Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 6 x^{18} - 21 x^{17} + 179 x^{16} + 90 x^{15} - 2109 x^{14} + 926 x^{13} + 12681 x^{12} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.31693\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.31693 | −0.760332 | −0.380166 | − | 0.924918i | \(-0.624133\pi\) | ||||
−0.380166 | + | 0.924918i | \(0.624133\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.28443 | −0.574416 | −0.287208 | − | 0.957868i | \(-0.592727\pi\) | ||||
−0.287208 | + | 0.957868i | \(0.592727\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02036 | 0.385659 | 0.192829 | − | 0.981232i | \(-0.438234\pi\) | ||||
0.192829 | + | 0.981232i | \(0.438234\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.26569 | −0.421895 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.40771 | −1.02746 | −0.513731 | − | 0.857951i | \(-0.671737\pi\) | ||||
−0.513731 | + | 0.857951i | \(0.671737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.32304 | −1.75370 | −0.876848 | − | 0.480768i | \(-0.840358\pi\) | ||||
−0.876848 | + | 0.480768i | \(0.840358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.69151 | 0.436747 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.36124 | 1.30029 | 0.650145 | − | 0.759810i | \(-0.274708\pi\) | ||||
0.650145 | + | 0.759810i | \(0.274708\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29090 | 0.525569 | 0.262785 | − | 0.964855i | \(-0.415359\pi\) | ||||
0.262785 | + | 0.964855i | \(0.415359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34374 | −0.293229 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.25279 | −1.30380 | −0.651898 | − | 0.758307i | \(-0.726027\pi\) | ||||
−0.651898 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.35023 | −0.670047 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61763 | 1.08111 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.07720 | −1.49990 | −0.749949 | − | 0.661495i | \(-0.769922\pi\) | ||||
−0.749949 | + | 0.661495i | \(0.769922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.34002 | −0.240675 | −0.120337 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120337 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.48773 | 0.781213 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.31058 | −0.221528 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.74614 | −1.27346 | −0.636729 | − | 0.771088i | \(-0.719713\pi\) | ||||
−0.636729 | + | 0.771088i | \(0.719713\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.32702 | 1.33339 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.95371 | 1.55451 | 0.777254 | − | 0.629187i | \(-0.216612\pi\) | ||||
0.777254 | + | 0.629187i | \(0.216612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.55335 | 0.236884 | 0.118442 | − | 0.992961i | \(-0.462210\pi\) | ||||
0.118442 | + | 0.992961i | \(0.462210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.62569 | 0.242343 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5709 | 1.68780 | 0.843898 | − | 0.536503i | \(-0.180255\pi\) | ||||
0.843898 | + | 0.536503i | \(0.180255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.95887 | −0.851267 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.06039 | −0.988653 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.43397 | −1.15850 | −0.579248 | − | 0.815152i | \(-0.696654\pi\) | ||||
−0.579248 | + | 0.815152i | \(0.696654\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37697 | 0.590191 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.01697 | −0.399607 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9358 | 1.68410 | 0.842051 | − | 0.539397i | \(-0.181348\pi\) | ||||
0.842051 | + | 0.539397i | \(0.181348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.212306 | 0.0271830 | 0.0135915 | − | 0.999908i | \(-0.495674\pi\) | ||||
0.0135915 | + | 0.999908i | \(0.495674\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.29145 | −0.162708 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.12152 | 1.00735 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62764 | −0.198848 | −0.0994240 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994240 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.23450 | 0.991318 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1685 | −1.32546 | −0.662729 | − | 0.748860i | \(-0.730602\pi\) | ||||
−0.662729 | + | 0.748860i | \(0.730602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7073 | −1.25319 | −0.626597 | − | 0.779343i | \(-0.715553\pi\) | ||||
−0.626597 | + | 0.779343i | \(0.715553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.41203 | 0.509458 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.47708 | −0.396250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1646 | 1.59365 | 0.796824 | − | 0.604212i | \(-0.206512\pi\) | ||||
0.796824 | + | 0.604212i | \(0.206512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.60098 | −0.400109 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.94879 | −0.213907 | −0.106954 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106954 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.88615 | −0.746907 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.6371 | 1.14042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.10583 | −0.435217 | −0.217608 | − | 0.976036i | \(-0.569826\pi\) | ||||
−0.217608 | + | 0.976036i | \(0.569826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.45176 | −0.676328 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76472 | 0.182993 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.94251 | −0.301895 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6029 | 1.38117 | 0.690583 | − | 0.723253i | \(-0.257354\pi\) | ||||
0.690583 | + | 0.723253i | \(0.257354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.31309 | 0.433482 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.708875 | −0.0705357 | −0.0352679 | − | 0.999378i | \(-0.511228\pi\) | ||||
−0.0352679 | + | 0.999378i | \(0.511228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.913943 | −0.0900535 | −0.0450267 | − | 0.998986i | \(-0.514337\pi\) | ||||
−0.0450267 | + | 0.998986i | \(0.514337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.72595 | 0.168435 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00141 | −0.290157 | −0.145078 | − | 0.989420i | \(-0.546343\pi\) | ||||
