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: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52988 | −0.894448 | −0.447224 | − | 0.894422i | \(-0.647587\pi\) | ||||
−0.447224 | + | 0.894422i | \(0.647587\pi\) | |||||||
\(3\) | 7.31543 | 1.40786 | 0.703928 | − | 0.710272i | \(-0.251428\pi\) | ||||
0.703928 | + | 0.710272i | \(0.251428\pi\) | |||||||
\(4\) | −1.59971 | −0.199964 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −18.5072 | −1.25925 | ||||||||
\(7\) | 2.79284 | 0.150799 | 0.0753996 | − | 0.997153i | \(-0.475977\pi\) | ||||
0.0753996 | + | 0.997153i | \(0.475977\pi\) | |||||||
\(8\) | 24.2861 | 1.07330 | ||||||||
\(9\) | 26.5155 | 0.982057 | ||||||||
\(10\) | −12.6494 | −0.400009 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −11.7026 | −0.281520 | ||||||||
\(13\) | 30.0745 | 0.641628 | 0.320814 | − | 0.947142i | \(-0.396044\pi\) | ||||
0.320814 | + | 0.947142i | \(0.396044\pi\) | |||||||
\(14\) | −7.06555 | −0.134882 | ||||||||
\(15\) | 36.5772 | 0.629612 | ||||||||
\(16\) | −48.6433 | −0.760051 | ||||||||
\(17\) | −93.2244 | −1.33001 | −0.665007 | − | 0.746837i | \(-0.731571\pi\) | ||||
−0.665007 | + | 0.746837i | \(0.731571\pi\) | |||||||
\(18\) | −67.0811 | −0.878398 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −7.99854 | −0.0894264 | ||||||||
\(21\) | 20.4308 | 0.212303 | ||||||||
\(22\) | 27.8287 | 0.269686 | ||||||||
\(23\) | −157.354 | −1.42655 | −0.713274 | − | 0.700885i | \(-0.752789\pi\) | ||||
−0.713274 | + | 0.700885i | \(0.752789\pi\) | |||||||
\(24\) | 177.663 | 1.51106 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −76.0848 | −0.573903 | ||||||||
\(27\) | −3.54404 | −0.0252611 | ||||||||
\(28\) | −4.46773 | −0.0301543 | ||||||||
\(29\) | −209.195 | −1.33954 | −0.669768 | − | 0.742570i | \(-0.733606\pi\) | ||||
−0.669768 | + | 0.742570i | \(0.733606\pi\) | |||||||
\(30\) | −92.5358 | −0.563155 | ||||||||
\(31\) | 151.518 | 0.877850 | 0.438925 | − | 0.898524i | \(-0.355359\pi\) | ||||
0.438925 | + | 0.898524i | \(0.355359\pi\) | |||||||
\(32\) | −71.2273 | −0.393479 | ||||||||
\(33\) | −80.4697 | −0.424484 | ||||||||
\(34\) | 235.847 | 1.18963 | ||||||||
\(35\) | 13.9642 | 0.0674395 | ||||||||
\(36\) | −42.4171 | −0.196376 | ||||||||
\(37\) | −440.562 | −1.95751 | −0.978755 | − | 0.205032i | \(-0.934270\pi\) | ||||
−0.978755 | + | 0.205032i | \(0.934270\pi\) | |||||||
\(38\) | 48.0677 | 0.205200 | ||||||||
\(39\) | 220.008 | 0.903319 | ||||||||
\(40\) | 121.431 | 0.479996 | ||||||||
\(41\) | −296.286 | −1.12859 | −0.564294 | − | 0.825574i | \(-0.690851\pi\) | ||||
−0.564294 | + | 0.825574i | \(0.690851\pi\) | |||||||
\(42\) | −51.6875 | −0.189894 | ||||||||
\(43\) | 514.211 | 1.82364 | 0.911818 | − | 0.410594i | \(-0.134678\pi\) | ||||
0.911818 | + | 0.410594i | \(0.134678\pi\) | |||||||
\(44\) | 17.5968 | 0.0602913 | ||||||||
\(45\) | 132.578 | 0.439189 | ||||||||
\(46\) | 398.087 | 1.27597 | ||||||||
\(47\) | 455.543 | 1.41378 | 0.706891 | − | 0.707323i | \(-0.250097\pi\) | ||||
0.706891 | + | 0.707323i | \(0.250097\pi\) | |||||||
\(48\) | −355.846 | −1.07004 | ||||||||
\(49\) | −335.200 | −0.977260 | ||||||||
\(50\) | −63.2470 | −0.178890 | ||||||||
\(51\) | −681.977 | −1.87247 | ||||||||
\(52\) | −48.1104 | −0.128302 | ||||||||
\(53\) | 37.2991 | 0.0966684 | 0.0483342 | − | 0.998831i | \(-0.484609\pi\) | ||||
0.0483342 | + | 0.998831i | \(0.484609\pi\) | |||||||
\(54\) | 8.96600 | 0.0225948 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 67.8272 | 0.161853 | ||||||||
\(57\) | −138.993 | −0.322984 | ||||||||
\(58\) | 529.238 | 1.19814 | ||||||||
\(59\) | 39.5060 | 0.0871735 | 0.0435868 | − | 0.999050i | \(-0.486122\pi\) | ||||
0.0435868 | + | 0.999050i | \(0.486122\pi\) | |||||||
\(60\) | −58.5128 | −0.125899 | ||||||||
\(61\) | −411.791 | −0.864335 | −0.432168 | − | 0.901793i | \(-0.642251\pi\) | ||||
−0.432168 | + | 0.901793i | \(0.642251\pi\) | |||||||
\(62\) | −383.321 | −0.785191 | ||||||||
\(63\) | 74.0537 | 0.148093 | ||||||||
\(64\) | 569.343 | 1.11200 | ||||||||
\(65\) | 150.372 | 0.286945 | ||||||||
\(66\) | 203.579 | 0.379679 | ||||||||
\(67\) | 227.684 | 0.415164 | 0.207582 | − | 0.978218i | \(-0.433441\pi\) | ||||
0.207582 | + | 0.978218i | \(0.433441\pi\) | |||||||
\(68\) | 149.132 | 0.265954 | ||||||||
\(69\) | −1151.11 | −2.00837 | ||||||||
\(70\) | −35.3278 | −0.0603211 | ||||||||
\(71\) | −364.300 | −0.608936 | −0.304468 | − | 0.952523i | \(-0.598479\pi\) | ||||
−0.304468 | + | 0.952523i | \(0.598479\pi\) | |||||||
\(72\) | 643.959 | 1.05405 | ||||||||
\(73\) | −293.949 | −0.471289 | −0.235644 | − | 0.971839i | \(-0.575720\pi\) | ||||
−0.235644 | + | 0.971839i | \(0.575720\pi\) | |||||||
\(74\) | 1114.57 | 1.75089 | ||||||||
\(75\) | 182.886 | 0.281571 | ||||||||
\(76\) | 30.3945 | 0.0458748 | ||||||||
\(77\) | −30.7212 | −0.0454677 | ||||||||
\(78\) | −556.593 | −0.807972 | ||||||||
\(79\) | 598.450 | 0.852290 | 0.426145 | − | 0.904655i | \(-0.359871\pi\) | ||||
0.426145 | + | 0.904655i | \(0.359871\pi\) | |||||||
\(80\) | −243.216 | −0.339905 | ||||||||
\(81\) | −741.846 | −1.01762 | ||||||||
\(82\) | 749.567 | 1.00946 | ||||||||
\(83\) | −68.9269 | −0.0911531 | −0.0455765 | − | 0.998961i | \(-0.514512\pi\) | ||||
−0.0455765 | + | 0.998961i | \(0.514512\pi\) | |||||||
\(84\) | −32.6834 | −0.0424530 | ||||||||
\(85\) | −466.122 | −0.594800 | ||||||||
\(86\) | −1300.89 | −1.63115 | ||||||||
\(87\) | −1530.35 | −1.88587 | ||||||||
\(88\) | −267.147 | −0.323613 | ||||||||
\(89\) | −896.631 | −1.06790 | −0.533948 | − | 0.845517i | \(-0.679292\pi\) | ||||
−0.533948 | + | 0.845517i | \(0.679292\pi\) | |||||||
\(90\) | −335.406 | −0.392832 | ||||||||
\(91\) | 83.9933 | 0.0967570 | ||||||||
\(92\) | 251.721 | 0.285258 | ||||||||
\(93\) | 1108.42 | 1.23589 | ||||||||
\(94\) | −1152.47 | −1.26455 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −521.058 | −0.553961 | ||||||||
\(97\) | −1202.45 | −1.25867 | −0.629334 | − | 0.777135i | \(-0.716672\pi\) | ||||
−0.629334 | + | 0.777135i | \(0.716672\pi\) | |||||||
\(98\) | 848.016 | 0.874107 | ||||||||
\(99\) | −291.671 | −0.296101 | ||||||||
\(100\) | −39.9927 | −0.0399927 | ||||||||
\(101\) | −1837.97 | −1.81074 | −0.905372 | − | 0.424619i | \(-0.860408\pi\) | ||||
−0.905372 | + | 0.424619i | \(0.860408\pi\) | |||||||
\(102\) | 1725.32 | 1.67482 | ||||||||
\(103\) | 625.355 | 0.598234 | 0.299117 | − | 0.954216i | \(-0.403308\pi\) | ||||
0.299117 | + | 0.954216i | \(0.403308\pi\) | |||||||
\(104\) | 730.392 | 0.688662 | ||||||||
\(105\) | 102.154 | 0.0949450 | ||||||||
\(106\) | −94.3623 | −0.0864648 | ||||||||
\(107\) | 1213.17 | 1.09609 | 0.548046 | − | 0.836448i | \(-0.315372\pi\) | ||||
0.548046 | + | 0.836448i | \(0.315372\pi\) | |||||||
\(108\) | 5.66943 | 0.00505131 | ||||||||
\(109\) | 1586.52 | 1.39414 | 0.697068 | − | 0.717005i | \(-0.254488\pi\) | ||||
0.697068 | + | 0.717005i | \(0.254488\pi\) | |||||||
\(110\) | 139.143 | 0.120607 | ||||||||
\(111\) | −3222.90 | −2.75589 | ||||||||
\(112\) | −135.853 | −0.114615 | ||||||||
\(113\) | 690.468 | 0.574812 | 0.287406 | − | 0.957809i | \(-0.407207\pi\) | ||||
0.287406 | + | 0.957809i | \(0.407207\pi\) | |||||||
