Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (of order \(6\), degree \(2\), not 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.e.649.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −2.86123 | − | 6.38854i | −0.408747 | − | 0.912648i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.98749 | + | 17.2988i | −0.907953 | + | 1.57262i | −0.0910503 | + | 0.995846i | \(0.529022\pi\) |
−0.816903 | + | 0.576775i | \(0.804311\pi\) | |||||||
\(12\) | 1.73205 | + | 3.00000i | 0.144338 | + | 0.250000i | ||||
\(13\) | 3.49788 | 0.269068 | 0.134534 | − | 0.990909i | \(-0.457046\pi\) | ||||
0.134534 | + | 0.990909i | \(0.457046\pi\) | |||||||
\(14\) | 8.02165 | + | 5.80113i | 0.572975 | + | 0.414367i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −9.12112 | + | 15.7982i | −0.536536 | + | 0.929308i | 0.462551 | + | 0.886593i | \(0.346934\pi\) |
−0.999087 | + | 0.0427155i | \(0.986399\pi\) | |||||||
\(18\) | 3.67423 | + | 2.12132i | 0.204124 | + | 0.117851i | ||||
\(19\) | 21.3143 | − | 12.3058i | 1.12180 | − | 0.647673i | 0.179942 | − | 0.983677i | \(-0.442409\pi\) |
0.941861 | + | 0.336004i | \(0.109076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0607 | + | 1.24079i | 0.574319 | + | 0.0590854i | ||||
\(22\) | − | 28.2489i | − | 1.28404i | ||||||
\(23\) | −21.8155 | + | 12.5952i | −0.948500 | + | 0.547617i | −0.892615 | − | 0.450820i | \(-0.851131\pi\) |
−0.0558853 | + | 0.998437i | \(0.517798\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.28401 | + | 2.47338i | −0.164770 | + | 0.0951299i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −13.9265 | − | 1.43274i | −0.497375 | − | 0.0511694i | ||||
\(29\) | 53.1223 | 1.83180 | 0.915902 | − | 0.401402i | \(-0.131477\pi\) | ||||
0.915902 | + | 0.401402i | \(0.131477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.0944 | + | 15.0656i | 0.841754 | + | 0.485987i | 0.857860 | − | 0.513883i | \(-0.171794\pi\) |
−0.0161061 | + | 0.999870i | \(0.505127\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −17.2988 | − | 29.9625i | −0.524207 | − | 0.907953i | ||||
\(34\) | − | 25.7984i | − | 0.758777i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −40.5034 | + | 23.3846i | −1.09469 | + | 0.632017i | −0.934820 | − | 0.355122i | \(-0.884439\pi\) |
−0.159866 | + | 0.987139i | \(0.551106\pi\) | |||||||
\(38\) | −17.4030 | + | 30.1429i | −0.457974 | + | 0.793234i | ||||
\(39\) | −3.02925 | + | 5.24682i | −0.0776732 | + | 0.134534i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 31.5250i | − | 0.768903i | −0.923145 | − | 0.384452i | \(-0.874391\pi\) | ||
0.923145 | − | 0.384452i | \(-0.125609\pi\) | |||||||
\(42\) | −15.6487 | + | 7.00855i | −0.372587 | + | 0.166870i | ||||
\(43\) | − | 64.4116i | − | 1.49794i | −0.662602 | − | 0.748972i | \(-0.730548\pi\) | ||
0.662602 | − | 0.748972i | \(-0.269452\pi\) | |||||||
\(44\) | 19.9750 | + | 34.5977i | 0.453977 | + | 0.786311i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.8123 | − | 30.8518i | 0.387223 | − | 0.670691i | ||||
\(47\) | −14.0313 | − | 24.3029i | −0.298538 | − | 0.517083i | 0.677264 | − | 0.735740i | \(-0.263166\pi\) |
−0.975802 | + | 0.218657i | \(0.929832\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −32.6268 | + | 36.5581i | −0.665852 | + | 0.746084i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.7982 | − | 27.3634i | −0.309769 | − | 0.536536i | ||||
\(52\) | 3.49788 | − | 6.05851i | 0.0672670 | − | 0.116510i | ||||
\(53\) | −56.1833 | − | 32.4374i | −1.06006 | − | 0.612027i | −0.134612 | − | 0.990898i | \(-0.542979\pi\) |
−0.925449 | + | 0.378872i | \(0.876312\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 18.0695 | − | 8.09277i | 0.322670 | − | 0.144514i | ||||
\(57\) | 42.6285i | 0.747869i | ||||||||
\(58\) | −65.0613 | + | 37.5631i | −1.12175 | + | 0.647640i | ||||
\(59\) | −86.7684 | − | 50.0958i | −1.47065 | − | 0.849081i | −0.471194 | − | 0.882029i | \(-0.656177\pi\) |
−0.999457 | + | 0.0329486i | \(0.989510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.94896 | − | 4.01198i | 0.113917 | − | 0.0657702i | −0.441959 | − | 0.897035i | \(-0.645716\pi\) |
0.555876 | + | 0.831265i | \(0.312383\pi\) | |||||||
\(62\) | −42.6119 | −0.687289 | ||||||||
\(63\) | −12.3061 | + | 17.0165i | −0.195334 | + | 0.270103i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 42.3733 | + | 24.4642i | 0.642020 | + | 0.370670i | ||||
\(67\) | −14.0844 | − | 8.13165i | −0.210215 | − | 0.121368i | 0.391196 | − | 0.920307i | \(-0.372061\pi\) |
−0.601411 | + | 0.798939i | \(0.705395\pi\) | |||||||
\(68\) | 18.2422 | + | 31.5965i | 0.268268 | + | 0.464654i | ||||
\(69\) | − | 43.6310i | − | 0.632333i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −107.725 | −1.51725 | −0.758625 | − | 0.651528i | \(-0.774128\pi\) | ||||
−0.758625 | + | 0.651528i | \(0.774128\pi\) | |||||||
\(72\) | 7.34847 | − | 4.24264i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 25.8303 | − | 44.7395i | 0.353840 | − | 0.612870i | −0.633078 | − | 0.774088i | \(-0.718209\pi\) |
0.986919 | + | 0.161218i | \(0.0515423\pi\) | |||||||
\(74\) | 33.0709 | − | 57.2804i | 0.446904 | − | 0.774060i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 49.2232i | − | 0.647673i | ||||||
\(77\) | 139.091 | + | 14.3095i | 1.80637 | + | 0.185838i | ||||
\(78\) | − | 8.56803i | − | 0.109846i | ||||||
\(79\) | −10.9877 | − | 19.0313i | −0.139085 | − | 0.240903i | 0.788065 | − | 0.615592i | \(-0.211083\pi\) |
−0.927151 | + | 0.374689i | \(0.877750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 22.2916 | + | 38.6101i | 0.271848 | + | 0.470855i | ||||
\(83\) | 0.417479 | 0.00502987 | 0.00251494 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251494 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(84\) | 14.2098 | − | 19.6489i | 0.169164 | − | 0.233916i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 45.5459 | + | 78.8878i | 0.529603 | + | 0.917300i | ||||
\(87\) | −46.0053 | + | 79.6835i | −0.528796 | + | 0.915902i | ||||
\(88\) | −48.9285 | − | 28.2489i | −0.556006 | − | 0.321010i | ||||
\(89\) | 96.3110 | − | 55.6052i | 1.08215 | − | 0.624778i | 0.150672 | − | 0.988584i | \(-0.451856\pi\) |
0.931475 | + | 0.363806i | \(0.118523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0082 | − | 22.3463i | −0.109981 | − | 0.245564i | ||||
\(92\) | 50.3807i | 0.547617i | ||||||||
\(93\) | −45.1968 | + | 26.0944i | −0.485987 | + | 0.280585i | ||||
\(94\) | 34.3695 | + | 19.8432i | 0.365633 | + | 0.211098i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | −74.2244 | −0.765200 | −0.382600 | − | 0.923914i | \(-0.624971\pi\) | ||||
−0.382600 | + | 0.923914i | \(0.624971\pi\) | |||||||
\(98\) | 14.1090 | − | 67.8449i | 0.143969 | − | 0.692295i | ||||
\(99\) | 59.9249 | 0.605302 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 75.8587 | + | 43.7970i | 0.751076 | + | 0.433634i | 0.826083 | − | 0.563549i | \(-0.190564\pi\) |
−0.0750065 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(102\) | 38.6976 | + | 22.3421i | 0.379388 | + | 0.219040i | ||||
\(103\) | −69.5206 | − | 120.413i | −0.674957 | − | 1.16906i | −0.976482 | − | 0.215601i | \(-0.930829\pi\) |
0.301525 | − | 0.953458i | \(-0.402504\pi\) | |||||||
\(104\) | 9.89350i | 0.0951299i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 91.7469 | 0.865537 | ||||||||
\(107\) | 131.800 | − | 76.0949i | 1.23178 | − | 0.711168i | 0.264378 | − | 0.964419i | \(-0.414833\pi\) |
0.967400 | + | 0.253252i | \(0.0815000\pi\) | |||||||
\(108\) | 5.19615 | − | 9.00000i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 32.3777 | − | 56.0798i | 0.297043 | − | 0.514494i | −0.678415 | − | 0.734679i | \(-0.737333\pi\) |
0.975458 | + | 0.220185i | \(0.0706662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 81.0068i | − | 0.729791i | ||||||
\(112\) | −16.4081 | + | 22.6887i | −0.146501 | + | 0.202577i | ||||
\(113\) | − | 3.25860i | − | 0.0288372i | −0.999896 | − | 0.0144186i | \(-0.995410\pi\) | ||
0.999896 | − | 0.0144186i | \(-0.00458974\pi\) | |||||||
\(114\) | −30.1429 | − | 52.2090i | −0.264411 | − | 0.457974i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 53.1223 | − | 92.0105i | 0.457951 | − | 0.793194i | ||||
\(117\) | −5.24682 | − | 9.08776i | −0.0448446 | − | 0.0776732i | ||||
\(118\) | 141.692 | 1.20078 | ||||||||
\(119\) | 127.025 | + | 13.0682i | 1.06744 | + | 0.109817i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139.000 | − | 240.755i | −1.14876 | − | 1.98971i | ||||
\(122\) | −5.67380 | + | 9.82731i | −0.0465066 | + | 0.0805517i | ||||
\(123\) | 47.2875 | + | 27.3015i | 0.384452 | + | 0.221963i | ||||
\(124\) | 52.1887 | − | 30.1312i | 0.420877 | − | 0.242993i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.03931 | − | 29.5426i | 0.0241215 | − | 0.234465i | ||||
\(127\) | − | 88.5772i | − | 0.697458i | −0.937224 | − | 0.348729i | \(-0.886613\pi\) | ||
