Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.666010 | 0.235470 | 0.117735 | − | 0.993045i | \(-0.462437\pi\) | ||||
0.117735 | + | 0.993045i | \(0.462437\pi\) | |||||||
\(3\) | −10.2430 | −1.97126 | −0.985630 | − | 0.168919i | \(-0.945973\pi\) | ||||
−0.985630 | + | 0.168919i | \(0.945973\pi\) | |||||||
\(4\) | −7.55643 | −0.944554 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −6.82192 | −0.464173 | ||||||||
\(7\) | 4.34789 | 0.234764 | 0.117382 | − | 0.993087i | \(-0.462550\pi\) | ||||
0.117382 | + | 0.993087i | \(0.462550\pi\) | |||||||
\(8\) | −10.3607 | −0.457884 | ||||||||
\(9\) | 77.9184 | 2.88587 | ||||||||
\(10\) | −3.33005 | −0.105305 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 77.4003 | 1.86196 | ||||||||
\(13\) | 15.3859 | 0.328253 | 0.164126 | − | 0.986439i | \(-0.447519\pi\) | ||||
0.164126 | + | 0.986439i | \(0.447519\pi\) | |||||||
\(14\) | 2.89574 | 0.0552799 | ||||||||
\(15\) | 51.2148 | 0.881574 | ||||||||
\(16\) | 53.5511 | 0.836736 | ||||||||
\(17\) | −111.405 | −1.58940 | −0.794698 | − | 0.607005i | \(-0.792371\pi\) | ||||
−0.794698 | + | 0.607005i | \(0.792371\pi\) | |||||||
\(18\) | 51.8944 | 0.679535 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 37.7822 | 0.422417 | ||||||||
\(21\) | −44.5353 | −0.462781 | ||||||||
\(22\) | −7.32611 | −0.0709969 | ||||||||
\(23\) | −182.322 | −1.65290 | −0.826451 | − | 0.563009i | \(-0.809644\pi\) | ||||
−0.826451 | + | 0.563009i | \(0.809644\pi\) | |||||||
\(24\) | 106.125 | 0.902609 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 10.2472 | 0.0772937 | ||||||||
\(27\) | −521.555 | −3.71753 | ||||||||
\(28\) | −32.8546 | −0.221747 | ||||||||
\(29\) | 6.29537 | 0.0403111 | 0.0201555 | − | 0.999797i | \(-0.493584\pi\) | ||||
0.0201555 | + | 0.999797i | \(0.493584\pi\) | |||||||
\(30\) | 34.1096 | 0.207584 | ||||||||
\(31\) | 10.5762 | 0.0612756 | 0.0306378 | − | 0.999531i | \(-0.490246\pi\) | ||||
0.0306378 | + | 0.999531i | \(0.490246\pi\) | |||||||
\(32\) | 118.551 | 0.654910 | ||||||||
\(33\) | 112.673 | 0.594357 | ||||||||
\(34\) | −74.1970 | −0.374255 | ||||||||
\(35\) | −21.7395 | −0.104990 | ||||||||
\(36\) | −588.785 | −2.72586 | ||||||||
\(37\) | −310.552 | −1.37985 | −0.689925 | − | 0.723881i | \(-0.742356\pi\) | ||||
−0.689925 | + | 0.723881i | \(0.742356\pi\) | |||||||
\(38\) | −12.6542 | −0.0540205 | ||||||||
\(39\) | −157.598 | −0.647072 | ||||||||
\(40\) | 51.8037 | 0.204772 | ||||||||
\(41\) | −291.283 | −1.10953 | −0.554765 | − | 0.832007i | \(-0.687192\pi\) | ||||
−0.554765 | + | 0.832007i | \(0.687192\pi\) | |||||||
\(42\) | −29.6610 | −0.108971 | ||||||||
\(43\) | 42.1352 | 0.149432 | 0.0747158 | − | 0.997205i | \(-0.476195\pi\) | ||||
0.0747158 | + | 0.997205i | \(0.476195\pi\) | |||||||
\(44\) | 83.1207 | 0.284794 | ||||||||
\(45\) | −389.592 | −1.29060 | ||||||||
\(46\) | −121.428 | −0.389209 | ||||||||
\(47\) | −40.5254 | −0.125771 | −0.0628856 | − | 0.998021i | \(-0.520030\pi\) | ||||
−0.0628856 | + | 0.998021i | \(0.520030\pi\) | |||||||
\(48\) | −548.522 | −1.64942 | ||||||||
\(49\) | −324.096 | −0.944886 | ||||||||
\(50\) | 16.6502 | 0.0470940 | ||||||||
\(51\) | 1141.12 | 3.13311 | ||||||||
\(52\) | −116.263 | −0.310053 | ||||||||
\(53\) | −337.809 | −0.875501 | −0.437751 | − | 0.899096i | \(-0.644225\pi\) | ||||
−0.437751 | + | 0.899096i | \(0.644225\pi\) | |||||||
\(54\) | −347.361 | −0.875367 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −45.0474 | −0.107495 | ||||||||
\(57\) | 194.616 | 0.452238 | ||||||||
\(58\) | 4.19278 | 0.00949204 | ||||||||
\(59\) | 425.860 | 0.939699 | 0.469850 | − | 0.882746i | \(-0.344308\pi\) | ||||
0.469850 | + | 0.882746i | \(0.344308\pi\) | |||||||
\(60\) | −387.001 | −0.832694 | ||||||||
\(61\) | −694.137 | −1.45697 | −0.728485 | − | 0.685062i | \(-0.759775\pi\) | ||||
−0.728485 | + | 0.685062i | \(0.759775\pi\) | |||||||
\(62\) | 7.04385 | 0.0144286 | ||||||||
\(63\) | 338.781 | 0.677498 | ||||||||
\(64\) | −349.452 | −0.682524 | ||||||||
\(65\) | −76.9296 | −0.146799 | ||||||||
\(66\) | 75.0411 | 0.139953 | ||||||||
\(67\) | −899.527 | −1.64022 | −0.820110 | − | 0.572206i | \(-0.806088\pi\) | ||||
−0.820110 | + | 0.572206i | \(0.806088\pi\) | |||||||
\(68\) | 841.826 | 1.50127 | ||||||||
\(69\) | 1867.52 | 3.25830 | ||||||||
\(70\) | −14.4787 | −0.0247219 | ||||||||
\(71\) | 745.640 | 1.24636 | 0.623178 | − | 0.782080i | \(-0.285841\pi\) | ||||
0.623178 | + | 0.782080i | \(0.285841\pi\) | |||||||
\(72\) | −807.292 | −1.32139 | ||||||||
\(73\) | 103.964 | 0.166686 | 0.0833429 | − | 0.996521i | \(-0.473440\pi\) | ||||
0.0833429 | + | 0.996521i | \(0.473440\pi\) | |||||||
\(74\) | −206.831 | −0.324913 | ||||||||
\(75\) | −256.074 | −0.394252 | ||||||||
\(76\) | 143.572 | 0.216696 | ||||||||
\(77\) | −47.8268 | −0.0707841 | ||||||||
\(78\) | −104.961 | −0.152366 | ||||||||
\(79\) | −866.127 | −1.23350 | −0.616752 | − | 0.787157i | \(-0.711552\pi\) | ||||
−0.616752 | + | 0.787157i | \(0.711552\pi\) | |||||||
\(80\) | −267.756 | −0.374200 | ||||||||
\(81\) | 3238.48 | 4.44236 | ||||||||
\(82\) | −193.997 | −0.261261 | ||||||||
\(83\) | 1270.56 | 1.68026 | 0.840132 | − | 0.542381i | \(-0.182477\pi\) | ||||
0.840132 | + | 0.542381i | \(0.182477\pi\) | |||||||
\(84\) | 336.528 | 0.437122 | ||||||||
\(85\) | 557.026 | 0.710800 | ||||||||
\(86\) | 28.0625 | 0.0351867 | ||||||||
\(87\) | −64.4833 | −0.0794636 | ||||||||
\(88\) | 113.968 | 0.138057 | ||||||||
\(89\) | −828.828 | −0.987142 | −0.493571 | − | 0.869706i | \(-0.664309\pi\) | ||||
−0.493571 | + | 0.869706i | \(0.664309\pi\) | |||||||
\(90\) | −259.472 | −0.303897 | ||||||||
\(91\) | 66.8964 | 0.0770620 | ||||||||
\(92\) | 1377.70 | 1.56126 | ||||||||
\(93\) | −108.332 | −0.120790 | ||||||||
\(94\) | −26.9903 | −0.0296153 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | −1214.32 | −1.29100 | ||||||||
\(97\) | 655.359 | 0.685996 | 0.342998 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342998 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(98\) | −215.851 | −0.222492 | ||||||||
\(99\) | −857.102 | −0.870121 | ||||||||
\(100\) | −188.911 | −0.188911 | ||||||||
\(101\) | −994.650 | −0.979915 | −0.489957 | − | 0.871746i | \(-0.662988\pi\) | ||||
−0.489957 | + | 0.871746i | \(0.662988\pi\) | |||||||
\(102\) | 759.997 | 0.737754 | ||||||||
\(103\) | 36.2047 | 0.0346345 | 0.0173173 | − | 0.999850i | \(-0.494487\pi\) | ||||
0.0173173 | + | 0.999850i | \(0.494487\pi\) | |||||||
\(104\) | −159.409 | −0.150302 | ||||||||
\(105\) | 222.677 | 0.206962 | ||||||||
\(106\) | −224.984 | −0.206154 | ||||||||
\(107\) | −411.866 | −0.372117 | −0.186059 | − | 0.982539i | \(-0.559571\pi\) | ||||
−0.186059 | + | 0.982539i | \(0.559571\pi\) | |||||||
\(108\) | 3941.10 | 3.51141 | ||||||||
\(109\) | −487.137 | −0.428067 | −0.214033 | − | 0.976826i | \(-0.568660\pi\) | ||||
−0.214033 | + | 0.976826i | \(0.568660\pi\) | |||||||
\(110\) | 36.6305 | 0.0317508 | ||||||||
\(111\) | 3180.97 | 2.72004 | ||||||||
\(112\) | 232.834 | 0.196436 | ||||||||
\(113\) | 1397.53 | 1.16344 | 0.581718 | − | 0.813391i | \(-0.302381\pi\) | ||||
0.581718 | + | 0.813391i | \(0.302381\pi\) | |||||||