\(114\) | 351.636 | 0.288892 | ||||||||
\(115\) | −786.771 | −0.637972 | ||||||||
\(116\) | 334.651 | 0.267858 | ||||||||
\(117\) | 797.441 | 0.630115 | ||||||||
\(118\) | −99.9453 | −0.0779722 | ||||||||
\(119\) | −260.361 | −0.200565 | ||||||||
\(120\) | 888.317 | 0.675765 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1041.78 | 0.773103 | ||||||||
\(123\) | −2167.46 | −1.58889 | ||||||||
\(124\) | −242.384 | −0.175538 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −187.347 | −0.132462 | ||||||||
\(127\) | −638.173 | −0.445895 | −0.222948 | − | 0.974830i | \(-0.571568\pi\) | ||||
−0.222948 | + | 0.974830i | \(0.571568\pi\) | |||||||
\(128\) | −870.550 | −0.601144 | ||||||||
\(129\) | 3761.67 | 2.56742 | ||||||||
\(130\) | −380.424 | −0.256657 | ||||||||
\(131\) | 162.200 | 0.108179 | 0.0540895 | − | 0.998536i | \(-0.482774\pi\) | ||||
0.0540895 | + | 0.998536i | \(0.482774\pi\) | |||||||
\(132\) | 128.728 | 0.0848814 | ||||||||
\(133\) | −53.0640 | −0.0345957 | ||||||||
\(134\) | −576.012 | −0.371342 | ||||||||
\(135\) | −17.7202 | −0.0112971 | ||||||||
\(136\) | −2264.06 | −1.42751 | ||||||||
\(137\) | 1192.01 | 0.743362 | 0.371681 | − | 0.928361i | \(-0.378782\pi\) | ||||
0.371681 | + | 0.928361i | \(0.378782\pi\) | |||||||
\(138\) | 2912.18 | 1.79639 | ||||||||
\(139\) | 483.185 | 0.294843 | 0.147422 | − | 0.989074i | \(-0.452903\pi\) | ||||
0.147422 | + | 0.989074i | \(0.452903\pi\) | |||||||
\(140\) | −22.3387 | −0.0134854 | ||||||||
\(141\) | 3332.49 | 1.99040 | ||||||||
\(142\) | 921.635 | 0.544661 | ||||||||
\(143\) | −330.819 | −0.193458 | ||||||||
\(144\) | −1289.80 | −0.746413 | ||||||||
\(145\) | −1045.98 | −0.599059 | ||||||||
\(146\) | 743.655 | 0.421543 | ||||||||
\(147\) | −2452.13 | −1.37584 | ||||||||
\(148\) | 704.770 | 0.391431 | ||||||||
\(149\) | −359.318 | −0.197560 | −0.0987801 | − | 0.995109i | \(-0.531494\pi\) | ||||
−0.0987801 | + | 0.995109i | \(0.531494\pi\) | |||||||
\(150\) | −462.679 | −0.251851 | ||||||||
\(151\) | 330.088 | 0.177895 | 0.0889475 | − | 0.996036i | \(-0.471650\pi\) | ||||
0.0889475 | + | 0.996036i | \(0.471650\pi\) | |||||||
\(152\) | −461.436 | −0.246233 | ||||||||
\(153\) | −2471.90 | −1.30615 | ||||||||
\(154\) | 77.7211 | 0.0406684 | ||||||||
\(155\) | 757.588 | 0.392587 | ||||||||
\(156\) | −351.948 | −0.180631 | ||||||||
\(157\) | −3721.78 | −1.89191 | −0.945957 | − | 0.324293i | \(-0.894874\pi\) | ||||
−0.945957 | + | 0.324293i | \(0.894874\pi\) | |||||||
\(158\) | −1514.01 | −0.762329 | ||||||||
\(159\) | 272.859 | 0.136095 | ||||||||
\(160\) | −356.136 | −0.175969 | ||||||||
\(161\) | −439.465 | −0.215122 | ||||||||
\(162\) | 1876.78 | 0.910209 | ||||||||
\(163\) | −631.831 | −0.303612 | −0.151806 | − | 0.988410i | \(-0.548509\pi\) | ||||
−0.151806 | + | 0.988410i | \(0.548509\pi\) | |||||||
\(164\) | 473.971 | 0.225676 | ||||||||
\(165\) | −402.349 | −0.189835 | ||||||||
\(166\) | 174.377 | 0.0815316 | ||||||||
\(167\) | 2185.74 | 1.01280 | 0.506401 | − | 0.862298i | \(-0.330975\pi\) | ||||
0.506401 | + | 0.862298i | \(0.330975\pi\) | |||||||
\(168\) | 496.185 | 0.227866 | ||||||||
\(169\) | −1292.52 | −0.588314 | ||||||||
\(170\) | 1179.23 | 0.532018 | ||||||||
\(171\) | −503.795 | −0.225299 | ||||||||
\(172\) | −822.587 | −0.364661 | ||||||||
\(173\) | 4065.62 | 1.78672 | 0.893362 | − | 0.449338i | \(-0.148340\pi\) | ||||
0.893362 | + | 0.449338i | \(0.148340\pi\) | |||||||
\(174\) | 3871.61 | 1.68681 | ||||||||
\(175\) | 69.8210 | 0.0301598 | ||||||||
\(176\) | 535.076 | 0.229164 | ||||||||
\(177\) | 289.003 | 0.122728 | ||||||||
\(178\) | 2268.37 | 0.955177 | ||||||||
\(179\) | −1911.11 | −0.798004 | −0.399002 | − | 0.916950i | \(-0.630643\pi\) | ||||
−0.399002 | + | 0.916950i | \(0.630643\pi\) | |||||||
\(180\) | −212.086 | −0.0878218 | ||||||||
\(181\) | −1127.61 | −0.463062 | −0.231531 | − | 0.972828i | \(-0.574373\pi\) | ||||
−0.231531 | + | 0.972828i | \(0.574373\pi\) | |||||||
\(182\) | −212.493 | −0.0865440 | ||||||||
\(183\) | −3012.43 | −1.21686 | ||||||||
\(184\) | −3821.52 | −1.53112 | ||||||||
\(185\) | −2202.81 | −0.875425 | ||||||||
\(186\) | −2804.16 | −1.10544 | ||||||||
\(187\) | 1025.47 | 0.401014 | ||||||||
\(188\) | −728.735 | −0.282705 | ||||||||
\(189\) | −9.89794 | −0.00380936 | ||||||||
\(190\) | 240.339 | 0.0917684 | ||||||||
\(191\) | 966.220 | 0.366038 | 0.183019 | − | 0.983109i | \(-0.441413\pi\) | ||||
0.183019 | + | 0.983109i | \(0.441413\pi\) | |||||||
\(192\) | 4164.99 | 1.56553 | ||||||||
\(193\) | 915.165 | 0.341321 | 0.170661 | − | 0.985330i | \(-0.445410\pi\) | ||||
0.170661 | + | 0.985330i | \(0.445410\pi\) | |||||||
\(194\) | 3042.07 | 1.12581 | ||||||||
\(195\) | 1100.04 | 0.403977 | ||||||||
\(196\) | 536.222 | 0.195416 | ||||||||
\(197\) | −4781.39 | −1.72924 | −0.864619 | − | 0.502429i | \(-0.832440\pi\) | ||||
−0.864619 | + | 0.502429i | \(0.832440\pi\) | |||||||
\(198\) | 737.892 | 0.264847 | ||||||||
\(199\) | −3438.46 | −1.22485 | −0.612427 | − | 0.790527i | \(-0.709807\pi\) | ||||
−0.612427 | + | 0.790527i | \(0.709807\pi\) | |||||||
\(200\) | 607.153 | 0.214661 | ||||||||
\(201\) | 1665.60 | 0.584491 | ||||||||
\(202\) | 4649.85 | 1.61962 | ||||||||
\(203\) | −584.248 | −0.202001 | ||||||||
\(204\) | 1090.96 | 0.374425 | ||||||||
\(205\) | −1481.43 | −0.504719 | ||||||||
\(206\) | −1582.07 | −0.535089 | ||||||||
\(207\) | −4172.33 | −1.40095 | ||||||||
\(208\) | −1462.92 | −0.487670 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | −258.438 | −0.0849233 | ||||||||
\(211\) | −2149.64 | −0.701362 | −0.350681 | − | 0.936495i | \(-0.614050\pi\) | ||||
−0.350681 | + | 0.936495i | \(0.614050\pi\) | |||||||
\(212\) | −59.6677 | −0.0193302 | ||||||||
\(213\) | −2665.01 | −0.857294 | ||||||||
\(214\) | −3069.18 | −0.980397 | ||||||||
\(215\) | 2571.05 | 0.815555 | ||||||||
\(216\) | −86.0710 | −0.0271129 | ||||||||
\(217\) | 423.164 | 0.132379 | ||||||||
\(218\) | −4013.70 | −1.24698 | ||||||||
\(219\) | −2150.36 | −0.663507 | ||||||||
\(220\) | 87.9840 | 0.0269631 | ||||||||
\(221\) | −2803.68 | −0.853374 | ||||||||
\(222\) | 8153.55 | 2.46500 | ||||||||
\(223\) | −1036.94 | −0.311383 | −0.155691 | − | 0.987806i | \(-0.549761\pi\) | ||||
−0.155691 | + | 0.987806i | \(0.549761\pi\) | |||||||
\(224\) | −198.926 | −0.0593363 | ||||||||
\(225\) | 662.888 | 0.196411 | ||||||||
\(226\) | −1746.80 | −0.514139 | ||||||||
\(227\) | −676.719 | −0.197865 | −0.0989326 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989326 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(228\) | 222.349 | 0.0645851 | ||||||||
\(229\) | 3166.82 | 0.913840 | 0.456920 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456920 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(230\) | 1990.44 | 0.570632 | ||||||||
\(231\) | −224.739 | −0.0640119 | ||||||||
\(232\) | −5080.53 | −1.43773 | ||||||||
\(233\) | 826.349 | 0.232343 | 0.116171 | − | 0.993229i | \(-0.462938\pi\) | ||||
0.116171 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(234\) | −2017.43 | −0.563605 | ||||||||
\(235\) | 2277.71 | 0.632262 | ||||||||
\(236\) | −63.1980 | −0.0174315 | ||||||||
