Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.40 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.81880i | 1.95470i | 0.211629 | + | 0.977350i | \(0.432123\pi\) | ||||
−0.211629 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −45.1337 | −2.82085 | ||||||||
\(5\) | 21.3172 | 0.852690 | 0.426345 | − | 0.904561i | \(-0.359801\pi\) | ||||
0.426345 | + | 0.904561i | \(0.359801\pi\) | |||||||
\(6\) | 40.6277i | 1.12855i | ||||||||
\(7\) | −30.7266 | −0.627073 | −0.313537 | − | 0.949576i | \(-0.601514\pi\) | ||||
−0.313537 | + | 0.949576i | \(0.601514\pi\) | |||||||
\(8\) | − | 227.790i | − | 3.55922i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 166.675i | 1.66675i | ||||||||
\(11\) | − | 207.480i | − | 1.71471i | −0.514728 | − | 0.857353i | \(-0.672107\pi\) | ||
0.514728 | − | 0.857353i | \(-0.327893\pi\) | |||||||
\(12\) | −234.521 | −1.62862 | ||||||||
\(13\) | − | 206.020i | − | 1.21905i | −0.792766 | − | 0.609526i | \(-0.791360\pi\) | ||
0.792766 | − | 0.609526i | \(-0.208640\pi\) | |||||||
\(14\) | − | 240.245i | − | 1.22574i | ||||||
\(15\) | 110.768 | 0.492301 | ||||||||
\(16\) | 1058.91 | 4.13636 | ||||||||
\(17\) | −391.490 | −1.35464 | −0.677318 | − | 0.735690i | \(-0.736858\pi\) | ||||
−0.677318 | + | 0.735690i | \(0.736858\pi\) | |||||||
\(18\) | 211.108i | 0.651567i | ||||||||
\(19\) | −321.627 | −0.890934 | −0.445467 | − | 0.895298i | \(-0.646962\pi\) | ||||
−0.445467 | + | 0.895298i | \(0.646962\pi\) | |||||||
\(20\) | −962.125 | −2.40531 | ||||||||
\(21\) | −159.660 | −0.362041 | ||||||||
\(22\) | 1622.24 | 3.35174 | ||||||||
\(23\) | − | 287.967i | − | 0.544360i | −0.962246 | − | 0.272180i | \(-0.912255\pi\) | ||
0.962246 | − | 0.272180i | \(-0.0877447\pi\) | |||||||
\(24\) | − | 1183.63i | − | 2.05492i | ||||||
\(25\) | −170.575 | −0.272921 | ||||||||
\(26\) | 1610.83 | 2.38288 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 1386.80 | 1.76888 | ||||||||
\(29\) | 1020.53 | 1.21347 | 0.606737 | − | 0.794902i | \(-0.292478\pi\) | ||||
0.606737 | + | 0.794902i | \(0.292478\pi\) | |||||||
\(30\) | 866.070i | 0.962300i | ||||||||
\(31\) | − | 560.747i | − | 0.583504i | −0.956494 | − | 0.291752i | \(-0.905762\pi\) | ||
0.956494 | − | 0.291752i | \(-0.0942381\pi\) | |||||||
\(32\) | 4634.75i | 4.52612i | ||||||||
\(33\) | − | 1078.10i | − | 0.989987i | ||||||
\(34\) | − | 3060.98i | − | 2.64791i | ||||||
\(35\) | −655.006 | −0.534699 | ||||||||
\(36\) | −1218.61 | −0.940284 | ||||||||
\(37\) | 1257.89i | 0.918838i | 0.888220 | + | 0.459419i | \(0.151942\pi\) | ||||
−0.888220 | + | 0.459419i | \(0.848058\pi\) | |||||||
\(38\) | − | 2514.74i | − | 1.74151i | ||||||
\(39\) | − | 1070.51i | − | 0.703820i | ||||||
\(40\) | − | 4855.86i | − | 3.03491i | ||||||
\(41\) | −1524.79 | −0.907076 | −0.453538 | − | 0.891237i | \(-0.649838\pi\) | ||||
−0.453538 | + | 0.891237i | \(0.649838\pi\) | |||||||
\(42\) | − | 1248.35i | − | 0.707681i | ||||||
\(43\) | 2155.53i | 1.16578i | 0.812550 | + | 0.582892i | \(0.198079\pi\) | ||||
−0.812550 | + | 0.582892i | \(0.801921\pi\) | |||||||
\(44\) | 9364.31i | 4.83694i | ||||||||
\(45\) | 575.565 | 0.284230 | ||||||||
\(46\) | 2251.55 | 1.06406 | ||||||||
\(47\) | 245.854i | 0.111296i | 0.998450 | + | 0.0556482i | \(0.0177225\pi\) | ||||
−0.998450 | + | 0.0556482i | \(0.982277\pi\) | |||||||
\(48\) | 5502.25 | 2.38813 | ||||||||
\(49\) | −1456.88 | −0.606779 | ||||||||
\(50\) | − | 1333.69i | − | 0.533478i | ||||||
\(51\) | −2034.24 | −0.782100 | ||||||||
\(52\) | 9298.43i | 3.43877i | ||||||||
\(53\) | −1142.98 | −0.406899 | −0.203449 | − | 0.979085i | \(-0.565215\pi\) | ||||
−0.203449 | + | 0.979085i | \(0.565215\pi\) | |||||||
\(54\) | 1096.95i | 0.376182i | ||||||||
\(55\) | − | 4422.89i | − | 1.46211i | ||||||
\(56\) | 6999.22i | 2.23189i | ||||||||
\(57\) | −1671.22 | −0.514381 | ||||||||
\(58\) | 7979.34i | 2.37198i | ||||||||
\(59\) | −3465.52 | + | 327.946i | −0.995552 | + | 0.0942101i | ||||
\(60\) | −4999.35 | −1.38871 | ||||||||
\(61\) | 518.066i | 0.139228i | 0.997574 | + | 0.0696138i | \(0.0221767\pi\) | ||||
−0.997574 | + | 0.0696138i | \(0.977823\pi\) | |||||||
\(62\) | 4384.37 | 1.14057 | ||||||||
\(63\) | −829.618 | −0.209024 | ||||||||
\(64\) | −19295.6 | −4.71085 | ||||||||
\(65\) | − | 4391.77i | − | 1.03947i | ||||||
\(66\) | 8429.41 | 1.93513 | ||||||||
\(67\) | − | 2495.71i | − | 0.555961i | −0.960587 | − | 0.277980i | \(-0.910335\pi\) | ||
0.960587 | − | 0.277980i | \(-0.0896650\pi\) | |||||||
\(68\) | 17669.4 | 3.82123 | ||||||||
\(69\) | − | 1496.32i | − | 0.314287i | ||||||
\(70\) | − | 5121.36i | − | 1.04518i | ||||||
\(71\) | 9311.79 | 1.84721 | 0.923606 | − | 0.383344i | \(-0.125228\pi\) | ||||
0.923606 | + | 0.383344i | \(0.125228\pi\) | |||||||
\(72\) | − | 6150.34i | − | 1.18641i | ||||||
\(73\) | − | 8005.70i | − | 1.50229i | −0.660138 | − | 0.751144i | \(-0.729502\pi\) | ||
0.660138 | − | 0.751144i | \(-0.270498\pi\) | |||||||
\(74\) | −9835.18 | −1.79605 | ||||||||
\(75\) | −886.336 | −0.157571 | ||||||||
\(76\) | 14516.2 | 2.51319 | ||||||||
\(77\) | 6375.14i | 1.07525i | ||||||||
\(78\) | 8370.11 | 1.37576 | ||||||||
\(79\) | 5130.68 | 0.822093 | 0.411047 | − | 0.911614i | \(-0.365163\pi\) | ||||
0.411047 | + | 0.911614i | \(0.365163\pi\) | |||||||
\(80\) | 22573.0 | 3.52703 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 11922.1i | − | 1.77306i | ||||||
\(83\) | − | 13428.1i | − | 1.94921i | −0.223939 | − | 0.974603i | \(-0.571892\pi\) | ||
0.223939 | − | 0.974603i | \(-0.428108\pi\) | |||||||
\(84\) | 7206.04 | 1.02126 | ||||||||
\(85\) | −8345.49 | −1.15508 | ||||||||
\(86\) | −16853.7 | −2.27876 | ||||||||
\(87\) | 5302.84 | 0.700600 | ||||||||
\(88\) | −47261.8 | −6.10302 | ||||||||
\(89\) | 3141.70i | 0.396630i | 0.980138 | + | 0.198315i | \(0.0635468\pi\) | ||||
−0.980138 | + | 0.198315i | \(0.936453\pi\) | |||||||
\(90\) | 4500.23i | 0.555584i | ||||||||
\(91\) | 6330.29i | 0.764435i | ||||||||
\(92\) | 12997.0i | 1.53556i | ||||||||
\(93\) | − | 2913.73i | − | 0.336886i | ||||||
\(94\) | −1922.28 | −0.217551 | ||||||||
\(95\) | −6856.20 | −0.759690 | ||||||||
\(96\) | 24082.9i | 2.61316i | ||||||||
\(97\) | − | 5322.39i | − | 0.565670i | −0.959169 | − | 0.282835i | \(-0.908725\pi\) | ||
0.959169 | − | 0.282835i | \(-0.0912749\pi\) | |||||||
\(98\) | − | 11391.0i | − | 1.18607i | ||||||
\(99\) | − | 5601.95i | − | 0.571569i | ||||||
\(100\) | 7698.69 | 0.769869 | ||||||||
\(101\) | 6022.91i | 0.590424i | 0.955432 | + | 0.295212i | \(0.0953902\pi\) | ||||
−0.955432 | + | 0.295212i | \(0.904610\pi\) | |||||||
\(102\) | − | 15905.3i | − | 1.52877i | ||||||
\(103\) | 3738.09i | 0.352350i | 0.984359 | + | 0.176175i | \(0.0563725\pi\) | ||||
−0.984359 | + | 0.176175i | \(0.943627\pi\) | |||||||
\(104\) | −46929.3 | −4.33888 | ||||||||
\(105\) | −3403.51 | −0.308708 | ||||||||
\(106\) | − | 8936.72i | − | 0.795365i | ||||||
\(107\) | 10702.1 | 0.934764 | 0.467382 | − | 0.884056i | \(-0.345197\pi\) | ||||
0.467382 | + | 0.884056i | \(0.345197\pi\) | |||||||
\(108\) | −6332.08 | −0.542873 | ||||||||
\(109\) | − | 21298.0i | − | 1.79261i | −0.443442 | − | 0.896303i | \(-0.646243\pi\) | ||
0.443442 | − | 0.896303i | \(-0.353757\pi\) | |||||||
\(110\) | 34581.7 | 2.85799 | ||||||||
\(111\) | 6536.18i | 0.530491i | ||||||||
\(112\) | −32536.6 | −2.59380 | ||||||||
\(113\) | 16771.3i | 1.31344i | 0.754135 | + | 0.656720i | \(0.228057\pi\) | ||||
−0.754135 | + | 0.656720i | \(0.771943\pi\) | |||||||
\(114\) | − | 13067.0i | − | 1.00546i | ||||||