−0.145078 | + | 0.989420i | \(0.546343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7818 | 1.22427 | 0.612137 | − | 0.790752i | \(-0.290310\pi\) | ||||
0.612137 | + | 0.790752i | \(0.290310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2011 | 0.968250 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.91713 | −0.368493 | −0.184246 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184246 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.03128 | 0.748921 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.00298 | 0.739876 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.47038 | 0.501468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.612476 | 0.0556796 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.1084 | −1.18194 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7253 | 0.959301 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.76931 | 0.778150 | 0.389075 | − | 0.921206i | \(-0.372795\pi\) | ||||
0.389075 | + | 0.921206i | \(0.372795\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.04566 | −0.180110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.48973 | −0.304899 | −0.152450 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152450 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.33754 | 0.202690 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.21546 | −0.621008 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.10500 | 0.265278 | 0.132639 | − | 0.991164i | \(-0.457655\pi\) | ||||
0.132639 | + | 0.991164i | \(0.457655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.59477 | 0.304904 | 0.152452 | − | 0.988311i | \(-0.451283\pi\) | ||||
0.152452 | + | 0.988311i | \(0.451283\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.2382 | −1.28329 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.5471 | 1.80186 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.3746 | 0.861565 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.84744 | 0.647246 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.2901 | −1.17069 | −0.585344 | − | 0.810785i | \(-0.699041\pi\) | ||||
−0.585344 | + | 0.810785i | \(0.699041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.83424 | 0.393405 | 0.196702 | − | 0.980463i | \(-0.436977\pi\) | ||||
0.196702 | + | 0.980463i | \(0.436977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.78564 | −0.548587 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.72117 | 0.138247 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3653 | 0.827240 | 0.413620 | − | 0.910450i | \(-0.364264\pi\) | ||||
0.413620 | + | 0.910450i | \(0.364264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.1070 | 0.880841 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.38007 | −0.502820 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.74307 | 0.449832 | 0.224916 | − | 0.974378i | \(-0.427789\pi\) | ||||
0.224916 | + | 0.974378i | \(0.427789\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.76418 | −0.448741 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.01822 | −0.543086 | −0.271543 | − | 0.962426i | \(-0.587534\pi\) | ||||
−0.271543 | + | 0.962426i | \(0.587534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9808 | 2.07545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.89956 | −0.221735 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.76197 | 0.286018 | 0.143009 | − | 0.989721i | \(-0.454322\pi\) | ||||
0.143009 | + | 0.989721i | \(0.454322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.41843 | −0.258409 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.0356 | −1.28048 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.7663 | −1.47740 | −0.738700 | − | 0.674035i | \(-0.764560\pi\) | ||||
−0.738700 | + | 0.674035i | \(0.764560\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9611 | 1.11205 | 0.556024 | − | 0.831167i | \(-0.312326\pi\) | ||||
0.556024 | + | 0.831167i | \(0.312326\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.279593 | −0.0206681 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.94939 | 0.731494 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.2695 | −1.33600 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.73198 | 0.416940 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6702 | 0.772071 | 0.386036 | − | 0.922484i | \(-0.373844\pi\) | ||||
0.386036 | + | 0.922484i | \(0.373844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3570 | 1.17740 | 0.588702 | − | 0.808350i | \(-0.299639\pi\) | ||||
0.588702 | + | 0.808350i | \(0.299639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.6955 | −0.765921 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.80928 | −0.413894 | −0.206947 | − | 0.978352i | \(-0.566353\pi\) | ||||
−0.206947 | + | 0.978352i | \(0.566353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.49860 | 0.389785 | 0.194893 | − | 0.980825i | \(-0.437564\pi\) | ||||
0.194893 | + | 0.980825i | \(0.437564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.14350 | 0.151191 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.24163 | −0.578449 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7849 | −0.892934 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.91406 | 0.550065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.80673 | −0.540003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.32109 | −0.641690 | −0.320845 | − | 0.947132i | \(-0.603967\pi\) | ||||
−0.320845 | + | 0.947132i | \(0.603967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.7082 | 1.00779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.99517 | −0.136070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.36730 | −0.0928184 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.1008 | 0.952843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.8993 | −2.28031 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.9589 | −1.53744 | −0.768721 | − | 0.639584i | \(-0.779106\pi\) | ||||
−0.768721 | + | 0.639584i | \(0.779106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.24034 | 0.282690 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.8349 | 1.78109 | 0.890546 | − | 0.454893i | \(-0.150323\pi\) | ||||
0.890546 | + | 0.454893i | \(0.150323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7770 | 1.57123 | 0.785613 | − | 0.618718i | \(-0.212348\pi\) | ||||