0.937224 | − | 0.348729i | \(-0.113387\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 96.6174 | + | 55.7821i | 0.748972 | + | 0.432419i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −108.361 | + | 62.5621i | −0.827181 | + | 0.477573i | −0.852887 | − | 0.522096i | \(-0.825150\pi\) |
0.0257055 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(132\) | −69.1953 | −0.524207 | ||||||||
\(133\) | −139.601 | − | 100.957i | −1.04963 | − | 0.759077i | ||||
\(134\) | 22.9998 | 0.171640 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −44.6842 | − | 25.7984i | −0.328560 | − | 0.189694i | ||||
\(137\) | 33.7349 | + | 19.4769i | 0.246240 | + | 0.142167i | 0.618042 | − | 0.786145i | \(-0.287926\pi\) |
−0.371801 | + | 0.928312i | \(0.621260\pi\) | |||||||
\(138\) | 30.8518 | + | 53.4368i | 0.223564 | + | 0.387223i | ||||
\(139\) | − | 98.9454i | − | 0.711837i | −0.934517 | − | 0.355919i | \(-0.884168\pi\) | ||
0.934517 | − | 0.355919i | \(-0.115832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48.6058 | 0.344722 | ||||||||
\(142\) | 131.935 | − | 76.1729i | 0.929122 | − | 0.536429i | ||||
\(143\) | −34.9351 | + | 60.5093i | −0.244301 | + | 0.423142i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 73.0593i | 0.500406i | ||||||||
\(147\) | −26.5815 | − | 80.6004i | −0.180827 | − | 0.548302i | ||||
\(148\) | 93.5385i | 0.632017i | ||||||||
\(149\) | −93.2324 | − | 161.483i | −0.625721 | − | 1.08378i | −0.988401 | − | 0.151867i | \(-0.951472\pi\) |
0.362680 | − | 0.931914i | \(-0.381862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −77.4202 | + | 134.096i | −0.512716 | + | 0.888051i | 0.487175 | + | 0.873304i | \(0.338027\pi\) |
−0.999891 | + | 0.0147462i | \(0.995306\pi\) | |||||||
\(152\) | 34.8060 | + | 60.2858i | 0.228987 | + | 0.396617i | ||||
\(153\) | 54.7267 | 0.357691 | ||||||||
\(154\) | −180.469 | + | 80.8265i | −1.17188 | + | 0.524847i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.05851 | + | 10.4936i | 0.0388366 | + | 0.0672670i | ||||
\(157\) | 25.1019 | − | 43.4777i | 0.159885 | − | 0.276928i | −0.774942 | − | 0.632032i | \(-0.782221\pi\) |
0.934827 | + | 0.355104i | \(0.115554\pi\) | |||||||
\(158\) | 26.9143 | + | 15.5390i | 0.170344 | + | 0.0983481i | ||||
\(159\) | 97.3123 | − | 56.1833i | 0.612027 | − | 0.353354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 142.884 | + | 103.331i | 0.887477 | + | 0.641810i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 100.295 | − | 57.9054i | 0.615308 | − | 0.355248i | −0.159732 | − | 0.987160i | \(-0.551063\pi\) |
0.775040 | + | 0.631912i | \(0.217730\pi\) | |||||||
\(164\) | −54.6029 | − | 31.5250i | −0.332945 | − | 0.192226i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.511306 | + | 0.295202i | −0.00308015 | + | 0.00177833i | ||||
\(167\) | 61.3210 | 0.367191 | 0.183596 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183596 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(168\) | −3.50949 | + | 34.1128i | −0.0208898 | + | 0.203052i | ||||
\(169\) | −156.765 | −0.927602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −63.9428 | − | 36.9174i | −0.373934 | − | 0.215891i | ||||
\(172\) | −111.564 | − | 64.4116i | −0.648629 | − | 0.374486i | ||||
\(173\) | −15.8508 | − | 27.4544i | −0.0916232 | − | 0.158696i | 0.816571 | − | 0.577245i | \(-0.195872\pi\) |
−0.908194 | + | 0.418549i | \(0.862539\pi\) | |||||||
\(174\) | − | 130.123i | − | 0.747831i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 79.8999 | 0.453977 | ||||||||
\(177\) | 150.287 | − | 86.7684i | 0.849081 | − | 0.490217i | ||||
\(178\) | −78.6376 | + | 136.204i | −0.441784 | + | 0.765193i | ||||
\(179\) | 65.9472 | − | 114.224i | 0.368420 | − | 0.638122i | −0.620899 | − | 0.783891i | \(-0.713232\pi\) |
0.989319 | + | 0.145768i | \(0.0465655\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 55.1431i | 0.304658i | 0.988330 | + | 0.152329i | \(0.0486773\pi\) | ||||
−0.988330 | + | 0.152329i | \(0.951323\pi\) | |||||||
\(182\) | 28.0588 | + | 20.2917i | 0.154169 | + | 0.111493i | ||||
\(183\) | 13.8979i | 0.0759449i | ||||||||
\(184\) | −35.6246 | − | 61.7035i | −0.193612 | − | 0.335345i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 36.9030 | − | 63.9179i | 0.198403 | − | 0.343645i | ||||
\(187\) | −182.194 | − | 315.569i | −0.974300 | − | 1.68754i | ||||
\(188\) | −56.1252 | −0.298538 | ||||||||
\(189\) | −14.8674 | − | 33.1958i | −0.0786633 | − | 0.175639i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −97.5822 | − | 169.017i | −0.510901 | − | 0.884907i | −0.999920 | − | 0.0126340i | \(-0.995978\pi\) |
0.489019 | − | 0.872273i | \(-0.337355\pi\) | |||||||
\(192\) | 6.92820 | − | 12.0000i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 302.035 | + | 174.380i | 1.56495 | + | 0.903523i | 0.996744 | + | 0.0806348i | \(0.0256947\pi\) |
0.568204 | + | 0.822888i | \(0.307639\pi\) | |||||||
\(194\) | 90.9060 | − | 52.4846i | 0.468588 | − | 0.270539i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 30.6937 | + | 93.0693i | 0.156601 | + | 0.474843i | ||||
\(197\) | − | 56.3808i | − | 0.286197i | −0.989708 | − | 0.143098i | \(-0.954293\pi\) | ||
0.989708 | − | 0.143098i | \(-0.0457066\pi\) | |||||||
\(198\) | −73.3927 | + | 42.3733i | −0.370670 | + | 0.214007i | ||||
\(199\) | −148.357 | − | 85.6540i | −0.745513 | − | 0.430422i | 0.0785571 | − | 0.996910i | \(-0.474969\pi\) |
−0.824070 | + | 0.566487i | \(0.808302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.3950 | − | 14.0844i | 0.121368 | − | 0.0700718i | ||||
\(202\) | −123.877 | −0.613251 | ||||||||
\(203\) | −151.995 | − | 339.374i | −0.748744 | − | 1.67179i | ||||
\(204\) | −63.1930 | −0.309769 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 170.290 | + | 98.3169i | 0.826650 | + | 0.477267i | ||||
\(207\) | 65.4465 | + | 37.7856i | 0.316167 | + | 0.182539i | ||||
\(208\) | −6.99576 | − | 12.1170i | −0.0336335 | − | 0.0582549i | ||||
\(209\) | 491.616i | 2.35223i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 162.038 | 0.767954 | 0.383977 | − | 0.923343i | \(-0.374554\pi\) | ||||
0.383977 | + | 0.923343i | \(0.374554\pi\) | |||||||
\(212\) | −112.367 | + | 64.8748i | −0.530031 | + | 0.306013i | ||||
\(213\) | 93.2923 | − | 161.587i | 0.437992 | − | 0.758625i | ||||
\(214\) | −107.614 | + | 186.394i | −0.502871 | + | 0.870999i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 21.5851 | − | 209.811i | 0.0994707 | − | 0.966870i | ||||
\(218\) | 91.5779i | 0.420082i | ||||||||
\(219\) | 44.7395 | + | 77.4910i | 0.204290 | + | 0.353840i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.9046 | + | 55.2604i | −0.144365 | + | 0.250047i | ||||
\(222\) | 57.2804 | + | 99.2126i | 0.258020 | + | 0.446904i | ||||
\(223\) | −365.329 | −1.63825 | −0.819123 | − | 0.573618i | \(-0.805539\pi\) | ||||
−0.819123 | + | 0.573618i | \(0.805539\pi\) | |||||||
\(224\) | 4.05241 | − | 39.3901i | 0.0180911 | − | 0.175849i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.30418 | + | 3.99096i | 0.0101955 | + | 0.0176591i | ||||
\(227\) | −128.937 | + | 223.325i | −0.568004 | + | 0.983811i | 0.428759 | + | 0.903419i | \(0.358951\pi\) |
−0.996763 | + | 0.0803928i | \(0.974383\pi\) | |||||||
\(228\) | 73.8347 | + | 42.6285i | 0.323837 | + | 0.186967i | ||||
\(229\) | 13.3634 | − | 7.71538i | 0.0583556 | − | 0.0336916i | −0.470538 | − | 0.882380i | \(-0.655940\pi\) |
0.528894 | + | 0.848688i | \(0.322607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −141.920 | + | 196.244i | −0.614374 | + | 0.849539i | ||||
\(232\) | 150.253i | 0.647640i | ||||||||
\(233\) | 108.553 | − | 62.6734i | 0.465895 | − | 0.268984i | −0.248625 | − | 0.968600i | \(-0.579979\pi\) |
0.714520 | + | 0.699615i | \(0.246645\pi\) | |||||||
\(234\) | 12.8520 | + | 7.42013i | 0.0549232 | + | 0.0317100i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −173.537 | + | 100.192i | −0.735326 | + | 0.424540i | ||||
\(237\) | 38.0626 | 0.160602 | ||||||||
\(238\) | −164.814 | + | 73.8151i | −0.692496 | + | 0.310148i | ||||
\(239\) | 3.62565 | 0.0151701 | 0.00758503 | − | 0.999971i | \(-0.497586\pi\) | ||||
0.00758503 | + | 0.999971i | \(0.497586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 83.6915 | + | 48.3193i | 0.347268 | + | 0.200495i | 0.663481 | − | 0.748193i | \(-0.269078\pi\) |
−0.316213 | + | 0.948688i | \(0.602412\pi\) | |||||||
\(242\) | 340.479 | + | 196.575i | 1.40694 | + | 0.812295i | ||||
\(243\) | −7.79423 | − | 13.5000i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | − | 16.0479i | − | 0.0657702i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −77.2202 | −0.313903 | ||||||||
\(247\) | 74.5548 | − | 43.0442i | 0.301841 | − | 0.174268i | ||||
\(248\) | −42.6119 | + | 73.8060i | −0.171822 | + | 0.297605i | ||||
\(249\) | −0.361548 | + | 0.626219i | −0.00145200 | + | 0.00251494i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 29.7311i | − | 0.118450i | −0.998245 | − | 0.0592252i | \(-0.981137\pi\) | ||
