Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(191,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.191");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.3 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.191 |
Dual form | 320.3.b.c.191.2 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 2.35114i | 0.783714i | 0.920026 | + | 0.391857i | \(0.128167\pi\) | ||||
−0.920026 | + | 0.391857i | \(0.871833\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 5.25731i | − 0.751044i | −0.926813 | − | 0.375522i | \(-0.877463\pi\) | ||||
0.926813 | − | 0.375522i | \(-0.122537\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.47214 | 0.385793 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 19.9192i | − 1.81084i | −0.424522 | − | 0.905418i | \(-0.639558\pi\) | ||||
0.424522 | − | 0.905418i | \(-0.360442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.47214 | 0.651703 | 0.325851 | − | 0.945421i | \(-0.394349\pi\) | ||||
0.325851 | + | 0.945421i | \(0.394349\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.25731i | 0.350487i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.8885 | 0.699326 | 0.349663 | − | 0.936876i | \(-0.386296\pi\) | ||||
0.349663 | + | 0.936876i | \(0.386296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.2169i | 0.800890i | 0.916321 | + | 0.400445i | \(0.131144\pi\) | ||||
−0.916321 | + | 0.400445i | \(0.868856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3607 | 0.588604 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.555029i | − 0.0241317i | −0.999927 | − | 0.0120659i | \(-0.996159\pi\) | ||||
0.999927 | − | 0.0120659i | \(-0.00384077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.3238i | 1.08606i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.9443 | 0.377389 | 0.188694 | − | 0.982036i | \(-0.439574\pi\) | ||||
0.188694 | + | 0.982036i | \(0.439574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.29451i | − 0.267565i | −0.991011 | − | 0.133782i | \(-0.957288\pi\) | ||||
0.991011 | − | 0.133782i | \(-0.0427123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 46.8328 | 1.41918 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 11.7557i | − 0.335877i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.3607 | 0.496235 | 0.248117 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248117 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.9192i | 0.510748i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.5836 | −0.355697 | −0.177849 | − | 0.984058i | \(-0.556914\pi\) | ||||
−0.177849 | + | 0.984058i | \(0.556914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 22.2703i | − 0.517915i | −0.965889 | − | 0.258957i | \(-0.916621\pi\) | ||||
0.965889 | − | 0.258957i | \(-0.0833789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.76393 | 0.172532 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 53.3902i | 1.13596i | 0.823042 | + | 0.567981i | \(0.192275\pi\) | ||||
−0.823042 | + | 0.567981i | \(0.807725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.3607 | 0.435932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 27.9516i | 0.548071i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 66.3607 | 1.25209 | 0.626044 | − | 0.779788i | \(-0.284673\pi\) | ||||
0.626044 | + | 0.779788i | \(0.284673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 44.5407i | − 0.809830i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −35.7771 | −0.627668 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 17.4370i | − 0.295543i | −0.989022 | − | 0.147771i | \(-0.952790\pi\) | ||||
0.989022 | − | 0.147771i | \(-0.0472100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −90.1378 | −1.47767 | −0.738834 | − | 0.673887i | \(-0.764623\pi\) | ||||
−0.738834 | + | 0.673887i | \(0.764623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 18.2541i | − 0.289748i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.9443 | 0.291450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 50.2220i | − 0.749582i | −0.927109 | − | 0.374791i | \(-0.877715\pi\) | ||||
0.927109 | − | 0.374791i | \(-0.122285\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.30495 | 0.0189123 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 80.7868i | − 1.13784i | −0.822392 | − | 0.568921i | \(-0.807361\pi\) | ||||
0.822392 | − | 0.568921i | \(-0.192639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55418 | −0.0760846 | −0.0380423 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380423 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.7557i | 0.156743i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −104.721 | −1.36002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 13.8448i | − 0.175251i | −0.996154 | − | 0.0876253i | \(-0.972072\pi\) | ||||
0.996154 | − | 0.0876253i | \(-0.0279278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −37.6950 | −0.465371 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.2155i | 0.918260i | 0.888369 | + | 0.459130i | \(0.151839\pi\) | ||||
−0.888369 | + | 0.459130i | \(0.848161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.5836 | 0.312748 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25.7315i | 0.295765i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111.443 | −1.25217 | −0.626083 | − | 0.779757i | \(-0.715343\pi\) | ||||
−0.626083 | + | 0.779757i | \(0.715343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 44.5407i | − 0.489458i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.5016 | 0.209694 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34.0260i | 0.358169i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −92.8328 | −0.957039 | −0.478520 | − | 0.878077i | \(-0.658826\pi\) | ||||
−0.478520 | + | 0.878077i | \(0.658826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 69.1621i | − 0.698607i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −64.1115 | −0.634767 | −0.317383 | − | 0.948297i | \(-0.602804\pi\) | ||||
−0.317383 | + | 0.948297i | \(0.602804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 137.769i | 1.33757i | 0.743458 | + | 0.668783i | \(0.233184\pi\) | ||||
−0.743458 | + | 0.668783i | \(0.766816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 27.6393 | 0.263232 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 51.3320i | 0.479739i | 0.970805 | + | 0.239869i | \(0.0771046\pi\) | ||||
−0.970805 | + | 0.239869i | \(0.922895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −133.469 | −1.22449 | −0.612243 | − | 0.790669i | \(-0.709733\pi\) | ||||
−0.612243 | + | 0.790669i | \(0.709733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 43.1685i | 0.388906i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 170.721 | 1.51081 | 0.755404 | − | 0.655259i | \(-0.227441\pi\) | ||||
