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 | 799.1 | ||
Root | \(-1.32288 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.799 |
Dual form | 1425.2.c.i.799.4 |
$q$-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 | \(-0.615027\pi\) | ||||
0.353553 | − | 0.935414i | \(-0.384973\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −5.00000 | −2.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.64575 | −1.08012 | ||||||||
\(7\) | 3.64575i | 1.37796i | 0.724778 | + | 0.688982i | \(0.241942\pi\) | ||||
−0.724778 | + | 0.688982i | \(0.758058\pi\) | |||||||
\(8\) | 7.93725i | 2.80624i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64575 | 1.70226 | 0.851129 | − | 0.524957i | \(-0.175918\pi\) | ||||
0.851129 | + | 0.524957i | \(0.175918\pi\) | |||||||
\(12\) | 5.00000i | 1.44338i | ||||||||
\(13\) | − 5.64575i | − 1.56585i | −0.622116 | − | 0.782925i | \(-0.713727\pi\) | ||||
0.622116 | − | 0.782925i | \(-0.286273\pi\) | |||||||
\(14\) | 9.64575 | 2.57794 | ||||||||
\(15\) | 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 | ||||||||
\(21\) | 3.64575 | 0.795568 | ||||||||
\(22\) | − 14.9373i | − 3.18463i | ||||||||
\(23\) | − 1.29150i | − 0.269297i | −0.990893 | − | 0.134648i | \(-0.957009\pi\) | ||||
0.990893 | − | 0.134648i | \(-0.0429905\pi\) | |||||||
\(24\) | 7.93725 | 1.62019 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.9373 | −2.92944 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 18.2288i | − 3.44491i | ||||||||
\(29\) | 6.93725 | 1.28822 | 0.644108 | − | 0.764935i | \(-0.277229\pi\) | ||||
0.644108 | + | 0.764935i | \(0.277229\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | − 5.64575i | − 0.982799i | ||||||||
\(34\) | 10.5830 | 1.81497 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.00000 | 0.833333 | ||||||||
\(37\) | 1.64575i | 0.270560i | 0.990807 | + | 0.135280i | \(0.0431934\pi\) | ||||
−0.990807 | + | 0.135280i | \(0.956807\pi\) | |||||||
\(38\) | − 2.64575i | − 0.429198i | ||||||||
\(39\) | −5.64575 | −0.904044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.35425 | −0.680019 | −0.340010 | − | 0.940422i | \(-0.610430\pi\) | ||||
−0.340010 | + | 0.940422i | \(0.610430\pi\) | |||||||
\(42\) | − 9.64575i | − 1.48837i | ||||||||
\(43\) | 0.354249i | 0.0540224i | 0.999635 | + | 0.0270112i | \(0.00859898\pi\) | ||||
−0.999635 | + | 0.0270112i | \(0.991401\pi\) | |||||||
\(44\) | −28.2288 | −4.25565 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.41699 | −0.503808 | ||||||||
\(47\) | − 9.29150i | − 1.35530i | −0.735382 | − | 0.677652i | \(-0.762997\pi\) | ||||
0.735382 | − | 0.677652i | \(-0.237003\pi\) | |||||||
\(48\) | − 11.0000i | − 1.58771i | ||||||||
\(49\) | −6.29150 | −0.898786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 28.2288i | 3.91462i | ||||||||
\(53\) | 0.708497i | 0.0973196i | 0.998815 | + | 0.0486598i | \(0.0154950\pi\) | ||||
−0.998815 | + | 0.0486598i | \(0.984505\pi\) | |||||||
\(54\) | 2.64575 | 0.360041 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −28.9373 | −3.86690 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | − 18.3542i | − 2.41003i | ||||||||
\(59\) | −0.708497 | −0.0922385 | −0.0461193 | − | 0.998936i | \(-0.514685\pi\) | ||||
−0.0461193 | + | 0.998936i | \(0.514685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.708497 | −0.0907138 | −0.0453569 | − | 0.998971i | \(-0.514443\pi\) | ||||
−0.0453569 | + | 0.998971i | \(0.514443\pi\) | |||||||
\(62\) | − 15.8745i | − 2.01606i | ||||||||
\(63\) | − 3.64575i | − 0.459321i | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.9373 | −1.83865 | ||||||||
\(67\) | − 14.5830i | − 1.78160i | −0.454398 | − | 0.890799i | \(-0.650146\pi\) | ||||
0.454398 | − | 0.890799i | \(-0.349854\pi\) | |||||||
\(68\) | − 20.0000i | − 2.42536i | ||||||||
\(69\) | −1.29150 | −0.155479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.29150 | −0.390629 | −0.195315 | − | 0.980741i | \(-0.562573\pi\) | ||||
−0.195315 | + | 0.980741i | \(0.562573\pi\) | |||||||
\(72\) | − 7.93725i | − 0.935414i | ||||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 4.35425 | 0.506171 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | 20.5830i | 2.34565i | ||||||||
\(78\) | 14.9373i | 1.69131i | ||||||||
\(79\) | 14.5830 | 1.64072 | 0.820358 | − | 0.571850i | \(-0.193774\pi\) | ||||
0.820358 | + | 0.571850i | \(0.193774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5203i | 1.27220i | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −18.2288 | −1.98892 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.937254 | 0.101067 | ||||||||
\(87\) | − 6.93725i | − 0.743752i | ||||||||
\(88\) | 44.8118i | 4.77695i | ||||||||
\(89\) | 1.06275 | 0.112651 | 0.0563254 | − | 0.998412i | \(-0.482062\pi\) | ||||
0.0563254 | + | 0.998412i | \(0.482062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.5830 | 2.15769 | ||||||||
\(92\) | 6.45751i | 0.673242i | ||||||||
\(93\) | − 6.00000i | − 0.622171i | ||||||||
\(94\) | −24.5830 | −2.53554 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.2288 | −1.35015 | ||||||||
\(97\) | − 12.9373i | − 1.31358i | −0.754074 | − | 0.656790i | \(-0.771914\pi\) | ||||
0.754074 | − | 0.656790i | \(-0.228086\pi\) | |||||||
\(98\) | 16.6458i | 1.68147i | ||||||||
\(99\) | −5.64575 | −0.567419 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29150 | −0.128509 | −0.0642547 | − | 0.997934i | \(-0.520467\pi\) | ||||
−0.0642547 | + | 0.997934i | \(0.520467\pi\) | |||||||
\(102\) | − 10.5830i | − 1.04787i | ||||||||
\(103\) | 10.5830i | 1.04277i | 0.853320 | + | 0.521387i | \(0.174585\pi\) | ||||
−0.853320 | + | 0.521387i | \(0.825415\pi\) | |||||||
\(104\) | 44.8118 | 4.39415 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.87451 | 0.182068 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | − 5.00000i | − 0.481125i | ||||||||
\(109\) | 5.29150 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.64575 | 0.156208 | ||||||||
\(112\) | 40.1033i | 3.78940i | ||||||||
\(113\) | − 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 | ||||||||
\(116\) | −34.6863 | −3.22054 | ||||||||
\(117\) | 5.64575i | 0.521950i | ||||||||
\(118\) | 1.87451i | 0.172562i | ||||||||
\(119\) | −14.5830 | −1.33682 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8745 | 1.89768 | ||||||||
\(122\) | 1.87451i | 0.169710i | ||||||||
\(123\) | 4.35425i | 0.392609i | ||||||||
\(124\) | −30.0000 | −2.69408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.64575 | −0.859312 | ||||||||
\(127\) | − 4.00000i | − 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 7.93725i | 0.701561i | ||||||||
