16732.3 | 1.62140 | ||||||||
\(475\) | −1143.54 | −0.110461 | ||||||||
\(476\) | 4618.31 | 0.444706 | ||||||||
\(477\) | 17897.8 | 1.71800 | ||||||||
\(478\) | −3941.36 | −0.377142 | ||||||||
\(479\) | −3790.83 | −0.361602 | −0.180801 | − | 0.983520i | \(-0.557869\pi\) | ||||
−0.180801 | + | 0.983520i | \(0.557869\pi\) | |||||||
\(480\) | −22234.0 | −2.11425 | ||||||||
\(481\) | 2504.63 | 0.237425 | ||||||||
\(482\) | 10381.6 | 0.981060 | ||||||||
\(483\) | −13257.0 | −1.24889 | ||||||||
\(484\) | −1721.91 | −0.161712 | ||||||||
\(485\) | 3943.23 | 0.369181 | ||||||||
\(486\) | −24293.6 | −2.26745 | ||||||||
\(487\) | 6937.25 | 0.645497 | 0.322748 | − | 0.946485i | \(-0.395393\pi\) | ||||
0.322748 | + | 0.946485i | \(0.395393\pi\) | |||||||
\(488\) | −1658.63 | −0.153858 | ||||||||
\(489\) | 28965.4 | 2.67865 | ||||||||
\(490\) | −2465.95 | −0.227347 | ||||||||
\(491\) | −3418.47 | −0.314203 | −0.157101 | − | 0.987582i | \(-0.550215\pi\) | ||||
−0.157101 | + | 0.987582i | \(0.550215\pi\) | |||||||
\(492\) | 328.200 | 0.0300739 | ||||||||
\(493\) | 13757.1 | 1.25677 | ||||||||
\(494\) | 916.911 | 0.0835097 | ||||||||
\(495\) | 46861.1 | 4.25505 | ||||||||
\(496\) | 2751.28 | 0.249065 | ||||||||
\(497\) | 1858.99 | 0.167781 | ||||||||
\(498\) | 26674.0 | 2.40018 | ||||||||
\(499\) | 8330.03 | 0.747301 | 0.373651 | − | 0.927570i | \(-0.378106\pi\) | ||||
0.373651 | + | 0.927570i | \(0.378106\pi\) | |||||||
\(500\) | 404.404 | 0.0361710 | ||||||||
\(501\) | 40747.9 | 3.63369 | ||||||||
\(502\) | −12055.7 | −1.07186 | ||||||||
\(503\) | −1435.22 | −0.127223 | −0.0636116 | − | 0.997975i | \(-0.520262\pi\) | ||||
−0.0636116 | + | 0.997975i | \(0.520262\pi\) | |||||||
\(504\) | −28162.4 | −2.48900 | ||||||||
\(505\) | 9712.69 | 0.855860 | ||||||||
\(506\) | 7429.88 | 0.652764 | ||||||||
\(507\) | 2215.54 | 0.194074 | ||||||||
\(508\) | 1164.71 | 0.101724 | ||||||||
\(509\) | −1358.45 | −0.118295 | −0.0591477 | − | 0.998249i | \(-0.518838\pi\) | ||||
−0.0591477 | + | 0.998249i | \(0.518838\pi\) | |||||||
\(510\) | 26323.8 | 2.28556 | ||||||||
\(511\) | 14884.2 | 1.28853 | ||||||||
\(512\) | −8096.75 | −0.698885 | ||||||||
\(513\) | 4172.55 | 0.359109 | ||||||||
\(514\) | 6570.67 | 0.563851 | ||||||||
\(515\) | −23902.6 | −2.04520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 407.972 | 0.0347052 | ||||||||
\(518\) | −1961.02 | −0.166336 | ||||||||
\(519\) | 7934.56 | 0.671076 | ||||||||
\(520\) | 16876.9 | 1.42328 | ||||||||
\(521\) | 852.637 | 0.0716981 | 0.0358490 | − | 0.999357i | \(-0.488586\pi\) | ||||
0.0358490 | + | 0.999357i | \(0.488586\pi\) | |||||||
\(522\) | −25505.4 | −2.13859 | ||||||||
\(523\) | −9749.01 | −0.815094 | −0.407547 | − | 0.913184i | \(-0.633616\pi\) | ||||
−0.407547 | + | 0.913184i | \(0.633616\pi\) | |||||||
\(524\) | −4537.57 | −0.378292 | ||||||||
\(525\) | −19015.0 | −1.58073 | ||||||||
\(526\) | −5922.19 | −0.490912 | ||||||||
\(527\) | 9313.42 | 0.769827 | ||||||||
\(528\) | 10045.6 | 0.827988 | ||||||||
\(529\) | −5448.21 | −0.447785 | ||||||||
\(530\) | 8397.71 | 0.688251 | ||||||||
\(531\) | 20343.4 | 1.66258 | ||||||||
\(532\) | 556.888 | 0.0453837 | ||||||||
\(533\) | −422.505 | −0.0343353 | ||||||||
\(534\) | 29216.6 | 2.36765 | ||||||||
\(535\) | 15246.1 | 1.23205 | ||||||||
\(536\) | −6678.90 | −0.538217 | ||||||||
\(537\) | 33098.1 | 2.65976 | ||||||||
\(538\) | −17390.4 | −1.39359 | ||||||||
\(539\) | −3185.55 | −0.254567 | ||||||||
\(540\) | 23350.0 | 1.86079 | ||||||||
\(541\) | 4019.47 | 0.319428 | 0.159714 | − | 0.987163i | \(-0.448943\pi\) | ||||
0.159714 | + | 0.987163i | \(0.448943\pi\) | |||||||
