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: | 3.3.58461.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 65x - 126 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(9.37106\) 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 | ||||||||
\(5\) | 21.3959 | 1.91371 | 0.956855 | − | 0.290567i | \(-0.0938438\pi\) | ||||
0.956855 | + | 0.290567i | \(0.0938438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.7035 | −0.293385 | −0.146693 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146693 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.31878 | −0.177478 | −0.0887390 | − | 0.996055i | \(-0.528284\pi\) | ||||
−0.0887390 | + | 0.996055i | \(0.528284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 64.1878 | 1.10488 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.48423 | −0.0211752 | −0.0105876 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105876 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 161.519 | 1.95026 | 0.975130 | − | 0.221635i | \(-0.0711395\pi\) | ||||
0.975130 | + | 0.221635i | \(0.0711395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 123.945 | 1.12367 | 0.561834 | − | 0.827250i | \(-0.310096\pi\) | ||||
0.561834 | + | 0.827250i | \(0.310096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 332.786 | 2.66228 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −222.817 | −1.42676 | −0.713381 | − | 0.700777i | \(-0.752837\pi\) | ||||
−0.713381 | + | 0.700777i | \(0.752837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 203.851 | 1.18105 | 0.590526 | − | 0.807018i | \(-0.298920\pi\) | ||||
0.590526 | + | 0.807018i | \(0.298920\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −32.1106 | −0.169386 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −341.224 | −1.51613 | −0.758066 | − | 0.652178i | \(-0.773856\pi\) | ||||
−0.758066 | + | 0.652178i | \(0.773856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −24.9563 | −0.102467 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −147.127 | −0.560422 | −0.280211 | − | 0.959938i | \(-0.590404\pi\) | ||||
−0.280211 | + | 0.959938i | \(0.590404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −51.3401 | −0.182077 | −0.0910383 | − | 0.995847i | \(-0.529019\pi\) | ||||
−0.0910383 | + | 0.995847i | \(0.529019\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 192.563 | 0.637903 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 269.510 | 0.836428 | 0.418214 | − | 0.908348i | \(-0.362656\pi\) | ||||
0.418214 | + | 0.908348i | \(0.362656\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.45269 | −0.0122255 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.500 | −1.12091 | −0.560457 | − | 0.828183i | \(-0.689375\pi\) | ||||
−0.560457 | + | 0.828183i | \(0.689375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −229.012 | −0.561454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 484.556 | 1.12598 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30.7341 | 0.0678176 | 0.0339088 | − | 0.999425i | \(-0.489204\pi\) | ||||
0.0339088 | + | 0.999425i | \(0.489204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 592.517 | 1.24367 | 0.621836 | − | 0.783147i | \(-0.286387\pi\) | ||||
0.621836 | + | 0.783147i | \(0.286387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −177.988 | −0.339641 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −414.052 | −0.754993 | −0.377497 | − | 0.926011i | \(-0.623215\pi\) | ||||
−0.377497 | + | 0.926011i | \(0.623215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 371.836 | 0.648750 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −294.854 | −0.492856 | −0.246428 | − | 0.969161i | \(-0.579257\pi\) | ||||
−0.246428 | + | 0.969161i | \(0.579257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 594.063 | 0.952462 | 0.476231 | − | 0.879320i | \(-0.342003\pi\) | ||||
0.476231 | + | 0.879320i | \(0.342003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 998.357 | 1.53707 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 831.386 | 1.18403 | 0.592014 | − | 0.805928i | \(-0.298333\pi\) | ||||
0.592014 | + | 0.805928i | \(0.298333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 326.218 | 0.431410 | 0.215705 | − | 0.976459i | \(-0.430795\pi\) | ||||
0.215705 | + | 0.976459i | \(0.430795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31.7564 | −0.0405232 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −668.451 | −0.823741 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1261.10 | 1.50198 | 0.750989 | − | 0.660315i | \(-0.229577\pi\) | ||||
0.750989 | + | 0.660315i | \(0.229577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 611.552 | 0.681881 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3455.84 | 3.73223 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1059.98 | 1.10953 | 0.554766 | − | 0.832007i | \(-0.312808\pi\) | ||||
0.554766 | + | 0.832007i | \(0.312808\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −96.3319 | −0.0977951 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −180.948 | −0.178267 | −0.0891337 | − | 0.996020i | \(-0.528410\pi\) | ||||
−0.0891337 | + | 0.996020i | \(0.528410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.0461 | 0.0641384 | 0.0320692 | − | 0.999486i | \(-0.489790\pi\) | ||||
0.0320692 | + | 0.999486i | \(0.489790\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1060.10 | 0.957794 | 0.478897 | − | 0.877871i | \(-0.341037\pi\) | ||||
0.478897 | + | 0.877871i | \(0.341037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −777.222 | −0.682976 | −0.341488 | − | 0.939886i | \(-0.610931\pi\) | ||||
−0.341488 | + | 0.939886i | \(0.610931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1023.67 | −0.875340 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1021.93 | −0.850749 | −0.425375 | − | 0.905017i | \(-0.639858\pi\) | ||||
