Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.5 | ||
Root | \(1.37720i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.i.639.2 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.75441i | 0.918135i | 0.888401 | + | 0.459068i | \(0.151816\pi\) | ||||
−0.888401 | + | 0.459068i | \(0.848184\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.54778 | − | 4.30219i | 0.509556 | − | 0.860437i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.84997 | −0.549995 | −0.274998 | − | 0.961445i | \(-0.588677\pi\) | ||||
−0.274998 | + | 0.961445i | \(0.588677\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41325 | 0.157028 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.19112 | −0.562829 | −0.281415 | − | 0.959586i | \(-0.590804\pi\) | ||||
−0.281415 | + | 0.959586i | \(0.590804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.1132 | −1.23948 | −0.619738 | − | 0.784809i | \(-0.712761\pi\) | ||||
−0.619738 | + | 0.784809i | \(0.712761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.8500 | + | 7.01762i | 0.789998 | + | 0.467842i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.20875i | 0.306397i | 0.988195 | + | 0.153198i | \(0.0489574\pi\) | ||||
−0.988195 | + | 0.153198i | \(0.951043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.2264 | 1.90665 | 0.953326 | − | 0.301944i | \(-0.0976357\pi\) | ||||
0.953326 | + | 0.301944i | \(0.0976357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 10.6044i | − | 0.504970i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22.0411 | −0.958308 | −0.479154 | − | 0.877731i | \(-0.659057\pi\) | ||||
−0.479154 | + | 0.877731i | \(0.659057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.0176 | − | 21.9221i | −0.480705 | − | 0.876882i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.6823i | 1.06231i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 20.0352i | − | 0.690871i | −0.938443 | − | 0.345435i | \(-0.887731\pi\) | ||
0.938443 | − | 0.345435i | \(-0.112269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.4175i | 0.852177i | 0.904681 | + | 0.426089i | \(0.140109\pi\) | ||||
−0.904681 | + | 0.426089i | \(0.859891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 17.0529i | − | 0.516754i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.80888 | + | 16.5633i | −0.280254 | + | 0.473237i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −69.3219 | −1.87357 | −0.936783 | − | 0.349911i | \(-0.886212\pi\) | ||||
−0.936783 | + | 0.349911i | \(0.886212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 44.3822i | − | 1.13801i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6220 | −0.283463 | −0.141732 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141732 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.8542i | 0.601261i | 0.953741 | + | 0.300630i | \(0.0971971\pi\) | ||||
−0.953741 | + | 0.300630i | \(0.902803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.60065 | − | 6.08006i | 0.0800144 | − | 0.135112i | ||||
\(46\) | 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 | ||||||||
\(51\) | −14.3470 | −0.281314 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.5751 | 0.746699 | 0.373350 | − | 0.927691i | \(-0.378209\pi\) | ||||
0.373350 | + | 0.927691i | \(0.378209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.7736 | + | 26.6354i | −0.286793 | + | 0.484280i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 99.7821i | 1.75056i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27.7736 | −0.470739 | −0.235370 | − | 0.971906i | \(-0.575630\pi\) | ||||
−0.235370 | + | 0.971906i | \(0.575630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 54.1954i | − | 0.888449i | −0.895916 | − | 0.444224i | \(-0.853479\pi\) | ||
0.895916 | − | 0.444224i | \(-0.146521\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.44096 | −0.0863645 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −41.0529 | + | 69.3219i | −0.631583 | + | 1.06649i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 107.507i | − | 1.60459i | −0.596931 | − | 0.802293i | \(-0.703613\pi\) | ||
0.596931 | − | 0.802293i | \(-0.296387\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 60.7101i | − | 0.879857i | ||||||
\(70\) | 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 | ||||||||
\(75\) | 60.3822 | − | 33.1014i | 0.805097 | − | 0.441352i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.8356 | 0.309554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 97.6530i | 1.23611i | 0.786133 | + | 0.618057i | \(0.212080\pi\) | ||||
−0.786133 | + | 0.618057i | \(0.787920\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −66.2835 | −0.818315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 126.163i | 1.52003i | 0.649904 | + | 0.760017i | \(0.274809\pi\) | ||||
−0.649904 | + | 0.760017i | \(0.725191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.4090 | + | 13.2707i | 0.263635 | + | 0.156126i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 55.1852 | 0.634313 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −133.635 | −1.50151 | −0.750757 | − | 0.660579i | \(-0.770311\pi\) | ||||
−0.750757 | + | 0.660579i | \(0.770311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.0352 | 0.681706 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −72.7645 | −0.782414 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 92.2969 | − | 155.853i | 0.971546 | − | 1.64055i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.40900i | − | 0.0660722i | −0.999454 | − | 0.0330361i | \(-0.989482\pi\) | ||
0.999454 | − | 0.0330361i | \(-0.0105176\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.74960 | −0.0883798 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 121.564i | − | 1.20361i | −0.798644 | − | 0.601803i | \(-0.794449\pi\) | ||
0.798644 | − | 0.601803i | \(-0.205551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.95891 | 0.0966884 | 0.0483442 | − | 0.998831i | \(-0.484606\pi\) | ||||
0.0483442 | + | 0.998831i | \(0.484606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −45.6220 | − | 27.0176i | −0.434495 | − | 0.257311i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 134.842i | − | 1.26020i | −0.776512 | − | 0.630102i | \(-0.783013\pi\) | ||
0.776512 | − | 0.630102i | \(-0.216987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 28.2306i | − | 0.258996i | −0.991580 | − | 0.129498i | \(-0.958663\pi\) | ||
