Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.4 | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.k.639.3 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73799i | 0.579331i | 0.957128 | + | 0.289666i | \(0.0935441\pi\) | ||||
−0.957128 | + | 0.289666i | \(0.906456\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.35996 | + | 3.70279i | −0.671991 | + | 0.740559i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.32638 | −1.04663 | −0.523313 | − | 0.852141i | \(-0.675304\pi\) | ||||
−0.523313 | + | 0.852141i | \(0.675304\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.97938 | 0.664375 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.9852 | 1.27138 | 0.635690 | − | 0.771944i | \(-0.280716\pi\) | ||||
0.635690 | + | 0.771944i | \(0.280716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.4106 | −0.954659 | −0.477329 | − | 0.878724i | \(-0.658395\pi\) | ||||
−0.477329 | + | 0.878724i | \(0.658395\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.43544 | − | 5.83959i | −0.429029 | − | 0.389306i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.07874i | 0.239926i | 0.992778 | + | 0.119963i | \(0.0382776\pi\) | ||||
−0.992778 | + | 0.119963i | \(0.961722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.9804 | −0.788440 | −0.394220 | − | 0.919016i | \(-0.628985\pi\) | ||||
−0.394220 | + | 0.919016i | \(0.628985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 12.7332i | − | 0.606343i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.8788 | −1.08168 | −0.540842 | − | 0.841124i | \(-0.681894\pi\) | ||||
−0.540842 | + | 0.841124i | \(0.681894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.42138 | − | 24.8825i | −0.0968551 | − | 0.995298i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.0341i | 0.964225i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.6447i | 1.47051i | 0.677792 | + | 0.735254i | \(0.262937\pi\) | ||||
−0.677792 | + | 0.735254i | \(0.737063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 27.9864i | − | 0.902787i | −0.892325 | − | 0.451393i | \(-0.850927\pi\) | ||
0.892325 | − | 0.451393i | \(-0.149073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.3062i | 0.736551i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.6163 | − | 27.1281i | 0.703324 | − | 0.775088i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12.4664 | −0.336929 | −0.168465 | − | 0.985708i | \(-0.553881\pi\) | ||||
−0.168465 | + | 0.985708i | \(0.553881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 21.5695i | − | 0.553064i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −75.4673 | −1.84067 | −0.920333 | − | 0.391136i | \(-0.872082\pi\) | ||||
−0.920333 | + | 0.391136i | \(0.872082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 20.5971i | − | 0.479002i | −0.970896 | − | 0.239501i | \(-0.923016\pi\) | ||
0.970896 | − | 0.239501i | \(-0.0769839\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.0904 | + | 22.1404i | −0.446454 | + | 0.492009i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.8709 | 0.678104 | 0.339052 | − | 0.940768i | \(-0.389894\pi\) | ||||
0.339052 | + | 0.940768i | \(0.389894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.67586 | 0.0954256 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.08883 | −0.138997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 88.3667 | 1.66730 | 0.833648 | − | 0.552296i | \(-0.186248\pi\) | ||||
0.833648 | + | 0.552296i | \(0.186248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.9896 | + | 51.7843i | −0.854357 | + | 0.941532i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 26.0358i | − | 0.456768i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 64.3508 | 1.09069 | 0.545345 | − | 0.838211i | \(-0.316398\pi\) | ||||
0.545345 | + | 0.838211i | \(0.316398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 44.1435i | − | 0.723664i | −0.932243 | − | 0.361832i | \(-0.882151\pi\) | ||
0.932243 | − | 0.361832i | \(-0.117849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −43.8072 | −0.695352 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 41.6990 | − | 45.9538i | 0.641523 | − | 0.706981i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 85.0952i | − | 1.27008i | −0.772481 | − | 0.635038i | \(-0.780984\pi\) | ||
0.772481 | − | 0.635038i | \(-0.219016\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 43.2391i | − | 0.626654i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 44.9608i | − | 0.633250i | −0.948551 | − | 0.316625i | \(-0.897450\pi\) | ||
0.948551 | − | 0.316625i | \(-0.102550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 51.8688i | − | 0.710531i | −0.934765 | − | 0.355265i | \(-0.884390\pi\) | ||
0.934765 | − | 0.355265i | \(-0.115610\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 43.2456 | − | 4.20834i | 0.576608 | − | 0.0561112i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −102.461 | −1.33066 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 145.130i | − | 1.83709i | −0.395316 | − | 0.918545i | \(-0.629365\pi\) | ||
0.395316 | − | 0.918545i | \(-0.370635\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.56734 | 0.105770 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 100.687i | − | 1.21309i | −0.795048 | − | 0.606547i | \(-0.792554\pi\) | ||
0.795048 | − | 0.606547i | \(-0.207446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1028 | − | 13.7044i | −0.177679 | − | 0.161228i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −74.1163 | −0.851911 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4980 | −0.174135 | −0.0870674 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870674 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 90.9245 | 0.999171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.6402 | 0.523013 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 50.3333 | − | 55.4692i | 0.529825 | − | 0.583886i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.492654i | − | 0.00507891i | −0.999997 | − | 0.00253946i | \(-0.999192\pi\) | ||
0.999997 | − | 0.00253946i | \(-0.000808335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 83.6227 | 0.844674 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 24.5991i | 0.243556i | 0.992557 | + | 0.121778i | \(0.0388595\pi\) | ||||
−0.992557 | + | 0.121778i | \(0.961140\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 45.2049 | 0.438882 | 0.219441 | − | 0.975626i | \(-0.429577\pi\) | ||||
0.219441 | + | 0.975626i | \(0.429577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 47.1484 | + | 42.7830i | 0.449033 | + | 0.407457i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 113.659i | − | 1.06223i | −0.847299 | − | 0.531116i | \(-0.821773\pi\) | ||
0.847299 | − | 0.531116i | \(-0.178227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 33.0086i | − | 0.302831i | −0.988470 | − | 0.151416i | \(-0.951617\pi\) | ||
0.988470 | − | 0.151416i | \(-0.0483832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 21.6665i | − | 0.195194i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 215.991i | 1.91142i | 0.294303 | + | 0.955712i | \(0.404912\pi\) | ||||
