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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 649.6 | ||
Character | \(\chi\) | \(=\) | 1050.649 |
Dual form | 1050.3.q.d.199.6 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(7\) | 6.34914 | − | 2.94762i | 0.907020 | − | 0.421088i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.87118 | − | 15.3653i | −0.806471 | − | 1.39685i | −0.915293 | − | 0.402788i | \(-0.868041\pi\) |
0.108822 | − | 0.994061i | \(-0.465292\pi\) | |||||||
\(12\) | 1.73205 | − | 3.00000i | 0.144338 | − | 0.250000i | ||||
\(13\) | −8.10715 | −0.623627 | −0.311813 | − | 0.950143i | \(-0.600936\pi\) | ||||
−0.311813 | + | 0.950143i | \(0.600936\pi\) | |||||||
\(14\) | −9.86035 | − | 0.879440i | −0.704311 | − | 0.0628172i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.93681 | + | 6.81875i | 0.231577 | + | 0.401103i | 0.958272 | − | 0.285857i | \(-0.0922781\pi\) |
−0.726695 | + | 0.686960i | \(0.758945\pi\) | |||||||
\(18\) | 3.67423 | − | 2.12132i | 0.204124 | − | 0.117851i | ||||
\(19\) | −17.5951 | − | 10.1585i | −0.926059 | − | 0.534660i | −0.0404958 | − | 0.999180i | \(-0.512894\pi\) |
−0.885563 | + | 0.464519i | \(0.846227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.91994 | − | 6.97100i | −0.472378 | − | 0.331952i | ||||
\(22\) | 25.0915i | 1.14052i | ||||||||
\(23\) | 28.2223 | + | 16.2941i | 1.22706 | + | 0.708441i | 0.966413 | − | 0.256995i | \(-0.0827323\pi\) |
0.260642 | + | 0.965435i | \(0.416066\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.92919 | + | 5.73262i | 0.381892 | + | 0.220485i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 11.4546 | + | 8.04941i | 0.409091 | + | 0.287479i | ||||
\(29\) | 25.0915 | 0.865224 | 0.432612 | − | 0.901580i | \(-0.357592\pi\) | ||||
0.432612 | + | 0.901580i | \(0.357592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.0686 | + | 26.5977i | −1.48608 | + | 0.857991i | −0.999874 | − | 0.0158519i | \(-0.994954\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −15.3653 | + | 26.6135i | −0.465616 | + | 0.806471i | ||||
\(34\) | − | 11.1350i | − | 0.327499i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −37.7270 | − | 21.7817i | −1.01965 | − | 0.588695i | −0.105647 | − | 0.994404i | \(-0.533691\pi\) |
−0.914002 | + | 0.405709i | \(0.867025\pi\) | |||||||
\(38\) | 14.3664 | + | 24.8833i | 0.378062 | + | 0.654822i | ||||
\(39\) | 7.02100 | + | 12.1607i | 0.180026 | + | 0.311813i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 70.3424i | − | 1.71567i | −0.513927 | − | 0.857834i | \(-0.671810\pi\) | ||
0.513927 | − | 0.857834i | \(-0.328190\pi\) | |||||||
\(42\) | 7.22016 | + | 15.5521i | 0.171908 | + | 0.370289i | ||||
\(43\) | − | 2.43179i | − | 0.0565533i | −0.999600 | − | 0.0282767i | \(-0.990998\pi\) | ||
0.999600 | − | 0.0282767i | \(-0.00900194\pi\) | |||||||
\(44\) | 17.7424 | − | 30.7307i | 0.403236 | − | 0.698424i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.0434 | − | 39.9123i | −0.500943 | − | 0.867659i | ||||
\(47\) | −7.69399 | + | 13.3264i | −0.163702 | + | 0.283540i | −0.936194 | − | 0.351485i | \(-0.885677\pi\) |
0.772492 | + | 0.635025i | \(0.219010\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 31.6231 | − | 37.4297i | 0.645370 | − | 0.763870i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.81875 | − | 11.8104i | 0.133701 | − | 0.231577i | ||||
\(52\) | −8.10715 | − | 14.0420i | −0.155907 | − | 0.270038i | ||||
\(53\) | 44.0765 | − | 25.4476i | 0.831632 | − | 0.480143i | −0.0227791 | − | 0.999741i | \(-0.507251\pi\) |
0.854411 | + | 0.519598i | \(0.173918\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.33712 | − | 17.9581i | −0.148877 | − | 0.320680i | ||||
\(57\) | 35.1902i | 0.617372i | ||||||||
\(58\) | −30.7307 | − | 17.7424i | −0.529839 | − | 0.305903i | ||||
\(59\) | −22.9688 | + | 13.2610i | −0.389302 | + | 0.224763i | −0.681858 | − | 0.731485i | \(-0.738828\pi\) |
0.292556 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.7553 | − | 16.6019i | −0.471399 | − | 0.272162i | 0.245426 | − | 0.969415i | \(-0.421072\pi\) |
−0.716825 | + | 0.697253i | \(0.754405\pi\) | |||||||
\(62\) | 75.2297 | 1.21338 | ||||||||
\(63\) | −1.86557 | + | 20.9170i | −0.0296123 | + | 0.332015i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 37.6372 | − | 21.7299i | 0.570261 | − | 0.329240i | ||||
\(67\) | −86.4589 | + | 49.9171i | −1.29043 | + | 0.745031i | −0.978731 | − | 0.205149i | \(-0.934232\pi\) |
−0.311701 | + | 0.950180i | \(0.600899\pi\) | |||||||
\(68\) | −7.87362 | + | 13.6375i | −0.115789 | + | 0.200552i | ||||
\(69\) | − | 56.4445i | − | 0.818037i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −97.0831 | −1.36737 | −0.683684 | − | 0.729778i | \(-0.739623\pi\) | ||||
−0.683684 | + | 0.729778i | \(0.739623\pi\) | |||||||
\(72\) | 7.34847 | + | 4.24264i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 27.0175 | + | 46.7957i | 0.370103 | + | 0.641037i | 0.989581 | − | 0.143977i | \(-0.0459890\pi\) |
−0.619478 | + | 0.785014i | \(0.712656\pi\) | |||||||
\(74\) | 30.8040 | + | 53.3541i | 0.416270 | + | 0.721001i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 40.6342i | − | 0.534660i | ||||||
\(77\) | −101.615 | − | 71.4078i | −1.31968 | − | 0.927374i | ||||
\(78\) | − | 19.8584i | − | 0.254595i | ||||||
\(79\) | −37.3591 | + | 64.7079i | −0.472900 | + | 0.819087i | −0.999519 | − | 0.0310142i | \(-0.990126\pi\) |
0.526619 | + | 0.850102i | \(0.323460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −49.7396 | + | 86.1515i | −0.606580 | + | 1.05063i | ||||
\(83\) | −85.2206 | −1.02675 | −0.513377 | − | 0.858163i | \(-0.671606\pi\) | ||||
−0.513377 | + | 0.858163i | \(0.671606\pi\) | |||||||
\(84\) | 2.15418 | − | 24.1528i | 0.0256450 | − | 0.287534i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.71954 | + | 2.97833i | −0.0199946 | + | 0.0346317i | ||||
\(87\) | −21.7299 | − | 37.6372i | −0.249769 | − | 0.432612i | ||||
\(88\) | −43.4597 | + | 25.0915i | −0.493861 | + | 0.285131i | ||||
\(89\) | 115.343 | + | 66.5932i | 1.29599 | + | 0.748238i | 0.979708 | − | 0.200428i | \(-0.0642332\pi\) |
0.316279 | + | 0.948666i | \(0.397567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −51.4734 | + | 23.8968i | −0.565642 | + | 0.262602i | ||||
\(92\) | 65.1765i | 0.708441i | ||||||||
\(93\) | 79.7931 | + | 46.0686i | 0.857991 | + | 0.495361i | ||||
\(94\) | 18.8464 | − | 10.8809i | 0.200493 | − | 0.115755i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | − | 4.89898i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 49.9973 | 0.515436 | 0.257718 | − | 0.966220i | \(-0.417029\pi\) | ||||
0.257718 | + | 0.966220i | \(0.417029\pi\) | |||||||
\(98\) | −65.1970 | + | 23.4809i | −0.665276 | + | 0.239601i | ||||
\(99\) | 53.2271 | 0.537647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −142.296 | + | 82.1544i | −1.40887 | + | 0.813410i | −0.995279 | − | 0.0970542i | \(-0.969058\pi\) |
−0.413588 | + | 0.910464i | \(0.635725\pi\) | |||||||
\(102\) | −16.7025 | + | 9.64318i | −0.163750 | + | 0.0945409i | ||||
\(103\) | 48.7198 | − | 84.3852i | 0.473008 | − | 0.819274i | −0.526515 | − | 0.850166i | \(-0.676502\pi\) |
0.999523 | + | 0.0308923i | \(0.00983487\pi\) | |||||||
\(104\) | 22.9305i | 0.220485i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −71.9766 | −0.679025 | ||||||||
\(107\) | 84.4097 | + | 48.7339i | 0.788875 | + | 0.455457i | 0.839567 | − | 0.543257i | \(-0.182809\pi\) |
−0.0506910 | + | 0.998714i | \(0.516142\pi\) | |||||||
\(108\) | 5.19615 | + | 9.00000i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −32.1284 | − | 55.6480i | −0.294756 | − | 0.510532i | 0.680172 | − | 0.733052i | \(-0.261905\pi\) |
−0.974928 | + | 0.222520i | \(0.928572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 75.4540i | 0.679766i | ||||||||
\(112\) | −2.48743 | + | 27.8893i | −0.0222092 | + | 0.249012i | ||||
\(113\) | 43.4647i | 0.384643i | 0.981332 | + | 0.192321i | \(0.0616016\pi\) | ||||
−0.981332 | + | 0.192321i | \(0.938398\pi\) | |||||||
\(114\) | 24.8833 | − | 43.0991i | 0.218274 | − | 0.378062i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 25.0915 | + | 43.4597i | 0.216306 | + | 0.374653i | ||||
\(117\) | 12.1607 | − | 21.0630i | 0.103938 | − | 0.180026i | ||||
\(118\) | 37.5079 | 0.317864 | ||||||||
\(119\) | 45.0944 | + | 31.6890i | 0.378945 | + | 0.266294i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −96.8957 | + | 167.828i | −0.800791 | + | 1.38701i | ||||
\(122\) | 23.4786 | + | 40.6662i | 0.192448 | + | 0.333329i | ||||
\(123\) | −105.514 | + | 60.9183i | −0.857834 | + | 0.495271i | ||||
\(124\) | −92.1372 | − | 53.1954i | −0.743042 | − | 0.428995i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 17.0754 | − | 24.2988i | 0.135519 | − | 0.192848i | ||||
\(127\) | 186.018i | 1.46471i | 0.680924 | + | 0.732354i | \(0.261578\pi\) | ||||
