Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(319,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.h (of order \(2\), degree \(1\), 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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.2 | ||
Root | \(-1.37720i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.319 |
Dual form | 320.3.h.g.319.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.75441 | −0.918135 | −0.459068 | − | 0.888401i | \(-0.651816\pi\) | ||||
−0.459068 | + | 0.888401i | \(0.651816\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.30219 | + | 2.54778i | −0.860437 | + | 0.509556i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.84997 | 0.549995 | 0.274998 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274998 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41325 | −0.157028 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.19112i | − | 0.562829i | −0.959586 | − | 0.281415i | \(-0.909196\pi\) | ||
0.959586 | − | 0.281415i | \(-0.0908037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.1132i | 1.23948i | 0.784809 | + | 0.619738i | \(0.212761\pi\) | ||||
−0.784809 | + | 0.619738i | \(0.787239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.8500 | − | 7.01762i | 0.789998 | − | 0.467842i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.20875i | − | 0.306397i | −0.988195 | − | 0.153198i | \(-0.951043\pi\) | ||
0.988195 | − | 0.153198i | \(-0.0489574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 36.2264i | − | 1.90665i | −0.301944 | − | 0.953326i | \(-0.597636\pi\) | ||
0.301944 | − | 0.953326i | \(-0.402364\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.6044 | −0.504970 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.0411 | 0.958308 | 0.479154 | − | 0.877731i | \(-0.340943\pi\) | ||||
0.479154 | + | 0.877731i | \(0.340943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0176 | − | 21.9221i | 0.480705 | − | 0.876882i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.6823 | 1.06231 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.0352 | 0.690871 | 0.345435 | − | 0.938443i | \(-0.387731\pi\) | ||||
0.345435 | + | 0.938443i | \(0.387731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 26.4175i | − | 0.852177i | −0.904681 | − | 0.426089i | \(-0.859891\pi\) | ||
0.904681 | − | 0.426089i | \(-0.140109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.0529i | 0.516754i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.5633 | + | 9.80888i | −0.473237 | + | 0.280254i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 69.3219i | − | 1.87357i | −0.349911 | − | 0.936783i | \(-0.613788\pi\) | ||
0.349911 | − | 0.936783i | \(-0.386212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 44.3822i | − | 1.13801i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6220 | 0.283463 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.8542 | 0.601261 | 0.300630 | − | 0.953741i | \(-0.402803\pi\) | ||||
0.300630 | + | 0.953741i | \(0.402803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.08006 | − | 3.60065i | 0.135112 | − | 0.0800144i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −66.1853 | −1.40820 | −0.704099 | − | 0.710102i | \(-0.748649\pi\) | ||||
−0.704099 | + | 0.710102i | \(0.748649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −34.1777 | −0.697505 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.3470i | 0.281314i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.5751i | 0.746699i | 0.927691 | + | 0.373350i | \(0.121791\pi\) | ||||
−0.927691 | + | 0.373350i | \(0.878209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.7736 | + | 26.6354i | 0.286793 | + | 0.484280i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 99.7821i | 1.75056i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 27.7736i | − | 0.470739i | −0.971906 | − | 0.235370i | \(-0.924370\pi\) | ||
0.971906 | − | 0.235370i | \(-0.0756301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.1954 | 0.888449 | 0.444224 | − | 0.895916i | \(-0.353479\pi\) | ||||
0.444224 | + | 0.895916i | \(0.353479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.44096 | −0.0863645 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −41.0529 | − | 69.3219i | −0.631583 | − | 1.06649i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 107.507 | 1.60459 | 0.802293 | − | 0.596931i | \(-0.203613\pi\) | ||||
0.802293 | + | 0.596931i | \(0.203613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −60.7101 | −0.879857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70.7997i | 0.997179i | 0.866838 | + | 0.498590i | \(0.166149\pi\) | ||||
−0.866838 | + | 0.498590i | \(0.833851\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37.4351i | 0.512810i | 0.966569 | + | 0.256405i | \(0.0825380\pi\) | ||||
−0.966569 | + | 0.256405i | \(0.917462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −33.1014 | + | 60.3822i | −0.441352 | + | 0.805097i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 23.8356i | − | 0.309554i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 97.6530i | − | 1.23611i | −0.786133 | − | 0.618057i | \(-0.787920\pi\) | ||
0.786133 | − | 0.618057i | \(-0.212080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −66.2835 | −0.818315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −126.163 | −1.52003 | −0.760017 | − | 0.649904i | \(-0.774809\pi\) | ||||
−0.760017 | + | 0.649904i | \(0.774809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2707 | + | 22.4090i | 0.156126 | + | 0.263635i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55.1852 | −0.634313 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 133.635 | 1.50151 | 0.750757 | − | 0.660579i | \(-0.229689\pi\) | ||||
0.750757 | + | 0.660579i | \(0.229689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.0352i | 0.681706i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 72.7645i | 0.782414i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 92.2969 | + | 155.853i | 0.971546 | + | 1.64055i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.40900i | 0.0660722i | 0.999454 | + | 0.0330361i | \(0.0105176\pi\) | ||||
−0.999454 | + | 0.0330361i | \(0.989482\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.74960i | 0.0883798i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −121.564 | −1.20361 | −0.601803 | − | 0.798644i | \(-0.705551\pi\) | ||||
−0.601803 | + | 0.798644i | \(0.705551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.95891 | −0.0966884 | −0.0483442 | − | 0.998831i | \(-0.515394\pi\) | ||||
−0.0483442 | + | 0.998831i | \(0.515394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 45.6220 | − | 27.0176i | 0.434495 | − | 0.257311i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −134.842 | −1.26020 | −0.630102 | − | 0.776512i | \(-0.716987\pi\) | ||||
−0.630102 | + | 0.776512i | \(0.716987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 28.2306 | 0.258996 | 0.129498 | − | 0.991580i | \(-0.458663\pi\) | ||||
0.129498 | + | 0.991580i | \(0.458663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 190.941i | 1.72019i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 190.052i | − | 1.68188i | −0.541130 | − | 0.840939i | \(-0.682003\pi\) | ||
