Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 21x^{4} + 5x^{3} + 101x^{2} + 29x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.52770\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62699 | 1.28234 | 0.641168 | − | 0.767401i | \(-0.278450\pi\) | ||||
0.641168 | + | 0.767401i | \(0.278450\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.15507 | 0.644383 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.4519 | −1.21229 | −0.606144 | − | 0.795355i | \(-0.707285\pi\) | ||||
−0.606144 | + | 0.795355i | \(0.707285\pi\) | |||||||
\(8\) | −10.3185 | −0.456020 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.4410 | 1.43742 | 0.718708 | − | 0.695312i | \(-0.244734\pi\) | ||||
0.718708 | + | 0.695312i | \(0.244734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84.8342 | 1.80991 | 0.904953 | − | 0.425512i | \(-0.139906\pi\) | ||||
0.904953 | + | 0.425512i | \(0.139906\pi\) | |||||||
\(14\) | −81.4328 | −1.55456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.6658 | −1.22915 | ||||||||
\(17\) | 45.4636 | 0.648620 | 0.324310 | − | 0.945951i | \(-0.394868\pi\) | ||||
0.324310 | + | 0.945951i | \(0.394868\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −85.6658 | −1.03437 | −0.517186 | − | 0.855873i | \(-0.673021\pi\) | ||||
−0.517186 | + | 0.855873i | \(0.673021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 190.203 | 1.84325 | ||||||||
\(23\) | 55.7673 | 0.505578 | 0.252789 | − | 0.967521i | \(-0.418652\pi\) | ||||
0.252789 | + | 0.967521i | \(0.418652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 307.693 | 2.32091 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.741 | −0.781179 | ||||||||
\(29\) | 96.5180 | 0.618033 | 0.309016 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309016 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 107.596 | 0.623382 | 0.311691 | − | 0.950183i | \(-0.399105\pi\) | ||||
0.311691 | + | 0.950183i | \(0.399105\pi\) | |||||||
\(32\) | −202.772 | −1.12017 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 164.896 | 0.831748 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.7139 | 0.363073 | 0.181536 | − | 0.983384i | \(-0.441893\pi\) | ||||
0.181536 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(38\) | −310.709 | −1.32641 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 248.066 | 0.944914 | 0.472457 | − | 0.881354i | \(-0.343367\pi\) | ||||
0.472457 | + | 0.881354i | \(0.343367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 292.163 | 1.03615 | 0.518075 | − | 0.855335i | \(-0.326649\pi\) | ||||
0.518075 | + | 0.855335i | \(0.326649\pi\) | |||||||
\(44\) | 270.337 | 0.926247 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 202.268 | 0.648320 | ||||||||
\(47\) | 240.137 | 0.745268 | 0.372634 | − | 0.927978i | \(-0.378455\pi\) | ||||
0.372634 | + | 0.927978i | \(0.378455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 161.088 | 0.469643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 437.326 | 1.16627 | ||||||||
\(53\) | 505.234 | 1.30942 | 0.654710 | − | 0.755881i | \(-0.272791\pi\) | ||||
0.654710 | + | 0.755881i | \(0.272791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 231.671 | 0.552827 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 350.070 | 0.792525 | ||||||||
\(59\) | 613.029 | 1.35270 | 0.676352 | − | 0.736579i | \(-0.263560\pi\) | ||||
0.676352 | + | 0.736579i | \(0.263560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 147.014 | 0.308577 | 0.154288 | − | 0.988026i | \(-0.450692\pi\) | ||||
0.154288 | + | 0.988026i | \(0.450692\pi\) | |||||||
\(62\) | 390.251 | 0.799385 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −106.125 | −0.207276 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55.7251 | 0.101611 | 0.0508053 | − | 0.998709i | \(-0.483821\pi\) | ||||
0.0508053 | + | 0.998709i | \(0.483821\pi\) | |||||||
\(68\) | 234.368 | 0.417960 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −541.270 | −0.904746 | −0.452373 | − | 0.891829i | \(-0.649422\pi\) | ||||
−0.452373 | + | 0.891829i | \(0.649422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −73.4510 | −0.117764 | −0.0588821 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588821 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(74\) | 296.376 | 0.465581 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −441.613 | −0.666533 | ||||||||
\(77\) | −1177.40 | −1.74256 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1222.46 | −1.74099 | −0.870494 | − | 0.492179i | \(-0.836200\pi\) | ||||
−0.870494 | + | 0.492179i | \(0.836200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 899.735 | 1.21170 | ||||||||
\(83\) | −718.235 | −0.949838 | −0.474919 | − | 0.880029i | \(-0.657523\pi\) | ||||
−0.474919 | + | 0.880029i | \(0.657523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1059.67 | 1.32869 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −541.115 | −0.655489 | ||||||||
\(89\) | −540.674 | −0.643948 | −0.321974 | − | 0.946749i | \(-0.604346\pi\) | ||||
−0.321974 | + | 0.946749i | \(0.604346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1904.69 | −2.19413 | ||||||||
\(92\) | 287.484 | 0.325786 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 870.975 | 0.955683 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1669.58 | 1.74763 | 0.873816 | − | 0.486256i | \(-0.161638\pi\) | ||||
0.873816 | + | 0.486256i | \(0.161638\pi\) | |||||||
\(98\) | 584.263 | 0.602240 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −261.609 | −0.257734 | −0.128867 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128867 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −557.014 | −0.532856 | −0.266428 | − | 0.963855i | \(-0.585844\pi\) | ||||
−0.266428 | + | 0.963855i | \(0.585844\pi\) | |||||||
\(104\) | −875.366 | −0.825352 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1832.48 | 1.67911 | ||||||||
\(107\) | 295.633 | 0.267102 | 0.133551 | − | 0.991042i | \(-0.457362\pi\) | ||||
0.133551 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1080.17 | 0.949190 | 0.474595 | − | 0.880204i | \(-0.342595\pi\) | ||||
