Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.4 | ||
Root | \(2.16644 - 1.81839i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.e.55.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16644 | + | 1.81839i | −0.765952 | + | 0.642898i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.38692 | − | 7.87886i | 0.173365 | − | 0.984858i | ||||
\(5\) | − | 4.47531i | − | 0.400284i | −0.979767 | − | 0.200142i | \(-0.935860\pi\) | ||
0.979767 | − | 0.200142i | \(-0.0641403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.9825 | − | 10.8869i | 0.808979 | − | 0.587837i | ||||
\(8\) | 11.3222 | + | 19.5910i | 0.500374 | + | 0.865810i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.13786 | + | 9.69549i | 0.257342 | + | 0.306598i | ||||
\(11\) | 7.61561i | 0.208745i | 0.994538 | + | 0.104372i | \(0.0332834\pi\) | ||||
−0.994538 | + | 0.104372i | \(0.966717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.3620i | 0.285074i | 0.989790 | + | 0.142537i | \(0.0455259\pi\) | ||||
−0.989790 | + | 0.142537i | \(0.954474\pi\) | |||||||
\(14\) | −12.6621 | + | 50.8298i | −0.241720 | + | 0.970346i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.1529 | − | 21.8547i | −0.939889 | − | 0.341480i | ||||
\(17\) | − | 55.3574i | − | 0.789773i | −0.918730 | − | 0.394886i | \(-0.870784\pi\) | ||
0.918730 | − | 0.394886i | \(-0.129216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −73.9099 | −0.892426 | −0.446213 | − | 0.894927i | \(-0.647228\pi\) | ||||
−0.446213 | + | 0.894927i | \(0.647228\pi\) | |||||||
\(20\) | −35.2603 | − | 6.20690i | −0.394223 | − | 0.0693952i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.8481 | − | 16.4988i | −0.134202 | − | 0.159888i | ||||
\(23\) | − | 133.446i | − | 1.20980i | −0.796301 | − | 0.604901i | \(-0.793213\pi\) | ||
0.796301 | − | 0.604901i | \(-0.206787\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.972 | 0.839773 | ||||||||
\(26\) | −24.2974 | − | 28.9480i | −0.183273 | − | 0.218353i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −64.9968 | − | 133.144i | −0.438687 | − | 0.898640i | ||||
\(29\) | −23.3760 | −0.149684 | −0.0748418 | − | 0.997195i | \(-0.523845\pi\) | ||||
−0.0748418 | + | 0.997195i | \(0.523845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −241.005 | −1.39632 | −0.698159 | − | 0.715943i | \(-0.745997\pi\) | ||||
−0.698159 | + | 0.715943i | \(0.745997\pi\) | |||||||
\(32\) | 170.058 | − | 62.0345i | 0.939446 | − | 0.342696i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 100.661 | + | 119.928i | 0.507743 | + | 0.604928i | ||||
\(35\) | −48.7222 | − | 67.0514i | −0.235302 | − | 0.323821i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 178.979 | 0.795240 | 0.397620 | − | 0.917550i | \(-0.369836\pi\) | ||||
0.397620 | + | 0.917550i | \(0.369836\pi\) | |||||||
\(38\) | 160.121 | − | 134.397i | 0.683556 | − | 0.573739i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 87.6760 | − | 50.6702i | 0.346570 | − | 0.200291i | ||||
\(41\) | − | 494.101i | − | 1.88209i | −0.338282 | − | 0.941045i | \(-0.609846\pi\) | ||
0.338282 | − | 0.941045i | \(-0.390154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 72.6137i | 0.257523i | 0.991676 | + | 0.128761i | \(0.0411001\pi\) | ||||
−0.991676 | + | 0.128761i | \(0.958900\pi\) | |||||||
\(44\) | 60.0023 | + | 10.5622i | 0.205584 | + | 0.0361890i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 242.657 | + | 289.103i | 0.777779 | + | 0.926650i | ||||
\(47\) | −59.7992 | −0.185587 | −0.0927937 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927937 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 105.951 | − | 326.226i | 0.308895 | − | 0.951096i | ||||
\(50\) | −227.415 | + | 190.879i | −0.643226 | + | 0.539888i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 105.277 | + | 18.5320i | 0.280757 | + | 0.0494218i | ||||
\(53\) | 569.477 | 1.47592 | 0.737960 | − | 0.674845i | \(-0.235789\pi\) | ||||
0.737960 | + | 0.674845i | \(0.235789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34.0822 | 0.0835572 | ||||||||
\(56\) | 382.920 | + | 170.260i | 0.913747 | + | 0.406284i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 50.6428 | − | 42.5068i | 0.114650 | − | 0.0962312i | ||||
\(59\) | −59.5343 | −0.131368 | −0.0656839 | − | 0.997840i | \(-0.520923\pi\) | ||||
−0.0656839 | + | 0.997840i | \(0.520923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 629.889i | − | 1.32212i | −0.750335 | − | 0.661058i | \(-0.770108\pi\) | ||
0.750335 | − | 0.661058i | \(-0.229892\pi\) | |||||||
\(62\) | 522.123 | − | 438.241i | 1.06951 | − | 0.897689i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −255.617 | + | 443.626i | −0.499253 | + | 0.866456i | ||||
\(65\) | 59.7992 | 0.114110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 599.636i | − | 1.09339i | −0.837332 | − | 0.546695i | \(-0.815886\pi\) | ||
0.837332 | − | 0.546695i | \(-0.184114\pi\) | |||||||
\(68\) | −436.153 | − | 76.7762i | −0.777814 | − | 0.136919i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 227.479 | + | 56.6667i | 0.388414 | + | 0.0967567i | ||||
\(71\) | 407.701i | 0.681482i | 0.940157 | + | 0.340741i | \(0.110678\pi\) | ||||
−0.940157 | + | 0.340741i | \(0.889322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 680.155i | − | 1.09050i | −0.838275 | − | 0.545248i | \(-0.816436\pi\) | ||
0.838275 | − | 0.545248i | \(-0.183564\pi\) | |||||||
\(74\) | −387.746 | + | 325.453i | −0.609116 | + | 0.511258i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −102.507 | + | 582.326i | −0.154715 | + | 0.878913i | ||||
\(77\) | 82.9103 | + | 114.101i | 0.122708 | + | 0.168870i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1084.52i | − | 1.54454i | −0.635296 | − | 0.772269i | \(-0.719122\pi\) | ||
0.635296 | − | 0.772269i | \(-0.280878\pi\) | |||||||
\(80\) | −97.8065 | + | 269.203i | −0.136689 | + | 0.376223i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 898.469 | + | 1070.44i | 1.20999 | + | 1.44159i | ||||
\(83\) | −935.224 | −1.23680 | −0.618398 | − | 0.785865i | \(-0.712218\pi\) | ||||
−0.618398 | + | 0.785865i | \(0.712218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −247.741 | −0.316133 | ||||||||
\(86\) | −132.040 | − | 157.313i | −0.165561 | − | 0.197250i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −149.198 | + | 86.2251i | −0.180733 | + | 0.104450i | ||||
\(89\) | 12.1437i | 0.0144633i | 0.999974 | + | 0.00723163i | \(0.00230192\pi\) | ||||
−0.999974 | + | 0.00723163i | \(0.997698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 145.471 | + | 200.197i | 0.167577 | + | 0.230619i | ||||
\(92\) | −1051.40 | − | 185.079i | −1.19148 | − | 0.209737i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 129.551 | − | 108.738i | 0.142151 | − | 0.119314i | ||||
\(95\) | 330.770i | 0.357224i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1433.48i | 1.50049i | 0.661160 | + | 0.750245i | \(0.270064\pi\) | ||||
−0.661160 | + | 0.750245i | \(0.729936\pi\) | |||||||
\(98\) | 363.669 | + | 899.409i | 0.374859 | + | 0.927082i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 145.587 | − | 827.057i | 0.145587 | − | 0.827057i | ||||
\(101\) | 1771.45i | 1.74521i | 0.488427 | + | 0.872605i | \(0.337571\pi\) | ||||
−0.488427 | + | 0.872605i | \(0.662429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1667.56 | −1.59524 | −0.797618 | − | 0.603163i | \(-0.793907\pi\) | ||||
−0.797618 | + | 0.603163i | \(0.793907\pi\) | |||||||
\(104\) | −261.776 | + | 151.287i | −0.246820 | + | 0.142643i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1233.74 | + | 1035.53i | −1.13048 | + | 0.948865i | ||||
\(107\) | − | 1105.21i | − | 0.998551i | −0.866443 | − | 0.499276i | \(-0.833600\pi\) | ||
0.866443 | − | 0.499276i | \(-0.166400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −353.412 | −0.310557 | −0.155279 | − | 0.987871i | \(-0.549628\pi\) | ||||
−0.155279 | + | 0.987871i | \(0.549628\pi\) | |||||||
\(110\) | −73.8370 | + | 61.9747i | −0.0640008 | + | 0.0537187i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1139.17 | + | 327.440i | −0.961085 | + | 0.276252i | ||||
\(113\) | −796.483 | −0.663070 | −0.331535 | − | 0.943443i | \(-0.607566\pi\) | ||||
−0.331535 | + | 0.943443i | \(0.607566\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −597.213 | −0.484264 | ||||||||