0.541130 | − | 0.840939i | \(-0.317997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −94.8249 | + | 56.1559i | −0.824564 | + | 0.488312i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 22.7719i | − | 0.194632i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 20.0535i | − | 0.168517i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 82.6700 | 0.683223 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32.0117 | −0.260258 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.15055 | + | 124.931i | 0.0332044 | + | 0.999449i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −60.0646 | −0.472950 | −0.236475 | − | 0.971638i | \(-0.575992\pi\) | ||||
−0.236475 | + | 0.971638i | \(0.575992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −71.2130 | −0.552039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 111.985i | 0.854848i | 0.904051 | + | 0.427424i | \(0.140579\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 139.470i | − | 1.04865i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −123.397 | + | 73.0763i | −0.914049 | + | 0.541306i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 42.6439i | − | 0.311269i | −0.987815 | − | 0.155635i | \(-0.950258\pi\) | ||
0.987815 | − | 0.155635i | \(-0.0497422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 222.332i | − | 1.59951i | −0.600325 | − | 0.799756i | \(-0.704962\pi\) | ||
0.600325 | − | 0.799756i | \(-0.295038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 182.301 | 1.29292 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 99.7587 | 0.697614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −86.1954 | + | 51.0454i | −0.594451 | + | 0.352037i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 94.1394 | 0.640404 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0981 | −0.134887 | −0.0674434 | − | 0.997723i | \(-0.521484\pi\) | ||||
−0.0674434 | + | 0.997723i | \(0.521484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 86.0522i | − | 0.569882i | −0.958545 | − | 0.284941i | \(-0.908026\pi\) | ||
0.958545 | − | 0.284941i | \(-0.0919741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.36126i | 0.0481128i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67.3060 | + | 113.653i | 0.434232 | + | 0.733245i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0342i | 0.102129i | 0.998695 | + | 0.0510643i | \(0.0162614\pi\) | ||||
−0.998695 | + | 0.0510643i | \(0.983739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 109.006i | − | 0.685571i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 84.8575 | 0.527065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 179.157 | 1.09912 | 0.549561 | − | 0.835454i | \(-0.314795\pi\) | ||||
0.549561 | + | 0.835454i | \(0.314795\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −43.4470 | − | 73.3646i | −0.263315 | − | 0.444634i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 137.800 | 0.825149 | 0.412574 | − | 0.910924i | \(-0.364630\pi\) | ||||
0.412574 | + | 0.910924i | \(0.364630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −90.6347 | −0.536300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 51.1969i | 0.299397i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 62.8895i | − | 0.363523i | −0.983343 | − | 0.181762i | \(-0.941820\pi\) | ||
0.983343 | − | 0.181762i | \(-0.0581799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 46.2675 | − | 84.3992i | 0.264385 | − | 0.482281i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 76.4998i | 0.432203i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 238.020i | − | 1.32972i | −0.746967 | − | 0.664861i | \(-0.768491\pi\) | ||
0.746967 | − | 0.664861i | \(-0.231509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −186.718 | −1.03159 | −0.515795 | − | 0.856712i | \(-0.672503\pi\) | ||||
−0.515795 | + | 0.856712i | \(0.672503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −149.276 | −0.815716 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 176.617 | + | 298.236i | 0.954687 | + | 1.61209i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.2480 | −0.172449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 110.426 | 0.584264 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 123.447i | − | 0.646319i | −0.946344 | − | 0.323160i | \(-0.895255\pi\) | ||
0.946344 | − | 0.323160i | \(-0.104745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 162.355i | 0.841220i | 0.907242 | + | 0.420610i | \(0.138184\pi\) | ||||
−0.907242 | + | 0.420610i | \(0.861816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 113.076 | + | 190.941i | 0.579878 | + | 0.979183i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 113.540i | 0.576344i | 0.957579 | + | 0.288172i | \(0.0930475\pi\) | ||||
−0.957579 | + | 0.288172i | \(0.906952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 325.928i | − | 1.63783i | −0.573915 | − | 0.818915i | \(-0.694576\pi\) | ||
0.573915 | − | 0.818915i | \(-0.305424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −296.118 | −1.47323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 77.1351 | 0.379976 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −50.0000 | + | 29.6103i | −0.243902 | + | 0.144441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −31.1496 | −0.150481 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −224.282 | −1.07312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 130.731i | − | 0.619580i | −0.950805 | − | 0.309790i | \(-0.899741\pi\) | ||
0.950805 | − | 0.309790i | \(-0.100259\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 195.011i | − | 0.915546i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −111.230 | + | 65.8709i | −0.517347 | + | 0.306376i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 101.707i | − | 0.468694i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 103.112i | − | 0.470829i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 83.9295 | 0.379772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −93.3889 | −0.418784 | −0.209392 | − | 0.977832i | \(-0.567149\pi\) | ||||
−0.209392 | + | 0.977832i | \(0.567149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.9839 | + | 30.9813i | −0.0754840 | + | 0.137695i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9957 | −0.0660602 | −0.0330301 | − | 0.999454i | \(-0.510516\pi\) | ||||
−0.0330301 | + | 0.999454i | \(0.510516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 144.106 | 0.629283 | 0.314641 | − | 0.949211i | \(-0.398116\pi\) | ||||
0.314641 | + | 0.949211i | \(0.398116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 65.6530i | 0.284212i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 126.528i | − | 0.543040i | −0.962433 | − | 0.271520i | \(-0.912474\pi\) | ||
0.962433 | − | 0.271520i | \(-0.0875263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 284.741 | − | 168.626i | 1.21167 | − | 0.717556i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 268.976i | 1.13492i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.65300i | − | 0.00691630i | −0.999994 | − | 0.00345815i | \(-0.998899\pi\) | ||
0.999994 | − | 0.00345815i | \(-0.00110077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 206.928 | 0.858622 | 0.429311 | − | 0.903157i | \(-0.358756\pi\) | ||||
