Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 7.15207 | 1.37642 | 0.688208 | − | 0.725513i | \(-0.258398\pi\) | ||||
0.688208 | + | 0.725513i | \(0.258398\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −8.30413 | −0.742744 | −0.371372 | − | 0.928484i | \(-0.621113\pi\) | ||||
−0.371372 | + | 0.928484i | \(0.621113\pi\) | |||||||
\(6\) | −14.3041 | −0.973273 | ||||||||
\(7\) | 35.1521 | 1.89803 | 0.949017 | − | 0.315226i | \(-0.102080\pi\) | ||||
0.949017 | + | 0.315226i | \(0.102080\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 24.1521 | 0.894521 | ||||||||
\(10\) | 16.6083 | 0.525200 | ||||||||
\(11\) | 18.3041 | 0.501719 | 0.250859 | − | 0.968024i | \(-0.419287\pi\) | ||||
0.250859 | + | 0.968024i | \(0.419287\pi\) | |||||||
\(12\) | 28.6083 | 0.688208 | ||||||||
\(13\) | −40.0645 | −0.854760 | −0.427380 | − | 0.904072i | \(-0.640563\pi\) | ||||
−0.427380 | + | 0.904072i | \(0.640563\pi\) | |||||||
\(14\) | −70.3041 | −1.34211 | ||||||||
\(15\) | −59.3917 | −1.02233 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −125.281 | −1.78736 | −0.893680 | − | 0.448706i | \(-0.851885\pi\) | ||||
−0.893680 | + | 0.448706i | \(0.851885\pi\) | |||||||
\(18\) | −48.3041 | −0.632522 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −33.2165 | −0.371372 | ||||||||
\(21\) | 251.410 | 2.61248 | ||||||||
\(22\) | −36.6083 | −0.354769 | ||||||||
\(23\) | 8.97688 | 0.0813830 | 0.0406915 | − | 0.999172i | \(-0.487044\pi\) | ||||
0.0406915 | + | 0.999172i | \(0.487044\pi\) | |||||||
\(24\) | −57.2165 | −0.486637 | ||||||||
\(25\) | −56.0413 | −0.448331 | ||||||||
\(26\) | 80.1289 | 0.604407 | ||||||||
\(27\) | −20.3686 | −0.145183 | ||||||||
\(28\) | 140.608 | 0.949017 | ||||||||
\(29\) | 153.410 | 0.982328 | 0.491164 | − | 0.871067i | \(-0.336572\pi\) | ||||
0.491164 | + | 0.871067i | \(0.336572\pi\) | |||||||
\(30\) | 118.783 | 0.722893 | ||||||||
\(31\) | −114.433 | −0.662993 | −0.331497 | − | 0.943456i | \(-0.607554\pi\) | ||||
−0.331497 | + | 0.943456i | \(0.607554\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 130.912 | 0.690573 | ||||||||
\(34\) | 250.562 | 1.26385 | ||||||||
\(35\) | −291.908 | −1.40975 | ||||||||
\(36\) | 96.6083 | 0.447261 | ||||||||
\(37\) | 83.5669 | 0.371306 | 0.185653 | − | 0.982615i | \(-0.440560\pi\) | ||||
0.185653 | + | 0.982615i | \(0.440560\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | −286.544 | −1.17651 | ||||||||
\(40\) | 66.4331 | 0.262600 | ||||||||
\(41\) | −355.088 | −1.35257 | −0.676285 | − | 0.736640i | \(-0.736411\pi\) | ||||
−0.676285 | + | 0.736640i | \(0.736411\pi\) | |||||||
\(42\) | −502.820 | −1.84730 | ||||||||
\(43\) | 467.299 | 1.65727 | 0.828633 | − | 0.559792i | \(-0.189119\pi\) | ||||
0.828633 | + | 0.559792i | \(0.189119\pi\) | |||||||
\(44\) | 73.2165 | 0.250859 | ||||||||
\(45\) | −200.562 | −0.664400 | ||||||||
\(46\) | −17.9538 | −0.0575464 | ||||||||
\(47\) | 166.083 | 0.515439 | 0.257720 | − | 0.966220i | \(-0.417029\pi\) | ||||
0.257720 | + | 0.966220i | \(0.417029\pi\) | |||||||
\(48\) | 114.433 | 0.344104 | ||||||||
\(49\) | 892.668 | 2.60253 | ||||||||
\(50\) | 112.083 | 0.317018 | ||||||||
\(51\) | −896.018 | −2.46015 | ||||||||
\(52\) | −160.258 | −0.427380 | ||||||||
\(53\) | 258.369 | 0.669616 | 0.334808 | − | 0.942286i | \(-0.391329\pi\) | ||||
0.334808 | + | 0.942286i | \(0.391329\pi\) | |||||||
\(54\) | 40.7372 | 0.102660 | ||||||||
\(55\) | −152.000 | −0.372649 | ||||||||
\(56\) | −281.217 | −0.671056 | ||||||||
\(57\) | −135.889 | −0.315771 | ||||||||
\(58\) | −306.820 | −0.694611 | ||||||||
\(59\) | −371.797 | −0.820404 | −0.410202 | − | 0.911995i | \(-0.634542\pi\) | ||||
−0.410202 | + | 0.911995i | \(0.634542\pi\) | |||||||
\(60\) | −237.567 | −0.511163 | ||||||||
\(61\) | −47.3090 | −0.0993000 | −0.0496500 | − | 0.998767i | \(-0.515811\pi\) | ||||
−0.0496500 | + | 0.998767i | \(0.515811\pi\) | |||||||
\(62\) | 228.866 | 0.468807 | ||||||||
\(63\) | 848.995 | 1.69783 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 332.701 | 0.634868 | ||||||||
\(66\) | −261.825 | −0.488309 | ||||||||
\(67\) | −755.539 | −1.37767 | −0.688834 | − | 0.724919i | \(-0.741877\pi\) | ||||
−0.688834 | + | 0.724919i | \(0.741877\pi\) | |||||||
\(68\) | −501.124 | −0.893680 | ||||||||
\(69\) | 64.2032 | 0.112017 | ||||||||
\(70\) | 583.815 | 0.996846 | ||||||||
\(71\) | 349.345 | 0.583939 | 0.291970 | − | 0.956428i | \(-0.405689\pi\) | ||||
0.291970 | + | 0.956428i | \(0.405689\pi\) | |||||||
\(72\) | −193.217 | −0.316261 | ||||||||
\(73\) | 54.8479 | 0.0879379 | 0.0439689 | − | 0.999033i | \(-0.486000\pi\) | ||||
0.0439689 | + | 0.999033i | \(0.486000\pi\) | |||||||
\(74\) | −167.134 | −0.262553 | ||||||||
\(75\) | −400.811 | −0.617090 | ||||||||
\(76\) | −76.0000 | −0.114708 | ||||||||
\(77\) | 643.428 | 0.952279 | ||||||||
\(78\) | 573.088 | 0.831915 | ||||||||
\(79\) | 438.820 | 0.624951 | 0.312475 | − | 0.949926i | \(-0.398842\pi\) | ||||
0.312475 | + | 0.949926i | \(0.398842\pi\) | |||||||
\(80\) | −132.866 | −0.185686 | ||||||||
\(81\) | −797.783 | −1.09435 | ||||||||
\(82\) | 710.175 | 0.956411 | ||||||||
\(83\) | 1073.09 | 1.41912 | 0.709558 | − | 0.704647i | \(-0.248895\pi\) | ||||
0.709558 | + | 0.704647i | \(0.248895\pi\) | |||||||
\(84\) | 1005.64 | 1.30624 | ||||||||
\(85\) | 1040.35 | 1.32755 | ||||||||
\(86\) | −934.598 | −1.17186 | ||||||||
\(87\) | 1097.20 | 1.35209 | ||||||||
\(88\) | −146.433 | −0.177384 | ||||||||
\(89\) | −501.521 | −0.597316 | −0.298658 | − | 0.954360i | \(-0.596539\pi\) | ||||
−0.298658 | + | 0.954360i | \(0.596539\pi\) | |||||||
\(90\) | 401.124 | 0.469802 | ||||||||
\(91\) | −1408.35 | −1.62236 | ||||||||
\(92\) | 35.9075 | 0.0406915 | ||||||||
\(93\) | −818.433 | −0.912554 | ||||||||
\(94\) | −332.165 | −0.364471 | ||||||||
\(95\) | 157.779 | 0.170397 | ||||||||
\(96\) | −228.866 | −0.243318 | ||||||||
\(97\) | −1437.56 | −1.50476 | −0.752380 | − | 0.658729i | \(-0.771094\pi\) | ||||
−0.752380 | + | 0.658729i | \(0.771094\pi\) | |||||||
\(98\) | −1785.34 | −1.84027 | ||||||||
\(99\) | 442.083 | 0.448798 | ||||||||
\(100\) | −224.165 | −0.224165 | ||||||||
\(101\) | 395.124 | 0.389270 | 0.194635 | − | 0.980876i | \(-0.437648\pi\) | ||||
0.194635 | + | 0.980876i | \(0.437648\pi\) | |||||||
\(102\) | 1792.04 | 1.73959 | ||||||||
\(103\) | 1285.68 | 1.22992 | 0.614958 | − | 0.788559i | \(-0.289173\pi\) | ||||
0.614958 | + | 0.788559i | \(0.289173\pi\) | |||||||
\(104\) | 320.516 | 0.302203 | ||||||||
\(105\) | −2087.74 | −1.94041 | ||||||||
\(106\) | −516.737 | −0.473490 | ||||||||
\(107\) | 1203.10 | 1.08699 | 0.543494 | − | 0.839413i | \(-0.317101\pi\) | ||||
0.543494 | + | 0.839413i | \(0.317101\pi\) | |||||||
\(108\) | −81.4744 | −0.0725915 | ||||||||
\(109\) | −1333.74 | −1.17201 | −0.586005 | − | 0.810307i | \(-0.699300\pi\) | ||||
−0.586005 | + | 0.810307i | \(0.699300\pi\) | |||||||
\(110\) | 304.000 | 0.263502 | ||||||||
\(111\) | 597.676 | 0.511071 | ||||||||
\(112\) | 562.433 | 0.474508 | ||||||||
\(113\) | 836.506 | 0.696388 | 0.348194 | − | 0.937422i | \(-0.386795\pi\) | ||||
0.348194 | + | 0.937422i | \(0.386795\pi\) | |||||||
\(114\) | 271.779 | 0.223284 | ||||||||
\(115\) | −74.5452 | −0.0604467 | ||||||||
\(116\) | 613.640 | 0.491164 | ||||||||
