Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [161,4,Mod(1,161)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(161, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("161.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 161 = 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 161.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: | \(9.49930751092\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 60x^{7} - 22x^{6} + 1179x^{5} + 694x^{4} - 7936x^{3} - 4352x^{2} + 11008x + 3072 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.264899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 161.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.264899 | −0.0936559 | −0.0468280 | − | 0.998903i | \(-0.514911\pi\) | ||||
−0.0468280 | + | 0.998903i | \(0.514911\pi\) | |||||||
\(3\) | −6.92505 | −1.33273 | −0.666364 | − | 0.745627i | \(-0.732150\pi\) | ||||
−0.666364 | + | 0.745627i | \(0.732150\pi\) | |||||||
\(4\) | −7.92983 | −0.991229 | ||||||||
\(5\) | −11.7130 | −1.04764 | −0.523821 | − | 0.851828i | \(-0.675494\pi\) | ||||
−0.523821 | + | 0.851828i | \(0.675494\pi\) | |||||||
\(6\) | 1.83444 | 0.124818 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 4.21980 | 0.186490 | ||||||||
\(9\) | 20.9564 | 0.776162 | ||||||||
\(10\) | 3.10276 | 0.0981179 | ||||||||
\(11\) | −55.2621 | −1.51474 | −0.757370 | − | 0.652986i | \(-0.773516\pi\) | ||||
−0.757370 | + | 0.652986i | \(0.773516\pi\) | |||||||
\(12\) | 54.9145 | 1.32104 | ||||||||
\(13\) | −76.7819 | −1.63811 | −0.819057 | − | 0.573712i | \(-0.805503\pi\) | ||||
−0.819057 | + | 0.573712i | \(0.805503\pi\) | |||||||
\(14\) | 1.85429 | 0.0353986 | ||||||||
\(15\) | 81.1131 | 1.39622 | ||||||||
\(16\) | 62.3208 | 0.973763 | ||||||||
\(17\) | 112.294 | 1.60208 | 0.801041 | − | 0.598609i | \(-0.204280\pi\) | ||||
0.801041 | + | 0.598609i | \(0.204280\pi\) | |||||||
\(18\) | −5.55133 | −0.0726922 | ||||||||
\(19\) | 98.4128 | 1.18829 | 0.594143 | − | 0.804359i | \(-0.297491\pi\) | ||||
0.594143 | + | 0.804359i | \(0.297491\pi\) | |||||||
\(20\) | 92.8820 | 1.03845 | ||||||||
\(21\) | 48.4754 | 0.503724 | ||||||||
\(22\) | 14.6389 | 0.141864 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −29.2223 | −0.248541 | ||||||||
\(25\) | 12.1943 | 0.0975541 | ||||||||
\(26\) | 20.3395 | 0.153419 | ||||||||
\(27\) | 41.8524 | 0.298314 | ||||||||
\(28\) | 55.5088 | 0.374649 | ||||||||
\(29\) | −195.047 | −1.24894 | −0.624470 | − | 0.781049i | \(-0.714685\pi\) | ||||
−0.624470 | + | 0.781049i | \(0.714685\pi\) | |||||||
\(30\) | −21.4868 | −0.130764 | ||||||||
\(31\) | −99.2668 | −0.575124 | −0.287562 | − | 0.957762i | \(-0.592845\pi\) | ||||
−0.287562 | + | 0.957762i | \(0.592845\pi\) | |||||||
\(32\) | −50.2671 | −0.277689 | ||||||||
\(33\) | 382.693 | 2.01874 | ||||||||
\(34\) | −29.7467 | −0.150045 | ||||||||
\(35\) | 81.9910 | 0.395972 | ||||||||
\(36\) | −166.181 | −0.769354 | ||||||||
\(37\) | −14.5629 | −0.0647060 | −0.0323530 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323530 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(38\) | −26.0694 | −0.111290 | ||||||||
\(39\) | 531.719 | 2.18316 | ||||||||
\(40\) | −49.4264 | −0.195375 | ||||||||
\(41\) | −329.303 | −1.25435 | −0.627176 | − | 0.778878i | \(-0.715789\pi\) | ||||
−0.627176 | + | 0.778878i | \(0.715789\pi\) | |||||||
\(42\) | −12.8411 | −0.0471767 | ||||||||
\(43\) | −275.032 | −0.975395 | −0.487697 | − | 0.873013i | \(-0.662163\pi\) | ||||
−0.487697 | + | 0.873013i | \(0.662163\pi\) | |||||||
\(44\) | 438.219 | 1.50145 | ||||||||
\(45\) | −245.462 | −0.813140 | ||||||||
\(46\) | 6.09268 | 0.0195286 | ||||||||
\(47\) | −4.09163 | −0.0126984 | −0.00634921 | − | 0.999980i | \(-0.502021\pi\) | ||||
−0.00634921 | + | 0.999980i | \(0.502021\pi\) | |||||||
\(48\) | −431.575 | −1.29776 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −3.23025 | −0.00913652 | ||||||||
\(51\) | −777.645 | −2.13514 | ||||||||
\(52\) | 608.868 | 1.62375 | ||||||||
\(53\) | −254.594 | −0.659832 | −0.329916 | − | 0.944010i | \(-0.607020\pi\) | ||||
−0.329916 | + | 0.944010i | \(0.607020\pi\) | |||||||
\(54\) | −11.0866 | −0.0279389 | ||||||||
\(55\) | 647.285 | 1.58691 | ||||||||
\(56\) | −29.5386 | −0.0704867 | ||||||||
\(57\) | −681.514 | −1.58366 | ||||||||
\(58\) | 51.6676 | 0.116971 | ||||||||
\(59\) | 207.145 | 0.457083 | 0.228542 | − | 0.973534i | \(-0.426604\pi\) | ||||
0.228542 | + | 0.973534i | \(0.426604\pi\) | |||||||
\(60\) | −643.213 | −1.38397 | ||||||||
\(61\) | 721.632 | 1.51468 | 0.757341 | − | 0.653020i | \(-0.226498\pi\) | ||||
0.757341 | + | 0.653020i | \(0.226498\pi\) | |||||||
\(62\) | 26.2957 | 0.0538638 | ||||||||
\(63\) | −146.695 | −0.293362 | ||||||||
\(64\) | −485.251 | −0.947755 | ||||||||
\(65\) | 899.347 | 1.71616 | ||||||||
\(66\) | −101.375 | −0.189067 | ||||||||
\(67\) | −514.780 | −0.938662 | −0.469331 | − | 0.883022i | \(-0.655505\pi\) | ||||
−0.469331 | + | 0.883022i | \(0.655505\pi\) | |||||||
\(68\) | −890.476 | −1.58803 | ||||||||
\(69\) | 159.276 | 0.277893 | ||||||||
\(70\) | −21.7193 | −0.0370851 | ||||||||
\(71\) | 1059.23 | 1.77053 | 0.885266 | − | 0.465085i | \(-0.153976\pi\) | ||||
0.885266 | + | 0.465085i | \(0.153976\pi\) | |||||||
\(72\) | 88.4317 | 0.144747 | ||||||||
\(73\) | −376.129 | −0.603049 | −0.301525 | − | 0.953458i | \(-0.597496\pi\) | ||||
−0.301525 | + | 0.953458i | \(0.597496\pi\) | |||||||
\(74\) | 3.85769 | 0.00606010 | ||||||||
\(75\) | −84.4459 | −0.130013 | ||||||||
\(76\) | −780.396 | −1.17786 | ||||||||
\(77\) | 386.835 | 0.572518 | ||||||||
\(78\) | −140.852 | −0.204466 | ||||||||
\(79\) | 849.401 | 1.20968 | 0.604842 | − | 0.796345i | \(-0.293236\pi\) | ||||
0.604842 | + | 0.796345i | \(0.293236\pi\) | |||||||
\(80\) | −729.963 | −1.02015 | ||||||||
\(81\) | −855.652 | −1.17373 | ||||||||
\(82\) | 87.2319 | 0.117477 | ||||||||
\(83\) | 204.086 | 0.269896 | 0.134948 | − | 0.990853i | \(-0.456913\pi\) | ||||
0.134948 | + | 0.990853i | \(0.456913\pi\) | |||||||
\(84\) | −384.401 | −0.499305 | ||||||||
\(85\) | −1315.30 | −1.67841 | ||||||||
\(86\) | 72.8557 | 0.0913515 | ||||||||
\(87\) | 1350.71 | 1.66450 | ||||||||
\(88\) | −233.195 | −0.282485 | ||||||||
\(89\) | −631.481 | −0.752099 | −0.376050 | − | 0.926599i | \(-0.622718\pi\) | ||||
−0.376050 | + | 0.926599i | \(0.622718\pi\) | |||||||
\(90\) | 65.0227 | 0.0761554 | ||||||||
\(91\) | 537.474 | 0.619149 | ||||||||
\(92\) | 182.386 | 0.206685 | ||||||||
\(93\) | 687.428 | 0.766483 | ||||||||
\(94\) | 1.08387 | 0.00118928 | ||||||||
\(95\) | −1152.71 | −1.24490 | ||||||||
\(96\) | 348.102 | 0.370084 | ||||||||
\(97\) | 988.987 | 1.03522 | 0.517610 | − | 0.855616i | \(-0.326822\pi\) | ||||
0.517610 | + | 0.855616i | \(0.326822\pi\) | |||||||
\(98\) | −12.9801 | −0.0133794 | ||||||||
\(99\) | −1158.09 | −1.17568 | ||||||||
\(100\) | −96.6984 | −0.0966984 | ||||||||
\(101\) | −179.498 | −0.176839 | −0.0884196 | − | 0.996083i | \(-0.528182\pi\) | ||||
−0.0884196 | + | 0.996083i | \(0.528182\pi\) | |||||||
\(102\) | 205.997 | 0.199968 | ||||||||
\(103\) | 1643.80 | 1.57251 | 0.786255 | − | 0.617903i | \(-0.212017\pi\) | ||||
0.786255 | + | 0.617903i | \(0.212017\pi\) | |||||||
\(104\) | −324.004 | −0.305492 | ||||||||
\(105\) | −567.792 | −0.527722 | ||||||||