\(237\) | 4377.92 | 1.19990 | ||||||||
\(238\) | 658.682 | 0.179395 | ||||||||
\(239\) | 2581.31 | 0.698623 | 0.349311 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349311 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(240\) | −1779.23 | −0.478537 | ||||||||
\(241\) | 3108.18 | 0.830770 | 0.415385 | − | 0.909646i | \(-0.363647\pi\) | ||||
0.415385 | + | 0.909646i | \(0.363647\pi\) | |||||||
\(242\) | −306.115 | −0.0813134 | ||||||||
\(243\) | −5331.23 | −1.40740 | ||||||||
\(244\) | 658.746 | 0.172836 | ||||||||
\(245\) | −1676.00 | −0.437044 | ||||||||
\(246\) | 5483.41 | 1.42118 | ||||||||
\(247\) | −571.415 | −0.147200 | ||||||||
\(248\) | 3679.77 | 0.942201 | ||||||||
\(249\) | −504.230 | −0.128330 | ||||||||
\(250\) | −316.235 | −0.0800018 | ||||||||
\(251\) | −1220.33 | −0.306878 | −0.153439 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153439 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(252\) | −118.464 | −0.0296133 | ||||||||
\(253\) | 1730.90 | 0.430121 | ||||||||
\(254\) | 1614.50 | 0.398830 | ||||||||
\(255\) | −3409.88 | −0.837393 | ||||||||
\(256\) | −2352.35 | −0.574305 | ||||||||
\(257\) | −6329.14 | −1.53619 | −0.768096 | − | 0.640335i | \(-0.778795\pi\) | ||||
−0.768096 | + | 0.640335i | \(0.778795\pi\) | |||||||
\(258\) | −9516.58 | −2.29642 | ||||||||
\(259\) | −1230.42 | −0.295191 | ||||||||
\(260\) | −240.552 | −0.0573785 | ||||||||
\(261\) | −5546.92 | −1.31550 | ||||||||
\(262\) | −410.345 | −0.0967604 | ||||||||
\(263\) | −2870.36 | −0.672980 | −0.336490 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336490 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(264\) | −1954.30 | −0.455601 | ||||||||
\(265\) | 186.496 | 0.0432314 | ||||||||
\(266\) | 134.245 | 0.0309440 | ||||||||
\(267\) | −6559.25 | −1.50344 | ||||||||
\(268\) | −364.227 | −0.0830176 | ||||||||
\(269\) | −8202.73 | −1.85922 | −0.929609 | − | 0.368548i | \(-0.879855\pi\) | ||||
−0.929609 | + | 0.368548i | \(0.879855\pi\) | |||||||
\(270\) | 44.8300 | 0.0101047 | ||||||||
\(271\) | −2243.52 | −0.502894 | −0.251447 | − | 0.967871i | \(-0.580906\pi\) | ||||
−0.251447 | + | 0.967871i | \(0.580906\pi\) | |||||||
\(272\) | 4534.74 | 1.01088 | ||||||||
\(273\) | 614.447 | 0.136220 | ||||||||
\(274\) | −3015.65 | −0.664898 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 1841.45 | 0.401602 | ||||||||
\(277\) | −2622.08 | −0.568757 | −0.284378 | − | 0.958712i | \(-0.591787\pi\) | ||||
−0.284378 | + | 0.958712i | \(0.591787\pi\) | |||||||
\(278\) | −1222.40 | −0.263722 | ||||||||
\(279\) | 4017.57 | 0.862099 | ||||||||
\(280\) | 339.136 | 0.0723831 | ||||||||
\(281\) | −3802.38 | −0.807228 | −0.403614 | − | 0.914929i | \(-0.632246\pi\) | ||||
−0.403614 | + | 0.914929i | \(0.632246\pi\) | |||||||
\(282\) | −8430.80 | −1.78031 | ||||||||
\(283\) | −5545.13 | −1.16475 | −0.582374 | − | 0.812921i | \(-0.697876\pi\) | ||||
−0.582374 | + | 0.812921i | \(0.697876\pi\) | |||||||
\(284\) | 582.774 | 0.121765 | ||||||||
\(285\) | −694.966 | −0.144443 | ||||||||
\(286\) | 836.933 | 0.173038 | ||||||||
\(287\) | −827.479 | −0.170190 | ||||||||
\(288\) | −1888.63 | −0.386419 | ||||||||
\(289\) | 3777.79 | 0.768938 | ||||||||
\(290\) | 2646.19 | 0.535827 | ||||||||
\(291\) | −8796.48 | −1.77202 | ||||||||
\(292\) | 470.232 | 0.0942406 | ||||||||
\(293\) | −3593.74 | −0.716549 | −0.358274 | − | 0.933616i | \(-0.616635\pi\) | ||||
−0.358274 | + | 0.933616i | \(0.616635\pi\) | |||||||
\(294\) | 6203.60 | 1.23062 | ||||||||
\(295\) | 197.530 | 0.0389852 | ||||||||
\(296\) | −10699.5 | −2.10100 | ||||||||
\(297\) | 38.9845 | 0.00761652 | ||||||||
\(298\) | 909.031 | 0.176707 | ||||||||
\(299\) | −4732.35 | −0.915313 | ||||||||
\(300\) | −292.564 | −0.0563040 | ||||||||
\(301\) | 1436.11 | 0.275003 | ||||||||
\(302\) | −835.082 | −0.159118 | ||||||||
\(303\) | −13445.6 | −2.54927 | ||||||||
\(304\) | 924.222 | 0.174368 | ||||||||
\(305\) | −2058.96 | −0.386543 | ||||||||
\(306\) | 6253.60 | 1.16828 | ||||||||
\(307\) | 7243.62 | 1.34663 | 0.673315 | − | 0.739356i | \(-0.264870\pi\) | ||||
0.673315 | + | 0.739356i | \(0.264870\pi\) | |||||||
\(308\) | 49.1450 | 0.00909188 | ||||||||
\(309\) | 4574.74 | 0.842227 | ||||||||
\(310\) | −1916.61 | −0.351148 | ||||||||
\(311\) | −7399.74 | −1.34920 | −0.674599 | − | 0.738184i | \(-0.735684\pi\) | ||||
−0.674599 | + | 0.738184i | \(0.735684\pi\) | |||||||
\(312\) | 5343.14 | 0.969537 | ||||||||
\(313\) | 1196.71 | 0.216109 | 0.108055 | − | 0.994145i | \(-0.465538\pi\) | ||||
0.108055 | + | 0.994145i | \(0.465538\pi\) | |||||||
\(314\) | 9415.66 | 1.69222 | ||||||||
\(315\) | 370.268 | 0.0662294 | ||||||||
\(316\) | −957.346 | −0.170427 | ||||||||
\(317\) | 6918.56 | 1.22582 | 0.612910 | − | 0.790153i | \(-0.289999\pi\) | ||||
0.612910 | + | 0.790153i | \(0.289999\pi\) | |||||||
\(318\) | −690.301 | −0.121730 | ||||||||
\(319\) | 2301.15 | 0.403885 | ||||||||
\(320\) | 2846.71 | 0.497300 | ||||||||
\(321\) | 8874.89 | 1.54314 | ||||||||
\(322\) | 1111.79 | 0.192416 | ||||||||
\(323\) | 1771.26 | 0.305126 | ||||||||
\(324\) | 1186.74 | 0.203487 | ||||||||
\(325\) | 751.862 | 0.128326 | ||||||||
\(326\) | 1598.46 | 0.271565 | ||||||||
\(327\) | 11606.1 | 1.96274 | ||||||||
\(328\) | −7195.63 | −1.21132 | ||||||||
\(329\) | 1272.26 | 0.213197 | ||||||||
\(330\) | 1017.89 | 0.169798 | ||||||||
\(331\) | 807.068 | 0.134020 | 0.0670098 | − | 0.997752i | \(-0.478654\pi\) | ||||
0.0670098 | + | 0.997752i | \(0.478654\pi\) | |||||||
\(332\) | 110.263 | 0.0182273 | ||||||||
\(333\) | −11681.7 | −1.92239 | ||||||||
\(334\) | −5529.67 | −0.905899 | ||||||||
\(335\) | 1138.42 | 0.185667 | ||||||||
\(336\) | −993.822 | −0.161361 | ||||||||
\(337\) | 7218.46 | 1.16681 | 0.583404 | − | 0.812182i | \(-0.301720\pi\) | ||||
0.583404 | + | 0.812182i | \(0.301720\pi\) | |||||||
\(338\) | 3269.93 | 0.526216 | ||||||||
\(339\) | 5051.07 | 0.809253 | ||||||||
\(340\) | 745.659 | 0.118938 | ||||||||
\(341\) | −1666.69 | −0.264682 | ||||||||
\(342\) | 1274.54 | 0.201518 | ||||||||
\(343\) | −1894.10 | −0.298169 | ||||||||
\(344\) | 12488.2 | 1.95732 | ||||||||
\(345\) | −5755.57 | −0.898172 | ||||||||
\(346\) | −10285.5 | −1.59813 | ||||||||
\(347\) | 6598.36 | 1.02080 | 0.510401 | − | 0.859936i | \(-0.329497\pi\) | ||||
0.510401 | + | 0.859936i | \(0.329497\pi\) | |||||||
\(348\) | 2448.12 | 0.377106 | ||||||||
\(349\) | 10762.2 | 1.65068 | 0.825342 | − | 0.564633i | \(-0.190982\pi\) | ||||
0.825342 | + | 0.564633i | \(0.190982\pi\) | |||||||
\(350\) | −176.639 | −0.0269764 | ||||||||
\(351\) | −106.585 | −0.0162083 | ||||||||
\(352\) | 783.500 | 0.118638 | ||||||||
\(353\) | −5983.40 | −0.902165 | −0.451082 | − | 0.892482i | \(-0.648962\pi\) | ||||
−0.451082 | + | 0.892482i | \(0.648962\pi\) | |||||||
\(354\) | −731.143 | −0.109774 | ||||||||
\(355\) | −1821.50 | −0.272324 | ||||||||
\(356\) | 1434.35 | 0.213540 | ||||||||
\(357\) | −1904.65 | −0.282367 | ||||||||
\(358\) | 4834.87 | 0.713773 | ||||||||
\(359\) | 4034.06 | 0.593062 | 0.296531 | − | 0.955023i | \(-0.404170\pi\) | ||||
0.296531 | + | 0.955023i | \(0.404170\pi\) | |||||||
