Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 294) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | 15.8995 | 1.42209 | 0.711047 | − | 0.703144i | \(-0.248221\pi\) | ||||
0.711047 | + | 0.703144i | \(0.248221\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −57.3970 | −1.57326 | −0.786629 | − | 0.617426i | \(-0.788176\pi\) | ||||
−0.786629 | + | 0.617426i | \(0.788176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.69848 | −0.121575 | −0.0607875 | − | 0.998151i | \(-0.519361\pi\) | ||||
−0.0607875 | + | 0.998151i | \(0.519361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.6985 | 0.821046 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 51.8995 | 0.740440 | 0.370220 | − | 0.928944i | \(-0.379282\pi\) | ||||
0.370220 | + | 0.928944i | \(0.379282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.2010 | 0.195619 | 0.0978096 | − | 0.995205i | \(-0.468816\pi\) | ||||
0.0978096 | + | 0.995205i | \(0.468816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 213.397 | 1.93462 | 0.967312 | − | 0.253590i | \(-0.0816114\pi\) | ||||
0.967312 | + | 0.253590i | \(0.0816114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 127.794 | 1.02235 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −218.191 | −1.39714 | −0.698570 | − | 0.715542i | \(-0.746180\pi\) | ||||
−0.698570 | + | 0.715542i | \(0.746180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −251.397 | −1.45652 | −0.728262 | − | 0.685299i | \(-0.759671\pi\) | ||||
−0.728262 | + | 0.685299i | \(0.759671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −172.191 | −0.908321 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 386.794 | 1.71861 | 0.859304 | − | 0.511464i | \(-0.170897\pi\) | ||||
0.859304 | + | 0.511464i | \(0.170897\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.0955 | −0.0701914 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 328.503 | 1.25130 | 0.625652 | − | 0.780102i | \(-0.284833\pi\) | ||||
0.625652 | + | 0.780102i | \(0.284833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37.5879 | 0.133305 | 0.0666523 | − | 0.997776i | \(-0.478768\pi\) | ||||
0.0666523 | + | 0.997776i | \(0.478768\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 143.095 | 0.474031 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −254.995 | −0.791379 | −0.395690 | − | 0.918384i | \(-0.629494\pi\) | ||||
−0.395690 | + | 0.918384i | \(0.629494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 155.698 | 0.427493 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 211.588 | 0.548374 | 0.274187 | − | 0.961676i | \(-0.411591\pi\) | ||||
0.274187 | + | 0.961676i | \(0.411591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −912.583 | −2.23732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 48.6030 | 0.112941 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −412.201 | −0.909559 | −0.454780 | − | 0.890604i | \(-0.650282\pi\) | ||||
−0.454780 | + | 0.890604i | \(0.650282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 836.693 | 1.75619 | 0.878095 | − | 0.478486i | \(-0.158814\pi\) | ||||
0.878095 | + | 0.478486i | \(0.158814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −90.6030 | −0.172891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 165.588 | 0.301937 | 0.150969 | − | 0.988539i | \(-0.451761\pi\) | ||||
0.150969 | + | 0.988539i | \(0.451761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 640.191 | 1.11696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 465.015 | 0.777284 | 0.388642 | − | 0.921389i | \(-0.372944\pi\) | ||||
0.388642 | + | 0.921389i | \(0.372944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −449.658 | −0.720938 | −0.360469 | − | 0.932771i | \(-0.617383\pi\) | ||||
−0.360469 | + | 0.932771i | \(0.617383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 383.382 | 0.590255 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 343.558 | 0.489282 | 0.244641 | − | 0.969614i | \(-0.421330\pi\) | ||||
0.244641 | + | 0.969614i | \(0.421330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1502.33 | 1.98677 | 0.993387 | − | 0.114812i | \(-0.0366265\pi\) | ||||
0.993387 | + | 0.114812i | \(0.0366265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 825.176 | 1.05298 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −654.573 | −0.806639 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 341.085 | 0.406236 | 0.203118 | − | 0.979154i | \(-0.434893\pi\) | ||||
0.203118 | + | 0.979154i | \(0.434893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −754.191 | −0.840924 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 257.588 | 0.278189 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 865.437 | 0.905895 | 0.452947 | − | 0.891537i | \(-0.350373\pi\) | ||||
0.452947 | + | 0.891537i | \(0.350373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −516.573 | −0.524419 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 243.256 | 0.239652 | 0.119826 | − | 0.992795i | \(-0.461766\pi\) | ||||
0.119826 | + | 0.992795i | \(0.461766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −953.346 | −0.912000 | −0.456000 | − | 0.889980i | \(-0.650718\pi\) | ||||
−0.456000 | + | 0.889980i | \(0.650718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1344.95 | 1.21516 | 0.607578 | − | 0.794260i | \(-0.292141\pi\) | ||||
0.607578 | + | 0.794260i | \(0.292141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1734.35 | 1.52404 | 0.762022 | − | 0.647551i | \(-0.224207\pi\) | ||||
0.762022 | + | 0.647551i | \(0.224207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1160.38 | 0.992239 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1441.18 | 1.19977 | 0.599887 | − | 0.800085i | \(-0.295212\pi\) | ||||
