Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.12 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.73 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.03383i | − 1.51691i | −0.651723 | − | 0.758457i | \(-0.725953\pi\) | ||||
0.651723 | − | 0.758457i | \(-0.274047\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.20412 | −1.30103 | ||||||||
\(5\) | 9.69466i | 1.93893i | 0.245227 | + | 0.969466i | \(0.421138\pi\) | ||||
−0.245227 | + | 0.969466i | \(0.578862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.465658 | −0.0665226 | −0.0332613 | − | 0.999447i | \(-0.510589\pi\) | ||||
−0.0332613 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(8\) | 3.65310i | 0.456637i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 29.4119 | 2.94119 | ||||||||
\(11\) | − 0.825606i | − 0.0750551i | −0.999296 | − | 0.0375276i | \(-0.988052\pi\) | ||||
0.999296 | − | 0.0375276i | \(-0.0119482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.5786 | 0.813739 | 0.406869 | − | 0.913486i | \(-0.366620\pi\) | ||||
0.406869 | + | 0.913486i | \(0.366620\pi\) | |||||||
\(14\) | 1.41273i | 0.100909i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.73361 | −0.608350 | ||||||||
\(17\) | 10.2606i | 0.603562i | 0.953377 | + | 0.301781i | \(0.0975812\pi\) | ||||
−0.953377 | + | 0.301781i | \(0.902419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2136 | 1.32703 | 0.663515 | − | 0.748163i | \(-0.269064\pi\) | ||||
0.663515 | + | 0.748163i | \(0.269064\pi\) | |||||||
\(20\) | − 50.4522i | − 2.52261i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.50475 | −0.113852 | ||||||||
\(23\) | − 0.704676i | − 0.0306381i | −0.999883 | − | 0.0153190i | \(-0.995124\pi\) | ||||
0.999883 | − | 0.0153190i | \(-0.00487639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −68.9864 | −2.75946 | ||||||||
\(26\) | − 32.0937i | − 1.23437i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.42334 | 0.0865479 | ||||||||
\(29\) | 8.67552i | 0.299156i | 0.988750 | + | 0.149578i | \(0.0477915\pi\) | ||||
−0.988750 | + | 0.149578i | \(0.952209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.9325 | −1.86879 | −0.934394 | − | 0.356240i | \(-0.884059\pi\) | ||||
−0.934394 | + | 0.356240i | \(0.884059\pi\) | |||||||
\(32\) | 44.1425i | 1.37945i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 31.1288 | 0.915552 | ||||||||
\(35\) | − 4.51440i | − 0.128983i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.5115 | −0.365177 | −0.182588 | − | 0.983189i | \(-0.558448\pi\) | ||||
−0.182588 | + | 0.983189i | \(0.558448\pi\) | |||||||
\(38\) | − 76.4937i | − 2.01299i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −35.4155 | −0.885388 | ||||||||
\(41\) | 10.5730i | 0.257878i | 0.991653 | + | 0.128939i | \(0.0411572\pi\) | ||||
−0.991653 | + | 0.128939i | \(0.958843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.4833 | −0.801937 | −0.400969 | − | 0.916092i | \(-0.631326\pi\) | ||||
−0.400969 | + | 0.916092i | \(0.631326\pi\) | |||||||
\(44\) | 4.29656i | 0.0976490i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.13787 | −0.0464754 | ||||||||
\(47\) | 62.5318i | 1.33046i | 0.746637 | + | 0.665232i | \(0.231667\pi\) | ||||
−0.746637 | + | 0.665232i | \(0.768333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.7832 | −0.995575 | ||||||||
\(50\) | 209.293i | 4.18586i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −55.0523 | −1.05870 | ||||||||
\(53\) | − 91.4802i | − 1.72604i | −0.505168 | − | 0.863021i | \(-0.668570\pi\) | ||||
0.505168 | − | 0.863021i | \(-0.331430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00397 | 0.145527 | ||||||||
\(56\) | − 1.70109i | − 0.0303767i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 26.3200 | 0.453794 | ||||||||
\(59\) | 17.6740i | 0.299559i | 0.988719 | + | 0.149779i | \(0.0478564\pi\) | ||||
−0.988719 | + | 0.149779i | \(0.952144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 67.4200 | 1.10525 | 0.552623 | − | 0.833431i | \(-0.313627\pi\) | ||||
0.552623 | + | 0.833431i | \(0.313627\pi\) | |||||||
\(62\) | 175.757i | 2.83479i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 94.9864 | 1.48416 | ||||||||
\(65\) | 102.556i | 1.57778i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −30.5164 | −0.455469 | −0.227734 | − | 0.973723i | \(-0.573132\pi\) | ||||
−0.227734 | + | 0.973723i | \(0.573132\pi\) | |||||||
\(68\) | − 53.3972i | − 0.785253i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.6959 | −0.195656 | ||||||||
\(71\) | 133.968i | 1.88687i | 0.331553 | + | 0.943437i | \(0.392427\pi\) | ||||
−0.331553 | + | 0.943437i | \(0.607573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.109 | 1.60423 | 0.802117 | − | 0.597167i | \(-0.203707\pi\) | ||||
0.802117 | + | 0.597167i | \(0.203707\pi\) | |||||||
\(74\) | 40.9917i | 0.553942i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −131.215 | −1.72651 | ||||||||
\(77\) | 0.384450i | 0.00499286i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −93.5817 | −1.18458 | −0.592289 | − | 0.805726i | \(-0.701776\pi\) | ||||
−0.592289 | + | 0.805726i | \(0.701776\pi\) | |||||||
\(80\) | − 94.3640i | − 1.17955i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 32.0767 | 0.391179 | ||||||||
\(83\) | 104.813i | 1.26281i | 0.775454 | + | 0.631404i | \(0.217521\pi\) | ||||
−0.775454 | + | 0.631404i | \(0.782479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −99.4726 | −1.17027 | ||||||||
\(86\) | 104.616i | 1.21647i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.01602 | 0.0342730 | ||||||||
\(89\) | − 5.45973i | − 0.0613453i | −0.999529 | − | 0.0306727i | \(-0.990235\pi\) | ||||
0.999529 | − | 0.0306727i | \(-0.00976494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.92601 | −0.0541320 | ||||||||
\(92\) | 3.66722i | 0.0398611i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 189.711 | 2.01820 | ||||||||
\(95\) | 244.437i | 2.57302i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −46.1082 | −0.475342 | −0.237671 | − | 0.971346i | \(-0.576384\pi\) | ||||
−0.237671 | + | 0.971346i | \(0.576384\pi\) | |||||||
\(98\) | 148.000i | 1.51020i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 359.013 | 3.59013 | ||||||||
\(101\) | 162.423i | 1.60815i | 0.594529 | + | 0.804074i | \(0.297339\pi\) | ||||
−0.594529 | + | 0.804074i | \(0.702661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −38.9286 | −0.377947 | −0.188974 | − | 0.981982i | \(-0.560516\pi\) | ||||
−0.188974 | + | 0.981982i | \(0.560516\pi\) | |||||||
\(104\) | 38.6447i | 0.371584i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −277.535 | −2.61826 | ||||||||
\(107\) | 4.84185i | 0.0452509i | 0.999744 | + | 0.0226255i | \(0.00720252\pi\) | ||||
−0.999744 | + | 0.0226255i | \(0.992797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −93.9791 | −0.862194 | −0.431097 | − | 0.902306i | \(-0.641873\pi\) | ||||
