Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(799,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1425.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.c (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: | \(11.3786822880\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 3x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 285) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.3 | ||
Root | \(1.32288 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.799 |
Dual form | 1425.2.c.i.799.2 |
$q$-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 \(\left(\mathbb{Z}/1425\mathbb{Z}\right)^\times\).
\(n\) | \(476\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.64575i | 1.87083i | 0.353553 | + | 0.935414i | \(0.384973\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −5.00000 | −2.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.64575 | 1.08012 | ||||||||
\(7\) | − 1.64575i | − 0.622036i | −0.950404 | − | 0.311018i | \(-0.899330\pi\) | ||||
0.950404 | − | 0.311018i | \(-0.100670\pi\) | |||||||
\(8\) | − 7.93725i | − 2.80624i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.354249 | 0.106810 | 0.0534050 | − | 0.998573i | \(-0.482993\pi\) | ||||
0.0534050 | + | 0.998573i | \(0.482993\pi\) | |||||||
\(12\) | 5.00000i | 1.44338i | ||||||||
\(13\) | − 0.354249i | − 0.0982509i | −0.998793 | − | 0.0491255i | \(-0.984357\pi\) | ||||
0.998793 | − | 0.0491255i | \(-0.0156434\pi\) | |||||||
\(14\) | 4.35425 | 1.16372 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.0000 | 2.75000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | − 2.64575i | − 0.623610i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64575 | −0.359132 | ||||||||
\(22\) | 0.937254i | 0.199823i | ||||||||
\(23\) | 9.29150i | 1.93741i | 0.248211 | + | 0.968706i | \(0.420158\pi\) | ||||
−0.248211 | + | 0.968706i | \(0.579842\pi\) | |||||||
\(24\) | −7.93725 | −1.62019 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.937254 | 0.183811 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 8.22876i | 1.55509i | ||||||||
\(29\) | −8.93725 | −1.65961 | −0.829803 | − | 0.558056i | \(-0.811547\pi\) | ||||
−0.829803 | + | 0.558056i | \(0.811547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 13.2288i | 2.33854i | ||||||||
\(33\) | − 0.354249i | − 0.0616668i | ||||||||
\(34\) | −10.5830 | −1.81497 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.00000 | 0.833333 | ||||||||
\(37\) | − 3.64575i | − 0.599358i | −0.954040 | − | 0.299679i | \(-0.903120\pi\) | ||||
0.954040 | − | 0.299679i | \(-0.0968795\pi\) | |||||||
\(38\) | 2.64575i | 0.429198i | ||||||||
\(39\) | −0.354249 | −0.0567252 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.64575 | −1.50641 | −0.753207 | − | 0.657784i | \(-0.771494\pi\) | ||||
−0.753207 | + | 0.657784i | \(0.771494\pi\) | |||||||
\(42\) | − 4.35425i | − 0.671875i | ||||||||
\(43\) | 5.64575i | 0.860969i | 0.902598 | + | 0.430485i | \(0.141657\pi\) | ||||
−0.902598 | + | 0.430485i | \(0.858343\pi\) | |||||||
\(44\) | −1.77124 | −0.267025 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24.5830 | −3.62457 | ||||||||
\(47\) | 1.29150i | 0.188385i | 0.995554 | + | 0.0941925i | \(0.0300269\pi\) | ||||
−0.995554 | + | 0.0941925i | \(0.969973\pi\) | |||||||
\(48\) | − 11.0000i | − 1.58771i | ||||||||
\(49\) | 4.29150 | 0.613072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 1.77124i | 0.245627i | ||||||||
\(53\) | 11.2915i | 1.55101i | 0.631343 | + | 0.775504i | \(0.282504\pi\) | ||||
−0.631343 | + | 0.775504i | \(0.717496\pi\) | |||||||
\(54\) | −2.64575 | −0.360041 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.0627 | −1.74558 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | − 23.6458i | − 3.10484i | ||||||||
\(59\) | −11.2915 | −1.47003 | −0.735014 | − | 0.678052i | \(-0.762825\pi\) | ||||
−0.735014 | + | 0.678052i | \(0.762825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2915 | −1.44573 | −0.722864 | − | 0.690990i | \(-0.757175\pi\) | ||||
−0.722864 | + | 0.690990i | \(0.757175\pi\) | |||||||
\(62\) | 15.8745i | 2.01606i | ||||||||
\(63\) | 1.64575i | 0.207345i | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.937254 | 0.115368 | ||||||||
\(67\) | 6.58301i | 0.804242i | 0.915587 | + | 0.402121i | \(0.131727\pi\) | ||||
−0.915587 | + | 0.402121i | \(0.868273\pi\) | |||||||
\(68\) | − 20.0000i | − 2.42536i | ||||||||
\(69\) | 9.29150 | 1.11857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.29150 | 0.865342 | 0.432671 | − | 0.901552i | \(-0.357571\pi\) | ||||
0.432671 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(72\) | 7.93725i | 0.935414i | ||||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 9.64575 | 1.12130 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | − 0.583005i | − 0.0664396i | ||||||||
\(78\) | − 0.937254i | − 0.106123i | ||||||||
\(79\) | −6.58301 | −0.740646 | −0.370323 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370323 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 25.5203i | − 2.81824i | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 8.22876 | 0.897831 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.9373 | −1.61073 | ||||||||
\(87\) | 8.93725i | 0.958174i | ||||||||
\(88\) | − 2.81176i | − 0.299735i | ||||||||
\(89\) | 16.9373 | 1.79535 | 0.897673 | − | 0.440663i | \(-0.145257\pi\) | ||||
0.897673 | + | 0.440663i | \(0.145257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.583005 | −0.0611156 | ||||||||
\(92\) | − 46.4575i | − 4.84353i | ||||||||
\(93\) | − 6.00000i | − 0.622171i | ||||||||
\(94\) | −3.41699 | −0.352436 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 13.2288 | 1.35015 | ||||||||
\(97\) | 2.93725i | 0.298233i | 0.988820 | + | 0.149116i | \(0.0476429\pi\) | ||||
−0.988820 | + | 0.149116i | \(0.952357\pi\) | |||||||
\(98\) | 11.3542i | 1.14695i | ||||||||
\(99\) | −0.354249 | −0.0356033 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.29150 | 0.924539 | 0.462270 | − | 0.886739i | \(-0.347035\pi\) | ||||
0.462270 | + | 0.886739i | \(0.347035\pi\) | |||||||
\(102\) | 10.5830i | 1.04787i | ||||||||
\(103\) | − 10.5830i | − 1.04277i | −0.853320 | − | 0.521387i | \(-0.825415\pi\) | ||||
0.853320 | − | 0.521387i | \(-0.174585\pi\) | |||||||
\(104\) | −2.81176 | −0.275716 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.8745 | −2.90167 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | − 5.00000i | − 0.481125i | ||||||||
\(109\) | −5.29150 | −0.506834 | −0.253417 | − | 0.967357i | \(-0.581554\pi\) | ||||
−0.253417 | + | 0.967357i | \(0.581554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.64575 | −0.346039 | ||||||||
\(112\) | − 18.1033i | − 1.71060i | ||||||||
