Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(1349,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1350.1349");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.b (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: | \(36.7848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1349.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.1349 |
Dual form | 1350.3.b.f.1349.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 8.24264i | − 1.17752i | −0.808308 | − | 0.588760i | \(-0.799616\pi\) | ||||
0.808308 | − | 0.588760i | \(-0.200384\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000i | 0.272727i | 0.990659 | + | 0.136364i | \(0.0435416\pi\) | ||||
−0.990659 | + | 0.136364i | \(0.956458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.4853i | − 1.03733i | −0.854978 | − | 0.518665i | \(-0.826429\pi\) | ||||
0.854978 | − | 0.518665i | \(-0.173571\pi\) | |||||||
\(14\) | 11.6569i | 0.832632i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 16.2426 | 0.955449 | 0.477725 | − | 0.878510i | \(-0.341462\pi\) | ||||
0.477725 | + | 0.878510i | \(0.341462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.9706 | −1.31424 | −0.657120 | − | 0.753786i | \(-0.728226\pi\) | ||||
−0.657120 | + | 0.753786i | \(0.728226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.24264i | − 0.192847i | ||||||||
\(23\) | 23.4853 | 1.02110 | 0.510550 | − | 0.859848i | \(-0.329442\pi\) | ||||
0.510550 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 19.0711i | 0.733503i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 16.4853i | − 0.588760i | ||||||||
\(29\) | − 40.9706i | − 1.41278i | −0.707824 | − | 0.706389i | \(-0.750323\pi\) | ||||
0.707824 | − | 0.706389i | \(-0.249677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.2132 | −0.426232 | −0.213116 | − | 0.977027i | \(-0.568361\pi\) | ||||
−0.213116 | + | 0.977027i | \(0.568361\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −22.9706 | −0.675605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 14.4558i | − 0.390698i | −0.980734 | − | 0.195349i | \(-0.937416\pi\) | ||||
0.980734 | − | 0.195349i | \(-0.0625840\pi\) | |||||||
\(38\) | 35.3137 | 0.929308 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.7868i | 0.360654i | 0.983607 | + | 0.180327i | \(0.0577155\pi\) | ||||
−0.983607 | + | 0.180327i | \(0.942284\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.9706i | 1.04583i | 0.852386 | + | 0.522914i | \(0.175155\pi\) | ||||
−0.852386 | + | 0.522914i | \(0.824845\pi\) | |||||||
\(44\) | 6.00000i | 0.136364i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.2132 | −0.722026 | ||||||||
\(47\) | 23.4853 | 0.499687 | 0.249843 | − | 0.968286i | \(-0.419621\pi\) | ||||
0.249843 | + | 0.968286i | \(0.419621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.9411 | −0.386554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 26.9706i | − 0.518665i | ||||||||
\(53\) | −74.9117 | −1.41343 | −0.706714 | − | 0.707499i | \(-0.749823\pi\) | ||||
−0.706714 | + | 0.707499i | \(0.749823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.3137i | 0.416316i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 57.9411i | 0.998985i | ||||||||
\(59\) | − 17.0589i | − 0.289133i | −0.989495 | − | 0.144567i | \(-0.953821\pi\) | ||||
0.989495 | − | 0.144567i | \(-0.0461788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.3675 | −1.56340 | −0.781701 | − | 0.623653i | \(-0.785648\pi\) | ||||
−0.781701 | + | 0.623653i | \(0.785648\pi\) | |||||||
\(62\) | 18.6863 | 0.301392 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 81.0955i | − 1.21038i | −0.796081 | − | 0.605190i | \(-0.793097\pi\) | ||||
0.796081 | − | 0.605190i | \(-0.206903\pi\) | |||||||
\(68\) | 32.4853 | 0.477725 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 89.4853i | 1.26036i | 0.776451 | + | 0.630178i | \(0.217018\pi\) | ||||
−0.776451 | + | 0.630178i | \(0.782982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.08831i | − 0.0697029i | −0.999393 | − | 0.0348515i | \(-0.988904\pi\) | ||||
0.999393 | − | 0.0348515i | \(-0.0110958\pi\) | |||||||
\(74\) | 20.4437i | 0.276266i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −49.9411 | −0.657120 | ||||||||
\(77\) | 24.7279 | 0.321142 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.81623 | 0.0229903 | 0.0114952 | − | 0.999934i | \(-0.496341\pi\) | ||||
0.0114952 | + | 0.999934i | \(0.496341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 20.9117i | − 0.255021i | ||||||||
\(83\) | 109.882 | 1.32388 | 0.661941 | − | 0.749556i | \(-0.269733\pi\) | ||||
0.661941 | + | 0.749556i | \(0.269733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 63.5980i | − 0.739511i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 8.48528i | − 0.0964237i | ||||||||
\(89\) | − 40.2426i | − 0.452165i | −0.974108 | − | 0.226082i | \(-0.927408\pi\) | ||||
0.974108 | − | 0.226082i | \(-0.0725918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −111.154 | −1.22148 | ||||||||
\(92\) | 46.9706 | 0.510550 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −33.2132 | −0.353332 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 160.765i | − 1.65737i | −0.559718 | − | 0.828683i | \(-0.689091\pi\) | ||||
0.559718 | − | 0.828683i | \(-0.310909\pi\) | |||||||
\(98\) | 26.7868 | 0.273335 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 171.037i | 1.69343i | 0.532046 | + | 0.846716i | \(0.321424\pi\) | ||||
−0.532046 | + | 0.846716i | \(0.678576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 117.095i | 1.13685i | 0.822735 | + | 0.568425i | \(0.192447\pi\) | ||||
−0.822735 | + | 0.568425i | \(0.807553\pi\) | |||||||
\(104\) | 38.1421i | 0.366751i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 105.941 | 0.999445 | ||||||||
\(107\) | −135.853 | −1.26965 | −0.634826 | − | 0.772655i | \(-0.718928\pi\) | ||||
−0.634826 | + | 0.772655i | \(0.718928\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −188.853 | −1.73259 | −0.866297 | − | 0.499529i | \(-0.833507\pi\) | ||||
−0.866297 | + | 0.499529i | \(0.833507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 32.9706i | − 0.294380i | ||||||||