0.998245 | − | 0.0592252i | \(-0.0188630\pi\) | |||||||
\(252\) | 17.1674 | + | 38.3312i | 0.0681245 | + | 0.152108i | ||||
\(253\) | − | 503.177i | − | 1.98884i | ||||||
\(254\) | 62.6336 | + | 108.484i | 0.246589 | + | 0.427104i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 220.811 | + | 382.457i | 0.859189 | + | 1.48816i | 0.872704 | + | 0.488250i | \(0.162364\pi\) |
−0.0135154 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(258\) | −157.776 | −0.611533 | ||||||||
\(259\) | 265.283 | + | 191.848i | 1.02426 | + | 0.740728i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −79.6835 | − | 138.016i | −0.305301 | − | 0.528796i | ||||
\(262\) | 88.4762 | − | 153.245i | 0.337695 | − | 0.584905i | ||||
\(263\) | 297.087 | + | 171.523i | 1.12961 | + | 0.652180i | 0.943836 | − | 0.330413i | \(-0.107188\pi\) |
0.185772 | + | 0.982593i | \(0.440521\pi\) | |||||||
\(264\) | 84.7466 | − | 48.9285i | 0.321010 | − | 0.185335i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 242.363 | + | 24.9341i | 0.911139 | + | 0.0937371i | ||||
\(267\) | 192.622i | 0.721431i | ||||||||
\(268\) | −28.1689 | + | 16.2633i | −0.105108 | + | 0.0606840i | ||||
\(269\) | −401.274 | − | 231.676i | −1.49172 | − | 0.861247i | −0.491769 | − | 0.870726i | \(-0.663650\pi\) |
−0.999955 | + | 0.00947852i | \(0.996983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 211.814 | − | 122.291i | 0.781600 | − | 0.451257i | −0.0553967 | − | 0.998464i | \(-0.517642\pi\) |
0.836997 | + | 0.547207i | \(0.184309\pi\) | |||||||
\(272\) | 72.9689 | 0.268268 | ||||||||
\(273\) | 42.1869 | + | 4.34015i | 0.154531 | + | 0.0158980i | ||||
\(274\) | −55.0889 | −0.201054 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −75.5711 | − | 43.6310i | −0.273808 | − | 0.158083i | ||||
\(277\) | −122.126 | − | 70.5092i | −0.440887 | − | 0.254546i | 0.263087 | − | 0.964772i | \(-0.415259\pi\) |
−0.703974 | + | 0.710226i | \(0.748593\pi\) | |||||||
\(278\) | 69.9650 | + | 121.183i | 0.251673 | + | 0.435910i | ||||
\(279\) | − | 90.3935i | − | 0.323991i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 84.9953 | 0.302475 | 0.151237 | − | 0.988497i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988497i | \(0.451674\pi\) | |||||||
\(282\) | −59.5297 | + | 34.3695i | −0.211098 | + | 0.121878i | ||||
\(283\) | −58.3392 | + | 101.047i | −0.206146 | + | 0.357055i | −0.950497 | − | 0.310733i | \(-0.899425\pi\) |
0.744351 | + | 0.667788i | \(0.232759\pi\) | |||||||
\(284\) | −107.725 | + | 186.585i | −0.379312 | + | 0.656988i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 98.8112i | − | 0.345494i | ||||||
\(287\) | −201.399 | + | 90.2003i | −0.701738 | + | 0.314287i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −21.8896 | − | 37.9138i | −0.0757424 | − | 0.131190i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 64.2802 | − | 111.337i | 0.220894 | − | 0.382600i | ||||
\(292\) | −51.6607 | − | 89.4789i | −0.176920 | − | 0.306435i | ||||
\(293\) | 131.882 | 0.450110 | 0.225055 | − | 0.974346i | \(-0.427744\pi\) | ||||
0.225055 | + | 0.974346i | \(0.427744\pi\) | |||||||
\(294\) | 89.5487 | + | 79.9189i | 0.304587 | + | 0.271833i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −66.1417 | − | 114.561i | −0.223452 | − | 0.387030i | ||||
\(297\) | −51.8965 | + | 89.8874i | −0.174736 | + | 0.302651i | ||||
\(298\) | 228.372 | + | 131.851i | 0.766348 | + | 0.442451i | ||||
\(299\) | −76.3080 | + | 44.0565i | −0.255211 | + | 0.147346i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −411.496 | + | 184.296i | −1.36710 | + | 0.612280i | ||||
\(302\) | − | 218.977i | − | 0.725090i | ||||||
\(303\) | −131.391 | + | 75.8587i | −0.433634 | + | 0.250359i | ||||
\(304\) | −85.2570 | − | 49.2232i | −0.280451 | − | 0.161918i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −67.0263 | + | 38.6976i | −0.219040 | + | 0.126463i | ||||
\(307\) | −429.871 | −1.40023 | −0.700115 | − | 0.714030i | \(-0.746868\pi\) | ||||
−0.700115 | + | 0.714030i | \(0.746868\pi\) | |||||||
\(308\) | 163.875 | − | 226.603i | 0.532063 | − | 0.735723i | ||||
\(309\) | 240.826 | 0.779373 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −217.786 | − | 125.739i | −0.700277 | − | 0.404305i | 0.107174 | − | 0.994240i | \(-0.465820\pi\) |
−0.807451 | + | 0.589935i | \(0.799153\pi\) | |||||||
\(312\) | −14.8403 | − | 8.56803i | −0.0475649 | − | 0.0274616i | ||||
\(313\) | −6.85166 | − | 11.8674i | −0.0218903 | − | 0.0379151i | 0.854873 | − | 0.518838i | \(-0.173635\pi\) |
−0.876763 | + | 0.480923i | \(0.840302\pi\) | |||||||
\(314\) | 70.9988i | 0.226111i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.9509 | −0.139085 | ||||||||
\(317\) | −28.5183 | + | 16.4651i | −0.0899632 | + | 0.0519403i | −0.544307 | − | 0.838886i | \(-0.683207\pi\) |
0.454343 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(318\) | −79.4551 | + | 137.620i | −0.249859 | + | 0.432768i | ||||
\(319\) | −530.558 | + | 918.954i | −1.66319 | + | 2.88073i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 263.601i | 0.821186i | ||||||||
\(322\) | −248.063 | − | 25.5204i | −0.770381 | − | 0.0792560i | ||||
\(323\) | 448.970i | 1.39000i | ||||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −81.8906 | + | 141.839i | −0.251198 | + | 0.435088i | ||||
\(327\) | 56.0798 | + | 97.1331i | 0.171498 | + | 0.297043i | ||||
\(328\) | 89.1662 | 0.271848 | ||||||||
\(329\) | −115.113 | + | 159.176i | −0.349888 | + | 0.483816i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 208.940 | + | 361.895i | 0.631240 | + | 1.09334i | 0.987299 | + | 0.158876i | \(0.0507869\pi\) |
−0.356059 | + | 0.934464i | \(0.615880\pi\) | |||||||
\(332\) | 0.417479 | − | 0.723095i | 0.00125747 | − | 0.00217800i | ||||
\(333\) | 121.510 | + | 70.1539i | 0.364895 | + | 0.210672i | ||||
\(334\) | −75.1025 | + | 43.3605i | −0.224858 | + | 0.129822i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −19.8232 | − | 44.2611i | −0.0589975 | − | 0.131729i | ||||
\(337\) | − | 286.688i | − | 0.850705i | −0.905028 | − | 0.425353i | \(-0.860150\pi\) | ||
0.905028 | − | 0.425353i | \(-0.139850\pi\) | |||||||
\(338\) | 191.997 | − | 110.849i | 0.568038 | − | 0.327957i | ||||
\(339\) | 4.88790 | + | 2.82203i | 0.0144186 | + | 0.00832458i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −521.234 | + | 300.935i | −1.52855 | + | 0.882507i | ||||
\(342\) | 104.418 | 0.305316 | ||||||||
\(343\) | 326.905 | + | 103.836i | 0.953077 | + | 0.302729i | ||||
\(344\) | 182.184 | 0.529603 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.8264 | + | 22.4164i | 0.112215 | + | 0.0647874i | ||||
\(347\) | −265.693 | − | 153.398i | −0.765685 | − | 0.442069i | 0.0656479 | − | 0.997843i | \(-0.479089\pi\) |
−0.831333 | + | 0.555774i | \(0.812422\pi\) | |||||||
\(348\) | 92.0105 | + | 159.367i | 0.264398 | + | 0.457951i | ||||
\(349\) | 340.162i | 0.974676i | 0.873214 | + | 0.487338i | \(0.162032\pi\) | ||||
−0.873214 | + | 0.487338i | \(0.837968\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.1755 | 0.0517821 | ||||||||
\(352\) | −97.8570 | + | 56.4978i | −0.278003 | + | 0.160505i | ||||
\(353\) | −187.501 | + | 324.761i | −0.531165 | + | 0.920004i | 0.468174 | + | 0.883636i | \(0.344912\pi\) |
−0.999338 | + | 0.0363676i | \(0.988421\pi\) | |||||||
\(354\) | −122.709 | + | 212.538i | −0.346636 | + | 0.600391i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 222.421i | − | 0.624778i | ||||||
\(357\) | −129.609 | + | 179.220i | −0.363051 | + | 0.502018i | ||||
\(358\) | 186.527i | 0.521025i | ||||||||
\(359\) | −164.750 | − | 285.356i | −0.458915 | − | 0.794863i | 0.539989 | − | 0.841672i | \(-0.318428\pi\) |
−0.998904 | + | 0.0468084i | \(0.985095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 122.365 | − | 211.942i | 0.338961 | − | 0.587098i | ||||
\(362\) | −38.9920 | − | 67.5362i | −0.107713 | − | 0.186564i | ||||
\(363\) | 481.509 | 1.32647 | ||||||||
\(364\) | −48.7132 | − | 5.01157i | −0.133828 | − | 0.0137681i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.82731 | − | 17.0214i | −0.0268506 | − | 0.0465066i | ||||
\(367\) | −13.5772 | + | 23.5163i | −0.0369950 | + | 0.0640772i | −0.883930 | − | 0.467619i | \(-0.845112\pi\) |
0.846935 | + | 0.531696i | \(0.178445\pi\) | |||||||
\(368\) | 87.2620 | + | 50.3807i | 0.237125 | + | 0.136904i | ||||
\(369\) | −81.9044 | + | 47.2875i | −0.221963 | + | 0.128151i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.4745 | + | 451.740i | −0.125268 | + | 1.21763i | ||||
\(372\) | 104.377i | 0.280585i | ||||||||
\(373\) | −110.416 | + | 63.7488i | −0.296022 | + | 0.170908i | −0.640654 | − | 0.767829i | \(-0.721337\pi\) |
0.344633 | + | 0.938738i | \(0.388004\pi\) | |||||||
\(374\) | 446.283 | + | 257.661i | 1.19327 | + | 0.688934i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 68.7390 | − | 39.6865i | 0.182817 | − | 0.105549i | ||||
\(377\) | 185.816 | 0.492880 | ||||||||
