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: | \(3\) |
Coefficient field: | 3.3.57516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 24x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.248072\) 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 | ||||||||
\(5\) | 12.4346 | 1.11218 | 0.556092 | − | 0.831120i | \(-0.312300\pi\) | ||||
0.556092 | + | 0.831120i | \(0.312300\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.3115 | −1.65315 | −0.826573 | − | 0.562829i | \(-0.809713\pi\) | ||||
−0.826573 | + | 0.562829i | \(0.809713\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.4269 | −0.777154 | −0.388577 | − | 0.921416i | \(-0.627033\pi\) | ||||
−0.388577 | + | 0.921416i | \(0.627033\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −37.3038 | −0.642120 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 48.7461 | 0.695451 | 0.347726 | − | 0.937596i | \(-0.386954\pi\) | ||||
0.347726 | + | 0.937596i | \(0.386954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.5500 | −0.610366 | −0.305183 | − | 0.952294i | \(-0.598718\pi\) | ||||
−0.305183 | + | 0.952294i | \(0.598718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −138.792 | −1.25827 | −0.629135 | − | 0.777296i | \(-0.716591\pi\) | ||||
−0.629135 | + | 0.777296i | \(0.716591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.6194 | 0.236955 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −61.1345 | −0.391462 | −0.195731 | − | 0.980658i | \(-0.562708\pi\) | ||||
−0.195731 | + | 0.980658i | \(0.562708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.16935 | −0.00677490 | −0.00338745 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338745 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 180.935 | 0.954444 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.5268 | 0.308923 | 0.154461 | − | 0.987999i | \(-0.450636\pi\) | ||||
0.154461 | + | 0.987999i | \(0.450636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 109.281 | 0.448690 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −308.115 | −1.17365 | −0.586823 | − | 0.809715i | \(-0.699622\pi\) | ||||
−0.586823 | + | 0.809715i | \(0.699622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −174.443 | −0.618657 | −0.309329 | − | 0.950955i | \(-0.600104\pi\) | ||||
−0.309329 | + | 0.950955i | \(0.600104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 111.911 | 0.370728 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 389.362 | 1.20839 | 0.604194 | − | 0.796837i | \(-0.293495\pi\) | ||||
0.604194 | + | 0.796837i | \(0.293495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −146.238 | −0.401519 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 314.935 | 0.816220 | 0.408110 | − | 0.912933i | \(-0.366188\pi\) | ||||
0.408110 | + | 0.912933i | \(0.366188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −749.950 | −1.83860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 151.650 | 0.352395 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 844.526 | 1.86352 | 0.931762 | − | 0.363068i | \(-0.118271\pi\) | ||||
0.931762 | + | 0.363068i | \(0.118271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 338.538 | 0.710579 | 0.355290 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355290 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −452.954 | −0.864339 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 971.550 | 1.77155 | 0.885774 | − | 0.464117i | \(-0.153628\pi\) | ||||
0.885774 | + | 0.464117i | \(0.153628\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 416.377 | 0.726463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 98.4698 | 0.164595 | 0.0822973 | − | 0.996608i | \(-0.473774\pi\) | ||||
0.0822973 | + | 0.996608i | \(0.473774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −710.235 | −1.13872 | −0.569361 | − | 0.822088i | \(-0.692809\pi\) | ||||
−0.569361 | + | 0.822088i | \(0.692809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −88.8581 | −0.136806 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 486.884 | 0.693402 | 0.346701 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346701 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 605.688 | 0.800999 | 0.400499 | − | 0.916297i | \(-0.368837\pi\) | ||||
0.400499 | + | 0.916297i | \(0.368837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 606.139 | 0.773470 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 183.403 | 0.226010 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −218.069 | −0.259722 | −0.129861 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129861 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50806 | 0.00391149 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −628.569 | −0.678840 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 782.288 | 0.818859 | 0.409429 | − | 0.912342i | \(-0.365728\pi\) | ||||
0.409429 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −542.804 | −0.551049 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 311.646 | 0.307029 | 0.153514 | − | 0.988146i | \(-0.450941\pi\) | ||||
0.153514 | + | 0.988146i | \(0.450941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −149.258 | −0.142784 | −0.0713922 | − | 0.997448i | \(-0.522744\pi\) | ||||
−0.0713922 | + | 0.997448i | \(0.522744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −851.519 | −0.769341 | −0.384670 | − | 0.923054i | \(-0.625685\pi\) | ||||
−0.384670 | + | 0.923054i | \(0.625685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1361.88 | 1.19674 | 0.598369 | − | 0.801221i | \(-0.295816\pi\) | ||||
0.598369 | + | 0.801221i | \(0.295816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −208.581 | −0.178357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1048.55 | 0.872917 | 0.436459 | − | 0.899724i | \(-0.356233\pi\) | ||||