−0.425375 | + | 0.905017i | \(0.639858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2651.92 | 2.15037 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −74.8690 | −0.0591593 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1216.43 | −0.913925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −441.380 | −0.323560 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4445.76 | 3.18113 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1176.21 | −0.821824 | −0.410912 | − | 0.911675i | \(-0.634790\pi\) | ||||
−0.410912 | + | 0.911675i | \(0.634790\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −154.020 | −0.105122 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1900.95 | −1.26784 | −0.633920 | − | 0.773398i | \(-0.718555\pi\) | ||||
−0.633920 | + | 0.773398i | \(0.718555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 577.690 | 0.368294 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −619.637 | −0.386417 | −0.193209 | − | 0.981158i | \(-0.561889\pi\) | ||||
−0.193209 | + | 0.981158i | \(0.561889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1248.11 | −0.761604 | −0.380802 | − | 0.924657i | \(-0.624352\pi\) | ||||
−0.380802 | + | 0.924657i | \(0.624352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 808.531 | 0.482912 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 89.0404 | 0.0520694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4767.38 | −2.73041 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 521.479 | 0.286720 | 0.143360 | − | 0.989671i | \(-0.454209\pi\) | ||||
0.143360 | + | 0.989671i | \(0.454209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1261.33 | −0.679773 | −0.339886 | − | 0.940467i | \(-0.610389\pi\) | ||||
−0.339886 | + | 0.940467i | \(0.610389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.3581 | −0.00705840 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4361.57 | 2.26019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 584.137 | 0.296938 | 0.148469 | − | 0.988917i | \(-0.452566\pi\) | ||||
0.148469 | + | 0.988917i | \(0.452566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1297.50 | −0.647160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −164.133 | −0.0788704 | −0.0394352 | − | 0.999222i | \(-0.512556\pi\) | ||||
−0.0394352 | + | 0.999222i | \(0.512556\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −687.036 | −0.324156 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3292.41 | 1.52560 | 0.762798 | − | 0.646636i | \(-0.223825\pi\) | ||||
0.762798 | + | 0.646636i | \(0.223825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2127.80 | −0.968502 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1453.67 | 0.650086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2602.09 | −1.14355 | −0.571773 | − | 0.820412i | \(-0.693744\pi\) | ||||
−0.571773 | + | 0.820412i | \(0.693744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 92.2023 | 0.0391545 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 302.031 | 0.126116 | 0.0630582 | − | 0.998010i | \(-0.479915\pi\) | ||||
0.0630582 | + | 0.998010i | \(0.479915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −609.020 | −0.250100 | −0.125050 | − | 0.992150i | \(-0.539909\pi\) | ||||
−0.125050 | + | 0.992150i | \(0.539909\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1777.55 | 0.718035 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7300.81 | −2.90144 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8865 | 0.00621249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4801.60 | 1.81901 | 0.909507 | − | 0.415688i | \(-0.136459\pi\) | ||||
0.909507 | + | 0.415688i | \(0.136459\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1912.28 | 0.713208 | 0.356604 | − | 0.934256i | \(-0.383935\pi\) | ||||
0.356604 | + | 0.934256i | \(0.383935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −533.964 | −0.196092 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4085.92 | 1.47771 | 0.738857 | − | 0.673862i | \(-0.235366\pi\) | ||||
0.738857 | + | 0.673862i | \(0.235366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 498.536 | 0.177589 | 0.0887946 | − | 0.996050i | \(-0.471699\pi\) | ||||
0.0887946 | + | 0.996050i | \(0.471699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1242.16 | −0.435896 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3147.91 | −1.07249 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1115.51 | 0.374556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1728.82 | −0.572177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2033.67 | 0.663523 | 0.331762 | − | 0.943363i | \(-0.392357\pi\) | ||||
0.331762 | + | 0.943363i | \(0.392357\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −884.563 | −0.284551 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1098.47 | −0.348442 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1782.19 | 0.549904 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3470 | 0.00375813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2858.45 | 0.858367 | 0.429184 | − | 0.903217i | \(-0.358801\pi\) | ||||
0.429184 | + | 0.903217i | \(0.358801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2995.07 | 0.887428 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2994.18 | −0.875467 | −0.437733 | − | 0.899105i | \(-0.644219\pi\) | ||||
−0.437733 | + | 0.899105i | \(0.644219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4174.68 | −1.20467 | −0.602337 | − | 0.798242i | \(-0.705764\pi\) | ||||
−0.602337 | + | 0.798242i | \(0.705764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2466.76 | −0.693576 | −0.346788 | − | 0.937944i | \(-0.612728\pi\) | ||||
−0.346788 | + | 0.937944i | \(0.612728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5766.42 | 1.60068 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2494.16 | 0.683599 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −447.762 | −0.121185 | −0.0605927 | − | 0.998163i | \(-0.519299\pi\) | ||||