\(378\) | 41.6817 | + | 30.1436i | 0.110269 | + | 0.0797449i | ||||
\(379\) | −319.795 | −0.843785 | −0.421893 | − | 0.906646i | \(-0.638634\pi\) | ||||
−0.421893 | + | 0.906646i | \(0.638634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 132.866 | + | 76.7101i | 0.348729 | + | 0.201339i | ||||
\(382\) | 239.027 | + | 138.002i | 0.625724 | + | 0.361262i | ||||
\(383\) | −204.471 | − | 354.155i | −0.533867 | − | 0.924686i | −0.999217 | − | 0.0395587i | \(-0.987405\pi\) |
0.465350 | − | 0.885127i | \(-0.345929\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −493.221 | −1.27777 | ||||||||
\(387\) | −167.346 | + | 96.6174i | −0.432419 | + | 0.249657i | ||||
\(388\) | −74.2244 | + | 128.560i | −0.191300 | + | 0.331341i | ||||
\(389\) | 193.576 | − | 335.284i | 0.497626 | − | 0.861913i | −0.502370 | − | 0.864652i | \(-0.667539\pi\) |
0.999996 | + | 0.00273932i | \(0.000871952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 459.529i | − | 1.17526i | ||||||
\(392\) | −103.402 | − | 92.2824i | −0.263780 | − | 0.235414i | ||||
\(393\) | − | 216.721i | − | 0.551454i | ||||||
\(394\) | 39.8672 | + | 69.0521i | 0.101186 | + | 0.175259i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 59.9249 | − | 103.793i | 0.151326 | − | 0.262104i | ||||
\(397\) | 15.0556 | + | 26.0771i | 0.0379234 | + | 0.0656853i | 0.884364 | − | 0.466798i | \(-0.154592\pi\) |
−0.846441 | + | 0.532483i | \(0.821259\pi\) | |||||||
\(398\) | 242.266 | 0.608709 | ||||||||
\(399\) | 272.334 | − | 121.970i | 0.682541 | − | 0.305689i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −68.3852 | − | 118.447i | −0.170537 | − | 0.295378i | 0.768071 | − | 0.640365i | \(-0.221217\pi\) |
−0.938608 | + | 0.344987i | \(0.887883\pi\) | |||||||
\(402\) | −19.9184 | + | 34.4997i | −0.0495482 | + | 0.0858201i | ||||
\(403\) | 91.2750 | + | 52.6977i | 0.226489 | + | 0.130763i | ||||
\(404\) | 151.717 | − | 87.5941i | 0.375538 | − | 0.216817i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 426.129 | + | 308.170i | 1.04958 | + | 0.759038i | ||||
\(407\) | − | 934.215i | − | 2.29537i | ||||||
\(408\) | 77.3952 | − | 44.6842i | 0.189694 | − | 0.109520i | ||||
\(409\) | 426.838 | + | 246.435i | 1.04361 | + | 0.602531i | 0.920855 | − | 0.389906i | \(-0.127493\pi\) |
0.122759 | + | 0.992437i | \(0.460826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −58.4306 | + | 33.7349i | −0.142167 | + | 0.0820801i | ||||
\(412\) | −278.082 | −0.674957 | ||||||||
\(413\) | −71.7744 | + | 697.659i | −0.173788 | + | 1.68925i | ||||
\(414\) | −106.874 | −0.258149 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.1361 | + | 9.89350i | 0.0411924 | + | 0.0237825i | ||||
\(417\) | 148.418 | + | 85.6892i | 0.355919 | + | 0.205490i | ||||
\(418\) | −347.625 | − | 602.104i | −0.831638 | − | 1.44044i | ||||
\(419\) | 311.640i | 0.743771i | 0.928279 | + | 0.371885i | \(0.121289\pi\) | ||||
−0.928279 | + | 0.371885i | \(0.878711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −539.935 | −1.28250 | −0.641252 | − | 0.767330i | \(-0.721585\pi\) | ||||
−0.641252 | + | 0.767330i | \(0.721585\pi\) | |||||||
\(422\) | −198.456 | + | 114.578i | −0.470274 | + | 0.271513i | ||||
\(423\) | −42.0939 | + | 72.9087i | −0.0995127 | + | 0.172361i | ||||
\(424\) | 91.7469 | − | 158.910i | 0.216384 | − | 0.374788i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 263.871i | 0.619414i | ||||||||
\(427\) | −45.5132 | − | 32.9145i | −0.106588 | − | 0.0770831i | ||||
\(428\) | − | 304.380i | − | 0.711168i | ||||||
\(429\) | −60.5093 | − | 104.805i | −0.141047 | − | 0.244301i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 314.021 | − | 543.900i | 0.728586 | − | 1.26195i | −0.228895 | − | 0.973451i | \(-0.573511\pi\) |
0.957481 | − | 0.288497i | \(-0.0931555\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 706.789 | 1.63231 | 0.816153 | − | 0.577836i | \(-0.196103\pi\) | ||||
0.816153 | + | 0.577836i | \(0.196103\pi\) | |||||||
\(434\) | 121.922 | + | 272.228i | 0.280927 | + | 0.627253i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −64.7554 | − | 112.160i | −0.148522 | − | 0.257247i | ||||
\(437\) | −309.987 | + | 536.914i | −0.709353 | + | 1.22864i | ||||
\(438\) | −109.589 | − | 63.2712i | −0.250203 | − | 0.144455i | ||||
\(439\) | −564.452 | + | 325.886i | −1.28577 | + | 0.742338i | −0.977896 | − | 0.209090i | \(-0.932950\pi\) |
−0.307871 | + | 0.951428i | \(0.599617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 143.921 | + | 29.9297i | 0.326351 | + | 0.0678677i | ||||
\(442\) | − | 90.2398i | − | 0.204162i | ||||||
\(443\) | 20.4605 | − | 11.8129i | 0.0461863 | − | 0.0266657i | −0.476729 | − | 0.879050i | \(-0.658178\pi\) |
0.522915 | + | 0.852385i | \(0.324844\pi\) | |||||||
\(444\) | −140.308 | − | 81.0068i | −0.316009 | − | 0.182448i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 447.435 | − | 258.326i | 1.00322 | − | 0.579207i | ||||
\(447\) | 322.967 | 0.722520 | ||||||||
\(448\) | 22.8898 | + | 51.1083i | 0.0510933 | + | 0.114081i | ||||
\(449\) | 55.1499 | 0.122828 | 0.0614141 | − | 0.998112i | \(-0.480439\pi\) | ||||
0.0614141 | + | 0.998112i | \(0.480439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 545.346 | + | 314.856i | 1.20919 | + | 0.698128i | ||||
\(452\) | −5.64407 | − | 3.25860i | −0.0124869 | − | 0.00720930i | ||||
\(453\) | −134.096 | − | 232.260i | −0.296017 | − | 0.512716i | ||||
\(454\) | − | 364.689i | − | 0.803279i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −120.572 | −0.264411 | ||||||||
\(457\) | 303.778 | − | 175.386i | 0.664723 | − | 0.383778i | −0.129351 | − | 0.991599i | \(-0.541290\pi\) |
0.794074 | + | 0.607821i | \(0.207956\pi\) | |||||||
\(458\) | −10.9112 | + | 18.8987i | −0.0238236 | + | 0.0412636i | ||||
\(459\) | −47.3947 | + | 82.0901i | −0.103256 | + | 0.178845i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 471.598i | − | 1.02299i | −0.859287 | − | 0.511494i | \(-0.829092\pi\) | ||
0.859287 | − | 0.511494i | \(-0.170908\pi\) | |||||||
\(462\) | 35.0510 | − | 340.701i | 0.0758680 | − | 0.737448i | ||||
\(463\) | − | 387.112i | − | 0.836094i | −0.908425 | − | 0.418047i | \(-0.862715\pi\) | ||
0.908425 | − | 0.418047i | \(-0.137285\pi\) | |||||||
\(464\) | −106.245 | − | 184.021i | −0.228975 | − | 0.396597i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −88.6336 | + | 153.518i | −0.190201 | + | 0.329437i | ||||
\(467\) | −146.673 | − | 254.045i | −0.314075 | − | 0.543994i | 0.665166 | − | 0.746696i | \(-0.268361\pi\) |
−0.979240 | + | 0.202702i | \(0.935028\pi\) | |||||||
\(468\) | −20.9873 | −0.0448446 | ||||||||
\(469\) | −11.6506 | + | 113.245i | −0.0248413 | + | 0.241461i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 43.4777 | + | 75.3056i | 0.0923094 | + | 0.159885i | ||||
\(472\) | 141.692 | − | 245.418i | 0.300195 | − | 0.519954i | ||||
\(473\) | 1114.25 | + | 643.310i | 2.35570 | + | 1.36006i | ||||
\(474\) | −46.6170 | + | 26.9143i | −0.0983481 | + | 0.0567813i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 149.660 | − | 206.946i | 0.314412 | − | 0.434760i | ||||
\(477\) | 194.625i | 0.408018i | ||||||||
\(478\) | −4.44049 | + | 2.56372i | −0.00928973 | + | 0.00536343i | ||||
\(479\) | 660.805 | + | 381.516i | 1.37955 | + | 0.796484i | 0.992105 | − | 0.125409i | \(-0.0400242\pi\) |
0.387445 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −141.676 | + | 81.7967i | −0.294545 | + | 0.170056i | ||||
\(482\) | −136.668 | −0.283543 | ||||||||
\(483\) | −278.738 | + | 124.838i | −0.577098 | + | 0.258464i | ||||
\(484\) | −555.999 | −1.14876 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 193.893 | + | 111.944i | 0.398138 | + | 0.229865i | 0.685680 | − | 0.727903i | \(-0.259505\pi\) |
−0.287542 | + | 0.957768i | \(0.592838\pi\) | |||||||
\(488\) | 11.3476 | + | 19.6546i | 0.0232533 | + | 0.0402759i | ||||
\(489\) | 200.590i | 0.410205i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −837.694 | −1.70610 | −0.853049 | − | 0.521830i | \(-0.825249\pi\) | ||||
−0.853049 | + | 0.521830i | \(0.825249\pi\) | |||||||
\(492\) | 94.5751 | − | 54.6029i | 0.192226 | − | 0.110982i | ||||
\(493\) | −484.535 | + | 839.239i | −0.982829 | + | 1.70231i | ||||
\(494\) | −60.8737 | + | 105.436i | −0.123226 | + | 0.213434i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 120.525i | − | 0.242993i | ||||||
\(497\) | 308.225 | + | 688.203i | 0.620171 | + | 1.38471i | ||||
\(498\) | − | 1.02261i | − | 0.00205344i | ||||||
\(499\) | 87.3234 | + | 151.249i | 0.174997 | + | 0.303103i | 0.940160 | − | 0.340733i | \(-0.110675\pi\) |
−0.765163 | + | 0.643836i | \(0.777342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.1055 | + | 91.9814i | −0.105999 | + | 0.183596i | ||||
\(502\) | 21.0230 | + | 36.4130i | 0.0418786 | + | 0.0725358i | ||||
\(503\) | −747.962 | −1.48700 | −0.743501 | − | 0.668734i | \(-0.766836\pi\) | ||||
−0.743501 | + | 0.668734i | \(0.766836\pi\) | |||||||