\(113\) | −69.2132 | −0.612506 | −0.306253 | − | 0.951950i | \(-0.599075\pi\) | ||||
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 81.9411i | − 0.706389i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.1249i | 0.204448i | ||||||||
\(119\) | − 133.882i | − 1.12506i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 112.000 | 0.925620 | ||||||||
\(122\) | 134.870 | 1.10549 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −26.4264 | −0.213116 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 206.919i | − 1.62928i | −0.579965 | − | 0.814641i | \(-0.696934\pi\) | ||||
0.579965 | − | 0.814641i | \(-0.303066\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 155.735i | − 1.18882i | −0.804163 | − | 0.594409i | \(-0.797386\pi\) | ||||
0.804163 | − | 0.594409i | \(-0.202614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 205.823i | 1.54754i | ||||||||
\(134\) | 114.686i | 0.855868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −45.9411 | −0.337802 | ||||||||
\(137\) | −23.1472 | −0.168958 | −0.0844788 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844788 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −61.0955 | −0.439536 | −0.219768 | − | 0.975552i | \(-0.570530\pi\) | ||||
−0.219768 | + | 0.975552i | \(0.570530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 126.551i | − 0.891206i | ||||||||
\(143\) | 40.4558 | 0.282908 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.19596i | 0.0492874i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 28.9117i | − 0.195349i | ||||||||
\(149\) | 140.007i | 0.939645i | 0.882761 | + | 0.469823i | \(0.155682\pi\) | ||||
−0.882761 | + | 0.469823i | \(0.844318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29.0883 | 0.192638 | 0.0963189 | − | 0.995351i | \(-0.469293\pi\) | ||||
0.0963189 | + | 0.995351i | \(0.469293\pi\) | |||||||
\(152\) | 70.6274 | 0.464654 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −34.9706 | −0.227082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 185.706i | − 1.18284i | −0.806364 | − | 0.591419i | \(-0.798568\pi\) | ||||
0.806364 | − | 0.591419i | \(-0.201432\pi\) | |||||||
\(158\) | −2.56854 | −0.0162566 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 193.581i | − 1.20236i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 241.698i | − 1.48281i | −0.671056 | − | 0.741406i | \(-0.734159\pi\) | ||||
0.671056 | − | 0.741406i | \(-0.265841\pi\) | |||||||
\(164\) | 29.5736i | 0.180327i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −155.397 | −0.936126 | ||||||||
\(167\) | −286.279 | −1.71425 | −0.857123 | − | 0.515111i | \(-0.827751\pi\) | ||||
−0.857123 | + | 0.515111i | \(0.827751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8528 | −0.0760522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 89.9411i | 0.522914i | ||||||||
\(173\) | −220.846 | −1.27656 | −0.638282 | − | 0.769802i | \(-0.720355\pi\) | ||||
−0.638282 | + | 0.769802i | \(0.720355\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000i | 0.0681818i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 56.9117i | 0.319729i | ||||||||
\(179\) | − 245.912i | − 1.37381i | −0.726748 | − | 0.686904i | \(-0.758969\pi\) | ||||
0.726748 | − | 0.686904i | \(-0.241031\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −267.309 | −1.47684 | −0.738422 | − | 0.674339i | \(-0.764429\pi\) | ||||
−0.738422 | + | 0.674339i | \(0.764429\pi\) | |||||||
\(182\) | 157.196 | 0.863714 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −66.4264 | −0.361013 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 48.7279i | 0.260577i | ||||||||
\(188\) | 46.9706 | 0.249843 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 346.441i | 1.81383i | 0.421318 | + | 0.906913i | \(0.361568\pi\) | ||||
−0.421318 | + | 0.906913i | \(0.638432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 34.9117i | − 0.180890i | −0.995901 | − | 0.0904448i | \(-0.971171\pi\) | ||||
0.995901 | − | 0.0904448i | \(-0.0288289\pi\) | |||||||
\(194\) | 227.355i | 1.17193i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.8823 | −0.193277 | ||||||||
\(197\) | −189.941 | −0.964168 | −0.482084 | − | 0.876125i | \(-0.660120\pi\) | ||||
−0.482084 | + | 0.876125i | \(0.660120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −137.213 | −0.689514 | −0.344757 | − | 0.938692i | \(-0.612039\pi\) | ||||
−0.344757 | + | 0.938692i | \(0.612039\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 241.882i | − 1.19744i | ||||||||
\(203\) | −337.706 | −1.66357 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 165.598i | − 0.803874i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 53.9411i | − 0.259332i | ||||||||
\(209\) | − 74.9117i | − 0.358429i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −173.706 | −0.823249 | −0.411625 | − | 0.911353i | \(-0.635039\pi\) | ||||
−0.411625 | + | 0.911353i | \(0.635039\pi\) | |||||||
\(212\) | −149.823 | −0.706714 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 192.125 | 0.897780 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 108.912i | 0.501897i | ||||||||
\(218\) | 267.078 | 1.22513 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 219.037i | − 0.991116i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 167.029i | 0.749011i | 0.927225 | + | 0.374505i | \(0.122188\pi\) | ||||
−0.927225 | + | 0.374505i | \(0.877812\pi\) | |||||||
\(224\) | 46.6274i | 0.208158i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 97.8823 | 0.433107 | ||||||||
\(227\) | 295.441 | 1.30150 | 0.650750 | − | 0.759292i | \(-0.274454\pi\) | ||||
0.650750 | + | 0.759292i | \(0.274454\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 189.485 | 0.827447 | 0.413723 | − | 0.910403i | \(-0.364228\pi\) | ||||
0.413723 | + | 0.910403i | \(0.364228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 115.882i | 0.499492i | ||||||||
\(233\) | −139.757 | −0.599817 | −0.299908 | − | 0.953968i | \(-0.596956\pi\) | ||||
−0.299908 | + | 0.953968i | \(0.596956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 34.1177i | − 0.144567i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 189.338i | 0.795538i | ||||||||