−0.294303 | + | 0.955712i | \(0.595088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.5915 | − | 92.1209i | 0.726883 | − | 0.801051i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −74.2075 | −0.634252 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 29.8824i | − | 0.251113i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 74.5855 | 0.616409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 131.162i | − | 1.06636i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 100.270 | + | 74.6381i | 0.802163 | + | 0.597105i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −113.998 | −0.897619 | −0.448810 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448810 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 35.7976 | 0.277501 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −35.7036 | −0.272547 | −0.136273 | − | 0.990671i | \(-0.543513\pi\) | ||||
−0.136273 | + | 0.990671i | \(0.543513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 109.752 | 0.825201 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −96.3988 | − | 87.4733i | −0.714065 | − | 0.647951i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 157.165i | 1.14719i | 0.819139 | + | 0.573595i | \(0.194452\pi\) | ||||
−0.819139 | + | 0.573595i | \(0.805548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38.7762 | −0.278965 | −0.139483 | − | 0.990225i | \(-0.544544\pi\) | ||||
−0.139483 | + | 0.990225i | \(0.544544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 55.3914i | 0.392847i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −173.564 | −1.21373 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −157.905 | − | 143.284i | −1.08900 | − | 0.988168i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.12661i | 0.0552831i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 50.5027i | 0.338944i | 0.985535 | + | 0.169472i | \(0.0542063\pi\) | ||||
−0.985535 | + | 0.169472i | \(0.945794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 280.148i | − | 1.85529i | −0.373467 | − | 0.927643i | \(-0.621831\pi\) | ||
0.373467 | − | 0.927643i | \(-0.378169\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.3883i | 0.159401i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 103.628 | + | 94.0331i | 0.668567 | + | 0.606665i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 109.217 | 0.695650 | 0.347825 | − | 0.937560i | \(-0.386920\pi\) | ||||
0.347825 | + | 0.937560i | \(0.386920\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 153.581i | 0.965917i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 182.271 | 1.13212 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 312.727i | 1.91857i | 0.282438 | + | 0.959286i | \(0.408857\pi\) | ||||
−0.282438 | + | 0.959286i | \(0.591143\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −90.0008 | − | 81.6677i | −0.545459 | − | 0.494956i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −163.812 | −0.980913 | −0.490456 | − | 0.871466i | \(-0.663170\pi\) | ||||
−0.490456 | + | 0.871466i | \(0.663170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.9778 | −0.0886262 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −89.5732 | −0.523820 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −120.423 | −0.696087 | −0.348043 | − | 0.937478i | \(-0.613154\pi\) | ||||
−0.348043 | + | 0.937478i | \(0.613154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.7399 | + | 182.298i | 0.101371 | + | 1.04171i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 111.841i | 0.631871i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 234.996 | 1.31283 | 0.656413 | − | 0.754401i | \(-0.272073\pi\) | ||||
0.656413 | + | 0.754401i | \(0.272073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 51.8066i | 0.286224i | 0.989706 | + | 0.143112i | \(0.0457109\pi\) | ||||
−0.989706 | + | 0.143112i | \(0.954289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 76.7211 | 0.419241 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.8865 | − | 46.1604i | 0.226413 | − | 0.249516i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 57.0420i | 0.305037i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 190.735i | − | 1.00918i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 259.662i | − | 1.35949i | −0.733450 | − | 0.679744i | \(-0.762091\pi\) | ||
0.733450 | − | 0.679744i | \(-0.237909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 246.349i | − | 1.27642i | −0.769861 | − | 0.638211i | \(-0.779675\pi\) | ||
0.769861 | − | 0.638211i | \(-0.220325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 79.8674 | + | 72.4726i | 0.409576 | + | 0.371654i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −176.610 | −0.896499 | −0.448249 | − | 0.893908i | \(-0.647952\pi\) | ||||
−0.448249 | + | 0.893908i | \(0.647952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 133.272i | 0.669711i | 0.942270 | + | 0.334855i | \(0.108687\pi\) | ||||
−0.942270 | + | 0.334855i | \(0.891313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 147.895 | 0.735795 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 312.431i | − | 1.53907i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 253.567 | − | 279.440i | 1.23691 | − | 1.36312i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −148.759 | −0.718645 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −209.503 | −1.00241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −93.5098 | −0.443174 | −0.221587 | − | 0.975141i | \(-0.571124\pi\) | ||||
−0.221587 | + | 0.975141i | \(0.571124\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 78.1416 | 0.366862 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 76.2668 | + | 69.2054i | 0.354729 | + | 0.321885i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 205.039i | 0.944880i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 90.1476 | 0.411633 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 50.6195i | − | 0.229048i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −275.006 | −1.23321 | −0.616606 | − | 0.787272i | \(-0.711493\pi\) | ||||
−0.616606 | + | 0.787272i | \(0.711493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.4783 | − | 148.782i | −0.0643482 | − | 0.661252i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 279.388i | − | 1.23078i | −0.788222 | − | 0.615391i | \(-0.788998\pi\) | ||
0.788222 | − | 0.615391i | \(-0.211002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 74.4214i | 0.324984i | 0.986710 | + | 0.162492i | \(0.0519532\pi\) | ||||
−0.986710 | + | 0.162492i | \(0.948047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 178.076i | − | 0.770893i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 345.559i | − | 1.48308i | −0.670907 | − | 0.741542i | \(-0.734095\pi\) | ||
0.670907 | − | 0.741542i | \(-0.265905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107.085 | + | 118.011i | −0.455680 | + | 0.502176i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 252.235 | 1.06428 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.25176i | 0.0136057i | 0.999977 | + | 0.00680284i | \(0.00216543\pi\) | ||||