0.474595 | + | 0.880204i | \(0.342595\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1766.20 | 1.49009 | ||||||||
\(113\) | −2191.08 | −1.82406 | −0.912032 | − | 0.410119i | \(-0.865487\pi\) | ||||
−0.912032 | + | 0.410119i | \(0.865487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 497.557 | 0.398250 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2223.45 | 1.73462 | ||||||||
\(119\) | −1020.74 | −0.786315 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1419.06 | 1.06616 | ||||||||
\(122\) | 533.218 | 0.395699 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 554.666 | 0.401697 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1029.13 | 0.719058 | 0.359529 | − | 0.933134i | \(-0.382937\pi\) | ||||
0.359529 | + | 0.933134i | \(0.382937\pi\) | |||||||
\(128\) | 1237.26 | 0.854370 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2502.10 | −1.66878 | −0.834388 | − | 0.551177i | \(-0.814179\pi\) | ||||
−0.834388 | + | 0.551177i | \(0.814179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1923.36 | 1.25396 | ||||||||
\(134\) | 202.114 | 0.130299 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −469.118 | −0.295784 | ||||||||
\(137\) | 539.139 | 0.336217 | 0.168109 | − | 0.985768i | \(-0.446234\pi\) | ||||
0.168109 | + | 0.985768i | \(0.446234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1050.00 | −0.640720 | −0.320360 | − | 0.947296i | \(-0.603804\pi\) | ||||
−0.320360 | + | 0.947296i | \(0.603804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1963.18 | −1.16019 | ||||||||
\(143\) | 4448.79 | 2.60159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −266.406 | −0.151013 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 421.241 | 0.233958 | ||||||||
\(149\) | −2464.13 | −1.35483 | −0.677415 | − | 0.735601i | \(-0.736900\pi\) | ||||
−0.677415 | + | 0.735601i | \(0.736900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 818.338 | 0.441029 | 0.220514 | − | 0.975384i | \(-0.429226\pi\) | ||||
0.220514 | + | 0.975384i | \(0.429226\pi\) | |||||||
\(152\) | 883.947 | 0.471694 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4270.42 | −2.23455 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 588.328 | 0.299068 | 0.149534 | − | 0.988757i | \(-0.452223\pi\) | ||||
0.149534 | + | 0.988757i | \(0.452223\pi\) | |||||||
\(158\) | −4433.87 | −2.23253 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1252.08 | −0.612906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1371.87 | 0.659220 | 0.329610 | − | 0.944117i | \(-0.393083\pi\) | ||||
0.329610 | + | 0.944117i | \(0.393083\pi\) | |||||||
\(164\) | 1278.80 | 0.608887 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2605.03 | −1.21801 | ||||||||
\(167\) | 482.446 | 0.223550 | 0.111775 | − | 0.993734i | \(-0.464346\pi\) | ||||
0.111775 | + | 0.993734i | \(0.464346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4999.84 | 2.27576 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1506.12 | 0.667678 | ||||||||
\(173\) | −1210.98 | −0.532192 | −0.266096 | − | 0.963947i | \(-0.585734\pi\) | ||||
−0.266096 | + | 0.963947i | \(0.585734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4125.32 | −1.76680 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1961.02 | −0.825757 | ||||||||
\(179\) | −1372.10 | −0.572936 | −0.286468 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286468 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1733.63 | 0.711931 | 0.355965 | − | 0.934499i | \(-0.384152\pi\) | ||||
0.355965 | + | 0.934499i | \(0.384152\pi\) | |||||||
\(182\) | −6908.29 | −2.81361 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −575.438 | −0.230553 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2384.16 | 0.932336 | ||||||||
\(188\) | 1237.92 | 0.480238 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4029.39 | −1.52648 | −0.763238 | − | 0.646118i | \(-0.776391\pi\) | ||||
−0.763238 | + | 0.646118i | \(0.776391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1095.49 | 0.408575 | 0.204288 | − | 0.978911i | \(-0.434512\pi\) | ||||
0.204288 | + | 0.978911i | \(0.434512\pi\) | |||||||
\(194\) | 6055.56 | 2.24105 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 830.417 | 0.302630 | ||||||||
\(197\) | −254.777 | −0.0921428 | −0.0460714 | − | 0.998938i | \(-0.514670\pi\) | ||||
−0.0460714 | + | 0.998938i | \(0.514670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 942.807 | 0.335848 | 0.167924 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167924 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −948.854 | −0.330501 | ||||||||
\(203\) | −2167.01 | −0.749234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2020.28 | −0.683301 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6673.55 | −2.22465 | ||||||||
\(209\) | −4492.40 | −1.48682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2624.31 | −0.856233 | −0.428117 | − | 0.903723i | \(-0.640823\pi\) | ||||
−0.428117 | + | 0.903723i | \(0.640823\pi\) | |||||||
\(212\) | 2604.51 | 0.843768 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1072.26 | 0.342515 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2415.74 | −0.755719 | ||||||||
\(218\) | 3917.77 | 1.21718 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3856.87 | 1.17394 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 976.561 | 0.293253 | 0.146626 | − | 0.989192i | \(-0.453159\pi\) | ||||
0.146626 | + | 0.989192i | \(0.453159\pi\) | |||||||
\(224\) | 4552.61 | 1.35797 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7947.02 | −2.33906 | ||||||||
\(227\) | 4591.31 | 1.34245 | 0.671224 | − | 0.741255i | \(-0.265769\pi\) | ||||
0.671224 | + | 0.741255i | \(0.265769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4640.73 | −1.33916 | −0.669581 | − | 0.742739i | \(-0.733526\pi\) | ||||
−0.669581 | + | 0.742739i | \(0.733526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −995.926 | −0.281835 | ||||||||
\(233\) | 3508.00 | 0.986339 | 0.493169 | − | 0.869933i | \(-0.335838\pi\) | ||||
