Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.391168.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 40x^{2} + 382 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.96955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.81338 | 0.698850 | 0.349425 | − | 0.936964i | \(-0.386377\pi\) | ||||
0.349425 | + | 0.936964i | \(0.386377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.7627 | 1.17213 | 0.586065 | − | 0.810264i | \(-0.300676\pi\) | ||||
0.586065 | + | 0.810264i | \(0.300676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.9493 | 0.233599 | 0.116799 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116799 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −23.4401 | −0.403481 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −80.2889 | −1.14547 | −0.572733 | − | 0.819742i | \(-0.694117\pi\) | ||||
−0.572733 | + | 0.819742i | \(0.694117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −112.675 | −1.36049 | −0.680246 | − | 0.732984i | \(-0.738127\pi\) | ||||
−0.680246 | + | 0.732984i | \(0.738127\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −70.1884 | −0.636317 | −0.318159 | − | 0.948037i | \(-0.603064\pi\) | ||||
−0.318159 | + | 0.948037i | \(0.603064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −63.9511 | −0.511609 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −147.010 | −0.941344 | −0.470672 | − | 0.882308i | \(-0.655989\pi\) | ||||
−0.470672 | + | 0.882308i | \(0.655989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 144.529 | 0.837363 | 0.418681 | − | 0.908133i | \(-0.362492\pi\) | ||||
0.418681 | + | 0.908133i | \(0.362492\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −128.288 | −0.676729 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.292803 | −0.00130099 | −0.000650494 | − | 1.00000i | \(-0.500207\pi\) | ||||
−0.000650494 | 1.00000i | \(0.500207\pi\) | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.8479 | −0.134868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 294.097 | 1.12025 | 0.560126 | − | 0.828408i | \(-0.310753\pi\) | ||||
0.560126 | + | 0.828408i | \(0.310753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 337.866 | 1.19823 | 0.599117 | − | 0.800661i | \(-0.295518\pi\) | ||||
0.599117 | + | 0.800661i | \(0.295518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 70.3204 | 0.232950 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −104.524 | −0.324391 | −0.162196 | − | 0.986759i | \(-0.551858\pi\) | ||||
−0.162196 | + | 0.986759i | \(0.551858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 240.867 | 0.661335 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −143.050 | −0.370743 | −0.185372 | − | 0.982668i | \(-0.559349\pi\) | ||||
−0.185372 | + | 0.982668i | \(0.559349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 334.121 | 0.819143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 338.024 | 0.785480 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −520.440 | −1.14840 | −0.574199 | − | 0.818716i | \(-0.694686\pi\) | ||||
−0.574199 | + | 0.818716i | \(0.694686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −399.902 | −0.839380 | −0.419690 | − | 0.907668i | \(-0.637861\pi\) | ||||
−0.419690 | + | 0.907668i | \(0.637861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 85.5509 | 0.163251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 137.813 | 0.251292 | 0.125646 | − | 0.992075i | \(-0.459900\pi\) | ||||
0.125646 | + | 0.992075i | \(0.459900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 210.565 | 0.367378 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 266.418 | 0.445324 | 0.222662 | − | 0.974896i | \(-0.428525\pi\) | ||||
0.222662 | + | 0.974896i | \(0.428525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −524.754 | −0.841340 | −0.420670 | − | 0.907214i | \(-0.638205\pi\) | ||||
−0.420670 | + | 0.907214i | \(0.638205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 191.853 | 0.295377 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 433.874 | 0.617907 | 0.308953 | − | 0.951077i | \(-0.400021\pi\) | ||||
0.308953 | + | 0.951077i | \(0.400021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −664.921 | −0.879332 | −0.439666 | − | 0.898161i | \(-0.644903\pi\) | ||||
−0.439666 | + | 0.898161i | \(0.644903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −627.328 | −0.800509 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 441.029 | 0.543485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −803.579 | −0.957069 | −0.478535 | − | 0.878069i | \(-0.658832\pi\) | ||||
−0.478535 | + | 0.878069i | \(0.658832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −433.588 | −0.483452 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −880.370 | −0.950780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −445.813 | −0.466654 | −0.233327 | − | 0.972398i | \(-0.574961\pi\) | ||||
−0.233327 | + | 0.972398i | \(0.574961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 384.864 | 0.390710 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1547.45 | −1.52453 | −0.762263 | − | 0.647267i | \(-0.775912\pi\) | ||||
−0.762263 | + | 0.647267i | \(0.775912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −679.600 | −0.650126 | −0.325063 | − | 0.945692i | \(-0.605386\pi\) | ||||
−0.325063 | + | 0.945692i | \(0.605386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1998.86 | 1.80595 | 0.902975 | − | 0.429693i | \(-0.141378\pi\) | ||||
0.902975 | + | 0.429693i | \(0.141378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1455.60 | −1.27909 | −0.639547 | − | 0.768752i | \(-0.720878\pi\) | ||||
−0.639547 | + | 0.768752i | \(0.720878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.878410 | 0.000751126 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 523.808 | 0.436068 | 0.218034 | − | 0.975941i | \(-0.430036\pi\) | ||||