\(360\) | 3219.80 | 0.471384 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 2852.71 | 0.414185 | ||||||||
\(363\) | 885.167 | 0.127987 | ||||||||
\(364\) | −134.365 | −0.0193479 | ||||||||
\(365\) | −1469.74 | −0.210767 | ||||||||
\(366\) | 7621.09 | 1.08842 | ||||||||
\(367\) | 5455.32 | 0.775928 | 0.387964 | − | 0.921675i | \(-0.373178\pi\) | ||||
0.387964 | + | 0.921675i | \(0.373178\pi\) | |||||||
\(368\) | 7654.22 | 1.08425 | ||||||||
\(369\) | −7856.18 | −1.10834 | ||||||||
\(370\) | 5572.84 | 0.783022 | ||||||||
\(371\) | 104.170 | 0.0145775 | ||||||||
\(372\) | −1773.14 | −0.247132 | ||||||||
\(373\) | −5023.06 | −0.697277 | −0.348639 | − | 0.937257i | \(-0.613356\pi\) | ||||
−0.348639 | + | 0.937257i | \(0.613356\pi\) | |||||||
\(374\) | −2594.31 | −0.358686 | ||||||||
\(375\) | 914.429 | 0.125922 | ||||||||
\(376\) | 11063.4 | 1.51742 | ||||||||
\(377\) | −6291.44 | −0.859484 | ||||||||
\(378\) | 25.0406 | 0.00340727 | ||||||||
\(379\) | 8955.56 | 1.21376 | 0.606882 | − | 0.794792i | \(-0.292420\pi\) | ||||
0.606882 | + | 0.794792i | \(0.292420\pi\) | |||||||
\(380\) | 151.972 | 0.0205158 | ||||||||
\(381\) | −4668.51 | −0.627756 | ||||||||
\(382\) | −2444.42 | −0.327402 | ||||||||
\(383\) | −7565.40 | −1.00933 | −0.504666 | − | 0.863315i | \(-0.668384\pi\) | ||||
−0.504666 | + | 0.863315i | \(0.668384\pi\) | |||||||
\(384\) | −6368.45 | −0.846324 | ||||||||
\(385\) | −153.606 | −0.0203338 | ||||||||
\(386\) | −2315.26 | −0.305294 | ||||||||
\(387\) | 13634.6 | 1.79092 | ||||||||
\(388\) | 1923.58 | 0.251688 | ||||||||
\(389\) | −10239.4 | −1.33460 | −0.667301 | − | 0.744788i | \(-0.732551\pi\) | ||||
−0.667301 | + | 0.744788i | \(0.732551\pi\) | |||||||
\(390\) | −2782.97 | −0.361336 | ||||||||
\(391\) | 14669.3 | 1.89733 | ||||||||
\(392\) | −8140.70 | −1.04890 | ||||||||
\(393\) | 1186.56 | 0.152300 | ||||||||
\(394\) | 12096.3 | 1.54671 | ||||||||
\(395\) | 2992.25 | 0.381156 | ||||||||
\(396\) | 466.588 | 0.0592095 | ||||||||
\(397\) | 6185.73 | 0.781997 | 0.390998 | − | 0.920391i | \(-0.372130\pi\) | ||||
0.390998 | + | 0.920391i | \(0.372130\pi\) | |||||||
\(398\) | 8698.89 | 1.09557 | ||||||||
\(399\) | −388.186 | −0.0487058 | ||||||||
\(400\) | −1216.08 | −0.152010 | ||||||||
\(401\) | 14441.7 | 1.79847 | 0.899233 | − | 0.437469i | \(-0.144125\pi\) | ||||
0.899233 | + | 0.437469i | \(0.144125\pi\) | |||||||
\(402\) | −4213.78 | −0.522796 | ||||||||
\(403\) | 4556.81 | 0.563253 | ||||||||
\(404\) | 2940.22 | 0.362083 | ||||||||
\(405\) | −3709.23 | −0.455094 | ||||||||
\(406\) | 1478.08 | 0.180679 | ||||||||
\(407\) | 4846.18 | 0.590212 | ||||||||
\(408\) | −16562.6 | −2.00973 | ||||||||
\(409\) | −4076.86 | −0.492879 | −0.246440 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246440 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(410\) | 3747.84 | 0.451445 | ||||||||
\(411\) | 8720.09 | 1.04655 | ||||||||
\(412\) | −1000.39 | −0.119625 | ||||||||
\(413\) | 110.334 | 0.0131457 | ||||||||
\(414\) | 10555.5 | 1.25308 | ||||||||
\(415\) | −344.634 | −0.0407649 | ||||||||
\(416\) | −2142.12 | −0.252467 | ||||||||
\(417\) | 3534.71 | 0.415097 | ||||||||
\(418\) | −528.745 | −0.0618702 | ||||||||
\(419\) | −7212.76 | −0.840970 | −0.420485 | − | 0.907299i | \(-0.638140\pi\) | ||||
−0.420485 | + | 0.907299i | \(0.638140\pi\) | |||||||
\(420\) | −163.417 | −0.0189855 | ||||||||
\(421\) | −1114.24 | −0.128990 | −0.0644949 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644949 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(422\) | 5438.34 | 0.627332 | ||||||||
\(423\) | 12079.0 | 1.38841 | ||||||||
\(424\) | 905.850 | 0.103755 | ||||||||
\(425\) | −2330.61 | −0.266003 | ||||||||
\(426\) | 6742.16 | 0.766804 | ||||||||
\(427\) | −1150.07 | −0.130341 | ||||||||
\(428\) | −1940.72 | −0.219179 | ||||||||
\(429\) | −2420.09 | −0.272361 | ||||||||
\(430\) | −6504.46 | −0.729471 | ||||||||
\(431\) | 11702.2 | 1.30783 | 0.653913 | − | 0.756570i | \(-0.273126\pi\) | ||||
0.653913 | + | 0.756570i | \(0.273126\pi\) | |||||||
\(432\) | 172.394 | 0.0191998 | ||||||||
\(433\) | 3023.18 | 0.335530 | 0.167765 | − | 0.985827i | \(-0.446345\pi\) | ||||
0.167765 | + | 0.985827i | \(0.446345\pi\) | |||||||
\(434\) | −1070.56 | −0.118406 | ||||||||
\(435\) | −7651.76 | −0.843388 | ||||||||
\(436\) | −2537.97 | −0.278776 | ||||||||
\(437\) | 2989.73 | 0.327273 | ||||||||
\(438\) | 5440.16 | 0.593472 | ||||||||
\(439\) | 7581.15 | 0.824211 | 0.412105 | − | 0.911136i | \(-0.364794\pi\) | ||||
0.412105 | + | 0.911136i | \(0.364794\pi\) | |||||||
\(440\) | −1335.74 | −0.144724 | ||||||||
\(441\) | −8888.01 | −0.959725 | ||||||||
\(442\) | 7092.96 | 0.763298 | ||||||||
\(443\) | 9398.82 | 1.00802 | 0.504008 | − | 0.863699i | \(-0.331858\pi\) | ||||
0.504008 | + | 0.863699i | \(0.331858\pi\) | |||||||
\(444\) | 5155.70 | 0.551078 | ||||||||
\(445\) | −4483.16 | −0.477578 | ||||||||
\(446\) | 2623.32 | 0.278516 | ||||||||
\(447\) | −2628.57 | −0.278136 | ||||||||
\(448\) | 1590.08 | 0.167688 | ||||||||
\(449\) | −8511.21 | −0.894586 | −0.447293 | − | 0.894388i | \(-0.647612\pi\) | ||||
−0.447293 | + | 0.894388i | \(0.647612\pi\) | |||||||
\(450\) | −1677.03 | −0.175680 | ||||||||
\(451\) | 3259.14 | 0.340282 | ||||||||
\(452\) | −1104.55 | −0.114942 | ||||||||
\(453\) | 2414.73 | 0.250451 | ||||||||
\(454\) | 1712.02 | 0.176980 | ||||||||
\(455\) | 419.966 | 0.0432710 | ||||||||
\(456\) | −3375.60 | −0.346660 | ||||||||
\(457\) | 15373.8 | 1.57364 | 0.786820 | − | 0.617182i | \(-0.211726\pi\) | ||||
0.786820 | + | 0.617182i | \(0.211726\pi\) | |||||||
\(458\) | −8011.68 | −0.817382 | ||||||||
\(459\) | 330.391 | 0.0335977 | ||||||||
\(460\) | 1258.60 | 0.127571 | ||||||||
\(461\) | 11658.4 | 1.17785 | 0.588923 | − | 0.808189i | \(-0.299552\pi\) | ||||
0.588923 | + | 0.808189i | \(0.299552\pi\) | |||||||
\(462\) | 568.563 | 0.0572553 | ||||||||
\(463\) | −10435.9 | −1.04751 | −0.523757 | − | 0.851868i | \(-0.675470\pi\) | ||||
−0.523757 | + | 0.851868i | \(0.675470\pi\) | |||||||
\(464\) | 10175.9 | 1.01812 | ||||||||
\(465\) | 5542.08 | 0.552705 | ||||||||
\(466\) | −2090.56 | −0.207819 | ||||||||
\(467\) | −17050.1 | −1.68948 | −0.844739 | − | 0.535179i | \(-0.820244\pi\) | ||||
−0.844739 | + | 0.535179i | \(0.820244\pi\) | |||||||
\(468\) | −1275.67 | −0.126000 | ||||||||
\(469\) | 635.884 | 0.0626064 | ||||||||
\(470\) | −5762.34 | −0.565525 | ||||||||
\(471\) | −27226.4 | −2.66354 | ||||||||
\(472\) | 959.446 | 0.0935638 | ||||||||
\(473\) | −5656.32 | −0.549847 | ||||||||
\(474\) | −11075.6 | −1.07325 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | 416.502 | 0.0401057 | ||||||||
\(477\) | 989.006 | 0.0949339 | ||||||||
\(478\) | −6530.39 | −0.624881 | ||||||||
\(479\) | 973.555 | 0.0928661 | 0.0464331 | − | 0.998921i | \(-0.485215\pi\) | ||||
0.0464331 | + | 0.998921i | \(0.485215\pi\) | |||||||
\(480\) | −2605.29 | −0.247739 | ||||||||
\(481\) | −13249.7 | −1.25599 | ||||||||
\(482\) | −7863.32 | −0.743080 | ||||||||
\(483\) | −3214.88 | −0.302861 | ||||||||
\(484\) | −193.565 | −0.0181785 | ||||||||
\(485\) | −6012.27 | −0.562893 | ||||||||
\(486\) | 13487.4 | 1.25885 | ||||||||