0.493169 | + | 0.869933i | \(0.335838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3160.20 | 0.871660 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3702.23 | −1.00832 | ||||||||
\(239\) | −889.109 | −0.240635 | −0.120317 | − | 0.992735i | \(-0.538391\pi\) | ||||
−0.120317 | + | 0.992735i | \(0.538391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6433.23 | 1.71951 | 0.859753 | − | 0.510710i | \(-0.170618\pi\) | ||||
0.859753 | + | 0.510710i | \(0.170618\pi\) | |||||||
\(242\) | 5146.93 | 1.36718 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 757.866 | 0.198842 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7267.39 | −1.87212 | ||||||||
\(248\) | −1110.24 | −0.284275 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4538.67 | 1.14135 | 0.570674 | − | 0.821177i | \(-0.306682\pi\) | ||||
0.570674 | + | 0.821177i | \(0.306682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2924.50 | 0.726725 | ||||||||
\(254\) | 3732.64 | 0.922074 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5336.53 | 1.30286 | ||||||||
\(257\) | −4469.84 | −1.08491 | −0.542453 | − | 0.840086i | \(-0.682505\pi\) | ||||
−0.542453 | + | 0.840086i | \(0.682505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1834.63 | −0.440149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9075.10 | −2.13993 | ||||||||
\(263\) | −1738.49 | −0.407603 | −0.203802 | − | 0.979012i | \(-0.565330\pi\) | ||||
−0.203802 | + | 0.979012i | \(0.565330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6976.01 | 1.60799 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 287.267 | 0.0654761 | ||||||||
\(269\) | −7058.43 | −1.59985 | −0.799926 | − | 0.600099i | \(-0.795128\pi\) | ||||
−0.799926 | + | 0.600099i | \(0.795128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5909.97 | −1.32474 | −0.662371 | − | 0.749176i | \(-0.730450\pi\) | ||||
−0.662371 | + | 0.749176i | \(0.730450\pi\) | |||||||
\(272\) | −3576.43 | −0.797254 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1955.45 | 0.431143 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5374.61 | −1.16581 | −0.582904 | − | 0.812541i | \(-0.698084\pi\) | ||||
−0.582904 | + | 0.812541i | \(0.698084\pi\) | |||||||
\(278\) | −3808.35 | −0.821618 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8132.88 | 1.72657 | 0.863286 | − | 0.504715i | \(-0.168402\pi\) | ||||
0.863286 | + | 0.504715i | \(0.168402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4016.36 | 0.843631 | 0.421816 | − | 0.906682i | \(-0.361393\pi\) | ||||
0.421816 | + | 0.906682i | \(0.361393\pi\) | |||||||
\(284\) | −2790.28 | −0.583003 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16135.7 | 3.33610 | ||||||||
\(287\) | −5569.56 | −1.14551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2846.06 | −0.579292 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −378.645 | −0.0758853 | ||||||||
\(293\) | −105.803 | −0.0210958 | −0.0105479 | − | 0.999944i | \(-0.503358\pi\) | ||||
−0.0105479 | + | 0.999944i | \(0.503358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −843.169 | −0.165568 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8937.39 | −1.73735 | ||||||||
\(299\) | 4730.98 | 0.915048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6559.62 | −1.25611 | ||||||||
\(302\) | 2968.10 | 0.565547 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6738.97 | 1.27140 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4638.61 | 0.862344 | 0.431172 | − | 0.902270i | \(-0.358100\pi\) | ||||
0.431172 | + | 0.902270i | \(0.358100\pi\) | |||||||
\(308\) | −6069.58 | −1.12288 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2931.33 | 0.534471 | 0.267235 | − | 0.963631i | \(-0.413890\pi\) | ||||
0.267235 | + | 0.963631i | \(0.413890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5131.09 | −0.926601 | −0.463301 | − | 0.886201i | \(-0.653335\pi\) | ||||
−0.463301 | + | 0.886201i | \(0.653335\pi\) | |||||||
\(314\) | 2133.86 | 0.383506 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6301.89 | −1.12186 | ||||||||
\(317\) | 7218.07 | 1.27889 | 0.639443 | − | 0.768838i | \(-0.279165\pi\) | ||||
0.639443 | + | 0.768838i | \(0.279165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5061.51 | 0.888370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4541.29 | −0.785951 | ||||||||
\(323\) | −3894.68 | −0.670915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4975.75 | 0.845341 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2559.69 | −0.430899 | ||||||||
\(329\) | −5391.53 | −0.903480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1540.33 | 0.255783 | 0.127892 | − | 0.991788i | \(-0.459179\pi\) | ||||
0.127892 | + | 0.991788i | \(0.459179\pi\) | |||||||
\(332\) | −3702.55 | −0.612060 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1749.83 | 0.286666 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10254.4 | 1.65754 | 0.828772 | − | 0.559587i | \(-0.189040\pi\) | ||||
0.828772 | + | 0.559587i | \(0.189040\pi\) | |||||||
\(338\) | 18134.4 | 2.91828 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5642.46 | 0.896059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4084.28 | 0.642946 | ||||||||
\(344\) | −3014.70 | −0.472505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4392.22 | −0.682448 | ||||||||
\(347\) | −7036.23 | −1.08854 | −0.544272 | − | 0.838909i | \(-0.683194\pi\) | ||||
−0.544272 | + | 0.838909i | \(0.683194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2916.17 | −0.447275 | −0.223637 | − | 0.974672i | \(-0.571793\pi\) | ||||
−0.223637 | + | 0.974672i | \(0.571793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10633.6 | −1.61015 | ||||||||
\(353\) | −1203.79 | −0.181505 | −0.0907525 | − | 0.995873i | \(-0.528927\pi\) | ||||
−0.0907525 | + | 0.995873i | \(0.528927\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2787.21 | −0.414949 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4976.59 | −0.734696 | ||||||||
\(359\) | 9039.30 | 1.32890 | 0.664451 | − | 0.747331i | \(-0.268665\pi\) | ||||
0.664451 | + | 0.747331i | \(0.268665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 479.632 | 0.0699275 | ||||||||