0.785613 | + | 0.618718i | \(0.212348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.57908 | 0.301282 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.34838 | 0.415896 | 0.207948 | − | 0.978140i | \(-0.433321\pi\) | ||||
0.207948 | + | 0.978140i | \(0.433321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8621 | −0.969497 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.6539 | −1.21170 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5726 | −1.33073 | −0.665366 | − | 0.746518i | \(-0.731724\pi\) | ||||
−0.665366 | + | 0.746518i | \(0.731724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.1473 | −1.10455 | −0.552277 | − | 0.833661i | \(-0.686241\pi\) | ||||
−0.552277 | + | 0.833661i | \(0.686241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.1106 | −0.776897 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.65377 | 0.488981 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.4855 | −0.921689 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.56643 | 0.162641 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.3077 | 1.33960 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.06860 | 0.567898 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0889 | 1.19073 | 0.595367 | − | 0.803454i | \(-0.297007\pi\) | ||||
0.595367 | + | 0.803454i | \(0.297007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.90383 | −0.491120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2232 | 0.632800 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.8459 | 1.65539 | 0.827695 | − | 0.561178i | \(-0.189652\pi\) | ||||
0.827695 | + | 0.561178i | \(0.189652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8329 | 0.665458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.40710 | 0.330909 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8198 | −1.08649 | −0.543246 | − | 0.839573i | \(-0.682805\pi\) | ||||
−0.543246 | + | 0.839573i | \(0.682805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9178 | 1.57440 | 0.787198 | − | 0.616700i | \(-0.211531\pi\) | ||||
0.787198 | + | 0.616700i | \(0.211531\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.49654 | 0.514234 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.4166 | 0.688448 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.255098 | 0.0153273 | 0.00766367 | − | 0.999971i | \(-0.497561\pi\) | ||||
0.00766367 | + | 0.999971i | \(0.497561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.69605 | 0.101540 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1427 | 1.44023 | 0.720115 | − | 0.693855i | \(-0.244089\pi\) | ||||
0.720115 | + | 0.693855i | \(0.244089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9395 | 1.83916 | 0.919581 | − | 0.392899i | \(-0.128528\pi\) | ||||
0.919581 | + | 0.392899i | \(0.128528\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.87509 | 0.229541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1563 | 0.599510 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7429 | 0.690756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.9141 | −1.05014 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.8506 | −1.39337 | −0.696684 | − | 0.717378i | \(-0.745342\pi\) | ||||
−0.696684 | + | 0.717378i | \(0.745342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.6152 | −0.967375 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.1432 | −1.11080 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.5366 | 2.28646 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58497 | 0.0913563 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.933542 | 0.0536306 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.272693 | −0.0156143 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2007 | 0.924622 | 0.462311 | − | 0.886718i | \(-0.347020\pi\) | ||||
0.462311 | + | 0.886718i | \(0.347020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.20360 | 0.0684705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.09690 | −0.345724 | −0.172862 | − | 0.984946i | \(-0.555301\pi\) | ||||
−0.172862 | + | 0.984946i | \(0.555301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.43223 | 0.250525 | 0.125262 | − | 0.992124i | \(-0.460023\pi\) | ||||
0.125262 | + | 0.992124i | \(0.460023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.65878 | 0.0934618 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.00439 | −0.449571 | −0.224786 | − | 0.974408i | \(-0.572168\pi\) | ||||
−0.224786 | + | 0.974408i | \(0.572168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.5247 | 1.54109 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.95265 | 0.220616 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2821 | 0.683393 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1837 | 1.17506 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8328 | −0.930854 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.8065 | 0.650913 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.8762 | 1.69711 | 0.848554 | − | 0.529109i | \(-0.177474\pi\) | ||||
0.848554 | + | 0.529109i | \(0.177474\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.80418 | 0.537266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.09060 | 0.114221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1121 | 1.36794 | 0.683971 | − | 0.729509i | \(-0.260252\pi\) | ||||
0.683971 | + | 0.729509i | \(0.260252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.15860 | 0.280177 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.56640 | 0.247285 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2227 | −0.713957 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.5767 | −0.569428 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.6440 | 1.16191 | 0.580956 | − | 0.813935i | \(-0.302679\pi\) | ||||
0.580956 | + | 0.813935i | \(0.302679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8202 | 1.70330 | 0.851648 | − | 0.524113i | \(-0.175603\pi\) | ||||
0.851648 | + | 0.524113i | \(0.175603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −35.5205 | −1.89594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.9369 | −1.00791 | −0.503954 | − | 0.863730i | \(-0.668122\pi\) | ||||
−0.503954 | + | 0.863730i | \(0.668122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3452 | 0.761364 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.20412 | −0.381282 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.4551 | −0.868468 | −0.434234 | − | 0.900800i | \(-0.642981\pi\) | ||||