\(115\) | − | 6138.65i | − | 0.464170i | ||||||
\(116\) | −46060.4 | −3.42303 | ||||||||
\(117\) | − | 5562.54i | − | 0.406351i | ||||||
\(118\) | −2564.14 | − | 27096.2i | −0.184153 | − | 1.94601i | ||||
\(119\) | 12029.2 | 0.849456 | ||||||||
\(120\) | − | 25231.8i | − | 1.75221i | ||||||
\(121\) | −28406.8 | −1.94022 | ||||||||
\(122\) | −4050.65 | −0.272148 | ||||||||
\(123\) | −7923.06 | −0.523700 | ||||||||
\(124\) | 25308.6i | 1.64598i | ||||||||
\(125\) | −16959.5 | −1.08541 | ||||||||
\(126\) | − | 6486.62i | − | 0.408580i | ||||||
\(127\) | 27235.6 | 1.68861 | 0.844305 | − | 0.535863i | \(-0.180014\pi\) | ||||
0.844305 | + | 0.535863i | \(0.180014\pi\) | |||||||
\(128\) | − | 76712.8i | − | 4.68218i | ||||||
\(129\) | 11200.5i | 0.673066i | ||||||||
\(130\) | 34338.4 | 2.03186 | ||||||||
\(131\) | − | 1718.72i | − | 0.100153i | −0.998745 | − | 0.0500763i | \(-0.984054\pi\) | ||
0.998745 | − | 0.0500763i | \(-0.0159465\pi\) | |||||||
\(132\) | 48658.4i | 2.79261i | ||||||||
\(133\) | 9882.51 | 0.558681 | ||||||||
\(134\) | 19513.4 | 1.08674 | ||||||||
\(135\) | 2990.73 | 0.164100 | ||||||||
\(136\) | 89177.6i | 4.82145i | ||||||||
\(137\) | 8888.26 | 0.473560 | 0.236780 | − | 0.971563i | \(-0.423908\pi\) | ||||
0.236780 | + | 0.971563i | \(0.423908\pi\) | |||||||
\(138\) | 11699.4 | 0.614336 | ||||||||
\(139\) | 2771.10 | 0.143424 | 0.0717121 | − | 0.997425i | \(-0.477154\pi\) | ||||
0.0717121 | + | 0.997425i | \(0.477154\pi\) | |||||||
\(140\) | 29562.8 | 1.50831 | ||||||||
\(141\) | 1277.49i | 0.0642570i | ||||||||
\(142\) | 72807.1i | 3.61074i | ||||||||
\(143\) | −42744.9 | −2.09032 | ||||||||
\(144\) | 28590.5 | 1.37879 | ||||||||
\(145\) | 21754.9 | 1.03472 | ||||||||
\(146\) | 62594.9 | 2.93652 | ||||||||
\(147\) | −7570.15 | −0.350324 | ||||||||
\(148\) | − | 56773.1i | − | 2.59191i | ||||||
\(149\) | − | 8123.08i | − | 0.365888i | −0.983123 | − | 0.182944i | \(-0.941437\pi\) | ||
0.983123 | − | 0.182944i | \(-0.0585627\pi\) | |||||||
\(150\) | − | 6930.08i | − | 0.308004i | ||||||
\(151\) | 2438.11i | 0.106930i | 0.998570 | + | 0.0534651i | \(0.0170266\pi\) | ||||
−0.998570 | + | 0.0534651i | \(0.982973\pi\) | |||||||
\(152\) | 73263.5i | 3.17103i | ||||||||
\(153\) | −10570.2 | −0.451546 | ||||||||
\(154\) | −49845.9 | −2.10179 | ||||||||
\(155\) | − | 11953.6i | − | 0.497547i | ||||||
\(156\) | 48316.1i | 1.98537i | ||||||||
\(157\) | − | 13811.6i | − | 0.560332i | −0.959952 | − | 0.280166i | \(-0.909611\pi\) | ||
0.959952 | − | 0.280166i | \(-0.0903895\pi\) | |||||||
\(158\) | 40115.8i | 1.60695i | ||||||||
\(159\) | −5939.09 | −0.234923 | ||||||||
\(160\) | 98800.0i | 3.85938i | ||||||||
\(161\) | 8848.23i | 0.341354i | ||||||||
\(162\) | 5699.91i | 0.217189i | ||||||||
\(163\) | −14070.7 | −0.529593 | −0.264796 | − | 0.964304i | \(-0.585305\pi\) | ||||
−0.264796 | + | 0.964304i | \(0.585305\pi\) | |||||||
\(164\) | 68819.5 | 2.55873 | ||||||||
\(165\) | − | 22982.0i | − | 0.844151i | ||||||
\(166\) | 104991. | 3.81011 | ||||||||
\(167\) | −37863.4 | −1.35765 | −0.678823 | − | 0.734302i | \(-0.737510\pi\) | ||||
−0.678823 | + | 0.734302i | \(0.737510\pi\) | |||||||
\(168\) | 36369.0i | 1.28858i | ||||||||
\(169\) | −13883.2 | −0.486089 | ||||||||
\(170\) | − | 65251.7i | − | 2.25784i | ||||||
\(171\) | −8683.93 | −0.296978 | ||||||||
\(172\) | − | 97287.2i | − | 3.28851i | ||||||
\(173\) | − | 13221.6i | − | 0.441765i | −0.975300 | − | 0.220883i | \(-0.929106\pi\) | ||
0.975300 | − | 0.220883i | \(-0.0708938\pi\) | |||||||
\(174\) | 41461.9i | 1.36946i | ||||||||
\(175\) | 5241.20 | 0.171141 | ||||||||
\(176\) | − | 219702.i | − | 7.09264i | ||||||
\(177\) | −18007.4 | + | 1704.05i | −0.574782 | + | 0.0543923i | ||||
\(178\) | −24564.3 | −0.775292 | ||||||||
\(179\) | 398.257i | 0.0124296i | 0.999981 | + | 0.00621480i | \(0.00197825\pi\) | ||||
−0.999981 | + | 0.00621480i | \(0.998022\pi\) | |||||||
\(180\) | −25977.4 | −0.801771 | ||||||||
\(181\) | 46013.5 | 1.40452 | 0.702260 | − | 0.711920i | \(-0.252174\pi\) | ||||
0.702260 | + | 0.711920i | \(0.252174\pi\) | |||||||
\(182\) | −49495.3 | −1.49424 | ||||||||
\(183\) | 2691.95i | 0.0803831i | ||||||||
\(184\) | −65596.0 | −1.93750 | ||||||||
\(185\) | 26814.7i | 0.783483i | ||||||||
\(186\) | 22781.8 | 0.658511 | ||||||||
\(187\) | 81226.2i | 2.32281i | ||||||||
\(188\) | − | 11096.3i | − | 0.313951i | ||||||
\(189\) | −4310.82 | −0.120680 | ||||||||
\(190\) | − | 53607.3i | − | 1.48497i | ||||||
\(191\) | 60179.4i | 1.64961i | 0.565418 | + | 0.824804i | \(0.308715\pi\) | ||||
−0.565418 | + | 0.824804i | \(0.691285\pi\) | |||||||
\(192\) | −100263. | −2.71981 | ||||||||
\(193\) | −31955.1 | −0.857879 | −0.428939 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428939 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(194\) | 41614.7 | 1.10572 | ||||||||
\(195\) | − | 22820.3i | − | 0.600140i | ||||||
\(196\) | 65754.2 | 1.71163 | ||||||||
\(197\) | −34993.6 | −0.901689 | −0.450844 | − | 0.892603i | \(-0.648877\pi\) | ||||
−0.450844 | + | 0.892603i | \(0.648877\pi\) | |||||||
\(198\) | 43800.5 | 1.11725 | ||||||||
\(199\) | 3731.67 | 0.0942317 | 0.0471159 | − | 0.998889i | \(-0.484997\pi\) | ||||
0.0471159 | + | 0.998889i | \(0.484997\pi\) | |||||||
\(200\) | 38855.4i | 0.971385i | ||||||||
\(201\) | − | 12968.1i | − | 0.320984i | ||||||
\(202\) | −47092.0 | −1.15410 | ||||||||
\(203\) | −31357.5 | −0.760938 | ||||||||
\(204\) | 91812.8 | 2.20619 | ||||||||
\(205\) | −32504.4 | −0.773454 | ||||||||
\(206\) | −29227.4 | −0.688740 | ||||||||
\(207\) | − | 7775.10i | − | 0.181453i | ||||||
\(208\) | − | 218156.i | − | 5.04244i | ||||||
\(209\) | 66731.1i | 1.52769i | ||||||||
\(210\) | − | 26611.4i | − | 0.603433i | ||||||
\(211\) | − | 13733.7i | − | 0.308476i | −0.988034 | − | 0.154238i | \(-0.950708\pi\) | ||
0.988034 | − | 0.154238i | \(-0.0492923\pi\) | |||||||
\(212\) | 51586.8 | 1.14780 | ||||||||
\(213\) | 48385.5 | 1.06649 | ||||||||
\(214\) | 83677.7i | 1.82718i | ||||||||
\(215\) | 45950.0i | 0.994052i | ||||||||
\(216\) | − | 31958.1i | − | 0.684973i | ||||||
\(217\) | 17229.8i | 0.365899i | ||||||||
\(218\) | 166524. | 3.50401 | ||||||||
\(219\) | − | 41598.8i | − | 0.867347i | ||||||
\(220\) | 199621.i | 4.12441i | ||||||||
\(221\) | 80654.7i | 1.65137i | ||||||||
\(222\) | −51105.1 | −1.03695 | ||||||||
\(223\) | −62492.9 | −1.25667 | −0.628335 | − | 0.777943i | \(-0.716263\pi\) | ||||
−0.628335 | + | 0.777943i | \(0.716263\pi\) | |||||||
\(224\) | − | 142410.i | − | 2.83821i | ||||||
\(225\) | −4605.54 | −0.0909735 | ||||||||
\(226\) | −131132. | −2.56738 | ||||||||
\(227\) | − | 15746.2i | − | 0.305579i | −0.988259 | − | 0.152790i | \(-0.951174\pi\) | ||
0.988259 | − | 0.152790i | \(-0.0488257\pi\) | |||||||
\(228\) | 75428.4 | 1.45099 | ||||||||
\(229\) | − | 50347.4i | − | 0.960078i | −0.877247 | − | 0.480039i | \(-0.840623\pi\) | ||
0.877247 | − | 0.480039i | \(-0.159377\pi\) | |||||||
\(230\) | 47996.9 | 0.907314 | ||||||||
\(231\) | 33126.2i | 0.620794i | ||||||||
\(232\) | − | 232467.i | − | 4.31903i | ||||||
\(233\) | 54304.7i | 1.00029i | 0.865942 | + | 0.500144i | \(0.166720\pi\) | ||||
−0.865942 | + | 0.500144i | \(0.833280\pi\) | |||||||
\(234\) | 43492.4 | 0.794294 | ||||||||
\(235\) | 5240.92i | 0.0949012i | ||||||||
\(236\) | 156411. | − | 14801.4i | 2.80831 | − | 0.265753i | ||||
\(237\) | 26659.8 | 0.474636 | ||||||||
\(238\) | 94053.6i | 1.66043i | ||||||||
