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 | 890.2 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.83 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.86719i | − 1.93359i | −0.255545 | − | 0.966797i | \(-0.582255\pi\) | ||||
0.255545 | − | 0.966797i | \(-0.417745\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.9551 | −2.73879 | ||||||||
\(5\) | − 9.44547i | − 1.88909i | −0.328376 | − | 0.944547i | \(-0.606501\pi\) | ||||
0.328376 | − | 0.944547i | \(-0.393499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.3204 | 1.61719 | 0.808597 | − | 0.588363i | \(-0.200227\pi\) | ||||
0.808597 | + | 0.588363i | \(0.200227\pi\) | |||||||
\(8\) | 26.8969i | 3.36211i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −36.5274 | −3.65274 | ||||||||
\(11\) | − 14.1873i | − 1.28975i | −0.764288 | − | 0.644875i | \(-0.776909\pi\) | ||||
0.764288 | − | 0.644875i | \(-0.223091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.8150 | 0.831925 | 0.415962 | − | 0.909382i | \(-0.363445\pi\) | ||||
0.415962 | + | 0.909382i | \(0.363445\pi\) | |||||||
\(14\) | − 43.7780i | − 3.12700i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 60.1947 | 3.76217 | ||||||||
\(17\) | 9.53381i | 0.560813i | 0.959881 | + | 0.280406i | \(0.0904692\pi\) | ||||
−0.959881 | + | 0.280406i | \(0.909531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.9634 | −1.31387 | −0.656933 | − | 0.753949i | \(-0.728146\pi\) | ||||
−0.656933 | + | 0.753949i | \(0.728146\pi\) | |||||||
\(20\) | 103.477i | 5.17383i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −54.8648 | −2.49385 | ||||||||
\(23\) | 13.0513i | 0.567448i | 0.958906 | + | 0.283724i | \(0.0915700\pi\) | ||||
−0.958906 | + | 0.283724i | \(0.908430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −64.2169 | −2.56868 | ||||||||
\(26\) | − 41.8237i | − 1.60860i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −124.016 | −4.42915 | ||||||||
\(29\) | − 18.2561i | − 0.629521i | −0.949171 | − | 0.314761i | \(-0.898076\pi\) | ||||
0.949171 | − | 0.314761i | \(-0.101924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.5312 | −1.24294 | −0.621472 | − | 0.783437i | \(-0.713465\pi\) | ||||
−0.621472 | + | 0.783437i | \(0.713465\pi\) | |||||||
\(32\) | − 125.197i | − 3.91240i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.8691 | 1.08438 | ||||||||
\(35\) | − 106.926i | − 3.05503i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −51.8983 | −1.40266 | −0.701329 | − | 0.712838i | \(-0.747410\pi\) | ||||
−0.701329 | + | 0.712838i | \(0.747410\pi\) | |||||||
\(38\) | 96.5383i | 2.54048i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 254.054 | 6.35134 | ||||||||
\(41\) | 18.2318i | 0.444679i | 0.974969 | + | 0.222339i | \(0.0713693\pi\) | ||||
−0.974969 | + | 0.222339i | \(0.928631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.3978 | −0.730180 | −0.365090 | − | 0.930972i | \(-0.618962\pi\) | ||||
−0.365090 | + | 0.930972i | \(0.618962\pi\) | |||||||
\(44\) | 155.424i | 3.53235i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 50.4719 | 1.09722 | ||||||||
\(47\) | − 4.56917i | − 0.0972164i | −0.998818 | − | 0.0486082i | \(-0.984521\pi\) | ||||
0.998818 | − | 0.0486082i | \(-0.0154786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 79.1505 | 1.61532 | ||||||||
\(50\) | 248.339i | 4.96678i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −118.480 | −2.27846 | ||||||||
\(53\) | − 31.5680i | − 0.595623i | −0.954625 | − | 0.297812i | \(-0.903743\pi\) | ||||
0.954625 | − | 0.297812i | \(-0.0962568\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −134.005 | −2.43646 | ||||||||
\(56\) | 304.482i | 5.43718i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −70.5998 | −1.21724 | ||||||||
\(59\) | − 62.5783i | − 1.06065i | −0.847795 | − | 0.530325i | \(-0.822070\pi\) | ||||
0.847795 | − | 0.530325i | \(-0.177930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 64.5712 | 1.05854 | 0.529272 | − | 0.848452i | \(-0.322465\pi\) | ||||
0.529272 | + | 0.848452i | \(0.322465\pi\) | |||||||
\(62\) | 149.008i | 2.40335i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −243.380 | −3.80282 | ||||||||
\(65\) | − 102.153i | − 1.57158i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.3116 | 1.10913 | 0.554564 | − | 0.832141i | \(-0.312885\pi\) | ||||
0.554564 | + | 0.832141i | \(0.312885\pi\) | |||||||
\(68\) | − 104.444i | − 1.53595i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −413.503 | −5.90719 | ||||||||
\(71\) | 111.127i | 1.56516i | 0.622547 | + | 0.782582i | \(0.286098\pi\) | ||||
−0.622547 | + | 0.782582i | \(0.713902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48.7312 | −0.667550 | −0.333775 | − | 0.942653i | \(-0.608323\pi\) | ||||
−0.333775 | + | 0.942653i | \(0.608323\pi\) | |||||||
\(74\) | 200.701i | 2.71217i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 273.478 | 3.59840 | ||||||||
\(77\) | − 160.605i | − 2.08578i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −63.2310 | −0.800393 | −0.400196 | − | 0.916429i | \(-0.631058\pi\) | ||||
−0.400196 | + | 0.916429i | \(0.631058\pi\) | |||||||
\(80\) | − 568.567i | − 7.10709i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 70.5059 | 0.859829 | ||||||||
\(83\) | 51.0401i | 0.614940i | 0.951558 | + | 0.307470i | \(0.0994824\pi\) | ||||
−0.951558 | + | 0.307470i | \(0.900518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 90.0514 | 1.05943 | ||||||||
\(86\) | 121.421i | 1.41187i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 381.593 | 4.33628 | ||||||||
\(89\) | − 19.4944i | − 0.219039i | −0.993985 | − | 0.109519i | \(-0.965069\pi\) | ||||
0.993985 | − | 0.109519i | \(-0.0349312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 122.430 | 1.34538 | ||||||||
\(92\) | − 142.979i | − 1.55412i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.6698 | −0.187977 | ||||||||
\(95\) | 235.791i | 2.48202i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 72.1446 | 0.743758 | 0.371879 | − | 0.928281i | \(-0.378714\pi\) | ||||
0.371879 | + | 0.928281i | \(0.378714\pi\) | |||||||
\(98\) | − 306.090i | − 3.12337i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 703.506 | 7.03506 | ||||||||
\(101\) | − 130.320i | − 1.29030i | −0.764055 | − | 0.645151i | \(-0.776794\pi\) | ||||
0.764055 | − | 0.645151i | \(-0.223206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41.3239 | 0.401203 | 0.200602 | − | 0.979673i | \(-0.435710\pi\) | ||||
0.200602 | + | 0.979673i | \(0.435710\pi\) | |||||||
\(104\) | 290.890i | 2.79702i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −122.080 | −1.15169 | ||||||||
\(107\) | − 169.058i | − 1.57999i | −0.613116 | − | 0.789993i | \(-0.710084\pi\) | ||||
0.613116 | − | 0.789993i | \(-0.289916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −67.9965 | −0.623821 | −0.311910 | − | 0.950111i | \(-0.600969\pi\) | ||||