\(106\) | 67.4416 | 0.0617972 | ||||||||
\(107\) | −992.701 | −0.896897 | −0.448449 | − | 0.893809i | \(-0.648023\pi\) | ||||
−0.448449 | + | 0.893809i | \(0.648023\pi\) | |||||||
\(108\) | −331.882 | −0.295698 | ||||||||
\(109\) | 21.3103 | 0.0187262 | 0.00936310 | − | 0.999956i | \(-0.497020\pi\) | ||||
0.00936310 | + | 0.999956i | \(0.497020\pi\) | |||||||
\(110\) | −171.465 | −0.148623 | ||||||||
\(111\) | 100.849 | 0.0862354 | ||||||||
\(112\) | −436.246 | −0.368048 | ||||||||
\(113\) | 613.931 | 0.511095 | 0.255548 | − | 0.966796i | \(-0.417744\pi\) | ||||
0.255548 | + | 0.966796i | \(0.417744\pi\) | |||||||
\(114\) | 180.532 | 0.148319 | ||||||||
\(115\) | 269.399 | 0.218448 | ||||||||
\(116\) | 1546.69 | 1.23798 | ||||||||
\(117\) | −1609.07 | −1.27144 | ||||||||
\(118\) | −54.8724 | −0.0428086 | ||||||||
\(119\) | −786.061 | −0.605530 | ||||||||
\(120\) | 342.281 | 0.260382 | ||||||||
\(121\) | 1722.90 | 1.29444 | ||||||||
\(122\) | −191.160 | −0.141859 | ||||||||
\(123\) | 2280.44 | 1.67171 | ||||||||
\(124\) | 787.169 | 0.570079 | ||||||||
\(125\) | 1321.29 | 0.945440 | ||||||||
\(126\) | 38.8593 | 0.0274751 | ||||||||
\(127\) | −960.519 | −0.671120 | −0.335560 | − | 0.942019i | \(-0.608926\pi\) | ||||
−0.335560 | + | 0.942019i | \(0.608926\pi\) | |||||||
\(128\) | 530.679 | 0.366452 | ||||||||
\(129\) | 1904.61 | 1.29994 | ||||||||
\(130\) | −238.236 | −0.160728 | ||||||||
\(131\) | −1991.37 | −1.32814 | −0.664071 | − | 0.747670i | \(-0.731173\pi\) | ||||
−0.664071 | + | 0.747670i | \(0.731173\pi\) | |||||||
\(132\) | −3034.69 | −2.00103 | ||||||||
\(133\) | −688.889 | −0.449130 | ||||||||
\(134\) | 136.365 | 0.0879113 | ||||||||
\(135\) | −490.216 | −0.312527 | ||||||||
\(136\) | 473.860 | 0.298773 | ||||||||
\(137\) | −2774.94 | −1.73050 | −0.865251 | − | 0.501338i | \(-0.832841\pi\) | ||||
−0.865251 | + | 0.501338i | \(0.832841\pi\) | |||||||
\(138\) | −42.1921 | −0.0260263 | ||||||||
\(139\) | −60.9410 | −0.0371867 | −0.0185933 | − | 0.999827i | \(-0.505919\pi\) | ||||
−0.0185933 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(140\) | −650.174 | −0.392498 | ||||||||
\(141\) | 28.3348 | 0.0169235 | ||||||||
\(142\) | −280.590 | −0.165821 | ||||||||
\(143\) | 4243.13 | 2.48132 | ||||||||
\(144\) | 1306.02 | 0.755798 | ||||||||
\(145\) | 2284.58 | 1.30844 | ||||||||
\(146\) | 99.6362 | 0.0564791 | ||||||||
\(147\) | −339.328 | −0.190390 | ||||||||
\(148\) | 115.481 | 0.0641384 | ||||||||
\(149\) | −625.084 | −0.343684 | −0.171842 | − | 0.985125i | \(-0.554972\pi\) | ||||
−0.171842 | + | 0.985125i | \(0.554972\pi\) | |||||||
\(150\) | 22.3696 | 0.0121765 | ||||||||
\(151\) | 2266.11 | 1.22128 | 0.610639 | − | 0.791909i | \(-0.290913\pi\) | ||||
0.610639 | + | 0.791909i | \(0.290913\pi\) | |||||||
\(152\) | 415.282 | 0.221604 | ||||||||
\(153\) | 2353.29 | 1.24348 | ||||||||
\(154\) | −102.472 | −0.0536197 | ||||||||
\(155\) | 1162.71 | 0.602524 | ||||||||
\(156\) | −4216.44 | −2.16401 | ||||||||
\(157\) | 2533.35 | 1.28779 | 0.643895 | − | 0.765114i | \(-0.277317\pi\) | ||||
0.643895 | + | 0.765114i | \(0.277317\pi\) | |||||||
\(158\) | −225.005 | −0.113294 | ||||||||
\(159\) | 1763.07 | 0.879377 | ||||||||
\(160\) | 588.778 | 0.290919 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 226.661 | 0.109927 | ||||||||
\(163\) | 2479.38 | 1.19141 | 0.595705 | − | 0.803203i | \(-0.296873\pi\) | ||||
0.595705 | + | 0.803203i | \(0.296873\pi\) | |||||||
\(164\) | 2611.31 | 1.24335 | ||||||||
\(165\) | −4482.48 | −2.11491 | ||||||||
\(166\) | −54.0622 | −0.0252773 | ||||||||
\(167\) | 440.669 | 0.204192 | 0.102096 | − | 0.994775i | \(-0.467445\pi\) | ||||
0.102096 | + | 0.994775i | \(0.467445\pi\) | |||||||
\(168\) | 204.556 | 0.0939396 | ||||||||
\(169\) | 3698.47 | 1.68342 | ||||||||
\(170\) | 348.423 | 0.157193 | ||||||||
\(171\) | 2062.38 | 0.922303 | ||||||||
\(172\) | 2180.96 | 0.966839 | ||||||||
\(173\) | −3111.52 | −1.36742 | −0.683712 | − | 0.729752i | \(-0.739636\pi\) | ||||
−0.683712 | + | 0.729752i | \(0.739636\pi\) | |||||||
\(174\) | −357.801 | −0.155890 | ||||||||
\(175\) | −85.3598 | −0.0368720 | ||||||||
\(176\) | −3443.98 | −1.47500 | ||||||||
\(177\) | −1434.49 | −0.609168 | ||||||||
\(178\) | 167.279 | 0.0704386 | ||||||||
\(179\) | 1846.07 | 0.770848 | 0.385424 | − | 0.922740i | \(-0.374055\pi\) | ||||
0.385424 | + | 0.922740i | \(0.374055\pi\) | |||||||
\(180\) | 1946.47 | 0.806008 | ||||||||
\(181\) | −2020.32 | −0.829665 | −0.414833 | − | 0.909898i | \(-0.636160\pi\) | ||||
−0.414833 | + | 0.909898i | \(0.636160\pi\) | |||||||
\(182\) | −142.376 | −0.0579870 | ||||||||
\(183\) | −4997.34 | −2.01866 | ||||||||
\(184\) | −97.0553 | −0.0388859 | ||||||||
\(185\) | 170.575 | 0.0677887 | ||||||||
\(186\) | −182.099 | −0.0717857 | ||||||||
\(187\) | −6205.62 | −2.42674 | ||||||||
\(188\) | 32.4459 | 0.0125870 | ||||||||
\(189\) | −292.967 | −0.112752 | ||||||||
\(190\) | 305.351 | 0.116592 | ||||||||
\(191\) | 279.890 | 0.106032 | 0.0530160 | − | 0.998594i | \(-0.483117\pi\) | ||||
0.0530160 | + | 0.998594i | \(0.483117\pi\) | |||||||
\(192\) | 3360.39 | 1.26310 | ||||||||
\(193\) | −4842.79 | −1.80617 | −0.903087 | − | 0.429458i | \(-0.858705\pi\) | ||||
−0.903087 | + | 0.429458i | \(0.858705\pi\) | |||||||
\(194\) | −261.982 | −0.0969546 | ||||||||
\(195\) | −6228.02 | −2.28717 | ||||||||
\(196\) | −388.562 | −0.141604 | ||||||||
\(197\) | −2838.58 | −1.02660 | −0.513301 | − | 0.858208i | \(-0.671578\pi\) | ||||
−0.513301 | + | 0.858208i | \(0.671578\pi\) | |||||||
\(198\) | 306.778 | 0.110110 | ||||||||
\(199\) | 3449.73 | 1.22887 | 0.614435 | − | 0.788968i | \(-0.289384\pi\) | ||||
0.614435 | + | 0.788968i | \(0.289384\pi\) | |||||||
\(200\) | 51.4573 | 0.0181929 | ||||||||
\(201\) | 3564.88 | 1.25098 | ||||||||
\(202\) | 47.5490 | 0.0165620 | ||||||||
\(203\) | 1365.33 | 0.472055 | ||||||||
\(204\) | 6166.59 | 2.11641 | ||||||||
\(205\) | 3857.12 | 1.31411 | ||||||||
\(206\) | −435.441 | −0.147275 | ||||||||
\(207\) | −481.997 | −0.161841 | ||||||||
\(208\) | −4785.11 | −1.59513 | ||||||||
\(209\) | −5438.49 | −1.79995 | ||||||||
\(210\) | 150.408 | 0.0494243 | ||||||||
\(211\) | 1249.39 | 0.407636 | 0.203818 | − | 0.979009i | \(-0.434665\pi\) | ||||
0.203818 | + | 0.979009i | \(0.434665\pi\) | |||||||
\(212\) | 2018.88 | 0.654045 | ||||||||
\(213\) | −7335.25 | −2.35964 | ||||||||
\(214\) | 262.966 | 0.0839998 | ||||||||
\(215\) | 3221.45 | 1.02186 | ||||||||
\(216\) | 176.608 | 0.0556328 | ||||||||
\(217\) | 694.868 | 0.217376 | ||||||||
\(218\) | −5.64508 | −0.00175382 | ||||||||
\(219\) | 2604.72 | 0.803700 | ||||||||
\(220\) | −5132.86 | −1.57299 | ||||||||
\(221\) | −8622.19 | −2.62439 | ||||||||
\(222\) | −26.7147 | −0.00807646 | ||||||||
\(223\) | 4170.14 | 1.25226 | 0.626128 | − | 0.779720i | \(-0.284639\pi\) | ||||
0.626128 | + | 0.779720i | \(0.284639\pi\) | |||||||
\(224\) | 351.870 | 0.104957 | ||||||||
\(225\) | 255.548 | 0.0757178 | ||||||||
\(226\) | −162.630 | −0.0478671 | ||||||||
\(227\) | −3259.90 | −0.953158 | −0.476579 | − | 0.879132i | \(-0.658123\pi\) | ||||
−0.476579 | + | 0.879132i | \(0.658123\pi\) | |||||||
\(228\) | 5404.29 | 1.56977 | ||||||||
\(229\) | 3715.07 | 1.07205 | 0.536023 | − | 0.844204i | \(-0.319926\pi\) | ||||