−0.999977 | + | 0.00680284i | \(0.997835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −395.249 | −1.64004 | −0.820018 | − | 0.572337i | \(-0.806037\pi\) | ||||
−0.820018 | + | 0.572337i | \(0.806037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 249.197i | 1.02550i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.7107 | + | 17.3137i | −0.0641252 | + | 0.0706683i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 185.915 | 0.752691 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 174.993 | 0.702783 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −366.962 | −1.46200 | −0.730999 | − | 0.682378i | \(-0.760946\pi\) | ||||
−0.730999 | + | 0.682378i | \(0.760946\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −347.934 | −1.37523 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.8182 | − | 26.2485i | 0.0934046 | − | 0.102935i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 354.526i | − | 1.37948i | −0.724058 | − | 0.689739i | \(-0.757725\pi\) | ||
0.724058 | − | 0.689739i | \(-0.242275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 91.3334 | 0.352639 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 254.989i | 0.976969i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 380.361 | 1.44624 | 0.723120 | − | 0.690722i | \(-0.242707\pi\) | ||||
0.723120 | + | 0.690722i | \(0.242707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −296.908 | + | 327.204i | −1.12041 | + | 1.23473i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 26.9354i | − | 0.100882i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 130.893i | 0.486591i | 0.969952 | + | 0.243295i | \(0.0782284\pi\) | ||||
−0.969952 | + | 0.243295i | \(0.921772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1591i | 0.107598i | 0.998552 | + | 0.0537991i | \(0.0171330\pi\) | ||||
−0.998552 | + | 0.0537991i | \(0.982867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 158.026i | 0.578851i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −33.8634 | − | 347.986i | −0.123140 | − | 1.26540i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −239.772 | −0.865601 | −0.432801 | − | 0.901490i | \(-0.642475\pi\) | ||||
−0.432801 | + | 0.901490i | \(0.642475\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 167.341i | − | 0.599789i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −38.7771 | −0.137997 | −0.0689984 | − | 0.997617i | \(-0.521980\pi\) | ||||
−0.0689984 | + | 0.997617i | \(0.521980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 105.503i | − | 0.372804i | −0.982474 | − | 0.186402i | \(-0.940317\pi\) | ||
0.982474 | − | 0.186402i | \(-0.0596826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 96.4051 | + | 87.4790i | 0.338263 | + | 0.306944i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 552.902 | 1.92649 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 272.364 | 0.942435 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.856230 | 0.00294237 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 116.858 | 0.398832 | 0.199416 | − | 0.979915i | \(-0.436096\pi\) | ||||
0.199416 | + | 0.979915i | \(0.436096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −216.216 | + | 238.278i | −0.732935 | + | 0.807721i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 364.091i | 1.22590i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 308.759 | 1.03264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 150.902i | 0.501336i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.7531 | −0.141099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 163.454 | + | 148.320i | 0.535916 | + | 0.486296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 440.306i | 1.43422i | 0.696960 | + | 0.717110i | \(0.254536\pi\) | ||||
−0.696960 | + | 0.717110i | \(0.745464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 78.5658i | 0.254258i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160.201i | 0.515115i | 0.966263 | + | 0.257558i | \(0.0829178\pi\) | ||||
−0.966263 | + | 0.257558i | \(0.917082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 529.200i | − | 1.69073i | −0.534186 | − | 0.845367i | \(-0.679382\pi\) | ||
0.534186 | − | 0.845367i | \(-0.320618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 147.190 | − | 162.209i | 0.467271 | − | 0.514949i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −428.110 | −1.35051 | −0.675253 | − | 0.737586i | \(-0.735965\pi\) | ||||
−0.675253 | + | 0.737586i | \(0.735965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 596.394i | 1.86957i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 197.538 | 0.615385 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 61.1010i | − | 0.189167i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.0507 | + | 308.805i | 0.0924636 | + | 0.950171i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 57.3688 | 0.175440 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −233.498 | −0.709721 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −649.786 | −1.96310 | −0.981550 | − | 0.191204i | \(-0.938761\pi\) | ||||
−0.981550 | + | 0.191204i | \(0.938761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −74.5412 | −0.223847 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 315.090 | + | 285.916i | 0.940567 | + | 0.853481i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 296.274i | 0.879152i | 0.898205 | + | 0.439576i | \(0.144871\pi\) | ||||
−0.898205 | + | 0.439576i | \(0.855129\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −375.391 | −1.10735 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 391.395i | − | 1.14779i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 324.736 | 0.946751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 160.106 | + | 145.282i | 0.464074 | + | 0.421106i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 510.003i | 1.46975i | 0.678203 | + | 0.734874i | \(0.262759\pi\) | ||||
−0.678203 | + | 0.734874i | \(0.737241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 380.141i | 1.08923i | 0.838686 | + | 0.544615i | \(0.183324\pi\) | ||||
−0.838686 | + | 0.544615i | \(0.816676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 323.098i | − | 0.920506i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 171.150i | 0.484844i | 0.970171 | + | 0.242422i | \(0.0779419\pi\) | ||||
−0.970171 | + | 0.242422i | \(0.922058\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 166.481 | + | 151.066i | 0.468959 | + | 0.425539i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 51.9355 | 0.145478 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 418.429i | 1.16554i | 0.812637 | + | 0.582770i | \(0.198031\pi\) | ||||
−0.812637 | + | 0.582770i | \(0.801969\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −136.589 | −0.378363 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 129.629i | 0.357105i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 192.059 | + | 174.277i | 0.526190 | + | 0.477471i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 304.286 | 0.829118 | 0.414559 | − | 0.910023i | \(-0.363936\pi\) | ||||