\(129\) | 0.354249 | 0.0311899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2288 | 1.06843 | 0.534216 | − | 0.845348i | \(-0.320607\pi\) | ||||
0.534216 | + | 0.845348i | \(0.320607\pi\) | |||||||
\(132\) | 28.2288i | 2.45700i | ||||||||
\(133\) | 3.64575i | 0.316127i | ||||||||
\(134\) | −38.5830 | −3.33306 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −31.7490 | −2.72246 | ||||||||
\(137\) | − 6.00000i | − 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 3.41699i | 0.290874i | ||||||||
\(139\) | 13.8745 | 1.17682 | 0.588410 | − | 0.808563i | \(-0.299754\pi\) | ||||
0.588410 | + | 0.808563i | \(0.299754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.29150 | −0.782486 | ||||||||
\(142\) | 8.70850i | 0.730801i | ||||||||
\(143\) | − 31.8745i | − 2.66548i | ||||||||
\(144\) | −11.0000 | −0.916667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26.4575 | 2.18964 | ||||||||
\(147\) | 6.29150i | 0.518914i | ||||||||
\(148\) | − 8.22876i | − 0.676400i | ||||||||
\(149\) | −0.583005 | −0.0477617 | −0.0238808 | − | 0.999715i | \(-0.507602\pi\) | ||||
−0.0238808 | + | 0.999715i | \(0.507602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5830 | 1.02399 | 0.511995 | − | 0.858988i | \(-0.328907\pi\) | ||||
0.511995 | + | 0.858988i | \(0.328907\pi\) | |||||||
\(152\) | 7.93725i | 0.643796i | ||||||||
\(153\) | − 4.00000i | − 0.323381i | ||||||||
\(154\) | 54.4575 | 4.38831 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 28.2288 | 2.26011 | ||||||||
\(157\) | 2.70850i | 0.216162i | 0.994142 | + | 0.108081i | \(0.0344705\pi\) | ||||
−0.994142 | + | 0.108081i | \(0.965529\pi\) | |||||||
\(158\) | − 38.5830i | − 3.06950i | ||||||||
\(159\) | 0.708497 | 0.0561875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.70850 | 0.371082 | ||||||||
\(162\) | − 2.64575i | − 0.207870i | ||||||||
\(163\) | − 7.64575i | − 0.598861i | −0.954118 | − | 0.299431i | \(-0.903203\pi\) | ||||
0.954118 | − | 0.299431i | \(-0.0967967\pi\) | |||||||
\(164\) | 21.7712 | 1.70005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8745 | 1.23210 | ||||||||
\(167\) | 10.7085i | 0.828648i | 0.910129 | + | 0.414324i | \(0.135982\pi\) | ||||
−0.910129 | + | 0.414324i | \(0.864018\pi\) | |||||||
\(168\) | 28.9373i | 2.23256i | ||||||||
\(169\) | −18.8745 | −1.45189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | − 1.77124i | − 0.135056i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | −18.3542 | −1.39143 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 62.1033 | 4.68121 | ||||||||
\(177\) | 0.708497i | 0.0532539i | ||||||||
\(178\) | − 2.81176i | − 0.210750i | ||||||||
\(179\) | −3.29150 | −0.246018 | −0.123009 | − | 0.992406i | \(-0.539254\pi\) | ||||
−0.123009 | + | 0.992406i | \(0.539254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70850 | 0.498639 | 0.249319 | − | 0.968421i | \(-0.419793\pi\) | ||||
0.249319 | + | 0.968421i | \(0.419793\pi\) | |||||||
\(182\) | − 54.4575i | − 4.03666i | ||||||||
\(183\) | 0.708497i | 0.0523736i | ||||||||
\(184\) | 10.2510 | 0.755713 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.8745 | −1.16398 | ||||||||
\(187\) | 22.5830i | 1.65143i | ||||||||
\(188\) | 46.4575i | 3.38826i | ||||||||
\(189\) | −3.64575 | −0.265189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2288 | −1.46370 | −0.731851 | − | 0.681465i | \(-0.761343\pi\) | ||||
−0.731851 | + | 0.681465i | \(0.761343\pi\) | |||||||
\(192\) | 13.0000i | 0.938194i | ||||||||
\(193\) | − 6.35425i | − 0.457389i | −0.973498 | − | 0.228694i | \(-0.926554\pi\) | ||||
0.973498 | − | 0.228694i | \(-0.0734457\pi\) | |||||||
\(194\) | −34.2288 | −2.45748 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.4575 | 2.24697 | ||||||||
\(197\) | − 17.1660i | − 1.22303i | −0.791234 | − | 0.611514i | \(-0.790561\pi\) | ||||
0.791234 | − | 0.611514i | \(-0.209439\pi\) | |||||||
\(198\) | 14.9373i | 1.06154i | ||||||||
\(199\) | 3.29150 | 0.233328 | 0.116664 | − | 0.993171i | \(-0.462780\pi\) | ||||
0.116664 | + | 0.993171i | \(0.462780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.5830 | −1.02861 | ||||||||
\(202\) | 3.41699i | 0.240419i | ||||||||
\(203\) | 25.2915i | 1.77512i | ||||||||
\(204\) | −20.0000 | −1.40028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.0000 | 1.95085 | ||||||||
\(207\) | 1.29150i | 0.0897656i | ||||||||
\(208\) | − 62.1033i | − 4.30609i | ||||||||
\(209\) | 5.64575 | 0.390525 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.5830 | −1.27931 | −0.639653 | − | 0.768663i | \(-0.720922\pi\) | ||||
−0.639653 | + | 0.768663i | \(0.720922\pi\) | |||||||
\(212\) | − 3.54249i | − 0.243299i | ||||||||
\(213\) | 3.29150i | 0.225530i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.93725 | −0.540062 | ||||||||
\(217\) | 21.8745i | 1.48494i | ||||||||
\(218\) | − 14.0000i | − 0.948200i | ||||||||
\(219\) | 10.0000 | 0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.5830 | 1.51910 | ||||||||
\(222\) | − 4.35425i | − 0.292238i | ||||||||
\(223\) | − 18.5830i | − 1.24441i | −0.782854 | − | 0.622205i | \(-0.786237\pi\) | ||||
0.782854 | − | 0.622205i | \(-0.213763\pi\) | |||||||
\(224\) | 48.2288 | 3.22242 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.5830 | −0.703971 | ||||||||
\(227\) | 21.2915i | 1.41317i | 0.707630 | + | 0.706583i | \(0.249764\pi\) | ||||
−0.707630 | + | 0.706583i | \(0.750236\pi\) | |||||||
\(228\) | 5.00000i | 0.331133i | ||||||||
\(229\) | −19.2915 | −1.27482 | −0.637409 | − | 0.770525i | \(-0.719994\pi\) | ||||
−0.637409 | + | 0.770525i | \(0.719994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.5830 | 1.35426 | ||||||||
\(232\) | 55.0627i | 3.61505i | ||||||||
\(233\) | − 18.0000i | − 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 14.9373 | 0.976479 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.54249 | 0.230596 | ||||||||
\(237\) | − 14.5830i | − 0.947268i | ||||||||
\(238\) | 38.5830i | 2.50096i | ||||||||
\(239\) | −10.3542 | −0.669761 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.58301 | −0.295217 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(242\) | − 55.2288i | − 3.55024i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 3.54249 | 0.226784 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.5203 | 0.734505 | ||||||||
\(247\) | − 5.64575i | − 0.359231i | ||||||||
\(248\) | 47.6235i | 3.02410i | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.6458 | −1.36627 | −0.683134 | − | 0.730293i | \(-0.739383\pi\) | ||||
−0.683134 | + | 0.730293i | \(0.739383\pi\) | |||||||