0.218034 | + | 0.975941i | \(0.430036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −548.409 | −0.444690 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 98.5436 | 0.0778663 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 497.645 | 0.373888 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −882.292 | −0.646777 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1476.35 | −1.05639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2496.08 | 1.74402 | 0.872011 | − | 0.489486i | \(-0.162815\pi\) | ||||
0.872011 | + | 0.489486i | \(0.162815\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1013.60 | −0.691801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −407.249 | −0.271615 | −0.135807 | − | 0.990735i | \(-0.543363\pi\) | ||||
−0.135807 | + | 0.990735i | \(0.543363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −210.961 | −0.134494 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 478.949 | 0.298682 | 0.149341 | − | 0.988786i | \(-0.452285\pi\) | ||||
0.149341 | + | 0.988786i | \(0.452285\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 123.985 | 0.0756569 | 0.0378284 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378284 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 313.572 | 0.187287 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 468.221 | 0.273808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1148.64 | −0.657858 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1645.37 | 0.904658 | 0.452329 | − | 0.891851i | \(-0.350593\pi\) | ||||
0.452329 | + | 0.891851i | \(0.350593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3044.79 | −1.64094 | −0.820470 | − | 0.571690i | \(-0.806288\pi\) | ||||
−0.820470 | + | 0.571690i | \(0.806288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −722.600 | −0.381822 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1129.26 | 0.585191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1408.22 | 0.715850 | 0.357925 | − | 0.933750i | \(-0.383484\pi\) | ||||
0.357925 | + | 0.933750i | \(0.383484\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 429.149 | 0.214049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2083.51 | −1.00119 | −0.500593 | − | 0.865683i | \(-0.666885\pi\) | ||||
−0.500593 | + | 0.865683i | \(0.666885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1002.36 | −0.472932 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.235 | 0.0853685 | 0.0426843 | − | 0.999089i | \(-0.486409\pi\) | ||||
0.0426843 | + | 0.999089i | \(0.486409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2077.11 | −0.945432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1014.07 | −0.453497 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3332.98 | −1.46475 | −0.732375 | − | 0.680902i | \(-0.761588\pi\) | ||||
−0.732375 | + | 0.680902i | \(0.761588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1561.32 | 0.663028 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3273.98 | −1.36709 | −0.683544 | − | 0.729909i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729909i | \(0.739562\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2708.05 | 1.11209 | 0.556043 | − | 0.831154i | \(-0.312319\pi\) | ||||
0.556043 | + | 0.831154i | \(0.312319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1199.71 | 0.484616 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.28778 | −0.000909196 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3433.37 | −1.34264 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −985.187 | −0.373223 | −0.186612 | − | 0.982434i | \(-0.559751\pi\) | ||||
−0.186612 | + | 0.982434i | \(0.559751\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4627.92 | −1.72604 | −0.863018 | − | 0.505172i | \(-0.831429\pi\) | ||||
−0.863018 | + | 0.505172i | \(0.831429\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −256.653 | −0.0942528 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3501.81 | −1.26647 | −0.633233 | − | 0.773961i | \(-0.718273\pi\) | ||||
−0.633233 | + | 0.773961i | \(0.718273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −169.661 | −0.0604368 | −0.0302184 | − | 0.999543i | \(-0.509620\pi\) | ||||
−0.0302184 | + | 0.999543i | \(0.509620\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −413.439 | −0.145083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2297.90 | 0.782888 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −631.696 | −0.212106 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4818.27 | −1.59467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1188.76 | −0.387857 | −0.193929 | − | 0.981016i | \(-0.562123\pi\) | ||||
−0.193929 | + | 0.981016i | \(0.562123\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −799.255 | −0.257108 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2639.88 | 0.837386 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1574.26 | 0.485748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −879.106 | −0.267580 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3395.54 | −1.01965 | −0.509826 | − | 0.860278i | \(-0.670290\pi\) | ||||
−0.509826 | + | 0.860278i | \(0.670290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −575.560 | −0.170536 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1198.05 | −0.350297 | −0.175148 | − | 0.984542i | \(-0.556041\pi\) | ||||
−0.175148 | + | 0.984542i | \(0.556041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5820.40 | −1.67958 | −0.839788 | − | 0.542914i | \(-0.817321\pi\) | ||||
−0.839788 | + | 0.542914i | \(0.817321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3488.08 | 0.980737 | 0.490368 | − | 0.871515i | \(-0.336862\pi\) | ||||
