Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
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: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.27399\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −9.87991 | −1.90139 | −0.950695 | − | 0.310128i | \(-0.899628\pi\) | ||||
−0.950695 | + | 0.310128i | \(0.899628\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.8209 | 1.50451 | 0.752255 | − | 0.658872i | \(-0.228966\pi\) | ||||
0.752255 | + | 0.658872i | \(0.228966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.21997 | 0.281852 | 0.140926 | − | 0.990020i | \(-0.454992\pi\) | ||||
0.140926 | + | 0.990020i | \(0.454992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 70.6126 | 2.61528 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.55158 | 0.234400 | 0.117200 | − | 0.993108i | \(-0.462608\pi\) | ||||
0.117200 | + | 0.993108i | \(0.462608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.3429 | 0.241996 | 0.120998 | − | 0.992653i | \(-0.461391\pi\) | ||||
0.120998 | + | 0.992653i | \(0.461391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −166.189 | −2.86066 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68.4740 | 0.976904 | 0.488452 | − | 0.872591i | \(-0.337562\pi\) | ||||
0.488452 | + | 0.872591i | \(0.337562\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.93014 | −0.0836780 | −0.0418390 | − | 0.999124i | \(-0.513322\pi\) | ||||
−0.0418390 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −51.5728 | −0.535910 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −132.042 | −1.19708 | −0.598538 | − | 0.801095i | \(-0.704251\pi\) | ||||
−0.598538 | + | 0.801095i | \(0.704251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 157.944 | 1.26355 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −430.889 | −3.07128 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.419319 | −0.00242941 | −0.00121471 | − | 0.999999i | \(-0.500387\pi\) | ||||
−0.00121471 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −84.4888 | −0.445685 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 87.8048 | 0.424049 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −395.483 | −1.75722 | −0.878609 | − | 0.477542i | \(-0.841528\pi\) | ||||
−0.878609 | + | 0.477542i | \(0.841528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −112.067 | −0.460128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −447.209 | −1.70347 | −0.851736 | − | 0.523971i | \(-0.824450\pi\) | ||||
−0.851736 | + | 0.523971i | \(0.824450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −184.132 | −0.653020 | −0.326510 | − | 0.945194i | \(-0.605873\pi\) | ||||
−0.326510 | + | 0.945194i | \(0.605873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1187.77 | 3.93472 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −97.2612 | −0.301851 | −0.150926 | − | 0.988545i | \(-0.548225\pi\) | ||||
−0.150926 | + | 0.988545i | \(0.548225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.752 | −0.920559 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −676.516 | −1.85748 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 209.547 | 0.543086 | 0.271543 | − | 0.962426i | \(-0.412466\pi\) | ||||
0.271543 | + | 0.962426i | \(0.412466\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 143.845 | 0.352657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 68.4691 | 0.159105 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −45.9651 | −0.101426 | −0.0507131 | − | 0.998713i | \(-0.516149\pi\) | ||||
−0.0507131 | + | 0.998713i | \(0.516149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −427.655 | −0.897634 | −0.448817 | − | 0.893624i | \(-0.648154\pi\) | ||||
−0.448817 | + | 0.893624i | \(0.648154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 368.596 | 0.737122 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 190.798 | 0.364085 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 405.055 | 0.738588 | 0.369294 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369294 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1304.57 | 2.27611 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −557.971 | −0.932662 | −0.466331 | − | 0.884610i | \(-0.654424\pi\) | ||||
−0.466331 | + | 0.884610i | \(0.654424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −381.988 | −0.612443 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1560.47 | −2.40250 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 44.6390 | 0.0660660 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 577.208 | 0.822038 | 0.411019 | − | 0.911627i | \(-0.365173\pi\) | ||||
0.411019 | + | 0.911627i | \(0.365173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2350.60 | 3.22442 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 353.745 | 0.467813 | 0.233907 | − | 0.972259i | \(-0.424849\pi\) | ||||
0.233907 | + | 0.972259i | \(0.424849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1151.80 | 1.46976 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −286.517 | −0.353079 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −277.871 | −0.330947 | −0.165473 | − | 0.986214i | \(-0.552915\pi\) | ||||
−0.165473 | + | 0.986214i | \(0.552915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 59.2095 | 0.0682070 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.14283 | 0.00461926 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −116.571 | −0.125894 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 677.917 | 0.709609 | 0.354804 | − | 0.934941i | \(-0.384547\pi\) | ||||
0.354804 | + | 0.934941i | \(0.384547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 603.849 | 0.613022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −567.816 | −0.559404 | −0.279702 | − | 0.960087i | \(-0.590236\pi\) | ||||
−0.279702 | + | 0.960087i | \(0.590236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 319.205 | 0.305362 | 0.152681 | − | 0.988276i | \(-0.451209\pi\) | ||||
0.152681 | + | 0.988276i | \(0.451209\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −867.503 | −0.806282 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 79.6547 | 0.0719674 | 0.0359837 | − | 0.999352i | \(-0.488544\pi\) | ||||
0.0359837 | + | 0.999352i | \(0.488544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1708.43 | 1.50126 | 0.750632 | − | 0.660721i | \(-0.229749\pi\) | ||||