\(114\) | 129.616 | 0.106488 | ||||||||
\(115\) | 911.610 | 0.739200 | ||||||||
\(116\) | −47.5705 | −0.0380760 | ||||||||
\(117\) | 1198.85 | 0.947294 | ||||||||
\(118\) | 283.627 | 0.221271 | ||||||||
\(119\) | −484.378 | −0.373133 | ||||||||
\(120\) | −530.623 | −0.403659 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −462.302 | −0.343073 | ||||||||
\(123\) | 2983.60 | 2.18717 | ||||||||
\(124\) | −79.9184 | −0.0578781 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 225.631 | 0.159530 | ||||||||
\(127\) | −2699.83 | −1.88638 | −0.943192 | − | 0.332248i | \(-0.892193\pi\) | ||||
−0.943192 | + | 0.332248i | \(0.892193\pi\) | |||||||
\(128\) | −1181.15 | −0.815624 | ||||||||
\(129\) | −431.590 | −0.294569 | ||||||||
\(130\) | −51.2359 | −0.0345668 | ||||||||
\(131\) | 2784.16 | 1.85689 | 0.928447 | − | 0.371465i | \(-0.121144\pi\) | ||||
0.928447 | + | 0.371465i | \(0.121144\pi\) | |||||||
\(132\) | −851.403 | −0.561402 | ||||||||
\(133\) | −82.6100 | −0.0538586 | ||||||||
\(134\) | −599.094 | −0.386223 | ||||||||
\(135\) | 2607.78 | 1.66253 | ||||||||
\(136\) | 1154.24 | 0.727759 | ||||||||
\(137\) | −2071.50 | −1.29183 | −0.645913 | − | 0.763411i | \(-0.723523\pi\) | ||||
−0.645913 | + | 0.763411i | \(0.723523\pi\) | |||||||
\(138\) | 1243.78 | 0.767232 | ||||||||
\(139\) | 491.030 | 0.299630 | 0.149815 | − | 0.988714i | \(-0.452132\pi\) | ||||
0.149815 | + | 0.988714i | \(0.452132\pi\) | |||||||
\(140\) | 164.273 | 0.0991685 | ||||||||
\(141\) | 415.101 | 0.247928 | ||||||||
\(142\) | 496.604 | 0.293479 | ||||||||
\(143\) | −169.245 | −0.0989720 | ||||||||
\(144\) | 4172.62 | 2.41471 | ||||||||
\(145\) | −31.4768 | −0.0180277 | ||||||||
\(146\) | 69.2410 | 0.0392495 | ||||||||
\(147\) | 3319.70 | 1.86262 | ||||||||
\(148\) | 2346.66 | 1.30334 | ||||||||
\(149\) | 243.919 | 0.134112 | 0.0670558 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670558 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(150\) | −170.548 | −0.0928345 | ||||||||
\(151\) | −2683.31 | −1.44612 | −0.723061 | − | 0.690785i | \(-0.757265\pi\) | ||||
−0.723061 | + | 0.690785i | \(0.757265\pi\) | |||||||
\(152\) | 196.854 | 0.105046 | ||||||||
\(153\) | −8680.52 | −4.58679 | ||||||||
\(154\) | −31.8531 | −0.0166675 | ||||||||
\(155\) | −52.8810 | −0.0274033 | ||||||||
\(156\) | 1190.87 | 0.611194 | ||||||||
\(157\) | −1489.89 | −0.757366 | −0.378683 | − | 0.925526i | \(-0.623623\pi\) | ||||
−0.378683 | + | 0.925526i | \(0.623623\pi\) | |||||||
\(158\) | −576.849 | −0.290453 | ||||||||
\(159\) | 3460.16 | 1.72584 | ||||||||
\(160\) | −592.757 | −0.292885 | ||||||||
\(161\) | −792.716 | −0.388042 | ||||||||
\(162\) | 2156.86 | 1.04604 | ||||||||
\(163\) | 239.149 | 0.114918 | 0.0574590 | − | 0.998348i | \(-0.481700\pi\) | ||||
0.0574590 | + | 0.998348i | \(0.481700\pi\) | |||||||
\(164\) | 2201.06 | 1.04801 | ||||||||
\(165\) | −563.363 | −0.265805 | ||||||||
\(166\) | 846.205 | 0.395652 | ||||||||
\(167\) | 394.272 | 0.182693 | 0.0913463 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913463 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(168\) | 461.419 | 0.211900 | ||||||||
\(169\) | −1960.27 | −0.892250 | ||||||||
\(170\) | 370.985 | 0.167372 | ||||||||
\(171\) | −1480.45 | −0.662063 | ||||||||
\(172\) | −318.392 | −0.141146 | ||||||||
\(173\) | −3760.11 | −1.65246 | −0.826230 | − | 0.563333i | \(-0.809519\pi\) | ||||
−0.826230 | + | 0.563333i | \(0.809519\pi\) | |||||||
\(174\) | −42.9465 | −0.0187113 | ||||||||
\(175\) | 108.697 | 0.0469528 | ||||||||
\(176\) | −589.062 | −0.252285 | ||||||||
\(177\) | −4362.07 | −1.85239 | ||||||||
\(178\) | −552.008 | −0.232442 | ||||||||
\(179\) | 1572.58 | 0.656649 | 0.328325 | − | 0.944565i | \(-0.393516\pi\) | ||||
0.328325 | + | 0.944565i | \(0.393516\pi\) | |||||||
\(180\) | 2943.92 | 1.21904 | ||||||||
\(181\) | 1578.45 | 0.648206 | 0.324103 | − | 0.946022i | \(-0.394938\pi\) | ||||
0.324103 | + | 0.946022i | \(0.394938\pi\) | |||||||
\(182\) | 44.5536 | 0.0181458 | ||||||||
\(183\) | 7110.02 | 2.87207 | ||||||||
\(184\) | 1888.99 | 0.756837 | ||||||||
\(185\) | 1552.76 | 0.617087 | ||||||||
\(186\) | −72.1500 | −0.0284424 | ||||||||
\(187\) | 1225.46 | 0.479221 | ||||||||
\(188\) | 306.228 | 0.118798 | ||||||||
\(189\) | −2267.67 | −0.872743 | ||||||||
\(190\) | 63.2709 | 0.0241587 | ||||||||
\(191\) | 2227.16 | 0.843728 | 0.421864 | − | 0.906659i | \(-0.361376\pi\) | ||||
0.421864 | + | 0.906659i | \(0.361376\pi\) | |||||||
\(192\) | 3579.43 | 1.34543 | ||||||||
\(193\) | −57.8787 | −0.0215865 | −0.0107933 | − | 0.999942i | \(-0.503436\pi\) | ||||
−0.0107933 | + | 0.999942i | \(0.503436\pi\) | |||||||
\(194\) | 436.476 | 0.161532 | ||||||||
\(195\) | 787.988 | 0.289379 | ||||||||
\(196\) | 2449.01 | 0.892496 | ||||||||
\(197\) | 2473.85 | 0.894694 | 0.447347 | − | 0.894360i | \(-0.352369\pi\) | ||||
0.447347 | + | 0.894360i | \(0.352369\pi\) | |||||||
\(198\) | −570.838 | −0.204887 | ||||||||
\(199\) | −3694.38 | −1.31602 | −0.658010 | − | 0.753009i | \(-0.728601\pi\) | ||||
−0.658010 | + | 0.753009i | \(0.728601\pi\) | |||||||
\(200\) | −259.018 | −0.0915768 | ||||||||
\(201\) | 9213.83 | 3.23330 | ||||||||
\(202\) | −662.447 | −0.230740 | ||||||||
\(203\) | 27.3716 | 0.00946359 | ||||||||
\(204\) | −8622.80 | −2.95940 | ||||||||
\(205\) | 1456.42 | 0.496197 | ||||||||
\(206\) | 24.1127 | 0.00815540 | ||||||||
\(207\) | −14206.2 | −4.77005 | ||||||||
\(208\) | 823.933 | 0.274661 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | 148.305 | 0.0487333 | ||||||||
\(211\) | 2678.20 | 0.873814 | 0.436907 | − | 0.899507i | \(-0.356074\pi\) | ||||
0.436907 | + | 0.899507i | \(0.356074\pi\) | |||||||
\(212\) | 2552.63 | 0.826958 | ||||||||
\(213\) | −7637.57 | −2.45689 | ||||||||
\(214\) | −274.307 | −0.0876225 | ||||||||
\(215\) | −210.676 | −0.0668279 | ||||||||
\(216\) | 5403.70 | 1.70220 | ||||||||
\(217\) | 45.9842 | 0.0143853 | ||||||||
\(218\) | −324.438 | −0.100797 | ||||||||
\(219\) | −1064.90 | −0.328581 | ||||||||
\(220\) | −415.604 | −0.127364 | ||||||||
\(221\) | −1714.07 | −0.521724 | ||||||||
\(222\) | 2118.56 | 0.640488 | ||||||||
\(223\) | 2932.58 | 0.880629 | 0.440315 | − | 0.897844i | \(-0.354867\pi\) | ||||
0.440315 | + | 0.897844i | \(0.354867\pi\) | |||||||
\(224\) | 515.449 | 0.153749 | ||||||||
\(225\) | 1947.96 | 0.577173 | ||||||||
\(226\) | 930.766 | 0.273954 | ||||||||
\(227\) | 6488.53 | 1.89718 | 0.948588 | − | 0.316513i | \(-0.102512\pi\) | ||||
0.948588 | + | 0.316513i | \(0.102512\pi\) | |||||||
\(228\) | −1470.61 | −0.427163 | ||||||||
\(229\) | −2031.56 | −0.586242 | −0.293121 | − | 0.956075i | \(-0.594694\pi\) | ||||
−0.293121 | + | 0.956075i | \(0.594694\pi\) | |||||||
\(230\) | 607.141 | 0.174059 | ||||||||
\(231\) | 489.889 | 0.139534 | ||||||||
\(232\) | −65.2246 | −0.0184578 | ||||||||
\(233\) | −6992.00 | −1.96593 | −0.982963 | − | 0.183803i | \(-0.941159\pi\) | ||||
−0.982963 | + | 0.183803i | \(0.941159\pi\) | |||||||
\(234\) | 798.443 | 0.223059 | ||||||||
\(235\) | 202.627 | 0.0562466 | ||||||||
\(236\) | −3217.98 | −0.887597 | ||||||||
\(237\) | 8871.71 | 2.43156 | ||||||||
