Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,4,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, 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("983.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(57.9988775356\) |
Analytic rank: | \(0\) |
Dimension: | \(136\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.25160 | −1.85672 | −0.928361 | − | 0.371680i | \(-0.878782\pi\) | ||||
−0.928361 | + | 0.371680i | \(0.878782\pi\) | |||||||
\(3\) | 3.19215 | 0.614329 | 0.307165 | − | 0.951656i | \(-0.400620\pi\) | ||||
0.307165 | + | 0.951656i | \(0.400620\pi\) | |||||||
\(4\) | 19.5793 | 2.44741 | ||||||||
\(5\) | −16.3542 | −1.46276 | −0.731382 | − | 0.681968i | \(-0.761124\pi\) | ||||
−0.731382 | + | 0.681968i | \(0.761124\pi\) | |||||||
\(6\) | −16.7639 | −1.14064 | ||||||||
\(7\) | −21.7601 | −1.17493 | −0.587467 | − | 0.809248i | \(-0.699875\pi\) | ||||
−0.587467 | + | 0.809248i | \(0.699875\pi\) | |||||||
\(8\) | −60.8100 | −2.68745 | ||||||||
\(9\) | −16.8102 | −0.622599 | ||||||||
\(10\) | 85.8857 | 2.71595 | ||||||||
\(11\) | −6.52197 | −0.178768 | −0.0893839 | − | 0.995997i | \(-0.528490\pi\) | ||||
−0.0893839 | + | 0.995997i | \(0.528490\pi\) | |||||||
\(12\) | 62.5001 | 1.50352 | ||||||||
\(13\) | 3.49094 | 0.0744778 | 0.0372389 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372389 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(14\) | 114.275 | 2.18153 | ||||||||
\(15\) | −52.2050 | −0.898619 | ||||||||
\(16\) | 162.715 | 2.54242 | ||||||||
\(17\) | 11.0219 | 0.157248 | 0.0786238 | − | 0.996904i | \(-0.474947\pi\) | ||||
0.0786238 | + | 0.996904i | \(0.474947\pi\) | |||||||
\(18\) | 88.2804 | 1.15599 | ||||||||
\(19\) | 84.4586 | 1.01980 | 0.509898 | − | 0.860235i | \(-0.329683\pi\) | ||||
0.509898 | + | 0.860235i | \(0.329683\pi\) | |||||||
\(20\) | −320.204 | −3.57999 | ||||||||
\(21\) | −69.4615 | −0.721797 | ||||||||
\(22\) | 34.2508 | 0.331922 | ||||||||
\(23\) | −189.072 | −1.71410 | −0.857049 | − | 0.515234i | \(-0.827705\pi\) | ||||
−0.857049 | + | 0.515234i | \(0.827705\pi\) | |||||||
\(24\) | −194.115 | −1.65098 | ||||||||
\(25\) | 142.460 | 1.13968 | ||||||||
\(26\) | −18.3330 | −0.138285 | ||||||||
\(27\) | −139.849 | −0.996811 | ||||||||
\(28\) | −426.048 | −2.87555 | ||||||||
\(29\) | −188.736 | −1.20853 | −0.604265 | − | 0.796784i | \(-0.706533\pi\) | ||||
−0.604265 | + | 0.796784i | \(0.706533\pi\) | |||||||
\(30\) | 274.160 | 1.66849 | ||||||||
\(31\) | −221.190 | −1.28151 | −0.640756 | − | 0.767745i | \(-0.721379\pi\) | ||||
−0.640756 | + | 0.767745i | \(0.721379\pi\) | |||||||
\(32\) | −368.035 | −2.03313 | ||||||||
\(33\) | −20.8191 | −0.109822 | ||||||||
\(34\) | −57.8827 | −0.291965 | ||||||||
\(35\) | 355.869 | 1.71865 | ||||||||
\(36\) | −329.132 | −1.52376 | ||||||||
\(37\) | −94.6529 | −0.420563 | −0.210282 | − | 0.977641i | \(-0.567438\pi\) | ||||
−0.210282 | + | 0.977641i | \(0.567438\pi\) | |||||||
\(38\) | −443.543 | −1.89348 | ||||||||
\(39\) | 11.1436 | 0.0457539 | ||||||||
\(40\) | 994.498 | 3.93110 | ||||||||
\(41\) | −464.280 | −1.76850 | −0.884248 | − | 0.467018i | \(-0.845328\pi\) | ||||
−0.884248 | + | 0.467018i | \(0.845328\pi\) | |||||||
\(42\) | 364.784 | 1.34018 | ||||||||
\(43\) | −414.429 | −1.46976 | −0.734882 | − | 0.678195i | \(-0.762763\pi\) | ||||
−0.734882 | + | 0.678195i | \(0.762763\pi\) | |||||||
\(44\) | −127.696 | −0.437519 | ||||||||
\(45\) | 274.917 | 0.910716 | ||||||||
\(46\) | 992.932 | 3.18260 | ||||||||
\(47\) | −449.696 | −1.39564 | −0.697818 | − | 0.716276i | \(-0.745845\pi\) | ||||
−0.697818 | + | 0.716276i | \(0.745845\pi\) | |||||||
\(48\) | 519.411 | 1.56189 | ||||||||
\(49\) | 130.501 | 0.380471 | ||||||||
\(50\) | −748.142 | −2.11607 | ||||||||
\(51\) | 35.1836 | 0.0966018 | ||||||||
\(52\) | 68.3502 | 0.182278 | ||||||||
\(53\) | 412.692 | 1.06958 | 0.534788 | − | 0.844986i | \(-0.320391\pi\) | ||||
0.534788 | + | 0.844986i | \(0.320391\pi\) | |||||||
\(54\) | 734.429 | 1.85080 | ||||||||
\(55\) | 106.662 | 0.261495 | ||||||||
\(56\) | 1323.23 | 3.15757 | ||||||||
\(57\) | 269.604 | 0.626491 | ||||||||
\(58\) | 991.165 | 2.24390 | ||||||||
\(59\) | 10.9547 | 0.0241726 | 0.0120863 | − | 0.999927i | \(-0.496153\pi\) | ||||
0.0120863 | + | 0.999927i | \(0.496153\pi\) | |||||||
\(60\) | −1022.14 | −2.19929 | ||||||||
\(61\) | −789.040 | −1.65617 | −0.828084 | − | 0.560604i | \(-0.810569\pi\) | ||||
−0.828084 | + | 0.560604i | \(0.810569\pi\) | |||||||
\(62\) | 1161.60 | 2.37941 | ||||||||
\(63\) | 365.791 | 0.731513 | ||||||||
\(64\) | 631.054 | 1.23253 | ||||||||
\(65\) | −57.0915 | −0.108943 | ||||||||
\(66\) | 109.334 | 0.203910 | ||||||||
\(67\) | 950.873 | 1.73385 | 0.866923 | − | 0.498442i | \(-0.166094\pi\) | ||||
0.866923 | + | 0.498442i | \(0.166094\pi\) | |||||||
\(68\) | 215.802 | 0.384850 | ||||||||
\(69\) | −603.547 | −1.05302 | ||||||||
\(70\) | −1868.88 | −3.19106 | ||||||||
\(71\) | −416.952 | −0.696944 | −0.348472 | − | 0.937319i | \(-0.613299\pi\) | ||||
−0.348472 | + | 0.937319i | \(0.613299\pi\) | |||||||
\(72\) | 1022.23 | 1.67320 | ||||||||
\(73\) | 931.949 | 1.49420 | 0.747099 | − | 0.664713i | \(-0.231446\pi\) | ||||
0.747099 | + | 0.664713i | \(0.231446\pi\) | |||||||
\(74\) | 497.079 | 0.780869 | ||||||||
\(75\) | 454.753 | 0.700138 | ||||||||
\(76\) | 1653.64 | 2.49586 | ||||||||
\(77\) | 141.919 | 0.210041 | ||||||||
\(78\) | −58.5217 | −0.0849523 | ||||||||
\(79\) | −1200.42 | −1.70959 | −0.854796 | − | 0.518964i | \(-0.826318\pi\) | ||||
−0.854796 | + | 0.518964i | \(0.826318\pi\) | |||||||
\(80\) | −2661.08 | −3.71897 | ||||||||
\(81\) | 7.45706 | 0.0102292 | ||||||||
\(82\) | 2438.21 | 3.28360 | ||||||||
\(83\) | −624.025 | −0.825248 | −0.412624 | − | 0.910901i | \(-0.635388\pi\) | ||||
−0.412624 | + | 0.910901i | \(0.635388\pi\) | |||||||
\(84\) | −1360.01 | −1.76654 | ||||||||
\(85\) | −180.255 | −0.230016 | ||||||||
\(86\) | 2176.42 | 2.72894 | ||||||||
\(87\) | −602.473 | −0.742435 | ||||||||
\(88\) | 396.601 | 0.480429 | ||||||||
\(89\) | −859.427 | −1.02358 | −0.511792 | − | 0.859109i | \(-0.671018\pi\) | ||||
−0.511792 | + | 0.859109i | \(0.671018\pi\) | |||||||
\(90\) | −1443.75 | −1.69095 | ||||||||
\(91\) | −75.9631 | −0.0875065 | ||||||||
\(92\) | −3701.90 | −4.19511 | ||||||||
\(93\) | −706.071 | −0.787271 | ||||||||
\(94\) | 2361.62 | 2.59131 | ||||||||
\(95\) | −1381.25 | −1.49172 | ||||||||
\(96\) | −1174.82 | −1.24901 | ||||||||
\(97\) | 1054.60 | 1.10391 | 0.551953 | − | 0.833876i | \(-0.313883\pi\) | ||||
0.551953 | + | 0.833876i | \(0.313883\pi\) | |||||||
\(98\) | −685.341 | −0.706428 | ||||||||
\(99\) | 109.635 | 0.111301 | ||||||||
\(100\) | 2789.27 | 2.78927 | ||||||||
\(101\) | −1997.46 | −1.96787 | −0.983934 | − | 0.178531i | \(-0.942866\pi\) | ||||
−0.983934 | + | 0.178531i | \(0.942866\pi\) | |||||||
\(102\) | −184.770 | −0.179363 | ||||||||
\(103\) | −1517.46 | −1.45164 | −0.725822 | − | 0.687882i | \(-0.758540\pi\) | ||||
−0.725822 | + | 0.687882i | \(0.758540\pi\) | |||||||
\(104\) | −212.284 | −0.200155 | ||||||||
\(105\) | 1135.99 | 1.05582 | ||||||||
\(106\) | −2167.29 | −1.98591 | ||||||||
\(107\) | 1254.83 | 1.13373 | 0.566864 | − | 0.823812i | \(-0.308157\pi\) | ||||