−0.0605927 | + | 0.998163i | \(0.519299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5404.61 | 1.44457 | 0.722286 | − | 0.691595i | \(-0.243092\pi\) | ||||
0.722286 | + | 0.691595i | \(0.243092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1343.64 | −0.346128 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 978.654 | 0.249075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6654.56 | −1.67343 | −0.836717 | − | 0.547635i | \(-0.815528\pi\) | ||||
−0.836717 | + | 0.547635i | \(0.815528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1326.65 | −0.329668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −95.2693 | −0.0233961 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5185.32 | −1.25857 | −0.629283 | − | 0.777177i | \(-0.716651\pi\) | ||||
−0.629283 | + | 0.777177i | \(0.716651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2005.35 | −0.475587 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1234.78 | 0.289504 | 0.144752 | − | 0.989468i | \(-0.453762\pi\) | ||||
0.144752 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9253.74 | −2.14510 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3783.29 | 0.867168 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2165.24 | 0.490771 | 0.245385 | − | 0.969426i | \(-0.421086\pi\) | ||||
0.245385 | + | 0.969426i | \(0.421086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1767.98 | −0.396300 | −0.198150 | − | 0.980172i | \(-0.563493\pi\) | ||||
−0.198150 | + | 0.980172i | \(0.563493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3561.98 | −0.781075 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5539.01 | −1.20147 | −0.600735 | − | 0.799449i | \(-0.705125\pi\) | ||||
−0.600735 | + | 0.799449i | \(0.705125\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1834.65 | 0.393684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4869.88 | 1.03385 | 0.516926 | − | 0.856030i | \(-0.327076\pi\) | ||||
0.516926 | + | 0.856030i | \(0.327076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8375.10 | 1.75918 | 0.879590 | − | 0.475732i | \(-0.157817\pi\) | ||||
0.879590 | + | 0.475732i | \(0.157817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10367.5 | 2.15480 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4910.80 | −0.999552 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3179.94 | 0.640588 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9398.40 | 1.87393 | 0.936963 | − | 0.349428i | \(-0.113624\pi\) | ||||
0.936963 | + | 0.349428i | \(0.113624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 657.585 | 0.129783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −288.996 | −0.0564620 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1031.07 | −0.199426 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −542.844 | −0.102923 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12677.5 | 2.38003 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −102.680 | −0.0190888 | −0.00954438 | − | 0.999954i | \(-0.503038\pi\) | ||||
−0.00954438 | + | 0.999954i | \(0.503038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 201.138 | 0.0370303 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5365.79 | −0.978347 | −0.489173 | − | 0.872187i | \(-0.662701\pi\) | ||||
−0.489173 | + | 0.872187i | \(0.662701\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4165.06 | −0.752150 | −0.376075 | − | 0.926589i | \(-0.622727\pi\) | ||||
−0.376075 | + | 0.926589i | \(0.622727\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2339.76 | 0.414556 | 0.207278 | − | 0.978282i | \(-0.433540\pi\) | ||||
0.207278 | + | 0.978282i | \(0.433540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2384.93 | 0.418591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3180.31 | 0.552983 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −239.731 | −0.0412971 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2768.37 | −0.472497 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2331.67 | −0.394316 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3721.80 | 0.618033 | 0.309016 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309016 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3071.02 | −0.505378 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8859.03 | −1.44484 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 632.972 | 0.102315 | 0.0511575 | − | 0.998691i | \(-0.483709\pi\) | ||||
0.0511575 | + | 0.998691i | \(0.483709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3065.78 | −0.491180 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2181.92 | −0.346504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7955.76 | 1.24152 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2699.12 | 0.417569 | 0.208784 | − | 0.977962i | \(-0.433049\pi\) | ||||
0.208784 | + | 0.977962i | \(0.433049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9047.70 | 1.38771 | 0.693857 | − | 0.720113i | \(-0.255910\pi\) | ||||
0.693857 | + | 0.720113i | \(0.255910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −224.607 | −0.0341556 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9024.27 | 1.36066 | 0.680331 | − | 0.732905i | \(-0.261836\pi\) | ||||
0.680331 | + | 0.732905i | \(0.261836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6308.68 | −0.943183 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5082.12 | −0.747142 | −0.373571 | − | 0.927602i | \(-0.621867\pi\) | ||||
−0.373571 | + | 0.927602i | \(0.621867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19229.3 | 2.80351 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3649.30 | −0.527655 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12710.5 | 1.82274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7142.75 | −1.01594 | −0.507968 | − | 0.861376i | \(-0.669603\pi\) | ||||