−0.434234 | + | 0.900800i | \(0.642981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7518 | −0.723777 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.806590 | −0.0423350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.7528 | 0.719854 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.04730 | −0.367866 | −0.183933 | − | 0.982939i | \(-0.558883\pi\) | ||||
−0.183933 | + | 0.982939i | \(0.558883\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.5983 | −0.655840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.60566 | −0.446784 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9354 | −0.566211 | −0.283106 | − | 0.959089i | \(-0.591365\pi\) | ||||
−0.283106 | + | 0.959089i | \(0.591365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.1245 | −0.729387 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.0725 | 2.63037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.20641 | −0.164702 | −0.0823511 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823511 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.5486 | −0.591652 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.5125 | 1.30363 | 0.651814 | − | 0.758379i | \(-0.274008\pi\) | ||||
0.651814 | + | 0.758379i | \(0.274008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.46607 | 0.227612 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.96605 | −0.0999402 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7967 | 1.00373 | 0.501866 | − | 0.864945i | \(-0.332647\pi\) | ||||
0.501866 | + | 0.864945i | \(0.332647\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.5227 | −1.69531 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.59574 | 0.231824 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.1935 | −0.915416 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8522 | −1.04654 | −0.523270 | − | 0.852167i | \(-0.675288\pi\) | ||||
−0.523270 | + | 0.852167i | \(0.675288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.07838 | −0.154112 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4625 | −1.52122 | −0.760612 | − | 0.649207i | \(-0.775101\pi\) | ||||
−0.760612 | + | 0.649207i | \(0.775101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.47301 | 0.422071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.62522 | 0.229829 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.3966 | 1.30843 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.9664 | 1.08617 | 0.543085 | − | 0.839678i | \(-0.317256\pi\) | ||||
0.543085 | + | 0.839678i | \(0.317256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.08907 | −0.201699 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.1992 | 0.649489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.50309 | 0.122872 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.73407 | −0.231828 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.11485 | −0.298730 | −0.149365 | − | 0.988782i | \(-0.547723\pi\) | ||||
−0.149365 | + | 0.988782i | \(0.547723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.04861 | −0.343528 | −0.171764 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171764 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.6452 | −0.712073 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.9614 | −0.871255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.216628 | 0.0104834 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.3761 | −1.37001 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.56669 | 0.0754646 | 0.0377323 | − | 0.999288i | \(-0.487987\pi\) | ||||
0.0377323 | + | 0.999288i | \(0.487987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.5996 | 1.08607 | 0.543034 | − | 0.839711i | \(-0.317276\pi\) | ||||
0.543034 | + | 0.839711i | \(0.317276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.6627 | −0.655076 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3245 | −0.685235 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.3805 | −1.25907 | −0.629537 | − | 0.776970i | \(-0.716756\pi\) | ||||
−0.629537 | + | 0.776970i | \(0.716756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.54206 | 0.359146 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1676 | −1.48082 | −0.740409 | − | 0.672157i | \(-0.765368\pi\) | ||||
−0.740409 | + | 0.672157i | \(0.765368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.27366 | 0.249995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.8191 | 0.890111 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.6847 | −0.504242 | −0.252121 | − | 0.967696i | \(-0.581128\pi\) | ||||
−0.252121 | + | 0.967696i | \(0.581128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.9193 | −1.59720 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.36637 | −0.299118 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.28685 | 0.388494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.95521 | −0.138239 | −0.0691194 | − | 0.997608i | \(-0.522019\pi\) | ||||
−0.0691194 | + | 0.997608i | \(0.522019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.1174 | 1.40576 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.6933 | 1.89528 | 0.947639 | − | 0.319344i | \(-0.103463\pi\) | ||||
0.947639 | + | 0.319344i | \(0.103463\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1764 | −0.658834 | −0.329417 | − | 0.944185i | \(-0.606852\pi\) | ||||
−0.329417 | + | 0.944185i | \(0.606852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.26666 | −0.105114 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.85700 | 0.317304 | 0.158652 | − | 0.987335i | \(-0.449285\pi\) | ||||
0.158652 | + | 0.987335i | \(0.449285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.66078 | −0.0766875 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.6504 | −0.628977 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.29337 | −0.243389 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.67506 | −0.352156 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6748 | 0.488764 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.6396 | −0.943048 | −0.471524 | − | 0.881853i | \(-0.656296\pi\) | ||||
−0.471524 | + | 0.881853i | \(0.656296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.9791 | 2.23326 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.40213 | 0.382310 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.4720 | −0.793363 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9244 | 1.53726 | 0.768631 | − | 0.639693i | \(-0.220938\pi\) | ||||
