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: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 79 x^{11} + 274 x^{10} - 747 x^{9} - 1422 x^{8} + 3287 x^{7} + 4161 x^{6} - 6861 x^{5} - 6676 x^{4} + 5599 x^{3} + 4627 x^{2} - 359 x - 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.87232\) 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 | ||||||||
\(3\) | −2.87232 | −1.65833 | −0.829166 | − | 0.559002i | \(-0.811184\pi\) | ||||
−0.829166 | + | 0.559002i | \(0.811184\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.801100 | −0.358263 | −0.179131 | − | 0.983825i | \(-0.557329\pi\) | ||||
−0.179131 | + | 0.983825i | \(0.557329\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.32848 | 1.63601 | 0.818007 | − | 0.575209i | \(-0.195079\pi\) | ||||
0.818007 | + | 0.575209i | \(0.195079\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.25020 | 1.75007 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.29679 | −1.59704 | −0.798521 | − | 0.601967i | \(-0.794384\pi\) | ||||
−0.798521 | + | 0.601967i | \(0.794384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.355175 | 0.0985078 | 0.0492539 | − | 0.998786i | \(-0.484316\pi\) | ||||
0.0492539 | + | 0.998786i | \(0.484316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.30101 | 0.594119 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.75803 | 1.63906 | 0.819531 | − | 0.573035i | \(-0.194234\pi\) | ||||
0.819531 | + | 0.573035i | \(0.194234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61157 | −0.599136 | −0.299568 | − | 0.954075i | \(-0.596843\pi\) | ||||
−0.299568 | + | 0.954075i | \(0.596843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.4328 | −2.71305 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.43653 | −0.925080 | −0.462540 | − | 0.886598i | \(-0.653062\pi\) | ||||
−0.462540 | + | 0.886598i | \(0.653062\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.35824 | −0.871648 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.46328 | −1.24386 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.80961 | 1.26451 | 0.632256 | − | 0.774759i | \(-0.282129\pi\) | ||||
0.632256 | + | 0.774759i | \(0.282129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0652340 | −0.0117164 | −0.00585819 | − | 0.999983i | \(-0.501865\pi\) | ||||
−0.00585819 | + | 0.999983i | \(0.501865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.2141 | 2.64843 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46755 | −0.586123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.99433 | −0.985462 | −0.492731 | − | 0.870182i | \(-0.664001\pi\) | ||||
−0.492731 | + | 0.870182i | \(0.664001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.02017 | −0.163359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.40285 | −1.31230 | −0.656152 | − | 0.754628i | \(-0.727817\pi\) | ||||
−0.656152 | + | 0.754628i | \(0.727817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.52917 | −0.690692 | −0.345346 | − | 0.938475i | \(-0.612239\pi\) | ||||
−0.345346 | + | 0.938475i | \(0.612239\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.20593 | −0.626984 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.41115 | −0.643432 | −0.321716 | − | 0.946836i | \(-0.604260\pi\) | ||||
−0.321716 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7358 | 1.67654 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.4112 | −2.71811 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.98971 | 1.37219 | 0.686096 | − | 0.727511i | \(-0.259323\pi\) | ||||
0.686096 | + | 0.727511i | \(0.259323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24326 | 0.572161 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50126 | 0.993566 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9609 | 1.68737 | 0.843683 | − | 0.536842i | \(-0.180383\pi\) | ||||
0.843683 | + | 0.536842i | \(0.180383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.45173 | −0.954096 | −0.477048 | − | 0.878877i | \(-0.658293\pi\) | ||||
−0.477048 | + | 0.878877i | \(0.658293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.7254 | 2.86313 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.284531 | −0.0352917 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.80450 | −0.464794 | −0.232397 | − | 0.972621i | \(-0.574657\pi\) | ||||
−0.232397 | + | 0.972621i | \(0.574657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.7431 | 1.53409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0301 | 1.78374 | 0.891872 | − | 0.452288i | \(-0.149392\pi\) | ||||
0.891872 | + | 0.452288i | \(0.149392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.56498 | −0.417249 | −0.208625 | − | 0.977996i | \(-0.566899\pi\) | ||||
−0.208625 | + | 0.977996i | \(0.566899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5182 | 1.44548 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.9271 | −2.61278 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7170 | 1.31826 | 0.659131 | − | 0.752028i | \(-0.270924\pi\) | ||||
0.659131 | + | 0.752028i | \(0.270924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.81398 | 0.312665 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.25692 | 0.577022 | 0.288511 | − | 0.957477i | \(-0.406840\pi\) | ||||
0.288511 | + | 0.957477i | \(0.406840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.41386 | −0.587215 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.5593 | −2.09698 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.90166 | 0.307576 | 0.153788 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153788 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.53737 | 0.161160 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.187373 | 0.0194296 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.09213 | 0.214648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2836 | −1.34874 | −0.674372 | − | 0.738392i | \(-0.735586\pi\) | ||||
−0.674372 | + | 0.738392i | \(0.735586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −27.8092 | −2.79493 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.25334 | −0.721735 | −0.360867 | − | 0.932617i | \(-0.617519\pi\) | ||||
−0.360867 | + | 0.932617i | \(0.617519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.92994 | −0.978426 | −0.489213 | − | 0.872164i | \(-0.662716\pi\) | ||||
