Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.5 | ||
Root | \(0.500000 + 1.56488i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.j.703.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.956810 | 0.191362 | 0.0956810 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956810 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.34610i | − 0.906586i | −0.891361 | − | 0.453293i | \(-0.850249\pi\) | ||||
0.891361 | − | 0.453293i | \(-0.149751\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 14.4991i | − 1.31810i | −0.752100 | − | 0.659049i | \(-0.770959\pi\) | ||||
0.752100 | − | 0.659049i | \(-0.229041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76367 | −0.135667 | −0.0678334 | − | 0.997697i | \(-0.521609\pi\) | ||||
−0.0678334 | + | 0.997697i | \(0.521609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.34309 | −0.0790056 | −0.0395028 | − | 0.999219i | \(-0.512577\pi\) | ||||
−0.0395028 | + | 0.999219i | \(0.512577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 13.0234i | − 0.685442i | −0.939437 | − | 0.342721i | \(-0.888651\pi\) | ||||
0.939437 | − | 0.342721i | \(-0.111349\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.19916i | 0.182572i | 0.995825 | + | 0.0912861i | \(0.0290978\pi\) | ||||
−0.995825 | + | 0.0912861i | \(0.970902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.0845 | −0.963381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.1690 | −1.31617 | −0.658087 | − | 0.752942i | \(-0.728634\pi\) | ||||
−0.658087 | + | 0.752942i | \(0.728634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.172759i | 0.00557288i | 0.999996 | + | 0.00278644i | \(0.000886953\pi\) | ||||
−0.999996 | + | 0.00278644i | \(0.999113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.07202i | − 0.173486i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.1937 | −0.410641 | −0.205320 | − | 0.978695i | \(-0.565824\pi\) | ||||
−0.205320 | + | 0.978695i | \(0.565824\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.3965 | 1.69260 | 0.846298 | − | 0.532709i | \(-0.178826\pi\) | ||||
0.846298 | + | 0.532709i | \(0.178826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.52734i | 0.128543i | 0.997932 | + | 0.0642713i | \(0.0204723\pi\) | ||||
−0.997932 | + | 0.0642713i | \(0.979528\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.7137i | 1.41944i | 0.704484 | + | 0.709720i | \(0.251179\pi\) | ||||
−0.704484 | + | 0.709720i | \(0.748821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.72695 | 0.178101 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31.6556 | −0.597275 | −0.298638 | − | 0.954367i | \(-0.596532\pi\) | ||||
−0.298638 | + | 0.954367i | \(0.596532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 13.8729i | − 0.252234i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.2410i | − 0.207475i | −0.994605 | − | 0.103738i | \(-0.966920\pi\) | ||||
0.994605 | − | 0.103738i | \(-0.0330802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −92.1017 | −1.50986 | −0.754932 | − | 0.655803i | \(-0.772330\pi\) | ||||
−0.754932 | + | 0.655803i | \(0.772330\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.68750 | −0.0259615 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.4583i | 0.394900i | 0.980313 | + | 0.197450i | \(0.0632661\pi\) | ||||
−0.980313 | + | 0.197450i | \(0.936734\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 85.4493i | 1.20351i | 0.798680 | + | 0.601755i | \(0.205532\pi\) | ||||
−0.798680 | + | 0.601755i | \(0.794468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −103.920 | −1.42356 | −0.711781 | − | 0.702401i | \(-0.752111\pi\) | ||||
−0.711781 | + | 0.702401i | \(0.752111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −92.0126 | −1.19497 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.3424i | 0.865093i | 0.901612 | + | 0.432547i | \(0.142385\pi\) | ||||
−0.901612 | + | 0.432547i | \(0.857615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 137.277i | − 1.65393i | −0.562251 | − | 0.826967i | \(-0.690064\pi\) | ||||
0.562251 | − | 0.826967i | \(-0.309936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.28509 | −0.0151187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 67.3405 | 0.756635 | 0.378317 | − | 0.925676i | \(-0.376503\pi\) | ||||
0.378317 | + | 0.925676i | \(0.376503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1924i | 0.122994i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 12.4609i | − 0.131168i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −95.6956 | −0.986553 | −0.493276 | − | 0.869873i | \(-0.664201\pi\) | ||||
−0.493276 | + | 0.869873i | \(0.664201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 73.9722 | 0.732398 | 0.366199 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366199 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59.6083i | 0.578721i | 0.957220 | + | 0.289361i | \(0.0934427\pi\) | ||||
−0.957220 | + | 0.289361i | \(0.906557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 137.299i | − 1.28317i | −0.767053 | − | 0.641583i | \(-0.778278\pi\) | ||||