0.436459 | + | 0.899724i | \(0.356233\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1725.83 | −1.39943 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −327.842 | −0.259051 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2306.48 | 1.73289 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 924.346 | 0.677605 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1186.02 | −0.848647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −488.408 | −0.341254 | −0.170627 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170627 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 523.328 | 0.357182 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1854.23 | −1.23668 | −0.618338 | − | 0.785912i | \(-0.712194\pi\) | ||||
−0.618338 | + | 0.785912i | \(0.712194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −335.734 | −0.214040 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −511.115 | −0.318741 | −0.159370 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159370 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2266.10 | 1.38279 | 0.691397 | − | 0.722475i | \(-0.256995\pi\) | ||||
0.691397 | + | 0.722475i | \(0.256995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1168.09 | −0.697663 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2196.96 | 1.28475 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −760.183 | −0.435378 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1507.90 | 0.829074 | 0.414537 | − | 0.910033i | \(-0.363944\pi\) | ||||
0.414537 | + | 0.910033i | \(0.363944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1591.83 | −0.857887 | −0.428943 | − | 0.903331i | \(-0.641114\pi\) | ||||
−0.428943 | + | 0.903331i | \(0.641114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 438.715 | 0.231817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5404 | −0.00753494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1164.16 | −0.591784 | −0.295892 | − | 0.955221i | \(-0.595617\pi\) | ||||
−0.295892 | + | 0.955221i | \(0.595617\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −944.805 | −0.471245 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1155.88 | 0.555432 | 0.277716 | − | 0.960663i | \(-0.410423\pi\) | ||||
0.277716 | + | 0.960663i | \(0.410423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2249.85 | 1.06152 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2890.61 | −1.33941 | −0.669707 | − | 0.742626i | \(-0.733580\pi\) | ||||
−0.669707 | + | 0.742626i | \(0.733580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −870.082 | −0.396032 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −454.950 | −0.203455 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1894.94 | −0.832770 | −0.416385 | − | 0.909188i | \(-0.636703\pi\) | ||||
−0.416385 | + | 0.909188i | \(0.636703\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2533.58 | −1.07591 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4288.49 | 1.79071 | 0.895355 | − | 0.445354i | \(-0.146922\pi\) | ||||
0.895355 | + | 0.445354i | \(0.146922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −383.732 | −0.157583 | −0.0787917 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787917 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1015.61 | −0.410253 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 864.539 | 0.343579 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2939.95 | −1.14968 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −385.311 | −0.145969 | −0.0729845 | − | 0.997333i | \(-0.523252\pi\) | ||||
−0.0729845 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 630.224 | 0.235049 | 0.117525 | − | 0.993070i | \(-0.462504\pi\) | ||||
0.117525 | + | 0.993070i | \(0.462504\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1358.86 | 0.499026 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1250.23 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1092.24 | −0.389081 | −0.194541 | − | 0.980894i | \(-0.562322\pi\) | ||||
−0.194541 | + | 0.980894i | \(0.562322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2914.65 | −1.02280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3831.29 | −1.30531 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1249.13 | −0.419423 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3048.75 | 1.00902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3620.05 | 1.18111 | 0.590556 | − | 0.806997i | \(-0.298909\pi\) | ||||
0.590556 | + | 0.806997i | \(0.298909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −295.409 | −0.0950287 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2169.13 | −0.688061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2130.70 | 0.657442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1775.67 | −0.540473 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −183.844 | −0.0552069 | −0.0276034 | − | 0.999619i | \(-0.508788\pi\) | ||||
−0.0276034 | + | 0.999619i | \(0.508788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 266.574 | 0.0789850 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2279.52 | 0.666506 | 0.333253 | − | 0.942837i | \(-0.391854\pi\) | ||||
0.333253 | + | 0.942837i | \(0.391854\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5412.67 | −1.56192 | −0.780960 | − | 0.624582i | \(-0.785270\pi\) | ||||
−0.780960 | + | 0.624582i | \(0.785270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1138.37 | 0.320073 | 0.160036 | − | 0.987111i | \(-0.448839\pi\) | ||||
0.160036 | + | 0.987111i | \(0.448839\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4841.56 | 1.34395 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1460.65 | −0.400336 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6226.36 | 1.68515 | 0.842573 | − | 0.538583i | \(-0.181040\pi\) | ||||
0.842573 | + | 0.538583i | \(0.181040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3196.20 | 0.854295 | 0.427147 | − | 0.904182i | \(-0.359519\pi\) | ||||