\(542\) | −8997.78 | −0.713077 | ||||||||
\(543\) | 41719.1 | 3.29712 | ||||||||
\(544\) | −11664.4 | −0.919317 | ||||||||
\(545\) | −9582.52 | −0.753156 | ||||||||
\(546\) | 15246.6 | 1.19505 | ||||||||
\(547\) | 4687.88 | 0.366434 | 0.183217 | − | 0.983073i | \(-0.441349\pi\) | ||||
0.183217 | + | 0.983073i | \(0.441349\pi\) | |||||||
\(548\) | 6951.74 | 0.541904 | ||||||||
\(549\) | 4789.68 | 0.372347 | ||||||||
\(550\) | 10657.0 | 0.826208 | ||||||||
\(551\) | 1658.87 | 0.128258 | ||||||||
\(552\) | 19742.8 | 1.52230 | ||||||||
\(553\) | −13082.5 | −1.00601 | ||||||||
\(554\) | 18102.6 | 1.38828 | ||||||||
\(555\) | 8670.60 | 0.663147 | ||||||||
\(556\) | 5431.52 | 0.414294 | ||||||||
\(557\) | 8917.98 | 0.678397 | 0.339198 | − | 0.940715i | \(-0.389844\pi\) | ||||
0.339198 | + | 0.940715i | \(0.389844\pi\) | |||||||
\(558\) | −17266.9 | −1.30998 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6080.06 | −0.458803 | ||||||||
\(561\) | 34005.5 | 2.55920 | ||||||||
\(562\) | −2732.05 | −0.205061 | ||||||||
\(563\) | 4096.21 | 0.306634 | 0.153317 | − | 0.988177i | \(-0.451004\pi\) | ||||
0.153317 | + | 0.988177i | \(0.451004\pi\) | |||||||
\(564\) | 329.591 | 0.0246069 | ||||||||
\(565\) | 29427.9 | 2.19122 | ||||||||
\(566\) | −19048.1 | −1.41458 | ||||||||
\(567\) | 38216.7 | 2.83060 | ||||||||
\(568\) | −2768.47 | −0.204511 | ||||||||
\(569\) | 2683.32 | 0.197699 | 0.0988495 | − | 0.995102i | \(-0.468484\pi\) | ||||
0.0988495 | + | 0.995102i | \(0.468484\pi\) | |||||||
\(570\) | 3174.19 | 0.233249 | ||||||||
\(571\) | 10667.4 | 0.781815 | 0.390908 | − | 0.920430i | \(-0.372161\pi\) | ||||
0.390908 | + | 0.920430i | \(0.372161\pi\) | |||||||
\(572\) | 6628.48 | 0.484529 | ||||||||
\(573\) | −35991.7 | −2.62404 | ||||||||
\(574\) | 330.803 | 0.0240548 | ||||||||
\(575\) | 9637.02 | 0.698942 | ||||||||
\(576\) | 35056.4 | 2.53591 | ||||||||
\(577\) | −21766.6 | −1.57046 | −0.785230 | − | 0.619205i | \(-0.787455\pi\) | ||||
−0.785230 | + | 0.619205i | \(0.787455\pi\) | |||||||
\(578\) | 3381.91 | 0.243372 | ||||||||
\(579\) | −31605.8 | −2.26855 | ||||||||
\(580\) | 9283.19 | 0.664592 | ||||||||
\(581\) | −20855.6 | −1.48922 | ||||||||
\(582\) | −5305.12 | −0.377843 | ||||||||
\(583\) | 10848.3 | 0.770653 | ||||||||
\(584\) | −22166.0 | −1.57061 | ||||||||
\(585\) | −48736.1 | −3.44443 | ||||||||
\(586\) | 2491.04 | 0.175604 | ||||||||
\(587\) | 24126.0 | 1.69640 | 0.848201 | − | 0.529675i | \(-0.177686\pi\) | ||||
0.848201 | + | 0.529675i | \(0.177686\pi\) | |||||||
\(588\) | −2573.53 | −0.180494 | ||||||||
\(589\) | 1123.04 | 0.0785635 | ||||||||
\(590\) | 9545.20 | 0.666050 | ||||||||
\(591\) | −917.551 | −0.0638629 | ||||||||
\(592\) | 1343.76 | 0.0932906 | ||||||||
\(593\) | 23547.7 | 1.63067 | 0.815337 | − | 0.578987i | \(-0.196552\pi\) | ||||
0.815337 | + | 0.578987i | \(0.196552\pi\) | |||||||
\(594\) | −38885.3 | −2.68600 | ||||||||
\(595\) | −20581.7 | −1.41810 | ||||||||
\(596\) | −7054.94 | −0.484868 | ||||||||
\(597\) | −957.791 | −0.0656613 | ||||||||
\(598\) | −7727.17 | −0.528407 | ||||||||
\(599\) | −10000.3 | −0.682139 | −0.341070 | − | 0.940038i | \(-0.610789\pi\) | ||||
−0.341070 | + | 0.940038i | \(0.610789\pi\) | |||||||
\(600\) | 28317.8 | 1.92678 | ||||||||
\(601\) | −4062.49 | −0.275728 | −0.137864 | − | 0.990451i | \(-0.544024\pi\) | ||||
−0.137864 | + | 0.990451i | \(0.544024\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19286.9 | 1.30252 | ||||||||
\(604\) | 766.857 | 0.0516605 | ||||||||
\(605\) | 7673.80 | 0.515676 | ||||||||
\(606\) | −13067.2 | −0.875939 | ||||||||
\(607\) | −12695.2 | −0.848902 | −0.424451 | − | 0.905451i | \(-0.639533\pi\) | ||||