0.490368 | + | 0.871515i | \(0.336862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −816.685 | −0.226701 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1301.62 | −0.356749 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4688.08 | 1.26882 | 0.634408 | − | 0.772999i | \(-0.281244\pi\) | ||||
0.634408 | + | 0.772999i | \(0.281244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6419.23 | −1.71576 | −0.857881 | − | 0.513848i | \(-0.828220\pi\) | ||||
−0.857881 | + | 0.513848i | \(0.828220\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1233.71 | −0.317809 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1994.76 | 0.507682 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5928.29 | 1.49080 | 0.745400 | − | 0.666618i | \(-0.232259\pi\) | ||||
0.745400 | + | 0.666618i | \(0.232259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3001.44 | −0.745846 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1881.98 | 0.462174 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 673.329 | 0.163428 | 0.0817142 | − | 0.996656i | \(-0.473961\pi\) | ||||
0.0817142 | + | 0.996656i | \(0.473961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1323.09 | −0.313781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5270.35 | −1.23568 | −0.617839 | − | 0.786304i | \(-0.711992\pi\) | ||||
−0.617839 | + | 0.786304i | \(0.711992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1117.70 | −0.259094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2410.74 | 0.552564 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4064.77 | −0.921313 | −0.460656 | − | 0.887579i | \(-0.652386\pi\) | ||||
−0.460656 | + | 0.887579i | \(0.652386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6524.19 | −1.46242 | −0.731211 | − | 0.682151i | \(-0.761045\pi\) | ||||
−0.731211 | + | 0.682151i | \(0.761045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2734.72 | −0.599672 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8345.83 | 1.81030 | 0.905149 | − | 0.425095i | \(-0.139759\pi\) | ||||
0.905149 | + | 0.425095i | \(0.139759\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1300.76 | 0.279121 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8161.43 | 1.73263 | 0.866316 | − | 0.499496i | \(-0.166481\pi\) | ||||
0.866316 | + | 0.499496i | \(0.166481\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8669.66 | 1.82105 | 0.910526 | − | 0.413451i | \(-0.135677\pi\) | ||||
0.910526 | + | 0.413451i | \(0.135677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2641.11 | 0.548933 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1533.31 | 0.312093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1337.44 | 0.269423 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −99.7900 | −0.0198969 | −0.00994846 | − | 0.999951i | \(-0.503167\pi\) | ||||
−0.00994846 | + | 0.999951i | \(0.503167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4066.39 | −0.802558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1154.59 | −0.225576 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −768.513 | −0.148643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4642.35 | 0.880186 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3124.58 | −0.586601 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8631.55 | 1.60465 | 0.802327 | − | 0.596885i | \(-0.203595\pi\) | ||||
0.802327 | + | 0.596885i | \(0.203595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2038.80 | 0.375351 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −863.980 | −0.157530 | −0.0787650 | − | 0.996893i | \(-0.525098\pi\) | ||||
−0.0787650 | + | 0.996893i | \(0.525098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −577.824 | −0.104347 | −0.0521734 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521734 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −196.879 | −0.0348828 | −0.0174414 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174414 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6286.52 | −1.10338 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5996.57 | −1.04267 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9046.53 | 1.55840 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −700.219 | −0.119511 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4366.80 | 0.738485 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4645.40 | −0.771402 | −0.385701 | − | 0.922624i | \(-0.626040\pi\) | ||||
−0.385701 | + | 0.922624i | \(0.626040\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.63523 | −0.000433663 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1076.79 | 0.175615 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7255.28 | −1.17276 | −0.586380 | − | 0.810036i | \(-0.699447\pi\) | ||||
−0.586380 | + | 0.810036i | \(0.699447\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1571.42 | −0.251764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6180.46 | 0.981498 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1645.23 | 0.256742 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3066.25 | 0.474366 | 0.237183 | − | 0.971465i | \(-0.423776\pi\) | ||||
0.237183 | + | 0.971465i | \(0.423776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −884.690 | −0.135692 | −0.0678458 | − | 0.997696i | \(-0.521613\pi\) | ||||
−0.0678458 | + | 0.997696i | \(0.521613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −295.631 | −0.0449561 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2463.28 | −0.371409 | −0.185704 | − | 0.982606i | \(-0.559457\pi\) | ||||
−0.185704 | + | 0.982606i | \(0.559457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2081.63 | 0.311215 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1999.23 | −0.293915 | −0.146957 | − | 0.989143i | \(-0.546948\pi\) | ||||