\(113\) | − 4.00000i | − 0.376288i | −0.982141 | − | 0.188144i | \(-0.939753\pi\) | ||||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | 2.64575 | 0.247797 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 44.6863 | 4.14902 | ||||||||
\(117\) | 0.354249i | 0.0327503i | ||||||||
\(118\) | − 29.8745i | − 2.75017i | ||||||||
\(119\) | 6.58301 | 0.603463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8745 | −0.988592 | ||||||||
\(122\) | − 29.8745i | − 2.70471i | ||||||||
\(123\) | 9.64575i | 0.869728i | ||||||||
\(124\) | −30.0000 | −2.69408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.35425 | −0.387907 | ||||||||
\(127\) | − 4.00000i | − 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | − 7.93725i | − 0.701561i | ||||||||
\(129\) | 5.64575 | 0.497081 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2288 | −1.24317 | −0.621586 | − | 0.783346i | \(-0.713511\pi\) | ||||
−0.621586 | + | 0.783346i | \(0.713511\pi\) | |||||||
\(132\) | 1.77124i | 0.154167i | ||||||||
\(133\) | − 1.64575i | − 0.142705i | ||||||||
\(134\) | −17.4170 | −1.50460 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31.7490 | 2.72246 | ||||||||
\(137\) | − 6.00000i | − 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 24.5830i | 2.09264i | ||||||||
\(139\) | −17.8745 | −1.51610 | −0.758048 | − | 0.652199i | \(-0.773847\pi\) | ||||
−0.758048 | + | 0.652199i | \(0.773847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.29150 | 0.108764 | ||||||||
\(142\) | 19.2915i | 1.61891i | ||||||||
\(143\) | − 0.125492i | − 0.0104942i | ||||||||
\(144\) | −11.0000 | −0.916667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26.4575 | −2.18964 | ||||||||
\(147\) | − 4.29150i | − 0.353957i | ||||||||
\(148\) | 18.2288i | 1.49839i | ||||||||
\(149\) | 20.5830 | 1.68623 | 0.843113 | − | 0.537737i | \(-0.180721\pi\) | ||||
0.843113 | + | 0.537737i | \(0.180721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.58301 | −0.698475 | −0.349238 | − | 0.937034i | \(-0.613559\pi\) | ||||
−0.349238 | + | 0.937034i | \(0.613559\pi\) | |||||||
\(152\) | − 7.93725i | − 0.643796i | ||||||||
\(153\) | − 4.00000i | − 0.323381i | ||||||||
\(154\) | 1.54249 | 0.124297 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.77124 | 0.141813 | ||||||||
\(157\) | 13.2915i | 1.06078i | 0.847755 | + | 0.530389i | \(0.177954\pi\) | ||||
−0.847755 | + | 0.530389i | \(0.822046\pi\) | |||||||
\(158\) | − 17.4170i | − 1.38562i | ||||||||
\(159\) | 11.2915 | 0.895474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2915 | 1.20514 | ||||||||
\(162\) | 2.64575i | 0.207870i | ||||||||
\(163\) | − 2.35425i | − 0.184399i | −0.995741 | − | 0.0921995i | \(-0.970610\pi\) | ||||
0.995741 | − | 0.0921995i | \(-0.0293898\pi\) | |||||||
\(164\) | 48.2288 | 3.76603 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.8745 | −1.23210 | ||||||||
\(167\) | 21.2915i | 1.64759i | 0.566891 | + | 0.823793i | \(0.308146\pi\) | ||||
−0.566891 | + | 0.823793i | \(0.691854\pi\) | |||||||
\(168\) | 13.0627i | 1.00781i | ||||||||
\(169\) | 12.8745 | 0.990347 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | − 28.2288i | − 2.15242i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | −23.6458 | −1.79258 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.89674 | 0.293727 | ||||||||
\(177\) | 11.2915i | 0.848721i | ||||||||
\(178\) | 44.8118i | 3.35878i | ||||||||
\(179\) | 7.29150 | 0.544992 | 0.272496 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272496 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2915 | 1.28527 | 0.642634 | − | 0.766174i | \(-0.277842\pi\) | ||||
0.642634 | + | 0.766174i | \(0.277842\pi\) | |||||||
\(182\) | − 1.54249i | − 0.114337i | ||||||||
\(183\) | 11.2915i | 0.834692i | ||||||||
\(184\) | 73.7490 | 5.43685 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.8745 | 1.16398 | ||||||||
\(187\) | 1.41699i | 0.103621i | ||||||||
\(188\) | − 6.45751i | − 0.470963i | ||||||||
\(189\) | 1.64575 | 0.119711 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.22876 | 0.450697 | 0.225349 | − | 0.974278i | \(-0.427648\pi\) | ||||
0.225349 | + | 0.974278i | \(0.427648\pi\) | |||||||
\(192\) | 13.0000i | 0.938194i | ||||||||
\(193\) | − 11.6458i | − 0.838280i | −0.907922 | − | 0.419140i | \(-0.862332\pi\) | ||||
0.907922 | − | 0.419140i | \(-0.137668\pi\) | |||||||
\(194\) | −7.77124 | −0.557943 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.4575 | −1.53268 | ||||||||
\(197\) | 25.1660i | 1.79300i | 0.443040 | + | 0.896502i | \(0.353900\pi\) | ||||
−0.443040 | + | 0.896502i | \(0.646100\pi\) | |||||||
\(198\) | − 0.937254i | − 0.0666077i | ||||||||
\(199\) | −7.29150 | −0.516881 | −0.258440 | − | 0.966027i | \(-0.583209\pi\) | ||||
−0.258440 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.58301 | 0.464329 | ||||||||
\(202\) | 24.5830i | 1.72965i | ||||||||
\(203\) | 14.7085i | 1.03233i | ||||||||
\(204\) | −20.0000 | −1.40028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.0000 | 1.95085 | ||||||||
\(207\) | − 9.29150i | − 0.645804i | ||||||||
\(208\) | − 3.89674i | − 0.270190i | ||||||||
\(209\) | 0.354249 | 0.0245039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.58301 | 0.177821 | 0.0889107 | − | 0.996040i | \(-0.471661\pi\) | ||||
0.0889107 | + | 0.996040i | \(0.471661\pi\) | |||||||
\(212\) | − 56.4575i | − 3.87752i | ||||||||
\(213\) | − 7.29150i | − 0.499606i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.93725 | 0.540062 | ||||||||
\(217\) | − 9.87451i | − 0.670325i | ||||||||
\(218\) | − 14.0000i | − 0.948200i | ||||||||
\(219\) | 10.0000 | 0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.41699 | 0.0953174 | ||||||||
\(222\) | − 9.64575i | − 0.647380i | ||||||||
\(223\) | 2.58301i | 0.172971i | 0.996253 | + | 0.0864854i | \(0.0275636\pi\) | ||||
−0.996253 | + | 0.0864854i | \(0.972436\pi\) | |||||||
\(224\) | 21.7712 | 1.45465 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5830 | 0.703971 | ||||||||
\(227\) | 10.7085i | 0.710748i | 0.934724 | + | 0.355374i | \(0.115646\pi\) | ||||
−0.934724 | + | 0.355374i | \(0.884354\pi\) | |||||||
\(228\) | 5.00000i | 0.331133i | ||||||||
\(229\) | −8.70850 | −0.575474 | −0.287737 | − | 0.957710i | \(-0.592903\pi\) | ||||
−0.287737 | + | 0.957710i | \(0.592903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.583005 | −0.0383589 | ||||||||
\(232\) | 70.9373i | 4.65726i | ||||||||
\(233\) | − 18.0000i | − 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | −0.937254 | −0.0612702 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 56.4575 | 3.67507 | ||||||||
\(237\) | 6.58301i | 0.427612i | ||||||||
\(238\) | 17.4170i | 1.12898i | ||||||||
\(239\) | −15.6458 | −1.01204 | −0.506020 | − | 0.862522i | \(-0.668884\pi\) | ||||
