Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 152x^{2} - 177x + 2922 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.46638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.726342 | −0.0649660 | −0.0324830 | − | 0.999472i | \(-0.510341\pi\) | ||||
−0.0324830 | + | 0.999472i | \(0.510341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −64.4895 | −1.76766 | −0.883832 | − | 0.467804i | \(-0.845045\pi\) | ||||
−0.883832 | + | 0.467804i | \(0.845045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −71.8475 | −1.53284 | −0.766420 | − | 0.642340i | \(-0.777964\pi\) | ||||
−0.766420 | + | 0.642340i | \(0.777964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.17903 | 0.0375081 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −48.9034 | −0.697694 | −0.348847 | − | 0.937180i | \(-0.613427\pi\) | ||||
−0.348847 | + | 0.937180i | \(0.613427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −34.3968 | −0.415325 | −0.207663 | − | 0.978201i | \(-0.566586\pi\) | ||||
−0.207663 | + | 0.978201i | \(0.566586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.903350 | −0.00818963 | −0.00409482 | − | 0.999992i | \(-0.501303\pi\) | ||||
−0.00409482 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.472 | −0.995779 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 226.686 | 1.45154 | 0.725769 | − | 0.687939i | \(-0.241484\pi\) | ||||
0.725769 | + | 0.687939i | \(0.241484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 275.795 | 1.59788 | 0.798940 | − | 0.601411i | \(-0.205395\pi\) | ||||
0.798940 | + | 0.601411i | \(0.205395\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 193.468 | 1.02056 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 295.209 | 1.31168 | 0.655839 | − | 0.754901i | \(-0.272315\pi\) | ||||
0.655839 | + | 0.754901i | \(0.272315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 215.543 | 0.884985 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −186.604 | −0.710798 | −0.355399 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355399 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −455.317 | −1.61477 | −0.807386 | − | 0.590023i | \(-0.799119\pi\) | ||||
−0.807386 | + | 0.590023i | \(0.799119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.53708 | −0.0216553 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −282.334 | −0.876228 | −0.438114 | − | 0.898920i | \(-0.644353\pi\) | ||||
−0.438114 | + | 0.898920i | \(0.644353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 146.710 | 0.402814 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 356.214 | 0.923204 | 0.461602 | − | 0.887087i | \(-0.347275\pi\) | ||||
0.461602 | + | 0.887087i | \(0.347275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.8414 | 0.114838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 103.191 | 0.239788 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −729.370 | −1.60942 | −0.804711 | − | 0.593667i | \(-0.797680\pi\) | ||||
−0.804711 | + | 0.593667i | \(0.797680\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −274.353 | −0.575856 | −0.287928 | − | 0.957652i | \(-0.592966\pi\) | ||||
−0.287928 | + | 0.957652i | \(0.592966\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 52.1859 | 0.0995825 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 193.272 | 0.352417 | 0.176209 | − | 0.984353i | \(-0.443617\pi\) | ||||
0.176209 | + | 0.984353i | \(0.443617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.71005 | 0.00472829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.5277 | 0.0677429 | 0.0338715 | − | 0.999426i | \(-0.489216\pi\) | ||||
0.0338715 | + | 0.999426i | \(0.489216\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 206.472 | 0.331038 | 0.165519 | − | 0.986207i | \(-0.447070\pi\) | ||||
0.165519 | + | 0.986207i | \(0.447070\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 373.417 | 0.574914 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 937.741 | 1.33549 | 0.667747 | − | 0.744388i | \(-0.267259\pi\) | ||||
0.667747 | + | 0.744388i | \(0.267259\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −911.607 | −1.20556 | −0.602782 | − | 0.797906i | \(-0.705941\pi\) | ||||
−0.602782 | + | 0.797906i | \(0.705941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.5206 | 0.0453264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −680.059 | −0.838045 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 949.975 | 1.13143 | 0.565715 | − | 0.824601i | \(-0.308600\pi\) | ||||
0.565715 | + | 0.824601i | \(0.308600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −827.385 | −0.922536 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.9839 | 0.0269820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39.4687 | −0.0413138 | −0.0206569 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206569 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −580.405 | −0.589221 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 316.874 | 0.312180 | 0.156090 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156090 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 322.634 | 0.308641 | 0.154321 | − | 0.988021i | \(-0.450681\pi\) | ||||
0.154321 | + | 0.988021i | \(0.450681\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 681.451 | 0.615686 | 0.307843 | − | 0.951437i | \(-0.400393\pi\) | ||||
0.307843 | + | 0.951437i | \(0.400393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −455.967 | −0.400677 | −0.200338 | − | 0.979727i | \(-0.564204\pi\) | ||||
−0.200338 | + | 0.979727i | \(0.564204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −885.627 | −0.757297 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −796.025 | −0.662688 | −0.331344 | − | 0.943510i | \(-0.607502\pi\) | ||||