−0.424451 | + | 0.905451i | \(0.639533\pi\) | |||||||
\(608\) | −1406.53 | −0.0938195 | ||||||||
\(609\) | 27584.1 | 1.83541 | ||||||||
\(610\) | 2247.34 | 0.149167 | ||||||||
\(611\) | −424.296 | −0.0280936 | ||||||||
\(612\) | 19861.1 | 1.31182 | ||||||||
\(613\) | −4025.43 | −0.265230 | −0.132615 | − | 0.991168i | \(-0.542337\pi\) | ||||
−0.132615 | + | 0.991168i | \(0.542337\pi\) | |||||||
\(614\) | −17039.4 | −1.11996 | ||||||||
\(615\) | −1462.64 | −0.0959013 | ||||||||
\(616\) | −17070.0 | −1.11651 | ||||||||
\(617\) | −21979.7 | −1.43415 | −0.717074 | − | 0.696997i | \(-0.754519\pi\) | ||||
−0.717074 | + | 0.696997i | \(0.754519\pi\) | |||||||
\(618\) | 32158.0 | 2.09318 | ||||||||
\(619\) | 3508.41 | 0.227811 | 0.113906 | − | 0.993492i | \(-0.463664\pi\) | ||||
0.113906 | + | 0.993492i | \(0.463664\pi\) | |||||||
\(620\) | 6284.63 | 0.407091 | ||||||||
\(621\) | −35163.7 | −2.27226 | ||||||||
\(622\) | 12525.0 | 0.807405 | ||||||||
\(623\) | −22843.6 | −1.46903 | ||||||||
\(624\) | −10447.5 | −0.670250 | ||||||||
\(625\) | −16498.5 | −1.05591 | ||||||||
\(626\) | −16228.4 | −1.03613 | ||||||||
\(627\) | 4100.47 | 0.261176 | ||||||||
\(628\) | −8531.28 | −0.542094 | ||||||||
\(629\) | 4548.78 | 0.288349 | ||||||||
\(630\) | 38158.2 | 2.41311 | ||||||||
\(631\) | −12163.9 | −0.767412 | −0.383706 | − | 0.923455i | \(-0.625352\pi\) | ||||
−0.383706 | + | 0.923455i | \(0.625352\pi\) | |||||||
\(632\) | 19482.9 | 1.22625 | ||||||||
\(633\) | 1054.53 | 0.0662143 | ||||||||
\(634\) | 18834.0 | 1.17980 | ||||||||
\(635\) | −5190.60 | −0.324382 | ||||||||
\(636\) | 8764.09 | 0.546413 | ||||||||
\(637\) | 3313.02 | 0.206070 | ||||||||
\(638\) | −15459.5 | −0.959321 | ||||||||
\(639\) | 7994.60 | 0.494932 | ||||||||
\(640\) | −1569.34 | −0.0969273 | ||||||||
\(641\) | 19508.5 | 1.20209 | 0.601045 | − | 0.799216i | \(-0.294751\pi\) | ||||
0.601045 | + | 0.799216i | \(0.294751\pi\) | |||||||
\(642\) | −20511.7 | −1.26095 | ||||||||
\(643\) | 8349.25 | 0.512072 | 0.256036 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256036 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(644\) | −4693.11 | −0.287165 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1665.25 | 0.101421 | ||||||||
\(647\) | −24420.9 | −1.48390 | −0.741952 | − | 0.670453i | \(-0.766100\pi\) | ||||
−0.741952 | + | 0.670453i | \(0.766100\pi\) | |||||||
\(648\) | −56913.6 | −3.45027 | ||||||||
\(649\) | 12330.6 | 0.745794 | ||||||||
\(650\) | −11083.4 | −0.668809 | ||||||||
\(651\) | 18674.1 | 1.12427 | ||||||||
\(652\) | 10254.0 | 0.615919 | ||||||||
\(653\) | 17813.5 | 1.06753 | 0.533763 | − | 0.845634i | \(-0.320777\pi\) | ||||
0.533763 | + | 0.845634i | \(0.320777\pi\) | |||||||
\(654\) | 12892.1 | 0.770825 | ||||||||
\(655\) | 20221.9 | 1.20632 | ||||||||
\(656\) | −226.678 | −0.0134913 | ||||||||
\(657\) | 64009.5 | 3.80099 | ||||||||
\(658\) | 332.205 | 0.0196819 | ||||||||
\(659\) | −10172.2 | −0.601294 | −0.300647 | − | 0.953735i | \(-0.597203\pi\) | ||||
−0.300647 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(660\) | 22946.7 | 1.35333 | ||||||||
\(661\) | −10378.7 | −0.610716 | −0.305358 | − | 0.952238i | \(-0.598776\pi\) | ||||
−0.305358 | + | 0.952238i | \(0.598776\pi\) | |||||||
\(662\) | −8486.54 | −0.498246 | ||||||||
\(663\) | −35366.1 | −2.07166 | ||||||||
\(664\) | 31058.9 | 1.81524 | ||||||||
\(665\) | −2481.80 | −0.144722 | ||||||||
\(666\) | −8433.36 | −0.490670 | ||||||||
\(667\) | −13979.9 | −0.811551 | ||||||||
\(668\) | 14425.2 | 0.835519 | ||||||||
\(669\) | −37442.8 | −2.16386 | ||||||||
\(670\) | 9049.47 | 0.521808 | ||||||||