0.755404 | + | 0.655259i | \(0.227441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.24108i | − 0.0107920i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 29.4164 | 0.251422 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 62.5018i | − 0.525225i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −275.774 | −2.27912 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 34.2881i | − 0.278765i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 198.637i | − 1.56407i | −0.623235 | − | 0.782035i | \(-0.714182\pi\) | ||||
0.623235 | − | 0.782035i | \(-0.285818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 52.3607 | 0.405897 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.77041i | − 0.0593161i | −0.999560 | − | 0.0296580i | \(-0.990558\pi\) | ||||
0.999560 | − | 0.0296580i | \(-0.00944183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.0000 | 0.601504 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 65.5699i | 0.485703i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.832816 | 0.00607895 | 0.00303947 | − | 0.999995i | \(-0.499033\pi\) | ||||
0.00303947 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 237.658i | 1.70977i | 0.518817 | + | 0.854885i | \(0.326373\pi\) | ||||
−0.518817 | + | 0.854885i | \(0.673627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −125.528 | −0.890269 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 168.758i | − 1.18013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.4721 | 0.168773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 50.2220i | 0.341646i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 36.9706 | 0.248125 | 0.124062 | − | 0.992274i | \(-0.460408\pi\) | ||||
0.124062 | + | 0.992274i | \(0.460408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 282.723i | 1.87234i | 0.351552 | + | 0.936168i | \(0.385654\pi\) | ||||
−0.351552 | + | 0.936168i | \(0.614346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 41.2786 | 0.269795 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 18.5471i | − 0.119659i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −204.748 | −1.30413 | −0.652063 | − | 0.758165i | \(-0.726096\pi\) | ||||
−0.652063 | + | 0.758165i | \(0.726096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 156.023i | 0.981279i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.91796 | −0.0181240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 107.235i | − 0.657885i | −0.944350 | − | 0.328943i | \(-0.893308\pi\) | ||||
0.944350 | − | 0.328943i | \(-0.106692\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 104.721 | 0.634675 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 33.2090i | 0.198856i | 0.995045 | + | 0.0994280i | \(0.0317013\pi\) | ||||
−0.995045 | + | 0.0994280i | \(0.968299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −97.2229 | −0.575284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 52.8352i | 0.308978i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 226.361 | 1.30844 | 0.654222 | − | 0.756303i | \(-0.272996\pi\) | ||||
0.654222 | + | 0.756303i | \(0.272996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 26.2866i | − 0.150209i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.9969 | 0.231621 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 224.337i | − 1.25328i | −0.779308 | − | 0.626641i | \(-0.784429\pi\) | ||||
0.779308 | − | 0.626641i | \(-0.215571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −86.2229 | −0.476370 | −0.238185 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238185 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 211.927i | − 1.15807i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.0557 | 0.221923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 236.810i | − 1.26636i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 154.164 | 0.815683 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 31.0198i | − 0.162407i | −0.996698 | − | 0.0812036i | \(-0.974124\pi\) | ||||
0.996698 | − | 0.0812036i | \(-0.0258764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.223 | 0.571103 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 44.5407i | 0.228414i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 172.525 | 0.875760 | 0.437880 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437880 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 272.208i | − 1.36788i | −0.729538 | − | 0.683940i | \(-0.760265\pi\) | ||||
0.729538 | − | 0.683940i | \(-0.239735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 118.079 | 0.587457 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 57.5374i | − 0.283436i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.6099 | −0.159073 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.92714i | − 0.00930984i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 303.108 | 1.45028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 205.266i | 0.972826i | 0.873729 | + | 0.486413i | \(0.161695\pi\) | ||||
−0.873729 | + | 0.486413i | \(0.838305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 189.941 | 0.891743 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 49.7980i | − 0.231618i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −43.6068 | −0.200953 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 13.0586i | − 0.0596285i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 100.721 | 0.455753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 235.731i | 1.05709i | 0.848905 | + | 0.528545i | \(0.177262\pi\) | ||||
−0.848905 | + | 0.528545i | \(0.822738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.3607 | 0.0771586 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 58.5165i | 0.257782i | 0.991659 | + | 0.128891i | \(0.0411417\pi\) | ||||
−0.991659 | + | 0.128891i | \(0.958858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −162.721 | −0.710574 | −0.355287 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355287 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 246.215i | − 1.06586i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 319.050 | 1.36931 | 0.684656 | − | 0.728867i | \(-0.259953\pi\) | ||||
0.684656 | + | 0.728867i | \(0.259953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 119.384i | 0.508017i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.5511 | 0.137346 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 236.810i | 0.990837i | 0.868654 | + | 0.495419i | \(0.164985\pi\) | ||||
−0.868654 | + | 0.495419i | \(0.835015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.917961 | −0.00380897 | −0.00190448 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190448 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 175.287i | 0.721347i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 47.7639 | 0.194955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 128.920i | 0.521942i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −179.193 | −0.719653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 136.690i | 0.544582i | 0.962215 | + | 0.272291i | \(0.0877813\pi\) | ||||