0.991580 | − | 0.129498i | \(-0.0413367\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 190.941i | − | 1.72019i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 190.052i | 1.68188i | 0.541130 | + | 0.840939i | \(0.317997\pi\) | ||||
−0.541130 | + | 0.840939i | \(0.682003\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −56.1559 | + | 94.8249i | −0.488312 | + | 0.824564i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.7719 | −0.194632 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 20.0535i | − | 0.168517i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −82.6700 | −0.683223 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 32.0117i | − | 0.260258i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124.931 | − | 4.15055i | −0.999449 | − | 0.0332044i | ||||
\(126\) | 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 | ||||||||
\(131\) | −111.985 | −0.854848 | −0.427424 | − | 0.904051i | \(-0.640579\pi\) | ||||
−0.427424 | + | 0.904051i | \(0.640579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −139.470 | −1.04865 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | −222.332 | −1.59951 | −0.799756 | − | 0.600325i | \(-0.795038\pi\) | ||||
−0.799756 | + | 0.600325i | \(0.795038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 182.301i | − | 1.29292i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 99.7587 | 0.697614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −86.1954 | − | 51.0454i | −0.594451 | − | 0.352037i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 94.1394i | − | 0.640404i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 20.0981i | − | 0.134887i | −0.997723 | − | 0.0674434i | \(-0.978516\pi\) | ||
0.997723 | − | 0.0674434i | \(-0.0214842\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 113.653 | + | 67.3060i | 0.733245 | + | 0.434232i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0342 | −0.102129 | −0.0510643 | − | 0.998695i | \(-0.516261\pi\) | ||||
−0.0510643 | + | 0.998695i | \(0.516261\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 109.006i | 0.685571i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 84.8575 | 0.527065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 179.157i | − | 1.09912i | −0.835454 | − | 0.549561i | \(-0.814795\pi\) | ||
0.835454 | − | 0.549561i | \(-0.185205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −73.3646 | − | 43.4470i | −0.444634 | − | 0.263315i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −137.800 | −0.825149 | −0.412574 | − | 0.910924i | \(-0.635370\pi\) | ||||
−0.412574 | + | 0.910924i | \(0.635370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 90.6347 | 0.536300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 51.1969 | 0.299397 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 62.8895 | 0.363523 | 0.181762 | − | 0.983343i | \(-0.441820\pi\) | ||||
0.181762 | + | 0.983343i | \(0.441820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 46.2675 | + | 84.3992i | 0.264385 | + | 0.482281i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 76.4998i | − | 0.432203i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 238.020 | 1.32972 | 0.664861 | − | 0.746967i | \(-0.268491\pi\) | ||||
0.664861 | + | 0.746967i | \(0.268491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 186.718i | − | 1.03159i | −0.856712 | − | 0.515795i | \(-0.827497\pi\) | ||
0.856712 | − | 0.515795i | \(-0.172503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 149.276 | 0.815716 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −176.617 | + | 298.236i | −0.954687 | + | 1.61209i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 32.2480i | − | 0.172449i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 110.426i | − | 0.584264i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 123.447i | 0.646319i | 0.946344 | + | 0.323160i | \(0.104745\pi\) | ||||
−0.946344 | + | 0.323160i | \(0.895255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 162.355i | − | 0.841220i | −0.907242 | − | 0.420610i | \(-0.861816\pi\) | ||
0.907242 | − | 0.420610i | \(-0.138184\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −190.941 | − | 113.076i | −0.979183 | − | 0.579878i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 113.540 | 0.576344 | 0.288172 | − | 0.957579i | \(-0.406952\pi\) | ||||
0.288172 | + | 0.957579i | \(0.406952\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 77.1351i | 0.379976i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.6103 | + | 50.0000i | −0.144441 | + | 0.243902i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −31.1496 | −0.150481 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −224.282 | −1.07312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 130.731 | 0.619580 | 0.309790 | − | 0.950805i | \(-0.399741\pi\) | ||||
0.309790 | + | 0.950805i | \(0.399741\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −195.011 | −0.915546 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 111.230 | + | 65.8709i | 0.517347 | + | 0.306376i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 101.707i | − | 0.468694i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −103.112 | −0.470829 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 83.9295i | − | 0.379772i | ||||||
\(222\) | 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 | ||||||||
\(227\) | 14.9957i | 0.0660602i | 0.999454 | + | 0.0330301i | \(0.0105157\pi\) | ||||
−0.999454 | + | 0.0330301i | \(0.989484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 144.106i | 0.629283i | 0.949211 | + | 0.314641i | \(0.101884\pi\) | ||||
−0.949211 | + | 0.314641i | \(0.898116\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | −168.626 | + | 284.741i | −0.717556 | + | 1.21167i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −268.976 | −1.13492 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65300i | 0.00691630i | 0.999994 | + | 0.00345815i | \(0.00110077\pi\) | ||||
−0.999994 | + | 0.00345815i | \(0.998899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 206.928 | 0.858622 | 0.429311 | − | 0.903157i | \(-0.358756\pi\) | ||||