\(504\) | −48.1299 | − | 34.8068i | −0.0954958 | − | 0.0690611i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 355.800 | + | 616.263i | 0.703162 | + | 1.21791i | ||||
\(507\) | 135.762 | − | 235.147i | 0.267776 | − | 0.463801i | ||||
\(508\) | −153.420 | − | 88.5772i | −0.302008 | − | 0.174365i | ||||
\(509\) | 203.021 | − | 117.214i | 0.398863 | − | 0.230284i | −0.287130 | − | 0.957892i | \(-0.592701\pi\) |
0.685993 | + | 0.727608i | \(0.259368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −359.726 | − | 37.0083i | −0.703965 | − | 0.0724233i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 110.752 | − | 63.9428i | 0.215891 | − | 0.124645i | ||||
\(514\) | −540.875 | − | 312.275i | −1.05229 | − | 0.607538i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 193.235 | − | 111.564i | 0.374486 | − | 0.216210i | ||||
\(517\) | 560.549 | 1.08423 | ||||||||
\(518\) | −460.561 | − | 47.3821i | −0.889114 | − | 0.0914712i | ||||
\(519\) | 54.9088 | 0.105797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 186.068 | + | 107.427i | 0.357137 | + | 0.206193i | 0.667824 | − | 0.744319i | \(-0.267226\pi\) |
−0.310687 | + | 0.950512i | \(0.600559\pi\) | |||||||
\(522\) | 195.184 | + | 112.689i | 0.373915 | + | 0.215880i | ||||
\(523\) | −462.520 | − | 801.108i | −0.884360 | − | 1.53176i | −0.846446 | − | 0.532475i | \(-0.821262\pi\) |
−0.0379137 | − | 0.999281i | \(-0.512071\pi\) | |||||||
\(524\) | 250.248i | 0.477573i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −485.141 | −0.922321 | ||||||||
\(527\) | −476.020 | + | 274.830i | −0.903263 | + | 0.521499i | ||||
\(528\) | −69.1953 | + | 119.850i | −0.131052 | + | 0.226988i | ||||
\(529\) | 52.7773 | − | 91.4130i | 0.0997681 | − | 0.172803i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 300.575i | 0.566054i | ||||||||
\(532\) | −314.464 | + | 140.839i | −0.591098 | + | 0.264734i | ||||
\(533\) | − | 110.271i | − | 0.206887i | ||||||
\(534\) | −136.204 | − | 235.913i | −0.255064 | − | 0.441784i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.9998 | − | 39.8368i | 0.0429100 | − | 0.0743224i | ||||
\(537\) | 114.224 | + | 197.842i | 0.212707 | + | 0.368420i | ||||
\(538\) | 655.277 | 1.21799 | ||||||||
\(539\) | −306.553 | − | 929.528i | −0.568744 | − | 1.72454i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 57.1560 | + | 98.9971i | 0.105649 | + | 0.182989i | 0.914003 | − | 0.405707i | \(-0.132975\pi\) |
−0.808354 | + | 0.588696i | \(0.799641\pi\) | |||||||
\(542\) | −172.945 | + | 299.550i | −0.319087 | + | 0.552675i | ||||
\(543\) | −82.7146 | − | 47.7553i | −0.152329 | − | 0.0879472i | ||||
\(544\) | −89.3683 | + | 51.5968i | −0.164280 | + | 0.0948471i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −54.7371 | + | 24.5151i | −0.100251 | + | 0.0448994i | ||||
\(547\) | − | 57.7698i | − | 0.105612i | −0.998605 | − | 0.0528060i | \(-0.983183\pi\) | ||
0.998605 | − | 0.0528060i | \(-0.0168165\pi\) | |||||||
\(548\) | 67.4699 | − | 38.9538i | 0.123120 | − | 0.0710835i | ||||
\(549\) | −20.8469 | − | 12.0359i | −0.0379725 | − | 0.0219234i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1132.26 | − | 653.712i | 2.05492 | − | 1.18641i | ||||
\(552\) | 123.407 | 0.223564 | ||||||||
\(553\) | −90.1438 | + | 124.648i | −0.163009 | + | 0.225404i | ||||
\(554\) | 199.430 | 0.359982 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −171.378 | − | 98.9454i | −0.308235 | − | 0.177959i | ||||
\(557\) | 351.738 | + | 203.076i | 0.631487 | + | 0.364589i | 0.781328 | − | 0.624121i | \(-0.214543\pi\) |
−0.149841 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(558\) | 63.9179 | + | 110.709i | 0.114548 | + | 0.198403i | ||||
\(559\) | − | 225.304i | − | 0.403049i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 631.139 | 1.12502 | ||||||||
\(562\) | −104.098 | + | 60.1008i | −0.185227 | + | 0.106941i | ||||
\(563\) | −214.146 | + | 370.911i | −0.380366 | + | 0.658813i | −0.991114 | − | 0.133012i | \(-0.957535\pi\) |
0.610749 | + | 0.791824i | \(0.290869\pi\) | |||||||
\(564\) | 48.6058 | − | 84.1878i | 0.0861805 | − | 0.149269i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 165.008i | − | 0.291534i | ||||||
\(567\) | 62.6692 | + | 6.44735i | 0.110528 | + | 0.0113710i | ||||
\(568\) | − | 304.691i | − | 0.536429i | ||||||
\(569\) | −457.897 | − | 793.100i | −0.804739 | − | 1.39385i | −0.916467 | − | 0.400110i | \(-0.868972\pi\) |
0.111728 | − | 0.993739i | \(-0.464362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 356.947 | − | 618.250i | 0.625125 | − | 1.08275i | −0.363391 | − | 0.931637i | \(-0.618381\pi\) |
0.988517 | − | 0.151112i | \(-0.0482855\pi\) | |||||||
\(572\) | 69.8701 | + | 121.019i | 0.122151 | + | 0.211571i | ||||
\(573\) | 338.035 | 0.589938 | ||||||||
\(574\) | 182.881 | − | 252.883i | 0.318608 | − | 0.440562i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 43.7973 | − | 75.8591i | 0.0759052 | − | 0.131472i | −0.825574 | − | 0.564293i | \(-0.809149\pi\) |
0.901480 | + | 0.432822i | \(0.142482\pi\) | |||||||
\(578\) | 53.6183 | + | 30.9565i | 0.0927652 | + | 0.0535580i | ||||
\(579\) | −523.140 | + | 302.035i | −0.903523 | + | 0.521649i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19450 | − | 2.66708i | −0.00205594 | − | 0.00459050i | ||||
\(582\) | 181.812i | 0.312392i | ||||||||
\(583\) | 1122.26 | − | 647.937i | 1.92497 | − | 1.11138i | ||||
\(584\) | 126.542 | + | 73.0593i | 0.216682 | + | 0.125101i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −161.522 | + | 93.2548i | −0.275635 | + | 0.159138i | ||||
\(587\) | 169.908 | 0.289452 | 0.144726 | − | 0.989472i | \(-0.453770\pi\) | ||||
0.144726 | + | 0.989472i | \(0.453770\pi\) | |||||||
\(588\) | −166.186 | − | 34.5598i | −0.282628 | − | 0.0587752i | ||||
\(589\) | 741.576 | 1.25904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 84.5712 | + | 48.8272i | 0.143098 | + | 0.0826179i | ||||
\(592\) | 162.014 | + | 93.5385i | 0.273671 | + | 0.158004i | ||||
\(593\) | −100.126 | − | 173.424i | −0.168847 | − | 0.292452i | 0.769168 | − | 0.639047i | \(-0.220671\pi\) |
−0.938015 | + | 0.346595i | \(0.887338\pi\) | |||||||
\(594\) | − | 146.785i | − | 0.247114i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −372.930 | −0.625721 | ||||||||
\(597\) | 256.962 | − | 148.357i | 0.430422 | − | 0.248504i | ||||
\(598\) | 62.3053 | − | 107.916i | 0.104189 | − | 0.180461i | ||||
\(599\) | −350.201 | + | 606.566i | −0.584643 | + | 1.01263i | 0.410277 | + | 0.911961i | \(0.365432\pi\) |
−0.994920 | + | 0.100671i | \(0.967901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1039.21i | 1.72914i | 0.502515 | + | 0.864569i | \(0.332408\pi\) | ||||
−0.502515 | + | 0.864569i | \(0.667592\pi\) | |||||||
\(602\) | 373.660 | − | 516.687i | 0.620698 | − | 0.858285i | ||||
\(603\) | 48.7899i | 0.0809119i | ||||||||
\(604\) | 154.840 | + | 268.191i | 0.256358 | + | 0.444025i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 107.280 | − | 185.815i | 0.177030 | − | 0.306626i | ||||
\(607\) | 30.5796 | + | 52.9655i | 0.0503783 | + | 0.0872578i | 0.890115 | − | 0.455736i | \(-0.150624\pi\) |
−0.839737 | + | 0.542994i | \(0.817291\pi\) | |||||||
\(608\) | 139.224 | 0.228987 | ||||||||
\(609\) | 640.692 | + | 65.9138i | 1.05204 | + | 0.108233i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.0798 | − | 85.0087i | −0.0803270 | − | 0.139130i | ||||
\(612\) | 54.7267 | − | 94.7894i | 0.0894227 | − | 0.154885i | ||||
\(613\) | −452.688 | − | 261.359i | −0.738479 | − | 0.426361i | 0.0830371 | − | 0.996546i | \(-0.473538\pi\) |
−0.821516 | + | 0.570185i | \(0.806871\pi\) | |||||||
\(614\) | 526.482 | − | 303.965i | 0.857462 | − | 0.495056i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −40.4734 | + | 393.408i | −0.0657036 | + | 0.638649i | ||||
\(617\) | − | 608.200i | − | 0.985738i | −0.870104 | − | 0.492869i | \(-0.835948\pi\) | ||
0.870104 | − | 0.492869i | \(-0.164052\pi\) | |||||||
\(618\) | −294.951 | + | 170.290i | −0.477267 | + | 0.275550i | ||||
\(619\) | −902.671 | − | 521.157i | −1.45827 | − | 0.841934i | −0.459346 | − | 0.888257i | \(-0.651916\pi\) |
−0.998927 | + | 0.0463229i | \(0.985250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −113.357 | + | 65.4465i | −0.182539 | + | 0.105389i | ||||
\(622\) | 355.643 | 0.571774 | ||||||||
\(623\) | −630.804 | − | 456.187i | −1.01253 | − | 0.732243i | ||||
\(624\) | 24.2340 | 0.0388366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.7831 | + | 9.68972i | 0.0268100 | + | 0.0154788i | ||||
\(627\) | −737.424 | − | 425.752i | −1.17611 | − | 0.679030i | ||||
\(628\) | −50.2037 | − | 86.9554i | −0.0799423 | − | 0.138464i | ||||
\(629\) | − | 853.176i | − | 1.35640i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −235.274 | −0.372859 | −0.186430 | − | 0.982468i | \(-0.559692\pi\) | ||||
−0.186430 | + | 0.982468i | \(0.559692\pi\) | |||||||