0.429311 | + | 0.903157i | \(0.358756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −75.5692 | −0.310984 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 147.039 | − | 87.0774i | 0.600159 | − | 0.355418i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 583.722 | 2.36325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 347.503 | 1.39560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 74.1206i | − | 0.295301i | −0.989040 | − | 0.147651i | \(-0.952829\pi\) | ||
0.989040 | − | 0.147651i | \(-0.0471711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 136.459i | − | 0.539364i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.5530 | − | 61.7235i | −0.143345 | − | 0.242053i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 274.682i | − | 1.06880i | −0.845231 | − | 0.534402i | \(-0.820537\pi\) | ||
0.845231 | − | 0.534402i | \(-0.179463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 266.887i | − | 1.03045i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.3148 | −0.108486 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 75.5382 | 0.287218 | 0.143609 | − | 0.989635i | \(-0.454129\pi\) | ||||
0.143609 | + | 0.989635i | \(0.454129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −100.829 | − | 170.259i | −0.380485 | − | 0.642488i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −368.084 | −1.37859 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −314.087 | −1.16761 | −0.583804 | − | 0.811895i | \(-0.698436\pi\) | ||||
−0.583804 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 128.158i | − | 0.472908i | −0.971643 | − | 0.236454i | \(-0.924015\pi\) | ||
0.971643 | − | 0.236454i | \(-0.0759852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 170.870i | − | 0.625898i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −135.722 | − | 74.4026i | −0.493535 | − | 0.270555i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 242.118i | 0.874073i | 0.899444 | + | 0.437037i | \(0.143972\pi\) | ||||
−0.899444 | + | 0.437037i | \(0.856028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37.3345i | 0.133815i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.8562 | 0.102691 | 0.0513456 | − | 0.998681i | \(-0.483649\pi\) | ||||
0.0513456 | + | 0.998681i | \(0.483649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 269.993 | 0.954039 | 0.477020 | − | 0.878893i | \(-0.341717\pi\) | ||||
0.477020 | + | 0.878893i | \(0.341717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −254.223 | − | 429.281i | −0.892011 | − | 1.50625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.7443 | 0.155904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 261.869 | 0.906121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.6530i | − | 0.0606632i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 353.448i | 1.20631i | 0.797625 | + | 0.603154i | \(0.206089\pi\) | ||||
−0.797625 | + | 0.603154i | \(0.793911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.7611 | + | 119.487i | 0.239868 | + | 0.405042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 177.576i | − | 0.597898i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 355.152i | 1.18780i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 99.5379 | 0.330691 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 334.837 | 1.10507 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −233.159 | + | 138.078i | −0.764454 | + | 0.452715i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −260.946 | −0.849985 | −0.424993 | − | 0.905197i | \(-0.639723\pi\) | ||||
−0.424993 | + | 0.905197i | \(0.639723\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.4309 | 0.0887730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 141.570i | 0.455208i | 0.973754 | + | 0.227604i | \(0.0730892\pi\) | ||||
−0.973754 | + | 0.227604i | \(0.926911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 365.950i | 1.16917i | 0.811333 | + | 0.584584i | \(0.198742\pi\) | ||||
−0.811333 | + | 0.584584i | \(0.801258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.4080 | − | 13.8624i | 0.0743113 | − | 0.0440076i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.22805i | − | 0.0291106i | −0.999894 | − | 0.0145553i | \(-0.995367\pi\) | ||
0.999894 | − | 0.0145553i | \(-0.00463326\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 124.041i | − | 0.388842i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 371.409 | 1.15704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −188.694 | −0.584192 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 353.234 | + | 193.642i | 1.08687 | + | 0.595822i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −77.7586 | −0.237794 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −254.811 | −0.774502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 53.3799i | 0.161268i | 0.996744 | + | 0.0806342i | \(0.0256946\pi\) | ||||
−0.996744 | + | 0.0806342i | \(0.974305\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 97.9692i | 0.294202i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −462.516 | + | 273.905i | −1.38065 | + | 0.817626i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 350.458i | − | 1.03994i | −0.854186 | − | 0.519968i | \(-0.825944\pi\) | ||
0.854186 | − | 0.519968i | \(-0.174056\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 523.481i | 1.54419i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −163.554 | −0.479630 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −320.232 | −0.933620 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 261.186 | − | 154.676i | 0.757062 | − | 0.448336i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 70.8302 | 0.204122 | 0.102061 | − | 0.994778i | \(-0.467456\pi\) | ||||
0.102061 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −373.045 | −1.06890 | −0.534449 | − | 0.845201i | \(-0.679481\pi\) | ||||
−0.534449 | + | 0.845201i | \(0.679481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 462.163i | 1.31670i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 543.568i | 1.53985i | 0.638132 | + | 0.769927i | \(0.279707\pi\) | ||||
−0.638132 | + | 0.769927i | \(0.720293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −180.382 | − | 304.594i | −0.508119 | − | 0.858010i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 55.2355i | 0.154721i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 500.805i | 1.39500i | 0.716585 | + | 0.697500i | \(0.245704\pi\) | ||||
−0.716585 | + | 0.697500i | \(0.754296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −951.350 | −2.63532 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −227.707 | −0.627291 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −95.3765 | − | 161.053i | −0.261305 | − | 0.441241i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −142.499 | −0.388281 | −0.194140 | − | 0.980974i | \(-0.562192\pi\) | ||||
−0.194140 | + | 0.980974i | \(0.562192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4248 | −0.0445116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 152.363i | 0.410681i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 160.000i | 0.428954i | 0.976729 | + | 0.214477i | \(0.0688047\pi\) | ||||
