Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(1471,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.d (of order \(2\), degree \(1\), 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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9144576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.2 | ||
Root | \(2.60168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1471 |
Dual form | 1568.3.d.i.1471.5 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.76873i | − 0.589578i | −0.955562 | − | 0.294789i | \(-0.904751\pi\) | ||||
0.955562 | − | 0.294789i | \(-0.0952494\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.20336 | −1.64067 | −0.820336 | − | 0.571882i | \(-0.806213\pi\) | ||||
−0.820336 | + | 0.571882i | \(0.806213\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.87158 | 0.652398 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10.5096i | − 0.955415i | −0.878519 | − | 0.477707i | \(-0.841468\pi\) | ||||
0.878519 | − | 0.477707i | \(-0.158532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.87158 | −0.451660 | −0.225830 | − | 0.974167i | \(-0.572509\pi\) | ||||
−0.225830 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.5096i | 0.967304i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.0168 | 1.58922 | 0.794612 | − | 0.607118i | \(-0.207675\pi\) | ||||
0.794612 | + | 0.607118i | \(0.207675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 12.3085i | − 0.647818i | −0.946088 | − | 0.323909i | \(-0.895003\pi\) | ||||
0.946088 | − | 0.323909i | \(-0.104997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.9139i | 1.82235i | 0.412025 | + | 0.911173i | \(0.364822\pi\) | ||||
−0.412025 | + | 0.911173i | \(0.635178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.2951 | 1.69180 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 26.3039i | − 0.974217i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.4235 | 1.25598 | 0.627992 | − | 0.778220i | \(-0.283877\pi\) | ||||
0.627992 | + | 0.778220i | \(0.283877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.64031i | 0.246462i | 0.992378 | + | 0.123231i | \(0.0393256\pi\) | ||||
−0.992378 | + | 0.123231i | \(0.960674\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.5886 | −0.563292 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.25684 | 0.196131 | 0.0980654 | − | 0.995180i | \(-0.468735\pi\) | ||||
0.0980654 | + | 0.995180i | \(0.468735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.3853i | 0.266289i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.1667 | −1.17480 | −0.587398 | − | 0.809298i | \(-0.699848\pi\) | ||||
−0.587398 | + | 0.809298i | \(0.699848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 23.4863i | − 0.546193i | −0.961987 | − | 0.273097i | \(-0.911952\pi\) | ||||
0.961987 | − | 0.273097i | \(-0.0880479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −48.1667 | −1.07037 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 59.1173i | − 1.25781i | −0.777480 | − | 0.628907i | \(-0.783502\pi\) | ||||
0.777480 | − | 0.628907i | \(-0.216498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 47.7855i | − 0.936971i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.06561 | −0.0767097 | −0.0383548 | − | 0.999264i | \(-0.512212\pi\) | ||||
−0.0383548 | + | 0.999264i | \(0.512212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 86.2137i | 1.56752i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.7705 | −0.381939 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26.8214i | 0.454601i | 0.973825 | + | 0.227300i | \(0.0729899\pi\) | ||||
−0.973825 | + | 0.227300i | \(0.927010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.370024 | 0.00606597 | 0.00303298 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303298 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.1667 | 0.741026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.08605i | 0.0311351i | 0.999879 | + | 0.0155676i | \(0.00495551\pi\) | ||||
−0.999879 | + | 0.0155676i | \(0.995044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 74.1346 | 1.07442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 121.781i | − 1.71523i | −0.514291 | − | 0.857616i | \(-0.671945\pi\) | ||||
0.514291 | − | 0.857616i | \(-0.328055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.1452 | −1.05678 | −0.528392 | − | 0.849001i | \(-0.677205\pi\) | ||||
−0.528392 | + | 0.849001i | \(0.677205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 74.8088i | − 0.997450i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 36.8101i | 0.465950i | 0.972483 | + | 0.232975i | \(0.0748461\pi\) | ||||
−0.972483 | + | 0.232975i | \(0.925154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.31965 | 0.0780204 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 98.2951i | − 1.18428i | −0.805836 | − | 0.592139i | \(-0.798284\pi\) | ||||
0.805836 | − | 0.592139i | \(-0.201716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −221.628 | −2.60739 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 64.4235i | − 0.740500i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −30.3458 | −0.340964 | −0.170482 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170482 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5137 | 0.145308 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 100.971i | 1.06286i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.87158 | −0.0605317 | −0.0302659 | − | 0.999542i | \(-0.509635\pi\) | ||||
−0.0302659 | + | 0.999542i | \(0.509635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 61.7077i | − 0.623310i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −153.317 | −1.51799 | −0.758993 | − | 0.651099i | \(-0.774308\pi\) | ||||
−0.758993 | + | 0.651099i | \(0.774308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 77.7269i | − 0.754630i | −0.926085 | − | 0.377315i | \(-0.876847\pi\) | ||||
0.926085 | − | 0.377315i | \(-0.123153\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 164.889i | − 1.54102i | −0.637427 | − | 0.770511i | \(-0.720001\pi\) | ||||