\(487\) | 6959.17 | 0.647536 | 0.323768 | − | 0.946137i | \(-0.395050\pi\) | ||||
0.323768 | + | 0.946137i | \(0.395050\pi\) | |||||||
\(488\) | −10000.8 | −0.927695 | ||||||||
\(489\) | −4622.11 | −0.427442 | ||||||||
\(490\) | 4240.08 | 0.390913 | ||||||||
\(491\) | 21221.7 | 1.95055 | 0.975276 | − | 0.220989i | \(-0.0709285\pi\) | ||||
0.975276 | + | 0.220989i | \(0.0709285\pi\) | |||||||
\(492\) | 3467.30 | 0.317720 | ||||||||
\(493\) | 19502.1 | 1.78160 | ||||||||
\(494\) | 1445.61 | 0.131662 | ||||||||
\(495\) | −1458.35 | −0.132421 | ||||||||
\(496\) | −7370.31 | −0.667211 | ||||||||
\(497\) | −1017.43 | −0.0918271 | ||||||||
\(498\) | 1275.64 | 0.114785 | ||||||||
\(499\) | 19202.6 | 1.72269 | 0.861347 | − | 0.508017i | \(-0.169621\pi\) | ||||
0.861347 | + | 0.508017i | \(0.169621\pi\) | |||||||
\(500\) | −199.964 | −0.0178853 | ||||||||
\(501\) | 15989.7 | 1.42588 | ||||||||
\(502\) | 3087.28 | 0.274486 | ||||||||
\(503\) | −18828.7 | −1.66905 | −0.834524 | − | 0.550971i | \(-0.814257\pi\) | ||||
−0.834524 | + | 0.550971i | \(0.814257\pi\) | |||||||
\(504\) | 1798.48 | 0.158949 | ||||||||
\(505\) | −9189.86 | −0.809789 | ||||||||
\(506\) | −4378.96 | −0.384720 | ||||||||
\(507\) | −9455.38 | −0.828261 | ||||||||
\(508\) | 1020.89 | 0.0891628 | ||||||||
\(509\) | 8686.23 | 0.756406 | 0.378203 | − | 0.925723i | \(-0.376542\pi\) | ||||
0.378203 | + | 0.925723i | \(0.376542\pi\) | |||||||
\(510\) | 8626.60 | 0.749004 | ||||||||
\(511\) | −820.952 | −0.0710700 | ||||||||
\(512\) | 12915.6 | 1.11483 | ||||||||
\(513\) | 67.3368 | 0.00579531 | ||||||||
\(514\) | 16012.0 | 1.37404 | ||||||||
\(515\) | 3126.78 | 0.267538 | ||||||||
\(516\) | −6017.58 | −0.513390 | ||||||||
\(517\) | −5010.97 | −0.426271 | ||||||||
\(518\) | 3112.81 | 0.264033 | ||||||||
\(519\) | 29741.8 | 2.51545 | ||||||||
\(520\) | 3651.96 | 0.307979 | ||||||||
\(521\) | 20241.2 | 1.70208 | 0.851040 | − | 0.525101i | \(-0.175973\pi\) | ||||
0.851040 | + | 0.525101i | \(0.175973\pi\) | |||||||
\(522\) | 14033.0 | 1.17665 | ||||||||
\(523\) | −20045.4 | −1.67596 | −0.837978 | − | 0.545705i | \(-0.816262\pi\) | ||||
−0.837978 | + | 0.545705i | \(0.816262\pi\) | |||||||
\(524\) | −259.472 | −0.0216318 | ||||||||
\(525\) | 510.771 | 0.0424607 | ||||||||
\(526\) | 7261.65 | 0.601945 | ||||||||
\(527\) | −14125.1 | −1.16755 | ||||||||
\(528\) | 3914.31 | 0.322630 | ||||||||
\(529\) | 12593.3 | 1.03504 | ||||||||
\(530\) | −471.811 | −0.0386683 | ||||||||
\(531\) | 1047.52 | 0.0856094 | ||||||||
\(532\) | 84.8869 | 0.00691788 | ||||||||
\(533\) | −8910.64 | −0.724133 | ||||||||
\(534\) | 16594.1 | 1.34475 | ||||||||
\(535\) | 6065.87 | 0.490188 | ||||||||
\(536\) | 5529.55 | 0.445597 | ||||||||
\(537\) | −13980.6 | −1.12347 | ||||||||
\(538\) | 20751.9 | 1.66297 | ||||||||
\(539\) | 3687.20 | 0.294655 | ||||||||
\(540\) | 28.3472 | 0.00225901 | ||||||||
\(541\) | −4019.89 | −0.319462 | −0.159731 | − | 0.987161i | \(-0.551063\pi\) | ||||
−0.159731 | + | 0.987161i | \(0.551063\pi\) | |||||||
\(542\) | 5675.85 | 0.449813 | ||||||||
\(543\) | −8248.92 | −0.651925 | ||||||||
\(544\) | 6640.12 | 0.523332 | ||||||||
\(545\) | 7932.59 | 0.623477 | ||||||||
\(546\) | −1554.48 | −0.121842 | ||||||||
\(547\) | −10463.0 | −0.817852 | −0.408926 | − | 0.912568i | \(-0.634097\pi\) | ||||
−0.408926 | + | 0.912568i | \(0.634097\pi\) | |||||||
\(548\) | −1906.87 | −0.148645 | ||||||||
\(549\) | −10918.9 | −0.848827 | ||||||||
\(550\) | 695.717 | 0.0539372 | ||||||||
\(551\) | 3974.71 | 0.307311 | ||||||||
\(552\) | −27956.1 | −2.15560 | ||||||||
\(553\) | 1671.38 | 0.128525 | ||||||||
\(554\) | 6633.55 | 0.508723 | ||||||||
\(555\) | −16114.5 | −1.23247 | ||||||||
\(556\) | −772.955 | −0.0589579 | ||||||||
\(557\) | 2301.85 | 0.175103 | 0.0875516 | − | 0.996160i | \(-0.472096\pi\) | ||||
0.0875516 | + | 0.996160i | \(0.472096\pi\) | |||||||
\(558\) | −10164.0 | −0.771102 | ||||||||
\(559\) | 15464.6 | 1.17010 | ||||||||
\(560\) | −679.264 | −0.0512574 | ||||||||
\(561\) | 7501.74 | 0.564570 | ||||||||
\(562\) | 9619.57 | 0.722023 | ||||||||
\(563\) | 23635.2 | 1.76928 | 0.884641 | − | 0.466273i | \(-0.154403\pi\) | ||||
0.884641 | + | 0.466273i | \(0.154403\pi\) | |||||||
\(564\) | −5331.01 | −0.398007 | ||||||||
\(565\) | 3452.34 | 0.257064 | ||||||||
\(566\) | 14028.5 | 1.04181 | ||||||||
\(567\) | −2071.86 | −0.153456 | ||||||||
\(568\) | −8847.43 | −0.653574 | ||||||||
\(569\) | 2213.32 | 0.163071 | 0.0815355 | − | 0.996670i | \(-0.474018\pi\) | ||||
0.0815355 | + | 0.996670i | \(0.474018\pi\) | |||||||
\(570\) | 1758.18 | 0.129197 | ||||||||
\(571\) | −3401.12 | −0.249269 | −0.124634 | − | 0.992203i | \(-0.539776\pi\) | ||||
−0.124634 | + | 0.992203i | \(0.539776\pi\) | |||||||
\(572\) | 529.215 | 0.0386846 | ||||||||
\(573\) | 7068.32 | 0.515328 | ||||||||
\(574\) | 2093.42 | 0.152226 | ||||||||
\(575\) | −3933.85 | −0.285310 | ||||||||
\(576\) | 15096.4 | 1.09204 | ||||||||
\(577\) | 18870.2 | 1.36149 | 0.680743 | − | 0.732523i | \(-0.261657\pi\) | ||||
0.680743 | + | 0.732523i | \(0.261657\pi\) | |||||||
\(578\) | −9557.36 | −0.687774 | ||||||||
\(579\) | 6694.83 | 0.480531 | ||||||||
\(580\) | 1673.26 | 0.119790 | ||||||||
\(581\) | −192.502 | −0.0137458 | ||||||||
\(582\) | 22254.0 | 1.58498 | ||||||||
\(583\) | −410.290 | −0.0291466 | ||||||||
\(584\) | −7138.87 | −0.505836 | ||||||||
\(585\) | 3987.21 | 0.281796 | ||||||||
\(586\) | 9091.74 | 0.640915 | ||||||||
\(587\) | −15453.5 | −1.08660 | −0.543300 | − | 0.839538i | \(-0.682825\pi\) | ||||
−0.543300 | + | 0.839538i | \(0.682825\pi\) | |||||||
\(588\) | 3922.70 | 0.275118 | ||||||||
\(589\) | −2878.83 | −0.201393 | ||||||||
\(590\) | −499.727 | −0.0348702 | ||||||||
\(591\) | −34977.9 | −2.43452 | ||||||||
\(592\) | 21430.4 | 1.48781 | ||||||||
\(593\) | −4246.51 | −0.294069 | −0.147035 | − | 0.989131i | \(-0.546973\pi\) | ||||
−0.147035 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(594\) | −98.6260 | −0.00681258 | ||||||||
\(595\) | −1301.80 | −0.0896954 | ||||||||
\(596\) | 574.804 | 0.0395049 | ||||||||
\(597\) | −25153.8 | −1.72442 | ||||||||
\(598\) | 11972.3 | 0.818700 | ||||||||
\(599\) | 3506.61 | 0.239192 | 0.119596 | − | 0.992823i | \(-0.461840\pi\) | ||||
0.119596 | + | 0.992823i | \(0.461840\pi\) | |||||||
\(600\) | 4441.58 | 0.302212 | ||||||||
\(601\) | 4288.64 | 0.291077 | 0.145539 | − | 0.989353i | \(-0.453509\pi\) | ||||
0.145539 | + | 0.989353i | \(0.453509\pi\) | |||||||
\(602\) | −3633.18 | −0.245976 | ||||||||
\(603\) | 6037.15 | 0.407715 | ||||||||
\(604\) | −528.044 | −0.0355725 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 34015.7 | 2.28018 | ||||||||
\(607\) | 3585.23 | 0.239736 | 0.119868 | − | 0.992790i | \(-0.461753\pi\) | ||||
0.119868 | + | 0.992790i | \(0.461753\pi\) | |||||||
\(608\) | 1353.32 | 0.0902702 | ||||||||
\(609\) | −4274.03 | −0.284388 | ||||||||
\(610\) | 5208.91 | 0.345742 | ||||||||
\(611\) | 13700.2 | 0.907122 | ||||||||
\(612\) | 3954.31 | 0.261182 | ||||||||
\(613\) | 22008.4 | 1.45010 | 0.725049 | − | 0.688697i | \(-0.241817\pi\) | ||||
0.725049 | + | 0.688697i | \(0.241817\pi\) | |||||||
\(614\) | −18325.5 | −1.20449 | ||||||||
