Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 2.22137 | 1.28251 | 0.641253 | − | 0.767330i | \(-0.278415\pi\) | ||||
0.641253 | + | 0.767330i | \(0.278415\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.27900 | −0.571987 | −0.285993 | − | 0.958232i | \(-0.592324\pi\) | ||||
−0.285993 | + | 0.958232i | \(0.592324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.396716 | 0.149945 | 0.0749723 | − | 0.997186i | \(-0.476113\pi\) | ||||
0.0749723 | + | 0.997186i | \(0.476113\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.93446 | 0.644821 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72422 | −0.821383 | −0.410691 | − | 0.911774i | \(-0.634713\pi\) | ||||
−0.410691 | + | 0.911774i | \(0.634713\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.91685 | 1.91839 | 0.959195 | − | 0.282747i | \(-0.0912456\pi\) | ||||
0.959195 | + | 0.282747i | \(0.0912456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.84113 | −0.733576 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0994799 | 0.0228222 | 0.0114111 | − | 0.999935i | \(-0.496368\pi\) | ||||
0.0114111 | + | 0.999935i | \(0.496368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.881251 | 0.192305 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.04990 | 1.26149 | 0.630745 | − | 0.775990i | \(-0.282749\pi\) | ||||
0.630745 | + | 0.775990i | \(0.282749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.36416 | −0.672831 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.36695 | −0.455519 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.610013 | −0.113277 | −0.0566383 | − | 0.998395i | \(-0.518038\pi\) | ||||
−0.0566383 | + | 0.998395i | \(0.518038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.40183 | −1.14980 | −0.574901 | − | 0.818223i | \(-0.694959\pi\) | ||||
−0.574901 | + | 0.818223i | \(0.694959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.05148 | −1.05343 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.507401 | −0.0857663 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3427 | 1.86473 | 0.932367 | − | 0.361513i | \(-0.117740\pi\) | ||||
0.932367 | + | 0.361513i | \(0.117740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.3648 | 2.46034 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.02962 | 0.316973 | 0.158487 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158487 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.63051 | 1.46864 | 0.734319 | − | 0.678804i | \(-0.237501\pi\) | ||||
0.734319 | + | 0.678804i | \(0.237501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.47418 | −0.368829 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.2148 | 1.92758 | 0.963789 | − | 0.266664i | \(-0.0859215\pi\) | ||||
0.963789 | + | 0.266664i | \(0.0859215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.84262 | −0.977517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22137 | 0.311053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.02927 | −0.141382 | −0.0706909 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706909 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.48428 | 0.469820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.220981 | 0.0292697 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.211649 | 0.0270989 | 0.0135494 | − | 0.999908i | \(-0.495687\pi\) | ||||
0.0135494 | + | 0.999908i | \(0.495687\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.767433 | 0.0966874 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.84666 | −1.09729 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.77777 | −1.07237 | −0.536187 | − | 0.844099i | \(-0.680136\pi\) | ||||
−0.536187 | + | 0.844099i | \(0.680136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.4390 | 1.61787 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.34794 | 0.634683 | 0.317342 | − | 0.948311i | \(-0.397210\pi\) | ||||
0.317342 | + | 0.948311i | \(0.397210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.43008 | −0.752583 | −0.376292 | − | 0.926501i | \(-0.622801\pi\) | ||||
−0.376292 | + | 0.926501i | \(0.622801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.47302 | −0.862910 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08074 | −0.123162 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.68797 | 0.414929 | 0.207465 | − | 0.978243i | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978243i | \(0.433479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0612 | −1.22903 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1769 | 1.33658 | 0.668292 | − | 0.743899i | \(-0.267025\pi\) | ||||
0.668292 | + | 0.743899i | \(0.267025\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.27900 | −0.138727 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.35506 | −0.145278 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.3468 | 1.30876 | 0.654378 | − | 0.756168i | \(-0.272931\pi\) | ||||
0.654378 | + | 0.756168i | \(0.272931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.74403 | 0.287652 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.2208 | −1.47463 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.127235 | −0.0130540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.49270 | 0.557699 | 0.278849 | − | 0.960335i | \(-0.410047\pi\) | ||||
0.278849 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.26990 | −0.529645 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.92668 | 0.390719 | 0.195360 | − | 0.980732i | \(-0.437413\pi\) | ||||
0.195360 | + | 0.980732i | \(0.437413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.2153 | −1.69628 | −0.848139 | − | 0.529773i | \(-0.822277\pi\) | ||||
−0.848139 | + | 0.529773i | \(0.822277\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.12712 | −0.109996 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.8408 | 1.91809 | 0.959043 | − | 0.283260i | \(-0.0914159\pi\) | ||||
0.959043 | + | 0.283260i | \(0.0914159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.60167 | −0.919673 | −0.459836 | − | 0.888004i | \(-0.652092\pi\) | ||||
−0.459836 | + | 0.888004i | \(0.652092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.1964 | 2.39153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.45903 | 0.795759 | 0.397879 | − | 0.917438i | \(-0.369746\pi\) | ||||