0.768631 | + | 0.639693i | \(0.220938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.56325 | −0.342022 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3239 | −1.32337 | −0.661685 | − | 0.749782i | \(-0.730158\pi\) | ||||
−0.661685 | + | 0.749782i | \(0.730158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.3038 | −1.95030 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.53987 | −0.248999 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.3959 | −0.511174 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.74198 | 0.391345 | 0.195672 | − | 0.980669i | \(-0.437311\pi\) | ||||
0.195672 | + | 0.980669i | \(0.437311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.24253 | 0.412926 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.56731 | −0.292822 | −0.146411 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146411 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.910503 | 0.0405168 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.5320 | −1.57803 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1486 | 1.51361 | 0.756804 | − | 0.653642i | \(-0.226760\pi\) | ||||
0.756804 | + | 0.653642i | \(0.226760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9253 | −0.483305 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.8694 | 0.568199 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.17390 | 0.0517281 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.4304 | −1.73415 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.95427 | −0.217468 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7659 | −0.822150 | −0.411075 | − | 0.911601i | \(-0.634847\pi\) | ||||
−0.411075 | + | 0.911601i | \(0.634847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5983 | −1.11934 | −0.559669 | − | 0.828716i | \(-0.689072\pi\) | ||||
−0.559669 | + | 0.828716i | \(0.689072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.50185 | 0.196477 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.18417 | −0.312947 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0973 | 0.699884 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.3727 | −0.710515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −62.9377 | −2.72613 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.85510 | 0.166671 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.0308 | 1.12331 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.3061 | 0.874645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.6658 | −1.10346 | −0.551729 | − | 0.834023i | \(-0.686032\pi\) | ||||
−0.551729 | + | 0.834023i | \(0.686032\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.7027 | −0.845525 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4174 | −0.703242 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9323 | −0.895000 | −0.447500 | − | 0.894284i | \(-0.647686\pi\) | ||||
−0.447500 | + | 0.894284i | \(0.647686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.268713 | −0.0114684 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.5041 | −0.788301 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4530 | 0.614604 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1027 | −0.556178 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.1674 | −1.53246 | −0.766230 | − | 0.642566i | \(-0.777870\pi\) | ||||
−0.766230 | + | 0.642566i | \(0.777870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.82190 | −0.415422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0598 | 1.01580 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.5029 | −1.74914 | −0.874569 | − | 0.484901i | \(-0.838856\pi\) | ||||
−0.874569 | + | 0.484901i | \(0.838856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.03129 | 0.211668 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.67429 | −0.154306 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7499 | −0.827958 | −0.413979 | − | 0.910286i | \(-0.635861\pi\) | ||||
−0.413979 | + | 0.910286i | \(0.635861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.83271 | 0.0766964 | 0.0383482 | − | 0.999264i | \(-0.487790\pi\) | ||||
0.0383482 | + | 0.999264i | \(0.487790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.0520 | −0.587030 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.9483 | 0.873604 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2668 | 1.63470 | 0.817349 | − | 0.576143i | \(-0.195443\pi\) | ||||
0.817349 | + | 0.576143i | \(0.195443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.5411 | −0.895217 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.98846 | −0.0824952 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.7405 | 1.19031 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.2793 | −0.424996 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.6019 | −1.38690 | −0.693449 | − | 0.720506i | \(-0.743910\pi\) | ||||
−0.693449 | + | 0.720506i | \(0.743910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.06986 | −0.126491 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.65044 | 0.314697 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0943 | −1.07157 | −0.535783 | − | 0.844356i | \(-0.679984\pi\) | ||||
−0.535783 | + | 0.844356i | \(0.679984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.02633 | −0.288051 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.24129 | −0.296366 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.7789 | 1.46189 | 0.730944 | − | 0.682438i | \(-0.239080\pi\) | ||||
0.730944 | + | 0.682438i | \(0.239080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.13530 | 0.168682 | 0.0843411 | − | 0.996437i | \(-0.473121\pi\) | ||||
0.0843411 | + | 0.996437i | \(0.473121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.06008 | 0.0838931 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.786684 | −0.0319833 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.4600 | −1.43928 | −0.719638 | − | 0.694349i | \(-0.755692\pi\) | ||||
−0.719638 | + | 0.694349i | \(0.755692\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.8537 | 0.439813 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −73.1636 | −2.95988 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4080 | −0.501156 | −0.250578 | − | 0.968096i | \(-0.580621\pi\) | ||||