\(117\) | −967.640 | −0.764601 | ||||||||
\(118\) | 743.594 | 0.580113 | ||||||||
\(119\) | −4403.89 | −3.39247 | ||||||||
\(120\) | 475.134 | 0.361447 | ||||||||
\(121\) | −995.959 | −0.748278 | ||||||||
\(122\) | 94.6181 | 0.0702157 | ||||||||
\(123\) | −2539.61 | −1.86170 | ||||||||
\(124\) | −457.732 | −0.331497 | ||||||||
\(125\) | 1503.39 | 1.07574 | ||||||||
\(126\) | −1697.99 | −1.20055 | ||||||||
\(127\) | −385.954 | −0.269668 | −0.134834 | − | 0.990868i | \(-0.543050\pi\) | ||||
−0.134834 | + | 0.990868i | \(0.543050\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 3342.16 | 2.28109 | ||||||||
\(130\) | −665.402 | −0.448920 | ||||||||
\(131\) | 1737.90 | 1.15909 | 0.579545 | − | 0.814940i | \(-0.303230\pi\) | ||||
0.579545 | + | 0.814940i | \(0.303230\pi\) | |||||||
\(132\) | 523.650 | 0.345287 | ||||||||
\(133\) | −667.889 | −0.435439 | ||||||||
\(134\) | 1511.08 | 0.974159 | ||||||||
\(135\) | 169.144 | 0.107834 | ||||||||
\(136\) | 1002.25 | 0.631927 | ||||||||
\(137\) | 41.7603 | 0.0260425 | 0.0130213 | − | 0.999915i | \(-0.495855\pi\) | ||||
0.0130213 | + | 0.999915i | \(0.495855\pi\) | |||||||
\(138\) | −128.406 | −0.0792078 | ||||||||
\(139\) | 1536.79 | 0.937763 | 0.468882 | − | 0.883261i | \(-0.344657\pi\) | ||||
0.468882 | + | 0.883261i | \(0.344657\pi\) | |||||||
\(140\) | −1167.63 | −0.704877 | ||||||||
\(141\) | 1187.83 | 0.709459 | ||||||||
\(142\) | −698.691 | −0.412907 | ||||||||
\(143\) | −733.345 | −0.428849 | ||||||||
\(144\) | 386.433 | 0.223630 | ||||||||
\(145\) | −1273.94 | −0.729619 | ||||||||
\(146\) | −109.696 | −0.0621815 | ||||||||
\(147\) | 6384.42 | 3.58216 | ||||||||
\(148\) | 334.268 | 0.185653 | ||||||||
\(149\) | 1656.65 | 0.910862 | 0.455431 | − | 0.890271i | \(-0.349485\pi\) | ||||
0.455431 | + | 0.890271i | \(0.349485\pi\) | |||||||
\(150\) | 801.623 | 0.436348 | ||||||||
\(151\) | −714.985 | −0.385329 | −0.192664 | − | 0.981265i | \(-0.561713\pi\) | ||||
−0.192664 | + | 0.981265i | \(0.561713\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | −3025.80 | −1.59883 | ||||||||
\(154\) | −1286.86 | −0.673363 | ||||||||
\(155\) | 950.268 | 0.492434 | ||||||||
\(156\) | −1146.18 | −0.588253 | ||||||||
\(157\) | 1684.23 | 0.856153 | 0.428077 | − | 0.903742i | \(-0.359191\pi\) | ||||
0.428077 | + | 0.903742i | \(0.359191\pi\) | |||||||
\(158\) | −877.640 | −0.441907 | ||||||||
\(159\) | 1847.87 | 0.921670 | ||||||||
\(160\) | 265.732 | 0.131300 | ||||||||
\(161\) | 315.556 | 0.154468 | ||||||||
\(162\) | 1595.57 | 0.773825 | ||||||||
\(163\) | 702.175 | 0.337415 | 0.168707 | − | 0.985666i | \(-0.446041\pi\) | ||||
0.168707 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(164\) | −1420.35 | −0.676285 | ||||||||
\(165\) | −1087.11 | −0.512920 | ||||||||
\(166\) | −2146.18 | −1.00347 | ||||||||
\(167\) | −282.506 | −0.130904 | −0.0654520 | − | 0.997856i | \(-0.520849\pi\) | ||||
−0.0654520 | + | 0.997856i | \(0.520849\pi\) | |||||||
\(168\) | −2011.28 | −0.923652 | ||||||||
\(169\) | −591.838 | −0.269385 | ||||||||
\(170\) | −2080.70 | −0.938720 | ||||||||
\(171\) | −458.889 | −0.205217 | ||||||||
\(172\) | 1869.20 | 0.828633 | ||||||||
\(173\) | 2183.44 | 0.959558 | 0.479779 | − | 0.877389i | \(-0.340717\pi\) | ||||
0.479779 | + | 0.877389i | \(0.340717\pi\) | |||||||
\(174\) | −2194.40 | −0.956073 | ||||||||
\(175\) | −1969.97 | −0.850947 | ||||||||
\(176\) | 292.866 | 0.125430 | ||||||||
\(177\) | −2659.12 | −1.12922 | ||||||||
\(178\) | 1003.04 | 0.422366 | ||||||||
\(179\) | −3198.51 | −1.33557 | −0.667786 | − | 0.744353i | \(-0.732758\pi\) | ||||
−0.667786 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(180\) | −802.248 | −0.332200 | ||||||||
\(181\) | −2151.05 | −0.883350 | −0.441675 | − | 0.897175i | \(-0.645616\pi\) | ||||
−0.441675 | + | 0.897175i | \(0.645616\pi\) | |||||||
\(182\) | 2816.70 | 1.14718 | ||||||||
\(183\) | −338.357 | −0.136678 | ||||||||
\(184\) | −71.8150 | −0.0287732 | ||||||||
\(185\) | −693.951 | −0.275785 | ||||||||
\(186\) | 1636.87 | 0.645273 | ||||||||
\(187\) | −2293.16 | −0.896751 | ||||||||
\(188\) | 664.331 | 0.257720 | ||||||||
\(189\) | −715.999 | −0.275562 | ||||||||
\(190\) | −315.557 | −0.120489 | ||||||||
\(191\) | −4435.52 | −1.68033 | −0.840165 | − | 0.542331i | \(-0.817542\pi\) | ||||
−0.840165 | + | 0.542331i | \(0.817542\pi\) | |||||||
\(192\) | 457.732 | 0.172052 | ||||||||
\(193\) | 2720.60 | 1.01468 | 0.507339 | − | 0.861746i | \(-0.330629\pi\) | ||||
0.507339 | + | 0.861746i | \(0.330629\pi\) | |||||||
\(194\) | 2875.11 | 1.06403 | ||||||||
\(195\) | 2379.50 | 0.873843 | ||||||||
\(196\) | 3570.67 | 1.30127 | ||||||||
\(197\) | 1254.08 | 0.453549 | 0.226775 | − | 0.973947i | \(-0.427182\pi\) | ||||
0.226775 | + | 0.973947i | \(0.427182\pi\) | |||||||
\(198\) | −884.165 | −0.317348 | ||||||||
\(199\) | 4155.19 | 1.48017 | 0.740084 | − | 0.672515i | \(-0.234786\pi\) | ||||
0.740084 | + | 0.672515i | \(0.234786\pi\) | |||||||
\(200\) | 448.331 | 0.158509 | ||||||||
\(201\) | −5403.67 | −1.89624 | ||||||||
\(202\) | −790.248 | −0.275256 | ||||||||
\(203\) | 5392.68 | 1.86449 | ||||||||
\(204\) | −3584.07 | −1.23007 | ||||||||
\(205\) | 2948.70 | 1.00461 | ||||||||
\(206\) | −2571.35 | −0.869683 | ||||||||
\(207\) | 216.810 | 0.0727988 | ||||||||
\(208\) | −641.032 | −0.213690 | ||||||||
\(209\) | −347.779 | −0.115102 | ||||||||
\(210\) | 4175.48 | 1.37208 | ||||||||
\(211\) | −633.437 | −0.206671 | −0.103335 | − | 0.994647i | \(-0.532952\pi\) | ||||
−0.103335 | + | 0.994647i | \(0.532952\pi\) | |||||||
\(212\) | 1033.47 | 0.334808 | ||||||||
\(213\) | 2498.54 | 0.803743 | ||||||||
\(214\) | −2406.19 | −0.768616 | ||||||||
\(215\) | −3880.52 | −1.23093 | ||||||||
\(216\) | 162.949 | 0.0513299 | ||||||||
\(217\) | −4022.56 | −1.25838 | ||||||||
\(218\) | 2667.48 | 0.828737 | ||||||||
\(219\) | 392.276 | 0.121039 | ||||||||
\(220\) | −608.000 | −0.186324 | ||||||||
\(221\) | 5019.32 | 1.52776 | ||||||||
\(222\) | −1195.35 | −0.361382 | ||||||||
\(223\) | −4798.34 | −1.44090 | −0.720449 | − | 0.693507i | \(-0.756064\pi\) | ||||
−0.720449 | + | 0.693507i | \(0.756064\pi\) | |||||||
\(224\) | −1124.87 | −0.335528 | ||||||||
\(225\) | −1353.51 | −0.401041 | ||||||||
\(226\) | −1673.01 | −0.492421 | ||||||||
\(227\) | 641.770 | 0.187647 | 0.0938233 | − | 0.995589i | \(-0.470091\pi\) | ||||
0.0938233 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(228\) | −543.557 | −0.157886 | ||||||||
\(229\) | −1231.34 | −0.355325 | −0.177662 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177662 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(230\) | 149.090 | 0.0427423 | ||||||||
\(231\) | 4601.84 | 1.31073 | ||||||||
\(232\) | −1227.28 | −0.347305 | ||||||||
\(233\) | 226.701 | 0.0637410 | 0.0318705 | − | 0.999492i | \(-0.489854\pi\) | ||||
0.0318705 | + | 0.999492i | \(0.489854\pi\) | |||||||
\(234\) | 1935.28 | 0.540655 | ||||||||
\(235\) | −1379.17 | −0.382840 | ||||||||
\(236\) | −1487.19 | −0.410202 | ||||||||
\(237\) | 3138.47 | 0.860192 | ||||||||
\(238\) | 8807.77 | 2.39884 | ||||||||
\(239\) | 2433.27 | 0.658557 | 0.329278 | − | 0.944233i | \(-0.393195\pi\) | ||||
0.329278 | + | 0.944233i | \(0.393195\pi\) | |||||||
\(240\) | −950.268 | −0.255581 | ||||||||