0.599887 | + | 0.800085i | \(0.295212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3392.90 | 2.75122 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −51.2864 | −0.0405250 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1963.41 | 1.47514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 985.508 | 0.722441 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 44.4222 | 0.0317860 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1184.70 | −0.827759 | −0.413880 | − | 0.910332i | \(-0.635827\pi\) | ||||
−0.413880 | + | 0.910332i | \(0.635827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 112.764 | 0.0769634 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 297.588 | 0.198476 | 0.0992381 | − | 0.995064i | \(-0.468359\pi\) | ||||
0.0992381 | + | 0.995064i | \(0.468359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 429.286 | 0.273682 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 620.985 | 0.387258 | 0.193629 | − | 0.981075i | \(-0.437974\pi\) | ||||
0.193629 | + | 0.981075i | \(0.437974\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −898.754 | −0.548426 | −0.274213 | − | 0.961669i | \(-0.588417\pi\) | ||||
−0.274213 | + | 0.961669i | \(0.588417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −764.985 | −0.456903 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 327.076 | 0.191269 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3469.13 | −1.98686 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3054.70 | −1.67954 | −0.839769 | − | 0.542945i | \(-0.817309\pi\) | ||||
−0.839769 | + | 0.542945i | \(0.817309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65.1455 | 0.0351090 | 0.0175545 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175545 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 467.095 | 0.246813 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3997.08 | −2.07131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1542.22 | −0.783966 | −0.391983 | − | 0.919973i | \(-0.628211\pi\) | ||||
−0.391983 | + | 0.919973i | \(0.628211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 634.764 | 0.316604 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2514.73 | 1.20840 | 0.604200 | − | 0.796833i | \(-0.293493\pi\) | ||||
0.604200 | + | 0.796833i | \(0.293493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2737.75 | −1.29172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 528.643 | 0.244956 | 0.122478 | − | 0.992471i | \(-0.460916\pi\) | ||||
0.122478 | + | 0.992471i | \(0.460916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2164.53 | −0.985220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 145.809 | 0.0652064 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −96.8439 | −0.0425602 | −0.0212801 | − | 0.999774i | \(-0.506774\pi\) | ||||
−0.0212801 | + | 0.999774i | \(0.506774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1236.60 | −0.525134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 534.542 | 0.223204 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2087.00 | −0.857049 | −0.428524 | − | 0.903530i | \(-0.640966\pi\) | ||||
−0.428524 | + | 0.903530i | \(0.640966\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2510.08 | 1.01394 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6149.83 | 2.44402 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2978.87 | −1.16490 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3387.69 | −1.28337 | −0.641687 | − | 0.766966i | \(-0.721765\pi\) | ||||
−0.641687 | + | 0.766966i | \(0.721765\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1908.35 | −0.711742 | −0.355871 | − | 0.934535i | \(-0.615816\pi\) | ||||
−0.355871 | + | 0.934535i | \(0.615816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −271.809 | −0.0998187 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2061.88 | −0.745699 | −0.372850 | − | 0.927892i | \(-0.621619\pi\) | ||||
−0.372850 | + | 0.927892i | \(0.621619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3171.50 | 1.12976 | 0.564878 | − | 0.825174i | \(-0.308923\pi\) | ||||
0.564878 | + | 0.825174i | \(0.308923\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 496.764 | 0.174323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5223.02 | 1.77947 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1920.57 | 0.644875 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −929.889 | −0.307760 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1349.97 | −0.440454 | −0.220227 | − | 0.975449i | \(-0.570680\pi\) | ||||
−0.220227 | + | 0.975449i | \(0.570680\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1395.05 | 0.448765 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 597.628 | 0.189572 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1348.97 | −0.416234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −295.748 | −0.0900190 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1361.85 | −0.408951 | −0.204476 | − | 0.978872i | \(-0.565549\pi\) | ||||
−0.204476 | + | 0.978872i | \(0.565549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1150.15 | 0.340784 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1861.81 | 0.544373 | 0.272186 | − | 0.962245i | \(-0.412253\pi\) | ||||
0.272186 | + | 0.962245i | \(0.412253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5358.78 | 1.54637 | 0.773184 | − | 0.634181i | \(-0.218663\pi\) | ||||
0.773184 | + | 0.634181i | \(0.218663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5441.12 | 1.52987 | 0.764935 | − | 0.644107i | \(-0.222771\pi\) | ||||
0.764935 | + | 0.644107i | \(0.222771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4054.29 | −1.12542 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1030.67 | 0.282487 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1157.28 | 0.313213 | 0.156607 | − | 0.987661i | \(-0.449945\pi\) | ||||
0.156607 | + | 0.987661i | \(0.449945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3969.38 | 1.06095 | 0.530477 | − | 0.847699i | \(-0.322013\pi\) | ||||