−0.146957 | + | 0.989143i | \(0.546948\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5836.59 | 0.850939 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1492.94 | −0.215865 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4100.10 | −0.587971 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6790.82 | 0.965880 | 0.482940 | − | 0.875653i | \(-0.339569\pi\) | ||||
0.482940 | + | 0.875653i | \(0.339569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2646.88 | 0.373417 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1222.01 | −0.169633 | −0.0848164 | − | 0.996397i | \(-0.527030\pi\) | ||||
−0.0848164 | + | 0.996397i | \(0.527030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4429.04 | 0.609906 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1609.65 | −0.219897 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10228.6 | 1.38630 | 0.693149 | − | 0.720794i | \(-0.256223\pi\) | ||||
0.693149 | + | 0.720794i | \(0.256223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7488.23 | −1.00691 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5452.92 | 0.727496 | 0.363748 | − | 0.931497i | \(-0.381497\pi\) | ||||
0.363748 | + | 0.931497i | \(0.381497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3040.79 | 0.399412 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14423.8 | 1.87999 | 0.939994 | − | 0.341190i | \(-0.110830\pi\) | ||||
0.939994 | + | 0.341190i | \(0.110830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5635.35 | 0.728880 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1221.75 | 0.156817 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3390.02 | 0.431824 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4462.35 | −0.564129 | −0.282064 | − | 0.959395i | \(-0.591019\pi\) | ||||
−0.282064 | + | 0.959395i | \(0.591019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12380.6 | 1.54179 | 0.770897 | − | 0.636960i | \(-0.219809\pi\) | ||||
0.770897 | + | 0.636960i | \(0.219809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1582.49 | 0.195607 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 632.884 | 0.0776500 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.5210 | −0.00152493 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10065.9 | −1.21694 | −0.608469 | − | 0.793578i | \(-0.708216\pi\) | ||||
−0.608469 | + | 0.793578i | \(0.708216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1436.85 | −0.172444 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5195.28 | −0.614521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −371.956 | −0.0436805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 645.188 | 0.0752256 | 0.0376128 | − | 0.999292i | \(-0.488025\pi\) | ||||
0.0376128 | + | 0.999292i | \(0.488025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16460.0 | −1.90549 | −0.952745 | − | 0.303770i | \(-0.901755\pi\) | ||||
−0.952745 | + | 0.303770i | \(0.901755\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −940.716 | −0.108130 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5134.56 | 0.586030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1404.66 | −0.158083 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4989.28 | 0.557599 | 0.278800 | − | 0.960349i | \(-0.410063\pi\) | ||||
0.278800 | + | 0.960349i | \(0.410063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12366.3 | 1.37248 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3445.92 | 0.379815 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7908.46 | 0.865705 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11733.7 | −1.27567 | −0.637836 | − | 0.770172i | \(-0.720170\pi\) | ||||
−0.637836 | + | 0.770172i | \(0.720170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4632.30 | −0.496811 | −0.248406 | − | 0.968656i | \(-0.579907\pi\) | ||||
−0.248406 | + | 0.968656i | \(0.579907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6278.67 | −0.668848 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4936.11 | −0.522304 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4057.84 | −0.426506 | −0.213253 | − | 0.976997i | \(-0.568406\pi\) | ||||
−0.213253 | + | 0.976997i | \(0.568406\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12576.4 | 1.31308 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9134.38 | 0.947397 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17692.3 | −1.81097 | −0.905484 | − | 0.424381i | \(-0.860492\pi\) | ||||
−0.905484 | + | 0.424381i | \(0.860492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2167.80 | 0.220445 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8120.88 | −0.820449 | −0.410225 | − | 0.911984i | \(-0.634550\pi\) | ||||
−0.410225 | + | 0.911984i | \(0.634550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19397.4 | −1.94703 | −0.973515 | − | 0.228624i | \(-0.926577\pi\) | ||||
−0.973515 | + | 0.228624i | \(0.926577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3387.79 | −0.337860 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11033.3 | 1.09327 | 0.546637 | − | 0.837370i | \(-0.315908\pi\) | ||||
0.546637 | + | 0.837370i | \(0.315908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4224.67 | −0.413296 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14448.1 | 1.40449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7205.67 | 0.696039 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1287.45 | −0.123581 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14170.5 | 1.35170 | 0.675852 | − | 0.737038i | \(-0.263776\pi\) | ||||
0.675852 | + | 0.737038i | \(0.263776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.20599 | −0.000303909 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3483.31 | −0.326121 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12929.3 | 1.20304 | 0.601522 | − | 0.798856i | \(-0.294561\pi\) | ||||