\(671\) | 2903.15 | 0.167026 | ||||||||
\(672\) | −23388.1 | −1.34258 | ||||||||
\(673\) | −20924.5 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(674\) | 6689.31 | 0.382289 | ||||||||
\(675\) | −50436.7 | −2.87601 | ||||||||
\(676\) | 784.324 | 0.0446247 | ||||||||
\(677\) | −9393.92 | −0.533290 | −0.266645 | − | 0.963795i | \(-0.585915\pi\) | ||||
−0.266645 | + | 0.963795i | \(0.585915\pi\) | |||||||
\(678\) | −39591.5 | −2.24263 | ||||||||
\(679\) | 4147.91 | 0.234436 | ||||||||
\(680\) | 30651.0 | 1.72855 | ||||||||
\(681\) | 21147.1 | 1.18996 | ||||||||
\(682\) | −10465.9 | −0.587626 | ||||||||
\(683\) | −4288.63 | −0.240263 | −0.120132 | − | 0.992758i | \(-0.538332\pi\) | ||||
−0.120132 | + | 0.992758i | \(0.538332\pi\) | |||||||
\(684\) | 2394.90 | 0.133876 | ||||||||
\(685\) | −30980.8 | −1.72805 | ||||||||
\(686\) | −14521.4 | −0.808207 | ||||||||
\(687\) | 8556.14 | 0.475163 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11282.4 | −0.623838 | ||||||||
\(690\) | −26750.1 | −1.47588 | ||||||||
\(691\) | −6084.89 | −0.334993 | −0.167496 | − | 0.985873i | \(-0.553568\pi\) | ||||
−0.167496 | + | 0.985873i | \(0.553568\pi\) | |||||||
\(692\) | 2808.92 | 0.154305 | ||||||||
\(693\) | 49293.4 | 2.70202 | ||||||||
\(694\) | 5601.86 | 0.306403 | ||||||||
\(695\) | −24205.9 | −1.32112 | ||||||||
\(696\) | −41079.1 | −2.23721 | ||||||||
\(697\) | −767.332 | −0.0416998 | ||||||||
\(698\) | −18409.9 | −0.998316 | ||||||||
\(699\) | 26639.2 | 1.44147 | ||||||||
\(700\) | −6731.51 | −0.363467 | ||||||||
\(701\) | 19240.3 | 1.03666 | 0.518329 | − | 0.855182i | \(-0.326554\pi\) | ||||
0.518329 | + | 0.855182i | \(0.326554\pi\) | |||||||
\(702\) | 40441.2 | 2.17429 | ||||||||
\(703\) | 548.504 | 0.0294270 | ||||||||
\(704\) | 21248.6 | 1.13755 | ||||||||
\(705\) | −1468.84 | −0.0784677 | ||||||||
\(706\) | −1697.53 | −0.0904922 | ||||||||
\(707\) | 10216.8 | 0.543485 | ||||||||
\(708\) | 9961.64 | 0.528787 | ||||||||
\(709\) | −22023.7 | −1.16660 | −0.583299 | − | 0.812258i | \(-0.698238\pi\) | ||||
−0.583299 | + | 0.812258i | \(0.698238\pi\) | |||||||
\(710\) | 3751.10 | 0.198276 | ||||||||
\(711\) | −56261.4 | −2.96761 | ||||||||
\(712\) | 34019.4 | 1.79063 | ||||||||
\(713\) | −9464.27 | −0.497110 | ||||||||
\(714\) | 27690.1 | 1.45137 | ||||||||
\(715\) | −29540.2 | −1.54509 | ||||||||
\(716\) | 11717.1 | 0.611575 | ||||||||
\(717\) | 18331.2 | 0.954801 | ||||||||
\(718\) | −14630.4 | −0.760449 | ||||||||
\(719\) | −9873.52 | −0.512128 | −0.256064 | − | 0.966660i | \(-0.582426\pi\) | ||||
−0.256064 | + | 0.966660i | \(0.582426\pi\) | |||||||
\(720\) | −26147.4 | −1.35341 | ||||||||
\(721\) | −25143.3 | −1.29873 | ||||||||
\(722\) | −14357.8 | −0.740085 | ||||||||
\(723\) | −48284.9 | −2.48373 | ||||||||
\(724\) | 14769.0 | 0.758129 | ||||||||
\(725\) | −20051.9 | −1.02719 | ||||||||
\(726\) | −10324.1 | −0.527774 | ||||||||
\(727\) | −22548.2 | −1.15030 | −0.575150 | − | 0.818048i | \(-0.695056\pi\) | ||||
−0.575150 | + | 0.818048i | \(0.695056\pi\) | |||||||
\(728\) | 17753.0 | 0.903803 | ||||||||
\(729\) | 50006.4 | 2.54059 | ||||||||
\(730\) | 30033.5 | 1.52272 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2345.38 | 0.118426 | ||||||||
\(733\) | 23342.2 | 1.17621 | 0.588106 | − | 0.808784i | \(-0.299874\pi\) | ||||
0.588106 | + | 0.808784i | \(0.299874\pi\) | |||||||
\(734\) | 22893.7 | 1.15125 | ||||||||
\(735\) | 11469.1 | 0.575570 | ||||||||
\(736\) | 11853.4 | 0.593642 | ||||||||
\(737\) | 11690.3 | 0.584282 | ||||||||
\(738\) | 1422.62 | 0.0709585 | ||||||||
\(739\) | 2588.54 | 0.128851 | 0.0644255 | − | 0.997923i | \(-0.479479\pi\) | ||||