−0.331344 | + | 0.943510i | \(0.607502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.656141 | 0.000532048 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −646.628 | −0.510947 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2827.89 | 2.12464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 559.813 | 0.410379 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 181.202 | 0.129658 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2333.92 | 1.63072 | 0.815362 | − | 0.578952i | \(-0.196538\pi\) | ||||
0.815362 | + | 0.578952i | \(0.196538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1365.95 | 0.932289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1886.98 | 1.25852 | 0.629259 | − | 0.777195i | \(-0.283358\pi\) | ||||
0.629259 | + | 0.777195i | \(0.283358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.6112 | 0.0125027 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2947.26 | 1.83797 | 0.918983 | − | 0.394297i | \(-0.129012\pi\) | ||||
0.918983 | + | 0.394297i | \(0.129012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −955.433 | −0.583013 | −0.291506 | − | 0.956569i | \(-0.594156\pi\) | ||||
−0.291506 | + | 0.956569i | \(0.594156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 847.003 | 0.505890 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4633.41 | 2.70955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −164.652 | −0.0943006 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2183.74 | 1.20066 | 0.600332 | − | 0.799751i | \(-0.295035\pi\) | ||||
0.600332 | + | 0.799751i | \(0.295035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 404.719 | 0.218116 | 0.109058 | − | 0.994035i | \(-0.465217\pi\) | ||||
0.109058 | + | 0.994035i | \(0.465217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −440.130 | −0.232565 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −200.322 | −0.103808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 929.582 | 0.472540 | 0.236270 | − | 0.971687i | \(-0.424075\pi\) | ||||
0.236270 | + | 0.971687i | \(0.424075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1068.64 | −0.533012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1425.68 | −0.685079 | −0.342540 | − | 0.939503i | \(-0.611287\pi\) | ||||
−0.342540 | + | 0.939503i | \(0.611287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −140.524 | −0.0663018 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4185.15 | −1.93926 | −0.969631 | − | 0.244572i | \(-0.921353\pi\) | ||||
−0.969631 | + | 0.244572i | \(0.921353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2965.07 | 1.34960 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −309.572 | −0.138442 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2235.55 | −0.982462 | −0.491231 | − | 0.871029i | \(-0.663453\pi\) | ||||
−0.491231 | + | 0.871029i | \(0.663453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2188.11 | 0.929200 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −941.479 | −0.393126 | −0.196563 | − | 0.980491i | \(-0.562978\pi\) | ||||
−0.196563 | + | 0.980491i | \(0.562978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 467.540 | 0.192000 | 0.0960000 | − | 0.995381i | \(-0.469395\pi\) | ||||
0.0960000 | + | 0.995381i | \(0.469395\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 823.058 | 0.332471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −214.423 | −0.0852144 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3153.75 | 1.23329 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 275.403 | 0.104332 | 0.0521660 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521660 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1640.30 | 0.611767 | 0.305884 | − | 0.952069i | \(-0.401048\pi\) | ||||
0.305884 | + | 0.952069i | \(0.401048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −156.558 | −0.0574940 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1303.88 | 0.471560 | 0.235780 | − | 0.971806i | \(-0.424236\pi\) | ||||
0.235780 | + | 0.971806i | \(0.424236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1327.36 | 0.472833 | 0.236417 | − | 0.971652i | \(-0.424027\pi\) | ||||
0.236417 | + | 0.971652i | \(0.424027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −579.817 | −0.203468 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 135.539 | 0.0461777 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.13015 | −0.00272988 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2218.23 | 0.734155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4753.28 | −1.55085 | −0.775426 | − | 0.631439i | \(-0.782465\pi\) | ||||
−0.775426 | + | 0.631439i | \(0.782465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −121.583 | −0.0391114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 330.716 | 0.104905 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −619.417 | −0.191125 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3513.58 | 1.06945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −513.149 | −0.154094 | −0.0770470 | − | 0.997027i | \(-0.524549\pi\) | ||||
−0.0770470 | + | 0.997027i | \(0.524549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1120.25 | −0.331926 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3309.34 | −0.967616 | −0.483808 | − | 0.875174i | \(-0.660747\pi\) | ||||
−0.483808 | + | 0.875174i | \(0.660747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5909.47 | 1.70528 | 0.852639 | − | 0.522501i | \(-0.175001\pi\) | ||||
0.852639 | + | 0.522501i | \(0.175001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −353.572 | −0.0994131 | −0.0497065 | − | 0.998764i | \(-0.515829\pi\) | ||||
−0.0497065 | + | 0.998764i | \(0.515829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 205.071 | 0.0569250 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2813.22 | −0.771048 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1652.55 | −0.447259 | −0.223629 | − | 0.974674i | \(-0.571791\pi\) | ||||
