Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.29725 | −1.32632 | −0.663159 | − | 0.748479i | \(-0.730785\pi\) | ||||
−0.663159 | + | 0.748479i | \(0.730785\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0563132 | −0.0251840 | −0.0125920 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125920 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(6\) | 2.29725 | 0.937848 | ||||||||
\(7\) | 2.55969 | 0.967471 | 0.483736 | − | 0.875214i | \(-0.339280\pi\) | ||||
0.483736 | + | 0.875214i | \(0.339280\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.27735 | 0.759117 | ||||||||
\(10\) | 0.0563132 | 0.0178078 | ||||||||
\(11\) | −4.38490 | −1.32210 | −0.661048 | − | 0.750343i | \(-0.729888\pi\) | ||||
−0.661048 | + | 0.750343i | \(0.729888\pi\) | |||||||
\(12\) | −2.29725 | −0.663159 | ||||||||
\(13\) | 2.08970 | 0.579579 | 0.289789 | − | 0.957090i | \(-0.406415\pi\) | ||||
0.289789 | + | 0.957090i | \(0.406415\pi\) | |||||||
\(14\) | −2.55969 | −0.684105 | ||||||||
\(15\) | 0.129365 | 0.0334020 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.33616 | 1.05167 | 0.525837 | − | 0.850586i | \(-0.323752\pi\) | ||||
0.525837 | + | 0.850586i | \(0.323752\pi\) | |||||||
\(18\) | −2.27735 | −0.536777 | ||||||||
\(19\) | 0.321301 | 0.0737115 | 0.0368558 | − | 0.999321i | \(-0.488266\pi\) | ||||
0.0368558 | + | 0.999321i | \(0.488266\pi\) | |||||||
\(20\) | −0.0563132 | −0.0125920 | ||||||||
\(21\) | −5.88024 | −1.28317 | ||||||||
\(22\) | 4.38490 | 0.934864 | ||||||||
\(23\) | 0.741876 | 0.154692 | 0.0773459 | − | 0.997004i | \(-0.475355\pi\) | ||||
0.0773459 | + | 0.997004i | \(0.475355\pi\) | |||||||
\(24\) | 2.29725 | 0.468924 | ||||||||
\(25\) | −4.99683 | −0.999366 | ||||||||
\(26\) | −2.08970 | −0.409824 | ||||||||
\(27\) | 1.66010 | 0.319487 | ||||||||
\(28\) | 2.55969 | 0.483736 | ||||||||
\(29\) | −2.18305 | −0.405383 | −0.202691 | − | 0.979243i | \(-0.564969\pi\) | ||||
−0.202691 | + | 0.979243i | \(0.564969\pi\) | |||||||
\(30\) | −0.129365 | −0.0236188 | ||||||||
\(31\) | −7.46270 | −1.34034 | −0.670170 | − | 0.742208i | \(-0.733779\pi\) | ||||
−0.670170 | + | 0.742208i | \(0.733779\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.0732 | 1.75352 | ||||||||
\(34\) | −4.33616 | −0.743645 | ||||||||
\(35\) | −0.144144 | −0.0243648 | ||||||||
\(36\) | 2.27735 | 0.379559 | ||||||||
\(37\) | 5.68263 | 0.934219 | 0.467109 | − | 0.884200i | \(-0.345295\pi\) | ||||
0.467109 | + | 0.884200i | \(0.345295\pi\) | |||||||
\(38\) | −0.321301 | −0.0521219 | ||||||||
\(39\) | −4.80056 | −0.768705 | ||||||||
\(40\) | 0.0563132 | 0.00890390 | ||||||||
\(41\) | 1.74954 | 0.273232 | 0.136616 | − | 0.990624i | \(-0.456377\pi\) | ||||
0.136616 | + | 0.990624i | \(0.456377\pi\) | |||||||
\(42\) | 5.88024 | 0.907341 | ||||||||
\(43\) | −0.974593 | −0.148624 | −0.0743120 | − | 0.997235i | \(-0.523676\pi\) | ||||
−0.0743120 | + | 0.997235i | \(0.523676\pi\) | |||||||
\(44\) | −4.38490 | −0.661048 | ||||||||
\(45\) | −0.128245 | −0.0191176 | ||||||||
\(46\) | −0.741876 | −0.109384 | ||||||||
\(47\) | 0.00455965 | 0.000665094 0 | 0.000332547 | − | 1.00000i | \(-0.499894\pi\) | ||||
0.000332547 | 1.00000i | \(0.499894\pi\) | ||||||||
\(48\) | −2.29725 | −0.331579 | ||||||||
\(49\) | −0.447997 | −0.0639995 | ||||||||
\(50\) | 4.99683 | 0.706658 | ||||||||
\(51\) | −9.96124 | −1.39485 | ||||||||
\(52\) | 2.08970 | 0.289789 | ||||||||
\(53\) | 11.8355 | 1.62573 | 0.812865 | − | 0.582452i | \(-0.197907\pi\) | ||||
0.812865 | + | 0.582452i | \(0.197907\pi\) | |||||||
\(54\) | −1.66010 | −0.225911 | ||||||||
\(55\) | 0.246928 | 0.0332957 | ||||||||
\(56\) | −2.55969 | −0.342053 | ||||||||
\(57\) | −0.738109 | −0.0977649 | ||||||||
\(58\) | 2.18305 | 0.286649 | ||||||||
\(59\) | 2.42707 | 0.315977 | 0.157989 | − | 0.987441i | \(-0.449499\pi\) | ||||
0.157989 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(60\) | 0.129365 | 0.0167010 | ||||||||
\(61\) | −4.05871 | −0.519665 | −0.259833 | − | 0.965654i | \(-0.583667\pi\) | ||||
−0.259833 | + | 0.965654i | \(0.583667\pi\) | |||||||
\(62\) | 7.46270 | 0.947763 | ||||||||
\(63\) | 5.82931 | 0.734424 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.117678 | −0.0145961 | ||||||||
\(66\) | −10.0732 | −1.23993 | ||||||||
\(67\) | −9.74948 | −1.19109 | −0.595544 | − | 0.803323i | \(-0.703063\pi\) | ||||
−0.595544 | + | 0.803323i | \(0.703063\pi\) | |||||||
\(68\) | 4.33616 | 0.525837 | ||||||||
\(69\) | −1.70427 | −0.205170 | ||||||||
\(70\) | 0.144144 | 0.0172285 | ||||||||
\(71\) | 0.760311 | 0.0902324 | 0.0451162 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451162 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(72\) | −2.27735 | −0.268389 | ||||||||
\(73\) | −16.3548 | −1.91418 | −0.957089 | − | 0.289793i | \(-0.906414\pi\) | ||||
−0.957089 | + | 0.289793i | \(0.906414\pi\) | |||||||
\(74\) | −5.68263 | −0.660592 | ||||||||
\(75\) | 11.4790 | 1.32548 | ||||||||
\(76\) | 0.321301 | 0.0368558 | ||||||||
\(77\) | −11.2240 | −1.27909 | ||||||||
\(78\) | 4.80056 | 0.543557 | ||||||||
\(79\) | −3.45286 | −0.388477 | −0.194239 | − | 0.980954i | \(-0.562224\pi\) | ||||
−0.194239 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(80\) | −0.0563132 | −0.00629601 | ||||||||
\(81\) | −10.6457 | −1.18286 | ||||||||
\(82\) | −1.74954 | −0.193204 | ||||||||
\(83\) | 0.0374441 | 0.00411003 | 0.00205501 | − | 0.999998i | \(-0.499346\pi\) | ||||
0.00205501 | + | 0.999998i | \(0.499346\pi\) | |||||||
\(84\) | −5.88024 | −0.641587 | ||||||||
\(85\) | −0.244183 | −0.0264854 | ||||||||
\(86\) | 0.974593 | 0.105093 | ||||||||
\(87\) | 5.01501 | 0.537666 | ||||||||
\(88\) | 4.38490 | 0.467432 | ||||||||
\(89\) | −11.5471 | −1.22399 | −0.611997 | − | 0.790860i | \(-0.709634\pi\) | ||||
−0.611997 | + | 0.790860i | \(0.709634\pi\) | |||||||
\(90\) | 0.128245 | 0.0135182 | ||||||||
\(91\) | 5.34898 | 0.560726 | ||||||||
\(92\) | 0.741876 | 0.0773459 | ||||||||
\(93\) | 17.1437 | 1.77772 | ||||||||
\(94\) | −0.00455965 | −0.000470292 0 | ||||||||
\(95\) | −0.0180935 | −0.00185635 | ||||||||
\(96\) | 2.29725 | 0.234462 | ||||||||
\(97\) | 8.86420 | 0.900023 | 0.450011 | − | 0.893023i | \(-0.351420\pi\) | ||||
0.450011 | + | 0.893023i | \(0.351420\pi\) | |||||||
\(98\) | 0.447997 | 0.0452545 | ||||||||
\(99\) | −9.98596 | −1.00363 | ||||||||
\(100\) | −4.99683 | −0.499683 | ||||||||
\(101\) | 16.5704 | 1.64882 | 0.824409 | − | 0.565994i | \(-0.191507\pi\) | ||||
0.824409 | + | 0.565994i | \(0.191507\pi\) | |||||||
\(102\) | 9.96124 | 0.986310 | ||||||||
\(103\) | −0.542195 | −0.0534241 | −0.0267120 | − | 0.999643i | \(-0.508504\pi\) | ||||
−0.0267120 | + | 0.999643i | \(0.508504\pi\) | |||||||
\(104\) | −2.08970 | −0.204912 | ||||||||
\(105\) | 0.331135 | 0.0323155 | ||||||||
\(106\) | −11.8355 | −1.14957 | ||||||||
\(107\) | 11.4189 | 1.10391 | 0.551955 | − | 0.833874i | \(-0.313882\pi\) | ||||
0.551955 | + | 0.833874i | \(0.313882\pi\) | |||||||
\(108\) | 1.66010 | 0.159743 | ||||||||
\(109\) | −1.21753 | −0.116618 | −0.0583090 | − | 0.998299i | \(-0.518571\pi\) | ||||
−0.0583090 | + | 0.998299i | \(0.518571\pi\) | |||||||
\(110\) | −0.246928 | −0.0235436 | ||||||||
\(111\) | −13.0544 | −1.23907 | ||||||||
\(112\) | 2.55969 | 0.241868 | ||||||||