0.0644255 | + | 0.997923i | \(0.479479\pi\) | |||||||
\(740\) | 3069.48 | 0.152482 | ||||||||
\(741\) | −4264.54 | −0.211420 | ||||||||
\(742\) | 8833.60 | 0.437051 | ||||||||
\(743\) | −8452.43 | −0.417348 | −0.208674 | − | 0.977985i | \(-0.566915\pi\) | ||||
−0.208674 | + | 0.977985i | \(0.566915\pi\) | |||||||
\(744\) | −27810.2 | −1.37039 | ||||||||
\(745\) | 31440.7 | 1.54617 | ||||||||
\(746\) | 4922.25 | 0.241577 | ||||||||
\(747\) | −89689.7 | −4.39300 | ||||||||
\(748\) | 12038.3 | 0.588454 | ||||||||
\(749\) | 16037.4 | 0.782370 | ||||||||
\(750\) | 2424.70 | 0.118050 | ||||||||
\(751\) | −3358.11 | −0.163168 | −0.0815841 | − | 0.996666i | \(-0.525998\pi\) | ||||
−0.0815841 | + | 0.996666i | \(0.525998\pi\) | |||||||
\(752\) | −227.639 | −0.0110387 | ||||||||
\(753\) | 56070.8 | 2.71359 | ||||||||
\(754\) | 16078.1 | 0.776563 | ||||||||
\(755\) | −3417.54 | −0.164738 | ||||||||
\(756\) | 24562.0 | 1.18163 | ||||||||
\(757\) | −14867.1 | −0.713810 | −0.356905 | − | 0.934141i | \(-0.616168\pi\) | ||||
−0.356905 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(758\) | −19465.4 | −0.932739 | ||||||||
\(759\) | −34556.3 | −1.65259 | ||||||||
\(760\) | 3695.98 | 0.176404 | ||||||||
\(761\) | 1721.42 | 0.0819991 | 0.0409995 | − | 0.999159i | \(-0.486946\pi\) | ||||
0.0409995 | + | 0.999159i | \(0.486946\pi\) | |||||||
\(762\) | 6983.30 | 0.331992 | ||||||||
\(763\) | −10079.9 | −0.478266 | ||||||||
\(764\) | −12741.4 | −0.603362 | ||||||||
\(765\) | −88512.0 | −4.18321 | ||||||||
\(766\) | 13590.7 | 0.641062 | ||||||||
\(767\) | −12824.0 | −0.603714 | ||||||||
\(768\) | 41407.0 | 1.94550 | ||||||||
\(769\) | 13213.3 | 0.619616 | 0.309808 | − | 0.950799i | \(-0.399735\pi\) | ||||
0.309808 | + | 0.950799i | \(0.399735\pi\) | |||||||
\(770\) | 23128.7 | 1.08247 | ||||||||
\(771\) | −30560.1 | −1.42749 | ||||||||
\(772\) | −11188.8 | −0.521623 | ||||||||
\(773\) | 26452.9 | 1.23085 | 0.615424 | − | 0.788196i | \(-0.288985\pi\) | ||||
0.615424 | + | 0.788196i | \(0.288985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13575.0 | −0.629196 | ||||||||
\(776\) | −6177.21 | −0.285759 | ||||||||
\(777\) | 9120.66 | 0.421109 | ||||||||
\(778\) | 15275.0 | 0.703901 | ||||||||
\(779\) | −92.5268 | −0.00425561 | ||||||||
\(780\) | −23864.8 | −1.09551 | ||||||||
\(781\) | 4845.73 | 0.222015 | ||||||||
\(782\) | −14033.7 | −0.641744 | ||||||||
\(783\) | 73165.8 | 3.33938 | ||||||||
\(784\) | 1777.46 | 0.0809704 | ||||||||
\(785\) | 38020.1 | 1.72866 | ||||||||
\(786\) | −27206.1 | −1.23462 | ||||||||
\(787\) | 22609.2 | 1.02405 | 0.512027 | − | 0.858970i | \(-0.328895\pi\) | ||||
0.512027 | + | 0.858970i | \(0.328895\pi\) | |||||||
\(788\) | −324.822 | −0.0146844 | ||||||||
\(789\) | 27544.0 | 1.24283 | ||||||||
\(790\) | −26398.1 | −1.18886 | ||||||||
\(791\) | 30955.3 | 1.39146 | ||||||||
\(792\) | −73409.5 | −3.29355 | ||||||||
\(793\) | −3019.31 | −0.135207 | ||||||||
\(794\) | 21620.6 | 0.966355 | ||||||||
\(795\) | −39057.7 | −1.74243 | ||||||||
\(796\) | −339.068 | −0.0150979 | ||||||||
\(797\) | 16151.3 | 0.717829 | 0.358915 | − | 0.933370i | \(-0.383147\pi\) | ||||
0.358915 | + | 0.933370i | \(0.383147\pi\) | |||||||
\(798\) | 3338.95 | 0.148117 | ||||||||
\(799\) | −770.584 | −0.0341193 | ||||||||
\(800\) | 17001.7 | 0.751377 | ||||||||
\(801\) | −98239.0 | −4.33346 | ||||||||
\(802\) | 9848.27 | 0.433609 | ||||||||
\(803\) | 38797.8 | 1.70504 | ||||||||
\(804\) | 9444.28 | 0.414271 | ||||||||
\(805\) | 20915.1 | 0.915727 | ||||||||
\(806\) | 10884.7 | 0.475678 | ||||||||
\(807\) | 80882.4 | 3.52812 | ||||||||
\(808\) | −15215.3 | −0.662465 | ||||||||