\(238\) | −322.601 | −0.0878617 | ||||||||
\(239\) | −924.735 | −0.250277 | −0.125138 | − | 0.992139i | \(-0.539937\pi\) | ||||
−0.125138 | + | 0.992139i | \(0.539937\pi\) | |||||||
\(240\) | 2742.61 | 0.737645 | ||||||||
\(241\) | 1737.40 | 0.464380 | 0.232190 | − | 0.972670i | \(-0.425411\pi\) | ||||
0.232190 | + | 0.972670i | \(0.425411\pi\) | |||||||
\(242\) | 80.5872 | 0.0214064 | ||||||||
\(243\) | −19089.6 | −5.03951 | ||||||||
\(244\) | 5245.20 | 1.37619 | ||||||||
\(245\) | 1620.48 | 0.422566 | ||||||||
\(246\) | 1987.11 | 0.515014 | ||||||||
\(247\) | −292.333 | −0.0753064 | ||||||||
\(248\) | −109.577 | −0.0280571 | ||||||||
\(249\) | −13014.3 | −3.31224 | ||||||||
\(250\) | −83.2512 | −0.0210611 | ||||||||
\(251\) | 6716.81 | 1.68909 | 0.844545 | − | 0.535485i | \(-0.179871\pi\) | ||||
0.844545 | + | 0.535485i | \(0.179871\pi\) | |||||||
\(252\) | −2559.97 | −0.639933 | ||||||||
\(253\) | 2005.54 | 0.498369 | ||||||||
\(254\) | −1798.11 | −0.444187 | ||||||||
\(255\) | −5705.60 | −1.40117 | ||||||||
\(256\) | 2008.96 | 0.490469 | ||||||||
\(257\) | −385.405 | −0.0935445 | −0.0467722 | − | 0.998906i | \(-0.514894\pi\) | ||||
−0.0467722 | + | 0.998906i | \(0.514894\pi\) | |||||||
\(258\) | −287.443 | −0.0693621 | ||||||||
\(259\) | −1350.25 | −0.323939 | ||||||||
\(260\) | 581.313 | 0.138660 | ||||||||
\(261\) | 490.525 | 0.116332 | ||||||||
\(262\) | 1854.28 | 0.437243 | ||||||||
\(263\) | −6938.45 | −1.62678 | −0.813390 | − | 0.581718i | \(-0.802381\pi\) | ||||
−0.813390 | + | 0.581718i | \(0.802381\pi\) | |||||||
\(264\) | −1167.37 | −0.272147 | ||||||||
\(265\) | 1689.04 | 0.391536 | ||||||||
\(266\) | −55.0190 | −0.0126821 | ||||||||
\(267\) | 8489.66 | 1.94591 | ||||||||
\(268\) | 6797.22 | 1.54928 | ||||||||
\(269\) | 5764.26 | 1.30652 | 0.653259 | − | 0.757135i | \(-0.273401\pi\) | ||||
0.653259 | + | 0.757135i | \(0.273401\pi\) | |||||||
\(270\) | 1736.80 | 0.391476 | ||||||||
\(271\) | −2934.60 | −0.657801 | −0.328901 | − | 0.944365i | \(-0.606678\pi\) | ||||
−0.328901 | + | 0.944365i | \(0.606678\pi\) | |||||||
\(272\) | −5965.87 | −1.32991 | ||||||||
\(273\) | −685.217 | −0.151909 | ||||||||
\(274\) | −1379.64 | −0.304186 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −14111.8 | −3.07764 | ||||||||
\(277\) | 746.505 | 0.161925 | 0.0809624 | − | 0.996717i | \(-0.474201\pi\) | ||||
0.0809624 | + | 0.996717i | \(0.474201\pi\) | |||||||
\(278\) | 327.031 | 0.0705539 | ||||||||
\(279\) | 824.081 | 0.176833 | ||||||||
\(280\) | 225.237 | 0.0480731 | ||||||||
\(281\) | 5041.44 | 1.07027 | 0.535137 | − | 0.844765i | \(-0.320260\pi\) | ||||
0.535137 | + | 0.844765i | \(0.320260\pi\) | |||||||
\(282\) | 276.461 | 0.0583795 | ||||||||
\(283\) | −2324.25 | −0.488207 | −0.244104 | − | 0.969749i | \(-0.578494\pi\) | ||||
−0.244104 | + | 0.969749i | \(0.578494\pi\) | |||||||
\(284\) | −5634.38 | −1.17725 | ||||||||
\(285\) | −973.082 | −0.202247 | ||||||||
\(286\) | −112.719 | −0.0233049 | ||||||||
\(287\) | −1266.47 | −0.260478 | ||||||||
\(288\) | 9237.33 | 1.88998 | ||||||||
\(289\) | 7498.13 | 1.52618 | ||||||||
\(290\) | −20.9639 | −0.00424497 | ||||||||
\(291\) | −6712.82 | −1.35228 | ||||||||
\(292\) | −785.597 | −0.157444 | ||||||||
\(293\) | 299.264 | 0.0596697 | 0.0298348 | − | 0.999555i | \(-0.490502\pi\) | ||||
0.0298348 | + | 0.999555i | \(0.490502\pi\) | |||||||
\(294\) | 2210.95 | 0.438590 | ||||||||
\(295\) | −2129.30 | −0.420246 | ||||||||
\(296\) | 3217.55 | 0.631811 | ||||||||
\(297\) | 5737.11 | 1.12088 | ||||||||
\(298\) | 162.452 | 0.0315793 | ||||||||
\(299\) | −2805.19 | −0.542570 | ||||||||
\(300\) | 1935.01 | 0.372392 | ||||||||
\(301\) | 183.199 | 0.0350812 | ||||||||
\(302\) | −1787.11 | −0.340518 | ||||||||
\(303\) | 10188.2 | 1.93167 | ||||||||
\(304\) | −1017.47 | −0.191960 | ||||||||
\(305\) | 3470.69 | 0.651577 | ||||||||
\(306\) | −5781.31 | −1.08005 | ||||||||
\(307\) | 7261.64 | 1.34998 | 0.674990 | − | 0.737827i | \(-0.264148\pi\) | ||||
0.674990 | + | 0.737827i | \(0.264148\pi\) | |||||||
\(308\) | 361.400 | 0.0668594 | ||||||||
\(309\) | −370.844 | −0.0682737 | ||||||||
\(310\) | −35.2193 | −0.00645265 | ||||||||
\(311\) | −6208.70 | −1.13204 | −0.566018 | − | 0.824393i | \(-0.691517\pi\) | ||||
−0.566018 | + | 0.824393i | \(0.691517\pi\) | |||||||
\(312\) | 1632.83 | 0.296284 | ||||||||
\(313\) | −1127.40 | −0.203592 | −0.101796 | − | 0.994805i | \(-0.532459\pi\) | ||||
−0.101796 | + | 0.994805i | \(0.532459\pi\) | |||||||
\(314\) | −992.284 | −0.178337 | ||||||||
\(315\) | −1693.90 | −0.302986 | ||||||||
\(316\) | 6544.83 | 1.16511 | ||||||||
\(317\) | −7253.45 | −1.28516 | −0.642578 | − | 0.766220i | \(-0.722135\pi\) | ||||
−0.642578 | + | 0.766220i | \(0.722135\pi\) | |||||||
\(318\) | 2304.50 | 0.406384 | ||||||||
\(319\) | −69.2491 | −0.0121542 | ||||||||
\(320\) | 1747.26 | 0.305234 | ||||||||
\(321\) | 4218.73 | 0.733540 | ||||||||
\(322\) | −527.957 | −0.0913723 | ||||||||
\(323\) | 2116.70 | 0.364633 | ||||||||
\(324\) | −24471.3 | −4.19605 | ||||||||
\(325\) | 384.648 | 0.0656506 | ||||||||
\(326\) | 159.276 | 0.0270597 | ||||||||
\(327\) | 4989.73 | 0.843831 | ||||||||
\(328\) | 3017.91 | 0.508036 | ||||||||
\(329\) | −176.200 | −0.0295266 | ||||||||
\(330\) | −375.205 | −0.0625890 | ||||||||
\(331\) | −5641.53 | −0.936817 | −0.468409 | − | 0.883512i | \(-0.655172\pi\) | ||||
−0.468409 | + | 0.883512i | \(0.655172\pi\) | |||||||
\(332\) | −9600.89 | −1.58710 | ||||||||
\(333\) | −24197.7 | −3.98206 | ||||||||
\(334\) | 262.589 | 0.0430186 | ||||||||
\(335\) | 4497.64 | 0.733529 | ||||||||
\(336\) | −2384.92 | −0.387226 | ||||||||
\(337\) | −1961.00 | −0.316980 | −0.158490 | − | 0.987361i | \(-0.550663\pi\) | ||||
−0.158490 | + | 0.987361i | \(0.550663\pi\) | |||||||
\(338\) | −1305.56 | −0.210098 | ||||||||
\(339\) | −14314.8 | −2.29343 | ||||||||
\(340\) | −4209.13 | −0.671389 | ||||||||
\(341\) | −116.338 | −0.0184753 | ||||||||
\(342\) | −985.994 | −0.155896 | ||||||||
\(343\) | −2900.46 | −0.456589 | ||||||||
\(344\) | −436.552 | −0.0684224 | ||||||||
\(345\) | −9337.59 | −1.45716 | ||||||||
\(346\) | −2504.27 | −0.389105 | ||||||||
\(347\) | −2007.00 | −0.310494 | −0.155247 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155247 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(348\) | 487.263 | 0.0750576 | ||||||||
\(349\) | 3057.04 | 0.468881 | 0.234441 | − | 0.972130i | \(-0.424674\pi\) | ||||
0.234441 | + | 0.972130i | \(0.424674\pi\) | |||||||
\(350\) | 72.3935 | 0.0110560 | ||||||||
\(351\) | −8024.61 | −1.22029 | ||||||||
\(352\) | −1304.07 | −0.197463 | ||||||||
\(353\) | 9203.36 | 1.38766 | 0.693832 | − | 0.720137i | \(-0.255921\pi\) | ||||
0.693832 | + | 0.720137i | \(0.255921\pi\) | |||||||
\(354\) | −2905.18 | −0.436183 | ||||||||
\(355\) | −3728.20 | −0.557387 | ||||||||
\(356\) | 6262.98 | 0.932409 | ||||||||
\(357\) | 4961.47 | 0.735543 | ||||||||
\(358\) | 1047.35 | 0.154621 | ||||||||
\(359\) | 10561.6 | 1.55270 | 0.776352 | − | 0.630300i | \(-0.217068\pi\) | ||||
0.776352 | + | 0.630300i | \(0.217068\pi\) | |||||||
\(360\) | 4036.46 | 0.590944 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 1051.26 | 0.152633 | ||||||||