0.414559 | + | 0.910023i | \(0.363936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −451.247 | −1.22289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −647.408 | −1.74504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −184.208 | −0.493856 | −0.246928 | − | 0.969034i | \(-0.579421\pi\) | ||||
−0.246928 | + | 0.969034i | \(0.579421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −129.721 | + | 174.269i | −0.345922 | + | 0.464718i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 529.245i | − | 1.40383i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −180.181 | −0.475410 | −0.237705 | − | 0.971337i | \(-0.576395\pi\) | ||||
−0.237705 | + | 0.971337i | \(0.576395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 198.127i | − | 0.520019i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −67.9402 | −0.177390 | −0.0886948 | − | 0.996059i | \(-0.528270\pi\) | ||||
−0.0886948 | + | 0.996059i | \(0.528270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 344.264 | − | 379.391i | 0.894192 | − | 0.985432i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 123.158i | − | 0.318237i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 547.634i | − | 1.40780i | −0.710299 | − | 0.703900i | \(-0.751440\pi\) | ||
0.710299 | − | 0.703900i | \(-0.248560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 101.474i | − | 0.259524i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 62.0527i | − | 0.157895i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 537.387 | + | 487.631i | 1.36047 | + | 1.23451i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 102.144 | 0.257289 | 0.128644 | − | 0.991691i | \(-0.458937\pi\) | ||||
0.128644 | + | 0.991691i | \(0.458937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 190.748i | 0.478065i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −260.718 | −0.650170 | −0.325085 | − | 0.945685i | \(-0.605393\pi\) | ||||
−0.325085 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 347.327i | 0.861853i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −28.7859 | + | 31.7231i | −0.0710763 | + | 0.0783286i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −174.345 | −0.428365 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 237.138 | 0.579800 | 0.289900 | − | 0.957057i | \(-0.406378\pi\) | ||||
0.289900 | + | 0.957057i | \(0.406378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −273.152 | −0.664604 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −471.458 | −1.14155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 372.823 | + | 338.303i | 0.898368 | + | 0.815189i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 67.3928i | − | 0.161613i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −378.980 | −0.904487 | −0.452244 | − | 0.891894i | \(-0.649376\pi\) | ||||
−0.452244 | + | 0.891894i | \(0.649376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 514.293i | − | 1.22160i | −0.791786 | − | 0.610799i | \(-0.790848\pi\) | ||
0.791786 | − | 0.610799i | \(-0.209152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 190.568 | 0.450515 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 101.489 | − | 9.87618i | 0.238798 | − | 0.0232381i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 323.412i | 0.757405i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 301.653i | − | 0.703155i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 747.351i | − | 1.73399i | −0.498315 | − | 0.866996i | \(-0.666048\pi\) | ||
0.498315 | − | 0.866996i | \(-0.333952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 604.587i | 1.39628i | 0.715963 | + | 0.698138i | \(0.245988\pi\) | ||||
−0.715963 | + | 0.698138i | \(0.754012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 249.027 | − | 274.437i | 0.572477 | − | 0.630890i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 372.692 | 0.852843 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 560.191i | 1.27606i | 0.770010 | + | 0.638031i | \(0.220251\pi\) | ||||
−0.770010 | + | 0.638031i | \(0.779749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 27.9587 | 0.0633984 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 63.4566i | 0.143243i | 0.997432 | + | 0.0716215i | \(0.0228174\pi\) | ||||
−0.997432 | + | 0.0716215i | \(0.977183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.0726 | − | 57.3859i | 0.117017 | − | 0.128957i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −87.7734 | −0.196361 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 684.142 | 1.52370 | 0.761851 | − | 0.647753i | \(-0.224291\pi\) | ||||
0.761851 | + | 0.647753i | \(0.224291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1055.42 | −2.34019 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 486.896 | 1.07483 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −305.503 | + | 336.675i | −0.671434 | + | 0.739945i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 98.0585i | − | 0.214570i | −0.994228 | − | 0.107285i | \(-0.965784\pi\) | ||
0.994228 | − | 0.107285i | \(-0.0342157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −106.186 | −0.231343 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 261.156i | 0.566499i | 0.959046 | + | 0.283249i | \(0.0914124\pi\) | ||||
−0.959046 | + | 0.283249i | \(0.908588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 485.876 | 1.04941 | 0.524704 | − | 0.851285i | \(-0.324176\pi\) | ||||
0.524704 | + | 0.851285i | \(0.324176\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −163.429 | + | 180.105i | −0.351460 | + | 0.387322i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 95.7017i | 0.204929i | 0.994737 | + | 0.102464i | \(0.0326727\pi\) | ||||
−0.994737 | + | 0.102464i | \(0.967327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 623.440i | 1.32930i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 189.818i | 0.403012i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 288.054i | − | 0.608994i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.2731 | + | 372.748i | 0.0763644 | + | 0.784733i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 528.378 | 1.10771 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 521.584i | − | 1.08890i | −0.838793 | − | 0.544451i | \(-0.816738\pi\) | ||
0.838793 | − | 0.544451i | \(-0.183262\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154.715 | 0.321652 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 316.786i | 0.655872i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.82420 | + | 1.65530i | 0.00376123 | + | 0.00341298i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 176.883 | 0.363209 | 0.181604 | − | 0.983372i | \(-0.441871\pi\) | ||||
0.181604 | + | 0.983372i | \(0.441871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −543.518 | −1.11149 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 196.467 | 0.400137 | 0.200068 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200068 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −173.937 | −0.352813 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −280.969 | + | 309.638i | −0.567614 | + | 0.625531i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 329.400i | 0.662776i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 220.261 | 0.441406 | 0.220703 | − | 0.975341i | \(-0.429165\pi\) | ||||
