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 | 1.16 | ||
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 | \(-0.622432\pi\) | ||||
−0.375218 | + | 0.926937i | \(0.622432\pi\) | |||||||
\(3\) | 9.87196 | 1.89986 | 0.949930 | − | 0.312463i | \(-0.101154\pi\) | ||||
0.949930 | + | 0.312463i | \(0.101154\pi\) | |||||||
\(4\) | −3.49478 | −0.436847 | ||||||||
\(5\) | −15.5747 | −1.39304 | −0.696520 | − | 0.717537i | \(-0.745269\pi\) | ||||
−0.696520 | + | 0.717537i | \(0.745269\pi\) | |||||||
\(6\) | −20.9537 | −1.42572 | ||||||||
\(7\) | −16.3831 | −0.884603 | −0.442302 | − | 0.896866i | \(-0.645838\pi\) | ||||
−0.442302 | + | 0.896866i | \(0.645838\pi\) | |||||||
\(8\) | 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 | \(-0.481298\pi\) | ||||
0.0587208 | + | 0.998274i | \(0.481298\pi\) | |||||||
\(20\) | 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 | \(-0.316131\pi\) | ||||
0.546049 | + | 0.837753i | \(0.316131\pi\) | |||||||
\(30\) | 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 | \(-0.460016\pi\) | ||||
0.125284 | + | 0.992121i | \(0.460016\pi\) | |||||||
\(38\) | −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 | \(-0.522729\pi\) | ||||
−0.0713454 | + | 0.997452i | \(0.522729\pi\) | |||||||
\(62\) | 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 | \(-0.530232\pi\) | ||||
−0.0948339 | + | 0.995493i | \(0.530232\pi\) | |||||||
\(72\) | 1718.99 | 2.81369 | ||||||||
\(73\) | −908.508 | −1.45661 | −0.728307 | − | 0.685251i | \(-0.759693\pi\) | ||||
−0.728307 | + | 0.685251i | \(0.759693\pi\) | |||||||
\(74\) | −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 | \(-0.188149\pi\) | ||||
0.830335 | + | 0.557265i | \(0.188149\pi\) | |||||||
\(90\) | 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 | \(-0.788103\pi\) | ||||
−0.786488 | + | 0.617605i | \(0.788103\pi\) | |||||||
\(114\) | −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 | \(-0.642538\pi\) | ||||
−0.432979 | + | 0.901404i | \(0.642538\pi\) | |||||||
\(132\) | −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 | \(-0.287033\pi\) | ||||
0.620245 | + | 0.784408i | \(0.287033\pi\) | |||||||
\(138\) | −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 | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(150\) | −2463.54 | −1.34098 | ||||||||
\(151\) | 219.429 | 0.118258 | 0.0591289 | − | 0.998250i | \(-0.481168\pi\) | ||||
0.0591289 | + | 0.998250i | \(0.481168\pi\) | |||||||
\(152\) | 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 | \(-0.713055\pi\) | ||||
−0.620462 | + | 0.784236i | \(0.713055\pi\) | |||||||
\(158\) | 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 | \(-0.250965\pi\) | ||||
0.704959 | + | 0.709248i | \(0.250965\pi\) | |||||||
\(164\) | −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 | \(-0.253189\pi\) | ||||
0.699988 | + | 0.714155i | \(0.253189\pi\) | |||||||
\(180\) | 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 | \(-0.742648\pi\) | ||||
−0.690588 | + | 0.723249i | \(0.742648\pi\) | |||||||
\(192\) | 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 | \(-0.505501\pi\) | ||||
−0.0172806 | + | 0.999851i | \(0.505501\pi\) | |||||||
\(200\) | 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 | \(-0.494453\pi\) | ||||
0.0174261 | + | 0.999848i | \(0.494453\pi\) | |||||||
\(212\) | −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 | \(-0.692855\pi\) | ||||
−0.569478 | + | 0.822006i | \(0.692855\pi\) | |||||||
\(224\) | 2369.14 | 0.706675 | ||||||||
\(225\) | 8283.48 | 2.45436 | ||||||||
\(226\) | 4010.50 | 1.18042 | ||||||||
\(227\) | 2142.14 | 0.626339 | 0.313170 | − | 0.949697i | \(-0.398609\pi\) | ||||
0.313170 | + | 0.949697i | \(0.398609\pi\) | |||||||
\(228\) | −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 | \(-0.376144\pi\) | ||||
0.379362 | + | 0.925248i | \(0.376144\pi\) | |||||||
\(234\) | 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 | \(-0.726768\pi\) | ||||
−0.653661 | + | 0.756788i | \(0.726768\pi\) | |||||||
\(242\) | −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 | \(-0.622592\pi\) | ||||
−0.375683 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(258\) | 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 | \(-0.393934\pi\) | ||||
0.327085 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(264\) | 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 | \(-0.875919\pi\) | ||||
−0.924981 | + | 0.380014i | \(0.875919\pi\) | |||||||
