Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.58366 | −1.62057 | −0.810283 | − | 0.586038i | \(-0.800687\pi\) | ||||
−0.810283 | + | 0.586038i | \(0.800687\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 13.0099 | 1.62624 | ||||||||
\(5\) | −16.2221 | −1.45095 | −0.725476 | − | 0.688248i | \(-0.758380\pi\) | ||||
−0.725476 | + | 0.688248i | \(0.758380\pi\) | |||||||
\(6\) | 13.7510 | 0.935635 | ||||||||
\(7\) | 3.97810 | 0.214797 | 0.107398 | − | 0.994216i | \(-0.465748\pi\) | ||||
0.107398 | + | 0.994216i | \(0.465748\pi\) | |||||||
\(8\) | −22.9636 | −1.01486 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 74.3567 | 2.35136 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −39.0297 | −0.938908 | ||||||||
\(13\) | −79.7218 | −1.70084 | −0.850418 | − | 0.526108i | \(-0.823651\pi\) | ||||
−0.850418 | + | 0.526108i | \(0.823651\pi\) | |||||||
\(14\) | −18.2342 | −0.348093 | ||||||||
\(15\) | 48.6664 | 0.837707 | ||||||||
\(16\) | 1.17823 | 0.0184099 | ||||||||
\(17\) | −16.3106 | −0.232700 | −0.116350 | − | 0.993208i | \(-0.537119\pi\) | ||||
−0.116350 | + | 0.993208i | \(0.537119\pi\) | |||||||
\(18\) | −41.2529 | −0.540189 | ||||||||
\(19\) | −57.2836 | −0.691672 | −0.345836 | − | 0.938295i | \(-0.612405\pi\) | ||||
−0.345836 | + | 0.938295i | \(0.612405\pi\) | |||||||
\(20\) | −211.048 | −2.35959 | ||||||||
\(21\) | −11.9343 | −0.124013 | ||||||||
\(22\) | 50.4202 | 0.488619 | ||||||||
\(23\) | 129.684 | 1.17570 | 0.587849 | − | 0.808971i | \(-0.299975\pi\) | ||||
0.587849 | + | 0.808971i | \(0.299975\pi\) | |||||||
\(24\) | 68.8909 | 0.585929 | ||||||||
\(25\) | 138.158 | 1.10526 | ||||||||
\(26\) | 365.417 | 2.75632 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 51.7546 | 0.349311 | ||||||||
\(29\) | 211.000 | 1.35109 | 0.675546 | − | 0.737318i | \(-0.263908\pi\) | ||||
0.675546 | + | 0.737318i | \(0.263908\pi\) | |||||||
\(30\) | −223.070 | −1.35756 | ||||||||
\(31\) | −129.512 | −0.750356 | −0.375178 | − | 0.926953i | \(-0.622418\pi\) | ||||
−0.375178 | + | 0.926953i | \(0.622418\pi\) | |||||||
\(32\) | 178.308 | 0.985025 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 74.7622 | 0.377106 | ||||||||
\(35\) | −64.5332 | −0.311660 | ||||||||
\(36\) | 117.089 | 0.542079 | ||||||||
\(37\) | −7.92892 | −0.0352299 | −0.0176149 | − | 0.999845i | \(-0.505607\pi\) | ||||
−0.0176149 | + | 0.999845i | \(0.505607\pi\) | |||||||
\(38\) | 262.568 | 1.12090 | ||||||||
\(39\) | 239.166 | 0.981978 | ||||||||
\(40\) | 372.519 | 1.47251 | ||||||||
\(41\) | −367.734 | −1.40074 | −0.700371 | − | 0.713779i | \(-0.746982\pi\) | ||||
−0.700371 | + | 0.713779i | \(0.746982\pi\) | |||||||
\(42\) | 54.7027 | 0.200971 | ||||||||
\(43\) | 196.158 | 0.695670 | 0.347835 | − | 0.937556i | \(-0.386917\pi\) | ||||
0.347835 | + | 0.937556i | \(0.386917\pi\) | |||||||
\(44\) | −143.109 | −0.490329 | ||||||||
\(45\) | −145.999 | −0.483651 | ||||||||
\(46\) | −594.428 | −1.90530 | ||||||||
\(47\) | −209.255 | −0.649425 | −0.324712 | − | 0.945813i | \(-0.605267\pi\) | ||||
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(48\) | −3.53470 | −0.0106290 | ||||||||
\(49\) | −327.175 | −0.953862 | ||||||||
\(50\) | −633.267 | −1.79115 | ||||||||
\(51\) | 48.9318 | 0.134350 | ||||||||
\(52\) | −1037.17 | −2.76596 | ||||||||
\(53\) | −220.297 | −0.570947 | −0.285473 | − | 0.958387i | \(-0.592151\pi\) | ||||
−0.285473 | + | 0.958387i | \(0.592151\pi\) | |||||||
\(54\) | 123.759 | 0.311878 | ||||||||
\(55\) | 178.443 | 0.437478 | ||||||||
\(56\) | −91.3515 | −0.217989 | ||||||||
\(57\) | 171.851 | 0.399337 | ||||||||
\(58\) | −967.150 | −2.18953 | ||||||||
\(59\) | 637.881 | 1.40754 | 0.703772 | − | 0.710426i | \(-0.251498\pi\) | ||||
0.703772 | + | 0.710426i | \(0.251498\pi\) | |||||||
\(60\) | 633.145 | 1.36231 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | 593.638 | 1.21600 | ||||||||
\(63\) | 35.8029 | 0.0715990 | ||||||||
\(64\) | −826.731 | −1.61471 | ||||||||
\(65\) | 1293.26 | 2.46783 | ||||||||
\(66\) | −151.261 | −0.282104 | ||||||||
\(67\) | −653.829 | −1.19221 | −0.596104 | − | 0.802907i | \(-0.703285\pi\) | ||||
−0.596104 | + | 0.802907i | \(0.703285\pi\) | |||||||
\(68\) | −212.199 | −0.378426 | ||||||||
\(69\) | −389.053 | −0.678789 | ||||||||
\(70\) | 295.798 | 0.505066 | ||||||||
\(71\) | 129.870 | 0.217081 | 0.108540 | − | 0.994092i | \(-0.465382\pi\) | ||||
0.108540 | + | 0.994092i | \(0.465382\pi\) | |||||||
\(72\) | −206.673 | −0.338286 | ||||||||
\(73\) | −658.004 | −1.05498 | −0.527490 | − | 0.849561i | \(-0.676867\pi\) | ||||
−0.527490 | + | 0.849561i | \(0.676867\pi\) | |||||||
\(74\) | 36.3434 | 0.0570924 | ||||||||
\(75\) | −414.473 | −0.638123 | ||||||||
\(76\) | −745.254 | −1.12482 | ||||||||
\(77\) | −43.7590 | −0.0647637 | ||||||||
\(78\) | −1096.25 | −1.59136 | ||||||||
\(79\) | 1058.66 | 1.50771 | 0.753853 | − | 0.657043i | \(-0.228193\pi\) | ||||
0.753853 | + | 0.657043i | \(0.228193\pi\) | |||||||
\(80\) | −19.1135 | −0.0267119 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1685.57 | 2.27000 | ||||||||
\(83\) | 797.979 | 1.05530 | 0.527648 | − | 0.849463i | \(-0.323074\pi\) | ||||
0.527648 | + | 0.849463i | \(0.323074\pi\) | |||||||
\(84\) | −155.264 | −0.201675 | ||||||||
\(85\) | 264.593 | 0.337637 | ||||||||
\(86\) | −899.121 | −1.12738 | ||||||||
\(87\) | −632.999 | −0.780053 | ||||||||
\(88\) | 252.600 | 0.305992 | ||||||||
\(89\) | 651.829 | 0.776334 | 0.388167 | − | 0.921589i | \(-0.373108\pi\) | ||||
0.388167 | + | 0.921589i | \(0.373108\pi\) | |||||||
\(90\) | 669.210 | 0.783788 | ||||||||
\(91\) | −317.141 | −0.365334 | ||||||||
\(92\) | 1687.18 | 1.91196 | ||||||||
\(93\) | 388.536 | 0.433218 | ||||||||
\(94\) | 959.152 | 1.05244 | ||||||||
\(95\) | 929.263 | 1.00358 | ||||||||
\(96\) | −534.925 | −0.568704 | ||||||||
\(97\) | 403.693 | 0.422565 | 0.211283 | − | 0.977425i | \(-0.432236\pi\) | ||||
0.211283 | + | 0.977425i | \(0.432236\pi\) | |||||||
\(98\) | 1499.66 | 1.54580 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 1797.42 | 1.79742 | ||||||||
\(101\) | −509.163 | −0.501620 | −0.250810 | − | 0.968036i | \(-0.580697\pi\) | ||||
−0.250810 | + | 0.968036i | \(0.580697\pi\) | |||||||
\(102\) | −224.287 | −0.217722 | ||||||||
\(103\) | 652.898 | 0.624582 | 0.312291 | − | 0.949986i | \(-0.398904\pi\) | ||||
0.312291 | + | 0.949986i | \(0.398904\pi\) | |||||||
\(104\) | 1830.70 | 1.72611 | ||||||||
\(105\) | 193.600 | 0.179937 | ||||||||
\(106\) | 1009.77 | 0.925257 | ||||||||
\(107\) | 248.959 | 0.224932 | 0.112466 | − | 0.993656i | \(-0.464125\pi\) | ||||
0.112466 | + | 0.993656i | \(0.464125\pi\) | |||||||
\(108\) | −351.267 | −0.312969 | ||||||||
\(109\) | 236.771 | 0.208060 | 0.104030 | − | 0.994574i | \(-0.466826\pi\) | ||||
0.104030 | + | 0.994574i | \(0.466826\pi\) | |||||||
\(110\) | −817.923 | −0.708963 | ||||||||
\(111\) | 23.7868 | 0.0203400 | ||||||||
\(112\) | 4.68713 | 0.00395439 | ||||||||
\(113\) | 1650.74 | 1.37423 | 0.687116 | − | 0.726548i | \(-0.258876\pi\) | ||||
0.687116 | + | 0.726548i | \(0.258876\pi\) | |||||||
\(114\) | −787.705 | −0.647152 | ||||||||