0.750632 | + | 0.660721i | \(0.229749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3907.34 | 3.34116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1050.31 | 0.874383 | 0.437191 | − | 0.899369i | \(-0.355973\pi\) | ||||
0.437191 | + | 0.899369i | \(0.355973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2221.08 | −1.80101 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 800.950 | 0.632887 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 357.432 | 0.275342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1257.87 | −0.945057 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4418.39 | 3.23896 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 554.143 | 0.396513 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 366.926 | 0.256373 | 0.128187 | − | 0.991750i | \(-0.459084\pi\) | ||||
0.128187 | + | 0.991750i | \(0.459084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1819.21 | 1.24165 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2310.86 | −1.54123 | −0.770614 | − | 0.637302i | \(-0.780050\pi\) | ||||
−0.770614 | + | 0.637302i | \(0.780050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36.1751 | −0.0235848 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7247.95 | −4.62077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1899.65 | 1.18466 | 0.592329 | − | 0.805696i | \(-0.298209\pi\) | ||||
0.592329 | + | 0.805696i | \(0.298209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1309.49 | −0.799061 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 960.932 | 0.573937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 96.9994 | 0.0567238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 487.807 | 0.279380 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3119.60 | 1.75034 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1782.98 | −0.980320 | −0.490160 | − | 0.871632i | \(-0.663062\pi\) | ||||
−0.490160 | + | 0.871632i | \(0.663062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1631.96 | −0.879515 | −0.439758 | − | 0.898116i | \(-0.644936\pi\) | ||||
−0.439758 | + | 0.898116i | \(0.644936\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4835.12 | 2.55488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.05333 | −0.00365508 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −852.817 | −0.433517 | −0.216759 | − | 0.976225i | \(-0.569548\pi\) | ||||
−0.216759 | + | 0.976225i | \(0.569548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2070.31 | −1.03262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −689.257 | −0.337398 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3280.24 | −1.57625 | −0.788123 | − | 0.615518i | \(-0.788947\pi\) | ||||
−0.788123 | + | 0.615518i | \(0.788947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1421.18 | −0.670538 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1682.26 | −0.779504 | −0.389752 | − | 0.920920i | \(-0.627439\pi\) | ||||
−0.389752 | + | 0.920920i | \(0.627439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2068.34 | −0.941438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −489.355 | −0.218842 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1590.22 | 0.698854 | 0.349427 | − | 0.936964i | \(-0.386376\pi\) | ||||
0.349427 | + | 0.936964i | \(0.386376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 824.462 | 0.356134 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 454.131 | 0.192851 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1794.60 | 0.749356 | 0.374678 | − | 0.927155i | \(-0.377753\pi\) | ||||
0.374678 | + | 0.927155i | \(0.377753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2353.41 | −0.966450 | −0.483225 | − | 0.875496i | \(-0.660535\pi\) | ||||
−0.483225 | + | 0.875496i | \(0.660535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4225.20 | 1.70675 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6652.40 | −2.64375 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 585.560 | 0.228986 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2249.23 | −0.865646 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2184.35 | −0.827508 | −0.413754 | − | 0.910389i | \(-0.635783\pi\) | ||||
−0.413754 | + | 0.910389i | \(0.635783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3109.71 | −1.15980 | −0.579901 | − | 0.814687i | \(-0.696909\pi\) | ||||
−0.579901 | + | 0.814687i | \(0.696909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1885.06 | −0.692267 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −923.756 | −0.334086 | −0.167043 | − | 0.985950i | \(-0.553422\pi\) | ||||
−0.167043 | + | 0.985950i | \(0.553422\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4548.71 | 1.62035 | 0.810174 | − | 0.586189i | \(-0.199372\pi\) | ||||
0.810174 | + | 0.586189i | \(0.199372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4001.91 | −1.40434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 151.379 | 0.0523386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7522.48 | −2.56289 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9323.85 | −3.13069 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −59.2636 | −0.0196141 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 318.664 | 0.103970 | 0.0519851 | − | 0.998648i | \(-0.483445\pi\) | ||||
0.0519851 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5512.70 | 1.77335 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3097.27 | −0.982475 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.18883 | −0.000684735 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3774.01 | 1.16449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 776.691 | 0.236407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1706.70 | 0.512509 | 0.256254 | − | 0.966609i | \(-0.417512\pi\) | ||||
0.256254 | + | 0.966609i | \(0.417512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11152.8 | 3.30454 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3043.63 | −0.889925 | −0.444962 | − | 0.895549i | \(-0.646783\pi\) | ||||
−0.444962 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2621.57 | 0.756500 | 0.378250 | − | 0.925704i | \(-0.376526\pi\) | ||||
0.378250 | + | 0.925704i | \(0.376526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −441.029 | −0.125617 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2778.73 | −0.781291 | −0.390646 | − | 0.920541i | \(-0.627748\pi\) | ||||
−0.390646 | + | 0.920541i | \(0.627748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1636.02 | −0.454138 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5702.76 | −1.56301 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4722.67 | 1.27818 | 0.639088 | − | 0.769133i | \(-0.279312\pi\) | ||||