−0.962215 | + | 0.272291i | \(0.912219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0557 | −0.0436985 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 62.5018i | 0.245105i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −274.944 | −1.06982 | −0.534911 | − | 0.844908i | \(-0.679655\pi\) | ||||
−0.534911 | + | 0.844908i | \(0.679655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 96.5278i | − 0.372694i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38.0000 | 0.145594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 406.385i | 1.54519i | 0.634899 | + | 0.772596i | \(0.281042\pi\) | ||||
−0.634899 | + | 0.772596i | \(0.718958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 148.387 | 0.559951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 262.018i | − 0.981339i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 348.525 | 1.29563 | 0.647816 | − | 0.761797i | \(-0.275683\pi\) | ||||
0.647816 | + | 0.761797i | \(0.275683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 247.849i | − 0.914571i | −0.889320 | − | 0.457286i | \(-0.848822\pi\) | ||||
0.889320 | − | 0.457286i | \(-0.151178\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 104.721 | 0.383595 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 99.5959i | − 0.362167i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 54.7539 | 0.197667 | 0.0988337 | − | 0.995104i | \(-0.468489\pi\) | ||||
0.0988337 | + | 0.995104i | \(0.468489\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 28.7997i | − 0.103225i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −50.3607 | −0.179220 | −0.0896098 | − | 0.995977i | \(-0.528562\pi\) | ||||
−0.0896098 | + | 0.995977i | \(0.528562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 147.336i | 0.520621i | 0.965525 | + | 0.260310i | \(0.0838249\pi\) | ||||
−0.965525 | + | 0.260310i | \(0.916175\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −80.0000 | −0.280702 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 76.6705i | 0.267145i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −147.663 | −0.510943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 218.263i | − 0.750045i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −178.859 | −0.610441 | −0.305220 | − | 0.952282i | \(-0.598730\pi\) | ||||
−0.305220 | + | 0.952282i | \(0.598730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 38.9904i | − 0.132171i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 584.105 | 1.96668 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.70228i | − 0.0157267i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −117.082 | −0.388977 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 150.735i | − 0.497475i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −201.554 | −0.660833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 284.550i | 0.926873i | 0.886130 | + | 0.463436i | \(0.153384\pi\) | ||||
−0.886130 | + | 0.463436i | \(0.846616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −323.915 | −1.04827 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 282.199i | 0.907392i | 0.891157 | + | 0.453696i | \(0.149895\pi\) | ||||
−0.891157 | + | 0.453696i | \(0.850105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −567.548 | −1.81325 | −0.906626 | − | 0.421935i | \(-0.861351\pi\) | ||||
−0.906626 | + | 0.421935i | \(0.861351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 40.8174i | − 0.129579i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −161.141 | −0.508331 | −0.254165 | − | 0.967161i | \(-0.581801\pi\) | ||||
−0.254165 | + | 0.967161i | \(0.581801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 218.001i | − 0.683389i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −120.689 | −0.375978 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 180.907i | 0.560083i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.3607 | 0.130341 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 313.805i | − 0.959647i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 280.689 | 0.853158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 331.966i | − 1.00292i | −0.865181 | − | 0.501459i | \(-0.832797\pi\) | ||||
0.865181 | − | 0.501459i | \(-0.167203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 63.7508 | 0.191444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 112.300i | − 0.335223i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −269.108 | −0.798541 | −0.399271 | − | 0.916833i | \(-0.630737\pi\) | ||||
−0.399271 | + | 0.916833i | \(0.630737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 401.390i | 1.18404i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −165.220 | −0.484516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 369.908i | − 1.07845i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.91796 | 0.00845786 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 503.075i | 1.44978i | 0.688863 | + | 0.724892i | \(0.258110\pi\) | ||||
−0.688863 | + | 0.724892i | \(0.741890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.504658 | 0.00144601 | 0.000723006 | − | 1.00000i | \(-0.499770\pi\) | ||||
0.000723006 | 1.00000i | \(0.499770\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 248.435i | 0.707791i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −335.994 | −0.951824 | −0.475912 | − | 0.879493i | \(-0.657882\pi\) | ||||
−0.475912 | + | 0.879493i | \(0.657882\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 180.645i | − 0.508859i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 146.950 | 0.411626 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 98.4859i | 0.274334i | 0.990548 | + | 0.137167i | \(0.0437997\pi\) | ||||
−0.990548 | + | 0.137167i | \(0.956200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129.446 | 0.358576 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 648.384i | − 1.78618i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4195 | −0.0340261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 498.473i | 1.35824i | 0.734029 | + | 0.679118i | \(0.237638\pi\) | ||||
−0.734029 | + | 0.679118i | \(0.762362\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −50.6362 | −0.137226 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 348.879i | − 0.940374i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −600.354 | −1.60953 | −0.804765 | − | 0.593594i | \(-0.797709\pi\) | ||||
−0.804765 | + | 0.593594i | \(0.797709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26.2866i | 0.0700975i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 92.7214 | 0.245945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 303.490i | − 0.800765i | −0.916348 | − | 0.400383i | \(-0.868877\pi\) | ||||