0.566864 | + | 0.823812i | \(0.308157\pi\) | |||||||
\(108\) | −2738.14 | −2.43961 | ||||||||
\(109\) | 1854.72 | 1.62982 | 0.814909 | − | 0.579589i | \(-0.196787\pi\) | ||||
0.814909 | + | 0.579589i | \(0.196787\pi\) | |||||||
\(110\) | −560.144 | −0.485524 | ||||||||
\(111\) | −302.146 | −0.258364 | ||||||||
\(112\) | −3540.70 | −2.98718 | ||||||||
\(113\) | 1711.19 | 1.42456 | 0.712280 | − | 0.701896i | \(-0.247663\pi\) | ||||
0.712280 | + | 0.701896i | \(0.247663\pi\) | |||||||
\(114\) | −1415.86 | −1.16322 | ||||||||
\(115\) | 3092.12 | 2.50732 | ||||||||
\(116\) | −3695.32 | −2.95777 | ||||||||
\(117\) | −58.6833 | −0.0463698 | ||||||||
\(118\) | −57.5299 | −0.0448818 | ||||||||
\(119\) | −239.838 | −0.184755 | ||||||||
\(120\) | 3174.59 | 2.41499 | ||||||||
\(121\) | −1288.46 | −0.968042 | ||||||||
\(122\) | 4143.72 | 3.07504 | ||||||||
\(123\) | −1482.05 | −1.08644 | ||||||||
\(124\) | −4330.75 | −3.13639 | ||||||||
\(125\) | −285.541 | −0.204316 | ||||||||
\(126\) | −1920.99 | −1.35822 | ||||||||
\(127\) | −1496.34 | −1.04550 | −0.522752 | − | 0.852485i | \(-0.675094\pi\) | ||||
−0.522752 | + | 0.852485i | \(0.675094\pi\) | |||||||
\(128\) | −369.762 | −0.255333 | ||||||||
\(129\) | −1322.92 | −0.902920 | ||||||||
\(130\) | 299.822 | 0.202278 | ||||||||
\(131\) | 856.080 | 0.570962 | 0.285481 | − | 0.958384i | \(-0.407847\pi\) | ||||
0.285481 | + | 0.958384i | \(0.407847\pi\) | |||||||
\(132\) | −407.624 | −0.268781 | ||||||||
\(133\) | −1837.83 | −1.19819 | ||||||||
\(134\) | −4993.61 | −3.21927 | ||||||||
\(135\) | 2287.11 | 1.45810 | ||||||||
\(136\) | −670.242 | −0.422594 | ||||||||
\(137\) | 1396.58 | 0.870933 | 0.435467 | − | 0.900205i | \(-0.356583\pi\) | ||||
0.435467 | + | 0.900205i | \(0.356583\pi\) | |||||||
\(138\) | 3169.59 | 1.95517 | ||||||||
\(139\) | 1021.52 | 0.623338 | 0.311669 | − | 0.950191i | \(-0.399112\pi\) | ||||
0.311669 | + | 0.950191i | \(0.399112\pi\) | |||||||
\(140\) | 6967.67 | 4.20625 | ||||||||
\(141\) | −1435.50 | −0.857380 | ||||||||
\(142\) | 2189.66 | 1.29403 | ||||||||
\(143\) | −22.7678 | −0.0133142 | ||||||||
\(144\) | −2735.27 | −1.58291 | ||||||||
\(145\) | 3086.62 | 1.76779 | ||||||||
\(146\) | −4894.23 | −2.77431 | ||||||||
\(147\) | 416.580 | 0.233734 | ||||||||
\(148\) | −1853.24 | −1.02929 | ||||||||
\(149\) | 1018.32 | 0.559895 | 0.279947 | − | 0.960015i | \(-0.409683\pi\) | ||||
0.279947 | + | 0.960015i | \(0.409683\pi\) | |||||||
\(150\) | −2388.18 | −1.29996 | ||||||||
\(151\) | 2022.90 | 1.09021 | 0.545103 | − | 0.838369i | \(-0.316491\pi\) | ||||
0.545103 | + | 0.838369i | \(0.316491\pi\) | |||||||
\(152\) | −5135.92 | −2.74065 | ||||||||
\(153\) | −185.280 | −0.0979022 | ||||||||
\(154\) | −745.300 | −0.389987 | ||||||||
\(155\) | 3617.38 | 1.87455 | ||||||||
\(156\) | 218.184 | 0.111979 | ||||||||
\(157\) | 1381.24 | 0.702133 | 0.351067 | − | 0.936351i | \(-0.385819\pi\) | ||||
0.351067 | + | 0.936351i | \(0.385819\pi\) | |||||||
\(158\) | 6304.12 | 3.17424 | ||||||||
\(159\) | 1317.37 | 0.657072 | ||||||||
\(160\) | 6018.92 | 2.97399 | ||||||||
\(161\) | 4114.23 | 2.01395 | ||||||||
\(162\) | −39.1615 | −0.0189927 | ||||||||
\(163\) | −113.309 | −0.0544483 | −0.0272242 | − | 0.999629i | \(-0.508667\pi\) | ||||
−0.0272242 | + | 0.999629i | \(0.508667\pi\) | |||||||
\(164\) | −9090.28 | −4.32824 | ||||||||
\(165\) | 340.480 | 0.160644 | ||||||||
\(166\) | 3277.13 | 1.53226 | ||||||||
\(167\) | −2529.48 | −1.17208 | −0.586039 | − | 0.810283i | \(-0.699313\pi\) | ||||
−0.586039 | + | 0.810283i | \(0.699313\pi\) | |||||||
\(168\) | 4223.95 | 1.93979 | ||||||||
\(169\) | −2184.81 | −0.994453 | ||||||||
\(170\) | 946.625 | 0.427076 | ||||||||
\(171\) | −1419.76 | −0.634924 | ||||||||
\(172\) | −8114.24 | −3.59712 | ||||||||
\(173\) | 99.8907 | 0.0438991 | 0.0219496 | − | 0.999759i | \(-0.493013\pi\) | ||||
0.0219496 | + | 0.999759i | \(0.493013\pi\) | |||||||
\(174\) | 3163.95 | 1.37850 | ||||||||
\(175\) | −3099.94 | −1.33905 | ||||||||
\(176\) | −1061.22 | −0.454504 | ||||||||
\(177\) | 34.9691 | 0.0148500 | ||||||||
\(178\) | 4513.37 | 1.90051 | ||||||||
\(179\) | −3488.73 | −1.45676 | −0.728379 | − | 0.685175i | \(-0.759726\pi\) | ||||
−0.728379 | + | 0.685175i | \(0.759726\pi\) | |||||||
\(180\) | 5382.69 | 2.22890 | ||||||||
\(181\) | 988.302 | 0.405856 | 0.202928 | − | 0.979194i | \(-0.434954\pi\) | ||||
0.202928 | + | 0.979194i | \(0.434954\pi\) | |||||||
\(182\) | 398.928 | 0.162475 | ||||||||
\(183\) | −2518.73 | −1.01743 | ||||||||
\(184\) | 11497.5 | 4.60655 | ||||||||
\(185\) | 1547.97 | 0.615185 | ||||||||
\(186\) | 3708.00 | 1.46174 | ||||||||
\(187\) | −71.8846 | −0.0281108 | ||||||||
\(188\) | −8804.73 | −3.41570 | ||||||||
\(189\) | 3043.12 | 1.17119 | ||||||||
\(190\) | 7253.79 | 2.76971 | ||||||||
\(191\) | 1005.98 | 0.381100 | 0.190550 | − | 0.981678i | \(-0.438973\pi\) | ||||
0.190550 | + | 0.981678i | \(0.438973\pi\) | |||||||
\(192\) | 2014.42 | 0.757178 | ||||||||
\(193\) | −1432.59 | −0.534300 | −0.267150 | − | 0.963655i | \(-0.586082\pi\) | ||||
−0.267150 | + | 0.963655i | \(0.586082\pi\) | |||||||
\(194\) | −5538.36 | −2.04964 | ||||||||
\(195\) | −182.244 | −0.0669272 | ||||||||
\(196\) | 2555.13 | 0.931169 | ||||||||
\(197\) | −2313.00 | −0.836521 | −0.418260 | − | 0.908327i | \(-0.637360\pi\) | ||||
−0.418260 | + | 0.908327i | \(0.637360\pi\) | |||||||
\(198\) | −575.762 | −0.206655 | ||||||||
\(199\) | 1726.88 | 0.615151 | 0.307575 | − | 0.951524i | \(-0.400482\pi\) | ||||
0.307575 | + | 0.951524i | \(0.400482\pi\) | |||||||
\(200\) | −8662.97 | −3.06282 | ||||||||
\(201\) | 3035.33 | 1.06515 | ||||||||
\(202\) | 10489.9 | 3.65378 | ||||||||
\(203\) | 4106.91 | 1.41994 | ||||||||
\(204\) | 688.871 | 0.236425 | ||||||||
\(205\) | 7592.92 | 2.58689 | ||||||||
\(206\) | 7969.07 | 2.69530 | ||||||||
\(207\) | 3178.34 | 1.06720 | ||||||||
\(208\) | 568.028 | 0.189354 | ||||||||
\(209\) | −550.836 | −0.182307 | ||||||||
\(210\) | −5965.75 | −1.96036 | ||||||||
\(211\) | 1869.97 | 0.610113 | 0.305057 | − | 0.952334i | \(-0.401325\pi\) | ||||
0.305057 | + | 0.952334i | \(0.401325\pi\) | |||||||
\(212\) | 8080.22 | 2.61770 | ||||||||
\(213\) | −1330.97 | −0.428153 | ||||||||
\(214\) | −6589.86 | −2.10502 | ||||||||
\(215\) | 6777.66 | 2.14992 | ||||||||
\(216\) | 8504.19 | 2.67887 | ||||||||
\(217\) | 4813.11 | 1.50569 | ||||||||
\(218\) | −9740.26 | −3.02612 | ||||||||
\(219\) | 2974.92 | 0.917929 | ||||||||
\(220\) | 2088.36 | 0.639987 | ||||||||
\(221\) | 38.4768 | 0.0117114 | ||||||||
\(222\) | 1586.75 | 0.479711 | ||||||||
\(223\) | 882.245 | 0.264930 | 0.132465 | − | 0.991188i | \(-0.457711\pi\) | ||||
0.132465 | + | 0.991188i | \(0.457711\pi\) | |||||||
\(224\) | 8008.48 | 2.38879 | ||||||||
\(225\) | −2394.77 | −0.709563 | ||||||||
\(226\) | −8986.49 | −2.64501 | ||||||||
\(227\) | 4527.35 | 1.32375 | 0.661875 | − | 0.749615i | \(-0.269761\pi\) | ||||
0.661875 | + | 0.749615i | \(0.269761\pi\) | |||||||
\(228\) | 5278.67 | 1.53328 | ||||||||
\(229\) | 4795.91 | 1.38394 | 0.691971 | − | 0.721925i | \(-0.256743\pi\) | ||||
0.691971 | + | 0.721925i | \(0.256743\pi\) | |||||||