−0.311910 | + | 0.950111i | \(0.600969\pi\) | |||||||
\(110\) | 518.224i | 4.71113i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 681.425 | 6.08415 | ||||||||
\(113\) | 44.6199i | 0.394866i | 0.980316 | + | 0.197433i | \(0.0632605\pi\) | ||||
−0.980316 | + | 0.197433i | \(0.936739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 123.276 | 1.07196 | ||||||||
\(116\) | 199.998i | 1.72412i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −242.002 | −2.05087 | ||||||||
\(119\) | 107.926i | 0.906943i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80.2783 | −0.663457 | ||||||||
\(122\) | − 249.709i | − 2.04679i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 422.115 | 3.40416 | ||||||||
\(125\) | 370.422i | 2.96338i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2694 | 0.0887357 | ||||||||
\(128\) | 440.411i | 3.44071i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −395.045 | −3.03881 | ||||||||
\(131\) | − 157.351i | − 1.20115i | −0.799567 | − | 0.600576i | \(-0.794938\pi\) | ||||
0.799567 | − | 0.600576i | \(-0.205062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −282.595 | −2.12477 | ||||||||
\(134\) | − 287.377i | − 2.14460i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −256.430 | −1.88551 | ||||||||
\(137\) | − 112.882i | − 0.823958i | −0.911193 | − | 0.411979i | \(-0.864838\pi\) | ||||
0.911193 | − | 0.411979i | \(-0.135162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −98.1690 | −0.706252 | −0.353126 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353126 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(140\) | 1171.39i | 8.36708i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 429.748 | 3.02639 | ||||||||
\(143\) | − 153.435i | − 1.07298i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −172.438 | −1.18922 | ||||||||
\(146\) | 188.453i | 1.29077i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 568.554 | 3.84158 | ||||||||
\(149\) | 198.203i | 1.33022i | 0.746744 | + | 0.665112i | \(0.231616\pi\) | ||||
−0.746744 | + | 0.665112i | \(0.768384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 272.334 | 1.80354 | 0.901768 | − | 0.432219i | \(-0.142269\pi\) | ||||
0.901768 | + | 0.432219i | \(0.142269\pi\) | |||||||
\(152\) | − 671.438i | − 4.41736i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −621.089 | −4.03305 | ||||||||
\(155\) | 363.946i | 2.34804i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5821 | −0.0992487 | −0.0496244 | − | 0.998768i | \(-0.515802\pi\) | ||||
−0.0496244 | + | 0.998768i | \(0.515802\pi\) | |||||||
\(158\) | 244.526i | 1.54764i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1182.54 | −7.39088 | ||||||||
\(161\) | 147.746i | 0.917674i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.264 | 1.36358 | 0.681790 | − | 0.731548i | \(-0.261202\pi\) | ||||
0.681790 | + | 0.731548i | \(0.261202\pi\) | |||||||
\(164\) | − 199.732i | − 1.21788i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 197.382 | 1.18905 | ||||||||
\(167\) | 0.247721i | 0.00148336i | 1.00000 | 0.000741679i | \(0.000236084\pi\) | |||||
−1.00000 | 0.000741679i | \(0.999764\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52.0354 | −0.307901 | ||||||||
\(170\) | − 348.246i | − 2.04850i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 343.967 | 1.99981 | ||||||||
\(173\) | − 177.674i | − 1.02702i | −0.858084 | − | 0.513509i | \(-0.828345\pi\) | ||||
0.858084 | − | 0.513509i | \(-0.171655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −726.958 | −4.15405 | ||||||||
\(176\) | − 853.997i | − 4.85226i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −75.3887 | −0.423532 | ||||||||
\(179\) | − 132.513i | − 0.740298i | −0.928972 | − | 0.370149i | \(-0.879307\pi\) | ||||
0.928972 | − | 0.370149i | \(-0.120693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4684 | 0.0909858 | 0.0454929 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454929 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(182\) | − 473.459i | − 2.60143i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −351.039 | −1.90782 | ||||||||
\(185\) | 490.204i | 2.64975i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 135.259 | 0.723308 | ||||||||
\(188\) | 50.0559i | 0.266255i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 911.850 | 4.79921 | ||||||||
\(191\) | − 89.1158i | − 0.466575i | −0.972408 | − | 0.233288i | \(-0.925052\pi\) | ||||
0.972408 | − | 0.233288i | \(-0.0749483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −263.571 | −1.36565 | −0.682826 | − | 0.730581i | \(-0.739249\pi\) | ||||
−0.682826 | + | 0.730581i | \(0.739249\pi\) | |||||||
\(194\) | − 278.997i | − 1.43813i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −867.105 | −4.42401 | ||||||||
\(197\) | − 188.222i | − 0.955444i | −0.878511 | − | 0.477722i | \(-0.841463\pi\) | ||||
0.878511 | − | 0.477722i | \(-0.158537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 87.7301 | 0.440855 | 0.220427 | − | 0.975403i | \(-0.429255\pi\) | ||||
0.220427 | + | 0.975403i | \(0.429255\pi\) | |||||||
\(200\) | − 1727.23i | − 8.63617i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −503.974 | −2.49492 | ||||||||
\(203\) | − 206.666i | − 1.01806i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 172.208 | 0.840040 | ||||||||
\(206\) | − 159.807i | − 0.775764i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 651.007 | 3.12984 | ||||||||
\(209\) | 354.163i | 1.69456i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 42.0224 | 0.199158 | 0.0995791 | − | 0.995030i | \(-0.468250\pi\) | ||||
0.0995791 | + | 0.995030i | \(0.468250\pi\) | |||||||
\(212\) | 345.833i | 1.63129i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −653.781 | −3.05505 | ||||||||
\(215\) | 296.567i | 1.37938i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −436.187 | −2.01008 | ||||||||
\(218\) | 262.955i | 1.20622i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1468.05 | 6.67295 | ||||||||
\(221\) | 103.108i | 0.466554i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 167.396 | 0.750656 | 0.375328 | − | 0.926892i | \(-0.377530\pi\) | ||||
0.375328 | + | 0.926892i | \(0.377530\pi\) | |||||||
\(224\) | − 1417.27i | − 6.32710i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 172.553 | 0.763511 | ||||||||
\(227\) | − 374.151i | − 1.64824i | −0.566412 | − | 0.824122i | \(-0.691669\pi\) | ||||
0.566412 | − | 0.824122i | \(-0.308331\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −144.506 | −0.631030 | −0.315515 | − | 0.948921i | \(-0.602177\pi\) | ||||
−0.315515 | + | 0.948921i | \(0.602177\pi\) | |||||||
\(230\) | − 476.731i | − 2.07274i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 491.032 | 2.11652 | ||||||||
\(233\) | 219.708i | 0.942955i | 0.881878 | + | 0.471477i | \(0.156279\pi\) | ||||