0.601522 | + | 0.798856i | \(0.294561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6250.54 | 0.578035 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 99.6829 | 0.00916217 | 0.00458109 | − | 0.999990i | \(-0.498542\pi\) | ||||
0.00458109 | + | 0.999990i | \(0.498542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11803.2 | 1.07828 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3007.09 | 0.273048 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6207.28 | −0.556865 | −0.278433 | − | 0.960456i | \(-0.589815\pi\) | ||||
−0.278433 | + | 0.960456i | \(0.589815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −552.705 | −0.0492875 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4743.31 | −0.420464 | −0.210232 | − | 0.977651i | \(-0.567422\pi\) | ||||
−0.210232 | + | 0.977651i | \(0.567422\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12090.8 | −1.06542 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6231.34 | 0.545845 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9836.46 | 0.856569 | 0.428284 | − | 0.903644i | \(-0.359118\pi\) | ||||
0.428284 | + | 0.903644i | \(0.359118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3042.22 | 0.261827 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5309.98 | −0.454341 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4469.72 | −0.380229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9998.94 | 0.845674 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2285.55 | 0.192192 | 0.0960958 | − | 0.995372i | \(-0.469364\pi\) | ||||
0.0960958 | + | 0.995372i | \(0.469364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7740.65 | −0.647180 | −0.323590 | − | 0.946197i | \(-0.604890\pi\) | ||||
−0.323590 | + | 0.946197i | \(0.604890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11604.1 | −0.959171 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7240.59 | −0.595100 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4683.96 | −0.382799 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3220.16 | 0.261689 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15617.8 | 1.26209 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9821.94 | 0.789289 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15682.4 | −1.24628 | −0.623141 | − | 0.782110i | \(-0.714144\pi\) | ||||
−0.623141 | + | 0.782110i | \(0.714144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8124.14 | −0.642063 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11373.2 | −0.893895 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3365.32 | −0.263054 | −0.131527 | − | 0.991313i | \(-0.541988\pi\) | ||||
−0.131527 | + | 0.991313i | \(0.541988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3599.12 | −0.279793 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16564.3 | 1.28069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.86335 | 0.000524924 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11968.8 | 0.910478 | 0.455239 | − | 0.890369i | \(-0.349554\pi\) | ||||
0.455239 | + | 0.890369i | \(0.349554\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3699.39 | 0.279906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10300.1 | 0.775171 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14981.4 | −1.12148 | −0.560740 | − | 0.827992i | \(-0.689483\pi\) | ||||
−0.560740 | + | 0.827992i | \(0.689483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4092.71 | 0.304746 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14947.7 | 1.10130 | 0.550652 | − | 0.834735i | \(-0.314379\pi\) | ||||
0.550652 | + | 0.834735i | \(0.314379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8138.91 | 0.596503 | 0.298251 | − | 0.954487i | \(-0.403597\pi\) | ||||
0.298251 | + | 0.954487i | \(0.403597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2955.56 | 0.215481 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4488.63 | 0.325545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4092.69 | 0.295288 | 0.147644 | − | 0.989041i | \(-0.452831\pi\) | ||||
0.147644 | + | 0.989041i | \(0.452831\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13883.8 | 0.996528 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6117.19 | −0.434559 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 769.958 | 0.0544169 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15877.4 | 1.11641 | 0.558203 | − | 0.829705i | \(-0.311491\pi\) | ||||
0.558203 | + | 0.829705i | \(0.311491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16284.8 | −1.13923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10505.4 | 0.731195 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21660.8 | −1.50000 | −0.750001 | − | 0.661436i | \(-0.769947\pi\) | ||||
−0.750001 | + | 0.661436i | \(0.769947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 508.982 | 0.0348932 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11674.4 | −0.796334 | −0.398167 | − | 0.917313i | \(-0.630354\pi\) | ||||
−0.398167 | + | 0.917313i | \(0.630354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5818.05 | −0.394881 | −0.197440 | − | 0.980315i | \(-0.563263\pi\) | ||||
−0.197440 | + | 0.980315i | \(0.563263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1240.32 | 0.0837640 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3888.29 | 0.261292 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19894.5 | 1.33030 | 0.665150 | − | 0.746710i | \(-0.268368\pi\) | ||||
0.665150 | + | 0.746710i | \(0.268368\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1144.46 | −0.0757774 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23979.8 | 1.57999 | 0.789996 | − | 0.613112i | \(-0.210083\pi\) | ||||
0.789996 | + | 0.613112i | \(0.210083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6893.69 | −0.452000 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16527.7 | −1.07841 | −0.539207 | − | 0.842173i | \(-0.681276\pi\) | ||||