\(363\) | −1239.40 | −0.179205 | ||||||||
\(364\) | −505.498 | −0.0727892 | ||||||||
\(365\) | −519.820 | −0.0745441 | ||||||||
\(366\) | 4735.34 | 0.676285 | ||||||||
\(367\) | −6210.01 | −0.883269 | −0.441634 | − | 0.897195i | \(-0.645601\pi\) | ||||
−0.441634 | + | 0.897195i | \(0.645601\pi\) | |||||||
\(368\) | −9763.54 | −1.38304 | ||||||||
\(369\) | −22696.3 | −3.20196 | ||||||||
\(370\) | 1034.15 | 0.145306 | ||||||||
\(371\) | −1468.76 | −0.205536 | ||||||||
\(372\) | 818.601 | 0.114093 | ||||||||
\(373\) | 83.0043 | 0.0115223 | 0.00576113 | − | 0.999983i | \(-0.498166\pi\) | ||||
0.00576113 | + | 0.999983i | \(0.498166\pi\) | |||||||
\(374\) | 816.167 | 0.112842 | ||||||||
\(375\) | 1280.37 | 0.176315 | ||||||||
\(376\) | 419.873 | 0.0575886 | ||||||||
\(377\) | 96.8601 | 0.0132322 | ||||||||
\(378\) | −1510.29 | −0.205505 | ||||||||
\(379\) | −4246.30 | −0.575509 | −0.287754 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(380\) | −717.861 | −0.0969092 | ||||||||
\(381\) | 27654.2 | 3.71855 | ||||||||
\(382\) | 1483.31 | 0.198672 | ||||||||
\(383\) | 4862.08 | 0.648670 | 0.324335 | − | 0.945942i | \(-0.394860\pi\) | ||||
0.324335 | + | 0.945942i | \(0.394860\pi\) | |||||||
\(384\) | 12098.5 | 1.60781 | ||||||||
\(385\) | 239.134 | 0.0316556 | ||||||||
\(386\) | −38.5478 | −0.00508298 | ||||||||
\(387\) | 3283.11 | 0.431240 | ||||||||
\(388\) | −4952.18 | −0.647960 | ||||||||
\(389\) | 7325.70 | 0.954827 | 0.477413 | − | 0.878679i | \(-0.341574\pi\) | ||||
0.477413 | + | 0.878679i | \(0.341574\pi\) | |||||||
\(390\) | 524.807 | 0.0681401 | ||||||||
\(391\) | 20311.6 | 2.62712 | ||||||||
\(392\) | 3357.87 | 0.432648 | ||||||||
\(393\) | −28518.0 | −3.66042 | ||||||||
\(394\) | 1647.61 | 0.210674 | ||||||||
\(395\) | 4330.63 | 0.551640 | ||||||||
\(396\) | 6476.63 | 0.821877 | ||||||||
\(397\) | −617.885 | −0.0781128 | −0.0390564 | − | 0.999237i | \(-0.512435\pi\) | ||||
−0.0390564 | + | 0.999237i | \(0.512435\pi\) | |||||||
\(398\) | −2460.50 | −0.309883 | ||||||||
\(399\) | 846.171 | 0.106169 | ||||||||
\(400\) | 1338.78 | 0.167347 | ||||||||
\(401\) | 7135.88 | 0.888651 | 0.444325 | − | 0.895865i | \(-0.353443\pi\) | ||||
0.444325 | + | 0.895865i | \(0.353443\pi\) | |||||||
\(402\) | 6136.50 | 0.761345 | ||||||||
\(403\) | 162.725 | 0.0201139 | ||||||||
\(404\) | 7516.00 | 0.925582 | ||||||||
\(405\) | −16192.4 | −1.98668 | ||||||||
\(406\) | 18.2297 | 0.00222839 | ||||||||
\(407\) | 3416.07 | 0.416040 | ||||||||
\(408\) | −11822.8 | −1.43460 | ||||||||
\(409\) | 8740.86 | 1.05674 | 0.528371 | − | 0.849013i | \(-0.322803\pi\) | ||||
0.528371 | + | 0.849013i | \(0.322803\pi\) | |||||||
\(410\) | 969.986 | 0.116840 | ||||||||
\(411\) | 21218.3 | 2.54652 | ||||||||
\(412\) | −273.579 | −0.0327142 | ||||||||
\(413\) | 1851.59 | 0.220608 | ||||||||
\(414\) | −9461.49 | −1.12320 | ||||||||
\(415\) | −6352.80 | −0.751437 | ||||||||
\(416\) | 1824.02 | 0.214976 | ||||||||
\(417\) | −5029.60 | −0.590649 | ||||||||
\(418\) | 139.196 | 0.0162878 | ||||||||
\(419\) | −8004.55 | −0.933288 | −0.466644 | − | 0.884445i | \(-0.654537\pi\) | ||||
−0.466644 | + | 0.884445i | \(0.654537\pi\) | |||||||
\(420\) | −1682.64 | −0.195487 | ||||||||
\(421\) | −83.8784 | −0.00971017 | −0.00485509 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485509 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(422\) | 1783.71 | 0.205757 | ||||||||
\(423\) | −3157.68 | −0.362959 | ||||||||
\(424\) | 3499.94 | 0.400878 | ||||||||
\(425\) | −2785.13 | −0.317879 | ||||||||
\(426\) | −5086.69 | −0.578524 | ||||||||
\(427\) | −3018.03 | −0.342044 | ||||||||
\(428\) | 3112.24 | 0.351485 | ||||||||
\(429\) | 1733.57 | 0.195099 | ||||||||
\(430\) | −140.312 | −0.0157360 | ||||||||
\(431\) | 13730.5 | 1.53451 | 0.767255 | − | 0.641342i | \(-0.221622\pi\) | ||||
0.767255 | + | 0.641342i | \(0.221622\pi\) | |||||||
\(432\) | −27929.9 | −3.11059 | ||||||||
\(433\) | 737.909 | 0.0818975 | 0.0409488 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409488 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(434\) | 30.6259 | 0.00338731 | ||||||||
\(435\) | 322.416 | 0.0355372 | ||||||||
\(436\) | 3681.02 | 0.404332 | ||||||||
\(437\) | 3464.12 | 0.379202 | ||||||||
\(438\) | −709.233 | −0.0773710 | ||||||||
\(439\) | 8355.23 | 0.908367 | 0.454184 | − | 0.890908i | \(-0.349931\pi\) | ||||
0.454184 | + | 0.890908i | \(0.349931\pi\) | |||||||
\(440\) | −569.840 | −0.0617411 | ||||||||
\(441\) | −25253.0 | −2.72681 | ||||||||
\(442\) | −1141.59 | −0.122850 | ||||||||
\(443\) | 11798.0 | 1.26533 | 0.632665 | − | 0.774426i | \(-0.281961\pi\) | ||||
0.632665 | + | 0.774426i | \(0.281961\pi\) | |||||||
\(444\) | −24036.8 | −2.56923 | ||||||||
\(445\) | 4144.14 | 0.441463 | ||||||||
\(446\) | 1953.13 | 0.207362 | ||||||||
\(447\) | −2498.45 | −0.264369 | ||||||||
\(448\) | −1519.38 | −0.160232 | ||||||||
\(449\) | 1784.73 | 0.187587 | 0.0937933 | − | 0.995592i | \(-0.470101\pi\) | ||||
0.0937933 | + | 0.995592i | \(0.470101\pi\) | |||||||
\(450\) | 1297.36 | 0.135907 | ||||||||
\(451\) | 3204.11 | 0.334536 | ||||||||
\(452\) | −10560.3 | −1.09893 | ||||||||
\(453\) | 27485.0 | 2.85068 | ||||||||
\(454\) | 4321.42 | 0.446728 | ||||||||
\(455\) | −334.482 | −0.0344632 | ||||||||
\(456\) | −2016.37 | −0.207073 | ||||||||
\(457\) | −15327.1 | −1.56887 | −0.784434 | − | 0.620213i | \(-0.787046\pi\) | ||||
−0.784434 | + | 0.620213i | \(0.787046\pi\) | |||||||
\(458\) | −1353.04 | −0.138042 | ||||||||
\(459\) | 58104.0 | 5.90863 | ||||||||
\(460\) | −6888.52 | −0.698215 | ||||||||
\(461\) | 2456.74 | 0.248203 | 0.124102 | − | 0.992270i | \(-0.460395\pi\) | ||||
0.124102 | + | 0.992270i | \(0.460395\pi\) | |||||||
\(462\) | 326.271 | 0.0328560 | ||||||||
\(463\) | 15389.3 | 1.54471 | 0.772355 | − | 0.635191i | \(-0.219079\pi\) | ||||
0.772355 | + | 0.635191i | \(0.219079\pi\) | |||||||
\(464\) | 337.124 | 0.0337297 | ||||||||
\(465\) | 541.659 | 0.0540190 | ||||||||
\(466\) | −4656.74 | −0.462917 | ||||||||
\(467\) | 2300.49 | 0.227953 | 0.113976 | − | 0.993483i | \(-0.463641\pi\) | ||||
0.113976 | + | 0.993483i | \(0.463641\pi\) | |||||||
\(468\) | −9059.00 | −0.894770 | ||||||||
\(469\) | −3911.05 | −0.385065 | ||||||||
\(470\) | 134.952 | 0.0132444 | ||||||||
\(471\) | 15260.9 | 1.49297 | ||||||||
\(472\) | −4412.22 | −0.430273 | ||||||||
\(473\) | −463.487 | −0.0450553 | ||||||||
\(474\) | 5908.64 | 0.572559 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | 3660.17 | 0.352445 | ||||||||
\(477\) | −26321.5 | −2.52658 | ||||||||
\(478\) | −615.882 | −0.0589326 | ||||||||
\(479\) | −6297.11 | −0.600673 | −0.300336 | − | 0.953833i | \(-0.597099\pi\) | ||||
−0.300336 | + | 0.953833i | \(0.597099\pi\) | |||||||
\(480\) | 6071.59 | 0.577352 | ||||||||
\(481\) | −4778.13 | −0.452940 | ||||||||
\(482\) | 1157.12 | 0.109348 | ||||||||
\(483\) | 8119.77 | 0.764932 | ||||||||
\(484\) | −914.328 | −0.0858685 | ||||||||
\(485\) | −3276.80 | −0.306787 | ||||||||
\(486\) | −12713.9 | −1.18665 | ||||||||
\(487\) | −5167.87 | −0.480860 | −0.240430 | − | 0.970667i | \(-0.577288\pi\) | ||||
−0.240430 | + | 0.970667i | \(0.577288\pi\) | |||||||