\(632\) | 53.8287 | − | 31.0780i | 0.0851720 | − | 0.0491741i | ||||
\(633\) | −140.329 | + | 243.057i | −0.221689 | + | 0.383977i | ||||
\(634\) | 23.2851 | − | 40.3310i | 0.0367273 | − | 0.0636136i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 224.733i | − | 0.353354i | ||||||
\(637\) | −114.125 | + | 127.876i | −0.179159 | + | 0.200747i | ||||
\(638\) | − | 1500.65i | − | 2.35211i | ||||||
\(639\) | 161.587 | + | 279.877i | 0.252875 | + | 0.437992i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 58.4900 | − | 101.308i | 0.0912481 | − | 0.158046i | −0.816788 | − | 0.576937i | \(-0.804248\pi\) |
0.908037 | + | 0.418891i | \(0.137581\pi\) | |||||||
\(642\) | −186.394 | − | 322.843i | −0.290333 | − | 0.502871i | ||||
\(643\) | −874.209 | −1.35958 | −0.679789 | − | 0.733408i | \(-0.737929\pi\) | ||||
−0.679789 | + | 0.733408i | \(0.737929\pi\) | |||||||
\(644\) | 321.859 | − | 144.151i | 0.499781 | − | 0.223837i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −317.470 | − | 549.874i | −0.491439 | − | 0.851198i | ||||
\(647\) | 5.84189 | − | 10.1185i | 0.00902920 | − | 0.0156390i | −0.861476 | − | 0.507799i | \(-0.830459\pi\) |
0.870505 | + | 0.492160i | \(0.163793\pi\) | |||||||
\(648\) | −22.0454 | − | 12.7279i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 1733.20 | − | 1000.66i | 2.67057 | − | 1.54185i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 296.023 | + | 214.079i | 0.454720 | + | 0.328847i | ||||
\(652\) | − | 231.622i | − | 0.355248i | ||||||
\(653\) | −552.641 | + | 319.067i | −0.846311 | + | 0.488618i | −0.859404 | − | 0.511296i | \(-0.829165\pi\) |
0.0130935 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(654\) | −137.367 | − | 79.3088i | −0.210041 | − | 0.121267i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −109.206 | + | 63.0500i | −0.166472 | + | 0.0961129i | ||||
\(657\) | −154.982 | −0.235894 | ||||||||
\(658\) | 28.4303 | − | 276.347i | 0.0432071 | − | 0.419980i | ||||
\(659\) | −870.363 | −1.32073 | −0.660367 | − | 0.750943i | \(-0.729599\pi\) | ||||
−0.660367 | + | 0.750943i | \(0.729599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 417.571 | + | 241.085i | 0.631727 | + | 0.364728i | 0.781420 | − | 0.624005i | \(-0.214495\pi\) |
−0.149694 | + | 0.988732i | \(0.547829\pi\) | |||||||
\(662\) | −511.797 | − | 295.486i | −0.773108 | − | 0.446354i | ||||
\(663\) | −55.2604 | − | 95.7138i | −0.0833490 | − | 0.144365i | ||||
\(664\) | 1.18081i | 0.00177833i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −198.425 | −0.297936 | ||||||||
\(667\) | −1158.89 | + | 669.085i | −1.73747 | + | 1.00313i | ||||
\(668\) | 61.3210 | − | 106.211i | 0.0917978 | − | 0.158999i | ||||
\(669\) | 316.384 | − | 547.993i | 0.472921 | − | 0.819123i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 160.279i | 0.238865i | ||||||||
\(672\) | 55.5756 | + | 40.1914i | 0.0827018 | + | 0.0598087i | ||||
\(673\) | 399.323i | 0.593347i | 0.954979 | + | 0.296674i | \(0.0958773\pi\) | ||||
−0.954979 | + | 0.296674i | \(0.904123\pi\) | |||||||
\(674\) | 202.719 | + | 351.119i | 0.300770 | + | 0.520948i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −156.765 | + | 271.525i | −0.231901 | + | 0.401664i | ||||
\(677\) | 70.6707 | + | 122.405i | 0.104388 | + | 0.180805i | 0.913488 | − | 0.406866i | \(-0.133378\pi\) |
−0.809100 | + | 0.587671i | \(0.800045\pi\) | |||||||
\(678\) | −7.98191 | −0.0117727 | ||||||||
\(679\) | 212.373 | + | 474.185i | 0.312773 | + | 0.698358i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −223.325 | − | 386.811i | −0.327937 | − | 0.568004i | ||||
\(682\) | 425.586 | − | 737.137i | 0.624026 | − | 1.08085i | ||||
\(683\) | 855.785 | + | 494.088i | 1.25298 | + | 0.723408i | 0.971700 | − | 0.236218i | \(-0.0759079\pi\) |
0.281279 | + | 0.959626i | \(0.409241\pi\) | |||||||
\(684\) | −127.886 | + | 73.8347i | −0.186967 | + | 0.107946i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −473.799 | + | 103.984i | −0.690669 | + | 0.151580i | ||||
\(687\) | 26.7268i | 0.0389037i | ||||||||
\(688\) | −223.128 | + | 128.823i | −0.324314 | + | 0.187243i | ||||
\(689\) | −196.522 | − | 113.462i | −0.285228 | − | 0.164677i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 303.829 | − | 175.415i | 0.439694 | − | 0.253857i | −0.263774 | − | 0.964585i | \(-0.584967\pi\) |
0.703468 | + | 0.710727i | \(0.251634\pi\) | |||||||
\(692\) | −63.4033 | −0.0916232 | ||||||||
\(693\) | −171.459 | − | 382.832i | −0.247415 | − | 0.552428i | ||||
\(694\) | 433.875 | 0.625180 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −225.379 | − | 130.123i | −0.323820 | − | 0.186958i | ||||
\(697\) | 498.040 | + | 287.543i | 0.714548 | + | 0.412544i | ||||
\(698\) | −240.531 | − | 416.611i | −0.344600 | − | 0.596864i | ||||
\(699\) | 217.107i | 0.310597i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 307.500 | 0.438659 | 0.219330 | − | 0.975651i | \(-0.429613\pi\) | ||||
0.219330 | + | 0.975651i | \(0.429613\pi\) | |||||||
\(702\) | −22.2604 | + | 12.8520i | −0.0317100 | + | 0.0183077i | ||||
\(703\) | −575.533 | + | 996.852i | −0.818681 | + | 1.41800i | ||||
\(704\) | 79.8999 | − | 138.391i | 0.113494 | − | 0.196578i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 530.333i | − | 0.751180i | ||||||
\(707\) | 62.7500 | − | 609.939i | 0.0887552 | − | 0.862715i | ||||
\(708\) | − | 347.074i | − | 0.490217i | ||||||
\(709\) | −49.0712 | − | 84.9938i | −0.0692118 | − | 0.119878i | 0.829343 | − | 0.558740i | \(-0.188715\pi\) |
−0.898555 | + | 0.438862i | \(0.855382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.9632 | + | 57.0939i | −0.0463617 | + | 0.0803009i | ||||
\(712\) | 157.275 | + | 272.409i | 0.220892 | + | 0.382597i | ||||
\(713\) | −759.016 | −1.06454 | ||||||||
\(714\) | 32.0105 | − | 311.147i | 0.0448326 | − | 0.435780i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −131.894 | − | 228.448i | −0.184210 | − | 0.319061i | ||||
\(717\) | −3.13990 | + | 5.43847i | −0.00437922 | + | 0.00758503i | ||||
\(718\) | 403.554 | + | 232.992i | 0.562053 | + | 0.324502i | ||||
\(719\) | −612.340 | + | 353.535i | −0.851655 | + | 0.491703i | −0.861209 | − | 0.508251i | \(-0.830292\pi\) |
0.00955403 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −570.349 | + | 788.664i | −0.791053 | + | 1.09385i | ||||
\(722\) | 346.100i | 0.479363i | ||||||||
\(723\) | −144.958 | + | 83.6915i | −0.200495 | + | 0.115756i | ||||
\(724\) | 95.5106 | + | 55.1431i | 0.131921 | + | 0.0761645i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −589.726 | + | 340.479i | −0.812295 | + | 0.468979i | ||||
\(727\) | 1353.85 | 1.86225 | 0.931123 | − | 0.364705i | \(-0.118830\pi\) | ||||
0.931123 | + | 0.364705i | \(0.118830\pi\) | |||||||
\(728\) | 63.2050 | − | 28.3076i | 0.0868201 | − | 0.0388840i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1017.59 | + | 587.506i | 1.39205 | + | 0.803701i | ||||
\(732\) | 24.0719 | + | 13.8979i | 0.0328851 | + | 0.0189862i | ||||
\(733\) | 276.517 | + | 478.941i | 0.377240 | + | 0.653398i | 0.990660 | − | 0.136359i | \(-0.0435400\pi\) |
−0.613420 | + | 0.789757i | \(0.710207\pi\) | |||||||
\(734\) | − | 38.4020i | − | 0.0523188i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −142.498 | −0.193612 | ||||||||
\(737\) | 281.336 | − | 162.429i | 0.381732 | − | 0.220393i | ||||
\(738\) | 66.8747 | − | 115.830i | 0.0906161 | − | 0.156952i | ||||
\(739\) | 466.739 | − | 808.416i | 0.631582 | − | 1.09393i | −0.355646 | − | 0.934621i | \(-0.615739\pi\) |
0.987228 | − | 0.159312i | \(-0.0509276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 149.110i | 0.201227i | ||||||||
\(742\) | −262.509 | − | 586.128i | −0.353785 | − | 0.789930i | ||||
\(743\) | − | 554.921i | − | 0.746865i | −0.927657 | − | 0.373432i | \(-0.878181\pi\) | ||
0.927657 | − | 0.373432i | \(-0.121819\pi\) | |||||||
\(744\) | −73.8060 | − | 127.836i | −0.0992016 | − | 0.171822i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 90.1544 | − | 156.152i | 0.120850 | − | 0.209319i | ||||
\(747\) | −0.626219 | − | 1.08464i | −0.000838312 | − | 0.00145200i | ||||
\(748\) | −728.776 | −0.974300 | ||||||||
\(749\) | −863.246 | − | 624.286i | −1.15253 | − | 0.833492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −363.974 | − | 630.421i | −0.484652 | − | 0.839442i | 0.515192 | − | 0.857075i | \(-0.327721\pi\) |
−0.999845 | + | 0.0176322i | \(0.994387\pi\) | |||||||
\(752\) | −56.1252 | + | 97.2117i | −0.0746345 | + | 0.129271i | ||||
\(753\) | 44.5966 | + | 25.7479i | 0.0592252 | + | 0.0341937i | ||||
\(754\) | −227.577 | + | 131.391i | −0.301826 | + | 0.174259i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −72.3642 | − | 7.44476i | −0.0957198 | − | 0.00984756i | ||||
\(757\) | 667.167i | 0.881330i | 0.897672 | + | 0.440665i | \(0.145257\pi\) | ||||
−0.897672 | + | 0.440665i | \(0.854743\pi\) | |||||||
\(758\) | 391.667 | − | 226.129i | 0.516711 | − | 0.298323i | ||||
