Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.45581.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 37x + 90 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.82712\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −13.1803 | −1.17888 | −0.589439 | − | 0.807813i | \(-0.700651\pi\) | ||||
−0.589439 | + | 0.807813i | \(0.700651\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −27.1877 | −1.46800 | −0.733998 | − | 0.679152i | \(-0.762348\pi\) | ||||
−0.733998 | + | 0.679152i | \(0.762348\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 26.3605 | 0.833593 | ||||||||
\(11\) | −25.5408 | −0.700077 | −0.350038 | − | 0.936735i | \(-0.613831\pi\) | ||||
−0.350038 | + | 0.936735i | \(0.613831\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −70.8493 | −1.51154 | −0.755771 | − | 0.654836i | \(-0.772738\pi\) | ||||
−0.755771 | + | 0.654836i | \(0.772738\pi\) | |||||||
\(14\) | 54.3753 | 1.03803 | ||||||||
\(15\) | 39.5408 | 0.680626 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −16.3679 | −0.233518 | −0.116759 | − | 0.993160i | \(-0.537250\pi\) | ||||
−0.116759 | + | 0.993160i | \(0.537250\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −93.5839 | −1.12998 | −0.564990 | − | 0.825098i | \(-0.691120\pi\) | ||||
−0.564990 | + | 0.825098i | \(0.691120\pi\) | |||||||
\(20\) | −52.7211 | −0.589439 | ||||||||
\(21\) | 81.5630 | 0.847548 | ||||||||
\(22\) | 51.0816 | 0.495029 | ||||||||
\(23\) | 42.9817 | 0.389665 | 0.194833 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194833 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 48.7195 | 0.389756 | ||||||||
\(26\) | 141.699 | 1.06882 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −108.751 | −0.733998 | ||||||||
\(29\) | −46.2217 | −0.295971 | −0.147985 | − | 0.988990i | \(-0.547279\pi\) | ||||
−0.147985 | + | 0.988990i | \(0.547279\pi\) | |||||||
\(30\) | −79.0816 | −0.481275 | ||||||||
\(31\) | 47.2024 | 0.273478 | 0.136739 | − | 0.990607i | \(-0.456338\pi\) | ||||
0.136739 | + | 0.990607i | \(0.456338\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 76.6224 | 0.404189 | ||||||||
\(34\) | 32.7358 | 0.165122 | ||||||||
\(35\) | 358.341 | 1.73059 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −272.669 | −1.21153 | −0.605763 | − | 0.795645i | \(-0.707132\pi\) | ||||
−0.605763 | + | 0.795645i | \(0.707132\pi\) | |||||||
\(38\) | 187.168 | 0.799016 | ||||||||
\(39\) | 212.548 | 0.872690 | ||||||||
\(40\) | 105.442 | 0.416797 | ||||||||
\(41\) | −8.26282 | −0.0314741 | −0.0157370 | − | 0.999876i | \(-0.505009\pi\) | ||||
−0.0157370 | + | 0.999876i | \(0.505009\pi\) | |||||||
\(42\) | −163.126 | −0.599307 | ||||||||
\(43\) | −408.690 | −1.44941 | −0.724705 | − | 0.689059i | \(-0.758024\pi\) | ||||
−0.724705 | + | 0.689059i | \(0.758024\pi\) | |||||||
\(44\) | −102.163 | −0.350038 | ||||||||
\(45\) | −118.622 | −0.392960 | ||||||||
\(46\) | −85.9633 | −0.275535 | ||||||||
\(47\) | 550.627 | 1.70888 | 0.854438 | − | 0.519554i | \(-0.173902\pi\) | ||||
0.854438 | + | 0.519554i | \(0.173902\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 396.169 | 1.15501 | ||||||||
\(50\) | −97.4389 | −0.275599 | ||||||||
\(51\) | 49.1038 | 0.134822 | ||||||||
\(52\) | −283.397 | −0.755771 | ||||||||
\(53\) | −45.1847 | −0.117106 | −0.0585528 | − | 0.998284i | \(-0.518649\pi\) | ||||
−0.0585528 | + | 0.998284i | \(0.518649\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 336.635 | 0.825306 | ||||||||
\(56\) | 217.501 | 0.519015 | ||||||||
\(57\) | 280.752 | 0.652394 | ||||||||
\(58\) | 92.4434 | 0.209283 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | 158.163 | 0.340313 | ||||||||
\(61\) | 507.849 | 1.06596 | 0.532979 | − | 0.846129i | \(-0.321073\pi\) | ||||
0.532979 | + | 0.846129i | \(0.321073\pi\) | |||||||
\(62\) | −94.4049 | −0.193378 | ||||||||
\(63\) | −244.689 | −0.489332 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 933.813 | 1.78193 | ||||||||
\(66\) | −153.245 | −0.285805 | ||||||||
\(67\) | −9.08450 | −0.0165649 | −0.00828245 | − | 0.999966i | \(-0.502636\pi\) | ||||
−0.00828245 | + | 0.999966i | \(0.502636\pi\) | |||||||
\(68\) | −65.4717 | −0.116759 | ||||||||
\(69\) | −128.945 | −0.224973 | ||||||||
\(70\) | −716.681 | −1.22371 | ||||||||
\(71\) | 57.0435 | 0.0953495 | 0.0476748 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476748 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −31.6317 | −0.0507153 | −0.0253576 | − | 0.999678i | \(-0.508072\pi\) | ||||
−0.0253576 | + | 0.999678i | \(0.508072\pi\) | |||||||
\(74\) | 545.337 | 0.856678 | ||||||||
\(75\) | −146.158 | −0.225026 | ||||||||
\(76\) | −374.335 | −0.564990 | ||||||||
\(77\) | 694.395 | 1.02771 | ||||||||
\(78\) | −425.096 | −0.617085 | ||||||||
\(79\) | 1066.85 | 1.51937 | 0.759686 | − | 0.650290i | \(-0.225353\pi\) | ||||
0.759686 | + | 0.650290i | \(0.225353\pi\) | |||||||
\(80\) | −210.884 | −0.294720 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 16.5256 | 0.0222555 | ||||||||
\(83\) | 1017.26 | 1.34528 | 0.672640 | − | 0.739969i | \(-0.265160\pi\) | ||||
0.672640 | + | 0.739969i | \(0.265160\pi\) | |||||||
\(84\) | 326.252 | 0.423774 | ||||||||
\(85\) | 215.734 | 0.275289 | ||||||||
\(86\) | 817.380 | 1.02489 | ||||||||
\(87\) | 138.665 | 0.170879 | ||||||||
\(88\) | 204.326 | 0.247514 | ||||||||
\(89\) | −41.5553 | −0.0494927 | −0.0247464 | − | 0.999694i | \(-0.507878\pi\) | ||||
−0.0247464 | + | 0.999694i | \(0.507878\pi\) | |||||||
\(90\) | 237.245 | 0.277864 | ||||||||
\(91\) | 1926.23 | 2.21894 | ||||||||
\(92\) | 171.927 | 0.194833 | ||||||||
\(93\) | −141.607 | −0.157892 | ||||||||
\(94\) | −1101.25 | −1.20836 | ||||||||
\(95\) | 1233.46 | 1.33211 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −1009.54 | −1.05674 | −0.528368 | − | 0.849015i | \(-0.677196\pi\) | ||||
−0.528368 | + | 0.849015i | \(0.677196\pi\) | |||||||
\(98\) | −792.337 | −0.816716 | ||||||||
\(99\) | −229.867 | −0.233359 | ||||||||
\(100\) | 194.878 | 0.194878 | ||||||||
\(101\) | −863.519 | −0.850726 | −0.425363 | − | 0.905023i | \(-0.639854\pi\) | ||||
−0.425363 | + | 0.905023i | \(0.639854\pi\) | |||||||
\(102\) | −98.2075 | −0.0953333 | ||||||||
\(103\) | −1870.17 | −1.78906 | −0.894532 | − | 0.447003i | \(-0.852491\pi\) | ||||
−0.894532 | + | 0.447003i | \(0.852491\pi\) | |||||||
\(104\) | 566.794 | 0.534411 | ||||||||
\(105\) | −1075.02 | −0.999156 | ||||||||
\(106\) | 90.3694 | 0.0828062 | ||||||||
\(107\) | −1147.67 | −1.03691 | −0.518457 | − | 0.855104i | \(-0.673493\pi\) | ||||
−0.518457 | + | 0.855104i | \(0.673493\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −1210.19 | −1.06345 | −0.531723 | − | 0.846918i | \(-0.678455\pi\) | ||||
−0.531723 | + | 0.846918i | \(0.678455\pi\) | |||||||
\(110\) | −673.269 | −0.583579 | ||||||||
\(111\) | 818.006 | 0.699475 | ||||||||
\(112\) | −435.003 | −0.366999 | ||||||||
\(113\) | 620.165 | 0.516285 | 0.258142 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258142 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(114\) | −561.503 | −0.461312 | ||||||||
\(115\) | −566.510 | −0.459368 | ||||||||
\(116\) | −184.887 | −0.147985 | ||||||||