−0.506020 | + | 0.862522i | \(0.668884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5830 | 1.06821 | 0.534103 | − | 0.845420i | \(-0.320650\pi\) | ||||
0.534103 | + | 0.845420i | \(0.320650\pi\) | |||||||
\(242\) | − 28.7712i | − 1.84949i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 56.4575 | 3.61432 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −25.5203 | −1.62711 | ||||||||
\(247\) | − 0.354249i | − 0.0225403i | ||||||||
\(248\) | − 47.6235i | − 3.02410i | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.3542 | −1.03227 | −0.516136 | − | 0.856507i | \(-0.672630\pi\) | ||||
−0.516136 | + | 0.856507i | \(0.672630\pi\) | |||||||
\(252\) | − 8.22876i | − 0.518363i | ||||||||
\(253\) | 3.29150i | 0.206935i | ||||||||
\(254\) | 10.5830 | 0.664037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.00000 | −0.312500 | ||||||||
\(257\) | 5.41699i | 0.337903i | 0.985624 | + | 0.168951i | \(0.0540381\pi\) | ||||
−0.985624 | + | 0.168951i | \(0.945962\pi\) | |||||||
\(258\) | 14.9373i | 0.929953i | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.93725 | 0.553202 | ||||||||
\(262\) | − 37.6458i | − 2.32576i | ||||||||
\(263\) | 4.58301i | 0.282600i | 0.989967 | + | 0.141300i | \(0.0451282\pi\) | ||||
−0.989967 | + | 0.141300i | \(0.954872\pi\) | |||||||
\(264\) | −2.81176 | −0.173052 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.35425 | 0.266976 | ||||||||
\(267\) | − 16.9373i | − 1.03654i | ||||||||
\(268\) | − 32.9150i | − 2.01061i | ||||||||
\(269\) | −4.22876 | −0.257832 | −0.128916 | − | 0.991656i | \(-0.541150\pi\) | ||||
−0.128916 | + | 0.991656i | \(0.541150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.70850 | −0.286021 | −0.143010 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143010 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(272\) | 44.0000i | 2.66789i | ||||||||
\(273\) | 0.583005i | 0.0352851i | ||||||||
\(274\) | 15.8745 | 0.959014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −46.4575 | −2.79641 | ||||||||
\(277\) | − 0.583005i | − 0.0350294i | −0.999847 | − | 0.0175147i | \(-0.994425\pi\) | ||||
0.999847 | − | 0.0175147i | \(-0.00557539\pi\) | |||||||
\(278\) | − 47.2915i | − 2.83636i | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.2288 | −1.92261 | −0.961303 | − | 0.275493i | \(-0.911159\pi\) | ||||
−0.961303 | + | 0.275493i | \(0.911159\pi\) | |||||||
\(282\) | 3.41699i | 0.203479i | ||||||||
\(283\) | − 11.5203i | − 0.684808i | −0.939553 | − | 0.342404i | \(-0.888759\pi\) | ||||
0.939553 | − | 0.342404i | \(-0.111241\pi\) | |||||||
\(284\) | −36.4575 | −2.16336 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.332021 | 0.0196328 | ||||||||
\(287\) | 15.8745i | 0.937043i | ||||||||
\(288\) | − 13.2288i | − 0.779512i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.93725 | 0.172185 | ||||||||
\(292\) | − 50.0000i | − 2.92603i | ||||||||
\(293\) | 5.41699i | 0.316464i | 0.987402 | + | 0.158232i | \(0.0505794\pi\) | ||||
−0.987402 | + | 0.158232i | \(0.949421\pi\) | |||||||
\(294\) | 11.3542 | 0.662193 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −28.9373 | −1.68194 | ||||||||
\(297\) | 0.354249i | 0.0205556i | ||||||||
\(298\) | 54.4575i | 3.15464i | ||||||||
\(299\) | 3.29150 | 0.190353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.29150 | 0.535553 | ||||||||
\(302\) | − 22.7085i | − 1.30673i | ||||||||
\(303\) | − 9.29150i | − 0.533783i | ||||||||
\(304\) | 11.0000 | 0.630893 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.5830 | 0.604990 | ||||||||
\(307\) | 24.4575i | 1.39586i | 0.716164 | + | 0.697932i | \(0.245896\pi\) | ||||
−0.716164 | + | 0.697932i | \(0.754104\pi\) | |||||||
\(308\) | 2.91503i | 0.166099i | ||||||||
\(309\) | −10.5830 | −0.602046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.9373 | 1.30065 | 0.650326 | − | 0.759655i | \(-0.274632\pi\) | ||||
0.650326 | + | 0.759655i | \(0.274632\pi\) | |||||||
\(312\) | 2.81176i | 0.159185i | ||||||||
\(313\) | 17.2915i | 0.977374i | 0.872459 | + | 0.488687i | \(0.162524\pi\) | ||||
−0.872459 | + | 0.488687i | \(0.837476\pi\) | |||||||
\(314\) | −35.1660 | −1.98453 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.9150 | 1.85161 | ||||||||
\(317\) | − 20.4575i | − 1.14901i | −0.818502 | − | 0.574504i | \(-0.805195\pi\) | ||||
0.818502 | − | 0.574504i | \(-0.194805\pi\) | |||||||
\(318\) | 29.8745i | 1.67528i | ||||||||
\(319\) | −3.16601 | −0.177263 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 40.4575i | 2.25461i | ||||||||
\(323\) | 4.00000i | 0.222566i | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.22876 | 0.344979 | ||||||||
\(327\) | 5.29150i | 0.292621i | ||||||||
\(328\) | 76.5608i | 4.22736i | ||||||||
\(329\) | 2.12549 | 0.117182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4170 | 0.627535 | 0.313767 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313767 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(332\) | − 30.0000i | − 1.64646i | ||||||||
\(333\) | 3.64575i | 0.199786i | ||||||||
\(334\) | −56.3320 | −3.08235 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.1033 | −0.987614 | ||||||||
\(337\) | − 14.9373i | − 0.813684i | −0.913499 | − | 0.406842i | \(-0.866630\pi\) | ||||
0.913499 | − | 0.406842i | \(-0.133370\pi\) | |||||||
\(338\) | 34.0627i | 1.85277i | ||||||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12549 | 0.115102 | ||||||||
\(342\) | − 2.64575i | − 0.143066i | ||||||||
\(343\) | − 18.5830i | − 1.00339i | ||||||||
\(344\) | 44.8118 | 2.41609 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 26.0000i | − 1.39575i | −0.716218 | − | 0.697877i | \(-0.754128\pi\) | ||||
0.716218 | − | 0.697877i | \(-0.245872\pi\) | |||||||
\(348\) | − 44.6863i | − 2.39544i | ||||||||
\(349\) | −23.1660 | −1.24005 | −0.620024 | − | 0.784583i | \(-0.712877\pi\) | ||||
−0.620024 | + | 0.784583i | \(0.712877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.354249 | 0.0189084 | ||||||||
\(352\) | 4.68627i | 0.249779i | ||||||||
\(353\) | 0.583005i | 0.0310302i | 0.999880 | + | 0.0155151i | \(0.00493881\pi\) | ||||
−0.999880 | + | 0.0155151i | \(0.995061\pi\) | |||||||
\(354\) | −29.8745 | −1.58781 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −84.6863 | −4.48836 | ||||||||
\(357\) | − 6.58301i | − 0.348410i | ||||||||
\(358\) | 19.2915i | 1.01959i | ||||||||
\(359\) | 36.1033 | 1.90546 | 0.952729 | − | 0.303822i | \(-0.0982629\pi\) | ||||
0.952729 | + | 0.303822i | \(0.0982629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 45.7490i | 2.40451i | ||||||||
\(363\) | 10.8745i | 0.570764i | ||||||||
\(364\) | 2.91503 | 0.152789 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −29.8745 | −1.56157 | ||||||||