−0.223629 | + | 0.974674i | \(0.571791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3106.95 | 0.830440 | 0.415220 | − | 0.909721i | \(-0.363705\pi\) | ||||
0.415220 | + | 0.909721i | \(0.363705\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2471.33 | 0.636627 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2734.82 | 0.696033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1771.77 | −0.445551 | −0.222776 | − | 0.974870i | \(-0.571512\pi\) | ||||
−0.222776 | + | 0.974870i | \(0.571512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58.2566 | 0.0144765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −106.562 | −0.0261692 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1478.13 | −0.358766 | −0.179383 | − | 0.983779i | \(-0.557410\pi\) | ||||
−0.179383 | + | 0.983779i | \(0.557410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2040.18 | 0.483846 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1431.97 | −0.335739 | −0.167869 | − | 0.985809i | \(-0.553689\pi\) | ||||
−0.167869 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −258.734 | −0.0599769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2849.93 | −0.653231 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −285.398 | −0.0646879 | −0.0323439 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323439 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5249.33 | 1.17666 | 0.588328 | − | 0.808622i | \(-0.299786\pi\) | ||||
0.588328 | + | 0.808622i | \(0.299786\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8027.16 | 1.76020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7147.87 | 1.55045 | 0.775224 | − | 0.631687i | \(-0.217637\pi\) | ||||
0.775224 | + | 0.631687i | \(0.217637\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2482.16 | 0.532627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4228.36 | 0.897661 | 0.448831 | − | 0.893617i | \(-0.351841\pi\) | ||||
0.448831 | + | 0.893617i | \(0.351841\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8342.38 | −1.75231 | −0.876154 | − | 0.482031i | \(-0.839899\pi\) | ||||
−0.876154 | + | 0.482031i | \(0.839899\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −74.9516 | −0.0155781 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2521.46 | −0.513223 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 118.406 | 0.0238525 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5038.84 | −1.00468 | −0.502342 | − | 0.864669i | \(-0.667528\pi\) | ||||
−0.502342 | + | 0.864669i | \(0.667528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 529.772 | 0.104558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1741.22 | 0.340187 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 64.9035 | 0.0125534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −950.623 | −0.180237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 199.274 | 0.0374111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4869.67 | 0.905300 | 0.452650 | − | 0.891688i | \(-0.350479\pi\) | ||||
0.452650 | + | 0.891688i | \(0.350479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −967.901 | −0.178194 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1452.84 | 0.264897 | 0.132449 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132449 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5696.27 | −1.02867 | −0.514333 | − | 0.857591i | \(-0.671960\pi\) | ||||
−0.514333 | + | 0.857591i | \(0.671960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3471.47 | −0.615070 | −0.307535 | − | 0.951537i | \(-0.599504\pi\) | ||||
−0.307535 | + | 0.951537i | \(0.599504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14618.9 | −2.56583 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2044.35 | −0.355466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1682.12 | 0.289770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8943.03 | 1.52637 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1367.90 | 0.231331 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6254.38 | 1.03859 | 0.519293 | − | 0.854597i | \(-0.326195\pi\) | ||||
0.519293 | + | 0.854597i | \(0.326195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2656.88 | 0.437226 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −140.382 | −0.0228951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8006.96 | 1.29426 | 0.647132 | − | 0.762378i | \(-0.275968\pi\) | ||||
0.647132 | + | 0.762378i | \(0.275968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2388.08 | 0.382603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17785.9 | −2.82451 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.96842 | −0.000307178 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7635.59 | 1.18127 | 0.590634 | − | 0.806940i | \(-0.298878\pi\) | ||||
0.590634 | + | 0.806940i | \(0.298878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10358.0 | 1.58869 | 0.794345 | − | 0.607468i | \(-0.207815\pi\) | ||||
0.794345 | + | 0.607468i | \(0.207815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1939.88 | 0.294995 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3384.23 | −0.510268 | −0.255134 | − | 0.966906i | \(-0.582120\pi\) | ||||
−0.255134 | + | 0.966906i | \(0.582120\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.4369 | −0.00440099 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8194.61 | −1.20472 | −0.602361 | − | 0.798224i | \(-0.705773\pi\) | ||||
−0.602361 | + | 0.798224i | \(0.705773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5675.86 | −0.827505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8483.67 | −1.22666 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −149.970 | −0.0215062 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −805.510 | −0.114570 | −0.0572851 | − | 0.998358i | \(-0.518244\pi\) | ||||