0.397879 | + | 0.917438i | \(0.369746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.73783 | −0.721556 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3804 | 1.23702 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.396716 | 0.0363669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.57863 | −0.325330 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.50853 | 0.406520 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6978 | 0.956837 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.74587 | −0.332392 | −0.166196 | − | 0.986093i | \(-0.553148\pi\) | ||||
−0.166196 | + | 0.986093i | \(0.553148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.3929 | 1.88354 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.87400 | 0.163732 | 0.0818659 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818659 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0394653 | 0.00342207 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.02733 | 0.260551 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5364 | −0.900183 | −0.450091 | − | 0.892982i | \(-0.648609\pi\) | ||||
−0.450091 | + | 0.892982i | \(0.648609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.2222 | 1.71523 | 0.857614 | − | 0.514294i | \(-0.171946\pi\) | ||||
0.857614 | + | 0.514294i | \(0.171946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.3549 | 2.47213 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8430 | −1.57573 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.780208 | 0.0647927 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.1999 | −1.25367 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.4874 | 1.26877 | 0.634387 | − | 0.773015i | \(-0.281252\pi\) | ||||
0.634387 | + | 0.773015i | \(0.281252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3085 | 0.838892 | 0.419446 | − | 0.907780i | \(-0.362224\pi\) | ||||
0.419446 | + | 0.907780i | \(0.362224\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.93446 | 0.156392 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.18795 | 0.657672 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5321 | −0.840553 | −0.420276 | − | 0.907396i | \(-0.638067\pi\) | ||||
−0.420276 | + | 0.907396i | \(0.638067\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.28640 | −0.181323 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.40009 | 0.189154 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0358 | −1.17770 | −0.588848 | − | 0.808244i | \(-0.700418\pi\) | ||||
−0.588848 | + | 0.808244i | \(0.700418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.73986 | 0.602547 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.55867 | 0.662290 | 0.331145 | − | 0.943580i | \(-0.392565\pi\) | ||||
0.331145 | + | 0.943580i | \(0.392565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.8428 | 2.68022 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.192440 | 0.0147163 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.7227 | −0.891258 | −0.445629 | − | 0.895218i | \(-0.647020\pi\) | ||||
−0.445629 | + | 0.895218i | \(0.647020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.33461 | −0.100887 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.22137 | 0.166968 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.43081 | −0.181687 | −0.0908437 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908437 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.29725 | 0.245082 | 0.122541 | − | 0.992463i | \(-0.460896\pi\) | ||||
0.122541 | + | 0.992463i | \(0.460896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.470150 | 0.0347545 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.5074 | −1.06660 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.72422 | −0.199215 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.939006 | −0.0683027 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4008 | 0.752578 | 0.376289 | − | 0.926502i | \(-0.377200\pi\) | ||||
0.376289 | + | 0.926502i | \(0.377200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.264170 | 0.0190154 | 0.00950768 | − | 0.999955i | \(-0.496974\pi\) | ||||
0.00950768 | + | 0.999955i | \(0.496974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.6517 | −1.40728 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.5349 | −1.53430 | −0.767150 | − | 0.641468i | \(-0.778326\pi\) | ||||
−0.767150 | + | 0.641468i | \(0.778326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.1327 | −1.07273 | −0.536365 | − | 0.843986i | \(-0.680203\pi\) | ||||
−0.536365 | + | 0.843986i | \(0.680203\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.4986 | −1.37533 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.242002 | −0.0169852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.59589 | −0.181305 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.7033 | 0.813435 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.271005 | −0.0187458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.28566 | 0.226194 | 0.113097 | − | 0.993584i | \(-0.463923\pi\) | ||||
0.113097 | + | 0.993584i | \(0.463923\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8797 | 0.813985 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.3174 | −0.840042 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.53971 | −0.172407 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.2835 | −0.965193 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.91685 | 0.465278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0572 | −1.07527 | −0.537636 | − | 0.843177i | \(-0.680683\pi\) | ||||
−0.537636 | + | 0.843177i | \(0.680683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.50783 | −0.433856 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.1971 | 1.47328 | 0.736638 | − | 0.676287i | \(-0.236412\pi\) | ||||
0.736638 | + | 0.676287i | \(0.236412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.96428 | 0.328049 | 0.164024 | − | 0.986456i | \(-0.447552\pi\) | ||||
0.164024 | + | 0.986456i | \(0.447552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.40072 | −0.157956 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7205 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289877\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9018 | −1.10255 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.19233 | 0.532149 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8155 | −1.15239 | −0.576194 | − | 0.817313i | \(-0.695463\pi\) | ||||