0.429311 | + | 0.903157i | \(0.358756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 75.5692i | 0.310984i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −87.0774 | + | 147.039i | −0.355418 | + | 0.600159i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −583.722 | −2.36325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −347.503 | −1.39560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −74.1206 | −0.295301 | −0.147651 | − | 0.989040i | \(-0.547171\pi\) | ||||
−0.147651 | + | 0.989040i | \(0.547171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 136.459 | 0.539364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.5530 | + | 61.7235i | −0.143345 | + | 0.242053i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 274.682i | 1.06880i | 0.845231 | + | 0.534402i | \(0.179463\pi\) | ||||
−0.845231 | + | 0.534402i | \(0.820537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 266.887 | 1.03045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 28.3148i | − | 0.108486i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −75.5382 | −0.287218 | −0.143609 | − | 0.989635i | \(-0.545871\pi\) | ||||
−0.143609 | + | 0.989635i | \(0.545871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 100.829 | − | 170.259i | 0.380485 | − | 0.642488i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 368.084i | − | 1.37859i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 314.087i | 1.16761i | 0.811895 | + | 0.583804i | \(0.198436\pi\) | ||||
−0.811895 | + | 0.583804i | \(0.801564\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 128.158i | 0.472908i | 0.971643 | + | 0.236454i | \(0.0759852\pi\) | ||||
−0.971643 | + | 0.236454i | \(0.924015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 170.870i | 0.625898i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 74.4026 | + | 135.722i | 0.270555 | + | 0.493535i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 242.118 | 0.874073 | 0.437037 | − | 0.899444i | \(-0.356028\pi\) | ||||
0.437037 | + | 0.899444i | \(0.356028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37.3345i | 0.133815i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.8562 | −0.102691 | −0.0513456 | − | 0.998681i | \(-0.516351\pi\) | ||||
−0.0513456 | + | 0.998681i | \(0.516351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 269.993i | 0.954039i | 0.878893 | + | 0.477020i | \(0.158283\pi\) | ||||
−0.878893 | + | 0.477020i | \(0.841717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 429.281 | + | 254.223i | 1.50625 | + | 0.892011i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.7443 | 0.155904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 261.869 | 0.906121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.6530 | 0.0606632 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 353.448 | 1.20631 | 0.603154 | − | 0.797625i | \(-0.293911\pi\) | ||||
0.603154 | + | 0.797625i | \(0.293911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −70.7611 | + | 119.487i | −0.239868 | + | 0.405042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 177.576i | − | 0.597898i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 355.152 | 1.18780 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 99.5379i | − | 0.330691i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 334.837 | 1.10507 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −233.159 | − | 138.078i | −0.764454 | − | 0.452715i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 260.946i | 0.849985i | 0.905197 | + | 0.424993i | \(0.139723\pi\) | ||||
−0.905197 | + | 0.424993i | \(0.860277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.4309i | 0.0887730i | ||||||||
\(310\) | 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 | ||||||||
\(315\) | −13.8624 | + | 23.4080i | −0.0440076 | + | 0.0743113i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.22805 | 0.0291106 | 0.0145553 | − | 0.999894i | \(-0.495367\pi\) | ||||
0.0145553 | + | 0.999894i | \(0.495367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 124.041i | 0.388842i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 371.409 | 1.15704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 188.694i | 0.584192i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 193.642 | + | 353.234i | 0.595822 | + | 1.08687i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 77.7586 | 0.237794 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 254.811 | 0.774502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 53.3799 | 0.161268 | 0.0806342 | − | 0.996744i | \(-0.474305\pi\) | ||||
0.0806342 | + | 0.996744i | \(0.474305\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −97.9692 | −0.294202 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −462.516 | − | 273.905i | −1.38065 | − | 0.817626i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 350.458i | 1.03994i | 0.854186 | + | 0.519968i | \(0.174056\pi\) | ||||
−0.854186 | + | 0.519968i | \(0.825944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −523.481 | −1.54419 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 163.554i | − | 0.479630i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 320.232 | 0.933620 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −261.186 | − | 154.676i | −0.757062 | − | 0.448336i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 70.8302i | 0.204122i | 0.994778 | + | 0.102061i | \(0.0325436\pi\) | ||||
−0.994778 | + | 0.102061i | \(0.967456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 373.045i | 1.06890i | 0.845201 | + | 0.534449i | \(0.179481\pi\) | ||||
−0.845201 | + | 0.534449i | \(0.820519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 462.163i | − | 1.31670i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 543.568i | − | 1.53985i | −0.638132 | − | 0.769927i | \(-0.720293\pi\) | ||
0.638132 | − | 0.769927i | \(-0.279707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 304.594 | + | 180.382i | 0.858010 | + | 0.508119i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 55.2355 | 0.154721 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − | 227.707i | − | 0.627291i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 161.053 | + | 95.3765i | 0.441241 | + | 0.261305i | ||||
\(366\) | 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 | ||||||||
\(371\) | −152.363 | −0.410681 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 160.000 | 0.428954 | 0.214477 | − | 0.976729i | \(-0.431195\pi\) | ||||