\(230\) | −16238.6 | −4.65540 | ||||||||
\(231\) | 453.025 | 0.129034 | ||||||||
\(232\) | 11477.0 | 3.24786 | ||||||||
\(233\) | 162.353 | 0.0456486 | 0.0228243 | − | 0.999739i | \(-0.492734\pi\) | ||||
0.0228243 | + | 0.999739i | \(0.492734\pi\) | |||||||
\(234\) | 308.181 | 0.0860959 | ||||||||
\(235\) | 7354.41 | 2.04148 | ||||||||
\(236\) | 214.486 | 0.0591604 | ||||||||
\(237\) | −3831.92 | −1.05025 | ||||||||
\(238\) | 1259.53 | 0.343039 | ||||||||
\(239\) | −1227.19 | −0.332136 | −0.166068 | − | 0.986114i | \(-0.553107\pi\) | ||||
−0.166068 | + | 0.986114i | \(0.553107\pi\) | |||||||
\(240\) | −8494.55 | −2.28467 | ||||||||
\(241\) | −2659.74 | −0.710908 | −0.355454 | − | 0.934694i | \(-0.615674\pi\) | ||||
−0.355454 | + | 0.934694i | \(0.615674\pi\) | |||||||
\(242\) | 6766.50 | 1.79738 | ||||||||
\(243\) | 3799.72 | 1.00309 | ||||||||
\(244\) | −15448.9 | −4.05333 | ||||||||
\(245\) | −2134.25 | −0.556539 | ||||||||
\(246\) | 7783.14 | 2.01721 | ||||||||
\(247\) | 294.840 | 0.0759522 | ||||||||
\(248\) | 13450.5 | 3.44399 | ||||||||
\(249\) | −1991.98 | −0.506974 | ||||||||
\(250\) | 1499.55 | 0.379359 | ||||||||
\(251\) | −4177.22 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(252\) | 7161.94 | 1.79032 | ||||||||
\(253\) | 1233.12 | 0.306426 | ||||||||
\(254\) | 7858.19 | 1.94121 | ||||||||
\(255\) | −575.400 | −0.141306 | ||||||||
\(256\) | −3106.59 | −0.758445 | ||||||||
\(257\) | −5934.53 | −1.44041 | −0.720205 | − | 0.693761i | \(-0.755952\pi\) | ||||
−0.720205 | + | 0.693761i | \(0.755952\pi\) | |||||||
\(258\) | 6947.45 | 1.67647 | ||||||||
\(259\) | 2059.66 | 0.494134 | ||||||||
\(260\) | −1117.81 | −0.266630 | ||||||||
\(261\) | 3172.68 | 0.752430 | ||||||||
\(262\) | −4495.79 | −1.06012 | ||||||||
\(263\) | −4269.77 | −1.00108 | −0.500542 | − | 0.865712i | \(-0.666866\pi\) | ||||
−0.500542 | + | 0.865712i | \(0.666866\pi\) | |||||||
\(264\) | 1266.01 | 0.295142 | ||||||||
\(265\) | −6749.24 | −1.56454 | ||||||||
\(266\) | 9651.53 | 2.22471 | ||||||||
\(267\) | −2743.42 | −0.628818 | ||||||||
\(268\) | 18617.4 | 4.24344 | ||||||||
\(269\) | −814.860 | −0.184695 | −0.0923473 | − | 0.995727i | \(-0.529437\pi\) | ||||
−0.0923473 | + | 0.995727i | \(0.529437\pi\) | |||||||
\(270\) | −12011.0 | −2.70728 | ||||||||
\(271\) | −4508.81 | −1.01067 | −0.505333 | − | 0.862924i | \(-0.668630\pi\) | ||||
−0.505333 | + | 0.862924i | \(0.668630\pi\) | |||||||
\(272\) | 1793.43 | 0.399790 | ||||||||
\(273\) | −242.486 | −0.0537578 | ||||||||
\(274\) | −7334.28 | −1.61708 | ||||||||
\(275\) | −929.118 | −0.203738 | ||||||||
\(276\) | −11817.0 | −2.57718 | ||||||||
\(277\) | 3450.20 | 0.748385 | 0.374192 | − | 0.927351i | \(-0.377920\pi\) | ||||
0.374192 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(278\) | −5364.60 | −1.15737 | ||||||||
\(279\) | 3718.24 | 0.797869 | ||||||||
\(280\) | −21640.4 | −4.61878 | ||||||||
\(281\) | 1003.25 | 0.212986 | 0.106493 | − | 0.994313i | \(-0.466038\pi\) | ||||
0.106493 | + | 0.994313i | \(0.466038\pi\) | |||||||
\(282\) | 7538.65 | 1.59192 | ||||||||
\(283\) | −1577.49 | −0.331351 | −0.165676 | − | 0.986180i | \(-0.552980\pi\) | ||||
−0.165676 | + | 0.986180i | \(0.552980\pi\) | |||||||
\(284\) | −8163.63 | −1.70571 | ||||||||
\(285\) | −4409.16 | −0.916408 | ||||||||
\(286\) | 119.567 | 0.0247208 | ||||||||
\(287\) | 10102.8 | 2.07787 | ||||||||
\(288\) | 6186.74 | 1.26582 | ||||||||
\(289\) | −4791.52 | −0.975273 | ||||||||
\(290\) | −16209.7 | −3.28230 | ||||||||
\(291\) | 3366.45 | 0.678161 | ||||||||
\(292\) | 18246.9 | 3.65692 | ||||||||
\(293\) | −3496.56 | −0.697171 | −0.348586 | − | 0.937277i | \(-0.613338\pi\) | ||||
−0.348586 | + | 0.937277i | \(0.613338\pi\) | |||||||
\(294\) | −2187.71 | −0.433979 | ||||||||
\(295\) | −179.156 | −0.0353588 | ||||||||
\(296\) | 5755.84 | 1.13024 | ||||||||
\(297\) | 912.088 | 0.178198 | ||||||||
\(298\) | −5347.83 | −1.03957 | ||||||||
\(299\) | −660.039 | −0.127662 | ||||||||
\(300\) | 8903.75 | 1.71353 | ||||||||
\(301\) | 9018.02 | 1.72688 | ||||||||
\(302\) | −10623.5 | −2.02421 | ||||||||
\(303\) | −6376.19 | −1.20892 | ||||||||
\(304\) | 13742.7 | 2.59276 | ||||||||
\(305\) | 12904.1 | 2.42258 | ||||||||
\(306\) | 973.019 | 0.181777 | ||||||||
\(307\) | −3774.37 | −0.701677 | −0.350838 | − | 0.936436i | \(-0.614103\pi\) | ||||
−0.350838 | + | 0.936436i | \(0.614103\pi\) | |||||||
\(308\) | 2778.67 | 0.514056 | ||||||||
\(309\) | −4843.95 | −0.891788 | ||||||||
\(310\) | −18997.1 | −3.48052 | ||||||||
\(311\) | 1945.44 | 0.354714 | 0.177357 | − | 0.984147i | \(-0.443245\pi\) | ||||
0.177357 | + | 0.984147i | \(0.443245\pi\) | |||||||
\(312\) | −677.641 | −0.122961 | ||||||||
\(313\) | −7045.82 | −1.27237 | −0.636187 | − | 0.771535i | \(-0.719489\pi\) | ||||
−0.636187 | + | 0.771535i | \(0.719489\pi\) | |||||||
\(314\) | −7253.72 | −1.30367 | ||||||||
\(315\) | −5982.22 | −1.07003 | ||||||||
\(316\) | −23503.4 | −4.18408 | ||||||||
\(317\) | −4684.02 | −0.829908 | −0.414954 | − | 0.909842i | \(-0.636202\pi\) | ||||
−0.414954 | + | 0.909842i | \(0.636202\pi\) | |||||||
\(318\) | −6918.32 | −1.22000 | ||||||||
\(319\) | 1230.93 | 0.216046 | ||||||||
\(320\) | −10320.4 | −1.80290 | ||||||||
\(321\) | 4005.60 | 0.696482 | ||||||||
\(322\) | −21606.3 | −3.73935 | ||||||||
\(323\) | 930.896 | 0.160360 | ||||||||
\(324\) | 146.004 | 0.0250350 | ||||||||
\(325\) | 497.318 | 0.0848807 | ||||||||
\(326\) | 595.056 | 0.101095 | ||||||||
\(327\) | 5920.55 | 1.00125 | ||||||||
\(328\) | 28232.8 | 4.75274 | ||||||||
\(329\) | 9785.42 | 1.63978 | ||||||||
\(330\) | −1788.06 | −0.298272 | ||||||||
\(331\) | 4675.61 | 0.776420 | 0.388210 | − | 0.921571i | \(-0.373094\pi\) | ||||
0.388210 | + | 0.921571i | \(0.373094\pi\) | |||||||
\(332\) | −12218.0 | −2.01973 | ||||||||
\(333\) | 1591.13 | 0.261842 | ||||||||
\(334\) | 13283.8 | 2.17622 | ||||||||
\(335\) | −15550.8 | −2.53621 | ||||||||
\(336\) | −11302.4 | −1.83511 | ||||||||
\(337\) | 4748.09 | 0.767493 | 0.383746 | − | 0.923439i | \(-0.374634\pi\) | ||||
0.383746 | + | 0.923439i | \(0.374634\pi\) | |||||||
\(338\) | 11473.8 | 1.84642 | ||||||||
\(339\) | 5462.37 | 0.875149 | ||||||||
\(340\) | −3529.26 | −0.562944 | ||||||||
\(341\) | 1442.59 | 0.229093 | ||||||||
\(342\) | 7456.04 | 1.17888 | ||||||||
\(343\) | 4623.99 | 0.727906 | ||||||||
\(344\) | 25201.4 | 3.94991 | ||||||||
\(345\) | 9870.52 | 1.54032 | ||||||||
\(346\) | −524.586 | −0.0815084 | ||||||||
\(347\) | −3303.33 | −0.511043 | −0.255522 | − | 0.966803i | \(-0.582247\pi\) | ||||
−0.255522 | + | 0.966803i | \(0.582247\pi\) | |||||||
\(348\) | −11796.0 | −1.81705 | ||||||||
\(349\) | 8912.11 | 1.36692 | 0.683459 | − | 0.729989i | \(-0.260475\pi\) | ||||
0.683459 | + | 0.729989i | \(0.260475\pi\) | |||||||
\(350\) | 16279.6 | 2.48624 | ||||||||
\(351\) | −488.203 | −0.0742403 | ||||||||
\(352\) | 2400.31 | 0.363458 | ||||||||
\(353\) | −8512.10 | −1.28344 | −0.641719 | − | 0.766940i | \(-0.721778\pi\) | ||||
−0.641719 | + | 0.766940i | \(0.721778\pi\) | |||||||
\(354\) | −183.644 | −0.0275722 | ||||||||
\(355\) | 6818.91 | 1.01946 | ||||||||
\(356\) | −16827.0 | −2.50514 | ||||||||
\(357\) | −765.598 | −0.113501 | ||||||||