\(116\) | −32.4207 | + | 184.177i | −0.0259499 | + | 0.147417i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 128.977 | − | 108.256i | 0.100621 | − | 0.0844561i | ||||
\(119\) | −602.670 | − | 829.392i | −0.464258 | − | 0.638910i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1273.00 | 0.956426 | ||||||||
\(122\) | 1145.38 | + | 1364.62i | 0.849985 | + | 1.01268i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −334.255 | + | 1898.85i | −0.242072 | + | 1.37517i | ||||
\(125\) | − | 1029.19i | − | 0.736431i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1382.89i | 0.966230i | 0.875557 | + | 0.483115i | \(0.160495\pi\) | ||||
−0.875557 | + | 0.483115i | \(0.839505\pi\) | |||||||
\(128\) | −252.905 | − | 1425.90i | −0.174639 | − | 0.984632i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −129.551 | + | 108.738i | −0.0874031 | + | 0.0733613i | ||||
\(131\) | 2930.78 | 1.95468 | 0.977342 | − | 0.211668i | \(-0.0678895\pi\) | ||||
0.977342 | + | 0.211668i | \(0.0678895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1107.36 | + | 804.649i | −0.721954 | + | 0.524601i | ||||
\(134\) | 1090.37 | + | 1299.07i | 0.702938 | + | 0.837485i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1084.51 | − | 626.765i | 0.683793 | − | 0.395181i | ||||
\(137\) | −1514.84 | −0.944685 | −0.472343 | − | 0.881415i | \(-0.656591\pi\) | ||||
−0.472343 | + | 0.881415i | \(0.656591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1121.88 | 0.684582 | 0.342291 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342291 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(140\) | −595.862 | + | 290.881i | −0.359711 | + | 0.175599i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −741.359 | − | 883.260i | −0.438123 | − | 0.521982i | ||||
\(143\) | −101.760 | −0.0595076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 104.615i | 0.0599159i | ||||||||
\(146\) | 1236.79 | + | 1473.52i | 0.701077 | + | 0.835267i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 248.229 | − | 1410.15i | 0.137867 | − | 0.783199i | ||||
\(149\) | 201.082 | 0.110559 | 0.0552796 | − | 0.998471i | \(-0.482395\pi\) | ||||
0.0552796 | + | 0.998471i | \(0.482395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1803.92i | 0.972192i | 0.873906 | + | 0.486096i | \(0.161579\pi\) | ||||
−0.873906 | + | 0.486096i | \(0.838421\pi\) | |||||||
\(152\) | −836.820 | − | 1447.97i | −0.446546 | − | 0.772671i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −387.100 | − | 96.4295i | −0.202555 | − | 0.0504578i | ||||
\(155\) | 1078.57i | 0.558923i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1163.09i | − | 0.591241i | −0.955305 | − | 0.295621i | \(-0.904474\pi\) | ||
0.955305 | − | 0.295621i | \(-0.0955265\pi\) | |||||||
\(158\) | 1972.09 | + | 2349.56i | 0.992980 | + | 1.18304i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −277.624 | − | 761.062i | −0.137176 | − | 0.376045i | ||||
\(161\) | −1452.81 | − | 1999.36i | −0.711166 | − | 0.978705i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1394.86i | − | 0.670271i | −0.942170 | − | 0.335135i | \(-0.891218\pi\) | ||
0.942170 | − | 0.335135i | \(-0.108782\pi\) | |||||||
\(164\) | −3892.96 | − | 685.279i | −1.85359 | − | 0.326288i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2026.11 | − | 1700.60i | 0.947327 | − | 0.795134i | ||||
\(167\) | −1161.55 | −0.538222 | −0.269111 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269111 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2018.46 | 0.918733 | ||||||||
\(170\) | 536.717 | − | 450.490i | 0.242143 | − | 0.203241i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 572.113 | + | 100.709i | 0.253623 | + | 0.0446454i | ||||
\(173\) | 2133.98i | 0.937825i | 0.883245 | + | 0.468913i | \(0.155354\pi\) | ||||
−0.883245 | + | 0.468913i | \(0.844646\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1572.74 | − | 1142.81i | 0.679359 | − | 0.493650i | ||||
\(176\) | 166.437 | − | 458.101i | 0.0712821 | − | 0.196197i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.0820 | − | 26.3086i | −0.00929839 | − | 0.0110782i | ||||
\(179\) | 2551.23i | 1.06530i | 0.846337 | + | 0.532648i | \(0.178803\pi\) | ||||
−0.846337 | + | 0.532648i | \(0.821197\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 715.321i | 0.293754i | 0.989155 | + | 0.146877i | \(0.0469221\pi\) | ||||
−0.989155 | + | 0.146877i | \(0.953078\pi\) | |||||||
\(182\) | −679.189 | − | 169.191i | −0.276620 | − | 0.0689081i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2614.35 | − | 1510.90i | 1.04746 | − | 0.605353i | ||||
\(185\) | − | 800.985i | − | 0.318322i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 421.580 | 0.164861 | ||||||||
\(188\) | −82.9367 | + | 471.149i | −0.0321743 | + | 0.182777i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −601.468 | − | 716.593i | −0.229658 | − | 0.273616i | ||||
\(191\) | − | 2766.30i | − | 1.04797i | −0.851727 | − | 0.523986i | \(-0.824444\pi\) | ||
0.851727 | − | 0.523986i | \(-0.175556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1182.88 | 0.441169 | 0.220584 | − | 0.975368i | \(-0.429204\pi\) | ||||
0.220584 | + | 0.975368i | \(0.429204\pi\) | |||||||
\(194\) | −2606.62 | − | 3105.54i | −0.964662 | − | 1.14930i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2423.34 | − | 1287.22i | −0.883143 | − | 0.469105i | ||||
\(197\) | 4748.28 | 1.71726 | 0.858631 | − | 0.512593i | \(-0.171315\pi\) | ||||
0.858631 | + | 0.512593i | \(0.171315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 918.553 | 0.327209 | 0.163604 | − | 0.986526i | \(-0.447688\pi\) | ||||
0.163604 | + | 0.986526i | \(0.447688\pi\) | |||||||
\(200\) | 1188.51 | + | 2056.50i | 0.420200 | + | 0.727083i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3221.19 | − | 3837.75i | −1.12199 | − | 1.33675i | ||||
\(203\) | −350.232 | + | 254.493i | −0.121091 | + | 0.0879895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2211.26 | −0.753370 | ||||||||
\(206\) | 3612.66 | − | 3032.27i | 1.22187 | − | 1.02557i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 292.023 | − | 803.764i | 0.0973468 | − | 0.267938i | ||||
\(209\) | − | 562.869i | − | 0.186289i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4595.79i | 1.49946i | 0.661742 | + | 0.749732i | \(0.269818\pi\) | ||||
−0.661742 | + | 0.749732i | \(0.730182\pi\) | |||||||
\(212\) | 789.819 | − | 4486.83i | 0.255873 | − | 1.45357i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2009.71 | + | 2394.38i | 0.641966 | + | 0.764842i | ||||
\(215\) | 324.969 | 0.103082 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3610.86 | + | 2623.80i | −1.12959 | + | 0.820807i | ||||
\(218\) | 765.646 | − | 642.641i | 0.237872 | − | 0.199657i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 47.2693 | − | 268.529i | 0.0144859 | − | 0.0822919i | ||||
\(221\) | 739.686 | 0.225143 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2989.01 | 0.897575 | 0.448787 | − | 0.893639i | \(-0.351856\pi\) | ||||
0.448787 | + | 0.893639i | \(0.351856\pi\) | |||||||
\(224\) | 1872.53 | − | 2780.84i | 0.558544 | − | 0.829475i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1725.53 | − | 1448.32i | 0.507879 | − | 0.426286i | ||||
\(227\) | 1938.17 | 0.566698 | 0.283349 | − | 0.959017i | \(-0.408554\pi\) | ||||
0.283349 | + | 0.959017i | \(0.408554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5281.13i | − | 1.52396i | −0.647600 | − | 0.761980i | \(-0.724227\pi\) | ||
0.647600 | − | 0.761980i | \(-0.275773\pi\) | |||||||
\(230\) | 1293.83 | − | 1085.97i | 0.370923 | − | 0.311332i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −264.667 | − | 457.961i | −0.0748977 | − | 0.129597i | ||||
\(233\) | 1490.57 | 0.419101 | 0.209550 | − | 0.977798i | \(-0.432800\pi\) | ||||
0.209550 | + | 0.977798i | \(0.432800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 267.620i | 0.0742876i | ||||||||
\(236\) | −82.5692 | + | 469.062i | −0.0227746 | + | 0.129379i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2813.81 | + | 700.940i | 0.766353 | + | 0.190904i | ||||
\(239\) | 2036.18i | 0.551085i | 0.961289 | + | 0.275543i | \(0.0888575\pi\) | ||||