\(239\) | − 260.397i | − 1.08953i | −0.838590 | − | 0.544764i | \(-0.816619\pi\) | ||||
0.838590 | − | 0.544764i | \(-0.183381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −85.8528 | −0.356236 | −0.178118 | − | 0.984009i | \(-0.557001\pi\) | ||||
−0.178118 | + | 0.984009i | \(0.557001\pi\) | |||||||
\(242\) | −158.392 | −0.654512 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −190.735 | −0.781701 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 336.735i | 1.36330i | ||||||||
\(248\) | 37.3726 | 0.150696 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 340.529i | − 1.35669i | −0.734744 | − | 0.678345i | \(-0.762698\pi\) | ||||
0.734744 | − | 0.678345i | \(-0.237302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 70.4558i | 0.278482i | ||||||||
\(254\) | 292.627i | 1.15208i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −375.889 | −1.46260 | −0.731302 | − | 0.682053i | \(-0.761087\pi\) | ||||
−0.731302 | + | 0.682053i | \(0.761087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −119.154 | −0.460055 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 220.243i | 0.840621i | ||||||||
\(263\) | 265.014 | 1.00766 | 0.503829 | − | 0.863803i | \(-0.331924\pi\) | ||||
0.503829 | + | 0.863803i | \(0.331924\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 291.078i | − 1.09428i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 162.191i | − 0.605190i | ||||||||
\(269\) | 157.706i | 0.586266i | 0.956072 | + | 0.293133i | \(0.0946979\pi\) | ||||
−0.956072 | + | 0.293133i | \(0.905302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −58.1766 | −0.214674 | −0.107337 | − | 0.994223i | \(-0.534232\pi\) | ||||
−0.107337 | + | 0.994223i | \(0.534232\pi\) | |||||||
\(272\) | 64.9706 | 0.238862 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.7351 | 0.119471 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 170.118i | − 0.614143i | −0.951686 | − | 0.307072i | \(-0.900651\pi\) | ||||
0.951686 | − | 0.307072i | \(-0.0993492\pi\) | |||||||
\(278\) | 86.4020 | 0.310799 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 222.323i | 0.791185i | 0.918426 | + | 0.395592i | \(0.129461\pi\) | ||||
−0.918426 | + | 0.395592i | \(0.870539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 24.9706i | − 0.0882352i | −0.999026 | − | 0.0441176i | \(-0.985952\pi\) | ||||
0.999026 | − | 0.0441176i | \(-0.0140476\pi\) | |||||||
\(284\) | 178.971i | 0.630178i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −57.2132 | −0.200046 | ||||||||
\(287\) | 121.882 | 0.424677 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.1766 | −0.0871163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 10.1766i | − 0.0348515i | ||||||||
\(293\) | −506.683 | −1.72929 | −0.864647 | − | 0.502379i | \(-0.832458\pi\) | ||||
−0.864647 | + | 0.502379i | \(0.832458\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 40.8873i | 0.138133i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 198.000i | − 0.664430i | ||||||||
\(299\) | − 316.706i | − 1.05922i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 370.676 | 1.23148 | ||||||||
\(302\) | −41.1371 | −0.136216 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −99.8823 | −0.328560 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 216.360i | − 0.704757i | −0.935858 | − | 0.352378i | \(-0.885373\pi\) | ||||
0.935858 | − | 0.352378i | \(-0.114627\pi\) | |||||||
\(308\) | 49.4558 | 0.160571 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 14.0437i | − 0.0451567i | −0.999745 | − | 0.0225783i | \(-0.992812\pi\) | ||||
0.999745 | − | 0.0225783i | \(-0.00718752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 372.617i | − 1.19047i | −0.803551 | − | 0.595235i | \(-0.797059\pi\) | ||||
0.803551 | − | 0.595235i | \(-0.202941\pi\) | |||||||
\(314\) | 262.627i | 0.836393i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63247 | 0.0114952 | ||||||||
\(317\) | 60.4996 | 0.190850 | 0.0954252 | − | 0.995437i | \(-0.469579\pi\) | ||||
0.0954252 | + | 0.995437i | \(0.469579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 122.912 | 0.385303 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 273.765i | 0.850200i | ||||||||
\(323\) | −405.588 | −1.25569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 341.813i | 1.04851i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 41.8234i | − 0.127510i | ||||||||
\(329\) | − 193.581i | − 0.588391i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 473.110 | 1.42933 | 0.714667 | − | 0.699465i | \(-0.246578\pi\) | ||||
0.714667 | + | 0.699465i | \(0.246578\pi\) | |||||||
\(332\) | 219.765 | 0.661941 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 404.860 | 1.21216 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 615.529i | 1.82650i | 0.407405 | + | 0.913248i | \(0.366434\pi\) | ||||
−0.407405 | + | 0.913248i | \(0.633566\pi\) | |||||||
\(338\) | 18.1766 | 0.0537770 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 39.6396i | − 0.116245i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 247.765i | − 0.722345i | ||||||||
\(344\) | − 127.196i | − 0.369756i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 312.323 | 0.902667 | ||||||||
\(347\) | 190.294 | 0.548399 | 0.274199 | − | 0.961673i | \(-0.411587\pi\) | ||||
0.274199 | + | 0.961673i | \(0.411587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 273.470 | 0.783582 | 0.391791 | − | 0.920054i | \(-0.371856\pi\) | ||||
0.391791 | + | 0.920054i | \(0.371856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 16.9706i | − 0.0482118i | ||||||||
\(353\) | 562.087 | 1.59232 | 0.796158 | − | 0.605089i | \(-0.206862\pi\) | ||||
0.796158 | + | 0.605089i | \(0.206862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 80.4853i | − 0.226082i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 347.772i | 0.971429i | ||||||||
\(359\) | 256.955i | 0.715753i | 0.933769 | + | 0.357877i | \(0.116499\pi\) | ||||
−0.933769 | + | 0.357877i | \(0.883501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 262.529 | 0.727227 | ||||||||
\(362\) | 378.032 | 1.04429 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −222.309 | −0.610738 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 190.177i | − 0.518192i | −0.965852 | − | 0.259096i | \(-0.916575\pi\) | ||||