−0.489213 | + | 0.872164i | \(0.662716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.95990 | 0.971987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.49608 | 0.241305 | 0.120653 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120653 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.89004 | 0.947294 | 0.473647 | − | 0.880715i | \(-0.342937\pi\) | ||||
0.473647 | + | 0.880715i | \(0.342937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.2176 | 1.63422 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.27604 | −0.778544 | −0.389272 | − | 0.921123i | \(-0.627273\pi\) | ||||
−0.389272 | + | 0.921123i | \(0.627273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.55410 | 0.331422 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.86474 | 0.172395 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.2520 | 2.68153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.0560 | 1.55054 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.1356 | 2.17624 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.49689 | 0.670542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9646 | 1.23915 | 0.619577 | − | 0.784936i | \(-0.287304\pi\) | ||||
0.619577 | + | 0.784936i | \(0.287304\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.0092 | 1.14540 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.7257 | −1.37396 | −0.686980 | − | 0.726676i | \(-0.741064\pi\) | ||||
−0.686980 | + | 0.726676i | \(0.741064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3042 | −0.980194 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.17773 | 0.445628 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.05086 | −0.773267 | −0.386634 | − | 0.922233i | \(-0.626362\pi\) | ||||
−0.386634 | + | 0.922233i | \(0.626362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.9944 | −1.27181 | −0.635903 | − | 0.771769i | \(-0.719372\pi\) | ||||
−0.635903 | + | 0.771769i | \(0.719372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6702 | 1.06702 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.88129 | −0.157321 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.45518 | −0.453028 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33.7089 | −2.78026 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5209 | 0.943830 | 0.471915 | − | 0.881644i | \(-0.343563\pi\) | ||||
0.471915 | + | 0.881644i | \(0.343563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.9441 | −1.46027 | −0.730133 | − | 0.683305i | \(-0.760542\pi\) | ||||
−0.730133 | + | 0.683305i | \(0.760542\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35.4810 | 2.86847 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0522590 | 0.00419754 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.18254 | −0.253994 | −0.126997 | − | 0.991903i | \(-0.540534\pi\) | ||||
−0.126997 | + | 0.991903i | \(0.540534\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.6936 | −2.27555 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.2034 | −1.51344 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.164487 | −0.0128836 | −0.00644180 | − | 0.999979i | \(-0.502051\pi\) | ||||
−0.00644180 | + | 0.999979i | \(0.502051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.1880 | −0.948833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.59809 | 0.123664 | 0.0618318 | − | 0.998087i | \(-0.480306\pi\) | ||||
0.0618318 | + | 0.998087i | \(0.480306\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8739 | −0.990296 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.7113 | −1.04853 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.673099 | 0.0511748 | 0.0255874 | − | 0.999673i | \(-0.491854\pi\) | ||||
0.0255874 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.8646 | −1.42603 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −37.2278 | −2.79821 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.6930 | −0.799235 | −0.399618 | − | 0.916682i | \(-0.630857\pi\) | ||||
−0.399618 | + | 0.916682i | \(0.630857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.73003 | −0.351580 | −0.175790 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175790 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.4037 | 1.58221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.80206 | 0.353054 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −35.7958 | −2.61765 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.9762 | −2.03497 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.50279 | 0.470525 | 0.235263 | − | 0.971932i | \(-0.424405\pi\) | ||||
0.235263 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2434 | −1.52914 | −0.764568 | − | 0.644543i | \(-0.777048\pi\) | ||||
−0.764568 | + | 0.644543i | \(0.777048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.817262 | 0.0585254 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1562 | 0.794845 | 0.397422 | − | 0.917636i | \(-0.369905\pi\) | ||||
0.397422 | + | 0.917636i | \(0.369905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1091 | 0.858388 | 0.429194 | − | 0.903212i | \(-0.358798\pi\) | ||||
0.429194 | + | 0.903212i | \(0.358798\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9277 | 0.770783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.4753 | 2.06876 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.73153 | 0.470150 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.2927 | −1.61895 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8330 | 0.956845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.4749 | −1.75377 | −0.876883 | − | 0.480703i | \(-0.840381\pi\) | ||||
−0.876883 | + | 0.480703i | \(0.840381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −43.1712 | −2.95804 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.62832 | 0.247450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.282364 | −0.0191681 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.2397 | 0.691938 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.40028 | 0.161460 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.59130 | −0.374421 | −0.187211 | − | 0.982320i | \(-0.559945\pi\) | ||||
−0.187211 | + | 0.982320i | \(0.559945\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.8816 | −1.52544 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.7847 | 1.57864 | 0.789321 | − | 0.613980i | \(-0.210433\pi\) | ||||
0.789321 | + | 0.613980i | \(0.210433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.73615 | −0.246892 | −0.123446 | − | 0.992351i | \(-0.539395\pi\) | ||||