0.536023 | + | 0.844204i | \(0.319926\pi\) | |||||||
\(230\) | −71.3635 | −0.0204590 | ||||||||
\(231\) | −2678.85 | −0.763011 | ||||||||
\(232\) | −823.057 | −0.232915 | ||||||||
\(233\) | −5851.29 | −1.64520 | −0.822598 | − | 0.568624i | \(-0.807476\pi\) | ||||
−0.822598 | + | 0.568624i | \(0.807476\pi\) | |||||||
\(234\) | 426.242 | 0.119078 | ||||||||
\(235\) | 47.9252 | 0.0133034 | ||||||||
\(236\) | −1642.62 | −0.453074 | ||||||||
\(237\) | −5882.15 | −1.61218 | ||||||||
\(238\) | 208.227 | 0.0567115 | ||||||||
\(239\) | 2342.48 | 0.633985 | 0.316993 | − | 0.948428i | \(-0.397327\pi\) | ||||
0.316993 | + | 0.948428i | \(0.397327\pi\) | |||||||
\(240\) | 5055.04 | 1.35959 | ||||||||
\(241\) | 3014.50 | 0.805731 | 0.402865 | − | 0.915259i | \(-0.368014\pi\) | ||||
0.402865 | + | 0.915259i | \(0.368014\pi\) | |||||||
\(242\) | −456.394 | −0.121232 | ||||||||
\(243\) | 4795.43 | 1.26595 | ||||||||
\(244\) | −5722.42 | −1.50140 | ||||||||
\(245\) | −573.937 | −0.149663 | ||||||||
\(246\) | −604.086 | −0.156565 | ||||||||
\(247\) | −7556.32 | −1.94655 | ||||||||
\(248\) | −418.886 | −0.107255 | ||||||||
\(249\) | −1413.31 | −0.359698 | ||||||||
\(250\) | −350.009 | −0.0885461 | ||||||||
\(251\) | −3717.17 | −0.934763 | −0.467381 | − | 0.884056i | \(-0.654802\pi\) | ||||
−0.467381 | + | 0.884056i | \(0.654802\pi\) | |||||||
\(252\) | 1163.26 | 0.290789 | ||||||||
\(253\) | 1271.03 | 0.315845 | ||||||||
\(254\) | 254.440 | 0.0628544 | ||||||||
\(255\) | 9108.55 | 2.23686 | ||||||||
\(256\) | 3741.43 | 0.913435 | ||||||||
\(257\) | −851.188 | −0.206598 | −0.103299 | − | 0.994650i | \(-0.532940\pi\) | ||||
−0.103299 | + | 0.994650i | \(0.532940\pi\) | |||||||
\(258\) | −504.530 | −0.121747 | ||||||||
\(259\) | 101.940 | 0.0244566 | ||||||||
\(260\) | −7131.66 | −1.70110 | ||||||||
\(261\) | −4087.47 | −0.969380 | ||||||||
\(262\) | 527.511 | 0.124388 | ||||||||
\(263\) | 6282.40 | 1.47296 | 0.736482 | − | 0.676458i | \(-0.236486\pi\) | ||||
0.736482 | + | 0.676458i | \(0.236486\pi\) | |||||||
\(264\) | 1614.89 | 0.376475 | ||||||||
\(265\) | 2982.05 | 0.691268 | ||||||||
\(266\) | 182.486 | 0.0420637 | ||||||||
\(267\) | 4373.04 | 1.00234 | ||||||||
\(268\) | 4082.12 | 0.930429 | ||||||||
\(269\) | 3572.08 | 0.809642 | 0.404821 | − | 0.914396i | \(-0.367334\pi\) | ||||
0.404821 | + | 0.914396i | \(0.367334\pi\) | |||||||
\(270\) | 129.858 | 0.0292700 | ||||||||
\(271\) | 97.7240 | 0.0219052 | 0.0109526 | − | 0.999940i | \(-0.496514\pi\) | ||||
0.0109526 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(272\) | 6998.28 | 1.56005 | ||||||||
\(273\) | −3722.03 | −0.825157 | ||||||||
\(274\) | 735.078 | 0.162072 | ||||||||
\(275\) | −673.880 | −0.147769 | ||||||||
\(276\) | −1263.03 | −0.275455 | ||||||||
\(277\) | −4764.37 | −1.03344 | −0.516721 | − | 0.856154i | \(-0.672847\pi\) | ||||
−0.516721 | + | 0.856154i | \(0.672847\pi\) | |||||||
\(278\) | 16.1432 | 0.00348275 | ||||||||
\(279\) | −2080.27 | −0.446390 | ||||||||
\(280\) | 345.985 | 0.0738449 | ||||||||
\(281\) | −2901.10 | −0.615890 | −0.307945 | − | 0.951404i | \(-0.599641\pi\) | ||||
−0.307945 | + | 0.951404i | \(0.599641\pi\) | |||||||
\(282\) | −7.50585 | −0.00158499 | ||||||||
\(283\) | −3015.38 | −0.633377 | −0.316688 | − | 0.948530i | \(-0.602571\pi\) | ||||
−0.316688 | + | 0.948530i | \(0.602571\pi\) | |||||||
\(284\) | −8399.53 | −1.75500 | ||||||||
\(285\) | 7982.57 | 1.65911 | ||||||||
\(286\) | −1124.00 | −0.232390 | ||||||||
\(287\) | 2305.12 | 0.474100 | ||||||||
\(288\) | −1053.42 | −0.215532 | ||||||||
\(289\) | 7697.04 | 1.56667 | ||||||||
\(290\) | −605.183 | −0.122543 | ||||||||
\(291\) | −6848.79 | −1.37967 | ||||||||
\(292\) | 2982.64 | 0.597760 | ||||||||
\(293\) | 2746.50 | 0.547619 | 0.273810 | − | 0.961784i | \(-0.411716\pi\) | ||||
0.273810 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(294\) | 89.8876 | 0.0178311 | ||||||||
\(295\) | −2426.28 | −0.478860 | ||||||||
\(296\) | −61.4523 | −0.0120670 | ||||||||
\(297\) | −2312.85 | −0.451869 | ||||||||
\(298\) | 165.584 | 0.0321880 | ||||||||
\(299\) | 1765.98 | 0.341570 | ||||||||
\(300\) | 669.642 | 0.128873 | ||||||||
\(301\) | 1925.22 | 0.368665 | ||||||||
\(302\) | −600.289 | −0.114380 | ||||||||
\(303\) | 1243.04 | 0.235679 | ||||||||
\(304\) | 6133.16 | 1.15711 | ||||||||
\(305\) | −8452.48 | −1.58684 | ||||||||
\(306\) | −623.383 | −0.116459 | ||||||||
\(307\) | 9858.98 | 1.83284 | 0.916420 | − | 0.400219i | \(-0.131066\pi\) | ||||
0.916420 | + | 0.400219i | \(0.131066\pi\) | |||||||
\(308\) | −3067.53 | −0.567496 | ||||||||
\(309\) | −11383.4 | −2.09573 | ||||||||
\(310\) | −308.001 | −0.0564300 | ||||||||
\(311\) | −5543.80 | −1.01080 | −0.505402 | − | 0.862884i | \(-0.668656\pi\) | ||||
−0.505402 | + | 0.862884i | \(0.668656\pi\) | |||||||
\(312\) | 2243.75 | 0.407138 | ||||||||
\(313\) | −8209.35 | −1.48249 | −0.741245 | − | 0.671234i | \(-0.765765\pi\) | ||||
−0.741245 | + | 0.671234i | \(0.765765\pi\) | |||||||
\(314\) | −671.081 | −0.120609 | ||||||||
\(315\) | 1718.23 | 0.307338 | ||||||||
\(316\) | −6735.60 | −1.19907 | ||||||||
\(317\) | 325.685 | 0.0577043 | 0.0288522 | − | 0.999584i | \(-0.490815\pi\) | ||||
0.0288522 | + | 0.999584i | \(0.490815\pi\) | |||||||
\(318\) | −467.037 | −0.0823589 | ||||||||
\(319\) | 10778.7 | 1.89182 | ||||||||
\(320\) | 5683.74 | 0.992909 | ||||||||
\(321\) | 6874.51 | 1.19532 | ||||||||
\(322\) | −42.6487 | −0.00738112 | ||||||||
\(323\) | 11051.2 | 1.90373 | ||||||||
\(324\) | 6785.18 | 1.16344 | ||||||||
\(325\) | −936.299 | −0.159805 | ||||||||
\(326\) | −656.785 | −0.111583 | ||||||||
\(327\) | −147.575 | −0.0249569 | ||||||||
\(328\) | −1389.59 | −0.233924 | ||||||||
\(329\) | 28.6414 | 0.00479955 | ||||||||
\(330\) | 1187.40 | 0.198074 | ||||||||
\(331\) | 3735.77 | 0.620352 | 0.310176 | − | 0.950679i | \(-0.399612\pi\) | ||||
0.310176 | + | 0.950679i | \(0.399612\pi\) | |||||||
\(332\) | −1618.37 | −0.267528 | ||||||||
\(333\) | −305.185 | −0.0502224 | ||||||||
\(334\) | −116.733 | −0.0191238 | ||||||||
\(335\) | 6029.61 | 0.983382 | ||||||||
\(336\) | 3021.03 | 0.490507 | ||||||||
\(337\) | −4319.35 | −0.698189 | −0.349095 | − | 0.937087i | \(-0.613511\pi\) | ||||
−0.349095 | + | 0.937087i | \(0.613511\pi\) | |||||||
\(338\) | −979.720 | −0.157662 | ||||||||
\(339\) | −4251.50 | −0.681150 | ||||||||
\(340\) | 10430.1 | 1.66369 | ||||||||
\(341\) | 5485.69 | 0.871164 | ||||||||
\(342\) | −546.321 | −0.0863792 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1160.58 | −0.181902 | ||||||||
\(345\) | −1865.60 | −0.291132 | ||||||||
\(346\) | 824.238 | 0.128067 | ||||||||
\(347\) | −4875.70 | −0.754298 | −0.377149 | − | 0.926153i | \(-0.623096\pi\) | ||||
−0.377149 | + | 0.926153i | \(0.623096\pi\) | |||||||
\(348\) | −10710.9 | −1.64990 | ||||||||
\(349\) | 11218.1 | 1.72060 | 0.860300 | − | 0.509788i | \(-0.170276\pi\) | ||||
0.860300 | + | 0.509788i | \(0.170276\pi\) | |||||||
\(350\) | 22.6117 | 0.00345328 | ||||||||
\(351\) | −3213.51 | −0.488673 | ||||||||
\(352\) | 2777.86 | 0.420627 | ||||||||
\(353\) | −3699.99 | −0.557878 | −0.278939 | − | 0.960309i | \(-0.589983\pi\) | ||||
−0.278939 | + | 0.960309i | \(0.589983\pi\) | |||||||
\(354\) | 379.994 | 0.0570522 | ||||||||
\(355\) | −12406.8 | −1.85488 | ||||||||