0.965852 | − | 0.259096i | \(-0.0834247\pi\) | |||||||
\(368\) | 93.9411 | 0.255275 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 617.470i | 1.66434i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 225.882i | − 0.605582i | −0.953057 | − | 0.302791i | \(-0.902082\pi\) | ||||
0.953057 | − | 0.302791i | \(-0.0979185\pi\) | |||||||
\(374\) | − 68.9117i | − 0.184256i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −66.4264 | −0.176666 | ||||||||
\(377\) | −552.500 | −1.46552 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 479.051 | 1.26399 | 0.631993 | − | 0.774974i | \(-0.282237\pi\) | ||||
0.631993 | + | 0.774974i | \(0.282237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 489.941i | − 1.28257i | ||||||||
\(383\) | 281.662 | 0.735410 | 0.367705 | − | 0.929943i | \(-0.380144\pi\) | ||||
0.367705 | + | 0.929943i | \(0.380144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 49.3726i | 0.127908i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 321.529i | − 0.828683i | ||||||||
\(389\) | − 632.382i | − 1.62566i | −0.582501 | − | 0.812830i | \(-0.697926\pi\) | ||||
0.582501 | − | 0.812830i | \(-0.302074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 381.463 | 0.975609 | ||||||||
\(392\) | 53.5736 | 0.136667 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 268.617 | 0.681770 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 511.632i | 1.28874i | 0.764712 | + | 0.644372i | \(0.222881\pi\) | ||||
−0.764712 | + | 0.644372i | \(0.777119\pi\) | |||||||
\(398\) | 194.049 | 0.487560 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 695.418i | − 1.73421i | −0.498125 | − | 0.867105i | \(-0.665978\pi\) | ||||
0.498125 | − | 0.867105i | \(-0.334022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 178.184i | 0.442143i | ||||||||
\(404\) | 342.073i | 0.846716i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 477.588 | 1.17632 | ||||||||
\(407\) | 43.3675 | 0.106554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 508.411 | 1.24306 | 0.621530 | − | 0.783391i | \(-0.286512\pi\) | ||||
0.621530 | + | 0.783391i | \(0.286512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 234.191i | 0.568425i | ||||||||
\(413\) | −140.610 | −0.340460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 76.2843i | 0.183376i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 105.941i | 0.253448i | ||||||||
\(419\) | 53.6468i | 0.128035i | 0.997949 | + | 0.0640176i | \(0.0203914\pi\) | ||||
−0.997949 | + | 0.0640176i | \(0.979609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 203.749 | 0.483965 | 0.241983 | − | 0.970281i | \(-0.422202\pi\) | ||||
0.241983 | + | 0.970281i | \(0.422202\pi\) | |||||||
\(422\) | 245.657 | 0.582125 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 211.882 | 0.499722 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 786.080i | 1.84094i | ||||||||
\(428\) | −271.706 | −0.634826 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 808.456i | 1.87577i | 0.346950 | + | 0.937884i | \(0.387218\pi\) | ||||
−0.346950 | + | 0.937884i | \(0.612782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 632.706i | 1.46121i | 0.682798 | + | 0.730607i | \(0.260763\pi\) | ||||
−0.682798 | + | 0.730607i | \(0.739237\pi\) | |||||||
\(434\) | − 154.024i | − 0.354895i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −377.706 | −0.866297 | ||||||||
\(437\) | −586.441 | −1.34197 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 41.8305 | 0.0952859 | 0.0476430 | − | 0.998864i | \(-0.484829\pi\) | ||||
0.0476430 | + | 0.998864i | \(0.484829\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 309.765i | 0.700825i | ||||||||
\(443\) | 487.617 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 236.215i | − 0.529631i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 65.9411i | − 0.147190i | ||||||||
\(449\) | − 26.7868i | − 0.0596588i | −0.999555 | − | 0.0298294i | \(-0.990504\pi\) | ||||
0.999555 | − | 0.0298294i | \(-0.00949640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3604 | −0.0983601 | ||||||||
\(452\) | −138.426 | −0.306253 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −417.816 | −0.920300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 523.382i | 1.14526i | 0.819815 | + | 0.572628i | \(0.194076\pi\) | ||||
−0.819815 | + | 0.572628i | \(0.805924\pi\) | |||||||
\(458\) | −267.973 | −0.585093 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 471.058i | 1.02182i | 0.859635 | + | 0.510909i | \(0.170691\pi\) | ||||
−0.859635 | + | 0.510909i | \(0.829309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 238.912i | − 0.516008i | −0.966144 | − | 0.258004i | \(-0.916935\pi\) | ||||
0.966144 | − | 0.258004i | \(-0.0830648\pi\) | |||||||
\(464\) | − 163.882i | − 0.353195i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 197.647 | 0.424135 | ||||||||
\(467\) | 472.882 | 1.01260 | 0.506298 | − | 0.862359i | \(-0.331014\pi\) | ||||
0.506298 | + | 0.862359i | \(0.331014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −668.441 | −1.42525 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 48.2498i | 0.102224i | ||||||||
\(473\) | −134.912 | −0.285226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 267.765i | − 0.562530i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 368.257i | 0.770412i | ||||||||
\(479\) | 179.647i | 0.375045i | 0.982260 | + | 0.187523i | \(0.0600458\pi\) | ||||
−0.982260 | + | 0.187523i | \(0.939954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −194.941 | −0.405283 | ||||||||
\(482\) | 121.414 | 0.251897 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 224.000 | 0.462810 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 368.874i | 0.757442i | 0.925511 | + | 0.378721i | \(0.123636\pi\) | ||||
−0.925511 | + | 0.378721i | \(0.876364\pi\) | |||||||
\(488\) | 269.740 | 0.552746 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 745.882i | 1.51911i | 0.650444 | + | 0.759554i | \(0.274583\pi\) | ||||
−0.650444 | + | 0.759554i | \(0.725417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 665.470i | − 1.34984i | ||||||||