−0.123446 | + | 0.992351i | \(0.539395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 65.8538 | 4.33286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.3122 | −1.85479 | −0.927397 | − | 0.374078i | \(-0.877959\pi\) | ||||
−0.927397 | + | 0.374078i | \(0.877959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53377 | 0.230518 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.6548 | −2.18612 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2022 | −1.63020 | −0.815098 | − | 0.579323i | \(-0.803317\pi\) | ||||
−0.815098 | + | 0.579323i | \(0.803317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.67062 | 0.300861 | 0.150431 | − | 0.988621i | \(-0.451934\pi\) | ||||
0.150431 | + | 0.988621i | \(0.451934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3072 | 0.725357 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.40153 | −0.600642 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.927566 | −0.0590196 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.0995 | −0.956895 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.4994 | 1.47739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.5503 | 0.973798 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3679 | 0.646730 | 0.323365 | − | 0.946274i | \(-0.395186\pi\) | ||||
0.323365 | + | 0.946274i | \(0.395186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.9464 | −1.61223 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 35.7518 | 2.21298 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.6365 | −1.70414 | −0.852070 | − | 0.523429i | \(-0.824653\pi\) | ||||
−0.852070 | + | 0.523429i | \(0.824653\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00276 | −0.491606 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.33449 | −0.510062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4810 | −0.760980 | −0.380490 | − | 0.924785i | \(-0.624245\pi\) | ||||
−0.380490 | + | 0.924785i | \(0.624245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.7491 | −1.32116 | −0.660581 | − | 0.750755i | \(-0.729690\pi\) | ||||
−0.660581 | + | 0.750755i | \(0.729690\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.41581 | −0.267257 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.0847 | 1.39206 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.24654 | −0.255150 | −0.127575 | − | 0.991829i | \(-0.540719\pi\) | ||||
−0.127575 | + | 0.991829i | \(0.540719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.342491 | −0.0205044 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.93757 | −0.592826 | −0.296413 | − | 0.955060i | \(-0.595790\pi\) | ||||
−0.296413 | + | 0.955060i | \(0.595790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.5140 | 1.81387 | 0.906933 | − | 0.421274i | \(-0.138417\pi\) | ||||
0.906933 | + | 0.421274i | \(0.138417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00926 | −0.355958 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.3716 | −2.14695 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.6709 | 1.68652 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.1547 | 2.23667 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1769 | −1.12033 | −0.560165 | − | 0.828381i | \(-0.689262\pi\) | ||||
−0.560165 | + | 0.828381i | \(0.689262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3830 | −0.604521 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.2346 | 1.98649 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.57574 | −0.0911277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.6045 | −1.12998 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.8339 | 1.19688 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.96958 | 0.341817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.2689 | −1.38510 | −0.692550 | − | 0.721369i | \(-0.743513\pi\) | ||||
−0.692550 | + | 0.721369i | \(0.743513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.5219 | 1.62255 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.6530 | 1.79488 | 0.897439 | − | 0.441139i | \(-0.145425\pi\) | ||||
0.897439 | + | 0.441139i | \(0.145425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4679 | −1.83519 | −0.917597 | − | 0.397512i | \(-0.869874\pi\) | ||||
−0.917597 | + | 0.397512i | \(0.869874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.2053 | −1.02575 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.47733 | 0.195307 | 0.0976533 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976533 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.0691 | −2.01948 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.16953 | −0.400164 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6491 | −0.982021 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.54794 | −0.0858641 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.4073 | −1.57093 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.0936 | −1.05266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.1784 | −1.10911 | −0.554554 | − | 0.832148i | \(-0.687111\pi\) | ||||
−0.554554 | + | 0.832148i | \(0.687111\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −31.4714 | −1.72462 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.04779 | 0.166519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5362 | −0.846313 | −0.423157 | − | 0.906057i | \(-0.639078\pi\) | ||||
−0.423157 | + | 0.906057i | \(0.639078\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.7714 | 1.29108 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.345531 | 0.0187115 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.4987 | 1.10683 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2085 | −0.549608 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.38220 | −0.181566 | −0.0907831 | − | 0.995871i | \(-0.528937\pi\) | ||||
−0.0907831 | + | 0.995871i | \(0.528937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7704 | 0.790640 | 0.395320 | − | 0.918543i | \(-0.370634\pi\) | ||||
0.395320 | + | 0.918543i | \(0.370634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.29559 | −0.122530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4231 | −0.607990 | −0.303995 | − | 0.952674i | \(-0.598321\pi\) | ||||
−0.303995 | + | 0.952674i | \(0.598321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0406 | −0.639049 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −84.0210 | −4.44686 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.7369 | −1.20001 | −0.600003 | − | 0.799998i | \(-0.704834\pi\) | ||||