\(367\) | − 1.64575i | − 0.0859075i | −0.999077 | − | 0.0429538i | \(-0.986323\pi\) | ||||
0.999077 | − | 0.0429538i | \(-0.0136768\pi\) | |||||||
\(368\) | 102.207i | 5.32788i | ||||||||
\(369\) | 9.64575 | 0.502138 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.5830 | 0.964782 | ||||||||
\(372\) | 30.0000i | 1.55543i | ||||||||
\(373\) | 5.06275i | 0.262139i | 0.991373 | + | 0.131070i | \(0.0418411\pi\) | ||||
−0.991373 | + | 0.131070i | \(0.958159\pi\) | |||||||
\(374\) | −3.74902 | −0.193857 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.2510 | 0.528654 | ||||||||
\(377\) | 3.16601i | 0.163058i | ||||||||
\(378\) | 4.35425i | 0.223958i | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 16.4797i | 0.843177i | ||||||||
\(383\) | − 18.5830i | − 0.949547i | −0.880108 | − | 0.474774i | \(-0.842530\pi\) | ||||
0.880108 | − | 0.474774i | \(-0.157470\pi\) | |||||||
\(384\) | −7.93725 | −0.405046 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.8118 | 1.56828 | ||||||||
\(387\) | − 5.64575i | − 0.286990i | ||||||||
\(388\) | − 14.6863i | − 0.745582i | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.1660 | −1.87957 | ||||||||
\(392\) | − 34.0627i | − 1.72043i | ||||||||
\(393\) | 14.2288i | 0.717746i | ||||||||
\(394\) | −66.5830 | −3.35440 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.77124 | 0.0890083 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | − 19.2915i | − 0.966996i | ||||||||
\(399\) | −1.64575 | −0.0823906 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.93725 | −0.246555 | −0.123277 | − | 0.992372i | \(-0.539340\pi\) | ||||
−0.123277 | + | 0.992372i | \(0.539340\pi\) | |||||||
\(402\) | 17.4170i | 0.868681i | ||||||||
\(403\) | − 2.12549i | − 0.105878i | ||||||||
\(404\) | −46.4575 | −2.31135 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −38.9150 | −1.93132 | ||||||||
\(407\) | − 1.29150i | − 0.0640174i | ||||||||
\(408\) | − 31.7490i | − 1.57181i | ||||||||
\(409\) | 6.70850 | 0.331714 | 0.165857 | − | 0.986150i | \(-0.446961\pi\) | ||||
0.165857 | + | 0.986150i | \(0.446961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | 52.9150i | 2.60694i | ||||||||
\(413\) | 18.5830i | 0.914410i | ||||||||
\(414\) | 24.5830 | 1.20819 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.68627 | 0.229763 | ||||||||
\(417\) | 17.8745i | 0.875318i | ||||||||
\(418\) | 0.937254i | 0.0458426i | ||||||||
\(419\) | −38.9373 | −1.90221 | −0.951105 | − | 0.308869i | \(-0.900050\pi\) | ||||
−0.951105 | + | 0.308869i | \(0.900050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5830 | 1.39305 | 0.696525 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696525 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(422\) | 6.83399i | 0.332673i | ||||||||
\(423\) | − 1.29150i | − 0.0627950i | ||||||||
\(424\) | 89.6235 | 4.35250 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 19.2915 | 0.934676 | ||||||||
\(427\) | 18.5830i | 0.899295i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.125492 | −0.00605882 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.29150 | 0.158546 | 0.0792731 | − | 0.996853i | \(-0.474740\pi\) | ||||
0.0792731 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(432\) | 11.0000i | 0.529238i | ||||||||
\(433\) | − 27.6458i | − 1.32857i | −0.747479 | − | 0.664285i | \(-0.768736\pi\) | ||||
0.747479 | − | 0.664285i | \(-0.231264\pi\) | |||||||
\(434\) | 26.1255 | 1.25406 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.4575 | 1.26709 | ||||||||
\(437\) | 9.29150i | 0.444473i | ||||||||
\(438\) | 26.4575i | 1.26419i | ||||||||
\(439\) | 1.41699 | 0.0676295 | 0.0338147 | − | 0.999428i | \(-0.489234\pi\) | ||||
0.0338147 | + | 0.999428i | \(0.489234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.29150 | −0.204357 | ||||||||
\(442\) | 3.74902i | 0.178322i | ||||||||
\(443\) | 26.7085i | 1.26896i | 0.772940 | + | 0.634480i | \(0.218786\pi\) | ||||
−0.772940 | + | 0.634480i | \(0.781214\pi\) | |||||||
\(444\) | 18.2288 | 0.865099 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.83399 | −0.323599 | ||||||||
\(447\) | − 20.5830i | − 0.973543i | ||||||||
\(448\) | 21.3948i | 1.01081i | ||||||||
\(449\) | 36.2288 | 1.70974 | 0.854870 | − | 0.518842i | \(-0.173637\pi\) | ||||
0.854870 | + | 0.518842i | \(0.173637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.41699 | −0.160900 | ||||||||
\(452\) | 20.0000i | 0.940721i | ||||||||
\(453\) | 8.58301i | 0.403265i | ||||||||
\(454\) | −28.3320 | −1.32969 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.93725 | −0.371696 | ||||||||
\(457\) | − 0.125492i | − 0.00587027i | −0.999996 | − | 0.00293514i | \(-0.999066\pi\) | ||||
0.999996 | − | 0.00293514i | \(-0.000934285\pi\) | |||||||
\(458\) | − 23.0405i | − 1.07661i | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.7490 | −1.75815 | −0.879073 | − | 0.476686i | \(-0.841838\pi\) | ||||
−0.879073 | + | 0.476686i | \(0.841838\pi\) | |||||||
\(462\) | − 1.54249i | − 0.0717630i | ||||||||
\(463\) | − 35.5203i | − 1.65077i | −0.564573 | − | 0.825383i | \(-0.690959\pi\) | ||||
0.564573 | − | 0.825383i | \(-0.309041\pi\) | |||||||
\(464\) | −98.3098 | −4.56392 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 47.6235 | 2.20612 | ||||||||
\(467\) | − 19.8745i | − 0.919683i | −0.888001 | − | 0.459841i | \(-0.847906\pi\) | ||||
0.888001 | − | 0.459841i | \(-0.152094\pi\) | |||||||
\(468\) | − 1.77124i | − 0.0818758i | ||||||||
\(469\) | 10.8340 | 0.500267 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2915 | 0.612440 | ||||||||
\(472\) | 89.6235i | 4.12526i | ||||||||
\(473\) | 2.00000i | 0.0919601i | ||||||||
\(474\) | −17.4170 | −0.799989 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −32.9150 | −1.50866 | ||||||||
\(477\) | − 11.2915i | − 0.517002i | ||||||||
\(478\) | − 41.3948i | − 1.89335i | ||||||||
\(479\) | −4.35425 | −0.198951 | −0.0994754 | − | 0.995040i | \(-0.531716\pi\) | ||||
−0.0994754 | + | 0.995040i | \(0.531716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.29150 | −0.0588875 | ||||||||
\(482\) | 43.8745i | 1.99843i | ||||||||
\(483\) | − 15.2915i | − 0.695787i | ||||||||
\(484\) | 54.3725 | 2.47148 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.64575 | 0.120014 | ||||||||
\(487\) | − 17.8745i | − 0.809971i | −0.914323 | − | 0.404986i | \(-0.867277\pi\) | ||||
0.914323 | − | 0.404986i | \(-0.132723\pi\) | |||||||
\(488\) | 89.6235i | 4.05707i | ||||||||
\(489\) | −2.35425 | −0.106463 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.77124 | −0.260453 | −0.130226 | − | 0.991484i | \(-0.541570\pi\) | ||||
−0.130226 | + | 0.991484i | \(0.541570\pi\) | |||||||
\(492\) | − 48.2288i | − 2.17432i | ||||||||