0.767053 | − | 0.641583i | \(-0.221722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −122.932 | −1.12782 | −0.563909 | − | 0.825837i | \(-0.690703\pi\) | ||||
−0.563909 | + | 0.825837i | \(0.690703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122.117 | 1.08068 | 0.540340 | − | 0.841447i | \(-0.318296\pi\) | ||||
0.540340 | + | 0.841447i | \(0.318296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.01780i | 0.0349374i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.52342i | 0.0716254i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −89.2230 | −0.737380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −46.9646 | −0.375716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 91.4995i | − 0.720469i | −0.932862 | − | 0.360234i | \(-0.882697\pi\) | ||||
0.932862 | − | 0.360234i | \(-0.117303\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 117.372i | 0.895972i | 0.894040 | + | 0.447986i | \(0.147859\pi\) | ||||
−0.894040 | + | 0.447986i | \(0.852141\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −82.6478 | −0.621412 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −56.4879 | −0.412320 | −0.206160 | − | 0.978518i | \(-0.566097\pi\) | ||||
−0.206160 | + | 0.978518i | \(0.566097\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 105.929i | 0.762080i | 0.924559 | + | 0.381040i | \(0.124434\pi\) | ||||
−0.924559 | + | 0.381040i | \(0.875566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.5715i | 0.178822i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.5205 | −0.251866 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −290.160 | −1.94739 | −0.973693 | − | 0.227865i | \(-0.926826\pi\) | ||||
−0.973693 | + | 0.227865i | \(0.926826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 188.866i | − 1.25077i | −0.780316 | − | 0.625385i | \(-0.784942\pi\) | ||||
0.780316 | − | 0.625385i | \(-0.215058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.165298i | 0.00106644i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −213.852 | −1.36211 | −0.681057 | − | 0.732231i | \(-0.738479\pi\) | ||||
−0.681057 | + | 0.732231i | \(0.738479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.6483 | 0.165518 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 304.944i | − 1.87082i | −0.353566 | − | 0.935410i | \(-0.615031\pi\) | ||||
0.353566 | − | 0.935410i | \(-0.384969\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 166.488i | − 0.996935i | −0.866908 | − | 0.498467i | \(-0.833896\pi\) | ||||
0.866908 | − | 0.498467i | \(-0.166104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −165.889 | −0.981595 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 313.389 | 1.81150 | 0.905749 | − | 0.423815i | \(-0.139310\pi\) | ||||
0.905749 | + | 0.423815i | \(0.139310\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 152.843i | 0.873388i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 144.278i | 0.806021i | 0.915195 | + | 0.403011i | \(0.132036\pi\) | ||||
−0.915195 | + | 0.403011i | \(0.867964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −120.016 | −0.663074 | −0.331537 | − | 0.943442i | \(-0.607567\pi\) | ||||
−0.331537 | + | 0.943442i | \(0.607567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.5375 | −0.0785810 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.4736i | 0.104137i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 257.420i | 1.34775i | 0.738846 | + | 0.673874i | \(0.235371\pi\) | ||||
−0.738846 | + | 0.673874i | \(0.764629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −289.234 | −1.49862 | −0.749310 | − | 0.662220i | \(-0.769615\pi\) | ||||
−0.749310 | + | 0.662220i | \(0.769615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 196.282 | 0.996357 | 0.498179 | − | 0.867074i | \(-0.334002\pi\) | ||||
0.498179 | + | 0.867074i | \(0.334002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 192.265i | − 0.966155i | −0.875578 | − | 0.483078i | \(-0.839519\pi\) | ||||
0.875578 | − | 0.483078i | \(-0.160481\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 242.225i | 1.19322i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 66.3992 | 0.323899 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −188.827 | −0.903479 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 20.0620i | − 0.0950804i | −0.998869 | − | 0.0475402i | \(-0.984862\pi\) | ||||
0.998869 | − | 0.0475402i | \(-0.0151382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.28861i | 0.0245982i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.09635 | 0.00505230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.36877 | 0.0107184 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 319.896i | 1.43451i | 0.696810 | + | 0.717256i | \(0.254602\pi\) | ||||
−0.696810 | + | 0.717256i | \(0.745398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 202.001i | − 0.889872i | −0.895562 | − | 0.444936i | \(-0.853226\pi\) | ||||
0.895562 | − | 0.444936i | \(-0.146774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −196.154 | −0.856568 | −0.428284 | − | 0.903644i | \(-0.640882\pi\) | ||||