0.639088 | + | 0.769133i | \(0.279312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4704.13 | −1.25734 | −0.628672 | − | 0.777671i | \(-0.716401\pi\) | ||||
−0.628672 | + | 0.777671i | \(0.716401\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11589.7 | −3.05959 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5311.24 | −1.38499 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −78.6076 | −0.0202497 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3494.96 | −0.889496 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4449.07 | −1.11882 | −0.559408 | − | 0.828893i | \(-0.688971\pi\) | ||||
−0.559408 | + | 0.828893i | \(0.688971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1129.17 | −0.280594 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11379.6 | −2.79459 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7226.68 | 1.75404 | 0.877019 | − | 0.480456i | \(-0.159529\pi\) | ||||
0.877019 | + | 0.480456i | \(0.159529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2064.41 | −0.495275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2047.77 | 0.485646 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4789.59 | −1.12296 | −0.561481 | − | 0.827490i | \(-0.689768\pi\) | ||||
−0.561481 | + | 0.827490i | \(0.689768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3524.78 | 0.817078 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2745.34 | 0.629259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 47.0448 | 0.0106631 | 0.00533154 | − | 0.999986i | \(-0.498303\pi\) | ||||
0.00533154 | + | 0.999986i | \(0.498303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7721.78 | 1.73087 | 0.865433 | − | 0.501025i | \(-0.167044\pi\) | ||||
0.865433 | + | 0.501025i | \(0.167044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −584.984 | −0.129688 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1350.67 | 0.296176 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7554.66 | 1.63868 | 0.819342 | − | 0.573305i | \(-0.194339\pi\) | ||||
0.819342 | + | 0.573305i | \(0.194339\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.6092 | −0.00635360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2094.83 | −0.444723 | −0.222361 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222361 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8200.83 | 1.72257 | 0.861287 | − | 0.508119i | \(-0.169659\pi\) | ||||
0.861287 | + | 0.508119i | \(0.169659\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1151.71 | 0.239374 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2334.42 | −0.480127 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −224.318 | −0.0456580 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6697.76 | −1.34924 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3518.87 | −0.701620 | −0.350810 | − | 0.936447i | \(-0.614094\pi\) | ||||
−0.350810 | + | 0.936447i | \(0.614094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −773.175 | −0.152597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3684.78 | −0.719907 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1497.74 | −0.289687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −961.163 | −0.184055 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5609.97 | 1.06364 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7193.56 | −1.35050 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8725.36 | 1.62209 | 0.811046 | − | 0.584982i | \(-0.198898\pi\) | ||||
0.811046 | + | 0.584982i | \(0.198898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3153.72 | −0.580611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2640.09 | 0.481370 | 0.240685 | − | 0.970603i | \(-0.422628\pi\) | ||||
0.240685 | + | 0.970603i | \(0.422628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1938.00 | −0.349976 | −0.174988 | − | 0.984571i | \(-0.555989\pi\) | ||||
−0.174988 | + | 0.984571i | \(0.555989\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6200.12 | 1.10901 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5546.11 | 0.982651 | 0.491326 | − | 0.870976i | \(-0.336512\pi\) | ||||
0.491326 | + | 0.870976i | \(0.336512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 247.996 | 0.0435270 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −786.981 | −0.136838 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −474.534 | −0.0817454 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1791.53 | 0.305774 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16879.1 | −2.85449 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −507.701 | −0.0850773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −185.492 | −0.0308023 | −0.0154012 | − | 0.999881i | \(-0.504903\pi\) | ||||
−0.0154012 | + | 0.999881i | \(0.504903\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27926.1 | −4.59562 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6813.41 | 1.11121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8508.32 | −1.37530 | −0.687652 | − | 0.726040i | \(-0.741359\pi\) | ||||
−0.687652 | + | 0.726040i | \(0.741359\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10377.0 | −1.66254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.58584 | −0.000569454 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3438.67 | −0.541313 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21944.0 | 3.42442 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7853.53 | −1.21498 | −0.607492 | − | 0.794326i | \(-0.707824\pi\) | ||||
−0.607492 | + | 0.794326i | \(0.707824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6328.33 | −0.970624 | −0.485312 | − | 0.874341i | \(-0.661294\pi\) | ||||
−0.485312 | + | 0.874341i | \(0.661294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4887.51 | −0.743237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7973.45 | −1.20222 | −0.601111 | − | 0.799166i | \(-0.705275\pi\) | ||||
−0.601111 | + | 0.799166i | \(0.705275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9385.59 | −1.40320 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3531.40 | −0.523533 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10059.4 | −1.47887 | −0.739435 | − | 0.673228i | \(-0.764907\pi\) | ||||