\(362\) | 6287.85 | 0.912934 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9818.80 | −1.41386 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3080.85 | −0.438199 | −0.219099 | − | 0.975703i | \(-0.570312\pi\) | ||||
−0.219099 | + | 0.975703i | \(0.570312\pi\) | |||||||
\(368\) | −4386.98 | −0.621433 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11343.5 | −1.58739 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6715.41 | 0.932201 | 0.466100 | − | 0.884732i | \(-0.345659\pi\) | ||||
0.466100 | + | 0.884732i | \(0.345659\pi\) | |||||||
\(374\) | 8647.32 | 1.19557 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2477.87 | −0.339857 | ||||||||
\(377\) | 8188.03 | 1.11858 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5898.85 | −0.799482 | −0.399741 | − | 0.916628i | \(-0.630900\pi\) | ||||
−0.399741 | + | 0.916628i | \(0.630900\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14614.6 | −1.95745 | ||||||||
\(383\) | 7272.18 | 0.970212 | 0.485106 | − | 0.874455i | \(-0.338781\pi\) | ||||
0.485106 | + | 0.874455i | \(0.338781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3973.33 | 0.523930 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8606.81 | 1.12615 | ||||||||
\(389\) | 4756.07 | 0.619904 | 0.309952 | − | 0.950752i | \(-0.399687\pi\) | ||||
0.309952 | + | 0.950752i | \(0.399687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2535.38 | 0.327928 | ||||||||
\(392\) | −1662.19 | −0.214166 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −924.075 | −0.118158 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3579.97 | 0.452578 | 0.226289 | − | 0.974060i | \(-0.427341\pi\) | ||||
0.226289 | + | 0.974060i | \(0.427341\pi\) | |||||||
\(398\) | 3419.55 | 0.430670 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11282.3 | −1.40502 | −0.702509 | − | 0.711674i | \(-0.747937\pi\) | ||||
−0.702509 | + | 0.711674i | \(0.747937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9127.84 | 1.12826 | ||||||||
\(404\) | −1348.61 | −0.166079 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7859.74 | −0.960769 | ||||||||
\(407\) | 4285.16 | 0.521886 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2402.70 | 0.290479 | 0.145240 | − | 0.989397i | \(-0.453605\pi\) | ||||
0.145240 | + | 0.989397i | \(0.453605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2871.44 | −0.343364 | ||||||||
\(413\) | −13763.7 | −1.63987 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −17202.0 | −2.02740 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16293.9 | −1.90661 | ||||||||
\(419\) | 3480.08 | 0.405759 | 0.202879 | − | 0.979204i | \(-0.434970\pi\) | ||||
0.202879 | + | 0.979204i | \(0.434970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5308.38 | −0.614524 | −0.307262 | − | 0.951625i | \(-0.599413\pi\) | ||||
−0.307262 | + | 0.951625i | \(0.599413\pi\) | |||||||
\(422\) | −9518.36 | −1.09798 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5213.28 | −0.597121 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3300.74 | −0.374084 | ||||||||
\(428\) | 1524.01 | 0.172116 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10783.8 | −1.20519 | −0.602595 | − | 0.798047i | \(-0.705867\pi\) | ||||
−0.602595 | + | 0.798047i | \(0.705867\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5480.10 | 0.608215 | 0.304107 | − | 0.952638i | \(-0.401642\pi\) | ||||
0.304107 | + | 0.952638i | \(0.401642\pi\) | |||||||
\(434\) | −8761.87 | −0.969085 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5568.36 | 0.611642 | ||||||||
\(437\) | −4777.35 | −0.522956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8264.22 | 0.898473 | 0.449237 | − | 0.893413i | \(-0.351696\pi\) | ||||
0.449237 | + | 0.893413i | \(0.351696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13988.8 | 1.50539 | ||||||||
\(443\) | 1252.96 | 0.134379 | 0.0671896 | − | 0.997740i | \(-0.478597\pi\) | ||||
0.0671896 | + | 0.997740i | \(0.478597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3541.98 | 0.376048 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2382.72 | 0.251278 | ||||||||
\(449\) | 1792.10 | 0.188362 | 0.0941808 | − | 0.995555i | \(-0.469977\pi\) | ||||
0.0941808 | + | 0.995555i | \(0.469977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13008.9 | 1.35823 | ||||||||
\(452\) | −11295.2 | −1.17540 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16652.6 | 1.72147 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11148.3 | 1.14113 | 0.570566 | − | 0.821252i | \(-0.306724\pi\) | ||||
0.570566 | + | 0.821252i | \(0.306724\pi\) | |||||||
\(458\) | −16831.9 | −1.71725 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9826.57 | 0.992775 | 0.496387 | − | 0.868101i | \(-0.334660\pi\) | ||||
0.496387 | + | 0.868101i | \(0.334660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11379.0 | −1.14217 | −0.571087 | − | 0.820889i | \(-0.693478\pi\) | ||||
−0.571087 | + | 0.820889i | \(0.693478\pi\) | |||||||
\(464\) | −7592.67 | −0.759657 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12723.5 | 1.26482 | ||||||||
\(467\) | −15503.0 | −1.53618 | −0.768089 | − | 0.640343i | \(-0.778792\pi\) | ||||
−0.768089 | + | 0.640343i | \(0.778792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1251.13 | −0.123181 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6325.56 | −0.616859 | ||||||||
\(473\) | 15321.3 | 1.48938 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5262.00 | −0.506688 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3224.79 | −0.308574 | ||||||||
\(479\) | 668.853 | 0.0638010 | 0.0319005 | − | 0.999491i | \(-0.489844\pi\) | ||||
0.0319005 | + | 0.999491i | \(0.489844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6932.13 | 0.657127 | ||||||||
\(482\) | 23333.3 | 2.20498 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7315.36 | 0.687017 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2418.99 | −0.225082 | −0.112541 | − | 0.993647i | \(-0.535899\pi\) | ||||