\(241\) | −901.336 | −0.240913 | −0.120457 | − | 0.992719i | \(-0.538436\pi\) | ||||
−0.120457 | + | 0.992719i | \(0.538436\pi\) | |||||||
\(242\) | 1991.92 | 0.529113 | ||||||||
\(243\) | −5155.85 | −1.36110 | ||||||||
\(244\) | −189.236 | −0.0496500 | ||||||||
\(245\) | −7412.83 | −1.93301 | ||||||||
\(246\) | 5079.22 | 1.31642 | ||||||||
\(247\) | 761.225 | 0.196095 | ||||||||
\(248\) | 915.465 | 0.234403 | ||||||||
\(249\) | 7674.79 | 1.95329 | ||||||||
\(250\) | −3006.78 | −0.760663 | ||||||||
\(251\) | −5675.92 | −1.42734 | −0.713668 | − | 0.700484i | \(-0.752967\pi\) | ||||
−0.713668 | + | 0.700484i | \(0.752967\pi\) | |||||||
\(252\) | 3395.98 | 0.848915 | ||||||||
\(253\) | 164.314 | 0.0408313 | ||||||||
\(254\) | 771.908 | 0.190684 | ||||||||
\(255\) | 7440.66 | 1.82726 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2035.88 | 0.494143 | 0.247072 | − | 0.968997i | \(-0.420532\pi\) | ||||
0.247072 | + | 0.968997i | \(0.420532\pi\) | |||||||
\(258\) | −6684.31 | −1.61297 | ||||||||
\(259\) | 2937.55 | 0.704751 | ||||||||
\(260\) | 1330.80 | 0.317434 | ||||||||
\(261\) | 3705.17 | 0.878713 | ||||||||
\(262\) | −3475.80 | −0.819601 | ||||||||
\(263\) | 1924.20 | 0.451147 | 0.225573 | − | 0.974226i | \(-0.427574\pi\) | ||||
0.225573 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(264\) | −1047.30 | −0.244155 | ||||||||
\(265\) | −2145.53 | −0.497354 | ||||||||
\(266\) | 1335.78 | 0.307902 | ||||||||
\(267\) | −3586.91 | −0.822155 | ||||||||
\(268\) | −3022.16 | −0.688834 | ||||||||
\(269\) | −829.280 | −0.187963 | −0.0939815 | − | 0.995574i | \(-0.529959\pi\) | ||||
−0.0939815 | + | 0.995574i | \(0.529959\pi\) | |||||||
\(270\) | −338.287 | −0.0762500 | ||||||||
\(271\) | −1223.13 | −0.274169 | −0.137085 | − | 0.990559i | \(-0.543773\pi\) | ||||
−0.137085 | + | 0.990559i | \(0.543773\pi\) | |||||||
\(272\) | −2004.50 | −0.446840 | ||||||||
\(273\) | −10072.6 | −2.23305 | ||||||||
\(274\) | −83.5207 | −0.0184148 | ||||||||
\(275\) | −1025.79 | −0.224936 | ||||||||
\(276\) | 256.813 | 0.0560084 | ||||||||
\(277\) | 1622.81 | 0.352004 | 0.176002 | − | 0.984390i | \(-0.443683\pi\) | ||||
0.176002 | + | 0.984390i | \(0.443683\pi\) | |||||||
\(278\) | −3073.59 | −0.663099 | ||||||||
\(279\) | −2763.80 | −0.593061 | ||||||||
\(280\) | 2335.26 | 0.498423 | ||||||||
\(281\) | 3618.96 | 0.768288 | 0.384144 | − | 0.923273i | \(-0.374497\pi\) | ||||
0.384144 | + | 0.923273i | \(0.374497\pi\) | |||||||
\(282\) | −2375.67 | −0.501663 | ||||||||
\(283\) | 2102.43 | 0.441613 | 0.220807 | − | 0.975318i | \(-0.429131\pi\) | ||||
0.220807 | + | 0.975318i | \(0.429131\pi\) | |||||||
\(284\) | 1397.38 | 0.291970 | ||||||||
\(285\) | 1128.44 | 0.234537 | ||||||||
\(286\) | 1466.69 | 0.303242 | ||||||||
\(287\) | −12482.1 | −2.56722 | ||||||||
\(288\) | −772.866 | −0.158130 | ||||||||
\(289\) | 10782.3 | 2.19465 | ||||||||
\(290\) | 2547.87 | 0.515918 | ||||||||
\(291\) | −10281.5 | −2.07118 | ||||||||
\(292\) | 219.392 | 0.0439689 | ||||||||
\(293\) | −5383.99 | −1.07350 | −0.536751 | − | 0.843741i | \(-0.680348\pi\) | ||||
−0.536751 | + | 0.843741i | \(0.680348\pi\) | |||||||
\(294\) | −12768.8 | −2.53297 | ||||||||
\(295\) | 3087.45 | 0.609350 | ||||||||
\(296\) | −668.535 | −0.131276 | ||||||||
\(297\) | −372.830 | −0.0728410 | ||||||||
\(298\) | −3313.31 | −0.644077 | ||||||||
\(299\) | −359.654 | −0.0695629 | ||||||||
\(300\) | −1603.25 | −0.308545 | ||||||||
\(301\) | 16426.5 | 3.14555 | ||||||||
\(302\) | 1429.97 | 0.272469 | ||||||||
\(303\) | 2825.95 | 0.535798 | ||||||||
\(304\) | −304.000 | −0.0573539 | ||||||||
\(305\) | 392.861 | 0.0737545 | ||||||||
\(306\) | 6051.59 | 1.13054 | ||||||||
\(307\) | 3692.85 | 0.686521 | 0.343260 | − | 0.939240i | \(-0.388469\pi\) | ||||
0.343260 | + | 0.939240i | \(0.388469\pi\) | |||||||
\(308\) | 2573.71 | 0.476139 | ||||||||
\(309\) | 9195.24 | 1.69288 | ||||||||
\(310\) | −1900.54 | −0.348204 | ||||||||
\(311\) | −4427.67 | −0.807299 | −0.403649 | − | 0.914914i | \(-0.632258\pi\) | ||||
−0.403649 | + | 0.914914i | \(0.632258\pi\) | |||||||
\(312\) | 2292.35 | 0.415958 | ||||||||
\(313\) | −7356.47 | −1.32847 | −0.664236 | − | 0.747523i | \(-0.731243\pi\) | ||||
−0.664236 | + | 0.747523i | \(0.731243\pi\) | |||||||
\(314\) | −3368.46 | −0.605392 | ||||||||
\(315\) | −7050.17 | −1.26105 | ||||||||
\(316\) | 1755.28 | 0.312475 | ||||||||
\(317\) | 1612.77 | 0.285747 | 0.142874 | − | 0.989741i | \(-0.454366\pi\) | ||||
0.142874 | + | 0.989741i | \(0.454366\pi\) | |||||||
\(318\) | −3695.74 | −0.651719 | ||||||||
\(319\) | 2808.04 | 0.492852 | ||||||||
\(320\) | −531.465 | −0.0928430 | ||||||||
\(321\) | 8604.62 | 1.49615 | ||||||||
\(322\) | −631.111 | −0.109225 | ||||||||
\(323\) | 2380.34 | 0.410048 | ||||||||
\(324\) | −3191.13 | −0.547177 | ||||||||
\(325\) | 2245.27 | 0.383215 | ||||||||
\(326\) | −1404.35 | −0.238588 | ||||||||
\(327\) | −9539.00 | −1.61317 | ||||||||
\(328\) | 2840.70 | 0.478206 | ||||||||
\(329\) | 5838.15 | 0.978321 | ||||||||
\(330\) | 2174.23 | 0.362689 | ||||||||
\(331\) | −2262.78 | −0.375752 | −0.187876 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187876 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(332\) | 4292.35 | 0.709558 | ||||||||
\(333\) | 2018.31 | 0.332141 | ||||||||
\(334\) | 565.012 | 0.0925631 | ||||||||
\(335\) | 6274.10 | 1.02326 | ||||||||
\(336\) | 4022.56 | 0.653121 | ||||||||
\(337\) | −2037.63 | −0.329367 | −0.164683 | − | 0.986346i | \(-0.552660\pi\) | ||||
−0.164683 | + | 0.986346i | \(0.552660\pi\) | |||||||
\(338\) | 1183.68 | 0.190484 | ||||||||
\(339\) | 5982.75 | 0.958520 | ||||||||
\(340\) | 4161.40 | 0.663776 | ||||||||
\(341\) | −2094.60 | −0.332636 | ||||||||
\(342\) | 917.779 | 0.145110 | ||||||||
\(343\) | 19322.0 | 3.04166 | ||||||||
\(344\) | −3738.39 | −0.585932 | ||||||||
\(345\) | −533.152 | −0.0831998 | ||||||||
\(346\) | −4366.87 | −0.678510 | ||||||||
\(347\) | −1844.33 | −0.285328 | −0.142664 | − | 0.989771i | \(-0.545567\pi\) | ||||
−0.142664 | + | 0.989771i | \(0.545567\pi\) | |||||||
\(348\) | 4388.79 | 0.676046 | ||||||||
\(349\) | −10156.9 | −1.55784 | −0.778918 | − | 0.627125i | \(-0.784231\pi\) | ||||
−0.778918 | + | 0.627125i | \(0.784231\pi\) | |||||||
\(350\) | 3939.94 | 0.601710 | ||||||||
\(351\) | 816.057 | 0.124097 | ||||||||
\(352\) | −585.732 | −0.0886922 | ||||||||
\(353\) | 1905.43 | 0.287296 | 0.143648 | − | 0.989629i | \(-0.454117\pi\) | ||||
0.143648 | + | 0.989629i | \(0.454117\pi\) | |||||||
\(354\) | 5318.23 | 0.798477 | ||||||||
\(355\) | −2901.01 | −0.433718 | ||||||||
\(356\) | −2006.08 | −0.298658 | ||||||||
\(357\) | −31496.9 | −4.66945 | ||||||||
\(358\) | 6397.01 | 0.944393 | ||||||||
\(359\) | −2496.50 | −0.367020 | −0.183510 | − | 0.983018i | \(-0.558746\pi\) | ||||
−0.183510 | + | 0.983018i | \(0.558746\pi\) | |||||||
\(360\) | 1604.50 | 0.234901 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 4302.10 | 0.624623 | ||||||||
\(363\) | −7123.16 | −1.02994 | ||||||||
\(364\) | −5633.40 | −0.811182 | ||||||||
\(365\) | −455.465 | −0.0653154 | ||||||||
\(366\) | 676.715 | 0.0966460 | ||||||||
\(367\) | −8748.42 | −1.24432 | −0.622158 | − | 0.782892i | \(-0.713744\pi\) | ||||
−0.622158 | + | 0.782892i | \(0.713744\pi\) | |||||||