\(493\) | − 35.7490i | − 1.61005i | ||||||||
\(494\) | 0.937254 | 0.0421690 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 66.0000 | 2.96349 | ||||||||
\(497\) | − 12.0000i | − 0.538274i | ||||||||
\(498\) | 15.8745i | 0.711354i | ||||||||
\(499\) | 31.0405 | 1.38956 | 0.694782 | − | 0.719220i | \(-0.255501\pi\) | ||||
0.694782 | + | 0.719220i | \(0.255501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.2915 | 0.951234 | ||||||||
\(502\) | − 43.2693i | − 1.93120i | ||||||||
\(503\) | − 2.00000i | − 0.0891756i | −0.999005 | − | 0.0445878i | \(-0.985803\pi\) | ||||
0.999005 | − | 0.0445878i | \(-0.0141974\pi\) | |||||||
\(504\) | 13.0627 | 0.581861 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.70850 | −0.387140 | ||||||||
\(507\) | − 12.8745i | − 0.571777i | ||||||||
\(508\) | 20.0000i | 0.887357i | ||||||||
\(509\) | 34.1033 | 1.51160 | 0.755800 | − | 0.654802i | \(-0.227248\pi\) | ||||
0.755800 | + | 0.654802i | \(0.227248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4575 | 0.728038 | ||||||||
\(512\) | − 29.1033i | − 1.28619i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | −14.3320 | −0.632158 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −28.2288 | −1.24270 | ||||||||
\(517\) | 0.457513i | 0.0201214i | ||||||||
\(518\) | − 15.8745i | − 0.697486i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1033 | 0.968362 | 0.484181 | − | 0.874968i | \(-0.339118\pi\) | ||||
0.484181 | + | 0.874968i | \(0.339118\pi\) | |||||||
\(522\) | 23.6458i | 1.03495i | ||||||||
\(523\) | − 23.2915i | − 1.01847i | −0.860629 | − | 0.509233i | \(-0.829929\pi\) | ||||
0.860629 | − | 0.509233i | \(-0.170071\pi\) | |||||||
\(524\) | 71.1438 | 3.10793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.1255 | −0.528697 | ||||||||
\(527\) | 24.0000i | 1.04546i | ||||||||
\(528\) | − 3.89674i | − 0.169584i | ||||||||
\(529\) | −63.3320 | −2.75357 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2915 | 0.490009 | ||||||||
\(532\) | 8.22876i | 0.356762i | ||||||||
\(533\) | 3.41699i | 0.148006i | ||||||||
\(534\) | 44.8118 | 1.93919 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 52.2510 | 2.25690 | ||||||||
\(537\) | − 7.29150i | − 0.314652i | ||||||||
\(538\) | − 11.1882i | − 0.482359i | ||||||||
\(539\) | 1.52026 | 0.0654822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | − 12.4575i | − 0.535096i | ||||||||
\(543\) | − 17.2915i | − 0.742049i | ||||||||
\(544\) | −52.9150 | −2.26871 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.54249 | −0.0660123 | ||||||||
\(547\) | − 1.87451i | − 0.0801482i | −0.999197 | − | 0.0400741i | \(-0.987241\pi\) | ||||
0.999197 | − | 0.0400741i | \(-0.0127594\pi\) | |||||||
\(548\) | 30.0000i | 1.28154i | ||||||||
\(549\) | 11.2915 | 0.481910 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.93725 | −0.380740 | ||||||||
\(552\) | − 73.7490i | − 3.13897i | ||||||||
\(553\) | 10.8340i | 0.460708i | ||||||||
\(554\) | 1.54249 | 0.0655340 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 89.3725 | 3.79024 | ||||||||
\(557\) | 11.4170i | 0.483754i | 0.970307 | + | 0.241877i | \(0.0777630\pi\) | ||||
−0.970307 | + | 0.241877i | \(0.922237\pi\) | |||||||
\(558\) | − 15.8745i | − 0.672022i | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41699 | 0.0598256 | ||||||||
\(562\) | − 85.2693i | − 3.59687i | ||||||||
\(563\) | 8.12549i | 0.342449i | 0.985232 | + | 0.171224i | \(0.0547723\pi\) | ||||
−0.985232 | + | 0.171224i | \(0.945228\pi\) | |||||||
\(564\) | −6.45751 | −0.271910 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.4797 | 1.28116 | ||||||||
\(567\) | − 1.64575i | − 0.0691151i | ||||||||
\(568\) | − 57.8745i | − 2.42836i | ||||||||
\(569\) | 7.06275 | 0.296086 | 0.148043 | − | 0.988981i | \(-0.452703\pi\) | ||||
0.148043 | + | 0.988981i | \(0.452703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7085 | 0.699229 | 0.349614 | − | 0.936894i | \(-0.386313\pi\) | ||||
0.349614 | + | 0.936894i | \(0.386313\pi\) | |||||||
\(572\) | 0.627461i | 0.0262354i | ||||||||
\(573\) | − 6.22876i | − 0.260210i | ||||||||
\(574\) | −42.0000 | −1.75305 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13.0000 | 0.541667 | ||||||||
\(577\) | 13.2915i | 0.553332i | 0.960966 | + | 0.276666i | \(0.0892296\pi\) | ||||
−0.960966 | + | 0.276666i | \(0.910770\pi\) | |||||||
\(578\) | 2.64575i | 0.110049i | ||||||||
\(579\) | −11.6458 | −0.483981 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.87451 | 0.409664 | ||||||||
\(582\) | 7.77124i | 0.322128i | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 79.3725 | 3.28446 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.3320 | −0.592050 | ||||||||
\(587\) | 33.2915i | 1.37409i | 0.726616 | + | 0.687044i | \(0.241092\pi\) | ||||
−0.726616 | + | 0.687044i | \(0.758908\pi\) | |||||||
\(588\) | 21.4575i | 0.884893i | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.1660 | 1.03519 | ||||||||
\(592\) | − 40.1033i | − 1.64823i | ||||||||
\(593\) | 3.41699i | 0.140319i | 0.997536 | + | 0.0701596i | \(0.0223508\pi\) | ||||
−0.997536 | + | 0.0701596i | \(0.977649\pi\) | |||||||
\(594\) | −0.937254 | −0.0384560 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −102.915 | −4.21556 | ||||||||
\(597\) | 7.29150i | 0.298421i | ||||||||
\(598\) | 8.70850i | 0.356117i | ||||||||
\(599\) | −9.41699 | −0.384768 | −0.192384 | − | 0.981320i | \(-0.561622\pi\) | ||||
−0.192384 | + | 0.981320i | \(0.561622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7085 | 0.926299 | 0.463149 | − | 0.886280i | \(-0.346719\pi\) | ||||
0.463149 | + | 0.886280i | \(0.346719\pi\) | |||||||
\(602\) | 24.5830i | 1.00193i | ||||||||
\(603\) | − 6.58301i | − 0.268081i | ||||||||
\(604\) | 42.9150 | 1.74619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.5830 | 0.998616 | ||||||||
\(607\) | 43.0405i | 1.74696i | 0.486859 | + | 0.873480i | \(0.338142\pi\) | ||||
−0.486859 | + | 0.873480i | \(0.661858\pi\) | |||||||
\(608\) | 13.2288i | 0.536497i | ||||||||
\(609\) | 14.7085 | 0.596018 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.457513 | 0.0185090 | ||||||||
\(612\) | 20.0000i | 0.808452i | ||||||||
\(613\) | − 30.4575i | − 1.23017i | −0.788462 | − | 0.615084i | \(-0.789122\pi\) | ||||
0.788462 | − | 0.615084i | \(-0.210878\pi\) | |||||||
\(614\) | −64.7085 | −2.61142 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.62746 | −0.186446 | ||||||||
\(617\) | − 12.0000i | − 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | − 28.0000i | − 1.12633i | ||||||||
\(619\) | −23.2915 | −0.936165 | −0.468082 | − | 0.883685i | \(-0.655055\pi\) | ||||
−0.468082 | + | 0.883685i | \(0.655055\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.29150 | −0.372855 | ||||||||