0.427147 | + | 0.904182i | \(0.359519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1841.38 | 0.474349 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1817.06 | −0.462457 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 239.608 | 0.0602546 | 0.0301273 | − | 0.999546i | \(-0.490409\pi\) | ||||
0.0301273 | + | 0.999546i | \(0.490409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8370.78 | 2.08010 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1818.42 | −0.446563 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −699.117 | −0.169688 | −0.0848439 | − | 0.996394i | \(-0.527039\pi\) | ||||
−0.0848439 | + | 0.996394i | \(0.527039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −550.210 | −0.130487 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 919.040 | 0.215477 | 0.107738 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107738 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3916.09 | 0.907787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 654.206 | 0.149950 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2779.17 | 0.629923 | 0.314961 | − | 0.949104i | \(-0.398008\pi\) | ||||
0.314961 | + | 0.949104i | \(0.398008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2226.98 | 0.499186 | 0.249593 | − | 0.968351i | \(-0.419703\pi\) | ||||
0.249593 | + | 0.968351i | \(0.419703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1786.39 | −0.391721 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7307.69 | 1.58511 | 0.792557 | − | 0.609797i | \(-0.208749\pi\) | ||||
0.792557 | + | 0.609797i | \(0.208749\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.5242 | −0.00225830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2730.61 | 0.579696 | 0.289848 | − | 0.957073i | \(-0.406395\pi\) | ||||
0.289848 | + | 0.957073i | \(0.406395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1769.85 | −0.371755 | −0.185878 | − | 0.982573i | \(-0.559513\pi\) | ||||
−0.185878 | + | 0.982573i | \(0.559513\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1885.71 | 0.391928 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2536.81 | −0.516347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2346.86 | −0.472768 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8228.81 | −1.64072 | −0.820362 | − | 0.571844i | \(-0.806228\pi\) | ||||
−0.820362 | + | 0.571844i | \(0.806228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10501.4 | 2.07258 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1628.41 | 0.318148 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5055.78 | 0.977870 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −934.937 | −0.177263 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4209.58 | 0.790295 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6019.62 | 1.11908 | 0.559541 | − | 0.828803i | \(-0.310977\pi\) | ||||
0.559541 | + | 0.828803i | \(0.310977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 447.773 | 0.0824366 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1193.71 | 0.217650 | 0.108825 | − | 0.994061i | \(-0.465291\pi\) | ||||
0.108825 | + | 0.994061i | \(0.465291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8846.04 | 1.59747 | 0.798734 | − | 0.601684i | \(-0.205503\pi\) | ||||
0.798734 | + | 0.601684i | \(0.205503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6081.43 | 1.07750 | 0.538750 | − | 0.842466i | \(-0.318897\pi\) | ||||
0.538750 | + | 0.842466i | \(0.318897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3687.11 | 0.647143 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2554.56 | 0.444179 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2464.12 | −0.424480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1078.94 | −0.184151 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4085.64 | −0.690936 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3053.30 | −0.507022 | −0.253511 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253511 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 625.742 | 0.102974 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12080.8 | 1.97029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3865.80 | 0.624877 | 0.312438 | − | 0.949938i | \(-0.398854\pi\) | ||||
0.312438 | + | 0.949938i | \(0.398854\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3145.66 | −0.503979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 70.5255 | 0.0111999 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5177.49 | 0.807961 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 99.5931 | 0.0154076 | 0.00770380 | − | 0.999970i | \(-0.497548\pi\) | ||||
0.00770380 | + | 0.999970i | \(0.497548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3607.34 | 0.553285 | 0.276643 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276643 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 983.526 | 0.149563 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7130.73 | −1.07516 | −0.537579 | − | 0.843214i | \(-0.680661\pi\) | ||||
−0.537579 | + | 0.843214i | \(0.680661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1224.43 | 0.183060 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6500.29 | 0.955632 | 0.477816 | − | 0.878460i | \(-0.341428\pi\) | ||||
0.477816 | + | 0.878460i | \(0.341428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4303.70 | −0.627453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6919.44 | −1.00049 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8831.49 | −1.26647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 824.886 | 0.117326 | 0.0586631 | − | 0.998278i | \(-0.481316\pi\) | ||||
0.0586631 | + | 0.998278i | \(0.481316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2773.04 | −0.391216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1333.85 | 0.185159 | 0.0925793 | − | 0.995705i | \(-0.470489\pi\) | ||||