\(113\) | 7.46015 | 0.701792 | 0.350896 | − | 0.936414i | \(-0.385877\pi\) | ||||
0.350896 | + | 0.936414i | \(0.385877\pi\) | |||||||
\(114\) | 0.738109 | 0.0691302 | ||||||||
\(115\) | −0.0417774 | −0.00389576 | ||||||||
\(116\) | −2.18305 | −0.202691 | ||||||||
\(117\) | 4.75899 | 0.439968 | ||||||||
\(118\) | −2.42707 | −0.223430 | ||||||||
\(119\) | 11.0992 | 1.01746 | ||||||||
\(120\) | −0.129365 | −0.0118094 | ||||||||
\(121\) | 8.22734 | 0.747940 | ||||||||
\(122\) | 4.05871 | 0.367459 | ||||||||
\(123\) | −4.01913 | −0.362393 | ||||||||
\(124\) | −7.46270 | −0.670170 | ||||||||
\(125\) | 0.562953 | 0.0503521 | ||||||||
\(126\) | −5.82931 | −0.519316 | ||||||||
\(127\) | −14.3321 | −1.27177 | −0.635885 | − | 0.771784i | \(-0.719365\pi\) | ||||
−0.635885 | + | 0.771784i | \(0.719365\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.23888 | 0.197123 | ||||||||
\(130\) | 0.117678 | 0.0103210 | ||||||||
\(131\) | 2.99206 | 0.261418 | 0.130709 | − | 0.991421i | \(-0.458275\pi\) | ||||
0.130709 | + | 0.991421i | \(0.458275\pi\) | |||||||
\(132\) | 10.0732 | 0.876760 | ||||||||
\(133\) | 0.822431 | 0.0713138 | ||||||||
\(134\) | 9.74948 | 0.842226 | ||||||||
\(135\) | −0.0934857 | −0.00804597 | ||||||||
\(136\) | −4.33616 | −0.371823 | ||||||||
\(137\) | 16.8733 | 1.44158 | 0.720791 | − | 0.693152i | \(-0.243779\pi\) | ||||
0.720791 | + | 0.693152i | \(0.243779\pi\) | |||||||
\(138\) | 1.70427 | 0.145077 | ||||||||
\(139\) | −15.9636 | −1.35401 | −0.677006 | − | 0.735978i | \(-0.736723\pi\) | ||||
−0.677006 | + | 0.735978i | \(0.736723\pi\) | |||||||
\(140\) | −0.144144 | −0.0121824 | ||||||||
\(141\) | −0.0104747 | −0.000882125 0 | ||||||||
\(142\) | −0.760311 | −0.0638039 | ||||||||
\(143\) | −9.16313 | −0.766259 | ||||||||
\(144\) | 2.27735 | 0.189779 | ||||||||
\(145\) | 0.122935 | 0.0102092 | ||||||||
\(146\) | 16.3548 | 1.35353 | ||||||||
\(147\) | 1.02916 | 0.0848837 | ||||||||
\(148\) | 5.68263 | 0.467109 | ||||||||
\(149\) | −6.61271 | −0.541734 | −0.270867 | − | 0.962617i | \(-0.587310\pi\) | ||||
−0.270867 | + | 0.962617i | \(0.587310\pi\) | |||||||
\(150\) | −11.4790 | −0.937253 | ||||||||
\(151\) | 10.0986 | 0.821811 | 0.410905 | − | 0.911678i | \(-0.365213\pi\) | ||||
0.410905 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(152\) | −0.321301 | −0.0260610 | ||||||||
\(153\) | 9.87496 | 0.798344 | ||||||||
\(154\) | 11.2240 | 0.904454 | ||||||||
\(155\) | 0.420248 | 0.0337552 | ||||||||
\(156\) | −4.80056 | −0.384353 | ||||||||
\(157\) | 7.00844 | 0.559334 | 0.279667 | − | 0.960097i | \(-0.409776\pi\) | ||||
0.279667 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(158\) | 3.45286 | 0.274695 | ||||||||
\(159\) | −27.1891 | −2.15623 | ||||||||
\(160\) | 0.0563132 | 0.00445195 | ||||||||
\(161\) | 1.89897 | 0.149660 | ||||||||
\(162\) | 10.6457 | 0.836407 | ||||||||
\(163\) | −15.7221 | −1.23145 | −0.615726 | − | 0.787960i | \(-0.711137\pi\) | ||||
−0.615726 | + | 0.787960i | \(0.711137\pi\) | |||||||
\(164\) | 1.74954 | 0.136616 | ||||||||
\(165\) | −0.567254 | −0.0441607 | ||||||||
\(166\) | −0.0374441 | −0.00290623 | ||||||||
\(167\) | 18.7636 | 1.45197 | 0.725986 | − | 0.687710i | \(-0.241384\pi\) | ||||
0.725986 | + | 0.687710i | \(0.241384\pi\) | |||||||
\(168\) | 5.88024 | 0.453670 | ||||||||
\(169\) | −8.63315 | −0.664088 | ||||||||
\(170\) | 0.244183 | 0.0187280 | ||||||||
\(171\) | 0.731716 | 0.0559557 | ||||||||
\(172\) | −0.974593 | −0.0743120 | ||||||||
\(173\) | 5.60033 | 0.425785 | 0.212893 | − | 0.977076i | \(-0.431712\pi\) | ||||
0.212893 | + | 0.977076i | \(0.431712\pi\) | |||||||
\(174\) | −5.01501 | −0.380187 | ||||||||
\(175\) | −12.7903 | −0.966858 | ||||||||
\(176\) | −4.38490 | −0.330524 | ||||||||
\(177\) | −5.57558 | −0.419086 | ||||||||
\(178\) | 11.5471 | 0.865494 | ||||||||
\(179\) | −10.3380 | −0.772702 | −0.386351 | − | 0.922352i | \(-0.626265\pi\) | ||||
−0.386351 | + | 0.922352i | \(0.626265\pi\) | |||||||
\(180\) | −0.128245 | −0.00955882 | ||||||||
\(181\) | −0.423949 | −0.0315119 | −0.0157560 | − | 0.999876i | \(-0.505015\pi\) | ||||
−0.0157560 | + | 0.999876i | \(0.505015\pi\) | |||||||
\(182\) | −5.34898 | −0.396493 | ||||||||
\(183\) | 9.32388 | 0.689241 | ||||||||
\(184\) | −0.741876 | −0.0546918 | ||||||||
\(185\) | −0.320007 | −0.0235274 | ||||||||
\(186\) | −17.1437 | −1.25703 | ||||||||
\(187\) | −19.0136 | −1.39041 | ||||||||
\(188\) | 0.00455965 | 0.000332547 0 | ||||||||
\(189\) | 4.24934 | 0.309094 | ||||||||
\(190\) | 0.0180935 | 0.00131264 | ||||||||
\(191\) | −9.33430 | −0.675407 | −0.337703 | − | 0.941253i | \(-0.609650\pi\) | ||||
−0.337703 | + | 0.941253i | \(0.609650\pi\) | |||||||
\(192\) | −2.29725 | −0.165790 | ||||||||
\(193\) | 8.70456 | 0.626568 | 0.313284 | − | 0.949659i | \(-0.398571\pi\) | ||||
0.313284 | + | 0.949659i | \(0.398571\pi\) | |||||||
\(194\) | −8.86420 | −0.636412 | ||||||||
\(195\) | 0.270335 | 0.0193591 | ||||||||
\(196\) | −0.447997 | −0.0319998 | ||||||||
\(197\) | 8.93519 | 0.636606 | 0.318303 | − | 0.947989i | \(-0.396887\pi\) | ||||
0.318303 | + | 0.947989i | \(0.396887\pi\) | |||||||
\(198\) | 9.98596 | 0.709671 | ||||||||
\(199\) | 11.6082 | 0.822884 | 0.411442 | − | 0.911436i | \(-0.365025\pi\) | ||||
0.411442 | + | 0.911436i | \(0.365025\pi\) | |||||||
\(200\) | 4.99683 | 0.353329 | ||||||||
\(201\) | 22.3970 | 1.57976 | ||||||||
\(202\) | −16.5704 | −1.16589 | ||||||||
\(203\) | −5.58793 | −0.392196 | ||||||||
\(204\) | −9.96124 | −0.697426 | ||||||||
\(205\) | −0.0985222 | −0.00688109 | ||||||||
\(206\) | 0.542195 | 0.0377765 | ||||||||
\(207\) | 1.68951 | 0.117429 | ||||||||
\(208\) | 2.08970 | 0.144895 | ||||||||
\(209\) | −1.40887 | −0.0974538 | ||||||||
\(210\) | −0.331135 | −0.0228505 | ||||||||
\(211\) | 17.8257 | 1.22717 | 0.613585 | − | 0.789628i | \(-0.289727\pi\) | ||||
0.613585 | + | 0.789628i | \(0.289727\pi\) | |||||||
\(212\) | 11.8355 | 0.812865 | ||||||||
\(213\) | −1.74662 | −0.119677 | ||||||||
\(214\) | −11.4189 | −0.780583 | ||||||||
\(215\) | 0.0548824 | 0.00374295 | ||||||||
\(216\) | −1.66010 | −0.112956 | ||||||||
\(217\) | −19.1022 | −1.29674 | ||||||||
\(218\) | 1.21753 | 0.0824614 | ||||||||
\(219\) | 37.5709 | 2.53881 | ||||||||
\(220\) | 0.246928 | 0.0166479 | ||||||||
\(221\) | 9.06128 | 0.609528 | ||||||||
\(222\) | 13.0544 | 0.876155 | ||||||||
\(223\) | −16.3876 | −1.09740 | −0.548698 | − | 0.836021i | \(-0.684876\pi\) | ||||
−0.548698 | + | 0.836021i | \(0.684876\pi\) | |||||||
\(224\) | −2.55969 | −0.171026 | ||||||||
\(225\) | −11.3795 | −0.758636 | ||||||||
\(226\) | −7.46015 | −0.496242 | ||||||||
\(227\) | −23.0524 | −1.53004 | −0.765019 | − | 0.644007i | \(-0.777271\pi\) | ||||
−0.765019 | + | 0.644007i | \(0.777271\pi\) | |||||||
\(228\) | −0.738109 | −0.0488824 | ||||||||
\(229\) | 9.30192 | 0.614688 | 0.307344 | − | 0.951599i | \(-0.400560\pi\) | ||||
0.307344 | + | 0.951599i | \(0.400560\pi\) | |||||||
\(230\) | 0.0417774 | 0.00275472 | ||||||||
\(231\) | 25.7843 | 1.69648 | ||||||||
\(232\) | 2.18305 | 0.143324 | ||||||||
\(233\) | 28.9954 | 1.89955 | 0.949776 | − | 0.312930i | \(-0.101310\pi\) | ||||
0.949776 | + | 0.312930i | \(0.101310\pi\) | |||||||
\(234\) | −4.75899 | −0.311105 | ||||||||
\(235\) | −0.000256769 0 | −1.67497e−5 0 | ||||||||
\(236\) | 2.42707 | 0.157989 | ||||||||