−0.881878 | + | 0.471477i | \(0.843721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −43.1580 | −0.183651 | ||||||||
\(236\) | 685.555i | 2.90489i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 417.371 | 1.75366 | ||||||||
\(239\) | − 434.872i | − 1.81955i | −0.415103 | − | 0.909774i | \(-0.636255\pi\) | ||||
0.415103 | − | 0.909774i | \(-0.363745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 198.766 | 0.824756 | 0.412378 | − | 0.911013i | \(-0.364698\pi\) | ||||
0.412378 | + | 0.911013i | \(0.364698\pi\) | |||||||
\(242\) | 310.451i | 1.28286i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −707.387 | −2.89913 | ||||||||
\(245\) | − 747.613i | − 3.05148i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −269.980 | −1.09304 | ||||||||
\(248\) | − 1036.37i | − 4.17891i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1432.49 | 5.72997 | ||||||||
\(251\) | 343.459i | 1.36836i | 0.729313 | + | 0.684180i | \(0.239840\pi\) | ||||
−0.729313 | + | 0.684180i | \(0.760160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 185.162 | 0.731867 | ||||||||
\(254\) | − 43.5810i | − 0.171579i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 729.632 | 2.85013 | ||||||||
\(257\) | 261.700i | 1.01829i | 0.860681 | + | 0.509144i | \(0.170038\pi\) | ||||
−0.860681 | + | 0.509144i | \(0.829962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −587.508 | −2.26837 | ||||||||
\(260\) | 1119.10i | 4.30423i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −608.506 | −2.32254 | ||||||||
\(263\) | 31.1538i | 0.118456i | 0.998244 | + | 0.0592278i | \(0.0188638\pi\) | ||||
−0.998244 | + | 0.0592278i | \(0.981136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −298.175 | −1.12519 | ||||||||
\(266\) | 1092.85i | 4.10845i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −814.094 | −3.03767 | ||||||||
\(269\) | 137.914i | 0.512693i | 0.966585 | + | 0.256346i | \(0.0825188\pi\) | ||||
−0.966585 | + | 0.256346i | \(0.917481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −194.468 | −0.717593 | −0.358797 | − | 0.933416i | \(-0.616813\pi\) | ||||
−0.358797 | + | 0.933416i | \(0.616813\pi\) | |||||||
\(272\) | 573.885i | 2.10987i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −436.537 | −1.59320 | ||||||||
\(275\) | 911.062i | 3.31295i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 205.748 | 0.742773 | 0.371386 | − | 0.928478i | \(-0.378883\pi\) | ||||
0.371386 | + | 0.928478i | \(0.378883\pi\) | |||||||
\(278\) | 379.638i | 1.36560i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2875.98 | 10.2713 | ||||||||
\(281\) | 94.8530i | 0.337555i | 0.985654 | + | 0.168778i | \(0.0539819\pi\) | ||||
−0.985654 | + | 0.168778i | \(0.946018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 193.502 | 0.683754 | 0.341877 | − | 0.939745i | \(-0.388937\pi\) | ||||
0.341877 | + | 0.939745i | \(0.388937\pi\) | |||||||
\(284\) | − 1217.41i | − 4.28665i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −593.364 | −2.07470 | ||||||||
\(287\) | 206.391i | 0.719132i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 198.106 | 0.685489 | ||||||||
\(290\) | 666.849i | 2.29948i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 533.857 | 1.82828 | ||||||||
\(293\) | − 354.078i | − 1.20846i | −0.796811 | − | 0.604229i | \(-0.793481\pi\) | ||||
0.796811 | − | 0.604229i | \(-0.206519\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −591.082 | −2.00367 | ||||||||
\(296\) | − 1395.90i | − 4.71589i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 766.490 | 2.57211 | ||||||||
\(299\) | 141.150i | 0.472074i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −355.434 | −1.18084 | ||||||||
\(302\) | − 1053.17i | − 3.48731i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1502.67 | −4.94298 | ||||||||
\(305\) | − 609.905i | − 1.99969i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 151.973 | 0.495026 | 0.247513 | − | 0.968885i | \(-0.420387\pi\) | ||||
0.247513 | + | 0.968885i | \(0.420387\pi\) | |||||||
\(308\) | 1759.45i | 5.71250i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1407.45 | 4.54015 | ||||||||
\(311\) | − 63.8741i | − 0.205383i | −0.994713 | − | 0.102691i | \(-0.967255\pi\) | ||||
0.994713 | − | 0.102691i | \(-0.0327454\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −37.0453 | −0.118356 | −0.0591778 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591778 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(314\) | 60.2587i | 0.191907i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 692.705 | 2.19211 | ||||||||
\(317\) | − 399.581i | − 1.26051i | −0.776389 | − | 0.630254i | \(-0.782951\pi\) | ||||
0.776389 | − | 0.630254i | \(-0.217049\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −259.004 | −0.811926 | ||||||||
\(320\) | 2298.84i | 7.18388i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 571.360 | 1.77441 | ||||||||
\(323\) | − 237.997i | − 0.736832i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −694.507 | −2.13695 | ||||||||
\(326\) | − 859.535i | − 2.63661i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −490.379 | −1.49506 | ||||||||
\(329\) | − 51.7246i | − 0.157218i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −37.3698 | −0.112900 | −0.0564498 | − | 0.998405i | \(-0.517978\pi\) | ||||
−0.0564498 | + | 0.998405i | \(0.517978\pi\) | |||||||
\(332\) | − 559.151i | − 1.68419i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.957984 | 0.00286821 | ||||||||
\(335\) | − 701.908i | − 2.09525i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −131.462 | −0.390094 | −0.195047 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195047 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(338\) | 201.231i | 0.595357i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −986.526 | −2.90155 | ||||||||
\(341\) | 546.653i | 1.60309i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 341.314 | 0.995085 | ||||||||
\(344\) | − 844.501i | − 2.45495i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −687.099 | −1.98583 | ||||||||
\(347\) | − 362.839i | − 1.04564i | −0.852442 | − | 0.522822i | \(-0.824879\pi\) | ||||
0.852442 | − | 0.522822i | \(-0.175121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −473.272 | −1.35608 | −0.678040 | − | 0.735025i | \(-0.737170\pi\) | ||||
−0.678040 | + | 0.735025i | \(0.737170\pi\) | |||||||
\(350\) | 2811.28i | 8.03224i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1776.20 | −5.04602 | ||||||||
\(353\) | 264.341i | 0.748841i | 0.927259 | + | 0.374420i | \(0.122158\pi\) | ||||
−0.927259 | + | 0.374420i | \(0.877842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1049.64 | 2.95674 | ||||||||
\(356\) | 213.565i | 0.599900i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −512.454 | −1.43144 | ||||||||