0.0925793 | + | 0.995705i | \(0.470489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3558.06 | 0.489967 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2226.94 | 0.304226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1338.29 | 0.181380 | 0.0906902 | − | 0.995879i | \(-0.471093\pi\) | ||||
0.0906902 | + | 0.995879i | \(0.471093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1465.22 | 0.197023 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 353.376 | 0.0471453 | 0.0235727 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235727 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1569.98 | −0.206219 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11737.2 | 1.52982 | 0.764908 | − | 0.644139i | \(-0.222784\pi\) | ||||
0.764908 | + | 0.644139i | \(0.222784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6765.59 | −0.875066 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5562.68 | 0.713996 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6054.21 | 0.771191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13281.4 | −1.67903 | −0.839516 | − | 0.543335i | \(-0.817161\pi\) | ||||
−0.839516 | + | 0.543335i | \(0.817161\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7482.36 | −0.931798 | −0.465899 | − | 0.884838i | \(-0.654269\pi\) | ||||
−0.465899 | + | 0.884838i | \(0.654269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.5959 | 0.00526514 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1007.20 | 0.123576 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4193.27 | −0.510694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13796.6 | 1.66797 | 0.833983 | − | 0.551791i | \(-0.186055\pi\) | ||||
0.833983 | + | 0.551791i | \(0.186055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1533.35 | 0.184025 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7531.49 | 0.890859 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6798.31 | −0.798357 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9497.56 | 1.10737 | 0.553683 | − | 0.832728i | \(-0.313222\pi\) | ||||
0.553683 | + | 0.832728i | \(0.313222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.367 | 0.0722797 | 0.0361399 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361399 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3504.26 | 0.402796 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1443.83 | 0.164791 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6590.88 | −0.741750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13397.3 | 1.49727 | 0.748636 | − | 0.662981i | \(-0.230709\pi\) | ||||
0.748636 | + | 0.662981i | \(0.230709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14057.3 | 1.56016 | 0.780079 | − | 0.625681i | \(-0.215179\pi\) | ||||
0.780079 | + | 0.625681i | \(0.215179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2280.55 | 0.251365 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7015.95 | 0.768006 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16368.8 | −1.77960 | −0.889798 | − | 0.456356i | \(-0.849155\pi\) | ||||
−0.889798 | + | 0.456356i | \(0.849155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1178.71 | 0.126416 | 0.0632078 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632078 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2711.60 | −0.288858 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4523.70 | −0.478666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12400.9 | −1.30342 | −0.651709 | − | 0.758469i | \(-0.725948\pi\) | ||||
−0.651709 | + | 0.758469i | \(0.725948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18582.9 | 1.94021 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4775.48 | 0.495301 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9925.58 | 1.01597 | 0.507986 | − | 0.861365i | \(-0.330390\pi\) | ||||
0.507986 | + | 0.861365i | \(0.330390\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1316.15 | −0.133840 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16010.3 | 1.61751 | 0.808755 | − | 0.588146i | \(-0.200142\pi\) | ||||
0.808755 | + | 0.588146i | \(0.200142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17372.4 | −1.74377 | −0.871883 | − | 0.489714i | \(-0.837101\pi\) | ||||
−0.871883 | + | 0.489714i | \(0.837101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 43.6213 | 0.00435030 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2108.06 | 0.208886 | 0.104443 | − | 0.994531i | \(-0.466694\pi\) | ||||
0.104443 | + | 0.994531i | \(0.466694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3492.48 | 0.341667 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10520.9 | 1.02273 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1497.26 | −0.144629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2834.41 | 0.272073 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2450.04 | −0.233706 | −0.116853 | − | 0.993149i | \(-0.537281\pi\) | ||||
−0.116853 | + | 0.993149i | \(0.537281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2532.65 | −0.240081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9727.44 | 0.910722 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −645.236 | −0.0600379 | −0.0300189 | − | 0.999549i | \(-0.509557\pi\) | ||||
−0.0300189 | + | 0.999549i | \(0.509557\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3467.64 | −0.320679 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11766.1 | −1.08146 | −0.540731 | − | 0.841196i | \(-0.681852\pi\) | ||||
−0.540731 | + | 0.841196i | \(0.681852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2980.07 | −0.272242 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6749.55 | −0.612868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.0209 | 0.00394919 | 0.00197459 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197459 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8671.83 | 0.773311 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8290.27 | 0.734880 | 0.367440 | − | 0.930047i | \(-0.380234\pi\) | ||||