−0.576194 | + | 0.817313i | \(0.695463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8145 | 1.40520 | 0.702598 | − | 0.711587i | \(-0.252023\pi\) | ||||
0.702598 | + | 0.711587i | \(0.252023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.4702 | −1.12071 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.75172 | 0.559127 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.688087 | 0.0437819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.0493 | 1.71418 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3241 | −0.651651 | −0.325825 | − | 0.945430i | \(-0.605642\pi\) | ||||
−0.325825 | + | 0.945430i | \(0.605642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.4812 | −1.03617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.84113 | −0.177918 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.2547 | 1.70010 | 0.850050 | − | 0.526702i | \(-0.176572\pi\) | ||||
0.850050 | + | 0.526702i | \(0.176572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.49985 | 0.279607 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.18005 | −0.0730431 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.06647 | −0.435737 | −0.217869 | − | 0.975978i | \(-0.569910\pi\) | ||||
−0.217869 | + | 0.975978i | \(0.569910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.31644 | 0.0808685 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.4267 | 1.67849 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.7138 | 1.26294 | 0.631471 | − | 0.775399i | \(-0.282451\pi\) | ||||
0.631471 | + | 0.775399i | \(0.282451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3390 | −1.05327 | −0.526636 | − | 0.850091i | \(-0.676547\pi\) | ||||
−0.526636 | + | 0.850091i | \(0.676547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.09548 | 0.368916 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.16469 | 0.552652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.95353 | 0.117376 | 0.0586881 | − | 0.998276i | \(-0.481308\pi\) | ||||
0.0586881 | + | 0.998276i | \(0.481308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.3841 | −0.741416 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1283 | −1.20075 | −0.600375 | − | 0.799718i | \(-0.704982\pi\) | ||||
−0.600375 | + | 0.799718i | \(0.704982\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0396 | −0.715681 | −0.357841 | − | 0.933783i | \(-0.616487\pi\) | ||||
−0.357841 | + | 0.933783i | \(0.616487\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.282635 | −0.0167419 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.805183 | 0.0475284 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2013 | 0.715252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5655 | −0.850926 | −0.425463 | − | 0.904976i | \(-0.639889\pi\) | ||||
−0.425463 | + | 0.904976i | \(0.639889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.27900 | −0.0744663 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.44808 | 0.374156 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 41.8462 | 2.42003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.82058 | 0.220214 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.72258 | 0.501099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.270699 | −0.0155002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.47762 | 0.426770 | 0.213385 | − | 0.976968i | \(-0.431551\pi\) | ||||
0.213385 | + | 0.976968i | \(0.431551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38.2416 | −2.17549 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00138 | 0.453717 | 0.226858 | − | 0.973928i | \(-0.427155\pi\) | ||||
0.226858 | + | 0.973928i | \(0.427155\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.7642 | −1.23019 | −0.615093 | − | 0.788455i | \(-0.710881\pi\) | ||||
−0.615093 | + | 0.788455i | \(0.710881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.981547 | −0.0553039 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.0400 | −0.788563 | −0.394282 | − | 0.918990i | \(-0.629007\pi\) | ||||
−0.394282 | + | 0.918990i | \(0.629007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.66181 | 0.0930435 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 44.0737 | 2.45996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0994799 | 0.00553521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.2694 | −1.29075 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.3288 | −1.17949 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.24253 | 0.289030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1586 | 0.778226 | 0.389113 | − | 0.921190i | \(-0.372781\pi\) | ||||
0.389113 | + | 0.921190i | \(0.372781\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.9421 | 1.20242 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.2268 | 0.613384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1952 | −0.773260 | −0.386630 | − | 0.922235i | \(-0.626361\pi\) | ||||
−0.386630 | + | 0.922235i | \(0.626361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.7906 | 1.02057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4400 | 0.944428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.49159 | −0.296518 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.1885 | −0.925400 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5947 | 0.837169 | 0.418584 | − | 0.908178i | \(-0.362526\pi\) | ||||
0.418584 | + | 0.908178i | \(0.362526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.2859 | −1.88881 | −0.944404 | − | 0.328786i | \(-0.893360\pi\) | ||||
−0.944404 | + | 0.328786i | \(0.893360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.3718 | −0.873863 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.27353 | −0.333906 | −0.166953 | − | 0.985965i | \(-0.553393\pi\) | ||||
−0.166953 | + | 0.985965i | \(0.553393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.84002 | −0.363031 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.881251 | 0.0466408 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.2386 | −1.80705 | −0.903523 | − | 0.428539i | \(-0.859028\pi\) | ||||