\(615\) | −10837.3 | −0.710572 | ||||||||
\(616\) | −746.099 | −0.0488007 | ||||||||
\(617\) | −29571.3 | −1.92949 | −0.964747 | − | 0.263181i | \(-0.915228\pi\) | ||||
−0.964747 | + | 0.263181i | \(0.915228\pi\) | |||||||
\(618\) | −11573.5 | −0.753327 | ||||||||
\(619\) | 8655.78 | 0.562044 | 0.281022 | − | 0.959701i | \(-0.409327\pi\) | ||||
0.281022 | + | 0.959701i | \(0.409327\pi\) | |||||||
\(620\) | −1211.92 | −0.0785030 | ||||||||
\(621\) | 557.670 | 0.0360363 | ||||||||
\(622\) | 18720.5 | 1.20679 | ||||||||
\(623\) | −2504.15 | −0.161038 | ||||||||
\(624\) | −10701.9 | −0.686569 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −3027.54 | −0.193298 | ||||||||
\(627\) | 1528.93 | 0.0973834 | ||||||||
\(628\) | 5953.76 | 0.378314 | ||||||||
\(629\) | 41071.1 | 2.60352 | ||||||||
\(630\) | −936.734 | −0.0592387 | ||||||||
\(631\) | 15795.8 | 0.996544 | 0.498272 | − | 0.867021i | \(-0.333968\pi\) | ||||
0.498272 | + | 0.867021i | \(0.333968\pi\) | |||||||
\(632\) | 14534.0 | 0.914767 | ||||||||
\(633\) | −15725.6 | −0.987417 | ||||||||
\(634\) | −17503.1 | −1.09643 | ||||||||
\(635\) | −3190.86 | −0.199410 | ||||||||
\(636\) | −436.495 | −0.0272141 | ||||||||
\(637\) | −10081.0 | −0.627037 | ||||||||
\(638\) | −5821.62 | −0.361254 | ||||||||
\(639\) | −9659.61 | −0.598010 | ||||||||
\(640\) | −4352.75 | −0.268840 | ||||||||
\(641\) | −11949.2 | −0.736295 | −0.368147 | − | 0.929767i | \(-0.620008\pi\) | ||||
−0.368147 | + | 0.929767i | \(0.620008\pi\) | |||||||
\(642\) | −22452.4 | −1.38026 | ||||||||
\(643\) | −9936.99 | −0.609451 | −0.304725 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304725 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(644\) | 703.016 | 0.0430166 | ||||||||
\(645\) | 18808.4 | 1.14818 | ||||||||
\(646\) | −4481.08 | −0.272919 | ||||||||
\(647\) | −384.498 | −0.0233635 | −0.0116818 | − | 0.999932i | \(-0.503719\pi\) | ||||
−0.0116818 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(648\) | −18016.5 | −1.09222 | ||||||||
\(649\) | −434.566 | −0.0262838 | ||||||||
\(650\) | −1902.12 | −0.114781 | ||||||||
\(651\) | 3095.63 | 0.186371 | ||||||||
\(652\) | 1010.75 | 0.0607114 | ||||||||
\(653\) | −4589.11 | −0.275016 | −0.137508 | − | 0.990501i | \(-0.543909\pi\) | ||||
−0.137508 | + | 0.990501i | \(0.543909\pi\) | |||||||
\(654\) | −29361.9 | −1.75557 | ||||||||
\(655\) | 810.998 | 0.0483791 | ||||||||
\(656\) | 14412.3 | 0.857784 | ||||||||
\(657\) | −7794.21 | −0.462833 | ||||||||
\(658\) | −3218.66 | −0.190694 | ||||||||
\(659\) | −27923.7 | −1.65061 | −0.825305 | − | 0.564687i | \(-0.808997\pi\) | ||||
−0.825305 | + | 0.564687i | \(0.808997\pi\) | |||||||
\(660\) | 643.641 | 0.0379601 | ||||||||
\(661\) | 1983.81 | 0.116734 | 0.0583671 | − | 0.998295i | \(-0.481411\pi\) | ||||
0.0583671 | + | 0.998295i | \(0.481411\pi\) | |||||||
\(662\) | −2041.79 | −0.119873 | ||||||||
\(663\) | −20510.1 | −1.20143 | ||||||||
\(664\) | −1673.97 | −0.0978350 | ||||||||
\(665\) | −265.320 | −0.0154717 | ||||||||
\(666\) | 29553.4 | 1.71947 | ||||||||
\(667\) | 32917.7 | 1.91091 | ||||||||
\(668\) | −3496.55 | −0.202524 | ||||||||
\(669\) | −7585.63 | −0.438382 | ||||||||
\(670\) | −2880.06 | −0.166069 | ||||||||
\(671\) | 4529.70 | 0.260607 | ||||||||
\(672\) | −1455.23 | −0.0835369 | ||||||||
\(673\) | −18166.4 | −1.04051 | −0.520254 | − | 0.854011i | \(-0.674163\pi\) | ||||
−0.520254 | + | 0.854011i | \(0.674163\pi\) | |||||||
\(674\) | −18261.8 | −1.04365 | ||||||||
\(675\) | −88.6010 | −0.00505223 | ||||||||
\(676\) | 2067.66 | 0.117641 | ||||||||
\(677\) | 13351.3 | 0.757948 | 0.378974 | − | 0.925407i | \(-0.376277\pi\) | ||||
0.378974 | + | 0.925407i | \(0.376277\pi\) | |||||||
\(678\) | −12778.6 | −0.723834 | ||||||||
\(679\) | −3358.26 | −0.189806 | ||||||||
\(680\) | −11320.3 | −0.638402 | ||||||||
\(681\) | −4950.49 | −0.278566 | ||||||||
\(682\) | 4216.53 | 0.236744 | ||||||||
\(683\) | 13189.1 | 0.738896 | 0.369448 | − | 0.929251i | \(-0.379547\pi\) | ||||
0.369448 | + | 0.929251i | \(0.379547\pi\) | |||||||
\(684\) | 805.926 | 0.0450517 | ||||||||
\(685\) | 5960.07 | 0.332442 | ||||||||
\(686\) | 4791.86 | 0.266697 | ||||||||
\(687\) | 23166.7 | 1.28655 | ||||||||
\(688\) | −25012.9 | −1.38606 | ||||||||
\(689\) | 1121.75 | 0.0620252 | ||||||||
\(690\) | 14560.9 | 0.803368 | ||||||||
\(691\) | −23878.4 | −1.31458 | −0.657292 | − | 0.753636i | \(-0.728298\pi\) | ||||
−0.657292 | + | 0.753636i | \(0.728298\pi\) | |||||||
\(692\) | −6503.80 | −0.357280 | ||||||||
\(693\) | −814.590 | −0.0446518 | ||||||||
\(694\) | −16693.1 | −0.913055 | ||||||||
\(695\) | 2415.93 | 0.131858 | ||||||||
\(696\) | −37166.3 | −2.02412 | ||||||||
\(697\) | 27621.1 | 1.50104 | ||||||||
\(698\) | −27227.1 | −1.47645 | ||||||||
\(699\) | 6045.10 | 0.327105 | ||||||||
\(700\) | −111.693 | −0.00603087 | ||||||||
\(701\) | −2769.78 | −0.149234 | −0.0746172 | − | 0.997212i | \(-0.523773\pi\) | ||||
−0.0746172 | + | 0.997212i | \(0.523773\pi\) | |||||||
\(702\) | 269.648 | 0.0144974 | ||||||||
\(703\) | 8370.67 | 0.449084 | ||||||||
\(704\) | −6262.77 | −0.335280 | ||||||||
\(705\) | 16662.5 | 0.890134 | ||||||||
\(706\) | 15137.3 | 0.806939 | ||||||||
\(707\) | −5133.16 | −0.273059 | ||||||||
\(708\) | −462.321 | −0.0245411 | ||||||||
\(709\) | −23939.3 | −1.26807 | −0.634034 | − | 0.773305i | \(-0.718602\pi\) | ||||
−0.634034 | + | 0.773305i | \(0.718602\pi\) | |||||||
\(710\) | 4608.18 | 0.243580 | ||||||||
\(711\) | 15868.2 | 0.836997 | ||||||||
\(712\) | −21775.7 | −1.14618 | ||||||||
\(713\) | −23841.9 | −1.25230 | ||||||||
\(714\) | 4818.54 | 0.252562 | ||||||||
\(715\) | −1654.10 | −0.0865171 | ||||||||
\(716\) | 3057.21 | 0.159572 | ||||||||
\(717\) | 18883.4 | 0.983560 | ||||||||
\(718\) | −10205.7 | −0.530463 | ||||||||
\(719\) | −18218.6 | −0.944976 | −0.472488 | − | 0.881337i | \(-0.656644\pi\) | ||||
−0.472488 | + | 0.881337i | \(0.656644\pi\) | |||||||
\(720\) | −6449.01 | −0.333806 | ||||||||
\(721\) | 1746.52 | 0.0902132 | ||||||||
\(722\) | −913.287 | −0.0470762 | ||||||||
\(723\) | 22737.7 | 1.16960 | ||||||||
\(724\) | 1803.84 | 0.0925955 | ||||||||
\(725\) | −5229.88 | −0.267907 | ||||||||
\(726\) | −2239.37 | −0.114478 | ||||||||
\(727\) | −21155.8 | −1.07926 | −0.539632 | − | 0.841901i | \(-0.681437\pi\) | ||||
−0.539632 | + | 0.841901i | \(0.681437\pi\) | |||||||
\(728\) | 2039.87 | 0.103850 | ||||||||
\(729\) | −18970.4 | −0.963798 | ||||||||
\(730\) | 3718.27 | 0.188520 | ||||||||
\(731\) | −47937.0 | −2.42546 | ||||||||
\(732\) | 4819.01 | 0.243328 | ||||||||
\(733\) | 18400.8 | 0.927218 | 0.463609 | − | 0.886040i | \(-0.346554\pi\) | ||||
0.463609 | + | 0.886040i | \(0.346554\pi\) | |||||||
\(734\) | −13801.3 | −0.694027 | ||||||||
\(735\) | −12260.7 | −0.615294 | ||||||||
\(736\) | 11207.9 | 0.561316 | ||||||||
\(737\) | −2504.52 | −0.125177 | ||||||||
\(738\) | 19875.2 | 0.991349 | ||||||||
\(739\) | 27770.3 | 1.38234 | 0.691169 | − | 0.722693i | \(-0.257096\pi\) | ||||
0.691169 | + | 0.722693i | \(0.257096\pi\) | |||||||
\(740\) | 3523.85 | 0.175053 | ||||||||
\(741\) | −4180.15 | −0.207236 | ||||||||
\(742\) | −263.539 | −0.0130388 | ||||||||