\(115\) | −2103.76 | −1.70588 | ||||||||
\(116\) | 2745.08 | 2.19720 | ||||||||
\(117\) | −717.497 | −0.566945 | ||||||||
\(118\) | −2923.83 | −2.28102 | ||||||||
\(119\) | −64.8852 | −0.0499833 | ||||||||
\(120\) | −1117.56 | −0.850155 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −279.603 | −0.207492 | ||||||||
\(123\) | 1103.20 | 0.808718 | ||||||||
\(124\) | −1684.94 | −1.22026 | ||||||||
\(125\) | −213.444 | −0.152728 | ||||||||
\(126\) | −164.108 | −0.116031 | ||||||||
\(127\) | −478.717 | −0.334483 | −0.167241 | − | 0.985916i | \(-0.553486\pi\) | ||||
−0.167241 | + | 0.985916i | \(0.553486\pi\) | |||||||
\(128\) | 2362.98 | 1.63172 | ||||||||
\(129\) | −588.474 | −0.401646 | ||||||||
\(130\) | −5927.85 | −3.99928 | ||||||||
\(131\) | −50.5922 | −0.0337425 | −0.0168712 | − | 0.999858i | \(-0.505371\pi\) | ||||
−0.0168712 | + | 0.999858i | \(0.505371\pi\) | |||||||
\(132\) | 429.327 | 0.283092 | ||||||||
\(133\) | −227.880 | −0.148569 | ||||||||
\(134\) | 2996.93 | 1.93205 | ||||||||
\(135\) | 437.998 | 0.279236 | ||||||||
\(136\) | 374.551 | 0.236158 | ||||||||
\(137\) | 933.261 | 0.581999 | 0.291000 | − | 0.956723i | \(-0.406012\pi\) | ||||
0.291000 | + | 0.956723i | \(0.406012\pi\) | |||||||
\(138\) | 1783.28 | 1.10002 | ||||||||
\(139\) | 86.8769 | 0.0530130 | 0.0265065 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265065 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(140\) | −839.570 | −0.506833 | ||||||||
\(141\) | 627.765 | 0.374945 | ||||||||
\(142\) | −595.279 | −0.351794 | ||||||||
\(143\) | 876.940 | 0.512821 | ||||||||
\(144\) | 10.6041 | 0.00613664 | ||||||||
\(145\) | −3422.87 | −1.96037 | ||||||||
\(146\) | 3016.06 | 1.70967 | ||||||||
\(147\) | 981.524 | 0.550713 | ||||||||
\(148\) | −103.154 | −0.0572922 | ||||||||
\(149\) | 1653.80 | 0.909293 | 0.454647 | − | 0.890672i | \(-0.349766\pi\) | ||||
0.454647 | + | 0.890672i | \(0.349766\pi\) | |||||||
\(150\) | 1899.80 | 1.03412 | ||||||||
\(151\) | 1556.69 | 0.838950 | 0.419475 | − | 0.907767i | \(-0.362214\pi\) | ||||
0.419475 | + | 0.907767i | \(0.362214\pi\) | |||||||
\(152\) | 1315.44 | 0.701950 | ||||||||
\(153\) | −146.796 | −0.0775668 | ||||||||
\(154\) | 200.576 | 0.104954 | ||||||||
\(155\) | 2100.96 | 1.08873 | ||||||||
\(156\) | 3111.52 | 1.59693 | ||||||||
\(157\) | −357.842 | −0.181904 | −0.0909518 | − | 0.995855i | \(-0.528991\pi\) | ||||
−0.0909518 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(158\) | −4852.54 | −2.44334 | ||||||||
\(159\) | 660.892 | 0.329636 | ||||||||
\(160\) | −2892.54 | −1.42922 | ||||||||
\(161\) | 515.896 | 0.252536 | ||||||||
\(162\) | −371.276 | −0.180063 | ||||||||
\(163\) | 1101.66 | 0.529377 | 0.264688 | − | 0.964334i | \(-0.414731\pi\) | ||||
0.264688 | + | 0.964334i | \(0.414731\pi\) | |||||||
\(164\) | −4784.18 | −2.27794 | ||||||||
\(165\) | −535.330 | −0.252578 | ||||||||
\(166\) | −3657.66 | −1.71018 | ||||||||
\(167\) | 2499.39 | 1.15813 | 0.579067 | − | 0.815280i | \(-0.303417\pi\) | ||||
0.579067 | + | 0.815280i | \(0.303417\pi\) | |||||||
\(168\) | 274.055 | 0.125856 | ||||||||
\(169\) | 4158.57 | 1.89284 | ||||||||
\(170\) | −1212.80 | −0.547163 | ||||||||
\(171\) | −515.553 | −0.230557 | ||||||||
\(172\) | 2552.00 | 1.13133 | ||||||||
\(173\) | −2049.10 | −0.900523 | −0.450261 | − | 0.892897i | \(-0.648669\pi\) | ||||
−0.450261 | + | 0.892897i | \(0.648669\pi\) | |||||||
\(174\) | 2901.45 | 1.26413 | ||||||||
\(175\) | 549.604 | 0.237407 | ||||||||
\(176\) | −12.9606 | −0.00555080 | ||||||||
\(177\) | −1913.64 | −0.812646 | ||||||||
\(178\) | −2987.76 | −1.25810 | ||||||||
\(179\) | 1188.44 | 0.496246 | 0.248123 | − | 0.968728i | \(-0.420186\pi\) | ||||
0.248123 | + | 0.968728i | \(0.420186\pi\) | |||||||
\(180\) | −1899.43 | −0.786530 | ||||||||
\(181\) | −1331.90 | −0.546959 | −0.273479 | − | 0.961878i | \(-0.588175\pi\) | ||||
−0.273479 | + | 0.961878i | \(0.588175\pi\) | |||||||
\(182\) | 1453.67 | 0.592049 | ||||||||
\(183\) | −183.000 | −0.0739221 | ||||||||
\(184\) | −2978.02 | −1.19317 | ||||||||
\(185\) | 128.624 | 0.0511169 | ||||||||
\(186\) | −1780.91 | −0.702059 | ||||||||
\(187\) | 179.417 | 0.0701618 | ||||||||
\(188\) | −2722.38 | −1.05612 | ||||||||
\(189\) | −107.409 | −0.0413377 | ||||||||
\(190\) | −4259.42 | −1.62637 | ||||||||
\(191\) | −99.9724 | −0.0378730 | −0.0189365 | − | 0.999821i | \(-0.506028\pi\) | ||||
−0.0189365 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(192\) | 2480.19 | 0.932252 | ||||||||
\(193\) | 407.993 | 0.152166 | 0.0760828 | − | 0.997102i | \(-0.475759\pi\) | ||||
0.0760828 | + | 0.997102i | \(0.475759\pi\) | |||||||
\(194\) | −1850.39 | −0.684796 | ||||||||
\(195\) | −3879.77 | −1.42480 | ||||||||
\(196\) | −4256.51 | −1.55121 | ||||||||
\(197\) | −1123.81 | −0.406439 | −0.203219 | − | 0.979133i | \(-0.565140\pi\) | ||||
−0.203219 | + | 0.979133i | \(0.565140\pi\) | |||||||
\(198\) | 453.782 | 0.162873 | ||||||||
\(199\) | 3456.17 | 1.23116 | 0.615582 | − | 0.788073i | \(-0.288921\pi\) | ||||
0.615582 | + | 0.788073i | \(0.288921\pi\) | |||||||
\(200\) | −3172.60 | −1.12168 | ||||||||
\(201\) | 1961.49 | 0.688322 | ||||||||
\(202\) | 2333.83 | 0.812908 | ||||||||
\(203\) | 839.377 | 0.290210 | ||||||||
\(204\) | 636.598 | 0.218484 | ||||||||
\(205\) | 5965.43 | 2.03241 | ||||||||
\(206\) | −2992.66 | −1.01218 | ||||||||
\(207\) | 1167.16 | 0.391899 | ||||||||
\(208\) | −93.9310 | −0.0313122 | ||||||||
\(209\) | 630.120 | 0.208547 | ||||||||
\(210\) | −887.394 | −0.291600 | ||||||||
\(211\) | 1623.45 | 0.529683 | 0.264841 | − | 0.964292i | \(-0.414680\pi\) | ||||
0.264841 | + | 0.964292i | \(0.414680\pi\) | |||||||
\(212\) | −2866.05 | −0.928495 | ||||||||
\(213\) | −389.610 | −0.125332 | ||||||||
\(214\) | −1141.14 | −0.364518 | ||||||||
\(215\) | −3182.10 | −1.00938 | ||||||||
\(216\) | 620.018 | 0.195310 | ||||||||
\(217\) | −515.211 | −0.161174 | ||||||||
\(218\) | −1085.28 | −0.337176 | ||||||||
\(219\) | 1974.01 | 0.609093 | ||||||||
\(220\) | 2321.53 | 0.711444 | ||||||||
\(221\) | 1300.31 | 0.395785 | ||||||||
\(222\) | −109.030 | −0.0329623 | ||||||||
\(223\) | −1227.51 | −0.368611 | −0.184306 | − | 0.982869i | \(-0.559004\pi\) | ||||
−0.184306 | + | 0.982869i | \(0.559004\pi\) | |||||||
\(224\) | 709.328 | 0.211580 | ||||||||
\(225\) | 1243.42 | 0.368420 | ||||||||
\(226\) | −7566.41 | −2.22704 | ||||||||
\(227\) | −657.451 | −0.192232 | −0.0961158 | − | 0.995370i | \(-0.530642\pi\) | ||||
−0.0961158 | + | 0.995370i | \(0.530642\pi\) | |||||||
\(228\) | 2235.76 | 0.649417 | ||||||||
\(229\) | −601.476 | −0.173566 | −0.0867831 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867831 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(230\) | 9642.89 | 2.76449 | ||||||||
\(231\) | 131.277 | 0.0373913 | ||||||||
\(232\) | −4845.32 | −1.37117 | ||||||||
\(233\) | 4374.82 | 1.23006 | 0.615030 | − | 0.788504i | \(-0.289144\pi\) | ||||
0.615030 | + | 0.788504i | \(0.289144\pi\) | |||||||
\(234\) | 3288.76 | 0.918772 | ||||||||
\(235\) | 3394.56 | 0.942284 | ||||||||
\(236\) | 8298.77 | 2.28900 | ||||||||
\(237\) | −3175.99 | −0.870475 | ||||||||