−0.903523 | + | 0.428539i | \(0.859028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9901 | −0.999479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.94945 | −0.417238 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.22408 | 0.430468 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.4773 | −1.38210 | −0.691052 | − | 0.722805i | \(-0.742852\pi\) | ||||
−0.691052 | + | 0.722805i | \(0.742852\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.92622 | 0.204391 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.408330 | −0.0211994 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2414 | 0.530281 | 0.265140 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265140 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.7636 | 1.22715 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.21937 | −0.217309 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.3706 | −1.09774 | −0.548868 | − | 0.835909i | \(-0.684941\pi\) | ||||
−0.548868 | + | 0.835909i | \(0.684941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.32094 | −0.426295 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.5666 | −0.795418 | −0.397709 | − | 0.917512i | \(-0.630195\pi\) | ||||
−0.397709 | + | 0.917512i | \(0.630195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.38227 | 0.0704470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.6299 | 0.947009 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.8120 | −1.56223 | −0.781115 | − | 0.624387i | \(-0.785349\pi\) | ||||
−0.781115 | + | 0.624387i | \(0.785349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.04990 | 0.305956 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.16283 | 0.209987 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.71692 | −0.237334 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5447 | −0.729976 | −0.364988 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364988 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0876668 | 0.00438883 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.07170 | −0.303206 | −0.151603 | − | 0.988441i | \(-0.548444\pi\) | ||||
−0.151603 | + | 0.988441i | \(0.548444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.2805 | −2.20577 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.1473 | 0.702987 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.9001 | −1.53166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8845 | 0.538206 | 0.269103 | − | 0.963111i | \(-0.413273\pi\) | ||||
0.269103 | + | 0.963111i | \(0.413273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.4051 | −1.15449 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.396716 | 0.0195211 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.5742 | −0.764509 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 44.9210 | 2.19979 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5499 | 0.661958 | 0.330979 | − | 0.943638i | \(-0.392621\pi\) | ||||
0.330979 | + | 0.943638i | \(0.392621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.98192 | −0.291541 | −0.145771 | − | 0.989318i | \(-0.546566\pi\) | ||||
−0.145771 | + | 0.989318i | \(0.546566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.5636 | 1.24294 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.36416 | −0.163186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0839646 | 0.00406333 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −41.8572 | −2.02089 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.8451 | 1.29308 | 0.646542 | − | 0.762879i | \(-0.276215\pi\) | ||||
0.646542 | + | 0.762879i | \(0.276215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.87008 | 0.426269 | 0.213135 | − | 0.977023i | \(-0.431633\pi\) | ||||
0.213135 | + | 0.977023i | \(0.431633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.73313 | 0.0830970 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.601843 | 0.0287900 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.1443 | −0.675069 | −0.337535 | − | 0.941313i | \(-0.609593\pi\) | ||||
−0.337535 | + | 0.941313i | \(0.609593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.2368 | −0.630323 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.7074 | −1.07886 | −0.539430 | − | 0.842031i | \(-0.681360\pi\) | ||||
−0.539430 | + | 0.842031i | \(0.681360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.7915 | −0.748591 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.4031 | 1.62721 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0320 | −1.03976 | −0.519878 | − | 0.854241i | \(-0.674023\pi\) | ||||
−0.519878 | + | 0.854241i | \(0.674023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.52913 | −0.260356 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.8989 | 1.07588 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.50961 | −0.164533 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9216 | 0.885117 | 0.442558 | − | 0.896740i | \(-0.354071\pi\) | ||||
0.442558 | + | 0.896740i | \(0.354071\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.36695 | −0.110480 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3814 | −0.576661 | −0.288331 | − | 0.957531i | \(-0.593100\pi\) | ||||
−0.288331 | + | 0.957531i | \(0.593100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.60847 | 0.353596 | 0.176798 | − | 0.984247i | \(-0.443426\pi\) | ||||
0.176798 | + | 0.984247i | \(0.443426\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.1884 | 0.843468 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.37688 | −0.433910 | −0.216955 | − | 0.976182i | \(-0.569613\pi\) | ||||
−0.216955 | + | 0.976182i | \(0.569613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.48228 | −0.160797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.3956 | −1.07801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.2356 | −1.20631 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.334666 | −0.0153555 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.99109 | −0.0911659 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9244 | 1.73281 | 0.866406 | − | 0.499340i | \(-0.166424\pi\) | ||||
0.866406 | + | 0.499340i | \(0.166424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 78.4560 | 3.57729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.33148 | 0.242591 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.02517 | −0.318996 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.3367 | 1.46531 | 0.732657 | − | 0.680598i | \(-0.238280\pi\) | ||||