−0.539207 | + | 0.842173i | \(0.681276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2135.87 | 0.138688 | 0.0693440 | − | 0.997593i | \(-0.477909\pi\) | ||||
0.0693440 | + | 0.997593i | \(0.477909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1895.09 | 0.122459 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3541.37 | −0.226648 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14454.8 | 0.920685 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.5089 | 0.00149024 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16460.9 | −1.03851 | −0.519253 | − | 0.854620i | \(-0.673790\pi\) | ||||
−0.519253 | + | 0.854620i | \(0.673790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3566.29 | 0.223930 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19502.8 | 1.21881 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2397.76 | 0.148441 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2506.10 | 0.154423 | 0.0772114 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772114 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15408.1 | 0.945002 | 0.472501 | − | 0.881330i | \(-0.343351\pi\) | ||||
0.472501 | + | 0.881330i | \(0.343351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7919.63 | −0.483465 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28067.4 | −1.70548 | −0.852738 | − | 0.522338i | \(-0.825060\pi\) | ||||
−0.852738 | + | 0.522338i | \(0.825060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22255.4 | −1.34607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3412.13 | 0.204482 | 0.102241 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3181.99 | −0.189818 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4722.79 | −0.280447 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18182.5 | −1.07479 | −0.537397 | − | 0.843329i | \(-0.680592\pi\) | ||||
−0.537397 | + | 0.843329i | \(0.680592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23113.9 | 1.36010 | 0.680049 | − | 0.733167i | \(-0.261958\pi\) | ||||
0.680049 | + | 0.733167i | \(0.261958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2637.32 | 0.154487 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10318.4 | 0.598994 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10186.6 | 0.588696 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17100.9 | −0.983862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13586.4 | 0.778183 | 0.389092 | − | 0.921199i | \(-0.372789\pi\) | ||||
0.389092 | + | 0.921199i | \(0.372789\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1726.68 | 0.0984591 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24054.6 | 1.36557 | 0.682786 | − | 0.730619i | \(-0.260768\pi\) | ||||
0.682786 | + | 0.730619i | \(0.260768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3594.15 | 0.202244 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21915.5 | 1.22778 | 0.613889 | − | 0.789393i | \(-0.289604\pi\) | ||||
0.613889 | + | 0.789393i | \(0.289604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3742.21 | 0.208734 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17461.2 | 0.969704 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1566.29 | −0.0866052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19309.5 | −1.06305 | −0.531524 | − | 0.847043i | \(-0.678381\pi\) | ||||
−0.531524 | + | 0.847043i | \(0.678381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 968.745 | 0.0528728 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23612.8 | −1.28321 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10464.2 | −0.566229 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10696.2 | 0.576305 | 0.288152 | − | 0.957585i | \(-0.406959\pi\) | ||||
0.288152 | + | 0.957585i | \(0.406959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.9915 | 0.00176998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2450.06 | 0.130886 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30425.4 | −1.61164 | −0.805818 | − | 0.592163i | \(-0.798274\pi\) | ||||
−0.805818 | + | 0.592163i | \(0.798274\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3904.86 | 0.205969 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10144.3 | −0.532828 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3658.39 | 0.191351 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14064.2 | −0.732551 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30084.9 | 1.56047 | 0.780235 | − | 0.625487i | \(-0.215100\pi\) | ||||
0.780235 | + | 0.625487i | \(0.215100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19257.7 | 0.990596 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9401.42 | 0.481600 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3894.17 | 0.198661 | 0.0993306 | − | 0.995054i | \(-0.468330\pi\) | ||||
0.0993306 | + | 0.995054i | \(0.468330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27126.9 | −1.37254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10760.8 | 0.542235 | 0.271117 | − | 0.962546i | \(-0.412607\pi\) | ||||
0.271117 | + | 0.962546i | \(0.412607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5893.26 | 0.294547 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13739.3 | −0.683907 | −0.341954 | − | 0.939717i | \(-0.611089\pi\) | ||||
−0.341954 | + | 0.939717i | \(0.611089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3701.12 | 0.183487 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26261.8 | 1.29670 | 0.648352 | − | 0.761341i | \(-0.275459\pi\) | ||||
0.648352 | + | 0.761341i | \(0.275459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12855.9 | 0.632220 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5984.29 | −0.293111 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15995.8 | 0.777222 | 0.388611 | − | 0.921402i | \(-0.372955\pi\) | ||||