0.916348 | − | 0.400383i | \(-0.131123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 467.023 | 1.22578 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 332.583i | − 0.868362i | −0.900826 | − | 0.434181i | \(-0.857038\pi\) | ||||
0.900826 | − | 0.434181i | \(-0.142962\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −234.164 | −0.608218 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 77.3256i | − 0.199808i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −392.354 | −1.00862 | −0.504312 | − | 0.863522i | \(-0.668254\pi\) | ||||
−0.504312 | + | 0.863522i | \(0.668254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 6.59849i | − 0.0168759i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.2693 | 0.0464868 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 30.9579i | − 0.0783744i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −334.190 | −0.841789 | −0.420895 | − | 0.907110i | \(-0.638284\pi\) | ||||
−0.420895 | + | 0.907110i | \(0.638284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 188.091i | 0.471407i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 121.003 | 0.301753 | 0.150877 | − | 0.988553i | \(-0.451790\pi\) | ||||
0.150877 | + | 0.988553i | \(0.451790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 70.2722i | − 0.174373i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −84.2887 | −0.208120 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 365.730i | − 0.898599i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −607.410 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.95807i | 0.00476415i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −91.6718 | −0.221966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.423i | 0.410658i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −558.768 | −1.33997 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 466.760i | 1.11398i | 0.830518 | + | 0.556992i | \(0.188045\pi\) | ||||
−0.830518 | + | 0.556992i | \(0.811955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 73.0883 | 0.173606 | 0.0868031 | − | 0.996225i | \(-0.472335\pi\) | ||||
0.0868031 | + | 0.996225i | \(0.472335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 185.378i | 0.438246i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 59.4427 | 0.139865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 473.882i | 1.10979i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 396.774 | 0.924881 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 463.630i | − 1.07571i | −0.843038 | − | 0.537853i | \(-0.819235\pi\) | ||||
0.843038 | − | 0.537853i | \(-0.180765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −99.8359 | −0.230568 | −0.115284 | − | 0.993333i | \(-0.536778\pi\) | ||||
−0.115284 | + | 0.993333i | \(0.536778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 57.5374i | 0.132270i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.44582 | 0.0193268 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 374.086i | 0.852133i | 0.904692 | + | 0.426066i | \(0.140101\pi\) | ||||
−0.904692 | + | 0.426066i | \(0.859899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 74.1672 | 0.168180 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 290.100i | 0.654854i | 0.944877 | + | 0.327427i | \(0.106182\pi\) | ||||
−0.944877 | + | 0.327427i | \(0.893818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −249.193 | −0.559985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 86.9231i | 0.194459i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 299.921 | 0.667976 | 0.333988 | − | 0.942577i | \(-0.391606\pi\) | ||||
0.333988 | + | 0.942577i | \(0.391606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 290.493i | 0.644109i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −664.721 | −1.46738 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 99.5959i | − 0.218892i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 822.328 | 1.79941 | 0.899703 | − | 0.436503i | \(-0.143783\pi\) | ||||
0.899703 | + | 0.436503i | \(0.143783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 348.617i | 0.759513i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 456.885 | 0.991075 | 0.495537 | − | 0.868587i | \(-0.334971\pi\) | ||||
0.495537 | + | 0.868587i | \(0.334971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 400.249i | 0.864469i | 0.901761 | + | 0.432234i | \(0.142275\pi\) | ||||
−0.901761 | + | 0.432234i | \(0.857725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 43.6068 | 0.0937781 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 913.145i | − 1.95534i | −0.210139 | − | 0.977672i | \(-0.567392\pi\) | ||||
0.210139 | − | 0.977672i | \(-0.432608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −264.033 | −0.562969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 481.391i | − 1.02206i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −443.607 | −0.937858 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 76.0845i | 0.160178i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 230.413 | 0.483047 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 526.131i | − 1.09840i | −0.835692 | − | 0.549198i | \(-0.814933\pi\) | ||||
0.835692 | − | 0.549198i | \(-0.185067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 155.554 | 0.323397 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.86054i | − 0.0142040i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −207.580 | −0.428001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 443.541i | 0.910762i | 0.890297 | + | 0.455381i | \(0.150497\pi\) | ||||
−0.890297 | + | 0.455381i | \(0.849503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 252.125 | 0.515594 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 287.163i | 0.584854i | 0.956288 | + | 0.292427i | \(0.0944628\pi\) | ||||
−0.956288 | + | 0.292427i | \(0.905537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 130.111 | 0.263918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 154.651i | − 0.312427i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −424.721 | −0.854570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 810.936i | − 1.62512i | −0.582876 | − | 0.812561i | \(-0.698073\pi\) | ||||
0.582876 | − | 0.812561i | \(-0.301927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −78.0789 | −0.155846 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 642.471i | 1.27728i | 0.769506 | + | 0.638639i | \(0.220502\pi\) | ||||
−0.769506 | + | 0.638639i | \(0.779498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −143.358 | −0.283876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 228.585i | − 0.450858i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 915.050 | 1.79774 | 0.898870 | − | 0.438216i | \(-0.144389\pi\) | ||||