0.732657 | + | 0.680598i | \(0.238280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.4000 | −1.51040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.86262 | 0.219447 | 0.109723 | − | 0.993962i | \(-0.465003\pi\) | ||||
0.109723 | + | 0.993962i | \(0.465003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.610013 | −0.0274736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.74021 | 0.302950 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.12161 | 0.0951674 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.7513 | 0.705127 | 0.352564 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352564 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.0119 | 0.849390 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.5110 | 0.602426 | 0.301213 | − | 0.953557i | \(-0.402608\pi\) | ||||
0.301213 | + | 0.953557i | \(0.402608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.02223 | −0.223486 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 77.3986 | 3.43739 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.5881 | 1.08985 | 0.544923 | − | 0.838486i | \(-0.316559\pi\) | ||||
0.544923 | + | 0.838486i | \(0.316559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.55091 | −0.112846 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.235464 | −0.0103960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0185 | 0.970249 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.0000 | −1.58328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.0403 | −1.14304 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.1171 | −0.968970 | −0.484485 | − | 0.874800i | \(-0.660993\pi\) | ||||
−0.484485 | + | 0.874800i | \(0.660993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.0750 | −1.62118 | −0.810588 | − | 0.585617i | \(-0.800852\pi\) | ||||
−0.810588 | + | 0.585617i | \(0.800852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.96467 | −0.129389 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.40183 | −0.278868 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.6012 | 0.591358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.93446 | 0.0839485 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.0386 | 0.608078 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.3765 | −1.09712 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.39972 | −0.233015 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6408 | 0.802915 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.6764 | 1.23290 | 0.616448 | − | 0.787396i | \(-0.288571\pi\) | ||||
0.616448 | + | 0.787396i | \(0.288571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.32439 | 0.314319 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.2805 | 0.526041 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5247 | 1.47617 | 0.738084 | − | 0.674708i | \(-0.235731\pi\) | ||||
0.738084 | + | 0.674708i | \(0.235731\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.409427 | 0.0174739 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0606840 | −0.00258523 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.46308 | 0.0622164 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.2262 | −1.36793 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9631 | −0.676378 | −0.338189 | − | 0.941078i | \(-0.609814\pi\) | ||||
−0.338189 | + | 0.941078i | \(0.609814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 66.6128 | 2.81742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.05148 | −0.255494 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.8342 | −1.80525 | −0.902623 | − | 0.430431i | \(-0.858362\pi\) | ||||
−0.902623 | + | 0.430431i | \(0.858362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8191 | −0.455164 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.38817 | −0.184286 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0189 | −1.09077 | −0.545385 | − | 0.838186i | \(-0.683616\pi\) | ||||
−0.545385 | + | 0.838186i | \(0.683616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.609323 | 0.0254994 | 0.0127497 | − | 0.999919i | \(-0.495942\pi\) | ||||
0.0127497 | + | 0.999919i | \(0.495942\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.1040 | 0.965185 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.3528 | −0.848770 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.6570 | −1.77583 | −0.887917 | − | 0.460003i | \(-0.847848\pi\) | ||||
−0.887917 | + | 0.460003i | \(0.847848\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.586817 | 0.0243873 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.83076 | 0.200414 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.80397 | 0.116129 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.1135 | −0.707558 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.1910 | −1.41121 | −0.705607 | − | 0.708604i | \(-0.749325\pi\) | ||||
−0.705607 | + | 0.708604i | \(0.749325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.636853 | −0.0262411 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.8369 | −1.96775 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.1643 | 1.19763 | 0.598817 | − | 0.800886i | \(-0.295638\pi\) | ||||
0.598817 | + | 0.800886i | \(0.295638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.507401 | −0.0208014 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −33.6153 | −1.37578 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.27404 | −0.297209 | −0.148605 | − | 0.988897i | \(-0.547478\pi\) | ||||
−0.148605 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4093 | −0.628560 | −0.314280 | − | 0.949330i | \(-0.601763\pi\) | ||||
−0.314280 | + | 0.949330i | \(0.601763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.9803 | −0.691490 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.57708 | 0.186085 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.3398 | 1.79969 | 0.899847 | − | 0.436205i | \(-0.143678\pi\) | ||||
0.899847 | + | 0.436205i | \(0.143678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.537575 | −0.0217836 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 91.4049 | 3.69785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5539 | 0.668605 | 0.334303 | − | 0.942466i | \(-0.391499\pi\) | ||||