0.214477 | + | 0.976729i | \(0.431195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.4323 | − | 344.111i | 0.0304862 | − | 0.917629i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 322.832i | 0.856317i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 192.796 | 0.508698 | 0.254349 | − | 0.967113i | \(-0.418139\pi\) | ||||
0.254349 | + | 0.967113i | \(0.418139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 165.442i | − | 0.434232i | ||||||
\(382\) | 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 | ||||||||
\(387\) | 36.5384i | 0.0944146i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 522.159i | 1.34231i | 0.741317 | + | 0.671155i | \(0.234202\pi\) | ||||
−0.741317 | + | 0.671155i | \(0.765798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 114.806i | − | 0.293623i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 308.452i | − | 0.784866i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 420.121 | + | 248.798i | 1.06360 | + | 0.629870i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 357.537 | 0.900598 | 0.450299 | − | 0.892878i | \(-0.351317\pi\) | ||||
0.450299 | + | 0.892878i | \(0.351317\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 425.670i | − | 1.05625i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −168.876 | + | 285.164i | −0.416977 | + | 0.704108i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 429.181 | 1.05450 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 63.2015 | 0.154527 | 0.0772634 | − | 0.997011i | \(-0.475382\pi\) | ||||
0.0772634 | + | 0.997011i | \(0.475382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 117.459 | 0.285787 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 106.928 | 0.258905 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 542.776 | + | 321.435i | 1.30789 | + | 0.774542i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 612.393i | − | 1.46857i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −673.390 | −1.60714 | −0.803568 | − | 0.595213i | \(-0.797068\pi\) | ||||
−0.803568 | + | 0.595213i | \(0.797068\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 84.6877i | − | 0.201158i | −0.994929 | − | 0.100579i | \(-0.967930\pi\) | ||
0.994929 | − | 0.100579i | \(-0.0320696\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −93.5363 | −0.221126 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 114.186 | − | 62.5968i | 0.268674 | − | 0.147286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 208.650i | 0.488643i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 274.776i | 0.640504i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 672.158i | 1.55953i | 0.626072 | + | 0.779766i | \(0.284662\pi\) | ||||
−0.626072 | + | 0.779766i | \(0.715338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 562.185i | − | 1.29835i | −0.760640 | − | 0.649174i | \(-0.775115\pi\) | ||
0.760640 | − | 0.649174i | \(-0.224885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 140.600 | − | 237.417i | 0.323218 | − | 0.545786i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −798.469 | −1.82716 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − | 461.625i | − | 1.04204i | −0.853544 | − | 0.521021i | \(-0.825551\pi\) | ||
0.853544 | − | 0.521021i | \(-0.174449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −340.472 | + | 574.922i | −0.765106 | + | 1.29196i | ||||
\(446\) | 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 | ||||||||
\(451\) | 71.9532 | 0.159542 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 237.023 | 0.523229 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | −149.399 | −0.325488 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 406.436i | − | 0.881639i | −0.897596 | − | 0.440820i | \(-0.854688\pi\) | ||
0.897596 | − | 0.440820i | \(-0.145312\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − | 594.738i | − | 1.27353i | −0.771058 | − | 0.636765i | \(-0.780272\pi\) | ||
0.771058 | − | 0.636765i | \(-0.219728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 413.899i | 0.882515i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 44.1647i | − | 0.0937679i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 160.067i | − | 0.338407i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −435.355 | − | 794.157i | −0.916537 | − | 1.67191i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 55.9294 | 0.117252 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 534.894i | − | 1.11669i | −0.829609 | − | 0.558344i | \(-0.811437\pi\) | ||
0.829609 | − | 0.558344i | \(-0.188563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1117.00 | 2.32224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 233.732i | 0.483917i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.5727 | − | 16.3287i | −0.0568510 | − | 0.0336675i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 264.298 | 0.542706 | 0.271353 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271353 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 493.471 | 1.00914 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −539.150 | −1.09807 | −0.549033 | − | 0.835801i | \(-0.685004\pi\) | ||||
−0.549033 | + | 0.835801i | \(0.685004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 104.359 | 0.211681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.2921 | + | 37.6424i | −0.0450345 | + | 0.0760453i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 272.577i | − | 0.548444i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 138.218 | 0.276991 | 0.138495 | − | 0.990363i | \(-0.455773\pi\) | ||||
0.138495 | + | 0.990363i | \(0.455773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 379.557i | − | 0.757598i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −389.170 | −0.773697 | −0.386848 | − | 0.922143i | \(-0.626436\pi\) | ||||
−0.386848 | + | 0.922143i | \(0.626436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −522.992 | − | 309.719i | −1.03563 | − | 0.613305i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 249.645i | 0.492396i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 468.599i | − | 0.920627i | −0.887756 | − | 0.460314i | \(-0.847737\pi\) | ||