−0.680924 | + | 0.732354i | \(0.738422\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −3.64769 | + | 2.10599i | −0.0282767 | + | 0.0163255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −78.0331 | − | 45.0524i | −0.595672 | − | 0.343912i | 0.171665 | − | 0.985155i | \(-0.445085\pi\) |
−0.767337 | + | 0.641244i | \(0.778419\pi\) | |||||||
\(132\) | −61.4613 | −0.465616 | ||||||||
\(133\) | −141.657 | − | 12.6343i | −1.06509 | − | 0.0949951i | ||||
\(134\) | 141.187 | 1.05363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.2864 | − | 11.1350i | 0.141811 | − | 0.0818749i | ||||
\(137\) | 9.38380 | − | 5.41774i | 0.0684949 | − | 0.0395456i | −0.465361 | − | 0.885121i | \(-0.654076\pi\) |
0.533856 | + | 0.845575i | \(0.320742\pi\) | |||||||
\(138\) | −39.9123 | + | 69.1302i | −0.289220 | + | 0.500943i | ||||
\(139\) | 222.126i | 1.59803i | 0.601314 | + | 0.799013i | \(0.294644\pi\) | ||||
−0.601314 | + | 0.799013i | \(0.705356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.6528 | 0.189027 | ||||||||
\(142\) | 118.902 | + | 68.6481i | 0.837338 | + | 0.483438i | ||||
\(143\) | 71.9200 | + | 124.569i | 0.502937 | + | 0.871112i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 76.4171i | − | 0.523405i | ||||||
\(147\) | −83.5309 | − | 15.0196i | −0.568237 | − | 0.102174i | ||||
\(148\) | − | 87.1268i | − | 0.588695i | ||||||
\(149\) | −4.33681 | + | 7.51157i | −0.0291061 | + | 0.0504132i | −0.880212 | − | 0.474582i | \(-0.842599\pi\) |
0.851105 | + | 0.524995i | \(0.175933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −106.283 | − | 184.088i | −0.703861 | − | 1.21912i | −0.967101 | − | 0.254392i | \(-0.918125\pi\) |
0.263240 | − | 0.964730i | \(-0.415209\pi\) | |||||||
\(152\) | −28.7327 | + | 49.7665i | −0.189031 | + | 0.327411i | ||||
\(153\) | −23.6209 | −0.154385 | ||||||||
\(154\) | 73.9601 | + | 159.309i | 0.480260 | + | 1.03448i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.0420 | + | 24.3214i | −0.0900128 | + | 0.155907i | ||||
\(157\) | −65.7193 | − | 113.829i | −0.418594 | − | 0.725027i | 0.577204 | − | 0.816600i | \(-0.304144\pi\) |
−0.995798 | + | 0.0915732i | \(0.970810\pi\) | |||||||
\(158\) | 91.5108 | − | 52.8338i | 0.579182 | − | 0.334391i | ||||
\(159\) | −76.3427 | − | 44.0765i | −0.480143 | − | 0.277211i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 227.216 | + | 20.2653i | 1.41128 | + | 0.125871i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | 38.8465 | + | 22.4281i | 0.238322 | + | 0.137595i | 0.614405 | − | 0.788990i | \(-0.289396\pi\) |
−0.376083 | + | 0.926586i | \(0.622729\pi\) | |||||||
\(164\) | 121.837 | − | 70.3424i | 0.742906 | − | 0.428917i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 104.374 | + | 60.2601i | 0.628756 | + | 0.363013i | ||||
\(167\) | −139.845 | −0.837398 | −0.418699 | − | 0.908125i | \(-0.637514\pi\) | ||||
−0.418699 | + | 0.908125i | \(0.637514\pi\) | |||||||
\(168\) | −19.7170 | + | 28.0578i | −0.117363 | + | 0.167011i | ||||
\(169\) | −103.274 | −0.611090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 52.7853 | − | 30.4756i | 0.308686 | − | 0.178220i | ||||
\(172\) | 4.21199 | − | 2.43179i | 0.0244883 | − | 0.0141383i | ||||
\(173\) | −72.4165 | + | 125.429i | −0.418593 | + | 0.725024i | −0.995798 | − | 0.0915753i | \(-0.970810\pi\) |
0.577206 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(174\) | 61.4613i | 0.353226i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 70.9695 | 0.403236 | ||||||||
\(177\) | 39.7831 | + | 22.9688i | 0.224763 | + | 0.129767i | ||||
\(178\) | −94.1770 | − | 163.119i | −0.529084 | − | 0.916401i | ||||
\(179\) | −16.2046 | − | 28.0672i | −0.0905284 | − | 0.156800i | 0.817205 | − | 0.576347i | \(-0.195522\pi\) |
−0.907734 | + | 0.419547i | \(0.862189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 119.139i | 0.658227i | 0.944290 | + | 0.329113i | \(0.106750\pi\) | ||||
−0.944290 | + | 0.329113i | \(0.893250\pi\) | |||||||
\(182\) | 79.9393 | + | 7.12975i | 0.439227 | + | 0.0391745i | ||||
\(183\) | 57.5107i | 0.314266i | ||||||||
\(184\) | 46.0868 | − | 79.8246i | 0.250472 | − | 0.433830i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −65.1508 | − | 112.845i | −0.350273 | − | 0.606691i | ||||
\(187\) | 69.8483 | − | 120.981i | 0.373520 | − | 0.646956i | ||||
\(188\) | −30.7760 | −0.163702 | ||||||||
\(189\) | 32.9911 | − | 15.3163i | 0.174556 | − | 0.0810384i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 122.229 | − | 211.706i | 0.639940 | − | 1.10841i | −0.345505 | − | 0.938417i | \(-0.612292\pi\) |
0.985445 | − | 0.169992i | \(-0.0543743\pi\) | |||||||
\(192\) | 6.92820 | + | 12.0000i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −221.323 | + | 127.781i | −1.14675 | + | 0.662077i | −0.948093 | − | 0.317992i | \(-0.896991\pi\) |
−0.198657 | + | 0.980069i | \(0.563658\pi\) | |||||||
\(194\) | −61.2339 | − | 35.3534i | −0.315639 | − | 0.182234i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 96.4532 | + | 17.3432i | 0.492108 | + | 0.0884856i | ||||
\(197\) | − | 351.495i | − | 1.78424i | −0.451802 | − | 0.892118i | \(-0.649218\pi\) | ||
0.451802 | − | 0.892118i | \(-0.350782\pi\) | |||||||
\(198\) | −65.1896 | − | 37.6372i | −0.329240 | − | 0.190087i | ||||
\(199\) | −266.168 | + | 153.672i | −1.33753 | + | 0.772222i | −0.986440 | − | 0.164121i | \(-0.947521\pi\) |
−0.351087 | + | 0.936343i | \(0.614188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 149.751 | + | 86.4589i | 0.745031 | + | 0.430144i | ||||
\(202\) | 232.368 | 1.15034 | ||||||||
\(203\) | 159.309 | − | 73.9601i | 0.784775 | − | 0.364335i | ||||
\(204\) | 27.2750 | 0.133701 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −119.339 | + | 68.9002i | −0.579314 | + | 0.334467i | ||||
\(207\) | −84.6668 | + | 48.8824i | −0.409018 | + | 0.236147i | ||||
\(208\) | 16.2143 | − | 28.0840i | 0.0779533 | − | 0.135019i | ||||
\(209\) | 360.473i | 1.72475i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −335.164 | −1.58845 | −0.794227 | − | 0.607621i | \(-0.792124\pi\) | ||||
−0.794227 | + | 0.607621i | \(0.792124\pi\) | |||||||
\(212\) | 88.1530 | + | 50.8952i | 0.415816 | + | 0.240071i | ||||
\(213\) | 84.0765 | + | 145.625i | 0.394725 | + | 0.683684i | ||||
\(214\) | −68.9202 | − | 119.373i | −0.322057 | − | 0.557819i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −214.096 | + | 304.665i | −0.986617 | + | 1.40399i | ||||
\(218\) | 90.8728i | 0.416847i | ||||||||
\(219\) | 46.7957 | − | 81.0526i | 0.213679 | − | 0.370103i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.9163 | − | 55.2806i | −0.144418 | − | 0.250139i | ||||
\(222\) | 53.3541 | − | 92.4119i | 0.240334 | − | 0.416270i | ||||
\(223\) | 50.9497 | 0.228474 | 0.114237 | − | 0.993454i | \(-0.463558\pi\) | ||||
0.114237 | + | 0.993454i | \(0.463558\pi\) | |||||||
\(224\) | 22.7672 | − | 32.3984i | 0.101639 | − | 0.144636i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.7342 | − | 53.2331i | 0.135992 | − | 0.235545i | ||||
\(227\) | −66.2128 | − | 114.684i | −0.291686 | − | 0.505215i | 0.682522 | − | 0.730865i | \(-0.260883\pi\) |
−0.974209 | + | 0.225649i | \(0.927550\pi\) | |||||||
\(228\) | −60.9513 | + | 35.1902i | −0.267330 | + | 0.154343i | ||||
\(229\) | −159.636 | − | 92.1659i | −0.697101 | − | 0.402471i | 0.109166 | − | 0.994024i | \(-0.465182\pi\) |
−0.806267 | + | 0.591552i | \(0.798515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1101 | + | 214.264i | −0.0827278 | + | 0.927551i | ||||
\(232\) | − | 70.9695i | − | 0.305903i | ||||||
\(233\) | 121.821 | + | 70.3332i | 0.522836 | + | 0.301859i | 0.738094 | − | 0.674698i | \(-0.235726\pi\) |
−0.215258 | + | 0.976557i | \(0.569059\pi\) | |||||||
\(234\) | −29.7876 | + | 17.1979i | −0.127297 | + | 0.0734951i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −45.9376 | − | 26.5221i | −0.194651 | − | 0.112382i | ||||
\(237\) | 129.416 | 0.546058 | ||||||||
\(238\) | −32.8217 | − | 70.6975i | −0.137906 | − | 0.297048i | ||||
\(239\) | 247.975 | 1.03755 | 0.518777 | − | 0.854910i | \(-0.326388\pi\) | ||||
0.518777 | + | 0.854910i | \(0.326388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −189.530 | + | 109.425i | −0.786431 | + | 0.454046i | −0.838705 | − | 0.544587i | \(-0.816687\pi\) |
0.0522735 | + | 0.998633i | \(0.483353\pi\) | |||||||
\(242\) | 237.345 | − | 137.031i | 0.980765 | − | 0.566245i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | − | 66.4076i | − | 0.272162i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 172.303 | 0.700419 | ||||||||
\(247\) | 142.646 | + | 82.3568i | 0.577515 | + | 0.333428i | ||||
\(248\) | 75.2297 | + | 130.302i | 0.303345 | + | 0.525410i | ||||
\(249\) | 73.8032 | + | 127.831i | 0.296399 | + | 0.513377i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 37.7083i | 0.150232i | 0.997175 | + | 0.0751161i | \(0.0239327\pi\) | ||||