0.334303 | + | 0.942466i | \(0.391499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.76641 | −0.232524 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.0175 | −1.16820 | −0.584100 | − | 0.811682i | \(-0.698552\pi\) | ||||
−0.584100 | + | 0.811682i | \(0.698552\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8516 | 0.838097 | 0.419048 | − | 0.907964i | \(-0.362364\pi\) | ||||
0.419048 | + | 0.907964i | \(0.362364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.3198 | −0.574633 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.89817 | 0.196241 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.13832 | 0.125533 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.602001 | −0.0240416 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3427 | 0.452264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.53794 | 0.180652 | 0.0903262 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903262 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.29865 | 0.290095 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.79097 | 0.190124 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.3294 | −1.87526 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3454 | 0.409257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.73898 | 0.147681 | 0.0738405 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738405 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1748 | −0.401256 | −0.200628 | − | 0.979667i | \(-0.564298\pi\) | ||||
−0.200628 | + | 0.979667i | \(0.564298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.3615 | −1.07736 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2698 | 0.403747 | 0.201874 | − | 0.979412i | \(-0.435297\pi\) | ||||
0.201874 | + | 0.979412i | \(0.435297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.72422 | −0.106935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.64162 | −0.221113 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.5592 | −0.726279 | −0.363139 | − | 0.931735i | \(-0.618295\pi\) | ||||
−0.363139 | + | 0.931735i | \(0.618295\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.39684 | −0.0936525 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4387 | −0.485282 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0530 | 0.625334 | 0.312667 | − | 0.949863i | \(-0.398778\pi\) | ||||
0.312667 | + | 0.949863i | \(0.398778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.4546 | −1.76798 | −0.883990 | − | 0.467505i | \(-0.845153\pi\) | ||||
−0.883990 | + | 0.467505i | \(0.845153\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.3648 | 0.596721 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0504761 | −0.00195738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.69052 | −0.142897 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.6690 | −1.37904 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.576578 | −0.0222585 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0557 | −0.811637 | −0.405819 | − | 0.913954i | \(-0.633014\pi\) | ||||
−0.405819 | + | 0.913954i | \(0.633014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.96278 | 0.306487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5944 | −0.445609 | −0.222804 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222804 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.17904 | 0.0836239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.3080 | 1.88948 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.6092 | −0.405950 | −0.202975 | − | 0.979184i | \(-0.565061\pi\) | ||||
−0.202975 | + | 0.979184i | \(0.565061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.4760 | 0.514893 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0275 | 0.420724 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.11934 | −0.271225 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9652 | 0.911680 | 0.455840 | − | 0.890062i | \(-0.349339\pi\) | ||||
0.455840 | + | 0.890062i | \(0.349339\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.09065 | −0.0794174 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.8643 | −0.981088 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.02962 | 0.0768773 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.5851 | 1.57289 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5614 | 0.436666 | 0.218333 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218333 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12837 | 0.0425574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.5450 | −1.41403 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.55778 | 0.0585862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.2618 | −1.02384 | −0.511920 | − | 0.859033i | \(-0.671066\pi\) | ||||
−0.511920 | + | 0.859033i | \(0.671066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.13424 | 0.267555 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.7304 | −1.45046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.1002 | 0.901298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.5747 | −1.47794 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.68485 | 0.0628343 | 0.0314172 | − | 0.999506i | \(-0.489998\pi\) | ||||
0.0314172 | + | 0.999506i | \(0.489998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.82961 | −0.254348 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.4580 | 1.80217 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.05218 | 0.0762160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.1113 | 1.67309 | 0.836544 | − | 0.547900i | \(-0.184573\pi\) | ||||
0.836544 | + | 0.547900i | \(0.184573\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.62400 | −0.208296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.63051 | 0.356197 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9390 | −0.551783 | −0.275892 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275892 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.4408 | 0.717083 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.9126 | 0.880830 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.2234 | −1.18536 | −0.592679 | − | 0.805439i | \(-0.701930\pi\) | ||||
−0.592679 | + | 0.805439i | \(0.701930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.52849 | 0.0561506 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7123 | −0.539743 | −0.269871 | − | 0.962896i | \(-0.586981\pi\) | ||||