\(368\) | 143.630 | 0.0203457 | ||||||||
\(369\) | −8576.10 | −1.20990 | ||||||||
\(370\) | 1387.90 | 0.195010 | ||||||||
\(371\) | 9082.19 | 1.27095 | ||||||||
\(372\) | −3273.73 | −0.456277 | ||||||||
\(373\) | 1460.62 | 0.202756 | 0.101378 | − | 0.994848i | \(-0.467675\pi\) | ||||
0.101378 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(374\) | 4586.32 | 0.634099 | ||||||||
\(375\) | 10752.4 | 1.48067 | ||||||||
\(376\) | −1328.66 | −0.182235 | ||||||||
\(377\) | −6146.29 | −0.839655 | ||||||||
\(378\) | 1432.00 | 0.194852 | ||||||||
\(379\) | 10581.0 | 1.43406 | 0.717029 | − | 0.697043i | \(-0.245501\pi\) | ||||
0.717029 | + | 0.697043i | \(0.245501\pi\) | |||||||
\(380\) | 631.114 | 0.0851986 | ||||||||
\(381\) | −2760.37 | −0.371176 | ||||||||
\(382\) | 8871.04 | 1.18817 | ||||||||
\(383\) | −2932.54 | −0.391242 | −0.195621 | − | 0.980680i | \(-0.562672\pi\) | ||||
−0.195621 | + | 0.980680i | \(0.562672\pi\) | |||||||
\(384\) | −915.465 | −0.121659 | ||||||||
\(385\) | −5343.11 | −0.707300 | ||||||||
\(386\) | −5441.20 | −0.717486 | ||||||||
\(387\) | 11286.2 | 1.48246 | ||||||||
\(388\) | −5750.23 | −0.752380 | ||||||||
\(389\) | −3631.19 | −0.473287 | −0.236644 | − | 0.971597i | \(-0.576047\pi\) | ||||
−0.236644 | + | 0.971597i | \(0.576047\pi\) | |||||||
\(390\) | −4759.00 | −0.617900 | ||||||||
\(391\) | −1124.63 | −0.145461 | ||||||||
\(392\) | −7141.34 | −0.920133 | ||||||||
\(393\) | 12429.6 | 1.59539 | ||||||||
\(394\) | −2508.15 | −0.320708 | ||||||||
\(395\) | −3644.02 | −0.464179 | ||||||||
\(396\) | 1768.33 | 0.224399 | ||||||||
\(397\) | −2005.32 | −0.253512 | −0.126756 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126756 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(398\) | −8310.37 | −1.04664 | ||||||||
\(399\) | −4776.79 | −0.599345 | ||||||||
\(400\) | −896.662 | −0.112083 | ||||||||
\(401\) | −8187.30 | −1.01959 | −0.509793 | − | 0.860297i | \(-0.670278\pi\) | ||||
−0.509793 | + | 0.860297i | \(0.670278\pi\) | |||||||
\(402\) | 10807.3 | 1.34085 | ||||||||
\(403\) | 4584.70 | 0.566700 | ||||||||
\(404\) | 1580.50 | 0.194635 | ||||||||
\(405\) | 6624.90 | 0.812825 | ||||||||
\(406\) | −10785.4 | −1.31839 | ||||||||
\(407\) | 1529.62 | 0.186291 | ||||||||
\(408\) | 7168.15 | 0.869794 | ||||||||
\(409\) | −15565.0 | −1.88175 | −0.940877 | − | 0.338747i | \(-0.889997\pi\) | ||||
−0.940877 | + | 0.338747i | \(0.889997\pi\) | |||||||
\(410\) | −5897.39 | −0.710369 | ||||||||
\(411\) | 298.673 | 0.0358454 | ||||||||
\(412\) | 5142.71 | 0.614958 | ||||||||
\(413\) | −13069.4 | −1.55715 | ||||||||
\(414\) | −433.620 | −0.0514765 | ||||||||
\(415\) | −8911.06 | −1.05404 | ||||||||
\(416\) | 1282.06 | 0.151102 | ||||||||
\(417\) | 10991.2 | 1.29075 | ||||||||
\(418\) | 695.557 | 0.0813895 | ||||||||
\(419\) | −1839.83 | −0.214514 | −0.107257 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107257 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(420\) | −8350.97 | −0.970204 | ||||||||
\(421\) | 4658.28 | 0.539266 | 0.269633 | − | 0.962963i | \(-0.413098\pi\) | ||||
0.269633 | + | 0.962963i | \(0.413098\pi\) | |||||||
\(422\) | 1266.87 | 0.146138 | ||||||||
\(423\) | 4011.24 | 0.461071 | ||||||||
\(424\) | −2066.95 | −0.236745 | ||||||||
\(425\) | 7020.92 | 0.801328 | ||||||||
\(426\) | −4997.08 | −0.568332 | ||||||||
\(427\) | −1663.01 | −0.188475 | ||||||||
\(428\) | 4812.38 | 0.543494 | ||||||||
\(429\) | −5244.94 | −0.590275 | ||||||||
\(430\) | 7761.03 | 0.870396 | ||||||||
\(431\) | 2820.47 | 0.315214 | 0.157607 | − | 0.987502i | \(-0.449622\pi\) | ||||
0.157607 | + | 0.987502i | \(0.449622\pi\) | |||||||
\(432\) | −325.898 | −0.0362957 | ||||||||
\(433\) | 8981.39 | 0.996809 | 0.498404 | − | 0.866945i | \(-0.333920\pi\) | ||||
0.498404 | + | 0.866945i | \(0.333920\pi\) | |||||||
\(434\) | 8045.12 | 0.889811 | ||||||||
\(435\) | −9111.28 | −1.00426 | ||||||||
\(436\) | −5334.96 | −0.586005 | ||||||||
\(437\) | −170.561 | −0.0186705 | ||||||||
\(438\) | −784.552 | −0.0855876 | ||||||||
\(439\) | 14131.1 | 1.53631 | 0.768157 | − | 0.640261i | \(-0.221174\pi\) | ||||
0.768157 | + | 0.640261i | \(0.221174\pi\) | |||||||
\(440\) | 1216.00 | 0.131751 | ||||||||
\(441\) | 21559.8 | 2.32802 | ||||||||
\(442\) | −10038.6 | −1.08029 | ||||||||
\(443\) | 1659.59 | 0.177990 | 0.0889951 | − | 0.996032i | \(-0.471634\pi\) | ||||
0.0889951 | + | 0.996032i | \(0.471634\pi\) | |||||||
\(444\) | 2390.71 | 0.255536 | ||||||||
\(445\) | 4164.70 | 0.443653 | ||||||||
\(446\) | 9596.68 | 1.01887 | ||||||||
\(447\) | 11848.5 | 1.25372 | ||||||||
\(448\) | 2249.73 | 0.237254 | ||||||||
\(449\) | −13732.6 | −1.44338 | −0.721692 | − | 0.692214i | \(-0.756635\pi\) | ||||
−0.721692 | + | 0.692214i | \(0.756635\pi\) | |||||||
\(450\) | 2707.03 | 0.283579 | ||||||||
\(451\) | −6499.57 | −0.678609 | ||||||||
\(452\) | 3346.02 | 0.348194 | ||||||||
\(453\) | −5113.62 | −0.530373 | ||||||||
\(454\) | −1283.54 | −0.132686 | ||||||||
\(455\) | 11695.1 | 1.20500 | ||||||||
\(456\) | 1087.11 | 0.111642 | ||||||||
\(457\) | −5273.37 | −0.539776 | −0.269888 | − | 0.962892i | \(-0.586987\pi\) | ||||
−0.269888 | + | 0.962892i | \(0.586987\pi\) | |||||||
\(458\) | 2462.69 | 0.251253 | ||||||||
\(459\) | 2551.80 | 0.259494 | ||||||||
\(460\) | −298.181 | −0.0302234 | ||||||||
\(461\) | 16402.4 | 1.65713 | 0.828565 | − | 0.559893i | \(-0.189158\pi\) | ||||
0.828565 | + | 0.559893i | \(0.189158\pi\) | |||||||
\(462\) | −9203.68 | −0.926827 | ||||||||
\(463\) | −5296.03 | −0.531593 | −0.265796 | − | 0.964029i | \(-0.585635\pi\) | ||||
−0.265796 | + | 0.964029i | \(0.585635\pi\) | |||||||
\(464\) | 2454.56 | 0.245582 | ||||||||
\(465\) | 6796.38 | 0.677795 | ||||||||
\(466\) | −453.402 | −0.0450717 | ||||||||
\(467\) | 3470.94 | 0.343931 | 0.171966 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171966 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(468\) | −3870.56 | −0.382301 | ||||||||
\(469\) | −26558.8 | −2.61486 | ||||||||
\(470\) | 2758.35 | 0.270709 | ||||||||
\(471\) | 12045.7 | 1.17842 | ||||||||
\(472\) | 2974.37 | 0.290057 | ||||||||
\(473\) | 8553.51 | 0.831481 | ||||||||
\(474\) | −6276.94 | −0.608248 | ||||||||
\(475\) | 1064.79 | 0.102854 | ||||||||
\(476\) | −17615.5 | −1.69623 | ||||||||
\(477\) | 6240.14 | 0.598986 | ||||||||
\(478\) | −4866.54 | −0.465670 | ||||||||
\(479\) | −16294.7 | −1.55433 | −0.777163 | − | 0.629300i | \(-0.783342\pi\) | ||||
−0.777163 | + | 0.629300i | \(0.783342\pi\) | |||||||
\(480\) | 1900.54 | 0.180723 | ||||||||
\(481\) | −3348.06 | −0.317378 | ||||||||
\(482\) | 1802.67 | 0.170352 | ||||||||
\(483\) | 2256.88 | 0.212612 | ||||||||
\(484\) | −3983.83 | −0.374139 | ||||||||
\(485\) | 11937.7 | 1.11765 | ||||||||
\(486\) | 10311.7 | 0.962445 | ||||||||
\(487\) | −2245.82 | −0.208969 | −0.104485 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104485 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(488\) | 378.472 | 0.0351079 | ||||||||
\(489\) | 5022.00 | 0.464423 | ||||||||
\(490\) | 14825.7 | 1.36685 | ||||||||
\(491\) | −7578.64 | −0.696577 | −0.348288 | − | 0.937387i | \(-0.613237\pi\) | ||||
−0.348288 | + | 0.937387i | \(0.613237\pi\) | |||||||
\(492\) | −10158.4 | −0.930849 | ||||||||