0.220703 | + | 0.975341i | \(0.429165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 284.705i | − | 0.568274i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −939.069 | −1.86694 | −0.933468 | − | 0.358661i | \(-0.883233\pi\) | ||||
−0.933468 | + | 0.358661i | \(0.883233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −91.0855 | − | 82.6520i | −0.180367 | − | 0.163667i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 26.0314i | − | 0.0513440i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 288.731i | − | 0.567251i | −0.958935 | − | 0.283625i | \(-0.908463\pi\) | ||
0.958935 | − | 0.283625i | \(-0.0915372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 380.010i | 0.743660i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 390.000i | − | 0.760233i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −151.886 | + | 167.384i | −0.294925 | + | 0.325018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 445.720 | 0.862128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 209.294i | − | 0.403265i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −674.737 | −1.29508 | −0.647541 | − | 0.762031i | \(-0.724202\pi\) | ||||
−0.647541 | + | 0.762031i | \(0.724202\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 447.061i | 0.854801i | 0.904063 | + | 0.427400i | \(0.140570\pi\) | ||||
−0.904063 | + | 0.427400i | \(0.859430\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −316.834 | + | 30.8319i | −0.603492 | + | 0.0587275i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 114.149 | 0.216602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 89.9523 | 0.170042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 384.777 | 0.724628 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 936.592 | 1.75721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 420.856 | + | 381.889i | 0.786646 | + | 0.713811i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 408.422i | 0.760562i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 65.3927 | 0.121322 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 229.726i | 0.424632i | 0.977201 | + | 0.212316i | \(0.0681006\pi\) | ||||
−0.977201 | + | 0.212316i | \(0.931899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −90.0395 | −0.165819 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 122.224 | + | 110.908i | 0.224264 | + | 0.203500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 218.904i | − | 0.400190i | −0.979776 | − | 0.200095i | \(-0.935875\pi\) | ||
0.979776 | − | 0.200095i | \(-0.0641251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 263.951i | − | 0.480784i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 638.833i | − | 1.15941i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1063.28i | 1.92275i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 80.2266 | + | 72.7985i | 0.144552 | + | 0.131168i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −193.072 | −0.346628 | −0.173314 | − | 0.984867i | \(-0.555448\pi\) | ||||
−0.173314 | + | 0.984867i | \(0.555448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 255.622i | 0.457284i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −99.1387 | −0.176718 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 184.168i | − | 0.327119i | −0.986533 | − | 0.163559i | \(-0.947702\pi\) | ||
0.986533 | − | 0.163559i | \(-0.0522975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −799.770 | − | 725.720i | −1.41552 | − | 1.28446i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −62.7676 | −0.110701 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −80.6773 | −0.141788 | −0.0708940 | − | 0.997484i | \(-0.522585\pi\) | ||||
−0.0708940 | + | 0.997484i | \(0.522585\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −905.670 | −1.58611 | −0.793056 | − | 0.609148i | \(-0.791511\pi\) | ||||
−0.793056 | + | 0.609148i | \(0.791511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 451.291 | 0.787594 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 60.2409 | + | 619.045i | 0.104767 | + | 1.07660i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 557.704i | − | 0.966557i | −0.875467 | − | 0.483279i | \(-0.839446\pi\) | ||
0.875467 | − | 0.483279i | \(-0.160554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 428.154 | 0.739471 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 737.670i | 1.26966i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1235.82 | 2.11977 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 249.334 | − | 274.775i | 0.426212 | − | 0.469701i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 188.682i | 0.321435i | 0.987000 | + | 0.160717i | \(0.0513808\pi\) | ||||
−0.987000 | + | 0.160717i | \(0.948619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 419.246i | 0.711793i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 306.948i | − | 0.519370i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 676.550i | 1.14089i | 0.821335 | + | 0.570446i | \(0.193230\pi\) | ||||
−0.821335 | + | 0.570446i | \(0.806770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 110.649 | + | 100.404i | 0.185964 | + | 0.168746i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −231.627 | −0.387985 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 565.309i | 0.943755i | 0.881664 | + | 0.471877i | \(0.156424\pi\) | ||||
−0.881664 | + | 0.471877i | \(0.843576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 891.353 | 1.48312 | 0.741559 | − | 0.670888i | \(-0.234087\pi\) | ||||
0.741559 | + | 0.670888i | \(0.234087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 508.816i | − | 0.843808i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −250.604 | + | 276.175i | −0.414221 | + | 0.456487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −112.539 | −0.185402 | −0.0927011 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0927011 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 543.004 | 0.891632 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −395.536 | −0.647358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −609.554 | −0.994379 | −0.497190 | − | 0.867642i | \(-0.665635\pi\) | ||||
−0.497190 | + | 0.867642i | \(0.665635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 485.665 | + | 440.698i | 0.789699 | + | 0.716582i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 599.080i | − | 0.970957i | −0.874249 | − | 0.485479i | \(-0.838645\pi\) | ||
0.874249 | − | 0.485479i | \(-0.161355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −358.707 | −0.579494 | −0.289747 | − | 0.957103i | \(-0.593571\pi\) | ||||
−0.289747 | + | 0.957103i | \(0.593571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 647.695i | − | 1.04299i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 113.544 | 0.182254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −613.274 | + | 120.500i | −0.981238 | + | 0.192800i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 364.115i | − | 0.580726i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 50.8472i | − | 0.0808381i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 827.851i | − | 1.31197i | −0.754776 | − | 0.655983i | \(-0.772254\pi\) | ||