−0.112541 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(488\) | −1516.97 | −0.140717 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6837.84 | −0.628487 | −0.314244 | − | 0.949342i | \(-0.601751\pi\) | ||||
−0.314244 | + | 0.949342i | \(0.601751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4388.06 | 0.400869 | ||||||||
\(494\) | −26358.8 | −2.40068 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8464.15 | −0.766233 | ||||||||
\(497\) | 12152.5 | 1.09681 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 437.043 | 0.0392079 | 0.0196039 | − | 0.999808i | \(-0.493759\pi\) | ||||
0.0196039 | + | 0.999808i | \(0.493759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16461.7 | 1.46359 | ||||||||
\(503\) | 6970.27 | 0.617871 | 0.308935 | − | 0.951083i | \(-0.400027\pi\) | ||||
0.308935 | + | 0.951083i | \(0.400027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10607.1 | 0.931906 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5305.23 | 0.463349 | ||||||||
\(509\) | −1570.36 | −0.136749 | −0.0683744 | − | 0.997660i | \(-0.521781\pi\) | ||||
−0.0683744 | + | 0.997660i | \(0.521781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1649.11 | 0.142764 | ||||||||
\(512\) | 9457.48 | 0.816339 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16212.1 | −1.39121 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12593.0 | 1.07126 | ||||||||
\(518\) | −6654.20 | −0.564418 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21269.3 | −1.78853 | −0.894265 | − | 0.447538i | \(-0.852301\pi\) | ||||
−0.894265 | + | 0.447538i | \(0.852301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13992.1 | −1.16985 | −0.584926 | − | 0.811087i | \(-0.698876\pi\) | ||||
−0.584926 | + | 0.811087i | \(0.698876\pi\) | |||||||
\(524\) | −12898.5 | −1.07533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6305.48 | −0.522684 | ||||||||
\(527\) | 4891.71 | 0.404338 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9057.00 | −0.744391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9915.05 | 0.808030 | ||||||||
\(533\) | 21044.5 | 1.71020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −575.002 | −0.0463364 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25600.9 | −2.05155 | ||||||||
\(539\) | 8447.60 | 0.675072 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16742.7 | −1.33054 | −0.665272 | − | 0.746601i | \(-0.731684\pi\) | ||||
−0.665272 | + | 0.746601i | \(0.731684\pi\) | |||||||
\(542\) | −21435.4 | −1.69876 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9218.74 | −0.726563 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6283.10 | −0.491126 | −0.245563 | − | 0.969381i | \(-0.578973\pi\) | ||||
−0.245563 | + | 0.969381i | \(0.578973\pi\) | |||||||
\(548\) | 2779.30 | 0.216653 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8268.30 | −0.639276 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27446.7 | 2.11058 | ||||||||
\(554\) | −19493.7 | −1.49496 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5412.83 | −0.412869 | ||||||||
\(557\) | 11043.6 | 0.840093 | 0.420047 | − | 0.907503i | \(-0.362014\pi\) | ||||
0.420047 | + | 0.907503i | \(0.362014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24785.4 | 1.87533 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29497.9 | 2.21404 | ||||||||
\(563\) | −22448.3 | −1.68043 | −0.840216 | − | 0.542252i | \(-0.817572\pi\) | ||||
−0.840216 | + | 0.542252i | \(0.817572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14567.3 | 1.08182 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5585.12 | 0.412582 | ||||||||
\(569\) | 7816.69 | 0.575910 | 0.287955 | − | 0.957644i | \(-0.407025\pi\) | ||||
0.287955 | + | 0.957644i | \(0.407025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11397.1 | −0.835294 | −0.417647 | − | 0.908609i | \(-0.637145\pi\) | ||||
−0.417647 | + | 0.908609i | \(0.637145\pi\) | |||||||
\(572\) | 22933.8 | 1.67642 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20200.8 | −1.46893 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10649.9 | −0.768393 | −0.384196 | − | 0.923251i | \(-0.625521\pi\) | ||||
−0.384196 | + | 0.923251i | \(0.625521\pi\) | |||||||
\(578\) | −10322.6 | −0.742846 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16125.7 | 1.15148 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26495.0 | 1.88218 | ||||||||
\(584\) | 757.907 | 0.0537028 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −383.746 | −0.0270519 | ||||||||
\(587\) | −16310.8 | −1.14688 | −0.573440 | − | 0.819247i | \(-0.694392\pi\) | ||||
−0.573440 | + | 0.819247i | \(0.694392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9217.32 | −0.644810 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6428.09 | −0.446272 | ||||||||
\(593\) | −24814.4 | −1.71839 | −0.859195 | − | 0.511648i | \(-0.829035\pi\) | ||||
−0.859195 | + | 0.511648i | \(0.829035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12702.8 | −0.873030 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17159.2 | 1.17340 | ||||||||
\(599\) | 22999.3 | 1.56883 | 0.784414 | − | 0.620238i | \(-0.212964\pi\) | ||||
0.784414 | + | 0.620238i | \(0.212964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15453.8 | 1.04887 | 0.524437 | − | 0.851449i | \(-0.324276\pi\) | ||||
0.524437 | + | 0.851449i | \(0.324276\pi\) | |||||||
\(602\) | −23791.7 | −1.61076 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4218.59 | 0.284192 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10510.2 | 0.702793 | 0.351396 | − | 0.936227i | \(-0.385707\pi\) | ||||
0.351396 | + | 0.936227i | \(0.385707\pi\) | |||||||
\(608\) | 17370.6 | 1.15867 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20371.8 | 1.34886 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18146.3 | 1.19563 | 0.597817 | − | 0.801633i | \(-0.296035\pi\) | ||||
0.597817 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(614\) | 16824.2 | 1.10581 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12149.1 | 0.794642 | ||||||||
\(617\) | −20368.1 | −1.32899 | −0.664495 | − | 0.747292i | \(-0.731353\pi\) | ||||