\(239\) | 44247.5 | 0.774628 | 0.387314 | − | 0.921948i | \(-0.373403\pi\) | ||||
0.387314 | + | 0.921948i | \(0.373403\pi\) | |||||||
\(240\) | 117293. | 2.03633 | ||||||||
\(241\) | 93615.1 | 1.61180 | 0.805902 | − | 0.592050i | \(-0.201681\pi\) | ||||
0.805902 | + | 0.592050i | \(0.201681\pi\) | |||||||
\(242\) | − | 222107.i | − | 3.79255i | ||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 23382.2i | − | 0.392741i | ||||||
\(245\) | −31056.6 | −0.517394 | ||||||||
\(246\) | − | 61948.8i | − | 1.02368i | ||||||
\(247\) | 66261.6i | 1.08610i | ||||||||
\(248\) | −127733. | −2.07682 | ||||||||
\(249\) | − | 69774.4i | − | 1.12537i | ||||||
\(250\) | − | 132603.i | − | 2.12164i | ||||||
\(251\) | −31025.2 | −0.492455 | −0.246228 | − | 0.969212i | \(-0.579191\pi\) | ||||
−0.246228 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(252\) | 37443.7 | 0.589627 | ||||||||
\(253\) | −59747.2 | −0.933419 | ||||||||
\(254\) | 212950.i | 3.30073i | ||||||||
\(255\) | −43364.4 | −0.666888 | ||||||||
\(256\) | 291072. | 4.44141 | ||||||||
\(257\) | −51107.2 | −0.773777 | −0.386889 | − | 0.922126i | \(-0.626450\pi\) | ||||
−0.386889 | + | 0.922126i | \(0.626450\pi\) | |||||||
\(258\) | −87574.4 | −1.31564 | ||||||||
\(259\) | − | 38650.6i | − | 0.576179i | ||||||
\(260\) | 198217.i | 2.93220i | ||||||||
\(261\) | 27554.4 | 0.404492 | ||||||||
\(262\) | 13438.3 | 0.195768 | ||||||||
\(263\) | 83386.8 | 1.20555 | 0.602776 | − | 0.797911i | \(-0.294061\pi\) | ||||
0.602776 | + | 0.797911i | \(0.294061\pi\) | |||||||
\(264\) | −245580. | −3.52358 | ||||||||
\(265\) | −24365.1 | −0.346958 | ||||||||
\(266\) | 77269.3i | 1.09205i | ||||||||
\(267\) | 16324.8i | 0.228994i | ||||||||
\(268\) | 112640.i | 1.56828i | ||||||||
\(269\) | − | 55398.4i | − | 0.765584i | −0.923835 | − | 0.382792i | \(-0.874963\pi\) | ||
0.923835 | − | 0.382792i | \(-0.125037\pi\) | |||||||
\(270\) | 23383.9i | 0.320767i | ||||||||
\(271\) | 33799.6 | 0.460228 | 0.230114 | − | 0.973164i | \(-0.426090\pi\) | ||||
0.230114 | + | 0.973164i | \(0.426090\pi\) | |||||||
\(272\) | −414552. | −5.60326 | ||||||||
\(273\) | 32893.1i | 0.441347i | ||||||||
\(274\) | 69495.5i | 0.925669i | ||||||||
\(275\) | 35390.9i | 0.467979i | ||||||||
\(276\) | 67534.3i | 0.886557i | ||||||||
\(277\) | 71567.4 | 0.932730 | 0.466365 | − | 0.884592i | \(-0.345563\pi\) | ||||
0.466365 | + | 0.884592i | \(0.345563\pi\) | |||||||
\(278\) | 21666.7i | 0.280351i | ||||||||
\(279\) | − | 15140.2i | − | 0.194501i | ||||||
\(280\) | 149204.i | 1.90311i | ||||||||
\(281\) | 121564. | 1.53955 | 0.769774 | − | 0.638316i | \(-0.220369\pi\) | ||||
0.769774 | + | 0.638316i | \(0.220369\pi\) | |||||||
\(282\) | −9988.46 | −0.125603 | ||||||||
\(283\) | − | 142151.i | − | 1.77491i | −0.460890 | − | 0.887457i | \(-0.652470\pi\) | ||
0.460890 | − | 0.887457i | \(-0.347530\pi\) | |||||||
\(284\) | −420275. | −5.21071 | ||||||||
\(285\) | −35625.9 | −0.438607 | ||||||||
\(286\) | − | 334214.i | − | 4.08594i | ||||||
\(287\) | 46851.7 | 0.568803 | ||||||||
\(288\) | 125138.i | 1.50871i | ||||||||
\(289\) | 69743.4 | 0.835041 | ||||||||
\(290\) | 170097.i | 2.02256i | ||||||||
\(291\) | − | 27655.9i | − | 0.326590i | ||||||
\(292\) | 361326.i | 4.23774i | ||||||||
\(293\) | −96135.1 | −1.11982 | −0.559908 | − | 0.828555i | \(-0.689164\pi\) | ||||
−0.559908 | + | 0.828555i | \(0.689164\pi\) | |||||||
\(294\) | − | 59189.5i | − | 0.684779i | ||||||
\(295\) | −73875.3 | + | 6990.89i | −0.848897 | + | 0.0803320i | ||||
\(296\) | 286535. | 3.27035 | ||||||||
\(297\) | − | 29108.6i | − | 0.329996i | ||||||
\(298\) | 63512.8 | 0.715202 | ||||||||
\(299\) | −59326.9 | −0.663604 | ||||||||
\(300\) | 40003.6 | 0.444484 | ||||||||
\(301\) | − | 66232.2i | − | 0.731032i | ||||||
\(302\) | −19063.1 | −0.209016 | ||||||||
\(303\) | 31296.0i | 0.340881i | ||||||||
\(304\) | −340574. | −3.68522 | ||||||||
\(305\) | 11043.7i | 0.118718i | ||||||||
\(306\) | − | 82646.5i | − | 0.882636i | ||||||
\(307\) | 35837.3 | 0.380240 | 0.190120 | − | 0.981761i | \(-0.439112\pi\) | ||||
0.190120 | + | 0.981761i | \(0.439112\pi\) | |||||||
\(308\) | − | 287733.i | − | 3.03311i | ||||||
\(309\) | 19423.7i | 0.203430i | ||||||||
\(310\) | 93462.6 | 0.972556 | ||||||||
\(311\) | −55265.8 | −0.571394 | −0.285697 | − | 0.958320i | \(-0.592225\pi\) | ||||
−0.285697 | + | 0.958320i | \(0.592225\pi\) | |||||||
\(312\) | −243852. | −2.50505 | ||||||||
\(313\) | 96714.2i | 0.987192i | 0.869691 | + | 0.493596i | \(0.164318\pi\) | ||||
−0.869691 | + | 0.493596i | \(0.835682\pi\) | |||||||
\(314\) | 107990. | 1.09528 | ||||||||
\(315\) | −17685.2 | −0.178233 | ||||||||
\(316\) | −231566. | −2.31900 | ||||||||
\(317\) | −132005. | −1.31363 | −0.656813 | − | 0.754053i | \(-0.728096\pi\) | ||||
−0.656813 | + | 0.754053i | \(0.728096\pi\) | |||||||
\(318\) | − | 46436.5i | − | 0.459204i | ||||||
\(319\) | − | 211740.i | − | 2.08075i | ||||||
\(320\) | −411330. | −4.01689 | ||||||||
\(321\) | 55609.8 | 0.539686 | ||||||||
\(322\) | −69182.6 | −0.667245 | ||||||||
\(323\) | 125914. | 1.20689 | ||||||||
\(324\) | −32902.4 | −0.313428 | ||||||||
\(325\) | 35141.9i | 0.332705i | ||||||||
\(326\) | − | 110016.i | − | 1.03519i | ||||||
\(327\) | − | 110667.i | − | 1.03496i | ||||||
\(328\) | 347333.i | 3.22848i | ||||||||
\(329\) | − | 7554.24i | − | 0.0697909i | ||||||
\(330\) | 179692. | 1.65006 | ||||||||
\(331\) | 53983.3 | 0.492724 | 0.246362 | − | 0.969178i | \(-0.420765\pi\) | ||||
0.246362 | + | 0.969178i | \(0.420765\pi\) | |||||||
\(332\) | 606058.i | 5.49842i | ||||||||
\(333\) | 33963.0i | 0.306279i | ||||||||
\(334\) | − | 296046.i | − | 2.65379i | ||||||
\(335\) | − | 53201.6i | − | 0.474062i | ||||||
\(336\) | −169065. | −1.49753 | ||||||||
\(337\) | 87020.3i | 0.766233i | 0.923700 | + | 0.383116i | \(0.125149\pi\) | ||||
−0.923700 | + | 0.383116i | \(0.874851\pi\) | |||||||
\(338\) | − | 108550.i | − | 0.950158i | ||||||
\(339\) | 87146.3i | 0.758315i | ||||||||
\(340\) | 376662. | 3.25832 | ||||||||
\(341\) | −116344. | −1.00054 | ||||||||
\(342\) | − | 67897.9i | − | 0.580503i | ||||||
\(343\) | 118539. | 1.00757 | ||||||||
\(344\) | 491010. | 4.14928 | ||||||||
\(345\) | − | 31897.4i | − | 0.267989i | ||||||
\(346\) | 103377. | 0.863519 | ||||||||
\(347\) | 74094.0i | 0.615353i | 0.951491 | + | 0.307677i | \(0.0995515\pi\) | ||||
−0.951491 | + | 0.307677i | \(0.900449\pi\) | |||||||
\(348\) | −239337. | −1.97629 | ||||||||
\(349\) | 27934.6i | 0.229347i | 0.993403 | + | 0.114673i | \(0.0365821\pi\) | ||||
−0.993403 | + | 0.114673i | \(0.963418\pi\) | |||||||
\(350\) | 40979.9i | 0.334530i | ||||||||
\(351\) | − | 28903.8i | − | 0.234607i | ||||||
\(352\) | 961615. | 7.76097 | ||||||||
\(353\) | 140969.i | 1.13129i | 0.824648 | + | 0.565647i | \(0.191373\pi\) | ||||
−0.824648 | + | 0.565647i | \(0.808627\pi\) | |||||||
\(354\) | −13323.7 | − | 140796.i | −0.106321 | − | 1.12353i | ||||
\(355\) | 198502. | 1.57510 | ||||||||
\(356\) | − | 141797.i | − | 1.11883i | ||||||
\(357\) | 62505.3 | 0.490434 | ||||||||
\(358\) | −3113.89 | −0.0242961 | ||||||||
\(359\) | −29736.8 | −0.230731 | −0.115365 | − | 0.993323i | \(-0.536804\pi\) | ||||
−0.115365 | + | 0.993323i | \(0.536804\pi\) | |||||||
\(360\) | − | 131108.i | − | 1.01164i | ||||||
\(361\) | −26877.0 | −0.206237 | ||||||||
\(362\) | 359770.i | 2.74542i | ||||||||
\(363\) | −147606. | −1.12019 | ||||||||
\(364\) | − | 285709.i | − | 2.15636i | ||||||
\(365\) | − | 170659.i | − | 1.28099i | ||||||
\(366\) | −21047.8 | −0.157125 | ||||||||