\(238\) | 297.411 | 0.0810013 | ||||||||
\(239\) | 3599.93 | 0.974310 | 0.487155 | − | 0.873316i | \(-0.338035\pi\) | ||||
0.487155 | + | 0.873316i | \(0.338035\pi\) | |||||||
\(240\) | 57.3404 | 0.0154221 | ||||||||
\(241\) | 4012.26 | 1.07242 | 0.536209 | − | 0.844085i | \(-0.319856\pi\) | ||||
0.536209 | + | 0.844085i | \(0.319856\pi\) | |||||||
\(242\) | −554.622 | −0.147324 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 793.604 | 0.208218 | ||||||||
\(245\) | 5307.47 | 1.38401 | ||||||||
\(246\) | −5056.70 | −1.31058 | ||||||||
\(247\) | 4566.76 | 1.17642 | ||||||||
\(248\) | 2974.07 | 0.761505 | ||||||||
\(249\) | −2393.94 | −0.609275 | ||||||||
\(250\) | 978.355 | 0.247506 | ||||||||
\(251\) | 726.525 | 0.182701 | 0.0913503 | − | 0.995819i | \(-0.470882\pi\) | ||||
0.0913503 | + | 0.995819i | \(0.470882\pi\) | |||||||
\(252\) | 465.791 | 0.116437 | ||||||||
\(253\) | −1426.53 | −0.354486 | ||||||||
\(254\) | 2194.28 | 0.542052 | ||||||||
\(255\) | −793.779 | −0.194935 | ||||||||
\(256\) | −4217.24 | −1.02960 | ||||||||
\(257\) | −5727.50 | −1.39016 | −0.695081 | − | 0.718932i | \(-0.744631\pi\) | ||||
−0.695081 | + | 0.718932i | \(0.744631\pi\) | |||||||
\(258\) | 2697.36 | 0.650893 | ||||||||
\(259\) | −31.5420 | −0.00756727 | ||||||||
\(260\) | 16825.2 | 4.01328 | ||||||||
\(261\) | 1899.00 | 0.450364 | ||||||||
\(262\) | 231.897 | 0.0546819 | ||||||||
\(263\) | −3815.81 | −0.894651 | −0.447325 | − | 0.894371i | \(-0.647623\pi\) | ||||
−0.447325 | + | 0.894371i | \(0.647623\pi\) | |||||||
\(264\) | −757.800 | −0.176664 | ||||||||
\(265\) | 3573.69 | 0.828416 | ||||||||
\(266\) | 1044.52 | 0.240766 | ||||||||
\(267\) | −1955.49 | −0.448217 | ||||||||
\(268\) | −8506.25 | −1.93881 | ||||||||
\(269\) | 1031.45 | 0.233786 | 0.116893 | − | 0.993144i | \(-0.462706\pi\) | ||||
0.116893 | + | 0.993144i | \(0.462706\pi\) | |||||||
\(270\) | −2007.63 | −0.452520 | ||||||||
\(271\) | −1355.75 | −0.303896 | −0.151948 | − | 0.988389i | \(-0.548555\pi\) | ||||
−0.151948 | + | 0.988389i | \(0.548555\pi\) | |||||||
\(272\) | −19.2177 | −0.00428399 | ||||||||
\(273\) | 951.423 | 0.210926 | ||||||||
\(274\) | −4277.75 | −0.943169 | ||||||||
\(275\) | −1519.73 | −0.333249 | ||||||||
\(276\) | −5061.54 | −1.10387 | ||||||||
\(277\) | 793.175 | 0.172048 | 0.0860239 | − | 0.996293i | \(-0.472584\pi\) | ||||
0.0860239 | + | 0.996293i | \(0.472584\pi\) | |||||||
\(278\) | −398.214 | −0.0859110 | ||||||||
\(279\) | −1165.61 | −0.250119 | ||||||||
\(280\) | 1481.92 | 0.316291 | ||||||||
\(281\) | −2136.81 | −0.453634 | −0.226817 | − | 0.973937i | \(-0.572832\pi\) | ||||
−0.226817 | + | 0.973937i | \(0.572832\pi\) | |||||||
\(282\) | −2877.46 | −0.607624 | ||||||||
\(283\) | 727.204 | 0.152748 | 0.0763742 | − | 0.997079i | \(-0.475666\pi\) | ||||
0.0763742 | + | 0.997079i | \(0.475666\pi\) | |||||||
\(284\) | 1689.60 | 0.353025 | ||||||||
\(285\) | −2787.79 | −0.579419 | ||||||||
\(286\) | −4019.59 | −0.831061 | ||||||||
\(287\) | −1462.88 | −0.300875 | ||||||||
\(288\) | 1604.78 | 0.328342 | ||||||||
\(289\) | −4646.96 | −0.945851 | ||||||||
\(290\) | 15689.2 | 3.17691 | ||||||||
\(291\) | −1211.08 | −0.243968 | ||||||||
\(292\) | −8560.57 | −1.71565 | ||||||||
\(293\) | −7465.12 | −1.48845 | −0.744227 | − | 0.667926i | \(-0.767182\pi\) | ||||
−0.744227 | + | 0.667926i | \(0.767182\pi\) | |||||||
\(294\) | −4498.97 | −0.892467 | ||||||||
\(295\) | −10347.8 | −2.04228 | ||||||||
\(296\) | 182.077 | 0.0357534 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −7580.46 | −1.47357 | ||||||||
\(299\) | −10338.7 | −1.99967 | ||||||||
\(300\) | −5392.25 | −1.03774 | ||||||||
\(301\) | 780.336 | 0.149428 | ||||||||
\(302\) | −7135.32 | −1.35957 | ||||||||
\(303\) | 1527.49 | 0.289610 | ||||||||
\(304\) | −67.4936 | −0.0127336 | ||||||||
\(305\) | −989.550 | −0.185775 | ||||||||
\(306\) | 672.860 | 0.125702 | ||||||||
\(307\) | −7738.58 | −1.43864 | −0.719322 | − | 0.694677i | \(-0.755547\pi\) | ||||
−0.719322 | + | 0.694677i | \(0.755547\pi\) | |||||||
\(308\) | −569.301 | −0.105321 | ||||||||
\(309\) | −1958.69 | −0.360603 | ||||||||
\(310\) | −9630.08 | −1.76436 | ||||||||
\(311\) | 6943.90 | 1.26609 | 0.633043 | − | 0.774117i | \(-0.281806\pi\) | ||||
0.633043 | + | 0.774117i | \(0.281806\pi\) | |||||||
\(312\) | −5492.11 | −0.996569 | ||||||||
\(313\) | 7632.13 | 1.37825 | 0.689127 | − | 0.724641i | \(-0.257994\pi\) | ||||
0.689127 | + | 0.724641i | \(0.257994\pi\) | |||||||
\(314\) | 1640.22 | 0.294787 | ||||||||
\(315\) | −580.799 | −0.103887 | ||||||||
\(316\) | 13773.1 | 2.45189 | ||||||||
\(317\) | −4942.99 | −0.875791 | −0.437896 | − | 0.899026i | \(-0.644276\pi\) | ||||
−0.437896 | + | 0.899026i | \(0.644276\pi\) | |||||||
\(318\) | −3029.30 | −0.534197 | ||||||||
\(319\) | −2321.00 | −0.407369 | ||||||||
\(320\) | 13411.3 | 2.34286 | ||||||||
\(321\) | −746.876 | −0.129865 | ||||||||
\(322\) | −2364.69 | −0.409252 | ||||||||
\(323\) | 934.331 | 0.160952 | ||||||||
\(324\) | 1053.80 | 0.180693 | ||||||||
\(325\) | −11014.2 | −1.87987 | ||||||||
\(326\) | −5049.61 | −0.857890 | ||||||||
\(327\) | −710.314 | −0.120124 | ||||||||
\(328\) | 8444.51 | 1.42156 | ||||||||
\(329\) | −832.436 | −0.139494 | ||||||||
\(330\) | 2453.77 | 0.409320 | ||||||||
\(331\) | 6861.55 | 1.13941 | 0.569706 | − | 0.821849i | \(-0.307057\pi\) | ||||
0.569706 | + | 0.821849i | \(0.307057\pi\) | |||||||
\(332\) | 10381.6 | 1.71616 | ||||||||
\(333\) | −71.3603 | −0.0117433 | ||||||||
\(334\) | −11456.3 | −1.87683 | ||||||||
\(335\) | 10606.5 | 1.72984 | ||||||||
\(336\) | −14.0614 | −0.00228307 | ||||||||
\(337\) | −2231.10 | −0.360641 | −0.180320 | − | 0.983608i | \(-0.557713\pi\) | ||||
−0.180320 | + | 0.983608i | \(0.557713\pi\) | |||||||
\(338\) | −19061.5 | −3.06747 | ||||||||
\(339\) | −4952.21 | −0.793413 | ||||||||
\(340\) | 3442.33 | 0.549078 | ||||||||
\(341\) | 1424.63 | 0.226241 | ||||||||
\(342\) | 2363.12 | 0.373634 | ||||||||
\(343\) | −2666.02 | −0.419684 | ||||||||
\(344\) | −4504.50 | −0.706007 | ||||||||
\(345\) | 6311.27 | 0.984890 | ||||||||
\(346\) | 9392.38 | 1.45936 | ||||||||
\(347\) | −2911.74 | −0.450463 | −0.225231 | − | 0.974305i | \(-0.572314\pi\) | ||||
−0.225231 | + | 0.974305i | \(0.572314\pi\) | |||||||
\(348\) | −8235.25 | −1.26855 | ||||||||
\(349\) | −6886.68 | −1.05626 | −0.528131 | − | 0.849163i | \(-0.677107\pi\) | ||||
−0.528131 | + | 0.849163i | \(0.677107\pi\) | |||||||
\(350\) | −2519.20 | −0.384733 | ||||||||
\(351\) | 2152.49 | 0.327326 | ||||||||
\(352\) | −1961.39 | −0.296996 | ||||||||
\(353\) | 6385.52 | 0.962796 | 0.481398 | − | 0.876502i | \(-0.340129\pi\) | ||||
0.481398 | + | 0.876502i | \(0.340129\pi\) | |||||||
\(354\) | 8771.49 | 1.31695 | ||||||||
\(355\) | −2106.77 | −0.314974 | ||||||||
\(356\) | 8480.22 | 1.26250 | ||||||||
\(357\) | 194.656 | 0.0288579 | ||||||||
\(358\) | −5447.40 | −0.804201 | ||||||||
\(359\) | −5381.57 | −0.791166 | −0.395583 | − | 0.918430i | \(-0.629457\pi\) | ||||
−0.395583 | + | 0.918430i | \(0.629457\pi\) | |||||||
\(360\) | 3352.67 | 0.490837 | ||||||||
\(361\) | −3577.58 | −0.521590 | ||||||||