−0.976729 | + | 0.214477i | \(0.931195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.4323 | − | 344.111i | −0.0304862 | − | 0.917629i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 322.832i | 0.856317i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 192.796i | 0.508698i | 0.967113 | + | 0.254349i | \(0.0818611\pi\) | ||||
−0.967113 | + | 0.254349i | \(0.918139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 165.442 | 0.434232 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −605.286 | −1.58038 | −0.790191 | − | 0.612861i | \(-0.790019\pi\) | ||||
−0.790191 | + | 0.612861i | \(0.790019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 60.7280 | + | 102.545i | 0.157735 | + | 0.266352i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36.5384 | −0.0944146 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 522.159 | 1.34231 | 0.671155 | − | 0.741317i | \(-0.265798\pi\) | ||||
0.671155 | + | 0.741317i | \(0.265798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 114.806i | − | 0.293623i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 308.452i | − | 0.784866i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 248.798 | + | 420.121i | 0.629870 | + | 1.06360i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 357.537i | − | 0.900598i | −0.892878 | − | 0.450299i | \(-0.851317\pi\) | ||
0.892878 | − | 0.450299i | \(-0.148683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 384.158i | 0.962802i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 262.506 | 0.654629 | 0.327315 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327315 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 425.670 | 1.05625 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 285.164 | − | 168.876i | 0.704108 | − | 0.416977i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −429.181 | −1.05450 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −63.2015 | −0.154527 | −0.0772634 | − | 0.997011i | \(-0.524618\pi\) | ||||
−0.0772634 | + | 0.997011i | \(0.524618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 117.459i | 0.285787i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 106.928i | − | 0.258905i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 542.776 | − | 321.435i | 1.30789 | − | 0.774542i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 612.393i | 1.46857i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 673.390i | 1.60714i | 0.595213 | + | 0.803568i | \(0.297068\pi\) | ||||
−0.595213 | + | 0.803568i | \(0.702932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −84.6877 | −0.201158 | −0.100579 | − | 0.994929i | \(-0.532070\pi\) | ||||
−0.100579 | + | 0.994929i | \(0.532070\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 93.5363 | 0.221126 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −114.186 | − | 62.5968i | −0.268674 | − | 0.147286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 208.650 | 0.488643 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −274.776 | −0.640504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 672.158i | − | 1.55953i | −0.626072 | − | 0.779766i | \(-0.715338\pi\) | ||
0.626072 | − | 0.779766i | \(-0.284662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 562.185i | 1.29835i | 0.760640 | + | 0.649174i | \(0.224885\pi\) | ||||
−0.760640 | + | 0.649174i | \(0.775115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 237.417 | − | 140.600i | 0.545786 | − | 0.323218i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 798.469i | − | 1.82716i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 384.842i | 0.876633i | 0.898821 | + | 0.438316i | \(0.144425\pi\) | ||||
−0.898821 | + | 0.438316i | \(0.855575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.3017 | 0.109528 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −461.625 | −1.04204 | −0.521021 | − | 0.853544i | \(-0.674449\pi\) | ||||
−0.521021 | + | 0.853544i | \(0.674449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −574.922 | + | 340.472i | −1.29196 | + | 0.765106i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 55.3584 | 0.123844 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 48.7390 | 0.108550 | 0.0542750 | − | 0.998526i | \(-0.482715\pi\) | ||||
0.0542750 | + | 0.998526i | \(0.482715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 71.9532i | − | 0.159542i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 237.023i | 0.523229i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −158.052 | − | 266.887i | −0.347368 | − | 0.586565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 762.588i | − | 1.66868i | −0.551248 | − | 0.834341i | \(-0.685848\pi\) | ||
0.551248 | − | 0.834341i | \(-0.314152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 149.399i | − | 0.325488i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 406.436 | 0.881639 | 0.440820 | − | 0.897596i | \(-0.354688\pi\) | ||||
0.440820 | + | 0.897596i | \(0.354688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 260.743 | 0.563159 | 0.281580 | − | 0.959538i | \(-0.409142\pi\) | ||||
0.281580 | + | 0.959538i | \(0.409142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −185.388 | − | 313.046i | −0.398684 | − | 0.673218i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 594.738 | 1.27353 | 0.636765 | − | 0.771058i | \(-0.280272\pi\) | ||||
0.636765 | + | 0.771058i | \(0.280272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 413.899 | 0.882515 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 44.1647i | − | 0.0937679i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 160.067i | − | 0.338407i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −794.157 | − | 435.355i | −1.67191 | − | 0.916537i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 55.9294i | − | 0.117252i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 534.894i | 1.11669i | 0.829609 | + | 0.558344i | \(0.188563\pi\) | ||||
−0.829609 | + | 0.558344i | \(0.811437\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1117.00 | 2.32224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −233.732 | −0.483917 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3287 | − | 27.5727i | −0.0336675 | − | 0.0568510i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −264.298 | −0.542706 | −0.271353 | − | 0.962480i | \(-0.587471\pi\) | ||||
−0.271353 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −493.471 | −1.00914 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 539.150i | − | 1.09807i | −0.835801 | − | 0.549033i | \(-0.814996\pi\) | ||
0.835801 | − | 0.549033i | \(-0.185004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 104.359i | − | 0.211681i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.2921 | − | 37.6424i | −0.0450345 | − | 0.0760453i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 272.577i | 0.548444i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 138.218i | − | 0.276991i | −0.990363 | − | 0.138495i | \(-0.955773\pi\) | ||
0.990363 | − | 0.138495i | \(-0.0442266\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −379.557 | −0.757598 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 389.170 | 0.773697 | 0.386848 | − | 0.922143i | \(-0.373564\pi\) | ||||