−0.997175 | + | 0.0751161i | \(0.976067\pi\) | |||||||
\(252\) | −38.0948 | + | 17.6857i | −0.151170 | + | 0.0701814i | ||||
\(253\) | − | 578.193i | − | 2.28535i | ||||||
\(254\) | 131.534 | − | 227.824i | 0.517852 | − | 0.896946i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 9.53153 | − | 16.5091i | 0.0370877 | − | 0.0642377i | −0.846886 | − | 0.531775i | \(-0.821525\pi\) |
0.883973 | + | 0.467537i | \(0.154859\pi\) | |||||||
\(258\) | 5.95665 | 0.0230878 | ||||||||
\(259\) | −303.738 | − | 27.0903i | −1.17273 | − | 0.104596i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −37.6372 | + | 65.1896i | −0.144204 | + | 0.249769i | ||||
\(262\) | 63.7137 | + | 110.355i | 0.243182 | + | 0.421204i | ||||
\(263\) | −207.590 | + | 119.852i | −0.789316 | + | 0.455712i | −0.839722 | − | 0.543017i | \(-0.817282\pi\) |
0.0504060 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(264\) | 75.2745 | + | 43.4597i | 0.285131 | + | 0.164620i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 164.560 | + | 115.641i | 0.618647 | + | 0.434739i | ||||
\(267\) | − | 230.686i | − | 0.863991i | ||||||
\(268\) | −172.918 | − | 99.8341i | −0.645216 | − | 0.372515i | ||||
\(269\) | −230.871 | + | 133.293i | −0.858256 | + | 0.495514i | −0.863428 | − | 0.504472i | \(-0.831687\pi\) |
0.00517171 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 316.324 | + | 182.630i | 1.16725 | + | 0.673911i | 0.953030 | − | 0.302875i | \(-0.0979464\pi\) |
0.214218 | + | 0.976786i | \(0.431280\pi\) | |||||||
\(272\) | −31.4945 | −0.115789 | ||||||||
\(273\) | 80.4224 | + | 56.5149i | 0.294588 | + | 0.207014i | ||||
\(274\) | −15.3237 | −0.0559259 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 97.7648 | − | 56.4445i | 0.354220 | − | 0.204509i | ||||
\(277\) | 368.004 | − | 212.467i | 1.32853 | − | 0.767030i | 0.343461 | − | 0.939167i | \(-0.388401\pi\) |
0.985073 | + | 0.172137i | \(0.0550673\pi\) | |||||||
\(278\) | 157.066 | − | 272.047i | 0.564987 | − | 0.978587i | ||||
\(279\) | − | 159.586i | − | 0.571994i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 144.818 | 0.515368 | 0.257684 | − | 0.966229i | \(-0.417041\pi\) | ||||
0.257684 | + | 0.966229i | \(0.417041\pi\) | |||||||
\(282\) | −32.6428 | − | 18.8464i | −0.115755 | − | 0.0668310i | ||||
\(283\) | −162.433 | − | 281.343i | −0.573969 | − | 0.994143i | −0.996153 | − | 0.0876331i | \(-0.972070\pi\) |
0.422184 | − | 0.906510i | \(-0.361264\pi\) | |||||||
\(284\) | −97.0831 | − | 168.153i | −0.341842 | − | 0.592088i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 203.420i | − | 0.711260i | ||||||
\(287\) | −207.342 | − | 446.614i | −0.722447 | − | 1.55614i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 113.503 | − | 196.593i | 0.392744 | − | 0.680253i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.2989 | − | 74.9959i | −0.148793 | − | 0.257718i | ||||
\(292\) | −54.0350 | + | 93.5914i | −0.185052 | + | 0.320519i | ||||
\(293\) | −171.836 | −0.586470 | −0.293235 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293235 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(294\) | 91.6835 | + | 77.4605i | 0.311849 | + | 0.263471i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −61.6080 | + | 106.708i | −0.208135 | + | 0.360500i | ||||
\(297\) | −46.0960 | − | 79.8406i | −0.155205 | − | 0.268824i | ||||
\(298\) | 10.6230 | − | 6.13317i | 0.0356475 | − | 0.0205811i | ||||
\(299\) | −228.802 | − | 132.099i | −0.765224 | − | 0.441802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.16799 | − | 15.4398i | −0.0238139 | − | 0.0512950i | ||||
\(302\) | 300.614i | 0.995410i | ||||||||
\(303\) | 246.463 | + | 142.296i | 0.813410 | + | 0.469622i | ||||
\(304\) | 70.3805 | − | 40.6342i | 0.231515 | − | 0.133665i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 28.9295 | + | 16.7025i | 0.0945409 | + | 0.0545832i | ||||
\(307\) | −114.101 | −0.371663 | −0.185832 | − | 0.982582i | \(-0.559498\pi\) | ||||
−0.185832 | + | 0.982582i | \(0.559498\pi\) | |||||||
\(308\) | 22.0665 | − | 247.411i | 0.0716444 | − | 0.803282i | ||||
\(309\) | −168.770 | −0.546182 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 134.405 | − | 77.5988i | 0.432171 | − | 0.249514i | −0.268100 | − | 0.963391i | \(-0.586396\pi\) |
0.700271 | + | 0.713877i | \(0.253063\pi\) | |||||||
\(312\) | 34.3957 | − | 19.8584i | 0.110243 | − | 0.0636486i | ||||
\(313\) | 212.548 | − | 368.143i | 0.679066 | − | 1.17618i | −0.296197 | − | 0.955127i | \(-0.595718\pi\) |
0.975263 | − | 0.221050i | \(-0.0709483\pi\) | |||||||
\(314\) | 185.882i | 0.591982i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −149.437 | −0.472900 | ||||||||
\(317\) | 12.4651 | + | 7.19672i | 0.0393220 | + | 0.0227026i | 0.519532 | − | 0.854451i | \(-0.326106\pi\) |
−0.480210 | + | 0.877153i | \(0.659440\pi\) | |||||||
\(318\) | 62.3336 | + | 107.965i | 0.196018 | + | 0.339512i | ||||
\(319\) | −222.591 | − | 385.539i | −0.697778 | − | 1.20859i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 168.819i | − | 0.525917i | ||||||
\(322\) | −263.952 | − | 185.486i | −0.819726 | − | 0.576043i | ||||
\(323\) | − | 159.969i | − | 0.495260i | ||||||
\(324\) | 9.00000 | − | 15.5885i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.7181 | − | 54.9373i | −0.0972947 | − | 0.168519i | ||||
\(327\) | −55.6480 | + | 96.3851i | −0.170177 | + | 0.294756i | ||||
\(328\) | −198.958 | −0.606580 | ||||||||
\(329\) | −9.56914 | + | 107.290i | −0.0290855 | + | 0.326109i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 42.5972 | − | 73.7805i | 0.128692 | − | 0.222902i | −0.794478 | − | 0.607293i | \(-0.792255\pi\) |
0.923170 | + | 0.384391i | \(0.125589\pi\) | |||||||
\(332\) | −85.2206 | − | 147.606i | −0.256689 | − | 0.444598i | ||||
\(333\) | 113.181 | − | 65.3451i | 0.339883 | − | 0.196232i | ||||
\(334\) | 171.275 | + | 98.8857i | 0.512800 | + | 0.296065i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 43.9881 | − | 20.4217i | 0.130917 | − | 0.0607788i | ||||
\(337\) | 122.057i | 0.362186i | 0.983466 | + | 0.181093i | \(0.0579635\pi\) | ||||
−0.983466 | + | 0.181093i | \(0.942036\pi\) | |||||||
\(338\) | 126.485 | + | 73.0259i | 0.374215 | + | 0.216053i | ||||
\(339\) | 65.1970 | − | 37.6415i | 0.192321 | − | 0.111037i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 817.366 | + | 471.906i | 2.39697 | + | 1.38389i | ||||
\(342\) | −86.1981 | −0.252041 | ||||||||
\(343\) | 90.4512 | − | 330.859i | 0.263706 | − | 0.964603i | ||||
\(344\) | −6.87815 | −0.0199946 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 177.383 | − | 102.412i | 0.512669 | − | 0.295990i | ||||
\(347\) | 213.607 | − | 123.326i | 0.615581 | − | 0.355406i | −0.159565 | − | 0.987187i | \(-0.551009\pi\) |
0.775147 | + | 0.631781i | \(0.217676\pi\) | |||||||
\(348\) | 43.4597 | − | 75.2745i | 0.124884 | − | 0.216306i | ||||
\(349\) | − | 265.448i | − | 0.760596i | −0.924864 | − | 0.380298i | \(-0.875821\pi\) | ||
0.924864 | − | 0.380298i | \(-0.124179\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −42.1260 | −0.120017 | ||||||||
\(352\) | −86.9195 | − | 50.1830i | −0.246930 | − | 0.142565i | ||||
\(353\) | 140.800 | + | 243.873i | 0.398867 | + | 0.690858i | 0.993586 | − | 0.113076i | \(-0.0360702\pi\) |
−0.594720 | + | 0.803933i | \(0.702737\pi\) | |||||||
\(354\) | −32.4828 | − | 56.2619i | −0.0917593 | − | 0.158932i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 266.373i | 0.748238i | ||||||||
\(357\) | 8.48060 | − | 95.0851i | 0.0237552 | − | 0.266345i | ||||
\(358\) | 45.8335i | 0.128026i | ||||||||
\(359\) | 3.21594 | − | 5.57016i | 0.00895804 | − | 0.0155158i | −0.861512 | − | 0.507738i | \(-0.830482\pi\) |
0.870470 | + | 0.492222i | \(0.163815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.8921 | + | 44.8463i | 0.0717231 | + | 0.124228i | ||||
\(362\) | 84.2440 | − | 145.915i | 0.232718 | − | 0.403080i | ||||
\(363\) | 335.657 | 0.924674 | ||||||||
\(364\) | −92.8638 | − | 65.2578i | −0.255120 | − | 0.179280i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 40.6662 | − | 70.4359i | 0.111110 | − | 0.192448i | ||||
\(367\) | −125.255 | − | 216.948i | −0.341295 | − | 0.591140i | 0.643379 | − | 0.765548i | \(-0.277532\pi\) |
−0.984673 | + | 0.174408i | \(0.944199\pi\) | |||||||
\(368\) | −112.889 | + | 65.1765i | −0.306764 | + | 0.177110i | ||||
\(369\) | 182.755 | + | 105.514i | 0.495271 | + | 0.285945i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 204.838 | − | 291.491i | 0.552124 | − | 0.785689i | ||||
\(372\) | 184.274i | 0.495361i | ||||||||
\(373\) | 366.119 | + | 211.379i | 0.981552 | + | 0.566700i | 0.902738 | − | 0.430190i | \(-0.141553\pi\) |
0.0788140 | + | 0.996889i | \(0.474887\pi\) | |||||||
\(374\) | −171.093 | + | 98.7804i | −0.457467 | + | 0.264119i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 37.6927 | + | 21.7619i | 0.100247 | + | 0.0578774i | ||||