\(622\) | 60.6863i | 2.43330i | ||||||||
\(623\) | − 27.8745i | − 1.11677i | ||||||||
\(624\) | −3.89674 | −0.155994 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −45.7490 | −1.82850 | ||||||||
\(627\) | − 0.354249i | − 0.0141473i | ||||||||
\(628\) | − 66.4575i | − 2.65194i | ||||||||
\(629\) | 14.5830 | 0.581462 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5830 | −0.580540 | −0.290270 | − | 0.956945i | \(-0.593745\pi\) | ||||
−0.290270 | + | 0.956945i | \(0.593745\pi\) | |||||||
\(632\) | 52.2510i | 2.07843i | ||||||||
\(633\) | − 2.58301i | − 0.102665i | ||||||||
\(634\) | 54.1255 | 2.14960 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −56.4575 | −2.23869 | ||||||||
\(637\) | − 1.52026i | − 0.0602349i | ||||||||
\(638\) | − 8.37648i | − 0.331628i | ||||||||
\(639\) | −7.29150 | −0.288447 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9373 | −0.668981 | −0.334491 | − | 0.942399i | \(-0.608564\pi\) | ||||
−0.334491 | + | 0.942399i | \(0.608564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 13.6458i | − 0.538136i | −0.963121 | − | 0.269068i | \(-0.913284\pi\) | ||||
0.963121 | − | 0.269068i | \(-0.0867156\pi\) | |||||||
\(644\) | −76.4575 | −3.01285 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5830 | −0.416383 | ||||||||
\(647\) | 3.41699i | 0.134336i | 0.997742 | + | 0.0671680i | \(0.0213963\pi\) | ||||
−0.997742 | + | 0.0671680i | \(0.978604\pi\) | |||||||
\(648\) | − 7.93725i | − 0.311805i | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.87451 | −0.387012 | ||||||||
\(652\) | 11.7712i | 0.460997i | ||||||||
\(653\) | 9.41699i | 0.368515i | 0.982878 | + | 0.184258i | \(0.0589881\pi\) | ||||
−0.982878 | + | 0.184258i | \(0.941012\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −106.103 | −4.14264 | ||||||||
\(657\) | − 10.0000i | − 0.390137i | ||||||||
\(658\) | 5.62352i | 0.219228i | ||||||||
\(659\) | −25.4170 | −0.990106 | −0.495053 | − | 0.868863i | \(-0.664851\pi\) | ||||
−0.495053 | + | 0.868863i | \(0.664851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.29150 | 0.0502336 | 0.0251168 | − | 0.999685i | \(-0.492004\pi\) | ||||
0.0251168 | + | 0.999685i | \(0.492004\pi\) | |||||||
\(662\) | 30.2065i | 1.17401i | ||||||||
\(663\) | − 1.41699i | − 0.0550315i | ||||||||
\(664\) | 47.6235 | 1.84815 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.64575 | −0.373765 | ||||||||
\(667\) | − 83.0405i | − 3.21534i | ||||||||
\(668\) | − 106.458i | − 4.11896i | ||||||||
\(669\) | 2.58301 | 0.0998648 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | − 21.7712i | − 0.839844i | ||||||||
\(673\) | − 13.0627i | − 0.503532i | −0.967788 | − | 0.251766i | \(-0.918989\pi\) | ||||
0.967788 | − | 0.251766i | \(-0.0810113\pi\) | |||||||
\(674\) | 39.5203 | 1.52226 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −64.3725 | −2.47587 | ||||||||
\(677\) | − 40.4575i | − 1.55491i | −0.628939 | − | 0.777454i | \(-0.716511\pi\) | ||||
0.628939 | − | 0.777454i | \(-0.283489\pi\) | |||||||
\(678\) | − 10.5830i | − 0.406438i | ||||||||
\(679\) | 4.83399 | 0.185511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.7085 | 0.410351 | ||||||||
\(682\) | 5.62352i | 0.215336i | ||||||||
\(683\) | 19.7490i | 0.755675i | 0.925872 | + | 0.377838i | \(0.123332\pi\) | ||||
−0.925872 | + | 0.377838i | \(0.876668\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 49.1660 | 1.87717 | ||||||||
\(687\) | 8.70850i | 0.332250i | ||||||||
\(688\) | 62.1033i | 2.36766i | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.0405 | −1.63734 | −0.818669 | − | 0.574265i | \(-0.805288\pi\) | ||||
−0.818669 | + | 0.574265i | \(0.805288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.583005i | 0.0221465i | ||||||||
\(694\) | 68.7895 | 2.61122 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 70.9373 | 2.68887 | ||||||||
\(697\) | − 38.5830i | − 1.46144i | ||||||||
\(698\) | − 61.2915i | − 2.31992i | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.5830 | 0.626331 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(702\) | 0.937254i | 0.0353744i | ||||||||
\(703\) | − 3.64575i | − 0.137502i | ||||||||
\(704\) | −4.60523 | −0.173566 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.54249 | −0.0580523 | ||||||||
\(707\) | − 15.2915i | − 0.575096i | ||||||||
\(708\) | − 56.4575i | − 2.12180i | ||||||||
\(709\) | 4.70850 | 0.176831 | 0.0884157 | − | 0.996084i | \(-0.471820\pi\) | ||||
0.0884157 | + | 0.996084i | \(0.471820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.58301 | 0.246882 | ||||||||
\(712\) | − 134.435i | − 5.03818i | ||||||||
\(713\) | 55.7490i | 2.08782i | ||||||||
\(714\) | 17.4170 | 0.651815 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −36.4575 | −1.36248 | ||||||||
\(717\) | 15.6458i | 0.584301i | ||||||||
\(718\) | 95.5203i | 3.56478i | ||||||||
\(719\) | −32.8118 | −1.22367 | −0.611836 | − | 0.790985i | \(-0.709569\pi\) | ||||
−0.611836 | + | 0.790985i | \(0.709569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.4170 | −0.648643 | ||||||||
\(722\) | 2.64575i | 0.0984647i | ||||||||
\(723\) | − 16.5830i | − 0.616729i | ||||||||
\(724\) | −86.4575 | −3.21317 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −28.7712 | −1.06780 | ||||||||
\(727\) | − 14.1033i | − 0.523061i | −0.965195 | − | 0.261531i | \(-0.915773\pi\) | ||||
0.965195 | − | 0.261531i | \(-0.0842272\pi\) | |||||||
\(728\) | 4.62746i | 0.171505i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.5830 | −0.835263 | ||||||||
\(732\) | − 56.4575i | − 2.08673i | ||||||||
\(733\) | 7.41699i | 0.273953i | 0.990574 | + | 0.136976i | \(0.0437385\pi\) | ||||
−0.990574 | + | 0.136976i | \(0.956262\pi\) | |||||||
\(734\) | 4.35425 | 0.160718 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −122.915 | −4.53071 | ||||||||
\(737\) | 2.33202i | 0.0859011i | ||||||||
\(738\) | 25.5203i | 0.939414i | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.354249 | −0.0130137 | ||||||||
\(742\) | 49.1660i | 1.80494i | ||||||||
\(743\) | − 10.5830i | − 0.388253i | −0.980977 | − | 0.194126i | \(-0.937813\pi\) | ||||
0.980977 | − | 0.194126i | \(-0.0621872\pi\) | |||||||
\(744\) | −47.6235 | −1.74596 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.3948 | −0.490417 | ||||||||
\(747\) | − 6.00000i | − 0.219529i | ||||||||
\(748\) | − 7.08497i | − 0.259052i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.5830 | −1.62686 | −0.813428 | − | 0.581665i | \(-0.802401\pi\) | ||||
−0.813428 | + | 0.581665i | \(0.802401\pi\) | |||||||
\(752\) | 14.2065i | 0.518059i | ||||||||
\(753\) | 16.3542i | 0.595982i | ||||||||
\(754\) | −8.37648 | −0.305053 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.22876 | −0.299277 | ||||||||