−0.269871 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.8084 | −0.725723 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.5557 | 0.861858 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.87118 | 0.287607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.41554 | 0.0881444 | 0.0440722 | − | 0.999028i | \(-0.485967\pi\) | ||||
0.0440722 | + | 0.999028i | \(0.485967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9336 | −0.835746 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.1846 | −0.479835 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.7957 | 1.15563 | 0.577816 | − | 0.816167i | \(-0.303905\pi\) | ||||
0.577816 | + | 0.816167i | \(0.303905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.6108 | −1.32889 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.87766 | −0.176815 | −0.0884075 | − | 0.996084i | \(-0.528178\pi\) | ||||
−0.0884075 | + | 0.996084i | \(0.528178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.80914 | −0.137900 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.47418 | −0.0894542 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.91685 | 0.249753 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.2749 | 1.77690 | 0.888449 | − | 0.458975i | \(-0.151783\pi\) | ||||
0.888449 | + | 0.458975i | \(0.151783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.5426 | 2.18039 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.5744 | −1.42339 | −0.711696 | − | 0.702487i | \(-0.752073\pi\) | ||||
−0.711696 | + | 0.702487i | \(0.752073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5367 | 0.773623 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.99580 | 0.358597 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.201906 | 0.00723404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.5690 | −0.521318 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.44387 | 0.0515997 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.4706 | 0.480785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0961 | 0.645057 | 0.322528 | − | 0.946560i | \(-0.395467\pi\) | ||||
0.322528 | + | 0.946560i | \(0.395467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6972 | −0.558835 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.35583 | 0.119320 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.46394 | 0.0519862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.92430 | 0.103714 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.6346 | 0.589227 | 0.294614 | − | 0.955616i | \(-0.404809\pi\) | ||||
0.294614 | + | 0.955616i | \(0.404809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2148 | 0.467507 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.8844 | 0.843913 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5169 | 0.618159 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.06972 | −0.108193 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.0129 | 1.61973 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.6645 | −0.585894 | −0.292947 | − | 0.956129i | \(-0.594636\pi\) | ||||
−0.292947 | + | 0.956129i | \(0.594636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2726 | −0.501180 | −0.250590 | − | 0.968093i | \(-0.580625\pi\) | ||||
−0.250590 | + | 0.968093i | \(0.580625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.5163 | −1.35083 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2308 | 0.673626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.958041 | 0.0335176 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.30822 | 0.185484 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.9263 | 0.800133 | 0.400066 | − | 0.916486i | \(-0.368987\pi\) | ||||
0.400066 | + | 0.916486i | \(0.368987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.5450 | 1.62246 | 0.811229 | − | 0.584729i | \(-0.198799\pi\) | ||||
0.811229 | + | 0.584729i | \(0.198799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.3581 | 0.708779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.80090 | −0.132170 | −0.0660851 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660851 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.7169 | 0.511138 | 0.255569 | − | 0.966791i | \(-0.417737\pi\) | ||||
0.255569 | + | 0.966791i | \(0.417737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.33950 | 0.150536 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.84262 | −0.237083 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9465 | −0.378821 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.1528 | 0.523757 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.7640 | 0.613283 | 0.306641 | − | 0.951825i | \(-0.400795\pi\) | ||||
0.306641 | + | 0.951825i | \(0.400795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6279 | −0.987168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.7122 | −1.53997 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.5640 | −1.53305 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41970 | −0.0487815 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.7444 | −0.917865 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 68.6224 | 2.35234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.35715 | 0.217665 | 0.108832 | − | 0.994060i | \(-0.465289\pi\) | ||||
0.108832 | + | 0.994060i | \(0.465289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.246131 | −0.00841751 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.1071 | −0.652685 | −0.326343 | − | 0.945252i | \(-0.605816\pi\) | ||||
−0.326343 | + | 0.945252i | \(0.605816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.9245 | −1.66928 | −0.834641 | − | 0.550795i | \(-0.814325\pi\) | ||||
−0.834641 | + | 0.550795i | \(0.814325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.78861 | 0.0609555 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.3956 | −0.762355 | −0.381177 | − | 0.924502i | \(-0.624481\pi\) | ||||
−0.381177 | + | 0.924502i | \(0.624481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9933 | 0.509788 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.22137 | 0.0754415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.0468 | −0.340816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.7145 | −2.05723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.6254 | 0.359616 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.24398 | 0.143473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.4743 | −0.488761 | −0.244381 | − | 0.969679i | \(-0.578585\pi\) | ||||