\(359\) | 54.6728i | 0.152292i | 0.997097 | + | 0.0761459i | \(0.0242615\pi\) | ||||
−0.997097 | + | 0.0761459i | \(0.975739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 262.173 | 0.726242 | ||||||||
\(362\) | − 63.6865i | − 0.175930i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1341.24 | −3.68472 | ||||||||
\(365\) | 460.289i | 1.26107i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −340.491 | −0.927769 | −0.463885 | − | 0.885896i | \(-0.653545\pi\) | ||||
−0.463885 | + | 0.885896i | \(0.653545\pi\) | |||||||
\(368\) | 785.620i | 2.13484i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1895.71 | 5.12355 | ||||||||
\(371\) | − 357.361i | − 0.963238i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 168.009 | 0.450426 | 0.225213 | − | 0.974310i | \(-0.427692\pi\) | ||||
0.225213 | + | 0.974310i | \(0.427692\pi\) | |||||||
\(374\) | − 523.071i | − 1.39859i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 122.896 | 0.326852 | ||||||||
\(377\) | − 197.440i | − 0.523714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6118 | 0.0781315 | 0.0390657 | − | 0.999237i | \(-0.487562\pi\) | ||||
0.0390657 | + | 0.999237i | \(0.487562\pi\) | |||||||
\(380\) | − 2583.13i | − 6.79771i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −344.628 | −0.902167 | ||||||||
\(383\) | − 670.916i | − 1.75174i | −0.482548 | − | 0.875870i | \(-0.660289\pi\) | ||||
0.482548 | − | 0.875870i | \(-0.339711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1516.99 | −3.94023 | ||||||||
\(386\) | 1019.28i | 2.64062i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −790.354 | −2.03700 | ||||||||
\(389\) | 651.906i | 1.67585i | 0.545785 | + | 0.837925i | \(0.316232\pi\) | ||||
−0.545785 | + | 0.837925i | \(0.683768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −124.429 | −0.318232 | ||||||||
\(392\) | 2128.90i | 5.43087i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −727.891 | −1.84744 | ||||||||
\(395\) | 597.247i | 1.51202i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −434.519 | −1.09451 | −0.547253 | − | 0.836967i | \(-0.684326\pi\) | ||||
−0.547253 | + | 0.836967i | \(0.684326\pi\) | |||||||
\(398\) | − 339.269i | − 0.852434i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3865.52 | −9.66379 | ||||||||
\(401\) | − 181.485i | − 0.452581i | −0.974060 | − | 0.226290i | \(-0.927340\pi\) | ||||
0.974060 | − | 0.226290i | \(-0.0726598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −416.716 | −1.03403 | ||||||||
\(404\) | 1427.68i | 3.53386i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −799.215 | −1.96851 | ||||||||
\(407\) | 736.295i | 1.80908i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 467.124 | 1.14211 | 0.571056 | − | 0.820911i | \(-0.306534\pi\) | ||||
0.571056 | + | 0.820911i | \(0.306534\pi\) | |||||||
\(410\) | − 665.962i | − 1.62430i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −452.710 | −1.09881 | ||||||||
\(413\) | − 708.409i | − 1.71528i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 482.097 | 1.16168 | ||||||||
\(416\) | − 1354.00i | − 3.25482i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1369.61 | 3.27659 | ||||||||
\(419\) | 457.963i | 1.09299i | 0.837462 | + | 0.546495i | \(0.184038\pi\) | ||||
−0.837462 | + | 0.546495i | \(0.815962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −656.507 | −1.55940 | −0.779699 | − | 0.626154i | \(-0.784628\pi\) | ||||
−0.779699 | + | 0.626154i | \(0.784628\pi\) | |||||||
\(422\) | − 162.508i | − 0.385091i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 849.081 | 2.00255 | ||||||||
\(425\) | − 612.232i | − 1.44055i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 730.968 | 1.71187 | ||||||||
\(428\) | 1852.06i | 4.32724i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1146.88 | 2.66716 | ||||||||
\(431\) | − 295.176i | − 0.684864i | −0.939543 | − | 0.342432i | \(-0.888749\pi\) | ||||
0.939543 | − | 0.342432i | \(-0.111251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 359.925 | 0.831236 | 0.415618 | − | 0.909539i | \(-0.363565\pi\) | ||||
0.415618 | + | 0.909539i | \(0.363565\pi\) | |||||||
\(434\) | 1686.82i | 3.88668i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 744.912 | 1.70851 | ||||||||
\(437\) | − 325.806i | − 0.745551i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 550.931 | 1.25497 | 0.627484 | − | 0.778630i | \(-0.284085\pi\) | ||||
0.627484 | + | 0.778630i | \(0.284085\pi\) | |||||||
\(440\) | − 3604.32i | − 8.19165i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 398.740 | 0.902126 | ||||||||
\(443\) | 487.185i | 1.09974i | 0.835250 | + | 0.549870i | \(0.185323\pi\) | ||||
−0.835250 | + | 0.549870i | \(0.814677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −184.134 | −0.413785 | ||||||||
\(446\) | − 647.353i | − 1.45146i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2755.15 | −6.14990 | ||||||||
\(449\) | − 433.451i | − 0.965371i | −0.875794 | − | 0.482685i | \(-0.839662\pi\) | ||||
0.875794 | − | 0.482685i | \(-0.160338\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 258.660 | 0.573525 | ||||||||
\(452\) | − 488.817i | − 1.08145i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1446.91 | −3.18704 | ||||||||
\(455\) | − 1156.41i | − 2.54156i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 544.259 | 1.19094 | 0.595469 | − | 0.803378i | \(-0.296966\pi\) | ||||
0.595469 | + | 0.803378i | \(0.296966\pi\) | |||||||
\(458\) | 558.831i | 1.22016i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1350.50 | −2.93588 | ||||||||
\(461\) | − 275.026i | − 0.596586i | −0.954474 | − | 0.298293i | \(-0.903583\pi\) | ||||
0.954474 | − | 0.298293i | \(-0.0964172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 221.762 | 0.478968 | 0.239484 | − | 0.970900i | \(-0.423022\pi\) | ||||
0.239484 | + | 0.970900i | \(0.423022\pi\) | |||||||
\(464\) | − 1098.92i | − 2.36836i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 849.654 | 1.82329 | ||||||||
\(467\) | − 387.031i | − 0.828761i | −0.910104 | − | 0.414380i | \(-0.863998\pi\) | ||||
0.910104 | − | 0.414380i | \(-0.136002\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 841.234 | 1.79368 | ||||||||
\(470\) | 166.900i | 0.355106i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1683.16 | 3.56602 | ||||||||
\(473\) | 445.448i | 0.941751i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1603.08 | 3.37490 | ||||||||
\(476\) | − 1182.35i | − 2.48392i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1681.73 | −3.51827 | ||||||||
\(479\) | 50.1545i | 0.104707i | 0.998629 | + | 0.0523533i | \(0.0166722\pi\) | ||||
−0.998629 | + | 0.0523533i | \(0.983328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −561.282 | −1.16691 | ||||||||
\(482\) | − 768.666i | − 1.59474i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 879.461 | 1.81707 | ||||||||