\(493\) | −19219.4 | −1.75577 | ||||||||
\(494\) | −1522.45 | −0.138660 | ||||||||
\(495\) | −3671.11 | −0.333342 | ||||||||
\(496\) | −1830.93 | −0.165748 | ||||||||
\(497\) | 12280.2 | 1.10834 | ||||||||
\(498\) | −15349.6 | −1.38119 | ||||||||
\(499\) | −10558.4 | −0.947209 | −0.473604 | − | 0.880738i | \(-0.657047\pi\) | ||||
−0.473604 | + | 0.880738i | \(0.657047\pi\) | |||||||
\(500\) | 6013.57 | 0.537870 | ||||||||
\(501\) | −2020.50 | −0.180178 | ||||||||
\(502\) | 11351.8 | 1.00928 | ||||||||
\(503\) | −5816.42 | −0.515590 | −0.257795 | − | 0.966200i | \(-0.582996\pi\) | ||||
−0.257795 | + | 0.966200i | \(0.582996\pi\) | |||||||
\(504\) | −6791.96 | −0.600274 | ||||||||
\(505\) | −3281.16 | −0.289128 | ||||||||
\(506\) | −328.628 | −0.0288721 | ||||||||
\(507\) | −4232.87 | −0.370785 | ||||||||
\(508\) | −1543.82 | −0.134834 | ||||||||
\(509\) | 18051.0 | 1.57190 | 0.785950 | − | 0.618290i | \(-0.212174\pi\) | ||||
0.785950 | + | 0.618290i | \(0.212174\pi\) | |||||||
\(510\) | −14881.3 | −1.29207 | ||||||||
\(511\) | 1928.02 | 0.166909 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 387.004 | 0.0333073 | ||||||||
\(514\) | −4071.76 | −0.349412 | ||||||||
\(515\) | −10676.4 | −0.913514 | ||||||||
\(516\) | 13368.6 | 1.14054 | ||||||||
\(517\) | 3040.00 | 0.258606 | ||||||||
\(518\) | −5875.10 | −0.498334 | ||||||||
\(519\) | 15616.1 | 1.32075 | ||||||||
\(520\) | −2661.61 | −0.224460 | ||||||||
\(521\) | −0.648976 | −5.45723e−5 0 | −2.72861e−5 | − | 1.00000i | \(-0.500009\pi\) | ||||
−2.72861e−5 | 1.00000i | \(0.500009\pi\) | ||||||||
\(522\) | −7410.34 | −0.621344 | ||||||||
\(523\) | 16912.1 | 1.41399 | 0.706994 | − | 0.707219i | \(-0.250051\pi\) | ||||
0.706994 | + | 0.707219i | \(0.250051\pi\) | |||||||
\(524\) | 6951.59 | 0.579545 | ||||||||
\(525\) | −14089.4 | −1.17126 | ||||||||
\(526\) | −3848.41 | −0.319009 | ||||||||
\(527\) | 14336.3 | 1.18501 | ||||||||
\(528\) | 2094.60 | 0.172643 | ||||||||
\(529\) | −12086.4 | −0.993377 | ||||||||
\(530\) | 4291.06 | 0.351682 | ||||||||
\(531\) | −8979.66 | −0.733868 | ||||||||
\(532\) | −2671.56 | −0.217719 | ||||||||
\(533\) | 14226.4 | 1.15612 | ||||||||
\(534\) | 7173.82 | 0.581351 | ||||||||
\(535\) | −9990.67 | −0.807354 | ||||||||
\(536\) | 6044.31 | 0.487079 | ||||||||
\(537\) | −22875.9 | −1.83830 | ||||||||
\(538\) | 1658.56 | 0.132910 | ||||||||
\(539\) | 16339.5 | 1.30574 | ||||||||
\(540\) | 676.575 | 0.0539169 | ||||||||
\(541\) | −8893.75 | −0.706788 | −0.353394 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353394 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(542\) | 2446.26 | 0.193867 | ||||||||
\(543\) | −15384.5 | −1.21586 | ||||||||
\(544\) | 4008.99 | 0.315963 | ||||||||
\(545\) | 11075.6 | 0.870505 | ||||||||
\(546\) | 20145.2 | 1.57900 | ||||||||
\(547\) | 16972.8 | 1.32670 | 0.663351 | − | 0.748308i | \(-0.269134\pi\) | ||||
0.663351 | + | 0.748308i | \(0.269134\pi\) | |||||||
\(548\) | 167.041 | 0.0130213 | ||||||||
\(549\) | −1142.61 | −0.0888260 | ||||||||
\(550\) | 2051.58 | 0.159054 | ||||||||
\(551\) | −2914.79 | −0.225362 | ||||||||
\(552\) | −513.626 | −0.0396039 | ||||||||
\(553\) | 15425.4 | 1.18618 | ||||||||
\(554\) | −3245.62 | −0.248905 | ||||||||
\(555\) | −4963.18 | −0.379595 | ||||||||
\(556\) | 6147.17 | 0.468882 | ||||||||
\(557\) | −17045.8 | −1.29669 | −0.648343 | − | 0.761348i | \(-0.724538\pi\) | ||||
−0.648343 | + | 0.761348i | \(0.724538\pi\) | |||||||
\(558\) | 5527.59 | 0.419358 | ||||||||
\(559\) | −18722.1 | −1.41657 | ||||||||
\(560\) | −4670.52 | −0.352438 | ||||||||
\(561\) | −16400.8 | −1.23430 | ||||||||
\(562\) | −7237.91 | −0.543261 | ||||||||
\(563\) | −6973.83 | −0.522046 | −0.261023 | − | 0.965333i | \(-0.584060\pi\) | ||||
−0.261023 | + | 0.965333i | \(0.584060\pi\) | |||||||
\(564\) | 4751.34 | 0.354730 | ||||||||
\(565\) | −6946.46 | −0.517238 | ||||||||
\(566\) | −4204.86 | −0.312268 | ||||||||
\(567\) | −28043.7 | −2.07712 | ||||||||
\(568\) | −2794.76 | −0.206454 | ||||||||
\(569\) | −21644.0 | −1.59466 | −0.797332 | − | 0.603541i | \(-0.793756\pi\) | ||||
−0.797332 | + | 0.603541i | \(0.793756\pi\) | |||||||
\(570\) | −2256.89 | −0.165843 | ||||||||
\(571\) | −13891.0 | −1.01807 | −0.509035 | − | 0.860746i | \(-0.669998\pi\) | ||||
−0.509035 | + | 0.860746i | \(0.669998\pi\) | |||||||
\(572\) | −2933.38 | −0.214425 | ||||||||
\(573\) | −31723.1 | −2.31283 | ||||||||
\(574\) | 24964.1 | 1.81530 | ||||||||
\(575\) | −503.076 | −0.0364865 | ||||||||
\(576\) | 1545.73 | 0.111815 | ||||||||
\(577\) | −2386.14 | −0.172160 | −0.0860798 | − | 0.996288i | \(-0.527434\pi\) | ||||
−0.0860798 | + | 0.996288i | \(0.527434\pi\) | |||||||
\(578\) | −21564.7 | −1.55185 | ||||||||
\(579\) | 19457.9 | 1.39662 | ||||||||
\(580\) | −5095.75 | −0.364809 | ||||||||
\(581\) | 37721.2 | 2.69353 | ||||||||
\(582\) | 20563.0 | 1.46454 | ||||||||
\(583\) | 4729.21 | 0.335959 | ||||||||
\(584\) | −438.783 | −0.0310907 | ||||||||
\(585\) | 8035.41 | 0.567903 | ||||||||
\(586\) | 10768.0 | 0.759080 | ||||||||
\(587\) | −826.851 | −0.0581393 | −0.0290697 | − | 0.999577i | \(-0.509254\pi\) | ||||
−0.0290697 | + | 0.999577i | \(0.509254\pi\) | |||||||
\(588\) | 25537.7 | 1.79108 | ||||||||
\(589\) | 2174.23 | 0.152101 | ||||||||
\(590\) | −6174.90 | −0.430876 | ||||||||
\(591\) | 8969.23 | 0.624272 | ||||||||
\(592\) | 1337.07 | 0.0928265 | ||||||||
\(593\) | 9789.50 | 0.677920 | 0.338960 | − | 0.940801i | \(-0.389925\pi\) | ||||
0.338960 | + | 0.940801i | \(0.389925\pi\) | |||||||
\(594\) | 745.659 | 0.0515064 | ||||||||
\(595\) | 36570.5 | 2.51974 | ||||||||
\(596\) | 6626.62 | 0.455431 | ||||||||
\(597\) | 29718.2 | 2.03733 | ||||||||
\(598\) | 719.308 | 0.0491884 | ||||||||
\(599\) | −23555.7 | −1.60678 | −0.803389 | − | 0.595455i | \(-0.796972\pi\) | ||||
−0.803389 | + | 0.595455i | \(0.796972\pi\) | |||||||
\(600\) | 3206.49 | 0.218174 | ||||||||
\(601\) | 12263.4 | 0.832334 | 0.416167 | − | 0.909288i | \(-0.363373\pi\) | ||||
0.416167 | + | 0.909288i | \(0.363373\pi\) | |||||||
\(602\) | −32853.1 | −2.22424 | ||||||||
\(603\) | −18247.8 | −1.23235 | ||||||||
\(604\) | −2859.94 | −0.192664 | ||||||||
\(605\) | 8270.57 | 0.555780 | ||||||||
\(606\) | −5651.91 | −0.378866 | ||||||||
\(607\) | 464.109 | 0.0310340 | 0.0155170 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155170 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | 38568.8 | 2.56632 | ||||||||
\(610\) | −785.721 | −0.0521523 | ||||||||
\(611\) | −6654.02 | −0.440577 | ||||||||
\(612\) | −12103.2 | −0.799415 | ||||||||
\(613\) | 11526.0 | 0.759427 | 0.379714 | − | 0.925104i | \(-0.376023\pi\) | ||||
0.379714 | + | 0.925104i | \(0.376023\pi\) | |||||||
\(614\) | −7385.69 | −0.485444 | ||||||||
\(615\) | 21089.3 | 1.38277 | ||||||||
\(616\) | −5147.43 | −0.336681 | ||||||||
\(617\) | 17632.5 | 1.15050 | 0.575249 | − | 0.817978i | \(-0.304905\pi\) | ||||
0.575249 | + | 0.817978i | \(0.304905\pi\) | |||||||
\(618\) | −18390.5 | −1.19705 | ||||||||
\(619\) | 16538.0 | 1.07386 | 0.536928 | − | 0.843628i | \(-0.319585\pi\) | ||||
0.536928 | + | 0.843628i | \(0.319585\pi\) | |||||||
\(620\) | 3801.07 | 0.246217 | ||||||||
\(621\) | −182.846 | −0.0118154 | ||||||||
\(622\) | 8855.33 | 0.570846 | ||||||||