−0.507968 | + | 0.861376i | \(0.669603\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1324.14 | −0.186807 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3819.86 | 0.530255 | 0.265127 | − | 0.964213i | \(-0.414586\pi\) | ||||
0.265127 | + | 0.964213i | \(0.414586\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13337.3 | 1.83663 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1853.57 | 0.253219 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5857.71 | 0.793906 | 0.396953 | − | 0.917839i | \(-0.370068\pi\) | ||||
0.396953 | + | 0.917839i | \(0.370068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3528.63 | −0.474480 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7404.66 | −0.987886 | −0.493943 | − | 0.869494i | \(-0.664445\pi\) | ||||
−0.493943 | + | 0.869494i | \(0.664445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −462.061 | −0.0606922 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7002.31 | −0.912677 | −0.456339 | − | 0.889806i | \(-0.650839\pi\) | ||||
−0.456339 | + | 0.889806i | \(0.650839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −183.963 | −0.0237939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5702.86 | −0.731988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17788.3 | 2.26589 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7423.72 | 0.938503 | 0.469252 | − | 0.883065i | \(-0.344524\pi\) | ||||
0.469252 | + | 0.883065i | \(0.344524\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2484.62 | −0.309417 | −0.154708 | − | 0.987960i | \(-0.549444\pi\) | ||||
−0.154708 | + | 0.987960i | \(0.549444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1695.79 | −0.209611 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1733.07 | 0.212634 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3652.31 | 0.444811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3509.66 | −0.424307 | −0.212153 | − | 0.977236i | \(-0.568048\pi\) | ||||
−0.212153 | + | 0.977236i | \(0.568048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1858.91 | −0.223098 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6979.73 | 0.825594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3744.32 | −0.439712 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6969.64 | 0.812624 | 0.406312 | − | 0.913734i | \(-0.366815\pi\) | ||||
0.406312 | + | 0.913734i | \(0.366815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12700.3 | −1.47024 | −0.735122 | − | 0.677935i | \(-0.762875\pi\) | ||||
−0.735122 | + | 0.677935i | \(0.762875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2425.59 | 0.278809 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −493.930 | −0.0563744 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 267.121 | 0.0300623 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −894.527 | −0.0999718 | −0.0499859 | − | 0.998750i | \(-0.515918\pi\) | ||||
−0.0499859 | + | 0.998750i | \(0.515918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15813.7 | −1.75510 | −0.877552 | − | 0.479482i | \(-0.840824\pi\) | ||||
−0.877552 | + | 0.479482i | \(0.840824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14302.1 | −1.57640 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20019.5 | 2.19144 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14221.9 | 1.54618 | 0.773090 | − | 0.634297i | \(-0.218710\pi\) | ||||
0.773090 | + | 0.634297i | \(0.218710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9422.08 | −1.01051 | −0.505256 | − | 0.862970i | \(-0.668602\pi\) | ||||
−0.505256 | + | 0.862970i | \(0.668602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26982.3 | 2.87435 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1564.44 | 0.165538 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3223.63 | −0.338825 | −0.169412 | − | 0.985545i | \(-0.554187\pi\) | ||||
−0.169412 | + | 0.985545i | \(0.554187\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1574.78 | 0.164420 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3783.99 | −0.392467 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6219.19 | 0.636589 | 0.318295 | − | 0.947992i | \(-0.396890\pi\) | ||||
0.318295 | + | 0.947992i | \(0.396890\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −40.0742 | −0.00407517 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10858.6 | −1.09704 | −0.548521 | − | 0.836137i | \(-0.684809\pi\) | ||||
−0.548521 | + | 0.836137i | \(0.684809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19067.3 | −1.91389 | −0.956946 | − | 0.290266i | \(-0.906256\pi\) | ||||
−0.956946 | + | 0.290266i | \(0.906256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13084.7 | 1.30492 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3919.79 | 0.388407 | 0.194204 | − | 0.980961i | \(-0.437788\pi\) | ||||
0.194204 | + | 0.980961i | \(0.437788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1752.41 | 0.171437 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 549.521 | 0.0534186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 53751.1 | 5.19214 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3892.50 | −0.373638 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8477.26 | −0.808634 | −0.404317 | − | 0.914619i | \(-0.632491\pi\) | ||||
−0.404317 | + | 0.914619i | \(0.632491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2838.57 | 0.269080 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22679.2 | 2.12332 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15250.3 | −1.41901 | −0.709505 | − | 0.704701i | \(-0.751081\pi\) | ||||
−0.709505 | + | 0.704701i | \(0.751081\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −492.399 | −0.0455359 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6524.81 | −0.599716 | −0.299858 | − | 0.953984i | \(-0.596939\pi\) | ||||