\(362\) | 6104.98 | 0.886383 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −4125.97 | −0.594120 | ||||||||
\(365\) | 10674.2 | 1.53073 | ||||||||
\(366\) | 838.809 | 0.119796 | ||||||||
\(367\) | 8673.70 | 1.23369 | 0.616844 | − | 0.787086i | \(-0.288411\pi\) | ||||
0.616844 | + | 0.787086i | \(0.288411\pi\) | |||||||
\(368\) | 152.798 | 0.0216445 | ||||||||
\(369\) | −3309.61 | −0.466914 | ||||||||
\(370\) | −589.568 | −0.0828383 | ||||||||
\(371\) | −876.364 | −0.122638 | ||||||||
\(372\) | 5054.81 | 0.704515 | ||||||||
\(373\) | 7643.56 | 1.06104 | 0.530521 | − | 0.847672i | \(-0.321996\pi\) | ||||
0.530521 | + | 0.847672i | \(0.321996\pi\) | |||||||
\(374\) | −822.385 | −0.113702 | ||||||||
\(375\) | 640.333 | 0.0881777 | ||||||||
\(376\) | 4805.25 | 0.659074 | ||||||||
\(377\) | −16821.3 | −2.29798 | ||||||||
\(378\) | 492.324 | 0.0669905 | ||||||||
\(379\) | 4039.97 | 0.547544 | 0.273772 | − | 0.961795i | \(-0.411729\pi\) | ||||
0.273772 | + | 0.961795i | \(0.411729\pi\) | |||||||
\(380\) | 12089.6 | 1.63206 | ||||||||
\(381\) | 1436.15 | 0.193114 | ||||||||
\(382\) | 458.239 | 0.0613758 | ||||||||
\(383\) | −10864.5 | −1.44948 | −0.724741 | − | 0.689021i | \(-0.758041\pi\) | ||||
−0.724741 | + | 0.689021i | \(0.758041\pi\) | |||||||
\(384\) | −7088.94 | −0.942073 | ||||||||
\(385\) | 709.865 | 0.0939690 | ||||||||
\(386\) | −1870.10 | −0.246595 | ||||||||
\(387\) | 1765.42 | 0.231890 | ||||||||
\(388\) | 5252.01 | 0.687192 | ||||||||
\(389\) | 2682.34 | 0.349614 | 0.174807 | − | 0.984603i | \(-0.444070\pi\) | ||||
0.174807 | + | 0.984603i | \(0.444070\pi\) | |||||||
\(390\) | 17783.5 | 2.30899 | ||||||||
\(391\) | −2115.23 | −0.273585 | ||||||||
\(392\) | 7513.12 | 0.968036 | ||||||||
\(393\) | 151.777 | 0.0194812 | ||||||||
\(394\) | 5151.18 | 0.658661 | ||||||||
\(395\) | −17173.8 | −2.18761 | ||||||||
\(396\) | −1287.98 | −0.163443 | ||||||||
\(397\) | −9484.81 | −1.19907 | −0.599533 | − | 0.800350i | \(-0.704647\pi\) | ||||
−0.599533 | + | 0.800350i | \(0.704647\pi\) | |||||||
\(398\) | −15841.9 | −1.99518 | ||||||||
\(399\) | 683.639 | 0.0857764 | ||||||||
\(400\) | 162.782 | 0.0203478 | ||||||||
\(401\) | −8668.93 | −1.07957 | −0.539783 | − | 0.841805i | \(-0.681494\pi\) | ||||
−0.539783 | + | 0.841805i | \(0.681494\pi\) | |||||||
\(402\) | −8990.78 | −1.11547 | ||||||||
\(403\) | 10324.9 | 1.27623 | ||||||||
\(404\) | −6624.16 | −0.815753 | ||||||||
\(405\) | −1313.99 | −0.161217 | ||||||||
\(406\) | −3847.41 | −0.470305 | ||||||||
\(407\) | 87.2181 | 0.0106222 | ||||||||
\(408\) | −1123.65 | −0.136346 | ||||||||
\(409\) | 11225.7 | 1.35715 | 0.678576 | − | 0.734530i | \(-0.262598\pi\) | ||||
0.678576 | + | 0.734530i | \(0.262598\pi\) | |||||||
\(410\) | −27343.5 | −3.29365 | ||||||||
\(411\) | −2799.78 | −0.336017 | ||||||||
\(412\) | 8494.14 | 1.01572 | ||||||||
\(413\) | 2537.55 | 0.302336 | ||||||||
\(414\) | −5349.85 | −0.635099 | ||||||||
\(415\) | −12944.9 | −1.53118 | ||||||||
\(416\) | −14215.1 | −1.67536 | ||||||||
\(417\) | −260.631 | −0.0306070 | ||||||||
\(418\) | −2888.25 | −0.337964 | ||||||||
\(419\) | 14523.3 | 1.69334 | 0.846671 | − | 0.532117i | \(-0.178603\pi\) | ||||
0.846671 | + | 0.532117i | \(0.178603\pi\) | |||||||
\(420\) | 2518.71 | 0.292620 | ||||||||
\(421\) | −16735.5 | −1.93739 | −0.968694 | − | 0.248259i | \(-0.920142\pi\) | ||||
−0.968694 | + | 0.248259i | \(0.920142\pi\) | |||||||
\(422\) | −7441.34 | −0.858386 | ||||||||
\(423\) | −1883.29 | −0.216475 | ||||||||
\(424\) | 5058.83 | 0.579430 | ||||||||
\(425\) | −2253.44 | −0.257194 | ||||||||
\(426\) | 1785.84 | 0.203108 | ||||||||
\(427\) | 242.664 | 0.0275019 | ||||||||
\(428\) | 3238.93 | 0.365793 | ||||||||
\(429\) | −2630.82 | −0.296077 | ||||||||
\(430\) | 14585.7 | 1.63577 | ||||||||
\(431\) | 17367.9 | 1.94102 | 0.970512 | − | 0.241055i | \(-0.0774933\pi\) | ||||
0.970512 | + | 0.241055i | \(0.0774933\pi\) | |||||||
\(432\) | −31.8123 | −0.00354299 | ||||||||
\(433\) | −15888.1 | −1.76336 | −0.881679 | − | 0.471850i | \(-0.843586\pi\) | ||||
−0.881679 | + | 0.471850i | \(0.843586\pi\) | |||||||
\(434\) | 2361.55 | 0.261193 | ||||||||
\(435\) | 10268.6 | 1.13182 | ||||||||
\(436\) | 3080.37 | 0.338355 | ||||||||
\(437\) | −7428.79 | −0.813197 | ||||||||
\(438\) | −9048.19 | −0.987076 | ||||||||
\(439\) | −8211.06 | −0.892693 | −0.446347 | − | 0.894860i | \(-0.647275\pi\) | ||||
−0.446347 | + | 0.894860i | \(0.647275\pi\) | |||||||
\(440\) | −4097.71 | −0.443979 | ||||||||
\(441\) | −2944.57 | −0.317954 | ||||||||
\(442\) | −5960.18 | −0.641396 | ||||||||
\(443\) | −7167.93 | −0.768756 | −0.384378 | − | 0.923176i | \(-0.625584\pi\) | ||||
−0.384378 | + | 0.923176i | \(0.625584\pi\) | |||||||
\(444\) | 309.463 | 0.0330776 | ||||||||
\(445\) | −10574.1 | −1.12642 | ||||||||
\(446\) | 5626.49 | 0.597359 | ||||||||
\(447\) | −4961.40 | −0.524981 | ||||||||
\(448\) | −3288.81 | −0.346834 | ||||||||
\(449\) | −12378.3 | −1.30104 | −0.650522 | − | 0.759487i | \(-0.725450\pi\) | ||||
−0.650522 | + | 0.759487i | \(0.725450\pi\) | |||||||
\(450\) | −5699.40 | −0.597050 | ||||||||
\(451\) | 4045.07 | 0.422339 | ||||||||
\(452\) | 21475.9 | 2.23483 | ||||||||
\(453\) | −4670.06 | −0.484368 | ||||||||
\(454\) | 3013.53 | 0.311524 | ||||||||
\(455\) | 5144.70 | 0.530082 | ||||||||
\(456\) | −3946.32 | −0.405271 | ||||||||
\(457\) | −6377.38 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(458\) | 2756.96 | 0.281276 | ||||||||
\(459\) | 440.387 | 0.0447832 | ||||||||
\(460\) | −27369.6 | −2.77417 | ||||||||
\(461\) | −4951.11 | −0.500209 | −0.250105 | − | 0.968219i | \(-0.580465\pi\) | ||||
−0.250105 | + | 0.968219i | \(0.580465\pi\) | |||||||
\(462\) | −601.729 | −0.0605952 | ||||||||
\(463\) | 12712.0 | 1.27597 | 0.637987 | − | 0.770047i | \(-0.279767\pi\) | ||||
0.637987 | + | 0.770047i | \(0.279767\pi\) | |||||||
\(464\) | 248.607 | 0.0248735 | ||||||||
\(465\) | −6302.88 | −0.628579 | ||||||||
\(466\) | −20052.7 | −1.99339 | ||||||||
\(467\) | 4980.38 | 0.493500 | 0.246750 | − | 0.969079i | \(-0.420637\pi\) | ||||
0.246750 | + | 0.969079i | \(0.420637\pi\) | |||||||
\(468\) | −9334.56 | −0.921987 | ||||||||
\(469\) | −2600.99 | −0.256083 | ||||||||
\(470\) | −15559.5 | −1.52703 | ||||||||
\(471\) | 1073.52 | 0.105022 | ||||||||
\(472\) | −14648.1 | −1.42846 | ||||||||
\(473\) | −2157.74 | −0.209753 | ||||||||
\(474\) | 14557.6 | 1.41066 | ||||||||
\(475\) | −7914.17 | −0.764478 | ||||||||
\(476\) | −844.149 | −0.0812847 | ||||||||
\(477\) | −1982.68 | −0.190316 | ||||||||
\(478\) | −16500.8 | −1.57893 | ||||||||
\(479\) | 1408.45 | 0.134350 | 0.0671752 | − | 0.997741i | \(-0.478601\pi\) | ||||
0.0671752 | + | 0.997741i | \(0.478601\pi\) | |||||||
\(480\) | 8677.63 | 0.825162 | ||||||||
\(481\) | 632.108 | 0.0599202 | ||||||||
\(482\) | −18390.8 | −1.73792 | ||||||||
\(483\) | −1547.69 | −0.145802 | ||||||||
\(484\) | 1574.20 | 0.147840 | ||||||||
\(485\) | −6548.77 | −0.613122 | ||||||||
\(486\) | 1113.83 | 0.103959 | ||||||||
\(487\) | −17539.5 | −1.63202 | −0.816008 | − | 0.578041i | \(-0.803817\pi\) | ||||