\(252\) | 18.2288i | 1.14830i | ||||||||
\(253\) | − 7.29150i | − 0.458413i | ||||||||
\(254\) | −10.5830 | −0.664037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.00000 | −0.312500 | ||||||||
\(257\) | 26.5830i | 1.65820i | 0.559099 | + | 0.829101i | \(0.311147\pi\) | ||||
−0.559099 | + | 0.829101i | \(0.688853\pi\) | |||||||
\(258\) | − 0.937254i | − 0.0583509i | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.93725 | −0.429405 | ||||||||
\(262\) | − 32.3542i | − 1.99885i | ||||||||
\(263\) | − 16.5830i | − 1.02255i | −0.859417 | − | 0.511276i | \(-0.829173\pi\) | ||||
0.859417 | − | 0.511276i | \(-0.170827\pi\) | |||||||
\(264\) | 44.8118 | 2.75797 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.64575 | 0.591419 | ||||||||
\(267\) | − 1.06275i | − 0.0650390i | ||||||||
\(268\) | 72.9150i | 4.45399i | ||||||||
\(269\) | 22.2288 | 1.35531 | 0.677656 | − | 0.735379i | \(-0.262996\pi\) | ||||
0.677656 | + | 0.735379i | \(0.262996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2915 | −0.928893 | −0.464446 | − | 0.885601i | \(-0.653747\pi\) | ||||
−0.464446 | + | 0.885601i | \(0.653747\pi\) | |||||||
\(272\) | 44.0000i | 2.66789i | ||||||||
\(273\) | − 20.5830i | − 1.24574i | ||||||||
\(274\) | −15.8745 | −0.959014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.45751 | 0.388697 | ||||||||
\(277\) | 20.5830i | 1.23671i | 0.785898 | + | 0.618356i | \(0.212201\pi\) | ||||
−0.785898 | + | 0.618356i | \(0.787799\pi\) | |||||||
\(278\) | − 36.7085i | − 2.20163i | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.77124 | −0.344284 | −0.172142 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172142 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(282\) | 24.5830i | 1.46390i | ||||||||
\(283\) | 25.5203i | 1.51702i | 0.651660 | + | 0.758511i | \(0.274073\pi\) | ||||
−0.651660 | + | 0.758511i | \(0.725927\pi\) | |||||||
\(284\) | 16.4575 | 0.976574 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −84.3320 | −4.98666 | ||||||||
\(287\) | − 15.8745i | − 0.937043i | ||||||||
\(288\) | 13.2288i | 0.779512i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9373 | −0.758395 | ||||||||
\(292\) | − 50.0000i | − 2.92603i | ||||||||
\(293\) | 26.5830i | 1.55300i | 0.630120 | + | 0.776498i | \(0.283006\pi\) | ||||
−0.630120 | + | 0.776498i | \(0.716994\pi\) | |||||||
\(294\) | 16.6458 | 0.970800 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.0627 | −0.759257 | ||||||||
\(297\) | 5.64575i | 0.327600i | ||||||||
\(298\) | 1.54249i | 0.0893539i | ||||||||
\(299\) | −7.29150 | −0.421678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29150 | −0.0744410 | ||||||||
\(302\) | − 33.2915i | − 1.91571i | ||||||||
\(303\) | 1.29150i | 0.0741949i | ||||||||
\(304\) | 11.0000 | 0.630893 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.5830 | −0.604990 | ||||||||
\(307\) | − 28.4575i | − 1.62416i | −0.583549 | − | 0.812078i | \(-0.698336\pi\) | ||||
0.583549 | − | 0.812078i | \(-0.301664\pi\) | |||||||
\(308\) | − 102.915i | − 5.86413i | ||||||||
\(309\) | 10.5830 | 0.602046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.06275 | 0.400492 | 0.200246 | − | 0.979746i | \(-0.435826\pi\) | ||||
0.200246 | + | 0.979746i | \(0.435826\pi\) | |||||||
\(312\) | − 44.8118i | − 2.53697i | ||||||||
\(313\) | 6.70850i | 0.379187i | 0.981863 | + | 0.189593i | \(0.0607170\pi\) | ||||
−0.981863 | + | 0.189593i | \(0.939283\pi\) | |||||||
\(314\) | 7.16601 | 0.404401 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −72.9150 | −4.10179 | ||||||||
\(317\) | 32.4575i | 1.82300i | 0.411305 | + | 0.911498i | \(0.365073\pi\) | ||||
−0.411305 | + | 0.911498i | \(0.634927\pi\) | |||||||
\(318\) | − 1.87451i | − 0.105117i | ||||||||
\(319\) | 39.1660 | 2.19288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 12.4575i | − 0.694230i | ||||||||
\(323\) | 4.00000i | 0.222566i | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.2288 | −1.12037 | ||||||||
\(327\) | − 5.29150i | − 0.292621i | ||||||||
\(328\) | − 34.5608i | − 1.90830i | ||||||||
\(329\) | 33.8745 | 1.86756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5830 | 1.79092 | 0.895462 | − | 0.445138i | \(-0.146845\pi\) | ||||
0.895462 | + | 0.445138i | \(0.146845\pi\) | |||||||
\(332\) | − 30.0000i | − 1.64646i | ||||||||
\(333\) | − 1.64575i | − 0.0901866i | ||||||||
\(334\) | 28.3320 | 1.55026 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 40.1033 | 2.18781 | ||||||||
\(337\) | 0.937254i | 0.0510555i | 0.999674 | + | 0.0255277i | \(0.00812661\pi\) | ||||
−0.999674 | + | 0.0255277i | \(0.991873\pi\) | |||||||
\(338\) | 49.9373i | 2.71623i | ||||||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.8745 | 1.83441 | ||||||||
\(342\) | 2.64575i | 0.143066i | ||||||||
\(343\) | 2.58301i | 0.139469i | ||||||||
\(344\) | −2.81176 | −0.151600 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 26.0000i | − 1.39575i | −0.716218 | − | 0.697877i | \(-0.754128\pi\) | ||||
0.716218 | − | 0.697877i | \(-0.245872\pi\) | |||||||
\(348\) | 34.6863i | 1.85938i | ||||||||
\(349\) | 19.1660 | 1.02593 | 0.512967 | − | 0.858409i | \(-0.328546\pi\) | ||||
0.512967 | + | 0.858409i | \(0.328546\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.64575 | 0.301348 | ||||||||
\(352\) | − 74.6863i | − 3.98079i | ||||||||
\(353\) | − 20.5830i | − 1.09552i | −0.836635 | − | 0.547761i | \(-0.815480\pi\) | ||||
0.836635 | − | 0.547761i | \(-0.184520\pi\) | |||||||
\(354\) | 1.87451 | 0.0996290 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.31373 | −0.281627 | ||||||||
\(357\) | 14.5830i | 0.771814i | ||||||||
\(358\) | 8.70850i | 0.460258i | ||||||||
\(359\) | −22.1033 | −1.16657 | −0.583283 | − | 0.812269i | \(-0.698232\pi\) | ||||
−0.583283 | + | 0.812269i | \(0.698232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 17.7490i | − 0.932868i | ||||||||
\(363\) | − 20.8745i | − 1.09563i | ||||||||
\(364\) | −102.915 | −5.39421 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.87451 | 0.0979821 | ||||||||
\(367\) | 3.64575i | 0.190307i | 0.995463 | + | 0.0951533i | \(0.0303341\pi\) | ||||
−0.995463 | + | 0.0951533i | \(0.969666\pi\) | |||||||
\(368\) | − 14.2065i | − 0.740567i | ||||||||
\(369\) | 4.35425 | 0.226673 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.58301 | −0.134103 | ||||||||
\(372\) | 30.0000i | 1.55543i | ||||||||
\(373\) | 20.9373i | 1.08409i | 0.840349 | + | 0.542045i | \(0.182350\pi\) | ||||
−0.840349 | + | 0.542045i | \(0.817650\pi\) | |||||||
\(374\) | 59.7490 | 3.08955 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 73.7490 | 3.80332 | ||||||||