0.530477 | + | 0.847699i | \(0.322013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −92.3212 | −0.0237824 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4506.99 | 1.14706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5978.75 | 1.50349 | 0.751744 | − | 0.659455i | \(-0.229213\pi\) | ||||
0.751744 | + | 0.659455i | \(0.229213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12248.3 | −3.04366 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2475.53 | 0.607935 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4650.15 | −1.12867 | −0.564335 | − | 0.825546i | \(-0.690868\pi\) | ||||
−0.564335 | + | 0.825546i | \(0.690868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1963.72 | −0.465713 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3695.37 | −0.866411 | −0.433205 | − | 0.901295i | \(-0.642618\pi\) | ||||
−0.433205 | + | 0.901295i | \(0.642618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3364.14 | 0.779840 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1023.26 | 0.234540 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7157.69 | 1.62235 | 0.811175 | − | 0.584804i | \(-0.198829\pi\) | ||||
0.811175 | + | 0.584804i | \(0.198829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4038.37 | 0.905216 | 0.452608 | − | 0.891710i | \(-0.350494\pi\) | ||||
0.452608 | + | 0.891710i | \(0.350494\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7334.98 | −1.60842 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2754.82 | −0.597550 | −0.298775 | − | 0.954324i | \(-0.596578\pi\) | ||||
−0.298775 | + | 0.954324i | \(0.596578\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2262.57 | −0.485508 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −772.742 | −0.164050 | −0.0820248 | − | 0.996630i | \(-0.526139\pi\) | ||||
−0.0820248 | + | 0.996630i | \(0.526139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6745.49 | −1.41688 | −0.708441 | − | 0.705770i | \(-0.750601\pi\) | ||||
−0.708441 | + | 0.705770i | \(0.750601\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 772.764 | 0.160613 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2219.44 | −0.451749 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2596.31 | 0.523019 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1922.69 | −0.383362 | −0.191681 | − | 0.981457i | \(-0.561394\pi\) | ||||
−0.191681 | + | 0.981457i | \(0.561394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6553.79 | −1.29348 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1549.72 | −0.302774 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1216.04 | −0.235202 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 729.768 | 0.138363 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13303.0 | 2.49747 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2016.68 | 0.374913 | 0.187456 | − | 0.982273i | \(-0.439976\pi\) | ||||
0.187456 | + | 0.982273i | \(0.439976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2860.04 | −0.526544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7149.99 | 1.30366 | 0.651831 | − | 0.758365i | \(-0.274001\pi\) | ||||
0.651831 | + | 0.758365i | \(0.274001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8596.49 | −1.55240 | −0.776202 | − | 0.630484i | \(-0.782856\pi\) | ||||
−0.776202 | + | 0.630484i | \(0.782856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2853.24 | −0.505532 | −0.252766 | − | 0.967527i | \(-0.581340\pi\) | ||||
−0.252766 | + | 0.967527i | \(0.581340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12523.5 | 2.19806 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4034.86 | 0.701570 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 840.824 | 0.144844 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −728.232 | −0.124292 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5203.05 | 0.879907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1619.12 | −0.268866 | −0.134433 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134433 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3481.15 | 0.572870 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2632.76 | 0.429383 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3278.67 | −0.529972 | −0.264986 | − | 0.964252i | \(-0.585367\pi\) | ||||
−0.264986 | + | 0.964252i | \(0.585367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4323.53 | 0.692690 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14429.4 | 2.29149 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10178.7 | 1.58842 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2850.30 | 0.440957 | 0.220479 | − | 0.975392i | \(-0.429238\pi\) | ||||
0.220479 | + | 0.975392i | \(0.429238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4725.32 | 0.724758 | 0.362379 | − | 0.932031i | \(-0.381965\pi\) | ||||
0.362379 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −153.859 | −0.0233971 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6727.44 | −1.01435 | −0.507175 | − | 0.861843i | \(-0.669310\pi\) | ||||
−0.507175 | + | 0.861843i | \(0.669310\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7393.51 | 1.10537 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7331.89 | 1.07789 | 0.538945 | − | 0.842341i | \(-0.318823\pi\) | ||||
0.538945 | + | 0.842341i | \(0.318823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6596.53 | −0.961733 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5890.24 | 0.851673 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7149.34 | −1.02524 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2774.43 | 0.394616 | 0.197308 | − | 0.980342i | \(-0.436780\pi\) | ||||
0.197308 | + | 0.980342i | \(0.436780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2956.52 | 0.417101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2527.35 | 0.350834 | 0.175417 | − | 0.984494i | \(-0.443873\pi\) | ||||