\(488\) | 7191.77 | 0.667123 | ||||||||
\(489\) | −2449.60 | −0.226533 | ||||||||
\(490\) | 1079.25 | 0.0995015 | ||||||||
\(491\) | −5003.25 | −0.459865 | −0.229932 | − | 0.973207i | \(-0.573851\pi\) | ||||
−0.229932 | + | 0.973207i | \(0.573851\pi\) | |||||||
\(492\) | −22545.4 | −2.06590 | ||||||||
\(493\) | −701.337 | −0.0640703 | ||||||||
\(494\) | −194.696 | −0.0177324 | ||||||||
\(495\) | 4285.51 | 0.389130 | ||||||||
\(496\) | 566.367 | 0.0512715 | ||||||||
\(497\) | 3241.96 | 0.292600 | ||||||||
\(498\) | −8667.65 | −0.779933 | ||||||||
\(499\) | 484.929 | 0.0435038 | 0.0217519 | − | 0.999763i | \(-0.493076\pi\) | ||||
0.0217519 | + | 0.999763i | \(0.493076\pi\) | |||||||
\(500\) | 944.554 | 0.0844835 | ||||||||
\(501\) | −4038.51 | −0.360134 | ||||||||
\(502\) | 4473.46 | 0.397730 | ||||||||
\(503\) | −1005.70 | −0.0891487 | −0.0445743 | − | 0.999006i | \(-0.514193\pi\) | ||||
−0.0445743 | + | 0.999006i | \(0.514193\pi\) | |||||||
\(504\) | −3510.02 | −0.310216 | ||||||||
\(505\) | 4973.25 | 0.438231 | ||||||||
\(506\) | 1335.71 | 0.117351 | ||||||||
\(507\) | 20079.0 | 1.75886 | ||||||||
\(508\) | 20401.0 | 1.78179 | ||||||||
\(509\) | −1588.13 | −0.138296 | −0.0691482 | − | 0.997606i | \(-0.522028\pi\) | ||||
−0.0691482 | + | 0.997606i | \(0.522028\pi\) | |||||||
\(510\) | −3799.99 | −0.329934 | ||||||||
\(511\) | 452.024 | 0.0391318 | ||||||||
\(512\) | 10787.2 | 0.931115 | ||||||||
\(513\) | 9909.55 | 0.852860 | ||||||||
\(514\) | −256.684 | −0.0220269 | ||||||||
\(515\) | −181.024 | −0.0154890 | ||||||||
\(516\) | 3261.28 | 0.278236 | ||||||||
\(517\) | 445.780 | 0.0379214 | ||||||||
\(518\) | −899.277 | −0.0762779 | ||||||||
\(519\) | 38514.7 | 3.25743 | ||||||||
\(520\) | 797.047 | 0.0672170 | ||||||||
\(521\) | −7824.63 | −0.657972 | −0.328986 | − | 0.944335i | \(-0.606707\pi\) | ||||
−0.328986 | + | 0.944335i | \(0.606707\pi\) | |||||||
\(522\) | 326.694 | 0.0273928 | ||||||||
\(523\) | 19970.3 | 1.66967 | 0.834837 | − | 0.550497i | \(-0.185562\pi\) | ||||
0.834837 | + | 0.550497i | \(0.185562\pi\) | |||||||
\(524\) | −21038.3 | −1.75394 | ||||||||
\(525\) | −1113.38 | −0.0925562 | ||||||||
\(526\) | −4621.08 | −0.383058 | ||||||||
\(527\) | −1178.24 | −0.0973912 | ||||||||
\(528\) | 6033.74 | 0.497320 | ||||||||
\(529\) | 21074.3 | 1.73209 | ||||||||
\(530\) | 1124.92 | 0.0921950 | ||||||||
\(531\) | 33182.3 | 2.71185 | ||||||||
\(532\) | 624.237 | 0.0508723 | ||||||||
\(533\) | −4481.66 | −0.364207 | ||||||||
\(534\) | 5654.20 | 0.458204 | ||||||||
\(535\) | 2059.33 | 0.166416 | ||||||||
\(536\) | 9319.76 | 0.751031 | ||||||||
\(537\) | −16107.9 | −1.29443 | ||||||||
\(538\) | 3839.05 | 0.307646 | ||||||||
\(539\) | 3565.05 | 0.284894 | ||||||||
\(540\) | −19705.5 | −1.57035 | ||||||||
\(541\) | −3253.06 | −0.258521 | −0.129260 | − | 0.991611i | \(-0.541260\pi\) | ||||
−0.129260 | + | 0.991611i | \(0.541260\pi\) | |||||||
\(542\) | −1954.47 | −0.154892 | ||||||||
\(543\) | −16168.0 | −1.27778 | ||||||||
\(544\) | −13207.3 | −1.04091 | ||||||||
\(545\) | 2435.69 | 0.191437 | ||||||||
\(546\) | −456.361 | −0.0357701 | ||||||||
\(547\) | 11588.5 | 0.905828 | 0.452914 | − | 0.891554i | \(-0.350384\pi\) | ||||
0.452914 | + | 0.891554i | \(0.350384\pi\) | |||||||
\(548\) | 15653.1 | 1.22020 | ||||||||
\(549\) | −54086.0 | −4.20462 | ||||||||
\(550\) | −183.153 | −0.0141994 | ||||||||
\(551\) | −119.612 | −0.00924799 | ||||||||
\(552\) | −19348.9 | −1.49192 | ||||||||
\(553\) | −3765.83 | −0.289583 | ||||||||
\(554\) | 497.180 | 0.0381284 | ||||||||
\(555\) | −15904.9 | −1.21644 | ||||||||
\(556\) | −3710.43 | −0.283017 | ||||||||
\(557\) | −19300.0 | −1.46817 | −0.734084 | − | 0.679059i | \(-0.762388\pi\) | ||||
−0.734084 | + | 0.679059i | \(0.762388\pi\) | |||||||
\(558\) | 548.846 | 0.0416389 | ||||||||
\(559\) | 648.289 | 0.0490514 | ||||||||
\(560\) | −1164.17 | −0.0878487 | ||||||||
\(561\) | −12552.3 | −0.944669 | ||||||||
\(562\) | 3357.65 | 0.252017 | ||||||||
\(563\) | 12068.0 | 0.903387 | 0.451694 | − | 0.892173i | \(-0.350820\pi\) | ||||
0.451694 | + | 0.892173i | \(0.350820\pi\) | |||||||
\(564\) | −3136.68 | −0.234181 | ||||||||
\(565\) | −6987.63 | −0.520304 | ||||||||
\(566\) | −1547.98 | −0.114958 | ||||||||
\(567\) | 14080.6 | 1.04291 | ||||||||
\(568\) | −7725.38 | −0.570686 | ||||||||
\(569\) | 15865.0 | 1.16889 | 0.584444 | − | 0.811434i | \(-0.301313\pi\) | ||||
0.584444 | + | 0.811434i | \(0.301313\pi\) | |||||||
\(570\) | −648.082 | −0.0476231 | ||||||||
\(571\) | −14742.2 | −1.08046 | −0.540230 | − | 0.841517i | \(-0.681663\pi\) | ||||
−0.540230 | + | 0.841517i | \(0.681663\pi\) | |||||||
\(572\) | 1278.89 | 0.0934844 | ||||||||
\(573\) | −22812.8 | −1.66321 | ||||||||
\(574\) | −843.480 | −0.0613348 | ||||||||
\(575\) | −4558.05 | −0.330580 | ||||||||
\(576\) | −27228.8 | −1.96967 | ||||||||
\(577\) | 9845.47 | 0.710351 | 0.355175 | − | 0.934800i | \(-0.384421\pi\) | ||||
0.355175 | + | 0.934800i | \(0.384421\pi\) | |||||||
\(578\) | 4993.83 | 0.359370 | ||||||||
\(579\) | 592.850 | 0.0425527 | ||||||||
\(580\) | 237.853 | 0.0170281 | ||||||||
\(581\) | 5524.26 | 0.394466 | ||||||||
\(582\) | −4470.80 | −0.318421 | ||||||||
\(583\) | 3715.89 | 0.263974 | ||||||||
\(584\) | −1077.14 | −0.0763228 | ||||||||
\(585\) | −5994.23 | −0.423643 | ||||||||
\(586\) | 199.313 | 0.0140504 | ||||||||
\(587\) | −16055.3 | −1.12892 | −0.564458 | − | 0.825462i | \(-0.690915\pi\) | ||||
−0.564458 | + | 0.825462i | \(0.690915\pi\) | |||||||
\(588\) | −25085.1 | −1.75934 | ||||||||
\(589\) | −200.948 | −0.0140576 | ||||||||
\(590\) | −1418.13 | −0.0989554 | ||||||||
\(591\) | −25339.6 | −1.76367 | ||||||||
\(592\) | −16630.4 | −1.15457 | ||||||||
\(593\) | −20716.8 | −1.43464 | −0.717318 | − | 0.696746i | \(-0.754630\pi\) | ||||
−0.717318 | + | 0.696746i | \(0.754630\pi\) | |||||||
\(594\) | 3820.97 | 0.263933 | ||||||||
\(595\) | 2421.89 | 0.166870 | ||||||||
\(596\) | −1843.16 | −0.126676 | ||||||||
\(597\) | 37841.5 | 2.59422 | ||||||||
\(598\) | −1868.28 | −0.127759 | ||||||||
\(599\) | −10546.3 | −0.719380 | −0.359690 | − | 0.933072i | \(-0.617118\pi\) | ||||
−0.359690 | + | 0.933072i | \(0.617118\pi\) | |||||||
\(600\) | 2653.12 | 0.180522 | ||||||||
\(601\) | −14403.3 | −0.977574 | −0.488787 | − | 0.872403i | \(-0.662561\pi\) | ||||
−0.488787 | + | 0.872403i | \(0.662561\pi\) | |||||||
\(602\) | 122.013 | 0.00826057 | ||||||||
\(603\) | −70089.7 | −4.73346 | ||||||||
\(604\) | 20276.2 | 1.36594 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | 6785.42 | 0.454849 | ||||||||
\(607\) | 489.614 | 0.0327394 | 0.0163697 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163697 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(608\) | −2252.48 | −0.150247 | ||||||||
\(609\) | −280.366 | −0.0186552 | ||||||||
\(610\) | 2311.51 | 0.153427 | ||||||||
\(611\) | −623.521 | −0.0412847 | ||||||||
\(612\) | 65593.7 | 4.33247 | ||||||||
\(613\) | 4970.44 | 0.327495 | 0.163747 | − | 0.986502i | \(-0.447642\pi\) | ||||
0.163747 | + | 0.986502i | \(0.447642\pi\) | |||||||
\(614\) | 4836.32 | 0.317880 | ||||||||
\(615\) | −14918.0 | −0.978134 | ||||||||