\(237\) | 7.93208 | 0.515244 | ||||||||
\(238\) | −11.0992 | −0.719455 | ||||||||
\(239\) | −8.61374 | −0.557177 | −0.278588 | − | 0.960411i | \(-0.589866\pi\) | ||||
−0.278588 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(240\) | 0.129365 | 0.00835050 | ||||||||
\(241\) | −6.65186 | −0.428484 | −0.214242 | − | 0.976781i | \(-0.568728\pi\) | ||||
−0.214242 | + | 0.976781i | \(0.568728\pi\) | |||||||
\(242\) | −8.22734 | −0.528873 | ||||||||
\(243\) | 19.4756 | 1.24936 | ||||||||
\(244\) | −4.05871 | −0.259833 | ||||||||
\(245\) | 0.0252281 | 0.00161177 | ||||||||
\(246\) | 4.01913 | 0.256250 | ||||||||
\(247\) | 0.671424 | 0.0427217 | ||||||||
\(248\) | 7.46270 | 0.473882 | ||||||||
\(249\) | −0.0860185 | −0.00545120 | ||||||||
\(250\) | −0.562953 | −0.0356043 | ||||||||
\(251\) | 7.33623 | 0.463059 | 0.231529 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231529 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(252\) | 5.82931 | 0.367212 | ||||||||
\(253\) | −3.25305 | −0.204518 | ||||||||
\(254\) | 14.3321 | 0.899277 | ||||||||
\(255\) | 0.560949 | 0.0351280 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.13605 | −0.382756 | −0.191378 | − | 0.981516i | \(-0.561296\pi\) | ||||
−0.191378 | + | 0.981516i | \(0.561296\pi\) | |||||||
\(258\) | −2.23888 | −0.139387 | ||||||||
\(259\) | 14.5458 | 0.903829 | ||||||||
\(260\) | −0.117678 | −0.00729807 | ||||||||
\(261\) | −4.97158 | −0.307733 | ||||||||
\(262\) | −2.99206 | −0.184850 | ||||||||
\(263\) | −8.49180 | −0.523627 | −0.261813 | − | 0.965119i | \(-0.584320\pi\) | ||||
−0.261813 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(264\) | −10.0732 | −0.619963 | ||||||||
\(265\) | −0.666495 | −0.0409424 | ||||||||
\(266\) | −0.822431 | −0.0504265 | ||||||||
\(267\) | 26.5266 | 1.62340 | ||||||||
\(268\) | −9.74948 | −0.595544 | ||||||||
\(269\) | −13.2993 | −0.810875 | −0.405438 | − | 0.914123i | \(-0.632881\pi\) | ||||
−0.405438 | + | 0.914123i | \(0.632881\pi\) | |||||||
\(270\) | 0.0934857 | 0.00568936 | ||||||||
\(271\) | 20.0373 | 1.21718 | 0.608589 | − | 0.793485i | \(-0.291736\pi\) | ||||
0.608589 | + | 0.793485i | \(0.291736\pi\) | |||||||
\(272\) | 4.33616 | 0.262918 | ||||||||
\(273\) | −12.2879 | −0.743700 | ||||||||
\(274\) | −16.8733 | −1.01935 | ||||||||
\(275\) | 21.9106 | 1.32126 | ||||||||
\(276\) | −1.70427 | −0.102585 | ||||||||
\(277\) | −14.1526 | −0.850346 | −0.425173 | − | 0.905112i | \(-0.639787\pi\) | ||||
−0.425173 | + | 0.905112i | \(0.639787\pi\) | |||||||
\(278\) | 15.9636 | 0.957431 | ||||||||
\(279\) | −16.9952 | −1.01748 | ||||||||
\(280\) | 0.144144 | 0.00861427 | ||||||||
\(281\) | 2.57606 | 0.153675 | 0.0768374 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768374 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(282\) | 0.0104747 | 0.000623757 0 | ||||||||
\(283\) | −23.8035 | −1.41497 | −0.707486 | − | 0.706727i | \(-0.750171\pi\) | ||||
−0.707486 | + | 0.706727i | \(0.750171\pi\) | |||||||
\(284\) | 0.760311 | 0.0451162 | ||||||||
\(285\) | 0.0415653 | 0.00246211 | ||||||||
\(286\) | 9.16313 | 0.541827 | ||||||||
\(287\) | 4.47828 | 0.264344 | ||||||||
\(288\) | −2.27735 | −0.134194 | ||||||||
\(289\) | 1.80229 | 0.106017 | ||||||||
\(290\) | −0.122935 | −0.00721897 | ||||||||
\(291\) | −20.3633 | −1.19372 | ||||||||
\(292\) | −16.3548 | −0.957089 | ||||||||
\(293\) | −7.61728 | −0.445006 | −0.222503 | − | 0.974932i | \(-0.571423\pi\) | ||||
−0.222503 | + | 0.974932i | \(0.571423\pi\) | |||||||
\(294\) | −1.02916 | −0.0600218 | ||||||||
\(295\) | −0.136676 | −0.00795758 | ||||||||
\(296\) | −5.68263 | −0.330296 | ||||||||
\(297\) | −7.27938 | −0.422392 | ||||||||
\(298\) | 6.61271 | 0.383064 | ||||||||
\(299\) | 1.55030 | 0.0896561 | ||||||||
\(300\) | 11.4790 | 0.662738 | ||||||||
\(301\) | −2.49465 | −0.143789 | ||||||||
\(302\) | −10.0986 | −0.581108 | ||||||||
\(303\) | −38.0664 | −2.18686 | ||||||||
\(304\) | 0.321301 | 0.0184279 | ||||||||
\(305\) | 0.228559 | 0.0130873 | ||||||||
\(306\) | −9.87496 | −0.564514 | ||||||||
\(307\) | 12.2067 | 0.696675 | 0.348338 | − | 0.937369i | \(-0.386746\pi\) | ||||
0.348338 | + | 0.937369i | \(0.386746\pi\) | |||||||
\(308\) | −11.2240 | −0.639545 | ||||||||
\(309\) | 1.24556 | 0.0708573 | ||||||||
\(310\) | −0.420248 | −0.0238685 | ||||||||
\(311\) | 1.91464 | 0.108569 | 0.0542846 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542846 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(312\) | 4.80056 | 0.271778 | ||||||||
\(313\) | −5.44385 | −0.307705 | −0.153852 | − | 0.988094i | \(-0.549168\pi\) | ||||
−0.153852 | + | 0.988094i | \(0.549168\pi\) | |||||||
\(314\) | −7.00844 | −0.395509 | ||||||||
\(315\) | −0.328267 | −0.0184958 | ||||||||
\(316\) | −3.45286 | −0.194239 | ||||||||
\(317\) | 7.14525 | 0.401317 | 0.200659 | − | 0.979661i | \(-0.435692\pi\) | ||||
0.200659 | + | 0.979661i | \(0.435692\pi\) | |||||||
\(318\) | 27.1891 | 1.52469 | ||||||||
\(319\) | 9.57246 | 0.535955 | ||||||||
\(320\) | −0.0563132 | −0.00314800 | ||||||||
\(321\) | −26.2322 | −1.46414 | ||||||||
\(322\) | −1.89897 | −0.105826 | ||||||||
\(323\) | 1.39321 | 0.0775205 | ||||||||
\(324\) | −10.6457 | −0.591429 | ||||||||
\(325\) | −10.4419 | −0.579211 | ||||||||
\(326\) | 15.7221 | 0.870768 | ||||||||
\(327\) | 2.79696 | 0.154672 | ||||||||
\(328\) | −1.74954 | −0.0966022 | ||||||||
\(329\) | 0.0116713 | 0.000643459 0 | ||||||||
\(330\) | 0.567254 | 0.0312263 | ||||||||
\(331\) | 0.951726 | 0.0523116 | 0.0261558 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261558 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(332\) | 0.0374441 | 0.00205501 | ||||||||
\(333\) | 12.9413 | 0.709182 | ||||||||
\(334\) | −18.7636 | −1.02670 | ||||||||
\(335\) | 0.549024 | 0.0299964 | ||||||||
\(336\) | −5.88024 | −0.320793 | ||||||||
\(337\) | −1.77919 | −0.0969185 | −0.0484592 | − | 0.998825i | \(-0.515431\pi\) | ||||
−0.0484592 | + | 0.998825i | \(0.515431\pi\) | |||||||
\(338\) | 8.63315 | 0.469581 | ||||||||
\(339\) | −17.1378 | −0.930799 | ||||||||
\(340\) | −0.244183 | −0.0132427 | ||||||||
\(341\) | 32.7232 | 1.77206 | ||||||||
\(342\) | −0.731716 | −0.0395667 | ||||||||
\(343\) | −19.0645 | −1.02939 | ||||||||
\(344\) | 0.974593 | 0.0525465 | ||||||||
\(345\) | 0.0959731 | 0.00516702 | ||||||||
\(346\) | −5.60033 | −0.301076 | ||||||||
\(347\) | −20.4216 | −1.09629 | −0.548144 | − | 0.836384i | \(-0.684665\pi\) | ||||
−0.548144 | + | 0.836384i | \(0.684665\pi\) | |||||||
\(348\) | 5.01501 | 0.268833 | ||||||||
\(349\) | 3.75534 | 0.201018 | 0.100509 | − | 0.994936i | \(-0.467953\pi\) | ||||
0.100509 | + | 0.994936i | \(0.467953\pi\) | |||||||
\(350\) | 12.7903 | 0.683672 | ||||||||
\(351\) | 3.46912 | 0.185168 | ||||||||
\(352\) | 4.38490 | 0.233716 | ||||||||
\(353\) | −30.1267 | −1.60348 | −0.801740 | − | 0.597673i | \(-0.796092\pi\) | ||||
−0.801740 | + | 0.597673i | \(0.796092\pi\) | |||||||
\(354\) | 5.57558 | 0.296339 | ||||||||
\(355\) | −0.0428156 | −0.00227241 | ||||||||
\(356\) | −11.5471 | −0.611997 | ||||||||
\(357\) | −25.4977 | −1.34948 | ||||||||
\(358\) | 10.3380 | 0.546383 | ||||||||
\(359\) | 35.3332 | 1.86481 | 0.932407 | − | 0.361410i | \(-0.117705\pi\) | ||||
0.932407 | + | 0.361410i | \(0.117705\pi\) | |||||||