\(367\) | − | 52026.5i | − | 0.386272i | −0.981172 | − | 0.193136i | \(-0.938134\pi\) | ||
0.981172 | − | 0.193136i | \(-0.0618658\pi\) | |||||||
\(368\) | − | 304930.i | − | 2.25167i | ||||||
\(369\) | −41169.4 | −0.302359 | ||||||||
\(370\) | −209659. | −1.53148 | ||||||||
\(371\) | 35119.8 | 0.255155 | ||||||||
\(372\) | 131507.i | 0.950306i | ||||||||
\(373\) | 70424.5 | 0.506181 | 0.253091 | − | 0.967443i | \(-0.418553\pi\) | ||||
0.253091 | + | 0.967443i | \(0.418553\pi\) | |||||||
\(374\) | −635091. | −4.54039 | ||||||||
\(375\) | −88124.0 | −0.626659 | ||||||||
\(376\) | 56003.0 | 0.396128 | ||||||||
\(377\) | − | 210250.i | − | 1.47929i | ||||||
\(378\) | − | 33705.5i | − | 0.235894i | ||||||
\(379\) | −39937.6 | −0.278038 | −0.139019 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139019 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(380\) | 309445. | 2.14297 | ||||||||
\(381\) | 141520. | 0.974919 | ||||||||
\(382\) | −470531. | −3.22449 | ||||||||
\(383\) | 155977. | 1.06332 | 0.531659 | − | 0.846959i | \(-0.321569\pi\) | ||||
0.531659 | + | 0.846959i | \(0.321569\pi\) | |||||||
\(384\) | − | 398612.i | − | 2.70326i | ||||||
\(385\) | 135900.i | 0.916852i | ||||||||
\(386\) | − | 249851.i | − | 1.67690i | ||||||
\(387\) | 58199.4i | 0.388595i | ||||||||
\(388\) | 240219.i | 1.59567i | ||||||||
\(389\) | −184572. | −1.21974 | −0.609870 | − | 0.792501i | \(-0.708778\pi\) | ||||
−0.609870 | + | 0.792501i | \(0.708778\pi\) | |||||||
\(390\) | 178428. | 1.17309 | ||||||||
\(391\) | 112736.i | 0.737411i | ||||||||
\(392\) | 331862.i | 2.15966i | ||||||||
\(393\) | − | 8930.73i | − | 0.0578232i | ||||||
\(394\) | − | 273608.i | − | 1.76253i | ||||||
\(395\) | 109372. | 0.700990 | ||||||||
\(396\) | 252836.i | 1.61231i | ||||||||
\(397\) | − | 216054.i | − | 1.37082i | −0.728155 | − | 0.685412i | \(-0.759622\pi\) | ||
0.728155 | − | 0.685412i | \(-0.240378\pi\) | |||||||
\(398\) | 29177.2i | 0.184195i | ||||||||
\(399\) | 51351.0 | 0.322555 | ||||||||
\(400\) | −180624. | −1.12890 | ||||||||
\(401\) | − | 186079.i | − | 1.15720i | −0.815611 | − | 0.578601i | \(-0.803599\pi\) | ||
0.815611 | − | 0.578601i | \(-0.196401\pi\) | |||||||
\(402\) | 101395. | 0.627428 | ||||||||
\(403\) | −115525. | −0.711321 | ||||||||
\(404\) | − | 271836.i | − | 1.66550i | ||||||
\(405\) | 15540.3 | 0.0947433 | ||||||||
\(406\) | − | 245178.i | − | 1.48741i | ||||||
\(407\) | 260986. | 1.57554 | ||||||||
\(408\) | 463380.i | 2.78367i | ||||||||
\(409\) | − | 142032.i | − | 0.849064i | −0.905413 | − | 0.424532i | \(-0.860439\pi\) | ||
0.905413 | − | 0.424532i | \(-0.139561\pi\) | |||||||
\(410\) | − | 254145.i | − | 1.51187i | ||||||
\(411\) | 46184.7 | 0.273410 | ||||||||
\(412\) | − | 168713.i | − | 0.993929i | ||||||
\(413\) | 106484. | − | 10076.6i | 0.624284 | − | 0.0590767i | ||||
\(414\) | 60792.0 | 0.354687 | ||||||||
\(415\) | − | 286250.i | − | 1.66207i | ||||||
\(416\) | 954850. | 5.51758 | ||||||||
\(417\) | 14399.0 | 0.0828060 | ||||||||
\(418\) | −521757. | −2.98618 | ||||||||
\(419\) | 305281.i | 1.73889i | 0.494032 | + | 0.869444i | \(0.335523\pi\) | ||||
−0.494032 | + | 0.869444i | \(0.664477\pi\) | |||||||
\(420\) | 153613. | 0.870821 | ||||||||
\(421\) | − | 40020.9i | − | 0.225799i | −0.993606 | − | 0.112900i | \(-0.963986\pi\) | ||
0.993606 | − | 0.112900i | \(-0.0360139\pi\) | |||||||
\(422\) | 107381. | 0.602978 | ||||||||
\(423\) | 6638.05i | 0.0370988i | ||||||||
\(424\) | 260359.i | 1.44824i | ||||||||
\(425\) | 66778.6 | 0.369708 | ||||||||
\(426\) | 378317.i | 2.08466i | ||||||||
\(427\) | − | 15918.4i | − | 0.0873059i | ||||||
\(428\) | −483025. | −2.63683 | ||||||||
\(429\) | −222109. | −1.20685 | ||||||||
\(430\) | −359274. | −1.94307 | ||||||||
\(431\) | 199954.i | 1.07641i | 0.842815 | + | 0.538203i | \(0.180897\pi\) | ||||
−0.842815 | + | 0.538203i | \(0.819103\pi\) | |||||||
\(432\) | 148561. | 0.796043 | ||||||||
\(433\) | −173422. | −0.924972 | −0.462486 | − | 0.886627i | \(-0.653042\pi\) | ||||
−0.462486 | + | 0.886627i | \(0.653042\pi\) | |||||||
\(434\) | −134717. | −0.715224 | ||||||||
\(435\) | 113042. | 0.597394 | ||||||||
\(436\) | 961254.i | 5.05668i | ||||||||
\(437\) | 92617.9i | 0.484989i | ||||||||
\(438\) | 325253. | 1.69540 | ||||||||
\(439\) | 236050. | 1.22483 | 0.612415 | − | 0.790536i | \(-0.290198\pi\) | ||||
0.612415 | + | 0.790536i | \(0.290198\pi\) | |||||||
\(440\) | −1.00749e6 | −5.20398 | ||||||||
\(441\) | −39335.7 | −0.202260 | ||||||||
\(442\) | −630623. | −3.22794 | ||||||||
\(443\) | − | 390579.i | − | 1.99022i | −0.0987629 | − | 0.995111i | \(-0.531489\pi\) | ||
0.0987629 | − | 0.995111i | \(-0.468511\pi\) | |||||||
\(444\) | − | 295002.i | − | 1.49644i | ||||||
\(445\) | 66972.4i | 0.338202i | ||||||||
\(446\) | − | 488620.i | − | 2.45641i | ||||||
\(447\) | − | 42208.8i | − | 0.211246i | ||||||
\(448\) | 592889. | 2.95405 | ||||||||
\(449\) | 297658. | 1.47647 | 0.738236 | − | 0.674543i | \(-0.235659\pi\) | ||||
0.738236 | + | 0.674543i | \(0.235659\pi\) | |||||||
\(450\) | − | 36009.8i | − | 0.177826i | ||||||
\(451\) | 316364.i | 1.55537i | ||||||||
\(452\) | − | 756951.i | − | 3.70502i | ||||||
\(453\) | 12668.8i | 0.0617361i | ||||||||
\(454\) | 123116. | 0.597316 | ||||||||
\(455\) | 134944.i | 0.651826i | ||||||||
\(456\) | 380688.i | 1.83080i | ||||||||
\(457\) | − | 138561.i | − | 0.663449i | −0.943376 | − | 0.331725i | \(-0.892370\pi\) | ||
0.943376 | − | 0.331725i | \(-0.107630\pi\) | |||||||
\(458\) | 393657. | 1.87666 | ||||||||
\(459\) | −54924.5 | −0.260700 | ||||||||
\(460\) | 277060.i | 1.30936i | ||||||||
\(461\) | −249929. | −1.17602 | −0.588010 | − | 0.808853i | \(-0.700089\pi\) | ||||
−0.588010 | + | 0.808853i | \(0.700089\pi\) | |||||||
\(462\) | −259007. | −1.21347 | ||||||||
\(463\) | 101021.i | 0.471248i | 0.971844 | + | 0.235624i | \(0.0757134\pi\) | ||||
−0.971844 | + | 0.235624i | \(0.924287\pi\) | |||||||
\(464\) | 1.08065e6 | 5.01937 | ||||||||
\(465\) | − | 62112.6i | − | 0.287259i | ||||||
\(466\) | −424597. | −1.95526 | ||||||||
\(467\) | − | 290164.i | − | 1.33048i | −0.746628 | − | 0.665242i | \(-0.768328\pi\) | ||
0.746628 | − | 0.665242i | \(-0.231672\pi\) | |||||||
\(468\) | 251058.i | 1.14626i | ||||||||
\(469\) | 76684.6i | 0.348628i | ||||||||
\(470\) | −40977.7 | −0.185503 | ||||||||
\(471\) | − | 71767.3i | − | 0.323508i | ||||||
\(472\) | 74702.8 | + | 789411.i | 0.335315 | + | 3.54339i | ||||
\(473\) | 447229. | 1.99898 | ||||||||
\(474\) | 208448.i | 0.927771i | ||||||||
\(475\) | 54861.7 | 0.243154 | ||||||||
\(476\) | −542920. | −2.39619 | ||||||||
\(477\) | −30860.4 | −0.135633 | ||||||||
\(478\) | 345963.i | 1.51417i | ||||||||
\(479\) | −90383.7 | −0.393930 | −0.196965 | − | 0.980411i | \(-0.563109\pi\) | ||||
−0.196965 | + | 0.980411i | \(0.563109\pi\) | |||||||
\(480\) | 513380.i | 2.22821i | ||||||||
\(481\) | 259150. | 1.12011 | ||||||||
\(482\) | 731958.i | 3.15059i | ||||||||
\(483\) | 45976.8i | 0.197081i | ||||||||
\(484\) | 1.28210e6 | 5.47308 | ||||||||
\(485\) | − | 113459.i | − | 0.482341i | ||||||
\(486\) | 29617.6i | 0.125394i | ||||||||
\(487\) | 151820. | 0.640132 | 0.320066 | − | 0.947395i | \(-0.396295\pi\) | ||||
0.320066 | + | 0.947395i | \(0.396295\pi\) | |||||||
\(488\) | 118010. | 0.495542 | ||||||||
\(489\) | −73113.7 | −0.305760 | ||||||||
\(490\) | − | 242825.i | − | 1.01135i | ||||||
\(491\) | −103785. | −0.430497 | −0.215249 | − | 0.976559i | \(-0.569056\pi\) | ||||