\(485\) | − 681.439i | − 1.40503i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 425.468 | 0.873650 | 0.436825 | − | 0.899546i | \(-0.356103\pi\) | ||||
0.436825 | + | 0.899546i | \(0.356103\pi\) | |||||||
\(488\) | 1736.76i | 3.55894i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2891.16 | −5.90033 | ||||||||
\(491\) | 537.662i | 1.09503i | 0.836794 | + | 0.547517i | \(0.184427\pi\) | ||||
−0.836794 | + | 0.547517i | \(0.815573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 174.050 | 0.353043 | ||||||||
\(494\) | 1044.06i | 2.11349i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2319.37 | −4.67616 | ||||||||
\(497\) | 1257.99i | 2.53117i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 215.600 | 0.432064 | 0.216032 | − | 0.976386i | \(-0.430688\pi\) | ||||
0.216032 | + | 0.976386i | \(0.430688\pi\) | |||||||
\(500\) | − 4058.03i | − 8.11606i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1328.22 | 2.64585 | ||||||||
\(503\) | 231.627i | 0.460491i | 0.973133 | + | 0.230245i | \(0.0739529\pi\) | ||||
−0.973133 | + | 0.230245i | \(0.926047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1230.94 | −2.43750 | ||||||||
\(506\) | − 716.058i | − 1.41513i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −123.458 | −0.243028 | ||||||||
\(509\) | − 663.901i | − 1.30432i | −0.758080 | − | 0.652162i | \(-0.773862\pi\) | ||||
0.758080 | − | 0.652162i | \(-0.226138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −551.654 | −1.07956 | ||||||||
\(512\) | − 1059.98i | − 2.07027i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1012.04 | 1.96896 | ||||||||
\(515\) | − 390.324i | − 0.757911i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −64.8240 | −0.125385 | ||||||||
\(518\) | 2272.00i | 4.38611i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2747.59 | 5.28384 | ||||||||
\(521\) | 629.316i | 1.20790i | 0.797022 | + | 0.603950i | \(0.206407\pi\) | ||||
−0.797022 | + | 0.603950i | \(0.793593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 464.271 | 0.887708 | 0.443854 | − | 0.896099i | \(-0.353611\pi\) | ||||
0.443854 | + | 0.896099i | \(0.353611\pi\) | |||||||
\(524\) | 1723.80i | 3.28970i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 120.478 | 0.229045 | ||||||||
\(527\) | − 367.350i | − 0.697058i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 358.663 | 0.678002 | ||||||||
\(530\) | 1153.10i | 2.17566i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3095.87 | 5.81931 | ||||||||
\(533\) | 197.178i | 0.369939i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1596.84 | −2.98474 | ||||||||
\(536\) | 1998.75i | 3.72901i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 533.341 | 0.991340 | ||||||||
\(539\) | − 1122.93i | − 2.08335i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −494.079 | −0.913270 | −0.456635 | − | 0.889654i | \(-0.650945\pi\) | ||||
−0.456635 | + | 0.889654i | \(0.650945\pi\) | |||||||
\(542\) | 752.044i | 1.38753i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1193.60 | 2.19412 | ||||||||
\(545\) | 642.259i | 1.17846i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −673.432 | −1.23114 | −0.615568 | − | 0.788084i | \(-0.711073\pi\) | ||||
−0.615568 | + | 0.788084i | \(0.711073\pi\) | |||||||
\(548\) | 1236.64i | 2.25665i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3523.25 | 6.40591 | ||||||||
\(551\) | 455.736i | 0.827106i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −715.798 | −1.29439 | ||||||||
\(554\) | − 795.667i | − 1.43622i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1075.46 | 1.93427 | ||||||||
\(557\) | − 201.163i | − 0.361154i | −0.983561 | − | 0.180577i | \(-0.942203\pi\) | ||||
0.983561 | − | 0.180577i | \(-0.0577965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −339.567 | −0.607455 | ||||||||
\(560\) | − 6436.38i | − 11.4935i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 366.814 | 0.652694 | ||||||||
\(563\) | 848.512i | 1.50713i | 0.657375 | + | 0.753563i | \(0.271667\pi\) | ||||
−0.657375 | + | 0.753563i | \(0.728333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 421.456 | 0.745939 | ||||||||
\(566\) | − 748.310i | − 1.32210i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2988.96 | −5.26225 | ||||||||
\(569\) | 1066.94i | 1.87511i | 0.347838 | + | 0.937555i | \(0.386916\pi\) | ||||
−0.347838 | + | 0.937555i | \(0.613084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −998.217 | −1.74819 | −0.874095 | − | 0.485754i | \(-0.838545\pi\) | ||||
−0.874095 | + | 0.485754i | \(0.838545\pi\) | |||||||
\(572\) | 1680.91i | 2.93865i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 798.152 | 1.39051 | ||||||||
\(575\) | − 838.115i | − 1.45759i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −433.529 | −0.751351 | −0.375675 | − | 0.926751i | \(-0.622589\pi\) | ||||
−0.375675 | + | 0.926751i | \(0.622589\pi\) | |||||||
\(578\) | − 766.115i | − 1.32546i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1889.08 | 3.25703 | ||||||||
\(581\) | 577.792i | 0.994478i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −447.864 | −0.768206 | ||||||||
\(584\) | − 1310.72i | − 2.24438i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1369.29 | −2.33667 | ||||||||
\(587\) | − 643.448i | − 1.09616i | −0.836425 | − | 0.548081i | \(-0.815358\pi\) | ||||
0.836425 | − | 0.548081i | \(-0.184642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 961.872 | 1.63306 | ||||||||
\(590\) | 2285.82i | 3.87428i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3124.00 | −5.27703 | ||||||||
\(593\) | − 398.873i | − 0.672635i | −0.941749 | − | 0.336318i | \(-0.890818\pi\) | ||||
0.941749 | − | 0.336318i | \(-0.109182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1019.41 | 1.71330 | ||||||||
\(596\) | − 2171.35i | − 3.64320i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 545.855 | 0.912800 | ||||||||
\(599\) | − 1145.77i | − 1.91280i | −0.292055 | − | 0.956402i | \(-0.594339\pi\) | ||||
0.292055 | − | 0.956402i | \(-0.405661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 260.499 | 0.433443 | 0.216722 | − | 0.976233i | \(-0.430464\pi\) | ||||
0.216722 | + | 0.976233i | \(0.430464\pi\) | |||||||
\(602\) | 1374.53i | 2.28327i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2983.46 | −4.93950 | ||||||||
\(605\) | 758.267i | 1.25333i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 938.733 | 1.54651 | 0.773256 | − | 0.634094i | \(-0.218627\pi\) | ||||
0.773256 | + | 0.634094i | \(0.218627\pi\) | |||||||
\(608\) | 3125.34i | 5.14036i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2358.62 | −3.86659 | ||||||||
\(611\) | − 49.4157i | − 0.0808767i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −608.571 | −0.992774 | −0.496387 | − | 0.868101i | \(-0.665340\pi\) | ||||
−0.496387 | + | 0.868101i | \(0.665340\pi\) | |||||||