0.887756 | − | 0.460314i | \(-0.152263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 144.124i | − | 0.282043i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1039.06i | 2.02545i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.3731 | − | 42.8451i | 0.0492682 | − | 0.0831943i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 409.761 | 0.792575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 173.223i | 0.333764i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 931.151 | 1.78724 | 0.893619 | − | 0.448826i | \(-0.148158\pi\) | ||||
0.893619 | + | 0.448826i | \(0.148158\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 227.656i | 0.435289i | 0.976028 | + | 0.217645i | \(0.0698374\pi\) | ||||
−0.976028 | + | 0.217645i | \(0.930163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −232.470 | + | 127.439i | −0.442799 | + | 0.242742i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −137.602 | −0.261104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −43.1902 | −0.0816451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.2511 | −0.0739191 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 187.267 | 0.351346 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −580.115 | − | 343.548i | −1.08433 | − | 0.642145i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 655.605i | 1.22087i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 211.599 | 0.392576 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 388.174i | 0.717511i | 0.933431 | + | 0.358756i | \(0.116799\pi\) | ||||
−0.933431 | + | 0.358756i | \(0.883201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 514.296 | 0.947139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −121.453 | − | 71.9254i | −0.222850 | − | 0.131973i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 473.059i | 0.864824i | 0.901676 | + | 0.432412i | \(0.142337\pi\) | ||||
−0.901676 | + | 0.432412i | \(0.857663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 76.5916i | − | 0.139511i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 725.804i | − | 1.31725i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 375.961i | − | 0.679857i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −821.463 | − | 486.475i | −1.48011 | − | 0.876532i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 419.101 | 0.752426 | 0.376213 | − | 0.926533i | \(-0.377226\pi\) | ||||
0.376213 | + | 0.926533i | \(0.377226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 416.594i | − | 0.745248i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 88.8241 | 0.158332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 145.910i | − | 0.259165i | −0.991569 | − | 0.129582i | \(-0.958636\pi\) | ||
0.991569 | − | 0.129582i | \(-0.0413637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 817.640 | + | 484.211i | 1.44715 | + | 0.857011i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 255.189 | 0.450069 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −950.513 | −1.67050 | −0.835249 | − | 0.549872i | \(-0.814677\pi\) | ||||
−0.835249 | + | 0.549872i | \(0.814677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −404.107 | −0.707717 | −0.353859 | − | 0.935299i | \(-0.615131\pi\) | ||||
−0.353859 | + | 0.935299i | \(0.615131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −340.023 | −0.593408 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 264.882 | + | 483.186i | 0.460664 | + | 0.840324i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 847.944i | − | 1.46957i | −0.678298 | − | 0.734787i | \(-0.737282\pi\) | ||
0.678298 | − | 0.734787i | \(-0.262718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 447.193 | 0.772354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 485.723i | − | 0.836011i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −245.014 | −0.420264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −58.0179 | + | 97.9692i | −0.0991760 | + | 0.167469i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 658.243i | 1.12137i | 0.828030 | + | 0.560684i | \(0.189462\pi\) | ||||
−0.828030 | + | 0.560684i | \(0.810538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 957.010i | 1.62480i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 312.735i | 0.529162i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 282.430i | 0.476274i | 0.971232 | + | 0.238137i | \(0.0765367\pi\) | ||||
−0.971232 | + | 0.238137i | \(0.923463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −86.2739 | − | 51.0920i | −0.144998 | − | 0.0858688i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 897.739 | 1.50375 | ||||||||
\(598\) | 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 | \(-0.423121\pi\) | ||||
0.239182 | + | 0.970975i | \(0.423121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 151.934i | − | 0.251964i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −210.625 | + | 355.662i | −0.348141 | + | 0.587871i | ||||
\(606\) | 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 | ||||||||
\(611\) | 1066.46 | 1.74543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −975.340 | −1.59109 | −0.795547 | − | 0.605892i | \(-0.792816\pi\) | ||||
−0.795547 | + | 0.605892i | \(0.792816\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 845.837 | 1.36646 | 0.683228 | − | 0.730205i | \(-0.260575\pi\) | ||||
0.683228 | + | 0.730205i | \(0.260575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 632.190i | − | 1.01802i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 514.489 | 0.825826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −336.153 | + | 526.902i | −0.537846 | + | 0.843043i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 617.764i | − | 0.985269i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 361.080i | − | 0.574055i | ||||||
\(630\) | 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 | ||||||||
\(635\) | −153.032 | + | 258.409i | −0.240995 | + | 0.406944i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 550.712 | 0.864541 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 118.227i | 0.183867i | 0.995765 | + | 0.0919335i | \(0.0293047\pi\) | ||||
−0.995765 | + | 0.0919335i | \(0.970695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −181.435 | + | 306.372i | −0.281295 | + | 0.474995i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 783.464 | 1.21092 | 0.605459 | − | 0.795876i | \(-0.292989\pi\) | ||||