−0.431097 | + | 0.902306i | \(0.641873\pi\) | |||||||
\(110\) | − 24.2827i | − 0.220752i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.53253 | 0.0404690 | ||||||||
\(113\) | 80.6426i | 0.713651i | 0.934171 | + | 0.356826i | \(0.116141\pi\) | ||||
−0.934171 | + | 0.356826i | \(0.883859\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.83159 | 0.0594052 | ||||||||
\(116\) | − 45.1484i | − 0.389211i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 53.6198 | 0.454405 | ||||||||
\(119\) | − 4.77791i | − 0.0401505i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.318 | 0.994367 | ||||||||
\(122\) | − 204.541i | − 1.67656i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 301.488 | 2.43135 | ||||||||
\(125\) | − 426.433i | − 3.41146i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2694 | 0.0887357 | ||||||||
\(128\) | − 111.602i | − 0.871894i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 311.137 | 2.39336 | ||||||||
\(131\) | − 34.3037i | − 0.261861i | −0.991392 | − | 0.130930i | \(-0.958204\pi\) | ||||
0.991392 | − | 0.130930i | \(-0.0417964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7409 | −0.0882775 | ||||||||
\(134\) | 92.5816i | 0.690907i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −37.4828 | −0.275609 | ||||||||
\(137\) | − 49.9509i | − 0.364605i | −0.983242 | − | 0.182303i | \(-0.941645\pi\) | ||||
0.983242 | − | 0.182303i | \(-0.0583551\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −124.555 | −0.896081 | −0.448040 | − | 0.894013i | \(-0.647878\pi\) | ||||
−0.448040 | + | 0.894013i | \(0.647878\pi\) | |||||||
\(140\) | 23.4935i | 0.167810i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 406.436 | 2.86223 | ||||||||
\(143\) | − 8.73377i | − 0.0610753i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −84.1062 | −0.580042 | ||||||||
\(146\) | − 355.289i | − 2.43349i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 70.3157 | 0.475106 | ||||||||
\(149\) | − 88.0919i | − 0.591221i | −0.955309 | − | 0.295610i | \(-0.904477\pi\) | ||||
0.955309 | − | 0.295610i | \(-0.0955230\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −186.337 | −1.23402 | −0.617010 | − | 0.786955i | \(-0.711656\pi\) | ||||
−0.617010 | + | 0.786955i | \(0.711656\pi\) | |||||||
\(152\) | 92.1077i | 0.605972i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.16636 | 0.00757375 | ||||||||
\(155\) | − 561.635i | − 3.62345i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 183.153 | 1.16658 | 0.583289 | − | 0.812265i | \(-0.301766\pi\) | ||||
0.583289 | + | 0.812265i | \(0.301766\pi\) | |||||||
\(158\) | 283.911i | 1.79690i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −427.946 | −2.67466 | ||||||||
\(161\) | 0.328138i | 0.00203813i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −199.823 | −1.22591 | −0.612954 | − | 0.790118i | \(-0.710019\pi\) | ||||
−0.612954 | + | 0.790118i | \(0.710019\pi\) | |||||||
\(164\) | − 55.0232i | − 0.335507i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 317.985 | 1.91557 | ||||||||
\(167\) | − 5.57997i | − 0.0334130i | −0.999860 | − | 0.0167065i | \(-0.994682\pi\) | ||||
0.999860 | − | 0.0167065i | \(-0.00531809\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57.0931 | −0.337829 | ||||||||
\(170\) | 301.783i | 1.77519i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 179.455 | 1.04334 | ||||||||
\(173\) | 106.519i | 0.615717i | 0.951432 | + | 0.307858i | \(0.0996123\pi\) | ||||
−0.951432 | + | 0.307858i | \(0.900388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.1241 | 0.183566 | ||||||||
\(176\) | 8.03613i | 0.0456598i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.5639 | −0.0930556 | ||||||||
\(179\) | 308.791i | 1.72509i | 0.505982 | + | 0.862544i | \(0.331130\pi\) | ||||
−0.505982 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 157.986 | 0.872849 | 0.436424 | − | 0.899741i | \(-0.356245\pi\) | ||||
0.436424 | + | 0.899741i | \(0.356245\pi\) | |||||||
\(182\) | 14.9447i | 0.0821137i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.57425 | 0.0139905 | ||||||||
\(185\) | − 130.990i | − 0.708053i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.47118 | 0.0453004 | ||||||||
\(188\) | − 325.423i | − 1.73097i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 741.580 | 3.90305 | ||||||||
\(191\) | − 151.699i | − 0.794233i | −0.917768 | − | 0.397117i | \(-0.870011\pi\) | ||||
0.917768 | − | 0.397117i | \(-0.129989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −101.412 | −0.525449 | −0.262724 | − | 0.964871i | \(-0.584621\pi\) | ||||
−0.262724 | + | 0.964871i | \(0.584621\pi\) | |||||||
\(194\) | 139.884i | 0.721054i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 253.873 | 1.29527 | ||||||||
\(197\) | − 60.6071i | − 0.307650i | −0.988098 | − | 0.153825i | \(-0.950841\pi\) | ||||
0.988098 | − | 0.153825i | \(-0.0491592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −93.6473 | −0.470590 | −0.235295 | − | 0.971924i | \(-0.575606\pi\) | ||||
−0.235295 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(200\) | − 252.014i | − 1.26007i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 492.764 | 2.43942 | ||||||||
\(203\) | − 4.03982i | − 0.0199006i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −102.502 | −0.500008 | ||||||||
\(206\) | 118.103i | 0.573314i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −102.968 | −0.495038 | ||||||||
\(209\) | − 20.8165i | − 0.0996005i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −193.953 | −0.919208 | −0.459604 | − | 0.888124i | \(-0.652009\pi\) | ||||
−0.459604 | + | 0.888124i | \(0.652009\pi\) | |||||||
\(212\) | 476.074i | 2.24563i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.6893 | 0.0686418 | ||||||||
\(215\) | − 334.304i | − 1.55490i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.9767 | 0.124317 | ||||||||
\(218\) | 285.117i | 1.30787i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −41.6536 | −0.189335 | ||||||||
\(221\) | 108.542i | 0.491142i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −96.5930 | −0.433152 | −0.216576 | − | 0.976266i | \(-0.569489\pi\) | ||||
−0.216576 | + | 0.976266i | \(0.569489\pi\) | |||||||
\(224\) | − 20.5553i | − 0.0917648i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 244.656 | 1.08255 | ||||||||
\(227\) | − 255.360i | − 1.12493i | −0.826820 | − | 0.562467i | \(-0.809852\pi\) | ||||
0.826820 | − | 0.562467i | \(-0.190148\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −153.818 | −0.671694 | −0.335847 | − | 0.941917i | \(-0.609022\pi\) | ||||
−0.335847 | + | 0.941917i | \(0.609022\pi\) | |||||||
\(230\) | − 20.7259i | − 0.0901126i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −31.6925 | −0.136606 | ||||||||
\(233\) | 345.735i | 1.48384i | 0.670488 | + | 0.741920i | \(0.266085\pi\) | ||||