−0.215249 | + | 0.976559i | \(0.569056\pi\) | |||||||
\(492\) | 357597. | 1.47728 | ||||||||
\(493\) | −399528. | −1.64382 | ||||||||
\(494\) | −518086. | −2.12299 | ||||||||
\(495\) | − | 119418.i | − | 0.487371i | ||||||
\(496\) | − | 593779.i | − | 2.41358i | ||||||
\(497\) | −286120. | −1.15834 | ||||||||
\(498\) | 545552. | 2.19977 | ||||||||
\(499\) | 469746. | 1.88652 | 0.943262 | − | 0.332049i | \(-0.107740\pi\) | ||||
0.943262 | + | 0.332049i | \(0.107740\pi\) | |||||||
\(500\) | 765443. | 3.06177 | ||||||||
\(501\) | −196744. | −0.783837 | ||||||||
\(502\) | − | 242580.i | − | 0.962602i | ||||||
\(503\) | − | 138093.i | − | 0.545801i | −0.962042 | − | 0.272901i | \(-0.912017\pi\) | ||
0.962042 | − | 0.272901i | \(-0.0879831\pi\) | |||||||
\(504\) | 188979.i | 0.743964i | ||||||||
\(505\) | 128392.i | 0.503448i | ||||||||
\(506\) | − | 467151.i | − | 1.82455i | ||||||
\(507\) | −72139.2 | −0.280644 | ||||||||
\(508\) | −1.22924e6 | −4.76332 | ||||||||
\(509\) | − | 123336.i | − | 0.476051i | −0.971259 | − | 0.238026i | \(-0.923500\pi\) | ||
0.971259 | − | 0.238026i | \(-0.0765002\pi\) | |||||||
\(510\) | − | 339058.i | − | 1.30357i | ||||||
\(511\) | 245988.i | 0.942045i | ||||||||
\(512\) | 1.04843e6i | 3.99944i | ||||||||
\(513\) | −45123.0 | −0.171460 | ||||||||
\(514\) | − | 399597.i | − | 1.51250i | ||||||
\(515\) | 79685.7i | 0.300446i | ||||||||
\(516\) | − | 505519.i | − | 1.89862i | ||||||
\(517\) | 51009.6 | 0.190841 | ||||||||
\(518\) | 302202. | 1.12626 | ||||||||
\(519\) | − | 68701.4i | − | 0.255053i | ||||||
\(520\) | −1.00040e6 | −3.69972 | ||||||||
\(521\) | −68858.9 | −0.253679 | −0.126840 | − | 0.991923i | \(-0.540483\pi\) | ||||
−0.126840 | + | 0.991923i | \(0.540483\pi\) | |||||||
\(522\) | 215442.i | 0.790660i | ||||||||
\(523\) | 269285. | 0.984482 | 0.492241 | − | 0.870459i | \(-0.336178\pi\) | ||||
0.492241 | + | 0.870459i | \(0.336178\pi\) | |||||||
\(524\) | 77572.1i | 0.282516i | ||||||||
\(525\) | 27234.1 | 0.0988084 | ||||||||
\(526\) | 651985.i | 2.35649i | ||||||||
\(527\) | 219527.i | 0.790435i | ||||||||
\(528\) | − | 1.14160e6i | − | 4.09494i | ||||||
\(529\) | 196916. | 0.703672 | ||||||||
\(530\) | − | 190506.i | − | 0.678199i | ||||||
\(531\) | −93569.0 | + | 8854.53i | −0.331851 | + | 0.0314034i | ||||
\(532\) | −446034. | −1.57596 | ||||||||
\(533\) | 314138.i | 1.10577i | ||||||||
\(534\) | −127640. | −0.447615 | ||||||||
\(535\) | 228139. | 0.797063 | ||||||||
\(536\) | −568498. | −1.97879 | ||||||||
\(537\) | 2069.40i | 0.00717623i | ||||||||
\(538\) | 433149. | 1.49649 | ||||||||
\(539\) | 302272.i | 1.04045i | ||||||||
\(540\) | −134982. | −0.462902 | ||||||||
\(541\) | − | 110046.i | − | 0.375993i | −0.982170 | − | 0.187997i | \(-0.939801\pi\) | ||
0.982170 | − | 0.187997i | \(-0.0601994\pi\) | |||||||
\(542\) | 264272.i | 0.899607i | ||||||||
\(543\) | 239093. | 0.810900 | ||||||||
\(544\) | − | 1.81446e6i | − | 6.13125i | ||||||
\(545\) | − | 454014.i | − | 1.52854i | ||||||
\(546\) | −257185. | −0.862701 | ||||||||
\(547\) | 163036. | 0.544889 | 0.272444 | − | 0.962172i | \(-0.412168\pi\) | ||||
0.272444 | + | 0.962172i | \(0.412168\pi\) | |||||||
\(548\) | −401159. | −1.33584 | ||||||||
\(549\) | 13987.8i | 0.0464092i | ||||||||
\(550\) | −276714. | −0.914758 | ||||||||
\(551\) | −328231. | −1.08113 | ||||||||
\(552\) | −340847. | −1.11862 | ||||||||
\(553\) | −157648. | −0.515513 | ||||||||
\(554\) | 559572.i | 1.82321i | ||||||||
\(555\) | 139333.i | 0.452344i | ||||||||
\(556\) | −125070. | −0.404578 | ||||||||
\(557\) | −447290. | −1.44171 | −0.720857 | − | 0.693084i | \(-0.756251\pi\) | ||||
−0.720857 | + | 0.693084i | \(0.756251\pi\) | |||||||
\(558\) | 118378. | 0.380192 | ||||||||
\(559\) | 444083. | 1.42115 | ||||||||
\(560\) | −693591. | −2.21171 | ||||||||
\(561\) | 422064.i | 1.34107i | ||||||||
\(562\) | 950487.i | 3.00936i | ||||||||
\(563\) | − | 50595.3i | − | 0.159622i | −0.996810 | − | 0.0798111i | \(-0.974568\pi\) | ||
0.996810 | − | 0.0798111i | \(-0.0254317\pi\) | |||||||
\(564\) | − | 57657.9i | − | 0.181259i | ||||||
\(565\) | 357518.i | 1.11996i | ||||||||
\(566\) | 1.11145e6 | 3.46943 | ||||||||
\(567\) | −22399.7 | −0.0696748 | ||||||||
\(568\) | − | 2.12114e6i | − | 6.57464i | ||||||
\(569\) | − | 596739.i | − | 1.84315i | −0.388204 | − | 0.921573i | \(-0.626904\pi\) | ||
0.388204 | − | 0.921573i | \(-0.373096\pi\) | |||||||
\(570\) | − | 278552.i | − | 0.857346i | ||||||
\(571\) | 2297.80i | 0.00704759i | 0.999994 | + | 0.00352379i | \(0.00112166\pi\) | ||||
−0.999994 | + | 0.00352379i | \(0.998878\pi\) | |||||||
\(572\) | 1.92923e6 | 5.89648 | ||||||||
\(573\) | 312701.i | 0.952402i | ||||||||
\(574\) | 366324.i | 1.11184i | ||||||||
\(575\) | 49120.0i | 0.148567i | ||||||||
\(576\) | −520982. | −1.57028 | ||||||||
\(577\) | −635182. | −1.90786 | −0.953931 | − | 0.300027i | \(-0.903004\pi\) | ||||
−0.953931 | + | 0.300027i | \(0.903004\pi\) | |||||||
\(578\) | 545310.i | 1.63225i | ||||||||
\(579\) | −166044. | −0.495296 | ||||||||
\(580\) | −981880. | −2.91879 | ||||||||
\(581\) | 412599.i | 1.22229i | ||||||||
\(582\) | 216236. | 0.638385 | ||||||||
\(583\) | 237145.i | 0.697712i | ||||||||
\(584\) | −1.82362e6 | −5.34698 | ||||||||
\(585\) | − | 118578.i | − | 0.346491i | ||||||
\(586\) | − | 751661.i | − | 2.18891i | ||||||
\(587\) | 46453.2i | 0.134815i | 0.997726 | + | 0.0674077i | \(0.0214728\pi\) | ||||
−0.997726 | + | 0.0674077i | \(0.978527\pi\) | |||||||
\(588\) | 341669. | 0.988213 | ||||||||
\(589\) | 180351.i | 0.519863i | ||||||||
\(590\) | −54660.4 | − | 577616.i | −0.157025 | − | 1.65934i | ||||
\(591\) | −181832. | −0.520590 | ||||||||
\(592\) | 1.33199e6i | 3.80064i | ||||||||
\(593\) | −292298. | −0.831221 | −0.415611 | − | 0.909543i | \(-0.636432\pi\) | ||||
−0.415611 | + | 0.909543i | \(0.636432\pi\) | |||||||
\(594\) | 227594. | 0.645042 | ||||||||
\(595\) | 256428. | 0.724323 | ||||||||
\(596\) | 366624.i | 1.03212i | ||||||||
\(597\) | 19390.3 | 0.0544047 | ||||||||
\(598\) | − | 463865.i | − | 1.29715i | ||||||
\(599\) | 239592. | 0.667758 | 0.333879 | − | 0.942616i | \(-0.391642\pi\) | ||||
0.333879 | + | 0.942616i | \(0.391642\pi\) | |||||||
\(600\) | 201899.i | 0.560829i | ||||||||
\(601\) | 235688.i | 0.652512i | 0.945281 | + | 0.326256i | \(0.105787\pi\) | ||||
−0.945281 | + | 0.326256i | \(0.894213\pi\) | |||||||
\(602\) | 517857. | 1.42895 | ||||||||
\(603\) | − | 67384.1i | − | 0.185320i | ||||||
\(604\) | − | 110041.i | − | 0.301634i | ||||||
\(605\) | −605554. | −1.65441 | ||||||||
\(606\) | −244697. | −0.666321 | ||||||||
\(607\) | 423021. | 1.14811 | 0.574056 | − | 0.818816i | \(-0.305369\pi\) | ||||
0.574056 | + | 0.818816i | \(0.305369\pi\) | |||||||
\(608\) | − | 1.49066e6i | − | 4.03247i | ||||||
\(609\) | −162938. | −0.439328 | ||||||||
\(610\) | −86348.7 | −0.232058 | ||||||||
\(611\) | 50650.7 | 0.135676 | ||||||||
\(612\) | 477073. | 1.27374 | ||||||||
\(613\) | − | 210522.i | − | 0.560243i | −0.959965 | − | 0.280122i | \(-0.909625\pi\) | ||
0.959965 | − | 0.280122i | \(-0.0903748\pi\) | |||||||
\(614\) | 280205.i | 0.743256i | ||||||||
\(615\) | −168898. | −0.446554 | ||||||||
\(616\) | 1.45219e6 | 3.82704 | ||||||||
\(617\) | −342587. | −0.899914 | −0.449957 | − | 0.893050i | \(-0.648561\pi\) | ||||
−0.449957 | + | 0.893050i | \(0.648561\pi\) | |||||||
\(618\) | −151870. | −0.397644 | ||||||||
\(619\) | −202870. | −0.529463 | −0.264732 | − | 0.964322i | \(-0.585283\pi\) | ||||