\(360\) | 0.128245 | 0.00675911 | ||||||||
\(361\) | −18.8968 | −0.994567 | ||||||||
\(362\) | 0.423949 | 0.0222823 | ||||||||
\(363\) | −18.9002 | −0.992006 | ||||||||
\(364\) | 5.34898 | 0.280363 | ||||||||
\(365\) | 0.920989 | 0.0482067 | ||||||||
\(366\) | −9.32388 | −0.487367 | ||||||||
\(367\) | −14.5194 | −0.757906 | −0.378953 | − | 0.925416i | \(-0.623716\pi\) | ||||
−0.378953 | + | 0.925416i | \(0.623716\pi\) | |||||||
\(368\) | 0.741876 | 0.0386730 | ||||||||
\(369\) | 3.98432 | 0.207415 | ||||||||
\(370\) | 0.320007 | 0.0166364 | ||||||||
\(371\) | 30.2952 | 1.57285 | ||||||||
\(372\) | 17.1437 | 0.888858 | ||||||||
\(373\) | −19.6147 | −1.01561 | −0.507805 | − | 0.861472i | \(-0.669543\pi\) | ||||
−0.507805 | + | 0.861472i | \(0.669543\pi\) | |||||||
\(374\) | 19.0136 | 0.983171 | ||||||||
\(375\) | −1.29324 | −0.0667828 | ||||||||
\(376\) | −0.00455965 | −0.000235146 0 | ||||||||
\(377\) | −4.56193 | −0.234951 | ||||||||
\(378\) | −4.24934 | −0.218563 | ||||||||
\(379\) | 23.2379 | 1.19365 | 0.596825 | − | 0.802371i | \(-0.296429\pi\) | ||||
0.596825 | + | 0.802371i | \(0.296429\pi\) | |||||||
\(380\) | −0.0180935 | −0.000928177 0 | ||||||||
\(381\) | 32.9244 | 1.68677 | ||||||||
\(382\) | 9.33430 | 0.477585 | ||||||||
\(383\) | −8.07250 | −0.412485 | −0.206243 | − | 0.978501i | \(-0.566124\pi\) | ||||
−0.206243 | + | 0.978501i | \(0.566124\pi\) | |||||||
\(384\) | 2.29725 | 0.117231 | ||||||||
\(385\) | 0.632058 | 0.0322127 | ||||||||
\(386\) | −8.70456 | −0.443051 | ||||||||
\(387\) | −2.21949 | −0.112823 | ||||||||
\(388\) | 8.86420 | 0.450011 | ||||||||
\(389\) | −25.1180 | −1.27353 | −0.636766 | − | 0.771057i | \(-0.719728\pi\) | ||||
−0.636766 | + | 0.771057i | \(0.719728\pi\) | |||||||
\(390\) | −0.270335 | −0.0136890 | ||||||||
\(391\) | 3.21689 | 0.162685 | ||||||||
\(392\) | 0.447997 | 0.0226273 | ||||||||
\(393\) | −6.87351 | −0.346723 | ||||||||
\(394\) | −8.93519 | −0.450148 | ||||||||
\(395\) | 0.194442 | 0.00978342 | ||||||||
\(396\) | −9.98596 | −0.501813 | ||||||||
\(397\) | −1.31879 | −0.0661882 | −0.0330941 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330941 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(398\) | −11.6082 | −0.581867 | ||||||||
\(399\) | −1.88933 | −0.0945847 | ||||||||
\(400\) | −4.99683 | −0.249841 | ||||||||
\(401\) | 26.0391 | 1.30033 | 0.650166 | − | 0.759792i | \(-0.274699\pi\) | ||||
0.650166 | + | 0.759792i | \(0.274699\pi\) | |||||||
\(402\) | −22.3970 | −1.11706 | ||||||||
\(403\) | −15.5948 | −0.776833 | ||||||||
\(404\) | 16.5704 | 0.824409 | ||||||||
\(405\) | 0.599495 | 0.0297891 | ||||||||
\(406\) | 5.58793 | 0.277324 | ||||||||
\(407\) | −24.9178 | −1.23513 | ||||||||
\(408\) | 9.96124 | 0.493155 | ||||||||
\(409\) | −27.2325 | −1.34656 | −0.673281 | − | 0.739386i | \(-0.735116\pi\) | ||||
−0.673281 | + | 0.739386i | \(0.735116\pi\) | |||||||
\(410\) | 0.0985222 | 0.00486566 | ||||||||
\(411\) | −38.7621 | −1.91200 | ||||||||
\(412\) | −0.542195 | −0.0267120 | ||||||||
\(413\) | 6.21254 | 0.305699 | ||||||||
\(414\) | −1.68951 | −0.0830350 | ||||||||
\(415\) | −0.00210860 | −0.000103507 0 | ||||||||
\(416\) | −2.08970 | −0.102456 | ||||||||
\(417\) | 36.6723 | 1.79585 | ||||||||
\(418\) | 1.40887 | 0.0689102 | ||||||||
\(419\) | −12.1085 | −0.591541 | −0.295770 | − | 0.955259i | \(-0.595576\pi\) | ||||
−0.295770 | + | 0.955259i | \(0.595576\pi\) | |||||||
\(420\) | 0.331135 | 0.0161577 | ||||||||
\(421\) | −11.8173 | −0.575940 | −0.287970 | − | 0.957639i | \(-0.592980\pi\) | ||||
−0.287970 | + | 0.957639i | \(0.592980\pi\) | |||||||
\(422\) | −17.8257 | −0.867741 | ||||||||
\(423\) | 0.0103839 | 0.000504884 0 | ||||||||
\(424\) | −11.8355 | −0.574783 | ||||||||
\(425\) | −21.6671 | −1.05101 | ||||||||
\(426\) | 1.74662 | 0.0846242 | ||||||||
\(427\) | −10.3890 | −0.502761 | ||||||||
\(428\) | 11.4189 | 0.551955 | ||||||||
\(429\) | 21.0500 | 1.01630 | ||||||||
\(430\) | −0.0548824 | −0.00264667 | ||||||||
\(431\) | −40.6471 | −1.95790 | −0.978951 | − | 0.204095i | \(-0.934575\pi\) | ||||
−0.978951 | + | 0.204095i | \(0.934575\pi\) | |||||||
\(432\) | 1.66010 | 0.0798717 | ||||||||
\(433\) | −3.45931 | −0.166244 | −0.0831220 | − | 0.996539i | \(-0.526489\pi\) | ||||
−0.0831220 | + | 0.996539i | \(0.526489\pi\) | |||||||
\(434\) | 19.1022 | 0.916934 | ||||||||
\(435\) | −0.282411 | −0.0135406 | ||||||||
\(436\) | −1.21753 | −0.0583090 | ||||||||
\(437\) | 0.238366 | 0.0114026 | ||||||||
\(438\) | −37.5709 | −1.79521 | ||||||||
\(439\) | −36.1447 | −1.72509 | −0.862546 | − | 0.505978i | \(-0.831132\pi\) | ||||
−0.862546 | + | 0.505978i | \(0.831132\pi\) | |||||||
\(440\) | −0.246928 | −0.0117718 | ||||||||
\(441\) | −1.02025 | −0.0485832 | ||||||||
\(442\) | −9.06128 | −0.431001 | ||||||||
\(443\) | 19.3661 | 0.920112 | 0.460056 | − | 0.887890i | \(-0.347829\pi\) | ||||
0.460056 | + | 0.887890i | \(0.347829\pi\) | |||||||
\(444\) | −13.0544 | −0.619535 | ||||||||
\(445\) | 0.650256 | 0.0308251 | ||||||||
\(446\) | 16.3876 | 0.775976 | ||||||||
\(447\) | 15.1910 | 0.718512 | ||||||||
\(448\) | 2.55969 | 0.120934 | ||||||||
\(449\) | −40.9853 | −1.93422 | −0.967109 | − | 0.254363i | \(-0.918134\pi\) | ||||
−0.967109 | + | 0.254363i | \(0.918134\pi\) | |||||||
\(450\) | 11.3795 | 0.536437 | ||||||||
\(451\) | −7.67156 | −0.361239 | ||||||||
\(452\) | 7.46015 | 0.350896 | ||||||||
\(453\) | −23.1989 | −1.08998 | ||||||||
\(454\) | 23.0524 | 1.08190 | ||||||||
\(455\) | −0.301218 | −0.0141213 | ||||||||
\(456\) | 0.738109 | 0.0345651 | ||||||||
\(457\) | −2.27000 | −0.106186 | −0.0530930 | − | 0.998590i | \(-0.516908\pi\) | ||||
−0.0530930 | + | 0.998590i | \(0.516908\pi\) | |||||||
\(458\) | −9.30192 | −0.434650 | ||||||||
\(459\) | 7.19847 | 0.335996 | ||||||||
\(460\) | −0.0417774 | −0.00194788 | ||||||||
\(461\) | 25.9596 | 1.20906 | 0.604529 | − | 0.796583i | \(-0.293361\pi\) | ||||
0.604529 | + | 0.796583i | \(0.293361\pi\) | |||||||
\(462\) | −25.7843 | −1.19959 | ||||||||
\(463\) | −20.1425 | −0.936103 | −0.468052 | − | 0.883701i | \(-0.655044\pi\) | ||||
−0.468052 | + | 0.883701i | \(0.655044\pi\) | |||||||
\(464\) | −2.18305 | −0.101346 | ||||||||
\(465\) | −0.965415 | −0.0447701 | ||||||||
\(466\) | −28.9954 | −1.34319 | ||||||||
\(467\) | 3.35104 | 0.155067 | 0.0775337 | − | 0.996990i | \(-0.475295\pi\) | ||||
0.0775337 | + | 0.996990i | \(0.475295\pi\) | |||||||
\(468\) | 4.75899 | 0.219984 | ||||||||
\(469\) | −24.9556 | −1.15234 | ||||||||
\(470\) | 0.000256769 0 | 1.18439e−5 0 | ||||||||
\(471\) | −16.1001 | −0.741855 | ||||||||
\(472\) | −2.42707 | −0.111715 | ||||||||
\(473\) | 4.27349 | 0.196495 | ||||||||
\(474\) | −7.93208 | −0.364333 | ||||||||
\(475\) | −1.60549 | −0.0736648 | ||||||||
\(476\) | 11.0992 | 0.508732 | ||||||||
\(477\) | 26.9536 | 1.23412 | ||||||||
\(478\) | 8.61374 | 0.393983 | ||||||||
\(479\) | −32.2923 | −1.47547 | −0.737736 | − | 0.675089i | \(-0.764105\pi\) | ||||
−0.737736 | + | 0.675089i | \(0.764105\pi\) | |||||||
\(480\) | −0.129365 | −0.00590470 | ||||||||
\(481\) | 11.8750 | 0.541453 | ||||||||
\(482\) | 6.65186 | 0.302984 | ||||||||
\(483\) | −4.36241 | −0.198496 | ||||||||
\(484\) | 8.22734 | 0.373970 | ||||||||
\(485\) | −0.499171 | −0.0226662 | ||||||||
\(486\) | −19.4756 | −0.883430 | ||||||||