\(377\) | − 39.1660i | − 2.01715i | ||||||||
\(378\) | 9.64575i | 0.496124i | ||||||||
\(379\) | −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 | ||||||||
\(382\) | 53.5203i | 2.73833i | ||||||||
\(383\) | 2.58301i | 0.131985i | 0.997820 | + | 0.0659927i | \(0.0210214\pi\) | ||||
−0.997820 | + | 0.0659927i | \(0.978979\pi\) | |||||||
\(384\) | 7.93725 | 0.405046 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.8118 | −0.855696 | ||||||||
\(387\) | − 0.354249i | − 0.0180075i | ||||||||
\(388\) | 64.6863i | 3.28395i | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.16601 | 0.261256 | ||||||||
\(392\) | − 49.9373i | − 2.52221i | ||||||||
\(393\) | − 12.2288i | − 0.616859i | ||||||||
\(394\) | −45.4170 | −2.28808 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 28.2288 | 1.41855 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | − 8.70850i | − 0.436518i | ||||||||
\(399\) | 3.64575 | 0.182516 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9373 | 0.546180 | 0.273090 | − | 0.961988i | \(-0.411954\pi\) | ||||
0.273090 | + | 0.961988i | \(0.411954\pi\) | |||||||
\(402\) | 38.5830i | 1.92435i | ||||||||
\(403\) | − 33.8745i | − 1.68741i | ||||||||
\(404\) | 6.45751 | 0.321273 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 66.9150 | 3.32094 | ||||||||
\(407\) | 9.29150i | 0.460563i | ||||||||
\(408\) | 31.7490i | 1.57181i | ||||||||
\(409\) | 17.2915 | 0.855010 | 0.427505 | − | 0.904013i | \(-0.359393\pi\) | ||||
0.427505 | + | 0.904013i | \(0.359393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | − 52.9150i | − 2.60694i | ||||||||
\(413\) | − 2.58301i | − 0.127101i | ||||||||
\(414\) | 3.41699 | 0.167936 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −74.6863 | −3.66180 | ||||||||
\(417\) | − 13.8745i | − 0.679438i | ||||||||
\(418\) | − 14.9373i | − 0.730605i | ||||||||
\(419\) | −23.0627 | −1.12669 | −0.563344 | − | 0.826222i | \(-0.690486\pi\) | ||||
−0.563344 | + | 0.826222i | \(0.690486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.41699 | 0.361482 | 0.180741 | − | 0.983531i | \(-0.442150\pi\) | ||||
0.180741 | + | 0.983531i | \(0.442150\pi\) | |||||||
\(422\) | 49.1660i | 2.39336i | ||||||||
\(423\) | 9.29150i | 0.451768i | ||||||||
\(424\) | −5.62352 | −0.273102 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.70850 | 0.421928 | ||||||||
\(427\) | − 2.58301i | − 0.125000i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.8745 | −1.53892 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.29150 | −0.351219 | −0.175610 | − | 0.984460i | \(-0.556190\pi\) | ||||
−0.175610 | + | 0.984460i | \(0.556190\pi\) | |||||||
\(432\) | 11.0000i | 0.529238i | ||||||||
\(433\) | − 22.3542i | − 1.07428i | −0.843494 | − | 0.537138i | \(-0.819505\pi\) | ||||
0.843494 | − | 0.537138i | \(-0.180495\pi\) | |||||||
\(434\) | 57.8745 | 2.77807 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.4575 | −1.26709 | ||||||||
\(437\) | − 1.29150i | − 0.0617809i | ||||||||
\(438\) | − 26.4575i | − 1.26419i | ||||||||
\(439\) | 22.5830 | 1.07783 | 0.538914 | − | 0.842361i | \(-0.318835\pi\) | ||||
0.538914 | + | 0.842361i | \(0.318835\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.29150 | 0.299595 | ||||||||
\(442\) | − 59.7490i | − 2.84197i | ||||||||
\(443\) | 37.2915i | 1.77177i | 0.463902 | + | 0.885886i | \(0.346449\pi\) | ||||
−0.463902 | + | 0.885886i | \(0.653551\pi\) | |||||||
\(444\) | −8.22876 | −0.390520 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −49.1660 | −2.32808 | ||||||||
\(447\) | 0.583005i | 0.0275752i | ||||||||
\(448\) | − 47.3948i | − 2.23919i | ||||||||
\(449\) | 9.77124 | 0.461133 | 0.230567 | − | 0.973057i | \(-0.425942\pi\) | ||||
0.230567 | + | 0.973057i | \(0.425942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.5830 | −1.15757 | ||||||||
\(452\) | 20.0000i | 0.940721i | ||||||||
\(453\) | − 12.5830i | − 0.591201i | ||||||||
\(454\) | 56.3320 | 2.64379 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.93725 | 0.371696 | ||||||||
\(457\) | − 31.8745i | − 1.49103i | −0.666491 | − | 0.745513i | \(-0.732204\pi\) | ||||
0.666491 | − | 0.745513i | \(-0.267796\pi\) | |||||||
\(458\) | 51.0405i | 2.38497i | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.7490 | 1.19925 | 0.599626 | − | 0.800281i | \(-0.295316\pi\) | ||||
0.599626 | + | 0.800281i | \(0.295316\pi\) | |||||||
\(462\) | − 54.4575i | − 2.53359i | ||||||||
\(463\) | 1.52026i | 0.0706524i | 0.999376 | + | 0.0353262i | \(0.0112470\pi\) | ||||
−0.999376 | + | 0.0353262i | \(0.988753\pi\) | |||||||
\(464\) | 76.3098 | 3.54259 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.6235 | −2.20612 | ||||||||
\(467\) | 11.8745i | 0.549487i | 0.961518 | + | 0.274743i | \(0.0885929\pi\) | ||||
−0.961518 | + | 0.274743i | \(0.911407\pi\) | |||||||
\(468\) | − 28.2288i | − 1.30487i | ||||||||
\(469\) | 53.1660 | 2.45498 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.70850 | 0.124801 | ||||||||
\(472\) | − 5.62352i | − 0.258844i | ||||||||
\(473\) | 2.00000i | 0.0919601i | ||||||||
\(474\) | −38.5830 | −1.77218 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 72.9150 | 3.34205 | ||||||||
\(477\) | − 0.708497i | − 0.0324399i | ||||||||
\(478\) | 27.3948i | 1.25301i | ||||||||
\(479\) | −9.64575 | −0.440726 | −0.220363 | − | 0.975418i | \(-0.570724\pi\) | ||||
−0.220363 | + | 0.975418i | \(0.570724\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.29150 | 0.423656 | ||||||||
\(482\) | 12.1255i | 0.552301i | ||||||||
\(483\) | − 4.70850i | − 0.214244i | ||||||||
\(484\) | −104.373 | −4.74421 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.64575 | −0.120014 | ||||||||
\(487\) | 13.8745i | 0.628714i | 0.949305 | + | 0.314357i | \(0.101789\pi\) | ||||
−0.949305 | + | 0.314357i | \(0.898211\pi\) | |||||||
\(488\) | − 5.62352i | − 0.254565i | ||||||||
\(489\) | −7.64575 | −0.345753 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2288 | −1.45446 | −0.727232 | − | 0.686392i | \(-0.759193\pi\) | ||||
−0.727232 | + | 0.686392i | \(0.759193\pi\) | |||||||
\(492\) | − 21.7712i | − 0.981523i | ||||||||
\(493\) | 27.7490i | 1.24975i | ||||||||
\(494\) | −14.9373 | −0.672059 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 66.0000 | 2.96349 | ||||||||
\(497\) | − 12.0000i | − 0.538274i | ||||||||
\(498\) | − 15.8745i | − 0.711354i | ||||||||
\(499\) | −43.0405 | −1.92676 | −0.963379 | − | 0.268143i | \(-0.913590\pi\) | ||||
−0.963379 | + | 0.268143i | \(0.913590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7085 | 0.478420 | ||||||||