\(616\) | 495.521 | 0.0324109 | ||||||||
\(617\) | −25969.2 | −1.69446 | −0.847229 | − | 0.531228i | \(-0.821731\pi\) | ||||
−0.847229 | + | 0.531228i | \(0.821731\pi\) | |||||||
\(618\) | −246.986 | −0.0160764 | ||||||||
\(619\) | 683.267 | 0.0443665 | 0.0221832 | − | 0.999754i | \(-0.492938\pi\) | ||||
0.0221832 | + | 0.999754i | \(0.492938\pi\) | |||||||
\(620\) | 399.592 | 0.0258839 | ||||||||
\(621\) | 95091.0 | 6.14472 | ||||||||
\(622\) | −4135.06 | −0.266561 | ||||||||
\(623\) | −3603.66 | −0.231746 | ||||||||
\(624\) | −8439.52 | −0.541428 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −750.859 | −0.0479399 | ||||||||
\(627\) | −2140.78 | −0.136355 | ||||||||
\(628\) | 11258.3 | 0.715373 | ||||||||
\(629\) | 34597.1 | 2.19313 | ||||||||
\(630\) | −1128.16 | −0.0713442 | ||||||||
\(631\) | −12579.4 | −0.793626 | −0.396813 | − | 0.917900i | \(-0.629884\pi\) | ||||
−0.396813 | + | 0.917900i | \(0.629884\pi\) | |||||||
\(632\) | 8973.71 | 0.564802 | ||||||||
\(633\) | −27432.7 | −1.72252 | ||||||||
\(634\) | −4830.87 | −0.302616 | ||||||||
\(635\) | 13499.1 | 0.843617 | ||||||||
\(636\) | −26146.5 | −1.63015 | ||||||||
\(637\) | −4986.51 | −0.310161 | ||||||||
\(638\) | −46.1205 | −0.00286196 | ||||||||
\(639\) | 58099.1 | 3.59681 | ||||||||
\(640\) | 5905.75 | 0.364758 | ||||||||
\(641\) | 26965.5 | 1.66158 | 0.830792 | − | 0.556583i | \(-0.187888\pi\) | ||||
0.830792 | + | 0.556583i | \(0.187888\pi\) | |||||||
\(642\) | 2809.71 | 0.172727 | ||||||||
\(643\) | 3846.15 | 0.235890 | 0.117945 | − | 0.993020i | \(-0.462369\pi\) | ||||
0.117945 | + | 0.993020i | \(0.462369\pi\) | |||||||
\(644\) | 5990.11 | 0.366527 | ||||||||
\(645\) | 2157.95 | 0.131735 | ||||||||
\(646\) | 1409.74 | 0.0858600 | ||||||||
\(647\) | −15946.5 | −0.968966 | −0.484483 | − | 0.874801i | \(-0.660992\pi\) | ||||
−0.484483 | + | 0.874801i | \(0.660992\pi\) | |||||||
\(648\) | −33553.0 | −2.03408 | ||||||||
\(649\) | −4684.46 | −0.283330 | ||||||||
\(650\) | 256.179 | 0.0154587 | ||||||||
\(651\) | −471.015 | −0.0283572 | ||||||||
\(652\) | −1807.12 | −0.108546 | ||||||||
\(653\) | 18804.9 | 1.12694 | 0.563471 | − | 0.826136i | \(-0.309466\pi\) | ||||
0.563471 | + | 0.826136i | \(0.309466\pi\) | |||||||
\(654\) | 3323.21 | 0.198697 | ||||||||
\(655\) | −13920.8 | −0.830428 | ||||||||
\(656\) | −15598.5 | −0.928384 | ||||||||
\(657\) | 8100.70 | 0.481033 | ||||||||
\(658\) | −117.351 | −0.00695262 | ||||||||
\(659\) | −15615.7 | −0.923065 | −0.461533 | − | 0.887123i | \(-0.652700\pi\) | ||||
−0.461533 | + | 0.887123i | \(0.652700\pi\) | |||||||
\(660\) | 4257.02 | 0.251067 | ||||||||
\(661\) | 21958.6 | 1.29212 | 0.646058 | − | 0.763288i | \(-0.276416\pi\) | ||||
0.646058 | + | 0.763288i | \(0.276416\pi\) | |||||||
\(662\) | −3757.31 | −0.220592 | ||||||||
\(663\) | 17557.2 | 1.02845 | ||||||||
\(664\) | −13163.9 | −0.769367 | ||||||||
\(665\) | 413.050 | 0.0240863 | ||||||||
\(666\) | −16115.9 | −0.937656 | ||||||||
\(667\) | −1147.78 | −0.0666302 | ||||||||
\(668\) | −2979.29 | −0.172563 | ||||||||
\(669\) | −30038.4 | −1.73595 | ||||||||
\(670\) | 2995.47 | 0.172724 | ||||||||
\(671\) | 7635.51 | 0.439293 | ||||||||
\(672\) | −5279.73 | −0.303080 | ||||||||
\(673\) | −10989.6 | −0.629447 | −0.314723 | − | 0.949183i | \(-0.601912\pi\) | ||||
−0.314723 | + | 0.949183i | \(0.601912\pi\) | |||||||
\(674\) | −1306.04 | −0.0746394 | ||||||||
\(675\) | −13038.9 | −0.743507 | ||||||||
\(676\) | 14812.7 | 0.842778 | ||||||||
\(677\) | −18922.0 | −1.07420 | −0.537099 | − | 0.843519i | \(-0.680480\pi\) | ||||
−0.537099 | + | 0.843519i | \(0.680480\pi\) | |||||||
\(678\) | −9533.81 | −0.540035 | ||||||||
\(679\) | 2849.43 | 0.161047 | ||||||||
\(680\) | −5771.20 | −0.325464 | ||||||||
\(681\) | −66461.8 | −3.73983 | ||||||||
\(682\) | −77.4824 | −0.00435037 | ||||||||
\(683\) | −6913.53 | −0.387319 | −0.193660 | − | 0.981069i | \(-0.562036\pi\) | ||||
−0.193660 | + | 0.981069i | \(0.562036\pi\) | |||||||
\(684\) | 11186.9 | 0.625354 | ||||||||
\(685\) | 10357.5 | 0.577722 | ||||||||
\(686\) | −1931.74 | −0.107513 | ||||||||
\(687\) | 20809.2 | 1.15564 | ||||||||
\(688\) | 2256.39 | 0.125035 | ||||||||
\(689\) | −5197.50 | −0.287386 | ||||||||
\(690\) | −6218.92 | −0.343116 | ||||||||
\(691\) | 9389.56 | 0.516926 | 0.258463 | − | 0.966021i | \(-0.416784\pi\) | ||||
0.258463 | + | 0.966021i | \(0.416784\pi\) | |||||||
\(692\) | 28413.0 | 1.56084 | ||||||||
\(693\) | −3726.59 | −0.204273 | ||||||||
\(694\) | −1336.68 | −0.0731119 | ||||||||
\(695\) | −2455.15 | −0.133999 | ||||||||
\(696\) | 668.094 | 0.0363851 | ||||||||
\(697\) | 32450.5 | 1.76348 | ||||||||
\(698\) | 2036.02 | 0.110407 | ||||||||
\(699\) | 71618.8 | 3.87535 | ||||||||
\(700\) | −821.364 | −0.0443495 | ||||||||
\(701\) | 32662.0 | 1.75981 | 0.879905 | − | 0.475149i | \(-0.157606\pi\) | ||||
0.879905 | + | 0.475149i | \(0.157606\pi\) | |||||||
\(702\) | −5344.47 | −0.287342 | ||||||||
\(703\) | 5900.49 | 0.316559 | ||||||||
\(704\) | 3843.98 | 0.205789 | ||||||||
\(705\) | −2075.50 | −0.110877 | ||||||||
\(706\) | 6129.53 | 0.326753 | ||||||||
\(707\) | −4324.63 | −0.230049 | ||||||||
\(708\) | 32961.7 | 1.74968 | ||||||||
\(709\) | −27679.7 | −1.46620 | −0.733098 | − | 0.680123i | \(-0.761926\pi\) | ||||
−0.733098 | + | 0.680123i | \(0.761926\pi\) | |||||||
\(710\) | −2483.02 | −0.131248 | ||||||||
\(711\) | −67487.2 | −3.55973 | ||||||||
\(712\) | 8587.27 | 0.451996 | ||||||||
\(713\) | −1928.27 | −0.101283 | ||||||||
\(714\) | 3304.39 | 0.173198 | ||||||||
\(715\) | 846.226 | 0.0442616 | ||||||||
\(716\) | −11883.1 | −0.620241 | ||||||||
\(717\) | 9472.03 | 0.493360 | ||||||||
\(718\) | 7034.13 | 0.365615 | ||||||||
\(719\) | 7449.56 | 0.386400 | 0.193200 | − | 0.981159i | \(-0.438113\pi\) | ||||
0.193200 | + | 0.981159i | \(0.438113\pi\) | |||||||
\(720\) | −20863.1 | −1.07989 | ||||||||
\(721\) | 157.414 | 0.00813095 | ||||||||
\(722\) | 240.429 | 0.0123932 | ||||||||
\(723\) | −17796.1 | −0.915415 | ||||||||
\(724\) | −11927.4 | −0.612265 | ||||||||
\(725\) | 157.384 | 0.00806221 | ||||||||
\(726\) | −825.452 | −0.0421975 | ||||||||
\(727\) | −3546.51 | −0.180926 | −0.0904628 | − | 0.995900i | \(-0.528835\pi\) | ||||
−0.0904628 | + | 0.995900i | \(0.528835\pi\) | |||||||
\(728\) | −693.095 | −0.0352855 | ||||||||
\(729\) | 108096. | 5.49183 | ||||||||
\(730\) | −346.205 | −0.0175529 | ||||||||
\(731\) | −4694.09 | −0.237506 | ||||||||
\(732\) | −53726.4 | −2.71282 | ||||||||
\(733\) | −3983.00 | −0.200703 | −0.100351 | − | 0.994952i | \(-0.531997\pi\) | ||||
−0.100351 | + | 0.994952i | \(0.531997\pi\) | |||||||
\(734\) | −4135.92 | −0.207983 | ||||||||
\(735\) | −16598.5 | −0.832987 | ||||||||
\(736\) | −21614.5 | −1.08250 | ||||||||
\(737\) | 9894.80 | 0.494545 | ||||||||
\(738\) | −15116.0 | −0.753965 | ||||||||
\(739\) | −8915.23 | −0.443778 | −0.221889 | − | 0.975072i | \(-0.571222\pi\) | ||||
−0.221889 | + | 0.975072i | \(0.571222\pi\) | |||||||
\(740\) | −11733.3 | −0.582872 | ||||||||
\(741\) | 2994.35 | 0.148448 | ||||||||
\(742\) | −978.205 | −0.0483976 | ||||||||
\(743\) | −13972.3 | −0.689898 | −0.344949 | − | 0.938622i | \(-0.612104\pi\) | ||||