−0.428284 | + | 0.903644i | \(0.640882\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −395.370 | −1.69687 | −0.848434 | − | 0.529301i | \(-0.822454\pi\) | ||||
−0.848434 | + | 0.529301i | \(0.822454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 63.8324i | 0.271627i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 449.180i | − 1.87941i | −0.341980 | − | 0.939707i | \(-0.611098\pi\) | ||||
0.341980 | − | 0.939707i | \(-0.388902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 187.767 | 0.779117 | 0.389558 | − | 0.921002i | \(-0.372628\pi\) | ||||
0.389558 | + | 0.921002i | \(0.372628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.35004 | 0.0340818 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.9689i | 0.0929917i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 57.1800i | 0.227809i | 0.993492 | + | 0.113904i | \(0.0363358\pi\) | ||||
−0.993492 | + | 0.113904i | \(0.963664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.8839 | 0.240648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 112.952 | 0.439501 | 0.219750 | − | 0.975556i | \(-0.429476\pi\) | ||||
0.219750 | + | 0.975556i | \(0.429476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96.4208i | 0.372281i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 48.0573i | − 0.182727i | −0.995818 | − | 0.0913636i | \(-0.970877\pi\) | ||||
0.995818 | − | 0.0913636i | \(-0.0291226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.2884 | −0.114296 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 196.360 | 0.729964 | 0.364982 | − | 0.931015i | \(-0.381075\pi\) | ||||
0.364982 | + | 0.931015i | \(0.381075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 242.829i | − 0.896050i | −0.894021 | − | 0.448025i | \(-0.852128\pi\) | ||||
0.894021 | − | 0.448025i | \(-0.147872\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 349.203i | 1.26983i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −228.132 | −0.823580 | −0.411790 | − | 0.911279i | \(-0.635096\pi\) | ||||
−0.411790 | + | 0.911279i | \(0.635096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −313.999 | −1.11743 | −0.558716 | − | 0.829359i | \(-0.688706\pi\) | ||||
−0.558716 | + | 0.829359i | \(0.688706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 522.669i | 1.84689i | 0.383735 | + | 0.923443i | \(0.374638\pi\) | ||||
−0.383735 | + | 0.923443i | \(0.625362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 440.397i | − 1.53449i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −287.196 | −0.993758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 173.891 | 0.593483 | 0.296742 | − | 0.954958i | \(-0.404100\pi\) | ||||
0.296742 | + | 0.954958i | \(0.404100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 11.7124i | − 0.0397029i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 7.40593i | − 0.0247690i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.0771 | 0.116535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −88.1239 | −0.288931 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 465.568i | − 1.51651i | −0.651959 | − | 0.758254i | \(-0.726053\pi\) | ||||
0.651959 | − | 0.758254i | \(-0.273947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 238.054i | − 0.765448i | −0.923863 | − | 0.382724i | \(-0.874986\pi\) | ||||
0.923863 | − | 0.382724i | \(-0.125014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.4041 | 0.317585 | 0.158793 | − | 0.987312i | \(-0.449240\pi\) | ||||
0.158793 | + | 0.987312i | \(0.449240\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 87.2285 | 0.275169 | 0.137584 | − | 0.990490i | \(-0.456066\pi\) | ||||
0.137584 | + | 0.990490i | \(0.456066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 553.415i | 1.73484i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.4916i | 0.0541537i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.4771 | 0.130699 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 423.372 | 1.28685 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0394i | 0.0756476i | 0.999284 | + | 0.0378238i | \(0.0120426\pi\) | ||||
−0.999284 | + | 0.0378238i | \(0.987957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.3156i | 0.0755689i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.5515 | −0.105494 | −0.0527471 | − | 0.998608i | \(-0.516798\pi\) | ||||
−0.0527471 | + | 0.998608i | \(0.516798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.50485 | 0.00734560 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 366.341i | − 1.06805i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 277.688i | 0.800254i | 0.916460 | + | 0.400127i | \(0.131034\pi\) | ||||
−0.916460 | + | 0.400127i | \(0.868966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 382.657 | 1.09644 | 0.548219 | − | 0.836335i | \(-0.315306\pi\) | ||||
0.548219 | + | 0.836335i | \(0.315306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −444.310 | −1.25867 | −0.629335 | − | 0.777134i | \(-0.716673\pi\) | ||||
−0.629335 | + | 0.777134i | \(0.716673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 81.7587i | 0.230306i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.9605i | 0.0305306i | 0.999883 | + | 0.0152653i | \(0.00485929\pi\) | ||||