0.898870 | + | 0.438216i | \(0.144389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.2000i | 0.0571429i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −446.217 | −0.869818 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 308.061i | 0.598177i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1063.49 | 2.05704 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 532.206i | 1.02544i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1006.98 | 1.93279 | 0.966396 | − | 0.257058i | \(-0.0827533\pi\) | ||||
0.966396 | + | 0.257058i | \(0.0827533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 774.173i | 1.48025i | 0.672467 | + | 0.740127i | \(0.265235\pi\) | ||||
−0.672467 | + | 0.740127i | \(0.734765\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 61.8034 | 0.117721 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 98.6096i | − 0.187115i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.692 | 0.999418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 60.5437i | − 0.114018i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −123.554 | −0.231809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 114.782i | 0.214546i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 527.449 | 0.982214 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 425.487i | − 0.789401i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 259.115 | 0.478955 | 0.239477 | − | 0.970902i | \(-0.423024\pi\) | ||||
0.239477 | + | 0.970902i | \(0.423024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 202.722i | − 0.373337i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −298.446 | −0.547607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 149.818i | 0.273890i | 0.990579 | + | 0.136945i | \(0.0437284\pi\) | ||||
−0.990579 | + | 0.136945i | \(0.956272\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −312.971 | −0.570074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 166.538i | 0.302247i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −72.7864 | −0.131621 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 96.5278i | 0.173924i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −511.698 | −0.918668 | −0.459334 | − | 0.888264i | \(-0.651912\pi\) | ||||
−0.459334 | + | 0.888264i | \(0.651912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 188.677i | − 0.337526i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 556.774 | 0.992467 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 490.726i | − 0.871627i | −0.900037 | − | 0.435814i | \(-0.856461\pi\) | ||||
0.900037 | − | 0.435814i | \(-0.143539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 381.745 | 0.675654 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 198.175i | 0.349514i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −232.748 | −0.409047 | −0.204523 | − | 0.978862i | \(-0.565564\pi\) | ||||
−0.204523 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 210.755i | 0.369098i | 0.982823 | + | 0.184549i | \(0.0590824\pi\) | ||||
−0.982823 | + | 0.184549i | \(0.940918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 72.9318 | 0.127281 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.77515i | − 0.00482634i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 341.712 | 0.592222 | 0.296111 | − | 0.955154i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955154i | \(0.404310\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 259.150i | 0.447581i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 400.689 | 0.689654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1321.85i | − 2.26733i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 65.7771 | 0.112439 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 618.412i | − 1.05351i | −0.850016 | − | 0.526756i | \(-0.823408\pi\) | ||||
0.850016 | − | 0.526756i | \(-0.176592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 126.217 | 0.214290 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 405.630i | 0.686345i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 120.663 | 0.203478 | 0.101739 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101739 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 139.758i | − 0.234888i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 640.000 | 1.07203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 849.927i | − 1.41891i | −0.704751 | − | 0.709455i | \(-0.748941\pi\) | ||||
0.704751 | − | 0.709455i | \(-0.251059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3576 | −0.0188978 | −0.00944890 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944890 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 174.378i | − 0.289183i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −616.649 | −1.01926 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1115.12i | − 1.83710i | −0.395305 | − | 0.918550i | \(-0.629361\pi\) | ||||
0.395305 | − | 0.918550i | \(-0.370639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 135.279 | 0.222132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 452.329i | 0.740309i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −499.475 | −0.814805 | −0.407402 | − | 0.913249i | \(-0.633565\pi\) | ||||
−0.407402 | + | 0.913249i | \(0.633565\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 76.6705i | − 0.124667i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 545.935 | 0.884822 | 0.442411 | − | 0.896813i | \(-0.354123\pi\) | ||||
0.442411 | + | 0.896813i | \(0.354123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 455.011i | − 0.735075i | −0.930009 | − | 0.367537i | \(-0.880201\pi\) | ||||
0.930009 | − | 0.367537i | \(-0.119799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.2755 | 0.0262086 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 585.889i | 0.940432i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 712.650i | 1.13660i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 218.282 | 0.347030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 267.706i | 0.424257i | 0.977242 | + | 0.212128i | \(0.0680395\pi\) | ||||
−0.977242 | + | 0.212128i | \(0.931960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −482.610 | −0.762417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 444.165i | − 0.699473i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 180.971 | 0.284098 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 280.503i | − 0.438971i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −418.571 | −0.652997 | −0.326499 | − | 0.945198i | \(-0.605869\pi\) | ||||
−0.326499 | + | 0.945198i | \(0.605869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 439.339i | − 0.683265i | −0.939834 | − | 0.341633i | \(-0.889020\pi\) | ||||
0.939834 | − | 0.341633i | \(-0.110980\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 117.082 | 0.181523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 419.644i | 0.648600i | 0.945954 | + | 0.324300i | \(0.105129\pi\) | ||||