0.388611 | + | 0.921402i | \(0.372955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17784.9 | −0.860713 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23790.1 | −1.14677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1837.00 | 0.0881993 | 0.0440997 | − | 0.999027i | \(-0.485958\pi\) | ||||
0.0440997 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9004.33 | 0.430615 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2992.29 | −0.142537 | −0.0712684 | − | 0.997457i | \(-0.522705\pi\) | ||||
−0.0712684 | + | 0.997457i | \(0.522705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5645.95 | −0.266836 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5698.44 | −0.268264 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27602.4 | 1.29437 | 0.647183 | − | 0.762335i | \(-0.275947\pi\) | ||||
0.647183 | + | 0.762335i | \(0.275947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2019.99 | −0.0943554 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29608.1 | 1.37766 | 0.688830 | − | 0.724923i | \(-0.258125\pi\) | ||||
0.688830 | + | 0.724923i | \(0.258125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9242.81 | −0.428402 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33137.3 | −1.52409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11392.8 | 0.521978 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3969.26 | 0.181162 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11003.0 | 0.500272 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6482.32 | 0.293608 | 0.146804 | − | 0.989166i | \(-0.453101\pi\) | ||||
0.146804 | + | 0.989166i | \(0.453101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15811.0 | 0.713420 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4378.64 | −0.196078 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3353.11 | 0.149588 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27622.2 | 1.22764 | 0.613821 | − | 0.789446i | \(-0.289632\pi\) | ||||
0.613821 | + | 0.789446i | \(0.289632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8392.12 | 0.371579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7232.21 | −0.319023 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22439.9 | −0.986160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12194.3 | 0.531920 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12740.7 | −0.553695 | −0.276848 | − | 0.960914i | \(-0.589290\pi\) | ||||
−0.276848 | + | 0.960914i | \(0.589290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2981.71 | −0.129102 | −0.0645511 | − | 0.997914i | \(-0.520562\pi\) | ||||
−0.0645511 | + | 0.997914i | \(0.520562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19572.6 | 0.844330 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16279.3 | −0.699679 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38069.0 | −1.63019 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39713.6 | 1.68820 | 0.844100 | − | 0.536185i | \(-0.180135\pi\) | ||||
0.844100 | + | 0.536185i | \(0.180135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19917.5 | 0.843596 | 0.421798 | − | 0.906690i | \(-0.361399\pi\) | ||||
0.421798 | + | 0.906690i | \(0.361399\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8204.16 | 0.346221 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9671.42 | −0.406660 | −0.203330 | − | 0.979110i | \(-0.565176\pi\) | ||||
−0.203330 | + | 0.979110i | \(0.565176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43001.4 | −1.80157 | −0.900784 | − | 0.434267i | \(-0.857007\pi\) | ||||
−0.900784 | + | 0.434267i | \(0.857007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25037.5 | −1.04518 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1439.50 | 0.0596598 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3902.29 | −0.161151 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29115.1 | 1.19805 | 0.599026 | − | 0.800730i | \(-0.295555\pi\) | ||||
0.599026 | + | 0.800730i | \(0.295555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2777.20 | −0.113871 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24484.3 | −1.00034 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16229.3 | −0.660715 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26009.0 | −1.05139 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.5514 | 0.000827841 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19860.6 | 0.797201 | 0.398601 | − | 0.917125i | \(-0.369496\pi\) | ||||
0.398601 | + | 0.917125i | \(0.369496\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7923.33 | −0.316927 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26027.5 | 1.03744 | 0.518719 | − | 0.854945i | \(-0.326409\pi\) | ||||
0.518719 | + | 0.854945i | \(0.326409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18974.5 | −0.753669 | −0.376835 | − | 0.926281i | \(-0.622988\pi\) | ||||
−0.376835 | + | 0.926281i | \(0.622988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21212.2 | −0.836699 | −0.418350 | − | 0.908286i | \(-0.637391\pi\) | ||||
−0.418350 | + | 0.908286i | \(0.637391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26041.8 | −1.02364 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4599.93 | −0.180187 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18553.6 | 0.724267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1508.96 | 0.0587015 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4012.32 | −0.155551 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13227.6 | 0.509310 | 0.254655 | − | 0.967032i | \(-0.418038\pi\) | ||||
0.254655 | + | 0.967032i | \(0.418038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 299.370 | 0.0114875 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7026.27 | 0.268696 | 0.134348 | − | 0.990934i | \(-0.457106\pi\) | ||||