\(494\) | − 476.215i | − 0.963999i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −52.8528 | −0.106558 | ||||||||
\(497\) | 737.595 | 1.48409 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 771.294 | 1.54568 | 0.772839 | − | 0.634602i | \(-0.218836\pi\) | ||||
0.772839 | + | 0.634602i | \(0.218836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 481.581i | 0.959324i | ||||||||
\(503\) | 32.2355 | 0.0640865 | 0.0320432 | − | 0.999486i | \(-0.489799\pi\) | ||||
0.0320432 | + | 0.999486i | \(0.489799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 99.6396i | − 0.196916i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 413.838i | − 0.814641i | ||||||||
\(509\) | 31.7574i | 0.0623917i | 0.999513 | + | 0.0311958i | \(0.00993155\pi\) | ||||
−0.999513 | + | 0.0311958i | \(0.990068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.9411 | −0.0820766 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 531.588 | 1.03422 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 70.4558i | 0.136278i | ||||||||
\(518\) | 168.510 | 0.325308 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 487.404i | − 0.935517i | −0.883856 | − | 0.467758i | \(-0.845062\pi\) | ||||
0.883856 | − | 0.467758i | \(-0.154938\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 304.353i | 0.581937i | 0.956733 | + | 0.290969i | \(0.0939775\pi\) | ||||
−0.956733 | + | 0.290969i | \(0.906022\pi\) | |||||||
\(524\) | − 311.470i | − 0.594409i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −374.787 | −0.712522 | ||||||||
\(527\) | −214.617 | −0.407243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5584 | 0.0426436 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 411.647i | 0.773772i | ||||||||
\(533\) | 199.404 | 0.374117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 229.373i | 0.427934i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 223.029i | − 0.414553i | ||||||||
\(539\) | − 56.8234i | − 0.105424i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 112.574 | 0.208084 | 0.104042 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104042 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(542\) | 82.2742 | 0.151797 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −91.8823 | −0.168901 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 157.470i | 0.287880i | 0.989586 | + | 0.143940i | \(0.0459772\pi\) | ||||
−0.989586 | + | 0.143940i | \(0.954023\pi\) | |||||||
\(548\) | −46.2944 | −0.0844788 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1023.06i | 1.85673i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 14.9706i | − 0.0270715i | ||||||||
\(554\) | 240.583i | 0.434265i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −122.191 | −0.219768 | ||||||||
\(557\) | 156.978 | 0.281827 | 0.140914 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140914 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 606.441 | 1.08487 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 314.412i | − 0.559452i | ||||||||
\(563\) | −81.3229 | −0.144446 | −0.0722229 | − | 0.997389i | \(-0.523009\pi\) | ||||
−0.0722229 | + | 0.997389i | \(0.523009\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 35.3137i | 0.0623917i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 253.103i | − 0.445603i | ||||||||
\(569\) | 479.022i | 0.841867i | 0.907092 | + | 0.420933i | \(0.138297\pi\) | ||||
−0.907092 | + | 0.420933i | \(0.861703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 631.418 | 1.10581 | 0.552906 | − | 0.833244i | \(-0.313519\pi\) | ||||
0.552906 | + | 0.833244i | \(0.313519\pi\) | |||||||
\(572\) | 80.9117 | 0.141454 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −172.368 | −0.300292 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 945.912i | − 1.63936i | −0.572820 | − | 0.819681i | \(-0.694151\pi\) | ||||
0.572820 | − | 0.819681i | \(-0.305849\pi\) | |||||||
\(578\) | 35.6051 | 0.0616006 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 905.720i | − 1.55890i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 224.735i | − 0.385480i | ||||||||
\(584\) | 14.3919i | 0.0246437i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 716.558 | 1.22280 | ||||||||
\(587\) | 847.529 | 1.44383 | 0.721916 | − | 0.691981i | \(-0.243262\pi\) | ||||
0.721916 | + | 0.691981i | \(0.243262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 329.941 | 0.560172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 57.8234i | − 0.0976746i | ||||||||
\(593\) | 268.118 | 0.452138 | 0.226069 | − | 0.974111i | \(-0.427413\pi\) | ||||
0.226069 | + | 0.974111i | \(0.427413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 280.014i | 0.469823i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 447.889i | 0.748979i | ||||||||
\(599\) | 817.176i | 1.36423i | 0.731243 | + | 0.682117i | \(0.238940\pi\) | ||||
−0.731243 | + | 0.682117i | \(0.761060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −602.706 | −1.00284 | −0.501419 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501419 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(602\) | −524.215 | −0.870790 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 58.1766 | 0.0963189 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 842.551i | 1.38806i | 0.719947 | + | 0.694029i | \(0.244166\pi\) | ||||
−0.719947 | + | 0.694029i | \(0.755834\pi\) | |||||||
\(608\) | 141.255 | 0.232327 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 316.706i | − 0.518340i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 50.8377i | − 0.0829326i | −0.999140 | − | 0.0414663i | \(-0.986797\pi\) | ||||
0.999140 | − | 0.0414663i | \(-0.0132029\pi\) | |||||||
\(614\) | 305.980i | 0.498338i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −69.9411 | −0.113541 | ||||||||
\(617\) | −167.272 | −0.271105 | −0.135553 | − | 0.990770i | \(-0.543281\pi\) | ||||
−0.135553 | + | 0.990770i | \(0.543281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −892.403 | −1.44169 | −0.720843 | − | 0.693099i | \(-0.756245\pi\) | ||||
−0.720843 | + | 0.693099i | \(0.756245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.8608i | 0.0319306i | ||||||||