\(117\) | −637.644 | −0.503848 | ||||||||
\(118\) | 118.000 | 0.0920575 | ||||||||
\(119\) | 445.006 | 0.342803 | ||||||||
\(120\) | −316.326 | −0.240638 | ||||||||
\(121\) | −678.667 | −0.509893 | ||||||||
\(122\) | −1015.70 | −0.753746 | ||||||||
\(123\) | 24.7885 | 0.0181716 | ||||||||
\(124\) | 188.810 | 0.136739 | ||||||||
\(125\) | 1005.40 | 0.719404 | ||||||||
\(126\) | 489.378 | 0.346010 | ||||||||
\(127\) | −1267.72 | −0.885763 | −0.442882 | − | 0.896580i | \(-0.646044\pi\) | ||||
−0.442882 | + | 0.896580i | \(0.646044\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1226.07 | 0.836817 | ||||||||
\(130\) | −1867.63 | −1.26001 | ||||||||
\(131\) | −1615.99 | −1.07778 | −0.538892 | − | 0.842375i | \(-0.681157\pi\) | ||||
−0.538892 | + | 0.842375i | \(0.681157\pi\) | |||||||
\(132\) | 306.490 | 0.202095 | ||||||||
\(133\) | 2544.33 | 1.65880 | ||||||||
\(134\) | 18.1690 | 0.0117132 | ||||||||
\(135\) | 355.867 | 0.226875 | ||||||||
\(136\) | 130.943 | 0.0825611 | ||||||||
\(137\) | −2033.70 | −1.26826 | −0.634128 | − | 0.773228i | \(-0.718641\pi\) | ||||
−0.634128 | + | 0.773228i | \(0.718641\pi\) | |||||||
\(138\) | 257.890 | 0.159080 | ||||||||
\(139\) | 2082.43 | 1.27072 | 0.635358 | − | 0.772218i | \(-0.280853\pi\) | ||||
0.635358 | + | 0.772218i | \(0.280853\pi\) | |||||||
\(140\) | 1433.36 | 0.865295 | ||||||||
\(141\) | −1651.88 | −0.986620 | ||||||||
\(142\) | −114.087 | −0.0674223 | ||||||||
\(143\) | 1809.55 | 1.05820 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 609.215 | 0.348914 | ||||||||
\(146\) | 63.2635 | 0.0358611 | ||||||||
\(147\) | −1188.51 | −0.666846 | ||||||||
\(148\) | −1090.67 | −0.605763 | ||||||||
\(149\) | −611.676 | −0.336312 | −0.168156 | − | 0.985760i | \(-0.553781\pi\) | ||||
−0.168156 | + | 0.985760i | \(0.553781\pi\) | |||||||
\(150\) | 292.317 | 0.159117 | ||||||||
\(151\) | −42.0765 | −0.0226764 | −0.0113382 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113382 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(152\) | 748.671 | 0.399508 | ||||||||
\(153\) | −147.311 | −0.0778393 | ||||||||
\(154\) | −1388.79 | −0.726700 | ||||||||
\(155\) | −622.141 | −0.322397 | ||||||||
\(156\) | 850.191 | 0.436345 | ||||||||
\(157\) | 251.374 | 0.127782 | 0.0638912 | − | 0.997957i | \(-0.479649\pi\) | ||||
0.0638912 | + | 0.997957i | \(0.479649\pi\) | |||||||
\(158\) | −2133.71 | −1.07436 | ||||||||
\(159\) | 135.554 | 0.0676110 | ||||||||
\(160\) | 421.769 | 0.208398 | ||||||||
\(161\) | −1168.57 | −0.572027 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −3291.77 | −1.58179 | −0.790893 | − | 0.611954i | \(-0.790384\pi\) | ||||
−0.790893 | + | 0.611954i | \(0.790384\pi\) | |||||||
\(164\) | −33.0513 | −0.0157370 | ||||||||
\(165\) | −1009.90 | −0.476490 | ||||||||
\(166\) | −2034.51 | −0.951257 | ||||||||
\(167\) | −1372.32 | −0.635887 | −0.317944 | − | 0.948110i | \(-0.602992\pi\) | ||||
−0.317944 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(168\) | −652.504 | −0.299653 | ||||||||
\(169\) | 2822.62 | 1.28476 | ||||||||
\(170\) | −431.467 | −0.194659 | ||||||||
\(171\) | −842.255 | −0.376660 | ||||||||
\(172\) | −1634.76 | −0.724705 | ||||||||
\(173\) | −1188.59 | −0.522354 | −0.261177 | − | 0.965291i | \(-0.584111\pi\) | ||||
−0.261177 | + | 0.965291i | \(0.584111\pi\) | |||||||
\(174\) | −277.330 | −0.120830 | ||||||||
\(175\) | −1324.57 | −0.572160 | ||||||||
\(176\) | −408.653 | −0.175019 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 83.1106 | 0.0349966 | ||||||||
\(179\) | −2.50060 | −0.00104416 | −0.000522078 | − | 1.00000i | \(-0.500166\pi\) | ||||
−0.000522078 | 1.00000i | \(0.500166\pi\) | ||||||||
\(180\) | −474.490 | −0.196480 | ||||||||
\(181\) | 1504.51 | 0.617841 | 0.308920 | − | 0.951088i | \(-0.400032\pi\) | ||||
0.308920 | + | 0.951088i | \(0.400032\pi\) | |||||||
\(182\) | −3852.45 | −1.56903 | ||||||||
\(183\) | −1523.55 | −0.615431 | ||||||||
\(184\) | −343.853 | −0.137767 | ||||||||
\(185\) | 3593.85 | 1.42824 | ||||||||
\(186\) | 283.215 | 0.111647 | ||||||||
\(187\) | 418.050 | 0.163480 | ||||||||
\(188\) | 2202.51 | 0.854438 | ||||||||
\(189\) | 734.067 | 0.282516 | ||||||||
\(190\) | −2466.92 | −0.941943 | ||||||||
\(191\) | 4474.89 | 1.69525 | 0.847623 | − | 0.530599i | \(-0.178033\pi\) | ||||
0.847623 | + | 0.530599i | \(0.178033\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −4906.36 | −1.82988 | −0.914942 | − | 0.403586i | \(-0.867764\pi\) | ||||
−0.914942 | + | 0.403586i | \(0.867764\pi\) | |||||||
\(194\) | 2019.08 | 0.747225 | ||||||||
\(195\) | −2801.44 | −1.02880 | ||||||||
\(196\) | 1584.67 | 0.577505 | ||||||||
\(197\) | −2489.12 | −0.900216 | −0.450108 | − | 0.892974i | \(-0.648615\pi\) | ||||
−0.450108 | + | 0.892974i | \(0.648615\pi\) | |||||||
\(198\) | 459.734 | 0.165010 | ||||||||
\(199\) | 185.142 | 0.0659517 | 0.0329758 | − | 0.999456i | \(-0.489502\pi\) | ||||
0.0329758 | + | 0.999456i | \(0.489502\pi\) | |||||||
\(200\) | −389.756 | −0.137799 | ||||||||
\(201\) | 27.2535 | 0.00956375 | ||||||||
\(202\) | 1727.04 | 0.601554 | ||||||||
\(203\) | 1256.66 | 0.434484 | ||||||||
\(204\) | 196.415 | 0.0674108 | ||||||||
\(205\) | 108.906 | 0.0371041 | ||||||||
\(206\) | 3740.35 | 1.26506 | ||||||||
\(207\) | 386.835 | 0.129888 | ||||||||
\(208\) | −1133.59 | −0.377886 | ||||||||
\(209\) | 2390.21 | 0.791072 | ||||||||
\(210\) | 2150.04 | 0.706510 | ||||||||
\(211\) | −5736.47 | −1.87164 | −0.935818 | − | 0.352483i | \(-0.885337\pi\) | ||||
−0.935818 | + | 0.352483i | \(0.885337\pi\) | |||||||
\(212\) | −180.739 | −0.0585528 | ||||||||
\(213\) | −171.130 | −0.0550501 | ||||||||
\(214\) | 2295.35 | 0.733209 | ||||||||
\(215\) | 5386.64 | 1.70868 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1283.32 | −0.401464 | ||||||||
\(218\) | 2420.39 | 0.751970 | ||||||||
\(219\) | 94.8952 | 0.0292805 | ||||||||
\(220\) | 1346.54 | 0.412653 | ||||||||
\(221\) | 1159.66 | 0.352972 | ||||||||
\(222\) | −1636.01 | −0.494603 | ||||||||
\(223\) | 4228.14 | 1.26967 | 0.634837 | − | 0.772646i | \(-0.281067\pi\) | ||||
0.634837 | + | 0.772646i | \(0.281067\pi\) | |||||||
\(224\) | 870.005 | 0.259507 | ||||||||
\(225\) | 438.475 | 0.129919 | ||||||||
\(226\) | −1240.33 | −0.365069 | ||||||||
\(227\) | 5589.59 | 1.63434 | 0.817168 | − | 0.576399i | \(-0.195543\pi\) | ||||
0.817168 | + | 0.576399i | \(0.195543\pi\) | |||||||
\(228\) | 1123.01 | 0.326197 | ||||||||
\(229\) | 2306.37 | 0.665543 | 0.332771 | − | 0.943008i | \(-0.392016\pi\) | ||||
0.332771 | + | 0.943008i | \(0.392016\pi\) | |||||||
\(230\) | 1133.02 | 0.324822 | ||||||||
\(231\) | −2083.18 | −0.593348 | ||||||||
\(232\) | 369.774 | 0.104642 | ||||||||
\(233\) | −1393.27 | −0.391744 | −0.195872 | − | 0.980629i | \(-0.562754\pi\) | ||||
−0.195872 | + | 0.980629i | \(0.562754\pi\) | |||||||
\(234\) | 1275.29 | 0.356274 | ||||||||
\(235\) | −7257.41 | −2.01456 | ||||||||
\(236\) | −236.000 | −0.0650945 | ||||||||
\(237\) | −3200.56 | −0.877210 | ||||||||
\(238\) | −890.011 | −0.242399 | ||||||||
\(239\) | −2293.76 | −0.620800 | −0.310400 | − | 0.950606i | \(-0.600463\pi\) | ||||