\(743\) | 37492.2 | 1.85122 | 0.925608 | − | 0.378483i | \(-0.123554\pi\) | ||||
0.925608 | + | 0.378483i | \(0.123554\pi\) | |||||||
\(744\) | 26919.1 | 1.32648 | ||||||||
\(745\) | −1796.59 | −0.0883516 | ||||||||
\(746\) | 12707.7 | 0.623678 | ||||||||
\(747\) | −1827.63 | −0.0895175 | ||||||||
\(748\) | −1640.45 | −0.0801883 | ||||||||
\(749\) | 3388.20 | 0.165290 | ||||||||
\(750\) | −2313.40 | −0.112631 | ||||||||
\(751\) | −9405.97 | −0.457029 | −0.228514 | − | 0.973541i | \(-0.573387\pi\) | ||||
−0.228514 | + | 0.973541i | \(0.573387\pi\) | |||||||
\(752\) | −22159.1 | −1.07455 | ||||||||
\(753\) | −8927.21 | −0.432040 | ||||||||
\(754\) | 15916.6 | 0.768763 | ||||||||
\(755\) | 1650.44 | 0.0795571 | ||||||||
\(756\) | 15.8338 | 0.000761733 0 | ||||||||
\(757\) | 3911.31 | 0.187793 | 0.0938963 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938963 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(758\) | −22656.5 | −1.08565 | ||||||||
\(759\) | 12662.3 | 0.605548 | ||||||||
\(760\) | −2307.18 | −0.110119 | ||||||||
\(761\) | −16994.1 | −0.809508 | −0.404754 | − | 0.914426i | \(-0.632643\pi\) | ||||
−0.404754 | + | 0.914426i | \(0.632643\pi\) | |||||||
\(762\) | 11810.8 | 0.561495 | ||||||||
\(763\) | 4430.89 | 0.210235 | ||||||||
\(764\) | −1545.67 | −0.0731942 | ||||||||
\(765\) | −12359.5 | −0.584128 | ||||||||
\(766\) | 19139.6 | 0.902794 | ||||||||
\(767\) | 1188.12 | 0.0559330 | ||||||||
\(768\) | −17208.5 | −0.808538 | ||||||||
\(769\) | 3264.54 | 0.153085 | 0.0765424 | − | 0.997066i | \(-0.475612\pi\) | ||||
0.0765424 | + | 0.997066i | \(0.475612\pi\) | |||||||
\(770\) | 388.605 | 0.0181875 | ||||||||
\(771\) | −46300.4 | −2.16273 | ||||||||
\(772\) | −1464.00 | −0.0682518 | ||||||||
\(773\) | −28840.6 | −1.34194 | −0.670972 | − | 0.741483i | \(-0.734123\pi\) | ||||
−0.670972 | + | 0.741483i | \(0.734123\pi\) | |||||||
\(774\) | −34493.8 | −1.60188 | ||||||||
\(775\) | 3787.94 | 0.175570 | ||||||||
\(776\) | −29202.9 | −1.35093 | ||||||||
\(777\) | −9001.04 | −0.415586 | ||||||||
\(778\) | 25904.6 | 1.19373 | ||||||||
\(779\) | 5629.43 | 0.258916 | ||||||||
\(780\) | −1759.74 | −0.0807806 | ||||||||
\(781\) | 4007.30 | 0.183601 | ||||||||
\(782\) | −37111.4 | −1.69706 | ||||||||
\(783\) | 741.396 | 0.0338382 | ||||||||
\(784\) | 16305.2 | 0.742767 | ||||||||
\(785\) | −18608.9 | −0.846089 | ||||||||
\(786\) | −3001.85 | −0.136225 | ||||||||
\(787\) | −11380.4 | −0.515462 | −0.257731 | − | 0.966217i | \(-0.582975\pi\) | ||||
−0.257731 | + | 0.966217i | \(0.582975\pi\) | |||||||
\(788\) | 7648.82 | 0.345784 | ||||||||
\(789\) | −20997.9 | −0.947458 | ||||||||
\(790\) | −7570.03 | −0.340924 | ||||||||
\(791\) | 1928.37 | 0.0866812 | ||||||||
\(792\) | −7083.55 | −0.317807 | ||||||||
\(793\) | −12384.4 | −0.554582 | ||||||||
\(794\) | −15649.1 | −0.699455 | ||||||||
\(795\) | 1364.30 | 0.0608636 | ||||||||
\(796\) | 5500.54 | 0.244926 | ||||||||
\(797\) | −24474.2 | −1.08773 | −0.543866 | − | 0.839172i | \(-0.683040\pi\) | ||||
−0.543866 | + | 0.839172i | \(0.683040\pi\) | |||||||
\(798\) | 982.063 | 0.0435647 | ||||||||
\(799\) | −42467.7 | −1.88035 | ||||||||
\(800\) | −1780.68 | −0.0786957 | ||||||||
\(801\) | −23774.7 | −1.04873 | ||||||||
\(802\) | −36535.8 | −1.60863 | ||||||||
\(803\) | 3233.44 | 0.142099 | ||||||||
\(804\) | −2664.48 | −0.116877 | ||||||||
\(805\) | −2197.33 | −0.0962056 | ||||||||
\(806\) | −11528.2 | −0.503801 | ||||||||
\(807\) | −60006.5 | −2.61751 | ||||||||
\(808\) | −44637.2 | −1.94348 | ||||||||
\(809\) | 19401.4 | 0.843162 | 0.421581 | − | 0.906791i | \(-0.361475\pi\) | ||||
0.421581 | + | 0.906791i | \(0.361475\pi\) | |||||||
\(810\) | 9383.90 | 0.407058 | ||||||||
\(811\) | −4251.69 | −0.184090 | −0.0920451 | − | 0.995755i | \(-0.529340\pi\) | ||||
−0.0920451 | + | 0.995755i | \(0.529340\pi\) | |||||||
\(812\) | 934.627 | 0.0403928 | ||||||||
\(813\) | −16412.3 | −0.708003 | ||||||||
\(814\) | −12260.2 | −0.527913 | ||||||||
\(815\) | −3159.15 | −0.135780 | ||||||||
\(816\) | 33173.6 | 1.42317 | ||||||||
\(817\) | −9770.00 | −0.418371 | ||||||||
\(818\) | 10314.0 | 0.440855 | ||||||||
\(819\) | 2227.13 | 0.0950209 | ||||||||
\(820\) | 2369.85 | 0.100925 | ||||||||
\(821\) | 13776.6 | 0.585636 | 0.292818 | − | 0.956168i | \(-0.405407\pi\) | ||||
0.292818 | + | 0.956168i | \(0.405407\pi\) | |||||||
\(822\) | −22060.8 | −0.936081 | ||||||||
\(823\) | 14914.8 | 0.631710 | 0.315855 | − | 0.948807i | \(-0.397709\pi\) | ||||
0.315855 | + | 0.948807i | \(0.397709\pi\) | |||||||
\(824\) | 15187.4 | 0.642087 | ||||||||
\(825\) | −2011.74 | −0.0848969 | ||||||||
\(826\) | −279.131 | −0.0117581 | ||||||||
\(827\) | −20855.9 | −0.876943 | −0.438472 | − | 0.898745i | \(-0.644480\pi\) | ||||
−0.438472 | + | 0.898745i | \(0.644480\pi\) | |||||||
\(828\) | 6674.51 | 0.280139 | ||||||||
\(829\) | −25184.2 | −1.05511 | −0.527554 | − | 0.849522i | \(-0.676891\pi\) | ||||
−0.527554 | + | 0.849522i | \(0.676891\pi\) | |||||||
\(830\) | 871.883 | 0.0364621 | ||||||||
\(831\) | −19181.7 | −0.800727 | ||||||||
\(832\) | 17122.7 | 0.713488 | ||||||||
\(833\) | 31248.8 | 1.29977 | ||||||||
\(834\) | −8942.39 | −0.371282 | ||||||||
\(835\) | 10928.7 | 0.452939 | ||||||||
\(836\) | −334.339 | −0.0138318 | ||||||||
\(837\) | −536.985 | −0.0221755 | ||||||||
\(838\) | 18247.4 | 0.752204 | ||||||||
\(839\) | 15722.2 | 0.646948 | 0.323474 | − | 0.946237i | \(-0.395149\pi\) | ||||
0.323474 | + | 0.946237i | \(0.395149\pi\) | |||||||
\(840\) | 2480.93 | 0.101905 | ||||||||
\(841\) | 19373.6 | 0.794357 | ||||||||
\(842\) | 2818.89 | 0.115375 | ||||||||
\(843\) | −27816.1 | −1.13646 | ||||||||
\(844\) | 3438.80 | 0.140247 | ||||||||
\(845\) | −6462.62 | −0.263102 | ||||||||
\(846\) | −30558.3 | −1.24186 | ||||||||
\(847\) | 337.934 | 0.0137090 | ||||||||
\(848\) | −1814.35 | −0.0734729 | ||||||||
\(849\) | −40565.0 | −1.63980 | ||||||||
\(850\) | 5896.16 | 0.237926 | ||||||||
\(851\) | 69324.2 | 2.79248 | ||||||||
\(852\) | 4263.24 | 0.171428 | ||||||||
\(853\) | 27788.1 | 1.11541 | 0.557706 | − | 0.830039i | \(-0.311682\pi\) | ||||
0.557706 | + | 0.830039i | \(0.311682\pi\) | |||||||
\(854\) | 2909.53 | 0.116583 | ||||||||
\(855\) | −2518.98 | −0.100757 | ||||||||
\(856\) | 29463.3 | 1.17644 | ||||||||
\(857\) | −38883.1 | −1.54985 | −0.774924 | − | 0.632054i | \(-0.782212\pi\) | ||||
−0.774924 | + | 0.632054i | \(0.782212\pi\) | |||||||
\(858\) | 6122.53 | 0.243613 | ||||||||
\(859\) | 28685.6 | 1.13939 | 0.569697 | − | 0.821855i | \(-0.307061\pi\) | ||||
0.569697 | + | 0.821855i | \(0.307061\pi\) | |||||||
\(860\) | −4112.94 | −0.163081 | ||||||||
\(861\) | −6053.37 | −0.239603 | ||||||||
\(862\) | −29605.0 | −1.16978 | ||||||||
\(863\) | −41287.5 | −1.62856 | −0.814278 | − | 0.580475i | \(-0.802867\pi\) | ||||
−0.814278 | + | 0.580475i | \(0.802867\pi\) | |||||||
\(864\) | 252.432 | 0.00993972 | ||||||||
\(865\) | 20328.1 | 0.799047 | ||||||||
\(866\) | −7648.27 | −0.300114 | ||||||||
\(867\) | 27636.2 | 1.08255 | ||||||||
\(868\) | −676.940 | −0.0264710 | ||||||||
\(869\) | −6582.95 | −0.256975 | ||||||||
\(870\) | 19358.0 | 0.754366 | ||||||||
\(871\) | 6847.47 | 0.266381 | ||||||||