0.637427 | − | 0.770511i | \(-0.279999\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 61.2596 | 0.562015 | 0.281008 | − | 0.959706i | \(-0.409331\pi\) | ||||
0.281008 | + | 0.959706i | \(0.409331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 12.8354i | − 0.115634i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79509 | −0.0866822 | −0.0433411 | − | 0.999060i | \(-0.513800\pi\) | ||||
−0.0433411 | + | 0.999060i | \(0.513800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 343.835i | − 2.98987i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −34.4754 | −0.294662 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5491 | 0.0871828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 85.1940i | 0.692634i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −141.878 | −1.13502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 125.705i | − 0.989802i | −0.868949 | − | 0.494901i | \(-0.835204\pi\) | ||||
0.868949 | − | 0.494901i | \(-0.164796\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −41.5411 | −0.322024 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 35.6173i | 0.271888i | 0.990717 | + | 0.135944i | \(0.0434067\pi\) | ||||
−0.990717 | + | 0.135944i | \(0.956593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 215.780i | 1.59837i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −119.500 | −0.872263 | −0.436131 | − | 0.899883i | \(-0.643652\pi\) | ||||
−0.436131 | + | 0.899883i | \(0.643652\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 47.3989i | 0.341000i | 0.985358 | + | 0.170500i | \(0.0545382\pi\) | ||||
−0.985358 | + | 0.170500i | \(0.945462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −104.563 | −0.741580 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 61.7077i | 0.431523i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −298.795 | −2.06066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −189.374 | −1.27097 | −0.635485 | − | 0.772114i | \(-0.719200\pi\) | ||||
−0.635485 | + | 0.772114i | \(0.719200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 245.307i | − 1.62455i | −0.583273 | − | 0.812276i | \(-0.698228\pi\) | ||||
0.583273 | − | 0.812276i | \(-0.301772\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 158.631 | 1.03681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 62.6762i | − 0.404363i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 220.718 | 1.40585 | 0.702924 | − | 0.711264i | \(-0.251877\pi\) | ||||
0.702924 | + | 0.711264i | \(0.251877\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.19099i | 0.0452263i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 272.034i | 1.66892i | 0.551067 | + | 0.834461i | \(0.314221\pi\) | ||||
−0.551067 | + | 0.834461i | \(0.685779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 152.489 | 0.924176 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 88.8674i | − 0.532140i | −0.963954 | − | 0.266070i | \(-0.914275\pi\) | ||||
0.963954 | − | 0.266070i | \(-0.0857252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −134.525 | −0.796003 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 72.2705i | − 0.422635i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −319.182 | −1.84498 | −0.922491 | − | 0.386019i | \(-0.873850\pi\) | ||||
−0.922491 | + | 0.386019i | \(0.873850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 47.4400 | 0.268023 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 139.436i | 0.778970i | 0.921033 | + | 0.389485i | \(0.127347\pi\) | ||||
−0.921033 | + | 0.389485i | \(0.872653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −73.1328 | −0.404048 | −0.202024 | − | 0.979381i | \(-0.564752\pi\) | ||||
−0.202024 | + | 0.979381i | \(0.564752\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 0.654474i | − 0.00357636i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −59.5305 | −0.321786 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 283.935i | − 1.51837i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 128.288i | − 0.671667i | −0.941921 | − | 0.335833i | \(-0.890982\pi\) | ||||
0.941921 | − | 0.335833i | \(-0.109018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 279.538 | 1.44838 | 0.724192 | − | 0.689598i | \(-0.242213\pi\) | ||||
0.724192 | + | 0.689598i | \(0.242213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 85.1940i | − 0.436892i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −99.0628 | −0.502857 | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 236.318i | 1.18753i | 0.804640 | + | 0.593763i | \(0.202359\pi\) | ||||
−0.804640 | + | 0.593763i | \(0.797641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.68967 | 0.0183566 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 395.128 | 1.92746 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 246.101i | 1.18889i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −129.357 | −0.618934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 389.683i | 1.84684i | 0.383791 | + | 0.923420i | \(0.374618\pi\) | ||||
−0.383791 | + | 0.923420i | \(0.625382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −215.399 | −1.01126 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 192.667i | 0.896124i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 136.449i | 0.623057i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −158.631 | −0.717788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 102.219i | 0.458379i | 0.973382 | + | 0.229190i | \(0.0736076\pi\) | ||||
−0.973382 | + | 0.229190i | \(0.926392\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 248.339 | 1.10373 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 230.982i | − 1.01754i | −0.860901 | − | 0.508772i | \(-0.830100\pi\) | ||||
0.860901 | − | 0.508772i | \(-0.169900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8044 | −0.0733817 | −0.0366909 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366909 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −120.615 | −0.517660 | −0.258830 | − | 0.965923i | \(-0.583337\pi\) | ||||