−0.600003 | + | 0.799998i | \(0.704834\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1797 | −0.641036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −48.9902 | −2.57132 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.85591 | 0.149485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.85042 | 0.253190 | 0.126595 | − | 0.991955i | \(-0.459595\pi\) | ||||
0.126595 | + | 0.991955i | \(0.459595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −44.1166 | −2.29662 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 43.2403 | 2.24492 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5539 | −0.960683 | −0.480341 | − | 0.877082i | \(-0.659487\pi\) | ||||
−0.480341 | + | 0.877082i | \(0.659487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21.5334 | −1.11198 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.41860 | 0.124564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8723 | −0.866673 | −0.433337 | − | 0.901232i | \(-0.642664\pi\) | ||||
−0.433337 | + | 0.901232i | \(0.642664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.1106 | −2.05493 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2439 | 1.03442 | 0.517208 | − | 0.855860i | \(-0.326971\pi\) | ||||
0.517208 | + | 0.855860i | \(0.326971\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.3669 | 0.936063 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.7791 | −1.20876 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.30439 | 0.218241 | 0.109121 | − | 0.994029i | \(-0.465196\pi\) | ||||
0.109121 | + | 0.994029i | \(0.465196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.9822 | −1.51626 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45.1692 | 2.27848 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.38647 | −0.472284 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3077 | 1.52110 | 0.760551 | − | 0.649279i | \(-0.224929\pi\) | ||||
0.760551 | + | 0.649279i | \(0.224929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 32.4691 | 1.62549 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.7892 | 0.788475 | 0.394238 | − | 0.919009i | \(-0.371009\pi\) | ||||
0.394238 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0231695 | −0.00115415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.25428 | −0.112016 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.7507 | 1.57382 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4833 | −0.518364 | −0.259182 | − | 0.965828i | \(-0.583453\pi\) | ||||
−0.259182 | + | 0.965828i | \(0.583453\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9969 | 1.28233 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 56.1011 | 2.76055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.21132 | −0.206726 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 43.0686 | 2.10908 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.1794 | −0.595001 | −0.297500 | − | 0.954722i | \(-0.596153\pi\) | ||||
−0.297500 | + | 0.954722i | \(0.596153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.5828 | −1.29556 | −0.647782 | − | 0.761826i | \(-0.724303\pi\) | ||||
−0.647782 | + | 0.761826i | \(0.724303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.1594 | −1.12605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.4531 | −1.42868 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.2547 | −1.56091 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.40365 | 0.260891 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8284 | 0.810598 | 0.405299 | − | 0.914184i | \(-0.367167\pi\) | ||||
0.405299 | + | 0.914184i | \(0.367167\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.73005 | −0.275369 | −0.137684 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137684 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.6690 | 0.751271 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.5863 | 0.554249 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2135 | −0.630648 | −0.315324 | − | 0.948984i | \(-0.602113\pi\) | ||||
−0.315324 | + | 0.948984i | \(0.602113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 61.6151 | 2.93405 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.21026 | 0.437593 | 0.218796 | − | 0.975771i | \(-0.429787\pi\) | ||||
0.218796 | + | 0.975771i | \(0.429787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.32452 | −0.110193 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.0917 | −1.56518 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7721 | 0.744332 | 0.372166 | − | 0.928166i | \(-0.378615\pi\) | ||||
0.372166 | + | 0.928166i | \(0.378615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.5081 | 2.09581 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 51.5410 | 2.42161 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.23159 | −0.0577377 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.7878 | −1.72086 | −0.860431 | − | 0.509567i | \(-0.829806\pi\) | ||||
−0.860431 | + | 0.509567i | \(0.829806\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −43.6790 | −2.03876 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9537 | −1.44166 | −0.720828 | − | 0.693114i | \(-0.756238\pi\) | ||||
−0.720828 | + | 0.693114i | \(0.756238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6966 | 0.497112 | 0.248556 | − | 0.968617i | \(-0.420044\pi\) | ||||
0.248556 | + | 0.968617i | \(0.420044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.150104 | −0.00696092 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.9092 | −1.15266 | −0.576331 | − | 0.817216i | \(-0.695516\pi\) | ||||
−0.576331 | + | 0.817216i | \(0.695516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4677 | −0.760410 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.14125 | 0.421207 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.9901 | 1.10306 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3819 | 0.522235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 52.4479 | 2.40143 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9085 | −1.04672 | −0.523359 | − | 0.852112i | \(-0.675321\pi\) | ||||
−0.523359 | + | 0.852112i | \(0.675321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.12904 | −0.0970757 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 55.1584 | 2.50979 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6415 | 0.483205 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4106 | 1.33272 | 0.666360 | − | 0.745630i | \(-0.267852\pi\) | ||||