−0.310400 | + | 0.950606i | \(0.600463\pi\) | |||||||
\(240\) | 632.653 | 0.170157 | ||||||||
\(241\) | −4418.38 | −1.18097 | −0.590483 | − | 0.807050i | \(-0.701063\pi\) | ||||
−0.590483 | + | 0.807050i | \(0.701063\pi\) | |||||||
\(242\) | 1357.33 | 0.360549 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 2031.40 | 0.532979 | ||||||||
\(245\) | −5221.61 | −1.36162 | ||||||||
\(246\) | −49.5769 | −0.0128492 | ||||||||
\(247\) | 6630.35 | 1.70801 | ||||||||
\(248\) | −377.619 | −0.0966890 | ||||||||
\(249\) | −3051.77 | −0.776698 | ||||||||
\(250\) | −2010.80 | −0.508696 | ||||||||
\(251\) | 2942.59 | 0.739978 | 0.369989 | − | 0.929036i | \(-0.379361\pi\) | ||||
0.369989 | + | 0.929036i | \(0.379361\pi\) | |||||||
\(252\) | −978.756 | −0.244666 | ||||||||
\(253\) | −1097.79 | −0.272795 | ||||||||
\(254\) | 2535.44 | 0.626329 | ||||||||
\(255\) | −647.201 | −0.158938 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5519.95 | −1.33979 | −0.669894 | − | 0.742457i | \(-0.733660\pi\) | ||||
−0.669894 | + | 0.742457i | \(0.733660\pi\) | |||||||
\(258\) | −2452.14 | −0.591719 | ||||||||
\(259\) | 7413.22 | 1.77851 | ||||||||
\(260\) | 3735.25 | 0.890963 | ||||||||
\(261\) | −415.995 | −0.0986570 | ||||||||
\(262\) | 3231.98 | 0.762109 | ||||||||
\(263\) | 5184.34 | 1.21551 | 0.607757 | − | 0.794123i | \(-0.292069\pi\) | ||||
0.607757 | + | 0.794123i | \(0.292069\pi\) | |||||||
\(264\) | −612.979 | −0.142903 | ||||||||
\(265\) | 595.547 | 0.138053 | ||||||||
\(266\) | −5088.65 | −1.17295 | ||||||||
\(267\) | 124.666 | 0.0285746 | ||||||||
\(268\) | −36.3380 | −0.00828245 | ||||||||
\(269\) | 5819.75 | 1.31910 | 0.659548 | − | 0.751663i | \(-0.270748\pi\) | ||||
0.659548 | + | 0.751663i | \(0.270748\pi\) | |||||||
\(270\) | −711.734 | −0.160425 | ||||||||
\(271\) | 5740.44 | 1.28674 | 0.643371 | − | 0.765554i | \(-0.277535\pi\) | ||||
0.643371 | + | 0.765554i | \(0.277535\pi\) | |||||||
\(272\) | −261.887 | −0.0583795 | ||||||||
\(273\) | −5778.68 | −1.28110 | ||||||||
\(274\) | 4067.41 | 0.896793 | ||||||||
\(275\) | −1244.33 | −0.272859 | ||||||||
\(276\) | −515.780 | −0.112487 | ||||||||
\(277\) | 3439.33 | 0.746027 | 0.373013 | − | 0.927826i | \(-0.378325\pi\) | ||||
0.373013 | + | 0.927826i | \(0.378325\pi\) | |||||||
\(278\) | −4164.86 | −0.898531 | ||||||||
\(279\) | 424.822 | 0.0911592 | ||||||||
\(280\) | −2866.72 | −0.611856 | ||||||||
\(281\) | −2630.81 | −0.558508 | −0.279254 | − | 0.960217i | \(-0.590087\pi\) | ||||
−0.279254 | + | 0.960217i | \(0.590087\pi\) | |||||||
\(282\) | 3303.76 | 0.697645 | ||||||||
\(283\) | −2835.99 | −0.595696 | −0.297848 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297848 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(284\) | 228.174 | 0.0476748 | ||||||||
\(285\) | −3700.38 | −0.769094 | ||||||||
\(286\) | −3619.10 | −0.748257 | ||||||||
\(287\) | 224.647 | 0.0462038 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −4645.09 | −0.945469 | ||||||||
\(290\) | −1218.43 | −0.246719 | ||||||||
\(291\) | 3028.62 | 0.610107 | ||||||||
\(292\) | −126.527 | −0.0253576 | ||||||||
\(293\) | −7754.35 | −1.54612 | −0.773062 | − | 0.634331i | \(-0.781276\pi\) | ||||
−0.773062 | + | 0.634331i | \(0.781276\pi\) | |||||||
\(294\) | 2377.01 | 0.471531 | ||||||||
\(295\) | 777.636 | 0.153477 | ||||||||
\(296\) | 2181.35 | 0.428339 | ||||||||
\(297\) | 689.602 | 0.134730 | ||||||||
\(298\) | 1223.35 | 0.237808 | ||||||||
\(299\) | −3045.22 | −0.588995 | ||||||||
\(300\) | −584.634 | −0.112513 | ||||||||
\(301\) | 11111.3 | 2.12773 | ||||||||
\(302\) | 84.1530 | 0.0160346 | ||||||||
\(303\) | 2590.56 | 0.491167 | ||||||||
\(304\) | −1497.34 | −0.282495 | ||||||||
\(305\) | −6693.59 | −1.25663 | ||||||||
\(306\) | 294.623 | 0.0550407 | ||||||||
\(307\) | 4407.11 | 0.819307 | 0.409653 | − | 0.912241i | \(-0.365650\pi\) | ||||
0.409653 | + | 0.912241i | \(0.365650\pi\) | |||||||
\(308\) | 2777.58 | 0.513855 | ||||||||
\(309\) | 5610.52 | 1.03292 | ||||||||
\(310\) | 1244.28 | 0.227969 | ||||||||
\(311\) | 1940.72 | 0.353853 | 0.176926 | − | 0.984224i | \(-0.443385\pi\) | ||||
0.176926 | + | 0.984224i | \(0.443385\pi\) | |||||||
\(312\) | −1700.38 | −0.308542 | ||||||||
\(313\) | 6120.82 | 1.10533 | 0.552667 | − | 0.833402i | \(-0.313610\pi\) | ||||
0.552667 | + | 0.833402i | \(0.313610\pi\) | |||||||
\(314\) | −502.749 | −0.0903559 | ||||||||
\(315\) | 3225.07 | 0.576863 | ||||||||
\(316\) | 4267.41 | 0.759686 | ||||||||
\(317\) | −3220.49 | −0.570602 | −0.285301 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285301 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(318\) | −271.108 | −0.0478082 | ||||||||
\(319\) | 1180.54 | 0.207202 | ||||||||
\(320\) | −843.537 | −0.147360 | ||||||||
\(321\) | 3443.02 | 0.598663 | ||||||||
\(322\) | 2337.14 | 0.404484 | ||||||||
\(323\) | 1531.77 | 0.263870 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −3451.74 | −0.589132 | ||||||||
\(326\) | 6583.54 | 1.11849 | ||||||||
\(327\) | 3630.58 | 0.613981 | ||||||||
\(328\) | 66.1026 | 0.0111278 | ||||||||
\(329\) | −14970.2 | −2.50862 | ||||||||
\(330\) | 2019.81 | 0.336930 | ||||||||
\(331\) | 21.1960 | 0.00351976 | 0.00175988 | − | 0.999998i | \(-0.499440\pi\) | ||||
0.00175988 | + | 0.999998i | \(0.499440\pi\) | |||||||
\(332\) | 4069.02 | 0.672640 | ||||||||
\(333\) | −2454.02 | −0.403842 | ||||||||
\(334\) | 2744.64 | 0.449640 | ||||||||
\(335\) | 119.736 | 0.0195280 | ||||||||
\(336\) | 1305.01 | 0.211887 | ||||||||
\(337\) | 7864.17 | 1.27118 | 0.635591 | − | 0.772026i | \(-0.280756\pi\) | ||||
0.635591 | + | 0.772026i | \(0.280756\pi\) | |||||||
\(338\) | −5645.24 | −0.908464 | ||||||||
\(339\) | −1860.49 | −0.298077 | ||||||||
\(340\) | 862.935 | 0.137645 | ||||||||
\(341\) | −1205.59 | −0.191455 | ||||||||
\(342\) | 1684.51 | 0.266339 | ||||||||
\(343\) | −1445.53 | −0.227555 | ||||||||
\(344\) | 3269.52 | 0.512444 | ||||||||
\(345\) | 1699.53 | 0.265216 | ||||||||
\(346\) | 2377.19 | 0.369360 | ||||||||
\(347\) | 11432.1 | 1.76862 | 0.884308 | − | 0.466904i | \(-0.154631\pi\) | ||||
0.884308 | + | 0.466904i | \(0.154631\pi\) | |||||||
\(348\) | 554.661 | 0.0854394 | ||||||||
\(349\) | 7424.04 | 1.13868 | 0.569341 | − | 0.822102i | \(-0.307199\pi\) | ||||
0.569341 | + | 0.822102i | \(0.307199\pi\) | |||||||
\(350\) | 2649.14 | 0.404578 | ||||||||
\(351\) | 1912.93 | 0.290897 | ||||||||
\(352\) | 817.306 | 0.123757 | ||||||||
\(353\) | −9914.93 | −1.49495 | −0.747476 | − | 0.664288i | \(-0.768735\pi\) | ||||
−0.747476 | + | 0.664288i | \(0.768735\pi\) | |||||||
\(354\) | −354.000 | −0.0531494 | ||||||||
\(355\) | −751.848 | −0.112406 | ||||||||
\(356\) | −166.221 | −0.0247464 | ||||||||
\(357\) | −1335.02 | −0.197918 | ||||||||
\(358\) | 5.00121 | 0.000738330 0 | ||||||||
\(359\) | −5706.08 | −0.838874 | −0.419437 | − | 0.907785i | \(-0.637772\pi\) | ||||
−0.419437 | + | 0.907785i | \(0.637772\pi\) | |||||||
\(360\) | 948.979 | 0.138932 | ||||||||
\(361\) | 1898.94 | 0.276854 | ||||||||
\(362\) | −3009.02 | −0.436879 | ||||||||
\(363\) | 2036.00 | 0.294387 | ||||||||
\(364\) | 7704.90 | 1.10947 | ||||||||
\(365\) | 416.915 | 0.0597872 | ||||||||