0.134348 | + | 0.990934i | \(0.457106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29986.9 | −1.14285 | −0.571427 | − | 0.820653i | \(-0.693610\pi\) | ||||
−0.571427 | + | 0.820653i | \(0.693610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12199.2 | 0.463357 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32874.6 | −1.24444 | −0.622222 | − | 0.782841i | \(-0.713770\pi\) | ||||
−0.622222 | + | 0.782841i | \(0.713770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3463.78 | 0.130237 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11777.2 | 0.441332 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25580.9 | −0.955390 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2305.54 | 0.0858191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21247.2 | −0.788247 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11485.3 | 0.424674 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21159.0 | 0.777181 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11380.2 | −0.416620 | −0.208310 | − | 0.978063i | \(-0.566796\pi\) | ||||
−0.208310 | + | 0.978063i | \(0.566796\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13927.1 | −0.508176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12842.6 | −0.467062 | −0.233531 | − | 0.972349i | \(-0.575028\pi\) | ||||
−0.233531 | + | 0.972349i | \(0.575028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28433.8 | −1.03069 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9373.75 | 0.338674 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12184.9 | 0.437369 | 0.218685 | − | 0.975796i | \(-0.429823\pi\) | ||||
0.218685 | + | 0.975796i | \(0.429823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25894.7 | −0.926447 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2917.09 | 0.104027 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7251 | 0.000665597 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6116.40 | −0.216709 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32603.6 | −1.15144 | −0.575721 | − | 0.817646i | \(-0.695279\pi\) | ||||
−0.575721 | + | 0.817646i | \(0.695279\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2591.94 | 0.0909499 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26826.2 | −0.938301 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15788.1 | −0.550453 | −0.275227 | − | 0.961379i | \(-0.588753\pi\) | ||||
−0.275227 | + | 0.961379i | \(0.588753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1733.47 | 0.0602446 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45207.2 | 1.56611 | 0.783057 | − | 0.621950i | \(-0.213659\pi\) | ||||
0.783057 | + | 0.621950i | \(0.213659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20642.2 | −0.712835 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36204.8 | 1.24234 | 0.621171 | − | 0.783675i | \(-0.286657\pi\) | ||||
0.621171 | + | 0.783675i | \(0.286657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5745.68 | −0.196536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 590.637 | 0.0201396 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41627.8 | 1.41496 | 0.707481 | − | 0.706733i | \(-0.249832\pi\) | ||||
0.707481 | + | 0.706733i | \(0.249832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7697.64 | −0.260827 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18859.6 | 0.637035 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8902.25 | −0.298824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17989.7 | 0.601983 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36159.7 | −1.20624 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36170.4 | −1.20286 | −0.601428 | − | 0.798927i | \(-0.705401\pi\) | ||||
−0.601428 | + | 0.798927i | \(0.705401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27139.6 | −0.899741 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7565.19 | 0.250029 | 0.125015 | − | 0.992155i | \(-0.460102\pi\) | ||||
0.125015 | + | 0.992155i | \(0.460102\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2100.66 | 0.0689998 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47949.1 | −1.57014 | −0.785070 | − | 0.619407i | \(-0.787373\pi\) | ||||
−0.785070 | + | 0.619407i | \(0.787373\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34363.2 | −1.12181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13100.4 | −0.426365 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10632.9 | −0.345001 | −0.172501 | − | 0.985009i | \(-0.555185\pi\) | ||||
−0.172501 | + | 0.985009i | \(0.555185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27361.0 | −0.885070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23714.3 | −0.762457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3411.06 | −0.109340 | −0.0546699 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546699 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13936.2 | 0.445369 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1325.62 | −0.0422362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17965.3 | −0.570678 | −0.285339 | − | 0.958427i | \(-0.592106\pi\) | ||||
−0.285339 | + | 0.958427i | \(0.592106\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.90569 | 0.000250375 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 | 1176.4.a.z.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 2352.4.a.co.1.3 | 4 | |||
7.6 | odd | 2 | 1176.4.a.be.1.2 | yes | 4 | ||
28.27 | even | 2 | 2352.4.a.cn.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.z.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1176.4.a.be.1.2 | yes | 4 | 7.6 | odd | 2 | ||
2352.4.a.cn.1.2 | 4 | 28.27 | even | 2 | |||
2352.4.a.co.1.3 | 4 | 4.3 | odd | 2 |