\(487\) | −25.6355 | −1.16166 | −0.580828 | − | 0.814027i | \(-0.697271\pi\) | ||||
−0.580828 | + | 0.814027i | \(0.697271\pi\) | |||||||
\(488\) | 4.05871 | 0.183729 | ||||||||
\(489\) | 36.1176 | 1.63330 | ||||||||
\(490\) | −0.0252281 | −0.00113969 | ||||||||
\(491\) | −30.8194 | −1.39086 | −0.695431 | − | 0.718593i | \(-0.744787\pi\) | ||||
−0.695431 | + | 0.718593i | \(0.744787\pi\) | |||||||
\(492\) | −4.01913 | −0.181196 | ||||||||
\(493\) | −9.46606 | −0.426330 | ||||||||
\(494\) | −0.671424 | −0.0302088 | ||||||||
\(495\) | 0.562341 | 0.0252754 | ||||||||
\(496\) | −7.46270 | −0.335085 | ||||||||
\(497\) | 1.94616 | 0.0872972 | ||||||||
\(498\) | 0.0860185 | 0.00385458 | ||||||||
\(499\) | −25.8260 | −1.15613 | −0.578065 | − | 0.815991i | \(-0.696192\pi\) | ||||
−0.578065 | + | 0.815991i | \(0.696192\pi\) | |||||||
\(500\) | 0.562953 | 0.0251760 | ||||||||
\(501\) | −43.1047 | −1.92577 | ||||||||
\(502\) | −7.33623 | −0.327432 | ||||||||
\(503\) | −21.8953 | −0.976265 | −0.488133 | − | 0.872770i | \(-0.662322\pi\) | ||||
−0.488133 | + | 0.872770i | \(0.662322\pi\) | |||||||
\(504\) | −5.82931 | −0.259658 | ||||||||
\(505\) | −0.933134 | −0.0415239 | ||||||||
\(506\) | 3.25305 | 0.144616 | ||||||||
\(507\) | 19.8325 | 0.880792 | ||||||||
\(508\) | −14.3321 | −0.635885 | ||||||||
\(509\) | −29.6657 | −1.31491 | −0.657454 | − | 0.753494i | \(-0.728367\pi\) | ||||
−0.657454 | + | 0.753494i | \(0.728367\pi\) | |||||||
\(510\) | −0.560949 | −0.0248393 | ||||||||
\(511\) | −41.8631 | −1.85191 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.533393 | 0.0235499 | ||||||||
\(514\) | 6.13605 | 0.270650 | ||||||||
\(515\) | 0.0305327 | 0.00134543 | ||||||||
\(516\) | 2.23888 | 0.0985613 | ||||||||
\(517\) | −0.0199936 | −0.000879318 0 | ||||||||
\(518\) | −14.5458 | −0.639104 | ||||||||
\(519\) | −12.8653 | −0.564726 | ||||||||
\(520\) | 0.117678 | 0.00516051 | ||||||||
\(521\) | −31.0025 | −1.35824 | −0.679122 | − | 0.734025i | \(-0.737639\pi\) | ||||
−0.679122 | + | 0.734025i | \(0.737639\pi\) | |||||||
\(522\) | 4.97158 | 0.217600 | ||||||||
\(523\) | −20.4078 | −0.892373 | −0.446186 | − | 0.894940i | \(-0.647218\pi\) | ||||
−0.446186 | + | 0.894940i | \(0.647218\pi\) | |||||||
\(524\) | 2.99206 | 0.130709 | ||||||||
\(525\) | 29.3826 | 1.28236 | ||||||||
\(526\) | 8.49180 | 0.370260 | ||||||||
\(527\) | −32.3594 | −1.40960 | ||||||||
\(528\) | 10.0732 | 0.438380 | ||||||||
\(529\) | −22.4496 | −0.976070 | ||||||||
\(530\) | 0.666495 | 0.0289507 | ||||||||
\(531\) | 5.52729 | 0.239864 | ||||||||
\(532\) | 0.822431 | 0.0356569 | ||||||||
\(533\) | 3.65602 | 0.158360 | ||||||||
\(534\) | −26.5266 | −1.14792 | ||||||||
\(535\) | −0.643037 | −0.0278009 | ||||||||
\(536\) | 9.74948 | 0.421113 | ||||||||
\(537\) | 23.7491 | 1.02485 | ||||||||
\(538\) | 13.2993 | 0.573375 | ||||||||
\(539\) | 1.96442 | 0.0846136 | ||||||||
\(540\) | −0.0934857 | −0.00402298 | ||||||||
\(541\) | 22.6070 | 0.971950 | 0.485975 | − | 0.873973i | \(-0.338465\pi\) | ||||
0.485975 | + | 0.873973i | \(0.338465\pi\) | |||||||
\(542\) | −20.0373 | −0.860675 | ||||||||
\(543\) | 0.973917 | 0.0417948 | ||||||||
\(544\) | −4.33616 | −0.185911 | ||||||||
\(545\) | 0.0685629 | 0.00293691 | ||||||||
\(546\) | 12.2879 | 0.525876 | ||||||||
\(547\) | 25.5181 | 1.09107 | 0.545537 | − | 0.838087i | \(-0.316326\pi\) | ||||
0.545537 | + | 0.838087i | \(0.316326\pi\) | |||||||
\(548\) | 16.8733 | 0.720791 | ||||||||
\(549\) | −9.24312 | −0.394487 | ||||||||
\(550\) | −21.9106 | −0.934271 | ||||||||
\(551\) | −0.701417 | −0.0298814 | ||||||||
\(552\) | 1.70427 | 0.0725387 | ||||||||
\(553\) | −8.83825 | −0.375841 | ||||||||
\(554\) | 14.1526 | 0.601285 | ||||||||
\(555\) | 0.735136 | 0.0312048 | ||||||||
\(556\) | −15.9636 | −0.677006 | ||||||||
\(557\) | 6.68743 | 0.283356 | 0.141678 | − | 0.989913i | \(-0.454750\pi\) | ||||
0.141678 | + | 0.989913i | \(0.454750\pi\) | |||||||
\(558\) | 16.9952 | 0.719464 | ||||||||
\(559\) | −2.03661 | −0.0861393 | ||||||||
\(560\) | −0.144144 | −0.00609121 | ||||||||
\(561\) | 43.6790 | 1.84413 | ||||||||
\(562\) | −2.57606 | −0.108665 | ||||||||
\(563\) | −39.1032 | −1.64800 | −0.824002 | − | 0.566587i | \(-0.808264\pi\) | ||||
−0.824002 | + | 0.566587i | \(0.808264\pi\) | |||||||
\(564\) | −0.0104747 | −0.000441063 0 | ||||||||
\(565\) | −0.420105 | −0.0176740 | ||||||||
\(566\) | 23.8035 | 1.00054 | ||||||||
\(567\) | −27.2497 | −1.14438 | ||||||||
\(568\) | −0.760311 | −0.0319020 | ||||||||
\(569\) | −30.8282 | −1.29239 | −0.646193 | − | 0.763174i | \(-0.723640\pi\) | ||||
−0.646193 | + | 0.763174i | \(0.723640\pi\) | |||||||
\(570\) | −0.0415653 | −0.00174098 | ||||||||
\(571\) | 36.5821 | 1.53091 | 0.765456 | − | 0.643488i | \(-0.222513\pi\) | ||||
0.765456 | + | 0.643488i | \(0.222513\pi\) | |||||||
\(572\) | −9.16313 | −0.383130 | ||||||||
\(573\) | 21.4432 | 0.895803 | ||||||||
\(574\) | −4.47828 | −0.186920 | ||||||||
\(575\) | −3.70703 | −0.154594 | ||||||||
\(576\) | 2.27735 | 0.0948897 | ||||||||
\(577\) | 2.25015 | 0.0936749 | 0.0468374 | − | 0.998903i | \(-0.485086\pi\) | ||||
0.0468374 | + | 0.998903i | \(0.485086\pi\) | |||||||
\(578\) | −1.80229 | −0.0749653 | ||||||||
\(579\) | −19.9965 | −0.831028 | ||||||||
\(580\) | 0.122935 | 0.00510458 | ||||||||
\(581\) | 0.0958453 | 0.00397633 | ||||||||
\(582\) | 20.3633 | 0.844085 | ||||||||
\(583\) | −51.8975 | −2.14937 | ||||||||
\(584\) | 16.3548 | 0.676764 | ||||||||
\(585\) | −0.267994 | −0.0110802 | ||||||||
\(586\) | 7.61728 | 0.314667 | ||||||||
\(587\) | 7.86640 | 0.324681 | 0.162341 | − | 0.986735i | \(-0.448096\pi\) | ||||
0.162341 | + | 0.986735i | \(0.448096\pi\) | |||||||
\(588\) | 1.02916 | 0.0424419 | ||||||||
\(589\) | −2.39777 | −0.0987985 | ||||||||
\(590\) | 0.136676 | 0.00562686 | ||||||||
\(591\) | −20.5264 | −0.844341 | ||||||||
\(592\) | 5.68263 | 0.233555 | ||||||||
\(593\) | −29.5875 | −1.21501 | −0.607506 | − | 0.794315i | \(-0.707830\pi\) | ||||
−0.607506 | + | 0.794315i | \(0.707830\pi\) | |||||||
\(594\) | 7.27938 | 0.298677 | ||||||||
\(595\) | −0.625033 | −0.0256238 | ||||||||
\(596\) | −6.61271 | −0.270867 | ||||||||
\(597\) | −26.6670 | −1.09141 | ||||||||
\(598\) | −1.55030 | −0.0633965 | ||||||||
\(599\) | 40.5026 | 1.65489 | 0.827445 | − | 0.561546i | \(-0.189793\pi\) | ||||
0.827445 | + | 0.561546i | \(0.189793\pi\) | |||||||
\(600\) | −11.4790 | −0.468627 | ||||||||
\(601\) | 32.0568 | 1.30763 | 0.653813 | − | 0.756656i | \(-0.273168\pi\) | ||||
0.653813 | + | 0.756656i | \(0.273168\pi\) | |||||||
\(602\) | 2.49465 | 0.101674 | ||||||||
\(603\) | −22.2030 | −0.904176 | ||||||||
\(604\) | 10.0986 | 0.410905 | ||||||||
\(605\) | −0.463308 | −0.0188361 | ||||||||
\(606\) | 38.0664 | 1.54634 | ||||||||
\(607\) | −23.7367 | −0.963443 | −0.481722 | − | 0.876324i | \(-0.659988\pi\) | ||||
−0.481722 | + | 0.876324i | \(0.659988\pi\) | |||||||
\(608\) | −0.321301 | −0.0130305 | ||||||||
\(609\) | 12.8369 | 0.520176 | ||||||||
\(610\) | −0.228559 | −0.00925409 | ||||||||
\(611\) | 0.00952831 | 0.000385474 0 | ||||||||
\(612\) | 9.87496 | 0.399172 | ||||||||
\(613\) | 41.1812 | 1.66329 | 0.831646 | − | 0.555306i | \(-0.187399\pi\) | ||||
0.831646 | + | 0.555306i | \(0.187399\pi\) | |||||||