0.367440 | + | 0.930047i | \(0.380234\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3875.19 | 0.341473 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2610.24 | 0.228649 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6915.04 | −0.602168 | −0.301084 | − | 0.953598i | \(-0.597349\pi\) | ||||
−0.301084 | + | 0.953598i | \(0.597349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1364.85 | 0.117465 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1855.96 | −0.158803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23483.0 | −1.99764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5684.81 | 0.480800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13399.3 | −1.12674 | −0.563371 | − | 0.826204i | \(-0.690496\pi\) | ||||
−0.563371 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9936.99 | −0.830811 | −0.415406 | − | 0.909636i | \(-0.636360\pi\) | ||||
−0.415406 | + | 0.909636i | \(0.636360\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −57.0014 | −0.00471161 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7096.33 | 0.583244 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7600.74 | 0.621175 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11223.7 | 0.912104 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10588.3 | −0.855649 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12865.5 | −1.03387 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9286.17 | 0.737973 | 0.368987 | − | 0.929435i | \(-0.379705\pi\) | ||||
0.368987 | + | 0.929435i | \(0.379705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1151.20 | 0.0909809 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16934.4 | 1.33099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16821.6 | 1.31488 | 0.657438 | − | 0.753508i | \(-0.271640\pi\) | ||||
0.657438 | + | 0.753508i | \(0.271640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3046.84 | 0.236860 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3090.35 | 0.238935 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2593.62 | −0.198366 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1805.94 | 0.137379 | 0.0686897 | − | 0.997638i | \(-0.478118\pi\) | ||||
0.0686897 | + | 0.997638i | \(0.478118\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6354.40 | 0.480792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8819.86 | 0.663770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12214.9 | 0.914381 | 0.457190 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457190 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13038.3 | 0.970845 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4283.77 | 0.315615 | 0.157808 | − | 0.987470i | \(-0.449557\pi\) | ||||
0.157808 | + | 0.987470i | \(0.449557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6359.94 | −0.466121 | −0.233060 | − | 0.972462i | \(-0.574874\pi\) | ||||
−0.233060 | + | 0.972462i | \(0.574874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1155.93 | 0.0842753 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4110.95 | −0.298153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14468.7 | −1.04392 | −0.521959 | − | 0.852971i | \(-0.674799\pi\) | ||||
−0.521959 | + | 0.852971i | \(0.674799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1890.67 | −0.135706 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18994.2 | −1.34933 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4076.59 | −0.288113 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11132.6 | −0.782777 | −0.391388 | − | 0.920226i | \(-0.628005\pi\) | ||||
−0.391388 | + | 0.920226i | \(0.628005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.1108 | 0.00413517 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3750.69 | 0.261054 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19775.6 | 1.36946 | 0.684728 | − | 0.728799i | \(-0.259921\pi\) | ||||
0.684728 | + | 0.728799i | \(0.259921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3276.73 | 0.224636 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23891.0 | 1.62965 | 0.814825 | − | 0.579707i | \(-0.196833\pi\) | ||||
0.814825 | + | 0.579707i | \(0.196833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19395.5 | −1.31641 | −0.658204 | − | 0.752840i | \(-0.728683\pi\) | ||||
−0.658204 | + | 0.752840i | \(0.728683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8743.95 | 0.590516 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28680.2 | 1.92730 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14596.7 | 0.976051 | 0.488025 | − | 0.872829i | \(-0.337717\pi\) | ||||
0.488025 | + | 0.872829i | \(0.337717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14183.2 | −0.939104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1979.80 | 0.130446 | 0.0652229 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652229 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11493.9 | 0.753622 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16262.4 | 1.06110 | 0.530551 | − | 0.847653i | \(-0.321985\pi\) | ||||
0.530551 | + | 0.847653i | \(0.321985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12021.0 | −0.780555 | −0.390278 | − | 0.920697i | \(-0.627621\pi\) | ||||
−0.390278 | + | 0.920697i | \(0.627621\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3747.39 | 0.242154 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18450.1 | −1.18081 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9146.24 | −0.582561 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3389.16 | 0.214841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25347.6 | −1.59916 | −0.799582 | − | 0.600557i | \(-0.794945\pi\) | ||||