\(358\) | 18321.4 | 2.70479 | ||||||||
\(359\) | −1173.62 | −0.172538 | −0.0862692 | − | 0.996272i | \(-0.527495\pi\) | ||||
−0.0862692 | + | 0.996272i | \(0.527495\pi\) | |||||||
\(360\) | −16717.7 | −2.44750 | ||||||||
\(361\) | 274.254 | 0.0399846 | ||||||||
\(362\) | −5190.17 | −0.753561 | ||||||||
\(363\) | −4112.97 | −0.594697 | ||||||||
\(364\) | −1487.31 | −0.214165 | ||||||||
\(365\) | −15241.3 | −2.18566 | ||||||||
\(366\) | 13227.4 | 1.88909 | ||||||||
\(367\) | 8023.73 | 1.14124 | 0.570621 | − | 0.821214i | \(-0.306703\pi\) | ||||
0.570621 | + | 0.821214i | \(0.306703\pi\) | |||||||
\(368\) | −30764.9 | −4.35797 | ||||||||
\(369\) | 7804.63 | 1.10106 | ||||||||
\(370\) | −8129.34 | −1.14223 | ||||||||
\(371\) | −8980.21 | −1.25668 | ||||||||
\(372\) | −13824.4 | −1.92678 | ||||||||
\(373\) | −3193.38 | −0.443289 | −0.221644 | − | 0.975128i | \(-0.571142\pi\) | ||||
−0.221644 | + | 0.975128i | \(0.571142\pi\) | |||||||
\(374\) | 377.509 | 0.0521939 | ||||||||
\(375\) | −911.489 | −0.125518 | ||||||||
\(376\) | 27346.0 | 3.75069 | ||||||||
\(377\) | −658.865 | −0.0900086 | ||||||||
\(378\) | −15981.2 | −2.17457 | ||||||||
\(379\) | 27.7049 | 0.00375490 | 0.00187745 | − | 0.999998i | \(-0.499402\pi\) | ||||
0.00187745 | + | 0.999998i | \(0.499402\pi\) | |||||||
\(380\) | −27044.0 | −3.65086 | ||||||||
\(381\) | −4776.55 | −0.642283 | ||||||||
\(382\) | −5283.00 | −0.707596 | ||||||||
\(383\) | −7807.42 | −1.04162 | −0.520810 | − | 0.853673i | \(-0.674370\pi\) | ||||
−0.520810 | + | 0.853673i | \(0.674370\pi\) | |||||||
\(384\) | −1180.34 | −0.156859 | ||||||||
\(385\) | −2320.96 | −0.307240 | ||||||||
\(386\) | 7523.38 | 0.992047 | ||||||||
\(387\) | 6966.63 | 0.915074 | ||||||||
\(388\) | 20648.4 | 2.70171 | ||||||||
\(389\) | 3570.87 | 0.465425 | 0.232712 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232712 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(390\) | 957.075 | 0.124265 | ||||||||
\(391\) | −2083.94 | −0.269538 | ||||||||
\(392\) | −7935.79 | −1.02249 | ||||||||
\(393\) | 2732.74 | 0.350759 | ||||||||
\(394\) | 12147.0 | 1.55319 | ||||||||
\(395\) | 19631.9 | 2.50073 | ||||||||
\(396\) | 2146.59 | 0.272399 | ||||||||
\(397\) | 13864.1 | 1.75269 | 0.876344 | − | 0.481686i | \(-0.159976\pi\) | ||||
0.876344 | + | 0.481686i | \(0.159976\pi\) | |||||||
\(398\) | −9068.86 | −1.14216 | ||||||||
\(399\) | −5866.62 | −0.736086 | ||||||||
\(400\) | 23180.4 | 2.89755 | ||||||||
\(401\) | −1546.00 | −0.192527 | −0.0962635 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962635 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(402\) | −15940.3 | −1.97769 | ||||||||
\(403\) | −772.160 | −0.0954442 | ||||||||
\(404\) | −39108.9 | −4.81619 | ||||||||
\(405\) | −121.954 | −0.0149629 | ||||||||
\(406\) | −21567.8 | −2.63644 | ||||||||
\(407\) | 617.323 | 0.0751832 | ||||||||
\(408\) | −2139.51 | −0.259612 | ||||||||
\(409\) | −12761.0 | −1.54276 | −0.771381 | − | 0.636374i | \(-0.780434\pi\) | ||||
−0.771381 | + | 0.636374i | \(0.780434\pi\) | |||||||
\(410\) | −39875.0 | −4.80314 | ||||||||
\(411\) | 4458.09 | 0.535040 | ||||||||
\(412\) | −29710.7 | −3.55278 | ||||||||
\(413\) | −238.376 | −0.0284012 | ||||||||
\(414\) | −16691.4 | −1.98149 | ||||||||
\(415\) | 10205.4 | 1.20714 | ||||||||
\(416\) | −1284.79 | −0.151423 | ||||||||
\(417\) | 3260.84 | 0.382935 | ||||||||
\(418\) | 2892.77 | 0.338493 | ||||||||
\(419\) | −4933.37 | −0.575205 | −0.287603 | − | 0.957750i | \(-0.592858\pi\) | ||||
−0.287603 | + | 0.957750i | \(0.592858\pi\) | |||||||
\(420\) | 22241.8 | 2.58403 | ||||||||
\(421\) | −373.053 | −0.0431864 | −0.0215932 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215932 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(422\) | −9820.33 | −1.13281 | ||||||||
\(423\) | 7559.47 | 0.868921 | ||||||||
\(424\) | −25095.8 | −2.87443 | ||||||||
\(425\) | 1570.18 | 0.179212 | ||||||||
\(426\) | 6989.73 | 0.794962 | ||||||||
\(427\) | 17169.6 | 1.94589 | ||||||||
\(428\) | 24568.7 | 2.77470 | ||||||||
\(429\) | −72.6781 | −0.00817933 | ||||||||
\(430\) | −35593.6 | −3.99180 | ||||||||
\(431\) | 16001.3 | 1.78829 | 0.894147 | − | 0.447773i | \(-0.147783\pi\) | ||||
0.894147 | + | 0.447773i | \(0.147783\pi\) | |||||||
\(432\) | −22755.5 | −2.53432 | ||||||||
\(433\) | −12904.4 | −1.43220 | −0.716101 | − | 0.697996i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697996i | \(0.754075\pi\) | |||||||
\(434\) | −25276.5 | −2.79565 | ||||||||
\(435\) | 9852.96 | 1.08601 | ||||||||
\(436\) | 36314.2 | 3.98884 | ||||||||
\(437\) | −15968.8 | −1.74803 | ||||||||
\(438\) | −15623.1 | −1.70434 | ||||||||
\(439\) | −14810.7 | −1.61020 | −0.805100 | − | 0.593140i | \(-0.797888\pi\) | ||||
−0.805100 | + | 0.593140i | \(0.797888\pi\) | |||||||
\(440\) | −6486.08 | −0.702754 | ||||||||
\(441\) | −2193.75 | −0.236881 | ||||||||
\(442\) | −202.065 | −0.0217449 | ||||||||
\(443\) | 2959.44 | 0.317398 | 0.158699 | − | 0.987327i | \(-0.449270\pi\) | ||||
0.158699 | + | 0.987327i | \(0.449270\pi\) | |||||||
\(444\) | −5915.82 | −0.632325 | ||||||||
\(445\) | 14055.2 | 1.49726 | ||||||||
\(446\) | −4633.20 | −0.491902 | ||||||||
\(447\) | 3250.64 | 0.343960 | ||||||||
\(448\) | −13731.8 | −1.44814 | ||||||||
\(449\) | 5227.49 | 0.549445 | 0.274722 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274722 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(450\) | 12576.4 | 1.31746 | ||||||||
\(451\) | 3028.02 | 0.316150 | ||||||||
\(452\) | 33503.9 | 3.48649 | ||||||||
\(453\) | 6457.39 | 0.669746 | ||||||||
\(454\) | −23775.9 | −2.45783 | ||||||||
\(455\) | 1242.32 | 0.128001 | ||||||||
\(456\) | −16394.6 | −1.68366 | ||||||||
\(457\) | −3459.45 | −0.354105 | −0.177053 | − | 0.984201i | \(-0.556656\pi\) | ||||
−0.177053 | + | 0.984201i | \(0.556656\pi\) | |||||||
\(458\) | −25186.2 | −2.56959 | ||||||||
\(459\) | −1541.40 | −0.156746 | ||||||||
\(460\) | 60541.7 | 6.13646 | ||||||||
\(461\) | 177.559 | 0.0179387 | 0.00896937 | − | 0.999960i | \(-0.497145\pi\) | ||||
0.00896937 | + | 0.999960i | \(0.497145\pi\) | |||||||
\(462\) | −2379.11 | −0.239580 | ||||||||
\(463\) | −5711.92 | −0.573338 | −0.286669 | − | 0.958030i | \(-0.592548\pi\) | ||||
−0.286669 | + | 0.958030i | \(0.592548\pi\) | |||||||
\(464\) | −30710.2 | −3.07259 | ||||||||
\(465\) | 11547.2 | 1.15159 | ||||||||
\(466\) | −852.614 | −0.0847567 | ||||||||
\(467\) | 287.505 | 0.0284886 | 0.0142443 | − | 0.999899i | \(-0.495466\pi\) | ||||
0.0142443 | + | 0.999899i | \(0.495466\pi\) | |||||||
\(468\) | −1148.98 | −0.113486 | ||||||||
\(469\) | −20691.1 | −2.03715 | ||||||||
\(470\) | −38622.4 | −3.79047 | ||||||||
\(471\) | 4409.12 | 0.431341 | ||||||||
\(472\) | −666.157 | −0.0649626 | ||||||||
\(473\) | 2702.89 | 0.262747 | ||||||||
\(474\) | 20123.7 | 1.95003 | ||||||||
\(475\) | 12032.0 | 1.16224 | ||||||||
\(476\) | −4695.86 | −0.452173 | ||||||||
\(477\) | −6937.42 | −0.665918 | ||||||||
\(478\) | 6444.74 | 0.616685 | ||||||||
\(479\) | −4273.72 | −0.407664 | −0.203832 | − | 0.979006i | \(-0.565340\pi\) | ||||
−0.203832 | + | 0.979006i | \(0.565340\pi\) | |||||||
\(480\) | 19213.3 | 1.82701 | ||||||||