\(623\) | −331.706 | −0.532433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 526.960i | 0.841790i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 371.411i | − 0.591419i | ||||||||
\(629\) | − 234.801i | − 0.373293i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −95.0294 | −0.150601 | −0.0753007 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753007 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(632\) | −5.13708 | −0.00812830 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −85.5593 | −0.134952 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 255.426i | 0.400983i | ||||||||
\(638\) | −173.823 | −0.272450 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1129.23i | − 1.76167i | −0.473428 | − | 0.880833i | \(-0.656983\pi\) | ||||
0.473428 | − | 0.880833i | \(-0.343017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1041.83i | − 1.62027i | −0.586247 | − | 0.810133i | \(-0.699395\pi\) | ||||
0.586247 | − | 0.810133i | \(-0.300605\pi\) | |||||||
\(644\) | − 387.161i | − 0.601182i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 573.588 | 0.887907 | ||||||||
\(647\) | −588.131 | −0.909013 | −0.454506 | − | 0.890744i | \(-0.650184\pi\) | ||||
−0.454506 | + | 0.890744i | \(0.650184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.1766 | 0.0788546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 483.397i | − 0.741406i | ||||||||
\(653\) | −127.861 | −0.195805 | −0.0979026 | − | 0.995196i | \(-0.531213\pi\) | ||||
−0.0979026 | + | 0.995196i | \(0.531213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 59.1472i | 0.0901634i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 273.765i | 0.416055i | ||||||||
\(659\) | − 1151.79i | − 1.74779i | −0.486115 | − | 0.873895i | \(-0.661587\pi\) | ||||
0.486115 | − | 0.873895i | \(-0.338413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 492.986 | 0.745818 | 0.372909 | − | 0.927868i | \(-0.378360\pi\) | ||||
0.372909 | + | 0.927868i | \(0.378360\pi\) | |||||||
\(662\) | −669.078 | −1.01069 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −310.794 | −0.468063 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 962.205i | − 1.44259i | ||||||||
\(668\) | −572.558 | −0.857123 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 286.103i | − 0.426382i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 620.088i | − 0.921379i | −0.887561 | − | 0.460690i | \(-0.847602\pi\) | ||||
0.887561 | − | 0.460690i | \(-0.152398\pi\) | |||||||
\(674\) | − 870.489i | − 1.29153i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.7056 | −0.0380261 | ||||||||
\(677\) | −733.581 | −1.08358 | −0.541788 | − | 0.840515i | \(-0.682252\pi\) | ||||
−0.541788 | + | 0.840515i | \(0.682252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1325.12 | −1.95158 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 56.0589i | 0.0821978i | ||||||||
\(683\) | 810.588 | 1.18681 | 0.593403 | − | 0.804906i | \(-0.297784\pi\) | ||||
0.593403 | + | 0.804906i | \(0.297784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 350.392i | 0.510775i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 179.882i | 0.261457i | ||||||||
\(689\) | 1010.21i | 1.46619i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −665.477 | −0.963064 | −0.481532 | − | 0.876428i | \(-0.659919\pi\) | ||||
−0.481532 | + | 0.876428i | \(0.659919\pi\) | |||||||
\(692\) | −441.691 | −0.638282 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −269.117 | −0.387776 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 240.177i | 0.344586i | ||||||||
\(698\) | −386.745 | −0.554076 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1210.32i | − 1.72656i | −0.504729 | − | 0.863278i | \(-0.668407\pi\) | ||||
0.504729 | − | 0.863278i | \(-0.331593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 360.971i | 0.513472i | ||||||||
\(704\) | 24.0000i | 0.0340909i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −794.912 | −1.12594 | ||||||||
\(707\) | 1409.79 | 1.99405 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 65.8671 | 0.0929014 | 0.0464507 | − | 0.998921i | \(-0.485209\pi\) | ||||
0.0464507 | + | 0.998921i | \(0.485209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 113.823i | 0.159864i | ||||||||
\(713\) | −310.316 | −0.435226 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 491.823i | − 0.686904i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 363.390i | − 0.506114i | ||||||||
\(719\) | 11.8385i | 0.0164653i | 0.999966 | + | 0.00823263i | \(0.00262056\pi\) | ||||
−0.999966 | + | 0.00823263i | \(0.997379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 965.176 | 1.33866 | ||||||||
\(722\) | −371.272 | −0.514227 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −534.617 | −0.738422 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 171.294i | − 0.235617i | −0.993036 | − | 0.117808i | \(-0.962413\pi\) | ||||
0.993036 | − | 0.117808i | \(-0.0375869\pi\) | |||||||
\(728\) | 314.392 | 0.431857 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 730.441i | 0.999235i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 197.191i | 0.269019i | 0.990912 | + | 0.134509i | \(0.0429459\pi\) | ||||
−0.990912 | + | 0.134509i | \(0.957054\pi\) | |||||||
\(734\) | 268.950i | 0.366417i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −132.853 | −0.180507 | ||||||||
\(737\) | 243.286 | 0.330104 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −140.728 | −0.190430 | −0.0952151 | − | 0.995457i | \(-0.530354\pi\) | ||||
−0.0952151 | + | 0.995457i | \(0.530354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 873.235i | − 1.17687i | ||||||||
\(743\) | 399.073 | 0.537111 | 0.268555 | − | 0.963264i | \(-0.413454\pi\) | ||||
0.268555 | + | 0.963264i | \(0.413454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 319.446i | 0.428211i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 97.4558i | 0.130289i | ||||||||
\(749\) | 1119.79i | 1.49504i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −93.8234 | −0.124931 | −0.0624656 | − | 0.998047i | \(-0.519896\pi\) | ||||
−0.0624656 | + | 0.998047i | \(0.519896\pi\) | |||||||