−0.258830 | + | 0.965923i | \(0.583337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 484.960i | 2.06366i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 65.1073 | 0.274714 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 109.863i | − 0.459679i | −0.973229 | − | 0.229840i | \(-0.926180\pi\) | ||||
0.973229 | − | 0.229840i | \(-0.0738202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 184.899 | 0.767214 | 0.383607 | − | 0.923496i | \(-0.374682\pi\) | ||||
0.383607 | + | 0.923496i | \(0.374682\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 247.913i | − 1.02022i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.2705i | 0.292593i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −173.858 | −0.698224 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 224.827i | − 0.895724i | −0.894103 | − | 0.447862i | \(-0.852186\pi\) | ||||
0.894103 | − | 0.447862i | \(-0.147814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 440.497 | 1.74110 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 392.002i | 1.53726i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 178.414 | 0.694219 | 0.347109 | − | 0.937825i | \(-0.387163\pi\) | ||||
0.347109 | + | 0.937825i | \(0.387163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 213.864 | 0.819400 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 288.613i | − 1.09739i | −0.836023 | − | 0.548694i | \(-0.815125\pi\) | ||||
0.836023 | − | 0.548694i | \(-0.184875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.3517 | 0.125855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 53.6736i | 0.201025i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 225.297 | 0.837536 | 0.418768 | − | 0.908093i | \(-0.362462\pi\) | ||||
0.418768 | + | 0.908093i | \(0.362462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 195.683i | − 0.722079i | −0.932551 | − | 0.361039i | \(-0.882422\pi\) | ||||
0.932551 | − | 0.361039i | \(-0.117578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 444.503i | − 1.61637i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −135.628 | −0.489633 | −0.244817 | − | 0.969569i | \(-0.578728\pi\) | ||||
−0.244817 | + | 0.969569i | \(0.578728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 44.8607i | 0.160791i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −372.495 | −1.32560 | −0.662802 | − | 0.748795i | \(-0.730633\pi\) | ||||
−0.662802 | + | 0.748795i | \(0.730633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 287.409i | − 1.01558i | −0.861481 | − | 0.507789i | \(-0.830463\pi\) | ||||
0.861481 | − | 0.507789i | \(-0.169537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 178.591 | 0.626637 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 440.907 | 1.52563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3853i | 0.0356882i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 131.947 | 0.450332 | 0.225166 | − | 0.974320i | \(-0.427708\pi\) | ||||
0.225166 | + | 0.974320i | \(0.427708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 220.026i | − 0.745850i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −276.442 | −0.930782 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 246.101i | − 0.823080i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 271.176i | 0.894971i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.03544 | −0.00995226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 47.8253i | 0.155783i | 0.996962 | + | 0.0778913i | \(0.0248187\pi\) | ||||
−0.996962 | + | 0.0778913i | \(0.975181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −137.478 | −0.444913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 227.499i | 0.731508i | 0.930712 | + | 0.365754i | \(0.119189\pi\) | ||||
−0.930712 | + | 0.365754i | \(0.880811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 123.097 | 0.393280 | 0.196640 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196640 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −480.295 | −1.51513 | −0.757563 | − | 0.652762i | \(-0.773610\pi\) | ||||
−0.757563 | + | 0.652762i | \(0.773610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 382.795i | − 1.19998i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −291.646 | −0.908553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 332.537i | − 1.02953i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −248.339 | −0.764120 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 108.352i | − 0.331352i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 474.392i | − 1.43321i | −0.697480 | − | 0.716604i | \(-0.745695\pi\) | ||||
0.697480 | − | 0.716604i | \(-0.254305\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 42.6091 | 0.127955 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 17.1126i | − 0.0510825i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −305.861 | −0.907599 | −0.453799 | − | 0.891104i | \(-0.649932\pi\) | ||||
−0.453799 | + | 0.891104i | \(0.649932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3249i | 0.0511059i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 80.2963 | 0.235473 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −608.153 | −1.76276 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 688.668i | − 1.98463i | −0.123722 | − | 0.992317i | \(-0.539483\pi\) | ||||
0.123722 | − | 0.992317i | \(-0.460517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 128.861 | 0.369228 | 0.184614 | − | 0.982811i | \(-0.440896\pi\) | ||||
0.184614 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 154.445i | 0.440015i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −95.0923 | −0.269383 | −0.134692 | − | 0.990888i | \(-0.543004\pi\) | ||||
−0.134692 | + | 0.990888i | \(0.543004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 999.016i | 2.81413i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.2145i | 0.100876i | 0.998727 | + | 0.0504380i | \(0.0160617\pi\) | ||||