\(481\) | −330.427 | −0.0313226 | ||||||||
\(482\) | 13967.9 | 1.31996 | ||||||||
\(483\) | 13133.2 | 1.23723 | ||||||||
\(484\) | −25227.2 | −2.36920 | ||||||||
\(485\) | −17247.2 | −1.61475 | ||||||||
\(486\) | −19954.6 | −1.86247 | ||||||||
\(487\) | 8386.70 | 0.780365 | 0.390183 | − | 0.920738i | \(-0.372412\pi\) | ||||
0.390183 | + | 0.920738i | \(0.372412\pi\) | |||||||
\(488\) | 47981.5 | 4.45086 | ||||||||
\(489\) | −361.700 | −0.0334492 | ||||||||
\(490\) | 11208.2 | 1.03334 | ||||||||
\(491\) | −1244.80 | −0.114413 | −0.0572066 | − | 0.998362i | \(-0.518219\pi\) | ||||
−0.0572066 | + | 0.998362i | \(0.518219\pi\) | |||||||
\(492\) | −29017.5 | −2.65897 | ||||||||
\(493\) | −2080.23 | −0.190038 | ||||||||
\(494\) | −1548.38 | −0.141022 | ||||||||
\(495\) | −1793.00 | −0.162807 | ||||||||
\(496\) | −35990.9 | −3.25815 | ||||||||
\(497\) | 9072.90 | 0.818864 | ||||||||
\(498\) | 10461.1 | 0.941310 | ||||||||
\(499\) | −14306.3 | −1.28345 | −0.641724 | − | 0.766936i | \(-0.721780\pi\) | ||||
−0.641724 | + | 0.766936i | \(0.721780\pi\) | |||||||
\(500\) | −5590.70 | −0.500047 | ||||||||
\(501\) | −8074.48 | −0.720042 | ||||||||
\(502\) | 21937.1 | 1.95040 | ||||||||
\(503\) | 18603.4 | 1.64907 | 0.824536 | − | 0.565810i | \(-0.191436\pi\) | ||||
0.824536 | + | 0.565810i | \(0.191436\pi\) | |||||||
\(504\) | −22243.7 | −1.96590 | ||||||||
\(505\) | 32666.9 | 2.87853 | ||||||||
\(506\) | −6475.87 | −0.568947 | ||||||||
\(507\) | −6974.25 | −0.610922 | ||||||||
\(508\) | −29297.4 | −2.55878 | ||||||||
\(509\) | −457.414 | −0.0398321 | −0.0199160 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199160 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(510\) | 3021.77 | 0.262365 | ||||||||
\(511\) | −20279.3 | −1.75558 | ||||||||
\(512\) | 19272.7 | 1.66355 | ||||||||
\(513\) | −11811.4 | −1.01654 | ||||||||
\(514\) | 31165.8 | 2.67444 | ||||||||
\(515\) | 24816.8 | 2.12341 | ||||||||
\(516\) | −25901.9 | −2.20982 | ||||||||
\(517\) | 2932.90 | 0.249495 | ||||||||
\(518\) | −10816.5 | −0.917470 | ||||||||
\(519\) | 318.866 | 0.0269685 | ||||||||
\(520\) | 3471.73 | 0.292780 | ||||||||
\(521\) | 12189.4 | 1.02500 | 0.512502 | − | 0.858686i | \(-0.328719\pi\) | ||||
0.512502 | + | 0.858686i | \(0.328719\pi\) | |||||||
\(522\) | −16661.7 | −1.39705 | ||||||||
\(523\) | 8493.84 | 0.710152 | 0.355076 | − | 0.934837i | \(-0.384455\pi\) | ||||
0.355076 | + | 0.934837i | \(0.384455\pi\) | |||||||
\(524\) | 16761.5 | 1.39738 | ||||||||
\(525\) | −9895.46 | −0.822616 | ||||||||
\(526\) | 22423.1 | 1.85873 | ||||||||
\(527\) | −2437.94 | −0.201515 | ||||||||
\(528\) | −3387.58 | −0.279215 | ||||||||
\(529\) | 23581.3 | 1.93814 | ||||||||
\(530\) | 35444.3 | 2.90491 | ||||||||
\(531\) | −184.151 | −0.0150499 | ||||||||
\(532\) | −35983.4 | −2.93248 | ||||||||
\(533\) | −1620.77 | −0.131714 | ||||||||
\(534\) | 14407.3 | 1.16754 | ||||||||
\(535\) | −20521.7 | −1.65838 | ||||||||
\(536\) | −57822.6 | −4.65962 | ||||||||
\(537\) | −11136.5 | −0.894929 | ||||||||
\(538\) | 4279.32 | 0.342927 | ||||||||
\(539\) | −851.126 | −0.0680159 | ||||||||
\(540\) | 44780.1 | 3.56857 | ||||||||
\(541\) | 10630.9 | 0.844840 | 0.422420 | − | 0.906400i | \(-0.361181\pi\) | ||||
0.422420 | + | 0.906400i | \(0.361181\pi\) | |||||||
\(542\) | 23678.5 | 1.87653 | ||||||||
\(543\) | 3154.81 | 0.249329 | ||||||||
\(544\) | −4056.46 | −0.319704 | ||||||||
\(545\) | −30332.5 | −2.38404 | ||||||||
\(546\) | 1273.44 | 0.0998133 | ||||||||
\(547\) | −2563.87 | −0.200408 | −0.100204 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100204 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(548\) | 27344.1 | 2.13154 | ||||||||
\(549\) | 13263.9 | 1.03113 | ||||||||
\(550\) | 4879.36 | 0.378285 | ||||||||
\(551\) | −15940.4 | −1.23245 | ||||||||
\(552\) | 36701.7 | 2.82994 | ||||||||
\(553\) | 26121.2 | 2.00866 | ||||||||
\(554\) | −18119.1 | −1.38954 | ||||||||
\(555\) | 4941.36 | 0.377926 | ||||||||
\(556\) | 20000.6 | 1.52557 | ||||||||
\(557\) | 8133.45 | 0.618717 | 0.309359 | − | 0.950945i | \(-0.399886\pi\) | ||||
0.309359 | + | 0.950945i | \(0.399886\pi\) | |||||||
\(558\) | −19526.7 | −1.48142 | ||||||||
\(559\) | −1446.75 | −0.109465 | ||||||||
\(560\) | 57905.2 | 4.36954 | ||||||||
\(561\) | −229.466 | −0.0172693 | ||||||||
\(562\) | −5268.69 | −0.395456 | ||||||||
\(563\) | 23461.2 | 1.75625 | 0.878126 | − | 0.478430i | \(-0.158794\pi\) | ||||
0.878126 | + | 0.478430i | \(0.158794\pi\) | |||||||
\(564\) | −28106.0 | −2.09836 | ||||||||
\(565\) | −27985.1 | −2.08379 | ||||||||
\(566\) | 8284.38 | 0.615227 | ||||||||
\(567\) | −162.266 | −0.0120186 | ||||||||
\(568\) | 25354.8 | 1.87300 | ||||||||
\(569\) | −19192.0 | −1.41401 | −0.707005 | − | 0.707208i | \(-0.749954\pi\) | ||||
−0.707005 | + | 0.707208i | \(0.749954\pi\) | |||||||
\(570\) | 23155.2 | 1.70152 | ||||||||
\(571\) | −11353.4 | −0.832094 | −0.416047 | − | 0.909343i | \(-0.636585\pi\) | ||||
−0.416047 | + | 0.909343i | \(0.636585\pi\) | |||||||
\(572\) | −445.777 | −0.0325855 | ||||||||
\(573\) | 3211.23 | 0.234121 | ||||||||
\(574\) | −53055.7 | −3.85802 | ||||||||
\(575\) | −26935.2 | −1.95352 | ||||||||
\(576\) | −10608.1 | −0.767371 | ||||||||
\(577\) | −18870.2 | −1.36148 | −0.680742 | − | 0.732523i | \(-0.738343\pi\) | ||||
−0.680742 | + | 0.732523i | \(0.738343\pi\) | |||||||
\(578\) | 25163.1 | 1.81081 | ||||||||
\(579\) | −4573.04 | −0.328237 | ||||||||
\(580\) | 60434.0 | 4.32652 | ||||||||
\(581\) | 13578.8 | 0.969613 | ||||||||
\(582\) | −17679.3 | −1.25916 | ||||||||
\(583\) | −2691.56 | −0.191206 | ||||||||
\(584\) | −56671.8 | −4.01558 | ||||||||
\(585\) | 959.718 | 0.0678281 | ||||||||
\(586\) | 18362.5 | 1.29445 | ||||||||
\(587\) | 16464.9 | 1.15771 | 0.578857 | − | 0.815429i | \(-0.303499\pi\) | ||||
0.578857 | + | 0.815429i | \(0.303499\pi\) | |||||||
\(588\) | 8156.35 | 0.572045 | ||||||||
\(589\) | −18681.4 | −1.30688 | ||||||||
\(590\) | 940.855 | 0.0656515 | ||||||||
\(591\) | −7383.45 | −0.513899 | ||||||||
\(592\) | −15401.5 | −1.06925 | ||||||||
\(593\) | 6169.75 | 0.427253 | 0.213627 | − | 0.976915i | \(-0.431472\pi\) | ||||
0.213627 | + | 0.976915i | \(0.431472\pi\) | |||||||
\(594\) | −4789.92 | −0.330864 | ||||||||
\(595\) | 3922.36 | 0.270254 | ||||||||
\(596\) | 19938.1 | 1.37030 | ||||||||
\(597\) | 5512.45 | 0.377905 | ||||||||
\(598\) | 3466.26 | 0.237033 | ||||||||
\(599\) | −4488.46 | −0.306166 | −0.153083 | − | 0.988213i | \(-0.548920\pi\) | ||||
−0.153083 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(600\) | −27653.5 | −1.88158 | ||||||||
\(601\) | 1010.49 | 0.0685835 | 0.0342917 | − | 0.999412i | \(-0.489082\pi\) | ||||
0.0342917 | + | 0.999412i | \(0.489082\pi\) | |||||||
\(602\) | −47359.0 | −3.20633 | ||||||||
\(603\) | −15984.4 | −1.07949 | ||||||||
\(604\) | 39607.0 | 2.66819 | ||||||||
\(605\) | 21071.8 | 1.41602 | ||||||||
\(606\) | 33485.2 | 2.24463 | ||||||||
\(607\) | −4640.78 | −0.310318 | −0.155159 | − | 0.987889i | \(-0.549589\pi\) | ||||
−0.155159 | + | 0.987889i | \(0.549589\pi\) | |||||||
\(608\) | −31083.8 | −2.07338 | ||||||||
\(609\) | 13109.9 | 0.872313 | ||||||||
\(610\) | −67767.3 | −4.49806 | ||||||||