−0.999883 | + | 0.0152653i | \(0.995141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 191.391 | 0.530170 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −99.4318 | −0.272416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 166.081i | 0.452538i | 0.974065 | + | 0.226269i | \(0.0726528\pi\) | ||||
−0.974065 | + | 0.226269i | \(0.927347\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 200.890i | 0.541482i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 240.406 | 0.644519 | 0.322259 | − | 0.946651i | \(-0.395558\pi\) | ||||
0.322259 | + | 0.946651i | \(0.395558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 67.3175 | 0.178561 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 224.504i | − 0.592359i | −0.955132 | − | 0.296179i | \(-0.904287\pi\) | ||||
0.955132 | − | 0.296179i | \(-0.0957127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 126.068i | 0.329160i | 0.986364 | + | 0.164580i | \(0.0526268\pi\) | ||||
−0.986364 | + | 0.164580i | \(0.947373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −88.0386 | −0.228672 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 435.033 | 1.11834 | 0.559169 | − | 0.829054i | \(-0.311120\pi\) | ||||
0.559169 | + | 0.829054i | \(0.311120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 5.63987i | − 0.0144242i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 65.3907i | 0.165546i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0620 | 0.0857985 | 0.0428993 | − | 0.999079i | \(-0.486341\pi\) | ||||
0.0428993 | + | 0.999079i | \(0.486341\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −152.431 | −0.380126 | −0.190063 | − | 0.981772i | \(-0.560869\pi\) | ||||
−0.190063 | + | 0.981772i | \(0.560869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.304690i | 0 0.000756055i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 220.294i | 0.541264i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 714.512 | 1.74697 | 0.873486 | − | 0.486849i | \(-0.161854\pi\) | ||||
0.873486 | + | 0.486849i | \(0.161854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −77.6830 | −0.188094 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 131.348i | − 0.316500i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 131.654i | − 0.314211i | −0.987582 | − | 0.157106i | \(-0.949784\pi\) | ||||
0.987582 | − | 0.157106i | \(-0.0502163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 55.5081 | 0.131848 | 0.0659241 | − | 0.997825i | \(-0.479000\pi\) | ||||
0.0659241 | + | 0.997825i | \(0.479000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.3478 | 0.0761124 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 584.487i | 1.36882i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 743.495i | 1.72505i | 0.506018 | + | 0.862523i | \(0.331117\pi\) | ||||
−0.506018 | + | 0.862523i | \(0.668883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 526.775 | 1.21657 | 0.608285 | − | 0.793719i | \(-0.291858\pi\) | ||||
0.608285 | + | 0.793719i | \(0.291858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 54.6873 | 0.125143 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 684.577i | − 1.55940i | −0.626152 | − | 0.779701i | \(-0.715371\pi\) | ||||
0.626152 | − | 0.779701i | \(-0.284629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 59.9868i | − 0.135410i | −0.997705 | − | 0.0677052i | \(-0.978432\pi\) | ||||
0.997705 | − | 0.0677052i | \(-0.0215677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 64.4321 | 0.144791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 78.3940 | 0.174597 | 0.0872985 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872985 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1006.18i | − 2.23101i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7090i | 0.0235363i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −64.6748 | −0.141520 | −0.0707602 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707602 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −321.909 | −0.698285 | −0.349143 | − | 0.937070i | \(-0.613527\pi\) | ||||
−0.349143 | + | 0.937070i | \(0.613527\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 520.291i | 1.12374i | 0.827226 | + | 0.561869i | \(0.189917\pi\) | ||||
−0.827226 | + | 0.561869i | \(0.810083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 454.944i | − 0.974185i | −0.873350 | − | 0.487093i | \(-0.838057\pi\) | ||||
0.873350 | − | 0.487093i | \(-0.161943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 167.907 | 0.358011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 80.1412 | 0.169432 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 313.662i | 0.660341i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 341.743i | − 0.713451i | −0.934209 | − | 0.356726i | \(-0.883893\pi\) | ||||
0.934209 | − | 0.356726i | \(-0.116107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.7966 | 0.0557103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −91.5625 | −0.188789 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 683.859i | − 1.40423i | −0.712065 | − | 0.702113i | \(-0.752240\pi\) | ||||