−0.739435 | + | 0.673228i | \(0.764907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6810.97 | −0.992998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12427.6 | 1.79692 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6425.40 | −0.921426 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3032.67 | −0.431346 | −0.215673 | − | 0.976466i | \(-0.569195\pi\) | ||||
−0.215673 | + | 0.976466i | \(0.569195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31578.6 | −4.45506 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1093.83 | 0.153070 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11109.4 | 1.54215 | 0.771077 | − | 0.636742i | \(-0.219718\pi\) | ||||
0.771077 | + | 0.636742i | \(0.219718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5474.89 | −0.753925 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 328.943 | 0.0449375 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4510.20 | −0.611275 | −0.305638 | − | 0.952148i | \(-0.598870\pi\) | ||||
−0.305638 | + | 0.952148i | \(0.598870\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3625.20 | −0.487466 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7810.96 | 1.04209 | 0.521047 | − | 0.853528i | \(-0.325542\pi\) | ||||
0.521047 | + | 0.853528i | \(0.325542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 750.869 | 0.0993970 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13002.0 | −1.70783 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9221.90 | −1.20198 | −0.600989 | − | 0.799258i | \(-0.705226\pi\) | ||||
−0.600989 | + | 0.799258i | \(0.705226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9041.46 | −1.16943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22831.1 | 2.93047 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9709.17 | 1.23676 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10034.3 | 1.26854 | 0.634268 | − | 0.773113i | \(-0.281301\pi\) | ||||
0.634268 | + | 0.773113i | \(0.281301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 357.407 | 0.0448439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8193.64 | −1.02038 | −0.510188 | − | 0.860063i | \(-0.670424\pi\) | ||||
−0.510188 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.75628 | −0.000587908 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 39539.3 | 4.85117 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3382.01 | −0.411892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3921.69 | 0.474120 | 0.237060 | − | 0.971495i | \(-0.423816\pi\) | ||||
0.237060 | + | 0.971495i | \(0.423816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18768.4 | −2.25250 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −239.936 | −0.0285872 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5950.31 | 0.703830 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12937.6 | 1.51933 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3026.66 | −0.352892 | −0.176446 | − | 0.984310i | \(-0.556460\pi\) | ||||
−0.176446 | + | 0.984310i | \(0.556460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4823.43 | −0.558384 | −0.279192 | − | 0.960235i | \(-0.590067\pi\) | ||||
−0.279192 | + | 0.960235i | \(0.590067\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6867.87 | −0.789426 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10815.0 | 1.23437 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2232.35 | −0.253000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −958.346 | −0.107854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2029.51 | −0.226816 | −0.113408 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113408 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −535.808 | −0.0594672 | −0.0297336 | − | 0.999558i | \(-0.509466\pi\) | ||||
−0.0297336 | + | 0.999558i | \(0.509466\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4819.49 | −0.531211 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 915.072 | 0.100169 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8791.74 | 0.955824 | 0.477912 | − | 0.878408i | \(-0.341394\pi\) | ||||
0.477912 | + | 0.878408i | \(0.341394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22296.1 | −2.40752 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13916.9 | −1.49258 | −0.746291 | − | 0.665619i | \(-0.768167\pi\) | ||||
−0.746291 | + | 0.665619i | \(0.768167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4674.05 | −0.497912 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17615.7 | 1.86397 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2129.54 | 0.223829 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3824.35 | −0.399294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16123.6 | 1.67230 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 995.958 | 0.102618 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1932.25 | 0.197783 | 0.0988915 | − | 0.995098i | \(-0.468470\pi\) | ||||
0.0988915 | + | 0.995098i | \(0.468470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29504.6 | −3.00035 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16518.3 | 1.66884 | 0.834418 | − | 0.551132i | \(-0.185804\pi\) | ||||
0.834418 | + | 0.551132i | \(0.185804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11535.2 | 1.15785 | 0.578926 | − | 0.815380i | \(-0.303472\pi\) | ||||
0.578926 | + | 0.815380i | \(0.303472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 69.6863 | 0.00694973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15667.8 | −1.55250 | −0.776250 | − | 0.630425i | \(-0.782880\pi\) | ||||
−0.776250 | + | 0.630425i | \(0.782880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2114.38 | 0.208172 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8425.75 | 0.824285 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1574.62 | −0.153068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1094.57 | −0.105731 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14796.7 | 1.42032 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4672.28 | 0.445682 | 0.222841 | − | 0.974855i | \(-0.428467\pi\) | ||||
0.222841 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4485.92 | −0.425239 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6809.80 | 0.641525 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11403.2 | 1.06761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8465.76 | −0.787722 | −0.393861 | − | 0.919170i | \(-0.628861\pi\) | ||||
−0.393861 | + | 0.919170i | \(0.628861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32408.4 | 2.99706 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12302.6 | 1.13077 | 0.565385 | − | 0.824827i | \(-0.308728\pi\) | ||||