\(809\) | 8389.19 | 0.364584 | 0.182292 | − | 0.983244i | \(-0.441648\pi\) | ||||
0.182292 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(810\) | 77114.2 | 3.34508 | ||||||||
\(811\) | −687.716 | −0.0297768 | −0.0148884 | − | 0.999889i | \(-0.504739\pi\) | ||||
−0.0148884 | + | 0.999889i | \(0.504739\pi\) | |||||||
\(812\) | 9765.04 | 0.422027 | ||||||||
\(813\) | 41848.6 | 1.80528 | ||||||||
\(814\) | −5111.67 | −0.220103 | ||||||||
\(815\) | −45697.7 | −1.96407 | ||||||||
\(816\) | −18974.3 | −0.814010 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −20786.7 | −0.888498 | ||||||||
\(819\) | −51265.8 | −2.18727 | ||||||||
\(820\) | −517.790 | −0.0220512 | ||||||||
\(821\) | −36524.3 | −1.55263 | −0.776313 | − | 0.630348i | \(-0.782912\pi\) | ||||
−0.776313 | + | 0.630348i | \(0.782912\pi\) | |||||||
\(822\) | 41680.8 | 1.76859 | ||||||||
\(823\) | −2950.87 | −0.124983 | −0.0624915 | − | 0.998045i | \(-0.519905\pi\) | ||||
−0.0624915 | + | 0.998045i | \(0.519905\pi\) | |||||||
\(824\) | 37444.3 | 1.58305 | ||||||||
\(825\) | −49565.4 | −2.09169 | ||||||||
\(826\) | 10040.6 | 0.422953 | ||||||||
\(827\) | −7907.73 | −0.332501 | −0.166251 | − | 0.986084i | \(-0.553166\pi\) | ||||
−0.166251 | + | 0.986084i | \(0.553166\pi\) | |||||||
\(828\) | −20182.8 | −0.847101 | ||||||||
\(829\) | −36919.5 | −1.54677 | −0.773383 | − | 0.633939i | \(-0.781437\pi\) | ||||
−0.773383 | + | 0.633939i | \(0.781437\pi\) | |||||||
\(830\) | −42082.7 | −1.75989 | ||||||||
\(831\) | −84194.9 | −3.51467 | ||||||||
\(832\) | −22098.8 | −0.920838 | ||||||||
\(833\) | 6016.93 | 0.250269 | ||||||||
\(834\) | 32565.9 | 1.35212 | ||||||||
\(835\) | −64286.6 | −2.66435 | ||||||||
\(836\) | 1451.61 | 0.0600538 | ||||||||
\(837\) | 49532.5 | 2.04551 | ||||||||
\(838\) | 22054.7 | 0.909149 | ||||||||
\(839\) | −21841.4 | −0.898747 | −0.449373 | − | 0.893344i | \(-0.648353\pi\) | ||||
−0.449373 | + | 0.893344i | \(0.648353\pi\) | |||||||
\(840\) | 61457.7 | 2.52440 | ||||||||
\(841\) | 4699.28 | 0.192680 | ||||||||
\(842\) | 2714.34 | 0.111095 | ||||||||
\(843\) | 12706.7 | 0.519149 | ||||||||
\(844\) | 373.313 | 0.0152251 | ||||||||
\(845\) | −3495.38 | −0.142302 | ||||||||
\(846\) | 1428.65 | 0.0580591 | ||||||||
\(847\) | 8072.11 | 0.327463 | ||||||||
\(848\) | −6053.10 | −0.245123 | ||||||||
\(849\) | 88592.4 | 3.58125 | ||||||||
\(850\) | −20129.0 | −0.812260 | ||||||||
\(851\) | −4622.46 | −0.186199 | ||||||||
\(852\) | 3914.75 | 0.157414 | ||||||||
\(853\) | −43215.2 | −1.73466 | −0.867328 | − | 0.497737i | \(-0.834165\pi\) | ||||
−0.867328 | + | 0.497737i | \(0.834165\pi\) | |||||||
\(854\) | 2363.99 | 0.0947236 | ||||||||
\(855\) | −10673.0 | −0.426911 | ||||||||
\(856\) | −23883.5 | −0.953646 | ||||||||
\(857\) | 14793.5 | 0.589657 | 0.294828 | − | 0.955550i | \(-0.404738\pi\) | ||||
0.294828 | + | 0.955550i | \(0.404738\pi\) | |||||||
\(858\) | 39742.6 | 1.58134 | ||||||||
\(859\) | 16459.1 | 0.653758 | 0.326879 | − | 0.945066i | \(-0.394003\pi\) | ||||
0.326879 | + | 0.945066i | \(0.394003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1538.56 | −0.0608989 | ||||||||
\(862\) | −17712.9 | −0.699890 | ||||||||
\(863\) | −32877.1 | −1.29681 | −0.648406 | − | 0.761295i | \(-0.724564\pi\) | ||||
−0.648406 | + | 0.761295i | \(0.724564\pi\) | |||||||
\(864\) | −62036.2 | −2.44272 | ||||||||
\(865\) | −12518.1 | −0.492055 | ||||||||
\(866\) | 18113.2 | 0.710752 | ||||||||
\(867\) | −15729.2 | −0.616139 | ||||||||
\(868\) | 6610.84 | 0.258510 | ||||||||
\(869\) | −34101.5 | −1.33120 | ||||||||
\(870\) | 55659.5 | 2.16900 | ||||||||
\(871\) | −12158.0 | −0.472972 | ||||||||