\(623\) | −17629.5 | −1.13372 | ||||||||
\(624\) | −4584.70 | −0.294126 | ||||||||
\(625\) | −5479.20 | −0.350669 | ||||||||
\(626\) | 14712.9 | 0.939372 | ||||||||
\(627\) | −2487.34 | −0.158428 | ||||||||
\(628\) | 6736.91 | 0.428077 | ||||||||
\(629\) | −10469.3 | −0.663657 | ||||||||
\(630\) | 14100.3 | 0.891700 | ||||||||
\(631\) | −8881.84 | −0.560349 | −0.280175 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280175 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(632\) | −3510.56 | −0.220953 | ||||||||
\(633\) | −4530.38 | −0.284465 | ||||||||
\(634\) | −3225.53 | −0.202054 | ||||||||
\(635\) | 3205.01 | 0.200295 | ||||||||
\(636\) | 7391.48 | 0.460835 | ||||||||
\(637\) | −35764.3 | −2.22454 | ||||||||
\(638\) | −5616.07 | −0.348499 | ||||||||
\(639\) | 8437.42 | 0.522346 | ||||||||
\(640\) | 1062.93 | 0.0656499 | ||||||||
\(641\) | 22459.3 | 1.38391 | 0.691956 | − | 0.721939i | \(-0.256749\pi\) | ||||
0.691956 | + | 0.721939i | \(0.256749\pi\) | |||||||
\(642\) | −17209.2 | −1.05794 | ||||||||
\(643\) | 19685.1 | 1.20731 | 0.603657 | − | 0.797244i | \(-0.293710\pi\) | ||||
0.603657 | + | 0.797244i | \(0.293710\pi\) | |||||||
\(644\) | 1262.22 | 0.0772338 | ||||||||
\(645\) | −27753.7 | −1.69427 | ||||||||
\(646\) | −4760.68 | −0.289948 | ||||||||
\(647\) | −11755.6 | −0.714312 | −0.357156 | − | 0.934045i | \(-0.616254\pi\) | ||||
−0.357156 | + | 0.934045i | \(0.616254\pi\) | |||||||
\(648\) | 6382.27 | 0.386912 | ||||||||
\(649\) | −6805.42 | −0.411612 | ||||||||
\(650\) | −4490.53 | −0.270974 | ||||||||
\(651\) | −28769.6 | −1.73206 | ||||||||
\(652\) | 2808.70 | 0.168707 | ||||||||
\(653\) | 18350.7 | 1.09972 | 0.549862 | − | 0.835256i | \(-0.314680\pi\) | ||||
0.549862 | + | 0.835256i | \(0.314680\pi\) | |||||||
\(654\) | 19078.0 | 1.14069 | ||||||||
\(655\) | −14431.7 | −0.860908 | ||||||||
\(656\) | −5681.40 | −0.338142 | ||||||||
\(657\) | 1324.69 | 0.0786623 | ||||||||
\(658\) | −11676.3 | −0.691777 | ||||||||
\(659\) | 14617.0 | 0.864034 | 0.432017 | − | 0.901866i | \(-0.357802\pi\) | ||||
0.432017 | + | 0.901866i | \(0.357802\pi\) | |||||||
\(660\) | −4348.46 | −0.256460 | ||||||||
\(661\) | −2932.29 | −0.172546 | −0.0862729 | − | 0.996272i | \(-0.527496\pi\) | ||||
−0.0862729 | + | 0.996272i | \(0.527496\pi\) | |||||||
\(662\) | 4525.56 | 0.265696 | ||||||||
\(663\) | 35898.5 | 2.10284 | ||||||||
\(664\) | −8584.70 | −0.501733 | ||||||||
\(665\) | 5546.24 | 0.323420 | ||||||||
\(666\) | −4036.63 | −0.234859 | ||||||||
\(667\) | 1377.14 | 0.0799448 | ||||||||
\(668\) | −1130.02 | −0.0654520 | ||||||||
\(669\) | −34318.0 | −1.98328 | ||||||||
\(670\) | −12548.2 | −0.723551 | ||||||||
\(671\) | −865.951 | −0.0498207 | ||||||||
\(672\) | −8045.12 | −0.461826 | ||||||||
\(673\) | 21271.4 | 1.21835 | 0.609177 | − | 0.793034i | \(-0.291500\pi\) | ||||
0.609177 | + | 0.793034i | \(0.291500\pi\) | |||||||
\(674\) | 4075.25 | 0.232898 | ||||||||
\(675\) | 1141.48 | 0.0650900 | ||||||||
\(676\) | −2367.35 | −0.134692 | ||||||||
\(677\) | −32878.2 | −1.86649 | −0.933245 | − | 0.359241i | \(-0.883036\pi\) | ||||
−0.933245 | + | 0.359241i | \(0.883036\pi\) | |||||||
\(678\) | −11965.5 | −0.677776 | ||||||||
\(679\) | −50533.1 | −2.85609 | ||||||||
\(680\) | −8322.80 | −0.469360 | ||||||||
\(681\) | 4589.98 | 0.258280 | ||||||||
\(682\) | 4189.20 | 0.235209 | ||||||||
\(683\) | −7771.01 | −0.435358 | −0.217679 | − | 0.976020i | \(-0.569849\pi\) | ||||
−0.217679 | + | 0.976020i | \(0.569849\pi\) | |||||||
\(684\) | −1835.56 | −0.102609 | ||||||||
\(685\) | −346.783 | −0.0193429 | ||||||||
\(686\) | −38643.9 | −2.15078 | ||||||||
\(687\) | −8806.65 | −0.489075 | ||||||||
\(688\) | 7476.79 | 0.414317 | ||||||||
\(689\) | −10351.4 | −0.572361 | ||||||||
\(690\) | 1066.30 | 0.0588312 | ||||||||
\(691\) | 3655.65 | 0.201255 | 0.100628 | − | 0.994924i | \(-0.467915\pi\) | ||||
0.100628 | + | 0.994924i | \(0.467915\pi\) | |||||||
\(692\) | 8733.74 | 0.479779 | ||||||||
\(693\) | 15540.1 | 0.851833 | ||||||||
\(694\) | 3688.66 | 0.201757 | ||||||||
\(695\) | −12761.7 | −0.696518 | ||||||||
\(696\) | −8777.59 | −0.478037 | ||||||||
\(697\) | 44485.7 | 2.41753 | ||||||||
\(698\) | 20313.8 | 1.10156 | ||||||||
\(699\) | 1621.38 | 0.0877342 | ||||||||
\(700\) | −7879.88 | −0.425473 | ||||||||
\(701\) | −28207.0 | −1.51977 | −0.759887 | − | 0.650055i | \(-0.774746\pi\) | ||||
−0.759887 | + | 0.650055i | \(0.774746\pi\) | |||||||
\(702\) | −1632.11 | −0.0877496 | ||||||||
\(703\) | −1587.77 | −0.0851834 | ||||||||
\(704\) | 1171.46 | 0.0627148 | ||||||||
\(705\) | −9863.94 | −0.526947 | ||||||||
\(706\) | −3810.85 | −0.203149 | ||||||||
\(707\) | 13889.4 | 0.738848 | ||||||||
\(708\) | −10636.5 | −0.564608 | ||||||||
\(709\) | 36417.7 | 1.92905 | 0.964524 | − | 0.263997i | \(-0.0850409\pi\) | ||||
0.964524 | + | 0.263997i | \(0.0850409\pi\) | |||||||
\(710\) | 5802.02 | 0.306685 | ||||||||
\(711\) | 10598.4 | 0.559031 | ||||||||
\(712\) | 4012.17 | 0.211183 | ||||||||
\(713\) | −1027.25 | −0.0539563 | ||||||||
\(714\) | 62993.8 | 3.30180 | ||||||||
\(715\) | 6089.80 | 0.318525 | ||||||||
\(716\) | −12794.0 | −0.667786 | ||||||||
\(717\) | 17402.9 | 0.906448 | ||||||||
\(718\) | 4993.00 | 0.259522 | ||||||||
\(719\) | 27227.6 | 1.41227 | 0.706133 | − | 0.708079i | \(-0.250438\pi\) | ||||
0.706133 | + | 0.708079i | \(0.250438\pi\) | |||||||
\(720\) | −3208.99 | −0.166100 | ||||||||
\(721\) | 45194.2 | 2.33442 | ||||||||
\(722\) | −722.000 | −0.0372161 | ||||||||
\(723\) | −6446.41 | −0.331597 | ||||||||
\(724\) | −8604.20 | −0.441675 | ||||||||
\(725\) | −8597.30 | −0.440408 | ||||||||
\(726\) | 14246.3 | 0.728279 | ||||||||
\(727\) | 27647.2 | 1.41043 | 0.705213 | − | 0.708996i | \(-0.250851\pi\) | ||||
0.705213 | + | 0.708996i | \(0.250851\pi\) | |||||||
\(728\) | 11266.8 | 0.573592 | ||||||||
\(729\) | −15334.8 | −0.779090 | ||||||||
\(730\) | 910.929 | 0.0461849 | ||||||||
\(731\) | −58543.7 | −2.96213 | ||||||||
\(732\) | −1353.43 | −0.0683391 | ||||||||
\(733\) | −32139.8 | −1.61952 | −0.809761 | − | 0.586760i | \(-0.800403\pi\) | ||||
−0.809761 | + | 0.586760i | \(0.800403\pi\) | |||||||
\(734\) | 17496.8 | 0.879864 | ||||||||
\(735\) | −53017.1 | −2.66063 | ||||||||
\(736\) | −287.260 | −0.0143866 | ||||||||
\(737\) | −13829.5 | −0.691202 | ||||||||
\(738\) | 17152.2 | 0.855530 | ||||||||
\(739\) | 16224.9 | 0.807635 | 0.403818 | − | 0.914839i | \(-0.367683\pi\) | ||||
0.403818 | + | 0.914839i | \(0.367683\pi\) | |||||||
\(740\) | −2775.80 | −0.137893 | ||||||||
\(741\) | 5444.33 | 0.269909 | ||||||||
\(742\) | −18164.4 | −0.898700 | ||||||||
\(743\) | 22463.2 | 1.10915 | 0.554573 | − | 0.832135i | \(-0.312882\pi\) | ||||
0.554573 | + | 0.832135i | \(0.312882\pi\) | |||||||
\(744\) | 6547.46 | 0.322637 | ||||||||
\(745\) | −13757.1 | −0.676538 | ||||||||
\(746\) | −2921.24 | −0.143370 | ||||||||
\(747\) | 25917.3 | 1.26943 | ||||||||
\(748\) | −9172.64 | −0.448376 | ||||||||
\(749\) | 42291.3 | 2.06314 | ||||||||
\(750\) | −21504.7 | −1.04699 | ||||||||
\(751\) | 9310.24 | 0.452377 | 0.226189 | − | 0.974083i | \(-0.427373\pi\) | ||||
0.226189 | + | 0.974083i | \(0.427373\pi\) | |||||||
\(752\) | 2657.32 | 0.128860 | ||||||||
\(753\) | −40594.6 | −1.96461 | ||||||||