0.754776 | − | 0.655983i | \(-0.227746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 162.519i | − | 0.256745i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 383.027 | − | 422.110i | 0.603193 | − | 0.664740i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −58.0300 | −0.0910989 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 268.837i | − | 0.420716i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 747.305 | 1.16584 | 0.582921 | − | 0.812529i | \(-0.301910\pi\) | ||||
0.582921 | + | 0.812529i | \(0.301910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 209.992i | 0.326582i | 0.986578 | + | 0.163291i | \(0.0522110\pi\) | ||||
−0.986578 | + | 0.163291i | \(0.947789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −120.278 | + | 132.551i | −0.186478 | + | 0.205506i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −703.401 | −1.08717 | −0.543586 | − | 0.839353i | \(-0.682934\pi\) | ||||
−0.543586 | + | 0.839353i | \(0.682934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 899.957 | 1.38668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −356.356 | −0.547399 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 235.011 | 0.359894 | 0.179947 | − | 0.983676i | \(-0.442407\pi\) | ||||
0.179947 | + | 0.983676i | \(0.442407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 119.963 | − | 132.203i | 0.183149 | − | 0.201837i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 310.143i | − | 0.472059i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 478.498 | 0.726097 | 0.363049 | − | 0.931770i | \(-0.381736\pi\) | ||||
0.363049 | + | 0.931770i | \(0.381736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 714.347i | 1.08071i | 0.841438 | + | 0.540354i | \(0.181709\pi\) | ||||
−0.841438 | + | 0.540354i | \(0.818291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 87.9764 | 0.132694 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −368.761 | + | 406.388i | −0.554528 | + | 0.611110i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1060.95i | − | 1.59063i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 477.959i | − | 0.714439i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 617.355i | − | 0.920052i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 54.3728i | − | 0.0807917i | −0.999184 | − | 0.0403958i | \(-0.987138\pi\) | ||
0.999184 | − | 0.0403958i | \(-0.0128619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 647.792 | − | 63.0383i | 0.959691 | − | 0.0933901i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1035.13 | −1.52899 | −0.764495 | − | 0.644629i | \(-0.777012\pi\) | ||||
−0.764495 | + | 0.644629i | \(0.777012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.60937i | 0.00531572i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 485.574 | 0.713031 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 99.8208i | − | 0.146151i | −0.997326 | − | 0.0730753i | \(-0.976719\pi\) | ||
0.997326 | − | 0.0730753i | \(-0.0232813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −581.950 | − | 528.068i | −0.849562 | − | 0.770902i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −129.344 | −0.188274 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1096.68 | −1.59170 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1201.63 | −1.73898 | −0.869489 | − | 0.493952i | \(-0.835552\pi\) | ||||
−0.869489 | + | 0.493952i | \(0.835552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −612.652 | −0.884057 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 130.286 | − | 143.580i | 0.187462 | − | 0.206590i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 307.812i | − | 0.441624i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 600.579 | 0.859197 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 357.520i | 0.510014i | 0.966939 | + | 0.255007i | \(0.0820777\pi\) | ||||
−0.966939 | + | 0.255007i | \(0.917922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 186.751 | 0.265648 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −205.103 | − | 186.113i | −0.290926 | − | 0.263990i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 180.222i | − | 0.254912i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 199.220i | 0.280988i | 0.990082 | + | 0.140494i | \(0.0448690\pi\) | ||||
−0.990082 | + | 0.140494i | \(0.955131\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 867.788i | − | 1.22052i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 696.266i | 0.976531i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 583.168 | − | 642.672i | 0.815619 | − | 0.898842i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.65154 | −0.00788220 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1102.66i | 1.53360i | 0.641888 | + | 0.766799i | \(0.278152\pi\) | ||||
−0.641888 | + | 0.766799i | \(0.721848\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −331.188 | −0.459345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 686.940i | − | 0.950125i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1061.11 | − | 103.259i | 1.46359 | − | 0.142426i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1126.09 | 1.54895 | 0.774476 | − | 0.632603i | \(-0.218014\pi\) | ||||
0.774476 | + | 0.632603i | \(0.218014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −355.996 | −0.488335 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 84.0103 | 0.114925 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1351.90 | 1.84434 | 0.922171 | − | 0.386784i | \(-0.126414\pi\) | ||||
0.922171 | + | 0.386784i | \(0.126414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.0912 | − | 27.3051i | −0.0409404 | − | 0.0371497i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1190.07i | − | 1.61475i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 167.536 | 0.226706 | 0.113353 | − | 0.993555i | \(-0.463841\pi\) | ||||
0.113353 | + | 0.993555i | \(0.463841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 323.119i | 0.436057i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −948.386 | −1.27643 | −0.638214 | − | 0.769859i | \(-0.720326\pi\) | ||||
−0.638214 | + | 0.769859i | \(0.720326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −187.001 | − | 169.687i | −0.251008 | − | 0.227768i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 602.044i | − | 0.805950i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 832.708i | 1.11176i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.4990i | 0.0699055i | 0.999389 | + | 0.0349528i | \(0.0111281\pi\) | ||||
−0.999389 | + | 0.0349528i | \(0.988872\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 637.777i | − | 0.846981i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1037.33 | + | 941.286i | 1.37395 | + | 1.24674i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 654.674 | 0.864827 | 0.432414 | − | 0.901675i | \(-0.357662\pi\) | ||||
0.432414 | + | 0.901675i | \(0.357662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 604.707i | − | 0.796716i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −88.5344 | −0.116340 | −0.0581698 | − | 0.998307i | \(-0.518526\pi\) | ||||