\(356\) | 5007.54 | 0.745502 | ||||||||
\(357\) | 5443.52 | 0.807007 | ||||||||
\(358\) | −489.022 | −0.0721945 | ||||||||
\(359\) | 1556.36 | 0.228807 | 0.114403 | − | 0.993434i | \(-0.463504\pi\) | ||||
0.114403 | + | 0.993434i | \(0.463504\pi\) | |||||||
\(360\) | −1035.80 | −0.151643 | ||||||||
\(361\) | 2826.07 | 0.412024 | ||||||||
\(362\) | 535.181 | 0.0777031 | ||||||||
\(363\) | −11931.2 | −1.72513 | ||||||||
\(364\) | −4262.07 | −0.613718 | ||||||||
\(365\) | 4405.60 | 0.631780 | ||||||||
\(366\) | 1323.79 | 0.189059 | ||||||||
\(367\) | −13384.4 | −1.90371 | −0.951856 | − | 0.306546i | \(-0.900827\pi\) | ||||
−0.951856 | + | 0.306546i | \(0.900827\pi\) | |||||||
\(368\) | −1433.38 | −0.203044 | ||||||||
\(369\) | −6900.99 | −0.973581 | ||||||||
\(370\) | −45.1851 | −0.00634882 | ||||||||
\(371\) | 1782.15 | 0.249393 | ||||||||
\(372\) | −5451.19 | −0.759760 | ||||||||
\(373\) | −708.946 | −0.0984125 | −0.0492062 | − | 0.998789i | \(-0.515669\pi\) | ||||
−0.0492062 | + | 0.998789i | \(0.515669\pi\) | |||||||
\(374\) | 1643.86 | 0.227279 | ||||||||
\(375\) | −9150.03 | −1.26001 | ||||||||
\(376\) | −17.2658 | −0.00236813 | ||||||||
\(377\) | 14976.1 | 2.04590 | ||||||||
\(378\) | 77.6065 | 0.0105599 | ||||||||
\(379\) | 6754.31 | 0.915423 | 0.457712 | − | 0.889101i | \(-0.348669\pi\) | ||||
0.457712 | + | 0.889101i | \(0.348669\pi\) | |||||||
\(380\) | 9140.78 | 1.23398 | ||||||||
\(381\) | 6651.64 | 0.894420 | ||||||||
\(382\) | −74.1425 | −0.00993052 | ||||||||
\(383\) | 4262.89 | 0.568730 | 0.284365 | − | 0.958716i | \(-0.408217\pi\) | ||||
0.284365 | + | 0.958716i | \(0.408217\pi\) | |||||||
\(384\) | −3674.98 | −0.488381 | ||||||||
\(385\) | −4530.99 | −0.599794 | ||||||||
\(386\) | 1282.85 | 0.169159 | ||||||||
\(387\) | −5763.68 | −0.757065 | ||||||||
\(388\) | −7842.50 | −1.02614 | ||||||||
\(389\) | 11230.0 | 1.46371 | 0.731857 | − | 0.681459i | \(-0.238654\pi\) | ||||
0.731857 | + | 0.681459i | \(0.238654\pi\) | |||||||
\(390\) | 1649.80 | 0.214207 | ||||||||
\(391\) | −2582.77 | −0.334057 | ||||||||
\(392\) | 206.770 | 0.0266415 | ||||||||
\(393\) | 13790.3 | 1.77005 | ||||||||
\(394\) | 751.938 | 0.0961475 | ||||||||
\(395\) | −9949.03 | −1.26732 | ||||||||
\(396\) | 9183.48 | 1.16537 | ||||||||
\(397\) | 1644.30 | 0.207872 | 0.103936 | − | 0.994584i | \(-0.466856\pi\) | ||||
0.103936 | + | 0.994584i | \(0.466856\pi\) | |||||||
\(398\) | −913.830 | −0.115091 | ||||||||
\(399\) | 4770.60 | 0.598568 | ||||||||
\(400\) | 759.956 | 0.0949945 | ||||||||
\(401\) | 7463.82 | 0.929489 | 0.464745 | − | 0.885445i | \(-0.346146\pi\) | ||||
0.464745 | + | 0.885445i | \(0.346146\pi\) | |||||||
\(402\) | −944.333 | −0.117162 | ||||||||
\(403\) | 7621.90 | 0.942119 | ||||||||
\(404\) | 1423.39 | 0.175288 | ||||||||
\(405\) | 10022.3 | 1.22965 | ||||||||
\(406\) | −361.674 | −0.0442107 | ||||||||
\(407\) | 804.775 | 0.0980128 | ||||||||
\(408\) | −3281.50 | −0.398183 | ||||||||
\(409\) | 3759.62 | 0.454526 | 0.227263 | − | 0.973833i | \(-0.427022\pi\) | ||||
0.227263 | + | 0.973833i | \(0.427022\pi\) | |||||||
\(410\) | −1021.75 | −0.123074 | ||||||||
\(411\) | 19216.6 | 2.30629 | ||||||||
\(412\) | −13035.1 | −1.55872 | ||||||||
\(413\) | −1450.01 | −0.172761 | ||||||||
\(414\) | 127.680 | 0.0151574 | ||||||||
\(415\) | −2390.46 | −0.282754 | ||||||||
\(416\) | 3859.60 | 0.454886 | ||||||||
\(417\) | 422.020 | 0.0495597 | ||||||||
\(418\) | 1440.65 | 0.168576 | ||||||||
\(419\) | −7619.80 | −0.888428 | −0.444214 | − | 0.895921i | \(-0.646517\pi\) | ||||
−0.444214 | + | 0.895921i | \(0.646517\pi\) | |||||||
\(420\) | 4502.49 | 0.523093 | ||||||||
\(421\) | 1487.35 | 0.172183 | 0.0860914 | − | 0.996287i | \(-0.472562\pi\) | ||||
0.0860914 | + | 0.996287i | \(0.472562\pi\) | |||||||
\(422\) | −330.961 | −0.0381776 | ||||||||
\(423\) | −85.7458 | −0.00985603 | ||||||||
\(424\) | −1074.33 | −0.123052 | ||||||||
\(425\) | 1369.35 | 0.156290 | ||||||||
\(426\) | 1943.10 | 0.220994 | ||||||||
\(427\) | −5051.43 | −0.572496 | ||||||||
\(428\) | 7871.95 | 0.889030 | ||||||||
\(429\) | −29383.9 | −3.30692 | ||||||||
\(430\) | −853.358 | −0.0957037 | ||||||||
\(431\) | −2649.29 | −0.296083 | −0.148042 | − | 0.988981i | \(-0.547297\pi\) | ||||
−0.148042 | + | 0.988981i | \(0.547297\pi\) | |||||||
\(432\) | 2608.27 | 0.290487 | ||||||||
\(433\) | −4224.97 | −0.468912 | −0.234456 | − | 0.972127i | \(-0.575331\pi\) | ||||
−0.234456 | + | 0.972127i | \(0.575331\pi\) | |||||||
\(434\) | −184.070 | −0.0203586 | ||||||||
\(435\) | −15820.8 | −1.74380 | ||||||||
\(436\) | −168.987 | −0.0185619 | ||||||||
\(437\) | −2263.49 | −0.247775 | ||||||||
\(438\) | −689.986 | −0.0752713 | ||||||||
\(439\) | −14831.9 | −1.61250 | −0.806251 | − | 0.591573i | \(-0.798507\pi\) | ||||
−0.806251 | + | 0.591573i | \(0.798507\pi\) | |||||||
\(440\) | 2731.41 | 0.295943 | ||||||||
\(441\) | 1026.86 | 0.110880 | ||||||||
\(442\) | 2284.01 | 0.245790 | ||||||||
\(443\) | −4704.72 | −0.504578 | −0.252289 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252289 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(444\) | −799.713 | −0.0854790 | ||||||||
\(445\) | 7396.53 | 0.787931 | ||||||||
\(446\) | −1104.67 | −0.117281 | ||||||||
\(447\) | 4328.74 | 0.458037 | ||||||||
\(448\) | 3396.76 | 0.358218 | ||||||||
\(449\) | 49.6103 | 0.00521438 | 0.00260719 | − | 0.999997i | \(-0.499170\pi\) | ||||
0.00260719 | + | 0.999997i | \(0.499170\pi\) | |||||||
\(450\) | −67.6943 | −0.00709142 | ||||||||
\(451\) | 18197.9 | 1.90002 | ||||||||
\(452\) | −4868.37 | −0.506612 | ||||||||
\(453\) | −15692.9 | −1.62763 | ||||||||
\(454\) | 863.543 | 0.0892689 | ||||||||
\(455\) | −6295.43 | −0.648646 | ||||||||
\(456\) | −2875.85 | −0.295338 | ||||||||
\(457\) | −6277.49 | −0.642557 | −0.321279 | − | 0.946985i | \(-0.604113\pi\) | ||||
−0.321279 | + | 0.946985i | \(0.604113\pi\) | |||||||
\(458\) | −984.117 | −0.100403 | ||||||||
\(459\) | 4699.79 | 0.477924 | ||||||||
\(460\) | −2136.29 | −0.216532 | ||||||||
\(461\) | −11140.2 | −1.12549 | −0.562744 | − | 0.826631i | \(-0.690254\pi\) | ||||
−0.562744 | + | 0.826631i | \(0.690254\pi\) | |||||||
\(462\) | 709.625 | 0.0714605 | ||||||||
\(463\) | −6821.86 | −0.684749 | −0.342374 | − | 0.939564i | \(-0.611231\pi\) | ||||
−0.342374 | + | 0.939564i | \(0.611231\pi\) | |||||||
\(464\) | −12155.5 | −1.21617 | ||||||||
\(465\) | −8051.84 | −0.803000 | ||||||||
\(466\) | 1550.00 | 0.154082 | ||||||||
\(467\) | 3374.34 | 0.334360 | 0.167180 | − | 0.985926i | \(-0.446534\pi\) | ||||
0.167180 | + | 0.985926i | \(0.446534\pi\) | |||||||
\(468\) | 12759.7 | 1.26029 | ||||||||
\(469\) | 3603.46 | 0.354781 | ||||||||
\(470\) | −12.6953 | −0.00124594 | ||||||||
\(471\) | −17543.6 | −1.71627 | ||||||||
\(472\) | 874.108 | 0.0852417 | ||||||||
\(473\) | 15198.8 | 1.47747 | ||||||||
\(474\) | 1558.17 | 0.150990 | ||||||||
\(475\) | 1200.07 | 0.115922 | ||||||||
\(476\) | 6233.33 | 0.600219 | ||||||||
\(477\) | −5335.36 | −0.512137 | ||||||||
\(478\) | −620.521 | −0.0593765 | ||||||||
\(479\) | 9644.40 | 0.919967 | 0.459983 | − | 0.887928i | \(-0.347855\pi\) | ||||
0.459983 | + | 0.887928i | \(0.347855\pi\) | |||||||
\(480\) | −4077.32 | −0.387715 | ||||||||
\(481\) | 1118.17 | 0.105996 | ||||||||
\(482\) | −798.538 | −0.0754615 | ||||||||