0.605459 | + | 0.795876i | \(0.292989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 171.950 | 0.264946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 280.141 | 0.430324 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.4352 | −0.0435455 | −0.0217727 | − | 0.999763i | \(-0.506931\pi\) | ||||
−0.0217727 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −285.314 | + | 481.781i | −0.435593 | + | 0.735543i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.9051i | 0.0805253i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −594.296 | −0.901814 | −0.450907 | − | 0.892571i | \(-0.648899\pi\) | ||||
−0.450907 | + | 0.892571i | \(0.648899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495.511i | 0.749638i | 0.927098 | + | 0.374819i | \(0.122295\pi\) | ||||
−0.927098 | + | 0.374819i | \(0.877705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 231.176 | 0.348682 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −355.340 | + | 600.028i | −0.534346 | + | 0.902297i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 441.599i | 0.662067i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 257.231i | − | 0.384501i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 335.530i | 0.500045i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 168.874i | 0.250927i | 0.992098 | + | 0.125464i | \(0.0400418\pi\) | ||||
−0.992098 | + | 0.125464i | \(0.959958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 628.775 | − | 344.693i | 0.931519 | − | 0.510657i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −895.899 | −1.32334 | −0.661668 | − | 0.749797i | \(-0.730151\pi\) | ||||
−0.661668 | + | 0.749797i | \(0.730151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.6745i | 0.0363394i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.3042 | −0.0606522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 359.410i | 0.526223i | 0.964765 | + | 0.263112i | \(0.0847487\pi\) | ||||
−0.964765 | + | 0.263112i | \(0.915251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −183.462 | − | 108.647i | −0.267828 | − | 0.158609i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −396.926 | −0.577767 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −637.680 | −0.925516 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −515.701 | −0.746311 | −0.373155 | − | 0.927769i | \(-0.621724\pi\) | ||||
−0.373155 | + | 0.927769i | \(0.621724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.6857 | 0.0486085 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −566.454 | + | 956.514i | −0.815041 | + | 1.37628i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 60.5360i | − | 0.0868523i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 348.510 | 0.498584 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1370.37i | − | 1.95488i | −0.211221 | − | 0.977438i | \(-0.567744\pi\) | ||
0.211221 | − | 0.977438i | \(-0.432256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2511.28 | −3.57224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −784.293 | − | 464.463i | −1.11247 | − | 0.658813i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 468.018i | 0.661978i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 662.128i | 0.933890i | 0.884286 | + | 0.466945i | \(0.154645\pi\) | ||||
−0.884286 | + | 0.466945i | \(0.845355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 138.008i | 0.194104i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 582.270i | − | 0.816649i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 254.163 | − | 429.181i | 0.355473 | − | 0.600253i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.55302 | −0.00635010 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 370.003i | 0.514608i | 0.966331 | + | 0.257304i | \(0.0828341\pi\) | ||||
−0.966331 | + | 0.257304i | \(0.917166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.3415 | −0.0531782 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 569.964i | 0.788331i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −439.214 | + | 240.776i | −0.605812 | + | 0.332105i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 607.695 | 0.835894 | 0.417947 | − | 0.908471i | \(-0.362750\pi\) | ||||
0.417947 | + | 0.908471i | \(0.362750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −804.700 | −1.10384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −134.668 | −0.184224 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1066.76 | 1.45533 | 0.727666 | − | 0.685931i | \(-0.240605\pi\) | ||||
0.727666 | + | 0.685931i | \(0.240605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −405.005 | − | 239.847i | −0.551027 | − | 0.326322i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 665.591i | 0.903108i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −558.366 | −0.755570 | −0.377785 | − | 0.925893i | \(-0.623314\pi\) | ||||
−0.377785 | + | 0.925893i | \(0.623314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1607.81i | − | 2.16978i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1112.00 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −86.4659 | − | 51.2056i | −0.116062 | − | 0.0687324i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 178.299i | 0.238687i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 519.137i | 0.693107i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1207.34i | − | 1.60764i | −0.594873 | − | 0.803820i | \(-0.702798\pi\) | ||
0.594873 | − | 0.803820i | \(-0.297202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 204.158i | − | 0.271127i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −370.213 | − | 219.242i | −0.490348 | − | 0.290387i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −87.7776 | −0.115955 | −0.0579773 | − | 0.998318i | \(-0.518465\pi\) | ||||
−0.0579773 | + | 0.998318i | \(0.518465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 375.864i | 0.495209i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −67.0202 | −0.0880686 | −0.0440343 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440343 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 108.687i | 0.142447i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.6695 | + | 18.7549i | 0.0413980 | + | 0.0245162i | ||||
\(766\) | 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 | ||||||||