0.565385 | + | 0.824827i | \(0.308728\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1985.74 | 0.181407 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10157.3 | 0.922297 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2912.59 | −0.262873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2781.31 | 0.249516 | 0.124758 | − | 0.992187i | \(-0.460185\pi\) | ||||
0.124758 | + | 0.992187i | \(0.460185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16620.6 | 1.48214 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13673.9 | −1.21211 | −0.606054 | − | 0.795424i | \(-0.707248\pi\) | ||||
−0.606054 | + | 0.795424i | \(0.707248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9551.18 | −0.841628 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20435.0 | 1.79004 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7431.68 | −0.647158 | −0.323579 | − | 0.946201i | \(-0.604886\pi\) | ||||
−0.323579 | + | 0.946201i | \(0.604886\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1993.97 | −0.172618 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2986.12 | 0.256999 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5369.33 | 0.459419 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −831.737 | −0.0707538 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15711.2 | −1.32879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7797.86 | 0.655721 | 0.327860 | − | 0.944726i | \(-0.393672\pi\) | ||||
0.327860 | + | 0.944726i | \(0.393672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16670.9 | 1.39382 | 0.696908 | − | 0.717160i | \(-0.254558\pi\) | ||||
0.696908 | + | 0.717160i | \(0.254558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8145.61 | −0.677149 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.7124 | −0.00237331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5268.18 | 0.432990 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3245.71 | −0.265258 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5072.64 | −0.412233 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1339.87 | 0.108276 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17730.5 | −1.42482 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2700.18 | −0.215779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13400.1 | −1.06491 | −0.532455 | − | 0.846458i | \(-0.678730\pi\) | ||||
−0.532455 | + | 0.846458i | \(0.678730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23251.5 | 1.83760 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28737.4 | 2.25867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17339.4 | 1.35535 | 0.677677 | − | 0.735360i | \(-0.262987\pi\) | ||||
0.677677 | + | 0.735360i | \(0.262987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30197.9 | −2.34757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −200.974 | −0.0155386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3013.01 | 0.231693 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 65725.1 | 5.02680 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7790.90 | 0.592659 | 0.296330 | − | 0.955086i | \(-0.404237\pi\) | ||||
0.296330 | + | 0.955086i | \(0.404237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2088.58 | −0.158028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5785.28 | −0.435392 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21514.2 | 1.61051 | 0.805253 | − | 0.592932i | \(-0.202030\pi\) | ||||
0.805253 | + | 0.592932i | \(0.202030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17667.3 | 1.31552 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12270.1 | 0.908808 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16993.5 | 1.25203 | 0.626015 | − | 0.779811i | \(-0.284685\pi\) | ||||
0.626015 | + | 0.779811i | \(0.284685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16791.4 | −1.23064 | −0.615321 | − | 0.788277i | \(-0.710973\pi\) | ||||
−0.615321 | + | 0.788277i | \(0.710973\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21581.2 | 1.57342 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20855.3 | −1.51256 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8108.87 | 0.585055 | 0.292527 | − | 0.956257i | \(-0.405504\pi\) | ||||
0.292527 | + | 0.956257i | \(0.405504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30723.7 | 2.20524 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1846.54 | 0.131854 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1791.96 | 0.127299 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13472.7 | 0.952185 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16076.3 | −1.13039 | −0.565197 | − | 0.824956i | \(-0.691200\pi\) | ||||
−0.565197 | + | 0.824956i | \(0.691200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.90594 | 0.000203289 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9126.63 | 0.635227 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4341.83 | −0.300671 | −0.150335 | − | 0.988635i | \(-0.548035\pi\) | ||||
−0.150335 | + | 0.988635i | \(0.548035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6012.34 | 0.414255 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44940.8 | −3.08091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10540.1 | −0.718960 | −0.359480 | − | 0.933153i | \(-0.617046\pi\) | ||||
−0.359480 | + | 0.933153i | \(0.617046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16485.6 | 1.11890 | 0.559451 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28602.0 | 1.93162 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21158.6 | −1.42185 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13326.5 | 0.891112 | 0.445556 | − | 0.895254i | \(-0.353006\pi\) | ||||
0.445556 | + | 0.895254i | \(0.353006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1495.61 | −0.0995161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1103.22 | −0.0730467 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20459.4 | −1.34804 | −0.674019 | − | 0.738714i | \(-0.735433\pi\) | ||||
−0.674019 | + | 0.738714i | \(0.735433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 74321.4 | 4.87305 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3108.50 | −0.202826 | −0.101413 | − | 0.994844i | \(-0.532336\pi\) | ||||
−0.101413 | + | 0.994844i | \(0.532336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10426.3 | −0.677012 | −0.338506 | − | 0.940964i | \(-0.609922\pi\) | ||||