−0.0572851 | + | 0.998358i | \(0.518244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1679.44 | −0.236933 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7905.71 | 1.09743 | 0.548716 | − | 0.836009i | \(-0.315117\pi\) | ||||
0.548716 | + | 0.836009i | \(0.315117\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −543.607 | −0.0748580 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16286.8 | −2.22497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3324.24 | 0.450540 | 0.225270 | − | 0.974296i | \(-0.427674\pi\) | ||||
0.225270 | + | 0.974296i | \(0.427674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7001.76 | −0.941499 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8470.76 | 1.13012 | 0.565060 | − | 0.825050i | \(-0.308853\pi\) | ||||
0.565060 | + | 0.825050i | \(0.308853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4097.85 | −0.538258 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7908.40 | −1.03078 | −0.515388 | − | 0.856957i | \(-0.672352\pi\) | ||||
−0.515388 | + | 0.856957i | \(0.672352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.1769 | 0.00571386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5660.93 | −0.726606 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −681.120 | −0.0867617 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9781.58 | 1.23658 | 0.618292 | − | 0.785949i | \(-0.287825\pi\) | ||||
0.618292 | + | 0.785949i | \(0.287825\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −795.653 | −0.0990849 | −0.0495424 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495424 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19815.2 | −2.44929 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −58.8337 | −0.00721844 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19037.9 | −2.31860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8584.72 | −1.03787 | −0.518933 | − | 0.854815i | \(-0.673671\pi\) | ||||
−0.518933 | + | 0.854815i | \(0.673671\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8841.78 | −1.06115 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 662.138 | 0.0783207 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2866.30 | 0.336603 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7447.09 | 0.868292 | 0.434146 | − | 0.900843i | \(-0.357050\pi\) | ||||
0.434146 | + | 0.900843i | \(0.357050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4446.76 | −0.514779 | −0.257390 | − | 0.966308i | \(-0.582862\pi\) | ||||
−0.257390 | + | 0.966308i | \(0.582862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2541.01 | −0.292076 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6087.12 | 0.694750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13900.2 | −1.56436 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8963.70 | −1.00178 | −0.500889 | − | 0.865512i | \(-0.666994\pi\) | ||||
−0.500889 | + | 0.865512i | \(0.666994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16173.6 | 1.79504 | 0.897520 | − | 0.440973i | \(-0.145367\pi\) | ||||
0.897520 | + | 0.440973i | \(0.145367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 493.955 | 0.0544445 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.0724 | 0.00340136 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6298.43 | 0.684755 | 0.342378 | − | 0.939562i | \(-0.388768\pi\) | ||||
0.342378 | + | 0.939562i | \(0.388768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16784.7 | −1.80015 | −0.900074 | − | 0.435738i | \(-0.856488\pi\) | ||||
−0.900074 | + | 0.435738i | \(0.856488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −690.007 | −0.0735044 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6551.22 | −0.693203 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2733.88 | 0.287349 | 0.143674 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143674 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12034.0 | 1.25645 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1214.16 | −0.125930 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9229.20 | 0.944691 | 0.472345 | − | 0.881414i | \(-0.343408\pi\) | ||||
0.472345 | + | 0.881414i | \(0.343408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1320.39 | 0.134271 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19726.7 | 1.99298 | 0.996491 | − | 0.0837048i | \(-0.0266753\pi\) | ||||
0.996491 | + | 0.0837048i | \(0.0266753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 368.924 | 0.0370310 | 0.0185155 | − | 0.999829i | \(-0.494106\pi\) | ||||
0.0185155 | + | 0.999829i | \(0.494106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 600.965 | 0.0599335 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13309.6 | 1.31883 | 0.659414 | − | 0.751780i | \(-0.270804\pi\) | ||||
0.659414 | + | 0.751780i | \(0.270804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2788.75 | −0.272821 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29363.2 | 2.85438 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4281.46 | 0.413572 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3205.93 | 0.307735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11562.8 | −1.10296 | −0.551479 | − | 0.834189i | \(-0.685936\pi\) | ||||
−0.551479 | + | 0.834189i | \(0.685936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21210.0 | −2.01059 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.6677 | 0.00268399 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2628.13 | 0.244542 | 0.122271 | − | 0.992497i | \(-0.460982\pi\) | ||||
0.122271 | + | 0.992497i | \(0.460982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4277.04 | 0.395531 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12319.9 | −1.13236 | −0.566181 | − | 0.824281i | \(-0.691580\pi\) | ||||