\(377\) | −203.420 | −0.539577 | ||||||||
\(378\) | −51.2359 | − | 4.56971i | −0.135545 | − | 0.0120892i | ||||
\(379\) | 510.205 | 1.34619 | 0.673093 | − | 0.739558i | \(-0.264965\pi\) | ||||
0.673093 | + | 0.739558i | \(0.264965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 279.027 | − | 161.096i | 0.732354 | − | 0.422825i | ||||
\(382\) | −299.398 | + | 172.857i | −0.783764 | + | 0.452506i | ||||
\(383\) | 134.443 | − | 232.862i | 0.351026 | − | 0.607995i | −0.635404 | − | 0.772180i | \(-0.719166\pi\) |
0.986429 | + | 0.164185i | \(0.0524996\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 361.419 | 0.936318 | ||||||||
\(387\) | 6.31798 | + | 3.64769i | 0.0163255 | + | 0.00942555i | ||||
\(388\) | 49.9973 | + | 86.5978i | 0.128859 | + | 0.223190i | ||||
\(389\) | −83.8883 | − | 145.299i | −0.215651 | − | 0.373519i | 0.737823 | − | 0.674995i | \(-0.235854\pi\) |
−0.953474 | + | 0.301476i | \(0.902521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 256.588i | 0.656234i | ||||||||
\(392\) | −105.867 | − | 89.4437i | −0.270069 | − | 0.228173i | ||||
\(393\) | 156.066i | 0.397115i | ||||||||
\(394\) | −248.544 | + | 430.491i | −0.630823 | + | 1.09262i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 53.2271 | + | 92.1920i | 0.134412 | + | 0.232808i | ||||
\(397\) | 181.784 | − | 314.858i | 0.457893 | − | 0.793094i | −0.540956 | − | 0.841051i | \(-0.681938\pi\) |
0.998849 | + | 0.0479565i | \(0.0152709\pi\) | |||||||
\(398\) | 434.650 | 1.09209 | ||||||||
\(399\) | 103.727 | + | 223.428i | 0.259968 | + | 0.559969i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −139.416 | + | 241.475i | −0.347670 | + | 0.602182i | −0.985835 | − | 0.167717i | \(-0.946360\pi\) |
0.638165 | + | 0.769900i | \(0.279694\pi\) | |||||||
\(402\) | −122.271 | − | 211.780i | −0.304158 | − | 0.526816i | ||||
\(403\) | 373.485 | − | 215.632i | 0.926761 | − | 0.535066i | ||||
\(404\) | −284.591 | − | 164.309i | −0.704434 | − | 0.406705i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −247.411 | − | 22.0665i | −0.609387 | − | 0.0543509i | ||||
\(407\) | 772.918i | 1.89906i | ||||||||
\(408\) | −33.4049 | − | 19.2864i | −0.0818749 | − | 0.0472705i | ||||
\(409\) | −337.862 | + | 195.065i | −0.826068 | + | 0.476931i | −0.852505 | − | 0.522720i | \(-0.824917\pi\) |
0.0264364 | + | 0.999650i | \(0.491584\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2532 | − | 9.38380i | −0.0395456 | − | 0.0228316i | ||||
\(412\) | 194.879 | 0.473008 | ||||||||
\(413\) | −106.744 | + | 151.899i | −0.258459 | + | 0.367795i | ||||
\(414\) | 138.260 | 0.333962 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −39.7167 | + | 22.9305i | −0.0954729 | + | 0.0551213i | ||||
\(417\) | 333.188 | − | 192.366i | 0.799013 | − | 0.461310i | ||||
\(418\) | 254.893 | − | 441.488i | 0.609792 | − | 1.05619i | ||||
\(419\) | − | 576.896i | − | 1.37684i | −0.725313 | − | 0.688419i | \(-0.758305\pi\) | ||
0.725313 | − | 0.688419i | \(-0.241695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 649.851 | 1.54359 | 0.771795 | − | 0.635871i | \(-0.219359\pi\) | ||||
0.771795 | + | 0.635871i | \(0.219359\pi\) | |||||||
\(422\) | 410.490 | + | 236.997i | 0.972725 | + | 0.561603i | ||||
\(423\) | −23.0820 | − | 39.9792i | −0.0545673 | − | 0.0945134i | ||||
\(424\) | −71.9766 | − | 124.667i | −0.169756 | − | 0.294026i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 237.804i | − | 0.558226i | ||||||
\(427\) | −231.508 | − | 20.6481i | −0.542172 | − | 0.0483561i | ||||
\(428\) | 194.936i | 0.455457i | ||||||||
\(429\) | 124.569 | − | 215.760i | 0.290371 | − | 0.502937i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −346.089 | − | 599.444i | −0.802991 | − | 1.39082i | −0.917639 | − | 0.397415i | \(-0.869907\pi\) |
0.114648 | − | 0.993406i | \(-0.463426\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 116.563 | 0.269200 | 0.134600 | − | 0.990900i | \(-0.457025\pi\) | ||||
0.134600 | + | 0.990900i | \(0.457025\pi\) | |||||||
\(434\) | 477.644 | − | 221.748i | 1.10056 | − | 0.510941i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 64.2567 | − | 111.296i | 0.147378 | − | 0.255266i | ||||
\(437\) | −331.049 | − | 573.394i | −0.757550 | − | 1.31212i | ||||
\(438\) | −114.626 | + | 66.1791i | −0.261702 | + | 0.151094i | ||||
\(439\) | −152.664 | − | 88.1408i | −0.347755 | − | 0.200776i | 0.315941 | − | 0.948779i | \(-0.397680\pi\) |
−0.663696 | + | 0.748002i | \(0.731013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.8104 | + | 138.304i | 0.112949 | + | 0.313614i | ||||
\(442\) | 90.2729i | 0.204237i | ||||||||
\(443\) | −284.069 | − | 164.007i | −0.641239 | − | 0.370219i | 0.143853 | − | 0.989599i | \(-0.454051\pi\) |
−0.785092 | + | 0.619380i | \(0.787384\pi\) | |||||||
\(444\) | −130.690 | + | 75.4540i | −0.294347 | + | 0.169942i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −62.4003 | − | 36.0268i | −0.139911 | − | 0.0807777i | ||||
\(447\) | 15.0231 | 0.0336088 | ||||||||
\(448\) | −50.7931 | + | 23.5809i | −0.113377 | + | 0.0526360i | ||||
\(449\) | 808.713 | 1.80114 | 0.900571 | − | 0.434709i | \(-0.143149\pi\) | ||||
0.900571 | + | 0.434709i | \(0.143149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1080.83 | + | 624.020i | −2.39653 | + | 1.38364i | ||||
\(452\) | −75.2830 | + | 43.4647i | −0.166555 | + | 0.0961607i | ||||
\(453\) | −184.088 | + | 318.849i | −0.406374 | + | 0.703861i | ||||
\(454\) | 187.278i | 0.412507i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 99.5330 | 0.218274 | ||||||||
\(457\) | 291.757 | + | 168.446i | 0.638418 | + | 0.368591i | 0.784005 | − | 0.620755i | \(-0.213174\pi\) |
−0.145587 | + | 0.989345i | \(0.546507\pi\) | |||||||
\(458\) | 130.342 | + | 225.760i | 0.284590 | + | 0.492925i | ||||
\(459\) | 20.4563 | + | 35.4313i | 0.0445670 | + | 0.0771924i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 614.879i | − | 1.33379i | −0.745150 | − | 0.666897i | \(-0.767622\pi\) | ||
0.745150 | − | 0.666897i | \(-0.232378\pi\) | |||||||
\(462\) | 174.913 | − | 248.906i | 0.378599 | − | 0.538758i | ||||
\(463\) | − | 818.194i | − | 1.76716i | −0.468283 | − | 0.883578i | \(-0.655127\pi\) | ||
0.468283 | − | 0.883578i | \(-0.344873\pi\) | |||||||
\(464\) | −50.1830 | + | 86.9195i | −0.108153 | + | 0.187326i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −99.4662 | − | 172.281i | −0.213447 | − | 0.369701i | ||||
\(467\) | −265.894 | + | 460.542i | −0.569367 | + | 0.986172i | 0.427262 | + | 0.904128i | \(0.359478\pi\) |
−0.996629 | + | 0.0820440i | \(0.973855\pi\) | |||||||
\(468\) | 48.6429 | 0.103938 | ||||||||
\(469\) | −401.803 | + | 571.778i | −0.856723 | + | 1.21914i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −113.829 | + | 197.158i | −0.241676 | + | 0.418594i | ||||
\(472\) | 37.5079 | + | 64.9656i | 0.0794659 | + | 0.137639i | ||||
\(473\) | −37.3653 | + | 21.5729i | −0.0789964 | + | 0.0456086i | ||||
\(474\) | −158.501 | − | 91.5108i | −0.334391 | − | 0.193061i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.79255 | + | 109.795i | −0.0205726 | + | 0.230661i | ||||
\(477\) | 152.685i | 0.320095i | ||||||||
\(478\) | −303.706 | − | 175.345i | −0.635369 | − | 0.366830i | ||||
\(479\) | −552.718 | + | 319.112i | −1.15390 | + | 0.666204i | −0.949834 | − | 0.312753i | \(-0.898749\pi\) |
−0.204065 | + | 0.978957i | \(0.565415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 305.858 | + | 176.587i | 0.635880 | + | 0.367126i | ||||
\(482\) | 309.501 | 0.642118 | ||||||||
\(483\) | −166.377 | − | 358.374i | −0.344466 | − | 0.741976i | ||||
\(484\) | −387.583 | −0.800791 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | − | 11.0227i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 336.754 | − | 194.425i | 0.691486 | − | 0.399230i | −0.112683 | − | 0.993631i | \(-0.535944\pi\) |
0.804168 | + | 0.594402i | \(0.202611\pi\) | |||||||
\(488\) | −46.9573 | + | 81.3324i | −0.0962239 | + | 0.166665i | ||||
\(489\) | − | 77.6931i | − | 0.158882i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 695.908 | 1.41733 | 0.708664 | − | 0.705546i | \(-0.249298\pi\) | ||||
0.708664 | + | 0.705546i | \(0.249298\pi\) | |||||||
\(492\) | −211.027 | − | 121.837i | −0.428917 | − | 0.247635i | ||||
\(493\) | 98.7804 | + | 171.093i | 0.200366 | + | 0.347044i | ||||
\(494\) | −116.470 | − | 201.732i | −0.235769 | − | 0.408365i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 212.782i | − | 0.428995i | ||||||
\(497\) | −616.394 | + | 286.164i | −1.24023 | + | 0.575782i | ||||
\(498\) | − | 208.747i | − | 0.419171i | ||||||
\(499\) | −265.395 | + | 459.678i | −0.531854 | + | 0.921199i | 0.467454 | + | 0.884017i | \(0.345171\pi\) |
−0.999309 | + | 0.0371815i | \(0.988162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 121.110 | + | 209.768i | 0.241736 | + | 0.418699i | ||||