0.712065 | − | 0.702113i | \(-0.247760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 419.194i | − 0.853756i | −0.904309 | − | 0.426878i | \(-0.859613\pi\) | ||||
0.904309 | − | 0.426878i | \(-0.140387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.2646 | 0.103985 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 542.270 | 1.09109 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 402.803i | − 0.807221i | −0.914931 | − | 0.403610i | \(-0.867755\pi\) | ||||
0.914931 | − | 0.403610i | \(-0.132245\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 321.360i | − 0.638887i | −0.947605 | − | 0.319444i | \(-0.896504\pi\) | ||||
0.947605 | − | 0.319444i | \(-0.103496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 70.7773 | 0.140153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −366.245 | −0.719539 | −0.359769 | − | 0.933041i | \(-0.617145\pi\) | ||||
−0.359769 | + | 0.933041i | \(0.617145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 659.488i | 1.29058i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 57.0338i | 0.110745i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 967.287 | 1.87096 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 660.982 | 1.26868 | 0.634340 | − | 0.773054i | \(-0.281272\pi\) | ||||
0.634340 | + | 0.773054i | \(0.281272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 197.073i | 0.376812i | 0.982091 | + | 0.188406i | \(0.0603321\pi\) | ||||
−0.982091 | + | 0.188406i | \(0.939668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 0.232032i | 0 0.000440289i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 511.367 | 0.966667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −122.392 | −0.229629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 131.369i | − 0.245549i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 126.533i | − 0.234755i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 777.149 | 1.43650 | 0.718252 | − | 0.695783i | \(-0.244942\pi\) | ||||
0.718252 | + | 0.695783i | \(0.244942\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −117.623 | −0.215821 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 400.931i | − 0.732963i | −0.930425 | − | 0.366482i | \(-0.880562\pi\) | ||||
0.930425 | − | 0.366482i | \(-0.119438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 497.090i | 0.902160i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 433.708 | 0.784282 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −553.074 | −0.992951 | −0.496476 | − | 0.868051i | \(-0.665373\pi\) | ||||
−0.496476 | + | 0.868051i | \(0.665373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 9.74839i | − 0.0174390i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 548.074i | − 0.973489i | −0.873545 | − | 0.486744i | \(-0.838184\pi\) | ||||
0.873545 | − | 0.486744i | \(-0.161816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 116.843 | 0.206801 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 627.765 | 1.10328 | 0.551639 | − | 0.834083i | \(-0.314003\pi\) | ||||
0.551639 | + | 0.834083i | \(0.314003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 652.428i | 1.14261i | 0.820739 | + | 0.571303i | \(0.193562\pi\) | ||||
−0.820739 | + | 0.571303i | \(0.806438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 101.135i | − 0.175887i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 300.791 | 0.521301 | 0.260651 | − | 0.965433i | \(-0.416063\pi\) | ||||
0.260651 | + | 0.965433i | \(0.416063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −871.171 | −1.49943 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 458.977i | 0.787267i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 513.527i | − 0.874833i | −0.899259 | − | 0.437417i | \(-0.855893\pi\) | ||||
0.899259 | − | 0.437417i | \(-0.144107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.24991 | 0.00381989 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −114.700 | −0.193423 | −0.0967116 | − | 0.995312i | \(-0.530832\pi\) | ||||
−0.0967116 | + | 0.995312i | \(0.530832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.15529i | 0.0137064i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 926.005i | 1.54592i | 0.634456 | + | 0.772959i | \(0.281224\pi\) | ||||
−0.634456 | + | 0.772959i | \(0.718776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −67.6176 | −0.112509 | −0.0562543 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562543 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −85.3694 | −0.141106 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 634.634i | 1.04552i | 0.852478 | + | 0.522762i | \(0.175098\pi\) | ||||
−0.852478 | + | 0.522762i | \(0.824902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 117.661i | − 0.192571i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −115.485 | −0.188394 | −0.0941969 | − | 0.995554i | \(-0.530028\pi\) | ||||
−0.0941969 | + | 0.995554i | \(0.530028\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −692.513 | −1.12239 | −0.561193 | − | 0.827685i | \(-0.689658\pi\) | ||||