0.175417 | + | 0.984494i | \(0.443873\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 133.267 | 0.0183516 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1243.36 | 0.169857 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3116.40 | −0.422371 | −0.211186 | − | 0.977446i | \(-0.567732\pi\) | ||||
−0.211186 | + | 0.977446i | \(0.567732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3554.11 | −0.477907 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1518.07 | 0.202532 | 0.101266 | − | 0.994859i | \(-0.467711\pi\) | ||||
0.101266 | + | 0.994859i | \(0.467711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 338.291 | 0.0444349 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3246.77 | −0.423182 | −0.211591 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211591 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11075.2 | 1.43247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 892.764 | 0.114590 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5462.39 | 0.695804 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1830.62 | 0.231427 | 0.115713 | − | 0.993283i | \(-0.463085\pi\) | ||||
0.115713 | + | 0.993283i | \(0.463085\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3385.81 | −0.421644 | −0.210822 | − | 0.977524i | \(-0.567614\pi\) | ||||
−0.210822 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1432.58 | 0.177077 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1287.86 | 0.158010 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22200.8 | −2.70382 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9253.17 | 1.11868 | 0.559340 | − | 0.828938i | \(-0.311055\pi\) | ||||
0.559340 | + | 0.828938i | \(0.311055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1862.95 | 0.223583 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23886.3 | 2.82538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2696.26 | −0.316634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3547.52 | −0.413622 | −0.206811 | − | 0.978381i | \(-0.566308\pi\) | ||||
−0.206811 | + | 0.978381i | \(0.566308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7848.87 | 0.908624 | 0.454312 | − | 0.890843i | \(-0.349885\pi\) | ||||
0.454312 | + | 0.890843i | \(0.349885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2294.95 | −0.263793 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6632.44 | 0.756990 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 981.227 | 0.110429 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4447.32 | 0.497030 | 0.248515 | − | 0.968628i | \(-0.420057\pi\) | ||||
0.248515 | + | 0.968628i | \(0.420057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6994.82 | −0.776327 | −0.388164 | − | 0.921590i | \(-0.626890\pi\) | ||||
−0.388164 | + | 0.921590i | \(0.626890\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10407.4 | −1.14712 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3457.25 | 0.378450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −636.182 | −0.0691647 | −0.0345823 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345823 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4474.24 | 0.479859 | 0.239929 | − | 0.970790i | \(-0.422876\pi\) | ||||
0.239929 | + | 0.970790i | \(0.422876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5423.08 | 0.577705 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9164.11 | −0.969681 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2389.42 | −0.251144 | −0.125572 | − | 0.992085i | \(-0.540077\pi\) | ||||
−0.125572 | + | 0.992085i | \(0.540077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18855.0 | −1.96862 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 195.436 | 0.0202702 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4438.34 | −0.454304 | −0.227152 | − | 0.973859i | \(-0.572941\pi\) | ||||
−0.227152 | + | 0.973859i | \(0.572941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1401.29 | 0.142498 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14079.8 | −1.42248 | −0.711240 | − | 0.702949i | \(-0.751866\pi\) | ||||
−0.711240 | + | 0.702949i | \(0.751866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4687.50 | −0.470511 | −0.235255 | − | 0.971934i | \(-0.575593\pi\) | ||||
−0.235255 | + | 0.971934i | \(0.575593\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11991.3 | −1.19587 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8447.26 | −0.837029 | −0.418514 | − | 0.908210i | \(-0.637449\pi\) | ||||
−0.418514 | + | 0.908210i | \(0.637449\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4626.66 | −0.452623 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2157.43 | −0.209723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2070.39 | 0.199992 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1904.29 | 0.182791 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4369.41 | 0.416792 | 0.208396 | − | 0.978045i | \(-0.433176\pi\) | ||||
0.208396 | + | 0.978045i | \(0.433176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2204.14 | −0.208940 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13760.0 | 1.28827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14477.7 | 1.34712 | 0.673561 | − | 0.739132i | \(-0.264764\pi\) | ||||
0.673561 | + | 0.739132i | \(0.264764\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7544.20 | 0.697670 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9306.12 | −0.855355 | −0.427677 | − | 0.903931i | \(-0.640668\pi\) | ||||
−0.427677 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11324.0 | −1.03450 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8213.25 | −0.745774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12237.5 | 1.09785 | 0.548926 | − | 0.835871i | \(-0.315037\pi\) | ||||