−0.670488 | + | 0.741920i | \(0.733915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −606.224 | −2.57968 | ||||||||
\(236\) | − 91.9775i | − 0.389735i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.4954 | −0.0609049 | ||||||||
\(239\) | − 17.6299i | − 0.0737652i | −0.999320 | − | 0.0368826i | \(-0.988257\pi\) | ||||
0.999320 | − | 0.0368826i | \(-0.0117428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 312.932 | 1.29847 | 0.649236 | − | 0.760587i | \(-0.275089\pi\) | ||||
0.649236 | + | 0.760587i | \(0.275089\pi\) | |||||||
\(242\) | − 365.025i | − 1.50837i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −350.862 | −1.43796 | ||||||||
\(245\) | − 472.936i | − 1.93035i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 266.725 | 1.07986 | ||||||||
\(248\) | − 211.633i | − 0.853359i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1293.72 | −5.17490 | ||||||||
\(251\) | − 230.937i | − 0.920066i | −0.887902 | − | 0.460033i | \(-0.847837\pi\) | ||||
0.887902 | − | 0.460033i | \(-0.152163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.581785 | −0.00229955 | ||||||||
\(254\) | − 34.1895i | − 0.134604i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 41.3626 | 0.161573 | ||||||||
\(257\) | 258.980i | 1.00770i | 0.863790 | + | 0.503852i | \(0.168084\pi\) | ||||
−0.863790 | + | 0.503852i | \(0.831916\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.29176 | 0.0242925 | ||||||||
\(260\) | − 533.714i | − 2.05274i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −104.072 | −0.397220 | ||||||||
\(263\) | 188.471i | 0.716620i | 0.933603 | + | 0.358310i | \(0.116647\pi\) | ||||
−0.933603 | + | 0.358310i | \(0.883353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 886.869 | 3.34668 | ||||||||
\(266\) | 35.6199i | 0.133909i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 158.811 | 0.592579 | ||||||||
\(269\) | − 66.7539i | − 0.248156i | −0.992272 | − | 0.124078i | \(-0.960403\pi\) | ||||
0.992272 | − | 0.124078i | \(-0.0395973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5305 | 0.0609980 | 0.0304990 | − | 0.999535i | \(-0.490290\pi\) | ||||
0.0304990 | + | 0.999535i | \(0.490290\pi\) | |||||||
\(272\) | − 99.8722i | − 0.367177i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −151.543 | −0.553075 | ||||||||
\(275\) | 56.9556i | 0.207111i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −304.859 | −1.10058 | −0.550288 | − | 0.834975i | \(-0.685482\pi\) | ||||
−0.550288 | + | 0.834975i | \(0.685482\pi\) | |||||||
\(278\) | 377.879i | 1.35928i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 16.4915 | 0.0588983 | ||||||||
\(281\) | 114.652i | 0.408014i | 0.978969 | + | 0.204007i | \(0.0653965\pi\) | ||||
−0.978969 | + | 0.204007i | \(0.934604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 213.495 | 0.754400 | 0.377200 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377200 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(284\) | − 697.186i | − 2.45488i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.4968 | −0.0926460 | ||||||||
\(287\) | − 4.92341i | − 0.0171547i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 183.721 | 0.635713 | ||||||||
\(290\) | 255.164i | 0.879875i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −609.450 | −2.08716 | ||||||||
\(293\) | − 499.490i | − 1.70475i | −0.522935 | − | 0.852373i | \(-0.675163\pi\) | ||||
0.522935 | − | 0.852373i | \(-0.324837\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −171.343 | −0.580824 | ||||||||
\(296\) | − 49.3590i | − 0.166753i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −267.256 | −0.896832 | ||||||||
\(299\) | − 7.45449i | − 0.0249314i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0574 | 0.0533470 | ||||||||
\(302\) | 565.315i | 1.87190i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −245.419 | −0.807300 | ||||||||
\(305\) | 653.614i | 2.14300i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 252.944 | 0.823922 | 0.411961 | − | 0.911202i | \(-0.364844\pi\) | ||||
0.411961 | + | 0.911202i | \(0.364844\pi\) | |||||||
\(308\) | − 2.00073i | − 0.00649586i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1703.91 | −5.49647 | ||||||||
\(311\) | 365.311i | 1.17463i | 0.809357 | + | 0.587317i | \(0.199816\pi\) | ||||
−0.809357 | + | 0.587317i | \(0.800184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 70.6417 | 0.225692 | 0.112846 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112846 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(314\) | − 555.654i | − 1.76960i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 487.010 | 1.54117 | ||||||||
\(317\) | − 219.350i | − 0.691955i | −0.938243 | − | 0.345978i | \(-0.887547\pi\) | ||||
0.938243 | − | 0.345978i | \(-0.112453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.16256 | 0.0224532 | ||||||||
\(320\) | 920.860i | 2.87769i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.995515 | 0.00309166 | ||||||||
\(323\) | 258.705i | 0.800945i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −729.780 | −2.24548 | ||||||||
\(326\) | 606.229i | 1.85960i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −38.6242 | −0.117757 | ||||||||
\(329\) | − 29.1184i | − 0.0885059i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198.861 | 0.600789 | 0.300394 | − | 0.953815i | \(-0.402882\pi\) | ||||
0.300394 | + | 0.953815i | \(0.402882\pi\) | |||||||
\(332\) | − 545.460i | − 1.64295i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.9287 | −0.0506847 | ||||||||
\(335\) | − 295.846i | − 0.883123i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 469.626 | 1.39355 | 0.696774 | − | 0.717291i | \(-0.254618\pi\) | ||||
0.696774 | + | 0.717291i | \(0.254618\pi\) | |||||||
\(338\) | 173.211i | 0.512458i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 517.667 | 1.52255 | ||||||||
\(341\) | 47.8294i | 0.140262i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.5335 | 0.132751 | ||||||||
\(344\) | − 125.971i | − 0.366195i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 323.160 | 0.933990 | ||||||||
\(347\) | 298.679i | 0.860745i | 0.902651 | + | 0.430373i | \(0.141618\pi\) | ||||
−0.902651 | + | 0.430373i | \(0.858382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −412.332 | −1.18147 | −0.590733 | − | 0.806867i | \(-0.701161\pi\) | ||||
−0.590733 | + | 0.806867i | \(0.701161\pi\) | |||||||
\(350\) | − 97.4589i | − 0.278454i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 36.4443 | 0.103535 | ||||||||
\(353\) | − 363.649i | − 1.03017i | −0.857140 | − | 0.515084i | \(-0.827761\pi\) | ||||
0.857140 | − | 0.515084i | \(-0.172239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1298.77 | −3.65852 | ||||||||
\(356\) | 28.4131i | 0.0798121i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 936.818 | 2.61681 | ||||||||
\(359\) | 415.792i | 1.15819i | 0.815259 | + | 0.579097i | \(0.196595\pi\) | ||||