−0.344949 | + | 0.938622i | \(0.612104\pi\) | |||||||
\(744\) | 1122.40 | 0.0553078 | ||||||||
\(745\) | −1219.60 | −0.0599765 | ||||||||
\(746\) | 55.2817 | 0.00271314 | ||||||||
\(747\) | 98999.9 | 4.84902 | ||||||||
\(748\) | −9260.09 | −0.452650 | ||||||||
\(749\) | −1790.75 | −0.0873599 | ||||||||
\(750\) | 852.739 | 0.0415169 | ||||||||
\(751\) | −37400.2 | −1.81725 | −0.908624 | − | 0.417614i | \(-0.862866\pi\) | ||||
−0.908624 | + | 0.417614i | \(0.862866\pi\) | |||||||
\(752\) | −2170.18 | −0.105237 | ||||||||
\(753\) | −68800.1 | −3.32964 | ||||||||
\(754\) | 64.5097 | 0.00311579 | ||||||||
\(755\) | 13416.5 | 0.646725 | ||||||||
\(756\) | 17135.5 | 0.824353 | ||||||||
\(757\) | −4311.96 | −0.207029 | −0.103515 | − | 0.994628i | \(-0.533009\pi\) | ||||
−0.103515 | + | 0.994628i | \(0.533009\pi\) | |||||||
\(758\) | −2828.08 | −0.135515 | ||||||||
\(759\) | −20542.7 | −0.982414 | ||||||||
\(760\) | −984.270 | −0.0469779 | ||||||||
\(761\) | 25152.1 | 1.19811 | 0.599056 | − | 0.800707i | \(-0.295543\pi\) | ||||
0.599056 | + | 0.800707i | \(0.295543\pi\) | |||||||
\(762\) | 18418.0 | 0.875608 | ||||||||
\(763\) | −2118.02 | −0.100495 | ||||||||
\(764\) | −16829.4 | −0.796946 | ||||||||
\(765\) | 43402.6 | 2.05127 | ||||||||
\(766\) | 3238.19 | 0.152742 | ||||||||
\(767\) | 6552.25 | 0.308459 | ||||||||
\(768\) | −20577.7 | −0.966842 | ||||||||
\(769\) | −39413.4 | −1.84822 | −0.924112 | − | 0.382122i | \(-0.875194\pi\) | ||||
−0.924112 | + | 0.382122i | \(0.875194\pi\) | |||||||
\(770\) | 159.266 | 0.00745394 | ||||||||
\(771\) | 3947.70 | 0.184401 | ||||||||
\(772\) | 437.357 | 0.0203897 | ||||||||
\(773\) | −22805.4 | −1.06113 | −0.530565 | − | 0.847644i | \(-0.678020\pi\) | ||||
−0.530565 | + | 0.847644i | \(0.678020\pi\) | |||||||
\(774\) | 2186.58 | 0.101544 | ||||||||
\(775\) | 264.405 | 0.0122551 | ||||||||
\(776\) | −6790.00 | −0.314107 | ||||||||
\(777\) | 13830.5 | 0.638568 | ||||||||
\(778\) | 4878.99 | 0.224833 | ||||||||
\(779\) | 5534.38 | 0.254544 | ||||||||
\(780\) | −5954.37 | −0.273334 | ||||||||
\(781\) | −8202.04 | −0.375790 | ||||||||
\(782\) | 13527.7 | 0.618607 | ||||||||
\(783\) | −3283.38 | −0.149858 | ||||||||
\(784\) | −17355.7 | −0.790620 | ||||||||
\(785\) | 7449.47 | 0.338704 | ||||||||
\(786\) | −18993.3 | −0.861919 | ||||||||
\(787\) | 6818.43 | 0.308832 | 0.154416 | − | 0.988006i | \(-0.450650\pi\) | ||||
0.154416 | + | 0.988006i | \(0.450650\pi\) | |||||||
\(788\) | −18693.5 | −0.845087 | ||||||||
\(789\) | 71070.3 | 3.20681 | ||||||||
\(790\) | 2884.24 | 0.129895 | ||||||||
\(791\) | 6076.30 | 0.273133 | ||||||||
\(792\) | 8880.21 | 0.398415 | ||||||||
\(793\) | −10679.9 | −0.478254 | ||||||||
\(794\) | −411.517 | −0.0183932 | ||||||||
\(795\) | −17300.8 | −0.771820 | ||||||||
\(796\) | 27916.4 | 1.24305 | ||||||||
\(797\) | 15742.9 | 0.699675 | 0.349838 | − | 0.936810i | \(-0.386237\pi\) | ||||
0.349838 | + | 0.936810i | \(0.386237\pi\) | |||||||
\(798\) | 563.558 | 0.0249997 | ||||||||
\(799\) | 4514.75 | 0.199900 | ||||||||
\(800\) | 2963.79 | 0.130982 | ||||||||
\(801\) | −64581.0 | −2.84876 | ||||||||
\(802\) | 4752.57 | 0.209251 | ||||||||
\(803\) | −1143.60 | −0.0502577 | ||||||||
\(804\) | −69623.7 | −3.05403 | ||||||||
\(805\) | 3963.58 | 0.173538 | ||||||||
\(806\) | 108.376 | 0.00473621 | ||||||||
\(807\) | −59043.1 | −2.57549 | ||||||||
\(808\) | 10305.3 | 0.448687 | ||||||||
\(809\) | −12949.3 | −0.562761 | −0.281381 | − | 0.959596i | \(-0.590792\pi\) | ||||
−0.281381 | + | 0.959596i | \(0.590792\pi\) | |||||||
\(810\) | −10784.3 | −0.467804 | ||||||||
\(811\) | 20025.2 | 0.867052 | 0.433526 | − | 0.901141i | \(-0.357269\pi\) | ||||
0.433526 | + | 0.901141i | \(0.357269\pi\) | |||||||
\(812\) | −206.832 | −0.00893887 | ||||||||
\(813\) | 30059.0 | 1.29670 | ||||||||
\(814\) | 2275.14 | 0.0979650 | ||||||||
\(815\) | −1195.75 | −0.0513929 | ||||||||
\(816\) | 61108.3 | 2.62159 | ||||||||
\(817\) | −800.569 | −0.0342820 | ||||||||
\(818\) | 5821.50 | 0.248831 | ||||||||
\(819\) | 5212.46 | 0.222391 | ||||||||
\(820\) | −11005.3 | −0.468685 | ||||||||
\(821\) | −32269.7 | −1.37177 | −0.685884 | − | 0.727711i | \(-0.740584\pi\) | ||||
−0.685884 | + | 0.727711i | \(0.740584\pi\) | |||||||
\(822\) | 14131.6 | 0.599630 | ||||||||
\(823\) | 35677.7 | 1.51111 | 0.755556 | − | 0.655084i | \(-0.227367\pi\) | ||||
0.755556 | + | 0.655084i | \(0.227367\pi\) | |||||||
\(824\) | −375.108 | −0.0158586 | ||||||||
\(825\) | 2816.82 | 0.118871 | ||||||||
\(826\) | 1233.18 | 0.0519465 | ||||||||
\(827\) | 39059.3 | 1.64235 | 0.821176 | − | 0.570675i | \(-0.193318\pi\) | ||||
0.821176 | + | 0.570675i | \(0.193318\pi\) | |||||||
\(828\) | 107348. | 4.50557 | ||||||||
\(829\) | −4550.98 | −0.190666 | −0.0953330 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953330 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(830\) | −4231.02 | −0.176941 | ||||||||
\(831\) | −7646.43 | −0.319196 | ||||||||
\(832\) | −5376.65 | −0.224041 | ||||||||
\(833\) | 36106.0 | 1.50180 | ||||||||
\(834\) | −3349.76 | −0.139080 | ||||||||
\(835\) | −1971.36 | −0.0817026 | ||||||||
\(836\) | −1579.29 | −0.0653362 | ||||||||
\(837\) | −5516.08 | −0.227794 | ||||||||
\(838\) | −5331.11 | −0.219761 | ||||||||
\(839\) | −47860.9 | −1.96942 | −0.984709 | − | 0.174205i | \(-0.944265\pi\) | ||||
−0.984709 | + | 0.174205i | \(0.944265\pi\) | |||||||
\(840\) | −2307.09 | −0.0947646 | ||||||||
\(841\) | −24349.4 | −0.998375 | ||||||||
\(842\) | −55.8638 | −0.00228645 | ||||||||
\(843\) | −51639.3 | −2.10979 | ||||||||
\(844\) | −20237.6 | −0.825365 | ||||||||
\(845\) | 9801.37 | 0.399026 | ||||||||
\(846\) | −2103.04 | −0.0854659 | ||||||||
\(847\) | 526.095 | 0.0213422 | ||||||||
\(848\) | −18090.0 | −0.732563 | ||||||||
\(849\) | 23807.3 | 0.962383 | ||||||||
\(850\) | −1854.92 | −0.0748510 | ||||||||
\(851\) | 56620.4 | 2.28076 | ||||||||
\(852\) | 57712.8 | 2.32067 | ||||||||
\(853\) | −21752.8 | −0.873155 | −0.436578 | − | 0.899667i | \(-0.643810\pi\) | ||||
−0.436578 | + | 0.899667i | \(0.643810\pi\) | |||||||
\(854\) | −2010.04 | −0.0805411 | ||||||||
\(855\) | 7402.25 | 0.296084 | ||||||||
\(856\) | 4267.23 | 0.170387 | ||||||||
\(857\) | 24128.7 | 0.961752 | 0.480876 | − | 0.876789i | \(-0.340319\pi\) | ||||
0.480876 | + | 0.876789i | \(0.340319\pi\) | |||||||
\(858\) | 1154.58 | 0.0459401 | ||||||||
\(859\) | 36459.9 | 1.44819 | 0.724095 | − | 0.689700i | \(-0.242258\pi\) | ||||
0.724095 | + | 0.689700i | \(0.242258\pi\) | |||||||
\(860\) | 1591.96 | 0.0631225 | ||||||||
\(861\) | 12972.4 | 0.513470 | ||||||||
\(862\) | 9144.63 | 0.361331 | ||||||||
\(863\) | 6415.63 | 0.253060 | 0.126530 | − | 0.991963i | \(-0.459616\pi\) | ||||
0.126530 | + | 0.991963i | \(0.459616\pi\) | |||||||
\(864\) | −61831.1 | −2.43465 | ||||||||
\(865\) | 18800.5 | 0.739003 | ||||||||
\(866\) | 491.454 | 0.0192844 | ||||||||
\(867\) | −76803.1 | −3.00850 | ||||||||
\(868\) | −347.477 | −0.0135877 | ||||||||
\(869\) | 9527.40 | 0.371916 | ||||||||
\(870\) | 214.732 | 0.00836794 | ||||||||
\(871\) | −13840.1 | −0.538407 | ||||||||
\(872\) | 5047.10 | 0.196005 | ||||||||