0.548926 | + | 0.835871i | \(0.315037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1585.93 | 0.141425 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5524.30 | −0.489694 | −0.244847 | − | 0.969562i | \(-0.578738\pi\) | ||||
−0.244847 | + | 0.969562i | \(0.578738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3867.65 | 0.340808 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6493.58 | −0.568817 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10079.6 | −0.877743 | −0.438871 | − | 0.898550i | \(-0.644622\pi\) | ||||
−0.438871 | + | 0.898550i | \(0.644622\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 437.427 | 0.0376470 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15157.7 | −1.29695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14635.9 | 1.24504 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −290.532 | −0.0245721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5706.61 | 0.479868 | 0.239934 | − | 0.970789i | \(-0.422874\pi\) | ||||
0.239934 | + | 0.970789i | \(0.422874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10657.3 | 0.891032 | 0.445516 | − | 0.895274i | \(-0.353020\pi\) | ||||
0.445516 | + | 0.895274i | \(0.353020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13047.4 | −1.07847 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33371.3 | 2.74277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3709.81 | −0.303186 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1871.97 | −0.152127 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21384.1 | 1.72807 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1603.63 | 0.128867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4010.48 | −0.318714 | −0.159357 | − | 0.987221i | \(-0.550942\pi\) | ||||
−0.159357 | + | 0.987221i | \(0.550942\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6261.01 | −0.494817 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27575.3 | 2.16733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17619.8 | 1.37728 | 0.688638 | − | 0.725105i | \(-0.258209\pi\) | ||||
0.688638 | + | 0.725105i | \(0.258209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7530.24 | 0.585397 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3534.91 | −0.273307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18449.5 | 1.41106 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10337.7 | −0.786395 | −0.393198 | − | 0.919454i | \(-0.628631\pi\) | ||||
−0.393198 | + | 0.919454i | \(0.628631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −214.194 | −0.0162065 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8936.62 | −0.672557 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24023.7 | 1.79836 | 0.899180 | − | 0.437580i | \(-0.144164\pi\) | ||||
0.899180 | + | 0.437580i | \(0.144164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22914.0 | 1.70619 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13179.2 | −0.971001 | −0.485501 | − | 0.874236i | \(-0.661363\pi\) | ||||
−0.485501 | + | 0.874236i | \(0.661363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7776.26 | −0.569924 | −0.284962 | − | 0.958539i | \(-0.591981\pi\) | ||||
−0.284962 | + | 0.958539i | \(0.591981\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10163.1 | −0.740956 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27270.8 | 1.97787 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20167.0 | 1.45505 | 0.727525 | − | 0.686081i | \(-0.240670\pi\) | ||||
0.727525 | + | 0.686081i | \(0.240670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5725.05 | −0.410924 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12144.5 | −0.862734 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −815.427 | −0.0576304 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8365.08 | 0.588184 | 0.294092 | − | 0.955777i | \(-0.404983\pi\) | ||||
0.294092 | + | 0.955777i | \(0.404983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4072.88 | −0.284924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6185.64 | −0.430530 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27621.9 | −1.91281 | −0.956403 | − | 0.292050i | \(-0.905663\pi\) | ||||
−0.956403 | + | 0.292050i | \(0.905663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9514.49 | 0.652265 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −538.318 | −0.0367197 | −0.0183598 | − | 0.999831i | \(-0.505844\pi\) | ||||
−0.0183598 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6958.64 | 0.472294 | 0.236147 | − | 0.971717i | \(-0.424115\pi\) | ||||
0.236147 | + | 0.971717i | \(0.424115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1490.29 | 0.100646 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31217.3 | 2.09779 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17297.6 | 1.15665 | 0.578326 | − | 0.815806i | \(-0.303706\pi\) | ||||
0.578326 | + | 0.815806i | \(0.303706\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1453.08 | 0.0962120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −839.158 | −0.0552908 | −0.0276454 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276454 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15669.1 | 1.02738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16040.0 | −1.04659 | −0.523295 | − | 0.852152i | \(-0.675297\pi\) | ||||
−0.523295 | + | 0.852152i | \(0.675297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5429.28 | 0.352538 | 0.176269 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176269 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5761.72 | 0.372318 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15268.0 | −0.977149 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2789.67 | −0.177685 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20074.4 | 1.27253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1807.86 | 0.114057 | 0.0570284 | − | 0.998373i | \(-0.481837\pi\) | ||||