−0.566181 | + | 0.824281i | \(0.691580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11085.7 | −1.01273 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 421.573 | 0.0382794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3305.81 | −0.296570 | −0.148285 | − | 0.988945i | \(-0.547375\pi\) | ||||
−0.148285 | + | 0.988945i | \(0.547375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12555.5 | 1.11963 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3072.72 | 0.272377 | 0.136189 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136189 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −230.159 | −0.0202811 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8895.20 | −0.779190 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13569.8 | −1.18167 | −0.590836 | − | 0.806791i | \(-0.701202\pi\) | ||||
−0.590836 | + | 0.806791i | \(0.701202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 928.715 | 0.0799294 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −234.342 | −0.0200512 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18207.6 | 1.54888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6706.66 | 0.567225 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10733.4 | 0.902566 | 0.451283 | − | 0.892381i | \(-0.350967\pi\) | ||||
0.451283 | + | 0.892381i | \(0.350967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8348.15 | −0.697971 | −0.348986 | − | 0.937128i | \(-0.613474\pi\) | ||||
−0.348986 | + | 0.937128i | \(0.613474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13487.3 | −1.11483 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12166.2 | −0.999933 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6564.33 | −0.536474 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13407.1 | 1.08954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −494.967 | −0.0399987 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2824.44 | 0.226971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23107.3 | −1.83634 | −0.918170 | − | 0.396186i | \(-0.870334\pi\) | ||||
−0.918170 | + | 0.396186i | \(0.870334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1402.62 | −0.110851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 331.188 | 0.0260304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13935.2 | 1.08926 | 0.544630 | − | 0.838676i | \(-0.316670\pi\) | ||||
0.544630 | + | 0.838676i | \(0.316670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2469.17 | −0.191952 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7797.29 | −0.602860 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 643.268 | 0.0491986 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15047.5 | −1.14467 | −0.572337 | − | 0.820018i | \(-0.693963\pi\) | ||||
−0.572337 | + | 0.820018i | \(0.693963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32713.4 | 2.47519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9461.25 | −0.712040 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15442.2 | −1.15597 | −0.577983 | − | 0.816049i | \(-0.696160\pi\) | ||||
−0.577983 | + | 0.816049i | \(0.696160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 578.187 | 0.0430522 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13362.1 | −0.984481 | −0.492240 | − | 0.870459i | \(-0.663822\pi\) | ||||
−0.492240 | + | 0.870459i | \(0.663822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22185.3 | −1.62596 | −0.812981 | − | 0.582290i | \(-0.802157\pi\) | ||||
−0.812981 | + | 0.582290i | \(0.802157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −826.208 | −0.0602362 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 112.442 | 0.00815507 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18951.4 | 1.36734 | 0.683671 | − | 0.729791i | \(-0.260383\pi\) | ||||
0.683671 | + | 0.729791i | \(0.260383\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4920.89 | −0.353204 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22972.1 | −1.63191 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 469.673 | 0.0331942 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19579.5 | −1.37672 | −0.688359 | − | 0.725371i | \(-0.741668\pi\) | ||||
−0.688359 | + | 0.725371i | \(0.741668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9486.48 | −0.663640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3911.63 | −0.272255 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5613.01 | −0.388699 | −0.194350 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194350 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3982.07 | −0.272990 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21925.5 | 1.49558 | 0.747790 | − | 0.663936i | \(-0.231115\pi\) | ||||
0.747790 | + | 0.663936i | \(0.231115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2067.51 | 0.140326 | 0.0701628 | − | 0.997536i | \(-0.477648\pi\) | ||||
0.0701628 | + | 0.997536i | \(0.477648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1739.45 | 0.117472 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2054.02 | −0.138029 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10167.2 | 0.679859 | 0.339930 | − | 0.940451i | \(-0.389597\pi\) | ||||
0.339930 | + | 0.940451i | \(0.389597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20285.0 | 1.34312 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18186.1 | −1.19825 | −0.599127 | − | 0.800654i | \(-0.704485\pi\) | ||||
−0.599127 | + | 0.800654i | \(0.704485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −406.616 | −0.0266607 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6584.41 | 0.429625 | 0.214812 | − | 0.976655i | \(-0.431086\pi\) | ||||
0.214812 | + | 0.976655i | \(0.431086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7779.72 | 0.505159 | 0.252579 | − | 0.967576i | \(-0.418721\pi\) | ||||