−0.264732 | + | 0.964322i | \(0.585283\pi\) | |||||||
\(620\) | 539508.i | 1.40351i | ||||||||
\(621\) | − | 40400.6i | − | 0.104762i | ||||||
\(622\) | − | 432112.i | − | 1.11690i | ||||||
\(623\) | − | 96533.8i | − | 0.248716i | ||||||
\(624\) | − | 1.13357e6i | − | 2.91125i | ||||||
\(625\) | −254919. | −0.652594 | ||||||||
\(626\) | −756189. | −1.92966 | ||||||||
\(627\) | 346745.i | 0.882013i | ||||||||
\(628\) | 623369.i | 1.58061i | ||||||||
\(629\) | − | 492451.i | − | 1.24469i | ||||||
\(630\) | − | 138277.i | − | 0.348392i | ||||||
\(631\) | −41966.6 | −0.105401 | −0.0527006 | − | 0.998610i | \(-0.516783\pi\) | ||||
−0.0527006 | + | 0.998610i | \(0.516783\pi\) | |||||||
\(632\) | − | 1.16872e6i | − | 2.92601i | ||||||
\(633\) | − | 71362.2i | − | 0.178099i | ||||||
\(634\) | − | 1.03212e6i | − | 2.56775i | ||||||
\(635\) | 580587. | 1.43986 | ||||||||
\(636\) | 268053. | 0.662683 | ||||||||
\(637\) | 300146.i | 0.739696i | ||||||||
\(638\) | 1.65555e6 | 4.06725 | ||||||||
\(639\) | 251418. | 0.615737 | ||||||||
\(640\) | − | 1.63531e6i | − | 3.99245i | ||||||
\(641\) | −336370. | −0.818656 | −0.409328 | − | 0.912387i | \(-0.634237\pi\) | ||||
−0.409328 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(642\) | 434802.i | 1.05492i | ||||||||
\(643\) | −387046. | −0.936140 | −0.468070 | − | 0.883691i | \(-0.655051\pi\) | ||||
−0.468070 | + | 0.883691i | \(0.655051\pi\) | |||||||
\(644\) | − | 399353.i | − | 0.962909i | ||||||
\(645\) | 238763.i | 0.573916i | ||||||||
\(646\) | 984495.i | 2.35911i | ||||||||
\(647\) | 640773. | 1.53072 | 0.765360 | − | 0.643602i | \(-0.222561\pi\) | ||||
0.765360 | + | 0.643602i | \(0.222561\pi\) | |||||||
\(648\) | − | 166059.i | − | 0.395469i | ||||||
\(649\) | 68042.0 | + | 719024.i | 0.161543 | + | 1.70708i | ||||
\(650\) | −274768. | −0.650338 | ||||||||
\(651\) | 89528.9i | 0.211252i | ||||||||
\(652\) | 635064. | 1.49390 | ||||||||
\(653\) | 59695.3 | 0.139995 | 0.0699977 | − | 0.997547i | \(-0.477701\pi\) | ||||
0.0699977 | + | 0.997547i | \(0.477701\pi\) | |||||||
\(654\) | 865287. | 2.02304 | ||||||||
\(655\) | − | 36638.4i | − | 0.0853991i | ||||||
\(656\) | −1.61462e6 | −3.75199 | ||||||||
\(657\) | − | 216154.i | − | 0.500763i | ||||||
\(658\) | 59065.1 | 0.136420 | ||||||||
\(659\) | − | 277090.i | − | 0.638043i | −0.947747 | − | 0.319022i | \(-0.896646\pi\) | ||
0.947747 | − | 0.319022i | \(-0.103354\pi\) | |||||||
\(660\) | 1.03726e6i | 2.38123i | ||||||||
\(661\) | −170596. | −0.390450 | −0.195225 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195225 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(662\) | 422085.i | 0.963128i | ||||||||
\(663\) | 419094.i | 0.953421i | ||||||||
\(664\) | −3.05879e6 | −6.93766 | ||||||||
\(665\) | 210668. | 0.476381 | ||||||||
\(666\) | −265550. | −0.598684 | ||||||||
\(667\) | − | 293879.i | − | 0.660568i | ||||||
\(668\) | 1.70891e6 | 3.82972 | ||||||||
\(669\) | −324723. | −0.725539 | ||||||||
\(670\) | 415973. | 0.926649 | ||||||||
\(671\) | 107488. | 0.238734 | ||||||||
\(672\) | − | 739984.i | − | 1.63864i | ||||||
\(673\) | 124494.i | 0.274864i | 0.990511 | + | 0.137432i | \(0.0438848\pi\) | ||||
−0.990511 | + | 0.137432i | \(0.956115\pi\) | |||||||
\(674\) | −680394. | −1.49775 | ||||||||
\(675\) | −23931.1 | −0.0525236 | ||||||||
\(676\) | 626599. | 1.37119 | ||||||||
\(677\) | 470982. | 1.02761 | 0.513804 | − | 0.857908i | \(-0.328236\pi\) | ||||
0.513804 | + | 0.857908i | \(0.328236\pi\) | |||||||
\(678\) | −681380. | −1.48228 | ||||||||
\(679\) | 163539.i | 0.354716i | ||||||||
\(680\) | 1.90102e6i | 4.11120i | ||||||||
\(681\) | − | 81819.6i | − | 0.176426i | ||||||
\(682\) | − | 909667.i | − | 1.95575i | ||||||
\(683\) | − | 543532.i | − | 1.16516i | −0.812775 | − | 0.582578i | \(-0.802044\pi\) | ||
0.812775 | − | 0.582578i | \(-0.197956\pi\) | |||||||
\(684\) | 391938. | 0.837731 | ||||||||
\(685\) | 189473. | 0.403800 | ||||||||
\(686\) | 926836.i | 1.96949i | ||||||||
\(687\) | − | 261613.i | − | 0.554301i | ||||||
\(688\) | 2.28251e6i | 4.82210i | ||||||||
\(689\) | 235476.i | 0.496031i | ||||||||
\(690\) | 249399. | 0.523838 | ||||||||
\(691\) | 466845.i | 0.977725i | 0.872361 | + | 0.488862i | \(0.162588\pi\) | ||||
−0.872361 | + | 0.488862i | \(0.837412\pi\) | |||||||
\(692\) | 596739.i | 1.24615i | ||||||||
\(693\) | 172129.i | 0.358416i | ||||||||
\(694\) | −579327. | −1.20283 | ||||||||
\(695\) | 59072.1 | 0.122296 | ||||||||
\(696\) | − | 1.20794e6i | − | 2.49359i | ||||||
\(697\) | 596942. | 1.22876 | ||||||||
\(698\) | −218415. | −0.448304 | ||||||||
\(699\) | 282175.i | 0.577517i | ||||||||
\(700\) | −236554. | −0.482764 | ||||||||
\(701\) | 661106.i | 1.34535i | 0.739939 | + | 0.672674i | \(0.234855\pi\) | ||||
−0.739939 | + | 0.672674i | \(0.765145\pi\) | |||||||
\(702\) | 225993. | 0.458586 | ||||||||
\(703\) | − | 404571.i | − | 0.818624i | ||||||
\(704\) | 4.00345e6i | 8.07773i | ||||||||
\(705\) | 27232.6i | 0.0547912i | ||||||||
\(706\) | −1.10221e6 | −2.21134 | ||||||||
\(707\) | − | 185064.i | − | 0.370239i | ||||||
\(708\) | 812738. | − | 76910.2i | 1.62138 | − | 0.153433i | ||||
\(709\) | −64729.8 | −0.128769 | −0.0643845 | − | 0.997925i | \(-0.520508\pi\) | ||||
−0.0643845 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(710\) | 1.55205e6i | 3.07884i | ||||||||
\(711\) | 138528. | 0.274031 | ||||||||
\(712\) | 715649. | 1.41169 | ||||||||
\(713\) | −161476. | −0.317636 | ||||||||
\(714\) | 488717.i | 0.958651i | ||||||||
\(715\) | −911203. | −1.78239 | ||||||||
\(716\) | − | 17974.8i | − | 0.0350621i | ||||||
\(717\) | 229917. | 0.447232 | ||||||||
\(718\) | − | 232506.i | − | 0.451009i | ||||||
\(719\) | − | 648569.i | − | 1.25458i | −0.778786 | − | 0.627290i | \(-0.784164\pi\) | ||
0.778786 | − | 0.627290i | \(-0.215836\pi\) | |||||||
\(720\) | 609471. | 1.17568 | ||||||||
\(721\) | − | 114859.i | − | 0.220950i | ||||||
\(722\) | − | 210146.i | − | 0.403131i | ||||||
\(723\) | 486439. | 0.930575 | ||||||||
\(724\) | −2.07676e6 | −3.96195 | ||||||||
\(725\) | −174078. | −0.331182 | ||||||||
\(726\) | − | 1.15410e6i | − | 2.18963i | ||||||
\(727\) | 201809. | 0.381831 | 0.190916 | − | 0.981606i | \(-0.438854\pi\) | ||||
0.190916 | + | 0.981606i | \(0.438854\pi\) | |||||||
\(728\) | 1.44198e6 | 2.72079 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 1.33435e6 | 2.50394 | ||||||||
\(731\) | − | 843870.i | − | 1.57921i | ||||||
\(732\) | − | 121497.i | − | 0.226749i | ||||||
\(733\) | −517718. | −0.963575 | −0.481787 | − | 0.876288i | \(-0.660012\pi\) | ||||
−0.481787 | + | 0.876288i | \(0.660012\pi\) | |||||||
\(734\) | 406785. | 0.755045 | ||||||||
\(735\) | −161375. | −0.298718 | ||||||||
\(736\) | 1.33465e6 | 2.46384 | ||||||||
\(737\) | −517808. | −0.953310 | ||||||||
\(738\) | − | 321896.i | − | 0.591020i | ||||||
\(739\) | 1.01019e6i | 1.84976i | 0.380263 | + | 0.924879i | \(0.375834\pi\) | ||||
−0.380263 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(740\) | − | 1.21025e6i | − | 2.21009i | ||||||
\(741\) | 344305.i | 0.627057i | ||||||||
\(742\) | 274595.i | 0.498752i | ||||||||
\(743\) | −521556. | −0.944765 | −0.472382 | − | 0.881394i | \(-0.656606\pi\) | ||||
−0.472382 | + | 0.881394i | \(0.656606\pi\) | |||||||
\(744\) | −663718. | −1.19905 | ||||||||
\(745\) | − | 173162.i | − | 0.311989i | ||||||
\(746\) | 550635.i | 0.989432i | ||||||||
\(747\) | − | 362558.i | − | 0.649735i | ||||||
\(748\) | − | 3.66603e6i | − | 6.55229i | ||||||
\(749\) | −328839. | −0.586165 | ||||||||