0.666360 | + | 0.745630i | \(0.267852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.472458 | 0.0213653 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0114 | 0.632328 | 0.316164 | − | 0.948705i | \(-0.397605\pi\) | ||||
0.316164 | + | 0.948705i | \(0.397605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.0195 | 2.07261 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.2780 | 1.00132 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 65.0575 | 2.91823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.66328 | 0.163991 | 0.0819954 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819954 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.59021 | −0.205075 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.92668 | 0.353433 | 0.176717 | − | 0.984262i | \(-0.443452\pi\) | ||||
0.176717 | + | 0.984262i | \(0.443452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.81066 | 0.258571 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.9778 | 1.64224 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.11458 | −0.359672 | −0.179836 | − | 0.983697i | \(-0.557557\pi\) | ||||
−0.179836 | + | 0.983697i | \(0.557557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4310 | −0.682626 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.8793 | 0.745240 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.95487 | 0.350534 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.3649 | 1.02759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.93335 | −0.0848648 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8551 | 1.26416 | 0.632082 | − | 0.774902i | \(-0.282201\pi\) | ||||
0.632082 | + | 0.774902i | \(0.282201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4433 | −1.06883 | −0.534415 | − | 0.845222i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845222i | \(0.679468\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 54.1850 | 2.36483 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.440853 | −0.0192039 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.31721 | −0.144226 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 68.0473 | 2.95300 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.98448 | −0.129272 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.99961 | −0.0864507 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.7138 | 1.32540 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −62.1619 | −2.67750 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.60751 | −0.327073 | −0.163536 | − | 0.986537i | \(-0.552290\pi\) | ||||
−0.163536 | + | 0.986537i | \(0.552290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5861 | 0.583037 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.92292 | −0.339380 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.3469 | 1.21203 | 0.606013 | − | 0.795455i | \(-0.292768\pi\) | ||||
0.606013 | + | 0.795455i | \(0.292768\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.1230 | −1.66973 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.7838 | −0.757615 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.7167 | 2.15669 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.7930 | −0.585482 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7882 | 1.00794 | 0.503969 | − | 0.863721i | \(-0.331872\pi\) | ||||
0.503969 | + | 0.863721i | \(0.331872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.60865 | −0.0680386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 102.817 | 4.34094 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.88451 | 0.121568 | 0.0607839 | − | 0.998151i | \(-0.480640\pi\) | ||||
0.0607839 | + | 0.998151i | \(0.480640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.62994 | 0.278924 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.1803 | 0.511523 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.34899 | 0.350008 | 0.175004 | − | 0.984568i | \(-0.444006\pi\) | ||||
0.175004 | + | 0.984568i | \(0.444006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.0203 | −1.08892 | −0.544458 | − | 0.838788i | \(-0.683265\pi\) | ||||
−0.544458 | + | 0.838788i | \(0.683265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.6781 | −0.780287 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.3355 | 0.806344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.4162 | 1.30787 | 0.653936 | − | 0.756550i | \(-0.273117\pi\) | ||||
0.653936 | + | 0.756550i | \(0.273117\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 61.0179 | 2.53582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.7545 | 0.944016 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.9134 | −2.19145 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.49384 | −0.0617628 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3674 | 0.923202 | 0.461601 | − | 0.887088i | \(-0.347275\pi\) | ||||
0.461601 | + | 0.887088i | \(0.347275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.170363 | 0.00701970 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.0441 | −1.31812 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.9886 | −1.23149 | −0.615743 | − | 0.787947i | \(-0.711144\pi\) | ||||
−0.615743 | + | 0.787947i | \(0.711144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.4338 | −0.960692 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.7810 | −1.42349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.82921 | 0.115598 | 0.0577991 | − | 0.998328i | \(-0.481592\pi\) | ||||
0.0577991 | + | 0.998328i | \(0.481592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.4709 | 1.44689 | 0.723443 | − | 0.690384i | \(-0.242558\pi\) | ||||
0.723443 | + | 0.690384i | \(0.242558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.9744 | −0.813420 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.6636 | −0.555502 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.67595 | −0.352146 | −0.176073 | − | 0.984377i | \(-0.556339\pi\) | ||||
−0.176073 | + | 0.984377i | \(0.556339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −84.6623 | −3.43069 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.56673 | −0.0633831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.42430 | 0.259475 | 0.129738 | − | 0.991548i | \(-0.458587\pi\) | ||||