\(366\) | 3047.09 | 0.435175 | ||||||||
\(367\) | 10571.3 | 1.50359 | 0.751796 | − | 0.659395i | \(-0.229188\pi\) | ||||
0.751796 | + | 0.659395i | \(0.229188\pi\) | |||||||
\(368\) | 687.707 | 0.0974163 | ||||||||
\(369\) | −74.3654 | −0.0104914 | ||||||||
\(370\) | −7187.69 | −1.00992 | ||||||||
\(371\) | 1228.47 | 0.171911 | ||||||||
\(372\) | −566.429 | −0.0789462 | ||||||||
\(373\) | 1164.85 | 0.161699 | 0.0808495 | − | 0.996726i | \(-0.474237\pi\) | ||||
0.0808495 | + | 0.996726i | \(0.474237\pi\) | |||||||
\(374\) | −836.100 | −0.115598 | ||||||||
\(375\) | −3016.19 | −0.415348 | ||||||||
\(376\) | −4405.01 | −0.604179 | ||||||||
\(377\) | 3274.78 | 0.447373 | ||||||||
\(378\) | −1468.13 | −0.199769 | ||||||||
\(379\) | −5178.94 | −0.701911 | −0.350956 | − | 0.936392i | \(-0.614143\pi\) | ||||
−0.350956 | + | 0.936392i | \(0.614143\pi\) | |||||||
\(380\) | 4933.84 | 0.666055 | ||||||||
\(381\) | 3803.16 | 0.511396 | ||||||||
\(382\) | −8949.79 | −1.19872 | ||||||||
\(383\) | 10634.4 | 1.41878 | 0.709392 | − | 0.704814i | \(-0.248970\pi\) | ||||
0.709392 | + | 0.704814i | \(0.248970\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −9152.31 | −1.21154 | ||||||||
\(386\) | 9812.72 | 1.29392 | ||||||||
\(387\) | −3678.21 | −0.483137 | ||||||||
\(388\) | −4038.17 | −0.528368 | ||||||||
\(389\) | −1177.81 | −0.153514 | −0.0767572 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767572 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(390\) | 5602.88 | 0.727468 | ||||||||
\(391\) | −703.521 | −0.0909938 | ||||||||
\(392\) | −3169.35 | −0.408358 | ||||||||
\(393\) | 4847.97 | 0.622259 | ||||||||
\(394\) | 4978.24 | 0.636549 | ||||||||
\(395\) | −14061.4 | −1.79116 | ||||||||
\(396\) | −919.469 | −0.116679 | ||||||||
\(397\) | −2986.65 | −0.377570 | −0.188785 | − | 0.982018i | \(-0.560455\pi\) | ||||
−0.188785 | + | 0.982018i | \(0.560455\pi\) | |||||||
\(398\) | −370.284 | −0.0466349 | ||||||||
\(399\) | −7632.98 | −0.957711 | ||||||||
\(400\) | 779.511 | 0.0974389 | ||||||||
\(401\) | −4191.02 | −0.521919 | −0.260960 | − | 0.965350i | \(-0.584039\pi\) | ||||
−0.260960 | + | 0.965350i | \(0.584039\pi\) | |||||||
\(402\) | −54.5070 | −0.00676259 | ||||||||
\(403\) | −3344.26 | −0.413373 | ||||||||
\(404\) | −3454.08 | −0.425363 | ||||||||
\(405\) | −1067.60 | −0.130987 | ||||||||
\(406\) | −2513.32 | −0.307227 | ||||||||
\(407\) | 6964.18 | 0.848161 | ||||||||
\(408\) | −392.830 | −0.0476666 | ||||||||
\(409\) | 582.890 | 0.0704696 | 0.0352348 | − | 0.999379i | \(-0.488782\pi\) | ||||
0.0352348 | + | 0.999379i | \(0.488782\pi\) | |||||||
\(410\) | −217.812 | −0.0262366 | ||||||||
\(411\) | 6101.11 | 0.732228 | ||||||||
\(412\) | −7480.69 | −0.894532 | ||||||||
\(413\) | 1604.07 | 0.191117 | ||||||||
\(414\) | −773.670 | −0.0918449 | ||||||||
\(415\) | −13407.7 | −1.58592 | ||||||||
\(416\) | 2267.18 | 0.267206 | ||||||||
\(417\) | −6247.29 | −0.733648 | ||||||||
\(418\) | −4780.41 | −0.559372 | ||||||||
\(419\) | 15862.1 | 1.84944 | 0.924718 | − | 0.380652i | \(-0.124300\pi\) | ||||
0.924718 | + | 0.380652i | \(0.124300\pi\) | |||||||
\(420\) | −4300.09 | −0.499578 | ||||||||
\(421\) | −1998.86 | −0.231398 | −0.115699 | − | 0.993284i | \(-0.536911\pi\) | ||||
−0.115699 | + | 0.993284i | \(0.536911\pi\) | |||||||
\(422\) | 11472.9 | 1.32345 | ||||||||
\(423\) | 4955.64 | 0.569625 | ||||||||
\(424\) | 361.478 | 0.0414031 | ||||||||
\(425\) | −797.436 | −0.0910149 | ||||||||
\(426\) | 342.261 | 0.0389263 | ||||||||
\(427\) | −13807.2 | −1.56482 | ||||||||
\(428\) | −4590.70 | −0.518457 | ||||||||
\(429\) | −5428.64 | −0.610950 | ||||||||
\(430\) | −10773.3 | −1.20822 | ||||||||
\(431\) | −8287.44 | −0.926199 | −0.463100 | − | 0.886306i | \(-0.653263\pi\) | ||||
−0.463100 | + | 0.886306i | \(0.653263\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −1060.75 | −0.117728 | −0.0588639 | − | 0.998266i | \(-0.518748\pi\) | ||||
−0.0588639 | + | 0.998266i | \(0.518748\pi\) | |||||||
\(434\) | 2566.65 | 0.283878 | ||||||||
\(435\) | −1827.64 | −0.201446 | ||||||||
\(436\) | −4840.78 | −0.531723 | ||||||||
\(437\) | −4022.39 | −0.440314 | ||||||||
\(438\) | −189.790 | −0.0207044 | ||||||||
\(439\) | 1340.69 | 0.145757 | 0.0728787 | − | 0.997341i | \(-0.476781\pi\) | ||||
0.0728787 | + | 0.997341i | \(0.476781\pi\) | |||||||
\(440\) | −2693.08 | −0.291790 | ||||||||
\(441\) | 3565.52 | 0.385004 | ||||||||
\(442\) | −2319.31 | −0.249589 | ||||||||
\(443\) | −16182.5 | −1.73556 | −0.867782 | − | 0.496945i | \(-0.834455\pi\) | ||||
−0.867782 | + | 0.496945i | \(0.834455\pi\) | |||||||
\(444\) | 3272.02 | 0.349737 | ||||||||
\(445\) | 547.710 | 0.0583459 | ||||||||
\(446\) | −8456.28 | −0.897795 | ||||||||
\(447\) | 1835.03 | 0.194170 | ||||||||
\(448\) | −1740.01 | −0.183499 | ||||||||
\(449\) | 993.687 | 0.104443 | 0.0522216 | − | 0.998636i | \(-0.483370\pi\) | ||||
0.0522216 | + | 0.998636i | \(0.483370\pi\) | |||||||
\(450\) | −876.950 | −0.0918663 | ||||||||
\(451\) | 211.039 | 0.0220342 | ||||||||
\(452\) | 2480.66 | 0.258142 | ||||||||
\(453\) | 126.230 | 0.0130922 | ||||||||
\(454\) | −11179.2 | −1.15565 | ||||||||
\(455\) | −25388.2 | −2.61586 | ||||||||
\(456\) | −2246.01 | −0.230656 | ||||||||
\(457\) | 833.216 | 0.0852871 | 0.0426436 | − | 0.999090i | \(-0.486422\pi\) | ||||
0.0426436 | + | 0.999090i | \(0.486422\pi\) | |||||||
\(458\) | −4612.74 | −0.470610 | ||||||||
\(459\) | 441.934 | 0.0449405 | ||||||||
\(460\) | −2266.04 | −0.229684 | ||||||||
\(461\) | −17336.5 | −1.75150 | −0.875748 | − | 0.482769i | \(-0.839631\pi\) | ||||
−0.875748 | + | 0.482769i | \(0.839631\pi\) | |||||||
\(462\) | 4166.37 | 0.419561 | ||||||||
\(463\) | 15278.3 | 1.53357 | 0.766785 | − | 0.641904i | \(-0.221855\pi\) | ||||
0.766785 | + | 0.641904i | \(0.221855\pi\) | |||||||
\(464\) | −739.547 | −0.0739927 | ||||||||
\(465\) | 1866.42 | 0.186136 | ||||||||
\(466\) | 2786.55 | 0.277005 | ||||||||
\(467\) | −15151.7 | −1.50136 | −0.750681 | − | 0.660665i | \(-0.770274\pi\) | ||||
−0.750681 | + | 0.660665i | \(0.770274\pi\) | |||||||
\(468\) | −2550.57 | −0.251924 | ||||||||
\(469\) | 246.986 | 0.0243172 | ||||||||
\(470\) | 14514.8 | 1.42451 | ||||||||
\(471\) | −754.123 | −0.0737753 | ||||||||
\(472\) | 472.000 | 0.0460287 | ||||||||
\(473\) | 10438.3 | 1.01470 | ||||||||
\(474\) | 6401.12 | 0.620281 | ||||||||
\(475\) | −4559.36 | −0.440416 | ||||||||
\(476\) | 1780.02 | 0.171402 | ||||||||
\(477\) | −406.662 | −0.0390352 | ||||||||
\(478\) | 4587.53 | 0.438972 | ||||||||
\(479\) | −18559.6 | −1.77038 | −0.885189 | − | 0.465231i | \(-0.845971\pi\) | ||||
−0.885189 | + | 0.465231i | \(0.845971\pi\) | |||||||
\(480\) | −1265.31 | −0.120319 | ||||||||
\(481\) | 19318.4 | 1.83127 | ||||||||
\(482\) | 8836.75 | 0.835069 | ||||||||
\(483\) | 3505.71 | 0.330260 | ||||||||
\(484\) | −2714.67 | −0.254946 | ||||||||
\(485\) | 13306.0 | 1.24576 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −12782.0 | −1.18934 | −0.594671 | − | 0.803969i | \(-0.702718\pi\) | ||||
−0.594671 | + | 0.803969i | \(0.702718\pi\) | |||||||
\(488\) | −4062.79 | −0.376873 | ||||||||