\(483\) | −1114.93 | −0.105034 | ||||||||
\(484\) | −13662.3 | −1.28309 | ||||||||
\(485\) | −11584.0 | −1.08454 | ||||||||
\(486\) | −1270.30 | −0.118564 | ||||||||
\(487\) | 587.142 | 0.0546323 | 0.0273162 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273162 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(488\) | 3045.14 | 0.282473 | ||||||||
\(489\) | −17169.8 | −1.58783 | ||||||||
\(490\) | 152.035 | 0.0140168 | ||||||||
\(491\) | 17831.2 | 1.63892 | 0.819461 | − | 0.573135i | \(-0.194273\pi\) | ||||
0.819461 | + | 0.573135i | \(0.194273\pi\) | |||||||
\(492\) | −18083.5 | −1.65705 | ||||||||
\(493\) | −21902.6 | −2.00090 | ||||||||
\(494\) | 2001.66 | 0.182306 | ||||||||
\(495\) | 13564.7 | 1.23170 | ||||||||
\(496\) | −6186.39 | −0.560034 | ||||||||
\(497\) | −7414.63 | −0.669198 | ||||||||
\(498\) | 374.384 | 0.0336878 | ||||||||
\(499\) | 7196.23 | 0.645586 | 0.322793 | − | 0.946470i | \(-0.395378\pi\) | ||||
0.322793 | + | 0.946470i | \(0.395378\pi\) | |||||||
\(500\) | −10477.6 | −0.937148 | ||||||||
\(501\) | −3051.66 | −0.272132 | ||||||||
\(502\) | 984.673 | 0.0875461 | ||||||||
\(503\) | 3011.39 | 0.266941 | 0.133471 | − | 0.991053i | \(-0.457388\pi\) | ||||
0.133471 | + | 0.991053i | \(0.457388\pi\) | |||||||
\(504\) | −619.022 | −0.0547092 | ||||||||
\(505\) | 2102.46 | 0.185264 | ||||||||
\(506\) | −336.694 | −0.0295808 | ||||||||
\(507\) | −25612.1 | −2.24354 | ||||||||
\(508\) | 7616.75 | 0.665233 | ||||||||
\(509\) | −6422.75 | −0.559299 | −0.279650 | − | 0.960102i | \(-0.590218\pi\) | ||||
−0.279650 | + | 0.960102i | \(0.590218\pi\) | |||||||
\(510\) | −2412.85 | −0.209495 | ||||||||
\(511\) | 2632.90 | 0.227931 | ||||||||
\(512\) | −5236.53 | −0.452001 | ||||||||
\(513\) | 4118.81 | 0.354483 | ||||||||
\(514\) | 225.479 | 0.0193491 | ||||||||
\(515\) | −19253.8 | −1.64743 | ||||||||
\(516\) | −15103.2 | −1.28853 | ||||||||
\(517\) | 226.112 | 0.0192348 | ||||||||
\(518\) | −27.0038 | −0.00229050 | ||||||||
\(519\) | 21547.4 | 1.82240 | ||||||||
\(520\) | 3795.06 | 0.320047 | ||||||||
\(521\) | −10457.6 | −0.879378 | −0.439689 | − | 0.898150i | \(-0.644911\pi\) | ||||
−0.439689 | + | 0.898150i | \(0.644911\pi\) | |||||||
\(522\) | 1082.77 | 0.0907882 | ||||||||
\(523\) | −5417.27 | −0.452927 | −0.226463 | − | 0.974020i | \(-0.572716\pi\) | ||||
−0.226463 | + | 0.974020i | \(0.572716\pi\) | |||||||
\(524\) | 15791.2 | 1.31649 | ||||||||
\(525\) | 591.121 | 0.0491403 | ||||||||
\(526\) | −1664.20 | −0.137952 | ||||||||
\(527\) | −11147.1 | −0.921396 | ||||||||
\(528\) | 23849.7 | 1.96577 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −789.943 | −0.0647414 | ||||||||
\(531\) | 4341.00 | 0.354771 | ||||||||
\(532\) | 5462.77 | 0.445190 | ||||||||
\(533\) | 25284.5 | 2.05477 | ||||||||
\(534\) | −1158.41 | −0.0938754 | ||||||||
\(535\) | 11627.5 | 0.939628 | ||||||||
\(536\) | −2172.27 | −0.175051 | ||||||||
\(537\) | −12784.1 | −1.02733 | ||||||||
\(538\) | −946.242 | −0.0758278 | ||||||||
\(539\) | −2707.84 | −0.216392 | ||||||||
\(540\) | 3887.33 | 0.309785 | ||||||||
\(541\) | 17716.7 | 1.40795 | 0.703975 | − | 0.710224i | \(-0.251406\pi\) | ||||
0.703975 | + | 0.710224i | \(0.251406\pi\) | |||||||
\(542\) | −25.8870 | −0.00205155 | ||||||||
\(543\) | 13990.8 | 1.10572 | ||||||||
\(544\) | −5644.71 | −0.444881 | ||||||||
\(545\) | −249.607 | −0.0196184 | ||||||||
\(546\) | 985.963 | 0.0772808 | ||||||||
\(547\) | 11555.7 | 0.903266 | 0.451633 | − | 0.892204i | \(-0.350842\pi\) | ||||
0.451633 | + | 0.892204i | \(0.350842\pi\) | |||||||
\(548\) | 22004.8 | 1.71532 | ||||||||
\(549\) | 15122.8 | 1.17564 | ||||||||
\(550\) | 178.510 | 0.0138395 | ||||||||
\(551\) | −19195.1 | −1.48410 | ||||||||
\(552\) | 672.113 | 0.0518244 | ||||||||
\(553\) | −5945.80 | −0.457218 | ||||||||
\(554\) | 1262.08 | 0.0967879 | ||||||||
\(555\) | −1181.24 | −0.0903439 | ||||||||
\(556\) | 483.251 | 0.0368605 | ||||||||
\(557\) | −4915.47 | −0.373923 | −0.186962 | − | 0.982367i | \(-0.559864\pi\) | ||||
−0.186962 | + | 0.982367i | \(0.559864\pi\) | |||||||
\(558\) | 551.062 | 0.0418070 | ||||||||
\(559\) | 21117.5 | 1.59781 | ||||||||
\(560\) | 5109.74 | 0.385582 | ||||||||
\(561\) | 42974.3 | 3.23418 | ||||||||
\(562\) | 768.498 | 0.0576818 | ||||||||
\(563\) | −17080.7 | −1.27862 | −0.639312 | − | 0.768947i | \(-0.720781\pi\) | ||||
−0.639312 | + | 0.768947i | \(0.720781\pi\) | |||||||
\(564\) | −224.690 | −0.0167751 | ||||||||
\(565\) | −7190.97 | −0.535445 | ||||||||
\(566\) | 798.770 | 0.0593195 | ||||||||
\(567\) | 5989.57 | 0.443630 | ||||||||
\(568\) | 4469.75 | 0.330187 | ||||||||
\(569\) | 26856.6 | 1.97871 | 0.989357 | − | 0.145507i | \(-0.0464813\pi\) | ||||
0.989357 | + | 0.145507i | \(0.0464813\pi\) | |||||||
\(570\) | −2114.57 | −0.155386 | ||||||||
\(571\) | 10125.2 | 0.742077 | 0.371039 | − | 0.928617i | \(-0.379002\pi\) | ||||
0.371039 | + | 0.928617i | \(0.379002\pi\) | |||||||
\(572\) | −33647.3 | −2.45955 | ||||||||
\(573\) | −1938.25 | −0.141312 | ||||||||
\(574\) | −610.623 | −0.0444023 | ||||||||
\(575\) | −280.468 | −0.0203414 | ||||||||
\(576\) | −10169.1 | −0.735612 | ||||||||
\(577\) | 10605.0 | 0.765147 | 0.382574 | − | 0.923925i | \(-0.375038\pi\) | ||||
0.382574 | + | 0.923925i | \(0.375038\pi\) | |||||||
\(578\) | −2038.94 | −0.146728 | ||||||||
\(579\) | 33536.6 | 2.40714 | ||||||||
\(580\) | −18116.3 | −1.29696 | ||||||||
\(581\) | −1428.60 | −0.102011 | ||||||||
\(582\) | 1814.24 | 0.129214 | ||||||||
\(583\) | 14069.4 | 0.999475 | ||||||||
\(584\) | −1587.19 | −0.112463 | ||||||||
\(585\) | 18847.1 | 1.33202 | ||||||||
\(586\) | −727.546 | −0.0512878 | ||||||||
\(587\) | −2267.45 | −0.159434 | −0.0797169 | − | 0.996818i | \(-0.525402\pi\) | ||||
−0.0797169 | + | 0.996818i | \(0.525402\pi\) | |||||||
\(588\) | 2690.81 | 0.188720 | ||||||||
\(589\) | −9769.12 | −0.683412 | ||||||||
\(590\) | 642.720 | 0.0448481 | ||||||||
\(591\) | 19657.4 | 1.36818 | ||||||||
\(592\) | −907.570 | −0.0630083 | ||||||||
\(593\) | 27734.2 | 1.92059 | 0.960294 | − | 0.278989i | \(-0.0899994\pi\) | ||||
0.960294 | + | 0.278989i | \(0.0899994\pi\) | |||||||
\(594\) | 612.671 | 0.0423202 | ||||||||
\(595\) | 9207.13 | 0.634379 | ||||||||
\(596\) | 4956.81 | 0.340669 | ||||||||
\(597\) | −23889.6 | −1.63775 | ||||||||
\(598\) | −467.808 | −0.0319901 | ||||||||
\(599\) | −8268.56 | −0.564014 | −0.282007 | − | 0.959412i | \(-0.591000\pi\) | ||||
−0.282007 | + | 0.959412i | \(0.591000\pi\) | |||||||
\(600\) | −356.344 | −0.0242462 | ||||||||
\(601\) | 1545.61 | 0.104903 | 0.0524515 | − | 0.998623i | \(-0.483297\pi\) | ||||
0.0524515 | + | 0.998623i | \(0.483297\pi\) | |||||||
\(602\) | −509.990 | −0.0345276 | ||||||||
\(603\) | −10787.9 | −0.728554 | ||||||||
\(604\) | −17969.8 | −1.21057 | ||||||||
\(605\) | −20180.3 | −1.35611 | ||||||||
\(606\) | −329.279 | −0.0220727 | ||||||||
\(607\) | 17902.6 | 1.19711 | 0.598554 | − | 0.801083i | \(-0.295742\pi\) | ||||
0.598554 | + | 0.801083i | \(0.295742\pi\) | |||||||
\(608\) | −4946.92 | −0.329974 | ||||||||
\(609\) | −9454.96 | −0.629120 | ||||||||
\(610\) | 2239.05 | 0.148617 | ||||||||
\(611\) | 314.163 | 0.0208015 | ||||||||
\(612\) | −18661.1 | −1.23257 | ||||||||
\(613\) | −13780.7 | −0.907986 | −0.453993 | − | 0.891005i | \(-0.650001\pi\) | ||||