−0.338506 | + | 0.940964i | \(0.609922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 56895.5 | 3.67655 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1450.48 | −0.0932780 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10421.8 | −0.666992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 585.519 | 0.0372941 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27080.3 | −1.71663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18018.2 | 1.13675 | 0.568377 | − | 0.822768i | \(-0.307572\pi\) | ||||
0.568377 | + | 0.822768i | \(0.307572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3148.37 | −0.197688 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6172.04 | 0.385716 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3581.53 | −0.222772 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −39399.8 | −2.43917 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15178.7 | 0.935295 | 0.467648 | − | 0.883915i | \(-0.345102\pi\) | ||||
0.467648 | + | 0.883915i | \(0.345102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23957.1 | −1.46932 | −0.734662 | − | 0.678433i | \(-0.762659\pi\) | ||||
−0.734662 | + | 0.678433i | \(0.762659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30600.7 | 1.86807 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12835.2 | −0.779915 | −0.389958 | − | 0.920833i | \(-0.627510\pi\) | ||||
−0.389958 | + | 0.920833i | \(0.627510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −393.074 | −0.0237743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.6255 | 0.00130195 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4355.97 | 0.261045 | 0.130523 | − | 0.991445i | \(-0.458335\pi\) | ||||
0.130523 | + | 0.991445i | \(0.458335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38870.8 | −2.31879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26973.2 | −1.60171 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32704.1 | 1.93319 | 0.966594 | − | 0.256313i | \(-0.0825079\pi\) | ||||
0.966594 | + | 0.256313i | \(0.0825079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2839.66 | 0.167095 | 0.0835475 | − | 0.996504i | \(-0.473375\pi\) | ||||
0.0835475 | + | 0.996504i | \(0.473375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7673.64 | −0.449501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −608.499 | −0.0354836 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3829.23 | −0.222291 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16862.1 | −0.974478 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3657.13 | −0.210405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18569.9 | −1.06362 | −0.531810 | − | 0.846864i | \(-0.678488\pi\) | ||||
−0.531810 | + | 0.846864i | \(0.678488\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −68056.1 | −3.88071 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18106.5 | −1.02790 | −0.513952 | − | 0.857819i | \(-0.671819\pi\) | ||||
−0.513952 | + | 0.857819i | \(0.671819\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3538.71 | 0.200005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30070.8 | 1.69209 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5510.97 | 0.308743 | 0.154371 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31953.9 | 1.78233 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25900.9 | −1.43840 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2376.87 | 0.131425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24652.0 | −1.35717 | −0.678587 | − | 0.734520i | \(-0.737408\pi\) | ||||
−0.678587 | + | 0.734520i | \(0.737408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3152.08 | 0.172781 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22026.9 | −1.20220 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30622.2 | −1.66413 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27453.6 | 1.48554 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3399.10 | 0.183142 | 0.0915708 | − | 0.995799i | \(-0.470811\pi\) | ||||
0.0915708 | + | 0.995799i | \(0.470811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2740.75 | 0.147041 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16163.8 | 0.863493 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2963.98 | −0.157669 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26329.1 | −1.39465 | −0.697327 | − | 0.716753i | \(-0.745627\pi\) | ||||
−0.697327 | + | 0.716753i | \(0.745627\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40758.2 | 2.14986 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 55.3678 | 0.00290819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1631.62 | 0.0853415 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46659.6 | −2.43031 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22345.6 | 1.15904 | 0.579521 | − | 0.814957i | \(-0.303240\pi\) | ||||
0.579521 | + | 0.814957i | \(0.303240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1666.24 | 0.0860668 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46476.4 | 2.39070 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4580.37 | 0.234635 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29862.8 | −1.52345 | −0.761727 | − | 0.647898i | \(-0.775648\pi\) | ||||
−0.761727 | + | 0.647898i | \(0.775648\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 51039.2 | 2.59306 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12608.2 | −0.637938 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 987.919 | 0.0497812 | 0.0248906 | − | 0.999690i | \(-0.492076\pi\) | ||||
0.0248906 | + | 0.999690i | \(0.492076\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 52474.6 | 2.63341 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3463.86 | 0.173125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35870.9 | 1.78556 | 0.892782 | − | 0.450489i | \(-0.148750\pi\) | ||||
0.892782 | + | 0.450489i | \(0.148750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 776.636 | 0.0385026 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8322.20 | 0.410918 | 0.205459 | − | 0.978666i | \(-0.434131\pi\) | ||||
0.205459 | + | 0.978666i | \(0.434131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29991.4 | −1.47490 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24978.8 | 1.22346 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 415.795 | 0.0202841 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20781.2 | 1.00974 | 0.504872 | − | 0.863194i | \(-0.331540\pi\) | ||||