0.129738 | + | 0.991548i | \(0.458587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.3351 | −0.779665 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.38475 | −0.136265 | −0.0681324 | − | 0.997676i | \(-0.521704\pi\) | ||||
−0.0681324 | + | 0.997676i | \(0.521704\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.5948 | 1.51106 | 0.755532 | − | 0.655112i | \(-0.227378\pi\) | ||||
0.755532 | + | 0.655112i | \(0.227378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.6745 | 1.15067 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5598 | 0.503198 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.7854 | 0.631417 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.7326 | −1.58677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.5098 | −1.61523 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.02277 | −0.0805251 | −0.0402626 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402626 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 73.1720 | 2.90833 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.1870 | −0.443943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.16825 | 0.165152 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 78.9110 | 3.12167 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.30542 | −0.209552 | −0.104776 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104776 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.5167 | 1.59782 | 0.798910 | − | 0.601450i | \(-0.205410\pi\) | ||||
0.798910 | + | 0.601450i | \(0.205410\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4217 | −0.410354 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.40204 | 0.330318 | 0.165159 | − | 0.986267i | \(-0.447186\pi\) | ||||
0.165159 | + | 0.986267i | \(0.447186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −68.6512 | −2.69479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.811040 | 0.0317872 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00801 | 0.274245 | 0.137122 | − | 0.990554i | \(-0.456215\pi\) | ||||
0.137122 | + | 0.990554i | \(0.456215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.5979 | 0.492239 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.7169 | −0.730214 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.3463 | −1.88330 | −0.941652 | − | 0.336589i | \(-0.890727\pi\) | ||||
−0.941652 | + | 0.336589i | \(0.890727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1898 | 1.01866 | 0.509332 | − | 0.860570i | \(-0.329892\pi\) | ||||
0.509332 | + | 0.860570i | \(0.329892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.89437 | −0.267755 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.05576 | 0.351167 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.2110 | −1.16978 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0600 | 0.620914 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.4702 | 1.52373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9702 | 1.54074 | 0.770369 | − | 0.637598i | \(-0.220072\pi\) | ||||
0.770369 | + | 0.637598i | \(0.220072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.1685 | 1.08421 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3948 | −0.399505 | −0.199753 | − | 0.979846i | \(-0.564014\pi\) | ||||
−0.199753 | + | 0.979846i | \(0.564014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.4978 | −2.20656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −68.3170 | −2.61791 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.414911 | 0.0158761 | 0.00793807 | − | 0.999968i | \(-0.497473\pi\) | ||||
0.00793807 | + | 0.999968i | \(0.497473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.25065 | 0.277033 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7314 | 0.409428 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.54810 | 0.135172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.96293 | −0.188799 | −0.0943994 | − | 0.995534i | \(-0.530093\pi\) | ||||
−0.0943994 | + | 0.995534i | \(0.530093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −120.372 | −4.57254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0120 | 0.455641 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.7867 | −2.15095 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 81.3216 | 3.07587 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.09222 | −0.154561 | −0.0772804 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772804 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.6546 | 0.590426 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.1501 | −0.382275 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.3960 | −1.18077 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1864 | −1.17123 | −0.585615 | − | 0.810589i | \(-0.699147\pi\) | ||||
−0.585615 | + | 0.810589i | \(0.699147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 61.5164 | 2.30705 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.289413 | 0.0108386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.50710 | 0.0563623 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 72.3887 | 2.70341 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.987492 | 0.0368272 | 0.0184136 | − | 0.999830i | \(-0.494138\pi\) | ||||
0.0184136 | + | 0.999830i | \(0.494138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.9816 | −1.60072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4155 | −0.498928 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.6779 | −1.10221 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.5550 | 1.72663 | 0.863314 | − | 0.504667i | \(-0.168385\pi\) | ||||
0.863314 | + | 0.504667i | \(0.168385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.9198 | −1.51555 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.6083 | −1.13209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0763 | 0.852341 | 0.426171 | − | 0.904643i | \(-0.359862\pi\) | ||||
0.426171 | + | 0.904643i | \(0.359862\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.0042 | 0.996064 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.1517 | 0.742296 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.9962 | 0.809145 | 0.404572 | − | 0.914506i | \(-0.367420\pi\) | ||||
0.404572 | + | 0.914506i | \(0.367420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.66426 | 0.0978741 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.69614 | −0.0622254 | −0.0311127 | − | 0.999516i | \(-0.509905\pi\) | ||||