−0.299858 | + | 0.953984i | \(0.596939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 330.711 | 0.0302120 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2061.11 | −0.187151 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7470.88 | 0.670226 | 0.335113 | − | 0.942178i | \(-0.391226\pi\) | ||||
0.335113 | + | 0.942178i | \(0.391226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9877.24 | 0.880804 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 928.803 | 0.0823325 | 0.0411663 | − | 0.999152i | \(-0.486893\pi\) | ||||
0.0411663 | + | 0.999152i | \(0.486893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3871.55 | −0.341152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6383.39 | −0.559165 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8947.97 | −0.779198 | −0.389599 | − | 0.920985i | \(-0.627386\pi\) | ||||
−0.389599 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4361.00 | 0.375328 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1434.51 | 0.122742 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2884.72 | −0.245396 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7806.28 | −0.660227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13141.0 | −1.10502 | −0.552510 | − | 0.833506i | \(-0.686330\pi\) | ||||
−0.552510 | + | 0.833506i | \(0.686330\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 821.254 | 0.0686633 | 0.0343317 | − | 0.999410i | \(-0.489070\pi\) | ||||
0.0343317 | + | 0.999410i | \(0.489070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −302.561 | −0.0250090 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3195.40 | 0.262629 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 276.607 | 0.0226059 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1223.91 | 0.0994626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22681.9 | 1.83294 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 906.092 | 0.0728133 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9933.49 | −0.789416 | −0.394708 | − | 0.918807i | \(-0.629154\pi\) | ||||
−0.394708 | + | 0.918807i | \(0.629154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1827.06 | −0.144395 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16629.4 | −1.30702 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22556.2 | 1.76313 | 0.881565 | − | 0.472063i | \(-0.156490\pi\) | ||||
0.881565 | + | 0.472063i | \(0.156490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5332.65 | 0.414558 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35989.1 | −2.78256 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21902.4 | −1.67515 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13146.5 | −1.00006 | −0.500032 | − | 0.866007i | \(-0.666678\pi\) | ||||
−0.500032 | + | 0.866007i | \(0.666678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 427.087 | 0.0323146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.6595 | 0.00358678 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24704.9 | −1.84935 | −0.924676 | − | 0.380754i | \(-0.875665\pi\) | ||||
−0.924676 | + | 0.380754i | \(0.875665\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21865.0 | −1.62809 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4375.65 | 0.322385 | 0.161192 | − | 0.986923i | \(-0.448466\pi\) | ||||
0.161192 | + | 0.986923i | \(0.448466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11284.7 | 0.827059 | 0.413529 | − | 0.910491i | \(-0.364296\pi\) | ||||
0.413529 | + | 0.910491i | \(0.364296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14404.8 | 1.05021 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41247.2 | 2.99152 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6831.44 | 0.492888 | 0.246444 | − | 0.969157i | \(-0.420738\pi\) | ||||
0.246444 | + | 0.969157i | \(0.420738\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5736.85 | 0.411771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4629.28 | 0.328860 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1601.89 | −0.113214 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1116.70 | 0.0785196 | 0.0392598 | − | 0.999229i | \(-0.487500\pi\) | ||||
0.0392598 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32925.7 | 2.30336 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12257.8 | 0.853159 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9724.17 | 0.673396 | 0.336698 | − | 0.941613i | \(-0.390690\pi\) | ||||
0.336698 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1495.61 | 0.102531 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 798.427 | 0.0544622 | 0.0272311 | − | 0.999629i | \(-0.491331\pi\) | ||||
0.0272311 | + | 0.999629i | \(0.491331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.5785 | −0.00173606 | −0.000868028 | − | 1.00000i | \(-0.500276\pi\) | ||||
−0.000868028 | 1.00000i | \(0.500276\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3726.47 | −0.251664 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26026.7 | −1.74899 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13746.8 | 0.919220 | 0.459610 | − | 0.888121i | \(-0.347989\pi\) | ||||
0.459610 | + | 0.888121i | \(0.347989\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2242.00 | −0.148448 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14443.4 | 0.951651 | 0.475825 | − | 0.879540i | \(-0.342149\pi\) | ||||
0.475825 | + | 0.879540i | \(0.342149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9443.73 | −0.619200 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27585.4 | 1.79991 | 0.899956 | − | 0.435980i | \(-0.143598\pi\) | ||||
0.899956 | + | 0.435980i | \(0.143598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17551.0 | −1.13963 | −0.569816 | − | 0.821772i | \(-0.692986\pi\) | ||||