−0.799582 | + | 0.600557i | \(0.794945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10860.1 | −0.681915 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6073.16 | −0.379537 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 886.228 | 0.0548648 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5111.60 | −0.314971 | −0.157485 | − | 0.987521i | \(-0.550339\pi\) | ||||
−0.157485 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10931.3 | −0.670435 | −0.335217 | − | 0.942141i | \(-0.608810\pi\) | ||||
−0.335217 | + | 0.942141i | \(0.608810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6507.38 | 0.397252 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18406.1 | −1.11842 | −0.559211 | − | 0.829025i | \(-0.688896\pi\) | ||||
−0.559211 | + | 0.829025i | \(0.688896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50934.7 | −3.08068 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19921.4 | 1.19385 | 0.596926 | − | 0.802296i | \(-0.296389\pi\) | ||||
0.596926 | + | 0.802296i | \(0.296389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23056.6 | −1.37541 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6392.11 | −0.379574 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18858.8 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25832.1 | −1.52005 | −0.760023 | − | 0.649896i | \(-0.774812\pi\) | ||||
−0.760023 | + | 0.649896i | \(0.774812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5327.01 | 0.312042 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8485.00 | 0.492564 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 551.533 | 0.0318737 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20417.7 | −1.17469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16275.0 | −0.932178 | −0.466089 | − | 0.884738i | \(-0.654337\pi\) | ||||
−0.466089 | + | 0.884738i | \(0.654337\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −799.723 | −0.0456020 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26271.8 | 1.49144 | 0.745720 | − | 0.666259i | \(-0.232105\pi\) | ||||
0.745720 | + | 0.666259i | \(0.232105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6838.55 | −0.384808 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8072.29 | 0.452237 | 0.226118 | − | 0.974100i | \(-0.427396\pi\) | ||||
0.226118 | + | 0.974100i | \(0.427396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6355.51 | −0.354499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16238.0 | 0.901774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11472.1 | −0.634328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24485.3 | −1.34799 | −0.673997 | − | 0.738734i | \(-0.735424\pi\) | ||||
−0.673997 | + | 0.738734i | \(0.735424\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28178.1 | 1.53792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15019.4 | −0.816214 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3415.10 | −0.184794 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 778.448 | 0.0419423 | 0.0209712 | − | 0.999780i | \(-0.493324\pi\) | ||||
0.0209712 | + | 0.999780i | \(0.493324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3514.58 | −0.188556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14524.7 | −0.775930 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24172.0 | −1.28039 | −0.640197 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640197 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4381.96 | 0.231134 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 162.297 | 0.00852466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27318.3 | 1.42888 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18679.1 | −0.972919 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −81.8835 | −0.00424720 | −0.00212360 | − | 0.999998i | \(-0.500676\pi\) | ||||
−0.00212360 | + | 0.999998i | \(0.500676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9588.59 | −0.493227 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1810.76 | −0.0927588 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32542.9 | −1.66018 | −0.830088 | − | 0.557632i | \(-0.811710\pi\) | ||||
−0.830088 | + | 0.557632i | \(0.811710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8503.40 | −0.430246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5068.94 | 0.255424 | 0.127712 | − | 0.991811i | \(-0.459237\pi\) | ||||
0.127712 | + | 0.991811i | \(0.459237\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −58595.6 | −2.92863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38428.5 | 1.91287 | 0.956437 | − | 0.291939i | \(-0.0943004\pi\) | ||||
0.956437 | + | 0.291939i | \(0.0943004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5524.14 | −0.273865 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21592.9 | −1.06617 | −0.533086 | − | 0.846061i | \(-0.678968\pi\) | ||||
−0.533086 | + | 0.846061i | \(0.678968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18750.1 | 0.922083 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5451.19 | 0.267000 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8112.60 | −0.394185 | −0.197093 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197093 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −718.823 | −0.0347880 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19793.7 | −0.954129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3108.01 | 0.149224 | 0.0746120 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746120 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25112.3 | −1.20095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7211.93 | 0.343538 | 0.171769 | − | 0.985137i | \(-0.445052\pi\) | ||||