\(757\) | 23.8745i | 0.867734i | 0.900977 | + | 0.433867i | \(0.142851\pi\) | ||||
−0.900977 | + | 0.433867i | \(0.857149\pi\) | |||||||
\(758\) | − 26.4575i | − 0.960980i | ||||||||
\(759\) | 3.29150 | 0.119474 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.7490 | 0.933401 | 0.466701 | − | 0.884415i | \(-0.345443\pi\) | ||||
0.466701 | + | 0.884415i | \(0.345443\pi\) | |||||||
\(762\) | − 10.5830i | − 0.383382i | ||||||||
\(763\) | 8.70850i | 0.315269i | ||||||||
\(764\) | −31.1438 | −1.12674 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 49.1660 | 1.77644 | ||||||||
\(767\) | 4.00000i | 0.144432i | ||||||||
\(768\) | 5.00000i | 0.180422i | ||||||||
\(769\) | 17.7490 | 0.640046 | 0.320023 | − | 0.947410i | \(-0.396309\pi\) | ||||
0.320023 | + | 0.947410i | \(0.396309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.41699 | 0.195088 | ||||||||
\(772\) | 58.2288i | 2.09570i | ||||||||
\(773\) | − 8.70850i | − 0.313223i | −0.987660 | − | 0.156611i | \(-0.949943\pi\) | ||||
0.987660 | − | 0.156611i | \(-0.0500570\pi\) | |||||||
\(774\) | 14.9373 | 0.536909 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.3137 | 0.836914 | ||||||||
\(777\) | 6.00000i | 0.215249i | ||||||||
\(778\) | 15.8745i | 0.569129i | ||||||||
\(779\) | −9.64575 | −0.345595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.58301 | 0.0924272 | ||||||||
\(782\) | − 98.3320i | − 3.51635i | ||||||||
\(783\) | − 8.93725i | − 0.319391i | ||||||||
\(784\) | 47.2065 | 1.68595 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37.6458 | −1.34278 | ||||||||
\(787\) | − 37.8745i | − 1.35008i | −0.737781 | − | 0.675040i | \(-0.764126\pi\) | ||||
0.737781 | − | 0.675040i | \(-0.235874\pi\) | |||||||
\(788\) | − 125.830i | − 4.48251i | ||||||||
\(789\) | 4.58301 | 0.163159 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.58301 | −0.234065 | ||||||||
\(792\) | 2.81176i | 0.0999116i | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | −5.29150 | −0.187788 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.4575 | 1.29220 | ||||||||
\(797\) | − 40.0000i | − 1.41687i | −0.705775 | − | 0.708436i | \(-0.749401\pi\) | ||||
0.705775 | − | 0.708436i | \(-0.250599\pi\) | |||||||
\(798\) | − 4.35425i | − 0.154139i | ||||||||
\(799\) | −5.16601 | −0.182760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.9373 | −0.598448 | ||||||||
\(802\) | − 13.0627i | − 0.461262i | ||||||||
\(803\) | 3.54249i | 0.125012i | ||||||||
\(804\) | −32.9150 | −1.16082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.62352 | 0.198080 | ||||||||
\(807\) | 4.22876i | 0.148859i | ||||||||
\(808\) | − 73.7490i | − 2.59448i | ||||||||
\(809\) | 19.4170 | 0.682665 | 0.341333 | − | 0.939943i | \(-0.389122\pi\) | ||||
0.341333 | + | 0.939943i | \(0.389122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3320 | 1.34602 | 0.673010 | − | 0.739634i | \(-0.265001\pi\) | ||||
0.673010 | + | 0.739634i | \(0.265001\pi\) | |||||||
\(812\) | − 73.5425i | − 2.58084i | ||||||||
\(813\) | 4.70850i | 0.165134i | ||||||||
\(814\) | 3.41699 | 0.119766 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 44.0000 | 1.54031 | ||||||||
\(817\) | 5.64575i | 0.197520i | ||||||||
\(818\) | 17.7490i | 0.620580i | ||||||||
\(819\) | 0.583005 | 0.0203719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.6235 | 1.66207 | 0.831036 | − | 0.556218i | \(-0.187748\pi\) | ||||
0.831036 | + | 0.556218i | \(0.187748\pi\) | |||||||
\(822\) | − 15.8745i | − 0.553687i | ||||||||
\(823\) | 4.22876i | 0.147405i | 0.997280 | + | 0.0737026i | \(0.0234816\pi\) | ||||
−0.997280 | + | 0.0737026i | \(0.976518\pi\) | |||||||
\(824\) | −84.0000 | −2.92628 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −49.1660 | −1.71070 | ||||||||
\(827\) | − 30.4575i | − 1.05911i | −0.848275 | − | 0.529556i | \(-0.822359\pi\) | ||||
0.848275 | − | 0.529556i | \(-0.177641\pi\) | |||||||
\(828\) | 46.4575i | 1.61451i | ||||||||
\(829\) | −2.70850 | −0.0940700 | −0.0470350 | − | 0.998893i | \(-0.514977\pi\) | ||||
−0.0470350 | + | 0.998893i | \(0.514977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.583005 | −0.0202242 | ||||||||
\(832\) | 4.60523i | 0.159658i | ||||||||
\(833\) | 17.1660i | 0.594767i | ||||||||
\(834\) | −47.2915 | −1.63757 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.77124 | −0.0612597 | ||||||||
\(837\) | 6.00000i | 0.207390i | ||||||||
\(838\) | − 103.018i | − 3.55871i | ||||||||
\(839\) | 12.4575 | 0.430081 | 0.215041 | − | 0.976605i | \(-0.431012\pi\) | ||||
0.215041 | + | 0.976605i | \(0.431012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.8745 | 1.75429 | ||||||||
\(842\) | 75.6235i | 2.60616i | ||||||||
\(843\) | 32.2288i | 1.11002i | ||||||||
\(844\) | −12.9150 | −0.444554 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.41699 | 0.117479 | ||||||||
\(847\) | 17.8967i | 0.614939i | ||||||||
\(848\) | 124.207i | 4.26527i | ||||||||
\(849\) | −11.5203 | −0.395374 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.8745 | 1.16120 | ||||||||
\(852\) | 36.4575i | 1.24901i | ||||||||
\(853\) | 14.7085i | 0.503609i | 0.967778 | + | 0.251805i | \(0.0810241\pi\) | ||||
−0.967778 | + | 0.251805i | \(0.918976\pi\) | |||||||
\(854\) | −49.1660 | −1.68243 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 31.0405i | − 1.06032i | −0.847896 | − | 0.530162i | \(-0.822131\pi\) | ||||
0.847896 | − | 0.530162i | \(-0.177869\pi\) | |||||||
\(858\) | − 0.332021i | − 0.0113350i | ||||||||
\(859\) | 34.3320 | 1.17139 | 0.585697 | − | 0.810530i | \(-0.300821\pi\) | ||||
0.585697 | + | 0.810530i | \(0.300821\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.8745 | 0.541002 | ||||||||
\(862\) | 8.70850i | 0.296613i | ||||||||
\(863\) | − 20.0000i | − 0.680808i | −0.940279 | − | 0.340404i | \(-0.889436\pi\) | ||||
0.940279 | − | 0.340404i | \(-0.110564\pi\) | |||||||
\(864\) | −13.2288 | −0.450051 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 73.1438 | 2.48553 | ||||||||
\(867\) | − 1.00000i | − 0.0339618i | ||||||||
\(868\) | 49.3725i | 1.67581i | ||||||||
\(869\) | −2.33202 | −0.0791084 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.33202 | 0.0790175 | ||||||||
\(872\) | 42.0000i | 1.42230i | ||||||||
\(873\) | − 2.93725i | − 0.0994110i | ||||||||
\(874\) | −24.5830 | −0.831533 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.0000 | −1.68934 | ||||||||
\(877\) | 25.0627i | 0.846309i | 0.906058 | + | 0.423154i | \(0.139077\pi\) | ||||
−0.906058 | + | 0.423154i | \(0.860923\pi\) | |||||||
\(878\) | 3.74902i | 0.126523i | ||||||||
\(879\) | 5.41699 | 0.182711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.125492 | −0.00422794 | −0.00211397 | − | 0.999998i | \(-0.500673\pi\) | ||||
−0.00211397 | + | 0.999998i | \(0.500673\pi\) | |||||||