0.386848 | + | 0.922143i | \(0.373564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 522.992 | − | 309.719i | 1.03563 | − | 0.613305i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 249.645 | 0.492396 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 468.599 | 0.920627 | 0.460314 | − | 0.887756i | \(-0.347737\pi\) | ||||
0.460314 | + | 0.887756i | \(0.347737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 144.124i | 0.282043i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1039.06i | − | 2.02545i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.8451 | − | 25.3731i | 0.0831943 | − | 0.0492682i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 409.761i | 0.792575i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 173.223i | 0.333764i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −931.151 | −1.78724 | −0.893619 | − | 0.448826i | \(-0.851842\pi\) | ||||
−0.893619 | + | 0.448826i | \(0.851842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 227.656 | 0.435289 | 0.217645 | − | 0.976028i | \(-0.430163\pi\) | ||||
0.217645 | + | 0.976028i | \(0.430163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −127.439 | + | 232.470i | −0.242742 | + | 0.442799i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −137.602 | −0.261104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −43.1902 | −0.0816451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.2511i | 0.0739191i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 187.267i | 0.351346i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 580.115 | − | 343.548i | 1.08433 | − | 0.642145i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 655.605i | 1.22087i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 211.599i | 0.392576i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −388.174 | −0.717511 | −0.358756 | − | 0.933431i | \(-0.616799\pi\) | ||||
−0.358756 | + | 0.933431i | \(0.616799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 514.296 | 0.947139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −121.453 | + | 71.9254i | −0.222850 | + | 0.131973i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −473.059 | −0.864824 | −0.432412 | − | 0.901676i | \(-0.642337\pi\) | ||||
−0.432412 | + | 0.901676i | \(0.642337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −76.5916 | −0.139511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 725.804i | − | 1.31725i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 375.961i | − | 0.679857i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −486.475 | − | 821.463i | −0.876532 | − | 1.48011i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 419.101i | − | 0.752426i | −0.926533 | − | 0.376213i | \(-0.877226\pi\) | ||
0.926533 | − | 0.376213i | \(-0.122774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 416.594i | 0.745248i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 88.8241 | 0.158332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 145.910 | 0.259165 | 0.129582 | − | 0.991569i | \(-0.458636\pi\) | ||||
0.129582 | + | 0.991569i | \(0.458636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 484.211 | + | 817.640i | 0.857011 | + | 1.44715i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −255.189 | −0.450069 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 950.513 | 1.67050 | 0.835249 | − | 0.549872i | \(-0.185323\pi\) | ||||
0.835249 | + | 0.549872i | \(0.185323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 404.107i | − | 0.707717i | −0.935299 | − | 0.353859i | \(-0.884869\pi\) | ||
0.935299 | − | 0.353859i | \(-0.115131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 340.023i | 0.593408i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 264.882 | − | 483.186i | 0.460664 | − | 0.840324i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 847.944i | 1.46957i | 0.678298 | + | 0.734787i | \(0.262718\pi\) | ||||
−0.678298 | + | 0.734787i | \(0.737282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 447.193i | − | 0.772354i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −485.723 | −0.836011 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 245.014 | 0.420264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 58.0179 | + | 97.9692i | 0.0991760 | + | 0.167469i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 658.243 | 1.12137 | 0.560684 | − | 0.828030i | \(-0.310538\pi\) | ||||
0.560684 | + | 0.828030i | \(0.310538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −957.010 | −1.62480 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 312.735i | − | 0.529162i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 282.430i | − | 0.476274i | −0.971232 | − | 0.238137i | \(-0.923463\pi\) | ||
0.971232 | − | 0.238137i | \(-0.0765367\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.0920 | + | 86.2739i | 0.0858688 | + | 0.144998i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 897.739i | 1.50375i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 498.597i | − | 0.832382i | −0.909277 | − | 0.416191i | \(-0.863365\pi\) | ||
0.909277 | − | 0.416191i | \(-0.136635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −287.496 | −0.478363 | −0.239182 | − | 0.970975i | \(-0.576879\pi\) | ||||
−0.239182 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −151.934 | −0.251964 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −355.662 | + | 210.625i | −0.587871 | + | 0.348141i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 844.260 | 1.39087 | 0.695437 | − | 0.718587i | \(-0.255211\pi\) | ||||
0.695437 | + | 0.718587i | \(0.255211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −212.461 | −0.348869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1066.46i | − | 1.74543i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 975.340i | − | 1.59109i | −0.605892 | − | 0.795547i | \(-0.707184\pi\) | ||
0.605892 | − | 0.795547i | \(-0.292816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 137.720 | − | 81.5588i | 0.223935 | − | 0.132616i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 319.229i | 0.517389i | 0.965959 | + | 0.258695i | \(0.0832923\pi\) | ||||
−0.965959 | + | 0.258695i | \(0.916708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 845.837i | 1.36646i | 0.730205 | + | 0.683228i | \(0.239425\pi\) | ||||
−0.730205 | + | 0.683228i | \(0.760575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 632.190 | 1.01802 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 514.489 | 0.825826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −336.153 | − | 526.902i | −0.537846 | − | 0.843043i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 617.764 | 0.985269 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −361.080 | −0.574055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 322.653i | 0.511335i | 0.966765 | + | 0.255668i | \(0.0822953\pi\) | ||||
−0.966765 | + | 0.255668i | \(0.917705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 360.087i | 0.568858i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 258.409 | − | 153.032i | 0.406944 | − | 0.240995i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 550.712i | − | 0.864541i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 100.058i | − | 0.156585i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 167.659 | 0.261558 | 0.130779 | − | 0.991412i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991412i | \(0.458252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −118.227 | −0.183867 | −0.0919335 | − | 0.995765i | \(-0.529305\pi\) | ||||