−0.0581698 | + | 0.998307i | \(0.518526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 241.834i | 0.316951i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −90.3050 | − | 81.9438i | −0.118046 | − | 0.107116i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −798.629 | −1.04124 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1308.40 | −1.70144 | −0.850718 | − | 0.525623i | \(-0.823832\pi\) | ||||
−0.850718 | + | 0.525623i | \(0.823832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 616.164 | 0.799175 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −604.591 | −0.782136 | −0.391068 | − | 0.920362i | \(-0.627894\pi\) | ||||
−0.391068 | + | 0.920362i | \(0.627894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −696.370 | + | 67.7656i | −0.898542 | + | 0.0874395i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 158.737i | 0.204295i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1130.53 | 1.45125 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 628.785i | − | 0.805102i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1110.22 | −1.41790 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −366.964 | + | 404.408i | −0.467471 | + | 0.515170i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1375.23i | 1.74743i | 0.486434 | + | 0.873717i | \(0.338297\pi\) | ||||
−0.486434 | + | 0.873717i | \(0.661703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 661.066i | 0.837852i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1582.43i | − | 2.00055i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 547.846i | 0.690852i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −568.678 | − | 516.025i | −0.715318 | − | 0.649088i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 924.699 | 1.16022 | 0.580112 | − | 0.814537i | \(-0.303009\pi\) | ||||
0.580112 | + | 0.814537i | \(0.303009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 129.993i | 0.162695i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −92.6683 | −0.115691 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 725.394i | − | 0.903355i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −612.423 | + | 674.913i | −0.760774 | + | 0.838401i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −227.491 | −0.281897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −241.708 | −0.298774 | −0.149387 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149387 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −61.5266 | −0.0758651 | −0.0379325 | − | 0.999280i | \(-0.512077\pi\) | ||||
−0.0379325 | + | 0.999280i | \(0.512077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.6783 | −0.0623350 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1157.96 | − | 1050.75i | −1.42082 | − | 1.28926i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 308.552i | 0.377664i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 543.672 | 0.663824 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 99.4438i | − | 0.121125i | −0.998164 | − | 0.0605626i | \(-0.980711\pi\) | ||
0.998164 | − | 0.0605626i | \(-0.0192895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −972.951 | −1.18220 | −0.591100 | − | 0.806598i | \(-0.701306\pi\) | ||||
−0.591100 | + | 0.806598i | \(0.701306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 604.797 | − | 58.8544i | 0.733088 | − | 0.0713387i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 364.016i | 0.440164i | 0.975481 | + | 0.220082i | \(0.0706325\pi\) | ||||
−0.975481 | + | 0.220082i | \(0.929368\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1013.84i | − | 1.22296i | −0.791258 | − | 0.611482i | \(-0.790574\pi\) | ||
0.791258 | − | 0.611482i | \(-0.209426\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 416.722i | − | 0.501470i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.0716i | 0.0228951i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 550.403 | − | 606.564i | 0.659165 | − | 0.726424i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 728.599 | 0.870489 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 377.536i | − | 0.449984i | −0.974361 | − | 0.224992i | \(-0.927764\pi\) | ||
0.974361 | − | 0.224992i | \(-0.0722355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −977.571 | −1.16239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 67.3944i | − | 0.0799459i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 50.3249 | − | 55.4598i | 0.0595561 | − | 0.0656330i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −546.442 | −0.645149 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 183.364 | 0.215977 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 310.148 | 0.364451 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −884.533 | −1.03697 | −0.518483 | − | 0.855088i | \(-0.673503\pi\) | ||||
−0.518483 | + | 0.855088i | \(0.673503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 300.962 | − | 331.671i | 0.352002 | − | 0.387919i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1036.74i | − | 1.20974i | −0.796326 | − | 0.604868i | \(-0.793226\pi\) | ||
0.796326 | − | 0.604868i | \(-0.206774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −658.011 | −0.766019 | −0.383010 | − | 0.923744i | \(-0.625112\pi\) | ||||
−0.383010 | + | 0.923744i | \(0.625112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 960.941i | 1.11607i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −496.875 | −0.575753 | −0.287877 | − | 0.957668i | \(-0.592949\pi\) | ||||
−0.287877 | + | 0.957668i | \(0.592949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 404.616 | − | 445.902i | 0.467764 | − | 0.515493i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 473.367i | 0.545982i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2029.67i | − | 2.33564i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1056.08i | 1.21249i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.94577i | − | 0.00337430i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −734.619 | − | 546.827i | −0.839565 | − | 0.624946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −288.006 | −0.328399 | −0.164199 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164199 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 203.098i | 0.231056i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 411.220 | 0.466765 | 0.233382 | − | 0.972385i | \(-0.425021\pi\) | ||||
0.233382 | + | 0.972385i | \(0.425021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 382.459i | − | 0.433136i | −0.976268 | − | 0.216568i | \(-0.930514\pi\) | ||
0.976268 | − | 0.216568i | \(-0.0694863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −414.125 | − | 375.782i | −0.467938 | − | 0.424612i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.7959 | −0.0234452 | −0.0117226 | − | 0.999931i | \(-0.503732\pi\) | ||||