0.171769 | + | 0.985137i | \(0.445052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5455.25 | 0.257823 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30763.5 | −1.44825 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7533.07 | 0.353250 | 0.176625 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176625 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2097.35 | 0.0979693 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24832.6 | 1.15546 | 0.577728 | − | 0.816229i | \(-0.303940\pi\) | ||||
0.577728 | + | 0.816229i | \(0.303940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.6355 | −0.00160535 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15575.2 | 0.716355 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5938.86 | −0.272099 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1650.63 | 0.0753368 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14475.9 | −0.658173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36313.1 | 1.64476 | 0.822378 | − | 0.568941i | \(-0.192647\pi\) | ||||
0.822378 | + | 0.568941i | \(0.192647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2757.12 | −0.124406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12331.9 | −0.552229 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11748.3 | −0.524111 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31665.7 | −1.40735 | −0.703675 | − | 0.710522i | \(-0.748459\pi\) | ||||
−0.703675 | + | 0.710522i | \(0.748459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18979.9 | 0.840375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1962.62 | −0.0865738 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42835.4 | 1.88247 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8337.52 | −0.363686 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12384.6 | 0.538219 | 0.269110 | − | 0.963110i | \(-0.413271\pi\) | ||||
0.269110 | + | 0.963110i | \(0.413271\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16742.4 | 0.724914 | 0.362457 | − | 0.932000i | \(-0.381938\pi\) | ||||
0.362457 | + | 0.932000i | \(0.381938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6680.94 | −0.288205 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14372.9 | 0.617744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8818.07 | 0.377607 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26456.3 | 1.12464 | 0.562322 | − | 0.826918i | \(-0.309908\pi\) | ||||
0.562322 | + | 0.826918i | \(0.309908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23098.5 | −0.978328 | −0.489164 | − | 0.872192i | \(-0.662698\pi\) | ||||
−0.489164 | + | 0.872192i | \(0.662698\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5359.17 | 0.226160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20647.6 | −0.868183 | −0.434092 | − | 0.900869i | \(-0.642931\pi\) | ||||
−0.434092 | + | 0.900869i | \(0.642931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23368.5 | 0.979037 | 0.489519 | − | 0.871993i | \(-0.337173\pi\) | ||||
0.489519 | + | 0.871993i | \(0.337173\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21923.1 | −0.915166 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35943.6 | −1.48968 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.5725 | 0.00130383 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16735.5 | 0.688645 | 0.344322 | − | 0.938851i | \(-0.388109\pi\) | ||||
0.344322 | + | 0.938851i | \(0.388109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20651.6 | −0.846758 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8191.84 | −0.334688 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10819.1 | −0.440460 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5309.55 | 0.214633 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9649.80 | −0.388708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10294.5 | 0.413219 | 0.206609 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5657.12 | −0.226280 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32788.6 | 1.30693 | 0.653463 | − | 0.756958i | \(-0.273315\pi\) | ||||
0.653463 | + | 0.756958i | \(0.273315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4909.76 | −0.195016 | −0.0975081 | − | 0.995235i | \(-0.531087\pi\) | ||||
−0.0975081 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17795.0 | −0.701909 | −0.350954 | − | 0.936393i | \(-0.614143\pi\) | ||||
−0.350954 | + | 0.936393i | \(0.614143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23562.8 | −0.926195 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7610.44 | 0.298113 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29364.7 | −1.14629 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35390.5 | −1.37677 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7040.59 | 0.272953 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34672.2 | 1.33500 | 0.667501 | − | 0.744609i | \(-0.267364\pi\) | ||||
0.667501 | + | 0.744609i | \(0.267364\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24686.4 | 0.947273 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40848.2 | −1.56210 | −0.781051 | − | 0.624467i | \(-0.785316\pi\) | ||||
−0.781051 | + | 0.624467i | \(0.785316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30035.1 | −1.14469 | −0.572345 | − | 0.820013i | \(-0.693966\pi\) | ||||
−0.572345 | + | 0.820013i | \(0.693966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31504.1 | −1.19661 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33210.7 | 1.25717 | 0.628583 | − | 0.777742i | \(-0.283635\pi\) | ||||
0.628583 | + | 0.777742i | \(0.283635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4885.23 | −0.183683 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19682.2 | −0.737559 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53325.7 | 1.99160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15167.3 | −0.564573 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71.4878 | 0.00265211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15351.9 | 0.567641 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4771.56 | −0.175262 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2497.83 | −0.0914433 | −0.0457217 | − | 0.998954i | \(-0.514559\pi\) | ||||