0.0570284 | + | 0.998373i | \(0.481837\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4049.91 | −0.254296 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18836.2 | −1.17715 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4185.14 | 0.259095 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5904.56 | −0.363832 | −0.181916 | − | 0.983314i | \(-0.558230\pi\) | ||||
−0.181916 | + | 0.983314i | \(0.558230\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8092.42 | −0.496320 | −0.248160 | − | 0.968719i | \(-0.579826\pi\) | ||||
−0.248160 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1792.88 | 0.109449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20192.7 | −1.22698 | −0.613490 | − | 0.789702i | \(-0.710235\pi\) | ||||
−0.613490 | + | 0.789702i | \(0.710235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23659.1 | 1.43097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21180.8 | −1.26933 | −0.634664 | − | 0.772789i | \(-0.718861\pi\) | ||||
−0.634664 | + | 0.772789i | \(0.718861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4731.50 | 0.282252 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4046.92 | −0.240313 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28411.3 | −1.67944 | −0.839718 | − | 0.543023i | \(-0.817280\pi\) | ||||
−0.839718 | + | 0.543023i | \(0.817280\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16704.9 | 0.982975 | 0.491488 | − | 0.870885i | \(-0.336453\pi\) | ||||
0.491488 | + | 0.870885i | \(0.336453\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −887.245 | −0.0519725 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46561.3 | −2.70294 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4085.55 | −0.236108 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48023.7 | −2.76294 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9047.09 | −0.518187 | −0.259093 | − | 0.965852i | \(-0.583424\pi\) | ||||
−0.259093 | + | 0.965852i | \(0.583424\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3450.44 | 0.196752 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7844.26 | −0.445316 | −0.222658 | − | 0.974897i | \(-0.571473\pi\) | ||||
−0.222658 | + | 0.974897i | \(0.571473\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5585.43 | 0.314294 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25766.1 | −1.44350 | −0.721751 | − | 0.692153i | \(-0.756662\pi\) | ||||
−0.721751 | + | 0.692153i | \(0.756662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9873.35 | 0.550717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16076.3 | 0.892796 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1205.73 | −0.0666686 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24674.1 | −1.35839 | −0.679195 | − | 0.733958i | \(-0.737671\pi\) | ||||
−0.679195 | + | 0.733958i | \(0.737671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14289.7 | −0.779914 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17049.1 | 0.926515 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16323.4 | 0.883271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29377.9 | 1.58286 | 0.791431 | − | 0.611258i | \(-0.209336\pi\) | ||||
0.791431 | + | 0.611258i | \(0.209336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6266.45 | 0.336193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12162.9 | −0.649759 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30594.3 | 1.62058 | 0.810291 | − | 0.586028i | \(-0.199309\pi\) | ||||
0.810291 | + | 0.586028i | \(0.199309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3092.02 | 0.163094 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53647.4 | −2.81782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5200.34 | 0.272002 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3471.83 | 0.180834 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1946.94 | −0.100985 | −0.0504927 | − | 0.998724i | \(-0.516079\pi\) | ||||
−0.0504927 | + | 0.998724i | \(0.516079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11908.1 | 0.612542 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27883.5 | −1.42837 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15750.6 | 0.803518 | 0.401759 | − | 0.915745i | \(-0.368399\pi\) | ||||
0.401759 | + | 0.915745i | \(0.368399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1950.79 | 0.0987040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14349.6 | −0.723074 | −0.361537 | − | 0.932358i | \(-0.617748\pi\) | ||||
−0.361537 | + | 0.932358i | \(0.617748\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9504.24 | −0.475025 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17758.1 | 0.883953 | 0.441976 | − | 0.897027i | \(-0.354278\pi\) | ||||
0.441976 | + | 0.897027i | \(0.354278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −276.964 | −0.0137308 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29187.6 | 1.44117 | 0.720586 | − | 0.693366i | \(-0.243873\pi\) | ||||
0.720586 | + | 0.693366i | \(0.243873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48568.2 | −2.38846 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13521.0 | 0.662258 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13781.9 | −0.669654 | −0.334827 | − | 0.942280i | \(-0.608678\pi\) | ||||
−0.334827 | + | 0.942280i | \(0.608678\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17936.3 | 0.868039 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1035.78 | 0.0499283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36952.7 | 1.77420 | 0.887099 | − | 0.461579i | \(-0.152717\pi\) | ||||
0.887099 | + | 0.461579i | \(0.152717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36745.0 | −1.75726 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28816.5 | −1.37266 | −0.686332 | − | 0.727288i | \(-0.740780\pi\) | ||||