−0.561193 | + | 0.827685i | \(0.689658\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 711.629i | 1.14964i | 0.818279 | + | 0.574821i | \(0.194928\pi\) | ||||
−0.818279 | + | 0.574821i | \(0.805072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 427.350i | − 0.685955i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 557.177 | 0.891483 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.4066 | 0.0324429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1036.16i | − 1.64210i | −0.570859 | − | 0.821048i | \(-0.693390\pi\) | ||||
0.570859 | − | 0.821048i | \(-0.306610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 87.5477i | − 0.137870i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.3915 | −0.0241624 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1024.87 | 1.59886 | 0.799431 | − | 0.600757i | \(-0.205134\pi\) | ||||
0.799431 | + | 0.600757i | \(0.205134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 824.393i | 1.28210i | 0.767498 | + | 0.641052i | \(0.221502\pi\) | ||||
−0.767498 | + | 0.641052i | \(0.778498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 414.268i | 0.640290i | 0.947369 | + | 0.320145i | \(0.103732\pi\) | ||||
−0.947369 | + | 0.320145i | \(0.896268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −177.484 | −0.273473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 796.975 | 1.22048 | 0.610241 | − | 0.792216i | \(-0.291072\pi\) | ||||
0.610241 | + | 0.792216i | \(0.291072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 112.303i | 0.171455i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 53.1521i | − 0.0806557i | −0.999187 | − | 0.0403279i | \(-0.987160\pi\) | ||||
0.999187 | − | 0.0403279i | \(-0.0128402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 649.763 | 0.983000 | 0.491500 | − | 0.870878i | \(-0.336449\pi\) | ||||
0.491500 | + | 0.870878i | \(0.336449\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −79.0783 | −0.118915 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 160.278i | − 0.240297i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1335.39i | 1.99015i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 829.302 | 1.23225 | 0.616123 | − | 0.787650i | \(-0.288702\pi\) | ||||
0.616123 | + | 0.787650i | \(0.288702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1166.76 | −1.72343 | −0.861716 | − | 0.507392i | \(-0.830610\pi\) | ||||
−0.861716 | + | 0.507392i | \(0.830610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 607.294i | 0.894395i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 690.100i | 1.01039i | 0.863004 | + | 0.505197i | \(0.168580\pi\) | ||||
−0.863004 | + | 0.505197i | \(0.831420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.0482 | −0.0789024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 55.8300 | 0.0810304 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 819.624i | − 1.18614i | −0.805150 | − | 0.593071i | \(-0.797915\pi\) | ||||
0.805150 | − | 0.593071i | \(-0.202085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 101.354i | 0.145833i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −93.2060 | −0.133725 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 378.889 | 0.540498 | 0.270249 | − | 0.962791i | \(-0.412894\pi\) | ||||
0.270249 | + | 0.962791i | \(0.412894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 197.874i | 0.281470i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 469.435i | − 0.663982i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 296.838 | 0.418672 | 0.209336 | − | 0.977844i | \(-0.432870\pi\) | ||||
0.209336 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.725445 | −0.00101745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.4671i | 0.0342197i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 523.144i | 0.727600i | 0.931477 | + | 0.363800i | \(0.118521\pi\) | ||||
−0.931477 | + | 0.363800i | \(0.881479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 378.280 | 0.524661 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 919.283 | 1.26798 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 636.546i | − 0.875579i | −0.899077 | − | 0.437790i | \(-0.855761\pi\) | ||||
0.899077 | − | 0.437790i | \(-0.144239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 7.42373i | − 0.0101556i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −420.326 | −0.573432 | −0.286716 | − | 0.958016i | \(-0.592564\pi\) | ||||
−0.286716 | + | 0.958016i | \(0.592564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 383.621 | 0.520517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 987.498i | − 1.33626i | −0.744044 | − | 0.668131i | \(-0.767095\pi\) | ||||
0.744044 | − | 0.668131i | \(-0.232905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 463.675i | − 0.624058i | −0.950073 | − | 0.312029i | \(-0.898991\pi\) | ||||
0.950073 | − | 0.312029i | \(-0.101009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −277.628 | −0.372656 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −871.313 | −1.16330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 326.135i | 0.434268i | 0.976142 | + | 0.217134i | \(0.0696709\pi\) | ||||