−0.998727 | + | 0.0504380i | \(0.983938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 209.500 | 0.580332 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 18.6586i | − 0.0514011i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 632.850 | 1.73384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8706i | 0.0650424i | 0.999471 | + | 0.0325212i | \(0.0103536\pi\) | ||||
−0.999471 | + | 0.0325212i | \(0.989646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −282.814 | −0.766435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −171.377 | −0.459456 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 250.944i | 0.669184i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −213.864 | −0.567277 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 22.8798i | − 0.0603689i | −0.999544 | − | 0.0301845i | \(-0.990391\pi\) | ||||
0.999544 | − | 0.0301845i | \(-0.00960947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −222.339 | −0.583566 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 564.774i | 1.47460i | 0.675563 | + | 0.737302i | \(0.263901\pi\) | ||||
−0.675563 | + | 0.737302i | \(0.736099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 137.902i | − 0.356335i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 119.522 | 0.307254 | 0.153627 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153627 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1132.38i | 2.89611i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 62.9975 | 0.160299 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 301.966i | − 0.764472i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 525.469 | 1.32360 | 0.661799 | − | 0.749681i | \(-0.269793\pi\) | ||||
0.661799 | + | 0.749681i | \(0.269793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −166.506 | −0.415226 | −0.207613 | − | 0.978211i | \(-0.566569\pi\) | ||||
−0.207613 | + | 0.978211i | \(0.566569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 44.8607i | − 0.111317i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −51.8424 | −0.128006 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 76.2662i | − 0.187386i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 475.345 | 1.16221 | 0.581106 | − | 0.813828i | \(-0.302620\pi\) | ||||
0.581106 | + | 0.813828i | \(0.302620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 211.364i | 0.514267i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 806.350i | 1.94301i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 83.8361 | 0.201046 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 370.547i | − 0.884360i | −0.896926 | − | 0.442180i | \(-0.854205\pi\) | ||||
0.896926 | − | 0.442180i | \(-0.145795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −248.779 | −0.590924 | −0.295462 | − | 0.955355i | \(-0.595474\pi\) | ||||
−0.295462 | + | 0.955355i | \(0.595474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 347.112i | − 0.820596i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1142.68 | 2.68865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 109.145 | 0.254416 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 66.0180i | − 0.153174i | −0.997063 | − | 0.0765870i | \(-0.975598\pi\) | ||||
0.997063 | − | 0.0765870i | \(-0.0244023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 753.932 | 1.74118 | 0.870591 | − | 0.492007i | \(-0.163737\pi\) | ||||
0.870591 | + | 0.492007i | \(0.163737\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 528.489i | 1.21492i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 515.899 | 1.18055 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 37.2376i | − 0.0848238i | −0.999100 | − | 0.0424119i | \(-0.986496\pi\) | ||||
0.999100 | − | 0.0424119i | \(-0.0135042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 562.222i | − 1.26912i | −0.772872 | − | 0.634562i | \(-0.781180\pi\) | ||||
0.772872 | − | 0.634562i | \(-0.218820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 248.937 | 0.559409 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 334.953i | 0.749335i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 265.855 | 0.592105 | 0.296052 | − | 0.955172i | \(-0.404330\pi\) | ||||
0.296052 | + | 0.955172i | \(0.404330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 506.211i | 1.12242i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −433.884 | −0.957801 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −66.0818 | −0.144599 | −0.0722995 | − | 0.997383i | \(-0.523034\pi\) | ||||
−0.0722995 | + | 0.997383i | \(0.523034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 710.646i | − 1.54825i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 59.0572 | 0.128107 | 0.0640534 | − | 0.997946i | \(-0.479597\pi\) | ||||
0.0640534 | + | 0.997946i | \(0.479597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 390.109i | − 0.842569i | −0.906929 | − | 0.421285i | \(-0.861579\pi\) | ||||
0.906929 | − | 0.421285i | \(-0.138421\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −110.858 | −0.238403 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 361.203i | − 0.773453i | −0.922194 | − | 0.386727i | \(-0.873606\pi\) | ||||
0.922194 | − | 0.386727i | \(-0.126394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 390.392i | − 0.828858i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −246.831 | −0.521841 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 520.591i | − 1.09598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.8716 | −0.0500452 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 96.4028i | − 0.201258i | −0.994924 | − | 0.100629i | \(-0.967914\pi\) | ||||
0.994924 | − | 0.100629i | \(-0.0320856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6091 | −0.0885845 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.1667 | 0.0993127 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 56.6871i | 0.116401i | 0.998305 | + | 0.0582003i | \(0.0185362\pi\) | ||||
−0.998305 | + | 0.0582003i | \(0.981464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 481.156 | 0.983960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 559.896i | 1.14032i | 0.821534 | + | 0.570159i | \(0.193118\pi\) | ||||