−0.453993 | + | 0.891005i | \(0.650001\pi\) | |||||||
\(614\) | −2611.63 | −0.171656 | ||||||||
\(615\) | −26710.8 | −1.75135 | ||||||||
\(616\) | 1632.36 | 0.106769 | ||||||||
\(617\) | 12935.0 | 0.843995 | 0.421998 | − | 0.906597i | \(-0.361329\pi\) | ||||
0.421998 | + | 0.906597i | \(0.361329\pi\) | |||||||
\(618\) | 3015.45 | 0.196277 | ||||||||
\(619\) | −28162.3 | −1.82866 | −0.914329 | − | 0.404971i | \(-0.867281\pi\) | ||||
−0.914329 | + | 0.404971i | \(0.867281\pi\) | |||||||
\(620\) | −9220.10 | −0.597239 | ||||||||
\(621\) | −962.604 | −0.0622029 | ||||||||
\(622\) | 1468.55 | 0.0946679 | ||||||||
\(623\) | 4420.37 | 0.284267 | ||||||||
\(624\) | 33137.2 | 2.12588 | ||||||||
\(625\) | −17000.6 | −1.08804 | ||||||||
\(626\) | 2174.65 | 0.138844 | ||||||||
\(627\) | 37661.9 | 2.39884 | ||||||||
\(628\) | −20089.0 | −1.27649 | ||||||||
\(629\) | −1635.33 | −0.103664 | ||||||||
\(630\) | −455.159 | −0.0287840 | ||||||||
\(631\) | 18619.8 | 1.17471 | 0.587356 | − | 0.809328i | \(-0.300169\pi\) | ||||
0.587356 | + | 0.809328i | \(0.300169\pi\) | |||||||
\(632\) | 3584.30 | 0.225594 | ||||||||
\(633\) | −8652.07 | −0.543268 | ||||||||
\(634\) | −86.2735 | −0.00540435 | ||||||||
\(635\) | 11250.5 | 0.703094 | ||||||||
\(636\) | −13980.9 | −0.871663 | ||||||||
\(637\) | −3762.32 | −0.234016 | ||||||||
\(638\) | −2855.26 | −0.177180 | ||||||||
\(639\) | 22197.7 | 1.37422 | ||||||||
\(640\) | −6215.84 | −0.383911 | ||||||||
\(641\) | 4403.53 | 0.271340 | 0.135670 | − | 0.990754i | \(-0.456681\pi\) | ||||
0.135670 | + | 0.990754i | \(0.456681\pi\) | |||||||
\(642\) | −1821.05 | −0.111949 | ||||||||
\(643\) | −9833.46 | −0.603101 | −0.301550 | − | 0.953450i | \(-0.597504\pi\) | ||||
−0.301550 | + | 0.953450i | \(0.597504\pi\) | |||||||
\(644\) | −1276.70 | −0.0781198 | ||||||||
\(645\) | −22308.7 | −1.36187 | ||||||||
\(646\) | −2927.45 | −0.178296 | ||||||||
\(647\) | 11633.7 | 0.706908 | 0.353454 | − | 0.935452i | \(-0.385007\pi\) | ||||
0.353454 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(648\) | −3610.68 | −0.218890 | ||||||||
\(649\) | −11447.2 | −0.692363 | ||||||||
\(650\) | 248.025 | 0.0149667 | ||||||||
\(651\) | −4812.00 | −0.289704 | ||||||||
\(652\) | −19661.0 | −1.18096 | ||||||||
\(653\) | 26410.4 | 1.58272 | 0.791361 | − | 0.611349i | \(-0.209373\pi\) | ||||
0.791361 | + | 0.611349i | \(0.209373\pi\) | |||||||
\(654\) | 39.0925 | 0.00233736 | ||||||||
\(655\) | 23324.9 | 1.39142 | ||||||||
\(656\) | −20522.4 | −1.22144 | ||||||||
\(657\) | −7882.31 | −0.468064 | ||||||||
\(658\) | −7.58708 | −0.000449506 0 | ||||||||
\(659\) | 6928.02 | 0.409525 | 0.204763 | − | 0.978812i | \(-0.434358\pi\) | ||||
0.204763 | + | 0.978812i | \(0.434358\pi\) | |||||||
\(660\) | 35545.3 | 2.09636 | ||||||||
\(661\) | −3672.24 | −0.216087 | −0.108044 | − | 0.994146i | \(-0.534459\pi\) | ||||
−0.108044 | + | 0.994146i | \(0.534459\pi\) | |||||||
\(662\) | −989.601 | −0.0580996 | ||||||||
\(663\) | 59709.1 | 3.49760 | ||||||||
\(664\) | 861.201 | 0.0503330 | ||||||||
\(665\) | 8068.96 | 0.470527 | ||||||||
\(666\) | 80.8433 | 0.00470362 | ||||||||
\(667\) | 4486.07 | 0.260422 | ||||||||
\(668\) | −3494.43 | −0.202401 | ||||||||
\(669\) | −28878.4 | −1.66892 | ||||||||
\(670\) | −1597.24 | −0.0920996 | ||||||||
\(671\) | −39878.9 | −2.29435 | ||||||||
\(672\) | −2436.72 | −0.139879 | ||||||||
\(673\) | −15522.8 | −0.889092 | −0.444546 | − | 0.895756i | \(-0.646635\pi\) | ||||
−0.444546 | + | 0.895756i | \(0.646635\pi\) | |||||||
\(674\) | 1144.19 | 0.0653896 | ||||||||
\(675\) | 510.358 | 0.0291018 | ||||||||
\(676\) | −29328.2 | −1.66865 | ||||||||
\(677\) | −5347.48 | −0.303575 | −0.151788 | − | 0.988413i | \(-0.548503\pi\) | ||||
−0.151788 | + | 0.988413i | \(0.548503\pi\) | |||||||
\(678\) | 1126.22 | 0.0637938 | ||||||||
\(679\) | −6922.91 | −0.391277 | ||||||||
\(680\) | −5550.31 | −0.313007 | ||||||||
\(681\) | 22575.0 | 1.27030 | ||||||||
\(682\) | −1453.15 | −0.0815896 | ||||||||
\(683\) | 7008.63 | 0.392647 | 0.196324 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196324 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(684\) | −16354.3 | −0.914213 | ||||||||
\(685\) | 32502.8 | 1.81295 | ||||||||
\(686\) | 90.8604 | 0.00505695 | ||||||||
\(687\) | −25727.0 | −1.42874 | ||||||||
\(688\) | −17140.2 | −0.949803 | ||||||||
\(689\) | 19548.2 | 1.08088 | ||||||||
\(690\) | 494.196 | 0.0272663 | ||||||||
\(691\) | −2542.80 | −0.139989 | −0.0699947 | − | 0.997547i | \(-0.522298\pi\) | ||||
−0.0699947 | + | 0.997547i | \(0.522298\pi\) | |||||||
\(692\) | 24673.8 | 1.35543 | ||||||||
\(693\) | 8106.66 | 0.444367 | ||||||||
\(694\) | 1291.57 | 0.0706445 | ||||||||
\(695\) | 713.801 | 0.0389583 | ||||||||
\(696\) | 5699.71 | 0.310412 | ||||||||
\(697\) | −36978.8 | −2.00957 | ||||||||
\(698\) | −2971.65 | −0.161144 | ||||||||
\(699\) | 40520.5 | 2.19260 | ||||||||
\(700\) | 676.889 | 0.0365485 | ||||||||
\(701\) | 5986.08 | 0.322527 | 0.161263 | − | 0.986911i | \(-0.448443\pi\) | ||||
0.161263 | + | 0.986911i | \(0.448443\pi\) | |||||||
\(702\) | 851.254 | 0.0457671 | ||||||||
\(703\) | −1433.17 | −0.0768892 | ||||||||
\(704\) | 26816.0 | 1.43560 | ||||||||
\(705\) | −331.885 | −0.0177298 | ||||||||
\(706\) | 980.125 | 0.0522486 | ||||||||
\(707\) | 1256.49 | 0.0668390 | ||||||||
\(708\) | 11375.2 | 0.603824 | ||||||||
\(709\) | −23850.9 | −1.26339 | −0.631693 | − | 0.775219i | \(-0.717640\pi\) | ||||
−0.631693 | + | 0.775219i | \(0.717640\pi\) | |||||||
\(710\) | 3286.55 | 0.173721 | ||||||||
\(711\) | 17800.4 | 0.938911 | ||||||||
\(712\) | −2664.72 | −0.140259 | ||||||||
\(713\) | 2283.14 | 0.119922 | ||||||||
\(714\) | −1441.98 | −0.0755810 | ||||||||
\(715\) | −49699.8 | −2.59953 | ||||||||
\(716\) | −14639.0 | −0.764087 | ||||||||
\(717\) | −16221.8 | −0.844929 | ||||||||
\(718\) | −412.279 | −0.0214291 | ||||||||
\(719\) | 16198.0 | 0.840173 | 0.420086 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420086 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(720\) | −15297.4 | −0.791806 | ||||||||
\(721\) | −11506.6 | −0.594353 | ||||||||
\(722\) | −748.623 | −0.0385885 | ||||||||
\(723\) | −20875.6 | −1.07382 | ||||||||
\(724\) | 16020.8 | 0.822388 | ||||||||
\(725\) | −2378.45 | −0.121839 | ||||||||
\(726\) | 3160.55 | 0.161569 | ||||||||
\(727\) | 14714.5 | 0.750662 | 0.375331 | − | 0.926891i | \(-0.377529\pi\) | ||||
0.375331 | + | 0.926891i | \(0.377529\pi\) | |||||||
\(728\) | 2268.03 | 0.115465 | ||||||||
\(729\) | −10106.0 | −0.513437 | ||||||||
\(730\) | −1167.04 | −0.0591699 | ||||||||
\(731\) | −30884.6 | −1.56266 | ||||||||
\(732\) | 39628.1 | 2.00095 | ||||||||
\(733\) | 22554.3 | 1.13651 | 0.568255 | − | 0.822852i | \(-0.307619\pi\) | ||||
0.568255 | + | 0.822852i | \(0.307619\pi\) | |||||||
\(734\) | 3545.53 | 0.178294 | ||||||||
\(735\) | 3974.54 | 0.199460 | ||||||||
\(736\) | 1156.14 | 0.0579022 | ||||||||
\(737\) | 28447.8 | 1.42183 | ||||||||
\(738\) | 1828.07 | 0.0911816 | ||||||||
\(739\) | −30940.6 | −1.54015 | −0.770073 | − | 0.637956i | \(-0.779780\pi\) | ||||
−0.770073 | + | 0.637956i | \(0.779780\pi\) | |||||||
\(740\) | −1352.63 | −0.0671941 | ||||||||
\(741\) | 52328.0 | 2.59422 | ||||||||
\(742\) | −472.091 | −0.0233572 | ||||||||