−0.0311127 | + | 0.999516i | \(0.509905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.22941 | −0.338139 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.5999 | 1.00983 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.8042 | 0.394778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.4070 | −1.00010 | −0.500049 | − | 0.865997i | \(-0.666685\pi\) | ||||
−0.500049 | + | 0.865997i | \(0.666685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.87232 | −0.104673 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3750 | 0.523159 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.88790 | 0.213999 | 0.107000 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.107000 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −67.4976 | −2.45001 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.02614 | 0.145947 | 0.0729737 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729737 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.8089 | 1.54979 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.4238 | −1.02767 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.60339 | 0.166219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.9600 | 1.40493 | 0.702467 | − | 0.711716i | \(-0.252082\pi\) | ||||
0.702467 | + | 0.711716i | \(0.252082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.7798 | −1.07249 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.0509 | −1.44053 | −0.720265 | − | 0.693699i | \(-0.755980\pi\) | ||||
−0.720265 | + | 0.693699i | \(0.755980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.284305 | 0.0102126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 74.5262 | 2.67361 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.9447 | 0.786249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −79.6112 | −2.84871 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −44.0124 | −1.57287 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.54953 | 0.0909967 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.2706 | −1.86324 | −0.931622 | − | 0.363428i | \(-0.881606\pi\) | ||||
−0.931622 | + | 0.363428i | \(0.881606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 79.3807 | 2.82603 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.8227 | −1.27371 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.64667 | −0.0939859 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.9865 | 0.815245 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.0948 | −1.56192 | −0.780959 | − | 0.624582i | \(-0.785269\pi\) | ||||
−0.780959 | + | 0.624582i | \(0.785269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.8107 | −1.05463 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.2343 | 0.538277 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.8830 | 0.666365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.3839 | 0.542211 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.8494 | 1.26196 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.50361 | 0.0528640 | 0.0264320 | − | 0.999651i | \(-0.491585\pi\) | ||||
0.0264320 | + | 0.999651i | \(0.491585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.3113 | −0.959031 | −0.479515 | − | 0.877533i | \(-0.659188\pi\) | ||||
−0.479515 | + | 0.877533i | \(0.659188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 62.4702 | 2.19093 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.131770 | 0.00461572 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.8283 | 0.413819 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.07149 | 0.282041 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.0473 | −1.85136 | −0.925681 | − | 0.378305i | \(-0.876507\pi\) | ||||
−0.925681 | + | 0.378305i | \(0.876507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.1868 | 1.71454 | 0.857271 | − | 0.514865i | \(-0.172158\pi\) | ||||
0.857271 | + | 0.514865i | \(0.172158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −66.3065 | −2.30849 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.26392 | −0.322138 | −0.161069 | − | 0.986943i | \(-0.551494\pi\) | ||||
−0.161069 | + | 0.986943i | \(0.551494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0625 | 0.384215 | 0.192107 | − | 0.981374i | \(-0.438468\pi\) | ||||
0.192107 | + | 0.981374i | \(0.438468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1974 | 0.423123 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 79.3107 | 2.74795 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.28023 | −0.0443041 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.421626 | 0.0145735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.3371 | −1.39259 | −0.696295 | − | 0.717756i | \(-0.745170\pi\) | ||||
−0.696295 | + | 0.717756i | \(0.745170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3708 | 0.598992 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.5438 | 0.983102 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3132 | 0.354786 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 73.8265 | 2.53671 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −87.6457 | −3.00799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.5940 | 0.911631 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.2519 | 1.82331 | 0.911655 | − | 0.410956i | \(-0.134805\pi\) | ||||
0.911655 | + | 0.410956i | \(0.134805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9841 | 0.375648 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.24507 | −0.145009 | −0.0725043 | − | 0.997368i | \(-0.523099\pi\) | ||||
−0.0725043 | + | 0.997368i | \(0.523099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.5555 | 1.11078 | 0.555390 | − | 0.831590i | \(-0.312569\pi\) | ||||
0.555390 | + | 0.831590i | \(0.312569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 104.471 | 3.56035 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.5375 | −1.78840 | −0.894199 | − | 0.447669i | \(-0.852254\pi\) | ||||
−0.894199 | + | 0.447669i | \(0.852254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.539220 | −0.0183340 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −82.3519 | −2.79682 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62.0623 | −2.10532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.35127 | −0.0457859 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −69.7415 | −2.36039 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.4502 | 1.09702 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.6449 | −1.74392 | −0.871962 | − | 0.489573i | \(-0.837153\pi\) | ||||