−0.250578 | + | 0.968096i | \(0.580621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.8368 | 0.678926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.4736 | −0.421653 | −0.210826 | − | 0.977524i | \(-0.567615\pi\) | ||||
−0.210826 | + | 0.977524i | \(0.567615\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7351 | 1.27554 | 0.637770 | − | 0.770227i | \(-0.279857\pi\) | ||||
0.637770 | + | 0.770227i | \(0.279857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.1258 | −1.40955 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.18941 | −0.167845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.97522 | 0.119009 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.2809 | 0.410581 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.5289 | −1.65586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.7008 | 1.89894 | 0.949470 | − | 0.313857i | \(-0.101621\pi\) | ||||
0.949470 | + | 0.313857i | \(0.101621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2753 | 0.487898 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.2636 | −0.446982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.6782 | 1.49286 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1358 | 0.559204 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2583 | 1.15563 | 0.577817 | − | 0.816166i | \(-0.303905\pi\) | ||||
0.577817 | + | 0.816166i | \(0.303905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3885 | 0.843481 | 0.421740 | − | 0.906717i | \(-0.361419\pi\) | ||||
0.421740 | + | 0.906717i | \(0.361419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.62751 | 0.103458 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.9187 | −0.861715 | −0.430857 | − | 0.902420i | \(-0.641789\pi\) | ||||
−0.430857 | + | 0.902420i | \(0.641789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.0816 | −1.73035 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80064 | 0.0705728 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.0864 | 0.512110 | 0.256055 | − | 0.966662i | \(-0.417577\pi\) | ||||
0.256055 | + | 0.966662i | \(0.417577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.48232 | 0.175139 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.5521 | 0.528717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.04943 | −0.0408800 | −0.0204400 | − | 0.999791i | \(-0.506507\pi\) | ||||
−0.0204400 | + | 0.999791i | \(0.506507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.93829 | 0.308764 | 0.154382 | − | 0.988011i | \(-0.450661\pi\) | ||||
0.154382 | + | 0.988011i | \(0.450661\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.6431 | 1.73380 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.00241 | −0.116429 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.5050 | 1.95556 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.2353 | 1.16897 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.723477 | −0.0279295 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2158 | −1.20328 | −0.601640 | − | 0.798767i | \(-0.705486\pi\) | ||||
−0.601640 | + | 0.798767i | \(0.705486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.8204 | −0.724396 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.1051 | 0.811135 | 0.405568 | − | 0.914065i | \(-0.367074\pi\) | ||||
0.405568 | + | 0.914065i | \(0.367074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8798 | 0.532659 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.3397 | −1.35422 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.8340 | 0.605872 | 0.302936 | − | 0.953011i | \(-0.402033\pi\) | ||||
0.302936 | + | 0.953011i | \(0.402033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.98816 | −0.152380 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.3127 | −1.19465 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.3284 | 2.03165 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7200 | 1.39689 | 0.698447 | − | 0.715662i | \(-0.253875\pi\) | ||||
0.698447 | + | 0.715662i | \(0.253875\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.40089 | 0.167176 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.61724 | −0.175142 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.3642 | 2.02131 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.36039 | −0.316219 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9385 | 0.677528 | 0.338764 | − | 0.940871i | \(-0.389991\pi\) | ||||
0.338764 | + | 0.940871i | \(0.389991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.7457 | −0.669290 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.5724 | 0.737139 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.723306 | −0.0272027 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.2917 | −1.21274 | −0.606371 | − | 0.795182i | \(-0.707375\pi\) | ||||
−0.606371 | + | 0.795182i | \(0.707375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.9280 | −0.672352 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.37887 | 0.313791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.6758 | −1.03502 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.0928 | 1.01180 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5719 | 0.431560 | 0.215780 | − | 0.976442i | \(-0.430771\pi\) | ||||
0.215780 | + | 0.976442i | \(0.430771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.932548 | −0.0347299 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.5819 | 0.839828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.0605 | 1.00500 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.59189 | −0.244480 | −0.122240 | − | 0.992501i | \(-0.539008\pi\) | ||||
−0.122240 | + | 0.992501i | \(0.539008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7518 | 0.990808 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.32788 | 0.308018 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.34073 | −0.234200 | −0.117100 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117100 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.0795 | −0.371788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.54653 | 0.204309 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9608 | −0.881411 | −0.440705 | − | 0.897652i | \(-0.645272\pi\) | ||||
−0.440705 | + | 0.897652i | \(0.645272\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.0764 | 0.700789 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.3846 | −1.48157 | −0.740784 | − | 0.671743i | \(-0.765546\pi\) | ||||