\(278\) | 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 | \(-0.257455\pi\) | ||||
0.690354 | + | 0.723471i | \(0.257455\pi\) | |||||||
\(314\) | 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 | \(-0.392286\pi\) | ||||
0.331971 | + | 0.943289i | \(0.392286\pi\) | |||||||
\(332\) | 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 | \(-0.565443\pi\) | ||||
−0.204150 | + | 0.978940i | \(0.565443\pi\) | |||||||
\(348\) | −5884.12 | −0.906386 | ||||||||
\(349\) | 8673.47 | 1.33032 | 0.665158 | − | 0.746702i | \(-0.268364\pi\) | ||||
0.665158 | + | 0.746702i | \(0.268364\pi\) | |||||||
\(350\) | 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 | \(-0.551458\pi\) | ||||
−0.160958 | + | 0.986961i | \(0.551458\pi\) | |||||||
\(374\) | 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 | \(-0.640474\pi\) | ||||
−0.427127 | + | 0.904192i | \(0.640474\pi\) | |||||||
\(384\) | 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 | \(-0.655384\pi\) | ||||
−0.468995 | + | 0.883201i | \(0.655384\pi\) | |||||||
\(390\) | −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 | \(-0.298343\pi\) | ||||
0.591988 | + | 0.805947i | \(0.298343\pi\) | |||||||
\(410\) | 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 | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795657i | \(0.707126\pi\) | |||||||
\(420\) | −8803.13 | −1.02274 | ||||||||
\(421\) | −1278.81 | −0.148041 | −0.0740206 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740206 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(422\) | −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 | \(-0.657031\pi\) | ||||
−0.473560 | + | 0.880762i | \(0.657031\pi\) | |||||||
\(434\) | −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 | \(-0.201379\pi\) | ||||
0.806464 | + | 0.591284i | \(0.201379\pi\) | |||||||
\(450\) | −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 | \(-0.181119\pi\) | ||||
0.842439 | + | 0.538792i | \(0.181119\pi\) | |||||||
\(458\) | 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 | \(-0.319997\pi\) | ||||
0.535834 | + | 0.844323i | \(0.319997\pi\) | |||||||
\(464\) | −4063.99 | −0.406608 | ||||||||
\(465\) | 17752.7 | 1.77045 | ||||||||
\(466\) | −5727.64 | −0.569373 | ||||||||
\(467\) | 6834.42 | 0.677215 | 0.338607 | − | 0.940928i | \(-0.390044\pi\) | ||||
0.338607 | + | 0.940928i | \(0.390044\pi\) | |||||||
\(468\) | 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 | \(-0.449785\pi\) | ||||
0.157101 | + | 0.987582i | \(0.449785\pi\) | |||||||
\(492\) | −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 | \(-0.621894\pi\) | ||||
−0.373651 | + | 0.927570i | \(0.621894\pi\) | |||||||
\(500\) | −404.404 | −0.0361710 | ||||||||
\(501\) | −40747.9 | −3.63369 | ||||||||
\(502\) | 12055.7 | 1.07186 | ||||||||
\(503\) | 1435.22 | 0.127223 | 0.0636116 | − | 0.997975i | \(-0.479738\pi\) | ||||
0.0636116 | + | 0.997975i | \(0.479738\pi\) | |||||||
\(504\) | −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 | \(-0.511414\pi\) | ||||
−0.0358490 | + | 0.999357i | \(0.511414\pi\) | |||||||
\(522\) | −25505.4 | −2.13859 | ||||||||
\(523\) | 9749.01 | 0.815094 | 0.407547 | − | 0.913184i | \(-0.366384\pi\) | ||||
0.407547 | + | 0.913184i | \(0.366384\pi\) | |||||||
\(524\) | 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 | \(-0.627839\pi\) | ||||
−0.390908 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(572\) | 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 | \(-0.212545\pi\) | ||||
0.785230 | + | 0.619205i | \(0.212545\pi\) | |||||||
\(578\) | −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 | \(-0.822314\pi\) | ||||
−0.848201 | + | 0.529675i | \(0.822314\pi\) | |||||||
\(588\) | 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 | \(-0.803448\pi\) | ||||
−0.815337 | + | 0.578987i | \(0.803448\pi\) | |||||||
\(594\) | −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 | \(-0.455976\pi\) | ||||
0.137864 | + | 0.990451i | \(0.455976\pi\) | |||||||
\(602\) | 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 | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(608\) | −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 | \(-0.374648\pi\) | ||||
0.383706 | + | 0.923455i | \(0.374648\pi\) | |||||||
\(632\) | −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 | \(-0.705249\pi\) | ||||
−0.601045 | + | 0.799216i | \(0.705249\pi\) | |||||||
\(642\) | −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 | \(-0.233900\pi\) | ||||