\(489\) | 9875.30 | 0.913245 | ||||||||
\(490\) | 10443.2 | 0.962809 | ||||||||
\(491\) | 7846.62 | 0.721207 | 0.360604 | − | 0.932719i | \(-0.382571\pi\) | ||||
0.360604 | + | 0.932719i | \(0.382571\pi\) | |||||||
\(492\) | 99.1539 | 0.00908578 | ||||||||
\(493\) | 756.553 | 0.0691145 | ||||||||
\(494\) | −13260.7 | −1.20775 | ||||||||
\(495\) | 3029.71 | 0.275102 | ||||||||
\(496\) | 755.239 | 0.0683694 | ||||||||
\(497\) | −1550.88 | −0.139973 | ||||||||
\(498\) | 6103.53 | 0.549209 | ||||||||
\(499\) | 20002.4 | 1.79445 | 0.897226 | − | 0.441571i | \(-0.145579\pi\) | ||||
0.897226 | + | 0.441571i | \(0.145579\pi\) | |||||||
\(500\) | 4021.59 | 0.359702 | ||||||||
\(501\) | 4116.96 | 0.367130 | ||||||||
\(502\) | −5885.18 | −0.523244 | ||||||||
\(503\) | 1592.53 | 0.141168 | 0.0705839 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705839 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(504\) | 1957.51 | 0.173005 | ||||||||
\(505\) | 11381.4 | 1.00290 | ||||||||
\(506\) | 2195.57 | 0.192895 | ||||||||
\(507\) | −8467.86 | −0.741757 | ||||||||
\(508\) | −5070.88 | −0.442882 | ||||||||
\(509\) | −6909.08 | −0.601649 | −0.300825 | − | 0.953679i | \(-0.597262\pi\) | ||||
−0.300825 | + | 0.953679i | \(0.597262\pi\) | |||||||
\(510\) | 1294.40 | 0.112386 | ||||||||
\(511\) | 859.993 | 0.0744498 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2526.76 | 0.217465 | ||||||||
\(514\) | 11039.9 | 0.947373 | ||||||||
\(515\) | 24649.4 | 2.10909 | ||||||||
\(516\) | 4904.28 | 0.418409 | ||||||||
\(517\) | −14063.4 | −1.19634 | ||||||||
\(518\) | −14826.4 | −1.25760 | ||||||||
\(519\) | 3565.78 | 0.301581 | ||||||||
\(520\) | −7470.50 | −0.630006 | ||||||||
\(521\) | 5022.19 | 0.422315 | 0.211158 | − | 0.977452i | \(-0.432277\pi\) | ||||
0.211158 | + | 0.977452i | \(0.432277\pi\) | |||||||
\(522\) | 831.991 | 0.0697610 | ||||||||
\(523\) | 1346.37 | 0.112567 | 0.0562835 | − | 0.998415i | \(-0.482075\pi\) | ||||
0.0562835 | + | 0.998415i | \(0.482075\pi\) | |||||||
\(524\) | −6463.97 | −0.538892 | ||||||||
\(525\) | 3973.70 | 0.330336 | ||||||||
\(526\) | −10368.7 | −0.859498 | ||||||||
\(527\) | −772.606 | −0.0638619 | ||||||||
\(528\) | 1225.96 | 0.101047 | ||||||||
\(529\) | −10319.6 | −0.848161 | ||||||||
\(530\) | −1191.09 | −0.0976185 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 10177.3 | 0.829402 | ||||||||
\(533\) | 585.415 | 0.0475744 | ||||||||
\(534\) | −249.332 | −0.0202053 | ||||||||
\(535\) | 15126.7 | 1.22240 | ||||||||
\(536\) | 72.6760 | 0.00585658 | ||||||||
\(537\) | 7.50181 | 0.000602844 0 | ||||||||
\(538\) | −11639.5 | −0.932741 | ||||||||
\(539\) | −10118.5 | −0.808596 | ||||||||
\(540\) | 1423.47 | 0.113438 | ||||||||
\(541\) | −15356.6 | −1.22039 | −0.610196 | − | 0.792251i | \(-0.708909\pi\) | ||||
−0.610196 | + | 0.792251i | \(0.708909\pi\) | |||||||
\(542\) | −11480.9 | −0.909864 | ||||||||
\(543\) | −4513.52 | −0.356711 | ||||||||
\(544\) | 523.774 | 0.0412805 | ||||||||
\(545\) | 15950.7 | 1.25367 | ||||||||
\(546\) | 11557.4 | 0.905878 | ||||||||
\(547\) | 13305.2 | 1.04002 | 0.520009 | − | 0.854160i | \(-0.325928\pi\) | ||||
0.520009 | + | 0.854160i | \(0.325928\pi\) | |||||||
\(548\) | −8134.82 | −0.634128 | ||||||||
\(549\) | 4570.64 | 0.355319 | ||||||||
\(550\) | 2488.67 | 0.192940 | ||||||||
\(551\) | 4325.61 | 0.334441 | ||||||||
\(552\) | 1031.56 | 0.0795401 | ||||||||
\(553\) | −29005.3 | −2.23043 | ||||||||
\(554\) | −6878.67 | −0.527521 | ||||||||
\(555\) | −10781.5 | −0.824596 | ||||||||
\(556\) | 8329.72 | 0.635358 | ||||||||
\(557\) | 5729.87 | 0.435875 | 0.217937 | − | 0.975963i | \(-0.430067\pi\) | ||||
0.217937 | + | 0.975963i | \(0.430067\pi\) | |||||||
\(558\) | −849.644 | −0.0644593 | ||||||||
\(559\) | 28955.4 | 2.19084 | ||||||||
\(560\) | 5733.45 | 0.432647 | ||||||||
\(561\) | −1254.15 | −0.0943855 | ||||||||
\(562\) | 5261.61 | 0.394925 | ||||||||
\(563\) | 6028.34 | 0.451269 | 0.225634 | − | 0.974212i | \(-0.427554\pi\) | ||||
0.225634 | + | 0.974212i | \(0.427554\pi\) | |||||||
\(564\) | −6607.52 | −0.493310 | ||||||||
\(565\) | −8173.94 | −0.608637 | ||||||||
\(566\) | 5671.97 | 0.421220 | ||||||||
\(567\) | −2202.20 | −0.163111 | ||||||||
\(568\) | −456.348 | −0.0337112 | ||||||||
\(569\) | 5645.33 | 0.415931 | 0.207965 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207965 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(570\) | 7400.76 | 0.543831 | ||||||||
\(571\) | −8432.15 | −0.617994 | −0.308997 | − | 0.951063i | \(-0.599993\pi\) | ||||
−0.308997 | + | 0.951063i | \(0.599993\pi\) | |||||||
\(572\) | 7238.19 | 0.529098 | ||||||||
\(573\) | −13424.7 | −0.978751 | ||||||||
\(574\) | −449.294 | −0.0326710 | ||||||||
\(575\) | 2094.04 | 0.151874 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7885.56 | 0.568943 | 0.284472 | − | 0.958684i | \(-0.408182\pi\) | ||||
0.284472 | + | 0.958684i | \(0.408182\pi\) | |||||||
\(578\) | 9290.18 | 0.668548 | ||||||||
\(579\) | 14719.1 | 1.05648 | ||||||||
\(580\) | 2436.86 | 0.174457 | ||||||||
\(581\) | −27656.8 | −1.97487 | ||||||||
\(582\) | −6057.25 | −0.431411 | ||||||||
\(583\) | 1154.05 | 0.0819829 | ||||||||
\(584\) | 253.054 | 0.0179306 | ||||||||
\(585\) | 8404.31 | 0.593975 | ||||||||
\(586\) | 15508.7 | 1.09327 | ||||||||
\(587\) | 10360.5 | 0.728490 | 0.364245 | − | 0.931303i | \(-0.381327\pi\) | ||||
0.364245 | + | 0.931303i | \(0.381327\pi\) | |||||||
\(588\) | −4754.02 | −0.333423 | ||||||||
\(589\) | −4417.39 | −0.309024 | ||||||||
\(590\) | −1555.27 | −0.108525 | ||||||||
\(591\) | 7467.37 | 0.519740 | ||||||||
\(592\) | −4362.70 | −0.302881 | ||||||||
\(593\) | −11986.1 | −0.830032 | −0.415016 | − | 0.909814i | \(-0.636224\pi\) | ||||
−0.415016 | + | 0.909814i | \(0.636224\pi\) | |||||||
\(594\) | −1379.20 | −0.0952684 | ||||||||
\(595\) | −5865.29 | −0.404124 | ||||||||
\(596\) | −2446.71 | −0.168156 | ||||||||
\(597\) | −555.427 | −0.0380772 | ||||||||
\(598\) | 6090.44 | 0.416483 | ||||||||
\(599\) | −6426.26 | −0.438347 | −0.219173 | − | 0.975686i | \(-0.570336\pi\) | ||||
−0.219173 | + | 0.975686i | \(0.570336\pi\) | |||||||
\(600\) | 1169.27 | 0.0795585 | ||||||||
\(601\) | 23916.6 | 1.62326 | 0.811630 | − | 0.584172i | \(-0.198580\pi\) | ||||
0.811630 | + | 0.584172i | \(0.198580\pi\) | |||||||
\(602\) | −22222.6 | −1.50453 | ||||||||
\(603\) | −81.7605 | −0.00552163 | ||||||||
\(604\) | −168.306 | −0.0113382 | ||||||||
\(605\) | 8945.02 | 0.601102 | ||||||||
\(606\) | −5181.11 | −0.347308 | ||||||||
\(607\) | −23005.0 | −1.53829 | −0.769145 | − | 0.639074i | \(-0.779318\pi\) | ||||
−0.769145 | + | 0.639074i | \(0.779318\pi\) | |||||||
\(608\) | 2994.68 | 0.199754 | ||||||||
\(609\) | −3769.98 | −0.250849 | ||||||||
\(610\) | 13387.2 | 0.888575 | ||||||||
\(611\) | −39011.5 | −2.58304 | ||||||||
\(612\) | −589.245 | −0.0389197 | ||||||||
\(613\) | 336.519 | 0.0221727 | 0.0110863 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110863 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(614\) | −8814.22 | −0.579337 | ||||||||
\(615\) | −326.719 | −0.0214221 | ||||||||
\(616\) | −5555.16 | −0.363350 | ||||||||