−0.821534 | + | 0.570159i | \(0.806882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 984.046 | 1.99604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 506.211i | 1.02265i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 372.698i | − 0.746890i | −0.927652 | − | 0.373445i | \(-0.878176\pi\) | ||||
0.927652 | − | 0.373445i | \(-0.121824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −157.183 | −0.313738 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 648.033i | − 1.28834i | −0.764884 | − | 0.644168i | \(-0.777204\pi\) | ||||
0.764884 | − | 0.644168i | \(-0.222796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1257.71 | 2.49052 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 237.938i | 0.469306i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 420.562 | 0.826251 | 0.413125 | − | 0.910674i | \(-0.364437\pi\) | ||||
0.413125 | + | 0.910674i | \(0.364437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −323.762 | −0.631115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 637.622i | 1.23810i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −621.297 | −1.20173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 564.548i | 1.08776i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 277.664 | 0.532943 | 0.266472 | − | 0.963843i | \(-0.414142\pi\) | ||||
0.266472 | + | 0.963843i | \(0.414142\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 653.025i | 1.24861i | 0.781179 | + | 0.624307i | \(0.214618\pi\) | ||||
−0.781179 | + | 0.624307i | \(0.785382\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 206.417i | 0.391683i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1227.78 | −2.32094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 157.484i | 0.296580i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 282.814 | 0.530609 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1352.65i | 2.52831i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 246.625 | 0.459264 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 266.287 | 0.492213 | 0.246107 | − | 0.969243i | \(-0.420849\pi\) | ||||
0.246107 | + | 0.969243i | \(0.420849\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 129.352i | 0.238218i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −502.535 | −0.922082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 291.492i | 0.532892i | 0.963850 | + | 0.266446i | \(0.0858493\pi\) | ||||
−0.963850 | + | 0.266446i | \(0.914151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.17263 | 0.00395742 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 448.320i | − 0.813648i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 105.294i | 0.189718i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −576.139 | −1.03436 | −0.517180 | − | 0.855876i | \(-0.673018\pi\) | ||||
−0.517180 | + | 0.855876i | \(0.673018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 137.902i | 0.246694i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −502.205 | −0.895196 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 575.149i | 1.02158i | 0.859706 | + | 0.510790i | \(0.170647\pi\) | ||||
−0.859706 | + | 0.510790i | \(0.829353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 80.3526 | 0.142217 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 857.219 | 1.50654 | 0.753268 | − | 0.657714i | \(-0.228477\pi\) | ||||
0.753268 | + | 0.657714i | \(0.228477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 295.010i | 0.516655i | 0.966057 | + | 0.258327i | \(0.0831713\pi\) | ||||
−0.966057 | + | 0.258327i | \(0.916829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −226.908 | −0.396000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1772.75i | 3.08305i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −566.402 | −0.981633 | −0.490817 | − | 0.871263i | \(-0.663302\pi\) | ||||
−0.490817 | + | 0.871263i | \(0.663302\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 494.429i | − 0.853936i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.7278i | 0.0732896i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 282.814 | 0.483443 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 882.011i | 1.50257i | 0.659975 | + | 0.751287i | \(0.270567\pi\) | ||||
−0.659975 | + | 0.751287i | \(0.729433\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 94.0411 | 0.159662 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 175.216i | 0.296473i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −925.083 | −1.56001 | −0.780003 | − | 0.625776i | \(-0.784782\pi\) | ||||
−0.780003 | + | 0.625776i | \(0.784782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 417.984 | 0.700140 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 151.848i | − 0.253502i | −0.991935 | − | 0.126751i | \(-0.959545\pi\) | ||||
0.991935 | − | 0.126751i | \(-0.0404550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 485.178 | 0.807284 | 0.403642 | − | 0.914917i | \(-0.367744\pi\) | ||||
0.403642 | + | 0.914917i | \(0.367744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2484i | 0.0203125i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −86.5382 | −0.143038 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 378.194i | 0.623054i | 0.950237 | + | 0.311527i | \(0.100840\pi\) | ||||
−0.950237 | + | 0.311527i | \(0.899160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 347.112i | 0.568105i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −614.281 | −1.00209 | −0.501045 | − | 0.865421i | \(-0.667051\pi\) | ||||
−0.501045 | + | 0.865421i | \(0.667051\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 698.877i | − 1.13639i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1193.13 | 1.93377 | 0.966883 | − | 0.255220i | \(-0.0821479\pi\) | ||||
0.966883 | + | 0.255220i | \(0.0821479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 488.526i | 0.789219i | 0.918849 | + | 0.394609i | \(0.129120\pi\) | ||||