\(743\) | 1548.59 | 0.0764632 | 0.0382316 | − | 0.999269i | \(-0.487828\pi\) | ||||
0.0382316 | + | 0.999269i | \(0.487828\pi\) | |||||||
\(744\) | 2900.81 | 0.142942 | ||||||||
\(745\) | 7321.60 | 0.360057 | ||||||||
\(746\) | 187.799 | 0.00921691 | ||||||||
\(747\) | 4276.91 | 0.209483 | ||||||||
\(748\) | 49209.5 | 2.40545 | ||||||||
\(749\) | 6948.91 | 0.338995 | ||||||||
\(750\) | 2423.83 | 0.118008 | ||||||||
\(751\) | 3631.60 | 0.176457 | 0.0882284 | − | 0.996100i | \(-0.471879\pi\) | ||||
0.0882284 | + | 0.996100i | \(0.471879\pi\) | |||||||
\(752\) | −254.994 | −0.0123652 | ||||||||
\(753\) | 25741.6 | 1.24578 | ||||||||
\(754\) | −3967.14 | −0.191611 | ||||||||
\(755\) | −26542.9 | −1.27946 | ||||||||
\(756\) | 2323.17 | 0.111763 | ||||||||
\(757\) | 10320.4 | 0.495513 | 0.247756 | − | 0.968822i | \(-0.420307\pi\) | ||||
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(758\) | −1789.21 | −0.0857348 | ||||||||
\(759\) | −8801.94 | −0.420936 | ||||||||
\(760\) | −4864.19 | −0.232162 | ||||||||
\(761\) | 28242.0 | 1.34530 | 0.672650 | − | 0.739961i | \(-0.265156\pi\) | ||||
0.672650 | + | 0.739961i | \(0.265156\pi\) | |||||||
\(762\) | −1762.01 | −0.0837677 | ||||||||
\(763\) | −149.172 | −0.00707784 | ||||||||
\(764\) | −2219.48 | −0.105102 | ||||||||
\(765\) | −27564.0 | −1.30272 | ||||||||
\(766\) | −1129.24 | −0.0532650 | ||||||||
\(767\) | −15905.0 | −0.748755 | ||||||||
\(768\) | −25909.6 | −1.21736 | ||||||||
\(769\) | −2021.61 | −0.0947997 | −0.0473998 | − | 0.998876i | \(-0.515093\pi\) | ||||
−0.0473998 | + | 0.998876i | \(0.515093\pi\) | |||||||
\(770\) | 1200.26 | 0.0561743 | ||||||||
\(771\) | 5894.52 | 0.275339 | ||||||||
\(772\) | 38402.5 | 1.79033 | ||||||||
\(773\) | 1544.52 | 0.0718661 | 0.0359330 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359330 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(774\) | 1526.79 | 0.0709036 | ||||||||
\(775\) | −1210.48 | −0.0561057 | ||||||||
\(776\) | 4173.32 | 0.193059 | ||||||||
\(777\) | −705.941 | −0.0325939 | ||||||||
\(778\) | −2974.82 | −0.137085 | ||||||||
\(779\) | −32407.6 | −1.49053 | ||||||||
\(780\) | 49387.2 | 2.26711 | ||||||||
\(781\) | −58535.4 | −2.68190 | ||||||||
\(782\) | 684.174 | 0.0312864 | ||||||||
\(783\) | −8163.16 | −0.372577 | ||||||||
\(784\) | 3053.72 | 0.139109 | ||||||||
\(785\) | −29673.1 | −1.34914 | ||||||||
\(786\) | −3653.04 | −0.165776 | ||||||||
\(787\) | −13130.7 | −0.594736 | −0.297368 | − | 0.954763i | \(-0.596109\pi\) | ||||
−0.297368 | + | 0.954763i | \(0.596109\pi\) | |||||||
\(788\) | 22509.5 | 1.01760 | ||||||||
\(789\) | −43506.0 | −1.96306 | ||||||||
\(790\) | 2635.49 | 0.118692 | ||||||||
\(791\) | −4297.52 | −0.193176 | ||||||||
\(792\) | −4886.92 | −0.219254 | ||||||||
\(793\) | −55408.3 | −2.48122 | ||||||||
\(794\) | −435.574 | −0.0194685 | ||||||||
\(795\) | −20650.9 | −0.921272 | ||||||||
\(796\) | −27355.8 | −1.21809 | ||||||||
\(797\) | −37425.0 | −1.66332 | −0.831658 | − | 0.555288i | \(-0.812608\pi\) | ||||
−0.831658 | + | 0.555288i | \(0.812608\pi\) | |||||||
\(798\) | −1263.73 | −0.0560594 | ||||||||
\(799\) | −459.467 | −0.0203439 | ||||||||
\(800\) | −612.970 | −0.0270897 | ||||||||
\(801\) | −13233.6 | −0.583751 | ||||||||
\(802\) | −1977.16 | −0.0870522 | ||||||||
\(803\) | 20785.7 | 0.913463 | ||||||||
\(804\) | −28268.9 | −1.24001 | ||||||||
\(805\) | −1885.79 | −0.0825658 | ||||||||
\(806\) | −2019.03 | −0.0882350 | ||||||||
\(807\) | −24736.9 | −1.07903 | ||||||||
\(808\) | −757.447 | −0.0329788 | ||||||||
\(809\) | 25725.0 | 1.11797 | 0.558987 | − | 0.829176i | \(-0.311190\pi\) | ||||
0.558987 | + | 0.829176i | \(0.311190\pi\) | |||||||
\(810\) | −2654.88 | −0.115164 | ||||||||
\(811\) | 12076.9 | 0.522908 | 0.261454 | − | 0.965216i | \(-0.415798\pi\) | ||||
0.261454 | + | 0.965216i | \(0.415798\pi\) | |||||||
\(812\) | −10826.8 | −0.467914 | ||||||||
\(813\) | −676.744 | −0.0291937 | ||||||||
\(814\) | −213.184 | −0.00917948 | ||||||||
\(815\) | −29040.9 | −1.24817 | ||||||||
\(816\) | −48463.5 | −2.07912 | ||||||||
\(817\) | −27066.7 | −1.15905 | ||||||||
\(818\) | −995.919 | −0.0425691 | ||||||||
\(819\) | 11263.5 | 0.480560 | ||||||||
\(820\) | −30586.3 | −1.30258 | ||||||||
\(821\) | −5025.21 | −0.213619 | −0.106809 | − | 0.994280i | \(-0.534063\pi\) | ||||
−0.106809 | + | 0.994280i | \(0.534063\pi\) | |||||||
\(822\) | −5090.46 | −0.215998 | ||||||||
\(823\) | −6388.20 | −0.270569 | −0.135285 | − | 0.990807i | \(-0.543195\pi\) | ||||
−0.135285 | + | 0.990807i | \(0.543195\pi\) | |||||||
\(824\) | 6936.50 | 0.293258 | ||||||||
\(825\) | 4666.66 | 0.196936 | ||||||||
\(826\) | 384.107 | 0.0161801 | ||||||||
\(827\) | 3250.99 | 0.136697 | 0.0683483 | − | 0.997662i | \(-0.478227\pi\) | ||||
0.0683483 | + | 0.997662i | \(0.478227\pi\) | |||||||
\(828\) | 3822.15 | 0.160421 | ||||||||
\(829\) | −26138.3 | −1.09508 | −0.547540 | − | 0.836780i | \(-0.684435\pi\) | ||||
−0.547540 | + | 0.836780i | \(0.684435\pi\) | |||||||
\(830\) | 633.230 | 0.0264816 | ||||||||
\(831\) | 32993.5 | 1.37730 | ||||||||
\(832\) | 37258.5 | 1.55253 | ||||||||
\(833\) | 5502.43 | 0.228869 | ||||||||
\(834\) | −111.793 | −0.00464156 | ||||||||
\(835\) | −5161.55 | −0.213920 | ||||||||
\(836\) | 43126.3 | 1.78416 | ||||||||
\(837\) | −4154.55 | −0.171568 | ||||||||
\(838\) | 2018.48 | 0.0832066 | ||||||||
\(839\) | 23507.5 | 0.967307 | 0.483654 | − | 0.875260i | \(-0.339309\pi\) | ||||
0.483654 | + | 0.875260i | \(0.339309\pi\) | |||||||
\(840\) | −2395.97 | −0.0984151 | ||||||||
\(841\) | 13654.2 | 0.559849 | ||||||||
\(842\) | −393.997 | −0.0161259 | ||||||||
\(843\) | 20090.3 | 0.820813 | ||||||||
\(844\) | −9907.42 | −0.404061 | ||||||||
\(845\) | −43320.1 | −1.76362 | ||||||||
\(846\) | 22.7140 | 0.000923076 0 | ||||||||
\(847\) | −12060.3 | −0.489252 | ||||||||
\(848\) | −15866.5 | −0.642520 | ||||||||
\(849\) | 20881.7 | 0.844118 | ||||||||
\(850\) | −362.739 | −0.0146375 | ||||||||
\(851\) | 334.946 | 0.0134921 | ||||||||
\(852\) | 58167.2 | 2.33894 | ||||||||
\(853\) | 19853.1 | 0.796901 | 0.398450 | − | 0.917190i | \(-0.369548\pi\) | ||||
0.398450 | + | 0.917190i | \(0.369548\pi\) | |||||||
\(854\) | 1338.12 | 0.0536176 | ||||||||
\(855\) | −24156.6 | −0.966244 | ||||||||
\(856\) | −4189.00 | −0.167263 | ||||||||
\(857\) | 16851.3 | 0.671678 | 0.335839 | − | 0.941919i | \(-0.390980\pi\) | ||||
0.335839 | + | 0.941919i | \(0.390980\pi\) | |||||||
\(858\) | 7783.77 | 0.309713 | ||||||||
\(859\) | 36623.8 | 1.45470 | 0.727350 | − | 0.686267i | \(-0.240752\pi\) | ||||
0.727350 | + | 0.686267i | \(0.240752\pi\) | |||||||
\(860\) | −25545.5 | −1.01290 | ||||||||
\(861\) | −15963.1 | −0.631846 | ||||||||
\(862\) | 701.795 | 0.0277300 | ||||||||
\(863\) | −93.2237 | −0.00367714 | −0.00183857 | − | 0.999998i | \(-0.500585\pi\) | ||||
−0.00183857 | + | 0.999998i | \(0.500585\pi\) | |||||||
\(864\) | −2103.80 | −0.0828387 | ||||||||
\(865\) | 36445.2 | 1.43257 | ||||||||
\(866\) | 1119.19 | 0.0439164 | ||||||||
\(867\) | −53302.4 | −2.08794 | ||||||||
\(868\) | −5510.18 | −0.215470 | ||||||||
\(869\) | −46939.7 | −1.83236 | ||||||||
\(870\) | 4190.92 | 0.163317 | ||||||||
\(871\) | 39525.8 | 1.53764 | ||||||||
\(872\) | 89.9251 | 0.00349226 | ||||||||
\(873\) | 20725.6 | 0.803499 | ||||||||