\(759\) | 754.765 | + | 435.764i | 0.994421 | + | 0.574129i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −630.061 | + | 363.766i | −0.827938 | + | 0.478010i | −0.853146 | − | 0.521672i | \(-0.825309\pi\) |
0.0252080 | + | 0.999682i | \(0.491975\pi\) | |||||||
\(762\) | −216.969 | −0.284736 | ||||||||
\(763\) | −450.908 | − | 46.3890i | −0.590967 | − | 0.0607981i | ||||
\(764\) | −390.329 | −0.510901 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 500.850 | + | 289.166i | 0.653851 | + | 0.377501i | ||||
\(767\) | −303.506 | − | 175.229i | −0.395705 | − | 0.228460i | ||||
\(768\) | −13.8564 | − | 24.0000i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | − | 1374.28i | − | 1.78709i | −0.448969 | − | 0.893547i | \(-0.648209\pi\) | ||
0.448969 | − | 0.893547i | \(-0.351791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −764.913 | −0.992106 | ||||||||
\(772\) | 604.070 | − | 348.760i | 0.782474 | − | 0.451761i | ||||
\(773\) | 46.3356 | − | 80.2556i | 0.0599425 | − | 0.103824i | −0.834497 | − | 0.551013i | \(-0.814242\pi\) |
0.894439 | + | 0.447189i | \(0.147575\pi\) | |||||||
\(774\) | 136.638 | − | 236.663i | 0.176534 | − | 0.305767i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 209.938i | − | 0.270539i | ||||||
\(777\) | −517.514 | + | 231.779i | −0.666042 | + | 0.298300i | ||||
\(778\) | 547.517i | 0.703749i | ||||||||
\(779\) | −387.940 | − | 671.932i | −0.497998 | − | 0.862558i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1075.90 | − | 1863.51i | 1.37759 | − | 2.38606i | ||||
\(782\) | 324.936 | + | 562.805i | 0.415519 | + | 0.719700i | ||||
\(783\) | 276.032 | 0.352531 | ||||||||
\(784\) | 191.894 | + | 39.9062i | 0.244763 | + | 0.0509008i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 153.245 | + | 265.428i | 0.194968 | + | 0.337695i | ||||
\(787\) | −418.113 | + | 724.193i | −0.531275 | + | 0.920195i | 0.468059 | + | 0.883697i | \(0.344953\pi\) |
−0.999334 | + | 0.0364974i | \(0.988380\pi\) | |||||||
\(788\) | −97.6544 | − | 56.3808i | −0.123927 | − | 0.0715492i | ||||
\(789\) | −514.570 | + | 297.087i | −0.652180 | + | 0.376536i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.8177 | + | 9.32360i | −0.0263182 | + | 0.0117871i | ||||
\(792\) | 169.493i | 0.214007i | ||||||||
\(793\) | 24.3066 | − | 14.0334i | 0.0306515 | − | 0.0176967i | ||||
\(794\) | −36.8785 | − | 21.2918i | −0.0464465 | − | 0.0268159i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −296.714 | + | 171.308i | −0.372757 | + | 0.215211i | ||||
\(797\) | 130.279 | 0.163462 | 0.0817310 | − | 0.996654i | \(-0.473955\pi\) | ||||
0.0817310 | + | 0.996654i | \(0.473955\pi\) | |||||||
\(798\) | −247.294 | + | 341.951i | −0.309892 | + | 0.428510i | ||||
\(799\) | 511.924 | 0.640706 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −288.933 | − | 166.816i | −0.360716 | − | 0.208259i | ||||
\(802\) | 167.509 | + | 96.7113i | 0.208864 | + | 0.120588i | ||||
\(803\) | 515.960 | + | 893.670i | 0.642541 | + | 1.11291i | ||||
\(804\) | − | 56.3377i | − | 0.0700718i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −149.052 | −0.184927 | ||||||||
\(807\) | 695.027 | − | 401.274i | 0.861247 | − | 0.497241i | ||||
\(808\) | −123.877 | + | 214.561i | −0.153313 | + | 0.265546i | ||||
\(809\) | 310.782 | − | 538.290i | 0.384156 | − | 0.665377i | −0.607496 | − | 0.794323i | \(-0.707826\pi\) |
0.991652 | + | 0.128946i | \(0.0411592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 445.846i | 0.549748i | 0.961480 | + | 0.274874i | \(0.0886361\pi\) | ||||
−0.961480 | + | 0.274874i | \(0.911364\pi\) | |||||||
\(812\) | −739.808 | − | 76.1107i | −0.911093 | − | 0.0937324i | ||||
\(813\) | 423.627i | 0.521067i | ||||||||
\(814\) | 660.590 | + | 1144.17i | 0.811535 | + | 1.40562i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −63.1930 | + | 109.453i | −0.0774423 | + | 0.134134i | ||||
\(817\) | −792.636 | − | 1372.89i | −0.970178 | − | 1.68040i | ||||
\(818\) | −697.023 | −0.852107 | ||||||||
\(819\) | −43.0451 | + | 59.5217i | −0.0525582 | + | 0.0726760i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −628.622 | − | 1088.81i | −0.765678 | − | 1.32619i | −0.939887 | − | 0.341485i | \(-0.889070\pi\) |
0.174209 | − | 0.984709i | \(-0.444263\pi\) | |||||||
\(822\) | 47.7084 | − | 82.6334i | 0.0580394 | − | 0.100527i | ||||
\(823\) | 104.219 | + | 60.1709i | 0.126633 | + | 0.0731117i | 0.561978 | − | 0.827152i | \(-0.310040\pi\) |
−0.435345 | + | 0.900264i | \(0.643374\pi\) | |||||||
\(824\) | 340.580 | − | 196.634i | 0.413325 | − | 0.238633i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −405.414 | − | 905.206i | −0.490816 | − | 1.09589i | ||||
\(827\) | 151.053i | 0.182652i | 0.995821 | + | 0.0913258i | \(0.0291105\pi\) | ||||
−0.995821 | + | 0.0913258i | \(0.970890\pi\) | |||||||
\(828\) | 130.893 | − | 75.5711i | 0.158083 | − | 0.0912695i | ||||
\(829\) | −217.640 | − | 125.654i | −0.262533 | − | 0.151573i | 0.362957 | − | 0.931806i | \(-0.381767\pi\) |
−0.625489 | + | 0.780233i | \(0.715101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 211.528 | − | 122.126i | 0.254546 | − | 0.146962i | ||||
\(832\) | −27.9831 | −0.0336335 | ||||||||
\(833\) | −279.961 | − | 848.896i | −0.336088 | − | 1.01908i | ||||
\(834\) | −242.366 | −0.290606 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 851.503 | + | 491.616i | 1.01854 | + | 0.588057i | ||||
\(837\) | 135.590 | + | 78.2831i | 0.161996 | + | 0.0935282i | ||||
\(838\) | −220.363 | − | 381.679i | −0.262963 | − | 0.455465i | ||||
\(839\) | 499.592i | 0.595461i | 0.954650 | + | 0.297730i | \(0.0962297\pi\) | ||||
−0.954650 | + | 0.297730i | \(0.903770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1980.98 | 2.35550 | ||||||||
\(842\) | 661.282 | − | 381.791i | 0.785371 | − | 0.453434i | ||||
\(843\) | −73.6081 | + | 127.493i | −0.0873169 | + | 0.151237i | ||||
\(844\) | 162.038 | − | 280.658i | 0.191988 | − | 0.332534i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 119.059i | − | 0.140732i | ||||||
\(847\) | −1140.36 | + | 1576.86i | −1.34635 | + | 1.86170i | ||||
\(848\) | 259.499i | 0.306013i | ||||||||
\(849\) | −101.047 | − | 175.018i | −0.119018 | − | 0.206146i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 589.068 | − | 1020.30i | 0.692206 | − | 1.19894i | ||||
\(852\) | −186.585 | − | 323.174i | −0.218996 | − | 0.379312i | ||||
\(853\) | 1265.99 | 1.48416 | 0.742082 | − | 0.670310i | \(-0.233839\pi\) | ||||
0.742082 | + | 0.670310i | \(0.233839\pi\) | |||||||
\(854\) | 79.0162 | + | 8.12911i | 0.0925248 | + | 0.00951886i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 215.229 | + | 372.788i | 0.251436 | + | 0.435499i | ||||
\(857\) | −184.810 | + | 320.100i | −0.215648 | + | 0.373513i | −0.953473 | − | 0.301479i | \(-0.902520\pi\) |
0.737825 | + | 0.674992i | \(0.235853\pi\) | |||||||
\(858\) | 148.217 | + | 85.5731i | 0.172747 | + | 0.0997355i | ||||
\(859\) | 1089.49 | − | 629.015i | 1.26832 | − | 0.732264i | 0.293649 | − | 0.955913i | \(-0.405130\pi\) |
0.974670 | + | 0.223649i | \(0.0717971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.1160 | − | 380.214i | 0.0454309 | − | 0.441596i | ||||
\(862\) | 888.184i | 1.03038i | ||||||||
\(863\) | 204.959 | − | 118.333i | 0.237496 | − | 0.137118i | −0.376530 | − | 0.926405i | \(-0.622883\pi\) |
0.614025 | + | 0.789286i | \(0.289549\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −865.636 | + | 499.775i | −0.999579 | + | 0.577107i | ||||
\(867\) | 75.8277 | 0.0874598 | ||||||||
\(868\) | −341.818 | − | 247.197i | −0.393799 | − | 0.284790i | ||||
\(869\) | 438.959 | 0.505132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.2657 | − | 28.4436i | −0.0565622 | − | 0.0326562i | ||||
\(872\) | 158.618 | + | 91.5779i | 0.181901 | + | 0.105021i | ||||
\(873\) | 111.337 | + | 192.841i | 0.127533 | + | 0.220894i | ||||
\(874\) | − | 876.777i | − | 1.00318i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 178.958 | 0.204290 | ||||||||
\(877\) | 697.611 | − | 402.766i | 0.795451 | − | 0.459254i | −0.0464269 | − | 0.998922i | \(-0.514783\pi\) |
0.841878 | + | 0.539668i | \(0.181450\pi\) | |||||||
\(878\) | 460.873 | − | 798.256i | 0.524912 | − | 0.909175i | ||||
\(879\) | −114.213 | + | 197.823i | −0.129936 | + | 0.225055i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 763.260i | 0.866356i | 0.901308 | + | 0.433178i | \(0.142608\pi\) | ||||
−0.901308 | + | 0.433178i | \(0.857392\pi\) | |||||||
\(882\) | −197.430 | + | 65.1112i | −0.223843 | + | 0.0738222i | ||||
\(883\) | − | 574.986i | − | 0.651173i | −0.945512 | − | 0.325587i | \(-0.894438\pi\) | ||
0.945512 | − | 0.325587i | \(-0.105562\pi\) | |||||||
\(884\) | 63.8092 | + | 110.521i | 0.0721823 | + | 0.125023i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.7060 | + | 28.9356i | −0.0188555 | + | 0.0326587i | ||||
\(887\) | −191.751 | − | 332.122i | −0.216179 | − | 0.374433i | 0.737458 | − | 0.675393i | \(-0.236026\pi\) |