\(614\) | − 587.708i | − 0.957179i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4319.77 | 7.01261 | ||||||||
\(617\) | − 5.41005i | − 0.00876832i | −0.999990 | − | 0.00438416i | \(-0.998604\pi\) | ||||
0.999990 | − | 0.00438416i | \(-0.00139553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 744.538 | 1.20281 | 0.601404 | − | 0.798945i | \(-0.294608\pi\) | ||||
0.601404 | + | 0.798945i | \(0.294608\pi\) | |||||||
\(620\) | − 3987.08i | − 6.43077i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −247.013 | −0.397127 | ||||||||
\(623\) | − 220.684i | − 0.354228i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1893.39 | 3.02942 | ||||||||
\(626\) | 143.261i | 0.228852i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 170.704 | 0.271821 | ||||||||
\(629\) | − 494.789i | − 0.786628i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 566.360 | 0.897560 | 0.448780 | − | 0.893642i | \(-0.351859\pi\) | ||||
0.448780 | + | 0.893642i | \(0.351859\pi\) | |||||||
\(632\) | − 1700.72i | − 2.69101i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1545.26 | −2.43731 | ||||||||
\(635\) | − 106.445i | − 0.167630i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 856.014 | 1.34382 | ||||||||
\(638\) | 1001.62i | 1.56993i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4159.89 | 6.49983 | ||||||||
\(641\) | 1034.40i | 1.61372i | 0.590740 | + | 0.806862i | \(0.298836\pi\) | ||||
−0.590740 | + | 0.806862i | \(0.701164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.47434 | 0.00851375 | 0.00425688 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425688 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(644\) | − 1618.57i | − 2.51331i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −920.379 | −1.42473 | ||||||||
\(647\) | − 639.245i | − 0.988015i | −0.869458 | − | 0.494007i | \(-0.835532\pi\) | ||||
0.869458 | − | 0.494007i | \(-0.164468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −887.815 | −1.36797 | ||||||||
\(650\) | 2685.79i | 4.13198i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2434.93 | −3.73456 | ||||||||
\(653\) | − 651.138i | − 0.997148i | −0.866847 | − | 0.498574i | \(-0.833857\pi\) | ||||
0.866847 | − | 0.498574i | \(-0.166143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1486.25 | −2.26909 | ||||||||
\(656\) | 1097.46i | 1.67296i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −200.029 | −0.303995 | ||||||||
\(659\) | − 296.523i | − 0.449958i | −0.974364 | − | 0.224979i | \(-0.927769\pi\) | ||||
0.974364 | − | 0.224979i | \(-0.0722314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 737.931 | 1.11639 | 0.558193 | − | 0.829711i | \(-0.311495\pi\) | ||||
0.558193 | + | 0.829711i | \(0.311495\pi\) | |||||||
\(662\) | 144.516i | 0.218302i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1372.82 | −2.06750 | ||||||||
\(665\) | 2669.24i | 4.01390i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 238.266 | 0.357221 | ||||||||
\(668\) | − 2.71382i | − 0.00406260i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2714.41 | −4.05136 | ||||||||
\(671\) | − 916.088i | − 1.36526i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −475.306 | −0.706250 | −0.353125 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353125 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(674\) | 508.388i | 0.754284i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 570.055 | 0.843277 | ||||||||
\(677\) | − 881.795i | − 1.30250i | −0.758862 | − | 0.651252i | \(-0.774244\pi\) | ||||
0.758862 | − | 0.651252i | \(-0.225756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 816.702 | 1.20280 | ||||||||
\(680\) | 2422.10i | 3.56191i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2114.01 | 3.09972 | ||||||||
\(683\) | − 161.438i | − 0.236366i | −0.992992 | − | 0.118183i | \(-0.962293\pi\) | ||||
0.992992 | − | 0.118183i | \(-0.0377070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1066.23 | −1.55653 | ||||||||
\(686\) | − 1319.93i | − 1.92409i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1889.98 | −2.74706 | ||||||||
\(689\) | − 341.409i | − 0.495514i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 366.744 | 0.530744 | 0.265372 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265372 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(692\) | 1946.44i | 2.81278i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1403.17 | −2.02185 | ||||||||
\(695\) | 927.252i | 1.33418i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −173.819 | −0.249382 | ||||||||
\(698\) | 1830.23i | 2.62211i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7963.94 | 11.3771 | ||||||||
\(701\) | − 140.809i | − 0.200869i | −0.994944 | − | 0.100435i | \(-0.967977\pi\) | ||||
0.994944 | − | 0.100435i | \(-0.0320233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1295.56 | 1.84290 | ||||||||
\(704\) | 3452.90i | 4.90469i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1022.26 | 1.44795 | ||||||||
\(707\) | − 1475.27i | − 2.08667i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 815.582 | 1.15033 | 0.575164 | − | 0.818038i | \(-0.304938\pi\) | ||||
0.575164 | + | 0.818038i | \(0.304938\pi\) | |||||||
\(710\) | − 4059.17i | − 5.71714i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 524.340 | 0.736432 | ||||||||
\(713\) | − 502.883i | − 0.705306i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1449.27 | −2.02695 | ||||||||
\(716\) | 1451.70i | 2.02752i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 211.430 | 0.294471 | ||||||||
\(719\) | − 1073.20i | − 1.49263i | −0.665593 | − | 0.746315i | \(-0.731821\pi\) | ||||
0.665593 | − | 0.746315i | \(-0.268179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 467.802 | 0.648823 | ||||||||
\(722\) | − 1013.87i | − 1.40426i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −180.414 | −0.249191 | ||||||||
\(725\) | 1172.35i | 1.61704i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −511.757 | −0.703930 | −0.351965 | − | 0.936013i | \(-0.614486\pi\) | ||||
−0.351965 | + | 0.936013i | \(0.614486\pi\) | |||||||
\(728\) | 3292.98i | 4.52332i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1780.02 | 2.43839 | ||||||||
\(731\) | − 299.340i | − 0.409494i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 630.537 | 0.860214 | 0.430107 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430107 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(734\) | 1316.74i | 1.79393i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1633.98 | 2.22008 | ||||||||
\(737\) | − 1054.28i | − 1.43050i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 253.573 | 0.343130 | 0.171565 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171565 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(740\) | − 5370.26i | − 7.25711i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1381.98 | −1.86251 | ||||||||