−0.918849 | + | 0.394609i | \(0.870880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1102.50 | 1.77536 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 106.497 | 0.170396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 228.799i | 0.364910i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 196.057 | 0.311696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 384.907i | − 0.609995i | −0.952353 | − | 0.304998i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304998i | \(-0.0986557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 689.246 | 1.08886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1031.20i | 1.62394i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 715.049i | − 1.11901i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1093.96 | 1.70665 | 0.853325 | − | 0.521380i | \(-0.174583\pi\) | ||||
0.853325 | + | 0.521380i | \(0.174583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 866.317i | − 1.34731i | −0.739048 | − | 0.673653i | \(-0.764724\pi\) | ||||
0.739048 | − | 0.673653i | \(-0.235276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 340.776 | 0.528335 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 37.1894i | − 0.0574798i | −0.999587 | − | 0.0287399i | \(-0.990851\pi\) | ||||
0.999587 | − | 0.0287399i | \(-0.00914946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 281.882 | 0.434332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1095.91 | −1.67827 | −0.839137 | − | 0.543920i | \(-0.816939\pi\) | ||||
−0.839137 | + | 0.543920i | \(0.816939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 292.181i | − 0.446079i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −452.964 | −0.689443 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.9021i | 0.0210957i | 0.999944 | + | 0.0105479i | \(0.00335755\pi\) | ||||
−0.999944 | + | 0.0105479i | \(0.996642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −101.621 | −0.153738 | −0.0768689 | − | 0.997041i | \(-0.524492\pi\) | ||||
−0.0768689 | + | 0.997041i | \(0.524492\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 280.576i | 0.423192i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1526.65i | 2.28884i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 180.798 | 0.270250 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 3.88879i | − 0.00579551i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −71.7077 | −0.106549 | −0.0532747 | − | 0.998580i | \(-0.516966\pi\) | ||||
−0.0532747 | + | 0.998580i | \(0.516966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1112.52i | − 1.64818i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1050.00 | −1.55095 | −0.775477 | − | 0.631376i | \(-0.782491\pi\) | ||||
−0.775477 | + | 0.631376i | \(0.782491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −408.547 | −0.599922 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 133.996i | − 0.196188i | −0.995177 | − | 0.0980939i | \(-0.968725\pi\) | ||||
0.995177 | − | 0.0980939i | \(-0.0312745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 980.301 | 1.43110 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.7225i | 0.0432643i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.8716 | 0.0346467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 450.798i | − 0.652385i | −0.945303 | − | 0.326193i | \(-0.894234\pi\) | ||||
0.945303 | − | 0.326193i | \(-0.105766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 388.831i | − 0.559468i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1301.31 | −1.86701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 213.335i | 0.305201i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −524.776 | −0.748611 | −0.374305 | − | 0.927306i | \(-0.622119\pi\) | ||||
−0.374305 | + | 0.927306i | \(0.622119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 89.3211i | − 0.127057i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 857.766 | 1.21669 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.4372 | −0.0626759 | −0.0313379 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313379 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 216.133i | 0.303985i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −320.236 | −0.449138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 506.211i | − 0.707987i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −194.319 | −0.271017 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 537.563i | 0.747654i | 0.927499 | + | 0.373827i | \(0.121955\pi\) | ||||
−0.927499 | + | 0.373827i | \(0.878045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 327.037i | − 0.452333i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1540.54 | 2.12488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 168.754i | 0.232124i | 0.993242 | + | 0.116062i | \(0.0370271\pi\) | ||||
−0.993242 | + | 0.116062i | \(0.962973\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −381.615 | −0.523477 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 634.525i | − 0.868023i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 201.692 | 0.275160 | 0.137580 | − | 0.990491i | \(-0.456068\pi\) | ||||
0.137580 | + | 0.990491i | \(0.456068\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.9235 | 0.0297470 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 221.788i | − 0.300119i | −0.988677 | − | 0.150059i | \(-0.952054\pi\) | ||||
0.988677 | − | 0.150059i | \(-0.0479465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 127.827 | 0.172507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 344.416i | − 0.463547i | −0.972770 | − | 0.231774i | \(-0.925547\pi\) | ||||
0.972770 | − | 0.231774i | \(-0.0744529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1553.51 | 2.08524 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 577.147i | − 0.772620i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1347.61i | − 1.79442i | −0.441603 | − | 0.897211i | \(-0.645590\pi\) | ||||
0.441603 | − | 0.897211i | \(-0.354410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −397.659 | −0.528099 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2012.34i | 2.66536i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −796.713 | −1.05246 | −0.526230 | − | 0.850342i | \(-0.676395\pi\) | ||||