\(752\) | 93.9411 | 0.124922 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 781.352 | 1.03628 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 763.573i | − 1.00868i | −0.863504 | − | 0.504341i | \(-0.831735\pi\) | ||||
0.863504 | − | 0.504341i | \(-0.168265\pi\) | |||||||
\(758\) | −677.480 | −0.893773 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 212.214i | − 0.278862i | −0.990232 | − | 0.139431i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139431i | \(-0.0445274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1556.65i | 2.04016i | ||||||||
\(764\) | 692.881i | 0.906913i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −398.330 | −0.520013 | ||||||||
\(767\) | −230.044 | −0.299927 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.79307 | −0.0101340 | −0.00506702 | − | 0.999987i | \(-0.501613\pi\) | ||||
−0.00506702 | + | 0.999987i | \(0.501613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 69.8234i | − 0.0904448i | ||||||||
\(773\) | −549.442 | −0.710791 | −0.355396 | − | 0.934716i | \(-0.615654\pi\) | ||||
−0.355396 | + | 0.934716i | \(0.615654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 454.711i | 0.585967i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 894.323i | 1.14952i | ||||||||
\(779\) | − 369.235i | − 0.473985i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −268.456 | −0.343733 | ||||||||
\(782\) | −539.470 | −0.689860 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −75.7645 | −0.0966384 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 332.764i | − 0.422825i | −0.977397 | − | 0.211413i | \(-0.932194\pi\) | ||||
0.977397 | − | 0.211413i | \(-0.0678064\pi\) | |||||||
\(788\) | −379.882 | −0.482084 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 570.500i | 0.721238i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1286.06i | 1.62176i | ||||||||
\(794\) | − 723.556i | − 0.911280i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −274.426 | −0.344757 | ||||||||
\(797\) | 656.029 | 0.823122 | 0.411561 | − | 0.911382i | \(-0.364984\pi\) | ||||
0.411561 | + | 0.911382i | \(0.364984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 381.463 | 0.477426 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 983.470i | 1.22627i | ||||||||
\(803\) | 15.2649 | 0.0190099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 251.990i | − 0.312643i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 483.765i | − 0.598718i | ||||||||
\(809\) | 475.736i | 0.588054i | 0.955797 | + | 0.294027i | \(0.0949956\pi\) | ||||
−0.955797 | + | 0.294027i | \(0.905004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −991.433 | −1.22248 | −0.611241 | − | 0.791445i | \(-0.709329\pi\) | ||||
−0.611241 | + | 0.791445i | \(0.709329\pi\) | |||||||
\(812\) | −675.411 | −0.831787 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −61.3310 | −0.0753452 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1122.94i | − 1.37447i | ||||||||
\(818\) | −719.002 | −0.878976 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1201.83i | − 1.46386i | −0.681379 | − | 0.731931i | \(-0.738619\pi\) | ||||
0.681379 | − | 0.731931i | \(-0.261381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 423.383i | − 0.514438i | −0.966353 | − | 0.257219i | \(-0.917194\pi\) | ||||
0.966353 | − | 0.257219i | \(-0.0828062\pi\) | |||||||
\(824\) | − 331.196i | − 0.401937i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 198.853 | 0.240742 | ||||||||
\(827\) | 225.323 | 0.272458 | 0.136229 | − | 0.990677i | \(-0.456502\pi\) | ||||
0.136229 | + | 0.990677i | \(0.456502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 602.279 | 0.726513 | 0.363256 | − | 0.931689i | \(-0.381665\pi\) | ||||
0.363256 | + | 0.931689i | \(0.381665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 107.882i | − 0.129666i | ||||||||
\(833\) | −307.654 | −0.369332 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 149.823i | − 0.179215i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 75.8680i | − 0.0905346i | ||||||||
\(839\) | 784.279i | 0.934779i | 0.884052 | + | 0.467389i | \(0.154805\pi\) | ||||
−0.884052 | + | 0.467389i | \(0.845195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.587 | −0.995942 | ||||||||
\(842\) | −288.145 | −0.342215 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −347.411 | −0.411625 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 923.176i | − 1.08994i | ||||||||
\(848\) | −299.647 | −0.353357 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 339.500i | − 0.398942i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 763.043i | 0.894540i | 0.894399 | + | 0.447270i | \(0.147604\pi\) | ||||
−0.894399 | + | 0.447270i | \(0.852396\pi\) | |||||||
\(854\) | − 1111.69i | − 1.30174i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 384.250 | 0.448890 | ||||||||
\(857\) | −527.294 | −0.615278 | −0.307639 | − | 0.951503i | \(-0.599539\pi\) | ||||
−0.307639 | + | 0.951503i | \(0.599539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 426.558 | 0.496576 | 0.248288 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248288 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 1143.33i | − 1.32637i | ||||||||
\(863\) | 705.442 | 0.817429 | 0.408715 | − | 0.912662i | \(-0.365977\pi\) | ||||
0.408715 | + | 0.912662i | \(0.365977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 894.781i | − 1.03323i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 217.823i | 0.250949i | ||||||||
\(869\) | 5.44870i | 0.00627008i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1093.60 | −1.25556 | ||||||||
\(872\) | 534.156 | 0.612565 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 829.352 | 0.948916 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 488.368i | 0.556862i | 0.960456 | + | 0.278431i | \(0.0898144\pi\) | ||||
−0.960456 | + | 0.278431i | \(0.910186\pi\) | |||||||
\(878\) | −59.1573 | −0.0673773 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 217.060i | − 0.246379i | −0.992383 | − | 0.123189i | \(-0.960688\pi\) | ||||
0.992383 | − | 0.123189i | \(-0.0393123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1392i | 0.0228077i | 0.999935 | + | 0.0114038i | \(0.00363003\pi\) | ||||