−0.945954 | + | 0.324300i | \(0.894871\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −347.331 | −0.535179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 102.526i | − 0.157490i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 370.085 | 0.566746 | 0.283373 | − | 0.959010i | \(-0.408547\pi\) | ||||
0.283373 | + | 0.959010i | \(0.408547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 17.3752i | − 0.0265270i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.2849 | −0.0293529 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 322.823i | 0.489868i | 0.969540 | + | 0.244934i | \(0.0787664\pi\) | ||||
−0.969540 | + | 0.244934i | \(0.921234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 812.735 | 1.22955 | 0.614777 | − | 0.788701i | \(-0.289246\pi\) | ||||
0.614777 | + | 0.788701i | \(0.289246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 236.810i | 0.357180i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 178.885 | 0.269001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.07439i | − 0.00910703i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −554.237 | −0.828456 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1795.47i | 2.67581i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 467.378 | 0.694469 | 0.347235 | − | 0.937778i | \(-0.387121\pi\) | ||||
0.347235 | + | 0.937778i | \(0.387121\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 146.619i | 0.217213i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −548.237 | −0.809803 | −0.404902 | − | 0.914360i | \(-0.632694\pi\) | ||||
−0.404902 | + | 0.914360i | \(0.632694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 488.051i | 0.718779i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −137.580 | −0.202027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 23.9663i | − 0.0350898i | −0.999846 | − | 0.0175449i | \(-0.994415\pi\) | ||||
0.999846 | − | 0.0175449i | \(-0.00558500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.86223 | 0.00271859 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 382.581i | − 0.556886i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 562.217 | 0.815989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 186.981i | 0.270595i | 0.990805 | + | 0.135298i | \(0.0431990\pi\) | ||||
−0.990805 | + | 0.135298i | \(0.956801\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −363.607 | −0.524685 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 531.420i | 0.764633i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −173.378 | −0.248748 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 750.130i | 1.07315i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 706.636 | 1.00804 | 0.504020 | − | 0.863692i | \(-0.331854\pi\) | ||||
0.504020 | + | 0.863692i | \(0.331854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.393i | 0.397429i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −280.689 | −0.398140 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 337.054i | 0.476738i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 188.597 | 0.266005 | 0.133002 | − | 0.991116i | \(-0.457538\pi\) | ||||
0.133002 | + | 0.991116i | \(0.457538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 48.0710i | − 0.0676104i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.60369 | −0.00645679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 377.354i | − 0.527769i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −556.774 | −0.776533 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 156.085i | 0.217086i | 0.994092 | + | 0.108543i | \(0.0346186\pi\) | ||||
−0.994092 | + | 0.108543i | \(0.965381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 724.296 | 1.00457 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.15825i | − 0.00298514i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 54.7214 | 0.0754777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 715.164i | − 0.983719i | −0.870675 | − | 0.491859i | \(-0.836317\pi\) | ||||
0.870675 | − | 0.491859i | \(-0.163683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −751.381 | −1.03070 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 264.762i | − 0.362191i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1233.29 | −1.68252 | −0.841259 | − | 0.540632i | \(-0.818185\pi\) | ||||
−0.841259 | + | 0.540632i | \(0.818185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 112.300i | 0.152789i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1000.38 | −1.35737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.55656i | − 0.0115786i | −0.999983 | − | 0.00578928i | \(-0.998157\pi\) | ||||
0.999983 | − | 0.00578928i | \(-0.00184280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −303.108 | −0.409053 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1010.56i | − 1.36011i | −0.733163 | − | 0.680053i | \(-0.761957\pi\) | ||||
0.733163 | − | 0.680053i | \(-0.238043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 82.6687 | 0.110965 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 264.631i | 0.354258i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 269.868 | 0.360305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1104.31i | − 1.47046i | −0.677820 | − | 0.735228i | \(-0.737075\pi\) | ||||
0.677820 | − | 0.735228i | \(-0.262925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −321.378 | −0.426796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 632.188i | 0.837335i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 875.633 | 1.15671 | 0.578357 | − | 0.815783i | \(-0.303694\pi\) | ||||
0.578357 | + | 0.815783i | \(0.303694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 25.9936i | − 0.0342471i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −647.207 | −0.850470 | −0.425235 | − | 0.905083i | \(-0.639808\pi\) | ||||
−0.425235 | + | 0.905083i | \(0.639808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 701.688i | 0.919644i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 92.3018 | 0.120656 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 147.729i | − 0.192606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 631.430 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 646.433i | − 0.838434i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 421.522 | 0.545306 | 0.272653 | − | 0.962112i | \(-0.412099\pi\) | ||||
0.272653 | + | 0.962112i | \(0.412099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 41.4725i | − 0.0535129i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 226.950 | 0.292086 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 221.917i | − 0.284874i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1609.21 | −2.06044 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 320.927i | 0.409869i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −457.830 | −0.583223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 838.633i | − 1.06561i | −0.846239 | − | 0.532804i | \(-0.821138\pi\) | ||||