0.252579 | + | 0.967576i | \(0.418721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.3905 | 0.00157610 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15427.4 | 0.987356 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6654.70 | −0.423865 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14436.7 | −0.915150 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3787.78 | 0.238969 | 0.119484 | − | 0.992836i | \(-0.461876\pi\) | ||||
0.119484 | + | 0.992836i | \(0.461876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14259.9 | 0.895384 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1695.22 | −0.105942 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 364.749 | 0.0225810 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19930.9 | −1.22812 | −0.614058 | − | 0.789261i | \(-0.710464\pi\) | ||||
−0.614058 | + | 0.789261i | \(0.710464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3185.18 | −0.195352 | −0.0976759 | − | 0.995218i | \(-0.531141\pi\) | ||||
−0.0976759 | + | 0.995218i | \(0.531141\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −992.148 | −0.0605671 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16943.0 | 1.02952 | 0.514759 | − | 0.857335i | \(-0.327881\pi\) | ||||
0.514759 | + | 0.857335i | \(0.327881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47036.7 | 2.84492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20078.8 | −1.20328 | −0.601640 | − | 0.798767i | \(-0.705486\pi\) | ||||
−0.601640 | + | 0.798767i | \(0.705486\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1370.59 | −0.0817609 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1858.25 | 0.110346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9442.46 | −0.558158 | −0.279079 | − | 0.960268i | \(-0.590029\pi\) | ||||
−0.279079 | + | 0.960268i | \(0.590029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −761.990 | −0.0448381 | −0.0224190 | − | 0.999749i | \(-0.507137\pi\) | ||||
−0.0224190 | + | 0.999749i | \(0.507137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10540.8 | −0.617449 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −204.777 | −0.0118876 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1539.45 | 0.0889663 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17692.8 | 1.01792 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16111.6 | −0.922818 | −0.461409 | − | 0.887188i | \(-0.652656\pi\) | ||||
−0.461409 | + | 0.887188i | \(0.652656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3360.76 | 0.191638 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31241.5 | −1.77357 | −0.886786 | − | 0.462180i | \(-0.847067\pi\) | ||||
−0.886786 | + | 0.462180i | \(0.847067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9928.03 | 0.558653 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30113.5 | −1.68706 | −0.843530 | − | 0.537082i | \(-0.819527\pi\) | ||||
−0.843530 | + | 0.537082i | \(0.819527\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2140.72 | −0.119405 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17728.4 | −0.984542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25593.1 | −1.41512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9750.85 | 0.536816 | 0.268408 | − | 0.963305i | \(-0.413502\pi\) | ||||
0.268408 | + | 0.963305i | \(0.413502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 693.971 | 0.0378760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9125.58 | 0.495920 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1060.71 | 0.0573962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11851.6 | 0.638559 | 0.319280 | − | 0.947661i | \(-0.396559\pi\) | ||||
0.319280 | + | 0.947661i | \(0.396559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10154.3 | −0.544773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −615.214 | −0.0328657 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1322.39 | 0.0700472 | 0.0350236 | − | 0.999386i | \(-0.488849\pi\) | ||||
0.0350236 | + | 0.999386i | \(0.488849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8439.67 | 0.445165 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −249.140 | −0.0130861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3365.44 | −0.176028 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4957.66 | 0.258225 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7301.56 | −0.378723 | −0.189362 | − | 0.981907i | \(-0.560642\pi\) | ||||
−0.189362 | + | 0.981907i | \(0.560642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9320.84 | −0.479455 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28216.2 | −1.44541 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6088.72 | 0.310616 | 0.155308 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155308 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22266.5 | 1.12662 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26578.5 | 1.33929 | 0.669644 | − | 0.742683i | \(-0.266447\pi\) | ||||
0.669644 | + | 0.742683i | \(0.266447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12464.0 | −0.622955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25219.8 | 1.25538 | 0.627689 | − | 0.778464i | \(-0.284001\pi\) | ||||
0.627689 | + | 0.778464i | \(0.284001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7413.98 | −0.367557 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2634.28 | 0.130071 | 0.0650353 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650353 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1586.14 | −0.0780023 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8204.46 | −0.401855 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5767.29 | 0.280228 | 0.140114 | − | 0.990135i | \(-0.455253\pi\) | ||||
0.140114 | + | 0.990135i | \(0.455253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5315.32 | 0.257239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −293.965 | −0.0141702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33378.7 | 1.60260 | 0.801302 | − | 0.598260i | \(-0.204141\pi\) | ||||