−0.0919335 | + | 0.995765i | \(0.529305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 306.372 | − | 181.435i | 0.474995 | − | 0.281295i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −783.464 | −1.21092 | −0.605459 | − | 0.795876i | \(-0.707011\pi\) | ||||
−0.605459 | + | 0.795876i | \(0.707011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −171.950 | −0.264946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 280.141i | 0.430324i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.4352i | 0.0435455i | 0.999763 | + | 0.0217727i | \(0.00693102\pi\) | ||||
−0.999763 | + | 0.0217727i | \(0.993069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −285.314 | − | 481.781i | −0.435593 | − | 0.735543i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 52.9051i | − | 0.0805253i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 594.296i | 0.901814i | 0.892571 | + | 0.450907i | \(0.148899\pi\) | ||||
−0.892571 | + | 0.450907i | \(0.851101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495.511 | 0.749638 | 0.374819 | − | 0.927098i | \(-0.377705\pi\) | ||||
0.374819 | + | 0.927098i | \(0.377705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −231.176 | −0.348682 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 355.340 | + | 600.028i | 0.534346 | + | 0.902297i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 441.599 | 0.662067 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 257.231 | 0.384501 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 335.530i | − | 0.500045i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 168.874i | − | 0.250927i | −0.992098 | − | 0.125464i | \(-0.959958\pi\) | ||
0.992098 | − | 0.125464i | \(-0.0400418\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 344.693 | − | 628.775i | 0.510657 | − | 0.931519i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 895.899i | − | 1.32334i | −0.749797 | − | 0.661668i | \(-0.769849\pi\) | ||
0.749797 | − | 0.661668i | \(-0.230151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.6745i | 0.0363394i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.3042 | 0.0606522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 359.410 | 0.526223 | 0.263112 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263112 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 108.647 | + | 183.462i | 0.158609 | + | 0.267828i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −396.926 | −0.577767 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −637.680 | −0.925516 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 515.701i | 0.746311i | 0.927769 | + | 0.373155i | \(0.121724\pi\) | ||||
−0.927769 | + | 0.373155i | \(0.878276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.6857i | 0.0486085i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 566.454 | + | 956.514i | 0.815041 | + | 1.37628i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 60.5360i | − | 0.0868523i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 348.510i | 0.498584i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1370.37 | 1.95488 | 0.977438 | − | 0.211221i | \(-0.0677441\pi\) | ||||
0.977438 | + | 0.211221i | \(0.0677441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2511.28 | −3.57224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −784.293 | + | 464.463i | −1.11247 | + | 0.658813i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −468.018 | −0.661978 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 662.128 | 0.933890 | 0.466945 | − | 0.884286i | \(-0.345355\pi\) | ||||
0.466945 | + | 0.884286i | \(0.345355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 138.008i | 0.194104i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 582.270i | − | 0.816649i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −429.181 | + | 254.163i | −0.600253 | + | 0.355473i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.55302i | 0.00635010i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 370.003i | − | 0.514608i | −0.966331 | − | 0.257304i | \(-0.917166\pi\) | ||
0.966331 | − | 0.257304i | \(-0.0828341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.3415 | −0.0531782 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −569.964 | −0.788331 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 240.776 | − | 439.214i | 0.332105 | − | 0.605812i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −607.695 | −0.835894 | −0.417947 | − | 0.908471i | \(-0.637250\pi\) | ||||
−0.417947 | + | 0.908471i | \(0.637250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 804.700 | 1.10384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 134.668i | − | 0.184224i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1066.76i | − | 1.45533i | −0.685931 | − | 0.727666i | \(-0.740605\pi\) | ||
0.685931 | − | 0.727666i | \(-0.259395\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −405.005 | + | 239.847i | −0.551027 | + | 0.326322i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 665.591i | − | 0.903108i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 558.366i | 0.755570i | 0.925893 | + | 0.377785i | \(0.123314\pi\) | ||||
−0.925893 | + | 0.377785i | \(0.876686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1607.81 | −2.16978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1112.00 | 1.49664 | 0.748319 | − | 0.663339i | \(-0.230861\pi\) | ||||
0.748319 | + | 0.663339i | \(0.230861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 86.4659 | − | 51.2056i | 0.116062 | − | 0.0687324i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 178.299 | 0.238687 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −519.137 | −0.693107 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1207.34i | 1.60764i | 0.594873 | + | 0.803820i | \(0.297202\pi\) | ||||
−0.594873 | + | 0.803820i | \(0.702798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 204.158i | 0.271127i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 219.242 | + | 370.213i | 0.290387 | + | 0.490348i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 87.7776i | − | 0.115955i | −0.998318 | − | 0.0579773i | \(-0.981535\pi\) | ||
0.998318 | − | 0.0579773i | \(-0.0184651\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 375.864i | 0.495209i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 67.0202 | 0.0880686 | 0.0440343 | − | 0.999030i | \(-0.485979\pi\) | ||||
0.0440343 | + | 0.999030i | \(0.485979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 108.687 | 0.142447 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.7549 | − | 31.6695i | −0.0245162 | − | 0.0413980i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 447.522 | 0.583470 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 342.869 | 0.445863 | 0.222932 | − | 0.974834i | \(-0.428437\pi\) | ||||
0.222932 | + | 0.974834i | \(0.428437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 756.587i | 0.981306i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 244.756i | 0.316631i | 0.987389 | + | 0.158316i | \(0.0506063\pi\) | ||||