\(617\) | 10401.1 | 0.678659 | 0.339329 | − | 0.940668i | \(-0.389800\pi\) | ||||
0.339329 | + | 0.940668i | \(0.389800\pi\) | |||||||
\(618\) | −11221.0 | −0.730383 | ||||||||
\(619\) | −13538.7 | −0.879106 | −0.439553 | − | 0.898217i | \(-0.644863\pi\) | ||||
−0.439553 | + | 0.898217i | \(0.644863\pi\) | |||||||
\(620\) | −2488.56 | −0.161199 | ||||||||
\(621\) | −1160.51 | −0.0749911 | ||||||||
\(622\) | −3881.44 | −0.250212 | ||||||||
\(623\) | 1129.79 | 0.0726551 | ||||||||
\(624\) | 3400.77 | 0.218172 | ||||||||
\(625\) | −19341.3 | −1.23785 | ||||||||
\(626\) | −12241.6 | −0.781589 | ||||||||
\(627\) | −7170.62 | −0.456726 | ||||||||
\(628\) | 1005.50 | 0.0638912 | ||||||||
\(629\) | 4463.02 | 0.282913 | ||||||||
\(630\) | −6450.13 | −0.407904 | ||||||||
\(631\) | 25233.4 | 1.59196 | 0.795978 | − | 0.605325i | \(-0.206957\pi\) | ||||
0.795978 | + | 0.605325i | \(0.206957\pi\) | |||||||
\(632\) | −8534.83 | −0.537179 | ||||||||
\(633\) | 17209.4 | 1.08059 | ||||||||
\(634\) | 6440.98 | 0.403476 | ||||||||
\(635\) | 16708.9 | 1.04421 | ||||||||
\(636\) | 542.217 | 0.0338055 | ||||||||
\(637\) | −28068.3 | −1.74585 | ||||||||
\(638\) | −2361.08 | −0.146514 | ||||||||
\(639\) | 513.391 | 0.0317832 | ||||||||
\(640\) | 1687.07 | 0.104199 | ||||||||
\(641\) | 26721.1 | 1.64652 | 0.823260 | − | 0.567664i | \(-0.192153\pi\) | ||||
0.823260 | + | 0.567664i | \(0.192153\pi\) | |||||||
\(642\) | −6886.05 | −0.423319 | ||||||||
\(643\) | −10266.9 | −0.629683 | −0.314842 | − | 0.949144i | \(-0.601951\pi\) | ||||
−0.314842 | + | 0.949144i | \(0.601951\pi\) | |||||||
\(644\) | −4674.28 | −0.286013 | ||||||||
\(645\) | −16159.9 | −0.986506 | ||||||||
\(646\) | −3063.55 | −0.186585 | ||||||||
\(647\) | 6973.79 | 0.423753 | 0.211876 | − | 0.977297i | \(-0.432043\pi\) | ||||
0.211876 | + | 0.977297i | \(0.432043\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 1506.91 | 0.0911422 | ||||||||
\(650\) | 6903.48 | 0.416580 | ||||||||
\(651\) | 3849.97 | 0.231785 | ||||||||
\(652\) | −13167.1 | −0.790893 | ||||||||
\(653\) | −5925.24 | −0.355088 | −0.177544 | − | 0.984113i | \(-0.556815\pi\) | ||||
−0.177544 | + | 0.984113i | \(0.556815\pi\) | |||||||
\(654\) | −7261.17 | −0.434150 | ||||||||
\(655\) | 21299.2 | 1.27058 | ||||||||
\(656\) | −132.205 | −0.00786851 | ||||||||
\(657\) | −284.686 | −0.0169051 | ||||||||
\(658\) | 29940.5 | 1.77386 | ||||||||
\(659\) | 2302.35 | 0.136095 | 0.0680476 | − | 0.997682i | \(-0.478323\pi\) | ||||
0.0680476 | + | 0.997682i | \(0.478323\pi\) | |||||||
\(660\) | −4039.62 | −0.238245 | ||||||||
\(661\) | −8569.20 | −0.504241 | −0.252121 | − | 0.967696i | \(-0.581128\pi\) | ||||
−0.252121 | + | 0.967696i | \(0.581128\pi\) | |||||||
\(662\) | −42.3921 | −0.00248884 | ||||||||
\(663\) | −3478.97 | −0.203789 | ||||||||
\(664\) | −8138.05 | −0.475629 | ||||||||
\(665\) | −33534.9 | −1.95553 | ||||||||
\(666\) | 4908.04 | 0.285559 | ||||||||
\(667\) | −1986.69 | −0.115330 | ||||||||
\(668\) | −5489.27 | −0.317944 | ||||||||
\(669\) | −12684.4 | −0.733047 | ||||||||
\(670\) | −239.472 | −0.0138084 | ||||||||
\(671\) | −12970.9 | −0.746252 | ||||||||
\(672\) | −2610.02 | −0.149827 | ||||||||
\(673\) | −4227.05 | −0.242111 | −0.121056 | − | 0.992646i | \(-0.538628\pi\) | ||||
−0.121056 | + | 0.992646i | \(0.538628\pi\) | |||||||
\(674\) | −15728.3 | −0.898862 | ||||||||
\(675\) | −1315.43 | −0.0750085 | ||||||||
\(676\) | 11290.5 | 0.642381 | ||||||||
\(677\) | 20850.6 | 1.18368 | 0.591841 | − | 0.806055i | \(-0.298401\pi\) | ||||
0.591841 | + | 0.806055i | \(0.298401\pi\) | |||||||
\(678\) | 3720.99 | 0.210772 | ||||||||
\(679\) | 27447.1 | 1.55128 | ||||||||
\(680\) | −1725.87 | −0.0973295 | ||||||||
\(681\) | −16768.8 | −0.943584 | ||||||||
\(682\) | 2411.18 | 0.135379 | ||||||||
\(683\) | 7979.20 | 0.447022 | 0.223511 | − | 0.974701i | \(-0.428248\pi\) | ||||
0.223511 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(684\) | −3369.02 | −0.188330 | ||||||||
\(685\) | 26804.8 | 1.49512 | ||||||||
\(686\) | 2891.06 | 0.160906 | ||||||||
\(687\) | −6919.11 | −0.384251 | ||||||||
\(688\) | −6539.04 | −0.362352 | ||||||||
\(689\) | 3201.30 | 0.177010 | ||||||||
\(690\) | −3399.06 | −0.187536 | ||||||||
\(691\) | 19.1250 | 0.00105289 | 0.000526447 | − | 1.00000i | \(-0.499832\pi\) | ||||
0.000526447 | 1.00000i | \(0.499832\pi\) | ||||||||
\(692\) | −4754.38 | −0.261177 | ||||||||
\(693\) | 6249.55 | 0.342570 | ||||||||
\(694\) | −22864.3 | −1.25060 | ||||||||
\(695\) | −27447.0 | −1.49802 | ||||||||
\(696\) | −1109.32 | −0.0604148 | ||||||||
\(697\) | 135.245 | 0.00734975 | ||||||||
\(698\) | −14848.1 | −0.805169 | ||||||||
\(699\) | 4179.82 | 0.226174 | ||||||||
\(700\) | −5298.27 | −0.286080 | ||||||||
\(701\) | 32156.1 | 1.73255 | 0.866277 | − | 0.499564i | \(-0.166507\pi\) | ||||
0.866277 | + | 0.499564i | \(0.166507\pi\) | |||||||
\(702\) | −3825.86 | −0.205695 | ||||||||
\(703\) | 25517.4 | 1.36900 | ||||||||
\(704\) | −1634.61 | −0.0875096 | ||||||||
\(705\) | 21772.2 | 1.16311 | ||||||||
\(706\) | 19829.9 | 1.05709 | ||||||||
\(707\) | 23477.1 | 1.24886 | ||||||||
\(708\) | 708.000 | 0.0375823 | ||||||||
\(709\) | 34125.4 | 1.80763 | 0.903814 | − | 0.427926i | \(-0.140756\pi\) | ||||
0.903814 | + | 0.427926i | \(0.140756\pi\) | |||||||
\(710\) | 1503.70 | 0.0794827 | ||||||||
\(711\) | 9601.68 | 0.506457 | ||||||||
\(712\) | 332.442 | 0.0174983 | ||||||||
\(713\) | 2028.84 | 0.106565 | ||||||||
\(714\) | 2670.03 | 0.139949 | ||||||||
\(715\) | −23850.3 | −1.24748 | ||||||||
\(716\) | −10.0024 | −0.000522078 0 | ||||||||
\(717\) | 6881.29 | 0.358419 | ||||||||
\(718\) | 11412.2 | 0.593173 | ||||||||
\(719\) | 22246.9 | 1.15392 | 0.576960 | − | 0.816772i | \(-0.304239\pi\) | ||||
0.576960 | + | 0.816772i | \(0.304239\pi\) | |||||||
\(720\) | −1897.96 | −0.0982399 | ||||||||
\(721\) | 50845.6 | 2.62634 | ||||||||
\(722\) | −3797.88 | −0.195765 | ||||||||
\(723\) | 13255.1 | 0.681831 | ||||||||
\(724\) | 6018.03 | 0.308920 | ||||||||
\(725\) | −2251.90 | −0.115356 | ||||||||
\(726\) | −4072.00 | −0.208163 | ||||||||
\(727\) | −2935.22 | −0.149740 | −0.0748702 | − | 0.997193i | \(-0.523854\pi\) | ||||
−0.0748702 | + | 0.997193i | \(0.523854\pi\) | |||||||
\(728\) | −15409.8 | −0.784513 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −833.830 | −0.0422759 | ||||||||
\(731\) | 6689.40 | 0.338463 | ||||||||
\(732\) | −6094.19 | −0.307715 | ||||||||
\(733\) | −9687.75 | −0.488166 | −0.244083 | − | 0.969754i | \(-0.578487\pi\) | ||||
−0.244083 | + | 0.969754i | \(0.578487\pi\) | |||||||
\(734\) | −21142.6 | −1.06320 | ||||||||
\(735\) | 15664.8 | 0.786130 | ||||||||
\(736\) | −1375.41 | −0.0688837 | ||||||||
\(737\) | 232.025 | 0.0115967 | ||||||||
\(738\) | 148.731 | 0.00741850 | ||||||||
\(739\) | −26669.2 | −1.32753 | −0.663764 | − | 0.747942i | \(-0.731042\pi\) | ||||
−0.663764 | + | 0.747942i | \(0.731042\pi\) | |||||||
\(740\) | 14375.4 | 0.714121 | ||||||||
\(741\) | −19891.0 | −0.986121 | ||||||||
\(742\) | −2456.93 | −0.121559 | ||||||||
\(743\) | 29864.3 | 1.47458 | 0.737291 | − | 0.675575i | \(-0.236105\pi\) | ||||
0.737291 | + | 0.675575i | \(0.236105\pi\) | |||||||