0.504872 | + | 0.863194i | \(0.331540\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43956.4 | 2.12730 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27451.0 | −1.32324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16424.7 | 0.788596 | 0.394298 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394298 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11156.1 | 0.533519 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 416.312 | 0.0198309 | 0.00991543 | − | 0.999951i | \(-0.496844\pi\) | ||||
0.00991543 | + | 0.999951i | \(0.496844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8917.95 | 0.423134 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 81331.3 | 3.84384 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −521.376 | −0.0245447 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37129.2 | −1.74111 | −0.870554 | − | 0.492073i | \(-0.836239\pi\) | ||||
−0.870554 | + | 0.492073i | \(0.836239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −71398.9 | −3.33511 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2182.83 | 0.101567 | 0.0507833 | − | 0.998710i | \(-0.483828\pi\) | ||||
0.0507833 | + | 0.998710i | \(0.483828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −66.2287 | −0.00306969 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20396.2 | 0.941711 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3099.22 | 0.142543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4771.53 | −0.218616 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12495.8 | −0.570322 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14345.2 | −0.652231 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7068.15 | −0.320143 | −0.160071 | − | 0.987105i | \(-0.551172\pi\) | ||||
−0.160071 | + | 0.987105i | \(0.551172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 47320.7 | 2.13519 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5482.61 | 0.246446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4850.84 | −0.217224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34824.5 | −1.55358 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15086.0 | −0.670482 | −0.335241 | − | 0.942132i | \(-0.608818\pi\) | ||||
−0.335241 | + | 0.942132i | \(0.608818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6659.86 | −0.294880 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19621.2 | −0.865519 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3266.60 | −0.143557 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11593.9 | −0.507619 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −464.798 | −0.0202747 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21798.3 | −0.947326 | −0.473663 | − | 0.880706i | \(-0.657069\pi\) | ||||
−0.473663 | + | 0.880706i | \(0.657069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5569.61 | −0.241153 | −0.120577 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120577 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −76290.4 | −3.29105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55176.6 | −2.37148 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1276.06 | 0.0546434 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4180.93 | 0.178381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21281.8 | −0.904676 | −0.452338 | − | 0.891847i | \(-0.649410\pi\) | ||||
−0.452338 | + | 0.891847i | \(0.649410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16799.0 | 0.711514 | 0.355757 | − | 0.934578i | \(-0.384223\pi\) | ||||
0.355757 | + | 0.934578i | \(0.384223\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13344.5 | −0.563145 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7360.62 | −0.309497 | −0.154748 | − | 0.987954i | \(-0.549457\pi\) | ||||
−0.154748 | + | 0.987954i | \(0.549457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11634.6 | 0.487438 | 0.243719 | − | 0.969846i | \(-0.421633\pi\) | ||||
0.243719 | + | 0.969846i | \(0.421633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −74639.4 | −3.11578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21620.8 | −0.899299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28297.2 | −1.17277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 180.680 | 0.00746141 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32151.0 | −1.32297 | −0.661486 | − | 0.749957i | \(-0.730074\pi\) | ||||
−0.661486 | + | 0.749957i | \(0.730074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20696.7 | 0.845592 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34791.4 | −1.41640 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6566.05 | −0.266366 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −81023.4 | −3.27528 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52220.6 | 2.10352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35044.9 | −1.40670 | −0.703349 | − | 0.710844i | \(-0.748313\pi\) | ||||
−0.703349 | + | 0.710844i | \(0.748313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8231.41 | −0.329249 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7143.05 | 0.284716 | 0.142358 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142358 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33960.3 | −1.34891 | −0.674454 | − | 0.738317i | \(-0.735621\pi\) | ||||
−0.674454 | + | 0.738317i | \(0.735621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23063.9 | 0.912909 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45823.4 | 1.80747 | 0.903736 | − | 0.428090i | \(-0.140814\pi\) | ||||
0.903736 | + | 0.428090i | \(0.140814\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26748.9 | 1.05143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2216.24 | 0.0868136 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4936.04 | 0.192685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4594.49 | 0.178735 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 47869.5 | 1.85583 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2892.61 | 0.111758 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21281.3 | 0.819406 | 0.409703 | − | 0.912219i | \(-0.365632\pi\) | ||||
0.409703 | + | 0.912219i | \(0.365632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34766.1 | 1.33405 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1359.32 | 0.0519826 | 0.0259913 | − | 0.999662i | \(-0.491726\pi\) | ||||