−0.871962 | + | 0.489573i | \(0.837153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.0822 | 1.85788 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.6645 | −0.561441 | −0.280721 | − | 0.959789i | \(-0.590573\pi\) | ||||
−0.280721 | + | 0.959789i | \(0.590573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.48960 | −0.319350 | −0.159675 | − | 0.987170i | \(-0.551045\pi\) | ||||
−0.159675 | + | 0.987170i | \(0.551045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.8232 | 1.00250 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.6151 | −0.524305 | −0.262152 | − | 0.965026i | \(-0.584432\pi\) | ||||
−0.262152 | + | 0.965026i | \(0.584432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 60.4454 | 2.02727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9051 | −0.499338 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.5200 | 0.385503 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.56620 | 0.286336 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.52604 | 0.151120 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.444218 | −0.0148155 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.5107 | 2.24911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 56.3102 | 1.87389 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.78923 | 0.125958 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4311 | −0.379562 | −0.189781 | − | 0.981826i | \(-0.560778\pi\) | ||||
−0.189781 | + | 0.981826i | \(0.560778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.0815 | −1.26308 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7068 | −0.354733 | −0.177367 | − | 0.984145i | \(-0.556758\pi\) | ||||
−0.177367 | + | 0.984145i | \(0.556758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8448 | −0.921529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.1465 | −0.566846 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −68.0684 | −2.24782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.67015 | 0.318989 | 0.159494 | − | 0.987199i | \(-0.449014\pi\) | ||||
0.159494 | + | 0.987199i | \(0.449014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 69.7080 | 2.29696 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.33831 | 0.175713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.1247 | 0.858976 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.1341 | −1.71231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.9009 | 0.981018 | 0.490509 | − | 0.871436i | \(-0.336811\pi\) | ||||
0.490509 | + | 0.871436i | \(0.336811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.6488 | −1.00447 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −90.9175 | −2.97650 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.6761 | 0.937807 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.9955 | 0.555218 | 0.277609 | − | 0.960694i | \(-0.410458\pi\) | ||||
0.277609 | + | 0.960694i | \(0.410458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 93.2581 | 3.04336 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8089 | −0.808748 | −0.404374 | − | 0.914594i | \(-0.632511\pi\) | ||||
−0.404374 | + | 0.914594i | \(0.632511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.2795 | 1.21399 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.4117 | 0.729054 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.82922 | −0.156929 | −0.0784643 | − | 0.996917i | \(-0.525002\pi\) | ||||
−0.0784643 | + | 0.996917i | \(0.525002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.26619 | −0.0411023 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.98800 | −0.323883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.65459 | 0.247956 | 0.123978 | − | 0.992285i | \(-0.460435\pi\) | ||||
0.123978 | + | 0.992285i | \(0.460435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.20938 | −0.168572 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 103.602 | 3.34897 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.1765 | −1.26508 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9957 | −0.999863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.1049 | 0.422300 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.0181 | 0.547833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3405 | −0.557632 | −0.278816 | − | 0.960345i | \(-0.589942\pi\) | ||||
−0.278816 | + | 0.960345i | \(0.589942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 50.6937 | 1.62852 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6264 | −0.565659 | −0.282830 | − | 0.959170i | \(-0.591273\pi\) | ||||
−0.282830 | + | 0.959170i | \(0.591273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −64.9029 | −2.08069 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.44617 | 0.142391 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.76153 | 0.0563564 | 0.0281782 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281782 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.3695 | −0.491211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 51.9247 | 1.65783 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.6266 | 0.881152 | 0.440576 | − | 0.897715i | \(-0.354774\pi\) | ||||
0.440576 | + | 0.897715i | \(0.354774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.93722 | −0.284763 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.8428 | 1.74567 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0938 | 0.638946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.7671 | −1.48560 | −0.742802 | − | 0.669511i | \(-0.766504\pi\) | ||||
−0.742802 | + | 0.669511i | \(0.766504\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 57.9589 | 1.83927 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.70057 | −0.307529 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0053 | 0.665243 | 0.332622 | − | 0.943060i | \(-0.392067\pi\) | ||||
0.332622 | + | 0.943060i | \(0.392067\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.7430 | 1.22577 |
(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.j.1.2 | 14 | ||
4.3 | odd | 2 | 1004.2.a.b.1.13 | ✓ | 14 | ||
12.11 | even | 2 | 9036.2.a.m.1.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.b.1.13 | ✓ | 14 | 4.3 | odd | 2 | ||
4016.2.a.j.1.2 | 14 | 1.1 | even | 1 | trivial | ||
9036.2.a.m.1.9 | 14 | 12.11 | even | 2 |