\(872\) | 15011.3 | 0.582968 | ||||||||
\(873\) | 17838.1 | 0.691557 | ||||||||
\(874\) | −1692.22 | −0.0654921 | ||||||||
\(875\) | −1895.80 | −0.0732453 | ||||||||
\(876\) | 31343.8 | 1.20891 | ||||||||
\(877\) | −13873.2 | −0.534168 | −0.267084 | − | 0.963673i | \(-0.586060\pi\) | ||||
−0.267084 | + | 0.963673i | \(0.586060\pi\) | |||||||
\(878\) | −29977.9 | −1.15228 | ||||||||
\(879\) | −11585.8 | −0.444572 | ||||||||
\(880\) | −15848.6 | −0.607108 | ||||||||
\(881\) | 36781.0 | 1.40657 | 0.703283 | − | 0.710910i | \(-0.251717\pi\) | ||||
0.703283 | + | 0.710910i | \(0.251717\pi\) | |||||||
\(882\) | −11155.3 | −0.425871 | ||||||||
\(883\) | 14471.7 | 0.551542 | 0.275771 | − | 0.961223i | \(-0.411067\pi\) | ||||
0.275771 | + | 0.961223i | \(0.411067\pi\) | |||||||
\(884\) | −12520.0 | −0.476349 | ||||||||
\(885\) | −44394.6 | −1.68622 | ||||||||
\(886\) | 12806.2 | 0.485591 | ||||||||
\(887\) | 29063.0 | 1.10016 | 0.550080 | − | 0.835112i | \(-0.314597\pi\) | ||||
0.550080 | + | 0.835112i | \(0.314597\pi\) | |||||||
\(888\) | −13582.8 | −0.513298 | ||||||||
\(889\) | −5460.03 | −0.205988 | ||||||||
\(890\) | −46094.1 | −1.73604 | ||||||||
\(891\) | 99617.4 | 3.74558 | ||||||||
\(892\) | −13255.1 | −0.497550 | ||||||||
\(893\) | −92.9191 | −0.00348199 | ||||||||
\(894\) | −42299.5 | −1.58245 | ||||||||
\(895\) | −52217.8 | −1.95022 | ||||||||
\(896\) | −1650.79 | −0.0615504 | ||||||||
\(897\) | 35939.0 | 1.33776 | ||||||||
\(898\) | −32571.8 | −1.21040 | ||||||||
\(899\) | 19692.5 | 0.730568 | ||||||||
\(900\) | −28948.9 | −1.07218 | ||||||||
\(901\) | −20490.5 | −0.757643 | ||||||||
\(902\) | 862.286 | 0.0318304 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46099.8 | −1.69608 | ||||||||
\(905\) | −65818.8 | −2.41756 | ||||||||
\(906\) | 4597.87 | 0.168603 | ||||||||
\(907\) | −5383.63 | −0.197090 | −0.0985450 | − | 0.995133i | \(-0.531419\pi\) | ||||
−0.0985450 | + | 0.995133i | \(0.531419\pi\) | |||||||
\(908\) | 7486.31 | 0.273614 | ||||||||
\(909\) | 43937.6 | 1.60321 | ||||||||
\(910\) | −24054.1 | −0.876248 | ||||||||
\(911\) | −11716.3 | −0.426100 | −0.213050 | − | 0.977041i | \(-0.568340\pi\) | ||||
−0.213050 | + | 0.977041i | \(0.568340\pi\) | |||||||
\(912\) | −2287.97 | −0.0830725 | ||||||||
\(913\) | −54363.2 | −1.97060 | ||||||||
\(914\) | −34938.2 | −1.26439 | ||||||||
\(915\) | −10452.3 | −0.377643 | ||||||||
\(916\) | 3028.96 | 0.109257 | ||||||||
\(917\) | 21271.6 | 0.766030 | ||||||||
\(918\) | 73447.2 | 2.64065 | ||||||||
\(919\) | 18077.4 | 0.648879 | 0.324439 | − | 0.945906i | \(-0.394824\pi\) | ||||
0.324439 | + | 0.945906i | \(0.394824\pi\) | |||||||
\(920\) | −31147.5 | −1.11620 | ||||||||
\(921\) | 79249.8 | 2.83537 | ||||||||
\(922\) | −3340.90 | −0.119335 | ||||||||
\(923\) | −5039.62 | −0.179719 | ||||||||
\(924\) | 24137.7 | 0.859386 | ||||||||
\(925\) | −6630.16 | −0.235674 | ||||||||
\(926\) | −22661.6 | −0.804217 | ||||||||
\(927\) | −108129. | −3.83110 | ||||||||
\(928\) | −24663.5 | −0.872435 | ||||||||
\(929\) | 2703.22 | 0.0954680 | 0.0477340 | − | 0.998860i | \(-0.484800\pi\) | ||||
0.0477340 | + | 0.998860i | \(0.484800\pi\) | |||||||
\(930\) | 37680.9 | 1.32861 | ||||||||
\(931\) | 725.537 | 0.0255408 | ||||||||
\(932\) | 9430.55 | 0.331446 | ||||||||
\(933\) | −58253.6 | −2.04409 | ||||||||
\(934\) | −14506.4 | −0.508206 | ||||||||
\(935\) | −53649.4 | −1.87649 | ||||||||
\(936\) | 76346.8 | 2.66610 | ||||||||
\(937\) | 5610.28 | 0.195603 | 0.0978015 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978015 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(938\) | 9519.19 | 0.331357 | ||||||||