−0.816008 | + | 0.578041i | \(0.803817\pi\) | |||||||
\(488\) | −1400.78 | −0.129939 | ||||||||
\(489\) | −3304.97 | −0.305636 | ||||||||
\(490\) | −24327.6 | −2.24288 | ||||||||
\(491\) | −17628.3 | −1.62027 | −0.810137 | − | 0.586240i | \(-0.800608\pi\) | ||||
−0.810137 | + | 0.586240i | \(0.800608\pi\) | |||||||
\(492\) | 14352.5 | 1.31517 | ||||||||
\(493\) | −3441.53 | −0.314399 | ||||||||
\(494\) | −20932.4 | −1.90647 | ||||||||
\(495\) | 1605.99 | 0.145826 | ||||||||
\(496\) | −152.595 | −0.0138140 | ||||||||
\(497\) | 516.635 | 0.0466283 | ||||||||
\(498\) | 10973.0 | 0.987371 | ||||||||
\(499\) | 8332.95 | 0.747563 | 0.373782 | − | 0.927517i | \(-0.378061\pi\) | ||||
0.373782 | + | 0.927517i | \(0.378061\pi\) | |||||||
\(500\) | −2776.89 | −0.248372 | ||||||||
\(501\) | −7498.16 | −0.668649 | ||||||||
\(502\) | −3330.14 | −0.296078 | ||||||||
\(503\) | 10603.3 | 0.939919 | 0.469959 | − | 0.882688i | \(-0.344269\pi\) | ||||
0.469959 | + | 0.882688i | \(0.344269\pi\) | |||||||
\(504\) | −822.164 | −0.0726629 | ||||||||
\(505\) | 8259.71 | 0.727826 | ||||||||
\(506\) | 6538.71 | 0.574468 | ||||||||
\(507\) | −12475.7 | −1.09283 | ||||||||
\(508\) | −6228.06 | −0.543948 | ||||||||
\(509\) | 856.192 | 0.0745580 | 0.0372790 | − | 0.999305i | \(-0.488131\pi\) | ||||
0.0372790 | + | 0.999305i | \(0.488131\pi\) | |||||||
\(510\) | 3638.41 | 0.315905 | ||||||||
\(511\) | −2617.60 | −0.226607 | ||||||||
\(512\) | 426.542 | 0.0368177 | ||||||||
\(513\) | 1546.66 | 0.133112 | ||||||||
\(514\) | 26252.9 | 2.25285 | ||||||||
\(515\) | −10591.4 | −0.906238 | ||||||||
\(516\) | −7655.99 | −0.653171 | ||||||||
\(517\) | 2301.80 | 0.195809 | ||||||||
\(518\) | 144.578 | 0.0122633 | ||||||||
\(519\) | 6147.31 | 0.519917 | ||||||||
\(520\) | −29697.9 | −2.50450 | ||||||||
\(521\) | −4899.62 | −0.412008 | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||||
−0.206004 | + | 0.978551i | \(0.566046\pi\) | |||||||
\(522\) | −8704.35 | −0.729845 | ||||||||
\(523\) | −2008.61 | −0.167936 | −0.0839681 | − | 0.996468i | \(-0.526759\pi\) | ||||
−0.0839681 | + | 0.996468i | \(0.526759\pi\) | |||||||
\(524\) | −658.199 | −0.0548732 | ||||||||
\(525\) | −1648.81 | −0.137067 | ||||||||
\(526\) | 17490.4 | 1.44984 | ||||||||
\(527\) | 2112.42 | 0.174608 | ||||||||
\(528\) | 38.8817 | 0.00320475 | ||||||||
\(529\) | 4651.01 | 0.382264 | ||||||||
\(530\) | −16380.6 | −1.34250 | ||||||||
\(531\) | 5740.93 | 0.469181 | ||||||||
\(532\) | −2964.69 | −0.241609 | ||||||||
\(533\) | 29316.4 | 2.38243 | ||||||||
\(534\) | 8963.28 | 0.726365 | ||||||||
\(535\) | −4038.64 | −0.326366 | ||||||||
\(536\) | 15014.3 | 1.20992 | ||||||||
\(537\) | −3565.32 | −0.286508 | ||||||||
\(538\) | −4727.81 | −0.378867 | ||||||||
\(539\) | 3598.92 | 0.287600 | ||||||||
\(540\) | 5698.30 | 0.454104 | ||||||||
\(541\) | −8895.89 | −0.706958 | −0.353479 | − | 0.935442i | \(-0.615001\pi\) | ||||
−0.353479 | + | 0.935442i | \(0.615001\pi\) | |||||||
\(542\) | 6214.27 | 0.492483 | ||||||||
\(543\) | 3995.71 | 0.315787 | ||||||||
\(544\) | −2908.32 | −0.229215 | ||||||||
\(545\) | −3840.94 | −0.301885 | ||||||||
\(546\) | −4361.00 | −0.341819 | ||||||||
\(547\) | 1736.07 | 0.135702 | 0.0678512 | − | 0.997695i | \(-0.478386\pi\) | ||||
0.0678512 | + | 0.997695i | \(0.478386\pi\) | |||||||
\(548\) | 12141.6 | 0.946469 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | 6965.93 | 0.540052 | ||||||||
\(551\) | −12086.8 | −0.934512 | ||||||||
\(552\) | 8934.07 | 0.688875 | ||||||||
\(553\) | 4211.46 | 0.323851 | ||||||||
\(554\) | −3635.64 | −0.278815 | ||||||||
\(555\) | −385.872 | −0.0295123 | ||||||||
\(556\) | 1130.26 | 0.0862116 | ||||||||
\(557\) | −6202.01 | −0.471791 | −0.235896 | − | 0.971778i | \(-0.575802\pi\) | ||||
−0.235896 | + | 0.971778i | \(0.575802\pi\) | |||||||
\(558\) | 5342.74 | 0.405334 | ||||||||
\(559\) | −15638.1 | −1.18322 | ||||||||
\(560\) | −76.0352 | −0.00573763 | ||||||||
\(561\) | −538.250 | −0.0405079 | ||||||||
\(562\) | 9794.38 | 0.735144 | ||||||||
\(563\) | 11792.8 | 0.882785 | 0.441393 | − | 0.897314i | \(-0.354485\pi\) | ||||
0.441393 | + | 0.897314i | \(0.354485\pi\) | |||||||
\(564\) | 8167.15 | 0.609750 | ||||||||
\(565\) | −26778.5 | −1.99394 | ||||||||
\(566\) | −3333.25 | −0.247539 | ||||||||
\(567\) | 322.226 | 0.0238663 | ||||||||
\(568\) | −2982.29 | −0.220306 | ||||||||
\(569\) | −720.606 | −0.0530920 | −0.0265460 | − | 0.999648i | \(-0.508451\pi\) | ||||
−0.0265460 | + | 0.999648i | \(0.508451\pi\) | |||||||
\(570\) | 12778.3 | 0.938987 | ||||||||
\(571\) | 6777.60 | 0.496731 | 0.248366 | − | 0.968666i | \(-0.420107\pi\) | ||||
0.248366 | + | 0.968666i | \(0.420107\pi\) | |||||||
\(572\) | 11408.9 | 0.833969 | ||||||||
\(573\) | 299.917 | 0.0218660 | ||||||||
\(574\) | 6705.34 | 0.487588 | ||||||||
\(575\) | 17916.9 | 1.29945 | ||||||||
\(576\) | −7440.57 | −0.538236 | ||||||||
\(577\) | −4736.39 | −0.341730 | −0.170865 | − | 0.985294i | \(-0.554656\pi\) | ||||
−0.170865 | + | 0.985294i | \(0.554656\pi\) | |||||||
\(578\) | 21300.1 | 1.53281 | ||||||||
\(579\) | −1223.98 | −0.0878528 | ||||||||
\(580\) | −44531.1 | −3.18802 | ||||||||
\(581\) | 3174.43 | 0.226674 | ||||||||
\(582\) | 5551.17 | 0.395367 | ||||||||
\(583\) | 2423.27 | 0.172147 | ||||||||
\(584\) | 15110.2 | 1.07066 | ||||||||
\(585\) | 11639.3 | 0.822610 | ||||||||
\(586\) | 34217.6 | 2.41214 | ||||||||
\(587\) | −17899.6 | −1.25860 | −0.629299 | − | 0.777163i | \(-0.716658\pi\) | ||||
−0.629299 | + | 0.777163i | \(0.716658\pi\) | |||||||
\(588\) | 12769.5 | 0.895589 | ||||||||
\(589\) | 7418.92 | 0.519000 | ||||||||
\(590\) | 47430.7 | 3.30965 | ||||||||
\(591\) | 3371.44 | 0.234658 | ||||||||
\(592\) | −9.34212 | −0.000648579 0 | ||||||||
\(593\) | 8710.21 | 0.603179 | 0.301590 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301590 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(594\) | −1361.35 | −0.0940348 | ||||||||
\(595\) | 1052.58 | 0.0725234 | ||||||||
\(596\) | 21515.8 | 1.47873 | ||||||||
\(597\) | −10368.5 | −0.710812 | ||||||||
\(598\) | 47388.9 | 3.24060 | ||||||||
\(599\) | 8887.52 | 0.606234 | 0.303117 | − | 0.952953i | \(-0.401973\pi\) | ||||
0.303117 | + | 0.952953i | \(0.401973\pi\) | |||||||
\(600\) | 9517.80 | 0.647604 | ||||||||
\(601\) | −193.942 | −0.0131632 | −0.00658158 | − | 0.999978i | \(-0.502095\pi\) | ||||
−0.00658158 | + | 0.999978i | \(0.502095\pi\) | |||||||
\(602\) | −3576.79 | −0.242158 | ||||||||
\(603\) | −5884.46 | −0.397403 | ||||||||
\(604\) | 20252.3 | 1.36433 | ||||||||
\(605\) | −1962.88 | −0.131905 | ||||||||
\(606\) | −7001.48 | −0.469333 | ||||||||
\(607\) | −2042.05 | −0.136547 | −0.0682736 | − | 0.997667i | \(-0.521749\pi\) | ||||
−0.0682736 | + | 0.997667i | \(0.521749\pi\) | |||||||
\(608\) | −10214.2 | −0.681314 | ||||||||
\(609\) | −2518.13 | −0.167553 | ||||||||
\(610\) | 4535.76 | 0.301061 | ||||||||
\(611\) | 16682.2 | 1.10456 | ||||||||
\(612\) | −1909.79 | −0.126142 | ||||||||
\(613\) | −19534.6 | −1.28710 | −0.643552 | − | 0.765402i | \(-0.722540\pi\) | ||||
−0.643552 | + | 0.765402i | \(0.722540\pi\) | |||||||
\(614\) | 35471.0 | 2.33142 | ||||||||