0.801302 | + | 0.598260i | \(0.204141\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −174.770 | −0.00835802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3626.09 | −0.172727 | −0.0863637 | − | 0.996264i | \(-0.527525\pi\) | ||||
−0.0863637 | + | 0.996264i | \(0.527525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 319.685 | 0.0151088 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52403.4 | 2.46698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3426.15 | −0.160663 | −0.0803316 | − | 0.996768i | \(-0.525598\pi\) | ||||
−0.0803316 | + | 0.996768i | \(0.525598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4434.38 | 0.207134 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13108.2 | −0.609920 | −0.304960 | − | 0.952365i | \(-0.598643\pi\) | ||||
−0.304960 | + | 0.952365i | \(0.598643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34328.9 | −1.59114 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6418.60 | 0.295212 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2613.61 | −0.119747 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6120.53 | −0.279348 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −675.194 | −0.0306990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39319.7 | −1.78094 | −0.890468 | − | 0.455045i | \(-0.849623\pi\) | ||||
−0.890468 | + | 0.455045i | \(0.849623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4295.92 | 0.193839 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19711.5 | 0.882696 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 776.201 | 0.0346277 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14597.8 | 0.648785 | 0.324393 | − | 0.945923i | \(-0.394840\pi\) | ||||
0.324393 | + | 0.945923i | \(0.394840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13807.1 | 0.611339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8549.78 | 0.377143 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13315.3 | −0.585164 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 856.194 | 0.0373475 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26827.4 | 1.16589 | 0.582943 | − | 0.812513i | \(-0.301901\pi\) | ||||
0.582943 | + | 0.812513i | \(0.301901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5177.09 | 0.224158 | 0.112079 | − | 0.993699i | \(-0.464249\pi\) | ||||
0.112079 | + | 0.993699i | \(0.464249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15748.0 | −0.679343 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1035.53 | 0.0445068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15661.5 | 0.670656 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20356.8 | 0.865355 | 0.432678 | − | 0.901549i | \(-0.357569\pi\) | ||||
0.432678 | + | 0.901549i | \(0.357569\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 57.5738 | 0.00243851 | 0.00121926 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121926 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24081.5 | −1.01625 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12296.6 | −0.517044 | −0.258522 | − | 0.966005i | \(-0.583235\pi\) | ||||
−0.258522 | + | 0.966005i | \(0.583235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22871.7 | −0.958224 | −0.479112 | − | 0.877754i | \(-0.659041\pi\) | ||||
−0.479112 | + | 0.877754i | \(0.659041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21443.6 | −0.895151 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3039.85 | 0.125986 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7446.47 | −0.307512 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37571.3 | −1.54601 | −0.773007 | − | 0.634398i | \(-0.781248\pi\) | ||||
−0.773007 | + | 0.634398i | \(0.781248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26997.6 | 1.10696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12685.1 | −0.518265 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2153.65 | −0.0876780 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25027.1 | 1.01170 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −266.677 | −0.0107422 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38354.5 | 1.53955 | 0.769774 | − | 0.638317i | \(-0.220369\pi\) | ||||
0.769774 | + | 0.638317i | \(0.220369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 224.855 | 0.00899401 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36545.7 | −1.45668 | −0.728341 | − | 0.685215i | \(-0.759708\pi\) | ||||
−0.728341 | + | 0.685215i | \(0.759708\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18564.3 | 0.737374 | 0.368687 | − | 0.929554i | \(-0.379807\pi\) | ||||
0.368687 | + | 0.929554i | \(0.379807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37457.7 | 1.47749 | 0.738746 | − | 0.673984i | \(-0.235418\pi\) | ||||
0.738746 | + | 0.673984i | \(0.235418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1623.78 | 0.0638266 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7564.39 | 0.296309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60474.4 | −2.36071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13886.1 | −0.540199 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −355.218 | −0.0137713 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27128.8 | −1.04455 | −0.522277 | − | 0.852776i | \(-0.674917\pi\) | ||||
−0.522277 | + | 0.852776i | \(0.674917\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15116.5 | 0.580055 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23647.8 | −0.904329 | −0.452165 | − | 0.891935i | \(-0.649348\pi\) | ||||
−0.452165 | + | 0.891935i | \(0.649348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4488.47 | −0.171063 | −0.0855316 | − | 0.996335i | \(-0.527259\pi\) | ||||
−0.0855316 | + | 0.996335i | \(0.527259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1589.32 | −0.0603664 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41026.8 | 1.55304 | 0.776520 | − | 0.630093i | \(-0.216983\pi\) | ||||