\(939\) | 75478.3 | 2.62315 | ||||||||
\(940\) | −519.985 | −0.0180426 | ||||||||
\(941\) | −1782.55 | −0.0617528 | −0.0308764 | − | 0.999523i | \(-0.509830\pi\) | ||||
−0.0308764 | + | 0.999523i | \(0.509830\pi\) | |||||||
\(942\) | −51151.3 | −1.76921 | ||||||||
\(943\) | 779.760 | 0.0269273 | ||||||||
\(944\) | −6880.21 | −0.237216 | ||||||||
\(945\) | −109462. | −3.76804 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17721.3 | −0.608094 | −0.304047 | − | 0.952657i | \(-0.598338\pi\) | ||||
−0.304047 | + | 0.952657i | \(0.598338\pi\) | |||||||
\(948\) | −27549.8 | −0.943855 | ||||||||
\(949\) | −40350.2 | −1.38021 | ||||||||
\(950\) | −2427.21 | −0.0828939 | ||||||||
\(951\) | −87596.9 | −2.98688 | ||||||||
\(952\) | 32242.0 | 1.09766 | ||||||||
\(953\) | −12699.3 | −0.431658 | −0.215829 | − | 0.976431i | \(-0.569245\pi\) | ||||
−0.215829 | + | 0.976431i | \(0.569245\pi\) | |||||||
\(954\) | 37989.0 | 1.28924 | ||||||||
\(955\) | 56782.9 | 1.92403 | ||||||||
\(956\) | 6489.45 | 0.219544 | ||||||||
\(957\) | 71901.9 | 2.42869 | ||||||||
\(958\) | −8046.22 | −0.271359 | ||||||||
\(959\) | −32588.9 | −1.09734 | ||||||||
\(960\) | −76502.2 | −2.57198 | ||||||||
\(961\) | −16459.4 | −0.552495 | ||||||||
\(962\) | 5316.21 | 0.178172 | ||||||||
\(963\) | 68969.1 | 2.30789 | ||||||||
\(964\) | −17093.4 | −0.571100 | ||||||||
\(965\) | 49863.4 | 1.66338 | ||||||||
\(966\) | −28138.6 | −0.937211 | ||||||||
\(967\) | 30667.6 | 1.01986 | 0.509929 | − | 0.860216i | \(-0.329671\pi\) | ||||
0.509929 | + | 0.860216i | \(0.329671\pi\) | |||||||
\(968\) | −12021.3 | −0.399151 | ||||||||
\(969\) | −7745.04 | −0.256766 | ||||||||
\(970\) | 8369.71 | 0.277047 | ||||||||
\(971\) | 38789.5 | 1.28199 | 0.640996 | − | 0.767544i | \(-0.278521\pi\) | ||||
0.640996 | + | 0.767544i | \(0.278521\pi\) | |||||||
\(972\) | 39999.3 | 1.31994 | ||||||||
\(973\) | −25462.3 | −0.838935 | ||||||||
\(974\) | 14724.7 | 0.484404 | ||||||||
\(975\) | 51548.6 | 1.69321 | ||||||||
\(976\) | −1619.89 | −0.0531263 | ||||||||
\(977\) | 34788.6 | 1.13919 | 0.569594 | − | 0.821926i | \(-0.307101\pi\) | ||||
0.569594 | + | 0.821926i | \(0.307101\pi\) | |||||||
\(978\) | 61480.4 | 2.01015 | ||||||||
\(979\) | −59545.1 | −1.94389 | ||||||||
\(980\) | 4060.18 | 0.132345 | ||||||||
\(981\) | −43348.7 | −1.41082 | ||||||||
\(982\) | −7255.89 | −0.235789 | ||||||||
\(983\) | −34284.6 | −1.11242 | −0.556210 | − | 0.831042i | \(-0.687745\pi\) | ||||
−0.556210 | + | 0.831042i | \(0.687745\pi\) | |||||||
\(984\) | 2291.28 | 0.0742309 | ||||||||
\(985\) | 1447.59 | 0.0468264 | ||||||||
\(986\) | 29200.1 | 0.943126 | ||||||||
\(987\) | −1545.08 | −0.0498283 | ||||||||
\(988\) | −1509.69 | −0.0486131 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 99465.0 | 3.19314 | ||||||||
\(991\) | −6213.41 | −0.199168 | −0.0995840 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995840 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(992\) | −16697.0 | −0.534404 | ||||||||
\(993\) | 39470.8 | 1.26140 | ||||||||
\(994\) | 3945.80 | 0.125909 | ||||||||
\(995\) | 1511.08 | 0.0481450 | ||||||||
\(996\) | −43918.7 | −1.39721 | ||||||||
\(997\) | −38148.6 | −1.21181 | −0.605907 | − | 0.795535i | \(-0.707190\pi\) | ||||
−0.605907 | + | 0.795535i | \(0.707190\pi\) | |||||||
\(998\) | 17680.9 | 0.560801 | ||||||||
\(999\) | 24192.3 | 0.766175 |
(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 | 1849.4.a.i.1.35 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.16 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.35 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.16 | yes | 50 | 43.42 | odd | 2 |