\(754\) | 12292.6 | 0.593726 | ||||||||
\(755\) | 5937.33 | 0.286201 | ||||||||
\(756\) | −2863.99 | −0.137781 | ||||||||
\(757\) | 28707.1 | 1.37830 | 0.689152 | − | 0.724617i | \(-0.257983\pi\) | ||||
0.689152 | + | 0.724617i | \(0.257983\pi\) | |||||||
\(758\) | −21161.9 | −1.01403 | ||||||||
\(759\) | 1175.18 | 0.0562009 | ||||||||
\(760\) | −1262.23 | −0.0602445 | ||||||||
\(761\) | −20820.3 | −0.991768 | −0.495884 | − | 0.868389i | \(-0.665156\pi\) | ||||
−0.495884 | + | 0.868389i | \(0.665156\pi\) | |||||||
\(762\) | 5520.73 | 0.262461 | ||||||||
\(763\) | −46883.7 | −2.22452 | ||||||||
\(764\) | −17742.1 | −0.840165 | ||||||||
\(765\) | 25126.6 | 1.18752 | ||||||||
\(766\) | 5865.08 | 0.276650 | ||||||||
\(767\) | 14895.8 | 0.701249 | ||||||||
\(768\) | 1830.93 | 0.0860260 | ||||||||
\(769\) | 28026.2 | 1.31424 | 0.657120 | − | 0.753786i | \(-0.271775\pi\) | ||||
0.657120 | + | 0.753786i | \(0.271775\pi\) | |||||||
\(770\) | 10686.2 | 0.500136 | ||||||||
\(771\) | 14560.8 | 0.680146 | ||||||||
\(772\) | 10882.4 | 0.507339 | ||||||||
\(773\) | −16405.1 | −0.763326 | −0.381663 | − | 0.924302i | \(-0.624648\pi\) | ||||
−0.381663 | + | 0.924302i | \(0.624648\pi\) | |||||||
\(774\) | −22572.5 | −1.04826 | ||||||||
\(775\) | 6412.98 | 0.297240 | ||||||||
\(776\) | 11500.5 | 0.532013 | ||||||||
\(777\) | 21009.6 | 0.970030 | ||||||||
\(778\) | 7262.38 | 0.334665 | ||||||||
\(779\) | 6746.66 | 0.310301 | ||||||||
\(780\) | 9517.99 | 0.436922 | ||||||||
\(781\) | 6394.47 | 0.292973 | ||||||||
\(782\) | 2249.26 | 0.102856 | ||||||||
\(783\) | −3124.75 | −0.142617 | ||||||||
\(784\) | 14282.7 | 0.650633 | ||||||||
\(785\) | −13986.1 | −0.635903 | ||||||||
\(786\) | −24859.1 | −1.12811 | ||||||||
\(787\) | −28468.8 | −1.28946 | −0.644730 | − | 0.764411i | \(-0.723030\pi\) | ||||
−0.644730 | + | 0.764411i | \(0.723030\pi\) | |||||||
\(788\) | 5016.30 | 0.226775 | ||||||||
\(789\) | 13762.0 | 0.620965 | ||||||||
\(790\) | 7288.04 | 0.328224 | ||||||||
\(791\) | 29404.9 | 1.32177 | ||||||||
\(792\) | −3536.66 | −0.158674 | ||||||||
\(793\) | 1895.41 | 0.0848777 | ||||||||
\(794\) | 4010.64 | 0.179260 | ||||||||
\(795\) | −15345.0 | −0.684566 | ||||||||
\(796\) | 16620.7 | 0.740084 | ||||||||
\(797\) | 7256.68 | 0.322515 | 0.161258 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161258 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(798\) | 9553.58 | 0.423801 | ||||||||
\(799\) | −20807.0 | −0.921275 | ||||||||
\(800\) | 1793.32 | 0.0792544 | ||||||||
\(801\) | −12112.8 | −0.534311 | ||||||||
\(802\) | 16374.6 | 0.720957 | ||||||||
\(803\) | 1003.94 | 0.0441201 | ||||||||
\(804\) | −21614.7 | −0.948122 | ||||||||
\(805\) | −2620.42 | −0.114730 | ||||||||
\(806\) | −9169.40 | −0.400718 | ||||||||
\(807\) | −5931.06 | −0.258715 | ||||||||
\(808\) | −3160.99 | −0.137628 | ||||||||
\(809\) | 10647.1 | 0.462711 | 0.231356 | − | 0.972869i | \(-0.425684\pi\) | ||||
0.231356 | + | 0.972869i | \(0.425684\pi\) | |||||||
\(810\) | −13249.8 | −0.574754 | ||||||||
\(811\) | −27076.9 | −1.17238 | −0.586190 | − | 0.810174i | \(-0.699373\pi\) | ||||
−0.586190 | + | 0.810174i | \(0.699373\pi\) | |||||||
\(812\) | 21570.7 | 0.932246 | ||||||||
\(813\) | −8747.91 | −0.377371 | ||||||||
\(814\) | −3059.24 | −0.131728 | ||||||||
\(815\) | −5830.96 | −0.250613 | ||||||||
\(816\) | −14336.3 | −0.615037 | ||||||||
\(817\) | −8878.69 | −0.380203 | ||||||||
\(818\) | 31129.9 | 1.33060 | ||||||||
\(819\) | −34014.5 | −1.45124 | ||||||||
\(820\) | 11794.8 | 0.502307 | ||||||||
\(821\) | 1880.29 | 0.0799301 | 0.0399650 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399650 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(822\) | −597.345 | −0.0253465 | ||||||||
\(823\) | 36904.5 | 1.56307 | 0.781537 | − | 0.623859i | \(-0.214436\pi\) | ||||
0.781537 | + | 0.623859i | \(0.214436\pi\) | |||||||
\(824\) | −10285.4 | −0.434841 | ||||||||
\(825\) | −7336.51 | −0.309605 | ||||||||
\(826\) | 26138.9 | 1.10107 | ||||||||
\(827\) | −23091.4 | −0.970939 | −0.485470 | − | 0.874254i | \(-0.661351\pi\) | ||||
−0.485470 | + | 0.874254i | \(0.661351\pi\) | |||||||
\(828\) | 867.240 | 0.0363994 | ||||||||
\(829\) | −15527.1 | −0.650515 | −0.325258 | − | 0.945625i | \(-0.605451\pi\) | ||||
−0.325258 | + | 0.945625i | \(0.605451\pi\) | |||||||
\(830\) | 17822.1 | 0.745319 | ||||||||
\(831\) | 11606.4 | 0.484504 | ||||||||
\(832\) | −2564.13 | −0.106845 | ||||||||
\(833\) | −111834. | −4.65166 | ||||||||
\(834\) | −21982.5 | −0.912700 | ||||||||
\(835\) | 2345.97 | 0.0972282 | ||||||||
\(836\) | −1391.11 | −0.0575511 | ||||||||
\(837\) | 2330.84 | 0.0962553 | ||||||||
\(838\) | 3679.66 | 0.151685 | ||||||||
\(839\) | 25695.1 | 1.05732 | 0.528661 | − | 0.848833i | \(-0.322694\pi\) | ||||
0.528661 | + | 0.848833i | \(0.322694\pi\) | |||||||
\(840\) | 16701.9 | 0.686038 | ||||||||
\(841\) | −854.386 | −0.0350316 | ||||||||
\(842\) | −9316.57 | −0.381319 | ||||||||
\(843\) | 25883.0 | 1.05748 | ||||||||
\(844\) | −2533.75 | −0.103335 | ||||||||
\(845\) | 4914.70 | 0.200084 | ||||||||
\(846\) | −8022.48 | −0.326027 | ||||||||
\(847\) | −35010.0 | −1.42026 | ||||||||
\(848\) | 4133.90 | 0.167404 | ||||||||
\(849\) | 15036.7 | 0.607843 | ||||||||
\(850\) | −14041.8 | −0.566625 | ||||||||
\(851\) | 750.170 | 0.0302180 | ||||||||
\(852\) | 9994.17 | 0.401872 | ||||||||
\(853\) | −4534.78 | −0.182026 | −0.0910129 | − | 0.995850i | \(-0.529010\pi\) | ||||
−0.0910129 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(854\) | 3326.02 | 0.133272 | ||||||||
\(855\) | 3810.68 | 0.152424 | ||||||||
\(856\) | −9624.77 | −0.384308 | ||||||||
\(857\) | 48754.1 | 1.94330 | 0.971651 | − | 0.236422i | \(-0.0759747\pi\) | ||||
0.971651 | + | 0.236422i | \(0.0759747\pi\) | |||||||
\(858\) | 10489.9 | 0.417387 | ||||||||
\(859\) | −11730.5 | −0.465937 | −0.232968 | − | 0.972484i | \(-0.574844\pi\) | ||||
−0.232968 | + | 0.972484i | \(0.574844\pi\) | |||||||
\(860\) | −15522.1 | −0.615463 | ||||||||
\(861\) | −89272.6 | −3.53357 | ||||||||
\(862\) | −5640.93 | −0.222890 | ||||||||
\(863\) | 9907.21 | 0.390783 | 0.195391 | − | 0.980725i | \(-0.437402\pi\) | ||||
0.195391 | + | 0.980725i | \(0.437402\pi\) | |||||||
\(864\) | 651.795 | 0.0256650 | ||||||||
\(865\) | −18131.5 | −0.712706 | ||||||||
\(866\) | −17962.8 | −0.704850 | ||||||||
\(867\) | 77116.0 | 3.02076 | ||||||||
\(868\) | −16090.2 | −0.629192 | ||||||||
\(869\) | 8032.22 | 0.313549 | ||||||||
\(870\) | 18222.6 | 0.710118 | ||||||||
\(871\) | 30270.3 | 1.17758 | ||||||||
\(872\) | 10669.9 | 0.414368 | ||||||||
\(873\) | −34720.0 | −1.34604 | ||||||||
\(874\) | 341.121 | 0.0132021 | ||||||||
\(875\) | 52847.3 | 2.04179 | ||||||||
\(876\) | 1569.10 | 0.0605195 | ||||||||
\(877\) | 23741.6 | 0.914136 | 0.457068 | − | 0.889432i | \(-0.348900\pi\) | ||||
0.457068 | + | 0.889432i | \(0.348900\pi\) | |||||||
\(878\) | −28262.3 | −1.08634 | ||||||||
\(879\) | −38506.7 | −1.47758 | ||||||||
\(880\) | −2432.00 | −0.0931622 | ||||||||
\(881\) | −24381.3 | −0.932378 | −0.466189 | − | 0.884685i | \(-0.654373\pi\) | ||||
−0.466189 | + | 0.884685i | \(0.654373\pi\) | |||||||
\(882\) | −43119.5 | −1.64616 | ||||||||