−0.815259 | + | 0.579097i | \(0.803405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 274.725 | 0.761010 | ||||||||
\(362\) | − 479.302i | − 1.32404i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 25.6356 | 0.0704274 | ||||||||
\(365\) | 1135.33i | 3.11050i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −53.1936 | −0.144942 | −0.0724708 | − | 0.997371i | \(-0.523088\pi\) | ||||
−0.0724708 | + | 0.997371i | \(0.523088\pi\) | |||||||
\(368\) | 6.85904i | 0.0186387i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −397.401 | −1.07406 | ||||||||
\(371\) | 42.5985i | 0.114821i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 394.389 | 1.05734 | 0.528671 | − | 0.848827i | \(-0.322691\pi\) | ||||
0.528671 | + | 0.848827i | \(0.322691\pi\) | |||||||
\(374\) | − 25.7001i | − 0.0687169i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −228.435 | −0.607539 | ||||||||
\(377\) | 91.7749i | 0.243435i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 357.810 | 0.944091 | 0.472045 | − | 0.881574i | \(-0.343516\pi\) | ||||
0.472045 | + | 0.881574i | \(0.343516\pi\) | |||||||
\(380\) | − 1272.08i | − 3.34758i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −460.228 | −1.20478 | ||||||||
\(383\) | 500.587i | 1.30702i | 0.756919 | + | 0.653508i | \(0.226704\pi\) | ||||
−0.756919 | + | 0.653508i | \(0.773296\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.72711 | −0.00968082 | ||||||||
\(386\) | 307.666i | 0.797061i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 239.953 | 0.618435 | ||||||||
\(389\) | − 44.6053i | − 0.114667i | −0.998355 | − | 0.0573333i | \(-0.981740\pi\) | ||||
0.998355 | − | 0.0573333i | \(-0.0182598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.23037 | 0.0184920 | ||||||||
\(392\) | − 178.210i | − 0.454617i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −183.872 | −0.466679 | ||||||||
\(395\) | − 907.242i | − 2.29682i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 213.697 | 0.538279 | 0.269139 | − | 0.963101i | \(-0.413261\pi\) | ||||
0.269139 | + | 0.963101i | \(0.413261\pi\) | |||||||
\(398\) | 284.110i | 0.713844i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 671.486 | 1.67872 | ||||||||
\(401\) | − 282.656i | − 0.704877i | −0.935835 | − | 0.352439i | \(-0.885353\pi\) | ||||
0.935835 | − | 0.352439i | \(-0.114647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −612.845 | −1.52071 | ||||||||
\(404\) | − 845.269i | − 2.09225i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.2561 | −0.0301875 | ||||||||
\(407\) | 11.1552i | 0.0274084i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 415.230 | 1.01523 | 0.507616 | − | 0.861584i | \(-0.330527\pi\) | ||||
0.507616 | + | 0.861584i | \(0.330527\pi\) | |||||||
\(410\) | 310.973i | 0.758470i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 202.589 | 0.491721 | ||||||||
\(413\) | − 8.23003i | − 0.0199274i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1016.13 | −2.44850 | ||||||||
\(416\) | 466.966i | 1.12251i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −63.1537 | −0.151085 | ||||||||
\(419\) | − 402.985i | − 0.961778i | −0.876782 | − | 0.480889i | \(-0.840314\pi\) | ||||
0.876782 | − | 0.480889i | \(-0.159686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 410.489 | 0.975033 | 0.487517 | − | 0.873114i | \(-0.337903\pi\) | ||||
0.487517 | + | 0.873114i | \(0.337903\pi\) | |||||||
\(422\) | 588.420i | 1.39436i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 334.186 | 0.788175 | ||||||||
\(425\) | − 707.839i | − 1.66550i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.3947 | −0.0735238 | ||||||||
\(428\) | − 25.1976i | − 0.0588728i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1014.22 | −2.35865 | ||||||||
\(431\) | − 481.326i | − 1.11677i | −0.829583 | − | 0.558383i | \(-0.811422\pi\) | ||||
0.829583 | − | 0.558383i | \(-0.188578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −716.958 | −1.65579 | −0.827896 | − | 0.560881i | \(-0.810462\pi\) | ||||
−0.827896 | + | 0.560881i | \(0.810462\pi\) | |||||||
\(434\) | − 81.8428i | − 0.188578i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 489.079 | 1.12174 | ||||||||
\(437\) | − 17.7674i | − 0.0406577i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 440.326 | 1.00302 | 0.501510 | − | 0.865152i | \(-0.332778\pi\) | ||||
0.501510 | + | 0.865152i | \(0.332778\pi\) | |||||||
\(440\) | 29.2393i | 0.0664529i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 329.299 | 0.745021 | ||||||||
\(443\) | 146.953i | 0.331723i | 0.986149 | + | 0.165862i | \(0.0530405\pi\) | ||||
−0.986149 | + | 0.165862i | \(0.946959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.9302 | 0.118944 | ||||||||
\(446\) | 293.047i | 0.657055i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −44.2312 | −0.0987303 | ||||||||
\(449\) | − 249.942i | − 0.556663i | −0.960485 | − | 0.278332i | \(-0.910219\pi\) | ||||
0.960485 | − | 0.278332i | \(-0.0897815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.72915 | 0.0193551 | ||||||||
\(452\) | − 419.674i | − 0.928482i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −774.718 | −1.70643 | ||||||||
\(455\) | − 47.7560i | − 0.104958i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 105.026 | 0.229815 | 0.114908 | − | 0.993376i | \(-0.463343\pi\) | ||||
0.114908 | + | 0.993376i | \(0.463343\pi\) | |||||||
\(458\) | 466.657i | 1.01890i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −35.5524 | −0.0772879 | ||||||||
\(461\) | − 125.250i | − 0.271692i | −0.990730 | − | 0.135846i | \(-0.956625\pi\) | ||||
0.990730 | − | 0.135846i | \(-0.0433753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 505.017 | 1.09075 | 0.545375 | − | 0.838192i | \(-0.316387\pi\) | ||||
0.545375 | + | 0.838192i | \(0.316387\pi\) | |||||||
\(464\) | − 84.4441i | − 0.181992i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1048.90 | 2.25086 | ||||||||
\(467\) | 78.9893i | 0.169142i | 0.996417 | + | 0.0845710i | \(0.0269520\pi\) | ||||
−0.996417 | + | 0.0845710i | \(0.973048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2102 | 0.0302990 | ||||||||
\(470\) | 1839.18i | 3.91315i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −64.5648 | −0.136790 | ||||||||
\(473\) | 28.4696i | 0.0601895i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1739.39 | −3.66188 | ||||||||
\(476\) | 24.8648i | 0.0522370i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −53.4861 | −0.111896 | ||||||||
\(479\) | 695.723i | 1.45245i | 0.687458 | + | 0.726225i | \(0.258727\pi\) | ||||
−0.687458 | + | 0.726225i | \(0.741273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −142.933 | −0.297159 | ||||||||
\(482\) | − 949.382i | − 1.96967i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −626.151 | −1.29370 | ||||||||