\(744\) | 1132.86 | 0.0558234 | ||||||||
\(745\) | 8062.06 | 0.396471 | ||||||||
\(746\) | −2329.70 | −0.114338 | ||||||||
\(747\) | 9155.30 | 0.448427 | ||||||||
\(748\) | 1672.20 | 0.0817402 | ||||||||
\(749\) | 31202.6 | 1.52219 | ||||||||
\(750\) | 6032.39 | 0.293696 | ||||||||
\(751\) | 7452.40 | 0.362106 | 0.181053 | − | 0.983473i | \(-0.442049\pi\) | ||||
0.181053 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(752\) | 8810.03 | 0.427219 | ||||||||
\(753\) | −8827.77 | −0.427227 | ||||||||
\(754\) | −6549.55 | −0.316340 | ||||||||
\(755\) | 554.580 | 0.0267327 | ||||||||
\(756\) | 2936.27 | 0.141258 | ||||||||
\(757\) | 7664.45 | 0.367991 | 0.183996 | − | 0.982927i | \(-0.441097\pi\) | ||||
0.183996 | + | 0.982927i | \(0.441097\pi\) | |||||||
\(758\) | 10357.9 | 0.496326 | ||||||||
\(759\) | 3293.36 | 0.157499 | ||||||||
\(760\) | −9867.68 | −0.470972 | ||||||||
\(761\) | 17753.5 | 0.845684 | 0.422842 | − | 0.906204i | \(-0.361033\pi\) | ||||
0.422842 | + | 0.906204i | \(0.361033\pi\) | |||||||
\(762\) | −7606.32 | −0.361611 | ||||||||
\(763\) | 32902.3 | 1.56113 | ||||||||
\(764\) | 17899.6 | 0.847623 | ||||||||
\(765\) | 1941.60 | 0.0917631 | ||||||||
\(766\) | −21268.9 | −1.00323 | ||||||||
\(767\) | 4180.11 | 0.196786 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −38103.4 | −1.78679 | −0.893396 | − | 0.449269i | \(-0.851684\pi\) | ||||
−0.893396 | + | 0.449269i | \(0.851684\pi\) | |||||||
\(770\) | 18304.6 | 0.856692 | ||||||||
\(771\) | 16559.9 | 0.773527 | ||||||||
\(772\) | −19625.4 | −0.914942 | ||||||||
\(773\) | −36223.3 | −1.68546 | −0.842730 | − | 0.538337i | \(-0.819053\pi\) | ||||
−0.842730 | + | 0.538337i | \(0.819053\pi\) | |||||||
\(774\) | 7356.42 | 0.341629 | ||||||||
\(775\) | 2299.68 | 0.106589 | ||||||||
\(776\) | 8076.33 | 0.373613 | ||||||||
\(777\) | −22239.7 | −1.02683 | ||||||||
\(778\) | 2355.61 | 0.108551 | ||||||||
\(779\) | 773.267 | 0.0355650 | ||||||||
\(780\) | −11205.8 | −0.514398 | ||||||||
\(781\) | −1456.94 | −0.0667520 | ||||||||
\(782\) | 1407.04 | 0.0643423 | ||||||||
\(783\) | 1247.99 | 0.0569596 | ||||||||
\(784\) | 6338.70 | 0.288753 | ||||||||
\(785\) | −3313.18 | −0.150640 | ||||||||
\(786\) | −9695.95 | −0.440004 | ||||||||
\(787\) | −12859.4 | −0.582450 | −0.291225 | − | 0.956655i | \(-0.594063\pi\) | ||||
−0.291225 | + | 0.956655i | \(0.594063\pi\) | |||||||
\(788\) | −9956.49 | −0.450108 | ||||||||
\(789\) | −15553.0 | −0.701777 | ||||||||
\(790\) | 28122.8 | 1.26654 | ||||||||
\(791\) | −16860.8 | −0.757904 | ||||||||
\(792\) | 1838.94 | 0.0825048 | ||||||||
\(793\) | −35980.7 | −1.61124 | ||||||||
\(794\) | 5973.29 | 0.266983 | ||||||||
\(795\) | −1786.64 | −0.0797051 | ||||||||
\(796\) | 740.569 | 0.0329758 | ||||||||
\(797\) | 25823.5 | 1.14770 | 0.573849 | − | 0.818961i | \(-0.305450\pi\) | ||||
0.573849 | + | 0.818961i | \(0.305450\pi\) | |||||||
\(798\) | 15266.0 | 0.677204 | ||||||||
\(799\) | −9012.61 | −0.399053 | ||||||||
\(800\) | −1559.02 | −0.0688997 | ||||||||
\(801\) | −373.998 | −0.0164976 | ||||||||
\(802\) | 8382.04 | 0.369053 | ||||||||
\(803\) | 807.900 | 0.0355046 | ||||||||
\(804\) | 109.014 | 0.00478187 | ||||||||
\(805\) | 15402.1 | 0.674350 | ||||||||
\(806\) | 6688.52 | 0.292299 | ||||||||
\(807\) | −17459.3 | −0.761580 | ||||||||
\(808\) | 6908.15 | 0.300777 | ||||||||
\(809\) | −19693.4 | −0.855850 | −0.427925 | − | 0.903814i | \(-0.640755\pi\) | ||||
−0.427925 | + | 0.903814i | \(0.640755\pi\) | |||||||
\(810\) | 2135.20 | 0.0926215 | ||||||||
\(811\) | −32605.0 | −1.41173 | −0.705866 | − | 0.708345i | \(-0.749442\pi\) | ||||
−0.705866 | + | 0.708345i | \(0.749442\pi\) | |||||||
\(812\) | 5026.64 | 0.217242 | ||||||||
\(813\) | −17221.3 | −0.742901 | ||||||||
\(814\) | −13928.4 | −0.599740 | ||||||||
\(815\) | 43386.4 | 1.86473 | ||||||||
\(816\) | 785.660 | 0.0337054 | ||||||||
\(817\) | 38246.8 | 1.63780 | ||||||||
\(818\) | −1165.78 | −0.0498295 | ||||||||
\(819\) | 17336.0 | 0.739646 | ||||||||
\(820\) | 435.625 | 0.0185520 | ||||||||
\(821\) | −13591.1 | −0.577751 | −0.288876 | − | 0.957367i | \(-0.593281\pi\) | ||||
−0.288876 | + | 0.957367i | \(0.593281\pi\) | |||||||
\(822\) | −12202.2 | −0.517763 | ||||||||
\(823\) | −16953.0 | −0.718035 | −0.359018 | − | 0.933331i | \(-0.616888\pi\) | ||||
−0.359018 | + | 0.933331i | \(0.616888\pi\) | |||||||
\(824\) | 14961.4 | 0.632530 | ||||||||
\(825\) | 3733.00 | 0.157535 | ||||||||
\(826\) | −3208.14 | −0.135140 | ||||||||
\(827\) | −20334.6 | −0.855023 | −0.427512 | − | 0.904010i | \(-0.640610\pi\) | ||||
−0.427512 | + | 0.904010i | \(0.640610\pi\) | |||||||
\(828\) | 1547.34 | 0.0649442 | ||||||||
\(829\) | 2011.07 | 0.0842551 | 0.0421275 | − | 0.999112i | \(-0.486586\pi\) | ||||
0.0421275 | + | 0.999112i | \(0.486586\pi\) | |||||||
\(830\) | 26815.4 | 1.12142 | ||||||||
\(831\) | −10318.0 | −0.430719 | ||||||||
\(832\) | −4534.35 | −0.188943 | ||||||||
\(833\) | −6484.46 | −0.269716 | ||||||||
\(834\) | 12494.6 | 0.518767 | ||||||||
\(835\) | 18087.5 | 0.749634 | ||||||||
\(836\) | 9560.83 | 0.395536 | ||||||||
\(837\) | −1274.47 | −0.0526308 | ||||||||
\(838\) | −31724.2 | −1.30775 | ||||||||
\(839\) | 39355.1 | 1.61941 | 0.809707 | − | 0.586834i | \(-0.199626\pi\) | ||||
0.809707 | + | 0.586834i | \(0.199626\pi\) | |||||||
\(840\) | 8600.17 | 0.353255 | ||||||||
\(841\) | −22252.6 | −0.912401 | ||||||||
\(842\) | 3997.71 | 0.163623 | ||||||||
\(843\) | 7892.42 | 0.322455 | ||||||||
\(844\) | −22945.9 | −0.935818 | ||||||||
\(845\) | −37202.9 | −1.51458 | ||||||||
\(846\) | −9911.28 | −0.402786 | ||||||||
\(847\) | 18451.4 | 0.748520 | ||||||||
\(848\) | −722.955 | −0.0292764 | ||||||||
\(849\) | 8507.96 | 0.343925 | ||||||||
\(850\) | 1594.87 | 0.0643573 | ||||||||
\(851\) | −11719.8 | −0.472089 | ||||||||
\(852\) | −684.522 | −0.0275250 | ||||||||
\(853\) | −39238.9 | −1.57505 | −0.787523 | − | 0.616285i | \(-0.788637\pi\) | ||||
−0.787523 | + | 0.616285i | \(0.788637\pi\) | |||||||
\(854\) | 27614.4 | 1.10650 | ||||||||
\(855\) | 11101.1 | 0.444036 | ||||||||
\(856\) | 9181.39 | 0.366605 | ||||||||
\(857\) | 31231.8 | 1.24487 | 0.622437 | − | 0.782670i | \(-0.286143\pi\) | ||||
0.622437 | + | 0.782670i | \(0.286143\pi\) | |||||||
\(858\) | 10857.3 | 0.432007 | ||||||||
\(859\) | −30254.4 | −1.20171 | −0.600853 | − | 0.799359i | \(-0.705172\pi\) | ||||
−0.600853 | + | 0.799359i | \(0.705172\pi\) | |||||||
\(860\) | 21546.6 | 0.854339 | ||||||||
\(861\) | −673.940 | −0.0266758 | ||||||||
\(862\) | 16574.9 | 0.654922 | ||||||||
\(863\) | −15484.2 | −0.610764 | −0.305382 | − | 0.952230i | \(-0.598784\pi\) | ||||
−0.305382 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 15666.0 | 0.615792 | ||||||||
\(866\) | 2121.49 | 0.0832462 | ||||||||
\(867\) | 13935.3 | 0.545867 | ||||||||
\(868\) | −5133.29 | −0.200732 | ||||||||
\(869\) | −27248.3 | −1.06368 | ||||||||
\(870\) | 3655.29 | 0.142443 | ||||||||
\(871\) | 643.630 | 0.0250385 | ||||||||
\(872\) | 9681.56 | 0.375985 | ||||||||
\(873\) | −9085.87 | −0.352245 | ||||||||
\(874\) | 8044.78 | 0.311349 | ||||||||
\(875\) | −27334.4 | −1.05608 | ||||||||