\(502\) | 57.2693i | 2.55605i | ||||||||
\(503\) | − 2.00000i | − 0.0891756i | −0.999005 | − | 0.0445878i | \(-0.985803\pi\) | ||||
0.999005 | − | 0.0445878i | \(-0.0141974\pi\) | |||||||
\(504\) | 28.9373 | 1.28897 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.2915 | −0.857612 | ||||||||
\(507\) | 18.8745i | 0.838246i | ||||||||
\(508\) | 20.0000i | 0.887357i | ||||||||
\(509\) | −24.1033 | −1.06836 | −0.534179 | − | 0.845371i | \(-0.679379\pi\) | ||||
−0.534179 | + | 0.845371i | \(0.679379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.4575 | −1.61279 | ||||||||
\(512\) | 29.1033i | 1.28619i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 70.3320 | 3.10221 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.77124 | −0.0779746 | ||||||||
\(517\) | − 52.4575i | − 2.30708i | ||||||||
\(518\) | 15.8745i | 0.697486i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1033 | −1.58171 | −0.790856 | − | 0.612002i | \(-0.790365\pi\) | ||||
−0.790856 | + | 0.612002i | \(0.790365\pi\) | |||||||
\(522\) | 18.3542i | 0.803344i | ||||||||
\(523\) | − 12.7085i | − 0.555704i | −0.960624 | − | 0.277852i | \(-0.910378\pi\) | ||||
0.960624 | − | 0.277852i | \(-0.0896224\pi\) | |||||||
\(524\) | −61.1438 | −2.67108 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.8745 | −1.91302 | ||||||||
\(527\) | 24.0000i | 1.04546i | ||||||||
\(528\) | − 62.1033i | − 2.70270i | ||||||||
\(529\) | 21.3320 | 0.927479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.708497 | 0.0307462 | ||||||||
\(532\) | − 18.2288i | − 0.790317i | ||||||||
\(533\) | 24.5830i | 1.06481i | ||||||||
\(534\) | −2.81176 | −0.121677 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 115.749 | 4.99960 | ||||||||
\(537\) | 3.29150i | 0.142039i | ||||||||
\(538\) | − 58.8118i | − 2.53556i | ||||||||
\(539\) | −35.5203 | −1.52997 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 40.4575i | 1.73780i | ||||||||
\(543\) | − 6.70850i | − 0.287889i | ||||||||
\(544\) | 52.9150 | 2.26871 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −54.4575 | −2.33057 | ||||||||
\(547\) | 29.8745i | 1.27734i | 0.769480 | + | 0.638671i | \(0.220515\pi\) | ||||
−0.769480 | + | 0.638671i | \(0.779485\pi\) | |||||||
\(548\) | 30.0000i | 1.28154i | ||||||||
\(549\) | 0.708497 | 0.0302379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.93725 | 0.295537 | ||||||||
\(552\) | − 10.2510i | − 0.436311i | ||||||||
\(553\) | 53.1660i | 2.26085i | ||||||||
\(554\) | 54.4575 | 2.31368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −69.3725 | −2.94205 | ||||||||
\(557\) | 32.5830i | 1.38059i | 0.723530 | + | 0.690293i | \(0.242518\pi\) | ||||
−0.723530 | + | 0.690293i | \(0.757482\pi\) | |||||||
\(558\) | 15.8745i | 0.672022i | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5830 | 0.953455 | ||||||||
\(562\) | 15.2693i | 0.644095i | ||||||||
\(563\) | 39.8745i | 1.68051i | 0.542191 | + | 0.840255i | \(0.317595\pi\) | ||||
−0.542191 | + | 0.840255i | \(0.682405\pi\) | |||||||
\(564\) | 46.4575 | 1.95621 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 67.5203 | 2.83809 | ||||||||
\(567\) | 3.64575i | 0.153107i | ||||||||
\(568\) | − 26.1255i | − 1.09620i | ||||||||
\(569\) | 22.9373 | 0.961580 | 0.480790 | − | 0.876836i | \(-0.340350\pi\) | ||||
0.480790 | + | 0.876836i | \(0.340350\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2915 | 1.14211 | 0.571057 | − | 0.820910i | \(-0.306534\pi\) | ||||
0.571057 | + | 0.820910i | \(0.306534\pi\) | |||||||
\(572\) | 159.373i | 6.66370i | ||||||||
\(573\) | 20.2288i | 0.845068i | ||||||||
\(574\) | −42.0000 | −1.75305 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13.0000 | 0.541667 | ||||||||
\(577\) | 2.70850i | 0.112756i | 0.998409 | + | 0.0563781i | \(0.0179552\pi\) | ||||
−0.998409 | + | 0.0563781i | \(0.982045\pi\) | |||||||
\(578\) | − 2.64575i | − 0.110049i | ||||||||
\(579\) | −6.35425 | −0.264074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8745 | −0.907508 | ||||||||
\(582\) | 34.2288i | 1.41883i | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | −79.3725 | −3.28446 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.3320 | 2.90539 | ||||||||
\(587\) | 22.7085i | 0.937280i | 0.883389 | + | 0.468640i | \(0.155256\pi\) | ||||
−0.883389 | + | 0.468640i | \(0.844744\pi\) | |||||||
\(588\) | − 31.4575i | − 1.29729i | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.1660 | −0.706115 | ||||||||
\(592\) | 18.1033i | 0.744040i | ||||||||
\(593\) | 24.5830i | 1.00950i | 0.863265 | + | 0.504752i | \(0.168416\pi\) | ||||
−0.863265 | + | 0.504752i | \(0.831584\pi\) | |||||||
\(594\) | 14.9373 | 0.612883 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.91503 | 0.119404 | ||||||||
\(597\) | − 3.29150i | − 0.134712i | ||||||||
\(598\) | 19.2915i | 0.788888i | ||||||||
\(599\) | −30.5830 | −1.24959 | −0.624794 | − | 0.780790i | \(-0.714817\pi\) | ||||
−0.624794 | + | 0.780790i | \(0.714817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.2915 | 1.35799 | 0.678994 | − | 0.734143i | \(-0.262416\pi\) | ||||
0.678994 | + | 0.734143i | \(0.262416\pi\) | |||||||
\(602\) | 3.41699i | 0.139266i | ||||||||
\(603\) | 14.5830i | 0.593866i | ||||||||
\(604\) | −62.9150 | −2.55998 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.41699 | 0.138806 | ||||||||
\(607\) | − 31.0405i | − 1.25990i | −0.776637 | − | 0.629948i | \(-0.783076\pi\) | ||||
0.776637 | − | 0.629948i | \(-0.216924\pi\) | |||||||
\(608\) | − 13.2288i | − 0.536497i | ||||||||
\(609\) | 25.2915 | 1.02486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.4575 | −2.12220 | ||||||||
\(612\) | 20.0000i | 0.808452i | ||||||||
\(613\) | 22.4575i | 0.907050i | 0.891243 | + | 0.453525i | \(0.149834\pi\) | ||||
−0.891243 | + | 0.453525i | \(0.850166\pi\) | |||||||
\(614\) | −75.2915 | −3.03852 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −163.373 | −6.58247 | ||||||||
\(617\) | − 12.0000i | − 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | − 28.0000i | − 1.12633i | ||||||||
\(619\) | −12.7085 | −0.510798 | −0.255399 | − | 0.966836i | \(-0.582207\pi\) | ||||
−0.255399 | + | 0.966836i | \(0.582207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.29150 | 0.0518262 | ||||||||
\(622\) | − 18.6863i | − 0.749251i | ||||||||
\(623\) | 3.87451i | 0.155229i | ||||||||
\(624\) | −62.1033 | −2.48612 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.7490 | 0.709393 | ||||||||
\(627\) | − 5.64575i | − 0.225470i | ||||||||
\(628\) | − 13.5425i | − 0.540404i | ||||||||