−0.0457217 | + | 0.998954i | \(0.514559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2804.81 | 0.102343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1895.00 | 0.0689180 | 0.0344590 | − | 0.999406i | \(-0.489029\pi\) | ||||
0.0344590 | + | 0.999406i | \(0.489029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36530.0 | −1.32417 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12628.8 | −0.456277 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6270.71 | −0.225083 | −0.112542 | − | 0.993647i | \(-0.535899\pi\) | ||||
−0.112542 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18058.9 | −0.646102 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3586.95 | −0.127915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2059.34 | 0.0732008 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1343.32 | −0.0475948 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31552.6 | 1.11432 | 0.557161 | − | 0.830404i | \(-0.311890\pi\) | ||||
0.557161 | + | 0.830404i | \(0.311890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3581.14 | −0.125661 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36557.2 | −1.27866 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22030.2 | 0.768084 | 0.384042 | − | 0.923316i | \(-0.374532\pi\) | ||||
0.384042 | + | 0.923316i | \(0.374532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26538.1 | −0.922299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32538.6 | 1.12724 | 0.563618 | − | 0.826036i | \(-0.309409\pi\) | ||||
0.563618 | + | 0.826036i | \(0.309409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42764.1 | 1.47677 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40711.0 | 1.39697 | 0.698485 | − | 0.715625i | \(-0.253858\pi\) | ||||
0.698485 | + | 0.715625i | \(0.253858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25871.7 | 0.884962 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18244.3 | −0.622095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52516.4 | −1.78507 | −0.892536 | − | 0.450976i | \(-0.851076\pi\) | ||||
−0.892536 | + | 0.450976i | \(0.851076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4791.18 | −0.162345 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11061.3 | −0.373628 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29789.6 | −0.999954 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7663.67 | −0.256447 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7836.58 | 0.261418 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14721.6 | −0.489570 | −0.244785 | − | 0.969577i | \(-0.578717\pi\) | ||||
−0.244785 | + | 0.969577i | \(0.578717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7392.35 | 0.245074 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13772.5 | 0.455181 | 0.227590 | − | 0.973757i | \(-0.426915\pi\) | ||||
0.227590 | + | 0.973757i | \(0.426915\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3236.83 | 0.106319 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24782.1 | 0.811513 | 0.405757 | − | 0.913981i | \(-0.367008\pi\) | ||||
0.405757 | + | 0.913981i | \(0.367008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13152.0 | 0.429358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12256.9 | 0.398912 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42804.7 | 1.38887 | 0.694435 | − | 0.719556i | \(-0.255655\pi\) | ||||
0.694435 | + | 0.719556i | \(0.255655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15546.1 | −0.502883 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24211.3 | 0.778438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −449.862 | −0.0144201 | −0.00721006 | − | 0.999974i | \(-0.502295\pi\) | ||||
−0.00721006 | + | 0.999974i | \(0.502295\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9159.89 | 0.292729 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13581.6 | −0.432730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21473.7 | 0.682127 | 0.341063 | − | 0.940040i | \(-0.389213\pi\) | ||||
0.341063 | + | 0.940040i | \(0.389213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1877.22 | −0.0594522 |
(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.cg.1.3 | 3 | ||
4.3 | odd | 2 | 147.4.a.m.1.2 | 3 | |||
7.3 | odd | 6 | 336.4.q.k.289.3 | 6 | |||
7.5 | odd | 6 | 336.4.q.k.193.3 | 6 | |||
7.6 | odd | 2 | 2352.4.a.ci.1.1 | 3 | |||
12.11 | even | 2 | 441.4.a.t.1.2 | 3 | |||
28.3 | even | 6 | 21.4.e.b.16.2 | yes | 6 | ||
28.11 | odd | 6 | 147.4.e.n.79.2 | 6 | |||
28.19 | even | 6 | 21.4.e.b.4.2 | ✓ | 6 | ||
28.23 | odd | 6 | 147.4.e.n.67.2 | 6 | |||
28.27 | even | 2 | 147.4.a.l.1.2 | 3 | |||
84.11 | even | 6 | 441.4.e.w.226.2 | 6 | |||
84.23 | even | 6 | 441.4.e.w.361.2 | 6 | |||
84.47 | odd | 6 | 63.4.e.c.46.2 | 6 | |||
84.59 | odd | 6 | 63.4.e.c.37.2 | 6 | |||
84.83 | odd | 2 | 441.4.a.s.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.2 | ✓ | 6 | 28.19 | even | 6 | ||
21.4.e.b.16.2 | yes | 6 | 28.3 | even | 6 | ||
63.4.e.c.37.2 | 6 | 84.59 | odd | 6 | |||
63.4.e.c.46.2 | 6 | 84.47 | odd | 6 | |||
147.4.a.l.1.2 | 3 | 28.27 | even | 2 | |||
147.4.a.m.1.2 | 3 | 4.3 | odd | 2 | |||
147.4.e.n.67.2 | 6 | 28.23 | odd | 6 | |||
147.4.e.n.79.2 | 6 | 28.11 | odd | 6 | |||
336.4.q.k.193.3 | 6 | 7.5 | odd | 6 | |||
336.4.q.k.289.3 | 6 | 7.3 | odd | 6 | |||
441.4.a.s.1.2 | 3 | 84.83 | odd | 2 | |||
441.4.a.t.1.2 | 3 | 12.11 | even | 2 | |||
441.4.e.w.226.2 | 6 | 84.11 | even | 6 | |||
441.4.e.w.361.2 | 6 | 84.23 | even | 6 | |||
2352.4.a.cg.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2352.4.a.ci.1.1 | 3 | 7.6 | odd | 2 |