−0.961289 | + | 0.275543i | \(0.911142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6102.51i | 1.63111i | 0.578681 | + | 0.815554i | \(0.303568\pi\) | ||||
−0.578681 | + | 0.815554i | \(0.696432\pi\) | |||||||
\(242\) | −2757.88 | + | 2314.81i | −0.732576 | + | 0.614884i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4962.81 | − | 873.606i | −1.30210 | − | 0.229209i | ||||
\(245\) | −1459.96 | − | 474.164i | −0.380708 | − | 0.123646i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 987.586i | − | 0.254407i | ||||||
\(248\) | −2728.70 | − | 4721.54i | −0.698680 | − | 1.20894i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1871.48 | + | 2229.69i | 0.473450 | + | 0.564071i | ||||
\(251\) | 1319.61 | 0.331846 | 0.165923 | − | 0.986139i | \(-0.446940\pi\) | ||||
0.165923 | + | 0.986139i | \(0.446940\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1016.27 | 0.252540 | ||||||||
\(254\) | −2514.62 | − | 2995.94i | −0.621187 | − | 0.740086i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3140.74 | + | 2629.25i | 0.766783 | + | 0.641906i | ||||
\(257\) | 4469.92i | 1.08492i | 0.840080 | + | 0.542462i | \(0.182508\pi\) | ||||
−0.840080 | + | 0.542462i | \(0.817492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2681.55 | − | 1948.52i | 0.643333 | − | 0.467472i | ||||
\(260\) | 82.9367 | − | 471.149i | 0.0197827 | − | 0.112382i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6349.36 | + | 5329.30i | −1.49719 | + | 1.25666i | ||||
\(263\) | 4673.64i | 1.09577i | 0.836552 | + | 0.547887i | \(0.184568\pi\) | ||||
−0.836552 | + | 0.547887i | \(0.815432\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2548.59i | − | 0.590787i | ||||||
\(266\) | 935.853 | − | 3756.83i | 0.215718 | − | 0.865962i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4724.45 | − | 831.647i | −1.07683 | − | 0.189556i | ||||
\(269\) | − | 4633.12i | − | 1.05013i | −0.851061 | − | 0.525067i | \(-0.824040\pi\) | ||
0.851061 | − | 0.525067i | \(-0.175960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3004.01 | −0.673359 | −0.336680 | − | 0.941619i | \(-0.609304\pi\) | ||||
−0.336680 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(272\) | −1209.82 | + | 3329.91i | −0.269691 | + | 0.742299i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3281.82 | − | 2754.58i | 0.723584 | − | 0.607336i | ||||
\(275\) | 799.423i | 0.175298i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8852.78 | −1.92026 | −0.960130 | − | 0.279552i | \(-0.909814\pi\) | ||||
−0.960130 | + | 0.279552i | \(0.909814\pi\) | |||||||
\(278\) | −2430.49 | + | 2040.02i | −0.524357 | + | 0.440116i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 761.965 | − | 1713.69i | 0.162629 | − | 0.365758i | ||||
\(281\) | −378.664 | −0.0803885 | −0.0401943 | − | 0.999192i | \(-0.512798\pi\) | ||||
−0.0401943 | + | 0.999192i | \(0.512798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1515.73 | 0.318378 | 0.159189 | − | 0.987248i | \(-0.449112\pi\) | ||||
0.159189 | + | 0.987248i | \(0.449112\pi\) | |||||||
\(284\) | 3212.22 | + | 565.449i | 0.671163 | + | 0.118145i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 220.457 | − | 185.039i | 0.0455800 | − | 0.0382573i | ||||
\(287\) | −5379.23 | − | 7402.88i | −1.10636 | − | 1.52257i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1848.56 | 0.376259 | ||||||||
\(290\) | −190.231 | − | 226.642i | −0.0385198 | − | 0.0458927i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5358.85 | − | 943.321i | −1.07398 | − | 0.189054i | ||||
\(293\) | 5745.66i | 1.14561i | 0.819690 | + | 0.572807i | \(0.194146\pi\) | ||||
−0.819690 | + | 0.572807i | \(0.805854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 266.434i | 0.0525844i | ||||||||
\(296\) | 2026.42 | + | 3506.38i | 0.397917 | + | 0.688527i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −435.633 | + | 365.646i | −0.0846830 | + | 0.0710782i | ||||
\(299\) | 1783.11 | 0.344883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 790.537 | + | 1087.93i | 0.151381 | + | 0.208331i | ||||
\(302\) | −3280.23 | − | 3908.08i | −0.625020 | − | 0.744652i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4445.90 | + | 1615.28i | 0.838782 | + | 0.304745i | ||||
\(305\) | −2818.95 | −0.529222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 591.984 | 0.110053 | 0.0550265 | − | 0.998485i | \(-0.482476\pi\) | ||||
0.0550265 | + | 0.998485i | \(0.482476\pi\) | |||||||
\(308\) | 1013.98 | − | 494.990i | 0.187586 | − | 0.0915736i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1961.27 | − | 2336.66i | −0.359330 | − | 0.428108i | ||||
\(311\) | 2628.66 | 0.479284 | 0.239642 | − | 0.970861i | \(-0.422970\pi\) | ||||
0.239642 | + | 0.970861i | \(0.422970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3781.59i | 0.682902i | 0.939900 | + | 0.341451i | \(0.110918\pi\) | ||||
−0.939900 | + | 0.341451i | \(0.889082\pi\) | |||||||
\(314\) | 2114.96 | + | 2519.77i | 0.380108 | + | 0.452863i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8544.81 | − | 1504.15i | −1.52115 | − | 0.267769i | ||||
\(317\) | −3073.59 | −0.544575 | −0.272288 | − | 0.962216i | \(-0.587780\pi\) | ||||
−0.272288 | + | 0.962216i | \(0.587780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 178.023i | − | 0.0312457i | ||||||
\(320\) | 1985.36 | + | 1143.97i | 0.346829 | + | 0.199843i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6783.04 | + | 1689.71i | 1.17393 | + | 0.292434i | ||||
\(323\) | 4091.46i | 0.704814i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1402.63i | 0.239397i | ||||||||
\(326\) | 2536.40 | + | 3021.89i | 0.430915 | + | 0.513395i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9679.96 | − | 5594.30i | 1.62953 | − | 0.941748i | ||||
\(329\) | −895.942 | + | 651.027i | −0.150136 | + | 0.109095i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6921.62i | 1.14939i | 0.818369 | + | 0.574693i | \(0.194878\pi\) | ||||
−0.818369 | + | 0.574693i | \(0.805122\pi\) | |||||||
\(332\) | −1297.08 | + | 7368.50i | −0.214417 | + | 1.21807i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2516.42 | − | 2112.14i | 0.412252 | − | 0.346022i | ||||
\(335\) | −2683.56 | −0.437667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8596.94 | 1.38963 | 0.694815 | − | 0.719189i | \(-0.255486\pi\) | ||||
0.694815 | + | 0.719189i | \(0.255486\pi\) | |||||||
\(338\) | −4372.86 | + | 3670.34i | −0.703705 | + | 0.590651i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −343.597 | + | 1951.92i | −0.0548064 | + | 0.311346i | ||||
\(341\) | − | 1835.40i | − | 0.291474i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1964.17 | − | 6041.16i | −0.309200 | − | 0.950997i | ||||
\(344\) | −1422.58 | + | 822.143i | −0.222966 | + | 0.128858i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3880.41 | − | 4623.15i | −0.602926 | − | 0.718329i | ||||
\(347\) | 4939.05i | 0.764098i | 0.924142 | + | 0.382049i | \(0.124781\pi\) | ||||
−0.924142 | + | 0.382049i | \(0.875219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 195.755i | − | 0.0300244i | −0.999887 | − | 0.0150122i | \(-0.995221\pi\) | ||
0.999887 | − | 0.0150122i | \(-0.00477872\pi\) | |||||||
\(350\) | −1329.16 | + | 5335.69i | −0.202990 | + | 0.814870i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 472.431 | + | 1295.09i | 0.0715359 | + | 0.196105i | ||||
\(353\) | − | 837.552i | − | 0.126284i | −0.998005 | − | 0.0631422i | \(-0.979888\pi\) | ||
0.998005 | − | 0.0631422i | \(-0.0201122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1824.59 | 0.272786 | ||||||||
\(356\) | 95.6785 | + | 16.8423i | 0.0142442 | + | 0.00250742i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4639.13 | − | 5527.09i | −0.684876 | − | 0.815965i | ||||
\(359\) | − | 5984.33i | − | 0.879779i | −0.898052 | − | 0.439890i | \(-0.855018\pi\) | ||
0.898052 | − | 0.439890i | \(-0.144982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1396.32 | −0.203576 | ||||||||
\(362\) | −1300.73 | − | 1549.70i | −0.188853 | − | 0.225001i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1779.08 | − | 868.488i | 0.256179 | − | 0.125058i | ||||
\(365\) | −3043.91 | −0.436508 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3550.58 | −0.505010 | −0.252505 | − | 0.967596i | \(-0.581254\pi\) | ||||
−0.252505 | + | 0.967596i | \(0.581254\pi\) | |||||||