\(883\) | 343.893 | 0.0131064 | 0.00655319 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655319 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(884\) | 20077.3 | 0.763882 | ||||||||
\(885\) | 22081.7 | 0.838719 | ||||||||
\(886\) | −3319.19 | −0.125858 | ||||||||
\(887\) | 33805.3 | 1.27967 | 0.639837 | − | 0.768511i | \(-0.279002\pi\) | ||||
0.639837 | + | 0.768511i | \(0.279002\pi\) | |||||||
\(888\) | −4781.41 | −0.180691 | ||||||||
\(889\) | −13567.1 | −0.511839 | ||||||||
\(890\) | −8329.39 | −0.313710 | ||||||||
\(891\) | −14602.7 | −0.549057 | ||||||||
\(892\) | −19193.4 | −0.720449 | ||||||||
\(893\) | −3155.57 | −0.118250 | ||||||||
\(894\) | −23697.0 | −0.886517 | ||||||||
\(895\) | 26560.8 | 0.991989 | ||||||||
\(896\) | −4499.46 | −0.167764 | ||||||||
\(897\) | −2572.27 | −0.0957475 | ||||||||
\(898\) | 27465.1 | 1.02063 | ||||||||
\(899\) | −17555.2 | −0.651277 | ||||||||
\(900\) | −5414.06 | −0.200521 | ||||||||
\(901\) | −32368.7 | −1.19684 | ||||||||
\(902\) | 12999.1 | 0.479849 | ||||||||
\(903\) | 117484. | 4.32958 | ||||||||
\(904\) | −6692.05 | −0.246210 | ||||||||
\(905\) | 17862.6 | 0.656103 | ||||||||
\(906\) | 10227.2 | 0.375030 | ||||||||
\(907\) | −26456.3 | −0.968540 | −0.484270 | − | 0.874919i | \(-0.660915\pi\) | ||||
−0.484270 | + | 0.874919i | \(0.660915\pi\) | |||||||
\(908\) | 2567.08 | 0.0938233 | ||||||||
\(909\) | 9543.06 | 0.348211 | ||||||||
\(910\) | −23390.2 | −0.852065 | ||||||||
\(911\) | −310.509 | −0.0112927 | −0.00564633 | − | 0.999984i | \(-0.501797\pi\) | ||||
−0.00564633 | + | 0.999984i | \(0.501797\pi\) | |||||||
\(912\) | −2174.23 | −0.0789429 | ||||||||
\(913\) | 19641.9 | 0.711997 | ||||||||
\(914\) | 10546.7 | 0.381679 | ||||||||
\(915\) | 2809.77 | 0.101517 | ||||||||
\(916\) | −4925.37 | −0.177662 | ||||||||
\(917\) | 61090.7 | 2.19999 | ||||||||
\(918\) | −5103.60 | −0.183490 | ||||||||
\(919\) | −17316.8 | −0.621575 | −0.310787 | − | 0.950479i | \(-0.600593\pi\) | ||||
−0.310787 | + | 0.950479i | \(0.600593\pi\) | |||||||
\(920\) | 596.361 | 0.0213711 | ||||||||
\(921\) | 26411.5 | 0.944938 | ||||||||
\(922\) | −32804.8 | −1.17177 | ||||||||
\(923\) | −13996.3 | −0.499128 | ||||||||
\(924\) | 18407.4 | 0.655366 | ||||||||
\(925\) | −4683.20 | −0.166468 | ||||||||
\(926\) | 10592.1 | 0.375893 | ||||||||
\(927\) | 31051.7 | 1.10019 | ||||||||
\(928\) | −4909.12 | −0.173653 | ||||||||
\(929\) | −36473.5 | −1.28811 | −0.644056 | − | 0.764978i | \(-0.722750\pi\) | ||||
−0.644056 | + | 0.764978i | \(0.722750\pi\) | |||||||
\(930\) | −13592.8 | −0.479273 | ||||||||
\(931\) | −16960.7 | −0.597061 | ||||||||
\(932\) | 906.803 | 0.0318705 | ||||||||
\(933\) | −31667.0 | −1.11118 | ||||||||
\(934\) | −6941.88 | −0.243196 | ||||||||
\(935\) | 19042.7 | 0.666057 | ||||||||
\(936\) | 7741.12 | 0.270327 | ||||||||
\(937\) | 4777.88 | 0.166581 | 0.0832905 | − | 0.996525i | \(-0.473457\pi\) | ||||
0.0832905 | + | 0.996525i | \(0.473457\pi\) | |||||||
\(938\) | 53117.5 | 1.84899 | ||||||||
\(939\) | −52613.9 | −1.82853 | ||||||||
\(940\) | −5516.69 | −0.191420 | ||||||||
\(941\) | 31366.5 | 1.08663 | 0.543315 | − | 0.839529i | \(-0.317169\pi\) | ||||
0.543315 | + | 0.839529i | \(0.317169\pi\) | |||||||
\(942\) | −24091.4 | −0.833271 | ||||||||
\(943\) | −3187.58 | −0.110076 | ||||||||
\(944\) | −5948.75 | −0.205101 | ||||||||
\(945\) | 5945.75 | 0.204672 | ||||||||
\(946\) | −17107.0 | −0.587946 | ||||||||
\(947\) | 26496.1 | 0.909195 | 0.454597 | − | 0.890697i | \(-0.349783\pi\) | ||||
0.454597 | + | 0.890697i | \(0.349783\pi\) | |||||||
\(948\) | 12553.9 | 0.430096 | ||||||||
\(949\) | −2197.45 | −0.0751658 | ||||||||
\(950\) | −2129.57 | −0.0727289 | ||||||||
\(951\) | 11534.6 | 0.393307 | ||||||||
\(952\) | 35231.1 | 1.19942 | ||||||||
\(953\) | −11928.3 | −0.405451 | −0.202725 | − | 0.979236i | \(-0.564980\pi\) | ||||
−0.202725 | + | 0.979236i | \(0.564980\pi\) | |||||||
\(954\) | −12480.3 | −0.423547 | ||||||||
\(955\) | 36833.1 | 1.24806 | ||||||||
\(956\) | 9733.07 | 0.329278 | ||||||||
\(957\) | 20083.3 | 0.678370 | ||||||||
\(958\) | 32589.3 | 1.09907 | ||||||||
\(959\) | 1467.96 | 0.0494296 | ||||||||
\(960\) | −3801.07 | −0.127791 | ||||||||
\(961\) | −16696.1 | −0.560440 | ||||||||
\(962\) | 6696.13 | 0.224420 | ||||||||
\(963\) | 29057.3 | 0.972333 | ||||||||
\(964\) | −3605.34 | −0.120457 | ||||||||
\(965\) | −22592.2 | −0.753647 | ||||||||
\(966\) | −4513.75 | −0.150339 | ||||||||
\(967\) | −58320.0 | −1.93945 | −0.969723 | − | 0.244209i | \(-0.921472\pi\) | ||||
−0.969723 | + | 0.244209i | \(0.921472\pi\) | |||||||
\(968\) | 7967.67 | 0.264556 | ||||||||
\(969\) | 17024.3 | 0.564397 | ||||||||
\(970\) | −23875.3 | −0.790300 | ||||||||
\(971\) | −27526.8 | −0.909760 | −0.454880 | − | 0.890553i | \(-0.650318\pi\) | ||||
−0.454880 | + | 0.890553i | \(0.650318\pi\) | |||||||
\(972\) | −20623.4 | −0.680551 | ||||||||
\(973\) | 54021.5 | 1.77991 | ||||||||
\(974\) | 4491.64 | 0.147763 | ||||||||
\(975\) | 16058.3 | 0.527464 | ||||||||
\(976\) | −756.945 | −0.0248250 | ||||||||
\(977\) | −36194.1 | −1.18521 | −0.592605 | − | 0.805493i | \(-0.701901\pi\) | ||||
−0.592605 | + | 0.805493i | \(0.701901\pi\) | |||||||
\(978\) | −10044.0 | −0.328397 | ||||||||
\(979\) | −9179.90 | −0.299684 | ||||||||
\(980\) | −29651.3 | −0.966507 | ||||||||
\(981\) | −32212.6 | −1.04839 | ||||||||
\(982\) | 15157.3 | 0.492554 | ||||||||
\(983\) | −58081.3 | −1.88454 | −0.942271 | − | 0.334850i | \(-0.891314\pi\) | ||||
−0.942271 | + | 0.334850i | \(0.891314\pi\) | |||||||
\(984\) | 20316.9 | 0.658210 | ||||||||
\(985\) | −10414.0 | −0.336871 | ||||||||
\(986\) | 38438.7 | 1.24152 | ||||||||
\(987\) | 41754.8 | 1.34658 | ||||||||
\(988\) | 3044.90 | 0.0980477 | ||||||||
\(989\) | 4194.89 | 0.134873 | ||||||||
\(990\) | 7342.23 | 0.235708 | ||||||||
\(991\) | 54921.4 | 1.76048 | 0.880240 | − | 0.474529i | \(-0.157382\pi\) | ||||
0.880240 | + | 0.474529i | \(0.157382\pi\) | |||||||
\(992\) | 3661.86 | 0.117202 | ||||||||
\(993\) | −16183.6 | −0.517190 | ||||||||
\(994\) | −24560.4 | −0.783712 | ||||||||
\(995\) | −34505.2 | −1.09939 | ||||||||
\(996\) | 30699.2 | 0.976647 | ||||||||
\(997\) | −33999.5 | −1.08001 | −0.540007 | − | 0.841661i | \(-0.681578\pi\) | ||||
−0.540007 | + | 0.841661i | \(0.681578\pi\) | |||||||
\(998\) | 21116.7 | 0.669778 | ||||||||
\(999\) | −1702.14 | −0.0539073 |
(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 | 38.4.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 342.4.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 304.4.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 950.4.b.g.799.1 | 4 | |||
5.3 | odd | 4 | 950.4.b.g.799.4 | 4 | |||
5.4 | even | 2 | 950.4.a.h.1.1 | 2 | |||
7.6 | odd | 2 | 1862.4.a.b.1.1 | 2 | |||
8.3 | odd | 2 | 1216.4.a.l.1.2 | 2 | |||
8.5 | even | 2 | 1216.4.a.j.1.1 | 2 | |||
19.18 | odd | 2 | 722.4.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
304.4.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
342.4.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
722.4.a.i.1.1 | 2 | 19.18 | odd | 2 | |||
950.4.a.h.1.1 | 2 | 5.4 | even | 2 | |||
950.4.b.g.799.1 | 4 | 5.2 | odd | 4 | |||
950.4.b.g.799.4 | 4 | 5.3 | odd | 4 | |||
1216.4.a.j.1.1 | 2 | 8.5 | even | 2 | |||
1216.4.a.l.1.2 | 2 | 8.3 | odd | 2 | |||
1862.4.a.b.1.1 | 2 | 7.6 | odd | 2 |