\(611\) | −1569.86 | −0.103944 | ||||||||
\(612\) | −3627.66 | −0.239607 | ||||||||
\(613\) | 8923.45 | 0.587953 | 0.293976 | − | 0.955813i | \(-0.405021\pi\) | ||||
0.293976 | + | 0.955813i | \(0.405021\pi\) | |||||||
\(614\) | 19821.5 | 1.30282 | ||||||||
\(615\) | 24237.7 | 1.58920 | ||||||||
\(616\) | −8630.06 | −0.564473 | ||||||||
\(617\) | −13366.0 | −0.872118 | −0.436059 | − | 0.899918i | \(-0.643626\pi\) | ||||
−0.436059 | + | 0.899918i | \(0.643626\pi\) | |||||||
\(618\) | 25438.5 | 1.65580 | ||||||||
\(619\) | 5687.05 | 0.369276 | 0.184638 | − | 0.982807i | \(-0.440889\pi\) | ||||
0.184638 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(620\) | 70825.9 | 4.58780 | ||||||||
\(621\) | 26441.5 | 1.70863 | ||||||||
\(622\) | −10216.7 | −0.658604 | ||||||||
\(623\) | 18701.2 | 1.20264 | ||||||||
\(624\) | 1813.23 | 0.116326 | ||||||||
\(625\) | −13137.7 | −0.840812 | ||||||||
\(626\) | 37001.8 | 2.36244 | ||||||||
\(627\) | −1758.35 | −0.111996 | ||||||||
\(628\) | 27043.7 | 1.71841 | ||||||||
\(629\) | −1043.26 | −0.0661325 | ||||||||
\(630\) | 31416.2 | 1.98675 | ||||||||
\(631\) | −25995.8 | −1.64006 | −0.820029 | − | 0.572322i | \(-0.806043\pi\) | ||||
−0.820029 | + | 0.572322i | \(0.806043\pi\) | |||||||
\(632\) | 72997.5 | 4.59444 | ||||||||
\(633\) | 5969.22 | 0.374811 | ||||||||
\(634\) | 24598.6 | 1.54091 | ||||||||
\(635\) | 24471.5 | 1.52932 | ||||||||
\(636\) | 25793.3 | 1.60813 | ||||||||
\(637\) | 455.572 | 0.0283366 | ||||||||
\(638\) | −6464.35 | −0.401138 | ||||||||
\(639\) | 7009.03 | 0.433917 | ||||||||
\(640\) | 6047.16 | 0.373492 | ||||||||
\(641\) | −18961.1 | −1.16836 | −0.584181 | − | 0.811624i | \(-0.698584\pi\) | ||||
−0.584181 | + | 0.811624i | \(0.698584\pi\) | |||||||
\(642\) | −21035.8 | −1.29317 | ||||||||
\(643\) | 5249.29 | 0.321947 | 0.160974 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160974 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(644\) | 80553.8 | 4.92898 | ||||||||
\(645\) | 21635.3 | 1.32076 | ||||||||
\(646\) | −4888.69 | −0.297745 | ||||||||
\(647\) | −7734.97 | −0.470005 | −0.235002 | − | 0.971995i | \(-0.575510\pi\) | ||||
−0.235002 | + | 0.971995i | \(0.575510\pi\) | |||||||
\(648\) | −453.464 | −0.0274903 | ||||||||
\(649\) | −71.4464 | −0.00432129 | ||||||||
\(650\) | −2611.72 | −0.157600 | ||||||||
\(651\) | 15364.2 | 0.924991 | ||||||||
\(652\) | −2218.52 | −0.133258 | ||||||||
\(653\) | 12141.7 | 0.727627 | 0.363813 | − | 0.931472i | \(-0.381475\pi\) | ||||
0.363813 | + | 0.931472i | \(0.381475\pi\) | |||||||
\(654\) | −31092.4 | −1.85903 | ||||||||
\(655\) | −14000.5 | −0.835183 | ||||||||
\(656\) | −75545.3 | −4.49627 | ||||||||
\(657\) | −15666.2 | −0.930286 | ||||||||
\(658\) | −51389.1 | −3.04461 | ||||||||
\(659\) | 3176.91 | 0.187792 | 0.0938960 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938960 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(660\) | 6666.36 | 0.393163 | ||||||||
\(661\) | −27717.3 | −1.63098 | −0.815490 | − | 0.578771i | \(-0.803532\pi\) | ||||
−0.815490 | + | 0.578771i | \(0.803532\pi\) | |||||||
\(662\) | −24554.5 | −1.44159 | ||||||||
\(663\) | 122.824 | 0.00719469 | ||||||||
\(664\) | 37946.9 | 2.21781 | ||||||||
\(665\) | 30056.2 | 1.75267 | ||||||||
\(666\) | −8355.99 | −0.486168 | ||||||||
\(667\) | 35684.7 | 2.07154 | ||||||||
\(668\) | −49525.5 | −2.86856 | ||||||||
\(669\) | 2816.26 | 0.162755 | ||||||||
\(670\) | 81666.4 | 4.70903 | ||||||||
\(671\) | 5146.09 | 0.296070 | ||||||||
\(672\) | 25564.3 | 1.46751 | ||||||||
\(673\) | 15612.4 | 0.894225 | 0.447113 | − | 0.894478i | \(-0.352452\pi\) | ||||
0.447113 | + | 0.894478i | \(0.352452\pi\) | |||||||
\(674\) | −24935.1 | −1.42502 | ||||||||
\(675\) | −19922.8 | −1.13604 | ||||||||
\(676\) | −42777.2 | −2.43384 | ||||||||
\(677\) | −5554.98 | −0.315355 | −0.157677 | − | 0.987491i | \(-0.550401\pi\) | ||||
−0.157677 | + | 0.987491i | \(0.550401\pi\) | |||||||
\(678\) | −28686.2 | −1.62491 | ||||||||
\(679\) | −22948.3 | −1.29702 | ||||||||
\(680\) | 10961.3 | 0.618156 | ||||||||
\(681\) | 14452.0 | 0.813218 | ||||||||
\(682\) | −7575.92 | −0.425362 | ||||||||
\(683\) | −4086.19 | −0.228922 | −0.114461 | − | 0.993428i | \(-0.536514\pi\) | ||||
−0.114461 | + | 0.993428i | \(0.536514\pi\) | |||||||
\(684\) | −27798.0 | −1.55392 | ||||||||
\(685\) | −22839.9 | −1.27397 | ||||||||
\(686\) | −24283.3 | −1.35152 | ||||||||
\(687\) | 15309.3 | 0.850196 | ||||||||
\(688\) | −67433.9 | −3.73677 | ||||||||
\(689\) | 1440.68 | 0.0796597 | ||||||||
\(690\) | −51836.1 | −2.85995 | ||||||||
\(691\) | −23164.0 | −1.27525 | −0.637627 | − | 0.770345i | \(-0.720084\pi\) | ||||
−0.637627 | + | 0.770345i | \(0.720084\pi\) | |||||||
\(692\) | 1955.79 | 0.107439 | ||||||||
\(693\) | −2385.68 | −0.130771 | ||||||||
\(694\) | 17347.8 | 0.948865 | ||||||||
\(695\) | −16706.1 | −0.911796 | ||||||||
\(696\) | 36636.4 | 1.99525 | ||||||||
\(697\) | −5117.25 | −0.278091 | ||||||||
\(698\) | −46802.9 | −2.53799 | ||||||||
\(699\) | 518.256 | 0.0280433 | ||||||||
\(700\) | −60694.7 | −3.27720 | ||||||||
\(701\) | 9795.28 | 0.527764 | 0.263882 | − | 0.964555i | \(-0.414997\pi\) | ||||
0.263882 | + | 0.964555i | \(0.414997\pi\) | |||||||
\(702\) | 2563.85 | 0.137844 | ||||||||
\(703\) | −7994.25 | −0.428889 | ||||||||
\(704\) | −4115.71 | −0.220336 | ||||||||
\(705\) | 23476.4 | 1.25414 | ||||||||
\(706\) | 44702.2 | 2.38299 | ||||||||
\(707\) | 43464.9 | 2.31212 | ||||||||
\(708\) | 684.672 | 0.0363440 | ||||||||
\(709\) | −24622.5 | −1.30426 | −0.652128 | − | 0.758109i | \(-0.726123\pi\) | ||||
−0.652128 | + | 0.758109i | \(0.726123\pi\) | |||||||
\(710\) | −35810.2 | −1.89286 | ||||||||
\(711\) | 20179.3 | 1.06439 | ||||||||
\(712\) | 52261.7 | 2.75083 | ||||||||
\(713\) | 41820.9 | 2.19664 | ||||||||
\(714\) | 4020.62 | 0.210739 | ||||||||
\(715\) | 372.349 | 0.0194756 | ||||||||
\(716\) | −68306.9 | −3.56529 | ||||||||
\(717\) | −3917.39 | −0.204041 | ||||||||
\(718\) | 6163.39 | 0.320356 | ||||||||
\(719\) | −11684.0 | −0.606033 | −0.303017 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303017 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(720\) | 44733.2 | 2.31543 | ||||||||
\(721\) | 33020.0 | 1.70559 | ||||||||
\(722\) | −1440.27 | −0.0742402 | ||||||||
\(723\) | −8490.29 | −0.436732 | ||||||||
\(724\) | 19350.3 | 0.993297 | ||||||||
\(725\) | −26887.3 | −1.37733 | ||||||||
\(726\) | 21599.7 | 1.10419 | ||||||||
\(727\) | −17381.1 | −0.886699 | −0.443350 | − | 0.896349i | \(-0.646210\pi\) | ||||
−0.443350 | + | 0.896349i | \(0.646210\pi\) | |||||||
\(728\) | 4619.31 | 0.235169 | ||||||||
\(729\) | 11927.9 | 0.606001 | ||||||||
\(730\) | 80041.1 | 4.05816 | ||||||||
\(731\) | −4567.81 | −0.231117 | ||||||||
\(732\) | −49315.1 | −2.49008 | ||||||||
\(733\) | −7832.92 | −0.394701 | −0.197350 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197350 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(734\) | −42137.5 | −2.11897 | ||||||||
\(735\) | −6812.83 | −0.341898 | ||||||||
\(736\) | 69585.3 | 3.48498 | ||||||||
\(737\) | −6201.56 | −0.309956 | ||||||||
\(738\) | −40986.8 | −2.04437 | ||||||||
\(739\) | −25124.2 | −1.25062 | −0.625309 | − | 0.780377i | \(-0.715027\pi\) | ||||