−0.569816 | + | 0.821772i | \(0.692986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3346.52 | 0.216250 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 53523.0 | 3.42547 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5186.47 | −0.330347 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 506.455 | 0.0321044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19726.5 | 1.24453 | 0.622265 | − | 0.782806i | \(-0.286212\pi\) | ||||
0.622265 | + | 0.782806i | \(0.286212\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6101.00 | 0.383085 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25166.1 | −1.57273 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2653.69 | −0.164285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1808.43 | −0.111433 | −0.0557166 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557166 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6017.67 | −0.369073 | −0.184536 | − | 0.982826i | \(-0.559078\pi\) | ||||
−0.184536 | + | 0.982826i | \(0.559078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3295.41 | −0.201173 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21123.6 | 1.28355 | 0.641774 | − | 0.766894i | \(-0.278199\pi\) | ||||
0.641774 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −328.964 | −0.0198967 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24226.0 | −1.45182 | −0.725908 | − | 0.687792i | \(-0.758580\pi\) | ||||
−0.725908 | + | 0.687792i | \(0.758580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40672.7 | −2.42628 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5346.56 | 0.317487 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11836.0 | −0.699643 | −0.349822 | − | 0.936816i | \(-0.613758\pi\) | ||||
−0.349822 | + | 0.936816i | \(0.613758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18763.4 | −1.10410 | −0.552051 | − | 0.833810i | \(-0.686155\pi\) | ||||
−0.552051 | + | 0.833810i | \(0.686155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.0409 | 0.00216976 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27617.1 | −1.60321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8575.35 | 0.495579 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6342.03 | −0.364875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2130.24 | −0.122013 | −0.0610065 | − | 0.998137i | \(-0.519431\pi\) | ||||
−0.0610065 | + | 0.998137i | \(0.519431\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8985.21 | 0.512357 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5386.83 | −0.305809 | −0.152904 | − | 0.988241i | \(-0.548863\pi\) | ||||
−0.152904 | + | 0.988241i | \(0.548863\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8982.55 | −0.505451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3421.99 | 0.191711 | 0.0958556 | − | 0.995395i | \(-0.469441\pi\) | ||||
0.0958556 | + | 0.995395i | \(0.469441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13257.7 | −0.739491 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12524.0 | −0.695519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3597.87 | 0.198938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3373.63 | −0.185730 | −0.0928648 | − | 0.995679i | \(-0.529602\pi\) | ||||
−0.0928648 | + | 0.995679i | \(0.529602\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26704.4 | −1.45749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 218.370 | 0.0118671 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7400.29 | −0.400436 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28103.0 | −1.51417 | −0.757087 | − | 0.653314i | \(-0.773378\pi\) | ||||
−0.757087 | + | 0.653314i | \(0.773378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55114.1 | −2.95685 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17299.3 | 0.924154 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30036.9 | −1.59106 | −0.795528 | − | 0.605917i | \(-0.792806\pi\) | ||||
−0.795528 | + | 0.605917i | \(0.792806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7482.47 | 0.394676 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25266.3 | 1.32711 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1905.10 | 0.0996458 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1343.29 | −0.0699665 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14102.6 | −0.731486 | −0.365743 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365743 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16213.8 | 0.834024 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −74150.3 | −3.79845 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3339.23 | −0.170351 | −0.0851756 | − | 0.996366i | \(-0.527145\pi\) | ||||
−0.0851756 | + | 0.996366i | \(0.527145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 76.2005 | 0.00385551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25436.3 | 1.28174 | 0.640868 | − | 0.767651i | \(-0.278575\pi\) | ||||
0.640868 | + | 0.767651i | \(0.278575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4431.83 | 0.221504 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21842.5 | 1.08727 | 0.543633 | − | 0.839323i | \(-0.317048\pi\) | ||||
0.543633 | + | 0.839323i | \(0.317048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4030.91 | −0.199837 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1480.51 | −0.0731019 | −0.0365510 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365510 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11157.5 | 0.548698 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2935.96 | 0.143803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7767.42 | −0.377413 | −0.188706 | − | 0.982034i | \(-0.560429\pi\) | ||||