−0.0117226 | + | 0.999931i | \(0.503732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 835.190 | 0.939472 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 119.816 | 0.134473 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −477.437 | −0.534644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −789.576 | + | 870.142i | −0.882208 | + | 0.972226i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 536.622i | 0.598241i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1193.47 | 1.32755 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 360.425i | 0.400028i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −262.267 | −0.290440 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −191.829 | − | 174.068i | −0.211966 | − | 0.192340i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 376.924i | − | 0.415572i | −0.978174 | − | 0.207786i | \(-0.933374\pi\) | ||
0.978174 | − | 0.207786i | \(-0.0666258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 147.087i | 0.161812i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1143.44i | − | 1.25515i | −0.778555 | − | 0.627577i | \(-0.784047\pi\) | ||
0.778555 | − | 0.627577i | \(-0.215953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1408.12i | − | 1.54230i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −257.780 | + | 284.083i | −0.281726 | + | 0.310473i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 261.578 | 0.285254 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 47.1893i | − | 0.0513485i | −0.999670 | − | 0.0256743i | \(-0.991827\pi\) | ||
0.999670 | − | 0.0256743i | \(-0.00817327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −765.248 | −0.830889 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 557.989i | 0.604538i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.1858 | + | 310.194i | 0.0326333 | + | 0.335345i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 270.297 | 0.291582 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 226.732 | 0.244061 | 0.122030 | − | 0.992526i | \(-0.461059\pi\) | ||||
0.122030 | + | 0.992526i | \(0.461059\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −70.0460 | −0.0752374 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −278.428 | −0.298423 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −211.215 | − | 191.659i | −0.225898 | − | 0.204983i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.3501i | 0.0580044i | 0.999579 | + | 0.0290022i | \(0.00923299\pi\) | ||||
−0.999579 | + | 0.0290022i | \(0.990767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 919.746 | 0.979495 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 787.840i | − | 0.837237i | −0.908162 | − | 0.418619i | \(-0.862514\pi\) | ||
0.908162 | − | 0.418619i | \(-0.137486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1877.53 | 1.99102 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 706.254 | + | 640.863i | 0.747359 | + | 0.678162i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1718.24i | − | 1.81440i | −0.420701 | − | 0.907199i | \(-0.638216\pi\) | ||
0.420701 | − | 0.907199i | \(-0.361784\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 643.721i | 0.678315i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 744.053i | − | 0.782390i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 968.692i | 1.01647i | 0.861220 | + | 0.508233i | \(0.169701\pi\) | ||||
−0.861220 | + | 0.508233i | \(0.830299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 961.476 | + | 872.454i | 1.00678 | + | 0.913564i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1036.53 | −1.08310 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1151.45i | − | 1.20068i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 177.762 | 0.184976 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 679.609i | − | 0.705721i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 912.181 | + | 827.724i | 0.945266 | + | 0.857745i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 527.058 | 0.545044 | 0.272522 | − | 0.962150i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 106.193 | 0.109591 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −591.749 | −0.609422 | −0.304711 | − | 0.952445i | \(-0.598560\pi\) | ||||
−0.304711 | + | 0.952445i | \(0.598560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 284.089 | 0.291972 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −536.702 | + | 52.2279i | −0.550464 | + | 0.0535671i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 590.566i | 0.604469i | 0.953234 | + | 0.302234i | \(0.0977325\pi\) | ||||
−0.953234 | + | 0.302234i | \(0.902267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −216.742 | −0.221392 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 197.371i | − | 0.201194i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1128.26 | −1.14777 | −0.573885 | − | 0.818936i | \(-0.694564\pi\) | ||||
−0.573885 | + | 0.818936i | \(0.694564\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 593.403 | − | 653.952i | 0.602440 | − | 0.663910i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 405.819i | − | 0.411164i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 512.430i | 0.518129i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 504.911i | − | 0.509496i | −0.967007 | − | 0.254748i | \(-0.918007\pi\) | ||
0.967007 | − | 0.254748i | \(-0.0819926\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1129.32i | − | 1.13729i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −493.481 | − | 447.790i | −0.495960 | − | 0.450040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1166.48 | 1.16999 | 0.584996 | − | 0.811036i | \(-0.301096\pi\) | ||||
0.584996 | + | 0.811036i | \(0.301096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 324.551i | − | 0.324875i |
(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 | 1280.3.e.k.639.4 | 24 | ||
4.3 | odd | 2 | 1280.3.e.l.639.21 | 24 | |||
5.4 | even | 2 | inner | 1280.3.e.k.639.21 | 24 | ||
8.3 | odd | 2 | inner | 1280.3.e.k.639.22 | 24 | ||
8.5 | even | 2 | 1280.3.e.l.639.3 | 24 | |||
16.3 | odd | 4 | 640.3.h.a.639.15 | yes | 24 | ||
16.5 | even | 4 | 640.3.h.b.639.15 | yes | 24 | ||
16.11 | odd | 4 | 640.3.h.b.639.10 | yes | 24 | ||
16.13 | even | 4 | 640.3.h.a.639.10 | yes | 24 | ||
20.19 | odd | 2 | 1280.3.e.l.639.4 | 24 | |||
40.19 | odd | 2 | inner | 1280.3.e.k.639.3 | 24 | ||
40.29 | even | 2 | 1280.3.e.l.639.22 | 24 | |||
80.19 | odd | 4 | 640.3.h.a.639.9 | ✓ | 24 | ||
80.29 | even | 4 | 640.3.h.a.639.16 | yes | 24 | ||
80.59 | odd | 4 | 640.3.h.b.639.16 | yes | 24 | ||
80.69 | even | 4 | 640.3.h.b.639.9 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.h.a.639.9 | ✓ | 24 | 80.19 | odd | 4 | ||
640.3.h.a.639.10 | yes | 24 | 16.13 | even | 4 | ||
640.3.h.a.639.15 | yes | 24 | 16.3 | odd | 4 | ||
640.3.h.a.639.16 | yes | 24 | 80.29 | even | 4 | ||
640.3.h.b.639.9 | yes | 24 | 80.69 | even | 4 | ||
640.3.h.b.639.10 | yes | 24 | 16.11 | odd | 4 | ||
640.3.h.b.639.15 | yes | 24 | 16.5 | even | 4 | ||
640.3.h.b.639.16 | yes | 24 | 80.59 | odd | 4 | ||
1280.3.e.k.639.3 | 24 | 40.19 | odd | 2 | inner | ||
1280.3.e.k.639.4 | 24 | 1.1 | even | 1 | trivial | ||
1280.3.e.k.639.21 | 24 | 5.4 | even | 2 | inner | ||
1280.3.e.k.639.22 | 24 | 8.3 | odd | 2 | inner | ||
1280.3.e.l.639.3 | 24 | 8.5 | even | 2 | |||
1280.3.e.l.639.4 | 24 | 20.19 | odd | 2 | |||
1280.3.e.l.639.21 | 24 | 4.3 | odd | 2 | |||
1280.3.e.l.639.22 | 24 | 40.29 | even | 2 |