−0.664495 | + | 0.747292i | \(0.731353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5632.50 | −0.365734 | −0.182867 | − | 0.983138i | \(-0.558538\pi\) | ||||
−0.182867 | + | 0.983138i | \(0.558538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10631.9 | 0.685370 | ||||||||
\(623\) | 12139.2 | 0.780650 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18610.4 | −1.18821 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3032.87 | 0.192715 | ||||||||
\(629\) | 3715.01 | 0.235496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10522.9 | 0.663882 | 0.331941 | − | 0.943300i | \(-0.392296\pi\) | ||||
0.331941 | + | 0.943300i | \(0.392296\pi\) | |||||||
\(632\) | 12614.1 | 0.793925 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26179.9 | 1.63996 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13665.7 | 0.850010 | ||||||||
\(638\) | 18358.0 | 1.13919 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17567.1 | 1.08246 | 0.541232 | − | 0.840874i | \(-0.317958\pi\) | ||||
0.541232 | + | 0.840874i | \(0.317958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11339.8 | 0.695489 | 0.347745 | − | 0.937589i | \(-0.386948\pi\) | ||||
0.347745 | + | 0.937589i | \(0.386948\pi\) | |||||||
\(644\) | −6454.57 | −0.394947 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14126.0 | −0.860338 | ||||||||
\(647\) | 12382.6 | 0.752411 | 0.376205 | − | 0.926536i | \(-0.377229\pi\) | ||||
0.376205 | + | 0.926536i | \(0.377229\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32147.9 | 1.94440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7072.06 | 0.424790 | ||||||||
\(653\) | −5075.83 | −0.304185 | −0.152092 | − | 0.988366i | \(-0.548601\pi\) | ||||
−0.152092 | + | 0.988366i | \(0.548601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19514.4 | −1.16144 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19555.0 | −1.15856 | ||||||||
\(659\) | −4410.87 | −0.260733 | −0.130367 | − | 0.991466i | \(-0.541615\pi\) | ||||
−0.130367 | + | 0.991466i | \(0.541615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16077.7 | −0.946065 | −0.473032 | − | 0.881045i | \(-0.656841\pi\) | ||||
−0.473032 | + | 0.881045i | \(0.656841\pi\) | |||||||
\(662\) | 5586.77 | 0.328000 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7411.15 | 0.433145 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5382.55 | 0.312464 | ||||||||
\(668\) | 2487.04 | 0.144052 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7709.56 | 0.443553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6603.48 | −0.378225 | −0.189113 | − | 0.981955i | \(-0.560561\pi\) | ||||
−0.189113 | + | 0.981955i | \(0.560561\pi\) | |||||||
\(674\) | 37192.6 | 2.12553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25774.5 | 1.46646 | ||||||||
\(677\) | −8956.50 | −0.508458 | −0.254229 | − | 0.967144i | \(-0.581822\pi\) | ||||
−0.254229 | + | 0.967144i | \(0.581822\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37485.3 | −2.11863 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20465.1 | 1.14905 | ||||||||
\(683\) | 6280.32 | 0.351844 | 0.175922 | − | 0.984404i | \(-0.443709\pi\) | ||||
0.175922 | + | 0.984404i | \(0.443709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14813.6 | 0.824472 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22983.3 | −1.27359 | ||||||||
\(689\) | 42861.1 | 2.36992 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16698.1 | −0.919284 | −0.459642 | − | 0.888104i | \(-0.652022\pi\) | ||||
−0.459642 | + | 0.888104i | \(0.652022\pi\) | |||||||
\(692\) | −6242.69 | −0.342936 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25520.3 | −1.39588 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11278.0 | 0.612890 | ||||||||
\(698\) | −10576.9 | −0.573556 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11420.7 | 0.615338 | 0.307669 | − | 0.951493i | \(-0.400451\pi\) | ||||
0.307669 | + | 0.951493i | \(0.400451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7000.09 | −0.375552 | ||||||||
\(704\) | −5565.33 | −0.297942 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4366.14 | −0.232750 | ||||||||
\(707\) | 5873.62 | 0.312447 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3436.21 | 0.182016 | 0.0910081 | − | 0.995850i | \(-0.470991\pi\) | ||||
0.0910081 | + | 0.995850i | \(0.470991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5578.97 | 0.293653 | ||||||||
\(713\) | 6000.36 | 0.315168 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7073.26 | −0.369190 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32785.5 | 1.70410 | ||||||||
\(719\) | −20029.0 | −1.03888 | −0.519441 | − | 0.854506i | \(-0.673860\pi\) | ||||
−0.519441 | + | 0.854506i | \(0.673860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12506.0 | 0.645976 | ||||||||
\(722\) | 1739.62 | 0.0896704 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8936.97 | 0.458757 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2639.99 | 0.134679 | 0.0673397 | − | 0.997730i | \(-0.478549\pi\) | ||||
0.0673397 | + | 0.997730i | \(0.478549\pi\) | |||||||
\(728\) | 19653.6 | 1.00057 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13282.8 | 0.672068 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19707.5 | −0.993060 | −0.496530 | − | 0.868020i | \(-0.665393\pi\) | ||||
−0.496530 | + | 0.868020i | \(0.665393\pi\) | |||||||
\(734\) | −11174.2 | −0.561918 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11308.0 | −0.566332 | ||||||||
\(737\) | 2922.28 | 0.146056 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11755.6 | −0.585163 | −0.292581 | − | 0.956241i | \(-0.594514\pi\) | ||||
−0.292581 | + | 0.956241i | \(0.594514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41142.6 | −2.03557 | ||||||||
\(743\) | −21494.4 | −1.06131 | −0.530655 | − | 0.847588i | \(-0.678054\pi\) | ||||
−0.530655 | + | 0.847588i | \(0.678054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24356.7 | 1.19539 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12290.5 | 0.600782 | ||||||||
\(749\) | −6637.53 | −0.323805 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36993.3 | 1.79748 | 0.898739 | − | 0.438483i | \(-0.144484\pi\) | ||||