0.846239 | − | 0.532804i | \(-0.178862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −955.469 | −1.21099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 897.535i | − 1.13468i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −763.659 | −0.963001 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 348.879i | 0.438841i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1213.57 | −1.52268 | −0.761339 | − | 0.648354i | \(-0.775458\pi\) | ||||
−0.761339 | + | 0.648354i | \(0.775458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 634.732i | 0.794408i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −386.944 | −0.483076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 110.635i | 0.137777i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.52476 | −0.00810529 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 819.431i | 1.01540i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −229.214 | −0.283330 | −0.141665 | − | 0.989915i | \(-0.545246\pi\) | ||||
−0.141665 | + | 0.989915i | \(0.545246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 454.225i | − 0.560080i | −0.959988 | − | 0.280040i | \(-0.909652\pi\) | ||||
0.959988 | − | 0.280040i | \(-0.0903478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 582.728 | 0.716762 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 239.785i | − 0.294215i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 338.885 | 0.414792 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 154.651i | − 0.188829i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1130.90 | −1.37747 | −0.688733 | − | 0.725015i | \(-0.741833\pi\) | ||||
−0.688733 | + | 0.725015i | \(0.741833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 780.148i | 0.947931i | 0.880543 | + | 0.473966i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473966i | \(0.842822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 234.164 | 0.283835 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 209.175i | − 0.252932i | −0.991971 | − | 0.126466i | \(-0.959636\pi\) | ||||
0.991971 | − | 0.126466i | \(-0.0403635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 508.525 | 0.613419 | 0.306710 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306710 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 128.734i | 0.154915i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 253.947 | 0.304859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.2575i | 0.0889311i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 243.226 | 0.290593 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 274.028i | − 0.326613i | −0.986575 | − | 0.163306i | \(-0.947784\pi\) | ||||
0.986575 | − | 0.163306i | \(-0.0522159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −721.223 | −0.857578 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 118.405i | − 0.140457i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −217.397 | −0.257275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1449.83i | 1.71172i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −346.407 | −0.408018 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 10.1907i | − 0.0119750i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1583.28 | 1.85613 | 0.928066 | − | 0.372416i | \(-0.121471\pi\) | ||||
0.928066 | + | 0.372416i | \(0.121471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 118.143i | 0.138179i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1007.38 | −1.17547 | −0.587735 | − | 0.809054i | \(-0.699980\pi\) | ||||
−0.587735 | + | 0.809054i | \(0.699980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 76.6086i | 0.0891835i | 0.999005 | + | 0.0445917i | \(0.0141987\pi\) | ||||
−0.999005 | + | 0.0445917i | \(0.985801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −180.263 | −0.209365 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 255.450i | − 0.296002i | −0.988987 | − | 0.148001i | \(-0.952716\pi\) | ||||
0.988987 | − | 0.148001i | \(-0.0472839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 506.158 | 0.585154 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 347.175i | − 0.400433i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −275.777 | −0.317350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 425.487i | − 0.488504i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −322.328 | −0.369219 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 58.7785i | − 0.0671755i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −601.522 | −0.685886 | −0.342943 | − | 0.939356i | \(-0.611424\pi\) | ||||
−0.342943 | + | 0.939356i | \(0.611424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 420.523i | − 0.478411i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 237.850 | 0.269977 | 0.134989 | − | 0.990847i | \(-0.456900\pi\) | ||||
0.134989 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.30294i | 0.00147559i | 1.00000 | 0.000737794i | \(0.000234847\pi\) | |||||
−1.00000 | 0.000737794i | \(0.999765\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 91.6718 | 0.103584 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 536.353i | − 0.604682i | −0.953200 | − | 0.302341i | \(-0.902232\pi\) | ||||
0.953200 | − | 0.302341i | \(-0.0977682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1044.30 | −1.17469 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 750.855i | 0.842710i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −812.433 | −0.909780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 501.634i | − 0.560485i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0557 | 0.0123252 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 90.7773i | − 0.100976i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 788.932 | 0.875618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 275.276i | − 0.304846i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −192.800 | −0.213039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 332.159i | − 0.366217i | −0.983093 | − | 0.183108i | \(-0.941384\pi\) | ||||
0.983093 | − | 0.183108i | \(-0.0586159\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −222.604 | −0.244889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1450.06i | − 1.59172i | −0.605478 | − | 0.795862i | \(-0.707018\pi\) | ||||
0.605478 | − | 0.795862i | \(-0.292982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1518.15 | 1.66282 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 473.882i | − 0.517904i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.8514 | −0.0445490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 814.405i | 0.886186i | 0.896476 | + | 0.443093i | \(0.146119\pi\) | ||||