\(629\) | −6.58301 | −0.262482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.58301 | 0.262065 | 0.131033 | − | 0.991378i | \(-0.458171\pi\) | ||||
0.131033 | + | 0.991378i | \(0.458171\pi\) | |||||||
\(632\) | 115.749i | 4.60425i | ||||||||
\(633\) | 18.5830i | 0.738608i | ||||||||
\(634\) | 85.8745 | 3.41051 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.54249 | −0.140469 | ||||||||
\(637\) | 35.5203i | 1.40736i | ||||||||
\(638\) | − 103.624i | − 4.10249i | ||||||||
\(639\) | 3.29150 | 0.130210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.06275 | −0.0419759 | −0.0209880 | − | 0.999780i | \(-0.506681\pi\) | ||||
−0.0209880 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.35425i | − 0.329459i | −0.986339 | − | 0.164730i | \(-0.947325\pi\) | ||||
0.986339 | − | 0.164730i | \(-0.0526752\pi\) | |||||||
\(644\) | −23.5425 | −0.927704 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5830 | 0.416383 | ||||||||
\(647\) | 24.5830i | 0.966458i | 0.875494 | + | 0.483229i | \(0.160536\pi\) | ||||
−0.875494 | + | 0.483229i | \(0.839464\pi\) | |||||||
\(648\) | 7.93725i | 0.311805i | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.8745 | 0.857330 | ||||||||
\(652\) | 38.2288i | 1.49715i | ||||||||
\(653\) | 30.5830i | 1.19681i | 0.801195 | + | 0.598403i | \(0.204198\pi\) | ||||
−0.801195 | + | 0.598403i | \(0.795802\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −47.8967 | −1.87005 | ||||||||
\(657\) | − 10.0000i | − 0.390137i | ||||||||
\(658\) | − 89.6235i | − 3.49389i | ||||||||
\(659\) | −46.5830 | −1.81462 | −0.907308 | − | 0.420466i | \(-0.861866\pi\) | ||||
−0.907308 | + | 0.420466i | \(0.861866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.29150 | −0.361398 | −0.180699 | − | 0.983538i | \(-0.557836\pi\) | ||||
−0.180699 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(662\) | − 86.2065i | − 3.35051i | ||||||||
\(663\) | − 22.5830i | − 0.877051i | ||||||||
\(664\) | −47.6235 | −1.84815 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.35425 | −0.168724 | ||||||||
\(667\) | − 8.95948i | − 0.346913i | ||||||||
\(668\) | − 53.5425i | − 2.07162i | ||||||||
\(669\) | −18.5830 | −0.718460 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | − 48.2288i | − 1.86046i | ||||||||
\(673\) | − 28.9373i | − 1.11545i | −0.830026 | − | 0.557725i | \(-0.811675\pi\) | ||||
0.830026 | − | 0.557725i | \(-0.188325\pi\) | |||||||
\(674\) | 2.47974 | 0.0955160 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 94.3725 | 3.62971 | ||||||||
\(677\) | 12.4575i | 0.478781i | 0.970923 | + | 0.239391i | \(0.0769476\pi\) | ||||
−0.970923 | + | 0.239391i | \(0.923052\pi\) | |||||||
\(678\) | 10.5830i | 0.406438i | ||||||||
\(679\) | 47.1660 | 1.81007 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.2915 | 0.815892 | ||||||||
\(682\) | − 89.6235i | − 3.43186i | ||||||||
\(683\) | − 43.7490i | − 1.67401i | −0.547196 | − | 0.837005i | \(-0.684305\pi\) | ||||
0.547196 | − | 0.837005i | \(-0.315695\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.83399 | 0.260923 | ||||||||
\(687\) | 19.2915i | 0.736017i | ||||||||
\(688\) | 3.89674i | 0.148562i | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0405 | 1.18084 | 0.590418 | − | 0.807097i | \(-0.298963\pi\) | ||||
0.590418 | + | 0.807097i | \(0.298963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 20.5830i | − 0.781884i | ||||||||
\(694\) | −68.7895 | −2.61122 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 55.0627 | 2.08715 | ||||||||
\(697\) | − 17.4170i | − 0.659716i | ||||||||
\(698\) | − 50.7085i | − 1.91934i | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.58301 | −0.173098 | −0.0865489 | − | 0.996248i | \(-0.527584\pi\) | ||||
−0.0865489 | + | 0.996248i | \(0.527584\pi\) | |||||||
\(702\) | − 14.9373i | − 0.563770i | ||||||||
\(703\) | 1.64575i | 0.0620707i | ||||||||
\(704\) | −73.3948 | −2.76617 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54.4575 | −2.04954 | ||||||||
\(707\) | − 4.70850i | − 0.177081i | ||||||||
\(708\) | − 3.54249i | − 0.133135i | ||||||||
\(709\) | 15.2915 | 0.574284 | 0.287142 | − | 0.957888i | \(-0.407295\pi\) | ||||
0.287142 | + | 0.957888i | \(0.407295\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5830 | −0.546905 | ||||||||
\(712\) | 8.43529i | 0.316126i | ||||||||
\(713\) | − 7.74902i | − 0.290203i | ||||||||
\(714\) | 38.5830 | 1.44393 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4575 | 0.615046 | ||||||||
\(717\) | 10.3542i | 0.386687i | ||||||||
\(718\) | 58.4797i | 2.18244i | ||||||||
\(719\) | 14.8118 | 0.552386 | 0.276193 | − | 0.961102i | \(-0.410927\pi\) | ||||
0.276193 | + | 0.961102i | \(0.410927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.5830 | −1.43691 | ||||||||
\(722\) | − 2.64575i | − 0.0984647i | ||||||||
\(723\) | 4.58301i | 0.170444i | ||||||||
\(724\) | −33.5425 | −1.24660 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −55.2288 | −2.04973 | ||||||||
\(727\) | 44.1033i | 1.63570i | 0.575432 | + | 0.817850i | \(0.304834\pi\) | ||||
−0.575432 | + | 0.817850i | \(0.695166\pi\) | |||||||
\(728\) | 163.373i | 6.05499i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41699 | −0.0524094 | ||||||||
\(732\) | − 3.54249i | − 0.130934i | ||||||||
\(733\) | 28.5830i | 1.05574i | 0.849326 | + | 0.527869i | \(0.177009\pi\) | ||||
−0.849326 | + | 0.527869i | \(0.822991\pi\) | |||||||
\(734\) | 9.64575 | 0.356031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.0850 | −0.629760 | ||||||||
\(737\) | − 82.3320i | − 3.03274i | ||||||||
\(738\) | − 11.5203i | − 0.424067i | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.64575 | −0.207402 | ||||||||
\(742\) | 6.83399i | 0.250884i | ||||||||
\(743\) | 10.5830i | 0.388253i | 0.980977 | + | 0.194126i | \(0.0621872\pi\) | ||||
−0.980977 | + | 0.194126i | \(0.937813\pi\) | |||||||
\(744\) | 47.6235 | 1.74596 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 55.3948 | 2.02815 | ||||||||
\(747\) | − 6.00000i | − 0.219529i | ||||||||
\(748\) | − 112.915i | − 4.12858i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4170 | −0.854498 | −0.427249 | − | 0.904134i | \(-0.640517\pi\) | ||||
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(752\) | − 102.207i | − 3.72709i | ||||||||
\(753\) | 21.6458i | 0.788815i | ||||||||
\(754\) | −103.624 | −3.77375 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.2288 | 0.662973 | ||||||||
\(757\) | − 7.87451i | − 0.286204i | −0.989708 | − | 0.143102i | \(-0.954292\pi\) | ||||
0.989708 | − | 0.143102i | \(-0.0457077\pi\) | |||||||
\(758\) | 26.4575i | 0.960980i | ||||||||