\(872\) | 38530.3 | 1.49633 | ||||||||
\(873\) | −31883.7 | −1.23608 | ||||||||
\(874\) | −7563.66 | −0.292728 | ||||||||
\(875\) | 349.105 | 0.0134879 | ||||||||
\(876\) | 3439.95 | 0.132677 | ||||||||
\(877\) | 5933.53 | 0.228462 | 0.114231 | − | 0.993454i | \(-0.463560\pi\) | ||||
0.114231 | + | 0.993454i | \(0.463560\pi\) | |||||||
\(878\) | −19179.4 | −0.737213 | ||||||||
\(879\) | −26289.8 | −1.00880 | ||||||||
\(880\) | 2675.38 | 0.102485 | ||||||||
\(881\) | 37757.9 | 1.44392 | 0.721961 | − | 0.691934i | \(-0.243241\pi\) | ||||
0.721961 | + | 0.691934i | \(0.243241\pi\) | |||||||
\(882\) | 22485.6 | 0.858423 | ||||||||
\(883\) | 24552.1 | 0.935725 | 0.467862 | − | 0.883801i | \(-0.345024\pi\) | ||||
0.467862 | + | 0.883801i | \(0.345024\pi\) | |||||||
\(884\) | 4485.07 | 0.170644 | ||||||||
\(885\) | 1445.02 | 0.0548855 | ||||||||
\(886\) | −23777.9 | −0.901618 | ||||||||
\(887\) | 17032.9 | 0.644767 | 0.322383 | − | 0.946609i | \(-0.395516\pi\) | ||||
0.322383 | + | 0.946609i | \(0.395516\pi\) | |||||||
\(888\) | −78271.7 | −2.95791 | ||||||||
\(889\) | −1782.31 | −0.0672406 | ||||||||
\(890\) | 11341.8 | 0.427168 | ||||||||
\(891\) | 8160.30 | 0.306824 | ||||||||
\(892\) | 1658.79 | 0.0622652 | ||||||||
\(893\) | −8655.31 | −0.324344 | ||||||||
\(894\) | 6649.96 | 0.248778 | ||||||||
\(895\) | −9555.53 | −0.356878 | ||||||||
\(896\) | −2431.31 | −0.0906521 | ||||||||
\(897\) | −34619.2 | −1.28863 | ||||||||
\(898\) | 21532.3 | 0.800160 | ||||||||
\(899\) | −31696.7 | −1.17591 | ||||||||
\(900\) | −1060.43 | −0.0392751 | ||||||||
\(901\) | −3477.19 | −0.128570 | ||||||||
\(902\) | −8245.24 | −0.304364 | ||||||||
\(903\) | 10505.8 | 0.387164 | ||||||||
\(904\) | 16768.8 | 0.616949 | ||||||||
\(905\) | −5638.03 | −0.207088 | ||||||||
\(906\) | −6108.99 | −0.224015 | ||||||||
\(907\) | 1450.32 | 0.0530947 | 0.0265474 | − | 0.999648i | \(-0.491549\pi\) | ||||
0.0265474 | + | 0.999648i | \(0.491549\pi\) | |||||||
\(908\) | 1082.55 | 0.0395658 | ||||||||
\(909\) | −48734.8 | −1.77825 | ||||||||
\(910\) | −1062.46 | −0.0387037 | ||||||||
\(911\) | 33935.1 | 1.23416 | 0.617081 | − | 0.786900i | \(-0.288315\pi\) | ||||
0.617081 | + | 0.786900i | \(0.288315\pi\) | |||||||
\(912\) | 6761.08 | 0.245484 | ||||||||
\(913\) | 758.195 | 0.0274837 | ||||||||
\(914\) | −38893.7 | −1.40754 | ||||||||
\(915\) | −15062.2 | −0.544196 | ||||||||
\(916\) | −5065.99 | −0.182735 | ||||||||
\(917\) | 452.998 | 0.0163133 | ||||||||
\(918\) | −835.850 | −0.0300514 | ||||||||
\(919\) | 19042.8 | 0.683528 | 0.341764 | − | 0.939786i | \(-0.388976\pi\) | ||||
0.341764 | + | 0.939786i | \(0.388976\pi\) | |||||||
\(920\) | −19107.6 | −0.684738 | ||||||||
\(921\) | 52990.2 | 1.89586 | ||||||||
\(922\) | −29494.4 | −1.05352 | ||||||||
\(923\) | −10956.1 | −0.390710 | ||||||||
\(924\) | 359.517 | 0.0128000 | ||||||||
\(925\) | −11014.0 | −0.391502 | ||||||||
\(926\) | 26401.6 | 0.936946 | ||||||||
\(927\) | 16581.6 | 0.587500 | ||||||||
\(928\) | 14900.4 | 0.527079 | ||||||||
\(929\) | −7512.08 | −0.265300 | −0.132650 | − | 0.991163i | \(-0.542349\pi\) | ||||
−0.132650 | + | 0.991163i | \(0.542349\pi\) | |||||||
\(930\) | −14020.8 | −0.494366 | ||||||||
\(931\) | 6368.80 | 0.224199 | ||||||||
\(932\) | −1321.92 | −0.0464601 | ||||||||
\(933\) | −54132.3 | −1.89948 | ||||||||
\(934\) | 43134.8 | 1.51115 | ||||||||
\(935\) | 5127.34 | 0.179339 | ||||||||
\(936\) | 19366.7 | 0.676305 | ||||||||
\(937\) | −3521.93 | −0.122792 | −0.0613962 | − | 0.998113i | \(-0.519555\pi\) | ||||
−0.0613962 | + | 0.998113i | \(0.519555\pi\) | |||||||
\(938\) | −1608.71 | −0.0559981 | ||||||||
\(939\) | 8754.47 | 0.304250 | ||||||||
\(940\) | −3643.68 | −0.126429 | ||||||||
\(941\) | −46438.0 | −1.60875 | −0.804376 | − | 0.594121i | \(-0.797500\pi\) | ||||
−0.804376 | + | 0.594121i | \(0.797500\pi\) | |||||||
\(942\) | 68879.6 | 2.38240 | ||||||||
\(943\) | 46621.8 | 1.60998 | ||||||||
\(944\) | −1921.70 | −0.0662563 | ||||||||
\(945\) | −49.4897 | −0.00170360 | ||||||||
\(946\) | 14309.8 | 0.491810 | ||||||||
\(947\) | 49642.1 | 1.70343 | 0.851717 | − | 0.524002i | \(-0.175561\pi\) | ||||
0.851717 | + | 0.524002i | \(0.175561\pi\) | |||||||
\(948\) | −7003.40 | −0.239936 | ||||||||
\(949\) | −8840.36 | −0.302392 | ||||||||
\(950\) | 1201.69 | 0.0410401 | ||||||||
\(951\) | 50612.2 | 1.72578 | ||||||||
\(952\) | −6323.15 | −0.215267 | ||||||||
\(953\) | 25629.0 | 0.871148 | 0.435574 | − | 0.900153i | \(-0.356546\pi\) | ||||
0.435574 | + | 0.900153i | \(0.356546\pi\) | |||||||
\(954\) | −2502.07 | −0.0849134 | ||||||||
\(955\) | 4831.10 | 0.163697 | ||||||||
\(956\) | −4129.34 | −0.139699 | ||||||||
\(957\) | 16833.9 | 0.568612 | ||||||||
\(958\) | −2462.98 | −0.0830639 | ||||||||
\(959\) | 3329.10 | 0.112098 | ||||||||
\(960\) | 20824.9 | 0.700127 | ||||||||
\(961\) | −6833.42 | −0.229379 | ||||||||
\(962\) | 33520.1 | 1.12342 | ||||||||
\(963\) | 32168.0 | 1.07643 | ||||||||
\(964\) | −4972.18 | −0.166124 | ||||||||
\(965\) | 4575.82 | 0.152644 | ||||||||
\(966\) | 8133.25 | 0.270893 | ||||||||
\(967\) | −31670.8 | −1.05322 | −0.526610 | − | 0.850107i | \(-0.676537\pi\) | ||||
−0.526610 | + | 0.850107i | \(0.676537\pi\) | |||||||
\(968\) | 2938.62 | 0.0975731 | ||||||||
\(969\) | 12957.6 | 0.429574 | ||||||||
\(970\) | 15210.3 | 0.503479 | ||||||||
\(971\) | 36224.6 | 1.19722 | 0.598612 | − | 0.801039i | \(-0.295719\pi\) | ||||
0.598612 | + | 0.801039i | \(0.295719\pi\) | |||||||
\(972\) | 8528.42 | 0.281429 | ||||||||
\(973\) | 1349.46 | 0.0444622 | ||||||||
\(974\) | −17605.9 | −0.579187 | ||||||||
\(975\) | 5500.20 | 0.180664 | ||||||||
\(976\) | 20030.9 | 0.656939 | ||||||||
\(977\) | −59720.8 | −1.95562 | −0.977809 | − | 0.209498i | \(-0.932817\pi\) | ||||
−0.977809 | + | 0.209498i | \(0.932817\pi\) | |||||||
\(978\) | 11693.4 | 0.382325 | ||||||||
\(979\) | 9862.94 | 0.321983 | ||||||||
\(980\) | 2681.11 | 0.0873928 | ||||||||
\(981\) | 42067.4 | 1.36912 | ||||||||
\(982\) | −53688.3 | −1.74467 | ||||||||
\(983\) | 47487.6 | 1.54081 | 0.770407 | − | 0.637553i | \(-0.220053\pi\) | ||||
0.770407 | + | 0.637553i | \(0.220053\pi\) | |||||||
\(984\) | −52639.1 | −1.70536 | ||||||||
\(985\) | −23906.9 | −0.773338 | ||||||||
\(986\) | −49337.9 | −1.59355 | ||||||||
\(987\) | 9307.12 | 0.300151 | ||||||||
\(988\) | 914.098 | 0.0294345 | ||||||||
\(989\) | −80913.2 | −2.60151 | ||||||||
\(990\) | 3689.46 | 0.118443 | ||||||||
\(991\) | 55419.6 | 1.77645 | 0.888224 | − | 0.459410i | \(-0.151939\pi\) | ||||
0.888224 | + | 0.459410i | \(0.151939\pi\) | |||||||
\(992\) | −10792.2 | −0.345415 | ||||||||
\(993\) | 5904.05 | 0.188680 | ||||||||
\(994\) | 2573.98 | 0.0821345 | ||||||||
\(995\) | −17192.3 | −0.547772 | ||||||||
\(996\) | 806.621 | 0.0256614 | ||||||||
\(997\) | −30231.2 | −0.960312 | −0.480156 | − | 0.877183i | \(-0.659420\pi\) | ||||
−0.480156 | + | 0.877183i | \(0.659420\pi\) | |||||||
\(998\) | −48580.1 | −1.54086 | ||||||||
\(999\) | 1561.37 | 0.0494490 |
(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.d.1.8 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.d.1.8 | ✓ | 22 | 1.1 | even | 1 | trivial |