\(874\) | 599.597 | 0.0232056 | ||||||||
\(875\) | −9249.05 | −0.357343 | ||||||||
\(876\) | −20654.9 | −0.796651 | ||||||||
\(877\) | 30806.3 | 1.18615 | 0.593075 | − | 0.805147i | \(-0.297914\pi\) | ||||
0.593075 | + | 0.805147i | \(0.297914\pi\) | |||||||
\(878\) | 3928.96 | 0.151020 | ||||||||
\(879\) | −19019.7 | −0.729827 | ||||||||
\(880\) | 40339.3 | 1.54527 | ||||||||
\(881\) | 30300.4 | 1.15874 | 0.579369 | − | 0.815066i | \(-0.303299\pi\) | ||||
0.579369 | + | 0.815066i | \(0.303299\pi\) | |||||||
\(882\) | −272.015 | −0.0103846 | ||||||||
\(883\) | −23271.1 | −0.886902 | −0.443451 | − | 0.896299i | \(-0.646246\pi\) | ||||
−0.443451 | + | 0.896299i | \(0.646246\pi\) | |||||||
\(884\) | 68372.5 | 2.60137 | ||||||||
\(885\) | 16802.1 | 0.638190 | ||||||||
\(886\) | 1246.28 | 0.0472567 | ||||||||
\(887\) | −1751.59 | −0.0663053 | −0.0331526 | − | 0.999450i | \(-0.510555\pi\) | ||||
−0.0331526 | + | 0.999450i | \(0.510555\pi\) | |||||||
\(888\) | 425.561 | 0.0160821 | ||||||||
\(889\) | 6723.63 | 0.253660 | ||||||||
\(890\) | −1959.33 | −0.0737944 | ||||||||
\(891\) | 47285.1 | 1.77790 | ||||||||
\(892\) | −33068.5 | −1.24127 | ||||||||
\(893\) | −402.669 | −0.0150894 | ||||||||
\(894\) | −1146.68 | −0.0428978 | ||||||||
\(895\) | −21623.0 | −0.807573 | ||||||||
\(896\) | −3714.75 | −0.138506 | ||||||||
\(897\) | −12229.5 | −0.455220 | ||||||||
\(898\) | −13.1417 | −0.000488357 0 | ||||||||
\(899\) | 19361.6 | 0.718295 | ||||||||
\(900\) | −2026.45 | −0.0750536 | ||||||||
\(901\) | −28589.4 | −1.05711 | ||||||||
\(902\) | −4820.62 | −0.177948 | ||||||||
\(903\) | −13332.3 | −0.491329 | ||||||||
\(904\) | 2590.66 | 0.0953143 | ||||||||
\(905\) | 23664.0 | 0.869192 | ||||||||
\(906\) | 4157.04 | 0.152437 | ||||||||
\(907\) | 38409.6 | 1.40614 | 0.703071 | − | 0.711120i | \(-0.251812\pi\) | ||||
0.703071 | + | 0.711120i | \(0.251812\pi\) | |||||||
\(908\) | 25850.4 | 0.944797 | ||||||||
\(909\) | −3761.64 | −0.137256 | ||||||||
\(910\) | 1667.65 | 0.0607496 | ||||||||
\(911\) | −45581.0 | −1.65770 | −0.828850 | − | 0.559471i | \(-0.811004\pi\) | ||||
−0.828850 | + | 0.559471i | \(0.811004\pi\) | |||||||
\(912\) | −42472.5 | −1.54211 | ||||||||
\(913\) | −11278.2 | −0.408822 | ||||||||
\(914\) | 1662.90 | 0.0601793 | ||||||||
\(915\) | 58533.9 | 2.11483 | ||||||||
\(916\) | −29459.8 | −1.06264 | ||||||||
\(917\) | 13939.6 | 0.501990 | ||||||||
\(918\) | −1244.97 | −0.0447604 | ||||||||
\(919\) | −44113.8 | −1.58344 | −0.791718 | − | 0.610886i | \(-0.790813\pi\) | ||||
−0.791718 | + | 0.610886i | \(0.790813\pi\) | |||||||
\(920\) | 1136.81 | 0.0407385 | ||||||||
\(921\) | −68274.0 | −2.44268 | ||||||||
\(922\) | 2951.02 | 0.105409 | ||||||||
\(923\) | −81330.0 | −2.90033 | ||||||||
\(924\) | 21242.8 | 0.756318 | ||||||||
\(925\) | −177.583 | −0.00631233 | ||||||||
\(926\) | 1807.10 | 0.0641308 | ||||||||
\(927\) | 34448.1 | 1.22052 | ||||||||
\(928\) | 9804.42 | 0.346817 | ||||||||
\(929\) | −14983.8 | −0.529173 | −0.264587 | − | 0.964362i | \(-0.585236\pi\) | ||||
−0.264587 | + | 0.964362i | \(0.585236\pi\) | |||||||
\(930\) | 2132.92 | 0.0752058 | ||||||||
\(931\) | 4822.23 | 0.169755 | ||||||||
\(932\) | 46399.7 | 1.63076 | ||||||||
\(933\) | 38391.2 | 1.34713 | ||||||||
\(934\) | −893.861 | −0.0313148 | ||||||||
\(935\) | 72686.5 | 2.54235 | ||||||||
\(936\) | −6789.96 | −0.237112 | ||||||||
\(937\) | 14492.9 | 0.505295 | 0.252647 | − | 0.967558i | \(-0.418699\pi\) | ||||
0.252647 | + | 0.967558i | \(0.418699\pi\) | |||||||
\(938\) | −954.552 | −0.0332273 | ||||||||
\(939\) | 56850.2 | 1.97576 | ||||||||
\(940\) | −380.039 | −0.0131867 | ||||||||
\(941\) | 39590.2 | 1.37152 | 0.685762 | − | 0.727826i | \(-0.259469\pi\) | ||||
0.685762 | + | 0.727826i | \(0.259469\pi\) | |||||||
\(942\) | 4647.27 | 0.160739 | ||||||||
\(943\) | 7573.96 | 0.261550 | ||||||||
\(944\) | 12909.4 | 0.445091 | ||||||||
\(945\) | 3431.52 | 0.118124 | ||||||||
\(946\) | −4026.16 | −0.138374 | ||||||||
\(947\) | −7209.23 | −0.247380 | −0.123690 | − | 0.992321i | \(-0.539473\pi\) | ||||
−0.123690 | + | 0.992321i | \(0.539473\pi\) | |||||||
\(948\) | 46644.4 | 1.59804 | ||||||||
\(949\) | 28879.9 | 0.987863 | ||||||||
\(950\) | −317.897 | −0.0108568 | ||||||||
\(951\) | −2255.38 | −0.0769041 | ||||||||
\(952\) | −3317.02 | −0.112926 | ||||||||
\(953\) | −6893.39 | −0.234312 | −0.117156 | − | 0.993114i | \(-0.537378\pi\) | ||||
−0.117156 | + | 0.993114i | \(0.537378\pi\) | |||||||
\(954\) | 1413.33 | 0.0479647 | ||||||||
\(955\) | −3278.35 | −0.111084 | ||||||||
\(956\) | −18575.5 | −0.628424 | ||||||||
\(957\) | −74643.0 | −2.52128 | ||||||||
\(958\) | −2554.79 | −0.0861603 | ||||||||
\(959\) | 19424.6 | 0.654069 | ||||||||
\(960\) | −39360.2 | −1.32328 | ||||||||
\(961\) | −19937.1 | −0.669232 | ||||||||
\(962\) | −296.201 | −0.00992713 | ||||||||
\(963\) | −20803.4 | −0.696138 | ||||||||
\(964\) | −23904.5 | −0.798663 | ||||||||
\(965\) | 56723.6 | 1.89222 | ||||||||
\(966\) | 295.345 | 0.00983702 | ||||||||
\(967\) | 50638.5 | 1.68400 | 0.841998 | − | 0.539480i | \(-0.181379\pi\) | ||||
0.841998 | + | 0.539480i | \(0.181379\pi\) | |||||||
\(968\) | 7270.28 | 0.241400 | ||||||||
\(969\) | −76530.2 | −2.53716 | ||||||||
\(970\) | 3068.59 | 0.101574 | ||||||||
\(971\) | 27159.4 | 0.897619 | 0.448809 | − | 0.893628i | \(-0.351848\pi\) | ||||
0.448809 | + | 0.893628i | \(0.351848\pi\) | |||||||
\(972\) | −38026.9 | −1.25485 | ||||||||
\(973\) | 426.587 | 0.0140552 | ||||||||
\(974\) | −155.533 | −0.00511664 | ||||||||
\(975\) | 6483.92 | 0.212976 | ||||||||
\(976\) | 44972.7 | 1.47494 | ||||||||
\(977\) | −11109.1 | −0.363778 | −0.181889 | − | 0.983319i | \(-0.558221\pi\) | ||||
−0.181889 | + | 0.983319i | \(0.558221\pi\) | |||||||
\(978\) | 4548.27 | 0.148709 | ||||||||
\(979\) | 34897.0 | 1.13924 | ||||||||
\(980\) | 4551.22 | 0.148350 | ||||||||
\(981\) | 446.587 | 0.0145346 | ||||||||
\(982\) | −4723.47 | −0.153495 | ||||||||
\(983\) | 27203.6 | 0.882666 | 0.441333 | − | 0.897343i | \(-0.354506\pi\) | ||||
0.441333 | + | 0.897343i | \(0.354506\pi\) | |||||||
\(984\) | 9622.98 | 0.311758 | ||||||||
\(985\) | 33248.3 | 1.07551 | ||||||||
\(986\) | 5801.99 | 0.187397 | ||||||||
\(987\) | −198.343 | −0.00639649 | ||||||||
\(988\) | 59920.4 | 1.92947 | ||||||||
\(989\) | 6325.73 | 0.203384 | ||||||||
\(990\) | −3593.29 | −0.115356 | ||||||||
\(991\) | −30907.6 | −0.990729 | −0.495364 | − | 0.868685i | \(-0.664965\pi\) | ||||
−0.495364 | + | 0.868685i | \(0.664965\pi\) | |||||||
\(992\) | 4989.85 | 0.159706 | ||||||||
\(993\) | −25870.4 | −0.826760 | ||||||||
\(994\) | 1964.13 | 0.0626744 | ||||||||
\(995\) | −40406.7 | −1.28742 | ||||||||
\(996\) | 11207.3 | 0.356543 | ||||||||
\(997\) | 12224.2 | 0.388309 | 0.194154 | − | 0.980971i | \(-0.437804\pi\) | ||||
0.194154 | + | 0.980971i | \(0.437804\pi\) | |||||||
\(998\) | −1906.27 | −0.0604629 | ||||||||
\(999\) | −609.491 | −0.0193027 |
(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 | 161.4.a.c.1.5 | ✓ | 9 | |
3.2 | odd | 2 | 1449.4.a.n.1.5 | 9 | |||
7.6 | odd | 2 | 1127.4.a.f.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.4.a.c.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial | |
1127.4.a.f.1.5 | 9 | 7.6 | odd | 2 | |||
1449.4.a.n.1.5 | 9 | 3.2 | odd | 2 |