\(615\) | −17896.3 | −1.17341 | ||||||||
\(616\) | 1004.87 | 0.0657260 | ||||||||
\(617\) | −25909.6 | −1.69057 | −0.845286 | − | 0.534315i | \(-0.820570\pi\) | ||||
−0.845286 | + | 0.534315i | \(0.820570\pi\) | |||||||
\(618\) | 8977.98 | 0.584381 | ||||||||
\(619\) | 5678.56 | 0.368724 | 0.184362 | − | 0.982858i | \(-0.440978\pi\) | ||||
0.184362 | + | 0.982858i | \(0.440978\pi\) | |||||||
\(620\) | 27333.3 | 1.77053 | ||||||||
\(621\) | −3501.48 | −0.226263 | ||||||||
\(622\) | −31828.4 | −2.05178 | ||||||||
\(623\) | 2593.04 | 0.166754 | ||||||||
\(624\) | 281.793 | 0.0180781 | ||||||||
\(625\) | −13807.2 | −0.883659 | ||||||||
\(626\) | −34983.1 | −2.23355 | ||||||||
\(627\) | −1890.36 | −0.120405 | ||||||||
\(628\) | −4655.48 | −0.295818 | ||||||||
\(629\) | 129.325 | 0.00819801 | ||||||||
\(630\) | 2662.18 | 0.168355 | ||||||||
\(631\) | 12122.5 | 0.764800 | 0.382400 | − | 0.923997i | \(-0.375098\pi\) | ||||
0.382400 | + | 0.923997i | \(0.375098\pi\) | |||||||
\(632\) | −24310.7 | −1.53011 | ||||||||
\(633\) | −4870.36 | −0.305812 | ||||||||
\(634\) | 22657.0 | 1.41928 | ||||||||
\(635\) | 7765.82 | 0.485318 | ||||||||
\(636\) | 8598.14 | 0.536067 | ||||||||
\(637\) | 26083.0 | 1.62236 | ||||||||
\(638\) | 10638.6 | 0.660170 | ||||||||
\(639\) | 1168.83 | 0.0723602 | ||||||||
\(640\) | −38332.6 | −2.36754 | ||||||||
\(641\) | 26350.5 | 1.62369 | 0.811843 | − | 0.583876i | \(-0.198465\pi\) | ||||
0.811843 | + | 0.583876i | \(0.198465\pi\) | |||||||
\(642\) | 3423.42 | 0.210454 | ||||||||
\(643\) | 11612.0 | 0.712182 | 0.356091 | − | 0.934451i | \(-0.384109\pi\) | ||||
0.356091 | + | 0.934451i | \(0.384109\pi\) | |||||||
\(644\) | 6711.76 | 0.410684 | ||||||||
\(645\) | 9546.31 | 0.582768 | ||||||||
\(646\) | −4282.65 | −0.260834 | ||||||||
\(647\) | −12052.1 | −0.732327 | −0.366164 | − | 0.930551i | \(-0.619329\pi\) | ||||
−0.366164 | + | 0.930551i | \(0.619329\pi\) | |||||||
\(648\) | −1860.05 | −0.112762 | ||||||||
\(649\) | −7016.70 | −0.424390 | ||||||||
\(650\) | 50485.2 | 3.04645 | ||||||||
\(651\) | 1545.63 | 0.0930539 | ||||||||
\(652\) | 14332.4 | 0.860892 | ||||||||
\(653\) | −27660.9 | −1.65766 | −0.828831 | − | 0.559499i | \(-0.810994\pi\) | ||||
−0.828831 | + | 0.559499i | \(0.810994\pi\) | |||||||
\(654\) | 3255.83 | 0.194668 | ||||||||
\(655\) | 820.713 | 0.0489587 | ||||||||
\(656\) | −433.277 | −0.0257875 | ||||||||
\(657\) | −5922.04 | −0.351660 | ||||||||
\(658\) | 3815.60 | 0.226060 | ||||||||
\(659\) | 33255.7 | 1.96580 | 0.982898 | − | 0.184149i | \(-0.0589530\pi\) | ||||
0.982898 | + | 0.184149i | \(0.0589530\pi\) | |||||||
\(660\) | −6964.59 | −0.410752 | ||||||||
\(661\) | 8330.75 | 0.490210 | 0.245105 | − | 0.969497i | \(-0.421178\pi\) | ||||
0.245105 | + | 0.969497i | \(0.421178\pi\) | |||||||
\(662\) | −31451.0 | −1.84649 | ||||||||
\(663\) | −3900.94 | −0.228506 | ||||||||
\(664\) | −18324.5 | −1.07098 | ||||||||
\(665\) | 3696.70 | 0.215567 | ||||||||
\(666\) | 327.091 | 0.0190308 | ||||||||
\(667\) | 27363.3 | 1.58848 | ||||||||
\(668\) | 32516.8 | 1.88340 | ||||||||
\(669\) | 3682.54 | 0.212818 | ||||||||
\(670\) | −48616.6 | −2.80332 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | −2127.98 | −0.122156 | ||||||||
\(673\) | −7169.40 | −0.410639 | −0.205320 | − | 0.978695i | \(-0.565823\pi\) | ||||
−0.205320 | + | 0.978695i | \(0.565823\pi\) | |||||||
\(674\) | 10226.6 | 0.584443 | ||||||||
\(675\) | −3730.26 | −0.212708 | ||||||||
\(676\) | 54102.6 | 3.07821 | ||||||||
\(677\) | 17876.2 | 1.01483 | 0.507415 | − | 0.861702i | \(-0.330601\pi\) | ||||
0.507415 | + | 0.861702i | \(0.330601\pi\) | |||||||
\(678\) | 22699.2 | 1.28578 | ||||||||
\(679\) | 1605.93 | 0.0907658 | ||||||||
\(680\) | −6076.02 | −0.342654 | ||||||||
\(681\) | 1972.35 | 0.110985 | ||||||||
\(682\) | −6530.02 | −0.366638 | ||||||||
\(683\) | −25975.2 | −1.45522 | −0.727608 | − | 0.685993i | \(-0.759368\pi\) | ||||
−0.727608 | + | 0.685993i | \(0.759368\pi\) | |||||||
\(684\) | −6707.29 | −0.374941 | ||||||||
\(685\) | −15139.5 | −0.844453 | ||||||||
\(686\) | 12220.1 | 0.680125 | ||||||||
\(687\) | 1804.43 | 0.100208 | ||||||||
\(688\) | 231.120 | 0.0128072 | ||||||||
\(689\) | 17562.5 | 0.971086 | ||||||||
\(690\) | −28928.7 | −1.59608 | ||||||||
\(691\) | −11074.9 | −0.609710 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(692\) | −26658.6 | −1.46446 | ||||||||
\(693\) | −393.831 | −0.0215879 | ||||||||
\(694\) | 13346.4 | 0.730005 | ||||||||
\(695\) | −1409.33 | −0.0769192 | ||||||||
\(696\) | 14536.0 | 0.791644 | ||||||||
\(697\) | 5997.97 | 0.325953 | ||||||||
\(698\) | 31566.2 | 1.71174 | ||||||||
\(699\) | −13124.5 | −0.710175 | ||||||||
\(700\) | 7150.29 | 0.386079 | ||||||||
\(701\) | 13647.6 | 0.735324 | 0.367662 | − | 0.929960i | \(-0.380158\pi\) | ||||
0.367662 | + | 0.929960i | \(0.380158\pi\) | |||||||
\(702\) | −9866.27 | −0.530454 | ||||||||
\(703\) | 454.197 | 0.0243675 | ||||||||
\(704\) | 9094.04 | 0.486853 | ||||||||
\(705\) | −10183.7 | −0.544028 | ||||||||
\(706\) | −29269.0 | −1.56028 | ||||||||
\(707\) | −2025.50 | −0.107746 | ||||||||
\(708\) | −24896.3 | −1.32155 | ||||||||
\(709\) | −12631.7 | −0.669101 | −0.334551 | − | 0.942378i | \(-0.608585\pi\) | ||||
−0.334551 | + | 0.942378i | \(0.608585\pi\) | |||||||
\(710\) | 9656.70 | 0.510436 | ||||||||
\(711\) | 9527.96 | 0.502569 | ||||||||
\(712\) | −14968.4 | −0.787869 | ||||||||
\(713\) | −16795.7 | −0.882191 | ||||||||
\(714\) | −892.234 | −0.0467661 | ||||||||
\(715\) | −14225.8 | −0.744079 | ||||||||
\(716\) | 15461.5 | 0.807014 | ||||||||
\(717\) | −10799.8 | −0.562518 | ||||||||
\(718\) | 24667.3 | 1.28214 | ||||||||
\(719\) | 19598.3 | 1.01654 | 0.508270 | − | 0.861198i | \(-0.330285\pi\) | ||||
0.508270 | + | 0.861198i | \(0.330285\pi\) | |||||||
\(720\) | −172.021 | −0.00890396 | ||||||||
\(721\) | 2597.29 | 0.134158 | ||||||||
\(722\) | 16398.4 | 0.845271 | ||||||||
\(723\) | −12036.8 | −0.619161 | ||||||||
\(724\) | −17327.9 | −0.889484 | ||||||||
\(725\) | 29151.2 | 1.49331 | ||||||||
\(726\) | 1663.87 | 0.0850577 | ||||||||
\(727\) | 3377.93 | 0.172325 | 0.0861627 | − | 0.996281i | \(-0.472540\pi\) | ||||
0.0861627 | + | 0.996281i | \(0.472540\pi\) | |||||||
\(728\) | 7282.71 | 0.370763 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −48927.0 | −2.48064 | ||||||||
\(731\) | −3199.46 | −0.161883 | ||||||||
\(732\) | −2380.81 | −0.120215 | ||||||||
\(733\) | −25011.2 | −1.26031 | −0.630157 | − | 0.776467i | \(-0.717010\pi\) | ||||
−0.630157 | + | 0.776467i | \(0.717010\pi\) | |||||||
\(734\) | −39757.2 | −1.99927 | ||||||||
\(735\) | −15922.4 | −0.799057 | ||||||||
\(736\) | 23123.8 | 1.15809 | ||||||||
\(737\) | 7192.12 | 0.359464 | ||||||||
\(738\) | 15170.1 | 0.756665 | ||||||||
\(739\) | 10710.5 | 0.533143 | 0.266572 | − | 0.963815i | \(-0.414109\pi\) | ||||
0.266572 | + | 0.963815i | \(0.414109\pi\) | |||||||
\(740\) | 1673.38 | 0.0831281 | ||||||||
\(741\) | −13700.3 | −0.679207 | ||||||||
\(742\) | 4016.95 | 0.198742 | ||||||||
\(743\) | 11349.4 | 0.560388 | 0.280194 | − | 0.959943i | \(-0.409601\pi\) | ||||