−0.188706 | + | 0.982034i | \(0.560429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19963.7 | −0.966158 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26987.3 | −1.30089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17950.6 | 0.861856 | 0.430928 | − | 0.902386i | \(-0.358186\pi\) | ||||
0.430928 | + | 0.902386i | \(0.358186\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3979.96 | −0.190334 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19870.2 | 0.946509 | 0.473255 | − | 0.880926i | \(-0.343079\pi\) | ||||
0.473255 | + | 0.880926i | \(0.343079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −285.808 | −0.0135077 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −255.670 | −0.0120361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13321.1 | 0.624668 | 0.312334 | − | 0.949972i | \(-0.398889\pi\) | ||||
0.312334 | + | 0.949972i | \(0.398889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15556.0 | −0.726633 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3413.53 | 0.158831 | 0.0794153 | − | 0.996842i | \(-0.474695\pi\) | ||||
0.0794153 | + | 0.996842i | \(0.474695\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67838.5 | 3.14430 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23763.7 | −1.09297 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3155.99 | 0.144597 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6016.06 | −0.274580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12498.1 | 0.568252 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4392.25 | 0.198941 | 0.0994706 | − | 0.995040i | \(-0.468285\pi\) | ||||
0.0994706 | + | 0.995040i | \(0.468285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3704.33 | 0.167145 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4929.02 | −0.220725 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27761.2 | −1.23848 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10628.2 | −0.472357 | −0.236179 | − | 0.971710i | \(-0.575895\pi\) | ||||
−0.236179 | + | 0.971710i | \(0.575895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −400.015 | −0.0177115 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11349.9 | 0.500659 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6358.57 | −0.279439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6495.73 | 0.283347 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31455.7 | 1.36702 | 0.683512 | − | 0.729939i | \(-0.260452\pi\) | ||||
0.683512 | + | 0.729939i | \(0.260452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15106.2 | 0.654070 | 0.327035 | − | 0.945012i | \(-0.393951\pi\) | ||||
0.327035 | + | 0.945012i | \(0.393951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5303.95 | −0.228804 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3511.77 | −0.150935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8292.39 | −0.355097 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44912.6 | −1.90921 | −0.954605 | − | 0.297875i | \(-0.903722\pi\) | ||||
−0.954605 | + | 0.297875i | \(0.903722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17546.9 | −0.743191 | −0.371595 | − | 0.928395i | \(-0.621189\pi\) | ||||
−0.371595 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10686.0 | −0.450954 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6540.96 | −0.275032 | −0.137516 | − | 0.990500i | \(-0.543912\pi\) | ||||
−0.137516 | + | 0.990500i | \(0.543912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7490.22 | −0.313807 | −0.156903 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156903 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16617.0 | −0.693668 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 70444.2 | 2.91955 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5503.96 | 0.227294 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35766.1 | 1.47173 | 0.735867 | − | 0.677127i | \(-0.236775\pi\) | ||||
0.735867 | + | 0.677127i | \(0.236775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25258.4 | 1.03565 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14609.6 | 0.596895 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45526.2 | −1.85343 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25125.3 | 1.01566 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42293.1 | −1.70363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25697.7 | −1.03150 | −0.515751 | − | 0.856738i | \(-0.672487\pi\) | ||||
−0.515751 | + | 0.856738i | \(0.672487\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31102.6 | 1.24408 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4707.36 | 0.187632 | 0.0938159 | − | 0.995590i | \(-0.470094\pi\) | ||||
0.0938159 | + | 0.995590i | \(0.470094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15093.5 | 0.599514 | 0.299757 | − | 0.954016i | \(-0.403094\pi\) | ||||
0.299757 | + | 0.954016i | \(0.403094\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42516.6 | 1.67704 | 0.838519 | − | 0.544873i | \(-0.183422\pi\) | ||||
0.838519 | + | 0.544873i | \(0.183422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55674.2 | −2.18842 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14732.4 | −0.577091 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8898.77 | −0.347376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3444.41 | 0.133995 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9539.81 | 0.369844 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4181.79 | −0.161014 | −0.0805069 | − | 0.996754i | \(-0.525654\pi\) | ||||
−0.0805069 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28195.2 | 1.08191 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3070.34 | 0.117415 | 0.0587073 | − | 0.998275i | \(-0.481302\pi\) | ||||
0.0587073 | + | 0.998275i | \(0.481302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −146.842 | −0.00559640 | −0.00279820 | − | 0.999996i | \(-0.500891\pi\) | ||||