\(368\) | −2916.42 | + | 8027.17i | −0.413123 | + | 1.13708i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1456.50 | + | 1735.28i | 0.204648 | + | 0.243819i | ||||
\(371\) | 8532.20 | − | 6199.84i | 1.19399 | − | 0.867600i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4863.68 | 0.675152 | 0.337576 | − | 0.941298i | \(-0.390393\pi\) | ||||
0.337576 | + | 0.941298i | \(0.390393\pi\) | |||||||
\(374\) | −913.328 | + | 766.597i | −0.126276 | + | 0.105989i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −677.056 | − | 1171.53i | −0.0928630 | − | 0.160683i | ||||
\(377\) | − | 312.351i | − | 0.0426708i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6050.73i | 0.820066i | 0.912071 | + | 0.410033i | \(0.134483\pi\) | ||||
−0.912071 | + | 0.410033i | \(0.865517\pi\) | |||||||
\(380\) | 2606.09 | + | 458.751i | 0.351815 | + | 0.0619301i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5030.22 | + | 5993.03i | 0.673739 | + | 0.802697i | ||||
\(383\) | −3136.38 | −0.418437 | −0.209219 | − | 0.977869i | \(-0.567092\pi\) | ||||
−0.209219 | + | 0.977869i | \(0.567092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 510.637 | − | 371.049i | 0.0675960 | − | 0.0491180i | ||||
\(386\) | −2562.64 | + | 2150.94i | −0.337914 | + | 0.283626i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11294.2 | + | 1988.12i | 1.47777 | + | 0.260132i | ||||
\(389\) | 4086.79 | 0.532669 | 0.266335 | − | 0.963881i | \(-0.414187\pi\) | ||||
0.266335 | + | 0.963881i | \(0.414187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7387.23 | −0.955469 | ||||||||
\(392\) | 7590.70 | − | 1617.89i | 0.978031 | − | 0.208459i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10286.9 | + | 8634.22i | −1.31534 | + | 1.10402i | ||||
\(395\) | −4853.58 | −0.618254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4953.21i | 0.626182i | 0.949723 | + | 0.313091i | \(0.101365\pi\) | ||||
−0.949723 | + | 0.313091i | \(0.898635\pi\) | |||||||
\(398\) | −1989.99 | + | 1670.29i | −0.250626 | + | 0.210362i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6314.35 | − | 2294.12i | −0.789293 | − | 0.286765i | ||||
\(401\) | −6920.41 | −0.861818 | −0.430909 | − | 0.902396i | \(-0.641807\pi\) | ||||
−0.430909 | + | 0.902396i | \(0.641807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3220.32i | − | 0.398053i | ||||||
\(404\) | 13957.0 | + | 2456.86i | 1.71878 | + | 0.302558i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 295.989 | − | 1188.20i | 0.0361816 | − | 0.145245i | ||||
\(407\) | 1363.03i | 0.166002i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15351.1i | − | 1.85590i | −0.372710 | − | 0.927948i | \(-0.621571\pi\) | ||
0.372710 | − | 0.927948i | \(-0.378429\pi\) | |||||||
\(410\) | 4790.55 | − | 4020.93i | 0.577045 | − | 0.484340i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2312.77 | + | 13138.4i | −0.276558 | + | 1.57108i | ||||
\(413\) | −891.973 | + | 648.143i | −0.106274 | + | 0.0772229i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4185.42i | 0.495070i | ||||||||
\(416\) | 828.907 | + | 2272.32i | 0.0976935 | + | 0.267811i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1023.51 | + | 1219.42i | 0.119765 | + | 0.142689i | ||||
\(419\) | 12665.4 | 1.47672 | 0.738358 | − | 0.674409i | \(-0.235601\pi\) | ||||
0.738358 | + | 0.674409i | \(0.235601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11040.6 | 1.27812 | 0.639059 | − | 0.769158i | \(-0.279324\pi\) | ||||
0.639059 | + | 0.769158i | \(0.279324\pi\) | |||||||
\(422\) | −8356.93 | − | 9956.49i | −0.964002 | − | 1.14852i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6447.71 | + | 11156.6i | 0.738511 | + | 1.27787i | ||||
\(425\) | − | 5810.95i | − | 0.663230i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6857.54 | − | 9437.32i | −0.777189 | − | 1.06956i | ||||
\(428\) | −8707.82 | − | 1532.84i | −0.983431 | − | 0.173114i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −704.025 | + | 590.920i | −0.0789560 | + | 0.0662713i | ||||
\(431\) | − | 11223.6i | − | 1.25434i | −0.778881 | − | 0.627171i | \(-0.784213\pi\) | ||
0.778881 | − | 0.627171i | \(-0.215787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3804.05i | − | 0.422196i | −0.977465 | − | 0.211098i | \(-0.932296\pi\) | ||
0.977465 | − | 0.211098i | \(-0.0677040\pi\) | |||||||
\(434\) | 3051.63 | − | 12250.3i | 0.337518 | − | 1.35491i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −490.154 | + | 2784.49i | −0.0538398 | + | 0.305855i | ||||
\(437\) | 9862.99i | 1.07966i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −729.294 | −0.0792877 | −0.0396438 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396438 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(440\) | 385.884 | + | 667.706i | 0.0418098 | + | 0.0723446i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1602.49 | + | 1345.04i | −0.172449 | + | 0.144744i | ||||
\(443\) | 3801.56i | 0.407714i | 0.979001 | + | 0.203857i | \(0.0653478\pi\) | ||||
−0.979001 | + | 0.203857i | \(0.934652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 54.3468 | 0.00578941 | ||||||||
\(446\) | −6475.52 | + | 5435.19i | −0.687499 | + | 0.577049i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 999.917 | + | 9429.50i | 0.105450 | + | 0.994425i | ||||
\(449\) | 14008.3 | 1.47237 | 0.736185 | − | 0.676780i | \(-0.236625\pi\) | ||||
0.736185 | + | 0.676780i | \(0.236625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3762.88 | 0.392876 | ||||||||
\(452\) | −1104.66 | + | 6275.38i | −0.114953 | + | 0.653029i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4198.92 | + | 3524.34i | −0.434064 | + | 0.364329i | ||||
\(455\) | 895.942 | − | 651.027i | 0.0923130 | − | 0.0670783i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15859.0 | −1.62331 | −0.811656 | − | 0.584136i | \(-0.801434\pi\) | ||||
−0.811656 | + | 0.584136i | \(0.801434\pi\) | |||||||
\(458\) | 9603.15 | + | 11441.3i | 0.979751 | + | 1.16728i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −828.286 | + | 4705.36i | −0.0839544 | + | 0.476931i | ||||
\(461\) | − | 7619.91i | − | 0.769836i | −0.922951 | − | 0.384918i | \(-0.874230\pi\) | ||
0.922951 | − | 0.384918i | \(-0.125770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5312.60i | − | 0.533255i | −0.963800 | − | 0.266628i | \(-0.914091\pi\) | ||
0.963800 | − | 0.266628i | \(-0.0859094\pi\) | |||||||
\(464\) | 1406.14 | + | 510.876i | 0.140686 | + | 0.0511139i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3229.23 | + | 2710.44i | −0.321011 | + | 0.269439i | ||||
\(467\) | −17971.9 | −1.78082 | −0.890408 | − | 0.455163i | \(-0.849581\pi\) | ||||
−0.890408 | + | 0.455163i | \(0.849581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6528.17 | − | 8984.05i | −0.642735 | − | 0.884530i | ||||
\(470\) | −486.637 | − | 579.782i | −0.0477594 | − | 0.0569008i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −674.057 | − | 1166.34i | −0.0657330 | − | 0.113740i | ||||
\(473\) | −552.997 | −0.0537565 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7758.44 | −0.749435 | ||||||||
\(476\) | −7370.52 | + | 3598.05i | −0.709721 | + | 0.346463i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3702.56 | − | 4411.26i | −0.354292 | − | 0.422105i | ||||
\(479\) | −11971.4 | −1.14194 | −0.570970 | − | 0.820971i | \(-0.693433\pi\) | ||||
−0.570970 | + | 0.820971i | \(0.693433\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2391.52i | 0.226702i | ||||||||
\(482\) | −11096.7 | − | 13220.7i | −1.04864 | − | 1.24935i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1765.55 | − | 10029.8i | 0.165811 | − | 0.941943i | ||||
\(485\) | 6415.25 | 0.600622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16208.1i | − | 1.50813i | −0.656802 | − | 0.754063i | \(-0.728091\pi\) | ||
0.656802 | − | 0.754063i | \(-0.271909\pi\) | |||||||
\(488\) | 12340.2 | − | 7131.71i | 1.14470 | − | 0.661552i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4025.13 | − | 1627.53i | 0.371096 | − | 0.150050i | ||||
\(491\) | 4844.19i | 0.445245i | 0.974905 | + | 0.222622i | \(0.0714617\pi\) | ||||
−0.974905 | + | 0.222622i | \(0.928538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1294.04i | 0.118216i | ||||||||