−0.625309 | + | 0.780377i | \(0.715027\pi\) | |||||||
\(740\) | 30308.2 | 1.50561 | ||||||||
\(741\) | 941.172 | 0.0466597 | ||||||||
\(742\) | 47160.5 | 2.33331 | ||||||||
\(743\) | 38845.7 | 1.91805 | 0.959026 | − | 0.283319i | \(-0.0914357\pi\) | ||||
0.959026 | + | 0.283319i | \(0.0914357\pi\) | |||||||
\(744\) | 42936.2 | 2.11575 | ||||||||
\(745\) | −16653.9 | −0.818994 | ||||||||
\(746\) | 16770.3 | 0.823064 | ||||||||
\(747\) | 10490.0 | 0.513799 | ||||||||
\(748\) | −1407.45 | −0.0687988 | ||||||||
\(749\) | −27305.2 | −1.33206 | ||||||||
\(750\) | 4786.78 | 0.233051 | ||||||||
\(751\) | −5345.96 | −0.259756 | −0.129878 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129878 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(752\) | −73172.3 | −3.54830 | ||||||||
\(753\) | −13334.3 | −0.645324 | ||||||||
\(754\) | 3460.09 | 0.167121 | ||||||||
\(755\) | −33082.9 | −1.59471 | ||||||||
\(756\) | 59582.2 | 2.86638 | ||||||||
\(757\) | −22152.0 | −1.06358 | −0.531788 | − | 0.846877i | \(-0.678480\pi\) | ||||
−0.531788 | + | 0.846877i | \(0.678480\pi\) | |||||||
\(758\) | −145.495 | −0.00697180 | ||||||||
\(759\) | 3936.31 | 0.188246 | ||||||||
\(760\) | 83993.9 | 4.00892 | ||||||||
\(761\) | 20608.5 | 0.981678 | 0.490839 | − | 0.871250i | \(-0.336690\pi\) | ||||
0.490839 | + | 0.871250i | \(0.336690\pi\) | |||||||
\(762\) | 25084.5 | 1.19254 | ||||||||
\(763\) | −40358.9 | −1.91493 | ||||||||
\(764\) | 19696.4 | 0.932709 | ||||||||
\(765\) | 3030.11 | 0.143208 | ||||||||
\(766\) | 41001.4 | 1.93400 | ||||||||
\(767\) | 38.2423 | 0.00180032 | ||||||||
\(768\) | −9916.71 | −0.465935 | ||||||||
\(769\) | −6404.10 | −0.300309 | −0.150155 | − | 0.988663i | \(-0.547977\pi\) | ||||
−0.150155 | + | 0.988663i | \(0.547977\pi\) | |||||||
\(770\) | 12188.8 | 0.570459 | ||||||||
\(771\) | −18943.9 | −0.884887 | ||||||||
\(772\) | −28049.1 | −1.30765 | ||||||||
\(773\) | −13210.2 | −0.614666 | −0.307333 | − | 0.951602i | \(-0.599437\pi\) | ||||
−0.307333 | + | 0.951602i | \(0.599437\pi\) | |||||||
\(774\) | −36586.0 | −1.69904 | ||||||||
\(775\) | −31510.7 | −1.46051 | ||||||||
\(776\) | −64130.4 | −2.96669 | ||||||||
\(777\) | 6574.73 | 0.303561 | ||||||||
\(778\) | −18752.8 | −0.864164 | ||||||||
\(779\) | −39212.4 | −1.80351 | ||||||||
\(780\) | −3568.22 | −0.163799 | ||||||||
\(781\) | 2719.34 | 0.124591 | ||||||||
\(782\) | 10944.0 | 0.500457 | ||||||||
\(783\) | 26394.4 | 1.20467 | ||||||||
\(784\) | 21234.6 | 0.967318 | ||||||||
\(785\) | −22589.1 | −1.02706 | ||||||||
\(786\) | −14351.2 | −0.651262 | ||||||||
\(787\) | −19340.7 | −0.876012 | −0.438006 | − | 0.898972i | \(-0.644315\pi\) | ||||
−0.438006 | + | 0.898972i | \(0.644315\pi\) | |||||||
\(788\) | −45287.0 | −2.04731 | ||||||||
\(789\) | −13629.7 | −0.614995 | ||||||||
\(790\) | −103099. | −4.64316 | ||||||||
\(791\) | −37235.6 | −1.67376 | ||||||||
\(792\) | −6666.93 | −0.299115 | ||||||||
\(793\) | −2754.49 | −0.123348 | ||||||||
\(794\) | −72808.5 | −3.25425 | ||||||||
\(795\) | −21544.6 | −0.961142 | ||||||||
\(796\) | 33811.1 | 1.50553 | ||||||||
\(797\) | 23294.1 | 1.03528 | 0.517641 | − | 0.855598i | \(-0.326810\pi\) | ||||
0.517641 | + | 0.855598i | \(0.326810\pi\) | |||||||
\(798\) | 30809.1 | 1.36671 | ||||||||
\(799\) | −4956.51 | −0.219460 | ||||||||
\(800\) | −52430.3 | −2.31711 | ||||||||
\(801\) | 14447.1 | 0.637283 | ||||||||
\(802\) | 8118.95 | 0.357469 | ||||||||
\(803\) | −6078.14 | −0.267115 | ||||||||
\(804\) | 59429.7 | 2.60687 | ||||||||
\(805\) | −67284.9 | −2.94594 | ||||||||
\(806\) | 4055.08 | 0.177213 | ||||||||
\(807\) | −2601.15 | −0.113463 | ||||||||
\(808\) | 121466. | 5.28854 | ||||||||
\(809\) | −42696.9 | −1.85555 | −0.927777 | − | 0.373135i | \(-0.878283\pi\) | ||||
−0.927777 | + | 0.373135i | \(0.878283\pi\) | |||||||
\(810\) | 640.455 | 0.0277818 | ||||||||
\(811\) | 16497.6 | 0.714313 | 0.357156 | − | 0.934045i | \(-0.383746\pi\) | ||||
0.357156 | + | 0.934045i | \(0.383746\pi\) | |||||||
\(812\) | 80410.4 | 3.47519 | ||||||||
\(813\) | −14392.8 | −0.620882 | ||||||||
\(814\) | −3241.94 | −0.139594 | ||||||||
\(815\) | 1853.08 | 0.0796450 | ||||||||
\(816\) | 5724.91 | 0.245603 | ||||||||
\(817\) | −35002.1 | −1.49886 | ||||||||
\(818\) | 67015.5 | 2.86448 | ||||||||
\(819\) | 1276.95 | 0.0544815 | ||||||||
\(820\) | 148664. | 6.33120 | ||||||||
\(821\) | −26383.0 | −1.12152 | −0.560762 | − | 0.827977i | \(-0.689492\pi\) | ||||
−0.560762 | + | 0.827977i | \(0.689492\pi\) | |||||||
\(822\) | −23412.1 | −0.993420 | ||||||||
\(823\) | −22798.2 | −0.965609 | −0.482805 | − | 0.875728i | \(-0.660382\pi\) | ||||
−0.482805 | + | 0.875728i | \(0.660382\pi\) | |||||||
\(824\) | 92276.4 | 3.90122 | ||||||||
\(825\) | −2965.88 | −0.125162 | ||||||||
\(826\) | 1251.86 | 0.0527332 | ||||||||
\(827\) | 13799.9 | 0.580254 | 0.290127 | − | 0.956988i | \(-0.406303\pi\) | ||||
0.290127 | + | 0.956988i | \(0.406303\pi\) | |||||||
\(828\) | 62229.7 | 2.61187 | ||||||||
\(829\) | −25392.7 | −1.06384 | −0.531920 | − | 0.846795i | \(-0.678529\pi\) | ||||
−0.531920 | + | 0.846795i | \(0.678529\pi\) | |||||||
\(830\) | −53594.8 | −2.24133 | ||||||||
\(831\) | 11013.6 | 0.459755 | ||||||||
\(832\) | 2202.97 | 0.0917960 | ||||||||
\(833\) | 1438.38 | 0.0598280 | ||||||||
\(834\) | −17124.6 | −0.711003 | ||||||||
\(835\) | 41367.6 | 1.71447 | ||||||||
\(836\) | −10785.0 | −0.446180 | ||||||||
\(837\) | 30933.1 | 1.27742 | ||||||||
\(838\) | 25908.1 | 1.06800 | ||||||||
\(839\) | 36314.1 | 1.49428 | 0.747140 | − | 0.664666i | \(-0.231426\pi\) | ||||
0.747140 | + | 0.664666i | \(0.231426\pi\) | |||||||
\(840\) | −69079.3 | −2.83745 | ||||||||
\(841\) | 11232.2 | 0.460544 | ||||||||
\(842\) | 1959.12 | 0.0801851 | ||||||||
\(843\) | 3202.54 | 0.130844 | ||||||||
\(844\) | 36612.7 | 1.49320 | ||||||||
\(845\) | 35730.9 | 1.45465 | ||||||||
\(846\) | −39699.3 | −1.61335 | ||||||||
\(847\) | 28037.1 | 1.13739 | ||||||||
\(848\) | 67151.2 | 2.71932 | ||||||||
\(849\) | −5035.60 | −0.203559 | ||||||||
\(850\) | −8245.96 | −0.332746 | ||||||||
\(851\) | 17896.2 | 0.720887 | ||||||||
\(852\) | −26059.5 | −1.04787 | ||||||||
\(853\) | 24198.9 | 0.971343 | 0.485671 | − | 0.874141i | \(-0.338575\pi\) | ||||
0.485671 | + | 0.874141i | \(0.338575\pi\) | |||||||
\(854\) | −90167.8 | −3.61297 | ||||||||
\(855\) | 23219.1 | 0.928745 | ||||||||
\(856\) | −76306.1 | −3.04683 | ||||||||
\(857\) | −5309.45 | −0.211630 | −0.105815 | − | 0.994386i | \(-0.533745\pi\) | ||||
−0.105815 | + | 0.994386i | \(0.533745\pi\) | |||||||
\(858\) | 381.677 | 0.0151867 | ||||||||
\(859\) | 23054.1 | 0.915710 | 0.457855 | − | 0.889027i | \(-0.348618\pi\) | ||||
0.457855 | + | 0.889027i | \(0.348618\pi\) | |||||||
\(860\) | 132702. | 5.26174 | ||||||||
\(861\) | 32249.5 | 1.27649 | ||||||||
\(862\) | −84032.4 | −3.32036 | ||||||||
\(863\) | −18397.8 | −0.725688 | −0.362844 | − | 0.931850i | \(-0.618194\pi\) | ||||
−0.362844 | + | 0.931850i | \(0.618194\pi\) | |||||||
\(864\) | 51469.3 | 2.02664 | ||||||||
\(865\) | −1633.63 | −0.0642140 | ||||||||
\(866\) | 67768.5 | 2.65920 | ||||||||
\(867\) | −15295.2 | −0.599139 | ||||||||
\(868\) | 94237.4 | 3.68505 | ||||||||