\(771\) | −756.587 | −0.981306 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 244.756 | 0.316631 | 0.158316 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158316 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 579.126 | − | 317.475i | 0.747259 | − | 0.409646i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 735.116i | 0.946095i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −421.023 | −0.540466 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 438.330i | − | 0.561242i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 574.657 | 0.733917 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.8516 | + | 68.9821i | −0.0520403 | + | 0.0878753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1120.38i | 1.42361i | 0.702376 | + | 0.711806i | \(0.252123\pi\) | ||||
−0.702376 | + | 0.711806i | \(0.747877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 208.063i | − | 0.263705i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 731.695i | − | 0.925025i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 873.260i | 1.10121i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 468.963 | + | 277.723i | 0.589891 | + | 0.349337i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1344.51 | −1.68696 | −0.843480 | − | 0.537161i | \(-0.819497\pi\) | ||||
−0.843480 | + | 0.537161i | \(0.819497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 344.742i | − | 0.431467i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −188.859 | −0.235779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 231.765i | − | 0.288624i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 216.198 | − | 365.073i | 0.268569 | − | 0.453507i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −865.122 | −1.07202 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −345.363 | −0.426901 | −0.213451 | − | 0.976954i | \(-0.568470\pi\) | ||||
−0.213451 | + | 0.976954i | \(0.568470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1275.44 | 1.57268 | 0.786338 | − | 0.617797i | \(-0.211975\pi\) | ||||
0.786338 | + | 0.617797i | \(0.211975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −352.999 | −0.434193 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −770.766 | − | 456.452i | −0.945725 | − | 0.560064i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 936.604i | 1.14639i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 87.6713 | 0.107047 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1257.99i | − | 1.53226i | −0.642684 | − | 0.766131i | \(-0.722179\pi\) | ||
0.642684 | − | 0.766131i | \(-0.277821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 206.093 | 0.250417 | 0.125208 | − | 0.992130i | \(-0.460040\pi\) | ||||
0.125208 | + | 0.992130i | \(0.460040\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −373.834 | + | 204.935i | −0.453132 | + | 0.248406i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 615.606i | − | 0.744384i | −0.928156 | − | 0.372192i | \(-0.878606\pi\) | ||
0.928156 | − | 0.372192i | \(-0.121394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1214.12i | − | 1.46456i | −0.681002 | − | 0.732281i | \(-0.738456\pi\) | ||
0.681002 | − | 0.732281i | \(-0.261544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 666.892i | 0.802518i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 178.023i | − | 0.213713i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −351.084 | + | 592.841i | −0.420460 | + | 0.709989i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −757.715 | −0.905275 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − | 79.4817i | − | 0.0942844i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 230.917 | − | 389.928i | 0.273275 | − | 0.461453i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 318.277 | 0.375769 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −743.671 | −0.875937 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1527.93 | 1.79545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 112.066 | 0.131379 | 0.0656893 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656893 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −719.610 | −0.837729 | −0.418865 | − | 0.908049i | \(-0.637572\pi\) | ||||
−0.418865 | + | 0.908049i | \(0.637572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 123.244i | 0.143141i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 721.293i | 0.831942i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 604.582i | − | 0.695721i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1732.28i | 1.98884i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.05752i | − | 0.0103752i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 480.981 | + | 15.9795i | 0.549692 | + | 0.0182623i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1427.99 | −1.62827 | −0.814135 | − | 0.580675i | \(-0.802789\pi\) | ||||
−0.814135 | + | 0.580675i | \(0.802789\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 800.458i | − | 0.906521i | −0.891378 | − | 0.453260i | \(-0.850261\pi\) | ||
0.891378 | − | 0.453260i | \(-0.149739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −329.117 | − | 194.905i | −0.371883 | − | 0.220231i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −591.672 | −0.667049 | −0.333524 | − | 0.942741i | \(-0.608238\pi\) | ||||
−0.333524 | + | 0.942741i | \(0.608238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 231.247 | 0.260120 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 410.369 | 0.460572 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2397.65 | −2.68494 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 606.424 | − | 1024.01i | 0.677568 | − | 1.14414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 978.233i | 1.09056i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 529.281 | 0.588744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 206.136i | 0.228786i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 274.168 | 0.303619 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −803.295 | − | 475.716i | −0.887618 | − | 0.525653i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 545.657i | − | 0.601606i | −0.953686 | − | 0.300803i | \(-0.902745\pi\) | ||
0.953686 | − | 0.300803i | \(-0.0972547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 171.801i | − | 0.189000i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 929.286i | − | 1.02007i | −0.860153 | − | 0.510036i | \(-0.829632\pi\) | ||