−0.00279820 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1972.75 | 0.0749304 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10739.3 | 0.406527 | 0.203263 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203263 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −866.987 | −0.0325984 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43531.0 | 1.63125 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6462.23 | 0.241350 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3093.22 | −0.115139 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45421.4 | −1.68508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 641.929 | 0.0237356 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13030.6 | −0.478619 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30615.1 | 1.12079 | 0.560396 | − | 0.828225i | \(-0.310649\pi\) | ||||
0.560396 | + | 0.828225i | \(0.310649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1628.53 | −0.0594225 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45026.6 | −1.63754 | −0.818770 | − | 0.574121i | \(-0.805344\pi\) | ||||
−0.818770 | + | 0.574121i | \(0.805344\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3491.69 | −0.126569 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 38032.4 | 1.37411 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22816.1 | 0.818970 | 0.409485 | − | 0.912317i | \(-0.365708\pi\) | ||||
0.409485 | + | 0.912317i | \(0.365708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −308.040 | −0.0110209 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2452.83 | 0.0874711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −113554. | −4.03638 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 603.415 | 0.0213795 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10944.1 | −0.386507 | −0.193254 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193254 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16097.4 | −0.564849 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 339.906 | 0.0118889 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10110.2 | −0.352494 | −0.176247 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176247 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12495.2 | −0.434254 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24417.0 | −0.845879 | −0.422939 | − | 0.906158i | \(-0.639002\pi\) | ||||
−0.422939 | + | 0.906158i | \(0.639002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18235.6 | −0.629728 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3131.71 | −0.107462 | −0.0537311 | − | 0.998555i | \(-0.517111\pi\) | ||||
−0.0537311 | + | 0.998555i | \(0.517111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4941.87 | −0.169041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7019.29 | 0.239344 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6544.00 | −0.222436 | −0.111218 | − | 0.993796i | \(-0.535475\pi\) | ||||
−0.111218 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 102735. | 3.48107 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7154.79 | 0.241674 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11764.0 | 0.394886 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9540.92 | 0.319265 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40915.0 | 1.36487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45805.7 | −1.52328 | −0.761640 | − | 0.648000i | \(-0.775605\pi\) | ||||
−0.761640 | + | 0.648000i | \(0.775605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −719.192 | −0.0238429 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34822.0 | 1.15087 | 0.575434 | − | 0.817848i | \(-0.304833\pi\) | ||||
0.575434 | + | 0.817848i | \(0.304833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8305.10 | −0.272796 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5213.81 | −0.170731 | −0.0853657 | − | 0.996350i | \(-0.527206\pi\) | ||||
−0.0853657 | + | 0.996350i | \(0.527206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13498.2 | −0.440658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6995.00 | −0.227659 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21152.9 | −0.686341 | −0.343171 | − | 0.939273i | \(-0.611501\pi\) | ||||
−0.343171 | + | 0.939273i | \(0.611501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 87422.0 | 2.82792 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6363.36 | −0.204594 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42635.1 | −1.36665 | −0.683324 | − | 0.730116i | \(-0.739466\pi\) | ||||
−0.683324 | + | 0.730116i | \(0.739466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11165.4 | 0.356821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10666.6 | 0.339854 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14197.8 | 0.451003 | 0.225502 | − | 0.974243i | \(-0.427598\pi\) | ||||
0.225502 | + | 0.974243i | \(0.427598\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9213.05 | −0.291780 |
(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.cj.1.3 | 3 | ||
4.3 | odd | 2 | 1176.4.a.x.1.3 | 3 | |||
7.3 | odd | 6 | 336.4.q.l.289.3 | 6 | |||
7.5 | odd | 6 | 336.4.q.l.193.3 | 6 | |||
7.6 | odd | 2 | 2352.4.a.ch.1.1 | 3 | |||
28.3 | even | 6 | 168.4.q.e.121.3 | yes | 6 | ||
28.19 | even | 6 | 168.4.q.e.25.3 | ✓ | 6 | ||
28.27 | even | 2 | 1176.4.a.y.1.1 | 3 | |||
84.47 | odd | 6 | 504.4.s.g.361.1 | 6 | |||
84.59 | odd | 6 | 504.4.s.g.289.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.e.25.3 | ✓ | 6 | 28.19 | even | 6 | ||
168.4.q.e.121.3 | yes | 6 | 28.3 | even | 6 | ||
336.4.q.l.193.3 | 6 | 7.5 | odd | 6 | |||
336.4.q.l.289.3 | 6 | 7.3 | odd | 6 | |||
504.4.s.g.289.1 | 6 | 84.59 | odd | 6 | |||
504.4.s.g.361.1 | 6 | 84.47 | odd | 6 | |||
1176.4.a.x.1.3 | 3 | 4.3 | odd | 2 | |||
1176.4.a.y.1.1 | 3 | 28.27 | even | 2 | |||
2352.4.a.ch.1.1 | 3 | 7.6 | odd | 2 | |||
2352.4.a.cj.1.3 | 3 | 1.1 | even | 1 | trivial |