\(750\) | − | 689024.i | − | 1.22493i | ||||||
\(751\) | − | 879845.i | − | 1.56001i | −0.625776 | − | 0.780003i | \(-0.715217\pi\) | ||
0.625776 | − | 0.780003i | \(-0.284783\pi\) | |||||||
\(752\) | 260336.i | 0.460362i | ||||||||
\(753\) | −161212. | −0.284319 | ||||||||
\(754\) | 1.64390e6 | 2.89157 | ||||||||
\(755\) | 51973.9i | 0.0911782i | ||||||||
\(756\) | 194563. | 0.340421 | ||||||||
\(757\) | −1.05871e6 | −1.84750 | −0.923748 | − | 0.383000i | \(-0.874891\pi\) | ||||
−0.923748 | + | 0.383000i | \(0.874891\pi\) | |||||||
\(758\) | − | 312264.i | − | 0.543481i | ||||||
\(759\) | −310456. | −0.538910 | ||||||||
\(760\) | 1.56178e6i | 2.70391i | ||||||||
\(761\) | −319446. | −0.551604 | −0.275802 | − | 0.961214i | \(-0.588943\pi\) | ||||
−0.275802 | + | 0.961214i | \(0.588943\pi\) | |||||||
\(762\) | 1.10652e6i | 1.90567i | ||||||||
\(763\) | 654414.i | 1.12410i | ||||||||
\(764\) | − | 2.71612e6i | − | 4.65330i | ||||||
\(765\) | −225328. | −0.385028 | ||||||||
\(766\) | 1.21955e6i | 2.07847i | ||||||||
\(767\) | 67563.3 | + | 713966.i | 0.114847 | + | 1.21363i | ||||
\(768\) | 1.51245e6 | 2.56425 | ||||||||
\(769\) | − | 547254.i | − | 0.925414i | −0.886511 | − | 0.462707i | \(-0.846878\pi\) | ||
0.886511 | − | 0.462707i | \(-0.153122\pi\) | |||||||
\(770\) | −1.06258e6 | −1.79217 | ||||||||
\(771\) | −265561. | −0.446741 | ||||||||
\(772\) | 1.44225e6 | 2.41995 | ||||||||
\(773\) | 385413.i | 0.645011i | 0.946568 | + | 0.322505i | \(0.104525\pi\) | ||||
−0.946568 | + | 0.322505i | \(0.895475\pi\) | |||||||
\(774\) | −455050. | −0.759586 | ||||||||
\(775\) | 95649.6i | 0.159250i | ||||||||
\(776\) | −1.21239e6 | −2.01335 | ||||||||
\(777\) | − | 200835.i | − | 0.332657i | ||||||
\(778\) | − | 1.44313e6i | − | 2.38423i | ||||||
\(779\) | 490415. | 0.808144 | ||||||||
\(780\) | 1.02996e6i | 1.69291i | ||||||||
\(781\) | − | 1.93201e6i | − | 3.16743i | ||||||
\(782\) | −881461. | −1.44142 | ||||||||
\(783\) | 143177. | 0.233533 | ||||||||
\(784\) | −1.54270e6 | −2.50986 | ||||||||
\(785\) | − | 294426.i | − | 0.477789i | ||||||
\(786\) | 69827.6 | 0.113027 | ||||||||
\(787\) | 1.03990e6 | 1.67896 | 0.839481 | − | 0.543389i | \(-0.182859\pi\) | ||||
0.839481 | + | 0.543389i | \(0.182859\pi\) | |||||||
\(788\) | 1.57939e6 | 2.54353 | ||||||||
\(789\) | 433290. | 0.696025 | ||||||||
\(790\) | 855158.i | 1.37023i | ||||||||
\(791\) | − | 515325.i | − | 0.823623i | ||||||
\(792\) | −1.27607e6 | −2.03434 | ||||||||
\(793\) | 106732. | 0.169726 | ||||||||
\(794\) | 1.68929e6 | 2.67955 | ||||||||
\(795\) | −126605. | −0.200316 | ||||||||
\(796\) | −168424. | −0.265814 | ||||||||
\(797\) | 436583.i | 0.687306i | 0.939097 | + | 0.343653i | \(0.111664\pi\) | ||||
−0.939097 | + | 0.343653i | \(0.888336\pi\) | |||||||
\(798\) | 401503.i | 0.630497i | ||||||||
\(799\) | − | 96249.2i | − | 0.150766i | ||||||
\(800\) | − | 790574.i | − | 1.23527i | ||||||
\(801\) | 84826.0i | 0.132210i | ||||||||
\(802\) | 1.45492e6 | 2.26198 | ||||||||
\(803\) | −1.66102e6 | −2.57598 | ||||||||
\(804\) | 585297.i | 0.905449i | ||||||||
\(805\) | 188620.i | 0.291069i | ||||||||
\(806\) | − | 903267.i | − | 1.39042i | ||||||
\(807\) | − | 287859.i | − | 0.442010i | ||||||
\(808\) | 1.37196e6 | 2.10145 | ||||||||
\(809\) | 43381.1i | 0.0662832i | 0.999451 | + | 0.0331416i | \(0.0105512\pi\) | ||||
−0.999451 | + | 0.0331416i | \(0.989449\pi\) | |||||||
\(810\) | 121506.i | 0.185195i | ||||||||
\(811\) | − | 112796.i | − | 0.171495i | −0.996317 | − | 0.0857476i | \(-0.972672\pi\) | ||
0.996317 | − | 0.0857476i | \(-0.0273279\pi\) | |||||||
\(812\) | 1.41528e6 | 2.14649 | ||||||||
\(813\) | 175628. | 0.265712 | ||||||||
\(814\) | 2.04060e6i | 3.07970i | ||||||||
\(815\) | −299949. | −0.451578 | ||||||||
\(816\) | −2.15408e6 | −3.23505 | ||||||||
\(817\) | − | 693279.i | − | 1.03864i | ||||||
\(818\) | 1.11052e6 | 1.65967 | ||||||||
\(819\) | 170918.i | 0.254812i | ||||||||
\(820\) | 1.46704e6 | 2.18180 | ||||||||
\(821\) | − | 606308.i | − | 0.899512i | −0.893152 | − | 0.449756i | \(-0.851511\pi\) | ||
0.893152 | − | 0.449756i | \(-0.148489\pi\) | |||||||
\(822\) | 361109.i | 0.534435i | ||||||||
\(823\) | 883912.i | 1.30500i | 0.757790 | + | 0.652499i | \(0.226279\pi\) | ||||
−0.757790 | + | 0.652499i | \(0.773721\pi\) | |||||||
\(824\) | 851500. | 1.25409 | ||||||||
\(825\) | 183897.i | 0.270188i | ||||||||
\(826\) | 78787.3 | + | 832574.i | 0.115477 | + | 1.22029i | ||||
\(827\) | −4182.48 | −0.00611537 | −0.00305769 | − | 0.999995i | \(-0.500973\pi\) | ||||
−0.00305769 | + | 0.999995i | \(0.500973\pi\) | |||||||
\(828\) | 350919.i | 0.511854i | ||||||||
\(829\) | 1.03471e6 | 1.50561 | 0.752803 | − | 0.658246i | \(-0.228701\pi\) | ||||
0.752803 | + | 0.658246i | \(0.228701\pi\) | |||||||
\(830\) | 2.23813e6 | 3.24884 | ||||||||
\(831\) | 371875. | 0.538512 | ||||||||
\(832\) | 3.97529e6i | 5.74277i | ||||||||
\(833\) | 570353. | 0.821965 | ||||||||
\(834\) | 112583.i | 0.161861i | ||||||||
\(835\) | −807143. | −1.15765 | ||||||||
\(836\) | − | 3.01182e6i | − | 4.30939i | ||||||
\(837\) | − | 78670.6i | − | 0.112295i | ||||||
\(838\) | −2.38693e6 | −3.39900 | ||||||||
\(839\) | 1.28432e6i | 1.82452i | 0.409611 | + | 0.912260i | \(0.365664\pi\) | ||||
−0.409611 | + | 0.912260i | \(0.634336\pi\) | |||||||
\(840\) | 775287.i | 1.09876i | ||||||||
\(841\) | 334205. | 0.472521 | ||||||||
\(842\) | 312916. | 0.441370 | ||||||||
\(843\) | 631667. | 0.888859 | ||||||||
\(844\) | 619851.i | 0.870166i | ||||||||
\(845\) | −295951. | −0.414483 | ||||||||
\(846\) | −51901.6 | −0.0725170 | ||||||||
\(847\) | 872843. | 1.21666 | ||||||||
\(848\) | −1.21031e6 | −1.68308 | ||||||||
\(849\) | − | 738639.i | − | 1.02475i | ||||||
\(850\) | 522128.i | 0.722669i | ||||||||
\(851\) | 362230. | 0.500179 | ||||||||
\(852\) | −2.18381e6 | −3.00841 | ||||||||
\(853\) | 131299. | 0.180452 | 0.0902262 | − | 0.995921i | \(-0.471241\pi\) | ||||
0.0902262 | + | 0.995921i | \(0.471241\pi\) | |||||||
\(854\) | 124463. | 0.170657 | ||||||||
\(855\) | −185117. | −0.253230 | ||||||||
\(856\) | − | 2.43784e6i | − | 3.32703i | ||||||
\(857\) | 41212.7i | 0.0561138i | 0.999606 | + | 0.0280569i | \(0.00893196\pi\) | ||||
−0.999606 | + | 0.0280569i | \(0.991068\pi\) | |||||||
\(858\) | − | 1.73663e6i | − | 2.35902i | ||||||
\(859\) | − | 794929.i | − | 1.07731i | −0.842525 | − | 0.538657i | \(-0.818932\pi\) | ||
0.842525 | − | 0.538657i | \(-0.181068\pi\) | |||||||
\(860\) | − | 2.07389e6i | − | 2.80407i | ||||||
\(861\) | 243449. | 0.328398 | ||||||||
\(862\) | −1.56340e6 | −2.10405 | ||||||||
\(863\) | − | 675152.i | − | 0.906525i | −0.891377 | − | 0.453263i | \(-0.850260\pi\) | ||
0.891377 | − | 0.453263i | \(-0.149740\pi\) | |||||||
\(864\) | 650237.i | 0.871052i | ||||||||
\(865\) | − | 281848.i | − | 0.376689i | ||||||
\(866\) | − | 1.35595e6i | − | 1.80804i | ||||||
\(867\) | 362397. | 0.482111 | ||||||||
\(868\) | − | 777646.i | − | 1.03215i | ||||||
\(869\) | − | 1.06451e6i | − | 1.40965i | ||||||
\(870\) | 883852.i | 1.16773i | ||||||||
\(871\) | −514165. | −0.677745 | ||||||||
\(872\) | −4.85147e6 | −6.38028 | ||||||||
\(873\) | − | 143704.i | − | 0.188557i | ||||||
\(874\) | −724161. | −0.948009 | ||||||||
\(875\) | 521107. | 0.680629 | ||||||||
\(876\) | 1.87751e6i | 2.44666i | ||||||||
\(877\) | 461113. | 0.599526 | 0.299763 | − | 0.954014i | \(-0.403092\pi\) | ||||
0.299763 | + | 0.954014i | \(0.403092\pi\) | |||||||
\(878\) | 1.84563e6i | 2.39418i | ||||||||