0.776520 | + | 0.630093i | \(0.216983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5223.65 | −0.196407 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9711.41 | 0.363919 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 683.836 | 0.0255398 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −194.710 | −0.00724771 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 62519.0 | 2.31938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17420.1 | −0.644114 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −339.594 | −0.0124735 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −736.305 | −0.0269555 | −0.0134777 | − | 0.999909i | \(-0.504290\pi\) | ||||
−0.0134777 | + | 0.999909i | \(0.504290\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2851.87 | 0.104060 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1287.54 | 0.0468256 | 0.0234128 | − | 0.999726i | \(-0.492547\pi\) | ||||
0.0234128 | + | 0.999726i | \(0.492547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58789.0 | 2.13103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −597.821 | −0.0215993 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34280.0 | 1.23046 | 0.615230 | − | 0.788348i | \(-0.289063\pi\) | ||||
0.615230 | + | 0.788348i | \(0.289063\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14609.0 | −0.522675 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2911.81 | −0.103839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36745.4 | −1.30614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2903.70 | 0.102880 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31475.8 | 1.11161 | 0.555806 | − | 0.831312i | \(-0.312410\pi\) | ||||
0.555806 | + | 0.831312i | \(0.312410\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4358.52 | −0.152939 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2290.70 | −0.0801219 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52560.6 | −1.83253 | −0.916264 | − | 0.400575i | \(-0.868810\pi\) | ||||
−0.916264 | + | 0.400575i | \(0.868810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17088.8 | 0.593900 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15976.7 | −0.553482 | −0.276741 | − | 0.960945i | \(-0.589254\pi\) | ||||
−0.276741 | + | 0.960945i | \(0.589254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 168.569 | 0.00582118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8504.43 | −0.291824 | −0.145912 | − | 0.989298i | \(-0.546612\pi\) | ||||
−0.145912 | + | 0.989298i | \(0.546612\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14834.5 | −0.507428 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10414.4 | 0.355111 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29417.5 | 0.999923 | 0.499961 | − | 0.866048i | \(-0.333348\pi\) | ||||
0.499961 | + | 0.866048i | \(0.333348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −200.036 | −0.00677804 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43856.6 | 1.48138 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46272.0 | 1.55322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6133.06 | 0.205229 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1191.42 | −0.0397441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3461.97 | 0.115129 | 0.0575643 | − | 0.998342i | \(-0.481667\pi\) | ||||
0.0575643 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5046.36 | −0.167299 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43558.8 | 1.43962 | 0.719809 | − | 0.694172i | \(-0.244229\pi\) | ||||
0.719809 | + | 0.694172i | \(0.244229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26829.1 | −0.881250 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5504.95 | −0.180265 | −0.0901325 | − | 0.995930i | \(-0.528729\pi\) | ||||
−0.0901325 | + | 0.995930i | \(0.528729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61263.4 | −1.99999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4103.71 | −0.133559 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30789.7 | 0.999023 | 0.499511 | − | 0.866307i | \(-0.333513\pi\) | ||||
0.499511 | + | 0.866307i | \(0.333513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −947.060 | −0.0306354 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 411.311 | 0.0132244 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21629.1 | −0.693312 | −0.346656 | − | 0.937992i | \(-0.612683\pi\) | ||||
−0.346656 | + | 0.937992i | \(0.612683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18763.1 | −0.599627 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −964.114 | −0.0307181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38195.8 | 1.21331 | 0.606656 | − | 0.794964i | \(-0.292510\pi\) | ||||
0.606656 | + | 0.794964i | \(0.292510\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7970.64 | −0.252432 |
(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 | 1176.4.a.ba.1.2 | 4 | ||
4.3 | odd | 2 | 2352.4.a.cp.1.2 | 4 | |||
7.3 | odd | 6 | 168.4.q.f.121.2 | yes | 8 | ||
7.5 | odd | 6 | 168.4.q.f.25.2 | ✓ | 8 | ||
7.6 | odd | 2 | 1176.4.a.bd.1.3 | 4 | |||
21.5 | even | 6 | 504.4.s.j.361.3 | 8 | |||
21.17 | even | 6 | 504.4.s.j.289.3 | 8 | |||
28.3 | even | 6 | 336.4.q.m.289.2 | 8 | |||
28.19 | even | 6 | 336.4.q.m.193.2 | 8 | |||
28.27 | even | 2 | 2352.4.a.cm.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.2 | ✓ | 8 | 7.5 | odd | 6 | ||
168.4.q.f.121.2 | yes | 8 | 7.3 | odd | 6 | ||
336.4.q.m.193.2 | 8 | 28.19 | even | 6 | |||
336.4.q.m.289.2 | 8 | 28.3 | even | 6 | |||
504.4.s.j.289.3 | 8 | 21.17 | even | 6 | |||
504.4.s.j.361.3 | 8 | 21.5 | even | 6 | |||
1176.4.a.ba.1.2 | 4 | 1.1 | even | 1 | trivial | ||
1176.4.a.bd.1.3 | 4 | 7.6 | odd | 2 | |||
2352.4.a.cm.1.3 | 4 | 28.27 | even | 2 | |||
2352.4.a.cp.1.2 | 4 | 4.3 | odd | 2 |