\(494\) | 1795.82 | + | 2139.54i | 0.163558 | + | 0.194864i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14497.2 | + | 5267.10i | 1.31238 | + | 0.476814i | ||||
\(497\) | 4438.60 | + | 6108.39i | 0.400600 | + | 0.551305i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3372.90i | − | 0.302589i | −0.988489 | − | 0.151294i | \(-0.951656\pi\) | ||
0.988489 | − | 0.151294i | \(-0.0483441\pi\) | |||||||
\(500\) | −8108.88 | − | 1427.41i | −0.725280 | − | 0.127671i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2858.86 | + | 2399.57i | −0.254178 | + | 0.213343i | ||||
\(503\) | −18916.6 | −1.67684 | −0.838420 | − | 0.545024i | \(-0.816520\pi\) | ||||
−0.838420 | + | 0.545024i | \(0.816520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7927.80 | 0.698579 | ||||||||
\(506\) | −2201.69 | + | 1847.98i | −0.193433 | + | 0.162357i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10895.6 | + | 1917.95i | 0.951599 | + | 0.167510i | ||||
\(509\) | − | 14473.0i | − | 1.26033i | −0.776463 | − | 0.630163i | \(-0.782988\pi\) | ||
0.776463 | − | 0.630163i | \(-0.217012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7404.78 | − | 10190.4i | −0.641033 | − | 0.882188i | ||||
\(512\) | −11585.2 | + | 14.9924i | −0.999999 | + | 0.00129410i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8128.05 | − | 9683.80i | −0.697496 | − | 0.831000i | ||||
\(515\) | 7462.83i | 0.638547i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 455.407i | − | 0.0387404i | ||||||
\(518\) | −2266.24 | + | 9097.45i | −0.192226 | + | 0.771658i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 677.056 | + | 1171.53i | 0.0570978 | + | 0.0987979i | ||||
\(521\) | − | 3641.31i | − | 0.306197i | −0.988211 | − | 0.153098i | \(-0.951075\pi\) | ||
0.988211 | − | 0.153098i | \(-0.0489251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16089.9 | 1.34525 | 0.672623 | − | 0.739985i | \(-0.265168\pi\) | ||||
0.672623 | + | 0.739985i | \(0.265168\pi\) | |||||||
\(524\) | 4064.76 | − | 23091.2i | 0.338874 | − | 1.92508i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8498.49 | − | 10125.2i | −0.704471 | − | 0.839311i | ||||
\(527\) | 13341.4i | 1.10277i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5640.87 | −0.463620 | ||||||||
\(530\) | 4634.32 | + | 5521.36i | 0.379815 | + | 0.452514i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4803.91 | + | 9840.69i | 0.391496 | + | 0.801970i | ||||
\(533\) | 6602.19 | 0.536534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4946.17 | −0.399704 | ||||||||
\(536\) | 11747.5 | − | 6789.17i | 0.946668 | − | 0.547104i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8424.81 | + | 10037.4i | 0.675129 | + | 0.804352i | ||||
\(539\) | 2484.41 | + | 806.882i | 0.198536 | + | 0.0644803i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18144.0 | 1.44190 | 0.720952 | − | 0.692985i | \(-0.243705\pi\) | ||||
0.720952 | + | 0.692985i | \(0.243705\pi\) | |||||||
\(542\) | 6508.00 | − | 5462.45i | 0.515761 | − | 0.432901i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3434.07 | − | 9413.96i | −0.270652 | − | 0.741949i | ||||
\(545\) | 1581.63i | 0.124311i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12520.2i | 0.978653i | 0.872101 | + | 0.489326i | \(0.162757\pi\) | ||||
−0.872101 | + | 0.489326i | \(0.837243\pi\) | |||||||
\(548\) | −2100.97 | + | 11935.2i | −0.163775 | + | 0.930381i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1453.66 | − | 1731.90i | −0.112699 | − | 0.134270i | ||||
\(551\) | 1727.72 | 0.133582 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11807.1 | − | 16248.9i | −0.907936 | − | 1.24950i | ||||
\(554\) | 19179.0 | − | 16097.8i | 1.47083 | − | 1.23453i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1555.96 | − | 8839.17i | 0.118683 | − | 0.674216i | ||||
\(557\) | −8252.03 | −0.627737 | −0.313869 | − | 0.949466i | \(-0.601625\pi\) | ||||
−0.313869 | + | 0.949466i | \(0.601625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −970.265 | −0.0734130 | ||||||||
\(560\) | 1465.40 | + | 5098.14i | 0.110579 | + | 0.384707i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 820.352 | − | 688.558i | 0.0615738 | − | 0.0516816i | ||||
\(563\) | 18486.4 | 1.38386 | 0.691928 | − | 0.721967i | \(-0.256762\pi\) | ||||
0.691928 | + | 0.721967i | \(0.256762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3564.51i | 0.265416i | ||||||||
\(566\) | −3283.74 | + | 2756.19i | −0.243862 | + | 0.204684i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7987.29 | + | 4616.06i | −0.590034 | + | 0.340996i | ||||
\(569\) | 22842.2 | 1.68294 | 0.841471 | − | 0.540302i | \(-0.181690\pi\) | ||||
0.841471 | + | 0.540302i | \(0.181690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7404.29i | 0.542662i | 0.962486 | + | 0.271331i | \(0.0874638\pi\) | ||||
−0.962486 | + | 0.271331i | \(0.912536\pi\) | |||||||
\(572\) | −141.133 | + | 801.752i | −0.0103165 | + | 0.0586065i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25115.1 | + | 6256.35i | 1.82628 | + | 0.454939i | ||||
\(575\) | − | 14008.1i | − | 1.01596i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 680.722i | 0.0491141i | 0.999698 | + | 0.0245570i | \(0.00781753\pi\) | ||||
−0.999698 | + | 0.0245570i | \(0.992182\pi\) | |||||||
\(578\) | −4004.79 | + | 3361.40i | −0.288196 | + | 0.241896i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 824.248 | + | 145.093i | 0.0590086 | + | 0.0103873i | ||||
\(581\) | −14012.0 | + | 10181.7i | −1.00054 | + | 0.727035i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4336.92i | 0.308090i | ||||||||
\(584\) | 13324.9 | − | 7700.83i | 0.944161 | − | 0.545655i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10447.8 | − | 12447.6i | −0.736513 | − | 0.877485i | ||||
\(587\) | 21647.2 | 1.52210 | 0.761052 | − | 0.648691i | \(-0.224683\pi\) | ||||
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17812.7 | 1.24611 | ||||||||
\(590\) | −484.481 | − | 577.214i | −0.0338064 | − | 0.0402771i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10766.1 | − | 3911.52i | −0.747438 | − | 0.271558i | ||||
\(593\) | − | 14571.9i | − | 1.00910i | −0.863383 | − | 0.504549i | \(-0.831659\pi\) | ||
0.863383 | − | 0.504549i | \(-0.168341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3711.79 | + | 2697.13i | −0.255745 | + | 0.185835i | ||||
\(596\) | 278.885 | − | 1584.30i | 0.0191671 | − | 0.108885i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3863.00 | + | 3242.39i | −0.264164 | + | 0.221724i | ||||
\(599\) | − | 23843.1i | − | 1.62638i | −0.581997 | − | 0.813191i | \(-0.697729\pi\) | ||
0.581997 | − | 0.813191i | \(-0.302271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3664.55i | 0.248719i | 0.992237 | + | 0.124360i | \(0.0396876\pi\) | ||||
−0.992237 | + | 0.124360i | \(0.960312\pi\) | |||||||
\(602\) | −3690.94 | − | 919.440i | −0.249886 | − | 0.0622485i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14212.8 | + | 2501.89i | 0.957470 | + | 0.168544i | ||||
\(605\) | − | 5697.08i | − | 0.382842i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1982.67 | 0.132577 | 0.0662885 | − | 0.997801i | \(-0.478884\pi\) | ||||
0.0662885 | + | 0.997801i | \(0.478884\pi\) | |||||||
\(608\) | −12569.0 | + | 4584.97i | −0.838387 | + | 0.305831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6107.09 | − | 5125.95i | 0.405358 | − | 0.340235i | ||||
\(611\) | − | 799.038i | − | 0.0529061i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10215.4 | −0.673077 | −0.336538 | − | 0.941670i | \(-0.609256\pi\) | ||||
−0.336538 | + | 0.941670i | \(0.609256\pi\) | |||||||
\(614\) | −1282.50 | + | 1076.46i | −0.0842954 | + | 0.0707529i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1296.63 | + | 2916.17i | −0.0848097 | + | 0.190740i | ||||
\(617\) | 10912.4 | 0.712022 | 0.356011 | − | 0.934482i | \(-0.384137\pi\) | ||||
0.356011 | + | 0.934482i | \(0.384137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6816.95 | 0.442644 | 0.221322 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221322 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(620\) | 8497.93 | + | 1495.89i | 0.550460 | + | 0.0968977i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5694.82 | + | 4779.92i | −0.367109 | + | 0.308131i | ||||