\(485\) | − 447.003i | − 0.921656i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −539.311 | −1.10741 | −0.553707 | − | 0.832711i | \(-0.686787\pi\) | ||||
−0.553707 | + | 0.832711i | \(0.686787\pi\) | |||||||
\(488\) | 246.292i | 0.504697i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1434.81 | −2.92818 | ||||||||
\(491\) | − 669.576i | − 1.36370i | −0.731493 | − | 0.681849i | \(-0.761176\pi\) | ||||
0.731493 | − | 0.681849i | \(-0.238824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −89.0156 | −0.180559 | ||||||||
\(494\) | − 809.197i | − 1.63805i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 563.892 | 1.13688 | ||||||||
\(497\) | − 62.3833i | − 0.125520i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 409.869 | 0.821382 | 0.410691 | − | 0.911775i | \(-0.365288\pi\) | ||||
0.410691 | + | 0.911775i | \(0.365288\pi\) | |||||||
\(500\) | 2219.21i | 4.43842i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −700.622 | −1.39566 | ||||||||
\(503\) | − 626.217i | − 1.24496i | −0.782634 | − | 0.622482i | \(-0.786125\pi\) | ||||
0.782634 | − | 0.622482i | \(-0.213875\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1574.64 | −3.11809 | ||||||||
\(506\) | 1.76504i | 0.00348822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −58.6475 | −0.115448 | ||||||||
\(509\) | − 957.198i | − 1.88055i | −0.340421 | − | 0.940273i | \(-0.610570\pi\) | ||||
0.340421 | − | 0.940273i | \(-0.389430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −54.5328 | −0.106718 | ||||||||
\(512\) | − 571.897i | − 1.11699i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 785.701 | 1.52860 | ||||||||
\(515\) | − 377.399i | − 0.732814i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.6266 | 0.0998581 | ||||||||
\(518\) | − 19.0881i | − 0.0368497i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −374.647 | −0.720475 | ||||||||
\(521\) | − 614.917i | − 1.18026i | −0.807307 | − | 0.590132i | \(-0.799076\pi\) | ||||
0.807307 | − | 0.590132i | \(-0.200924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1029.64 | 1.96871 | 0.984356 | − | 0.176194i | \(-0.0563785\pi\) | ||||
0.984356 | + | 0.176194i | \(0.0563785\pi\) | |||||||
\(524\) | 178.521i | 0.340688i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 571.789 | 1.08705 | ||||||||
\(527\) | − 594.419i | − 1.12793i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.503 | 0.999061 | ||||||||
\(530\) | − 2690.61i | − 5.07662i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 61.1011 | 0.114852 | ||||||||
\(533\) | 111.848i | 0.209846i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.9401 | −0.0877384 | ||||||||
\(536\) | − 111.479i | − 0.207984i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −202.520 | −0.376431 | ||||||||
\(539\) | 40.2757i | 0.0747230i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 674.507 | 1.24678 | 0.623390 | − | 0.781911i | \(-0.285755\pi\) | ||||
0.623390 | + | 0.781911i | \(0.285755\pi\) | |||||||
\(542\) | − 50.1506i | − 0.0925288i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −452.927 | −0.832586 | ||||||||
\(545\) | − 911.095i | − 1.67173i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 378.731 | 0.692378 | 0.346189 | − | 0.938165i | \(-0.387476\pi\) | ||||
0.346189 | + | 0.938165i | \(0.387476\pi\) | |||||||
\(548\) | 259.951i | 0.474363i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 172.794 | 0.314170 | ||||||||
\(551\) | 218.741i | 0.396989i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.5771 | 0.0788012 | ||||||||
\(554\) | 924.891i | 1.66948i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 648.201 | 1.16583 | ||||||||
\(557\) | 326.784i | 0.586686i | 0.956007 | + | 0.293343i | \(0.0947678\pi\) | ||||
−0.956007 | + | 0.293343i | \(0.905232\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −364.785 | −0.652568 | ||||||||
\(560\) | 43.9414i | 0.0784667i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 347.834 | 0.618922 | ||||||||
\(563\) | 164.132i | 0.291531i | 0.989319 | + | 0.145766i | \(0.0465645\pi\) | ||||
−0.989319 | + | 0.145766i | \(0.953435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −781.802 | −1.38372 | ||||||||
\(566\) | − 647.708i | − 1.14436i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −489.398 | −0.861617 | ||||||||
\(569\) | − 450.365i | − 0.791502i | −0.918358 | − | 0.395751i | \(-0.870484\pi\) | ||||
0.918358 | − | 0.395751i | \(-0.129516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −614.662 | −1.07647 | −0.538233 | − | 0.842796i | \(-0.680908\pi\) | ||||
−0.538233 | + | 0.842796i | \(0.680908\pi\) | |||||||
\(572\) | 45.4516i | 0.0794608i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.9368 | −0.0260223 | ||||||||
\(575\) | 48.6130i | 0.0845444i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 498.675 | 0.864254 | 0.432127 | − | 0.901813i | \(-0.357763\pi\) | ||||
0.432127 | + | 0.901813i | \(0.357763\pi\) | |||||||
\(578\) | − 557.378i | − 0.964322i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 437.699 | 0.754653 | ||||||||
\(581\) | − 48.8071i | − 0.0840053i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −75.5266 | −0.129548 | ||||||||
\(584\) | 427.811i | 0.732553i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1515.37 | −2.58595 | ||||||||
\(587\) | 773.400i | 1.31755i | 0.752342 | + | 0.658773i | \(0.228924\pi\) | ||||
−0.752342 | + | 0.658773i | \(0.771076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1460.68 | −2.47994 | ||||||||
\(590\) | 519.826i | 0.881061i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 131.516 | 0.222156 | ||||||||
\(593\) | 1037.15i | 1.74899i | 0.485032 | + | 0.874496i | \(0.338808\pi\) | ||||
−0.485032 | + | 0.874496i | \(0.661192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46.3202 | 0.0778491 | ||||||||
\(596\) | 458.441i | 0.769196i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.6157 | −0.0378188 | ||||||||
\(599\) | 266.824i | 0.445448i | 0.974882 | + | 0.222724i | \(0.0714949\pi\) | ||||
−0.974882 | + | 0.222724i | \(0.928505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −603.952 | −1.00491 | −0.502456 | − | 0.864603i | \(-0.667570\pi\) | ||||
−0.502456 | + | 0.864603i | \(0.667570\pi\) | |||||||
\(602\) | − 48.7155i | − 0.0809228i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 969.721 | 1.60550 | ||||||||
\(605\) | 1166.45i | 1.92801i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −270.545 | −0.445708 | −0.222854 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222854 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(608\) | 1112.99i | 1.83058i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1982.95 | 3.25074 | ||||||||
\(611\) | 661.499i | 1.08265i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −290.634 | −0.474117 | −0.237059 | − | 0.971495i | \(-0.576183\pi\) | ||||
−0.237059 | + | 0.971495i | \(0.576183\pi\) | |||||||