0.280194 | + | 0.959943i | \(0.409601\pi\) | |||||||
\(744\) | −8922.20 | −0.439655 | ||||||||
\(745\) | −26828.2 | −1.31934 | ||||||||
\(746\) | −35035.5 | −1.71949 | ||||||||
\(747\) | 7181.81 | 0.351765 | ||||||||
\(748\) | 2334.19 | 0.114100 | ||||||||
\(749\) | 990.381 | 0.0483148 | ||||||||
\(750\) | −2935.07 | −0.142898 | ||||||||
\(751\) | 4149.89 | 0.201640 | 0.100820 | − | 0.994905i | \(-0.467853\pi\) | ||||
0.100820 | + | 0.994905i | \(0.467853\pi\) | |||||||
\(752\) | −246.551 | −0.0119558 | ||||||||
\(753\) | −2179.57 | −0.105482 | ||||||||
\(754\) | 77103.0 | 3.72404 | ||||||||
\(755\) | −25252.8 | −1.21728 | ||||||||
\(756\) | −1397.37 | −0.0672249 | ||||||||
\(757\) | 1194.12 | 0.0573327 | 0.0286664 | − | 0.999589i | \(-0.490874\pi\) | ||||
0.0286664 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(758\) | −18517.8 | −0.887332 | ||||||||
\(759\) | 4279.58 | 0.204663 | ||||||||
\(760\) | −21339.3 | −1.01850 | ||||||||
\(761\) | −4267.65 | −0.203288 | −0.101644 | − | 0.994821i | \(-0.532410\pi\) | ||||
−0.101644 | + | 0.994821i | \(0.532410\pi\) | |||||||
\(762\) | −6582.83 | −0.312954 | ||||||||
\(763\) | 941.899 | 0.0446907 | ||||||||
\(764\) | −1300.63 | −0.0615905 | ||||||||
\(765\) | 2381.34 | 0.112546 | ||||||||
\(766\) | 49799.3 | 2.34898 | ||||||||
\(767\) | −50853.1 | −2.39400 | ||||||||
\(768\) | 12651.7 | 0.594440 | ||||||||
\(769\) | 12460.3 | 0.584304 | 0.292152 | − | 0.956372i | \(-0.405629\pi\) | ||||
0.292152 | + | 0.956372i | \(0.405629\pi\) | |||||||
\(770\) | −3253.78 | −0.152283 | ||||||||
\(771\) | 17182.5 | 0.802610 | ||||||||
\(772\) | 5307.94 | 0.247457 | ||||||||
\(773\) | 6865.85 | 0.319466 | 0.159733 | − | 0.987160i | \(-0.448937\pi\) | ||||
0.159733 | + | 0.987160i | \(0.448937\pi\) | |||||||
\(774\) | −8092.09 | −0.375793 | ||||||||
\(775\) | −17893.1 | −0.829339 | ||||||||
\(776\) | −9270.27 | −0.428844 | ||||||||
\(777\) | 94.6260 | 0.00436897 | ||||||||
\(778\) | −12294.9 | −0.566573 | ||||||||
\(779\) | 21065.1 | 0.968854 | ||||||||
\(780\) | −50475.5 | −2.31707 | ||||||||
\(781\) | −1428.57 | −0.0654523 | ||||||||
\(782\) | 9695.49 | 0.443363 | ||||||||
\(783\) | −5696.99 | −0.260018 | ||||||||
\(784\) | −385.489 | −0.0175605 | ||||||||
\(785\) | 5804.95 | 0.263933 | ||||||||
\(786\) | −695.692 | −0.0315706 | ||||||||
\(787\) | −25953.2 | −1.17552 | −0.587758 | − | 0.809037i | \(-0.699989\pi\) | ||||
−0.587758 | + | 0.809037i | \(0.699989\pi\) | |||||||
\(788\) | −14620.7 | −0.660966 | ||||||||
\(789\) | 11447.4 | 0.516527 | ||||||||
\(790\) | 78718.6 | 3.54517 | ||||||||
\(791\) | 6566.79 | 0.295181 | ||||||||
\(792\) | 2273.40 | 0.101997 | ||||||||
\(793\) | −4863.03 | −0.217770 | ||||||||
\(794\) | 43475.1 | 1.94317 | ||||||||
\(795\) | −10721.1 | −0.478286 | ||||||||
\(796\) | 44964.4 | 2.00216 | ||||||||
\(797\) | −36630.5 | −1.62800 | −0.814001 | − | 0.580863i | \(-0.802715\pi\) | ||||
−0.814001 | + | 0.580863i | \(0.802715\pi\) | |||||||
\(798\) | −3133.57 | −0.139006 | ||||||||
\(799\) | 3413.07 | 0.151121 | ||||||||
\(800\) | 24634.7 | 1.08871 | ||||||||
\(801\) | 5866.46 | 0.258778 | ||||||||
\(802\) | 39735.4 | 1.74951 | ||||||||
\(803\) | 7238.05 | 0.318089 | ||||||||
\(804\) | 25518.7 | 1.11937 | ||||||||
\(805\) | −8368.94 | −0.366418 | ||||||||
\(806\) | −47325.9 | −2.06822 | ||||||||
\(807\) | −3094.35 | −0.134977 | ||||||||
\(808\) | 11692.2 | 0.509073 | ||||||||
\(809\) | −20199.6 | −0.877849 | −0.438925 | − | 0.898524i | \(-0.644641\pi\) | ||||
−0.438925 | + | 0.898524i | \(0.644641\pi\) | |||||||
\(810\) | 6022.89 | 0.261263 | ||||||||
\(811\) | 27715.6 | 1.20003 | 0.600017 | − | 0.799987i | \(-0.295161\pi\) | ||||
0.600017 | + | 0.799987i | \(0.295161\pi\) | |||||||
\(812\) | 10920.2 | 0.471951 | ||||||||
\(813\) | 4067.24 | 0.175454 | ||||||||
\(814\) | −399.778 | −0.0172140 | ||||||||
\(815\) | −17871.2 | −0.768100 | ||||||||
\(816\) | 57.6532 | 0.00247336 | ||||||||
\(817\) | −11236.7 | −0.481176 | ||||||||
\(818\) | −51454.7 | −2.19935 | ||||||||
\(819\) | −2854.27 | −0.121778 | ||||||||
\(820\) | 77609.6 | 3.30518 | ||||||||
\(821\) | −19695.3 | −0.837236 | −0.418618 | − | 0.908162i | \(-0.637485\pi\) | ||||
−0.418618 | + | 0.908162i | \(0.637485\pi\) | |||||||
\(822\) | 12833.2 | 0.544539 | ||||||||
\(823\) | 2782.00 | 0.117830 | 0.0589152 | − | 0.998263i | \(-0.481236\pi\) | ||||
0.0589152 | + | 0.998263i | \(0.481236\pi\) | |||||||
\(824\) | −14992.9 | −0.633863 | ||||||||
\(825\) | 4559.20 | 0.192401 | ||||||||
\(826\) | −11631.3 | −0.489956 | ||||||||
\(827\) | 25074.1 | 1.05431 | 0.527153 | − | 0.849771i | \(-0.323260\pi\) | ||||
0.527153 | + | 0.849771i | \(0.323260\pi\) | |||||||
\(828\) | 15184.6 | 0.637321 | ||||||||
\(829\) | −8669.64 | −0.363219 | −0.181610 | − | 0.983371i | \(-0.558131\pi\) | ||||
−0.181610 | + | 0.983371i | \(0.558131\pi\) | |||||||
\(830\) | 59335.0 | 2.48138 | ||||||||
\(831\) | −2379.52 | −0.0993318 | ||||||||
\(832\) | 65908.5 | 2.74635 | ||||||||
\(833\) | 5336.42 | 0.221964 | ||||||||
\(834\) | 1194.64 | 0.0496008 | ||||||||
\(835\) | −40545.4 | −1.68040 | ||||||||
\(836\) | 8197.80 | 0.339147 | ||||||||
\(837\) | 3496.82 | 0.144406 | ||||||||
\(838\) | −66569.9 | −2.74417 | ||||||||
\(839\) | −38859.9 | −1.59904 | −0.799518 | − | 0.600642i | \(-0.794912\pi\) | ||||
−0.799518 | + | 0.600642i | \(0.794912\pi\) | |||||||
\(840\) | −4445.75 | −0.182611 | ||||||||
\(841\) | 20131.9 | 0.825449 | ||||||||
\(842\) | 76709.9 | 3.13967 | ||||||||
\(843\) | 6410.42 | 0.261906 | ||||||||
\(844\) | 21120.9 | 0.861389 | ||||||||
\(845\) | −67460.9 | −2.74642 | ||||||||
\(846\) | 8632.37 | 0.350812 | ||||||||
\(847\) | 481.350 | 0.0195270 | ||||||||
\(848\) | −259.562 | −0.0105111 | ||||||||
\(849\) | −2181.61 | −0.0881893 | ||||||||
\(850\) | 10329.0 | 0.416801 | ||||||||
\(851\) | −1028.26 | −0.0414197 | ||||||||
\(852\) | −5068.79 | −0.203819 | ||||||||
\(853\) | −6284.73 | −0.252268 | −0.126134 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126134 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(854\) | −1112.29 | −0.0445687 | ||||||||
\(855\) | 8363.37 | 0.334528 | ||||||||
\(856\) | −5717.00 | −0.228275 | ||||||||
\(857\) | 8942.69 | 0.356449 | 0.178224 | − | 0.983990i | \(-0.442965\pi\) | ||||
0.178224 | + | 0.983990i | \(0.442965\pi\) | |||||||
\(858\) | 12058.8 | 0.479813 | ||||||||
\(859\) | −11753.8 | −0.466863 | −0.233431 | − | 0.972373i | \(-0.574995\pi\) | ||||
−0.233431 | + | 0.972373i | \(0.574995\pi\) | |||||||
\(860\) | −41398.8 | −1.64150 | ||||||||
\(861\) | 4388.64 | 0.173710 | ||||||||
\(862\) | −79608.3 | −3.14556 | ||||||||
\(863\) | 43212.4 | 1.70448 | 0.852240 | − | 0.523150i | \(-0.175243\pi\) | ||||
0.852240 | + | 0.523150i | \(0.175243\pi\) | |||||||
\(864\) | −4814.33 | −0.189568 | ||||||||
\(865\) | 33240.8 | 1.30662 | ||||||||
\(866\) | 72825.6 | 2.85764 | ||||||||
\(867\) | 13940.9 | 0.546087 | ||||||||
\(868\) | −6702.84 | −0.262107 | ||||||||
\(869\) | −11645.3 | −0.454591 | ||||||||
\(870\) | −47067.7 | −1.83419 | ||||||||
\(871\) | 52124.5 | 2.02775 | ||||||||
\(872\) | −5437.13 | −0.211152 | ||||||||