−0.740784 | + | 0.671743i | \(0.765546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3546 | 0.672462 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.46655 | 0.0902465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.06251 | −0.111902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5929 | −0.532503 | −0.266251 | − | 0.963904i | \(-0.585785\pi\) | ||||
−0.266251 | + | 0.963904i | \(0.585785\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.31693 | −0.0479917 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.20925 | −0.225978 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6202 | −0.567727 | −0.283863 | − | 0.958865i | \(-0.591616\pi\) | ||||
−0.283863 | + | 0.958865i | \(0.591616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.0608 | −1.01854 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.6289 | 1.47280 | 0.736399 | − | 0.676548i | \(-0.236525\pi\) | ||||
0.736399 | + | 0.676548i | \(0.236525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0420 | 0.472152 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.71570 | 0.315117 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −81.7938 | −2.95340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.1395 | −0.473824 | −0.236912 | − | 0.971531i | \(-0.576135\pi\) | ||||
−0.236912 | + | 0.971531i | \(0.576135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1388 | −0.905353 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.3078 | −1.44977 | −0.724886 | − | 0.688869i | \(-0.758108\pi\) | ||||
−0.724886 | + | 0.688869i | \(0.758108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.48938 | 0.161263 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.4088 | 0.373414 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.8030 | 0.817002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.0590 | 1.36186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.3747 | −1.62156 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.3135 | −0.475179 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4714 | 0.444557 | 0.222279 | − | 0.974983i | \(-0.428651\pi\) | ||||
0.222279 | + | 0.974983i | \(0.428651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.3543 | −1.25865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.99687 | −0.142112 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34242 | −0.0476707 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.2662 | −0.505969 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5834 | −0.516570 | −0.258285 | − | 0.966069i | \(-0.583157\pi\) | ||||
−0.258285 | + | 0.966069i | \(0.583157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.0346 | 2.19463 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.19669 | 0.183616 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.4873 | 1.28761 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.19478 | 0.288828 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.4675 | 0.826095 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.7020 | −1.29037 | −0.645186 | − | 0.764025i | \(-0.723220\pi\) | ||||
−0.645186 | + | 0.764025i | \(0.723220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.80062 | −0.309032 | −0.154516 | − | 0.987990i | \(-0.549382\pi\) | ||||
−0.154516 | + | 0.987990i | \(0.549382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.1321 | −1.19706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.37659 | −0.258391 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.55858 | 0.124499 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.16590 | 0.285340 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.9979 | −0.523432 | −0.261716 | − | 0.965145i | \(-0.584288\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.68961 | 0.302901 | 0.151450 | − | 0.988465i | \(-0.451606\pi\) | ||||
0.151450 | + | 0.988465i | \(0.451606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.0349 | −0.523449 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9115 | 0.448976 | 0.224488 | − | 0.974477i | \(-0.427929\pi\) | ||||
0.224488 | + | 0.974477i | \(0.427929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.2578 | −1.78026 | −0.890128 | − | 0.455711i | \(-0.849385\pi\) | ||||
−0.890128 | + | 0.455711i | \(0.849385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.335947 | −0.0116539 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.9469 | −1.10690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.01443 | 0.311957 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.52774 | −0.260197 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.57114 | 0.295909 | 0.147954 | − | 0.988994i | \(-0.452731\pi\) | ||||
0.147954 | + | 0.988994i | \(0.452731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.2412 | 1.24970 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.7943 | −1.09505 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.6551 | −1.19217 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.624944 | 0.0214733 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.7453 | −1.39837 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.4349 | 1.66033 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.0161 | −1.54132 | −0.770661 | − | 0.637245i | \(-0.780074\pi\) | ||||
−0.770661 | + | 0.637245i | \(0.780074\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.72430 | 0.127368 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.6140 | −1.52398 | −0.761992 | − | 0.647587i | \(-0.775778\pi\) | ||||
−0.761992 | + | 0.647587i | \(0.775778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.0606 | −1.26449 | −0.632245 | − | 0.774768i | \(-0.717866\pi\) | ||||
−0.632245 | + | 0.774768i | \(0.717866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.3752 | −0.455826 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.7527 | 0.536229 | 0.268114 | − | 0.963387i | \(-0.413599\pi\) | ||||
0.268114 | + | 0.963387i | \(0.413599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.83200 | −0.164293 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.4646 | −0.525204 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.2690 | −1.63741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2916 | 0.348719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.2170 | −0.582707 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9436 | 0.369963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.05982 | 0.204626 | 0.102313 | − | 0.994752i | \(-0.467376\pi\) | ||||