\(882\) | − 11.3542i | − 0.382317i | ||||||||
\(883\) | 10.8118i | 0.363845i | 0.983313 | + | 0.181922i | \(0.0582320\pi\) | ||||
−0.983313 | + | 0.181922i | \(0.941768\pi\) | |||||||
\(884\) | −7.08497 | −0.238293 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −70.6640 | −2.37400 | ||||||||
\(887\) | 24.0000i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(888\) | 28.9373i | 0.971071i | ||||||||
\(889\) | −6.58301 | −0.220787 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.354249 | 0.0118678 | ||||||||
\(892\) | − 12.9150i | − 0.432427i | ||||||||
\(893\) | 1.29150i | 0.0432185i | ||||||||
\(894\) | 54.4575 | 1.82133 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.0627 | −0.436396 | ||||||||
\(897\) | − 3.29150i | − 0.109900i | ||||||||
\(898\) | 95.8523i | 3.19863i | ||||||||
\(899\) | −53.6235 | −1.78844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.1660 | −1.50470 | ||||||||
\(902\) | − 9.04052i | − 0.301016i | ||||||||
\(903\) | − 9.29150i | − 0.309202i | ||||||||
\(904\) | −31.7490 | −1.05596 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22.7085 | −0.754439 | ||||||||
\(907\) | 47.0405i | 1.56195i | 0.624559 | + | 0.780977i | \(0.285279\pi\) | ||||
−0.624559 | + | 0.780977i | \(0.714721\pi\) | |||||||
\(908\) | − 53.5425i | − 1.77687i | ||||||||
\(909\) | −9.29150 | −0.308180 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.5830 | 0.880734 | 0.440367 | − | 0.897818i | \(-0.354848\pi\) | ||||
0.440367 | + | 0.897818i | \(0.354848\pi\) | |||||||
\(912\) | − 11.0000i | − 0.364246i | ||||||||
\(913\) | 2.12549i | 0.0703435i | ||||||||
\(914\) | 0.332021 | 0.0109823 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.5425 | 1.43868 | ||||||||
\(917\) | 23.4170i | 0.773297i | ||||||||
\(918\) | − 10.5830i | − 0.349291i | ||||||||
\(919\) | −14.8340 | −0.489328 | −0.244664 | − | 0.969608i | \(-0.578678\pi\) | ||||
−0.244664 | + | 0.969608i | \(0.578678\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4575 | 0.805902 | ||||||||
\(922\) | − 99.8745i | − 3.28919i | ||||||||
\(923\) | − 2.58301i | − 0.0850207i | ||||||||
\(924\) | 2.91503 | 0.0958973 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 93.9778 | 3.08830 | ||||||||
\(927\) | 10.5830i | 0.347591i | ||||||||
\(928\) | − 118.229i | − 3.88105i | ||||||||
\(929\) | 11.8745 | 0.389590 | 0.194795 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194795 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.29150 | 0.140648 | ||||||||
\(932\) | 90.0000i | 2.94805i | ||||||||
\(933\) | − 22.9373i | − 0.750932i | ||||||||
\(934\) | 52.5830 | 1.72057 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.81176 | 0.0919053 | ||||||||
\(937\) | − 20.1255i | − 0.657471i | −0.944422 | − | 0.328736i | \(-0.893378\pi\) | ||||
0.944422 | − | 0.328736i | \(-0.106622\pi\) | |||||||
\(938\) | 28.6640i | 0.935914i | ||||||||
\(939\) | 17.2915 | 0.564287 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7712 | −0.383732 | −0.191866 | − | 0.981421i | \(-0.561454\pi\) | ||||
−0.191866 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(942\) | 35.1660i | 1.14577i | ||||||||
\(943\) | − 89.6235i | − 2.91854i | ||||||||
\(944\) | −124.207 | −4.04258 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.29150 | −0.172042 | ||||||||
\(947\) | − 11.4170i | − 0.371002i | −0.982644 | − | 0.185501i | \(-0.940609\pi\) | ||||
0.982644 | − | 0.185501i | \(-0.0593909\pi\) | |||||||
\(948\) | − 32.9150i | − 1.06903i | ||||||||
\(949\) | 3.54249 | 0.114994 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.4575 | −0.663380 | ||||||||
\(952\) | − 52.2510i | − 1.69346i | ||||||||
\(953\) | − 10.5830i | − 0.342817i | −0.985200 | − | 0.171409i | \(-0.945168\pi\) | ||||
0.985200 | − | 0.171409i | \(-0.0548318\pi\) | |||||||
\(954\) | 29.8745 | 0.967223 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 78.2288 | 2.53010 | ||||||||
\(957\) | 3.16601i | 0.102343i | ||||||||
\(958\) | − 11.5203i | − 0.372203i | ||||||||
\(959\) | −9.87451 | −0.318864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | − 3.41699i | − 0.110168i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −82.9150 | −2.67051 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 40.4575 | 1.30170 | ||||||||
\(967\) | 41.6458i | 1.33924i | 0.742705 | + | 0.669619i | \(0.233542\pi\) | ||||
−0.742705 | + | 0.669619i | \(0.766458\pi\) | |||||||
\(968\) | 86.3137i | 2.77423i | ||||||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 5.00000i | 0.160375i | ||||||||
\(973\) | 29.4170i | 0.943066i | ||||||||
\(974\) | 47.2915 | 1.51532 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −124.207 | −3.97575 | ||||||||
\(977\) | 51.0405i | 1.63293i | 0.577394 | + | 0.816465i | \(0.304070\pi\) | ||||
−0.577394 | + | 0.816465i | \(0.695930\pi\) | |||||||
\(978\) | − 6.22876i | − 0.199174i | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.29150 | 0.168945 | ||||||||
\(982\) | − 15.2693i | − 0.487262i | ||||||||
\(983\) | 34.4575i | 1.09902i | 0.835486 | + | 0.549512i | \(0.185186\pi\) | ||||
−0.835486 | + | 0.549512i | \(0.814814\pi\) | |||||||
\(984\) | 76.5608 | 2.44067 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 94.5830 | 3.01214 | ||||||||
\(987\) | − 2.12549i | − 0.0676552i | ||||||||
\(988\) | 1.77124i | 0.0563508i | ||||||||
\(989\) | −52.4575 | −1.66805 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.7490 | −1.13560 | −0.567802 | − | 0.823165i | \(-0.692206\pi\) | ||||
−0.567802 | + | 0.823165i | \(0.692206\pi\) | |||||||
\(992\) | 79.3725i | 2.52008i | ||||||||
\(993\) | − 11.4170i | − 0.362307i | ||||||||
\(994\) | 31.7490 | 1.00702 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.0000 | −0.950586 | ||||||||
\(997\) | − 26.7085i | − 0.845867i | −0.906161 | − | 0.422933i | \(-0.861000\pi\) | ||||
0.906161 | − | 0.422933i | \(-0.139000\pi\) | |||||||
\(998\) | 82.1255i | 2.59964i | ||||||||
\(999\) | 3.64575 | 0.115346 |
(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 | 1425.2.c.i.799.3 | 4 | ||
5.2 | odd | 4 | 285.2.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1425.2.a.p.1.2 | 2 | |||
5.4 | even | 2 | inner | 1425.2.c.i.799.2 | 4 | ||
15.2 | even | 4 | 855.2.a.g.1.2 | 2 | |||
15.8 | even | 4 | 4275.2.a.u.1.1 | 2 | |||
20.7 | even | 4 | 4560.2.a.bo.1.1 | 2 | |||
95.37 | even | 4 | 5415.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
855.2.a.g.1.2 | 2 | 15.2 | even | 4 | |||
1425.2.a.p.1.2 | 2 | 5.3 | odd | 4 | |||
1425.2.c.i.799.2 | 4 | 5.4 | even | 2 | inner | ||
1425.2.c.i.799.3 | 4 | 1.1 | even | 1 | trivial | ||
4275.2.a.u.1.1 | 2 | 15.8 | even | 4 | |||
4560.2.a.bo.1.1 | 2 | 20.7 | even | 4 | |||
5415.2.a.s.1.2 | 2 | 95.37 | even | 4 |