0.898739 | + | 0.438483i | \(0.144484\pi\) | |||||||
\(752\) | −18890.6 | −0.916049 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29697.9 | 1.43440 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34002.3 | 1.63254 | 0.816272 | − | 0.577668i | \(-0.196037\pi\) | ||||
0.816272 | + | 0.577668i | \(0.196037\pi\) | |||||||
\(758\) | −21395.1 | −1.02520 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20068.2 | 0.955943 | 0.477971 | − | 0.878375i | \(-0.341372\pi\) | ||||
0.477971 | + | 0.878375i | \(0.341372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24251.9 | −1.15069 | ||||||||
\(764\) | −20771.8 | −0.983635 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26376.2 | 1.24414 | ||||||||
\(767\) | 52005.8 | 2.44827 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7422.88 | −0.348083 | −0.174042 | − | 0.984738i | \(-0.555683\pi\) | ||||
−0.174042 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5647.32 | 0.263279 | ||||||||
\(773\) | 2410.40 | 0.112155 | 0.0560777 | − | 0.998426i | \(-0.482141\pi\) | ||||
0.0560777 | + | 0.998426i | \(0.482141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17227.7 | −0.796955 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17250.2 | 0.794924 | ||||||||
\(779\) | −21250.8 | −0.977393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28384.8 | −1.30050 | ||||||||
\(782\) | 9195.82 | 0.420514 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12672.1 | −0.577263 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17506.7 | −0.792945 | −0.396472 | − | 0.918047i | \(-0.629766\pi\) | ||||
−0.396472 | + | 0.918047i | \(0.629766\pi\) | |||||||
\(788\) | −1313.39 | −0.0593753 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49193.8 | 2.21129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12471.8 | 0.558495 | ||||||||
\(794\) | 12984.5 | 0.580356 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4860.23 | 0.216415 | ||||||||
\(797\) | −19875.1 | −0.883327 | −0.441663 | − | 0.897181i | \(-0.645611\pi\) | ||||
−0.441663 | + | 0.897181i | \(0.645611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10917.5 | 0.483396 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −40920.9 | −1.80170 | ||||||||
\(803\) | −3851.84 | −0.169276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33106.6 | 1.44681 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2699.43 | 0.117532 | ||||||||
\(809\) | 23451.1 | 1.01916 | 0.509578 | − | 0.860425i | \(-0.329802\pi\) | ||||
0.509578 | + | 0.860425i | \(0.329802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2190.02 | 0.0948237 | 0.0474118 | − | 0.998875i | \(-0.484903\pi\) | ||||
0.0474118 | + | 0.998875i | \(0.484903\pi\) | |||||||
\(812\) | −11171.1 | −0.482794 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15542.2 | 0.669233 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25028.4 | −1.07177 | ||||||||
\(818\) | 8714.58 | 0.372492 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17276.4 | −0.734411 | −0.367205 | − | 0.930140i | \(-0.619685\pi\) | ||||
−0.367205 | + | 0.930140i | \(0.619685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17501.7 | −0.741277 | −0.370639 | − | 0.928777i | \(-0.620861\pi\) | ||||
−0.370639 | + | 0.928777i | \(0.620861\pi\) | |||||||
\(824\) | 5747.57 | 0.242993 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −49920.7 | −2.10286 | ||||||||
\(827\) | 16849.9 | 0.708499 | 0.354250 | − | 0.935151i | \(-0.384736\pi\) | ||||
0.354250 | + | 0.935151i | \(0.384736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25450.3 | 1.06626 | 0.533128 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533128 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9003.06 | −0.375150 | ||||||||
\(833\) | 7323.62 | 0.304620 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23158.6 | −0.958084 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12622.2 | 0.520319 | ||||||||
\(839\) | −17571.1 | −0.723028 | −0.361514 | − | 0.932367i | \(-0.617740\pi\) | ||||
−0.361514 | + | 0.932367i | \(0.617740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15073.3 | −0.618036 | ||||||||
\(842\) | −19253.4 | −0.788025 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13528.5 | −0.551743 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31860.6 | −1.29250 | ||||||||
\(848\) | −39744.6 | −1.60948 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4556.97 | 0.183561 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40906.9 | −1.64200 | −0.821001 | − | 0.570927i | \(-0.806584\pi\) | ||||
−0.821001 | + | 0.570927i | \(0.806584\pi\) | |||||||
\(854\) | −11971.7 | −0.479701 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3050.50 | −0.121804 | ||||||||
\(857\) | −32541.9 | −1.29709 | −0.648547 | − | 0.761174i | \(-0.724623\pi\) | ||||
−0.648547 | + | 0.761174i | \(0.724623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36358.6 | −1.44417 | −0.722084 | − | 0.691806i | \(-0.756815\pi\) | ||||
−0.722084 | + | 0.691806i | \(0.756815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39112.7 | −1.54546 | ||||||||
\(863\) | 36628.0 | 1.44476 | 0.722382 | − | 0.691494i | \(-0.243047\pi\) | ||||
0.722382 | + | 0.691494i | \(0.243047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19876.3 | 0.779935 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12453.3 | −0.486973 | ||||||||
\(869\) | −64107.3 | −2.50252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4727.39 | 0.183905 | ||||||||
\(872\) | −11145.8 | −0.432849 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17327.4 | −0.670605 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7837.47 | −0.301770 | −0.150885 | − | 0.988551i | \(-0.548212\pi\) | ||||
−0.150885 | + | 0.988551i | \(0.548212\pi\) | |||||||
\(878\) | 29974.3 | 1.15214 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49066.1 | −1.87637 | −0.938183 | − | 0.346140i | \(-0.887492\pi\) | ||||
−0.938183 | + | 0.346140i | \(0.887492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13551.9 | −0.516486 | −0.258243 | − | 0.966080i | \(-0.583144\pi\) | ||||