\(759\) | −7.29150 | −0.264665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7490 | −1.36840 | −0.684200 | − | 0.729294i | \(-0.739849\pi\) | ||||
−0.684200 | + | 0.729294i | \(0.739849\pi\) | |||||||
\(762\) | 10.5830i | 0.383382i | ||||||||
\(763\) | 19.2915i | 0.698399i | ||||||||
\(764\) | 101.144 | 3.65925 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.83399 | 0.246922 | ||||||||
\(767\) | 4.00000i | 0.144432i | ||||||||
\(768\) | 5.00000i | 0.180422i | ||||||||
\(769\) | −45.7490 | −1.64975 | −0.824876 | − | 0.565314i | \(-0.808755\pi\) | ||||
−0.824876 | + | 0.565314i | \(0.808755\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5830 | 0.957364 | ||||||||
\(772\) | 31.7712i | 1.14347i | ||||||||
\(773\) | − 19.2915i | − 0.693867i | −0.937890 | − | 0.346934i | \(-0.887223\pi\) | ||||
0.937890 | − | 0.346934i | \(-0.112777\pi\) | |||||||
\(774\) | −0.937254 | −0.0336889 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 102.686 | 3.68622 | ||||||||
\(777\) | 6.00000i | 0.215249i | ||||||||
\(778\) | − 15.8745i | − 0.569129i | ||||||||
\(779\) | −4.35425 | −0.156007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5830 | −0.664952 | ||||||||
\(782\) | − 13.6680i | − 0.488766i | ||||||||
\(783\) | 6.93725i | 0.247917i | ||||||||
\(784\) | −69.2065 | −2.47166 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.3542 | −1.15404 | ||||||||
\(787\) | − 6.12549i | − 0.218350i | −0.994023 | − | 0.109175i | \(-0.965179\pi\) | ||||
0.994023 | − | 0.109175i | \(-0.0348209\pi\) | |||||||
\(788\) | 85.8301i | 3.05757i | ||||||||
\(789\) | −16.5830 | −0.590371 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5830 | 0.518512 | ||||||||
\(792\) | − 44.8118i | − 1.59232i | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | 5.29150 | 0.187788 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.4575 | −0.583321 | ||||||||
\(797\) | − 40.0000i | − 1.41687i | −0.705775 | − | 0.708436i | \(-0.749401\pi\) | ||||
0.705775 | − | 0.708436i | \(-0.250599\pi\) | |||||||
\(798\) | − 9.64575i | − 0.341456i | ||||||||
\(799\) | 37.1660 | 1.31484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.06275 | −0.0375503 | ||||||||
\(802\) | − 28.9373i | − 1.02181i | ||||||||
\(803\) | 56.4575i | 1.99234i | ||||||||
\(804\) | 72.9150 | 2.57151 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −89.6235 | −3.15685 | ||||||||
\(807\) | − 22.2288i | − 0.782489i | ||||||||
\(808\) | − 10.2510i | − 0.360628i | ||||||||
\(809\) | 40.5830 | 1.42682 | 0.713411 | − | 0.700746i | \(-0.247149\pi\) | ||||
0.713411 | + | 0.700746i | \(0.247149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3320 | −1.62694 | −0.813469 | − | 0.581609i | \(-0.802423\pi\) | ||||
−0.813469 | + | 0.581609i | \(0.802423\pi\) | |||||||
\(812\) | − 126.458i | − 4.43779i | ||||||||
\(813\) | 15.2915i | 0.536296i | ||||||||
\(814\) | 24.5830 | 0.861634 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 44.0000 | 1.54031 | ||||||||
\(817\) | 0.354249i | 0.0123936i | ||||||||
\(818\) | − 45.7490i | − 1.59958i | ||||||||
\(819\) | −20.5830 | −0.719228 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.6235 | −1.66207 | −0.831036 | − | 0.556218i | \(-0.812252\pi\) | ||||
−0.831036 | + | 0.556218i | \(0.812252\pi\) | |||||||
\(822\) | 15.8745i | 0.553687i | ||||||||
\(823\) | − 22.2288i | − 0.774846i | −0.921902 | − | 0.387423i | \(-0.873365\pi\) | ||||
0.921902 | − | 0.387423i | \(-0.126635\pi\) | |||||||
\(824\) | −84.0000 | −2.92628 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.83399 | −0.237785 | ||||||||
\(827\) | 22.4575i | 0.780924i | 0.920619 | + | 0.390462i | \(0.127685\pi\) | ||||
−0.920619 | + | 0.390462i | \(0.872315\pi\) | |||||||
\(828\) | − 6.45751i | − 0.224414i | ||||||||
\(829\) | −13.2915 | −0.461633 | −0.230816 | − | 0.972997i | \(-0.574140\pi\) | ||||
−0.230816 | + | 0.972997i | \(0.574140\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.5830 | 0.714017 | ||||||||
\(832\) | 73.3948i | 2.54451i | ||||||||
\(833\) | − 25.1660i | − 0.871951i | ||||||||
\(834\) | −36.7085 | −1.27111 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.2288 | −0.976312 | ||||||||
\(837\) | 6.00000i | 0.207390i | ||||||||
\(838\) | 61.0183i | 2.10784i | ||||||||
\(839\) | −40.4575 | −1.39675 | −0.698374 | − | 0.715733i | \(-0.746093\pi\) | ||||
−0.698374 | + | 0.715733i | \(0.746093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.1255 | 0.659500 | ||||||||
\(842\) | − 19.6235i | − 0.676271i | ||||||||
\(843\) | 5.77124i | 0.198772i | ||||||||
\(844\) | 92.9150 | 3.19827 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.5830 | 0.845181 | ||||||||
\(847\) | 76.1033i | 2.61494i | ||||||||
\(848\) | 7.79347i | 0.267629i | ||||||||
\(849\) | 25.5203 | 0.875853 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.12549 | 0.0728609 | ||||||||
\(852\) | − 16.4575i | − 0.563825i | ||||||||
\(853\) | 25.2915i | 0.865965i | 0.901402 | + | 0.432982i | \(0.142539\pi\) | ||||
−0.901402 | + | 0.432982i | \(0.857461\pi\) | |||||||
\(854\) | −6.83399 | −0.233854 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0405i | 1.47024i | 0.677939 | + | 0.735118i | \(0.262873\pi\) | ||||
−0.677939 | + | 0.735118i | \(0.737127\pi\) | |||||||
\(858\) | 84.3320i | 2.87905i | ||||||||
\(859\) | −50.3320 | −1.71731 | −0.858653 | − | 0.512557i | \(-0.828698\pi\) | ||||
−0.858653 | + | 0.512557i | \(0.828698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.8745 | −0.541002 | ||||||||
\(862\) | 19.2915i | 0.657071i | ||||||||
\(863\) | − 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 | ||||||||
\(866\) | −59.1438 | −2.00979 | ||||||||
\(867\) | − 1.00000i | − 0.0339618i | ||||||||
\(868\) | − 109.373i | − 3.71235i | ||||||||
\(869\) | 82.3320 | 2.79292 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −82.3320 | −2.78971 | ||||||||
\(872\) | 42.0000i | 1.42230i | ||||||||
\(873\) | 12.9373i | 0.437860i | ||||||||
\(874\) | −3.41699 | −0.115582 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.0000 | −1.68934 | ||||||||
\(877\) | 40.9373i | 1.38235i | 0.722686 | + | 0.691176i | \(0.242907\pi\) | ||||
−0.722686 | + | 0.691176i | \(0.757093\pi\) | |||||||
\(878\) | − 59.7490i | − 2.01643i | ||||||||
\(879\) | 26.5830 | 0.896623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8745 | −1.07388 | −0.536940 | − | 0.843621i | \(-0.680420\pi\) | ||||
−0.536940 | + | 0.843621i | \(0.680420\pi\) | |||||||
\(882\) | − 16.6458i | − 0.560492i | ||||||||
\(883\) | − 36.8118i | − 1.23881i | −0.785070 | − | 0.619407i | \(-0.787373\pi\) | ||||