0.741952 | + | 0.670453i | \(0.233900\pi\) | |||||||
\(648\) | 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 | \(-0.679223\pi\) | ||||
−0.533763 | + | 0.845634i | \(0.679223\pi\) | |||||||
\(654\) | 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 | \(-0.295468\pi\) | ||||
0.599243 | + | 0.800567i | \(0.295468\pi\) | |||||||
\(674\) | −6689.31 | −0.382289 | ||||||||
\(675\) | 50436.7 | 2.87601 | ||||||||
\(676\) | 784.324 | 0.0446247 | ||||||||
\(677\) | 9393.92 | 0.533290 | 0.266645 | − | 0.963795i | \(-0.414085\pi\) | ||||
0.266645 | + | 0.963795i | \(0.414085\pi\) | |||||||
\(678\) | 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 | \(-0.446432\pi\) | ||||
0.167496 | + | 0.985873i | \(0.446432\pi\) | |||||||
\(692\) | 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 | \(-0.304944\pi\) | ||||
0.575150 | + | 0.818048i | \(0.304944\pi\) | |||||||
\(728\) | 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 | \(-0.700126\pi\) | ||||
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(734\) | −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 | \(-0.520521\pi\) | ||||
−0.0644255 | + | 0.997923i | \(0.520521\pi\) | |||||||
\(740\) | 3069.48 | 0.152482 | ||||||||
\(741\) | −4264.54 | −0.211420 | ||||||||
\(742\) | 8833.60 | 0.437051 | ||||||||
\(743\) | 8452.43 | 0.417348 | 0.208674 | − | 0.977985i | \(-0.433085\pi\) | ||||
0.208674 | + | 0.977985i | \(0.433085\pi\) | |||||||
\(744\) | −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 | \(-0.474002\pi\) | ||||
0.0815841 | + | 0.996666i | \(0.474002\pi\) | |||||||
\(752\) | −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 | \(-0.383832\pi\) | ||||
0.356905 | + | 0.934141i | \(0.383832\pi\) | |||||||
\(758\) | 19465.4 | 0.932739 | ||||||||
\(759\) | 34556.3 | 1.65259 | ||||||||
\(760\) | −3695.98 | −0.176404 | ||||||||
\(761\) | −1721.42 | −0.0819991 | −0.0409995 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409995 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(762\) | 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 | \(-0.711015\pi\) | ||||
−0.615424 | + | 0.788196i | \(0.711015\pi\) | |||||||
\(774\) | 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 | \(-0.495261\pi\) | ||||
0.0148884 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(812\) | 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 | \(-0.218563\pi\) | ||||
0.773383 | + | 0.633939i | \(0.218563\pi\) | |||||||
\(830\) | −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 | \(-0.351647\pi\) | ||||
0.449373 | + | 0.893344i | \(0.351647\pi\) | |||||||
\(840\) | 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 | \(-0.605997\pi\) | ||||
−0.326879 | + | 0.945066i | \(0.605997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1538.56 | −0.0608989 | ||||||||
\(862\) | 17712.9 | 0.699890 | ||||||||
\(863\) | 32877.1 | 1.29681 | 0.648406 | − | 0.761295i | \(-0.275436\pi\) | ||||
0.648406 | + | 0.761295i | \(0.275436\pi\) | |||||||
\(864\) | −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 | \(-0.685403\pi\) | ||||
−0.550080 | + | 0.835112i | \(0.685403\pi\) | |||||||
\(888\) | 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 | \(-0.431660\pi\) | ||||
0.213050 | + | 0.977041i | \(0.431660\pi\) | |||||||
\(912\) | −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 | \(-0.515200\pi\) | ||||
−0.0477340 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(930\) | −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 | \(-0.531181\pi\) | ||||
−0.0978015 | + | 0.995206i | \(0.531181\pi\) | |||||||
\(938\) | 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 | \(-0.430755\pi\) | ||||
0.215829 | + | 0.976431i | \(0.430755\pi\) | |||||||
\(954\) | −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 | \(-0.312255\pi\) | ||||
0.556210 | + | 0.831042i | \(0.312255\pi\) | |||||||
\(984\) | 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 | \(-0.468249\pi\) | ||||
0.0995840 | + | 0.995029i | \(0.468249\pi\) | |||||||
\(992\) | 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 | \(-0.292810\pi\) | ||||
0.605907 | + | 0.795535i | \(0.292810\pi\) | |||||||
\(998\) | 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.j.1.16 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.35 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.35 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.16 | yes | 50 | 1.1 | even | 1 | trivial |