0.860153 | − | 0.510036i | \(-0.170368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 781.089i | − | 0.855520i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 380.323 | − | 642.213i | 0.415653 | − | 0.701873i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 431.139 | 0.470163 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − | 1140.81i | − | 1.23598i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 833.085 | + | 1519.68i | 0.900632 | + | 1.64290i | ||||
\(926\) | 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 | ||||||||
\(931\) | −1238.14 | −1.32990 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −389.940 | −0.417943 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −1007.97 | −1.07346 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1121.33i | − | 1.19163i | −0.803120 | − | 0.595817i | \(-0.796828\pi\) | ||
0.803120 | − | 0.595817i | \(-0.203172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 256.161 | 0.271645 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −475.073 | − | 281.341i | −0.502723 | − | 0.297716i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1395.22i | 1.47331i | 0.676271 | + | 0.736653i | \(0.263595\pi\) | ||||
−0.676271 | + | 0.736653i | \(0.736405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 603.199i | − | 0.635615i | ||||||
\(950\) | 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 | ||||||||
\(955\) | 531.092 | + | 314.516i | 0.556117 | + | 0.329336i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −341.658 | −0.357010 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 164.178i | 0.171197i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 263.116 | 0.273794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 190.565i | − | 0.197887i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −698.484 | − | 413.646i | −0.723817 | − | 0.428649i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 140.846 | 0.145653 | 0.0728263 | − | 0.997345i | \(-0.476798\pi\) | ||||
0.0728263 | + | 0.997345i | \(0.476798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −519.740 | −0.536367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1144.98 | −1.17918 | −0.589588 | − | 0.807704i | \(-0.700710\pi\) | ||||
−0.589588 | + | 0.807704i | \(0.700710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 855.971 | 0.879724 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −972.950 | + | 533.369i | −0.997898 | + | 0.547045i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 55.8912i | − | 0.0572070i | −0.999591 | − | 0.0286035i | \(-0.990894\pi\) | ||
0.999591 | − | 0.0286035i | \(-0.00910602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 827.349 | 0.845096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 39.8969i | − | 0.0406696i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1028.74 | 1.04653 | 0.523267 | − | 0.852169i | \(-0.324713\pi\) | ||||
0.523267 | + | 0.852169i | \(0.324713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 289.275 | − | 488.469i | 0.293680 | − | 0.495908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 701.853i | 0.711098i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 569.855i | − | 0.576193i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 666.207i | 0.672257i | 0.941816 | + | 0.336129i | \(0.109118\pi\) | ||||
−0.941816 | + | 0.336129i | \(0.890882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 147.030i | 0.148066i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1402.20 | − | 830.394i | −1.40925 | − | 0.834567i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 737.006 | 0.739224 | 0.369612 | − | 0.929186i | \(-0.379491\pi\) | ||||
0.369612 | + | 0.929186i | \(0.379491\pi\) | |||||||
\(998\) | 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 | 1280.3.e.i.639.5 | 6 | ||
4.3 | odd | 2 | 1280.3.e.h.639.2 | 6 | |||
5.4 | even | 2 | 1280.3.e.f.639.2 | 6 | |||
8.3 | odd | 2 | 1280.3.e.f.639.5 | 6 | |||
8.5 | even | 2 | 1280.3.e.g.639.2 | 6 | |||
16.3 | odd | 4 | 320.3.h.f.319.5 | 6 | |||
16.5 | even | 4 | 160.3.h.a.159.6 | yes | 6 | ||
16.11 | odd | 4 | 160.3.h.b.159.2 | yes | 6 | ||
16.13 | even | 4 | 320.3.h.g.319.1 | 6 | |||
20.19 | odd | 2 | 1280.3.e.g.639.5 | 6 | |||
40.19 | odd | 2 | inner | 1280.3.e.i.639.2 | 6 | ||
40.29 | even | 2 | 1280.3.e.h.639.5 | 6 | |||
48.5 | odd | 4 | 1440.3.j.a.1279.1 | 6 | |||
48.11 | even | 4 | 1440.3.j.b.1279.1 | 6 | |||
80.3 | even | 4 | 1600.3.b.v.1151.5 | 6 | |||
80.13 | odd | 4 | 1600.3.b.v.1151.2 | 6 | |||
80.19 | odd | 4 | 320.3.h.g.319.2 | 6 | |||
80.27 | even | 4 | 800.3.b.i.351.5 | 6 | |||
80.29 | even | 4 | 320.3.h.f.319.6 | 6 | |||
80.37 | odd | 4 | 800.3.b.i.351.2 | 6 | |||
80.43 | even | 4 | 800.3.b.h.351.2 | 6 | |||
80.53 | odd | 4 | 800.3.b.h.351.5 | 6 | |||
80.59 | odd | 4 | 160.3.h.a.159.5 | ✓ | 6 | ||
80.67 | even | 4 | 1600.3.b.w.1151.2 | 6 | |||
80.69 | even | 4 | 160.3.h.b.159.1 | yes | 6 | ||
80.77 | odd | 4 | 1600.3.b.w.1151.5 | 6 | |||
240.59 | even | 4 | 1440.3.j.a.1279.2 | 6 | |||
240.149 | odd | 4 | 1440.3.j.b.1279.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.5 | ✓ | 6 | 80.59 | odd | 4 | ||
160.3.h.a.159.6 | yes | 6 | 16.5 | even | 4 | ||
160.3.h.b.159.1 | yes | 6 | 80.69 | even | 4 | ||
160.3.h.b.159.2 | yes | 6 | 16.11 | odd | 4 | ||
320.3.h.f.319.5 | 6 | 16.3 | odd | 4 | |||
320.3.h.f.319.6 | 6 | 80.29 | even | 4 | |||
320.3.h.g.319.1 | 6 | 16.13 | even | 4 | |||
320.3.h.g.319.2 | 6 | 80.19 | odd | 4 | |||
800.3.b.h.351.2 | 6 | 80.43 | even | 4 | |||
800.3.b.h.351.5 | 6 | 80.53 | odd | 4 | |||
800.3.b.i.351.2 | 6 | 80.37 | odd | 4 | |||
800.3.b.i.351.5 | 6 | 80.27 | even | 4 | |||
1280.3.e.f.639.2 | 6 | 5.4 | even | 2 | |||
1280.3.e.f.639.5 | 6 | 8.3 | odd | 2 | |||
1280.3.e.g.639.2 | 6 | 8.5 | even | 2 | |||
1280.3.e.g.639.5 | 6 | 20.19 | odd | 2 | |||
1280.3.e.h.639.2 | 6 | 4.3 | odd | 2 | |||
1280.3.e.h.639.5 | 6 | 40.29 | even | 2 | |||
1280.3.e.i.639.2 | 6 | 40.19 | odd | 2 | inner | ||
1280.3.e.i.639.5 | 6 | 1.1 | even | 1 | trivial | ||
1440.3.j.a.1279.1 | 6 | 48.5 | odd | 4 | |||
1440.3.j.a.1279.2 | 6 | 240.59 | even | 4 | |||
1440.3.j.b.1279.1 | 6 | 48.11 | even | 4 | |||
1440.3.j.b.1279.2 | 6 | 240.149 | odd | 4 | |||
1600.3.b.v.1151.2 | 6 | 80.13 | odd | 4 | |||
1600.3.b.v.1151.5 | 6 | 80.3 | even | 4 | |||
1600.3.b.w.1151.2 | 6 | 80.67 | even | 4 | |||
1600.3.b.w.1151.5 | 6 | 80.77 | odd | 4 |