\(876\) | 379.581 | 0.0146402 | ||||||||
\(877\) | −19408.1 | −0.747282 | −0.373641 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373641 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(878\) | −2681.38 | −0.103066 | ||||||||
\(879\) | 23263.1 | 0.892655 | ||||||||
\(880\) | 5386.15 | 0.206326 | ||||||||
\(881\) | 50319.8 | 1.92431 | 0.962155 | − | 0.272504i | \(-0.0878517\pi\) | ||||
0.962155 | + | 0.272504i | \(0.0878517\pi\) | |||||||
\(882\) | −7131.04 | −0.272239 | ||||||||
\(883\) | −2696.79 | −0.102780 | −0.0513898 | − | 0.998679i | \(-0.516365\pi\) | ||||
−0.0513898 | + | 0.998679i | \(0.516365\pi\) | |||||||
\(884\) | 4638.62 | 0.176486 | ||||||||
\(885\) | −2332.91 | −0.0886100 | ||||||||
\(886\) | 32365.0 | 1.22723 | ||||||||
\(887\) | 6398.55 | 0.242212 | 0.121106 | − | 0.992640i | \(-0.461356\pi\) | ||||
0.121106 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(888\) | −6544.05 | −0.247302 | ||||||||
\(889\) | 34466.3 | 1.30030 | ||||||||
\(890\) | −1095.42 | −0.0412568 | ||||||||
\(891\) | −2068.81 | −0.0777863 | ||||||||
\(892\) | 16912.6 | 0.634837 | ||||||||
\(893\) | −51529.8 | −1.93099 | ||||||||
\(894\) | −3670.06 | −0.137299 | ||||||||
\(895\) | 32.9586 | 0.00123093 | ||||||||
\(896\) | 3480.02 | 0.129754 | ||||||||
\(897\) | 9135.66 | 0.340057 | ||||||||
\(898\) | −1987.37 | −0.0738525 | ||||||||
\(899\) | −2181.78 | −0.0809414 | ||||||||
\(900\) | 1753.90 | 0.0649593 | ||||||||
\(901\) | 739.580 | 0.0273463 | ||||||||
\(902\) | −422.078 | −0.0155806 | ||||||||
\(903\) | −33334.0 | −1.22844 | ||||||||
\(904\) | −4961.32 | −0.182534 | ||||||||
\(905\) | −19829.8 | −0.728360 | ||||||||
\(906\) | −252.459 | −0.00925760 | ||||||||
\(907\) | 51527.9 | 1.88639 | 0.943195 | − | 0.332240i | \(-0.107804\pi\) | ||||
0.943195 | + | 0.332240i | \(0.107804\pi\) | |||||||
\(908\) | 22358.4 | 0.817168 | ||||||||
\(909\) | −7771.67 | −0.283575 | ||||||||
\(910\) | 50776.4 | 1.84969 | ||||||||
\(911\) | 42103.4 | 1.53123 | 0.765614 | − | 0.643300i | \(-0.222435\pi\) | ||||
0.765614 | + | 0.643300i | \(0.222435\pi\) | |||||||
\(912\) | 4492.03 | 0.163098 | ||||||||
\(913\) | −25981.5 | −0.941800 | ||||||||
\(914\) | −1666.43 | −0.0603071 | ||||||||
\(915\) | 20080.8 | 0.725518 | ||||||||
\(916\) | 9225.48 | 0.332771 | ||||||||
\(917\) | 43935.0 | 1.58218 | ||||||||
\(918\) | −883.868 | −0.0317778 | ||||||||
\(919\) | −25405.8 | −0.911928 | −0.455964 | − | 0.889998i | \(-0.650705\pi\) | ||||
−0.455964 | + | 0.889998i | \(0.650705\pi\) | |||||||
\(920\) | 4532.08 | 0.162411 | ||||||||
\(921\) | −13221.3 | −0.473027 | ||||||||
\(922\) | 34672.9 | 1.23849 | ||||||||
\(923\) | −4041.49 | −0.144125 | ||||||||
\(924\) | −8332.74 | −0.296674 | ||||||||
\(925\) | −13284.3 | −0.472199 | ||||||||
\(926\) | −30556.6 | −1.08440 | ||||||||
\(927\) | −16831.6 | −0.596355 | ||||||||
\(928\) | 1479.09 | 0.0523208 | ||||||||
\(929\) | −27234.2 | −0.961813 | −0.480907 | − | 0.876772i | \(-0.659692\pi\) | ||||
−0.480907 | + | 0.876772i | \(0.659692\pi\) | |||||||
\(930\) | −3732.84 | −0.131618 | ||||||||
\(931\) | −37075.0 | −1.30514 | ||||||||
\(932\) | −5573.10 | −0.195872 | ||||||||
\(933\) | −5822.16 | −0.204297 | ||||||||
\(934\) | 30303.4 | 1.06162 | ||||||||
\(935\) | −5510.01 | −0.192724 | ||||||||
\(936\) | 5101.15 | 0.178137 | ||||||||
\(937\) | 52145.3 | 1.81805 | 0.909025 | − | 0.416742i | \(-0.136828\pi\) | ||||
0.909025 | + | 0.416742i | \(0.136828\pi\) | |||||||
\(938\) | −493.972 | −0.0171949 | ||||||||
\(939\) | −18362.5 | −0.638165 | ||||||||
\(940\) | −29029.6 | −1.00728 | ||||||||
\(941\) | −35478.1 | −1.22907 | −0.614534 | − | 0.788890i | \(-0.710656\pi\) | ||||
−0.614534 | + | 0.788890i | \(0.710656\pi\) | |||||||
\(942\) | 1508.25 | 0.0521670 | ||||||||
\(943\) | −355.150 | −0.0122643 | ||||||||
\(944\) | −944.000 | −0.0325472 | ||||||||
\(945\) | −9675.20 | −0.333052 | ||||||||
\(946\) | −20876.5 | −0.717500 | ||||||||
\(947\) | 15928.3 | 0.546568 | 0.273284 | − | 0.961933i | \(-0.411890\pi\) | ||||
0.273284 | + | 0.961933i | \(0.411890\pi\) | |||||||
\(948\) | −12802.2 | −0.438605 | ||||||||
\(949\) | 2241.09 | 0.0766583 | ||||||||
\(950\) | 9118.71 | 0.311421 | ||||||||
\(951\) | 9661.47 | 0.329437 | ||||||||
\(952\) | −3560.04 | −0.121199 | ||||||||
\(953\) | −9122.33 | −0.310075 | −0.155037 | − | 0.987909i | \(-0.549550\pi\) | ||||
−0.155037 | + | 0.987909i | \(0.549550\pi\) | |||||||
\(954\) | 813.325 | 0.0276021 | ||||||||
\(955\) | −58980.3 | −1.99849 | ||||||||
\(956\) | −9175.05 | −0.310400 | ||||||||
\(957\) | −3541.62 | −0.119628 | ||||||||
\(958\) | 37119.3 | 1.25185 | ||||||||
\(959\) | 55291.7 | 1.86179 | ||||||||
\(960\) | 2530.61 | 0.0850783 | ||||||||
\(961\) | −27562.9 | −0.925210 | ||||||||
\(962\) | −38636.8 | −1.29491 | ||||||||
\(963\) | −10329.1 | −0.345638 | ||||||||
\(964\) | −17673.5 | −0.590483 | ||||||||
\(965\) | 64667.1 | 2.15721 | ||||||||
\(966\) | −7011.43 | −0.233529 | ||||||||
\(967\) | −39017.8 | −1.29755 | −0.648773 | − | 0.760982i | \(-0.724718\pi\) | ||||
−0.648773 | + | 0.760982i | \(0.724718\pi\) | |||||||
\(968\) | 5429.34 | 0.180274 | ||||||||
\(969\) | −4595.32 | −0.152346 | ||||||||
\(970\) | −26612.1 | −0.880888 | ||||||||
\(971\) | −4022.40 | −0.132940 | −0.0664700 | − | 0.997788i | \(-0.521174\pi\) | ||||
−0.0664700 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −56616.4 | −1.86540 | ||||||||
\(974\) | 25564.1 | 0.840992 | ||||||||
\(975\) | 10355.2 | 0.340136 | ||||||||
\(976\) | 8125.58 | 0.266489 | ||||||||
\(977\) | 5543.33 | 0.181522 | 0.0907610 | − | 0.995873i | \(-0.471070\pi\) | ||||
0.0907610 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(978\) | −19750.6 | −0.645762 | ||||||||
\(979\) | 1061.36 | 0.0346487 | ||||||||
\(980\) | −20886.4 | −0.680809 | ||||||||
\(981\) | −10891.7 | −0.354482 | ||||||||
\(982\) | −15693.2 | −0.509971 | ||||||||
\(983\) | −48179.0 | −1.56325 | −0.781624 | − | 0.623750i | \(-0.785608\pi\) | ||||
−0.781624 | + | 0.623750i | \(0.785608\pi\) | |||||||
\(984\) | −198.308 | −0.00642461 | ||||||||
\(985\) | 32807.3 | 1.06125 | ||||||||
\(986\) | −1513.11 | −0.0488713 | ||||||||
\(987\) | 44910.7 | 1.44835 | ||||||||
\(988\) | 26521.4 | 0.854006 | ||||||||
\(989\) | −17566.2 | −0.564784 | ||||||||
\(990\) | −6059.42 | −0.194526 | ||||||||
\(991\) | −13100.7 | −0.419936 | −0.209968 | − | 0.977708i | \(-0.567336\pi\) | ||||
−0.209968 | + | 0.977708i | \(0.567336\pi\) | |||||||
\(992\) | −1510.48 | −0.0483445 | ||||||||
\(993\) | −63.5881 | −0.00203213 | ||||||||
\(994\) | 3101.76 | 0.0989756 | ||||||||
\(995\) | −2440.22 | −0.0777490 | ||||||||
\(996\) | −12207.1 | −0.388349 | ||||||||
\(997\) | 31014.5 | 0.985195 | 0.492598 | − | 0.870257i | \(-0.336047\pi\) | ||||
0.492598 | + | 0.870257i | \(0.336047\pi\) | |||||||
\(998\) | −40004.9 | −1.26887 | ||||||||
\(999\) | 7362.05 | 0.233158 |
(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 | 354.4.a.e.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 1062.4.a.j.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.a.e.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1062.4.a.j.1.3 | 3 | 3.2 | odd | 2 |