\(869\) | 7829.10 | 0.305620 | ||||||||
\(870\) | −51743.8 | −2.01641 | ||||||||
\(871\) | 3319.44 | 0.129133 | ||||||||
\(872\) | −112786. | −4.38005 | ||||||||
\(873\) | −17728.1 | −0.687290 | ||||||||
\(874\) | 83861.6 | 3.24561 | ||||||||
\(875\) | 6213.39 | 0.240058 | ||||||||
\(876\) | 58246.9 | 2.24655 | ||||||||
\(877\) | 2044.74 | 0.0787296 | 0.0393648 | − | 0.999225i | \(-0.487467\pi\) | ||||
0.0393648 | + | 0.999225i | \(0.487467\pi\) | |||||||
\(878\) | 77780.0 | 2.98969 | ||||||||
\(879\) | −11161.5 | −0.428293 | ||||||||
\(880\) | 17355.4 | 0.664832 | ||||||||
\(881\) | 13291.6 | 0.508293 | 0.254147 | − | 0.967166i | \(-0.418205\pi\) | ||||
0.254147 | + | 0.967166i | \(0.418205\pi\) | |||||||
\(882\) | 11520.7 | 0.439821 | ||||||||
\(883\) | 39342.5 | 1.49941 | 0.749707 | − | 0.661770i | \(-0.230195\pi\) | ||||
0.749707 | + | 0.661770i | \(0.230195\pi\) | |||||||
\(884\) | 753.350 | 0.0286628 | ||||||||
\(885\) | −571.892 | −0.0217220 | ||||||||
\(886\) | −15541.8 | −0.589320 | ||||||||
\(887\) | −36087.9 | −1.36608 | −0.683040 | − | 0.730381i | \(-0.739342\pi\) | ||||
−0.683040 | + | 0.730381i | \(0.739342\pi\) | |||||||
\(888\) | 18373.5 | 0.694341 | ||||||||
\(889\) | 32560.5 | 1.22840 | ||||||||
\(890\) | −73812.5 | −2.78000 | ||||||||
\(891\) | −48.6347 | −0.00182865 | ||||||||
\(892\) | 17273.8 | 0.648395 | ||||||||
\(893\) | −37980.7 | −1.42326 | ||||||||
\(894\) | −17071.1 | −0.638638 | ||||||||
\(895\) | 57055.3 | 2.13089 | ||||||||
\(896\) | 8046.05 | 0.300000 | ||||||||
\(897\) | −2106.94 | −0.0784267 | ||||||||
\(898\) | −27452.7 | −1.02017 | ||||||||
\(899\) | 41746.4 | 1.54875 | ||||||||
\(900\) | −46888.1 | −1.73659 | ||||||||
\(901\) | 4548.65 | 0.168188 | ||||||||
\(902\) | −15901.9 | −0.587003 | ||||||||
\(903\) | 28786.9 | 1.06087 | ||||||||
\(904\) | −104057. | −3.82843 | ||||||||
\(905\) | −16162.9 | −0.593671 | ||||||||
\(906\) | −33911.7 | −1.24353 | ||||||||
\(907\) | −8155.39 | −0.298561 | −0.149281 | − | 0.988795i | \(-0.547696\pi\) | ||||
−0.149281 | + | 0.988795i | \(0.547696\pi\) | |||||||
\(908\) | 88642.5 | 3.23976 | ||||||||
\(909\) | 33577.7 | 1.22519 | ||||||||
\(910\) | −6524.14 | −0.237663 | ||||||||
\(911\) | 18432.4 | 0.670354 | 0.335177 | − | 0.942155i | \(-0.391204\pi\) | ||||
0.335177 | + | 0.942155i | \(0.391204\pi\) | |||||||
\(912\) | 43868.7 | 1.59281 | ||||||||
\(913\) | 4069.87 | 0.147528 | ||||||||
\(914\) | 18167.6 | 0.657475 | ||||||||
\(915\) | 41191.9 | 1.48826 | ||||||||
\(916\) | 93900.6 | 3.38708 | ||||||||
\(917\) | −18628.4 | −0.670843 | ||||||||
\(918\) | 8094.82 | 0.291034 | ||||||||
\(919\) | −27174.8 | −0.975425 | −0.487712 | − | 0.873004i | \(-0.662169\pi\) | ||||
−0.487712 | + | 0.873004i | \(0.662169\pi\) | |||||||
\(920\) | −188032. | −6.73829 | ||||||||
\(921\) | −12048.4 | −0.431061 | ||||||||
\(922\) | −932.470 | −0.0333072 | ||||||||
\(923\) | −1455.55 | −0.0519069 | ||||||||
\(924\) | 8869.93 | 0.315800 | ||||||||
\(925\) | −13484.2 | −0.479307 | ||||||||
\(926\) | 29996.7 | 1.06453 | ||||||||
\(927\) | 25508.7 | 0.903793 | ||||||||
\(928\) | 69461.5 | 2.45709 | ||||||||
\(929\) | −45169.7 | −1.59523 | −0.797616 | − | 0.603166i | \(-0.793906\pi\) | ||||
−0.797616 | + | 0.603166i | \(0.793906\pi\) | |||||||
\(930\) | −60641.4 | −2.13818 | ||||||||
\(931\) | 11022.0 | 0.388002 | ||||||||
\(932\) | 3178.77 | 0.111721 | ||||||||
\(933\) | 6210.14 | 0.217911 | ||||||||
\(934\) | −1509.86 | −0.0528953 | ||||||||
\(935\) | 1175.61 | 0.0411195 | ||||||||
\(936\) | 3568.53 | 0.124616 | ||||||||
\(937\) | −33372.6 | −1.16354 | −0.581769 | − | 0.813354i | \(-0.697639\pi\) | ||||
−0.581769 | + | 0.813354i | \(0.697639\pi\) | |||||||
\(938\) | 108661. | 3.78243 | ||||||||
\(939\) | −22491.3 | −0.781657 | ||||||||
\(940\) | 143994. | 4.99636 | ||||||||
\(941\) | 38628.6 | 1.33821 | 0.669105 | − | 0.743168i | \(-0.266678\pi\) | ||||
0.669105 | + | 0.743168i | \(0.266678\pi\) | |||||||
\(942\) | −23155.0 | −0.800880 | ||||||||
\(943\) | 87782.4 | 3.03138 | ||||||||
\(944\) | 1782.50 | 0.0614571 | ||||||||
\(945\) | −49767.8 | −1.71317 | ||||||||
\(946\) | −14194.5 | −0.487847 | ||||||||
\(947\) | −20614.4 | −0.707367 | −0.353684 | − | 0.935365i | \(-0.615071\pi\) | ||||
−0.353684 | + | 0.935365i | \(0.615071\pi\) | |||||||
\(948\) | −75026.4 | −2.57040 | ||||||||
\(949\) | 3253.38 | 0.111285 | ||||||||
\(950\) | −63187.0 | −2.15796 | ||||||||
\(951\) | −14952.1 | −0.509837 | ||||||||
\(952\) | 14584.5 | 0.496520 | ||||||||
\(953\) | −38022.3 | −1.29241 | −0.646203 | − | 0.763166i | \(-0.723644\pi\) | ||||
−0.646203 | + | 0.763166i | \(0.723644\pi\) | |||||||
\(954\) | 36432.6 | 1.23642 | ||||||||
\(955\) | −16452.0 | −0.557459 | ||||||||
\(956\) | −24027.6 | −0.812876 | ||||||||
\(957\) | 3929.31 | 0.132724 | ||||||||
\(958\) | 22443.9 | 0.756919 | ||||||||
\(959\) | −30389.7 | −1.02329 | ||||||||
\(960\) | −32944.2 | −1.10757 | ||||||||
\(961\) | 19134.0 | 0.642273 | ||||||||
\(962\) | 1735.27 | 0.0581574 | ||||||||
\(963\) | −21093.9 | −0.705858 | ||||||||
\(964\) | −52075.9 | −1.73989 | ||||||||
\(965\) | 23428.8 | 0.781555 | ||||||||
\(966\) | −68970.5 | −2.29719 | ||||||||
\(967\) | −11846.4 | −0.393956 | −0.196978 | − | 0.980408i | \(-0.563113\pi\) | ||||
−0.196978 | + | 0.980408i | \(0.563113\pi\) | |||||||
\(968\) | 78351.4 | 2.60156 | ||||||||
\(969\) | 2971.56 | 0.0985141 | ||||||||
\(970\) | 90575.4 | 2.99815 | ||||||||
\(971\) | 6248.67 | 0.206518 | 0.103259 | − | 0.994654i | \(-0.467073\pi\) | ||||
0.103259 | + | 0.994654i | \(0.467073\pi\) | |||||||
\(972\) | 74395.9 | 2.45499 | ||||||||
\(973\) | −22228.3 | −0.732381 | ||||||||
\(974\) | −44043.6 | −1.44892 | ||||||||
\(975\) | 1587.51 | 0.0521447 | ||||||||
\(976\) | −128389. | −4.21068 | ||||||||
\(977\) | −38809.5 | −1.27086 | −0.635428 | − | 0.772160i | \(-0.719176\pi\) | ||||
−0.635428 | + | 0.772160i | \(0.719176\pi\) | |||||||
\(978\) | 1899.51 | 0.0621059 | ||||||||
\(979\) | 5605.15 | 0.182984 | ||||||||
\(980\) | −41787.1 | −1.36208 | ||||||||
\(981\) | −31178.2 | −1.01472 | ||||||||
\(982\) | 6537.17 | 0.212433 | ||||||||
\(983\) | −983.000 | −0.0318950 | ||||||||
\(984\) | 90123.4 | 2.91975 | ||||||||
\(985\) | 37827.3 | 1.22363 | ||||||||
\(986\) | 10924.5 | 0.352848 | ||||||||
\(987\) | 31236.5 | 1.00736 | ||||||||
\(988\) | 5772.76 | 0.185887 | ||||||||
\(989\) | 78357.1 | 2.51932 | ||||||||
\(990\) | 9416.12 | 0.302287 | ||||||||
\(991\) | −47518.7 | −1.52319 | −0.761595 | − | 0.648053i | \(-0.775583\pi\) | ||||
−0.761595 | + | 0.648053i | \(0.775583\pi\) | |||||||
\(992\) | 81405.7 | 2.60548 | ||||||||
\(993\) | 14925.3 | 0.476977 | ||||||||
\(994\) | −47647.3 | −1.52040 | ||||||||
\(995\) | −28241.7 | −0.899820 | ||||||||
\(996\) | −39001.6 | −1.24078 | ||||||||
\(997\) | −45562.4 | −1.44732 | −0.723659 | − | 0.690158i | \(-0.757541\pi\) | ||||
−0.723659 | + | 0.690158i | \(0.757541\pi\) | |||||||
\(998\) | 75131.2 | 2.38300 | ||||||||
\(999\) | 13237.1 | 0.419222 |
(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 | 983.4.a.b.1.6 | ✓ | 136 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.4.a.b.1.6 | ✓ | 136 | 1.1 | even | 1 | trivial |