−0.987389 | + | 0.158316i | \(0.949394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −579.126 | − | 317.475i | −0.747259 | − | 0.409646i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 735.116i | 0.946095i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 421.023i | − | 0.540466i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 438.330 | 0.561242 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 574.657 | 0.733917 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.8516 | − | 68.9821i | −0.0520403 | − | 0.0878753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1120.38 | −1.42361 | −0.711806 | − | 0.702376i | \(-0.752123\pi\) | ||||
−0.711806 | + | 0.702376i | \(0.752123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −208.063 | −0.263705 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 731.695i | − | 0.925025i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 873.260i | 1.10121i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 277.723 | + | 468.963i | 0.349337 | + | 0.589891i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1344.51i | 1.68696i | 0.537161 | + | 0.843480i | \(0.319497\pi\) | ||||
−0.537161 | + | 0.843480i | \(0.680503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 344.742i | 0.431467i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −188.859 | −0.235779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 231.765 | 0.288624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −365.073 | + | 216.198i | −0.453507 | + | 0.268569i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 865.122 | 1.07202 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 345.363 | 0.426901 | 0.213451 | − | 0.976954i | \(-0.431530\pi\) | ||||
0.213451 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1275.44i | 1.57268i | 0.617797 | + | 0.786338i | \(0.288025\pi\) | ||||
−0.617797 | + | 0.786338i | \(0.711975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 352.999i | 0.434193i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −770.766 | + | 456.452i | −0.945725 | + | 0.560064i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 936.604i | − | 1.14639i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 87.6713i | − | 0.107047i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1257.99 | −1.53226 | −0.766131 | − | 0.642684i | \(-0.777821\pi\) | ||||
−0.766131 | + | 0.642684i | \(0.777821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −206.093 | −0.250417 | −0.125208 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125208 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 373.834 | + | 204.935i | 0.453132 | + | 0.248406i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −615.606 | −0.744384 | −0.372192 | − | 0.928156i | \(-0.621394\pi\) | ||||
−0.372192 | + | 0.928156i | \(0.621394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1214.12 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 666.892i | − | 0.802518i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 178.023i | 0.213713i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −592.841 | + | 351.084i | −0.709989 | + | 0.420460i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 757.715i | − | 0.905275i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1338.99i | 1.59593i | 0.602701 | + | 0.797967i | \(0.294091\pi\) | ||||
−0.602701 | + | 0.797967i | \(0.705909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −439.589 | −0.522698 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −79.4817 | −0.0942844 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 389.928 | − | 230.917i | 0.461453 | − | 0.273275i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 318.277 | 0.375769 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −743.671 | −0.875937 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1527.93i | − | 1.79545i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 112.066i | 0.131379i | 0.997840 | + | 0.0656893i | \(0.0209246\pi\) | ||||
−0.997840 | + | 0.0656893i | \(0.979075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −130.438 | − | 220.259i | −0.152560 | − | 0.257612i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1089.15i | − | 1.27089i | −0.772148 | − | 0.635443i | \(-0.780817\pi\) | ||
0.772148 | − | 0.635443i | \(-0.219183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 719.610i | − | 0.837729i | −0.908049 | − | 0.418865i | \(-0.862428\pi\) | ||
0.908049 | − | 0.418865i | \(-0.137572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −123.244 | −0.143141 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −114.135 | −0.132254 | −0.0661269 | − | 0.997811i | \(-0.521064\pi\) | ||||
−0.0661269 | + | 0.997811i | \(0.521064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 160.229 | + | 270.563i | 0.185236 | + | 0.312789i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −721.293 | −0.831942 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −604.582 | −0.695721 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1732.28i | 1.98884i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.05752i | − | 0.0103752i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.9795 | + | 480.981i | 0.0182623 | + | 0.549692i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1427.99i | 1.62827i | 0.580675 | + | 0.814135i | \(0.302789\pi\) | ||||
−0.580675 | + | 0.814135i | \(0.697211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 973.539i | − | 1.10755i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 364.165 | 0.413354 | 0.206677 | − | 0.978409i | \(-0.433735\pi\) | ||||
0.206677 | + | 0.978409i | \(0.433735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 800.458 | 0.906521 | 0.453260 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453260 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −194.905 | − | 329.117i | −0.220231 | − | 0.371883i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 591.672 | 0.667049 | 0.333524 | − | 0.942741i | \(-0.391762\pi\) | ||||
0.333524 | + | 0.942741i | \(0.391762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −231.247 | −0.260120 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 410.369i | 0.460572i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2397.65i | 2.68494i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 606.424 | + | 1024.01i | 0.677568 | + | 1.14414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 978.233i | − | 1.09056i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 529.281i | − | 0.588744i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 206.136 | 0.228786 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −274.168 | −0.303619 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 803.295 | − | 475.716i | 0.887618 | − | 0.525653i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −545.657 | −0.601606 | −0.300803 | − | 0.953686i | \(-0.597255\pi\) | ||||
−0.300803 | + | 0.953686i | \(0.597255\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 171.801 | 0.189000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 929.286i | 1.02007i | 0.860153 | + | 0.510036i | \(0.170368\pi\) | ||||