−0.526230 | + | 0.850342i | \(0.676395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 779.122i | − 1.02651i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −814.559 | −1.07038 | −0.535190 | − | 0.844732i | \(-0.679760\pi\) | ||||
−0.535190 | + | 0.844732i | \(0.679760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1301.31 | −1.70106 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 157.484i | − 0.205325i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 60.5653 | 0.0787585 | 0.0393792 | − | 0.999224i | \(-0.487462\pi\) | ||||
0.0393792 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 315.567i | − 0.409296i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −998.420 | −1.29162 | −0.645809 | − | 0.763499i | \(-0.723480\pi\) | ||||
−0.645809 | + | 0.763499i | \(0.723480\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 323.148i | 0.416965i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 592.861i | 0.761054i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1279.87 | −1.63876 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 958.079i | − 1.22360i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1810.63 | −2.30654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 753.969i | 0.958029i | 0.877807 | + | 0.479014i | \(0.159006\pi\) | ||||
−0.877807 | + | 0.479014i | \(0.840994\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −510.480 | −0.646996 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.17263 | −0.00273975 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 58.9903i | − 0.0742016i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 335.856 | 0.421400 | 0.210700 | − | 0.977551i | \(-0.432426\pi\) | ||||
0.210700 | + | 0.977551i | \(0.432426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1597.16i | − 1.99895i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −178.178 | −0.222444 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 810.762i | 1.00967i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 398.491i | − 0.493793i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 749.689 | 0.926686 | 0.463343 | − | 0.886179i | \(-0.346650\pi\) | ||||
0.463343 | + | 0.886179i | \(0.346650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 790.284i | 0.974456i | 0.873275 | + | 0.487228i | \(0.161992\pi\) | ||||
−0.873275 | + | 0.487228i | \(0.838008\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −346.112 | −0.425722 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2231.59i | − 2.73815i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −289.082 | −0.353834 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 919.096 | 1.11948 | 0.559742 | − | 0.828667i | \(-0.310900\pi\) | ||||
0.559742 | + | 0.828667i | \(0.310900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 971.193i | − 1.18006i | −0.807380 | − | 0.590032i | \(-0.799115\pi\) | ||||
0.807380 | − | 0.590032i | \(-0.200885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −786.207 | −0.952979 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 110.492i | − 0.133606i | −0.997766 | − | 0.0668029i | \(-0.978720\pi\) | ||||
0.997766 | − | 0.0668029i | \(-0.0212799\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −495.972 | −0.598278 | −0.299139 | − | 0.954210i | \(-0.596699\pi\) | ||||
−0.299139 | + | 0.954210i | \(0.596699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 239.891i | 0.288677i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 729.011i | 0.873067i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 200.970 | 0.240107 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 529.377i | − 0.630962i | −0.948932 | − | 0.315481i | \(-0.897834\pi\) | ||||
0.948932 | − | 0.315481i | \(-0.102166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 485.672 | 0.577493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 658.844i | 0.781547i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1103.55 | 1.30598 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −508.350 | −0.598763 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 304.163i | 0.357418i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1122.77 | 1.31626 | 0.658132 | − | 0.752902i | \(-0.271347\pi\) | ||||
0.658132 | + | 0.752902i | \(0.271347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 592.861i | 0.693405i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −669.932 | −0.781717 | −0.390859 | − | 0.920451i | \(-0.627822\pi\) | ||||
−0.390859 | + | 0.920451i | \(0.627822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 234.046i | − 0.272464i | −0.990677 | − | 0.136232i | \(-0.956501\pi\) | ||||
0.990677 | − | 0.136232i | \(-0.0434992\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 51.7036i | − 0.0599115i | −0.999551 | − | 0.0299557i | \(-0.990463\pi\) | ||||
0.999551 | − | 0.0299557i | \(-0.00953663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2618.36 | 3.02701 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 779.847i | − 0.899478i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 386.858 | 0.445176 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 12.2484i | − 0.0140625i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.4754 | −0.0394908 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −108.325 | −0.123518 | −0.0617590 | − | 0.998091i | \(-0.519671\pi\) | ||||
−0.0617590 | + | 0.998091i | \(0.519671\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 233.379i | − 0.265506i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 901.643 | 1.02343 | 0.511716 | − | 0.859155i | \(-0.329010\pi\) | ||||
0.511716 | + | 0.859155i | \(0.329010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 391.049i | − 0.442864i | −0.975176 | − | 0.221432i | \(-0.928927\pi\) | ||||
0.975176 | − | 0.221432i | \(-0.0710731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −389.167 | −0.439737 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1296.88i | − 1.46209i | −0.682328 | − | 0.731047i | \(-0.739032\pi\) | ||||