−0.953637 | + | 0.300960i | \(0.902693\pi\) | |||||||
\(888\) | 229.122 | 0.258020 | ||||||||
\(889\) | −565.879 | + | 253.440i | −0.636534 | + | 0.285084i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −89.8874 | − | 155.690i | −0.100884 | − | 0.174736i | ||||
\(892\) | −365.329 | + | 632.768i | −0.409561 | + | 0.709381i | ||||
\(893\) | −598.133 | − | 345.332i | −0.669802 | − | 0.386710i | ||||
\(894\) | −395.552 | + | 228.372i | −0.442451 | + | 0.255449i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −64.1732 | − | 46.4091i | −0.0716219 | − | 0.0517958i | ||||
\(897\) | − | 152.616i | − | 0.170141i | ||||||
\(898\) | −67.5445 | + | 38.9968i | −0.0752166 | + | 0.0434263i | ||||
\(899\) | 1386.19 | + | 800.319i | 1.54193 | + | 0.890232i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1024.91 | − | 591.731i | 1.13752 | − | 0.656749i | ||||
\(902\) | −890.547 | −0.987302 | ||||||||
\(903\) | 79.9215 | − | 776.849i | 0.0885066 | − | 0.860298i | ||||
\(904\) | 9.21672 | 0.0101955 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 328.466 | + | 189.640i | 0.362545 | + | 0.209316i | ||||
\(907\) | 1006.70 | + | 581.220i | 1.10993 | + | 0.640816i | 0.938810 | − | 0.344435i | \(-0.111930\pi\) |
0.171115 | + | 0.985251i | \(0.445263\pi\) | |||||||
\(908\) | 257.874 | + | 446.650i | 0.284002 | + | 0.491906i | ||||
\(909\) | − | 262.782i | − | 0.289089i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1070.03 | 1.17457 | 0.587284 | − | 0.809381i | \(-0.300197\pi\) | ||||
0.587284 | + | 0.809381i | \(0.300197\pi\) | |||||||
\(912\) | 147.669 | − | 85.2570i | 0.161918 | − | 0.0934836i | ||||
\(913\) | −4.16957 | + | 7.22190i | −0.00456689 | + | 0.00791008i | ||||
\(914\) | −248.034 | + | 429.607i | −0.271372 | + | 0.470030i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 30.8615i | − | 0.0336916i | ||||||
\(917\) | 709.725 | + | 513.262i | 0.773964 | + | 0.559719i | ||||
\(918\) | − | 134.053i | − | 0.146027i | ||||||
\(919\) | 583.360 | + | 1010.41i | 0.634777 | + | 1.09947i | 0.986562 | + | 0.163386i | \(0.0522415\pi\) |
−0.351785 | + | 0.936081i | \(0.614425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 372.279 | − | 644.806i | 0.404212 | − | 0.700115i | ||||
\(922\) | 333.470 | + | 577.587i | 0.361681 | + | 0.626450i | ||||
\(923\) | −376.808 | −0.408243 | ||||||||
\(924\) | 197.984 | + | 442.057i | 0.214268 | + | 0.478416i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 273.729 | + | 474.113i | 0.295604 | + | 0.512001i | ||||
\(927\) | −208.562 | + | 361.239i | −0.224986 | + | 0.389686i | ||||
\(928\) | 260.245 | + | 150.253i | 0.280437 | + | 0.161910i | ||||
\(929\) | −194.325 | + | 112.194i | −0.209177 | + | 0.120768i | −0.600929 | − | 0.799303i | \(-0.705202\pi\) |
0.391752 | + | 0.920071i | \(0.371869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −245.539 | + | 1180.71i | −0.263737 | + | 1.26821i | ||||
\(932\) | − | 250.694i | − | 0.268984i | ||||||
\(933\) | 377.217 | − | 217.786i | 0.404305 | − | 0.233426i | ||||
\(934\) | 359.274 | + | 207.427i | 0.384662 | + | 0.222084i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 25.7041 | − | 14.8403i | 0.0274616 | − | 0.0158550i | ||||
\(937\) | 644.185 | 0.687497 | 0.343749 | − | 0.939062i | \(-0.388303\pi\) | ||||
0.343749 | + | 0.939062i | \(0.388303\pi\) | |||||||
\(938\) | −65.8076 | − | 146.935i | −0.0701573 | − | 0.156647i | ||||
\(939\) | 23.7349 | 0.0252767 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −266.097 | − | 153.631i | −0.282781 | − | 0.163264i | 0.351901 | − | 0.936037i | \(-0.385535\pi\) |
−0.634682 | + | 0.772774i | \(0.718869\pi\) | |||||||
\(942\) | −106.498 | − | 61.4868i | −0.113055 | − | 0.0652726i | ||||
\(943\) | 397.063 | + | 687.734i | 0.421064 | + | 0.729305i | ||||
\(944\) | 400.766i | 0.424540i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1819.56 | −1.92342 | ||||||||
\(947\) | −850.013 | + | 490.755i | −0.897585 | + | 0.518221i | −0.876416 | − | 0.481555i | \(-0.840072\pi\) |
−0.0211694 | + | 0.999776i | \(0.506739\pi\) | |||||||
\(948\) | 38.0626 | − | 65.9264i | 0.0401504 | − | 0.0695426i | ||||
\(949\) | 90.3515 | − | 156.493i | 0.0952071 | − | 0.164903i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 57.0367i | − | 0.0599755i | ||||||
\(952\) | −36.9625 | + | 359.281i | −0.0388262 | + | 0.377397i | ||||
\(953\) | − | 1258.67i | − | 1.32075i | −0.750936 | − | 0.660375i | \(-0.770397\pi\) | ||
0.750936 | − | 0.660375i | \(-0.229603\pi\) | |||||||
\(954\) | −137.620 | − | 238.365i | −0.144256 | − | 0.249859i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.62565 | − | 6.27980i | 0.00379252 | − | 0.00656883i | ||||
\(957\) | −918.954 | − | 1591.68i | −0.960245 | − | 1.66319i | ||||
\(958\) | −1079.09 | −1.12640 | ||||||||
\(959\) | 27.9054 | − | 271.245i | 0.0290984 | − | 0.282841i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5559 | − | 45.9962i | −0.0276336 | − | 0.0478628i | ||||
\(962\) | 115.678 | − | 200.360i | 0.120247 | − | 0.208275i | ||||
\(963\) | −395.401 | − | 228.285i | −0.410593 | − | 0.237056i | ||||
\(964\) | 167.383 | − | 96.6387i | 0.173634 | − | 0.100248i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 253.109 | − | 349.993i | 0.262018 | − | 0.362311i | ||||
\(967\) | − | 992.744i | − | 1.02662i | −0.858202 | − | 0.513311i | \(-0.828419\pi\) | ||
0.858202 | − | 0.513311i | \(-0.171581\pi\) | |||||||
\(968\) | 680.957 | − | 393.151i | 0.703468 | − | 0.406147i | ||||
\(969\) | −673.455 | − | 388.820i | −0.695000 | − | 0.401259i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −309.667 | + | 178.787i | −0.318916 | + | 0.184126i | −0.650909 | − | 0.759155i | \(-0.725612\pi\) |
0.331993 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −632.116 | + | 283.105i | −0.649657 | + | 0.290961i | ||||
\(974\) | −316.626 | −0.325078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.7958 | − | 16.0479i | −0.0284793 | − | 0.0164426i | ||||
\(977\) | 759.804 | + | 438.673i | 0.777691 | + | 0.449000i | 0.835611 | − | 0.549321i | \(-0.185114\pi\) |
−0.0579204 | + | 0.998321i | \(0.518447\pi\) | |||||||
\(978\) | −141.839 | − | 245.672i | −0.145029 | − | 0.251198i | ||||
\(979\) | 2221.43i | 2.26908i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −194.266 | −0.198029 | ||||||||
\(982\) | 1025.96 | − | 592.339i | 1.04477 | − | 0.603197i | ||||
\(983\) | −720.104 | + | 1247.26i | −0.732557 | + | 1.26883i | 0.223229 | + | 0.974766i | \(0.428340\pi\) |
−0.955787 | + | 0.294061i | \(0.904993\pi\) | |||||||
\(984\) | −77.2202 | + | 133.749i | −0.0784758 | + | 0.135924i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1370.47i | − | 1.38993i | ||||||
\(987\) | −139.072 | − | 310.520i | −0.140904 | − | 0.314610i | ||||
\(988\) | − | 172.177i | − | 0.174268i | ||||||
\(989\) | 811.276 | + | 1405.17i | 0.820299 | + | 1.42080i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −577.181 | + | 999.706i | −0.582423 | + | 1.00879i | 0.412769 | + | 0.910836i | \(0.364562\pi\) |
−0.995191 | + | 0.0979496i | \(0.968772\pi\) | |||||||
\(992\) | 85.2239 | + | 147.612i | 0.0859111 | + | 0.148802i | ||||
\(993\) | −723.791 | −0.728893 | ||||||||
\(994\) | −864.130 | − | 624.925i | −0.869346 | − | 0.628697i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.723095 | + | 1.25244i | 0.000725999 | + | 0.00125747i | ||||
\(997\) | −812.451 | + | 1407.21i | −0.814896 | + | 1.41144i | 0.0945072 | + | 0.995524i | \(0.469872\pi\) |
−0.909403 | + | 0.415916i | \(0.863461\pi\) | |||||||
\(998\) | −213.898 | − | 123.494i | −0.214326 | − | 0.123741i | ||||
\(999\) | −210.462 | + | 121.510i | −0.210672 | + | 0.121632i |
(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 | 1050.3.q.e.199.1 | 32 | ||
5.2 | odd | 4 | 1050.3.p.i.451.4 | 16 | |||
5.3 | odd | 4 | 210.3.o.b.31.7 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1050.3.q.e.199.10 | 32 | ||
7.5 | odd | 6 | inner | 1050.3.q.e.649.10 | 32 | ||
15.8 | even | 4 | 630.3.v.c.451.1 | 16 | |||
35.3 | even | 12 | 1470.3.f.d.391.2 | 16 | |||
35.12 | even | 12 | 1050.3.p.i.901.4 | 16 | |||
35.18 | odd | 12 | 1470.3.f.d.391.8 | 16 | |||
35.19 | odd | 6 | inner | 1050.3.q.e.649.1 | 32 | ||
35.33 | even | 12 | 210.3.o.b.61.7 | yes | 16 | ||
105.68 | odd | 12 | 630.3.v.c.271.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.7 | ✓ | 16 | 5.3 | odd | 4 | ||
210.3.o.b.61.7 | yes | 16 | 35.33 | even | 12 | ||
630.3.v.c.271.1 | 16 | 105.68 | odd | 12 | |||
630.3.v.c.451.1 | 16 | 15.8 | even | 4 | |||
1050.3.p.i.451.4 | 16 | 5.2 | odd | 4 | |||
1050.3.p.i.901.4 | 16 | 35.12 | even | 12 | |||
1050.3.q.e.199.1 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.q.e.199.10 | 32 | 5.4 | even | 2 | inner | ||
1050.3.q.e.649.1 | 32 | 35.19 | odd | 6 | inner | ||
1050.3.q.e.649.10 | 32 | 7.5 | odd | 6 | inner | ||
1470.3.f.d.391.2 | 16 | 35.3 | even | 12 | |||
1470.3.f.d.391.8 | 16 | 35.18 | odd | 12 |