−0.860153 | + | 0.510036i | \(0.829632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 781.089i | 0.855520i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 642.213 | − | 380.323i | 0.701873 | − | 0.415653i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 431.139i | 0.470163i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 171.353i | − | 0.186456i | −0.995645 | − | 0.0932278i | \(-0.970282\pi\) | ||
0.995645 | − | 0.0932278i | \(-0.0297185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 718.750 | 0.780402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1140.81 | −1.23598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1519.68 | − | 833.085i | −1.64290 | − | 0.900632i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0744 | 0.0151828 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1178.62 | −1.26870 | −0.634350 | − | 0.773046i | \(-0.718732\pi\) | ||||
−0.634350 | + | 0.773046i | \(0.718732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1238.14i | 1.32990i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 389.940i | − | 0.417943i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 138.737 | − | 82.1609i | 0.148382 | − | 0.0878726i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 412.624i | − | 0.440367i | −0.975458 | − | 0.220183i | \(-0.929334\pi\) | ||
0.975458 | − | 0.220183i | \(-0.0706656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1007.97i | − | 1.07346i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1121.33 | 1.19163 | 0.595817 | − | 0.803120i | \(-0.296828\pi\) | ||||
0.595817 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 256.161 | 0.271645 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −475.073 | + | 281.341i | −0.502723 | + | 0.297716i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1395.22 | −1.47331 | −0.736653 | − | 0.676271i | \(-0.763595\pi\) | ||||
−0.736653 | + | 0.676271i | \(0.763595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −603.199 | −0.635615 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.4178i | 0.0267275i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 476.331i | 0.499822i | 0.968269 | + | 0.249911i | \(0.0804014\pi\) | ||||
−0.968269 | + | 0.249911i | \(0.919599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 314.516 | + | 531.092i | 0.329336 | + | 0.556117i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 341.658i | 0.357010i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 164.178i | − | 0.171197i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 263.116 | 0.273794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 190.565 | 0.197887 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −413.646 | − | 698.484i | −0.428649 | − | 0.723817i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −140.846 | −0.145653 | −0.0728263 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728263 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 519.740 | 0.536367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1144.98i | − | 1.17918i | −0.807704 | − | 0.589588i | \(-0.799290\pi\) | ||
0.807704 | − | 0.589588i | \(-0.200710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 855.971i | − | 0.879724i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −972.950 | − | 533.369i | −0.997898 | − | 0.547045i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.8912i | 0.0572070i | 0.999591 | + | 0.0286035i | \(0.00910602\pi\) | ||||
−0.999591 | + | 0.0286035i | \(0.990894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 827.349i | − | 0.845096i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.8969 | −0.0406696 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1028.74 | −1.04653 | −0.523267 | − | 0.852169i | \(-0.675287\pi\) | ||||
−0.523267 | + | 0.852169i | \(0.675287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −289.275 | − | 488.469i | −0.293680 | − | 0.495908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 701.853 | 0.711098 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 569.855 | 0.576193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 666.207i | − | 0.672257i | −0.941816 | − | 0.336129i | \(-0.890882\pi\) | ||
0.941816 | − | 0.336129i | \(-0.109118\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 147.030i | − | 0.148066i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 830.394 | + | 1402.20i | 0.834567 | + | 1.40925i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 737.006i | 0.739224i | 0.929186 | + | 0.369612i | \(0.120509\pi\) | ||||
−0.929186 | + | 0.369612i | \(0.879491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1988.31i | − | 1.99030i |
(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 | 320.3.h.g.319.2 | 6 | ||
4.3 | odd | 2 | 320.3.h.f.319.6 | 6 | |||
5.2 | odd | 4 | 1600.3.b.v.1151.5 | 6 | |||
5.3 | odd | 4 | 1600.3.b.w.1151.2 | 6 | |||
5.4 | even | 2 | 320.3.h.f.319.5 | 6 | |||
8.3 | odd | 2 | 160.3.h.b.159.1 | yes | 6 | ||
8.5 | even | 2 | 160.3.h.a.159.5 | ✓ | 6 | ||
16.3 | odd | 4 | 1280.3.e.h.639.5 | 6 | |||
16.5 | even | 4 | 1280.3.e.g.639.5 | 6 | |||
16.11 | odd | 4 | 1280.3.e.f.639.2 | 6 | |||
16.13 | even | 4 | 1280.3.e.i.639.2 | 6 | |||
20.3 | even | 4 | 1600.3.b.w.1151.5 | 6 | |||
20.7 | even | 4 | 1600.3.b.v.1151.2 | 6 | |||
20.19 | odd | 2 | inner | 320.3.h.g.319.1 | 6 | ||
24.5 | odd | 2 | 1440.3.j.a.1279.2 | 6 | |||
24.11 | even | 2 | 1440.3.j.b.1279.2 | 6 | |||
40.3 | even | 4 | 800.3.b.i.351.2 | 6 | |||
40.13 | odd | 4 | 800.3.b.i.351.5 | 6 | |||
40.19 | odd | 2 | 160.3.h.a.159.6 | yes | 6 | ||
40.27 | even | 4 | 800.3.b.h.351.5 | 6 | |||
40.29 | even | 2 | 160.3.h.b.159.2 | yes | 6 | ||
40.37 | odd | 4 | 800.3.b.h.351.2 | 6 | |||
80.19 | odd | 4 | 1280.3.e.g.639.2 | 6 | |||
80.29 | even | 4 | 1280.3.e.f.639.5 | 6 | |||
80.59 | odd | 4 | 1280.3.e.i.639.5 | 6 | |||
80.69 | even | 4 | 1280.3.e.h.639.2 | 6 | |||
120.29 | odd | 2 | 1440.3.j.b.1279.1 | 6 | |||
120.59 | even | 2 | 1440.3.j.a.1279.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.5 | ✓ | 6 | 8.5 | even | 2 | ||
160.3.h.a.159.6 | yes | 6 | 40.19 | odd | 2 | ||
160.3.h.b.159.1 | yes | 6 | 8.3 | odd | 2 | ||
160.3.h.b.159.2 | yes | 6 | 40.29 | even | 2 | ||
320.3.h.f.319.5 | 6 | 5.4 | even | 2 | |||
320.3.h.f.319.6 | 6 | 4.3 | odd | 2 | |||
320.3.h.g.319.1 | 6 | 20.19 | odd | 2 | inner | ||
320.3.h.g.319.2 | 6 | 1.1 | even | 1 | trivial | ||
800.3.b.h.351.2 | 6 | 40.37 | odd | 4 | |||
800.3.b.h.351.5 | 6 | 40.27 | even | 4 | |||
800.3.b.i.351.2 | 6 | 40.3 | even | 4 | |||
800.3.b.i.351.5 | 6 | 40.13 | odd | 4 | |||
1280.3.e.f.639.2 | 6 | 16.11 | odd | 4 | |||
1280.3.e.f.639.5 | 6 | 80.29 | even | 4 | |||
1280.3.e.g.639.2 | 6 | 80.19 | odd | 4 | |||
1280.3.e.g.639.5 | 6 | 16.5 | even | 4 | |||
1280.3.e.h.639.2 | 6 | 80.69 | even | 4 | |||
1280.3.e.h.639.5 | 6 | 16.3 | odd | 4 | |||
1280.3.e.i.639.2 | 6 | 16.13 | even | 4 | |||
1280.3.e.i.639.5 | 6 | 80.59 | odd | 4 | |||
1440.3.j.a.1279.1 | 6 | 120.59 | even | 2 | |||
1440.3.j.a.1279.2 | 6 | 24.5 | odd | 2 | |||
1440.3.j.b.1279.1 | 6 | 120.29 | odd | 2 | |||
1440.3.j.b.1279.2 | 6 | 24.11 | even | 2 | |||
1600.3.b.v.1151.2 | 6 | 20.7 | even | 4 | |||
1600.3.b.v.1151.5 | 6 | 5.2 | odd | 4 | |||
1600.3.b.w.1151.2 | 6 | 5.3 | odd | 4 | |||
1600.3.b.w.1151.5 | 6 | 20.3 | even | 4 |