0.682328 | − | 0.731047i | \(-0.260968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 66.4167i | − 0.0745418i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −727.647 | −0.814835 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1143.84i | − 1.27803i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −435.287 | −0.485270 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 278.287i | 0.309552i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −109.840 | −0.121909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 599.934 | 0.662911 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 461.509i | − 0.508831i | −0.967095 | − | 0.254415i | \(-0.918117\pi\) | ||||
0.967095 | − | 0.254415i | \(-0.0818830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −900.210 | −0.990330 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 119.595i | − 0.131279i | −0.997843 | − | 0.0656395i | \(-0.979091\pi\) | ||||
0.997843 | − | 0.0656395i | \(-0.0209087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1033.04 | −1.13148 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.36889i | 0.00586764i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 707.698i | − 0.770074i | −0.922901 | − | 0.385037i | \(-0.874189\pi\) | ||||
0.922901 | − | 0.385037i | \(-0.125811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 84.5902 | 0.0918460 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 715.049i | 0.774701i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 306.929 | 0.331815 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 456.380i | − 0.492319i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −397.056 | −0.427401 | −0.213701 | − | 0.976899i | \(-0.568552\pi\) | ||||
−0.213701 | + | 0.976899i | \(0.568552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 402.385 | 0.431281 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2329.22i | 2.49114i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1227.51 | −1.31004 | −0.655020 | − | 0.755612i | \(-0.727340\pi\) | ||||
−0.655020 | + | 0.755612i | \(0.727340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 217.725i | − 0.231869i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −687.041 | −0.730118 | −0.365059 | − | 0.930984i | \(-0.618951\pi\) | ||||
−0.365059 | + | 0.930984i | \(0.618951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2018.86i | − 2.14089i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 133.564i | 0.141039i | 0.997510 | + | 0.0705194i | \(0.0224657\pi\) | ||||
−0.997510 | + | 0.0705194i | \(0.977534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 452.964 | 0.477307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 849.514i | 0.893285i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1030.34 | 1.08115 | 0.540575 | − | 0.841296i | \(-0.318207\pi\) | ||||
0.540575 | + | 0.841296i | \(0.318207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1052.40i | 1.10198i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −677.063 | −0.707485 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 902.626 | 0.939257 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 968.161i | − 1.00536i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2293.15 | −2.37632 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 337.880i | 0.349410i | 0.984621 | + | 0.174705i | \(0.0558972\pi\) | ||||
−0.984621 | + | 0.174705i | \(0.944103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −588.170 | −0.606986 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1679.34i | − 1.72950i | −0.502202 | − | 0.864750i | \(-0.667477\pi\) | ||||
0.502202 | − | 0.864750i | \(-0.332523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 439.246i | 0.450508i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1109.36 | −1.13547 | −0.567737 | − | 0.823210i | \(-0.692181\pi\) | ||||
−0.567737 | + | 0.823210i | \(0.692181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 318.921i | 0.325762i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 359.691 | 0.366657 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 416.403i | − 0.423604i | −0.977313 | − | 0.211802i | \(-0.932067\pi\) | ||||
0.977313 | − | 0.211802i | \(-0.0679333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 812.648 | 0.825023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 984.404 | 0.995353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1194.84i | 1.20569i | 0.797858 | + | 0.602846i | \(0.205967\pi\) | ||||
−0.797858 | + | 0.602846i | \(0.794033\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −839.073 | −0.844988 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1938.60i | − 1.94834i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1677.13 | 1.68218 | 0.841090 | − | 0.540895i | \(-0.181914\pi\) | ||||
0.841090 | + | 0.540895i | \(0.181914\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 190.883i | − 0.191074i |
(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 | 1568.3.d.i.1471.2 | 6 | ||
4.3 | odd | 2 | inner | 1568.3.d.i.1471.5 | 6 | ||
7.2 | even | 3 | 224.3.r.d.95.5 | yes | 12 | ||
7.4 | even | 3 | 224.3.r.d.191.2 | yes | 12 | ||
7.6 | odd | 2 | 1568.3.d.l.1471.5 | 6 | |||
28.11 | odd | 6 | 224.3.r.d.191.5 | yes | 12 | ||
28.23 | odd | 6 | 224.3.r.d.95.2 | ✓ | 12 | ||
28.27 | even | 2 | 1568.3.d.l.1471.2 | 6 | |||
56.11 | odd | 6 | 448.3.r.f.191.2 | 12 | |||
56.37 | even | 6 | 448.3.r.f.319.2 | 12 | |||
56.51 | odd | 6 | 448.3.r.f.319.5 | 12 | |||
56.53 | even | 6 | 448.3.r.f.191.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.d.95.2 | ✓ | 12 | 28.23 | odd | 6 | ||
224.3.r.d.95.5 | yes | 12 | 7.2 | even | 3 | ||
224.3.r.d.191.2 | yes | 12 | 7.4 | even | 3 | ||
224.3.r.d.191.5 | yes | 12 | 28.11 | odd | 6 | ||
448.3.r.f.191.2 | 12 | 56.11 | odd | 6 | |||
448.3.r.f.191.5 | 12 | 56.53 | even | 6 | |||
448.3.r.f.319.2 | 12 | 56.37 | even | 6 | |||
448.3.r.f.319.5 | 12 | 56.51 | odd | 6 | |||
1568.3.d.i.1471.2 | 6 | 1.1 | even | 1 | trivial | ||
1568.3.d.i.1471.5 | 6 | 4.3 | odd | 2 | inner | ||
1568.3.d.l.1471.2 | 6 | 28.27 | even | 2 | |||
1568.3.d.l.1471.5 | 6 | 7.6 | odd | 2 |