0.102313 | + | 0.994752i | \(0.467376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.4097 | 1.05942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.4775 | −1.26265 | −0.631324 | − | 0.775519i | \(-0.717488\pi\) | ||||
−0.631324 | + | 0.775519i | \(0.717488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.74089 | −0.327807 | −0.163903 | − | 0.986476i | \(-0.552409\pi\) | ||||
−0.163903 | + | 0.986476i | \(0.552409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.8811 | 0.735526 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.8151 | 0.933940 | 0.466970 | − | 0.884273i | \(-0.345346\pi\) | ||||
0.466970 | + | 0.884273i | \(0.345346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.94783 | 0.300100 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.2711 | 0.411097 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.5079 | 0.887054 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.3884 | 0.848641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −52.0671 | −1.73847 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.8236 | 0.360988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.2165 | −1.50638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.08730 | −0.0694611 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2165 | −0.638777 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9267 | −0.628452 | −0.314226 | − | 0.949348i | \(-0.601745\pi\) | ||||
−0.314226 | + | 0.949348i | \(0.601745\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.897214 | 0.0297587 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.37167 | 0.244234 | 0.122117 | − | 0.992516i | \(-0.461032\pi\) | ||||
0.122117 | + | 0.992516i | \(0.461032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.64090 | 0.219782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.359118 | 0.0118721 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.56077 | −0.117587 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.9676 | 0.988540 | 0.494270 | − | 0.869308i | \(-0.335435\pi\) | ||||
0.494270 | + | 0.869308i | \(0.335435\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.3352 | −0.703020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 70.6189 | 2.32445 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9514 | 0.853276 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.15677 | 0.0379932 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.27346 | 0.304252 | 0.152126 | − | 0.988361i | \(-0.451388\pi\) | ||||
0.152126 | + | 0.988361i | \(0.451388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6512 | −0.447400 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.02922 | 0.262865 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.4660 | 0.767420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.16311 | 0.299346 | 0.149673 | − | 0.988736i | \(-0.452178\pi\) | ||||
0.149673 | + | 0.988736i | \(0.452178\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.83696 | −0.190482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.4655 | 1.57993 | 0.789965 | − | 0.613152i | \(-0.210099\pi\) | ||||
0.789965 | + | 0.613152i | \(0.210099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.2384 | −2.02676 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.36235 | −0.239497 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2316 | −0.527455 | −0.263727 | − | 0.964597i | \(-0.584952\pi\) | ||||
−0.263727 | + | 0.964597i | \(0.584952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.7026 | 2.19772 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5412 | 0.341823 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7780 | −1.22375 | −0.611874 | − | 0.790955i | \(-0.709584\pi\) | ||||
−0.611874 | + | 0.790955i | \(0.709584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.7052 | −0.443490 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.2483 | −1.17174 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.16821 | 0.102307 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2043 | −0.942076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.79884 | 0.122416 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0095 | −0.676319 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6664 | −0.375167 | −0.187583 | − | 0.982249i | \(-0.560066\pi\) | ||||
−0.187583 | + | 0.982249i | \(0.560066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.1747 | −0.519605 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.7485 | 1.82115 | 0.910574 | − | 0.413347i | \(-0.135640\pi\) | ||||
0.910574 | + | 0.413347i | \(0.135640\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.66795 | 0.117589 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.8975 | −0.893434 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.8276 | −0.506371 | −0.253185 | − | 0.967418i | \(-0.581478\pi\) | ||||
−0.253185 | + | 0.967418i | \(0.581478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.9915 | 0.447169 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1777 | −0.516515 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0625 | −0.703685 | −0.351842 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351842 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.46163 | 0.237747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.5484 | −0.494910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.71277 | −0.308848 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2127 | 0.387949 | 0.193974 | − | 0.981007i | \(-0.437862\pi\) | ||||
0.193974 | + | 0.981007i | \(0.437862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.6618 | −1.29036 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.06258 | −0.223899 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.0107 | −1.14047 | −0.570236 | − | 0.821481i | \(-0.693148\pi\) | ||||
−0.570236 | + | 0.821481i | \(0.693148\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.5149 | −1.37675 |
(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 | 4016.2.a.l.1.6 | 19 | ||
4.3 | odd | 2 | 2008.2.a.c.1.14 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.c.1.14 | ✓ | 19 | 4.3 | odd | 2 | ||
4016.2.a.l.1.6 | 19 | 1.1 | even | 1 | trivial |