\(502\) | 26.6638 | − | 46.1830i | 0.0531151 | − | 0.0919980i | ||||
\(503\) | −694.388 | −1.38049 | −0.690247 | − | 0.723574i | \(-0.742498\pi\) | ||||
−0.690247 | + | 0.723574i | \(0.742498\pi\) | |||||||
\(504\) | 59.1621 | + | 5.27664i | 0.117385 | + | 0.0104695i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −408.844 | + | 708.139i | −0.807992 | + | 1.39948i | ||||
\(507\) | 89.4381 | + | 154.911i | 0.176406 | + | 0.305545i | ||||
\(508\) | −322.192 | + | 186.018i | −0.634237 | + | 0.366177i | ||||
\(509\) | 246.728 | + | 142.448i | 0.484730 | + | 0.279859i | 0.722386 | − | 0.691491i | \(-0.243046\pi\) |
−0.237656 | + | 0.971349i | \(0.576379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 309.474 | + | 217.475i | 0.605624 | + | 0.425588i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −91.4269 | − | 52.7853i | −0.178220 | − | 0.102895i | ||||
\(514\) | −23.3474 | + | 13.4796i | −0.0454229 | + | 0.0262250i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.29538 | − | 4.21199i | −0.0141383 | − | 0.00816277i | ||||
\(517\) | 273.019 | 0.528084 | ||||||||
\(518\) | 352.846 | + | 247.954i | 0.681170 | + | 0.478676i | ||||
\(519\) | 250.858 | 0.483349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 450.682 | − | 260.201i | 0.865033 | − | 0.499427i | −0.000661748 | − | 1.00000i | \(-0.500211\pi\) |
0.865694 | + | 0.500573i | \(0.166877\pi\) | |||||||
\(522\) | 92.1920 | − | 53.2271i | 0.176613 | − | 0.101968i | ||||
\(523\) | −85.7878 | + | 148.589i | −0.164030 | + | 0.284109i | −0.936310 | − | 0.351173i | \(-0.885783\pi\) |
0.772280 | + | 0.635282i | \(0.219116\pi\) | |||||||
\(524\) | − | 180.210i | − | 0.343912i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 338.993 | 0.644473 | ||||||||
\(527\) | −362.727 | − | 209.420i | −0.688286 | − | 0.397382i | ||||
\(528\) | −61.4613 | − | 106.454i | −0.116404 | − | 0.201618i | ||||
\(529\) | 266.498 | + | 461.587i | 0.503776 | + | 0.872566i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 79.5663i | − | 0.149842i | ||||||
\(532\) | −119.774 | − | 257.992i | −0.225139 | − | 0.484947i | ||||
\(533\) | 570.276i | 1.06994i | ||||||||
\(534\) | −163.119 | + | 282.531i | −0.305467 | + | 0.529084i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 141.187 | + | 244.543i | 0.263408 | + | 0.456236i | ||||
\(537\) | −28.0672 | + | 48.6137i | −0.0522666 | + | 0.0905284i | ||||
\(538\) | 377.011 | 0.700763 | ||||||||
\(539\) | −855.654 | − | 153.855i | −1.58748 | − | 0.285444i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 188.929 | − | 327.235i | 0.349222 | − | 0.604871i | −0.636889 | − | 0.770955i | \(-0.719779\pi\) |
0.986111 | + | 0.166085i | \(0.0531125\pi\) | |||||||
\(542\) | −258.278 | − | 447.350i | −0.476527 | − | 0.825369i | ||||
\(543\) | 178.709 | − | 103.177i | 0.329113 | − | 0.190014i | ||||
\(544\) | 38.5727 | + | 22.2700i | 0.0709057 | + | 0.0409374i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −58.5349 | − | 126.084i | −0.107207 | − | 0.230922i | ||||
\(547\) | 982.972i | 1.79702i | 0.438950 | + | 0.898511i | \(0.355350\pi\) | ||||
−0.438950 | + | 0.898511i | \(0.644650\pi\) | |||||||
\(548\) | 18.7676 | + | 10.8355i | 0.0342475 | + | 0.0197728i | ||||
\(549\) | 86.2660 | − | 49.8057i | 0.157133 | − | 0.0907208i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −441.488 | − | 254.893i | −0.801248 | − | 0.462601i | ||||
\(552\) | −159.649 | −0.289220 | ||||||||
\(553\) | −46.4642 | + | 520.960i | −0.0840220 | + | 0.942061i | ||||
\(554\) | −600.948 | −1.08474 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −384.733 | + | 222.126i | −0.691965 | + | 0.399506i | ||||
\(557\) | 312.143 | − | 180.216i | 0.560401 | − | 0.323548i | −0.192905 | − | 0.981217i | \(-0.561791\pi\) |
0.753306 | + | 0.657670i | \(0.228458\pi\) | |||||||
\(558\) | −112.845 | + | 195.452i | −0.202230 | + | 0.350273i | ||||
\(559\) | 19.7149i | 0.0352682i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −241.962 | −0.431304 | ||||||||
\(562\) | −177.366 | − | 102.402i | −0.315597 | − | 0.182210i | ||||
\(563\) | −337.825 | − | 585.130i | −0.600044 | − | 1.03931i | −0.992814 | − | 0.119670i | \(-0.961816\pi\) |
0.392770 | − | 0.919637i | \(-0.371517\pi\) | |||||||
\(564\) | 26.6528 | + | 46.1640i | 0.0472567 | + | 0.0818510i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 459.430i | 0.811715i | ||||||||
\(567\) | −51.5455 | − | 36.2224i | −0.0909092 | − | 0.0638842i | ||||
\(568\) | 274.593i | 0.483438i | ||||||||
\(569\) | 500.576 | − | 867.022i | 0.879746 | − | 1.52376i | 0.0281265 | − | 0.999604i | \(-0.491046\pi\) |
0.851620 | − | 0.524160i | \(-0.175621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −363.407 | − | 629.439i | −0.636439 | − | 1.10235i | −0.986208 | − | 0.165509i | \(-0.947073\pi\) |
0.349769 | − | 0.936836i | \(-0.386260\pi\) | |||||||
\(572\) | −143.840 | + | 249.138i | −0.251468 | + | 0.435556i | ||||
\(573\) | −423.412 | −0.738940 | ||||||||
\(574\) | −61.8619 | + | 693.601i | −0.107773 | + | 1.20836i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 33.5564 | + | 58.1213i | 0.0581566 | + | 0.100730i | 0.893638 | − | 0.448789i | \(-0.148144\pi\) |
−0.835481 | + | 0.549519i | \(0.814811\pi\) | |||||||
\(578\) | −278.025 | + | 160.518i | −0.481011 | + | 0.277712i | ||||
\(579\) | 383.342 | + | 221.323i | 0.662077 | + | 0.382250i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −541.078 | + | 251.198i | −0.931287 | + | 0.432354i | ||||
\(582\) | 122.468i | 0.210426i | ||||||||
\(583\) | −782.021 | − | 451.500i | −1.34137 | − | 0.774443i | ||||
\(584\) | 132.358 | − | 76.4171i | 0.226641 | − | 0.130851i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 210.455 | + | 121.506i | 0.359138 | + | 0.207349i | ||||
\(587\) | 964.783 | 1.64358 | 0.821791 | − | 0.569788i | \(-0.192975\pi\) | ||||
0.821791 | + | 0.569788i | \(0.192975\pi\) | |||||||
\(588\) | −57.5161 | − | 159.699i | −0.0978165 | − | 0.271598i | ||||
\(589\) | 1080.78 | 1.83493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −527.242 | + | 304.403i | −0.892118 | + | 0.515065i | ||||
\(592\) | 150.908 | − | 87.1268i | 0.254912 | − | 0.147174i | ||||
\(593\) | 0.846966 | − | 1.46699i | 0.00142827 | − | 0.00247384i | −0.865310 | − | 0.501236i | \(-0.832879\pi\) |
0.866739 | + | 0.498763i | \(0.166212\pi\) | |||||||
\(594\) | 130.379i | 0.219494i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.3472 | −0.0291061 | ||||||||
\(597\) | 461.016 | + | 266.168i | 0.772222 | + | 0.445842i | ||||
\(598\) | 186.816 | + | 323.575i | 0.312402 | + | 0.541095i | ||||
\(599\) | 46.3714 | + | 80.3177i | 0.0774147 | + | 0.134086i | 0.902134 | − | 0.431456i | \(-0.142000\pi\) |
−0.824719 | + | 0.565543i | \(0.808667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 393.426i | − | 0.654618i | −0.944917 | − | 0.327309i | \(-0.893858\pi\) | ||
0.944917 | − | 0.327309i | \(-0.106142\pi\) | |||||||
\(602\) | −2.13862 | + | 23.9783i | −0.00355252 | + | 0.0398311i | ||||
\(603\) | − | 299.502i | − | 0.496687i | ||||||
\(604\) | 212.566 | − | 368.175i | 0.351930 | − | 0.609561i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −201.236 | − | 348.552i | −0.332073 | − | 0.575168i | ||||
\(607\) | 148.539 | − | 257.278i | 0.244711 | − | 0.423851i | −0.717340 | − | 0.696724i | \(-0.754640\pi\) |
0.962050 | + | 0.272872i | \(0.0879737\pi\) | |||||||
\(608\) | −114.931 | −0.189031 | ||||||||
\(609\) | −248.906 | − | 174.913i | −0.408713 | − | 0.287213i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 62.3763 | − | 108.039i | 0.102089 | − | 0.176823i | ||||
\(612\) | −23.6209 | − | 40.9125i | −0.0385962 | − | 0.0668505i | ||||
\(613\) | −876.111 | + | 505.823i | −1.42922 | + | 0.825160i | −0.997059 | − | 0.0766368i | \(-0.975582\pi\) |
−0.432160 | + | 0.901797i | \(0.642248\pi\) | |||||||
\(614\) | 139.744 | + | 80.6813i | 0.227596 | + | 0.131403i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −201.972 | + | 287.412i | −0.327876 | + | 0.466578i | ||||
\(617\) | − | 467.794i | − | 0.758174i | −0.925361 | − | 0.379087i | \(-0.876238\pi\) | ||
0.925361 | − | 0.379087i | \(-0.123762\pi\) | |||||||
\(618\) | 206.701 | + | 119.339i | 0.334467 | + | 0.193105i | ||||
\(619\) | 919.996 | − | 531.160i | 1.48626 | − | 0.858094i | 0.486385 | − | 0.873745i | \(-0.338315\pi\) |
0.999878 | + | 0.0156508i | \(0.00498201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 146.647 | + | 84.6668i | 0.236147 | + | 0.136339i | ||||
\(622\) | −219.483 | −0.352866 | ||||||||
\(623\) | 928.619 | + | 82.8231i | 1.49056 | + | 0.132942i | ||||
\(624\) | −56.1680 | −0.0900128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −520.633 | + | 300.588i | −0.831682 | + | 0.480172i | ||||
\(627\) | 540.710 | − | 312.179i | 0.862376 | − | 0.497893i | ||||
\(628\) | 131.439 | − | 227.658i | 0.209297 | − | 0.362513i | ||||