−0.976142 | + | 0.217134i | \(0.930329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 180.709i | − 0.239350i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 404.389 | 0.534199 | 0.267100 | − | 0.963669i | \(-0.413935\pi\) | ||||
0.267100 | + | 0.963669i | \(0.413935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −322.469 | −0.423744 | −0.211872 | − | 0.977297i | \(-0.567956\pi\) | ||||
−0.211872 | + | 0.977297i | \(0.567956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 780.140i | 1.02246i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.5891i | 0.0281475i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −520.611 | −0.676997 | −0.338499 | − | 0.940967i | \(-0.609919\pi\) | ||||
−0.338499 | + | 0.940967i | \(0.609919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −664.521 | −0.859666 | −0.429833 | − | 0.902909i | \(-0.641427\pi\) | ||||
−0.429833 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.16083i | − 0.00536881i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 903.777i | − 1.16018i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1238.93 | 1.58634 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −204.616 | −0.260657 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 711.537i | − 0.904113i | −0.891989 | − | 0.452057i | \(-0.850690\pi\) | ||||
0.891989 | − | 0.452057i | \(-0.149310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 774.966i | − 0.979729i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 162.437 | 0.204838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 691.498 | 0.867626 | 0.433813 | − | 0.901003i | \(-0.357168\pi\) | ||||
0.433813 | + | 0.901003i | \(0.357168\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 89.6028i | − 0.112144i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1506.74i | 1.87639i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.4974 | 0.0316738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −646.526 | −0.799167 | −0.399583 | − | 0.916697i | \(-0.630845\pi\) | ||||
−0.399583 | + | 0.916697i | \(0.630845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 391.295i | − 0.482485i | −0.970465 | − | 0.241243i | \(-0.922445\pi\) | ||||
0.970465 | − | 0.241243i | \(-0.0775549\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 291.773i | − 0.358004i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.9847 | 0.0881085 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −271.408 | −0.330582 | −0.165291 | − | 0.986245i | \(-0.552856\pi\) | ||||
−0.165291 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1135.15i | − 1.37928i | −0.724152 | − | 0.689641i | \(-0.757769\pi\) | ||||
0.724152 | − | 0.689641i | \(-0.242231\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 266.279i | 0.321982i | 0.986956 | + | 0.160991i | \(0.0514690\pi\) | ||||
−0.986956 | + | 0.160991i | \(0.948531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −723.241 | −0.872426 | −0.436213 | − | 0.899844i | \(-0.643681\pi\) | ||||
−0.436213 | + | 0.899844i | \(0.643681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.7211 | −0.0140710 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 159.298i | − 0.190776i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1162.52i | − 1.38560i | −0.721131 | − | 0.692799i | \(-0.756377\pi\) | ||||
0.721131 | − | 0.692799i | \(-0.243623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 615.875 | 0.732312 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −158.725 | −0.187840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 566.218i | 0.668498i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 63.8008i | − 0.0749716i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −770.807 | −0.903642 | −0.451821 | − | 0.892109i | \(-0.649225\pi\) | ||||
−0.451821 | + | 0.892109i | \(0.649225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 383.535 | 0.447532 | 0.223766 | − | 0.974643i | \(-0.428165\pi\) | ||||
0.223766 | + | 0.974643i | \(0.428165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 338.150i | 0.393655i | 0.980438 | + | 0.196828i | \(0.0630640\pi\) | ||||
−0.980438 | + | 0.196828i | \(0.936936\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 783.026i | − 0.907331i | −0.891172 | − | 0.453665i | \(-0.850116\pi\) | ||||
0.891172 | − | 0.453665i | \(-0.149884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 299.854 | 0.346652 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 990.901 | 1.14028 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 46.6637i | − 0.0535749i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 298.042i | 0.340619i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1668.78 | −1.90283 | −0.951414 | − | 0.307916i | \(-0.900369\pi\) | ||||
−0.951414 | + | 0.307916i | \(0.900369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1269.86 | 1.44139 | 0.720695 | − | 0.693252i | \(-0.243823\pi\) | ||||
0.720695 | + | 0.693252i | \(0.243823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 471.136i | 0.533562i | 0.963757 | + | 0.266781i | \(0.0859601\pi\) | ||||