\(614\) | −12.2067 | −0.492624 | ||||||||
\(615\) | 0.226330 | 0.00912651 | ||||||||
\(616\) | 11.2240 | 0.452227 | ||||||||
\(617\) | 2.48579 | 0.100074 | 0.0500370 | − | 0.998747i | \(-0.484066\pi\) | ||||
0.0500370 | + | 0.998747i | \(0.484066\pi\) | |||||||
\(618\) | −1.24556 | −0.0501037 | ||||||||
\(619\) | 16.1042 | 0.647283 | 0.323641 | − | 0.946180i | \(-0.395093\pi\) | ||||
0.323641 | + | 0.946180i | \(0.395093\pi\) | |||||||
\(620\) | 0.420248 | 0.0168776 | ||||||||
\(621\) | 1.23159 | 0.0494220 | ||||||||
\(622\) | −1.91464 | −0.0767701 | ||||||||
\(623\) | −29.5571 | −1.18418 | ||||||||
\(624\) | −4.80056 | −0.192176 | ||||||||
\(625\) | 24.9524 | 0.998098 | ||||||||
\(626\) | 5.44385 | 0.217580 | ||||||||
\(627\) | 3.23653 | 0.129255 | ||||||||
\(628\) | 7.00844 | 0.279667 | ||||||||
\(629\) | 24.6408 | 0.982493 | ||||||||
\(630\) | 0.328267 | 0.0130785 | ||||||||
\(631\) | −9.97969 | −0.397285 | −0.198643 | − | 0.980072i | \(-0.563653\pi\) | ||||
−0.198643 | + | 0.980072i | \(0.563653\pi\) | |||||||
\(632\) | 3.45286 | 0.137347 | ||||||||
\(633\) | −40.9500 | −1.62762 | ||||||||
\(634\) | −7.14525 | −0.283774 | ||||||||
\(635\) | 0.807087 | 0.0320283 | ||||||||
\(636\) | −27.1891 | −1.07812 | ||||||||
\(637\) | −0.936180 | −0.0370928 | ||||||||
\(638\) | −9.57246 | −0.378977 | ||||||||
\(639\) | 1.73150 | 0.0684970 | ||||||||
\(640\) | 0.0563132 | 0.00222597 | ||||||||
\(641\) | −41.5643 | −1.64169 | −0.820845 | − | 0.571151i | \(-0.806497\pi\) | ||||
−0.820845 | + | 0.571151i | \(0.806497\pi\) | |||||||
\(642\) | 26.2322 | 1.03530 | ||||||||
\(643\) | −13.7650 | −0.542840 | −0.271420 | − | 0.962461i | \(-0.587493\pi\) | ||||
−0.271420 | + | 0.962461i | \(0.587493\pi\) | |||||||
\(644\) | 1.89897 | 0.0748299 | ||||||||
\(645\) | −0.126079 | −0.00496434 | ||||||||
\(646\) | −1.39321 | −0.0548153 | ||||||||
\(647\) | 10.4816 | 0.412073 | 0.206036 | − | 0.978544i | \(-0.433943\pi\) | ||||
0.206036 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(648\) | 10.6457 | 0.418204 | ||||||||
\(649\) | −10.6424 | −0.417753 | ||||||||
\(650\) | 10.4419 | 0.409564 | ||||||||
\(651\) | 43.8824 | 1.71989 | ||||||||
\(652\) | −15.7221 | −0.615726 | ||||||||
\(653\) | 3.27766 | 0.128265 | 0.0641324 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641324 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(654\) | −2.79696 | −0.109370 | ||||||||
\(655\) | −0.168493 | −0.00658355 | ||||||||
\(656\) | 1.74954 | 0.0683081 | ||||||||
\(657\) | −37.2455 | −1.45309 | ||||||||
\(658\) | −0.0116713 | −0.000454994 0 | ||||||||
\(659\) | −13.6413 | −0.531390 | −0.265695 | − | 0.964057i | \(-0.585601\pi\) | ||||
−0.265695 | + | 0.964057i | \(0.585601\pi\) | |||||||
\(660\) | −0.567254 | −0.0220803 | ||||||||
\(661\) | 22.0279 | 0.856784 | 0.428392 | − | 0.903593i | \(-0.359080\pi\) | ||||
0.428392 | + | 0.903593i | \(0.359080\pi\) | |||||||
\(662\) | −0.951726 | −0.0369899 | ||||||||
\(663\) | −20.8160 | −0.808427 | ||||||||
\(664\) | −0.0374441 | −0.00145311 | ||||||||
\(665\) | −0.0463137 | −0.00179597 | ||||||||
\(666\) | −12.9413 | −0.501467 | ||||||||
\(667\) | −1.61955 | −0.0627094 | ||||||||
\(668\) | 18.7636 | 0.725986 | ||||||||
\(669\) | 37.6464 | 1.45550 | ||||||||
\(670\) | −0.549024 | −0.0212107 | ||||||||
\(671\) | 17.7970 | 0.687047 | ||||||||
\(672\) | 5.88024 | 0.226835 | ||||||||
\(673\) | −27.7400 | −1.06930 | −0.534649 | − | 0.845074i | \(-0.679556\pi\) | ||||
−0.534649 | + | 0.845074i | \(0.679556\pi\) | |||||||
\(674\) | 1.77919 | 0.0685317 | ||||||||
\(675\) | −8.29525 | −0.319284 | ||||||||
\(676\) | −8.63315 | −0.332044 | ||||||||
\(677\) | 13.9859 | 0.537523 | 0.268761 | − | 0.963207i | \(-0.413386\pi\) | ||||
0.268761 | + | 0.963207i | \(0.413386\pi\) | |||||||
\(678\) | 17.1378 | 0.658174 | ||||||||
\(679\) | 22.6896 | 0.870746 | ||||||||
\(680\) | 0.244183 | 0.00936399 | ||||||||
\(681\) | 52.9570 | 2.02932 | ||||||||
\(682\) | −32.7232 | −1.25303 | ||||||||
\(683\) | −28.1723 | −1.07798 | −0.538992 | − | 0.842311i | \(-0.681195\pi\) | ||||
−0.538992 | + | 0.842311i | \(0.681195\pi\) | |||||||
\(684\) | 0.731716 | 0.0279779 | ||||||||
\(685\) | −0.950189 | −0.0363049 | ||||||||
\(686\) | 19.0645 | 0.727888 | ||||||||
\(687\) | −21.3688 | −0.815271 | ||||||||
\(688\) | −0.974593 | −0.0371560 | ||||||||
\(689\) | 24.7327 | 0.942239 | ||||||||
\(690\) | −0.0959731 | −0.00365363 | ||||||||
\(691\) | 24.9303 | 0.948394 | 0.474197 | − | 0.880419i | \(-0.342738\pi\) | ||||
0.474197 | + | 0.880419i | \(0.342738\pi\) | |||||||
\(692\) | 5.60033 | 0.212893 | ||||||||
\(693\) | −25.5609 | −0.970980 | ||||||||
\(694\) | 20.4216 | 0.775192 | ||||||||
\(695\) | 0.898959 | 0.0340995 | ||||||||
\(696\) | −5.01501 | −0.190094 | ||||||||
\(697\) | 7.58629 | 0.287351 | ||||||||
\(698\) | −3.75534 | −0.142142 | ||||||||
\(699\) | −66.6097 | −2.51941 | ||||||||
\(700\) | −12.7903 | −0.483429 | ||||||||
\(701\) | −5.79349 | −0.218817 | −0.109408 | − | 0.993997i | \(-0.534896\pi\) | ||||
−0.109408 | + | 0.993997i | \(0.534896\pi\) | |||||||
\(702\) | −3.46912 | −0.130933 | ||||||||
\(703\) | 1.82584 | 0.0688627 | ||||||||
\(704\) | −4.38490 | −0.165262 | ||||||||
\(705\) | 0.000589862 0 | 2.22155e−5 0 | ||||||||
\(706\) | 30.1267 | 1.13383 | ||||||||
\(707\) | 42.4151 | 1.59518 | ||||||||
\(708\) | −5.57558 | −0.209543 | ||||||||
\(709\) | 24.7620 | 0.929957 | 0.464978 | − | 0.885322i | \(-0.346062\pi\) | ||||
0.464978 | + | 0.885322i | \(0.346062\pi\) | |||||||
\(710\) | 0.0428156 | 0.00160684 | ||||||||
\(711\) | −7.86338 | −0.294900 | ||||||||
\(712\) | 11.5471 | 0.432747 | ||||||||
\(713\) | −5.53640 | −0.207340 | ||||||||
\(714\) | 25.4977 | 0.954226 | ||||||||
\(715\) | 0.516005 | 0.0192975 | ||||||||
\(716\) | −10.3380 | −0.386351 | ||||||||
\(717\) | 19.7879 | 0.738993 | ||||||||
\(718\) | −35.3332 | −1.31862 | ||||||||
\(719\) | −25.0866 | −0.935571 | −0.467785 | − | 0.883842i | \(-0.654948\pi\) | ||||
−0.467785 | + | 0.883842i | \(0.654948\pi\) | |||||||
\(720\) | −0.128245 | −0.00477941 | ||||||||
\(721\) | −1.38785 | −0.0516863 | ||||||||
\(722\) | 18.8968 | 0.703265 | ||||||||
\(723\) | 15.2810 | 0.568306 | ||||||||
\(724\) | −0.423949 | −0.0157560 | ||||||||
\(725\) | 10.9083 | 0.405125 | ||||||||
\(726\) | 18.9002 | 0.701454 | ||||||||
\(727\) | −49.6479 | −1.84134 | −0.920669 | − | 0.390343i | \(-0.872356\pi\) | ||||
−0.920669 | + | 0.390343i | \(0.872356\pi\) | |||||||
\(728\) | −5.34898 | −0.198247 | ||||||||
\(729\) | −12.8031 | −0.474187 | ||||||||
\(730\) | −0.920989 | −0.0340873 | ||||||||
\(731\) | −4.22599 | −0.156304 | ||||||||
\(732\) | 9.32388 | 0.344620 | ||||||||
\(733\) | 15.2739 | 0.564155 | 0.282077 | − | 0.959392i | \(-0.408977\pi\) | ||||
0.282077 | + | 0.959392i | \(0.408977\pi\) | |||||||
\(734\) | 14.5194 | 0.535920 | ||||||||
\(735\) | −0.0579553 | −0.00213771 | ||||||||
\(736\) | −0.741876 | −0.0273459 | ||||||||
\(737\) | 42.7505 | 1.57473 | ||||||||
\(738\) | −3.98432 | −0.146665 | ||||||||
\(739\) | −2.20308 | −0.0810415 | −0.0405208 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405208 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(740\) | −0.320007 | −0.0117637 | ||||||||
\(741\) | −1.54243 | −0.0566625 | ||||||||
\(742\) | −30.2952 | −1.11217 | ||||||||