\(873\) | 51064.5 | 1.97969 | ||||||||
\(874\) | 2307.13 | 0.0892906 | ||||||||
\(875\) | −543.487 | −0.0209979 | ||||||||
\(876\) | 8046.84 | 0.310362 | ||||||||
\(877\) | 2230.38 | 0.0858775 | 0.0429388 | − | 0.999078i | \(-0.486328\pi\) | ||||
0.0429388 | + | 0.999078i | \(0.486328\pi\) | |||||||
\(878\) | 5564.66 | 0.213893 | ||||||||
\(879\) | −3065.36 | −0.117624 | ||||||||
\(880\) | 2945.31 | 0.112825 | ||||||||
\(881\) | −1477.52 | −0.0565028 | −0.0282514 | − | 0.999601i | \(-0.508994\pi\) | ||||
−0.0282514 | + | 0.999601i | \(0.508994\pi\) | |||||||
\(882\) | −16818.8 | −0.642083 | ||||||||
\(883\) | −22570.9 | −0.860217 | −0.430109 | − | 0.902777i | \(-0.641525\pi\) | ||||
−0.430109 | + | 0.902777i | \(0.641525\pi\) | |||||||
\(884\) | 12952.3 | 0.492796 | ||||||||
\(885\) | 21810.4 | 0.828415 | ||||||||
\(886\) | 7857.60 | 0.297947 | ||||||||
\(887\) | 40168.8 | 1.52056 | 0.760280 | − | 0.649595i | \(-0.225061\pi\) | ||||
0.760280 | + | 0.649595i | \(0.225061\pi\) | |||||||
\(888\) | −32957.2 | −1.24546 | ||||||||
\(889\) | −11738.6 | −0.442855 | ||||||||
\(890\) | 2760.04 | 0.103951 | ||||||||
\(891\) | −35623.3 | −1.33942 | ||||||||
\(892\) | −22159.9 | −0.831802 | ||||||||
\(893\) | 769.983 | 0.0288539 | ||||||||
\(894\) | −1664.00 | −0.0622509 | ||||||||
\(895\) | −7862.91 | −0.293663 | ||||||||
\(896\) | −5135.51 | −0.191479 | ||||||||
\(897\) | 28733.5 | 1.06955 | ||||||||
\(898\) | 1188.64 | 0.0441710 | ||||||||
\(899\) | 66.5811 | 0.00247008 | ||||||||
\(900\) | −14719.6 | −0.545171 | ||||||||
\(901\) | 37633.6 | 1.39152 | ||||||||
\(902\) | 2133.97 | 0.0787732 | ||||||||
\(903\) | −1876.51 | −0.0691542 | ||||||||
\(904\) | −14479.4 | −0.532719 | ||||||||
\(905\) | −7892.25 | −0.289886 | ||||||||
\(906\) | 18305.3 | 0.671250 | ||||||||
\(907\) | −9829.85 | −0.359862 | −0.179931 | − | 0.983679i | \(-0.557587\pi\) | ||||
−0.179931 | + | 0.983679i | \(0.557587\pi\) | |||||||
\(908\) | −49030.1 | −1.79199 | ||||||||
\(909\) | −77501.5 | −2.82790 | ||||||||
\(910\) | −222.768 | −0.00811504 | ||||||||
\(911\) | 2662.85 | 0.0968434 | 0.0484217 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484217 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(912\) | 10421.9 | 0.378404 | ||||||||
\(913\) | −13976.2 | −0.506619 | ||||||||
\(914\) | −10208.0 | −0.369421 | ||||||||
\(915\) | −35550.1 | −1.28443 | ||||||||
\(916\) | 15351.4 | 0.553738 | ||||||||
\(917\) | 12105.2 | 0.435932 | ||||||||
\(918\) | 38697.8 | 1.39131 | ||||||||
\(919\) | 35978.4 | 1.29142 | 0.645711 | − | 0.763582i | \(-0.276561\pi\) | ||||
0.645711 | + | 0.763582i | \(0.276561\pi\) | |||||||
\(920\) | −9444.94 | −0.338468 | ||||||||
\(921\) | −74380.7 | −2.66116 | ||||||||
\(922\) | 1636.21 | 0.0584444 | ||||||||
\(923\) | 11472.4 | 0.409120 | ||||||||
\(924\) | −3701.81 | −0.131797 | ||||||||
\(925\) | −7763.80 | −0.275970 | ||||||||
\(926\) | 10249.4 | 0.363733 | ||||||||
\(927\) | 2821.01 | 0.0999507 | ||||||||
\(928\) | 746.325 | 0.0264001 | ||||||||
\(929\) | −35971.3 | −1.27038 | −0.635189 | − | 0.772357i | \(-0.719078\pi\) | ||||
−0.635189 | + | 0.772357i | \(0.719078\pi\) | |||||||
\(930\) | 360.750 | 0.0127198 | ||||||||
\(931\) | 6157.82 | 0.216772 | ||||||||
\(932\) | 52834.5 | 1.85692 | ||||||||
\(933\) | 63595.5 | 2.23154 | ||||||||
\(934\) | 1532.15 | 0.0536760 | ||||||||
\(935\) | −6127.29 | −0.214314 | ||||||||
\(936\) | −12420.9 | −0.433751 | ||||||||
\(937\) | 38333.1 | 1.33649 | 0.668244 | − | 0.743942i | \(-0.267046\pi\) | ||||
0.668244 | + | 0.743942i | \(0.267046\pi\) | |||||||
\(938\) | −2604.80 | −0.0906712 | ||||||||
\(939\) | 11547.9 | 0.401333 | ||||||||
\(940\) | −1531.14 | −0.0531279 | ||||||||
\(941\) | −20686.8 | −0.716653 | −0.358326 | − | 0.933596i | \(-0.616653\pi\) | ||||
−0.358326 | + | 0.933596i | \(0.616653\pi\) | |||||||
\(942\) | 10163.9 | 0.351549 | ||||||||
\(943\) | 53107.3 | 1.83395 | ||||||||
\(944\) | 22805.3 | 0.786280 | ||||||||
\(945\) | 11338.3 | 0.390303 | ||||||||
\(946\) | −308.687 | −0.0106092 | ||||||||
\(947\) | −54586.6 | −1.87310 | −0.936550 | − | 0.350533i | \(-0.886000\pi\) | ||||
−0.936550 | + | 0.350533i | \(0.886000\pi\) | |||||||
\(948\) | −67038.5 | −2.29674 | ||||||||
\(949\) | 1599.58 | 0.0547151 | ||||||||
\(950\) | −316.355 | −0.0108041 | ||||||||
\(951\) | 74296.9 | 2.53338 | ||||||||
\(952\) | 5018.51 | 0.170852 | ||||||||
\(953\) | 39163.8 | 1.33121 | 0.665604 | − | 0.746305i | \(-0.268174\pi\) | ||||
0.665604 | + | 0.746305i | \(0.268174\pi\) | |||||||
\(954\) | −17530.4 | −0.594934 | ||||||||
\(955\) | −11135.8 | −0.377326 | ||||||||
\(956\) | 6987.69 | 0.236400 | ||||||||
\(957\) | 709.316 | 0.0239592 | ||||||||
\(958\) | −4193.94 | −0.141440 | ||||||||
\(959\) | −9006.65 | −0.303274 | ||||||||
\(960\) | −17897.1 | −0.601696 | ||||||||
\(961\) | −29679.1 | −0.996245 | ||||||||
\(962\) | −3182.28 | −0.106654 | ||||||||
\(963\) | −32091.9 | −1.07388 | ||||||||
\(964\) | −13128.5 | −0.438632 | ||||||||
\(965\) | 289.394 | 0.00965379 | ||||||||
\(966\) | 5407.84 | 0.180119 | ||||||||
\(967\) | 23663.7 | 0.786943 | 0.393471 | − | 0.919337i | \(-0.371274\pi\) | ||||
0.393471 | + | 0.919337i | \(0.371274\pi\) | |||||||
\(968\) | −1253.65 | −0.0416258 | ||||||||
\(969\) | −21681.3 | −0.718786 | ||||||||
\(970\) | −2182.38 | −0.0722391 | ||||||||
\(971\) | 33344.5 | 1.10204 | 0.551018 | − | 0.834493i | \(-0.314240\pi\) | ||||
0.551018 | + | 0.834493i | \(0.314240\pi\) | |||||||
\(972\) | 144250. | 4.76009 | ||||||||
\(973\) | 2134.94 | 0.0703424 | ||||||||
\(974\) | −3441.85 | −0.113228 | ||||||||
\(975\) | −3939.94 | −0.129414 | ||||||||
\(976\) | −37171.8 | −1.21910 | ||||||||
\(977\) | 8943.73 | 0.292871 | 0.146436 | − | 0.989220i | \(-0.453220\pi\) | ||||
0.146436 | + | 0.989220i | \(0.453220\pi\) | |||||||
\(978\) | −1631.46 | −0.0533418 | ||||||||
\(979\) | 9117.11 | 0.297634 | ||||||||
\(980\) | −12245.0 | −0.399136 | ||||||||
\(981\) | −37956.9 | −1.23534 | ||||||||
\(982\) | −3332.22 | −0.108284 | ||||||||
\(983\) | 17462.5 | 0.566599 | 0.283300 | − | 0.959031i | \(-0.408571\pi\) | ||||
0.283300 | + | 0.959031i | \(0.408571\pi\) | |||||||
\(984\) | −30912.3 | −1.00147 | ||||||||
\(985\) | −12369.3 | −0.400119 | ||||||||
\(986\) | −467.097 | −0.0150866 | ||||||||
\(987\) | 1804.81 | 0.0582045 | ||||||||
\(988\) | 2208.99 | 0.0711309 | ||||||||
\(989\) | −7682.18 | −0.246996 | ||||||||
\(990\) | 2854.19 | 0.0916285 | ||||||||
\(991\) | 9370.69 | 0.300373 | 0.150186 | − | 0.988658i | \(-0.452013\pi\) | ||||
0.150186 | + | 0.988658i | \(0.452013\pi\) | |||||||
\(992\) | 1253.82 | 0.0401300 | ||||||||
\(993\) | 57786.0 | 1.84671 | ||||||||
\(994\) | 2159.18 | 0.0688984 | ||||||||
\(995\) | 18471.9 | 0.588542 | ||||||||
\(996\) | 98341.6 | 3.12859 | ||||||||
\(997\) | 10592.9 | 0.336489 | 0.168244 | − | 0.985745i | \(-0.446190\pi\) | ||||
0.168244 | + | 0.985745i | \(0.446190\pi\) | |||||||
\(998\) | 322.968 | 0.0102438 | ||||||||
\(999\) | 161970. | 5.12963 |
(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 | 1045.4.a.g.1.12 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.g.1.12 | ✓ | 23 | 1.1 | even | 1 | trivial |