\(614\) | − 767.389i | − 1.24982i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.40443 | −0.00227993 | ||||||||
\(617\) | − 1097.41i | − 1.77862i | −0.457302 | − | 0.889311i | \(-0.651184\pi\) | ||||
0.457302 | − | 0.889311i | \(-0.348816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −540.438 | −0.873083 | −0.436542 | − | 0.899684i | \(-0.643797\pi\) | ||||
−0.436542 | + | 0.899684i | \(0.643797\pi\) | |||||||
\(620\) | 2922.82i | 4.71422i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1108.29 | 1.78182 | ||||||||
\(623\) | 2.54237i | 0.00408085i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2409.46 | 3.85514 | ||||||||
\(626\) | − 214.315i | − 0.342356i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −953.149 | −1.51775 | ||||||||
\(629\) | − 138.636i | − 0.220407i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1145.02 | 1.81462 | 0.907310 | − | 0.420463i | \(-0.138132\pi\) | ||||
0.907310 | + | 0.420463i | \(0.138132\pi\) | |||||||
\(632\) | − 341.863i | − 0.540923i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −665.470 | −1.04964 | ||||||||
\(635\) | 109.253i | 0.172052i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −516.058 | −0.810138 | ||||||||
\(638\) | − 21.7300i | − 0.0340595i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1081.95 | 1.69054 | ||||||||
\(641\) | − 904.089i | − 1.41044i | −0.708991 | − | 0.705218i | \(-0.750849\pi\) | ||||
0.708991 | − | 0.705218i | \(-0.249151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 101.162 | 0.157328 | 0.0786642 | − | 0.996901i | \(-0.474934\pi\) | ||||
0.0786642 | + | 0.996901i | \(0.474934\pi\) | |||||||
\(644\) | − 1.70767i | − 0.00265166i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 784.868 | 1.21497 | ||||||||
\(647\) | 799.354i | 1.23548i | 0.786384 | + | 0.617738i | \(0.211951\pi\) | ||||
−0.786384 | + | 0.617738i | \(0.788049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.5918 | 0.0224834 | ||||||||
\(650\) | 2214.03i | 3.40620i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1039.90 | 1.59494 | ||||||||
\(653\) | 405.770i | 0.621394i | 0.950509 | + | 0.310697i | \(0.100562\pi\) | ||||
−0.950509 | + | 0.310697i | \(0.899438\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 332.563 | 0.507730 | ||||||||
\(656\) | − 102.914i | − 0.156880i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −88.3403 | −0.134256 | ||||||||
\(659\) | 87.7483i | 0.133154i | 0.997781 | + | 0.0665768i | \(0.0212077\pi\) | ||||
−0.997781 | + | 0.0665768i | \(0.978792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −252.832 | −0.382499 | −0.191250 | − | 0.981541i | \(-0.561254\pi\) | ||||
−0.191250 | + | 0.981541i | \(0.561254\pi\) | |||||||
\(662\) | − 603.310i | − 0.911345i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −382.892 | −0.576645 | ||||||||
\(665\) | − 113.824i | − 0.171164i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.11343 | 0.00916556 | ||||||||
\(668\) | 29.0388i | 0.0434713i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −897.547 | −1.33962 | ||||||||
\(671\) | − 55.6624i | − 0.0829544i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.5389 | −0.0305184 | −0.0152592 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152592 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(674\) | − 1424.76i | − 2.11389i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 297.119 | 0.439526 | ||||||||
\(677\) | 201.518i | 0.297663i | 0.988863 | + | 0.148832i | \(0.0475512\pi\) | ||||
−0.988863 | + | 0.148832i | \(0.952449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.4707 | 0.0316210 | ||||||||
\(680\) | − 363.383i | − 0.534387i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 145.106 | 0.212766 | ||||||||
\(683\) | 638.072i | 0.934219i | 0.884199 | + | 0.467110i | \(0.154705\pi\) | ||||
−0.884199 | + | 0.467110i | \(0.845295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 484.257 | 0.706945 | ||||||||
\(686\) | − 138.141i | − 0.201372i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 335.647 | 0.487859 | ||||||||
\(689\) | − 967.733i | − 1.40455i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1306.30 | 1.89045 | 0.945226 | − | 0.326417i | \(-0.105841\pi\) | ||||
0.945226 | + | 0.326417i | \(0.105841\pi\) | |||||||
\(692\) | − 554.338i | − 0.801066i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 906.140 | 1.30568 | ||||||||
\(695\) | − 1207.52i | − 1.73744i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −108.485 | −0.155646 | ||||||||
\(698\) | 1250.94i | 1.79218i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −167.178 | −0.238825 | ||||||||
\(701\) | 1065.94i | 1.52059i | 0.649576 | + | 0.760297i | \(0.274947\pi\) | ||||
−0.649576 | + | 0.760297i | \(0.725053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −340.674 | −0.484601 | ||||||||
\(704\) | − 78.4214i | − 0.111394i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1103.25 | −1.56268 | ||||||||
\(707\) | − 75.6336i | − 0.106978i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 472.012 | 0.665744 | 0.332872 | − | 0.942972i | \(-0.391982\pi\) | ||||
0.332872 | + | 0.942972i | \(0.391982\pi\) | |||||||
\(710\) | 3940.26i | 5.54966i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.9449 | 0.0280126 | ||||||||
\(713\) | 40.8236i | 0.0572561i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.6709 | 0.118421 | ||||||||
\(716\) | − 1606.98i | − 2.24439i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1261.44 | 1.75688 | ||||||||
\(719\) | − 209.385i | − 0.291217i | −0.989342 | − | 0.145609i | \(-0.953486\pi\) | ||||
0.989342 | − | 0.145609i | \(-0.0465140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1274 | 0.0251420 | ||||||||
\(722\) | − 833.468i | − 1.15439i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −822.176 | −1.13560 | ||||||||
\(725\) | − 598.492i | − 0.825507i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 973.645 | 1.33926 | 0.669632 | − | 0.742693i | \(-0.266452\pi\) | ||||
0.669632 | + | 0.742693i | \(0.266452\pi\) | |||||||
\(728\) | − 17.9952i | − 0.0247187i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3444.41 | 4.71836 | ||||||||
\(731\) | − 353.818i | − 0.484019i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 666.657 | 0.909491 | 0.454746 | − | 0.890621i | \(-0.349730\pi\) | ||||
0.454746 | + | 0.890621i | \(0.349730\pi\) | |||||||
\(734\) | 161.380i | 0.219864i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31.1062 | 0.0422638 | ||||||||
\(737\) | 25.1945i | 0.0341853i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1070.77 | 1.44894 | 0.724472 | − | 0.689304i | \(-0.242084\pi\) | ||||
0.724472 | + | 0.689304i | \(0.242084\pi\) | |||||||
\(740\) | 681.687i | 0.921198i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 129.237 | 0.174173 | ||||||||