−0.686332 | + | 0.727288i | \(0.740780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7426.58 | 0.350992 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2348.92 | 0.110580 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25285.2 | −1.18571 | −0.592854 | − | 0.805310i | \(-0.701999\pi\) | ||||
−0.592854 | + | 0.805310i | \(0.701999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13950.4 | −0.651638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18418.2 | 0.856995 | 0.428497 | − | 0.903543i | \(-0.359043\pi\) | ||||
0.428497 | + | 0.903543i | \(0.359043\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32127.0 | −1.48908 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5322.07 | 0.244779 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26690.5 | −1.22287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5891.15 | −0.268880 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24520.5 | −1.11487 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11075.8 | −0.501664 | −0.250832 | − | 0.968031i | \(-0.580704\pi\) | ||||
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11086.1 | −0.500223 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4767.88 | −0.213509 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10092.4 | 0.450241 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4838.83 | 0.215057 | 0.107528 | − | 0.994202i | \(-0.465706\pi\) | ||||
0.107528 | + | 0.994202i | \(0.465706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13234.1 | −0.585969 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3069.77 | 0.135412 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25809.0 | 1.13422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21473.1 | 0.936664 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31509.9 | −1.36938 | −0.684690 | − | 0.728834i | \(-0.740062\pi\) | ||||
−0.684690 | + | 0.728834i | \(0.740062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29463.3 | 1.27570 | 0.637851 | − | 0.770160i | \(-0.279823\pi\) | ||||
0.637851 | + | 0.770160i | \(0.279823\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12115.1 | 0.522627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39983.0 | 1.71846 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 608.962 | 0.0260770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3502.22 | 0.148877 | 0.0744386 | − | 0.997226i | \(-0.476284\pi\) | ||||
0.0744386 | + | 0.997226i | \(0.476284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39993.0 | −1.69389 | −0.846943 | − | 0.531684i | \(-0.821560\pi\) | ||||
−0.846943 | + | 0.531684i | \(0.821560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22005.0 | −0.928623 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10733.6 | 0.451322 | 0.225661 | − | 0.974206i | \(-0.427546\pi\) | ||||
0.225661 | + | 0.974206i | \(0.427546\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14537.5 | −0.609056 | −0.304528 | − | 0.952503i | \(-0.598499\pi\) | ||||
−0.304528 | + | 0.952503i | \(0.598499\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8264.47 | −0.344996 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8405.16 | 0.348351 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6787.72 | −0.280308 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7353.57 | −0.302591 | −0.151295 | − | 0.988489i | \(-0.548344\pi\) | ||||
−0.151295 | + | 0.988489i | \(0.548344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23218.3 | 0.951998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2318.23 | −0.0947141 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34414.9 | −1.40107 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20236.5 | −0.818037 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 82540.7 | 3.32486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19293.6 | 0.774442 | 0.387221 | − | 0.921987i | \(-0.373435\pi\) | ||||
0.387221 | + | 0.921987i | \(0.373435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2318.29 | 0.0927297 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14161.6 | −0.564468 | −0.282234 | − | 0.959346i | \(-0.591076\pi\) | ||||
−0.282234 | + | 0.959346i | \(0.591076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8219.13 | −0.326465 | −0.163232 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163232 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2574.95 | −0.101567 | −0.0507835 | − | 0.998710i | \(-0.516172\pi\) | ||||
−0.0507835 | + | 0.998710i | \(0.516172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1539.77 | −0.0605246 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6658.33 | −0.260817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19719.2 | −0.769766 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −943.600 | −0.0367080 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7788.93 | 0.301965 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30981.1 | 1.19288 | 0.596442 | − | 0.802656i | \(-0.296581\pi\) | ||||
0.596442 | + | 0.802656i | \(0.296581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5768.08 | −0.221334 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41781.8 | −1.59780 | −0.798902 | − | 0.601461i | \(-0.794585\pi\) | ||||
−0.798902 | + | 0.601461i | \(0.794585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39289.6 | 1.49740 | 0.748699 | − | 0.662911i | \(-0.230679\pi\) | ||||
0.748699 | + | 0.662911i | \(0.230679\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19661.4 | −0.746790 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5832.44 | −0.220783 | −0.110391 | − | 0.993888i | \(-0.535210\pi\) | ||||