0.0259913 | + | 0.999662i | \(0.491726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47928.2 | 1.82663 | 0.913313 | − | 0.407257i | \(-0.133515\pi\) | ||||
0.913313 | + | 0.407257i | \(0.133515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7638.90 | 0.290146 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3100.58 | 0.117370 | 0.0586851 | − | 0.998277i | \(-0.481309\pi\) | ||||
0.0586851 | + | 0.998277i | \(0.481309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1915.34 | 0.0722593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20101.3 | 0.755803 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 674.033 | 0.0252583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30186.8 | 1.12741 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14797.5 | 0.550808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.1602 | −0.000451131 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14348.5 | 0.530543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9496.21 | 0.349960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39586.5 | −1.45403 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23428.1 | −0.857680 | −0.428840 | − | 0.903380i | \(-0.641078\pi\) | ||||
−0.428840 | + | 0.903380i | \(0.641078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40094.9 | −1.46300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12868.3 | −0.467999 | −0.234000 | − | 0.972237i | \(-0.575181\pi\) | ||||
−0.234000 | + | 0.972237i | \(0.575181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3025.07 | 0.109655 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 71071.7 | 2.56782 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12062.6 | −0.434398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3938.41 | 0.141367 | 0.0706834 | − | 0.997499i | \(-0.477482\pi\) | ||||
0.0706834 | + | 0.997499i | \(0.477482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −86205.7 | −3.08423 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6328.99 | −0.225700 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −62464.1 | −2.22033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22539.9 | 0.798607 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15856.7 | −0.560001 | −0.280001 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2188.20 | 0.0770306 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26083.9 | −0.915271 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9849.67 | 0.344512 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18559.7 | −0.647085 | −0.323542 | − | 0.946214i | \(-0.604874\pi\) | ||||
−0.323542 | + | 0.946214i | \(0.604874\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19147.3 | 0.665441 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24125.6 | −0.835785 | −0.417892 | − | 0.908497i | \(-0.637231\pi\) | ||||
−0.417892 | + | 0.908497i | \(0.637231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59050.6 | 2.03919 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37834.1 | −1.30237 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6883.31 | 0.236196 | 0.118098 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118098 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4332.84 | −0.148209 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54795.0 | −1.86840 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37573.8 | 1.27716 | 0.638580 | − | 0.769555i | \(-0.279522\pi\) | ||||
0.638580 | + | 0.769555i | \(0.279522\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36742.8 | −1.24499 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2450.18 | −0.0827617 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9916.13 | 0.333898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29790.8 | −0.999994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5624.63 | 0.188215 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −52308.2 | −1.74493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1584.28 | −0.0526856 | −0.0263428 | − | 0.999653i | \(-0.508386\pi\) | ||||
−0.0263428 | + | 0.999653i | \(0.508386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4688.35 | 0.155430 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36569.1 | −1.20861 | −0.604304 | − | 0.796754i | \(-0.706549\pi\) | ||||
−0.604304 | + | 0.796754i | \(0.706549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6835.50 | −0.225217 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17700.2 | −0.581395 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33583.0 | −1.09971 | −0.549854 | − | 0.835261i | \(-0.685317\pi\) | ||||
−0.549854 | + | 0.835261i | \(0.685317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2376.23 | −0.0775738 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 120637. | 3.92623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25900.6 | −0.840387 | −0.420193 | − | 0.907435i | \(-0.638038\pi\) | ||||
−0.420193 | + | 0.907435i | \(0.638038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15538.4 | −0.502635 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5016.04 | 0.161765 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24313.2 | 0.781714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29604.3 | 0.948951 | 0.474475 | − | 0.880269i | \(-0.342638\pi\) | ||||
0.474475 | + | 0.880269i | \(0.342638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1832.65 | 0.0585672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 76513.5 | 2.43783 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39267.2 | −1.24735 | −0.623673 | − | 0.781685i | \(-0.714360\pi\) | ||||
−0.623673 | + | 0.781685i | \(0.714360\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 170409. | 5.39691 |
(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 | 1856.4.a.y.1.1 | 5 | ||
4.3 | odd | 2 | 1856.4.a.bb.1.5 | 5 | |||
8.3 | odd | 2 | 464.4.a.l.1.1 | 5 | |||
8.5 | even | 2 | 29.4.a.b.1.3 | ✓ | 5 | ||
24.5 | odd | 2 | 261.4.a.f.1.3 | 5 | |||
40.29 | even | 2 | 725.4.a.c.1.3 | 5 | |||
56.13 | odd | 2 | 1421.4.a.e.1.3 | 5 | |||
232.173 | even | 2 | 841.4.a.b.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.3 | ✓ | 5 | 8.5 | even | 2 | ||
261.4.a.f.1.3 | 5 | 24.5 | odd | 2 | |||
464.4.a.l.1.1 | 5 | 8.3 | odd | 2 | |||
725.4.a.c.1.3 | 5 | 40.29 | even | 2 | |||
841.4.a.b.1.3 | 5 | 232.173 | even | 2 | |||
1421.4.a.e.1.3 | 5 | 56.13 | odd | 2 | |||
1856.4.a.y.1.1 | 5 | 1.1 | even | 1 | trivial | ||
1856.4.a.bb.1.5 | 5 | 4.3 | odd | 2 |