\(629\) | − | 343.002i | − | 0.545313i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −970.749 | −1.53843 | −0.769215 | − | 0.638990i | \(-0.779352\pi\) | ||||
−0.769215 | + | 0.638990i | \(0.779352\pi\) | |||||||
\(632\) | 183.022 | + | 105.668i | 0.289591 | + | 0.167196i | ||||
\(633\) | 290.260 | + | 502.746i | 0.458547 | + | 0.794227i | ||||
\(634\) | −10.1777 | − | 17.6283i | −0.0160531 | − | 0.0278049i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 176.306i | − | 0.277211i | ||||||
\(637\) | −256.373 | + | 303.448i | −0.402470 | + | 0.476370i | ||||
\(638\) | 629.583i | 0.986807i | ||||||||
\(639\) | 145.625 | − | 252.229i | 0.227895 | − | 0.394725i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −523.506 | − | 906.739i | −0.816702 | − | 1.41457i | −0.908099 | − | 0.418755i | \(-0.862467\pi\) |
0.0913975 | − | 0.995814i | \(-0.470867\pi\) | |||||||
\(642\) | −119.373 | + | 206.761i | −0.185940 | + | 0.322057i | ||||
\(643\) | 704.161 | 1.09512 | 0.547559 | − | 0.836767i | \(-0.315557\pi\) | ||||
0.547559 | + | 0.836767i | \(0.315557\pi\) | |||||||
\(644\) | 192.115 | + | 413.815i | 0.298316 | + | 0.642570i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −113.115 | + | 195.921i | −0.175101 | + | 0.303284i | ||||
\(647\) | 188.237 | + | 326.037i | 0.290939 | + | 0.503921i | 0.974032 | − | 0.226411i | \(-0.0726991\pi\) |
−0.683093 | + | 0.730331i | \(0.739366\pi\) | |||||||
\(648\) | −22.0454 | + | 12.7279i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 407.521 | + | 235.282i | 0.627921 | + | 0.362530i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 642.410 | + | 57.2962i | 0.986805 | + | 0.0880127i | ||||
\(652\) | 89.7122i | 0.137595i | ||||||||
\(653\) | 23.5767 | + | 13.6120i | 0.0361052 | + | 0.0208454i | 0.517944 | − | 0.855415i | \(-0.326698\pi\) |
−0.481839 | + | 0.876260i | \(0.660031\pi\) | |||||||
\(654\) | 136.309 | − | 78.6981i | 0.208424 | − | 0.120334i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 243.673 | + | 140.685i | 0.371453 | + | 0.214459i | ||||
\(657\) | −162.105 | −0.246735 | ||||||||
\(658\) | 87.5852 | − | 124.636i | 0.133108 | − | 0.189417i | ||||
\(659\) | −501.943 | −0.761674 | −0.380837 | − | 0.924642i | \(-0.624364\pi\) | ||||
−0.380837 | + | 0.924642i | \(0.624364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −748.339 | + | 432.054i | −1.13213 | + | 0.653637i | −0.944470 | − | 0.328597i | \(-0.893424\pi\) |
−0.187662 | + | 0.982234i | \(0.560091\pi\) | |||||||
\(662\) | −104.341 | + | 60.2415i | −0.157615 | + | 0.0909992i | ||||
\(663\) | −55.2806 | + | 95.7489i | −0.0833796 | + | 0.144418i | ||||
\(664\) | 241.040i | 0.363013i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −184.824 | −0.277513 | ||||||||
\(667\) | 708.139 | + | 408.844i | 1.06168 | + | 0.612960i | ||||
\(668\) | −139.845 | − | 242.219i | −0.209350 | − | 0.362604i | ||||
\(669\) | −44.1237 | − | 76.4245i | −0.0659547 | − | 0.114237i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 589.114i | 0.877964i | ||||||||
\(672\) | −68.3145 | − | 6.09294i | −0.101659 | − | 0.00906688i | ||||
\(673\) | 726.018i | 1.07878i | 0.842057 | + | 0.539389i | \(0.181345\pi\) | ||||
−0.842057 | + | 0.539389i | \(0.818655\pi\) | |||||||
\(674\) | 86.3071 | − | 149.488i | 0.128052 | − | 0.221793i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −103.274 | − | 178.876i | −0.152772 | − | 0.264610i | ||||
\(677\) | −220.550 | + | 382.003i | −0.325775 | + | 0.564259i | −0.981669 | − | 0.190594i | \(-0.938959\pi\) |
0.655894 | + | 0.754853i | \(0.272292\pi\) | |||||||
\(678\) | −106.466 | −0.157030 | ||||||||
\(679\) | 317.440 | − | 147.373i | 0.467510 | − | 0.217044i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −114.684 | + | 198.638i | −0.168405 | + | 0.291686i | ||||
\(682\) | −667.376 | − | 1155.93i | −0.978557 | − | 1.69491i | ||||
\(683\) | −1030.09 | + | 594.725i | −1.50819 | + | 0.870754i | −0.508235 | + | 0.861218i | \(0.669702\pi\) |
−0.999955 | + | 0.00953518i | \(0.996965\pi\) | |||||||
\(684\) | 105.571 | + | 60.9513i | 0.154343 | + | 0.0891100i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −344.732 | + | 341.259i | −0.502525 | + | 0.497462i | ||||
\(687\) | 319.272i | 0.464734i | ||||||||
\(688\) | 8.42398 | + | 4.86359i | 0.0122442 | + | 0.00706917i | ||||
\(689\) | −357.335 | + | 206.307i | −0.518628 | + | 0.299430i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0369 | + | 21.3832i | 0.0535989 | + | 0.0309453i | 0.526560 | − | 0.850138i | \(-0.323482\pi\) |
−0.472961 | + | 0.881083i | \(0.656815\pi\) | |||||||
\(692\) | −289.666 | −0.418593 | ||||||||
\(693\) | 337.946 | − | 156.893i | 0.487657 | − | 0.226397i | ||||
\(694\) | −348.818 | −0.502620 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −106.454 | + | 61.4613i | −0.152951 | + | 0.0883065i | ||||
\(697\) | 479.648 | − | 276.925i | 0.688160 | − | 0.397309i | ||||
\(698\) | −187.700 | + | 325.106i | −0.268911 | + | 0.465768i | ||||
\(699\) | − | 243.642i | − | 0.348557i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 368.695 | 0.525956 | 0.262978 | − | 0.964802i | \(-0.415295\pi\) | ||||
0.262978 | + | 0.964802i | \(0.415295\pi\) | |||||||
\(702\) | 51.5936 | + | 29.7876i | 0.0734951 | + | 0.0424324i | ||||
\(703\) | 442.541 | + | 766.503i | 0.629503 | + | 1.09033i | ||||
\(704\) | 70.9695 | + | 122.923i | 0.100809 | + | 0.174606i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 398.243i | − | 0.564083i | ||||||
\(707\) | −661.295 | + | 941.043i | −0.935353 | + | 1.33104i | ||||
\(708\) | 91.8752i | 0.129767i | ||||||||
\(709\) | −93.3436 | + | 161.676i | −0.131655 | + | 0.228034i | −0.924315 | − | 0.381631i | \(-0.875363\pi\) |
0.792660 | + | 0.609665i | \(0.208696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −112.077 | − | 194.124i | −0.157633 | − | 0.273029i | ||||
\(712\) | 188.354 | − | 326.239i | 0.264542 | − | 0.458201i | ||||
\(713\) | −1733.55 | −2.43134 | ||||||||
\(714\) | −77.6219 | + | 110.458i | −0.108714 | + | 0.154704i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.4092 | − | 56.1343i | 0.0452642 | − | 0.0783999i | ||||
\(717\) | −214.753 | − | 371.963i | −0.299516 | − | 0.518777i | ||||
\(718\) | −7.87740 | + | 4.54802i | −0.0109713 | + | 0.00633429i | ||||
\(719\) | 447.220 | + | 258.203i | 0.622003 | + | 0.359113i | 0.777648 | − | 0.628700i | \(-0.216412\pi\) |
−0.155646 | + | 0.987813i | \(0.549746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.5936 | − | 679.381i | 0.0840411 | − | 0.942275i | ||||
\(722\) | − | 73.2338i | − | 0.101432i | ||||||
\(723\) | 328.275 | + | 189.530i | 0.454046 | + | 0.262144i | ||||
\(724\) | −206.355 | + | 119.139i | −0.285020 | + | 0.164557i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −411.094 | − | 237.345i | −0.566245 | − | 0.326922i | ||||
\(727\) | −986.117 | −1.35642 | −0.678210 | − | 0.734868i | \(-0.737244\pi\) | ||||
−0.678210 | + | 0.734868i | \(0.737244\pi\) | |||||||
\(728\) | 67.5902 | + | 145.589i | 0.0928437 | + | 0.199985i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5818 | − | 9.57351i | 0.0226837 | − | 0.0130965i | ||||
\(732\) | −99.6114 | + | 57.5107i | −0.136081 | + | 0.0785665i | ||||
\(733\) | −583.073 | + | 1009.91i | −0.795461 | + | 1.37778i | 0.127085 | + | 0.991892i | \(0.459438\pi\) |
−0.922546 | + | 0.385887i | \(0.873896\pi\) | |||||||
\(734\) | 354.275i | 0.482664i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 184.347 | 0.250472 | ||||||||
\(737\) | 1533.99 | + | 885.647i | 2.08139 | + | 1.20169i | ||||
\(738\) | −149.219 | − | 258.454i | −0.202193 | − | 0.350209i | ||||
\(739\) | −519.556 | − | 899.897i | −0.703053 | − | 1.21772i | −0.967390 | − | 0.253292i | \(-0.918487\pi\) |
0.264337 | − | 0.964430i | \(-0.414847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 285.292i | − | 0.385010i | ||||||
\(742\) | −456.989 | + | 212.159i | −0.615889 | + | 0.285929i | ||||
\(743\) | − | 320.811i | − | 0.431778i | −0.976418 | − | 0.215889i | \(-0.930735\pi\) | ||
0.976418 | − | 0.215889i | \(-0.0692650\pi\) | |||||||
\(744\) | 130.302 | − | 225.689i | 0.175137 | − | 0.303345i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −298.935 | − | 517.771i | −0.400717 | − | 0.694062i | ||||
\(747\) | 127.831 | − | 221.410i | 0.171126 | − | 0.296399i | ||||
\(748\) | 279.393 | 0.373520 | ||||||||
\(749\) | 679.578 | + | 60.6112i | 0.907313 | + | 0.0809228i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 560.762 | − | 971.268i | 0.746687 | − | 1.29330i | −0.202715 | − | 0.979238i | \(-0.564977\pi\) |
0.949402 | − | 0.314062i | \(-0.101690\pi\) | |||||||
\(752\) | −30.7760 | − | 53.3055i | −0.0409255 | − | 0.0708850i | ||||
\(753\) | 56.5624 | − | 32.6563i | 0.0751161 | − | 0.0433683i | ||||
\(754\) | 249.138 | + | 143.840i | 0.330422 | + | 0.190769i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 59.5196 | + | 41.8260i | 0.0787297 | + | 0.0553254i | ||||