\(743\) | − 486.119i | − 0.654265i | −0.944979 | − | 0.327132i | \(-0.893918\pi\) | ||||
0.944979 | − | 0.327132i | \(-0.106082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 854.021 | 1.14634 | ||||||||
\(746\) | − 1196.51i | − 1.60390i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −44.0851 | −0.0589372 | ||||||||
\(749\) | − 2.25465i | − 0.00301021i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −945.864 | −1.25947 | −0.629737 | − | 0.776809i | \(-0.716837\pi\) | ||||
−0.629737 | + | 0.776809i | \(0.716837\pi\) | |||||||
\(752\) | − 608.660i | − 0.809388i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 278.429 | 0.369270 | ||||||||
\(755\) | − 1806.47i | − 2.39268i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1232.83 | −1.62858 | −0.814290 | − | 0.580458i | \(-0.802873\pi\) | ||||
−0.814290 | + | 0.580458i | \(0.802873\pi\) | |||||||
\(758\) | − 1085.54i | − 1.43210i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −892.953 | −1.17494 | ||||||||
\(761\) | 1036.56i | 1.36210i | 0.732235 | + | 0.681052i | \(0.238477\pi\) | ||||
−0.732235 | + | 0.681052i | \(0.761523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.7621 | 0.0573554 | ||||||||
\(764\) | 789.458i | 1.03332i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1518.70 | 1.98263 | ||||||||
\(767\) | 186.966i | 0.243763i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 255.317 | 0.332012 | 0.166006 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166006 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(770\) | 11.3074i | 0.0146850i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 527.758 | 0.683625 | ||||||||
\(773\) | − 355.381i | − 0.459743i | −0.973221 | − | 0.229871i | \(-0.926169\pi\) | ||||
0.973221 | − | 0.229871i | \(-0.0738305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3996.55 | 5.15684 | ||||||||
\(776\) | − 168.438i | − 0.217059i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −135.325 | −0.173939 | ||||||||
\(779\) | 266.583i | 0.342212i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 110.605 | 0.141620 | ||||||||
\(782\) | − 21.9357i | − 0.0280508i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 474.836 | 0.605658 | ||||||||
\(785\) | 1775.60i | 2.26191i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 149.041 | 0.189378 | 0.0946892 | − | 0.995507i | \(-0.469814\pi\) | ||||
0.0946892 | + | 0.995507i | \(0.469814\pi\) | |||||||
\(788\) | 315.407i | 0.400262i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2752.42 | −3.48407 | ||||||||
\(791\) | − 37.5519i | − 0.0474739i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 713.210 | 0.899382 | ||||||||
\(794\) | − 648.319i | − 0.816523i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 487.352 | 0.612251 | ||||||||
\(797\) | 1254.91i | 1.57454i | 0.616605 | + | 0.787272i | \(0.288507\pi\) | ||||
−0.616605 | + | 0.787272i | \(0.711493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −641.611 | −0.803017 | ||||||||
\(800\) | − 3045.23i | − 3.80654i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −857.530 | −1.06924 | ||||||||
\(803\) | − 96.6860i | − 0.120406i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.18119 | −0.00395178 | ||||||||
\(806\) | 1859.27i | 2.30678i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −593.347 | −0.734341 | ||||||||
\(809\) | − 495.041i | − 0.611917i | −0.952045 | − | 0.305958i | \(-0.901023\pi\) | ||||
0.952045 | − | 0.305958i | \(-0.0989769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 378.712 | 0.466969 | 0.233485 | − | 0.972360i | \(-0.424987\pi\) | ||||
0.233485 | + | 0.972360i | \(0.424987\pi\) | |||||||
\(812\) | 21.0237i | 0.0258913i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.8430 | 0.0415762 | ||||||||
\(815\) | − 1937.22i | − 2.37695i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −869.448 | −1.06420 | ||||||||
\(818\) | − 1259.74i | − 1.54002i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 533.431 | 0.650526 | ||||||||
\(821\) | − 26.1980i | − 0.0319099i | −0.999873 | − | 0.0159549i | \(-0.994921\pi\) | ||||
0.999873 | − | 0.0159549i | \(-0.00507883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1424.46 | −1.73081 | −0.865405 | − | 0.501074i | \(-0.832939\pi\) | ||||
−0.865405 | + | 0.501074i | \(0.832939\pi\) | |||||||
\(824\) | − 142.210i | − 0.172585i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.9685 | −0.0302282 | ||||||||
\(827\) | − 691.197i | − 0.835789i | −0.908496 | − | 0.417894i | \(-0.862768\pi\) | ||||
0.908496 | − | 0.417894i | \(-0.137232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 954.895 | 1.15186 | 0.575932 | − | 0.817498i | \(-0.304639\pi\) | ||||
0.575932 | + | 0.817498i | \(0.304639\pi\) | |||||||
\(830\) | 3082.76i | 3.71416i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1004.82 | 1.20772 | ||||||||
\(833\) | − 500.542i | − 0.600891i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.0959 | 0.0647855 | ||||||||
\(836\) | 108.332i | 0.129583i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1222.59 | −1.45893 | ||||||||
\(839\) | 197.809i | 0.235767i | 0.993027 | + | 0.117884i | \(0.0376110\pi\) | ||||
−0.993027 | + | 0.117884i | \(0.962389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 765.735 | 0.910506 | ||||||||
\(842\) | − 1245.35i | − 1.47904i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1009.35 | 1.19592 | ||||||||
\(845\) | − 553.498i | − 0.655027i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −56.0272 | −0.0661478 | ||||||||
\(848\) | 890.432i | 1.05004i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2147.46 | −2.52643 | ||||||||
\(851\) | 9.52126i | 0.0111883i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 221.837 | 0.260066 | 0.130033 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130033 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(854\) | 95.2461i | 0.111529i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.6878 | −0.0206633 | ||||||||
\(857\) | 1660.75i | 1.93787i | 0.247325 | + | 0.968933i | \(0.420448\pi\) | ||||
−0.247325 | + | 0.968933i | \(0.579552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −638.952 | −0.743832 | −0.371916 | − | 0.928266i | \(-0.621299\pi\) | ||||
−0.371916 | + | 0.928266i | \(0.621299\pi\) | |||||||
\(860\) | 1739.76i | 2.02297i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1460.26 | −1.69404 | ||||||||
\(863\) | − 419.217i | − 0.485767i | −0.970055 | − | 0.242884i | \(-0.921907\pi\) | ||||
0.970055 | − | 0.242884i | \(-0.0780933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1032.66 | −1.19383 | ||||||||
\(866\) | 2175.13i | 2.51170i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −140.390 | −0.161740 | ||||||||
\(869\) | 77.2616i | 0.0889087i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −322.821 | −0.370633 | ||||||||