\(743\) | 1027.89i | 1.38343i | 0.722172 | + | 0.691714i | \(0.243144\pi\) | ||||
−0.722172 | + | 0.691714i | \(0.756856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1872.12 | 2.51292 | ||||||||
\(746\) | − 649.723i | − 0.870942i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1481.78 | −1.98099 | ||||||||
\(749\) | − 1913.80i | − 2.55514i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1089.29 | −1.45045 | −0.725224 | − | 0.688513i | \(-0.758264\pi\) | ||||
−0.725224 | + | 0.688513i | \(0.758264\pi\) | |||||||
\(752\) | − 275.040i | − 0.365744i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −763.539 | −1.01265 | ||||||||
\(755\) | − 2572.32i | − 3.40705i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1244.71 | 1.64427 | 0.822136 | − | 0.569291i | \(-0.192782\pi\) | ||||
0.822136 | + | 0.569291i | \(0.192782\pi\) | |||||||
\(758\) | − 114.514i | − 0.151075i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6342.05 | −8.34480 | ||||||||
\(761\) | − 1341.43i | − 1.76272i | −0.472446 | − | 0.881359i | \(-0.656629\pi\) | ||||
0.472446 | − | 0.881359i | \(-0.343371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −769.744 | −1.00884 | ||||||||
\(764\) | 976.277i | 1.27785i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2594.56 | −3.38715 | ||||||||
\(767\) | − 676.786i | − 0.882380i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 381.351 | 0.495905 | 0.247953 | − | 0.968772i | \(-0.420242\pi\) | ||||
0.247953 | + | 0.968772i | \(0.420242\pi\) | |||||||
\(770\) | 5866.48i | 7.61880i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2887.46 | 3.74023 | ||||||||
\(773\) | − 419.868i | − 0.543167i | −0.962415 | − | 0.271584i | \(-0.912453\pi\) | ||||
0.962415 | − | 0.271584i | \(-0.0875474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2474.36 | 3.19272 | ||||||||
\(776\) | 1940.46i | 2.50060i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2521.04 | 3.24042 | ||||||||
\(779\) | − 455.129i | − 0.584248i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1576.58 | 2.01867 | ||||||||
\(782\) | 481.190i | 0.615332i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4764.44 | 6.07709 | ||||||||
\(785\) | 147.180i | 0.187490i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1063.32 | −1.35110 | −0.675551 | − | 0.737313i | \(-0.736094\pi\) | ||||
−0.675551 | + | 0.737313i | \(0.736094\pi\) | |||||||
\(788\) | 2062.00i | 2.61676i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2309.67 | 2.92363 | ||||||||
\(791\) | 505.113i | 0.638575i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 698.338 | 0.880628 | ||||||||
\(794\) | 1680.37i | 2.11633i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −961.096 | −1.20741 | ||||||||
\(797\) | 324.161i | 0.406727i | 0.979103 | + | 0.203363i | \(0.0651873\pi\) | ||||
−0.979103 | + | 0.203363i | \(0.934813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.5616 | 0.0545202 | ||||||||
\(800\) | 8039.74i | 10.0497i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −701.836 | −0.875108 | ||||||||
\(803\) | 691.362i | 0.860973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1395.53 | 1.73357 | ||||||||
\(806\) | 1611.52i | 1.99940i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3505.21 | 4.33814 | ||||||||
\(809\) | − 149.456i | − 0.184741i | −0.995725 | − | 0.0923707i | \(-0.970556\pi\) | ||||
0.995725 | − | 0.0923707i | \(-0.0294445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 873.810 | 1.07745 | 0.538724 | − | 0.842483i | \(-0.318907\pi\) | ||||
0.538724 | + | 0.842483i | \(0.318907\pi\) | |||||||
\(812\) | 2264.05i | 2.78824i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2847.39 | 3.49803 | ||||||||
\(815\) | − 2099.38i | − 2.57593i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 783.796 | 0.959359 | ||||||||
\(818\) | − 1806.46i | − 2.20838i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1886.57 | −2.30069 | ||||||||
\(821\) | 671.265i | 0.817619i | 0.912620 | + | 0.408809i | \(0.134056\pi\) | ||||
−0.912620 | + | 0.408809i | \(0.865944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1205.43 | −1.46467 | −0.732337 | − | 0.680942i | \(-0.761571\pi\) | ||||
−0.732337 | + | 0.680942i | \(0.761571\pi\) | |||||||
\(824\) | 1111.48i | 1.34889i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2739.55 | −3.31665 | ||||||||
\(827\) | − 380.902i | − 0.460583i | −0.973122 | − | 0.230291i | \(-0.926032\pi\) | ||||
0.973122 | − | 0.230291i | \(-0.0739679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1532.03 | 1.84804 | 0.924020 | − | 0.382343i | \(-0.124883\pi\) | ||||
0.924020 | + | 0.382343i | \(0.124883\pi\) | |||||||
\(830\) | − 1864.36i | − 2.24622i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2632.16 | −3.16366 | ||||||||
\(833\) | 754.606i | 0.905889i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.33984 | 0.00280220 | ||||||||
\(836\) | − 3879.91i | − 4.64104i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1771.03 | 2.11340 | ||||||||
\(839\) | 270.488i | 0.322394i | 0.986922 | + | 0.161197i | \(0.0515354\pi\) | ||||
−0.986922 | + | 0.161197i | \(0.948465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 507.714 | 0.603703 | ||||||||
\(842\) | 2538.83i | 3.01524i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −460.361 | −0.545452 | ||||||||
\(845\) | 491.498i | 0.581655i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −908.779 | −1.07294 | ||||||||
\(848\) | − 1900.23i | − 2.24083i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2367.62 | −2.78543 | ||||||||
\(851\) | − 677.342i | − 0.795936i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −929.016 | −1.08912 | −0.544558 | − | 0.838723i | \(-0.683303\pi\) | ||||
−0.544558 | + | 0.838723i | \(0.683303\pi\) | |||||||
\(854\) | − 2826.79i | − 3.31006i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4547.14 | 5.31208 | ||||||||
\(857\) | 207.368i | 0.241969i | 0.992654 | + | 0.120985i | \(0.0386052\pi\) | ||||
−0.992654 | + | 0.120985i | \(0.961395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −493.994 | −0.575080 | −0.287540 | − | 0.957769i | \(-0.592837\pi\) | ||||
−0.287540 | + | 0.957769i | \(0.592837\pi\) | |||||||
\(860\) | − 3248.93i | − 3.77783i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1141.50 | −1.32425 | ||||||||
\(863\) | − 294.120i | − 0.340811i | −0.985374 | − | 0.170405i | \(-0.945492\pi\) | ||||
0.985374 | − | 0.170405i | \(-0.0545077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1678.21 | −1.94013 | ||||||||
\(866\) | − 1391.90i | − 1.60727i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4778.50 | 5.50518 | ||||||||
\(869\) | 897.075i | 1.03231i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 803.681 | 0.922711 | ||||||||