−0.258243 | + | 0.966080i | \(0.583144\pi\) | |||||||
\(884\) | 19882.4 | 0.756468 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4544.48 | 0.172319 | ||||||||
\(887\) | −39447.1 | −1.49324 | −0.746620 | − | 0.665251i | \(-0.768325\pi\) | ||||
−0.746620 | + | 0.665251i | \(0.768325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23105.9 | −0.871706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5034.24 | 0.188967 | ||||||||
\(893\) | −20571.5 | −0.770885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −27778.8 | −1.03574 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6499.92 | 0.241543 | ||||||||
\(899\) | 10385.0 | 0.385271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22969.8 | 0.849316 | ||||||||
\(902\) | 47183.0 | 1.74171 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22608.7 | 0.831809 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22027.4 | −0.806403 | −0.403202 | − | 0.915111i | \(-0.632103\pi\) | ||||
−0.403202 | + | 0.915111i | \(0.632103\pi\) | |||||||
\(908\) | 23668.5 | 0.865051 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25475.9 | 0.926512 | 0.463256 | − | 0.886224i | \(-0.346681\pi\) | ||||
0.463256 | + | 0.886224i | \(0.346681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37665.0 | −1.36531 | ||||||||
\(914\) | 40435.0 | 1.46331 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23923.3 | −0.862934 | ||||||||
\(917\) | 56176.9 | 2.02304 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53379.4 | 1.91602 | 0.958011 | − | 0.286733i | \(-0.0925691\pi\) | ||||
0.958011 | + | 0.286733i | \(0.0925691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35640.9 | 1.27307 | ||||||||
\(923\) | −45918.2 | −1.63750 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −41271.5 | −1.46465 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19571.1 | −0.692300 | ||||||||
\(929\) | 25713.7 | 0.908114 | 0.454057 | − | 0.890973i | \(-0.349976\pi\) | ||||
0.454057 | + | 0.890973i | \(0.349976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13799.7 | −0.485786 | ||||||||
\(932\) | 18084.0 | 0.635580 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −56229.4 | −1.96990 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35971.8 | 1.25416 | 0.627080 | − | 0.778955i | \(-0.284250\pi\) | ||||
0.627080 | + | 0.778955i | \(0.284250\pi\) | |||||||
\(938\) | −4537.85 | −0.157960 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34548.6 | −1.19687 | −0.598434 | − | 0.801172i | \(-0.704210\pi\) | ||||
−0.598434 | + | 0.801172i | \(0.704210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13834.0 | 0.477728 | ||||||||
\(944\) | −48224.4 | −1.66268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55570.4 | 1.90988 | ||||||||
\(947\) | −4988.80 | −0.171187 | −0.0855936 | − | 0.996330i | \(-0.527279\pi\) | ||||
−0.0855936 | + | 0.996330i | \(0.527279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6231.15 | −0.213142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10532.6 | 0.358575 | ||||||||
\(953\) | 5720.11 | 0.194431 | 0.0972154 | − | 0.995263i | \(-0.469006\pi\) | ||||
0.0972154 | + | 0.995263i | \(0.469006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4583.42 | −0.155061 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2425.92 | 0.0818142 | ||||||||
\(959\) | −12104.7 | −0.407592 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18214.1 | −0.611394 | ||||||||
\(962\) | 25142.8 | 0.842657 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33163.7 | 1.10802 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47265.0 | −1.57181 | −0.785904 | − | 0.618348i | \(-0.787802\pi\) | ||||
−0.785904 | + | 0.618348i | \(0.787802\pi\) | |||||||
\(968\) | −14642.7 | −0.486191 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42574.9 | −1.40710 | −0.703549 | − | 0.710647i | \(-0.748402\pi\) | ||||
−0.703549 | + | 0.710647i | \(0.748402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23574.5 | 0.776737 | ||||||||
\(974\) | −8773.66 | −0.288631 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11565.0 | −0.379288 | ||||||||
\(977\) | −40481.5 | −1.32561 | −0.662804 | − | 0.748793i | \(-0.730634\pi\) | ||||
−0.662804 | + | 0.748793i | \(0.730634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28353.5 | −0.925620 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24800.8 | −0.805932 | ||||||||
\(983\) | 35891.9 | 1.16457 | 0.582285 | − | 0.812985i | \(-0.302159\pi\) | ||||
0.582285 | + | 0.812985i | \(0.302159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15915.4 | 0.514048 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37463.9 | −1.20636 | ||||||||
\(989\) | 16293.2 | 0.523855 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2150.76 | 0.0689416 | 0.0344708 | − | 0.999406i | \(-0.489025\pi\) | ||||
0.0344708 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(992\) | −21817.5 | −0.698292 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 44077.2 | 1.40648 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18757.6 | 0.595847 | 0.297924 | − | 0.954590i | \(-0.403706\pi\) | ||||
0.297924 | + | 0.954590i | \(0.403706\pi\) | |||||||
\(998\) | 1585.15 | 0.0502776 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.4.a.bc.1.5 | 6 | ||
3.2 | odd | 2 | inner | 675.4.a.bc.1.2 | 6 | ||
5.2 | odd | 4 | 135.4.b.c.109.9 | yes | 12 | ||
5.3 | odd | 4 | 135.4.b.c.109.3 | ✓ | 12 | ||
5.4 | even | 2 | 675.4.a.bb.1.2 | 6 | |||
15.2 | even | 4 | 135.4.b.c.109.4 | yes | 12 | ||
15.8 | even | 4 | 135.4.b.c.109.10 | yes | 12 | ||
15.14 | odd | 2 | 675.4.a.bb.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.b.c.109.3 | ✓ | 12 | 5.3 | odd | 4 | ||
135.4.b.c.109.4 | yes | 12 | 15.2 | even | 4 | ||
135.4.b.c.109.9 | yes | 12 | 5.2 | odd | 4 | ||
135.4.b.c.109.10 | yes | 12 | 15.8 | even | 4 | ||
675.4.a.bb.1.2 | 6 | 5.4 | even | 2 | |||
675.4.a.bb.1.5 | 6 | 15.14 | odd | 2 | |||
675.4.a.bc.1.2 | 6 | 3.2 | odd | 2 | inner | ||
675.4.a.bc.1.5 | 6 | 1.1 | even | 1 | trivial |