\(872\) | − 343.315i | − 0.393710i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.9033 | −0.0616742 | ||||||||
\(875\) | 198.572i | 0.226939i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1354.65 | 1.54465 | 0.772323 | − | 0.635230i | \(-0.219095\pi\) | ||||
0.772323 | + | 0.635230i | \(0.219095\pi\) | |||||||
\(878\) | − 1335.87i | − 1.52150i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −77.9075 | −0.0885313 | ||||||||
\(881\) | 563.515i | 0.639631i | 0.947480 | + | 0.319816i | \(0.103621\pi\) | ||||
−0.947480 | + | 0.319816i | \(0.896379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1272.91 | −1.44157 | −0.720785 | − | 0.693159i | \(-0.756219\pi\) | ||||
−0.720785 | + | 0.693159i | \(0.756219\pi\) | |||||||
\(884\) | − 564.868i | − 0.638991i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 445.832 | 0.503196 | ||||||||
\(887\) | 716.899i | 0.808229i | 0.914708 | + | 0.404114i | \(0.132420\pi\) | ||||
−0.914708 | + | 0.404114i | \(0.867580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.24770 | −0.00590293 | ||||||||
\(890\) | − 160.581i | − 0.180428i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 502.682 | 0.563544 | ||||||||
\(893\) | 1576.65i | 1.76557i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2993.62 | −3.34483 | ||||||||
\(896\) | 51.9686i | 0.0580007i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −758.281 | −0.844411 | ||||||||
\(899\) | − 502.594i | − 0.559059i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 938.638 | 1.04177 | ||||||||
\(902\) | − 26.4827i | − 0.0293600i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −294.595 | −0.325880 | ||||||||
\(905\) | 1531.62i | 1.69239i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1550.93 | 1.70996 | 0.854981 | − | 0.518660i | \(-0.173569\pi\) | ||||
0.854981 | + | 0.518660i | \(0.173569\pi\) | |||||||
\(908\) | 1328.92i | 1.46357i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −144.884 | −0.159213 | ||||||||
\(911\) | − 472.805i | − 0.518996i | −0.965744 | − | 0.259498i | \(-0.916443\pi\) | ||||
0.965744 | − | 0.259498i | \(-0.0835571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 86.5343 | 0.0947802 | ||||||||
\(914\) | − 318.630i | − 0.348610i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 800.487 | 0.873894 | ||||||||
\(917\) | 15.9738i | 0.0174196i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1256.65 | −1.36741 | −0.683704 | − | 0.729759i | \(-0.739632\pi\) | ||||
−0.683704 | + | 0.729759i | \(0.739632\pi\) | |||||||
\(920\) | 24.9565i | 0.0271266i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −379.988 | −0.412134 | ||||||||
\(923\) | 1417.19i | 1.53542i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 932.113 | 1.00769 | ||||||||
\(926\) | − 1532.14i | − 1.65457i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −382.959 | −0.412671 | ||||||||
\(929\) | − 1347.86i | − 1.45087i | −0.688291 | − | 0.725435i | \(-0.741639\pi\) | ||||
0.688291 | − | 0.725435i | \(-0.258361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1230.00 | −1.32116 | ||||||||
\(932\) | − 1799.25i | − 1.93052i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 239.640 | 0.256574 | ||||||||
\(935\) | 82.1252i | 0.0878344i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 89.2394 | 0.0952395 | 0.0476198 | − | 0.998866i | \(-0.484836\pi\) | ||||
0.0476198 | + | 0.998866i | \(0.484836\pi\) | |||||||
\(938\) | − 43.1114i | − 0.0459609i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3154.86 | 3.35624 | ||||||||
\(941\) | 1728.75i | 1.83715i | 0.395252 | + | 0.918573i | \(0.370657\pi\) | ||||
−0.395252 | + | 0.918573i | \(0.629343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.45055 | 0.00790090 | ||||||||
\(944\) | − 172.032i | − 0.182237i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 86.3720 | 0.0913024 | ||||||||
\(947\) | − 1500.82i | − 1.58482i | −0.609992 | − | 0.792408i | \(-0.708827\pi\) | ||||
0.609992 | − | 0.792408i | \(-0.291173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1238.85 | 1.30543 | ||||||||
\(950\) | 5277.02i | 5.55476i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.4542 | 0.0183342 | ||||||||
\(953\) | 847.145i | 0.888924i | 0.895798 | + | 0.444462i | \(0.146605\pi\) | ||||
−0.895798 | + | 0.444462i | \(0.853395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1470.67 | 1.53996 | ||||||||
\(956\) | 91.7480i | 0.0959708i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2110.71 | 2.20324 | ||||||||
\(959\) | 23.2601i | 0.0242545i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2395.17 | 2.49237 | ||||||||
\(962\) | 433.635i | 0.450764i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1628.53 | −1.68935 | ||||||||
\(965\) | − 983.151i | − 1.01881i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1781.12 | −1.84191 | −0.920953 | − | 0.389673i | \(-0.872588\pi\) | ||||
−0.920953 | + | 0.389673i | \(0.872588\pi\) | |||||||
\(968\) | 439.535i | 0.454065i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1356.13 | −1.39807 | ||||||||
\(971\) | 821.559i | 0.846096i | 0.906107 | + | 0.423048i | \(0.139040\pi\) | ||||
−0.906107 | + | 0.423048i | \(0.860960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.0002 | 0.0596096 | ||||||||
\(974\) | 1636.18i | 1.67985i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −656.240 | −0.672377 | ||||||||
\(977\) | 195.226i | 0.199822i | 0.994996 | + | 0.0999111i | \(0.0318558\pi\) | ||||
−0.994996 | + | 0.0999111i | \(0.968144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.50759 | −0.00460428 | ||||||||
\(980\) | 2461.22i | 2.51145i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2031.38 | −2.06861 | ||||||||
\(983\) | 288.267i | 0.293253i | 0.989192 | + | 0.146626i | \(0.0468415\pi\) | ||||
−0.989192 | + | 0.146626i | \(0.953158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 587.565 | 0.596513 | ||||||||
\(986\) | 270.058i | 0.273893i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1388.07 | −1.40493 | ||||||||
\(989\) | 24.2996i | 0.0245698i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 575.624 | 0.580852 | 0.290426 | − | 0.956898i | \(-0.406203\pi\) | ||||
0.290426 | + | 0.956898i | \(0.406203\pi\) | |||||||
\(992\) | − 2557.28i | − 2.57791i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −189.260 | −0.190403 | ||||||||
\(995\) | − 907.879i | − 0.912441i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 181.307 | 0.181853 | 0.0909265 | − | 0.995858i | \(-0.471017\pi\) | ||||
0.0909265 | + | 0.995858i | \(0.471017\pi\) | |||||||
\(998\) | − 1243.47i | − 1.24597i | ||||||||
\(999\) | 0 | 0 |
(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 | 1143.3.b.a.890.12 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.73 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.12 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.73 | yes | 84 | 3.2 | odd | 2 | inner |