\(623\) | 132.207 | + | 181.943i | 0.00850204 | + | 0.0117005i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8515.49 | 0.544991 | ||||||||
\(626\) | −6876.41 | − | 8192.59i | −0.439036 | − | 0.523070i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9163.85 | − | 1613.12i | −0.582289 | − | 0.102501i | ||||
\(629\) | − | 9907.79i | − | 0.628059i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27480.9i | 1.73375i | 0.498527 | + | 0.866874i | \(0.333875\pi\) | ||||
−0.498527 | + | 0.866874i | \(0.666125\pi\) | |||||||
\(632\) | 21246.9 | − | 12279.2i | 1.33728 | − | 0.772846i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6658.76 | − | 5588.99i | 0.417118 | − | 0.350106i | ||||
\(635\) | 6188.84 | 0.386766 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4359.04 | + | 1415.72i | 0.271132 | + | 0.0880579i | ||||
\(638\) | 323.715 | + | 385.676i | 0.0200878 | + | 0.0239327i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6381.35 | + | 1131.83i | −0.394133 | + | 0.0699053i | ||||
\(641\) | −31255.0 | −1.92589 | −0.962946 | − | 0.269694i | \(-0.913077\pi\) | ||||
−0.962946 | + | 0.269694i | \(0.913077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3994.76 | −0.245004 | −0.122502 | − | 0.992468i | \(-0.539092\pi\) | ||||
−0.122502 | + | 0.992468i | \(0.539092\pi\) | |||||||
\(644\) | −17767.6 | + | 8673.57i | −1.08718 | + | 0.530724i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7439.87 | − | 8863.90i | −0.453123 | − | 0.539854i | ||||
\(647\) | −12996.2 | −0.789697 | −0.394848 | − | 0.918746i | \(-0.629203\pi\) | ||||
−0.394848 | + | 0.918746i | \(0.629203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 453.390i | − | 0.0274223i | ||||||
\(650\) | −2550.53 | − | 3038.72i | −0.153908 | − | 0.183367i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10989.9 | − | 1934.56i | −0.660121 | − | 0.116201i | ||||
\(653\) | −18282.4 | −1.09563 | −0.547814 | − | 0.836600i | \(-0.684540\pi\) | ||||
−0.547814 | + | 0.836600i | \(0.684540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13116.2i | − | 0.782428i | ||||||
\(656\) | −10798.4 | + | 29721.6i | −0.642695 | + | 1.76896i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 757.182 | − | 3039.58i | 0.0448602 | − | 0.180084i | ||||
\(659\) | 19470.9i | 1.15095i | 0.817818 | + | 0.575477i | \(0.195184\pi\) | ||||
−0.817818 | + | 0.575477i | \(0.804816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25139.3i | 1.47928i | 0.673000 | + | 0.739642i | \(0.265005\pi\) | ||||
−0.673000 | + | 0.739642i | \(0.734995\pi\) | |||||||
\(662\) | −12586.2 | − | 14995.3i | −0.738937 | − | 0.880374i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10588.8 | − | 18322.0i | −0.618860 | − | 1.07083i | ||||
\(665\) | 3601.06 | + | 4955.76i | 0.209989 | + | 0.288987i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3119.44i | 0.181087i | ||||||||
\(668\) | −1610.97 | + | 9151.66i | −0.0933089 | + | 0.530072i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5813.76 | − | 4879.75i | 0.335232 | − | 0.281375i | ||||
\(671\) | 4796.99 | 0.275985 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12277.8 | 0.703232 | 0.351616 | − | 0.936144i | \(-0.385632\pi\) | ||||
0.351616 | + | 0.936144i | \(0.385632\pi\) | |||||||
\(674\) | −18624.8 | + | 15632.6i | −1.06439 | + | 0.893390i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2799.44 | − | 15903.1i | 0.159276 | − | 0.904821i | ||||
\(677\) | 8737.50i | 0.496026i | 0.968757 | + | 0.248013i | \(0.0797776\pi\) | ||||
−0.968757 | + | 0.248013i | \(0.920222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15606.1 | + | 21477.1i | 0.882044 | + | 1.21387i | ||||
\(680\) | −2804.97 | − | 4853.51i | −0.158185 | − | 0.273711i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3337.48 | + | 3976.29i | 0.187388 | + | 0.223255i | ||||
\(683\) | − | 21358.4i | − | 1.19657i | −0.801284 | − | 0.598284i | \(-0.795849\pi\) | ||
0.801284 | − | 0.598284i | \(-0.204151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6779.40i | 0.378142i | ||||||||
\(686\) | 15240.4 | + | 9516.18i | 0.848226 | + | 0.529635i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1586.95 | − | 4367.92i | 0.0879388 | − | 0.242043i | ||||
\(689\) | 7609.37i | 0.420746i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27244.9 | 1.49992 | 0.749961 | − | 0.661483i | \(-0.230072\pi\) | ||||
0.749961 | + | 0.661483i | \(0.230072\pi\) | |||||||
\(692\) | 16813.4 | + | 2959.66i | 0.923624 | + | 0.162586i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8981.11 | − | 10700.1i | −0.491237 | − | 0.585262i | ||||
\(695\) | − | 5020.78i | − | 0.274027i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27352.2 | −1.48642 | ||||||||
\(698\) | 355.959 | + | 424.092i | 0.0193026 | + | 0.0229973i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6822.82 | − | 13976.4i | −0.368397 | − | 0.754653i | ||||
\(701\) | −9913.36 | −0.534126 | −0.267063 | − | 0.963679i | \(-0.586053\pi\) | ||||
−0.267063 | + | 0.963679i | \(0.586053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13228.3 | −0.709693 | ||||||||
\(704\) | −3378.48 | − | 1946.68i | −0.180868 | − | 0.104216i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1522.99 | + | 1814.50i | 0.0811879 | + | 0.0967277i | ||||
\(707\) | 19285.6 | + | 26540.8i | 1.02590 | + | 1.41184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4521.15 | −0.239486 | −0.119743 | − | 0.992805i | \(-0.538207\pi\) | ||||
−0.119743 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(710\) | −3952.86 | + | 3317.81i | −0.208941 | + | 0.175374i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −237.908 | + | 137.493i | −0.0125224 | + | 0.00723703i | ||||
\(713\) | 32161.2i | 1.68927i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 455.407i | 0.0238199i | ||||||||
\(716\) | 20100.8 | + | 3538.35i | 1.04916 | + | 0.184685i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10881.8 | + | 12964.7i | 0.565608 | + | 0.673869i | ||||
\(719\) | −14246.5 | −0.738948 | −0.369474 | − | 0.929241i | \(-0.620462\pi\) | ||||
−0.369474 | + | 0.929241i | \(0.620462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24984.2 | + | 18154.5i | −1.29051 | + | 0.937738i | ||||
\(722\) | 3025.05 | − | 2539.06i | 0.155929 | − | 0.130878i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5635.91 | + | 992.093i | 0.289305 | + | 0.0509266i | ||||
\(725\) | −2453.82 | −0.125700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13979.5 | 0.713164 | 0.356582 | − | 0.934264i | \(-0.383942\pi\) | ||||
0.356582 | + | 0.934264i | \(0.383942\pi\) | |||||||
\(728\) | −2275.01 | + | 5116.58i | −0.115821 | + | 0.260485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6594.44 | − | 5535.01i | 0.334344 | − | 0.280630i | ||||
\(731\) | 4019.70 | 0.203384 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22386.3i | 1.12805i | 0.825759 | + | 0.564023i | \(0.190747\pi\) | ||||
−0.825759 | + | 0.564023i | \(0.809253\pi\) | |||||||
\(734\) | 7692.11 | − | 6456.33i | 0.386813 | − | 0.324670i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8278.27 | − | 22693.6i | −0.414594 | − | 1.13654i | ||||
\(737\) | 4566.59 | 0.228240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19233.7i | − | 0.957406i | −0.877977 | − | 0.478703i | \(-0.841107\pi\) | ||
0.877977 | − | 0.478703i | \(-0.158893\pi\) | |||||||
\(740\) | −6310.85 | − | 1110.90i | −0.313502 | − | 0.0551859i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7210.77 | + | 28946.4i | −0.356760 | + | 1.43215i | ||||
\(743\) | 10980.6i | 0.542181i | 0.962554 | + | 0.271090i | \(0.0873842\pi\) | ||||
−0.962554 | + | 0.271090i | \(0.912616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 899.906i | − | 0.0442550i | ||||||
\(746\) | −10536.9 | + | 8844.07i | −0.517134 | + | 0.434054i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 584.698 | − | 3321.57i | 0.0285811 | − | 0.162365i | ||||
\(749\) | −12032.3 | − | 16558.9i | −0.586985 | − | 0.807807i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3799.25i | 0.184603i | 0.995731 | + | 0.0923014i | \(0.0294223\pi\) | ||||
−0.995731 | + | 0.0923014i | \(0.970578\pi\) | |||||||
\(752\) | 3597.09 | + | 1306.89i | 0.174432 | + | 0.0633743i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 567.976 | + | 676.690i | 0.0274330 | + | 0.0326838i | ||||