\(743\) | 21.7624 | 0.798385 | 0.399193 | − | 0.916867i | \(-0.369290\pi\) | ||||
0.399193 | + | 0.916867i | \(0.369290\pi\) | |||||||
\(744\) | −17.1437 | −0.628517 | ||||||||
\(745\) | 0.372383 | 0.0136431 | ||||||||
\(746\) | 19.6147 | 0.718145 | ||||||||
\(747\) | 0.0852734 | 0.00311999 | ||||||||
\(748\) | −19.0136 | −0.695207 | ||||||||
\(749\) | 29.2289 | 1.06800 | ||||||||
\(750\) | 1.29324 | 0.0472226 | ||||||||
\(751\) | −25.9286 | −0.946148 | −0.473074 | − | 0.881023i | \(-0.656856\pi\) | ||||
−0.473074 | + | 0.881023i | \(0.656856\pi\) | |||||||
\(752\) | 0.00455965 | 0.000166273 0 | ||||||||
\(753\) | −16.8531 | −0.614163 | ||||||||
\(754\) | 4.56193 | 0.166136 | ||||||||
\(755\) | −0.568683 | −0.0206965 | ||||||||
\(756\) | 4.24934 | 0.154547 | ||||||||
\(757\) | 47.0934 | 1.71164 | 0.855820 | − | 0.517274i | \(-0.173053\pi\) | ||||
0.855820 | + | 0.517274i | \(0.173053\pi\) | |||||||
\(758\) | −23.2379 | −0.844038 | ||||||||
\(759\) | 7.47307 | 0.271255 | ||||||||
\(760\) | 0.0180935 | 0.000656320 0 | ||||||||
\(761\) | 5.38781 | 0.195308 | 0.0976539 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976539 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(762\) | −32.9244 | −1.19273 | ||||||||
\(763\) | −3.11649 | −0.112825 | ||||||||
\(764\) | −9.33430 | −0.337703 | ||||||||
\(765\) | −0.556091 | −0.0201055 | ||||||||
\(766\) | 8.07250 | 0.291671 | ||||||||
\(767\) | 5.07185 | 0.183134 | ||||||||
\(768\) | −2.29725 | −0.0828948 | ||||||||
\(769\) | 49.3387 | 1.77920 | 0.889600 | − | 0.456741i | \(-0.150983\pi\) | ||||
0.889600 | + | 0.456741i | \(0.150983\pi\) | |||||||
\(770\) | −0.632058 | −0.0227778 | ||||||||
\(771\) | 14.0960 | 0.507656 | ||||||||
\(772\) | 8.70456 | 0.313284 | ||||||||
\(773\) | −9.45718 | −0.340151 | −0.170076 | − | 0.985431i | \(-0.554401\pi\) | ||||
−0.170076 | + | 0.985431i | \(0.554401\pi\) | |||||||
\(774\) | 2.21949 | 0.0797780 | ||||||||
\(775\) | 37.2898 | 1.33949 | ||||||||
\(776\) | −8.86420 | −0.318206 | ||||||||
\(777\) | −33.4152 | −1.19876 | ||||||||
\(778\) | 25.1180 | 0.900523 | ||||||||
\(779\) | 0.562129 | 0.0201404 | ||||||||
\(780\) | 0.270335 | 0.00967955 | ||||||||
\(781\) | −3.33389 | −0.119296 | ||||||||
\(782\) | −3.21689 | −0.115036 | ||||||||
\(783\) | −3.62409 | −0.129514 | ||||||||
\(784\) | −0.447997 | −0.0159999 | ||||||||
\(785\) | −0.394668 | −0.0140863 | ||||||||
\(786\) | 6.87351 | 0.245170 | ||||||||
\(787\) | 31.7788 | 1.13279 | 0.566395 | − | 0.824134i | \(-0.308338\pi\) | ||||
0.566395 | + | 0.824134i | \(0.308338\pi\) | |||||||
\(788\) | 8.93519 | 0.318303 | ||||||||
\(789\) | 19.5078 | 0.694495 | ||||||||
\(790\) | −0.194442 | −0.00691792 | ||||||||
\(791\) | 19.0957 | 0.678963 | ||||||||
\(792\) | 9.98596 | 0.354836 | ||||||||
\(793\) | −8.48150 | −0.301187 | ||||||||
\(794\) | 1.31879 | 0.0468021 | ||||||||
\(795\) | 1.53110 | 0.0543027 | ||||||||
\(796\) | 11.6082 | 0.411442 | ||||||||
\(797\) | −16.8671 | −0.597464 | −0.298732 | − | 0.954337i | \(-0.596564\pi\) | ||||
−0.298732 | + | 0.954337i | \(0.596564\pi\) | |||||||
\(798\) | 1.88933 | 0.0668815 | ||||||||
\(799\) | 0.0197714 | 0.000699461 0 | ||||||||
\(800\) | 4.99683 | 0.176665 | ||||||||
\(801\) | −26.2969 | −0.929155 | ||||||||
\(802\) | −26.0391 | −0.919473 | ||||||||
\(803\) | 71.7139 | 2.53073 | ||||||||
\(804\) | 22.3970 | 0.789880 | ||||||||
\(805\) | −0.106937 | −0.00376904 | ||||||||
\(806\) | 15.5948 | 0.549304 | ||||||||
\(807\) | 30.5519 | 1.07548 | ||||||||
\(808\) | −16.5704 | −0.582946 | ||||||||
\(809\) | −16.1194 | −0.566727 | −0.283363 | − | 0.959013i | \(-0.591450\pi\) | ||||
−0.283363 | + | 0.959013i | \(0.591450\pi\) | |||||||
\(810\) | −0.599495 | −0.0210641 | ||||||||
\(811\) | −36.2136 | −1.27163 | −0.635816 | − | 0.771840i | \(-0.719336\pi\) | ||||
−0.635816 | + | 0.771840i | \(0.719336\pi\) | |||||||
\(812\) | −5.58793 | −0.196098 | ||||||||
\(813\) | −46.0306 | −1.61437 | ||||||||
\(814\) | 24.9178 | 0.873367 | ||||||||
\(815\) | 0.885364 | 0.0310129 | ||||||||
\(816\) | −9.96124 | −0.348713 | ||||||||
\(817\) | −0.313138 | −0.0109553 | ||||||||
\(818\) | 27.2325 | 0.952164 | ||||||||
\(819\) | 12.1815 | 0.425657 | ||||||||
\(820\) | −0.0985222 | −0.00344054 | ||||||||
\(821\) | −12.1007 | −0.422316 | −0.211158 | − | 0.977452i | \(-0.567723\pi\) | ||||
−0.211158 | + | 0.977452i | \(0.567723\pi\) | |||||||
\(822\) | 38.7621 | 1.35199 | ||||||||
\(823\) | −11.0862 | −0.386439 | −0.193220 | − | 0.981156i | \(-0.561893\pi\) | ||||
−0.193220 | + | 0.981156i | \(0.561893\pi\) | |||||||
\(824\) | 0.542195 | 0.0188883 | ||||||||
\(825\) | −50.3341 | −1.75241 | ||||||||
\(826\) | −6.21254 | −0.216162 | ||||||||
\(827\) | −31.3593 | −1.09047 | −0.545236 | − | 0.838283i | \(-0.683560\pi\) | ||||
−0.545236 | + | 0.838283i | \(0.683560\pi\) | |||||||
\(828\) | 1.68951 | 0.0587146 | ||||||||
\(829\) | 48.8170 | 1.69548 | 0.847742 | − | 0.530408i | \(-0.177961\pi\) | ||||
0.847742 | + | 0.530408i | \(0.177961\pi\) | |||||||
\(830\) | 0.00210860 | 7.31905e−5 0 | ||||||||
\(831\) | 32.5120 | 1.12783 | ||||||||
\(832\) | 2.08970 | 0.0724474 | ||||||||
\(833\) | −1.94259 | −0.0673066 | ||||||||
\(834\) | −36.6723 | −1.26986 | ||||||||
\(835\) | −1.05664 | −0.0365665 | ||||||||
\(836\) | −1.40887 | −0.0487269 | ||||||||
\(837\) | −12.3888 | −0.428221 | ||||||||
\(838\) | 12.1085 | 0.418282 | ||||||||
\(839\) | −39.0010 | −1.34646 | −0.673232 | − | 0.739431i | \(-0.735095\pi\) | ||||
−0.673232 | + | 0.739431i | \(0.735095\pi\) | |||||||
\(840\) | −0.331135 | −0.0114252 | ||||||||
\(841\) | −24.2343 | −0.835665 | ||||||||
\(842\) | 11.8173 | 0.407251 | ||||||||
\(843\) | −5.91785 | −0.203822 | ||||||||
\(844\) | 17.8257 | 0.613585 | ||||||||
\(845\) | 0.486160 | 0.0167244 | ||||||||
\(846\) | −0.0103839 | −0.000357007 0 | ||||||||
\(847\) | 21.0594 | 0.723610 | ||||||||
\(848\) | 11.8355 | 0.406433 | ||||||||
\(849\) | 54.6826 | 1.87670 | ||||||||
\(850\) | 21.6671 | 0.743174 | ||||||||
\(851\) | 4.21581 | 0.144516 | ||||||||
\(852\) | −1.74662 | −0.0598384 | ||||||||
\(853\) | −41.2530 | −1.41247 | −0.706237 | − | 0.707975i | \(-0.749609\pi\) | ||||
−0.706237 | + | 0.707975i | \(0.749609\pi\) | |||||||
\(854\) | 10.3890 | 0.355506 | ||||||||
\(855\) | −0.0412053 | −0.00140919 | ||||||||
\(856\) | −11.4189 | −0.390291 | ||||||||
\(857\) | −9.51628 | −0.325070 | −0.162535 | − | 0.986703i | \(-0.551967\pi\) | ||||
−0.162535 | + | 0.986703i | \(0.551967\pi\) | |||||||
\(858\) | −21.0500 | −0.718635 | ||||||||
\(859\) | −27.2919 | −0.931189 | −0.465594 | − | 0.884998i | \(-0.654159\pi\) | ||||
−0.465594 | + | 0.884998i | \(0.654159\pi\) | |||||||
\(860\) | 0.0548824 | 0.00187148 | ||||||||
\(861\) | −10.2877 | −0.350604 | ||||||||
\(862\) | 40.6471 | 1.38445 | ||||||||
\(863\) | 1.90861 | 0.0649697 | 0.0324849 | − | 0.999472i | \(-0.489658\pi\) | ||||
0.0324849 | + | 0.999472i | \(0.489658\pi\) | |||||||
\(864\) | −1.66010 | −0.0564778 | ||||||||
\(865\) | −0.315372 | −0.0107230 | ||||||||
\(866\) | 3.45931 | 0.117552 | ||||||||
\(867\) | −4.14031 | −0.140612 | ||||||||
\(868\) | −19.1022 | −0.648370 | ||||||||
\(869\) | 15.1404 | 0.513604 | ||||||||
\(870\) | 0.282411 | 0.00957464 | ||||||||
\(871\) | −20.3735 | −0.690329 | ||||||||
\(872\) | 1.21753 | 0.0412307 | ||||||||