\(757\) | 769.996i | 1.01717i | 0.861012 | + | 0.508584i | \(0.169831\pi\) | ||||
−0.861012 | + | 0.508584i | \(0.830169\pi\) | |||||||
\(758\) | −624.871 | − | 360.769i | −0.824367 | − | 0.475949i | ||||
\(759\) | −867.289 | + | 500.730i | −1.14267 | + | 0.659723i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −874.305 | − | 504.780i | −1.14889 | − | 0.663311i | −0.200273 | − | 0.979740i | \(-0.564183\pi\) |
−0.948616 | + | 0.316429i | \(0.897516\pi\) | |||||||
\(762\) | −455.649 | −0.597964 | ||||||||
\(763\) | −368.016 | − | 258.615i | −0.482328 | − | 0.338944i | ||||
\(764\) | 488.914 | 0.639940 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −329.317 | + | 190.131i | −0.429917 | + | 0.248213i | ||||
\(767\) | 186.211 | − | 107.509i | 0.242779 | − | 0.140169i | ||||
\(768\) | −13.8564 | + | 24.0000i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 817.903i | − | 1.06359i | −0.846872 | − | 0.531797i | \(-0.821517\pi\) | ||
0.846872 | − | 0.531797i | \(-0.178483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.0182 | −0.0428252 | ||||||||
\(772\) | −442.646 | − | 255.562i | −0.573375 | − | 0.331038i | ||||
\(773\) | −642.220 | − | 1112.36i | −0.830815 | − | 1.43901i | −0.897393 | − | 0.441233i | \(-0.854541\pi\) |
0.0665776 | − | 0.997781i | \(-0.478792\pi\) | |||||||
\(774\) | −5.15861 | − | 8.93498i | −0.00666487 | − | 0.0115439i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 141.414i | − | 0.182234i | ||||||
\(777\) | 222.410 | + | 479.068i | 0.286241 | + | 0.616561i | ||||
\(778\) | 237.272i | 0.304977i | ||||||||
\(779\) | −714.576 | + | 1237.68i | −0.917300 | + | 1.58881i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 861.242 | + | 1491.71i | 1.10274 | + | 1.91001i | ||||
\(782\) | 181.435 | − | 314.254i | 0.232014 | − | 0.401860i | ||||
\(783\) | 130.379 | 0.166512 | ||||||||
\(784\) | 66.4139 | + | 184.405i | 0.0847116 | + | 0.235210i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 110.355 | − | 191.141i | 0.140401 | − | 0.243182i | ||||
\(787\) | −401.113 | − | 694.748i | −0.509673 | − | 0.882780i | −0.999937 | − | 0.0112060i | \(-0.996433\pi\) |
0.490264 | − | 0.871574i | \(-0.336900\pi\) | |||||||
\(788\) | 608.807 | − | 351.495i | 0.772597 | − | 0.446059i | ||||
\(789\) | 359.556 | + | 207.590i | 0.455712 | + | 0.263105i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 128.117 | + | 275.963i | 0.161969 | + | 0.348879i | ||||
\(792\) | − | 150.549i | − | 0.190087i | ||||||
\(793\) | 233.124 | + | 134.594i | 0.293977 | + | 0.169728i | ||||
\(794\) | −445.277 | + | 257.081i | −0.560802 | + | 0.323779i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −532.336 | − | 307.344i | −0.668764 | − | 0.386111i | ||||
\(797\) | −1242.74 | −1.55927 | −0.779636 | − | 0.626233i | \(-0.784596\pi\) | ||||
−0.779636 | + | 0.626233i | \(0.784596\pi\) | |||||||
\(798\) | 30.9477 | − | 346.988i | 0.0387816 | − | 0.434822i | ||||
\(799\) | −121.159 | −0.151638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −346.029 | + | 199.780i | −0.431996 | + | 0.249413i | ||||
\(802\) | 341.497 | − | 197.164i | 0.425807 | − | 0.245840i | ||||
\(803\) | 479.355 | − | 830.267i | 0.596955 | − | 1.03396i | ||||
\(804\) | 345.836i | 0.430144i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −609.898 | −0.756697 | ||||||||
\(807\) | 399.880 | + | 230.871i | 0.495514 | + | 0.286085i | ||||
\(808\) | 232.368 | + | 402.473i | 0.287584 | + | 0.498110i | ||||
\(809\) | 55.3589 | + | 95.8845i | 0.0684288 | + | 0.118522i | 0.898210 | − | 0.439567i | \(-0.144868\pi\) |
−0.829781 | + | 0.558089i | \(0.811535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 437.207i | 0.539096i | 0.962987 | + | 0.269548i | \(0.0868743\pi\) | ||||
−0.962987 | + | 0.269548i | \(0.913126\pi\) | |||||||
\(812\) | 287.412 | + | 201.972i | 0.353956 | + | 0.248734i | ||||
\(813\) | − | 632.649i | − | 0.778165i | ||||||
\(814\) | 546.535 | − | 946.627i | 0.671419 | − | 1.16293i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 27.2750 | + | 47.2417i | 0.0334253 | + | 0.0578943i | ||||
\(817\) | −24.7035 | + | 42.7877i | −0.0302368 | + | 0.0523717i | ||||
\(818\) | 551.726 | 0.674482 | ||||||||
\(819\) | 15.1245 | − | 169.577i | 0.0184670 | − | 0.207054i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 340.004 | − | 588.903i | 0.414133 | − | 0.717300i | −0.581204 | − | 0.813758i | \(-0.697418\pi\) |
0.995337 | + | 0.0964580i | \(0.0307513\pi\) | |||||||
\(822\) | 13.2707 | + | 22.9855i | 0.0161444 | + | 0.0279629i | ||||
\(823\) | 435.049 | − | 251.176i | 0.528613 | − | 0.305195i | −0.211838 | − | 0.977305i | \(-0.567945\pi\) |
0.740452 | + | 0.672110i | \(0.234612\pi\) | |||||||
\(824\) | −238.677 | − | 137.800i | −0.289657 | − | 0.167234i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 238.143 | − | 110.559i | 0.288309 | − | 0.133849i | ||||
\(827\) | 404.323i | 0.488904i | 0.969661 | + | 0.244452i | \(0.0786080\pi\) | ||||
−0.969661 | + | 0.244452i | \(0.921392\pi\) | |||||||
\(828\) | −169.334 | − | 97.7648i | −0.204509 | − | 0.118073i | ||||
\(829\) | 587.862 | − | 339.402i | 0.709122 | − | 0.409412i | −0.101614 | − | 0.994824i | \(-0.532401\pi\) |
0.810736 | + | 0.585412i | \(0.199067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −637.402 | − | 368.004i | −0.767030 | − | 0.442845i | ||||
\(832\) | 64.8572 | 0.0779533 | ||||||||
\(833\) | 379.718 | + | 68.2768i | 0.455844 | + | 0.0819650i | ||||
\(834\) | −544.094 | −0.652391 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −624.358 | + | 360.473i | −0.746840 | + | 0.431188i | ||||
\(837\) | −239.379 | + | 138.206i | −0.285997 | + | 0.165120i | ||||
\(838\) | −407.927 | + | 706.550i | −0.486786 | + | 0.843138i | ||||
\(839\) | − | 230.404i | − | 0.274617i | −0.990528 | − | 0.137309i | \(-0.956155\pi\) | ||
0.990528 | − | 0.137309i | \(-0.0438452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −211.417 | −0.251388 | ||||||||
\(842\) | −795.902 | − | 459.514i | −0.945252 | − | 0.545742i | ||||
\(843\) | −125.416 | − | 217.228i | −0.148774 | − | 0.257684i | ||||
\(844\) | −335.164 | − | 580.521i | −0.397113 | − | 0.687821i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 65.2857i | 0.0771698i | ||||||||
\(847\) | −120.511 | + | 1351.18i | −0.142280 | + | 1.59525i | ||||
\(848\) | 203.581i | 0.240071i | ||||||||
\(849\) | −281.343 | + | 487.300i | −0.331381 | + | 0.573969i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −709.828 | − | 1229.46i | −0.834111 | − | 1.44472i | ||||
\(852\) | −168.153 | + | 291.249i | −0.197363 | + | 0.341842i | ||||
\(853\) | −234.440 | −0.274842 | −0.137421 | − | 0.990513i | \(-0.543881\pi\) | ||||
−0.137421 | + | 0.990513i | \(0.543881\pi\) | |||||||
\(854\) | 268.937 | + | 188.989i | 0.314915 | + | 0.221299i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 137.840 | − | 238.747i | 0.161029 | − | 0.278910i | ||||
\(857\) | −309.636 | − | 536.305i | −0.361302 | − | 0.625794i | 0.626873 | − | 0.779121i | \(-0.284334\pi\) |
−0.988175 | + | 0.153327i | \(0.951001\pi\) | |||||||
\(858\) | −305.131 | + | 176.167i | −0.355630 | + | 0.205323i | ||||
\(859\) | 546.499 | + | 315.521i | 0.636204 | + | 0.367313i | 0.783151 | − | 0.621832i | \(-0.213611\pi\) |
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −490.357 | + | 697.792i | −0.569520 | + | 0.810444i | ||||
\(862\) | 978.888i | 1.13560i | ||||||||
\(863\) | 1103.50 | + | 637.108i | 1.27868 | + | 0.738247i | 0.976606 | − | 0.215036i | \(-0.0689870\pi\) |
0.302076 | + | 0.953284i | \(0.402320\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −142.760 | − | 82.4228i | −0.164850 | − | 0.0951764i | ||||
\(867\) | −393.186 | −0.453502 | ||||||||
\(868\) | −741.791 | − | 66.1600i | −0.854598 | − | 0.0762212i | ||||
\(869\) | 1325.68 | 1.52552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 700.935 | − | 404.685i | 0.804747 | − | 0.464621i | ||||
\(872\) | −157.396 | + | 90.8728i | −0.180500 | + | 0.104212i | ||||
\(873\) | −74.9959 | + | 129.897i | −0.0859060 | + | 0.148793i | ||||
\(874\) | 936.349i | 1.07134i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 187.183 | 0.213679 | ||||||||
\(877\) | −1.86172 | − | 1.07486i | −0.00212283 | − | 0.00122562i | 0.498938 | − | 0.866638i | \(-0.333723\pi\) |
−0.501061 | + | 0.865412i | \(0.667057\pi\) | |||||||
\(878\) | 124.650 | + | 215.900i | 0.141970 | + | 0.245900i | ||||
\(879\) | 148.814 | + | 257.754i | 0.169299 | + | 0.293235i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 839.378i | 0.952756i | 0.879241 | + | 0.476378i | \(0.158051\pi\) | ||||
−0.879241 | + | 0.476378i | \(0.841949\pi\) | |||||||
\(882\) | 36.7904 | − | 204.608i | 0.0417125 | − | 0.231982i | ||||
\(883\) | 1326.53i | 1.50230i | 0.660131 | + | 0.751150i | \(0.270501\pi\) | ||||