\(873\) | 3633.24 | 0.140855 | ||||||||
\(874\) | 34051.0 | 1.31784 | ||||||||
\(875\) | −849.102 | −0.0328056 | ||||||||
\(876\) | 25681.7 | 0.990530 | ||||||||
\(877\) | −28589.3 | −1.10079 | −0.550395 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550395 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(878\) | 37636.6 | 1.44667 | ||||||||
\(879\) | 22395.4 | 0.859360 | ||||||||
\(880\) | 210.248 | 0.00805394 | ||||||||
\(881\) | 30596.4 | 1.17006 | 0.585028 | − | 0.811013i | \(-0.301083\pi\) | ||||
0.585028 | + | 0.811013i | \(0.301083\pi\) | |||||||
\(882\) | 13496.9 | 0.515266 | ||||||||
\(883\) | −4764.07 | −0.181567 | −0.0907836 | − | 0.995871i | \(-0.528937\pi\) | ||||
−0.0907836 | + | 0.995871i | \(0.528937\pi\) | |||||||
\(884\) | 16916.9 | 0.643640 | ||||||||
\(885\) | 31043.4 | 1.17911 | ||||||||
\(886\) | 32855.3 | 1.24582 | ||||||||
\(887\) | 21955.5 | 0.831110 | 0.415555 | − | 0.909568i | \(-0.363587\pi\) | ||||
0.415555 | + | 0.909568i | \(0.363587\pi\) | |||||||
\(888\) | −546.230 | −0.0206422 | ||||||||
\(889\) | −1904.38 | −0.0718459 | ||||||||
\(890\) | 48467.8 | 1.82544 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | −15969.8 | −0.599449 | ||||||||
\(893\) | 11986.9 | 0.449189 | ||||||||
\(894\) | 22741.4 | 0.850766 | ||||||||
\(895\) | −19279.0 | −0.720030 | ||||||||
\(896\) | 9400.16 | 0.350488 | ||||||||
\(897\) | 31016.0 | 1.15451 | ||||||||
\(898\) | 56738.0 | 2.10843 | ||||||||
\(899\) | −27327.0 | −1.01380 | ||||||||
\(900\) | 16176.7 | 0.599139 | ||||||||
\(901\) | 3593.18 | 0.132859 | ||||||||
\(902\) | −18541.2 | −0.684429 | ||||||||
\(903\) | −2341.01 | −0.0862722 | ||||||||
\(904\) | −37906.9 | −1.39465 | ||||||||
\(905\) | 21606.3 | 0.793610 | ||||||||
\(906\) | 21406.0 | 0.784951 | ||||||||
\(907\) | −7846.51 | −0.287254 | −0.143627 | − | 0.989632i | \(-0.545877\pi\) | ||||
−0.143627 | + | 0.989632i | \(0.545877\pi\) | |||||||
\(908\) | −8553.37 | −0.312614 | ||||||||
\(909\) | −4582.47 | −0.167207 | ||||||||
\(910\) | −23581.6 | −0.859034 | ||||||||
\(911\) | −26447.4 | −0.961844 | −0.480922 | − | 0.876763i | \(-0.659698\pi\) | ||||
−0.480922 | + | 0.876763i | \(0.659698\pi\) | |||||||
\(912\) | 202.481 | 0.00735176 | ||||||||
\(913\) | −8777.76 | −0.318184 | ||||||||
\(914\) | 29231.7 | 1.05788 | ||||||||
\(915\) | 2968.65 | 0.107257 | ||||||||
\(916\) | −7825.14 | −0.282260 | ||||||||
\(917\) | −201.261 | −0.00724778 | ||||||||
\(918\) | −2018.58 | −0.0725742 | ||||||||
\(919\) | 33796.3 | 1.21310 | 0.606549 | − | 0.795046i | \(-0.292553\pi\) | ||||
0.606549 | + | 0.795046i | \(0.292553\pi\) | |||||||
\(920\) | 48309.9 | 1.73123 | ||||||||
\(921\) | 23215.7 | 0.830602 | ||||||||
\(922\) | 22694.2 | 0.810622 | ||||||||
\(923\) | −10353.5 | −0.369219 | ||||||||
\(924\) | 1707.90 | 0.0608072 | ||||||||
\(925\) | −1095.44 | −0.0389382 | ||||||||
\(926\) | −58267.4 | −2.06780 | ||||||||
\(927\) | 5876.08 | 0.208194 | ||||||||
\(928\) | 37623.0 | 1.33086 | ||||||||
\(929\) | −45691.8 | −1.61367 | −0.806834 | − | 0.590778i | \(-0.798821\pi\) | ||||
−0.806834 | + | 0.590778i | \(0.798821\pi\) | |||||||
\(930\) | 28890.2 | 1.01865 | ||||||||
\(931\) | 18741.8 | 0.659760 | ||||||||
\(932\) | 56915.9 | 2.00037 | ||||||||
\(933\) | −20831.7 | −0.730975 | ||||||||
\(934\) | −22828.4 | −0.799751 | ||||||||
\(935\) | −2910.52 | −0.101801 | ||||||||
\(936\) | 16476.3 | 0.575369 | ||||||||
\(937\) | 28028.5 | 0.977216 | 0.488608 | − | 0.872503i | \(-0.337505\pi\) | ||||
0.488608 | + | 0.872503i | \(0.337505\pi\) | |||||||
\(938\) | 11922.1 | 0.414999 | ||||||||
\(939\) | −22896.4 | −0.795735 | ||||||||
\(940\) | 44162.9 | 1.53238 | ||||||||
\(941\) | 21039.8 | 0.728881 | 0.364441 | − | 0.931227i | \(-0.381260\pi\) | ||||
0.364441 | + | 0.931227i | \(0.381260\pi\) | |||||||
\(942\) | −4920.67 | −0.170195 | ||||||||
\(943\) | −47689.3 | −1.64685 | ||||||||
\(944\) | 751.574 | 0.0259128 | ||||||||
\(945\) | 1742.40 | 0.0599790 | ||||||||
\(946\) | 9890.33 | 0.339918 | ||||||||
\(947\) | −54566.5 | −1.87241 | −0.936205 | − | 0.351455i | \(-0.885687\pi\) | ||||
−0.936205 | + | 0.351455i | \(0.885687\pi\) | |||||||
\(948\) | −41319.3 | −1.41560 | ||||||||
\(949\) | 52457.3 | 1.79435 | ||||||||
\(950\) | 36275.8 | 1.23889 | ||||||||
\(951\) | 14829.0 | 0.505638 | ||||||||
\(952\) | 1490.00 | 0.0507260 | ||||||||
\(953\) | 20333.0 | 0.691135 | 0.345568 | − | 0.938394i | \(-0.387686\pi\) | ||||
0.345568 | + | 0.938394i | \(0.387686\pi\) | |||||||
\(954\) | 9087.90 | 0.308419 | ||||||||
\(955\) | 1621.77 | 0.0549519 | ||||||||
\(956\) | 46834.7 | 1.58446 | ||||||||
\(957\) | 6962.99 | 0.235195 | ||||||||
\(958\) | −6455.86 | −0.217724 | ||||||||
\(959\) | 3712.60 | 0.125012 | ||||||||
\(960\) | −40234.0 | −1.35265 | ||||||||
\(961\) | −13017.7 | −0.436966 | ||||||||
\(962\) | −2897.36 | −0.0971048 | ||||||||
\(963\) | 2240.63 | 0.0749774 | ||||||||
\(964\) | 52199.1 | 1.74401 | ||||||||
\(965\) | −6618.51 | −0.220785 | ||||||||
\(966\) | 7094.07 | 0.236282 | ||||||||
\(967\) | −56345.3 | −1.87378 | −0.936889 | − | 0.349627i | \(-0.886308\pi\) | ||||
−0.936889 | + | 0.349627i | \(0.886308\pi\) | |||||||
\(968\) | −2778.60 | −0.0922599 | ||||||||
\(969\) | −2802.99 | −0.0929258 | ||||||||
\(970\) | 30017.3 | 0.993605 | ||||||||
\(971\) | −58451.1 | −1.93181 | −0.965903 | − | 0.258904i | \(-0.916639\pi\) | ||||
−0.965903 | + | 0.258904i | \(0.916639\pi\) | |||||||
\(972\) | −3161.40 | −0.104323 | ||||||||
\(973\) | 345.604 | 0.0113870 | ||||||||
\(974\) | 80395.1 | 2.64479 | ||||||||
\(975\) | 33042.5 | 1.08534 | ||||||||
\(976\) | 71.8723 | 0.00235715 | ||||||||
\(977\) | 43020.4 | 1.40875 | 0.704373 | − | 0.709830i | \(-0.251228\pi\) | ||||
0.704373 | + | 0.709830i | \(0.251228\pi\) | |||||||
\(978\) | 15148.8 | 0.495303 | ||||||||
\(979\) | −7170.12 | −0.234073 | ||||||||
\(980\) | 69049.7 | 2.25073 | ||||||||
\(981\) | 2130.94 | 0.0693534 | ||||||||
\(982\) | 80802.1 | 2.62576 | ||||||||
\(983\) | 5497.83 | 0.178386 | 0.0891930 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891930 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(984\) | −25333.5 | −0.820735 | ||||||||
\(985\) | 18230.7 | 0.589723 | ||||||||
\(986\) | 15774.8 | 0.509505 | ||||||||
\(987\) | 2497.31 | 0.0805371 | ||||||||
\(988\) | 59413.0 | 1.91314 | ||||||||
\(989\) | 25438.6 | 0.817898 | ||||||||
\(990\) | −7361.31 | −0.236321 | ||||||||
\(991\) | −22617.8 | −0.725003 | −0.362502 | − | 0.931983i | \(-0.618077\pi\) | ||||
−0.362502 | + | 0.931983i | \(0.618077\pi\) | |||||||
\(992\) | −23093.1 | −0.739119 | ||||||||
\(993\) | −20584.7 | −0.657839 | ||||||||
\(994\) | −2368.08 | −0.0755642 | ||||||||
\(995\) | −56066.5 | −1.78636 | ||||||||
\(996\) | −31144.9 | −0.990826 | ||||||||
\(997\) | 23209.6 | 0.737266 | 0.368633 | − | 0.929575i | \(-0.379826\pi\) | ||||
0.368633 | + | 0.929575i | \(0.379826\pi\) | |||||||
\(998\) | −38195.4 | −1.21148 | ||||||||
\(999\) | 214.081 | 0.00678000 |
(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 | 2013.4.a.b.1.5 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.b.1.5 | ✓ | 36 | 1.1 | even | 1 | trivial |