−0.963757 | + | 0.266781i | \(0.914040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 686.179i | 0.773596i | 0.922165 | + | 0.386798i | \(0.126419\pi\) | ||||
−0.922165 | + | 0.386798i | \(0.873581\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −580.666 | −0.653167 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 868.839 | 0.972944 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 138.046i | 0.154242i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6.59406i | − 0.00733488i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.5165 | 0.0471881 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −114.833 | −0.126887 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 406.300i | 0.447960i | 0.974594 | + | 0.223980i | \(0.0719051\pi\) | ||||
−0.974594 | + | 0.223980i | \(0.928095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1340.86i | − 1.47186i | −0.677060 | − | 0.735928i | \(-0.736746\pi\) | ||||
0.677060 | − | 0.735928i | \(-0.263254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1990.38 | −2.18005 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 744.857 | 0.812276 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1568.33i | − 1.70656i | −0.521452 | − | 0.853281i | \(-0.674609\pi\) | ||||
0.521452 | − | 0.853281i | \(-0.325391\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 150.704i | − 0.163276i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 365.933 | 0.395603 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1252.87 | −1.34862 | −0.674312 | − | 0.738446i | \(-0.735560\pi\) | ||||
−0.674312 | + | 0.738446i | \(0.735560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 113.655i | − 0.122078i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.6326i | 0.0199279i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −423.086 | −0.451532 | −0.225766 | − | 0.974182i | \(-0.572489\pi\) | ||||
−0.225766 | + | 0.974182i | \(0.572489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 449.433 | 0.477612 | 0.238806 | − | 0.971067i | \(-0.423244\pi\) | ||||
0.238806 | + | 0.971067i | \(0.423244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 291.407i | 0.309021i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 723.129i | 0.763599i | 0.924245 | + | 0.381800i | \(0.124696\pi\) | ||||
−0.924245 | + | 0.381800i | \(0.875304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 183.280 | 0.193130 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −921.421 | −0.966863 | −0.483432 | − | 0.875382i | \(-0.660610\pi\) | ||||
−0.483432 | + | 0.875382i | \(0.660610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 246.302i | 0.257908i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 358.478i | 0.373804i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.970 | 0.999969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −276.742 | −0.286779 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 317.463i | 0.328297i | 0.986436 | + | 0.164148i | \(0.0524876\pi\) | ||||
−0.986436 | + | 0.164148i | \(0.947512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 559.532i | − 0.576243i | −0.957594 | − | 0.288122i | \(-0.906969\pi\) | ||||
0.957594 | − | 0.288122i | \(-0.0930307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 672.237 | 0.690891 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1742.63 | −1.78366 | −0.891829 | − | 0.452372i | \(-0.850578\pi\) | ||||
−0.891829 | + | 0.452372i | \(0.850578\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 976.374i | − 0.997318i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1071.37i | − 1.08989i | −0.838470 | − | 0.544947i | \(-0.816550\pi\) | ||||
0.838470 | − | 0.544947i | \(-0.183450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 187.805 | 0.190665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.2102 | −0.0234683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1167.78i | 1.17839i | 0.807992 | + | 0.589193i | \(0.200554\pi\) | ||||
−0.807992 | + | 0.589193i | \(0.799446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 183.961i | − 0.184885i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1320.67 | −1.32464 | −0.662321 | − | 0.749220i | \(-0.730429\pi\) | ||||
−0.662321 | + | 0.749220i | \(0.730429\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.g.j.703.5 | 8 | ||
3.2 | odd | 2 | 1728.3.g.m.703.3 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.j.703.6 | 8 | ||
8.3 | odd | 2 | 864.3.g.d.703.4 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.d.703.3 | yes | 8 | ||
12.11 | even | 2 | 1728.3.g.m.703.4 | 8 | |||
24.5 | odd | 2 | 864.3.g.b.703.5 | ✓ | 8 | ||
24.11 | even | 2 | 864.3.g.b.703.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.b.703.5 | ✓ | 8 | 24.5 | odd | 2 | ||
864.3.g.b.703.6 | yes | 8 | 24.11 | even | 2 | ||
864.3.g.d.703.3 | yes | 8 | 8.5 | even | 2 | ||
864.3.g.d.703.4 | yes | 8 | 8.3 | odd | 2 | ||
1728.3.g.j.703.5 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.j.703.6 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.g.m.703.3 | 8 | 3.2 | odd | 2 | |||
1728.3.g.m.703.4 | 8 | 12.11 | even | 2 |