\(755\) | 8073.10 | 0.389153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16774.7 | −0.805400 | −0.402700 | − | 0.915332i | \(-0.631928\pi\) | ||||
−0.402700 | + | 0.915332i | \(0.631928\pi\) | |||||||
\(758\) | −11002.6 | − | 13108.5i | −0.527218 | − | 0.628131i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6480.12 | + | 3745.03i | −0.309288 | + | 0.178745i | ||||
\(761\) | 37256.0i | 1.77468i | 0.461119 | + | 0.887338i | \(0.347448\pi\) | ||||
−0.461119 | + | 0.887338i | \(0.652552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5295.00 | + | 3847.56i | −0.251235 | + | 0.182557i | ||||
\(764\) | −21795.3 | − | 3836.64i | −1.03210 | − | 0.181682i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6794.77 | − | 5703.15i | 0.320503 | − | 0.269012i | ||||
\(767\) | − | 795.498i | − | 0.0374495i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3677.87i | 0.172468i | 0.996275 | + | 0.0862338i | \(0.0274832\pi\) | ||||
−0.996275 | + | 0.0862338i | \(0.972517\pi\) | |||||||
\(770\) | −431.552 | + | 1732.39i | −0.0201975 | + | 0.0810794i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1640.56 | − | 9319.75i | 0.0764832 | − | 0.434488i | ||||
\(773\) | 1000.27i | 0.0465421i | 0.999729 | + | 0.0232711i | \(0.00740808\pi\) | ||||
−0.999729 | + | 0.0232711i | \(0.992592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25298.7 | −1.17259 | ||||||||
\(776\) | −28083.3 | + | 16230.1i | −1.29914 | + | 0.750805i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8853.78 | + | 7431.37i | −0.407999 | + | 0.342452i | ||||
\(779\) | 36519.0i | 1.67963i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3104.89 | −0.142256 | ||||||||
\(782\) | 16004.0 | − | 13432.9i | 0.731843 | − | 0.614269i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13502.8 | + | 17307.9i | −0.615107 | + | 0.788443i | ||||
\(785\) | −5205.20 | −0.236664 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29106.1 | 1.31832 | 0.659161 | − | 0.752002i | \(-0.270912\pi\) | ||||
0.659161 | + | 0.752002i | \(0.270912\pi\) | |||||||
\(788\) | 6585.48 | − | 37411.0i | 0.297713 | − | 1.69126i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10515.0 | − | 8825.70i | 0.473553 | − | 0.397474i | ||||
\(791\) | −11933.3 | + | 8671.23i | −0.536410 | + | 0.389777i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8416.59 | 0.376900 | ||||||||
\(794\) | −9006.86 | − | 10730.8i | −0.402571 | − | 0.479626i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1273.96 | − | 7237.15i | 0.0567265 | − | 0.322254i | ||||
\(797\) | 26054.3i | 1.15796i | 0.815343 | + | 0.578978i | \(0.196548\pi\) | ||||
−0.815343 | + | 0.578978i | \(0.803452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3310.33i | 0.146572i | ||||||||
\(800\) | 17851.3 | − | 6511.86i | 0.788922 | − | 0.287786i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14992.7 | − | 12584.0i | 0.660111 | − | 0.554061i | ||||
\(803\) | 5179.80 | 0.227635 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8947.75 | + | 6501.79i | −0.391760 | + | 0.284668i | ||||
\(806\) | 5855.79 | + | 6976.62i | 0.255907 | + | 0.304890i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34704.6 | + | 20056.7i | −1.51102 | + | 0.873257i | ||||
\(809\) | 29749.3 | 1.29287 | 0.646433 | − | 0.762971i | \(-0.276260\pi\) | ||||
0.646433 | + | 0.762971i | \(0.276260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2585.38 | 0.111942 | 0.0559709 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559709 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(812\) | 1519.37 | + | 3112.39i | 0.0656642 | + | 0.134512i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2478.52 | − | 2952.92i | −0.106722 | − | 0.127150i | ||||
\(815\) | −6242.44 | −0.268299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5366.87i | − | 0.229820i | ||||||
\(818\) | 27914.2 | + | 33257.2i | 1.19315 | + | 1.42153i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3066.84 | + | 17422.2i | −0.130608 | + | 0.741962i | ||||
\(821\) | 3421.88 | 0.145462 | 0.0727311 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727311 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 16719.6i | − | 0.708150i | −0.935217 | − | 0.354075i | \(-0.884796\pi\) | ||
0.935217 | − | 0.354075i | \(-0.115204\pi\) | |||||||
\(824\) | −18880.3 | − | 32669.2i | −0.798214 | − | 1.38117i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 753.828 | − | 3026.12i | 0.0317543 | − | 0.127472i | ||||
\(827\) | 2715.80i | 0.114193i | 0.998369 | + | 0.0570966i | \(0.0181843\pi\) | ||||
−0.998369 | + | 0.0570966i | \(0.981816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2183.04i | 0.0914599i | 0.998954 | + | 0.0457299i | \(0.0145614\pi\) | ||||
−0.998954 | + | 0.0457299i | \(0.985439\pi\) | |||||||
\(830\) | −7610.72 | − | 9067.45i | −0.318279 | − | 0.379200i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5927.74 | − | 3415.56i | −0.247004 | − | 0.142324i | ||||
\(833\) | −18059.0 | − | 5865.17i | −0.751150 | − | 0.243957i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5198.28i | 0.215442i | ||||||||
\(836\) | −4434.77 | − | 780.654i | −0.183468 | − | 0.0322960i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27438.8 | + | 23030.6i | −1.13109 | + | 0.949378i | ||||
\(839\) | −18292.1 | −0.752696 | −0.376348 | − | 0.926478i | \(-0.622820\pi\) | ||||
−0.376348 | + | 0.926478i | \(0.622820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23842.6 | −0.977595 | ||||||||
\(842\) | −23918.9 | + | 20076.2i | −0.978977 | + | 0.821699i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 36209.6 | + | 6373.99i | 1.47676 | + | 0.259955i | ||||
\(845\) | − | 9033.22i | − | 0.367754i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19072.8 | − | 13859.0i | 0.773729 | − | 0.562222i | ||||
\(848\) | −34255.7 | − | 12445.8i | −1.38720 | − | 0.503996i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10566.6 | + | 12589.1i | 0.426389 | + | 0.508002i | ||||
\(851\) | − | 23884.0i | − | 0.962083i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39811.6i | − | 1.59804i | −0.601307 | − | 0.799018i | \(-0.705353\pi\) | ||
0.601307 | − | 0.799018i | \(-0.294647\pi\) | |||||||
\(854\) | 32017.2 | + | 7975.71i | 1.28291 | + | 0.319582i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21652.3 | − | 12513.4i | 0.864555 | − | 0.499649i | ||||
\(857\) | 8630.80i | 0.344017i | 0.985095 | + | 0.172008i | \(0.0550256\pi\) | ||||
−0.985095 | + | 0.172008i | \(0.944974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1012.27 | −0.0402073 | −0.0201036 | − | 0.999798i | \(-0.506400\pi\) | ||||
−0.0201036 | + | 0.999798i | \(0.506400\pi\) | |||||||
\(860\) | 450.705 | − | 2560.38i | 0.0178708 | − | 0.101521i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20408.9 | + | 24315.2i | 0.806414 | + | 0.960766i | ||||
\(863\) | − | 18567.1i | − | 0.732367i | −0.930543 | − | 0.366184i | \(-0.880664\pi\) | ||
0.930543 | − | 0.366184i | \(-0.119336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9550.24 | 0.375396 | ||||||||
\(866\) | 6917.25 | + | 8241.25i | 0.271429 | + | 0.323382i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15664.6 | + | 32088.5i | 0.612546 | + | 1.25479i | ||||
\(869\) | 8259.31 | 0.322414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8012.34 | 0.311697 | ||||||||
\(872\) | −4001.39 | − | 6923.71i | −0.155395 | − | 0.268884i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17934.8 | − | 21367.6i | −0.694110 | − | 0.826967i | ||||
\(875\) | −11204.7 | − | 15419.9i | −0.432902 | − | 0.595758i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2228.75 | −0.0858149 | −0.0429075 | − | 0.999079i | \(-0.513662\pi\) | ||||
−0.0429075 | + | 0.999079i | \(0.513662\pi\) | |||||||
\(878\) | 1579.97 | − | 1326.14i | 0.0607305 | − | 0.0509739i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2050.14 | − | 744.856i | −0.0785345 | − | 0.0285331i | ||||
\(881\) | − | 28095.1i | − | 1.07440i | −0.843454 | − | 0.537201i | \(-0.819482\pi\) | ||
0.843454 | − | 0.537201i | \(-0.180518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29038.8i | 1.10672i | 0.832942 | + | 0.553361i | \(0.186655\pi\) | ||||
−0.832942 | + | 0.553361i | \(0.813345\pi\) | |||||||