0.785070 | − | 0.619407i | \(-0.212627\pi\) | |||||||
\(884\) | −112.915 | −3.79774 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 98.6640 | 3.31468 | ||||||||
\(887\) | 24.0000i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(888\) | 13.0627i | 0.438357i | ||||||||
\(889\) | 14.5830 | 0.489098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.64575 | 0.189140 | ||||||||
\(892\) | 92.9150i | 3.11103i | ||||||||
\(893\) | − 9.29150i | − 0.310928i | ||||||||
\(894\) | 1.54249 | 0.0515885 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28.9373 | −0.966726 | ||||||||
\(897\) | 7.29150i | 0.243456i | ||||||||
\(898\) | − 25.8523i | − 0.862702i | ||||||||
\(899\) | 41.6235 | 1.38822 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.83399 | −0.0944139 | ||||||||
\(902\) | 65.0405i | 2.16561i | ||||||||
\(903\) | 1.29150i | 0.0429785i | ||||||||
\(904\) | 31.7490 | 1.05596 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −33.2915 | −1.10604 | ||||||||
\(907\) | − 27.0405i | − 0.897866i | −0.893566 | − | 0.448933i | \(-0.851804\pi\) | ||||
0.893566 | − | 0.448933i | \(-0.148196\pi\) | |||||||
\(908\) | − 106.458i | − 3.53292i | ||||||||
\(909\) | 1.29150 | 0.0428364 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.41699 | 0.179473 | 0.0897365 | − | 0.995966i | \(-0.471398\pi\) | ||||
0.0897365 | + | 0.995966i | \(0.471398\pi\) | |||||||
\(912\) | − 11.0000i | − 0.364246i | ||||||||
\(913\) | 33.8745i | 1.12108i | ||||||||
\(914\) | −84.3320 | −2.78946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 96.4575 | 3.18705 | ||||||||
\(917\) | 44.5830i | 1.47226i | ||||||||
\(918\) | 10.5830i | 0.349291i | ||||||||
\(919\) | −57.1660 | −1.88573 | −0.942866 | − | 0.333171i | \(-0.891881\pi\) | ||||
−0.942866 | + | 0.333171i | \(0.891881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4575 | −0.937707 | ||||||||
\(922\) | − 68.1255i | − 2.24359i | ||||||||
\(923\) | 18.5830i | 0.611667i | ||||||||
\(924\) | −102.915 | −3.38566 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.02223 | 0.132179 | ||||||||
\(927\) | − 10.5830i | − 0.347591i | ||||||||
\(928\) | − 91.7712i | − 3.01254i | ||||||||
\(929\) | −19.8745 | −0.652061 | −0.326031 | − | 0.945359i | \(-0.605711\pi\) | ||||
−0.326031 | + | 0.945359i | \(0.605711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.29150 | −0.206196 | ||||||||
\(932\) | 90.0000i | 2.94805i | ||||||||
\(933\) | − 7.06275i | − 0.231224i | ||||||||
\(934\) | 31.4170 | 1.02800 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44.8118 | −1.46472 | ||||||||
\(937\) | − 51.8745i | − 1.69467i | −0.531062 | − | 0.847333i | \(-0.678207\pi\) | ||||
0.531062 | − | 0.847333i | \(-0.321793\pi\) | |||||||
\(938\) | − 140.664i | − 4.59284i | ||||||||
\(939\) | 6.70850 | 0.218924 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.2288 | −1.24622 | −0.623111 | − | 0.782133i | \(-0.714131\pi\) | ||||
−0.623111 | + | 0.782133i | \(0.714131\pi\) | |||||||
\(942\) | − 7.16601i | − 0.233481i | ||||||||
\(943\) | 5.62352i | 0.183127i | ||||||||
\(944\) | −7.79347 | −0.253656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.29150 | 0.172042 | ||||||||
\(947\) | − 32.5830i | − 1.05881i | −0.848371 | − | 0.529403i | \(-0.822416\pi\) | ||||
0.848371 | − | 0.529403i | \(-0.177584\pi\) | |||||||
\(948\) | 72.9150i | 2.36817i | ||||||||
\(949\) | 56.4575 | 1.83269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.4575 | 1.05251 | ||||||||
\(952\) | − 115.749i | − 3.75145i | ||||||||
\(953\) | 10.5830i | 0.342817i | 0.985200 | + | 0.171409i | \(0.0548318\pi\) | ||||
−0.985200 | + | 0.171409i | \(0.945168\pi\) | |||||||
\(954\) | −1.87451 | −0.0606894 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 51.7712 | 1.67440 | ||||||||
\(957\) | − 39.1660i | − 1.26606i | ||||||||
\(958\) | 25.5203i | 0.824522i | ||||||||
\(959\) | 21.8745 | 0.706365 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | − 24.5830i | − 0.792588i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.9150 | 0.738043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.4575 | −0.400814 | ||||||||
\(967\) | 36.3542i | 1.16907i | 0.811367 | + | 0.584537i | \(0.198724\pi\) | ||||
−0.811367 | + | 0.584537i | \(0.801276\pi\) | |||||||
\(968\) | 165.686i | 5.32536i | ||||||||
\(969\) | 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 | ||||||||
\(973\) | 50.5830i | 1.62162i | ||||||||
\(974\) | 36.7085 | 1.17622 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.79347 | −0.249463 | ||||||||
\(977\) | − 23.0405i | − 0.737131i | −0.929602 | − | 0.368566i | \(-0.879849\pi\) | ||||
0.929602 | − | 0.368566i | \(-0.120151\pi\) | |||||||
\(978\) | 20.2288i | 0.646844i | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.29150 | −0.168945 | ||||||||
\(982\) | 85.2693i | 2.72105i | ||||||||
\(983\) | − 18.4575i | − 0.588703i | −0.955697 | − | 0.294352i | \(-0.904896\pi\) | ||||
0.955697 | − | 0.294352i | \(-0.0951037\pi\) | |||||||
\(984\) | −34.5608 | −1.10176 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 73.4170 | 2.33807 | ||||||||
\(987\) | − 33.8745i | − 1.07824i | ||||||||
\(988\) | 28.2288i | 0.898076i | ||||||||
\(989\) | 0.457513 | 0.0145481 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7490 | 0.881477 | 0.440738 | − | 0.897636i | \(-0.354717\pi\) | ||||
0.440738 | + | 0.897636i | \(0.354717\pi\) | |||||||
\(992\) | − 79.3725i | − 2.52008i | ||||||||
\(993\) | − 32.5830i | − 1.03399i | ||||||||
\(994\) | −31.7490 | −1.00702 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.0000 | −0.950586 | ||||||||
\(997\) | − 37.2915i | − 1.18103i | −0.807025 | − | 0.590517i | \(-0.798924\pi\) | ||||
0.807025 | − | 0.590517i | \(-0.201076\pi\) | |||||||
\(998\) | 113.875i | 3.60463i | ||||||||
\(999\) | −1.64575 | −0.0520693 |
(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.799.1 | 4 | ||
5.2 | odd | 4 | 285.2.a.d.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1425.2.a.p.1.1 | 2 | |||
5.4 | even | 2 | inner | 1425.2.c.i.799.4 | 4 | ||
15.2 | even | 4 | 855.2.a.g.1.1 | 2 | |||
15.8 | even | 4 | 4275.2.a.u.1.2 | 2 | |||
20.7 | even | 4 | 4560.2.a.bo.1.2 | 2 | |||
95.37 | even | 4 | 5415.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.d.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
855.2.a.g.1.1 | 2 | 15.2 | even | 4 | |||
1425.2.a.p.1.1 | 2 | 5.3 | odd | 4 | |||
1425.2.c.i.799.1 | 4 | 1.1 | even | 1 | trivial | ||
1425.2.c.i.799.4 | 4 | 5.4 | even | 2 | inner | ||
4275.2.a.u.1.2 | 2 | 15.8 | even | 4 | |||
4560.2.a.bo.1.2 | 2 | 20.7 | even | 4 | |||
5415.2.a.s.1.1 | 2 | 95.37 | even | 4 |