−0.999935 | + | 0.0114038i | \(0.996370\pi\) | |||||||
\(884\) | − 438.073i | − 0.495558i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −689.595 | −0.778324 | ||||||||
\(887\) | −63.5727 | −0.0716716 | −0.0358358 | − | 0.999358i | \(-0.511409\pi\) | ||||
−0.0358358 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1705.56 | −1.91851 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 334.059i | 0.374505i | ||||||||
\(893\) | −586.441 | −0.656709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 93.2548i | 0.104079i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.8823i | 0.0421851i | ||||||||
\(899\) | 541.352i | 0.602172i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1216.76 | −1.35046 | ||||||||
\(902\) | 62.7351 | 0.0695511 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 195.765 | 0.216554 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 582.558i | − 0.642292i | −0.947030 | − | 0.321146i | \(-0.895932\pi\) | ||||
0.947030 | − | 0.321146i | \(-0.104068\pi\) | |||||||
\(908\) | 590.881 | 0.650750 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1683.69i | − 1.84818i | −0.382179 | − | 0.924088i | \(-0.624826\pi\) | ||||
0.382179 | − | 0.924088i | \(-0.375174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 329.647i | 0.361059i | ||||||||
\(914\) | − 740.174i | − 0.809818i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 378.971 | 0.413723 | ||||||||
\(917\) | −1283.67 | −1.39986 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1299.32 | −1.41384 | −0.706922 | − | 0.707292i | \(-0.749917\pi\) | ||||
−0.706922 | + | 0.707292i | \(0.749917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 666.177i | − 0.722534i | ||||||||
\(923\) | 1206.73 | 1.30740 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 337.872i | 0.364873i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 231.765i | 0.249746i | ||||||||
\(929\) | 1636.74i | 1.76183i | 0.473272 | + | 0.880916i | \(0.343073\pi\) | ||||
−0.473272 | + | 0.880916i | \(0.656927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 472.971 | 0.508024 | ||||||||
\(932\) | −279.515 | −0.299908 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −668.756 | −0.716013 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1084.38i | − 1.15729i | −0.815579 | − | 0.578645i | \(-0.803582\pi\) | ||||
0.815579 | − | 0.578645i | \(-0.196418\pi\) | |||||||
\(938\) | 945.318 | 1.00780 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 773.138i | 0.821614i | 0.911722 | + | 0.410807i | \(0.134753\pi\) | ||||
−0.911722 | + | 0.410807i | \(0.865247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 347.272i | 0.368263i | ||||||||
\(944\) | − 68.2355i | − 0.0722834i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190.794 | 0.201685 | ||||||||
\(947\) | 849.442 | 0.896982 | 0.448491 | − | 0.893787i | \(-0.351962\pi\) | ||||
0.448491 | + | 0.893787i | \(0.351962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −68.6173 | −0.0723049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 378.676i | 0.397769i | ||||||||
\(953\) | −1537.35 | −1.61317 | −0.806586 | − | 0.591117i | \(-0.798687\pi\) | ||||
−0.806586 | + | 0.591117i | \(0.798687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 520.794i | − 0.544764i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 254.059i | − 0.265197i | ||||||||
\(959\) | 190.794i | 0.198951i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −786.411 | −0.818326 | ||||||||
\(962\) | 275.688 | 0.286578 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −171.706 | −0.178118 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 974.234i | − 1.00748i | −0.863855 | − | 0.503740i | \(-0.831957\pi\) | ||||
0.863855 | − | 0.503740i | \(-0.168043\pi\) | |||||||
\(968\) | −316.784 | −0.327256 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 771.500i | 0.794541i | 0.917702 | + | 0.397271i | \(0.130043\pi\) | ||||
−0.917702 | + | 0.397271i | \(0.869957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 503.588i | 0.517562i | ||||||||
\(974\) | − 521.667i | − 0.535592i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −381.470 | −0.390851 | ||||||||
\(977\) | −580.118 | −0.593775 | −0.296887 | − | 0.954913i | \(-0.595949\pi\) | ||||
−0.296887 | + | 0.954913i | \(0.595949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 120.728 | 0.123318 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 1054.84i | − 1.07417i | ||||||||
\(983\) | 1086.02 | 1.10480 | 0.552398 | − | 0.833580i | \(-0.313713\pi\) | ||||
0.552398 | + | 0.833580i | \(0.313713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 941.117i | 0.954480i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 673.470i | 0.681650i | ||||||||
\(989\) | 1056.15i | 1.06789i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −159.294 | −0.160740 | −0.0803701 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803701 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(992\) | 74.7452 | 0.0753479 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1043.12 | −1.04941 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 100.427i | 0.100729i | 0.998731 | + | 0.0503647i | \(0.0160384\pi\) | ||||
−0.998731 | + | 0.0503647i | \(0.983962\pi\) | |||||||
\(998\) | −1090.77 | −1.09296 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.3.b.f.1349.1 | 4 | ||
3.2 | odd | 2 | 1350.3.b.a.1349.3 | 4 | |||
5.2 | odd | 4 | 1350.3.d.n.701.2 | yes | 4 | ||
5.3 | odd | 4 | 1350.3.d.l.701.3 | yes | 4 | ||
5.4 | even | 2 | 1350.3.b.a.1349.4 | 4 | |||
15.2 | even | 4 | 1350.3.d.n.701.4 | yes | 4 | ||
15.8 | even | 4 | 1350.3.d.l.701.1 | ✓ | 4 | ||
15.14 | odd | 2 | inner | 1350.3.b.f.1349.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.3.b.a.1349.3 | 4 | 3.2 | odd | 2 | |||
1350.3.b.a.1349.4 | 4 | 5.4 | even | 2 | |||
1350.3.b.f.1349.1 | 4 | 1.1 | even | 1 | trivial | ||
1350.3.b.f.1349.2 | 4 | 15.14 | odd | 2 | inner | ||
1350.3.d.l.701.1 | ✓ | 4 | 15.8 | even | 4 | ||
1350.3.d.l.701.3 | yes | 4 | 5.3 | odd | 4 | ||
1350.3.d.n.701.2 | yes | 4 | 5.2 | odd | 4 | ||
1350.3.d.n.701.4 | yes | 4 | 15.2 | even | 4 |