\(884\) | 1025.89 | − | 5827.89i | 0.0390320 | − | 0.221734i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6912.71 | − | 8235.84i | −0.262119 | − | 0.312290i | ||||
\(887\) | 45085.5 | 1.70668 | 0.853338 | − | 0.521357i | \(-0.174574\pi\) | ||||
0.853338 | + | 0.521357i | \(0.174574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15055.3 | + | 20719.1i | 0.567986 | + | 0.781660i | ||||
\(890\) | −117.739 | + | 98.8237i | −0.00443441 | + | 0.00372200i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4145.52 | − | 23550.0i | 0.155608 | − | 0.883983i | ||||
\(893\) | 4419.75 | 0.165623 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11417.5 | 0.426421 | ||||||||
\(896\) | −19312.8 | − | 18610.2i | −0.720083 | − | 0.693888i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30348.2 | + | 25472.6i | −1.12776 | + | 0.946583i | ||||
\(899\) | 5633.75 | 0.209006 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31524.8i | − | 1.16564i | ||||||
\(902\) | −8152.06 | + | 6842.39i | −0.300924 | + | 0.252579i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9017.91 | − | 15603.9i | −0.331782 | − | 0.574092i | ||||
\(905\) | 3201.28 | 0.117585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9186.50i | − | 0.336309i | −0.985761 | − | 0.168155i | \(-0.946219\pi\) | ||
0.985761 | − | 0.168155i | \(-0.0537808\pi\) | |||||||
\(908\) | 2688.08 | − | 15270.5i | 0.0982457 | − | 0.558117i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −757.182 | + | 3039.58i | −0.0275828 | + | 0.110727i | ||||
\(911\) | − | 13945.1i | − | 0.507158i | −0.967315 | − | 0.253579i | \(-0.918392\pi\) | ||
0.967315 | − | 0.253579i | \(-0.0816077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7122.30i | − | 0.258175i | ||||||
\(914\) | 34357.6 | − | 28837.9i | 1.24338 | − | 1.04362i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41609.3 | − | 7324.50i | −1.50088 | − | 0.264201i | ||||
\(917\) | 43910.4 | − | 31907.1i | 1.58130 | − | 1.14904i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16186.3i | − | 0.580996i | −0.956876 | − | 0.290498i | \(-0.906179\pi\) | ||
0.956876 | − | 0.290498i | \(-0.0938209\pi\) | |||||||
\(920\) | −6761.74 | − | 11700.0i | −0.242313 | − | 0.419281i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13856.0 | + | 16508.1i | 0.494926 | + | 0.589658i | ||||
\(923\) | −5447.71 | −0.194273 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18787.7 | 0.667821 | ||||||||
\(926\) | 9660.37 | + | 11509.4i | 0.342829 | + | 0.408448i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3975.28 | + | 1450.12i | −0.140620 | + | 0.0512959i | ||||
\(929\) | − | 12983.8i | − | 0.458541i | −0.973363 | − | 0.229271i | \(-0.926366\pi\) | ||
0.973363 | − | 0.229271i | \(-0.0736341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7830.84 | + | 24111.3i | −0.275666 | + | 0.848783i | ||||
\(932\) | 2067.30 | − | 11744.0i | 0.0726574 | − | 0.412755i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38935.1 | − | 32679.9i | 1.36402 | − | 1.14488i | ||||
\(935\) | − | 1886.70i | − | 0.0659912i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14063.8i | − | 0.490335i | −0.969481 | − | 0.245168i | \(-0.921157\pi\) | ||
0.969481 | − | 0.245168i | \(-0.0788430\pi\) | |||||||
\(938\) | 30479.4 | + | 7592.64i | 1.06097 | + | 0.264295i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2108.54 | + | 371.167i | 0.0731628 | + | 0.0128789i | ||||
\(941\) | − | 16064.3i | − | 0.556517i | −0.960506 | − | 0.278259i | \(-0.910243\pi\) | ||
0.960506 | − | 0.278259i | \(-0.0897572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −65935.9 | −2.27696 | ||||||||
\(944\) | 3581.16 | + | 1301.10i | 0.123471 | + | 0.0448594i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1198.03 | − | 1005.56i | 0.0411749 | − | 0.0345599i | ||||
\(947\) | 4913.13i | 0.168591i | 0.996441 | + | 0.0842953i | \(0.0268639\pi\) | ||||
−0.996441 | + | 0.0842953i | \(0.973136\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9088.25 | 0.310871 | ||||||||
\(950\) | 16808.2 | − | 14107.9i | 0.574031 | − | 0.481810i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9425.13 | − | 21197.4i | 0.320872 | − | 0.721652i | ||||
\(953\) | 1609.89 | 0.0547215 | 0.0273607 | − | 0.999626i | \(-0.491290\pi\) | ||||
0.0273607 | + | 0.999626i | \(0.491290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12380.1 | −0.419487 | ||||||||
\(956\) | 16042.8 | + | 2824.02i | 0.542741 | + | 0.0955389i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25935.4 | − | 21768.8i | 0.874672 | − | 0.734151i | ||||
\(959\) | −22696.2 | + | 16491.9i | −0.764231 | + | 0.555321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28292.5 | 0.949701 | ||||||||
\(962\) | −4348.71 | − | 5181.07i | −0.145746 | − | 0.173643i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48080.8 | + | 8463.68i | 1.60641 | + | 0.282777i | ||||
\(965\) | − | 5293.75i | − | 0.176593i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9176.82i | − | 0.305177i | −0.988290 | − | 0.152589i | \(-0.951239\pi\) | ||
0.988290 | − | 0.152589i | \(-0.0487610\pi\) | |||||||
\(968\) | 14413.1 | + | 24939.4i | 0.478570 | + | 0.828083i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13898.3 | + | 11665.4i | −0.460048 | + | 0.386139i | ||||
\(971\) | −9484.07 | −0.313448 | −0.156724 | − | 0.987642i | \(-0.550093\pi\) | ||||
−0.156724 | + | 0.987642i | \(0.550093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16808.6 | − | 12213.8i | 0.553813 | − | 0.402423i | ||||
\(974\) | 29472.6 | + | 35113.8i | 0.969571 | + | 1.15515i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13766.0 | + | 37889.7i | −0.451476 | + | 1.24264i | ||||
\(977\) | −10671.9 | −0.349461 | −0.174731 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174731 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −92.4817 | −0.00301913 | ||||||||
\(980\) | −5760.72 | + | 10845.2i | −0.187775 | + | 0.353508i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8808.62 | − | 10494.6i | −0.286247 | − | 0.341036i | ||||
\(983\) | 18046.5 | 0.585547 | 0.292774 | − | 0.956182i | \(-0.405422\pi\) | ||||
0.292774 | + | 0.956182i | \(0.405422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 21250.0i | − | 0.687393i | ||||||
\(986\) | −2353.06 | − | 2803.45i | −0.0760008 | − | 0.0905478i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7781.05 | − | 1369.70i | −0.250555 | − | 0.0441053i | ||||
\(989\) | 9690.01 | 0.311552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 13201.9i | − | 0.423181i | −0.977358 | − | 0.211590i | \(-0.932136\pi\) | ||
0.977358 | − | 0.211590i | \(-0.0678643\pi\) | |||||||
\(992\) | −40984.9 | + | 14950.7i | −1.31177 | + | 0.478512i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20723.4 | − | 5162.35i | −0.661273 | − | 0.164728i | ||||
\(995\) | − | 4110.81i | − | 0.130976i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 30223.1i | − | 0.960054i | −0.877254 | − | 0.480027i | \(-0.840627\pi\) | ||
0.877254 | − | 0.480027i | \(-0.159373\pi\) | |||||||
\(998\) | 6133.25 | + | 7307.19i | 0.194534 | + | 0.231768i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.b.e.55.4 | 12 | ||
3.2 | odd | 2 | 84.4.b.b.55.9 | yes | 12 | ||
4.3 | odd | 2 | 252.4.b.f.55.3 | 12 | |||
7.6 | odd | 2 | 252.4.b.f.55.4 | 12 | |||
12.11 | even | 2 | 84.4.b.a.55.10 | yes | 12 | ||
21.20 | even | 2 | 84.4.b.a.55.9 | ✓ | 12 | ||
24.5 | odd | 2 | 1344.4.b.g.895.6 | 12 | |||
24.11 | even | 2 | 1344.4.b.h.895.6 | 12 | |||
28.27 | even | 2 | inner | 252.4.b.e.55.3 | 12 | ||
84.83 | odd | 2 | 84.4.b.b.55.10 | yes | 12 | ||
168.83 | odd | 2 | 1344.4.b.g.895.7 | 12 | |||
168.125 | even | 2 | 1344.4.b.h.895.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.9 | ✓ | 12 | 21.20 | even | 2 | ||
84.4.b.a.55.10 | yes | 12 | 12.11 | even | 2 | ||
84.4.b.b.55.9 | yes | 12 | 3.2 | odd | 2 | ||
84.4.b.b.55.10 | yes | 12 | 84.83 | odd | 2 | ||
252.4.b.e.55.3 | 12 | 28.27 | even | 2 | inner | ||
252.4.b.e.55.4 | 12 | 1.1 | even | 1 | trivial | ||
252.4.b.f.55.3 | 12 | 4.3 | odd | 2 | |||
252.4.b.f.55.4 | 12 | 7.6 | odd | 2 | |||
1344.4.b.g.895.6 | 12 | 24.5 | odd | 2 | |||
1344.4.b.g.895.7 | 12 | 168.83 | odd | 2 | |||
1344.4.b.h.895.6 | 12 | 24.11 | even | 2 | |||
1344.4.b.h.895.7 | 12 | 168.125 | even | 2 |