−0.896476 | + | 0.443093i | \(0.853881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −669.017 | −0.726403 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 684.437i | − 0.741535i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 91.8034 | 0.0992469 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 478.353i | 0.516023i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 400.039 | 0.430612 | 0.215306 | − | 0.976547i | \(-0.430925\pi\) | ||||
0.215306 | + | 0.976547i | \(0.430925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 325.043i | 0.349134i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −663.489 | −0.711135 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 529.524i | − 0.566335i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 249.279 | 0.266039 | 0.133020 | − | 0.991113i | \(-0.457533\pi\) | ||||
0.133020 | + | 0.991113i | \(0.457533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1334.39i | − 1.42107i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −724.229 | −0.769638 | −0.384819 | − | 0.922992i | \(-0.625736\pi\) | ||||
−0.384819 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.09432i | 0.00858358i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 344.721 | 0.364785 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1141.54i | 1.20542i | 0.797959 | + | 0.602712i | \(0.205913\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.0557 | −0.0495845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 378.865i | − 0.398386i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1295.33 | 1.35921 | 0.679604 | − | 0.733579i | \(-0.262152\pi\) | ||||
0.679604 | + | 0.733579i | \(0.262152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 69.3623i | − 0.0726307i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 512.551 | 0.535581 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 4.37837i | − 0.00456556i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 892.201 | 0.928409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 178.232i | 0.185080i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 246.466 | 0.255405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 398.477i | − 0.412075i | −0.978544 | − | 0.206037i | \(-0.933943\pi\) | ||||
0.978544 | − | 0.206037i | \(-0.0660569\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −425.337 | −0.438945 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 928.093i | 0.955811i | 0.878411 | + | 0.477906i | \(0.158604\pi\) | ||||
−0.878411 | + | 0.477906i | \(0.841396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1249.44 | 1.28411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 99.5959i | 0.102150i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1378.05 | −1.41049 | −0.705247 | − | 0.708962i | \(-0.749164\pi\) | ||||
−0.705247 | + | 0.708962i | \(0.749164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2219.85i | 2.26747i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −463.423 | −0.472398 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 311.291i | 0.316675i | 0.987385 | + | 0.158337i | \(0.0506134\pi\) | ||||
−0.987385 | + | 0.158337i | \(0.949387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 385.777 | 0.391652 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 659.939i | 0.668631i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.3607 | −0.0124982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 961.147i | 0.969876i | 0.874549 | + | 0.484938i | \(0.161158\pi\) | ||||
−0.874549 | + | 0.484938i | \(0.838842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 780.498 | 0.786000 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 608.676i | − 0.611735i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1089.68 | 1.09296 | 0.546479 | − | 0.837473i | \(-0.315968\pi\) | ||||
0.546479 | + | 0.837473i | \(0.315968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 538.404i | 0.538943i |
(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 | 320.3.b.c.191.3 | 4 | ||
3.2 | odd | 2 | 2880.3.e.e.2431.1 | 4 | |||
4.3 | odd | 2 | inner | 320.3.b.c.191.2 | 4 | ||
5.2 | odd | 4 | 1600.3.h.n.1599.5 | 8 | |||
5.3 | odd | 4 | 1600.3.h.n.1599.3 | 8 | |||
5.4 | even | 2 | 1600.3.b.s.1151.2 | 4 | |||
8.3 | odd | 2 | 20.3.b.a.11.3 | ✓ | 4 | ||
8.5 | even | 2 | 20.3.b.a.11.4 | yes | 4 | ||
12.11 | even | 2 | 2880.3.e.e.2431.2 | 4 | |||
16.3 | odd | 4 | 1280.3.g.e.1151.5 | 8 | |||
16.5 | even | 4 | 1280.3.g.e.1151.6 | 8 | |||
16.11 | odd | 4 | 1280.3.g.e.1151.4 | 8 | |||
16.13 | even | 4 | 1280.3.g.e.1151.3 | 8 | |||
20.3 | even | 4 | 1600.3.h.n.1599.6 | 8 | |||
20.7 | even | 4 | 1600.3.h.n.1599.4 | 8 | |||
20.19 | odd | 2 | 1600.3.b.s.1151.3 | 4 | |||
24.5 | odd | 2 | 180.3.c.a.91.1 | 4 | |||
24.11 | even | 2 | 180.3.c.a.91.2 | 4 | |||
40.3 | even | 4 | 100.3.d.b.99.1 | 8 | |||
40.13 | odd | 4 | 100.3.d.b.99.7 | 8 | |||
40.19 | odd | 2 | 100.3.b.f.51.2 | 4 | |||
40.27 | even | 4 | 100.3.d.b.99.8 | 8 | |||
40.29 | even | 2 | 100.3.b.f.51.1 | 4 | |||
40.37 | odd | 4 | 100.3.d.b.99.2 | 8 | |||
120.29 | odd | 2 | 900.3.c.k.451.4 | 4 | |||
120.53 | even | 4 | 900.3.f.e.199.2 | 8 | |||
120.59 | even | 2 | 900.3.c.k.451.3 | 4 | |||
120.77 | even | 4 | 900.3.f.e.199.7 | 8 | |||
120.83 | odd | 4 | 900.3.f.e.199.8 | 8 | |||
120.107 | odd | 4 | 900.3.f.e.199.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.b.a.11.3 | ✓ | 4 | 8.3 | odd | 2 | ||
20.3.b.a.11.4 | yes | 4 | 8.5 | even | 2 | ||
100.3.b.f.51.1 | 4 | 40.29 | even | 2 | |||
100.3.b.f.51.2 | 4 | 40.19 | odd | 2 | |||
100.3.d.b.99.1 | 8 | 40.3 | even | 4 | |||
100.3.d.b.99.2 | 8 | 40.37 | odd | 4 | |||
100.3.d.b.99.7 | 8 | 40.13 | odd | 4 | |||
100.3.d.b.99.8 | 8 | 40.27 | even | 4 | |||
180.3.c.a.91.1 | 4 | 24.5 | odd | 2 | |||
180.3.c.a.91.2 | 4 | 24.11 | even | 2 | |||
320.3.b.c.191.2 | 4 | 4.3 | odd | 2 | inner | ||
320.3.b.c.191.3 | 4 | 1.1 | even | 1 | trivial | ||
900.3.c.k.451.3 | 4 | 120.59 | even | 2 | |||
900.3.c.k.451.4 | 4 | 120.29 | odd | 2 | |||
900.3.f.e.199.1 | 8 | 120.107 | odd | 4 | |||
900.3.f.e.199.2 | 8 | 120.53 | even | 4 | |||
900.3.f.e.199.7 | 8 | 120.77 | even | 4 | |||
900.3.f.e.199.8 | 8 | 120.83 | odd | 4 | |||
1280.3.g.e.1151.3 | 8 | 16.13 | even | 4 | |||
1280.3.g.e.1151.4 | 8 | 16.11 | odd | 4 | |||
1280.3.g.e.1151.5 | 8 | 16.3 | odd | 4 | |||
1280.3.g.e.1151.6 | 8 | 16.5 | even | 4 | |||
1600.3.b.s.1151.2 | 4 | 5.4 | even | 2 | |||
1600.3.b.s.1151.3 | 4 | 20.19 | odd | 2 | |||
1600.3.h.n.1599.3 | 8 | 5.3 | odd | 4 | |||
1600.3.h.n.1599.4 | 8 | 20.7 | even | 4 | |||
1600.3.h.n.1599.5 | 8 | 5.2 | odd | 4 | |||
1600.3.h.n.1599.6 | 8 | 20.3 | even | 4 | |||
2880.3.e.e.2431.1 | 4 | 3.2 | odd | 2 | |||
2880.3.e.e.2431.2 | 4 | 12.11 | even | 2 |