−0.110391 | + | 0.993888i | \(0.535210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4649.15 | −0.174806 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4131.18 | −0.154809 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8498.95 | 0.317418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3648.12 | −0.135794 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54852.5 | 2.03497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10981.3 | 0.406038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33182.3 | −1.21880 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42387.9 | −1.55178 | −0.775892 | − | 0.630866i | \(-0.782700\pi\) | ||||
−0.775892 | + | 0.630866i | \(0.782700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2189.30 | 0.0798841 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2275.12 | −0.0827423 | −0.0413711 | − | 0.999144i | \(-0.513173\pi\) | ||||
−0.0413711 | + | 0.999144i | \(0.513173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86229.3 | −3.12571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39909.0 | 1.44191 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31284.3 | 1.12293 | 0.561465 | − | 0.827500i | \(-0.310238\pi\) | ||||
0.561465 | + | 0.827500i | \(0.310238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6050.05 | 0.216456 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2649.88 | −0.0944983 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49429.9 | 1.75702 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8580.12 | −0.304000 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32196.6 | 1.13707 | 0.568535 | − | 0.822659i | \(-0.307511\pi\) | ||||
0.568535 | + | 0.822659i | \(0.307511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21450.0 | 0.752669 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −47362.6 | −1.65660 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22293.6 | 0.777269 | 0.388635 | − | 0.921392i | \(-0.372947\pi\) | ||||
0.388635 | + | 0.921392i | \(0.372947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25789.5 | −0.896281 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31809.7 | −1.10198 | −0.550991 | − | 0.834511i | \(-0.685750\pi\) | ||||
−0.550991 | + | 0.834511i | \(0.685750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70101.4 | 2.42080 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18982.6 | −0.651376 | −0.325688 | − | 0.945477i | \(-0.605596\pi\) | ||||
−0.325688 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2562.37 | 0.0876481 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8559.71 | −0.291869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9254.58 | 0.314570 | 0.157285 | − | 0.987553i | \(-0.449726\pi\) | ||||
0.157285 | + | 0.987553i | \(0.449726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −53862.5 | −1.82508 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37570.5 | 1.26905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33409.4 | 1.12146 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12104.6 | 0.405052 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30341.8 | −1.01216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15317.5 | −0.509387 | −0.254694 | − | 0.967022i | \(-0.581975\pi\) | ||||
−0.254694 | + | 0.967022i | \(0.581975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2522.47 | 0.0836259 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22432.6 | −0.741398 | −0.370699 | − | 0.928753i | \(-0.620882\pi\) | ||||
−0.370699 | + | 0.928753i | \(0.620882\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2184.70 | −0.0717603 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −627.864 | −0.0205600 | −0.0102800 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102800 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19577.3 | −0.639114 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15609.2 | 0.508015 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45032.6 | −1.46116 | −0.730579 | − | 0.682828i | \(-0.760750\pi\) | ||||
−0.730579 | + | 0.682828i | \(0.760750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32782.8 | −1.06045 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8021.14 | 0.257894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31981.0 | 1.02514 | 0.512569 | − | 0.858646i | \(-0.328694\pi\) | ||||
0.512569 | + | 0.858646i | \(0.328694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4857.35 | −0.155230 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50425.2 | 1.60662 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12378.8 | 0.393221 | 0.196611 | − | 0.980482i | \(-0.437007\pi\) | ||||
0.196611 | + | 0.980482i | \(0.437007\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10443.4 | 0.330746 |
(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 | 2352.4.a.cd.1.2 | 2 | ||
4.3 | odd | 2 | 294.4.a.j.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 2352.4.a.bn.1.1 | 2 | |||
12.11 | even | 2 | 882.4.a.bc.1.1 | 2 | |||
28.3 | even | 6 | 294.4.e.n.79.2 | 4 | |||
28.11 | odd | 6 | 294.4.e.o.79.1 | 4 | |||
28.19 | even | 6 | 294.4.e.n.67.2 | 4 | |||
28.23 | odd | 6 | 294.4.e.o.67.1 | 4 | |||
28.27 | even | 2 | 294.4.a.k.1.1 | yes | 2 | ||
84.11 | even | 6 | 882.4.g.bd.667.2 | 4 | |||
84.23 | even | 6 | 882.4.g.bd.361.2 | 4 | |||
84.47 | odd | 6 | 882.4.g.y.361.1 | 4 | |||
84.59 | odd | 6 | 882.4.g.y.667.1 | 4 | |||
84.83 | odd | 2 | 882.4.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.j.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
294.4.a.k.1.1 | yes | 2 | 28.27 | even | 2 | ||
294.4.e.n.67.2 | 4 | 28.19 | even | 6 | |||
294.4.e.n.79.2 | 4 | 28.3 | even | 6 | |||
294.4.e.o.67.1 | 4 | 28.23 | odd | 6 | |||
294.4.e.o.79.1 | 4 | 28.11 | odd | 6 | |||
882.4.a.bc.1.1 | 2 | 12.11 | even | 2 | |||
882.4.a.bi.1.2 | 2 | 84.83 | odd | 2 | |||
882.4.g.y.361.1 | 4 | 84.47 | odd | 6 | |||
882.4.g.y.667.1 | 4 | 84.59 | odd | 6 | |||
882.4.g.bd.361.2 | 4 | 84.23 | even | 6 | |||
882.4.g.bd.667.2 | 4 | 84.11 | even | 6 | |||
2352.4.a.bn.1.1 | 2 | 7.6 | odd | 2 | |||
2352.4.a.cd.1.2 | 2 | 1.1 | even | 1 | trivial |