−0.244381 | + | 0.969679i | \(0.578585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.3553 | −1.09132 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.8222 | −1.34164 | −0.670822 | − | 0.741619i | \(-0.734058\pi\) | ||||
−0.670822 | + | 0.741619i | \(0.734058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.57968 | 0.255076 | 0.127538 | − | 0.991834i | \(-0.459292\pi\) | ||||
0.127538 | + | 0.991834i | \(0.459292\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.84113 | −0.0955035 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9178 | −0.937388 | −0.468694 | − | 0.883360i | \(-0.655275\pi\) | ||||
−0.468694 | + | 0.883360i | \(0.655275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.48605 | −0.0498404 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.1332 | 1.00950 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.31461 | 0.0439917 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.10901 | 0.103923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 92.9557 | 3.10370 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.90520 | 0.130246 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.02927 | −0.0342901 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48690 | 0.282426 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.21718 | −0.140184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.6241 | 1.84697 | 0.923484 | − | 0.383636i | \(-0.125328\pi\) | ||||
0.923484 | + | 0.383636i | \(0.125328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.59601 | 0.251944 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6289 | −1.44549 | −0.722745 | − | 0.691115i | \(-0.757120\pi\) | ||||
−0.722745 | + | 0.691115i | \(0.757120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.1724 | −1.09785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.601322 | −0.0198791 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.743445 | 0.0245507 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.9904 | 0.362539 | 0.181270 | − | 0.983433i | \(-0.441979\pi\) | ||||
0.181270 | + | 0.983433i | \(0.441979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.6105 | 0.547335 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.9909 | 1.21757 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.1587 | −1.25465 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.3024 | −1.09380 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.7940 | −1.73211 | −0.866057 | − | 0.499945i | \(-0.833354\pi\) | ||||
−0.866057 | + | 0.499945i | \(0.833354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.680702 | −0.0223091 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.7740 | 0.581894 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.48428 | 0.113948 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43513 | −0.112221 | −0.0561104 | − | 0.998425i | \(-0.517870\pi\) | ||||
−0.0561104 | + | 0.998425i | \(0.517870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.3462 | −1.57772 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.4484 | −1.41638 | −0.708189 | − | 0.706023i | \(-0.750488\pi\) | ||||
−0.708189 | + | 0.706023i | \(0.750488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2790 | 0.399859 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.20099 | 0.0390682 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.28586 | 0.139272 | 0.0696359 | − | 0.997572i | \(-0.477816\pi\) | ||||
0.0696359 | + | 0.997572i | \(0.477816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.4759 | −1.44375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.1879 | −1.01134 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.844400 | −0.0273528 | −0.0136764 | − | 0.999906i | \(-0.504353\pi\) | ||||
−0.0136764 | + | 0.999906i | \(0.504353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.3027 | −0.430465 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.69149 | 0.119329 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.17995 | −0.134978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.98339 | 0.322045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.3814 | 1.23682 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.337873 | −0.0108765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8215 | 0.508786 | 0.254393 | − | 0.967101i | \(-0.418124\pi\) | ||||
0.254393 | + | 0.967101i | \(0.418124\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.220981 | 0.00709893 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.5299 | −1.26857 | −0.634287 | − | 0.773098i | \(-0.718706\pi\) | ||||
−0.634287 | + | 0.773098i | \(0.718706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.02249 | 0.257189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −51.6897 | −1.65540 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.71814 | −0.246925 | −0.123463 | − | 0.992349i | \(-0.539400\pi\) | ||||
−0.123463 | + | 0.992349i | \(0.539400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.6353 | −1.07499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.5741 | −0.593024 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.0438 | 0.798772 | 0.399386 | − | 0.916783i | \(-0.369223\pi\) | ||||
0.399386 | + | 0.916783i | \(0.369223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.5432 | 0.877599 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.6456 | 0.370683 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.2636 | 1.85267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.2669 | −0.897928 | −0.448964 | − | 0.893550i | \(-0.648207\pi\) | ||||
−0.448964 | + | 0.893550i | \(0.648207\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.4514 | 0.998080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3548 | 0.613588 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0420885 | −0.00133296 | −0.000666478 | − | 1.00000i | \(-0.500212\pi\) | ||||
−0.000666478 | 1.00000i | \(0.500212\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.8477 | −0.849422 |
(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 | 4012.2.a.j.1.16 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.j.1.16 | ✓ | 21 | 1.1 | even | 1 | trivial |