\(879\) | −499533. | −0.646526 | ||||||||
\(880\) | − | 4.68343e6i | − | 6.04782i | ||||||
\(881\) | − | 39808.0i | − | 0.0512883i | −0.999671 | − | 0.0256442i | \(-0.991836\pi\) | ||
0.999671 | − | 0.0256442i | \(-0.00816368\pi\) | |||||||
\(882\) | − | 307558.i | − | 0.395357i | ||||||
\(883\) | −206390. | −0.264708 | −0.132354 | − | 0.991203i | \(-0.542254\pi\) | ||||
−0.132354 | + | 0.991203i | \(0.542254\pi\) | |||||||
\(884\) | − | 3.64024e6i | − | 4.65828i | ||||||
\(885\) | −383867. | + | 36325.7i | −0.490111 | + | 0.0463797i | ||||
\(886\) | 3.05386e6 | 3.89029 | ||||||||
\(887\) | − | 488379.i | − | 0.620740i | −0.950616 | − | 0.310370i | \(-0.899547\pi\) | ||
0.950616 | − | 0.310370i | \(-0.100453\pi\) | |||||||
\(888\) | 1.48888e6 | 1.88814 | ||||||||
\(889\) | −836857. | −1.05888 | ||||||||
\(890\) | −523644. | −0.661083 | ||||||||
\(891\) | − | 151253.i | − | 0.190523i | ||||||
\(892\) | 2.82053e6 | 3.54488 | ||||||||
\(893\) | − | 79073.2i | − | 0.0991577i | ||||||
\(894\) | 330022. | 0.412922 | ||||||||
\(895\) | 8489.74i | 0.0105986i | ||||||||
\(896\) | 2.35712e6i | 2.93607i | ||||||||
\(897\) | −308271. | −0.383132 | ||||||||
\(898\) | 2.32733e6i | 2.88606i | ||||||||
\(899\) | − | 572260.i | − | 0.708067i | ||||||
\(900\) | 207865. | 0.256623 | ||||||||
\(901\) | 447464. | 0.551200 | ||||||||
\(902\) | −2.47358e6 | −3.04028 | ||||||||
\(903\) | − | 344153.i | − | 0.422062i | ||||||
\(904\) | 3.82034e6 | 4.67482 | ||||||||
\(905\) | 980880. | 1.19762 | ||||||||
\(906\) | −99054.9 | −0.120676 | ||||||||
\(907\) | −664689. | −0.807986 | −0.403993 | − | 0.914762i | \(-0.632378\pi\) | ||||
−0.403993 | + | 0.914762i | \(0.632378\pi\) | |||||||
\(908\) | 710683.i | 0.861994i | ||||||||
\(909\) | 162619.i | 0.196808i | ||||||||
\(910\) | −1.05510e6 | −1.27412 | ||||||||
\(911\) | 467295. | 0.563060 | 0.281530 | − | 0.959552i | \(-0.409158\pi\) | ||||
0.281530 | + | 0.959552i | \(0.409158\pi\) | |||||||
\(912\) | −1.76967e6 | −2.12766 | ||||||||
\(913\) | −2.78605e6 | −3.34232 | ||||||||
\(914\) | 1.08338e6 | 1.29684 | ||||||||
\(915\) | 57384.9i | 0.0685418i | ||||||||
\(916\) | 2.27236e6i | 2.70824i | ||||||||
\(917\) | 52810.4i | 0.0628030i | ||||||||
\(918\) | − | 429444.i | − | 0.509590i | ||||||
\(919\) | 32821.0i | 0.0388616i | 0.999811 | + | 0.0194308i | \(0.00618541\pi\) | ||||
−0.999811 | + | 0.0194308i | \(0.993815\pi\) | |||||||
\(920\) | −1.39833e6 | −1.65209 | ||||||||
\(921\) | 186216. | 0.219532 | ||||||||
\(922\) | − | 1.95415e6i | − | 2.29877i | ||||||
\(923\) | − | 1.91841e6i | − | 2.25185i | ||||||
\(924\) | − | 1.49511e6i | − | 1.75117i | ||||||
\(925\) | − | 214565.i | − | 0.250770i | ||||||
\(926\) | −789863. | −0.921149 | ||||||||
\(927\) | 100928.i | 0.117450i | ||||||||
\(928\) | 4.72991e6i | 5.49233i | ||||||||
\(929\) | 1.32545e6i | 1.53579i | 0.640577 | + | 0.767894i | \(0.278695\pi\) | ||||
−0.640577 | + | 0.767894i | \(0.721305\pi\) | |||||||
\(930\) | 485646. | 0.561505 | ||||||||
\(931\) | 468571. | 0.540600 | ||||||||
\(932\) | − | 2.45097e6i | − | 2.82167i | ||||||
\(933\) | −287169. | −0.329894 | ||||||||
\(934\) | 2.26873e6 | 2.60070 | ||||||||
\(935\) | 1.73152e6i | 1.98063i | ||||||||
\(936\) | −1.26709e6 | −1.44629 | ||||||||
\(937\) | 45039.7i | 0.0512998i | 0.999671 | + | 0.0256499i | \(0.00816552\pi\) | ||||
−0.999671 | + | 0.0256499i | \(0.991834\pi\) | |||||||
\(938\) | −599582. | −0.681463 | ||||||||
\(939\) | 502542.i | 0.569956i | ||||||||
\(940\) | − | 236542.i | − | 0.267702i | ||||||
\(941\) | − | 517189.i | − | 0.584077i | −0.956407 | − | 0.292038i | \(-0.905667\pi\) | ||
0.956407 | − | 0.292038i | \(-0.0943335\pi\) | |||||||
\(942\) | 561134. | 0.632361 | ||||||||
\(943\) | 439090.i | 0.493776i | ||||||||
\(944\) | −3.66966e6 | + | 347264.i | −4.11796 | + | 0.389687i | ||||
\(945\) | −91894.8 | −0.102903 | ||||||||
\(946\) | 3.49680e6i | 3.90740i | ||||||||
\(947\) | 510466. | 0.569203 | 0.284601 | − | 0.958646i | \(-0.408139\pi\) | ||||
0.284601 | + | 0.958646i | \(0.408139\pi\) | |||||||
\(948\) | −1.20325e6 | −1.33888 | ||||||||
\(949\) | −1.64933e6 | −1.83137 | ||||||||
\(950\) | 428953.i | 0.475294i | ||||||||
\(951\) | −685918. | −0.758422 | ||||||||
\(952\) | − | 2.74012e6i | − | 3.02340i | ||||||
\(953\) | −26017.8 | −0.0286473 | −0.0143237 | − | 0.999897i | \(-0.504560\pi\) | ||||
−0.0143237 | + | 0.999897i | \(0.504560\pi\) | |||||||
\(954\) | − | 241291.i | − | 0.265122i | ||||||
\(955\) | 1.28286e6i | 1.40660i | ||||||||
\(956\) | −1.99705e6 | −2.18511 | ||||||||
\(957\) | − | 1.10023e6i | − | 1.20132i | ||||||
\(958\) | − | 706692.i | − | 0.770015i | ||||||
\(959\) | −273106. | −0.296957 | ||||||||
\(960\) | −2.13733e6 | −2.31915 | ||||||||
\(961\) | 609084. | 0.659524 | ||||||||
\(962\) | 2.02624e6i | 2.18948i | ||||||||
\(963\) | 288957. | 0.311588 | ||||||||
\(964\) | −4.22519e6 | −4.54666 | ||||||||
\(965\) | −681195. | −0.731504 | ||||||||
\(966\) | −359483. | −0.385234 | ||||||||
\(967\) | − | 262570.i | − | 0.280797i | −0.990095 | − | 0.140399i | \(-0.955162\pi\) | ||
0.990095 | − | 0.140399i | \(-0.0448384\pi\) | |||||||
\(968\) | 6.47078e6i | 6.90567i | ||||||||
\(969\) | 654267. | 0.696799 | ||||||||
\(970\) | 887110. | 0.942832 | ||||||||
\(971\) | −787423. | −0.835160 | −0.417580 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417580 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(972\) | −170966. | −0.180958 | ||||||||
\(973\) | −85146.4 | −0.0899374 | ||||||||
\(974\) | 1.18705e6i | 1.25127i | ||||||||
\(975\) | 182603.i | 0.192087i | ||||||||
\(976\) | 548584.i | 0.575895i | ||||||||
\(977\) | 252812.i | 0.264855i | 0.991193 | + | 0.132428i | \(0.0422772\pi\) | ||||
−0.991193 | + | 0.132428i | \(0.957723\pi\) | |||||||
\(978\) | − | 571662.i | − | 0.597670i | ||||||
\(979\) | 651839. | 0.680103 | ||||||||
\(980\) | 1.40170e6 | 1.45949 | ||||||||
\(981\) | − | 575045.i | − | 0.597535i | ||||||
\(982\) | − | 811472.i | − | 0.841493i | ||||||
\(983\) | 1.29505e6i | 1.34023i | 0.742256 | + | 0.670116i | \(0.233756\pi\) | ||||
−0.742256 | + | 0.670116i | \(0.766244\pi\) | |||||||
\(984\) | 1.80480e6i | 1.86397i | ||||||||
\(985\) | −745968. | −0.768861 | ||||||||
\(986\) | − | 3.12383e6i | − | 3.21317i | ||||||
\(987\) | − | 39253.0i | − | 0.0402938i | ||||||
\(988\) | − | 2.99063e6i | − | 3.06372i | ||||||
\(989\) | 620722. | 0.634607 | ||||||||
\(990\) | 933706. | 0.952664 | ||||||||
\(991\) | − | 1.07822e6i | − | 1.09789i | −0.835857 | − | 0.548947i | \(-0.815029\pi\) | ||
0.835857 | − | 0.548947i | \(-0.184971\pi\) | |||||||
\(992\) | 2.59892e6 | 2.64101 | ||||||||
\(993\) | 280506. | 0.284474 | ||||||||
\(994\) | − | 2.23711e6i | − | 2.26420i | ||||||
\(995\) | 79548.9 | 0.0803504 | ||||||||
\(996\) | 3.14917e6i | 3.17452i | ||||||||
\(997\) | 565271. | 0.568678 | 0.284339 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284339 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(998\) | 3.67285e6i | 3.68759i | ||||||||
\(999\) | 176477.i | 0.176830i |
(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 | 177.5.c.a.58.40 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.1 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.1 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.40 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.1 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.40 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.1 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.40 | 40 | 177.176 | even | 2 |