\(873\) | 20.1869 | 0.683223 | ||||||||
\(874\) | −0.238366 | −0.00806284 | ||||||||
\(875\) | 1.44099 | 0.0487142 | ||||||||
\(876\) | 37.5709 | 1.26940 | ||||||||
\(877\) | 37.0912 | 1.25248 | 0.626241 | − | 0.779629i | \(-0.284593\pi\) | ||||
0.626241 | + | 0.779629i | \(0.284593\pi\) | |||||||
\(878\) | 36.1447 | 1.21982 | ||||||||
\(879\) | 17.4988 | 0.590219 | ||||||||
\(880\) | 0.246928 | 0.00832393 | ||||||||
\(881\) | 13.4848 | 0.454315 | 0.227158 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227158 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(882\) | 1.02025 | 0.0343535 | ||||||||
\(883\) | 15.8342 | 0.532865 | 0.266432 | − | 0.963854i | \(-0.414155\pi\) | ||||
0.266432 | + | 0.963854i | \(0.414155\pi\) | |||||||
\(884\) | 9.06128 | 0.304764 | ||||||||
\(885\) | 0.313979 | 0.0105543 | ||||||||
\(886\) | −19.3661 | −0.650618 | ||||||||
\(887\) | 38.2121 | 1.28304 | 0.641518 | − | 0.767108i | \(-0.278305\pi\) | ||||
0.641518 | + | 0.767108i | \(0.278305\pi\) | |||||||
\(888\) | 13.0544 | 0.438077 | ||||||||
\(889\) | −36.6857 | −1.23040 | ||||||||
\(890\) | −0.650256 | −0.0217966 | ||||||||
\(891\) | 46.6804 | 1.56385 | ||||||||
\(892\) | −16.3876 | −0.548698 | ||||||||
\(893\) | 0.00146502 | 4.90251e−5 0 | ||||||||
\(894\) | −15.1910 | −0.508064 | ||||||||
\(895\) | 0.582168 | 0.0194597 | ||||||||
\(896\) | −2.55969 | −0.0855132 | ||||||||
\(897\) | −3.56142 | −0.118912 | ||||||||
\(898\) | 40.9853 | 1.36770 | ||||||||
\(899\) | 16.2915 | 0.543350 | ||||||||
\(900\) | −11.3795 | −0.379318 | ||||||||
\(901\) | 51.3206 | 1.70974 | ||||||||
\(902\) | 7.67156 | 0.255435 | ||||||||
\(903\) | 5.73084 | 0.190710 | ||||||||
\(904\) | −7.46015 | −0.248121 | ||||||||
\(905\) | 0.0238739 | 0.000793597 0 | ||||||||
\(906\) | 23.1989 | 0.770733 | ||||||||
\(907\) | −36.6452 | −1.21678 | −0.608392 | − | 0.793637i | \(-0.708185\pi\) | ||||
−0.608392 | + | 0.793637i | \(0.708185\pi\) | |||||||
\(908\) | −23.0524 | −0.765019 | ||||||||
\(909\) | 37.7367 | 1.25165 | ||||||||
\(910\) | 0.301218 | 0.00998529 | ||||||||
\(911\) | 29.7821 | 0.986724 | 0.493362 | − | 0.869824i | \(-0.335768\pi\) | ||||
0.493362 | + | 0.869824i | \(0.335768\pi\) | |||||||
\(912\) | −0.738109 | −0.0244412 | ||||||||
\(913\) | −0.164189 | −0.00543385 | ||||||||
\(914\) | 2.27000 | 0.0750848 | ||||||||
\(915\) | −0.525057 | −0.0173579 | ||||||||
\(916\) | 9.30192 | 0.307344 | ||||||||
\(917\) | 7.65874 | 0.252914 | ||||||||
\(918\) | −7.19847 | −0.237585 | ||||||||
\(919\) | −3.42036 | −0.112827 | −0.0564137 | − | 0.998407i | \(-0.517967\pi\) | ||||
−0.0564137 | + | 0.998407i | \(0.517967\pi\) | |||||||
\(920\) | 0.0417774 | 0.00137736 | ||||||||
\(921\) | −28.0419 | −0.924013 | ||||||||
\(922\) | −25.9596 | −0.854934 | ||||||||
\(923\) | 1.58882 | 0.0522968 | ||||||||
\(924\) | 25.7843 | 0.848240 | ||||||||
\(925\) | −28.3951 | −0.933626 | ||||||||
\(926\) | 20.1425 | 0.661925 | ||||||||
\(927\) | −1.23477 | −0.0405551 | ||||||||
\(928\) | 2.18305 | 0.0716622 | ||||||||
\(929\) | −33.1208 | −1.08666 | −0.543329 | − | 0.839520i | \(-0.682836\pi\) | ||||
−0.543329 | + | 0.839520i | \(0.682836\pi\) | |||||||
\(930\) | 0.965415 | 0.0316572 | ||||||||
\(931\) | −0.143942 | −0.00471751 | ||||||||
\(932\) | 28.9954 | 0.949776 | ||||||||
\(933\) | −4.39840 | −0.143997 | ||||||||
\(934\) | −3.35104 | −0.109649 | ||||||||
\(935\) | 1.07072 | 0.0350162 | ||||||||
\(936\) | −4.75899 | −0.155552 | ||||||||
\(937\) | −60.1823 | −1.96607 | −0.983035 | − | 0.183416i | \(-0.941285\pi\) | ||||
−0.983035 | + | 0.183416i | \(0.941285\pi\) | |||||||
\(938\) | 24.9556 | 0.814830 | ||||||||
\(939\) | 12.5059 | 0.408114 | ||||||||
\(940\) | −0.000256769 0 | −8.37487e−6 0 | ||||||||
\(941\) | 12.9648 | 0.422641 | 0.211320 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211320 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(942\) | 16.1001 | 0.524571 | ||||||||
\(943\) | 1.29794 | 0.0422668 | ||||||||
\(944\) | 2.42707 | 0.0789943 | ||||||||
\(945\) | −0.239294 | −0.00778424 | ||||||||
\(946\) | −4.27349 | −0.138943 | ||||||||
\(947\) | −14.2582 | −0.463329 | −0.231665 | − | 0.972796i | \(-0.574417\pi\) | ||||
−0.231665 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(948\) | 7.93208 | 0.257622 | ||||||||
\(949\) | −34.1765 | −1.10942 | ||||||||
\(950\) | 1.60549 | 0.0520889 | ||||||||
\(951\) | −16.4144 | −0.532274 | ||||||||
\(952\) | −11.0992 | −0.359728 | ||||||||
\(953\) | 40.9505 | 1.32652 | 0.663259 | − | 0.748390i | \(-0.269173\pi\) | ||||
0.663259 | + | 0.748390i | \(0.269173\pi\) | |||||||
\(954\) | −26.9536 | −0.872655 | ||||||||
\(955\) | 0.525645 | 0.0170095 | ||||||||
\(956\) | −8.61374 | −0.278588 | ||||||||
\(957\) | −21.9903 | −0.710846 | ||||||||
\(958\) | 32.2923 | 1.04332 | ||||||||
\(959\) | 43.1904 | 1.39469 | ||||||||
\(960\) | 0.129365 | 0.00417525 | ||||||||
\(961\) | 24.6918 | 0.796511 | ||||||||
\(962\) | −11.8750 | −0.382865 | ||||||||
\(963\) | 26.0050 | 0.837998 | ||||||||
\(964\) | −6.65186 | −0.214242 | ||||||||
\(965\) | −0.490182 | −0.0157795 | ||||||||
\(966\) | 4.36241 | 0.140358 | ||||||||
\(967\) | −23.2470 | −0.747572 | −0.373786 | − | 0.927515i | \(-0.621940\pi\) | ||||
−0.373786 | + | 0.927515i | \(0.621940\pi\) | |||||||
\(968\) | −8.22734 | −0.264437 | ||||||||
\(969\) | −3.20056 | −0.102817 | ||||||||
\(970\) | 0.499171 | 0.0160274 | ||||||||
\(971\) | 9.45928 | 0.303563 | 0.151781 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151781 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(972\) | 19.4756 | 0.624679 | ||||||||
\(973\) | −40.8617 | −1.30997 | ||||||||
\(974\) | 25.6355 | 0.821414 | ||||||||
\(975\) | 23.9876 | 0.768218 | ||||||||
\(976\) | −4.05871 | −0.129916 | ||||||||
\(977\) | −25.0764 | −0.802265 | −0.401133 | − | 0.916020i | \(-0.631383\pi\) | ||||
−0.401133 | + | 0.916020i | \(0.631383\pi\) | |||||||
\(978\) | −36.1176 | −1.15491 | ||||||||
\(979\) | 50.6330 | 1.61824 | ||||||||
\(980\) | 0.0252281 | 0.000805883 0 | ||||||||
\(981\) | −2.77274 | −0.0885267 | ||||||||
\(982\) | 30.8194 | 0.983488 | ||||||||
\(983\) | 24.1186 | 0.769263 | 0.384632 | − | 0.923070i | \(-0.374329\pi\) | ||||
0.384632 | + | 0.923070i | \(0.374329\pi\) | |||||||
\(984\) | 4.01913 | 0.128125 | ||||||||
\(985\) | −0.503169 | −0.0160323 | ||||||||
\(986\) | 9.46606 | 0.301461 | ||||||||
\(987\) | −0.0268119 | −0.000853431 0 | ||||||||
\(988\) | 0.671424 | 0.0213608 | ||||||||
\(989\) | −0.723027 | −0.0229909 | ||||||||
\(990\) | −0.562341 | −0.0178724 | ||||||||
\(991\) | 16.4183 | 0.521545 | 0.260772 | − | 0.965400i | \(-0.416023\pi\) | ||||
0.260772 | + | 0.965400i | \(0.416023\pi\) | |||||||
\(992\) | 7.46270 | 0.236941 | ||||||||
\(993\) | −2.18635 | −0.0693818 | ||||||||
\(994\) | −1.94616 | −0.0617285 | ||||||||
\(995\) | −0.653696 | −0.0207235 | ||||||||
\(996\) | −0.0860185 | −0.00272560 | ||||||||
\(997\) | −13.5308 | −0.428525 | −0.214263 | − | 0.976776i | \(-0.568735\pi\) | ||||
−0.214263 | + | 0.976776i | \(0.568735\pi\) | |||||||
\(998\) | 25.8260 | 0.817507 | ||||||||
\(999\) | 9.43374 | 0.298470 |
(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 | 6002.2.a.b.1.10 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.b.1.10 | ✓ | 56 | 1.1 | even | 1 | trivial |