\(872\) | − 1828.89i | − 2.09735i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1259.95 | −1.44159 | ||||||||
\(875\) | 4193.31i | 4.79236i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1303.57 | −1.48640 | −0.743198 | − | 0.669071i | \(-0.766692\pi\) | ||||
−0.743198 | + | 0.669071i | \(0.766692\pi\) | |||||||
\(878\) | − 2130.55i | − 2.42660i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8066.41 | −9.16637 | ||||||||
\(881\) | − 1042.89i | − 1.18376i | −0.806026 | − | 0.591880i | \(-0.798386\pi\) | ||||
0.806026 | − | 0.591880i | \(-0.201614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −895.269 | −1.01390 | −0.506948 | − | 0.861977i | \(-0.669226\pi\) | ||||
−0.506948 | + | 0.861977i | \(0.669226\pi\) | |||||||
\(884\) | − 1129.57i | − 1.27779i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1884.04 | 2.12645 | ||||||||
\(887\) | − 490.009i | − 0.552434i | −0.961095 | − | 0.276217i | \(-0.910919\pi\) | ||||
0.961095 | − | 0.276217i | \(-0.0890808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 127.574 | 0.143503 | ||||||||
\(890\) | 712.082i | 0.800092i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1833.85 | −2.05589 | ||||||||
\(893\) | 114.062i | 0.127729i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1251.65 | −1.39849 | ||||||||
\(896\) | 4985.61i | 5.56430i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1676.24 | −1.86663 | ||||||||
\(899\) | 703.431i | 0.782459i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 300.964 | 0.334033 | ||||||||
\(902\) | − 1000.29i | − 1.10896i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1200.13 | −1.32758 | ||||||||
\(905\) | − 155.552i | − 0.171881i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1592.09 | −1.75534 | −0.877668 | − | 0.479270i | \(-0.840902\pi\) | ||||
−0.877668 | + | 0.479270i | \(0.840902\pi\) | |||||||
\(908\) | 4098.88i | 4.51419i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4472.05 | −4.91434 | ||||||||
\(911\) | − 804.999i | − 0.883643i | −0.897103 | − | 0.441821i | \(-0.854332\pi\) | ||||
0.897103 | − | 0.441821i | \(-0.145668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 724.118 | 0.793120 | ||||||||
\(914\) | − 2104.75i | − 2.30279i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1583.08 | 1.72826 | ||||||||
\(917\) | − 1781.27i | − 1.94250i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 828.169 | 0.901164 | 0.450582 | − | 0.892735i | \(-0.351217\pi\) | ||||
0.450582 | + | 0.892735i | \(0.351217\pi\) | |||||||
\(920\) | 3315.73i | 3.60406i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1063.58 | −1.15355 | ||||||||
\(923\) | 1201.84i | 1.30210i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3332.75 | 3.60297 | ||||||||
\(926\) | − 857.597i | − 0.926131i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2285.60 | −2.46294 | ||||||||
\(929\) | − 229.494i | − 0.247033i | −0.992342 | − | 0.123517i | \(-0.960583\pi\) | ||||
0.992342 | − | 0.123517i | \(-0.0394173\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1975.87 | −2.12231 | ||||||||
\(932\) | − 2406.94i | − 2.58255i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1496.72 | −1.60249 | ||||||||
\(935\) | − 1277.58i | − 1.36640i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1193.95 | −1.27423 | −0.637115 | − | 0.770769i | \(-0.719872\pi\) | ||||
−0.637115 | + | 0.770769i | \(0.719872\pi\) | |||||||
\(938\) | − 3253.21i | − 3.46824i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 472.802 | 0.502981 | ||||||||
\(941\) | 1658.41i | 1.76239i | 0.472752 | + | 0.881196i | \(0.343261\pi\) | ||||
−0.472752 | + | 0.881196i | \(0.656739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −237.949 | −0.252332 | ||||||||
\(944\) | − 3766.88i | − 3.99034i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1722.63 | 1.82096 | ||||||||
\(947\) | 106.033i | 0.111968i | 0.998432 | + | 0.0559839i | \(0.0178295\pi\) | ||||
−0.998432 | + | 0.0559839i | \(0.982170\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −527.028 | −0.555351 | ||||||||
\(950\) | − 6199.39i | − 6.52568i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2902.88 | −3.04924 | ||||||||
\(953\) | − 1530.38i | − 1.60586i | −0.596073 | − | 0.802930i | \(-0.703273\pi\) | ||||
0.596073 | − | 0.802930i | \(-0.296727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −841.741 | −0.881404 | ||||||||
\(956\) | 4764.09i | 4.98336i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 193.957 | 0.202460 | ||||||||
\(959\) | − 1277.87i | − 1.33250i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 523.656 | 0.544907 | ||||||||
\(962\) | 2170.58i | 2.25632i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2177.51 | −2.25883 | ||||||||
\(965\) | 2489.55i | 2.57984i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 886.692 | 0.916951 | 0.458475 | − | 0.888707i | \(-0.348396\pi\) | ||||
0.458475 | + | 0.888707i | \(0.348396\pi\) | |||||||
\(968\) | − 2159.24i | − 2.23062i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2635.25 | −2.71676 | ||||||||
\(971\) | 819.330i | 0.843800i | 0.906642 | + | 0.421900i | \(0.138637\pi\) | ||||
−0.906642 | + | 0.421900i | \(0.861363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1111.31 | −1.14215 | ||||||||
\(974\) | − 1645.36i | − 1.68928i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3886.84 | 3.98242 | ||||||||
\(977\) | 841.090i | 0.860890i | 0.902617 | + | 0.430445i | \(0.141643\pi\) | ||||
−0.902617 | + | 0.430445i | \(0.858357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −276.573 | −0.282505 | ||||||||
\(980\) | 8190.22i | 8.35736i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2079.24 | 2.11735 | ||||||||
\(983\) | 1409.80i | 1.43418i | 0.696980 | + | 0.717091i | \(0.254527\pi\) | ||||
−0.696980 | + | 0.717091i | \(0.745473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1777.85 | −1.80492 | ||||||||
\(986\) | − 673.086i | − 0.682643i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2957.67 | 2.99360 | ||||||||
\(989\) | − 409.782i | − 0.414340i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1664.02 | −1.67913 | −0.839567 | − | 0.543256i | \(-0.817191\pi\) | ||||
−0.839567 | + | 0.543256i | \(0.817191\pi\) | |||||||
\(992\) | 4823.98i | 4.86288i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4864.90 | 4.89426 | ||||||||
\(995\) | − 828.652i | − 0.832816i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −193.171 | −0.193752 | −0.0968761 | − | 0.995296i | \(-0.530885\pi\) | ||||
−0.0968761 | + | 0.995296i | \(0.530885\pi\) | |||||||
\(998\) | − 833.765i | − 0.835436i | ||||||||
\(999\) | 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.890.2 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.83 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.2 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.83 | yes | 84 | 3.2 | odd | 2 | inner |