−0.660131 | + | 0.751150i | \(0.729499\pi\) | |||||||
\(884\) | 63.8326 | − | 110.561i | 0.0722088 | − | 0.125069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 231.941 | + | 401.734i | 0.261785 | + | 0.453424i | ||||
\(887\) | −508.507 | + | 880.761i | −0.573289 | + | 0.992966i | 0.422936 | + | 0.906160i | \(0.360999\pi\) |
−0.996225 | + | 0.0868064i | \(0.972334\pi\) | |||||||
\(888\) | 213.416 | 0.240334 | ||||||||
\(889\) | 548.309 | + | 1181.05i | 0.616771 | + | 1.32852i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −79.8406 | + | 138.288i | −0.0896079 | + | 0.155205i | ||||
\(892\) | 50.9497 | + | 88.2474i | 0.0571185 | + | 0.0989321i | ||||
\(893\) | 270.753 | − | 156.320i | 0.303195 | − | 0.175050i | ||||
\(894\) | −18.3995 | − | 10.6230i | −0.0205811 | − | 0.0118825i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 78.8828 | + | 7.03552i | 0.0880389 | + | 0.00785214i | ||||
\(897\) | 457.604i | 0.510150i | ||||||||
\(898\) | −990.467 | − | 571.846i | −1.10297 | − | 0.636800i | ||||
\(899\) | −1155.93 | + | 667.376i | −1.28579 | + | 0.742354i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 347.042 | + | 200.365i | 0.385174 | + | 0.222380i | ||||
\(902\) | 1765.00 | 1.95676 | ||||||||
\(903\) | −16.9520 | + | 24.1232i | −0.0187730 | + | 0.0267146i | ||||
\(904\) | 122.937 | 0.135992 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 450.921 | − | 260.339i | 0.497705 | − | 0.287350i | ||||
\(907\) | 535.675 | − | 309.272i | 0.590601 | − | 0.340984i | −0.174734 | − | 0.984616i | \(-0.555907\pi\) |
0.765335 | + | 0.643632i | \(0.222573\pi\) | |||||||
\(908\) | 132.426 | − | 229.368i | 0.145843 | − | 0.252608i | ||||
\(909\) | − | 492.926i | − | 0.542273i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 821.498 | 0.901754 | 0.450877 | − | 0.892586i | \(-0.351111\pi\) | ||||
0.450877 | + | 0.892586i | \(0.351111\pi\) | |||||||
\(912\) | −121.903 | − | 70.3805i | −0.133665 | − | 0.0771716i | ||||
\(913\) | 756.008 | + | 1309.44i | 0.828048 | + | 1.43422i | ||||
\(914\) | −238.218 | − | 412.607i | −0.260633 | − | 0.451429i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 368.664i | − | 0.402471i | ||||||
\(917\) | −628.240 | − | 56.0324i | −0.685104 | − | 0.0611041i | ||||
\(918\) | − | 57.8591i | − | 0.0630273i | ||||||
\(919\) | 408.435 | − | 707.430i | 0.444434 | − | 0.769782i | −0.553579 | − | 0.832797i | \(-0.686738\pi\) |
0.998013 | + | 0.0630149i | \(0.0200716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 98.8141 | + | 171.151i | 0.107290 | + | 0.185832i | ||||
\(922\) | −434.785 | + | 753.069i | −0.471567 | + | 0.816778i | ||||
\(923\) | 787.067 | 0.852727 | ||||||||
\(924\) | −390.227 | + | 181.164i | −0.422323 | + | 0.196065i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −578.550 | + | 1002.08i | −0.624784 | + | 1.08216i | ||||
\(927\) | 146.159 | + | 253.156i | 0.157669 | + | 0.273091i | ||||
\(928\) | 122.923 | − | 70.9695i | 0.132460 | − | 0.0764757i | ||||
\(929\) | −109.848 | − | 63.4209i | −0.118243 | − | 0.0682679i | 0.439712 | − | 0.898139i | \(-0.355081\pi\) |
−0.557955 | + | 0.829871i | \(0.688414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −936.643 | + | 337.334i | −1.00606 | + | 0.362335i | ||||
\(932\) | 281.333i | 0.301859i | ||||||||
\(933\) | −232.796 | − | 134.405i | −0.249514 | − | 0.144057i | ||||
\(934\) | 651.305 | − | 376.031i | 0.697329 | − | 0.402603i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −59.5751 | − | 34.3957i | −0.0636486 | − | 0.0367476i | ||||
\(937\) | 1128.69 | 1.20458 | 0.602289 | − | 0.798278i | \(-0.294255\pi\) | ||||
0.602289 | + | 0.798278i | \(0.294255\pi\) | |||||||
\(938\) | 896.414 | − | 416.165i | 0.955666 | − | 0.443672i | ||||
\(939\) | −736.287 | −0.784118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 232.437 | − | 134.197i | 0.247010 | − | 0.142611i | −0.371384 | − | 0.928479i | \(-0.621117\pi\) |
0.618395 | + | 0.785868i | \(0.287783\pi\) | |||||||
\(942\) | 278.823 | − | 160.979i | 0.295991 | − | 0.170890i | ||||
\(943\) | 1146.17 | − | 1985.22i | 1.21545 | − | 2.10522i | ||||
\(944\) | − | 106.088i | − | 0.112382i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 61.0173 | 0.0645003 | ||||||||
\(947\) | 769.482 | + | 444.261i | 0.812547 | + | 0.469124i | 0.847840 | − | 0.530253i | \(-0.177903\pi\) |
−0.0352923 | + | 0.999377i | \(0.511236\pi\) | |||||||
\(948\) | 129.416 | + | 224.155i | 0.136515 | + | 0.236450i | ||||
\(949\) | −219.035 | − | 379.380i | −0.230806 | − | 0.399768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 24.9302i | − | 0.0262147i | ||||||
\(952\) | 89.6301 | − | 127.546i | 0.0941492 | − | 0.133977i | ||||
\(953\) | 300.519i | 0.315340i | 0.987492 | + | 0.157670i | \(0.0503983\pi\) | ||||
−0.987492 | + | 0.157670i | \(0.949602\pi\) | |||||||
\(954\) | 107.965 | − | 187.001i | 0.113171 | − | 0.196018i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 247.975 | + | 429.506i | 0.259388 | + | 0.449274i | ||||
\(957\) | −385.539 | + | 667.773i | −0.402862 | + | 0.697778i | ||||
\(958\) | 902.585 | 0.942155 | ||||||||
\(959\) | 43.6096 | − | 62.0578i | 0.0454741 | − | 0.0647110i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 934.376 | − | 1618.39i | 0.972296 | − | 1.68407i | ||||
\(962\) | −249.732 | − | 432.549i | −0.259597 | − | 0.449635i | ||||
\(963\) | −253.229 | + | 146.202i | −0.262958 | + | 0.151819i | ||||
\(964\) | −379.060 | − | 218.850i | −0.393216 | − | 0.227023i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −49.6396 | + | 556.563i | −0.0513867 | + | 0.576152i | ||||
\(967\) | − | 391.420i | − | 0.404778i | −0.979305 | − | 0.202389i | \(-0.935130\pi\) | ||
0.979305 | − | 0.202389i | \(-0.0648705\pi\) | |||||||
\(968\) | 474.690 | + | 274.062i | 0.490382 | + | 0.283122i | ||||
\(969\) | −239.954 | + | 138.537i | −0.247630 | + | 0.142969i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1370.55 | − | 791.285i | −1.41148 | − | 0.814918i | −0.415951 | − | 0.909387i | \(-0.636551\pi\) |
−0.995528 | + | 0.0944692i | \(0.969885\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | 654.741 | + | 1410.31i | 0.672910 | + | 1.44944i | ||||
\(974\) | −549.916 | −0.564596 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 115.021 | − | 66.4076i | 0.117850 | − | 0.0680406i | ||||
\(977\) | 737.340 | − | 425.703i | 0.754698 | − | 0.435725i | −0.0726910 | − | 0.997355i | \(-0.523159\pi\) |
0.827389 | + | 0.561630i | \(0.189825\pi\) | |||||||
\(978\) | −54.9373 | + | 95.1542i | −0.0561731 | + | 0.0972947i | ||||
\(979\) | − | 2363.04i | − | 2.41373i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 192.770 | 0.196504 | ||||||||
\(982\) | −852.310 | − | 492.082i | −0.867933 | − | 0.501101i | ||||
\(983\) | 113.507 | + | 196.599i | 0.115470 | + | 0.199999i | 0.917967 | − | 0.396656i | \(-0.129829\pi\) |
−0.802498 | + | 0.596655i | \(0.796496\pi\) | |||||||
\(984\) | 172.303 | + | 298.437i | 0.175105 | + | 0.303290i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 279.393i | − | 0.283360i | ||||||
\(987\) | 169.222 | − | 78.5621i | 0.171451 | − | 0.0795969i | ||||
\(988\) | 329.427i | 0.333428i | ||||||||
\(989\) | 39.6240 | − | 68.6307i | 0.0400647 | − | 0.0693940i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −276.368 | − | 478.683i | −0.278878 | − | 0.483031i | 0.692228 | − | 0.721679i | \(-0.256629\pi\) |
−0.971106 | + | 0.238648i | \(0.923296\pi\) | |||||||
\(992\) | −150.459 | + | 260.603i | −0.151673 | + | 0.262705i | ||||
\(993\) | −147.561 | −0.148601 | ||||||||
\(994\) | 957.274 | + | 85.3788i | 0.963052 | + | 0.0858942i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −147.606 | + | 255.662i | −0.148199 | + | 0.256689i | ||||
\(997\) | 134.953 | + | 233.746i | 0.135359 | + | 0.234449i | 0.925735 | − | 0.378174i | \(-0.123448\pi\) |
−0.790375 | + | 0.612623i | \(0.790114\pi\) | |||||||
\(998\) | 650.083 | − | 375.326i | 0.651386 | − | 0.376078i | ||||
\(999\) | −196.035 | − | 113.181i | −0.196232 | − | 0.113294i |
(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.d.649.6 | 24 | ||
5.2 | odd | 4 | 1050.3.p.e.901.6 | yes | 12 | ||
5.3 | odd | 4 | 1050.3.p.f.901.1 | yes | 12 | ||
5.4 | even | 2 | inner | 1050.3.q.d.649.9 | 24 | ||
7.3 | odd | 6 | inner | 1050.3.q.d.199.9 | 24 | ||
35.3 | even | 12 | 1050.3.p.f.451.1 | yes | 12 | ||
35.17 | even | 12 | 1050.3.p.e.451.6 | ✓ | 12 | ||
35.24 | odd | 6 | inner | 1050.3.q.d.199.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.e.451.6 | ✓ | 12 | 35.17 | even | 12 | ||
1050.3.p.e.901.6 | yes | 12 | 5.2 | odd | 4 | ||
1050.3.p.f.451.1 | yes | 12 | 35.3 | even | 12 | ||
1050.3.p.f.901.1 | yes | 12 | 5.3 | odd | 4 | ||
1050.3.q.d.199.6 | 24 | 35.24 | odd | 6 | inner | ||
1050.3.q.d.199.9 | 24 | 7.3 | odd | 6 | inner | ||
1050.3.q.d.649.6 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.q.d.649.9 | 24 | 5.4 | even | 2 | inner |